EUROPEAN THOUGHT IN THE NINETEENTH

CENTURY

TotovTOs ovv fiOi 6 (rvyypa(fiev<; earw, . . .

$€VO<i iv TOtS /3ty8Xt'otS KOI aTToAtS.

— LUCIAN.

A HISTORY

OF

EUROPEAN THOUGHT

IN THE

NINETEENTH CENTURY

BY

JOHN thp:odoiie mekz

VOL. II.

WILLIAM BLACKWOOD AND SONS

EDINBDilGH AND LONDON

M C M 1 I 1

All liiohU rrsfrveit

^llY OF TO525.

79787'

PREFACE.

In this second volume I have carried out the programme
which I put forward in the preface to the first volume, thus
finishing the first portion of my undertakiui,' — Tlie History
of Scientific Thought in the Nineteenth Century. The
two volumes form a work complete in itself, and for this
reason I have attached an alphabetical index.

In addition to the names I mentioned in the preface to
the first volume, I have to add those of other friends
who have been of great help to me in the course of
my work. With Professor Sampson, F.K.S., of Durham
University, I have liad many helpful discussions on the
subjects of this volume, notably on chapters viii. and
xiii., which he read in proof. Mr Arthur Berry, M.A.,
of King's College, Cambridge, has read over chapter
xiii., and made valuable suggestions. Mr Archibald S.
Percival, M.B., of Cambridge, has read over chapters
vi. and x. Professor F. G. Weiss, D.Sc, of Victoria
University, has read chapters viii. and i.v. Mr Thomas
Whittaker has continued his revision, much to the bonetit
of the book ; and Dr Spence Watson has given the finishing

VI PREFACE.

touches to the last pages, in which I endeavour to secure
in advance the interest of my readers for the subsequent
portions of this work. To all these friends I wish to
express my sense of obligation and my sincere thanks.
I find it impossible to express how much this book owes
to my beloved wife, my constant helpmate on the long
course of this arduous enterprise.

It is unnecessary for me to lighten the work of my
critics by pointing out the many defects of which I myself
am painfully conscious ; but, in the case of the last chapter
on " The Development of Mathematical Thought," I wish
to say that this is — so far as I know — the first attempt
to give to this abstract region of thought a place in a
general history of intellectual progress. I sincerely hope
that it will be followed by other and more successful
attempts to perform this very difficult task. It is now
abundantly clear that mathematical thought will play an
increasingly important part in the progress of science and
culture, and it is no longer permissible to consider it merely
an interesting specialty apart from the general course of
intellectual development. A due appreciation of its im-
portance and power will in future be expected, not only
from the practical thinker who applies science, but likewise
from the philosopher who assigns to science its place in
the comprehensive scheme of human culture.

J. THEO. MEEZ,

The Qpabbies,
Nkwcastle-upon-Ttne, October 1903.

CONTENTS OF THE SECOND YOIXME.

CHAPTER VI.

ON THE KINETIC OK MECHANICAL VIEW OF NATURE.

The idea of motion in ancient philosophy, 3 ; Descartes' development of the
kinetic view, 6 ; Huygens and Newton, 7 ; Revival of the kinetic view
in the nineteenth century, 7 ; Young and Fresnel, 8 ; UnduLttorj- and
emission theories, 11 ; Doth theories kinetic, 11 ; Undulatory theory
prepared by acoustics, 12 ; Newton's authority on the side of the emission
theory, 14; But also suggests the other theory, 15; Biot, BrewHter,
and Laplace against the undulatory theory, 16 ; Euler the suceeabor of
Huygens, 16; Young, 16; His "general law of the interference of
light," 18 ; Theory of the luminiferous ether, 18 ; Brougham's attack on
Young, 19 ; Augustin Fresnel, 21 ; Difficulties presented by the jwliir-
isation of light, 22 ; Fresnel's Memoir on Ditfi-action, 25 ; Young and
Fresnel introduce the conception of transverse vibrations, 28 ; Mechani-
cal difference between light and sound, 30 ; The proi)ertie8 of the ether,
31 ; Other kinetic theories, 34 ; Kinetic theory of ga.ses, 34 ; Vortex
motion, 35 ; Faraday's researches, 35 ; Problems aa to tlie nature of the
ether, 36 ; The theory of elasticity, 40 ; The problem of the ether may
be treated mathematically, 44 ; or experimentally, 44 ; Necessity of
combining the two methods, 44 ; Spectrum analysis, 45 ; Tl>e rlue
furnished by the phenomena on which it depends, 47 ; Sir 0. St<>ki>«,
47 ; (iustav KirchhofF, 48 ; Explanation of fluorescence, 52 ; View of (he
ether as an "elastic solid," 54 ; Lord Kelvin's rcseiux-lies, 55 ; Tyndull'*
' Heat,' 57 ; Lord Kelvin's vortex theory of rnalltT, 57 ; Heiuiholi*'*
investigations, 58 ; Earlier researches on vortex motion, (51 ; IufluoiKX»
of Helmholtz's investigations in England, 62 ; Difl^icultjos of liio vort<«x
ring theory, 64 ; Modern view of electrical plienomcna : KanuUy, 6«3 ;

Vlll CONTENTS.

" Lines of force," 68 ; Development of the conception by Lord Kelvin,
71 ; Clerk-Maxwell, 76 ; His series of works on the theory of electricity,
78; His conception of "tubes of force," 80; " Electrotonic state" of
matter, 81 ; Correspondence between velocities of light and electricity,
84 ; " Elastic disturbances " of the same medium, 85 ; Consequences on
the lines of the theory of Energy, 87 ; Destructive effect of the new
theories on the astronomical view, 89 ; Lord Kelvin on the vibrations
of the ether, 91 ; Indefiniteness of the electro-magnetic theory, 93.

CHAPTER VII.

ON THE PHYSICAL VIEW OF NATDRE.

Recapitulation, 95 ; Insufficiency of the astronomical, atomic, and kinetic
views, 96 ; The conception of energy, 96 ; The term first used by Young,
98 ; Watt introduces the term " power," 99 ; Poncelet introduces the
term "mechanical work," 101 ; Black, Rumford, and Davy, 102; Cor-
relation of forces, 105 ; Liebig, 105 ; Johannes Miiller, 106 ; F. Mohr,
107 ; Mayer, 108 ; Joule, 110 ; Helmholtz, 112 ; "Work" and "energy"
introduced by Clausius and Thomson, 115; Sadi Carnot, 117; Carnot
introduces the idea of "availability," 119 ; Thomson introduces the idea
of "dissipation," 119; Fourier, 120; His influence on Carnot, 122;
Clapeyron's graphical method, 123 ; Perpetual motion impossible, 124 ;
Application by William and James Thomson, 126 ; The two laws of
thermodynamics, 128 ; Summary statement of Thomson (Lord Kelvin),
132 ; Rankine, Zeuuer, and Hirn, 133 ; Revolutions brought about by
idea of energy, 137; Helmholtz on "tension," 138; "Potential" and
"actual" energy, 139 ; The Scotch school, 141 ; Thomson and Tait, 144;
Clerk - Maxwell, 145 ; Faraday, 146 ; Helmholtz on electro-dynamics,
149; Ostwald's physical chemistry, 153; The factor of "cost" in
industry, 155 ; Berthelot and Ostwald, 157 ; Arrhenius, 159 ; Graham
and Andrews, 161 ; Dissociation, 163 ; Hittorf and Kohlrausch, 164 ;
Victor Meyer on change of chemical views, 165 ; Ostwald's journal, 166 ;
Willard Gibbs, 167 ; Entropy, 169 ; Horstmann, 170 ; Helmholtz's "free
energy," 173 ; Kelvin's "available energy," 174 ; Ostwald's ' Allgemeine
Chemie,' 176 ; " Kinetics" and "energetics," 180 ; Criticism of mechani-
cal view, 183 ; The outcome, 187 ; Recent triumphs of atomic view, 188 ;
Modern electrical researches, 189; The term "electron," 193; Diffi-
culties of Clerk-Maxwell's theory, 194 ; What are electric charges 1
195 ; Dr Larmor's position, 195 ; Objections raised by atomists, 198 ;
Artificial character of modern dynamical explanations, 199; The phil-
osophic problem raised, 199.

CONTENTS. ix

CHAPTEE VIII.

ON THE MORPHOLOGICAL VIEW OK NATURE.

The abstract sciences, 200 ; Convenience and usefulness of the process of
abstraction, "201 ; Interest opposed to the spirit of abstraction, '202 ;
Tlie descriptive sciences, 203 ; The breaking down of old landmarks,
204 ; The spirit of exploration, 206 ; The medical interest, 207 ; Physical
science applied to medicine, 208 ; Schwann, 209 ; Darwin, 209 ; Herbert
Spencer, 210 LJ^Hiewell's divisions abandoned. 210 ; Divisions of natural
history, 211 ; Morphology and genetics, 213; Other aspects, 215; Life
and mind, 216 ; Vitalistic and psycho-physical aspects, 218 ; Morphology
defined, 219 ; Artificial and natural systems, 220 ; Linnaeus and liuffon,
221 ; Morphology of crystals, 222 ; Morphology on a large scale, 224 ;
Humboldt, 225 ; Morphology on a minute scale, 227 ; Its improvement,
230 ; Morphology and classification, 231 ; Study of separate organs, 233 ;
Outdoor studies, 234 ; Jussieu, 235 ; Problem of organisation, 236 ;
Cuvier, 237; "Types," 238; De Candolle, 239; Regularity and sym-
metry, 241 ; Goethe's metamorphosis, 243; The ideal type, 245; Paltcon-
tology, 247 ; Cuvier's catastrophism, 250 ; Study of analogies, 250 ;
Geoffroy Saint-Hilaire, 253 ; Cuvier and Geoffroy, 255 ; Richard Owen,
257 ; Study of homology, 258 ; The cellular theory, 260 ; Hugo von
Mohl, 262 ; Schleiden and Schwann, 263 ; Transition to tlie study of
development, 264 ; Affinity, 267 ; Insufficiency of the morphological
view, 270; Herbert Spencer's "physiological units," 272; Change of
scientific interests, 273 ; The morphological period, 274.

CHAPTER IX.

ON THE GENETIC VIEW OP NATURE.

Statics and dynamics of living forms, 276; "Evolution," 278; "Genesis,"
279 ; Leibniz's ' Protogaa,' 280 ; Kant's nebular theory, 282 ; Laplace,
284; "Cyclical" view, 286; Supplanted by genetic view, 290; Geology,
290 ; Hutton, 292 ; Lyell, 293 ; Embryology, 296 ; Epigenesis and evolu-
tion, 298; C. F. Wolff, 298; Pander and K. E. von Baer, 299; Von
Baer's comprehensive views, 302 ; Von Baer's views in modern terms,
306 ; Phylotaxy and phylogenesis, 308 ; Lamarck, 309 ; The term
"Biology," 312 ; "Environment," 314 ; The "Natur-philosophie," 315 ;
Lamarck and Von Baer, 816; The 'Vestiges,' 318; Popular influence,
320 ; Genetic view in Germany and France, 321 ; Apologetic literature
in England, 324 ; Mansel and Darwin, 326 ; Triumph of the genetic
view, 328; Humboldt's 'Kosmos' and the 'Origin of Species,' 329;

CONTENTS.

"Variation," 331 ; Malthus, 332 ; "Struggle for existence," 333 ; Out-
door studies, 334; "Natural selection" and "sexual selection," 336;
Meaning of natural classification, 336 ; Fertilisation of plants and
"Mimicry," 338; The judicial method, 339; Darwin and Newton
compared, 341 ; Unsolved problems, 343 ; Genetic view on a large
scale, 345 ; Phi1nsophica1 theories, 346 ; Herbert Spencer, 346 ; Haeckel,
347 ; CombinesTTarwin and Lamarck, 350 ; Philosophical problems, 352 ;
Problem of life, 352 ; Genetic view strengthened by physics and chem-
istry, 355 ; The heat of the sun, 357 ; Spectrum Analysis, 359 ; Genesis
of the cosmos — Faye and Lockyer, 360 ; Palseontology and geophysics,
363 ; Dissipation of energy, 364 ; Mystery of the actual processes of
Nature, 366. ' "^

CHAPTER X.

ON THE VITALISTIC VIEW OF NATURE.

The cosmical and the terrestrial views, 369 ; Vagueness of biological theories,
370 ; Impossibility of prediction, 372 ; Oscillation of biological thought,
374 ; The unknown factor, 375 ; The purely scientific aspect, 377 ; In-
fluence of medicine, 379 ; Practice urges the question : What is life ?
381 ; Bichat, 381 ; His Vitalism, 383 ; His definition of life, 383 ; Vital-
ism and Darwinism, 386 ; The extreme vitalism, 388 ; Attack from the
side of chemi.stry, 389 ; Change in organic chemistry, 393 ; Influence of
Liebig, 394 ; " Stoflwechsel" and "Kreislauf des Lebens," 395 ; "Auto-
nomy of the Cell," 395; "Division of Physiological Labour," 396;
Johannes Miiller, 397 ; Influence of doctrine of energy, 399 ; Mechanism,
399 ; Lotze and Du Bois-Reymond, 401 ; Liebig's vitalism, 405 ; Darwin,
406 ; Lotze and Claude Bernard, 409 ; Darwinism and final causes, 411 ;
"Natural result" against "purpose," 413; Organisation and individua-
tion, 415 ; Biology and economics, 415 ; The cellular theory, 417 ;
Schwann, 419; Circulation of matter and energy, 420; "Metabolism,"
422 ; Structural analysis of morphological elements, 423 ; Synthesis of
organic substances, 425; The "physical" method, 428; Properties of
the living substance, 429 ; Environment, 430 ; The "internal medium,"
432; Natural selection within the organism, 435 ; Mobility of living
matter, 438 ; Anabolism and Catabolism, 442 ; Reproduction, 443 ; The
protoplasmic theory, 444 ; Spencers law of limit of growth, 445 ; Fusion
of two elements, 446 ; New problems, 448 ; Weismann on heredity, 450 ;
Biogenesis, 451 ; The ubiquity of life, 452 ; The continuity of living
forms, 453 ; " Pangenesis," 454 ; Germ-substance and body-substance,
457 ; Germ-plasma and body-plasma, 458 ; DiSerentiation of germ-
plasma, 459 ; Weismann v. Lamarck, 460 ; Two aspects of the problem
of life, 462 ; Transition to psycho-physics, 464.

C'UN TENTS. Xi

CHAPTER XI.

ON THE rSYCHO-PHYSICAL VIEW OF NATURE.

Abstract and concrete sciences, 405 ; Their different nieth<Hl«, 466 ; Inner
experience, 468 ; P.sycho-physics, 469 ; Cabaniw'rt simile, 470 ; Preporcl
by Locke and Haller, 471 ; Berkeley's 'Theory of Vision,' 472 ; BcruouUi
and Euler, 474 ; Animal electricity, 475 ; Phrenology, 476 ; Dr Young'*
colour theory, 480 ; Charles Bell, 481 ; Miiller's "8i>ecific ener><ie»," 482 ;
Hehnholtz, 485; "Timbre" defined, 488; Analogy between h'>un<l and
colour, 489 ; Helmholtz and Kant, 491 ; The brothers Wel)er, 492 ;
Fechner's Psycho-physics, 493 ; Influence of Herbart, 494 ; I lis attitck
on the "faculty-psychology," 495; Unity of mental life, 496; Mathe-
matical psychology, 498 ; Lotze's physiology of the soul, 500 ; Two nidf*
of Lotze's doctrine, 502 ; The p.sycho-physics of vision, 504 ; Wheat-
stone's stereoscope, 505 ; Localisation of sensations, 507 ; Lotze's " local
signs," 508 ; Fechner, 508 ; Wundt, 511 ; Physiological i)8ychology, 512 ;
Wundt, Fechner, and Lotze compared, 515 ; The unity of consciouHnew.
516 ; Doctrine of parallelism, 518 ; Miinsterberg, 521 ; Phenomenon of
centrali-sation, 524 ; Externali.sation and growth of mind, 525; Wundt's
treatment of central problem, 525 ; Introspective nietlKKl, 527 ; Tlie
"objective mind," 529; Its study prepared by Herder, 5:51; His
'History of Mankind,' 534; Separation of natural and mental sciences,
534 ; The problem of language, 536 ; The exact treatment, 53S ;
Phonetics, 539; The dividing line between man and brute, 541 ; Sum-
mary, 543 ; The three facts impressed by psycho-physics, 545 ; Trani>i-
tiou to statistics, 546.

CHAPTER XII.

ON THE STATISTICAL VIEW OF NATURE.

Life and Mind as limiting conceptions, 548 ; Results of abstract science, 550 ;
. Uncertainty in the concrete, 552 ; Scientific spirit in businetw, 553 ; The
science of large numbers, 555 ; Belief in general order, 556j Rju-onj«_
" Method of In.stances," 557j General idea underlying enumci-ation,
561 ; Doctrine of averages, 561 ;~ Statistics in France, Germany, an<l
England, 562 ; John Graunt and Halley, 564 ; Probability, Co-oiKration,
E.iuitable Distribution, 566 ; The Science of Chances, 568 ; Condorcet,
570 ; Laplace, 572 ; Four applications, 574 ; Theory of Krn.r, 574 ;
Method of Least Squares : Gauss, 576 ; Laplace, 578 ; guetolet, 579 ;
The "mean man," 580; Social statistics and freewill, 5S3 ; Buckle,

Xll CONTENTS.

584 ; Criticism of pretension of statistics, 586 ; Historical criticism,
588 ; Application in physics, 589 ; Clausius and Clerk - Maxwell, 590 ;
Mathematical representation of experimental laws, 592 ; Irreversibility
of natural processes, 593 ; Lord Kelvin, 594 ; " Availability " a theorem
in probability, 597; "Selection" as conceived by Clerk-Maxwell, 598;
Statistical knowledge of nature, 600 ; As opposed to historical and
mechanical knowledge, 603 ; Sameness and variation, 607 ; Darwin,
608; Galton, 609; "Pangenesis," 610; Lends itself to statistical
treatment, 611 ; Problem of Heredity, 613 ; Mr Bateson's historical
treatment, 615; "Particulate" descent, 615; Application of theory
of error, 618 ; Difference in application to living and lifeless units,
620 ; Professor Pearson : The mathematical problem, 621 ; Statistical
knowledge one-sided, 624 ; Critical methods, 626 ; The instrument
of exact research, 626.

CHAPTER XIII.

ON THE DEVELOPMENT OF MATHEMATICAL THOUGHT DURING
THE NINETEENTH CENTURY.

History of thought, 627 ; Difference between thought and knowledge, 628 ;
Pojjular prejudices regarding mathematics, 628 ; Use of mathematics,
630 ; Twofold interest in mathematics, 632 ; Origin of mathematics,
634 ; Gauss, 636 ; Cauchy, 636 ; Process of generalisation, 638 ; Inverse
operations, 639 ; Modern terms indicative of modern thought, 643 ;
Complex quantities, 644 ; The continuous, 644 ; The infinite, 644 ;
Doctrine of series : Gauss, 645 ; Cauchy's Analysis, 647 ; Revision of
fundamentals, 649 ; Extension of conception of number, 650 ; The
geometrical and the logical problems, 651 ; Quaternions, 654 ; Founda-
tions of geometry, 656 ; Descriptive geometry, 658 ; Poncelet, 659 ;
Cliaracter of modern geometry, 662 ; Method of projection, 663 ; Law
of continuity, 664 ; Ideal elements, 664 ; Principle of duality, 665 ;
Reciprocity, 666 ; Steiuer, 667-; Mutual influence of metrical and pro-
jective geometry, 668 ; Pliicker, Chasles, Cayley, 671 ; Historical aqd
logical foundations, 671 ; Generalised co-ordinates, 673 ; Ideal elements,
674 ; Invariants, 676 ; Theory of forms, 678 ; Theory of numbers, 680 ;
Symmetry, 681 ; Determinants, 682 ; Calculus of operations, 684 ; Prin-
ciple of substitution, 686 ; General solution of equations, 687 ; Theory
of groups, 689 ; Continuous and discontinuous groups, 691 ; Theory of
functions, 693 ; Physical analogies, 696 ; The potential, 698 ; Riemann,
700 ; Weierstrass, 702 ; Riemann and Weierstrass compared, 707 ; Ex-
amination of foundations, 709 ; Non-Euclidean geometry, 712 ; Curva-

CONTENTS. Xlll

ture of space, 715 ; Generalised conceptions, 717 ; Klein's exposition,
718; Sophus Lie, 719; Theory of numbers, 721; Gauss's tlie<>ry of
congruences, 723 ; Generalised conception of number, 726 ; Process of
inversion, 727 ; Rummer's ideal numbers, 728 ; Modern algebra, 730 ;
Algebraical and transcendental numbers, 730 ; Counting and measuring,
732 ; Georg Cantor's theory of the transfinite, 735 ; Corresix)ndence,
736 ; Arithmetising tendency in mathematics, 738.

RETROSPECT AND PROSPECT.

Order and Unity, 742 ; Philosophical problems, 743 ; Individuality, 746 ;
Practical interests attaching to Order and Unity, 748 ; The geographical
centre of philosophic thought, 750.

Index ......... 753

ERRATA.

p.

Y Read Miller instead of Millar.

47 ; text, 1. 4 from below

48 ; 2nd col. of notes, 1. 8 from below

100 ; 2nd col. of notes, 1. 10 from below \ „ , ^, , • . , /■ r.. i

> Read Chasles instead of Charles.

101 ; 2nd col. of notes, 1. 2 from below J

361 ; 1st col. of notes, 1. 5 from above . Read Secchi instead o/Seechi.

f Read C. Hauptmann instead of
407 ; 2nd col. of notes, last word . | Kaufmann.

572 ; text, 1. 5 from above . . . .Read Stirling instead o/ Sterling.

CHAPTER VI.

ON THE KINETIC OR MECHANICAL VIEW OF NATURE.

It was a favourite idea witli the philosophers of antiquity i-
that every thing is in motion, that rest is to be found '""tionin
nowhere in nature, and that the entire process of life and i''"'''*op'^>-
sensation in particular is Ijrought about by the communi-
cation and transference of minute movements of a purely
mechanical kind. Out of the deep conviction that every-
thing around us and in us is in a perpetual flux — a doc-
trme which is usually fathered upon Heraclitus of Ephe-
sus ^ — two distinct problems resulted, and occupied the
thinkers of antiquity : the problem of explaining the
apparent rest and permanency of many observable pheno-

^ Tlie doctrine of Heraclitus (b.c.
500; is placed by Zeller (' Philo-
sophie der Griechen,' vol. i.) in
direct o])po.sition to that of the
Eleatic School (Parmenides, Zeno)
and of Pythagorais. The Eleatics
argued from the unity of all exist-
ence to the impossibility of the mul-
tiplieity and the change of things.
Heraclitus sets out from the concep-
tion that everything is in continual
motion and flow {Ki.vii(T%ai, iv Kivr\aii
tlvai). Our knowledge of Herac-
litus is derived mainly from refer-
ences in tlie writings of Plato and
Ari8t<jtle. K very full account i'^

given by Zeller, and by E. Pfleiderer
( ' Die Philosophic des Heraklit von
Ephesus,' Berlin, 1S8C), who sums
up the fundamental idea in the
beautiful versesof i;oethe(Gedichte,
" Eins und Alles ") :—

" Uiul uiMZUscliiifft'ii (las Gfschall'iie
Daiiiit sicli's niclit zuiii .Starien wall'ne,
Wiikt fwigts, UlifiiHii^;f.s Thuii.
Und was iiiclit war, nun will es werdeu,
Zu reincn .Sinmen, farbij,'en Erden.
In keineni Fallo darl' I's rulin.

Es soil sicli regen, scliatletid liandtdn,
Erst sich gcstalteii, dann verwandk-n ;
Nur sclieinbar stclit's Monieute still.
Uas Ewige regt sich fort in Allen :
Denn Alles muss in Niclits zerfullen,
Wenn es im Sein V>eharren will."

4 SCIENTIFIC THOUGHT.

mena and properties of natural objects, and the higher
ethical problem of fixing upon that which is lastingly
real and important in the continuous change of sensation
and opinion. The latter formed the central interest of
that course of reasoning which began with Socrates and
culminated in Plato and Aristotle ; the former was the
problem of natural philosophy of which Epicurus and
Lucretius stand out as the great representatives. In
a well-known passage of the second book of his great
poem, Lucretius explains the apparent rest of natural
things by the simile of a flock of lustily dancing sheep,
which at a distance looks like a white spot on a green
hillside/ This tendency of philosophic reasoning to see
motion where common-sense only sees rest, to reduce
theoretically the apparently permanent properties of
things to a play of intricate but imperceptible modes
of motion, has governed still more markedly modern
scientific thought. I shall comprise all efforts to give
more definite " expression to this general idea under

1 ' De Natura Rerum,' ii. 308— Omnia qute nobis longe eonfusa videntur

Et velut in viridi candor oonsistere

"Illud in his rebus non est mirabile, colli."

quare,

Omnia cuni rerum primordiasint inmotu, o rpj^j^ ^^^^^ definite expression is

Sumnia tamen summa videatur stare ; ... . . ',

quigtg ! entn-ely a que.stion or niatneniatics.

Prseterquam siquid proprio dat corpora ; It is interesting to note how Le

™ot"s. , . ^ ., ^aEre, in his ' Lucrece Neutonien '

Omms^^en.m longe nostris ab seHsibus ^ ^g^^^.^ ^^^^ ^-gg^^ ..^^.g^^^ ^j^^^

Primorum natura jacet ; quapropter, ubi [ if Epicurus bad had but a part of

the geometrical knowledge of his
contemporary Euclid, and concep-
tions of cosmography the same as
those of many then living, he might

ipsa
Cernere jam nequeas, motus quoque sur-

pere debent ;
Prsesertim cum, qu» possimus cernere,

celent ^ ^. ^

Ssepe tamen motus spatio diducta lo- ; Y^^ye discovCTed the laws of imi-

Nan?sa"i"'in colli toiidentes pabula l»ta ; versal gravity, and not only _ the

Lanigerse reptant pecudes quo quamque laws, but, what was the despair of

vncantes Newton, its mechanical cau.se "

Invitai.t herb* pemraantes rore recenti, /'ATinirn ' T.noretiu* ' vol ii n 13.5^

Et satiati agni ludunt blaudeque coru«- (Munro i^ucretius ^ol u p. i60).

cant; I Lionardo da Vinci (1452-1519) says :

KINETIC OK MECHANICAL VIEW OF NATURE. 5

the name of the kinetic ^ theory or view oi uaiuie.
It has frequently been phiced in opposition to the atomic
theory, and the history of the natural philosophy of the
earlier ages, down to Newton, has in recent years been
written from this point of view.^ If everything is
motion, there must still be something that moves, and
the question arises, What is it that moves ? The
system of Epicurus, and the great poem in which it has
found a classical expression, are really more occupied with
describing the final elements of matter — the so-called
nature of things — than with studying the different modes
of their motion. In the atomic theory, in the conception
of an infinite number of moving particles, the kinetic
tendency of thought repeatedly found botli in auricnt

" There is no certainty in science
■where some mathematics are not
appHcable "' (quoted by Lasswitz,
' Geschichte der Atomistik,' 1890,
vol. ii. p. 11) ; and Leibniz, in a
letter to Foucher dated 1693, con-
demns his earlier tract entitled
' Hypothesis Physica ' as a ''juvenile
attempt of one who had not yet
fathomed mathematics " (Ger-
hardt's edition of Leibniz's ' Philo-
so])hische Schriften,' vol. i. p. 415).
1 The word " kinetic " seems to
have been introduced into scientific-
literature Ijy Ampere, who uses the
term " cin(5mati([ue " to denote that
portion of mechanics where ' ' les
mouvements sont considores en eux-
memes, tels que nous les observons
dans les corps qui nous environ -
nent, et sjiecialement dans les
appareils appek's machines " ( ' Essai
sur la Philosojihie des Sciences,'
1834). In English text-books the
term kinematics, following Thom-
son and Tait ( ' Natural Philnsophy,'
Preface), is used to dcuDte what
PVench writers call " cincmatique

pure," formerly called "phoro-
nomie," the doctrine of the purely
geometrical properties of motion,
without reference to the cause of
motion ; the consideration of the
latter being the special study of
"kinetics," which, together with
" statics," is comprised in the term
"dynamics." The acceptance of
the word " kinetic " to denote the
view that motion is at the bottom
of all natural jirocesses dates prob-
ably from the writings of Thomson
(Lord Kelvin), Tait, and Clerk
Maxwell, who, under the influence
of Newton and the great French
school of Lagrange, Ampere, Poin-
sot, Poncelet, and others, have re-
formed English, and subse<iuently
also German, thought and nomen-
clature in these subject-s.

- I refer to the highly interesting
and important work of Professor
Kurd Liisswiti!, ' (Jcschichte der
Atomistik vnm ^littelalter bis
Newton,' 2 vols., Hamburg and
Leipzig, 1890.

SCIENTIFIC THOUGHT.

Descartes'
develop-
ment of
the kinetic
view.

and modern times a convenient resting-place ; but the
repose which it afforded has never l^een long enjoyed ;
every new attempt to attach permanent, ultimate, or
intrinsic properties to matter, or to its particles, has pro-
voked the desire to explain these properties by going still
farther back, and to see in them, through the dissecting
microscope of the mind's eye, a still more hidden motion.
Two of the most suggestive ideas by which physical
science has benefited in the nineteenth century are the
successful explanation of the dead pressure of gases by
a rapid translational, and of the rigidity of solid bodies
by a rapid rotational, motion of matter. The second
of these suggestions is far from being exhausted in its
capabilities ; the working out of the ultimate problems
which it suggests will be one of the principal tasks of
the coming acre.

The kinetic view of nature, however useful and suggest-
ive it may have shown itself to be in recent times, did not
yield any fruits of real knowledge either in the hands of
the ancients or even in those of the first great philoso-
pher of modern times, in those of Descartes. Just like
attraction and atomism, the kinetic theory had to be
worked out by the instruments of measurement and calcu-
lation, by the exact method, before it led to any actual
results. The kinetic view of nature was made scientifi-
cally possible when Newton, in the First Book of the
' Principia,' laid down for all time the laws of motion.
And yet we can hardly say that Newton himself developed
this promising vein of exploration ; for, even while open-
ing out an endless vista of research, he also, in the enun-
ciation of the so-called law of gravitation, afforded only

KINETIC OR MECHANICAL VIEW OF NATUKK.

one of those convenient resting-places, those preliminary
or provisional bases of thought, from which definite prob-
lems could be attacked and solved. His immediate
intluence lay, therefore, rather in discountenancing the
attempts towards a kinetic view of nature, which belonged
to the school of Descartes, and found an eminent exponent
in Huvsens as well as in others of his contemporaries and ■.'..
rivals ; ^ in fact, he launched into existence what I have an.i n. wto.,.
termed the astronomical view of nature, under the sway
of which the promising beginnings of the kinetic view
were for a long period almost forgotten, but which has
the merit of having built up the most perfect of all
physical sciences, namely, physical astronomy.

The sporadic beginnings of a genuine kinetic view of ^^^..J^^ ^^
natural phenomena, after having been cultivated with "eJ'!" tile
more or less success by Huygens and Euler," and early ccntun-.

' Among these, of whom Lasswitz
gives an exhaustive account, must
be mentioned specially Robert
Hooke (1635-1703). "In the his-
tory of tlie corpuscular theory Hooke
represents quite an original idea,
which would have been of the most
far-reaching importance if Hooke
himself had got beyond a mere
sketch to an exhaustive theory, or
if his conceptions had, through
Huygens' principles of dynamics,
been domiciled in science. Tiie
deviation from kinetic theories
caused by Newton's discoveries
brushed away, with much useless
hypothetical rubbish, likewise
Hooke's more valuable and legiti-
mate suggestions. The doctrine
owing to which we place Hooke
between Borelli and Huygens is his
vibratory theory of matter. It is
given in various writings, but most
clearly in his Lectures ' l)e Potentia
Restitutiva, or of Spring explaining

the Power of Springing Bodies,'
London, 1678 " {op. cit., vol. ii. p.
329 sq.)

- Leonhard Euler (1707-83),
one of the greatest analytical
talents of all times, whose writings
contain the beginnings of a very
large portion of subsequent mathe-
matical work in pure and applied
science, was in physics a great
opponent of Newton's philosophy
as it was then generally expounded
on the continent of Europe. There
it was identified in mechauios
with the theory of action at a
distance, and, in optics, with the
corpuscular theory of light. To
both Euler opposed his ether
theory, of which he gave a popular
account in his celel)rated ' Lettres ii
une princesse d'Allemagne [Princess
of Anhalt - Dessau] sur quelques
sujets de physique et de philoso-
phie" (Petersburg, 176S-7'2, 3 parts).
He had given a seientirtc exposi-

8

SCIENTIFIC THOUGHT.

Young and
Fresnel.

in the nineteenth century by Eumford and Young, were
united into a consistent physical theory by Augustin
Fresnel, who has been termed the Newton of optics, and
who consistently, and all but completely, worked out one
great example of this kind of reasoning. He has the
glory of having not only established the undulatory
theory of light on a firm foundation, but still more of
having impressed natural philosophers with the import-
ance of studying the laws of regular vibratory motion and
the phenomena of periodicity in the most general manner.
His work was carried through, as was that of Newton,
by a combination of observation, measurement, and calcu-
lation ; of experimental skill with mathematical ability.

tion of the same twenty-five years
before in his Berhn memoir, " Sur
la lumiere et les eouleurs" (1745).
Euler was as much opposed to
Descartes' and Leibniz's views as
he was to those of Newton, and
though he admits having forerun-
ners, he hardly refers to the
principal one, viz., Huygens, whose
well - known and useful prin-
ciple he absolutely ignores. In
fact, in spite of his great name and
reputation, his ideas on the ether as
continuously filling space, and his
attempts to explain the phenomena
of light, heat, magnetism, and
even gravitation by means of this
continuum remained isolated, and
had hardly any influence on physi-
cal science. His great friend and
correspondent, Daniel Bernoulli,
remained a firm believer in action
at a distance, and thought Euler
had put forward his hypotheses
with too much assurance. It is,
nevertheless, remarkable how
closelj- the terms in which Euler, in
his posthumous work ' Auleitung
zur Naturlehre' (edited by the
Petersburg Academy in the second

volume of the ' ' Opera posthuma
. . . anno 1844 detecta," 1862),
describes his ether as continuously
filling empty space and existing in
a strained (gcwaltsam) condition,
agree with quite modern ideas on
the subject. Accordingly Euler's
ether theory has in recent times
been studied again by several
writers abroad, of whom I will only
mention E. Cherbuliez, ' Ueber
physikalische Arbeiten
(Bern, 1872) ; F. Rosen-
' Die Geschichte der

(vol. ii., 1884, p. 333 sqq.);
C. Isenkrahe in ' Zeitschrift fiir
Mathematik und Physik ' (Hist. Lit.
Abth., vol. xxvi.) and ' Abhand-

zur Geschichte der Mathe-

vi. ; and E. Miething, ' L.
Lehre vom Aether ' (Berlin,

The first-mentioned author
tries to answer the question why
Euler's ideas remained so isolated.
He says (p. 49): "If we combine
the results of Huygens' and Euler's
investigations, we see that in the
'fifties of the eighteenth century the
undulatory system formed a largely
developed scientific doctrine. , . .

eniige
Eulers '
berger,
Physik'

lungen
matik,
Eulers
1894)

KINETIC OR MECHANICAL VIEW OF NATURE. 9

There is not, indeed, to be found in Fresnel's work .my
central and simple formula — like the gravitation formuhi
of Newton — out of which everything else Hows with
mathematical necessity. His work lay rather in combin-
ing u number of fruitful suggestions thrown out by
contemporary or earlier writers into a consistent whole,
correcting and enlarging them as was found necessary,
and following them out into their logical consequences.
Thus he was able to reveal in a special branch of physical
science new phenomena which had remained unoljserved
or unexplained till that time. In order to understand
how the kinetic view of nature has become firmly estab-
lished in the minds of physicists, it will l)e useful to enum-

In a certain sense Euler carried
further the work of Huygeus, . . .
but as he neglected the useful idea
of a wave-surface and anxiously
avoided Huygens' principle, lie
made the theory which he wished
to defend unfruitful. . . . We think
that Euler did more harm than
good to the progress of that theory.
. . . Euler's theory of light had no
great number of followers." In
England Euler's theory was known
and generally condemned. Priest-
ley, in his ' History of Optics '
(1772), refers to it at some length.
In the well-known attacks in which
Lord Brougham treated so unfairly
and superficially the discoveries of
Dr Young, it is suggested that the
latter borrowed his ideas from
Euler, whose natural philoso])hy is
held in little esteem. The fact is
that Young really went back to
Huygens and Newton, and that he
well knew that his own opinion,
as stated in the first Bakerian
Lecture (1802), "was precisely the
theory of Hooke and Huygens, with
the adoption of some suggestions

made by Newton himself as not in
themselves improbable " (Young's
'Miscellaneous Works,' ed. Peacock,
vol. i. p. 200). In spite of the
great admiration which Young had
for Euler as a mathematician, he
admits that Euler "added no
argumentative evidence whatever to
the [uudulatoryj theory, but has
done a real injury to the cau.se
which he endeavoured to support "
(' Lectures on Natural Philosophy,'
ed. Kelland, vol. i. p. 380). A more
recent and well-informed writer on
this subject, M. Verdet, says of
Euler : " Bien qu'il a donnc? de la
plupart des pln^nomcnes connus de
son temps les explications les plus
inexactes, il ne m3rite pas moins de
conserver dans I'histoire de I'ojitique
une place ominente jiour avoir dit
d'une maniore exjjrcssc que les
ondulations lumineusessont ])Oriod-
iques comnie les vibrations sonores,
et ([ue la cause des differences de
coloration est au fond la monie, que
la cause des differences de toualit«5 "
('(Kuvres de Fresnel,' vol. i. p.
xix).

10

SCIENTIFIC THOUGHT.

erate shortly the different suggestions which Fresnel
assimilated and worked up into his celebrated physical
theory of light.

That light consisted in the motion of something was
in the beginning of the nineteenth century a generally
accepted notion among natural philosaphers. It had
been so ever since Olaus Eomer^ in the seventeenth
century, from the observation of the hitherto unexplained
delay in the disappearance of Jupiter's satellites during
eclipses, had inferred, and Bradley'^ had later on con-

^ The moons of Jupiter, of which
two are visible to the naked eye,
were clearly seen and described as
one of the first discoveries with his
telescope by Gahleo in 1610, and
published in his ' Sidereus Nuncius.'
Owing to their continual and rapid
change of position and their fre-
quent eclipses, they were very soon
considered to furnish a valuable
means of determining the longi-
tude at sea, and were repeatedly
and very minutely observed. In
the course of such observations by
Cassini and Romer at Paris, the
latter found, in 1675, that the period
of occultation of the nearest moon
varied. This variation he traced
to the fact that the earth was
moving towards or away from
Jupiter. If light takes time to
travel, the visibility of the pheno-
menon is necessarily thus antici-
pated or postj^oned. This was the
first occasion on which data for the
calculation of the velocity of light
were forthcoming ; the terrestrial
experiments of Galileo having been
inconclusive. Romer's explanation
and calculation were accepted by
most astronomers ; they were con-
firmed by

- the phenomenon of aberration,
discovered by Bradley. It is ana-
logous to the observation we can

make in a moving railway train
if it rains ; the drops at the win-
dow, though they be descending
perpendicularly, yet appearing in
a slanting direction, in propor-
tion to the velocity of the train.
Both phenomena involve the mo-
tion of light itself and the motion
of the observer, who receives the
luminous impression and locates it
in space and time. The principle
involved in Romer's discovery was
later enunciated by Doppler, who
maintained that the very shoi-t
periods which belong to different
coloui's of the spectrum, according
to the undulatory theory, must
suffer (like the longer periods in
Riimer's occultations) by the mo-
tion of the luminous object or of
the observer in the line of sight. Al-
though this theory was admitted
in acoustics, it took some time
before it was admitted in optics.
Bolzano, Professor of Religious Phil-
osophj' and a colleague of Doppler
at Prague, foretold as early as 1842
the great utility of the principle,
and wrote : "I foresee with con-
fidence that use will be hereafter
made of it in order to solve — by
observing the changes which the
colour of stars undergoes in time
— the questions whether and in
which direction and with what

KINETIC OK MECHANICAL VIEW OF NATLKE. 11

firmed, tliat light takes time to travel from one point
ill space to another. Wherever time is involved in a
phenomenon, motion of something is suggested, and
this something, as well as the nature of its motion,
become subjects of speculation. At the beginning of 5.
the nineteenth century two distinct theories existed andemusion

theoriea.

regarding these matters. Both had succeeded in ex-
])laining and calculating satisfactorily a large number
of the phenomena of light as exhibited by mirrors and
lenses, as well as in optical instruments and crystals.
One of these theories, the so-called emission, emanation,
or corpuscular theory of light, held that luminous
bodies send out minute particles which travel in
straight lines, and, impinging upon the eye, create the
sensation of light. The rival hypothesis, the undul-
atory or vibratory theory, held light to consist in
the periodic wave-motion of a substance called ether,
which was supposed to exist everywhere, filling all
space and interpenetrating all ponderable matter. Both e.
theories are kinetic or mechanical theories, and for their theories

kinetic.

development require the analysis of certain modes of
motion. Both liad to formulate their respective
notions as to the something that moved. Both could
point to analogies in other domains of natural science.
There existed at that time similar corpuscular ex-
planations of the phenomena of heat, of electricity

velocity tliey move, how (li.staut William Huggins (1S6S), Kox-Tiil-

they are from u.s, and mucli else ' bot, and others. That Doppler's

he-sidex," a jjrediction which, since principle i.s really none otiier than

the invention of spectrum analysis U()mer".s was )-emarked by P. G.

and various controversies connected Tait in 'Light' ^•2nd eil., p. '220).

witli the subject, has been brilliantly ^ See also Hoscnborgor, ' Gescli. d.

verified by the discoveries of Sir Physik,' vol. iii. p. 708 Kq(j.

prepared by
acoustics.

12 SCIENTIFIC THOUGHT.

and of magnetism. On the other side there was the
highly developed theory of sound, which had succeeded
in explaining and analysing the properties of sound-
ing bodies by studying experimentally and mathe-
matically the vibrations of sounding strings, membranes
and plates, and also of the air in organ-pipes and other
7. musical instruments. Acoustics, the branch of science

Undulatory

DreuSed bv ^^hich treats of these phenomena, was, next to physical
astronomy, the furthest developed and best founded of
the physical sciences. By following up the elemen-
tary and primitive experience, known already to the
ancients, that sound is everywhere to be traced to the
vibrations or the tremor of some body which has been
struck or otherwise excited, a very complete theory,
substantiated by many experiments, had been built up.
Common-sense and everyday experience had originally
suggested this line of inquiry and explanation.-^ No
other physical science was so early in possession of the
right road of inquiry. In astronomy and optics the
suggestion of common-sense, which regards the earth
as stationary and light as an emission travelling in
straight lines, had indeed allowed a certain amount of
definite knowledge, based upon measurement and cal-

1 Acoustics is probably the only I covery, like universal gravitation, or

phj'sical science where this has luminiferous undulations, we take

been the case; as is well re- our stand upon acknowledged truths,

marked by "\Miewell in his ' History the production and propagation of

of the Inductive Sciences.' He sound by the motion of bodies

there contrasts acoustics with as- ; and of air; and we connect these

tronomy and optics. He might i with other truths, the laws of

have added dynamics, where Gal- motion, and the known properties

ileo's principle of inertia similarly of bodies, as for instance their

reversed the dicta of common-sense. elasticitj\ Instead of epochs of

Whewell says (vol. ii. p. 237) of i discovery, we have solutions of

acoustics : " Instead of having to problems. "
travel gradually towards a great dis-

kine:tic or mechanical view of nature. 13

dilation, to be accumulated. A real physical theory,
however, was impossible until the notions suggested
by common - sense were completely reversed, and an
ideal construction put in the place of a seemingly
obvious theory. This was done in astronomy at one
stroke by Copernicus ; in optics only gradually, tenta-
tively, and hesitatingly. The purely geometrical rela-
tions of straight lines, which light seemed to resemble ;
of pencils of rays, which were bent back or altered in
their direction at the surface of plane or curved mirrors
and of transparent bodies ; seemed to flow quite easily
and naturally when in the seventeenth century the
simple law of refraction had been added to that of
reflexion, known already to the ancients. The sciences
of catoptrics and dioptrics, with their application to the
telescope and microscope, were thus so complete and
useful that to many it must have seemed ditticult and
unnecessary to plunge into a new theory ; ^ especially

' It has always been the aim of process" (Tait, 'Light,' "ind ed.. p.

" geometrical optics " to free itself 160). Owing to the difBculties
from every hyi)othesis on the physi- i which liave more and more jire-
cal nature of light, and to deduce ' sented themselves in the fundamen-

properties of light from a tew simple tal conceptions f)f the wave-theory

geometrical const ructions. Precisely and the vibrating ether, of whicli

in the same way all geometrical and we shall learn more in the sequel of

many jjhysical i)roperties of the this chapter, the desire to bring the

stellar system can be deduced from j)henomena of refraction under a

the kinematical formula of attrac- purely geometrical formula, and to

tion, without discussing the nature emancipate the optics of crj'stals

of gravitation. This desideratum from physical hypotheses, has be-

— so far as optics is concerned — come very pronounced. Huygens'

was before the mind of .Sir W. U. geometiical coustiut-tioM of the

Hamilton, when, during tlie yeai's ordinary and extraordinary raj'.s in

1824-33, he discovered and elabor- uniaxial crystals answered well,

ated the theory of the " character- For luaxial crystals Fresnel had in-

istic function, by the helj) of which troduced the wave-surface, towliicli

all optical problems, whether on the corresponds Hamilton's i-haracter-
corjmscular or on the uiidulatory ' istic function. For didactic pur-

tlieory, are solved by one coniiium poses, and for the practical applica-

14

SCIENTIFIC THOUGHT.

8.
Newton's
authority
on the
Bide of the
emission
theory,

as that theory failed for a long time to explain the
apparently fundamental fact, viz., that light travels in
straight hnes, accompanied by well - marked shadows.
The contrary view, according to which light is a tremor
propagated like sound, was unable to explain the ex-
istence of clearly marked shadows. And so it came
about that Newton, to whom both theories were qiute
familiar, and to whom we owe great discoveries telling
severally in favour of each of these theories, in the
end threw the weight of his authority into the scale
of the corpuscular or emission theory. For many this
was quite sufficient to suppress for a long time all
claims which the tremor or wave theory put forward,
the fact being forgotten or overlooked that Newton
himself had pronounced the pure emission theory to
be insufficient, and had modified and complicated it by

tion to crystallography, it became a
desideratum to reach the geometri-
cal conception of the wave-surface
by purely geometrical methods.
This has been done in an admir-
able treatise entitled ' The Optical
Indicati-ix,' by Mr L. Fletcher. He
has shown that the construction of
the ray, a conception easily defined
geometrically, gives an easier ap-
proach than the construction of
the wave, which introduces phj'si-
cally doubtful definitions ; and
he demonstrates how " a simple
generalisation, involving no refer-
ence either to the constitution
of the luminiferous ether or to
the nature of the physical change
involved in the transmission of
light," will lead to the ray surface
(p. IS). For his purpose he starts
from a surface of reference, which
in singly refractive substances is
a sphere, in uniaxial crystals a

spheroid, and by inference in biaxial
crystals an ellipsoid with three un-
equal axes. This beautiful con-
struction was arrived at, as the
author tells us, before the detailed
history of Fresnel's theorj' had
come to his notice. It is now
known through Verdet, one of the
editors of Fresnel's ' Works ' (1868),
that Fresnel arrived at his wave-
surface by a purelj' geometiical
generalisation of Huygens' con-
struction, and that the conception
of the ether was subsequently
fixed so as to allow the wave surface
to be deduced therefrom (p. 24) ;
surely an interesting case in the
history of scientific thought. As
to the insufficiency of purely geo-
metrical optics for explaining the
phenomena connected with optical
instruments, see Czapski, ' Theorie
der optischen Instrumente,' Bres-
lau, 1893, p. 2.

KINETIC OK MECHANICAL VIEW OF NATURE. 15

suggesting tluiL the rays of light were possessed of tits of
eusy transmission and reflexion, i.e., of regular periodic
changes which could be measured and numbered. To
this amplification of the simple geometrical emission
theory Newton was driven by his own immortal researches,
which revealed the wonderful regularly arranged colours
of thin plates known as Newton's rings. In reading,
after the lapse of nearly two centuries, the reflections of
Newton on the nature of light, reflections which he never 9.
gathered up mto a compact and exhaustive treatise, as he minpests
did the theory of gravitation,^ we recognise that he had t'-eory.
clearly before his mind the two fundamental phenomena
peculiar to light, namely, its property of travelling in
straight lines, and its periodicity, as revealed by certain
delicate experiments of his own. Which of the two
theories should in the end prevail depended on the more
intimate knowledge — to be gained by experiment and
calculation — of the two kinds of motion involved ; of
rectilinear motion of particles under the influence of
contending forces, and of the more complicated periodic
motion pecuhar to waves, tremors, or oscillations. The
first kind of motion, being more easily studied and
also more nearly related to other prevailing studies,
received earlier attention ; the second — especially so

^ It is now sufficiently known
and recognised that Newton, both
in the theory of gravitation and
that of Hglit, did not pro[io8e to do
more than give a preliminary formu-
lation which was applicable as a
ba-sis for e.\perimentand calculation.
His further speculations are con-
tained mostly in the well - known
'yu<?riea' to the 'Opticks,' which

were extended in later editions, and
among which, " to show that " he
" did not take gravity for an esseu-
tial property of bodies," he adiled
one (juestion concerning its cause,
choosing to projiose it by way of a
question, because " he was not yet
satisfied about it for want of experi-
ments" (Advertisement to second
edition, 1717).

16

SCIENTIFIC THOUGHT.

10.
Biot,
Brewster,
and Laplace

against the
undulatory
theory.

11.
Euler the
successor
of Huygens.

12.
Young.

far as the mathematical side was concerned — was
studied later. The former theory has been furthered
more by the ingenuity of physical observers, the
latter more by mathematical reasoning applied to the
invention of crucial experiments which pure observa-
tion would probably never have suggested. Since the
time of Newton, whose name has been used in a one-
sided way to discredit the vibratory theory, although,
as already stated, his discoveries contributed equally to
the formation of both views, the development of the
corpuscular theory owes most to the experimental
labours of Biot in France and Brewster in this country ;
whilst no doubt Laplace's great predilection for atomic
and astronomical explanation of all natural phenomena
gave it great support in the eyes of his many followers
and admirers. The vibratory theory was first made
the subject of detailed study by Huygens, Newton's
contemporary ; it was accepted on purely mathematical
grounds by Euler : the lines of reasoning on which its
ultimate success depended were elaborated by Lagrange's
and d'Alembert's mathematical study of \dbrations ; but
the first great step in advance, based upon experiment
and calculation alike, was taken by Dr Young, who
from 1793 onward studied the subject, and who in
1801 published his 'Principle of Interferences.' Young
was led to his reflections on the phenomena of light by
an inquiry into the nature of sound,^ a province where

^ In his ' Reply to the Edinburgh degree in physic at Gottiugen, it

Reviewers ' (published as a pam- was necessary, besides publishing a

phlet in 1804, see Works, ed. medical dissertation, to deliver a

Peacock, vol. i. pp. 192-215), Young lecture upon some subject connected

gives the following history of his with medical studies, and I chose

speculations: "When I took a for this the Formation of the Human

KINETIC OR MECHANICAL VIEW OF NATURE. 17

the theory of vibrations iuid idready acliieved so much.
He was thus more interested in the physical nature than
in the geometrical properties of rays of light. He was
imp«ressed by the analogies which exist between many
phenomena of sound and light, and acquainted with the
writings of the Continental mathematicians, among whom
Euler was conspicuous as favouring the undulatory or
ether theory of Huygeus. He noticed that in Xewton's
writings were to be found the germs of both theories,
also that the arguments by which Newton convinced him-
self that a theory of undulations could not explain the
rectilinear propagation of light, were untenable.^ On re-
flecting in May 1801 on Xewton's beautiful experiments,

Voice. . . . Wheu I began the out-
line of an essay on the human voice,
I found myself at a loss for a per-
fect conception of what sound was,
and during the three years that I
passed at Emmanuel College, Cam-
bridge, I collected all the informa-
tion relating to it that I could
procure from books, and I made a
variety of original experiments on
sounds of all kinds, and on the
motions of fluids in general. In
the course of these inquiries 1
learned to my surprise how much
further our neighbours on the
Continent were advanced in the
investigation of tlie motions of
sounding bodies and of elastic fluids
than any of our countrymen ; and
in making some experiments on the
production of sounds, I was so
forcibly impressed with tlie resem-
blance of the phenomena that I saw
to those of the colours of thin plates,
with which 1 was already acquainted,
tliat I began to suspect the exist-
ence of a closer analogy between
tliem than I could before have
easily believed " (p. 199). This led

VOL. II.

to his 'Outlines of Experiments
and Inquiries respecting Sound and
Light ' (ibid., p. 64).

i Works, vol. i. p. 200. " New-
ton's arguments from experiment
appear to me to have been sutti-
ciently obviated by what Lambert
has advanced in the ' Memoirs of
Berlin.' . . . The demonstration is
attempted in the ' Principia' : to me
it appears to be defective. . . .
The celebrated Laplace, in com-
paring the opinions respecting
light, is contented to call the
Newtonian doctrine a hypothesis,
which, on account of the facility
of its application to the plienomena,
is extremely probable. If he had
considered the undulatory system
as demonstrably absurd, he would
not have expressed himself in so
undecided a maimer. . . . !Mucli
as I venerate tiio name of Newton,
1 am not tiierefore obliged to be-
lieve that he was infallible. I see
. . . with regret that he was liable
to err, and that his autliority hn.s,
j)erhaps, sometimes even retarded
the progress of science," &c., &c.

B

18

SCIENTIFIC THOUGHT.

13.
His

' ' general
law of the

he " discovered a law which appeared to account for a
greater variety of interesting phenomena than any other
optical principle that had yet been made known." ^ This
principle he familiarly illustrated by the well - known
observation that two series of waves of water entering a
channel reinforce or destroy each other according as their
elevations coincide or alternate in time. He main-
tained that similar effects take place whenever two
portions of light are thus mixed, and this he called
" the general law of the interference of light." He
SYight.^^*^^ showed " " that this law agrees most accurately with
the measures recorded in Newton's ' Opticks,' relative to
the colours of transparent substances, and with a great
diversity of other experiments never before explained." ^
In three papers Young entered " minutely into the con-
sequences of the law of the interference of light.'
Especially in the case of the remarkable phenomena
discovered by Grimaldi, where Ught seems to bend round
the edge of screening surfaces, he showed how under
certain conditions light added to light would create
darkness, and, if removed, would leave light ; and he
^^ boldly generalised the undulatory theory by maintaining
^t^7 that * " a luminiferous ether pervades the universe, rare
ether!' ^™"*' and clastic in a high degree," that the sensation of

»/

1 Works, vol. i. p. 202.

- Ibid., p. 203.

' ' ' This, I assert, is a most
powerful argument in favour of
the theory which I had before
revived : there was nothing that
could have led to it in auj^ author
with whom I am acquainted, ex-
cept some imperfect hints in those
inexhaustible but neglected mines

of nascent inventions, the works of
the great Dr Robert Hooke, which
had never occurred to me at the
time that I discovered the law "
(ibid., p. 203).

■^ The sentences in quotation
marks are the headings of the
different paragraphs in the " Baker-
ian Lecture " of November 12, ISOl.
Works, vol. i. p. 140 sqq.

KINETIC OR MECHANICAL VIEW OF NATURE. 10

different colours depends on tlie difterent frequency of
vibrations excited by light in the retina, and " that all
material bodies have an attraction for the ethereal
medium by means of which it is accumulated within
their substance." In all his conclusions, while differing
from Xewton's doctrines, he sees the strongest proofs of
llie admirable accuracy of Newton's experiments, " but
scarcely any remaining hope to explain the affections
of light by a comparison with the motions of projectiles." ^
Although Young thus estabhshed " a theory of the nature
of light which satisfactorily removes almost every diffi-
culty that has hitherto attended the subject," "' his view
was only tardily accepted. Wollaston,^ with the hesi-
tancy which also characterised liis adhesion to the
atomic theory of Dalton, did not avowedly adopt Young's
views, though he furnished some capital experimental
support for the vibratory theory of light.''

Brougham, in the ' Edinburgh Eeview,' ridiculed ,

O ' o ' Brougliani s

Young's theories, and persuaded the public that they yo^ng"''
stood in contradiction with Newton's discoveries, on
which they were really as much founded as those of
the opposite school. Through such disfavour, arising
largely from a want of skill in grasping the intricate
mathematical problems whicli were involved, the doctrine
of the interference of light, the mainstay of the undula-

Vj.

1 Works, vol. i. p. 169.

- ' Lectures,' ed. Kelland, Preface,
p. ix.

' " Whatever disposition Dr Wol-
laston may liave felt to view this
theory with favour, lie was re-
strained from adopting its con-
clusions by the habitual caution

of his character, or rather by the
want of that bold and enterprising
spirit of speculation which is more
or less essential to those who
make great revolutions in science"
(Peacock, ' Life of Young," p. 375).
* Ibid., p. 374.

20

SCIENTIFIC THOUGHT.

tory theory was, like the atomic theory of Dalton, driven
ovit of the country. Little was heard of it, or of Young's
great contribution, till it was taken up abroad, and in the
very place where the brilliant development by Laplace of
one side of Newton's suggestions had given plausibility
to that form of the projectile theory of light accord-
ing to which its material particles were supposed sub-
ject to attractive forces when they arrived in the
neighbourhood of ponderable matter. Young had
indeed shown that the introduction of such forces
could easily be dispensed with as a basis of many of
Laplace's calculations, and that the results could be
got without making use of molecular attraction. He had
emancipated himself from a belief in the infallibility of
Laplace's methods.^ He was also one of the first to

s/

1 On the 20th December 1804,
Young presented to the Royal
Society his important " Memoir on
the Cohesion of the Fluids. " It was
printed in the ' Transactions' in 1 805.
In December 1805 Laplace read
before the Institute of France, and
subsequently published in a supple-
ment to the ' Mecanique celeste,' his
celebrated theory of capillary
attraction. Young bases his inves-
tigation entirely on the existence
of a surface tension, an ojbservable
and measurable property ; whereas
Laplace falls back upon the hypo-
thesis of an attraction of the
smallest particles of matter, just
as he had employed the idea of
an attraction of matter on the
smallest particles of light to explain
atmospheric refraction according to
the projectile theory adopted by
him. In the sequel this attraction
is reduced to an action which is
insensible at sensible distances. In
a supplement to his memoir, which

appeared anonymously in the fii'st
number of the ' Quarterly Review '
(1809), Young, evidently annoj-ed
that some of his results had been
reproduced without acknowledg-
ment (see Peacock, ' Life of Young,'
p. 205), reviewed the treatise of
Laplace " with a severity which,
though excessive, can hardly be
considered unprovoked or un-
merited" (ibid., p. 206). Inter
alia he says : " The point on which
M. Laplace seems to rest the most
material part of his claim to origi-
nality is the deduction of all the
phenomena of capillary action from
the simple consideration of molec-
ular attraction. To us it; does
not appear that the fundamental
principle from which he sets out
is at all a necessary consequence
of the established properties of
matter ; and we conceive that this
mode of stating the question is but
partially justified by the coincidence
of the results derived from it with

KINETIC OR MECHANICAL VIEW OF NATURE. 21

emancipate himself from the astronomical view of
phenomena. In France the matter stood quite difierently,
and nothing hetter proves the genius of Augustin Fresnel 1.5.

. . . AuKUBtin

than the fact that he ventured against the opp(Jsition of FrcHnei.
great authorities to go his own way, starting from the
beginning and devising many ingenious appeals to nature
herself — i.e., to experiment — in order to establish a
correct view. It is well known that his labours had to
wait many years for their deserved appreciation.^ It is,
however, only just to remark that Arago, an admirer of
Laplace and an intimate friend of Biot, the great
supporter of the projectile theory of light, was the first
to recognise the importance of Fresnel's work, and that
it was largely owing to his co-operation and influence
that the undulatory theory of light trimnplied in the end.
Fresnel's own labours began with the study of the
same phenomena which had led Young to the discovery
of " interference " — -viz., the bands and coloured fringes
observable round the shadows of small screening objects,
or the images of small apertures through which rays of
light are allowed to enter : the phenomena of diftraction
or inflection of light. But whilst Young still explained
these phenomena as arising from the interference of
direct " portions " of light and such as were reflected at
the edge of the screening obstacle, Fresnel showed th.iL the
principle of interference had a much wider application, that
it was adequate to exphiin why a periodic wave-motion,
such as was conceived by Huygens, only sent out rays of

experiment, since he has not de-
monsstratod that a similar coinci-
dence might not be obtained by
proceeding on totally different

grounds" ('Quarterly Review,' No.
l,p. 109).

' See the first volume of this
work, p. 241 note'-.

22

SCIENTIFIC THOUGHT.

light in the direction which was in a straight line from
the origin or centre of light ; that the lateral or secondary
waves destroyed each other almost entirely by interference
or overlapping ; and that the so-called inflection, bending,
or lateral spreading of light, was occasioned by an incom-
plete coincidence or overlapping of these lateral undula-
tions. It appears that about the year 1815 Fresnel had,
through a study of the phenomena of diffraction, arrived
at a conviction, entertained by Young fifteen years earher,
that the projectile theory of light could not explain
them. He had also, by a more rigorous and minute
study of Young's principle of interference, explained the
reason of the rectilinear propagation of light. Yet these
presented rcsults did uot materially affect the adherents of the

by the ''

ofughf '^'^ projectile theory, who had been during late years very
active in studying another class of optical phenomena,
those of polarisation — the power which light possesses
of acquiring, either by refraction or reflexion, a difter-
ence not discernible merely by the eye. This differ-
ence consists in the fact that a ray of light very fre-
quently— as Newton had already expressed it — possesses
I " sides," just as a flat strip or narrow tape has sides if
compared with an ordinary thread or wire, which has no
sides ; or as a wire drawn through a specially shaped die
acquires sides or edges. This property was later termed
polarity,^ a term which implies that the particles of light

17.
Difficulties

1 The word "polarity" was in-
troduced by Malus in 1810. It is
unfortunate, as it suggests the cor-
puscular nature of light. Newton's
conception of "sidedness" ("later-
ality," formed by analogy on Lord
Kelvin's term " chirality " to de-
scribe right- or left - handedness,

see vol. i. p. 432) is a better de-
scription of the phenomenon. It is
contained in the 26th query to the
second edition of the ' Opticks '
(1717). Huygens had long before,
in his ' Traite de la Lumiere '
(written in 1678, published in 1690),
after having given a correct rule for

KINETIC OR MECHANICAL VIEW OF NATURE. 23

have unequal properties in different directions ; and ilie
process of revealing it was termed polarisation. Huygens
had discovered this property, which he found was given
to rays of light if they passed through certain crystals,
notaljly througli Iceland spar, which has the capacity
of di^^ding the rays so that objects seen througli tliem
appear double. He could not explain it on his
hypothesis of undulations, though he had invented a geo-
metrical construction of the double refraction which had
led him to its discovery. Malus showed in 1808 that
double refraction was not a necessary accompaniment of
polarisation, l)ut that ordinary reflexion was enough tu
give these sides to rays of light. Although the projectile
theory gave no complete explanation of this property,
still the supposition that this one- or many-sitledness
was owing to certain geometrical shapes of the i»ro-
jected particles suggested that double refraction might
be explained by the different attraction or repulsion
which these particles suffered according to tlie aspect

determining the course of the ordl- liglit " (Works, vol. i. |i. 247). And

uary and extraordinary rays in Ice- Plains himself, in writing to Young

land spar, described the pheno- as Foreign Secretary of the Royal

menon fully, admitting at the same Society, by whom he had been

time that he could not explain it. awarded the Rumford Medal, >ay8 :

When Malus discovered that light " Je ne regarde pa.s la connaissance
might acquire this peculiar pro- , de ces phononienes counue plus

perty by reflexion, Young wrote
in a review ('Quarterly Review,'
May 1810): "The discovery . . .
appears to us to be by far the most
important and interesting that has
been made in France, concerning

favorable au sj'stome de roniis.sion
qu'h celui des ondulations. lis do-
montrent ^galement linsuffisanoe
des deux hypotheses ; en etlet com-
ment expliijuer dan.s I'une ou dans
I'autre pounjuoi un rayon polarii«^

the properties of light, at least since ' pent traverser sous uiie certaine

the time of Huygens ; and it is so inelinaison uu corps diaphnne, eu

much the more deserving of notice, se ddrobant totalement k la n.^-

as it greatly influences the general flexion partielle qui a lieu h la sur-

balance of evidence in the com- face de ces corps dans les ciui ordi-

parison of the undulatory and the naires ?" (quoted l>y Peacock, 'Life

projectile theories of the nature of of Young,' p. 248 note).

24 SCIENTIFIC THOUGHT.

which they presented when approaching ponderable or
attracting substances. Nothing of this kind seemed
imaginable on the undulatory theory, which, reasoning
from the analogy of sound, considered light to consist
in a rapid to-and-fro motion of the ether in the direc-
tion of the rays of light. Sidedness or " laterahty "
seemed inconceivable. Eays of light possessing this
property would (as Fresnel and Arago showed in 1816)
eventually even lose their capabihty of interference, that
main property discovered by Young, the principal argu-
ment for the vibratory theory. " Every day in that
remarkable period — when so many great observers were
endeavouring to outstrip each other in the career of
discovery — was making known modifications and phe-
nomena of polarised light which no existing theory was
yet competent to explain. It was polarisation which
still continued to cast a dark cloud over the hopes and
fortunes of the undulating theory." ^ Thus it was
natural that the representatives of the astronomical view
of nature, who, headed by Laplace, had given so many
real and some apparent explanations of complicated phe-
nomena, and to whom the conceptions of the projectile
theory of light seemed more promising, should think it
time to attack the very stronghold of the \abratory theory,
namely, the phenomena of interference, exhibited mainly
in diffraction, and, by a minute experimental and mathe-
matical analysis, show whether these phenomena could
not be brought within the pale of their fundamental con-
ceptions. For the discoveries of Young and Fresnel had
not shaken them. Accordingly the Paris Academy of

1 Peacock in ' Life of Young,' p. 383.

KINETIC OR MECHANICAL VIEW OF NATURE. 25

Sciences in 1817 issued for the competition on the j^iand
mathematical prize for 1 S 1 0 the subject of DilTraction,
" jiersuaded that a deeper investigation of these phenijmena,
which seemed opposed to their cherished doctrine, wcjidd
give occasion for new triumphs." ^ In this lliey were
doomed to disappointment. At the request of Arag(j and
Ampere, Fresnel entered for this competition, and his
* Meinoire sur la Diffraction ' was crowned the following
year. In it he viewed the subject from a much more
general point of view, examining the two rival systems —
that of emission and that of undulations — as to their
capacity for explaining the phenomena of diffraction.
The result seemed decisive in favour of the latter theory,
and the impression produced was all the greater because
Poisson," one of the judges and a believer in the emission
theory, drew certain apparently very paradoxical conse-

18.

1 Yerdet in ' Qiuvres de Fresnel,'
vol. i.. Preface, p. xxxv., &c.

- The commissinn cousisted of
Biot, Arago, Laplace, Gay-Lussac,
and Poissuii. Arago drew up the
report, which is published in the
first volume of the ' Oiuvres de
Fresnel,' No. 13. It closes with
the following note: "M. Poisson,
depuis le rajjport de la commission,
ayant fait remarquer ii M. Fresnel
que I'intdgrale qui represente
rintensit(5 de la luniicre difYractie
peut aisomeut s'obtenir pour le
centre de I'ombre d'un ecran ou
d'une ouverture circulaires, celui-ci
fit le calcul pour ce dernier cas, et
trouva (|ue I'expression gendi-ale
d'intensite devenait alors seinlilable
h celle de la lumierc reflechie dans
le phononiene des anneaux colorcs ;
que 868 minima dtaient tout h fait
nul et devaient presenter ainsi un
jioir h. peu prds parfait dans une

lumicre sensiblenient honn)g6ne ; du
moins pour les trois premiers ordres,
oil le d^faut d'homogoneitA? de la
lumi6re rouge employee ne se fais-
ait pas encore trop sentir : c'est
aussi ce que Texperience a confirmo ;
en plarant le foyer de la loupe du
micrometre aux distances calculoes
ou appercevait comme une tache
d'encre au centre de I'ouverture
circulaire. . . . Ou peut rcgarder
cette experience comme une verifi-
cation des foi-mules de M. Fresnel,"
&c. ('Qiuvres,' vol. i. p. 245).
See also the note which Fresnel
attached to his memoir (il>id., p.
365). The memoir was crowned in
1819, Imt not publislied till 1826.
An abstract of the first and a re-
print of the second ]>art had been
publislied in tiie 11th vol uf the
' Annales de Chimie et ile Pliysique.'
Fresnel sent two co]iie8 to Vounp,
19th September 1819.

26

SCIENTIFIC THOUGHT.

quences from Fresnel's calculations : Fresnel was invited
to prove by experiment these astonishing results, and he
found them actually confirmed. So far as the phenomena
of diffraction — erroneously termed infiection — are con-
cerned, this work of Fresnel established the fact " that
the theory of undulations foretells the phenomena as
exactly as the theory of gravitation foretells the move-
ments of the heavenly bodies."^ It was, however,
quite different if we consider that other larger class of
phenomena^ which revealed the fact that rays of light

1 See Schwerd, ' Die Beugungs-
erscheinnugenausdeuFundamental-
gesetzen der Undulations - theorie
aualytisch entwickelt ' (Mannheim,
1835), Preface, p. x.

- The history of the final estab-
lishment of the wave theory of
light has been written by Whewell
in the second volume of the
' History of the Inductive Sciences. '
The main sources which existed at
that time were the memoirs of
Young and Fresnel, and the ' Life
of Dr Young ' by Peacock. This
^ history has been written again with
ampler materials by M. Verdet as
an introduction to the edition of
the complete works of Fresnel, pub-
lished in 1866. It is well to read
both accounts, as some points which
remain obscure in the earlier are
fully explained in the later. There
is no doubt that Young suggested
that the phenomena of " sided-
ness," which rays of light exhibit,
lead to the conception of a lateral
or transverse movement ; he also
hinted that in biaxial crystals the
shape of the wave might be that
of an almond or an amygdaloid
(article " Chromatics," reprinted in
Works, vol. i. pp. 317, 322), v?hat we
now call an ellipsoid ; but M. Ver-
det is right in characterising Young's
suggestions as vague, and vindicat-

ing for Fresnel the full merit of
having defined transverse vibrations
and of having introduced the ellip-
soid of elasticity as a geometrically
perfect means of finding by con-
struction the paths of rays in biaxial
crystals. The method was quite
independent of the theoretical views
regarding light which were con-
tained in the same memoir, the
consideration of which was referred
to a commission consisting of
Ampere, Arago, Fourier, and Pois-
son. Of these Ampere had sug-
gested transverse vibrations as a
means of explaining the phenomena
of polarisation ( ' CEuvres de Fresnel, *
vol. i. p. 394). Arago, though a great
friend of Fresnel and a believer
in the wave theory, never to the
end of his life accepted the
hypothesis of transverse vibrations
(ibid., p. Iv.) Poisson, a supporter
of Laplace's molecular theorj% re-
tired from the commission ; and
Arago, who composed the Report
to the Academy, confined himself
to pronouncing on the experimental
portion, which fully confirmed the
general law of double refraction an-
nounced by the author ; refraining
from the expression of any opinion as
to the theoretical portion, it being
premature to do so (see ' CEuvres
de Fresnel,' vol. ii. p. 463). Im-

KINETIC OK MECHANICAL VIEW OF NA'ITKK. 2

~ I

have sides, the phenomena of " laterality " (niLsleacUngly
called polarisation). The believers in the emission theory
studied them wiih predilection, l>iot at their head. Al-
though to Yoinig their explanati<jns were unconvincing,
their results were so perplexing that he wrote to l^rewster
in September 1815, "With respect to my own funda-
mental hypotheses respecting the nature of light, 1 be-
come less and less fond of dwelling on them, as 1 learn
more and more facts like those which j\lr Malus dis-
covered ; because, although they may not Ite incompat-
il)le with these facts, they certainly give us no assistance
in explaining them." ^ "When Young wrote this, Fresnel
had not yet presented his first memoir on DiHraction to
the Institute ; his own labours on that matter were more
than ten years old ; the phenomena of polarisation had
meantime absorbed the attention of opticians. In the
summer of 1816 Arago and Gay-Lussac paid a visit to

mediately after the reading of fraction, ils font disiKiraitre une

Arago's report, Laplace, " who had ^ difficulte qui ne pouvait luauquer de

thought for a long time that his rcsulter de toute dtudetaut soit ])eu

analysis had made the phenomena approfondie de ses ecrits imprimos.

of double refraction depend on his ... Un a vu au contraire que cette

emission theory," proclaimed the loi s'est manifesto Ji Fresnel coniiue

great importance of the memoir, , le rdsultatd'une generalisation toute

and declared that he placed these semblable aux g(?n<5ralisations iiui

researches above anything that had ont ameue la plupart dcs grandes

for a long time been communicated , ducouvertes. Lorsqu'il a voulu

to the Academy ( 'Qiuvres de Fres- ensuite se renclre compte de la loi

nel', vol. i. p. Lxxxvi., and vol. ii. par une thdorie mecanique, il n'e.st

p. 459). We are indebted to M.
Verdet for having shown that the
discovery of this law by Fresnel is
independent of the theoretical con-
siderations by which he tried

pas etonnant qu'il ait, [leut-ctre h
son insu, conduit cette thoorie vers
le but qu'il couuaissj\it il'avance,
et qu'il ait itc determine, dans le
choix dcs hyp<'th^ses au.viliaiies

synthetically to prove it. On this moins par leur vraisemblance intriu-

point he says : " En r(5vdlant la suque tiue par leur accord avec ce

sdrie de generalisations et de con- qu'il utait en droit de considiVer

jectures par lesquelles Fresnel est comme la verito " (ibid., vol. ii, p.

arrive peu ii j)eu a la ducouverte 327. Cf. vol. i. p. Ixxxiv. )
dea lois g(5n(jrales de la double re- ' Works, vol. i. p. 36 L

28

SCIENTIFIC THOUGHT.

10.
Young and
Fresnel
introduce
the concep-
tion of
transverse
vibrations.

England and to Young, who learnt from them that,
mainly owing to Fresnel's labours, his own researches
had " attracted much more notice in Paris than in
London, . . . leading to some very warm discussions
among the members of the Institute on some public
occasions." ^ It is likely that this visit, as well as the
discovery of Arago that rays of light when polarised
— i.e., possessed of laterality — lose under certain condi-
tions their power of interference, induced Young to
resume seriously the consideration of the subject. In
January 1817, long before Fresnel had made up his
mind to adopt a similar conclusion (suggested to him
by Ampere), Young announced in a letter to Arago
that in the assumption of transverse vibrations, after the
manner of the vibrations of a stretched string, lay the
possibility of explaining polarisation or " laterality," and
the non - interference of rays whose sides are perpen-
dicular to each other. By introducing this conception
of a lateral or transverse movement into physical optics
— a conception shortly afterwards adopted by Fresnel —
the data were provided for a complete mechanical or
kinetic explanation of all phenomena of homogeneous
rays of light — i.e., of such rays as, on passing through
refracting substances, are not divided into several
colours.

Two great problems now presented themselves, one of
which Fresnel attacked with great success. The other is
hardly yet solved. Inasmuch as these tw^o problems
have largely occupied physicists and mathematicians all
through the century, and guided their reasonings in other

1 Peacock, ' Life of Young,' p. 389.

KINETIC OR MECHANICAL VIEW OF NATL'UE. 29

l)ianches of research, it will l)e useful to deHue them
more clearly.

Ever since Newton laid down the general laws of
motion, it has been seen with increasing clearness t<i Yte
the object of mathematical physics to describe the exist-
ing- ol)servable or supposed forms of miitJMii in nature by
having recourse to the fundamental laws of motion
coupled with the smallest possible number of assumptions
as to the ultimate constitution of matter or of the
iniiving substance. As soon as any definite assumption
was made, it became necessary to follow it into all
possible consequences, and not to make any new assump-
tions so long as the capabilities of the old ones were un-
exhausted, or so long as it was not shown either that the
new assumption w^as based upon observable facts, or
did not involve latent contradictions with those already
admitted. Newton had led the way by making one
great assumption in addition to laying down the laws of
motion. This was the property of gravitation. Heed-
less of Newton's warning that this assumption, though
proved by experiment, did involve certain seeming
absurdities which called for further examination, philo-
sophers like Boscovich, and mathematicians like Laplace,
busied themselves with drawing all the consequences of
the assumption, and they saw the most hopeful way of
further progress in an extension of it into the realm
of molecular physics. Young was probably one of the
first to see the futility or the mere semblance of truth
in the astronomical view of nature. He approached both
by experiment and mathematically the great class of
phenomena of small, extremely rapid, periodic move-

30

SCIENTIFIC THOUGHT.

20.
Mechanical
difference
between
light and
sound.

ments ; and he applied his results for the purpose of
gaining a new basis for the theory of light. His specu-
lations were, however, not confined to this. He had
started by studying sound and had shown its analogy
with light ; but when he ultimately ventured on the bold
assumption of a lateral to-and-fro tremor, he showed
where the nature of light differed from that of sound.
It was in this : that the tremor of sound was that of an
elastic fluid such as air, or of any substance in which the
movement is carried forward by alternate compression
and expansion. But the phenomena of light seemed to
require for their explanation two seemingly incompatible
assmnptions : first, a substance more subtle than air, incap-
able of impeding the motion of matter in it ; and, secondly,
a substance having vibrations resembling the tremors
of what we term sohd bodies, e.g., stretched strings.
Young is one of the founders of the theory of elasticity.-^

^ The hi.story of the theories of
elasticity has been written by Isaac
Todhunter and continued by Pro-
fessor Karl Pearson. A perusal of
the earlier portion of the work
shows how imperfect were the ideas
which existed at the time when
Fresnel approached the problem in
the interest of the wave theoi-y
of light. The greatest mathemat-
icians, like Euler, had handled the
subject, and had damaged their rep-
utation, especially in this country,
by serious errors or by conclusions
which agreed ill with experience.
Young was one of the earliest writers
on elasticity in the nineteenth cen-
tury ; having given considerable at-
telition to the subject in his Lec-
tures on Natural Philosophy (de-
livered in 1802, published in 1807).
He there introduces the modulus of
elasticity, a term which, with some

change of meaning, survives in mod-
ern treatises. His name, as well as
that of Hooke (" Ut tensio sic vis '"),
appears accordingly at the portal of
the science. Young, though Tod-
hunter has a significant remark on
his obscurity of style, stands out
prominently, if compared with con-
temjDorary writers in this country,
by his thorough knowledge of the
labours of Continental mathemati-
cians, among whom he assigns special
merit to Coulomb. In general, Tod-
hunter has little to say in praise of
English science in this department
during the earlier part of the cen-
turj', and he considers the " perusal
of English text-books on practical
mechanics published in the first
half of the century a dispiriting
task," in consequence of a " want of
clear thinking, of scientific accuracy,
and of knowledge of the work ac-

'!'

KINETIC OR MECHANICAL VIEW OF NATURE. 31

He must have fully realised the difticulty of imagining a
substance more subtle than air and yet endowed with the
property of rigidity, known to us only in solid Ixidies.
The elaboration of the theory of light pressed upon
physicists and mathematicians a more careful study of
the different states in which matter can exist. The
different properties which this hypothetical substance 21.
called ether must possess had to be mathematically de-
fined ; and, further, it had to be shown whether it
would be physically possible for a body, subject to the
empirical laws of motion, to possess certain of the pro-
perties of what we term solids, and yet to be in other
respects the very opposite of a solid. Tlie solution of the
first problem was a purely mathematical performance, in
which many eminent mathematicians, such as Cauchy,
Neumann, Green, M'Cullagh, and Stokes,^ have been

complished abroad " (vol. i. p. 10.')). : brothers Weber, whose ' Wellenlehre

"It is difficult to picture the re- auf Experimente gegriindet' ap-

markable scientific ignorance of peared in 1825. In it wave-motion,

practical men iu England in the ' such a,s the theories of sound and

first quarter of the century. One light had made specially interesting

can only trust that there may be a and important, was experimentally

closer union of practice and theory examined and illustrated. The

in our own day " (p. 106). This I theory of elasticity now received a

passage was probably written iu the ' new ally, viz., tlie ela-stic theory

'seventies. " of light or of the ether. Thougli

According to Todhuntor, the true , suggested by Fresnel, its real

theory of elasticity was founded founder was Cauchy.

in France between the years 1820 j ^ The natural philosojiher to whiun

and 1830, by Xavier, Poisson, and , we are most indebted for l>ringing

Cauchy on the one side ; by the ex- clearness and definiteness into our

perimeutal work of Savart on the | ideas and our language in these

other. It had been allied with very intricate subjects is Sir Ceoi-ge

theoretical acoustics since Euler's Stokes. In two ])apers, |)ublishcd

time. Chladni in Germany fur- respectively in 184.') and 1849 (see

thered that branch of the subject in ' Matliematical and Thysical I'ajwrs,'

three celebrated works: ' Theorie vol. i. pp. In-l'ld, and vol. ii. pp.

des Klanges' (1787), ' Akustik ' 8-13), he haa done more than any

(1802), 'Beitriige zur Akustik' other writer to fix for nearly half

(1817). Chladni infiuenced the a century the conceptionn and tlie

32

SCIENTIFIC THOUGHT.

engaged. The solution of the latter prohlem involved
experiment as well as calculation. The different states
and properties of matter had to be studied from quite
novel points of view : they had to be defined in terms
of the different kinds of motion and of inertia, i.e.,
resistance to motion or capacity for motion. The popular
conceptions of solidity, rigidity, fluidity, expansion, pres-
sure, weight, required to be translated into the language
of ordinary dynamics, that it might appear to what

vocabulary of physical optics. He
has, however, whilst working inde-
pendently, been careful to point
out to what extent his views
agree with or are anticipated by
the important writings of Cauchy
and Poisson in France. Up to his
time the ether was universally
spoken of as a fluid. Stokes led
up to the "elastic solid" and the
" jelly " theory of the ether. "Un-
doubtedly," he says, " it does vio-
lence to the ideas that we should
have been likely to form a priori
of the nature of the ether to assert
that it must be regarded as an
elastic solid in treating of the
vibrations of light. When, how-
ever, we consider . . . the diffi-
culty of explaining these phenomena
by any vibrations due to the con-
densation and rarefaction of an
elastic fluid such as air, it seems
reasonable to suspend our judg-
ment and be content to learn from
phenomena the existence of forces
which we should not beforehand
have expected. . . . The following
illustration is advanced, not so
much as explaining the real nature
of the ether, as for the sake of
offering a plausible mode of con-
ceiving how the apparently opposite
properties of solidity and fluidity
which we must attribute to the
ether may be reconciled. Suppose
a small quantity of glue dissolved

in a little water so as to form a
stiff jelly. This jelly forms, in fact,
an elastic solid : it may be con-
strained . . . and return to its
original form when the constraining
force is removed, by virtue of its
elasticity ; but if we constrain it
too far it will break. Suppose now
the quantity of water to be ' in-
creased ' . . . till we have a pint
or a quart of glue-water. The jelly
will then become thinner. . . . At
last it will become so far fluid as to
mend itself again as soon as it is
dislocated. Yet there seems hardly
sufficient reason for supposing that
at a certain stage of the dilution the
tangential force whereby it resists
constraint ceases all of a sudden.
In order that the medium . . .
should have to be treated as an
elastic solid, it is only necessary that
the amount of constraint should
be very small. The medium would,
however, be what we should call a
fluid as regards the motion of solid
bodies through it. . . . Conceive
now a medium having similar pro-
perties, but incomparably rarer
than air, and we have a medium
such as we may conceive the ether
to be, a fluid as regards the motion
of the earth and planets through it,
an elastic solid as regards the small
vibrations which constitute light "
( ' Papers,' vol. ii. p. 11 sqq.)

KINETIC OR iVIECHANICAL VIEW oF NAnUK. MM

extent these various properties could exist separately or
were mutually dependent.^

In the domain of sound and light the early part of
the century was thus, as we have seen, witness of a
useful interpretation of these various modifications as
merely different kinds of motion : both were considered
to be vibrations, the frequency of which marked the
position of a note or a tint in the musical or chromatic

' That is to say, the number of
independent constants hiid to Ije
fixed which would permit isotropic
or anisotropic bodies (i.e., bodies
which are either equal in all direc-
tions, or unequal in the three direc-
tions) to be mathematically defined,
and in consequence their behaviour
studied, if subjected to strains and
displacements. Over these defini-
tions there arose the gi-eat contro-
versies of those who believed in a
small number of constants (one
constant in isotropic and fifteen in
anisotropic bodies against two and
twenty-one respectively). A good
account of these controversies and of
their mathematical and physical sig-
nificance will be found in the first
volume of Todhunter's ' History of
Elasticity,' by Professor Karl Pear-
son, p. 496 sqq. The former theory
is termed the rari- (few) constant
theory, the latter the multi- (many)
constant theory. The rari-constant
theory is based upon the assump-
tion that a body consists of mole-
cules, and that the action between
two molecules ... is in the line
joining them. It is an outcome of
the atomic and action - at - a - dis-
tance theory in vogue on the Conti-
nent, and is accordingly mainly
represented by Navier, Poisson,
Cauchy, and others, notably Saint-
Venant. The other school, mainly
represented by mathematical physi-
cists in this countrj', starts not from
a mathematical formula (which,

VOL. II.

after all, loses its precision as the
active forces are reduced to the
vague statement that they act t-en-
sibly only at insensible distances)
but from physical data. It is an
analogue to Young's theory of cap-
illarity as against Laplace (see
above, p. 20, note). '"The .some-
what unsatisfactory nature of the
results of those investigations pro-
duced, especiallj' in this country, a
reaction in favour of the opiXM-ite
method of treating bodies as if they
were, so far at least as our experi-
ments are concerned, truly continu-
ous. This method, in the hands of
Green, Stokes, and others, has led
to results the value of which does
not at all depend on what theory
we adopt as to the ultimate con-
stitution of bodies " (Clerk Maxwell,
'Scientific Papers,' vol. ii. p. 253).
" After the French mathematicians
had attempted, with more or less
ingenuity, to construct a theory of
elastic solids from the hypothesis
that they consist of atoms in equi-
librium under the action of their
mutual forces, Stokes and otiiers
showed that all the results of this
hypothesis, so far at least as they
agreed with facts, miglit be deduced
from the postulate that ehu-itic
bodies exist, and from the liyi)oth-
esis that the smallest portions into
which we can divide tliem are
sensiblj' homogeneous" (id. ibid.,
p. 449).

34 SCIENTIFIC THOUGHT.

scale, and the amplitude or height of the wave-motion

22. of which decided its intensity. There was floating about

other "

theories ^^® vaguc idea that heat also was to be interpreted
as a mode of motion ; still vaguer were the kinetic
notions as to electricity and magnetism ; whilst some
early attempts to explain gravity, not as an inherent
property of matter, but as a consequence of the motion
of matter itself, which was possessed merely of inertia,
had been half forgotten.

There is no doubt that the successful development of
the undulatory theory of hght induced many minds to
dream of an ultimate kinetic explanation or interpretation
of all natural phenomena, when in the course of the
tliird quarter of the century this direction of thought
received a great impetus through three independent
branches of research of a purely theoretical kind. These
have led to a very remarkable development of the kinetic
view of natui^e ; in fact it is mainly through them that
this view has become possible not only in special depart-
ments, but on a universal scale. They have, each in
its own way, led to a great extension of our experi-
mental knowledge ; one of them has likewise led to many
practical appHcations. AMiat most interests us here is
the peculiar direction which they have given to a great
volume of mathematical and physical thought of our day.

23. The first of these hues of research was connected with

Kmetic '

theoiyof and grew out of, the atomic hypothesis. It cuhninated
in the kinetic theory of gases, in which the names of
Joule, Clausius, and Clerk Maxwell are prominent. Of
this I have treated already in the fifth chapter. It
rests on a study of the average effect produced by a

KINETIC OR MECHANICAL VIEW OF NATURE. 35

swarm of Ijodies, subject to a transverse movement in
straight lines like projectiles, and continually encounter-
ing each other on their way. Tlie second line of research 2*.

Voricx

in ((ucstioii is the study of bodies subject to rapid move- '""»j<'«».
nient round an axis, but immersed in ;i medium which
is itself movable like water, but not in a r(jt;iry but
merely in a flowing motion. The whole .series of in-
vestigations which started 1)}' detining vortex or whirUng
motion as distinct from transverse, Howing, or projectile
motion, and from vibratory to - and - fro motion, was
initiated by Helmholt/^ in 1857 in a purely mathe-
matical paper, and then applied and greatly extended
by Sir William Thomson in the conception of the vortex
atom. The third branch of research had its origin in 2i.
experimental investigations carried on for many yeare on r^-starehe*.
peculiar lines, and quite independently, by Faraday: it
was put into mathematical language by (Jlerk Maxwell
in his celebrated treatise on electricity and magnetism
which appeared in 1872. It will be my object to show
in how far these ditferent investigations have confirmed
and developed the kinetic view of natural phenomena.
But before doing this it will be well to realise what
specific problems presented themselves to theoretical
physicists when once the undulatory conception of light
had taken hold of their minds ; what pecuhar dithculties
were involved ; and into what distinct new lines of
reasoning they were conducted.

We saw above that when the gravitational explana-
tion of a large class of phenomena had a century earlier
gradually gained ground, a great variety of researches
was suggested by it, and new lines of reasoning opened

36 SCIENTIFIC THOUGHT.

out, which in the course of the eighteenth century com-
bined to estabhsh what I termed the astronomical view
of nature. The undulatory theory of hght, estabhshed
by Young and Fresnel during the first quarter of the
nineteenth century, was a breaking away from what
then seemed to many Continental philosophers a prom-
ising line of thought, a unifying principle in natural
philosophy. As long as light was thought to consist of
particles, however minute, which were projected from
luminous centres, the mechanical laws of impact, of at-
traction and repulsion, could be applied ; and they went
a considerable way in apparently explaining the ordinary
phenomena of light, such as motion in straight lines, re-
liexion, and refraction. They failed indeed in the case
of diffraction or inflection, and still more in those pheno-
mena which were misleadingly grouped under the term
polarisation. The new theory seemed specially adapted
to these more recently discovered phenomena, but it had
to be admitted that the explanation of reflexion and
refraction of light at the surface of polished, transparent,
•2«. or opaque bodies met with considerable difficulties. The

Problems

uature'of ^^^ theory had introduced the conception of an all-

the ether, pervading, apparently imponderable substance, the ether.

The reintroduction of this conception into physical

science was repugnant to many thinkers of the then

prevailing school,^ and it became more so when it hhd —

1 One of the crucial tests for i measured the speed of light in
deciding between the corpuscular various media. He proved that

and the wave theory of light was
the relative speed with which light
travels in air and in water, i.e., in
a refracting substance. Foucault,
in 1850, by a very ingenious method,
improved since by Mitchelson,

light moves faster in air than in
water, whereas on the corpuscular
theory the speed of light in water
must be to its speed in air as 4 to 3
approximately. "This finally dis-
posed of the corpuscular theory "

KINETIC OR MECHANICAL VIEW OF NATUUH 37

for the purpose of serving as the carrier of a definite
kind of wave - motion — to he endowed with most mys-
terious, seemingly contra(Hctory properties.^ Neverthe-
less the development of this conception, the desire to
define more minutely the properties of this fictitious
sul)stance of wliich we have no direct perception, wime
in the course of the century to guide more and more the
work of experimentalists as well as theorists. We meet
with objections in the beginning, when the conception was
first introduced, such as were urged by many chemical
philosophers when Dal ton reintroduced and formulated

(Tait, 'Light,' p. 192). Sir G. G.
Stokes tells us " that in a course
of conversation with Sir David
Brewster, who had just returned
from France, where lie witnessed
the celebrated experiment by which
F(»ucault had just proved experi-
mentally that light travels faster
in air than in water, he asked him
wliat his objection was to the
theory of undulations, and he
found he was staggered by the
idea in limine of filling space with
some substance merely in order
that 'that little twinkling star,'
as he expressed himself, should be
able to send his light to us"
('Burnett Lectures on Light,' p.
15).

^ It is known that the two phil-
osophers who in the middle of the
century did more than any others to
introduce the positive or exact spirit
into general thinking and into
philosophical literature, Auguste
Comte and John Stuart Mill, were
both opposed to the theory of an
ether. Huxley, in speaking of
Comte, exclaims : " What is to be
thought of the contemporary of
Young and of Fresnel who never
misses an opportunity of casting
scorn upon the hypothesis of an
ether — the fundamental basis not

only of the undulatory theory of
light, but of so much else in
modern physics, and whose con-
tempt for the intellects of .some of
the strongest men of his generation
was such that he puts forward the
mere existence of niglit :« a refuta-
tion of the undulatory theory ? "
(See 'Philosophic Positive,' vol. ii.
p. 440, anil Huxley, ' Lay Sermons,'
J). 134.^ The fourteenth chapter
of Mill's 'System of Logic,' written
originally in the beginning of the
'forties, but subsequently anno-
tated with reference to some of
AVliewell's criticisms, contains a
lengthy discussion of the hypoth-
esis of an ether. Mill says (vol. ii.
]). 21, seventh edition): " What has
most contributed to accredit the
hypothesis of a physical medium
for the conveyance of light is the
certiiin fact that light travels, that
its communication is not instan-
taneous but requires time, and that
it is intercepted by intervening
objects. There are analogies be-
tween its j)henomena iind those of
the mechanical motion of a solid or
fluid substance. But we are not
entitled to ivs^iume that mechanical
motion is the only i)owcr in nature
capable of exhibiting the.se attri-
butes."

38 SCIENTIFIC THOUGHT.

the atomic view of matter. Similar uncertainties in
the definitions exist in both theories all through the
century, down to the most recent times. There are
those who still look upon both conceptions as merely
convenient symbolisms, as ideal instruments of thought
or scientific shorthand ; and on the other side we have it
as emphatically stated, that the question, What is ether ?
" is the question of the physical world at the present
time," " that it is not unanswerable," in fact, " that it
is not far from being answered," that " it is probably
a simpler question " than the other question. What is
matter ? ^ The whole domain of physical science is even
divided into two portions, the physics of matter and the
physics of ether,^ and the older, more empirical, and
common - sense divisions, treating separately of light,
electricity, and magnetism, are assembled in one great
doctrine, the " doctrine of the ether." It is, indeed,
somewhat astounding, if not disheartening, to hear at the
same time from an authority who has done more than
any other living philosopher to enlighten us in these

^ Professor 0. Lodge, in the | - See inter alia Professor Paul
Preface to the first edition of \ Drude's ' Physik des Aethers '
' Modern Views of Electricity,' i (Stuttgart, 1894). In the Preface,
\>. xi. " It is simpler," he con- p. vi, he speaks of the philosophical
tiuues, "partly because ether is "desire of using the i<ame funda-
one, while matter is apparently mental conceptions for the physics
mauj' ; partly because the presence of the Pother as for the physics of
of matter so modifies the ether that matter, whereby it remains an open
no complete theory of the properties question whether it is more service-
of matter can possibly be given , able to reduce the equations in the
without a preliminary and fairly ' physics of the sether to those ex-
complete knowledge of the pro- i pressions which can be got from the
perties and constitution of undis- | observable phenomena in the
turbed ether in free space. When | physics of matter (the equations
this has been attained, the resultant of dynamics), or whether the
and combined effect we call matter i opposite road can be chosen with
may begin to be understood." ' advantage."

KINETIC OK MECHANICAL VIEW UF NATURE. 39

matters, that at llie present iiKJiiient he knows us little
as to the true nature of these agencies or substances as
he did fifty years ago.^

Viewed from the position which we occupy in this
history of thought — i.e., in relation to the development
of ideas — the conception of an ether has, however, like
the atomic theory, had the most marked influence on
scientific research and reasoning. In digging for a hidden
treasure, in trying to describe the atoms or the ether,
many practically useful conceptions, applicable to tangible
phenomena, have been discovered. The atomic theory
led at once to an enormous increase of our knowledge of
difierent forms of matter, the knowledge of the elements,
and of their ininiiuerable possible compounds. The con-
ception of the ether has led similarly to an enormous ex-
tension of knowledge of the difierent possible forms of
motion. It is in this sense that we are greatly indebted
to these abstract conceptions : both have guided our ideas
in trying to uudcrstaud and grasp the endless variety
of phenomena. Let us see how from the early years
of the undulatory theory of light our knowledge
regarding the different forms of motion has grown, how
that theory has contributed to the kinetic view of nature.

^ Lord Kelvin, in referring to first session as professor. Some-
fifty years of scientific labour, said thing of .sadness must come of
(see the publication by James failure ; but . . . wliat splendid

Maclehose & Sons of tiie proceedings
at his jubilee in 1896, p. 70) : "I
know no more of electric and
magnetic force, or of the relation
between ether, electricity, and
ponderaljle matter, or of chemical
affinity, than I knew and tried to

compensation for j)hilosophical fail-
ures we have had iu the admirable
discoveries by observation and ex-
periment on the proi)ertie8 of
matter, and in the exquisitely
beneficent applications of science t4)
the use of mankind with which

teach to my students of natural these fifty years have so abounded.'
philosophy fifty years ago in my .

40 SCIENTIFIC THOUGHT.

It was recognised by Young, and still more clearly by
Fresnel, that the medium which they supposed to be the
carrier of light could not have the ordinary properties of
either a solid, a liquid, or a gas. It offered apparently
no resistance to the motion of the heavenly bodies, its
waves were not like those which in air produced sound ; it
propagated its waves at a speed much greater than any
other velocity known at that time ; at the same time the
wave-motion was not that of a body possessing the pro-
perties of a gas — i.e., an elastic, compressible fluid : it was
that of a body offering resistance to change of form rather
than to change of bulk. It was evident that the different
properties, which we see roughly assembled to constitute
the three forms of ponderable matter with which we
are practically acquainted, the solid, the liquid, and the
gaseous, cannot be assembled in any similar manner in
this imponderable substance, the ether. It was bound to
'^ have inertia — i.e., mass — otherwise the laws of motion could
not be employed in dealing with it, and mathematical
thinking about it would be impossible. A more perfect
description of the elementary movements which con-
stituted light evidently required a minute experimental
study, and a closer mathematical definition of the dif-
ferent properties of matter, known popularly but not
very clearly under the terms compressibility, rigidity,
27. mobility, elasticity, viscosity, &c., and of the inter-de-

The theory

of elasticity, pendcucc of thcsc clearly defined properties one on the
other. Just about the time when the vibratory theory
of light began to be seriously entertained by natural
philosophers, a beginning had also been made in this
study : the theory of elasticity had been founded in

KINETIC OR MFX'HANICAL VIEW OF NATIKK. 41

France by Na\'ier and I'oisson. One of the greatest
analysts of the century, Augustin L'auchy, had like-
wise applied himself to it; and when Fi-esnel, in ihe
\ear 1S26, brought out his great memoir on double
refraction in crystals, in which he was obliged to enter
more closely into the properties of the luminiferous ether
and its relation to ponderable matter, Cauchy was induced
to devote himself more specially to the mathematical
problems which presented themselves. Before his time
the theory of elasticity had been studied more as con-
nected with questions of practical engineering, such as
the strength of materials, the stability of buildings, the
construction of macliines, or with the properties of nnisical
and sounding bodies. A new interest was created by
Fresnel's researches.^ The ([uestion arose, \hi\\ mv we
to describe the vibrations of an imponderable substance,
endowed with mass (density) and rigidity, and what con-
ceptions can we form of the change of these vibrations
if there is present likewise ponderable matter ? Evi-
dently upon the clearness and correctness of these
notions depends the explanation of the phenomena observ-
able when rays of light fall upon the surfaces of trans-
parent or opaque bodies. We have to ask: In wliat
terms (viz., of different kinds of motion) can we define
and describe, and accordingly calculate the phenomena
of reflexion, refraction, scattering (i.e., dispersion), and
absorption (i.r., extinction) of light ? A tolerably clear

1 See Verdet iu ' ffiuvres de
Fresnel,' vol. i. p. Ixxx : " Les
seuls ecrits antdrieurs a Fresnel
oil I'on trouve des notions justes
8ur les in(5galites d't'^liisticito qui
peuvent exister dans les corps et

sur leur repartition rt^Kuli6re ]mr
rapport h, certains axes ou plans de
symdtrie sont ceux du grand miiu'"-
ralogiste allemand Samuel Christian
Weis" (' Mdm. de I'AwkI. dc Herlin.'
ISl.'i).

42

SCIENTIFIC THOUGHT.

definition of the kind of motion constituting a pencil of
homogeneous Hght in the free ether or in atmospheric
air had been given by Fresnel. Experimentally the
velocity of a wave motion of this kind was known ; it
was subsequently ascertained that this speed was not
the same in air as in the free ether, the so-called
vacuum. It was also known that this speed in an
elastic medium, such as the ether was supposed to be,
depends upon the density and the rigidity of the medium.
But when rays of light — i.e., the wave-motions of the
ether — arrive at the surface of liquid or solid bodies,
various changes are known to take place. These changes
had been to some extent described and brought into
measurable terms by experiment, and it had been shown
in a general way by Huygens, and more completely by
Fresnel, how these observed changes of reflexion, refrac-
tion, and dispersion could be translated into the language
of the vibratory theory. Complicated and yet very elegant
geometrical constructions, at which Fresnel arrived by an
intuitive or tentative process/ enabled the course of rays
inside transparent, doubly-refracting substances, such as
crystals, to be calculated ; a whole geometry of rays was
developed out of these representations ; new phenomena

^ The equation of the wave-sur-
face was not expHcitly given by
Fresnel himself. M. Verdet says
(' CEuvres de Fresnel,' vol. i. p.
Ixxv) : " Fresnel n'a pu lui-meme
venir a bout de ces ditficulles et n'a
su obtenir I'equation de la surface
del'onde qu'eu la supposant a priori
du quatrieme degre, et calculant la
valeur de ses coefficients de maniere
qu'ils satisfissent ti certaines condi-
tions faciles h d^duire de la con-

sideration des ondes planes normales
aux trois plans de sym(5tiie du
milieu. Ampere est le premier qui
ait eSectue le calcul d'une maniere
rigoureuse." However, "the con-
struction yields the wave-surface in
sucli a way that its singularities
are not obvious, and were only I'e-
marked by Sir W. R. Hamilton
several years after Fresnel's death "
(Fletcher, 'The Optical Indicat-
rix,' p. 31).

KINETIC UK MECHANICAL VIEW OF NATCRE. 4:'.

of refraction, such as conical refraction, were mathe-
matically foretold and experimentally verified.' The
real ]ihysical question, however, remained unanswered;
and it remains only partially answered up to the present
day." How is it tliat the luminiferous ether, wlien ex-
isting inside ponderable matter, like air permeating a
grove of trees — as Young put it — is so changed that its
waves travel with variously altered speeds, that in
different directions the rays acquire diftierent pro-
perties, are differently maintained or partially extin-
guished (absorbed) ? It was natural to suppose that
the particles of ponderable matter must in some way
affect the ether, changing its density or its rigidity, and
that they themselves are affected by the movements
of the ether which tills their interstices. The question
can only be exhaustively answered l)y a complete know-

^ The subsequent sug2;estioii of
the phenomena of inner and outer
conical refraction, experimentally
verified by Hum]>Iirey Lloyd in
1833 (see his 'Miscellaneous Pajiers,'
No. 1, or Transactions, Royal Irish
Academy, vol. xvii.), was jjopularly
regarded as a complete proof of
the correctness of the wave-surface,
and of Fresnel's entire theory. But
as to the first point, Sir G. G.
Stokes showed (Brit. Assoc. Repoi-t
on Double Refraction, 1862, p.
270) that conical refraction " must
be a property of the wave-sur-
face resulting from any reasonable
theory." And as the wave-surface
itself can Ijo geometrically con-
structed without any reference to
the mechanical theory of the ether
(as Mr Fletcher has most exhaus-
tively shown), the prediction of
conical refraction cannot be re-
garded as a proof of Fresnel's

theory. Todhunter- Pearson says :
" But for Cauchy's magnificent
molecular researches, it might have
been possible for Fresnel to com-
pletely sacriticc the infant theorj*
of elasticitj- to that fiimsy sujx?r-
stition, the mechanical dogma, ou
which he has endeavoured to base
his great discoveries in light.
Cauchy inspired Green, and Green
and his followers have done soiue-
thing, if not all, to reconcile Fres-
nel's I'e.sults with the now fully
developed theory of elasticity, the
growth of which his dogma at one
time seriou.sIy threatened to check "
(' Hist, of Elasticit}-,' vol. i. p.
167).

- In 1862 Sir G. G. Stokes "ex-
pressed his belief that the true
dynamical theory of double refrac-
tion had yet to be found " (Report,
I-. 268).

44 SCIENTIFIC THOUGHT.

ledge of the mechanism of the ether on the one side, of
ponderable matter on the other. Two ways are open by
which a solution of this ultimate or fundamental problem

28. can be solved. The one is purely mathematical. It

The problem

of the ether meaus the analysis of all the possible modes of motion of

may be ^ x

mlthe** a given mechanical system, and of the mutual iniiuence
niaticaiiy, ^j-j^gj-^ ^-^q interconnected mechanical systems, that of the
ether and that of ponderable matter, exert on each other.
This is a perfectly definite though a very intricate prob-
lem. It is a problem which can be compared with —
though it transcends in complexity — the analytical prob-
lem suggested by the gravitational view of physical
astronomy : to calculate mathematically the movements
of any number of bodies attracting each other according

29. to Newton's formula. The other way is the experi-

or experi-
mentally, mental method — to observe how under methodically

altered conditions rays of light are modified in colour
(wave-frequency), in direction, in intensity (amplitude of
wave-motion), in laterality (polarisation), and in other
ways ; and then to translate these conditions and altera-
tions into the now fairly well-established language of
the vibratory theory ; gaining in this way indications as
to the changes which the wave-motion is capable of, and
inferring from these possible changes the original con-
stitution (usvially called the constants) of the primary
substances — the ether and the ponderable matter which
come into interaction.

30. It may in general be stated that neither of these two

Necessity of .

combining mcthods has for any length of time been pursued alone,

the two J >=> f '

methods. ij^^ ^j^^^ progrcss lias nearly always depended upon an
alternating employment or a combination of both. On

KINETIC OK MhXHANICAL VIEW OF NATLllK. 45

the one side we have a great volume of purely analytical
reasoning begun l>y Cauchy in 1- ranee, and purHued
under varying assumptions by Green and MacCJuUagh in
England, by F. Neumann and others in (Jermany. On
the other side we have the purely experimental work
beginning with WoUaston and Brewster in England, the
refined methods for measuring the speed of light invented
]jy Fizeau and Foucault, the beautiful contrivances for
experimental research and verification of Jamin and
nianv others. Out of so many fruitful conceptions
which have resulted in an enormous accumulati(jn of new
knowledge of actual phenomena of light and wave-motion
— the real and sole end and aim of all theory — I will for
the purpose of illustration single out one which in llie
middle of the century opened out an entirely new field
of iniiuirv, formino- almost a new science by itself. I 8i.

^ ■' ■" Spectrum

refer to spectrum analysis. analysis.

The phenomena of dispersion (rainbow scattering) and
absorption (partial or complete extinction) of light were
among the earliest known, and had been among the
longest studied, properties of bodies. I>eing, besides,
connected with the physiological, subjective, and artistic
effects of light, they have always commanded special
interest. And yet, so far as either the emission or
the undulatory theory is concerned, they have always
presented special ditticulties. When the wave theory
was first propounded, it was generally understood on
the analogy of the phenomenon of sound that diflerence
of colour depends upon difierence of frequency, or where
the velocity of propagation (as in vacuo or in atmospheric
air) is the same, on the length of the waves. Thr ditli-

46

SCIENTIFIC THOUGHT.

ciUty arose of explaining how in refracting substances,
be they fluid, amorphous (singly refracting), or crystalline
(including doubly refracting), these different rays, with
different wave-lengths, come to travel with different
velocities, and hence take different courses ; how, further,
some of these rays come to be extinguished or reflected
(or both) in varying degrees.

Now, although the complete answer to this general
question has not yet been given, a principle has been
recognised which gives us a clue to the possible explana-
tion of a large class of phenomena, and wliich is thus of
remarkable fruitfulness. It was first laid down by
Euler,-^ a pure mathematician, whose physical reasoning-
was frequently suggestive but never particularly clear and
definite; it was probably first applied to optical phenomena
by Sir George Stokes ; ' and it was later on used by him

^ In the last section of his treatise
on light and colours ( ' Berlin Me-
moirs,' 1745 ; published in Latin,
1746), Euler treats of luminous,
reflecting, refracting, and opaque
bodies, and he there mentions the
analogy which exists with musical
resonance. " The smallest particles
[of opaque bodies] are similar to
Stretched strings, which are, as it
were, specially receptive for certain
vibrations, which they can assume
without being struck, if only they
are afifected by the undulatory
movement of the air." "In his
expositions upon light and colours,
Euler always starts with the analogy
of sound and light ; he follows it
with absolute consistency " (Cher-
buliez, ' Eulers physicalische Ar-
beiten,' p. 44). This analogy was
exactly what was absent in the in-
vestigations of Brewster, who re-
mained to the end an adherent of the

projectile theory. Balfour Stewart
came nearest to the true explana-
tion in his memoir of 1858 ( ' Trans,
of the Royal Societj* of Edin-
burgh,' 1861); but this referred to
radiant heat and to Provost's theory
of exchanges. It contains the
words : " The absorption of a plate
equals its radiation, and that for
every description of heat " (p. 13).
Had this statement been distinctly
applied to luminous rays, spectrum
analysis would have been his dis-
covery, although his theoretical
proof might be regarded as in-
sufficient (see Scheiner's treatise
on Astronomical Spectroscopy,
transl. by Frost, 1894, p. 112; also
Rosen berger's ' Geschichte der
Physik,' vol. iii., 1890, p. iS2'sq.)

^ See the references given on
p. 277 of the first volume of tliis
history.

KINETIC OR MECHANICAL VI KW OF NATfl'.K. 47

in giving a mechanical explanation of the dark and bright

lines of the spectrum, upon which Kirchhoff and liunseu [^',^1'/'***

founded spectrum analysis about the year 1860. ',.

Wollaston ^ had in 1802, on examining the solar "^^
spectrum (the succession of rainbow coloui-s expanded on
a white screen placed behind a prism uf white glass
through which a narrow beam of sunlight is made t(j pasij),
noticed that with a sufficient enlargement black lines in
great number could be detected. Fraunhofer,'- in ^lunich,
made a special study of them, named them by letters of
the alphabet, and compared the solar spectrum with the
spectra of artificial terrestrial sources where light is
created by combustion or incandescence. He found that
these spectra differed, the peculiar colour exhibited by
various flames being defined in the spectra by special
bright lines of different colours. Thus notably the two
dark lines called by him D in the solar spectrum were
replaced in the spectrum of a flame in which a volatile
salt of sodium was present, by two bright lines : Brewster
found the same coincidence of others of Fraunhofer's
lines with the bright lines of a flame in which nitre was
volatilised. Very similar and very accurate observations
of A. Millar as to the identity of the dark Hues D in the
solar spectrimi with the two bright lines of the sodium
flame were explained by Sir G. Stokes about the year ss.

^ ' Sir G.

1850 by the following theoretical reasoning: The sodium stokes.

1 "A method of examining re- after him in his investigations of

fractive and dispersive powers by the "refractive and dispersive

prismatic reflection" ('Trans, of i)o\vers of various kinds of gbss"

the Royal Society,' 1802). tor the purpose of improving the

3 Fraunhofer, whose epitaph, achromatic telescoiie (' Denkschrif-

" approximavit sidera," describes ten der Miinchener Akadcmie,' vol.

beautifully his life-work, was led to i., 1814-15).
the discovery of the lines named

48

SCIENTIFIC THOUGHT.

34.
Gustav
Kirchhofl.

flame which emits the two bright lines in its own spectrum

destroys them (replacing them by two dark lines) in the

spectrum of a ray of light which passes through the

sodium tiame.^ Foucault had in 1849 already shown

the direct reversal of the sodium line in the spectrum of

the electric arc. These earlier anticipations remained

partly unnoticed, partly unknown, or were looked upon

as isolated cases, and it was reserved for Gustav Kirch-

hoff to put this remarkable property of emission and

absorption of special colours by coloured flames into

practical language, and express it in a general way. He

wrote in 1859:^ "I conclude that coloured flames in

the spectra of which bright lines present themselves, so

weaken rays of the colour of these lines, when such rays

pass through them, that in place of the bright lines, dark

ones appear as soon as there is brought behind the flame

a source of light of sufflcient intensity, in which these

lines are otherwise wanting." And when he concluded

further that the dark lines of the solar spectrum which

are not evoked by the atmosphere of the earth, exist

in consequence of the presence in the sun's atmosphere

of those substances which in the spectrum of a flame

produce bright lines at the same place, " he at once gave

^ From this lie inferred that the
presence of sodium vapour in the at-
mosphere of the sun wt)uld explain
by absorption the two dark lines in
the solar spectrum. Lord Kelvin
reports that in consequence of this
observation of Stokes he regularly
taught his Glasgow students that
sodium must be in the sun's at-
mosphere. See the reprint of the
correspondence ou this subject in
the ' Gesammelte Abhandlungen ' of

Kirehhoff, 1882, p. 639, where it
will also be seen that Sir W.
Crookes claimed a similar anticipa-
tion for Millar in 1846. See also
Sir W. Thomson's ninth Baltimore
Lecture.

" See the translations of Fou-
cault's and Kirchhoif's memoirs
sent by Sir G. Stokes to the
' Philosophical Magazine ' of March.
1860, p. 194 sqq.

KINETIC OR MECHANICAL VIEW uF NAT! KK. 49

birth to two great applications of lii.s principle — tlie
search, through the study of the spectra of distant stellar
sources of light, after the ingredients which are jtresent
in those distant luminaries, and the search, through the
study of the flames of terrestrial substances, for new
sj)ectral lines announcing yet undiscovered elements." '
AMiilst in these two independent directions an enormous
amount of new knnwledge has been accumulated, the
mechanical explanation througli which Sir (!. Stokes
anticipated these phenomena, and llie further applications
of this principle by him, have done much to confirm the
conviction, that in looking upon liglit as a vibratory mode
of motion, we are on the road towards an adequate
description of these phenomena.

' To this principle we owe the
spectrum analysis of stellar at-
mospheres and the discovery of
new chemical elements, of which
no fewer than six have been iden-
tified by tliis method, lieginning
with cicsium and rubidium (found
by Kirchhoff and Bunsen in the
waters of some mineral springs).
The suggestion of Doppler, men-
tioned above (p. 10, note), has only
become fruitful through the inven-
tion of the sjiectroscope. Colour
differences originating through the
change of the frecjuency of vibra-
tions depending on cosmical veloc-
ities in the line of sight, could
not be discovered by the most
sensitive eye. In the spectrum,
however, shown by the spectro-
scope, "not only tiie colours of the
bright lines have been altered, but
their position in the spectrum
relatively to a fixed point of
reference as well. . . . The measure-
ment of the displacement of spectral
lines in conseciuence of the altere<l
refraiigiljility of the rays is the only

VOL. II.

method yet known which possesses
sufficient accuracy for determining
the motions of objects in the line
of sight. Thus far it has not been
possible to produce in the laboratory
velocities high enough to occasion
a perceptible displacement of the
lines" (Scheiner, /oc. cit., p. 148).
And as Doppler's principle in
acoustics was proved directly bj-
Buys Ballot through the whistle on
moving railway trains, so it has
been proved directly in optics by
observing the displacetnent in the
lines of the solar spectrum, wlieu
this is deiived from the nuter rays
of the sun's disc, the light-giving
parts moving in the line of sight
towards or away from tiie observer
in consec|uence of the rotation of
the .sun round its axis. " The re-
sulting velocity of the surface of
the sun is found to agree very
closely with the results of direct
observations of the revolution of
the spots, thus practically furnish-
ing a ])roof of the correctness of
Doppler's principle" (ibid., p. 149).

D

50 SCIENTIFIC THOUGHT.

We have seen above how the vibratory theory of light
was arrived at — mainly in the hands of Young — through
dwellincr on the analogy of certain optical phenomena,
notably those of interference, with the properties exhibited
bv sound. Amons the latter none were more remarkable
than those known popularly as consonance and resonance.
Sir George Stokes, on the appearance of Kirchhoff s memoir
on the relation of emission and absorption of certain rays
of light, gave the mechanical explanation in the following
words : 1 " In describing the result of a prismatic analysis
of the voltaic aixj formed between charcoal poles, ]\I.
Foucault ' found that the arc presents us with a mediimi
which emits the rays D on its own account, and which at
the same time absorbs them when they come from another
quarter.' . . . The remarkable phenomena discovered by
Foucault, and rediscovered and extended by Kirchhoff,
that a bodv mav be at the s:ime time a source of lisht,
giving out rays of a definite refrangibility, and an ab-
sorbincf medium extinguishing ravs of the same refransri-
bOity which traverse it, seems readily to admit of a
d3mamical illustration borrowed from sound. "We know
that a stretched sti-ins which on being struck gives out a
certain note, is capable of being thrown into the same
state of vibration by aerial vibrations corresponding to the
same note. Suppose now a portion of space to contain a
great number of such stretched stiings, forming thus the
analogue of a 'medium." It is evident that such a
medium, on being agitated, would give out the note above
mentioned, while on the other hand, if that note were
sounded in air at a distance, the incident A"ibrations would

1 'Phil. Mag.,' March 1860, pp. 194, 196.

KINETIC OR MECHANICAL VIEW OF NATURE. 51

throw the strings into vibration, and consequently wouM
themselves be gradually extinguished, since otherwise
there would be a creation of vis viva. The optical applica-
tion of this illustration is too obvious to need comment."
Already ten years before Kircldiofl" gave t(j the
researches into the spectrum their popular celebrity and
practical importance, Stokes ^ had made an extensive ex-

' The memoir of Sir G. Stokes
" on the chauge of the refrangi-
ViiHty of light," iu the ' Phiios.
Transactions' (Maj' 1852), forms a
landmark in optical science, and
wliilst dealing with the less obvious
— though very frequent and general
— phenomena of fluorescence and
phosphorescence, really indicated
the line of reasoning which has
become so fruitful and suggestive
in his own hands and in those
of other eminent natural phil-
osophers. On page r)4!} of that
meinoii- he wrote : '' All believers
in the undulatory theory of light
are agreed in regarding the pro-
duction of light in the first instance
as due to vibratory movements
among the molecules of the self-
luminous body. . . . Nothing then
seems more natural than to suppose
that the incident vibrations of the
luminiferous ether produce vibra-
tory movements among the ultimate
molecules of sensitive substances,
and that the molecules in turn,
swinging on their own account, pro-
duce vibrations in the luminiferous
ether, and thus cause the sensation
of light. The periodic times of
these vibrations depend upon the
j)eriods in which the molecules are
disjiosed to swing, not upon the
jjeriodic time of the incident vibra-
tions." Referring, then, to the
dynamical difficulties which attach
to such a view, he proceeds to point
out " that we have no right to re-
gard the molecular vibrations as

indefinitely small. The excursions
of the atoms may be, and d(jubtles8
are, e.\cessively small compared
with the linear dimensions of a
complex molecule. It is well
known that chemical changes take
place under the influence of light,
especially the more refrangible rays,
which would not otherwise happen.
In such cases it is plain that the
molecular disturbances nmst not be
regarded as indefinitely small.
But vibrations may very well take
place which do not go to the
length of complete disruption and
yet which ought by no means to be
regarded as indefinitely small. . . .
Certainly we cannot affirm that in
the disturbance comrauniciited back
again to the luminiferous ether
none but periodic vibrations would
be produced having the same
period as the incident vibrations.
Ilather, it seems that a sort of
irregular motion must be produced
in the molecules, periodic only in
the sense that the molecules ret;iin
the same mean state ; and thattlie
disturbance which the molecules in
turn communicate to the ctiier
must be such as cannot be expreseetl
by circular functions of a given
peritxl, namely, that of the incident
vibrations." St<jkes then refers to
the probable internal vibration of
the atoms in the compound mole-
cules, as " it is chiefly among organic
compounds . . . having a compli-
cated structure that internal dis-
persion (fluorescence) is found."

52 SCIENTIFIC THOUGHT.

amination into the question how vibrations of the
hmiiniferous medium can be mechanically transferred to
the compound molecules of a transparent body, and
retransf erred again to those of the ether itself — t.^.,
the question of the absorption and emission of light. He
showed that vibrations of a certain period, corresponding
to a definite tint of colour, could eventually give rise to
vibrations of altered period in the emitted light ; that
this period, however, must always be longer — i.e., that
the new colour must always be of a lower order in the
35. scale of refrangibility. He was thus not only able to
tionor' explain mechanically the peculiar luminosity which he

flUOr6SC6IlC6

* termed fluorescence,^ and which had been observed by
Herschel and Brewster in certain minerals and solutions,
and independently studied by E. Becquerel in France,
but he also showed how, by means of such substances,
rays of light which, owing to the frequency of their
vibrations, transcend the perceptive powers of the
• human eye, can be made visible by giving rise to
secondary waves of less frequency. The line of reason-

1 The term fluorescence was
coined by Sir G. Stokes by analogy
with opalescence as involving no

the term radiation was not yet
generally used to embrace the
invisible chemical (ultra-violet) and

theoretical suggestion, in place of caloric (infra-red) rays; that photo
the earlier names of " internal i graphy, which more than any other

dispersion" or " epipolised light "
used by Brewster and Herschel.
He, however, very soon favoured
the term " degraded light," sug-
gested by William Thomson (Lord
Kelvin) (see the second memoir,
1853, p. 387). The latter was at
that time occupied with his cele-
brated and not less epoch-making
researches referiing to the dissipa-
tion or degradation of energy, of
which more in the next chapter. If

we remember that fifty yeai's ago ' times.

process has familiarised us with
chemical radiation, was a compara-
tively recent invention ; that the
ideas of conservation, conversion,
and degradation of energy were
quite new ; that the general term
energy had not even been invented,
— we must indeed regard the words
of Sir G. Stokes as containing a
prophetic programme of the ideas
and problems of the whole subse-
quent period down to quite recent

KINETIC OR MECHANICAl- MKW OF NATUUK. 53

in!4 liere employed gave tlie ehie to all subseiiuent
attempts to deal with the ditticult problem of the inter-
action of the ether and ponderable matter ; uf ihe pos-
sible alteration of the density or the rijj^iility (called the
elastic constants) of the ether when Hllinj^ the interstices
of transparent bodies ; of the meciianical differences which
make some bodies transparent for some and opa([ue for
other rays of light. ]\Iany possible modiKcations were
tlieoretically foreseen, giving rise to remarkaltle unex-
pected phenomena, and these were frequently verified by
subsequent experience. The whole theory of light
entered upon a new phase as it became more and more
evident that the study of the vibrations of the elastic
medium was not suilicient, but that it must be supple-
mented by that of the interaction of two vibrating
systems, the ether and the molecules of the ponderable
substance, which give rise to tlie phenomena of })arlial
reflexion, refraction, dispersion, and partial or eomjilete
absorption. This more complicated problem in the
theory of elasticity had already presented itself in its
simpler form in the tlieory of the pendulum. To the
principle of optical consonance which had been employed
to explain the phenomena of absorption of liglit was
added, in order to explain the phenomena of tUsper-
sion, the principle of tlie free and forced vibrations
of a vibrating system.^

1 " If to the l)ob of a pendulum, Anomalous dispersion such as wiu

executing horizontal vibrations, foreseen by Sellmciei- and Lord

another pendulum be attached, exe- Kelvin and discovered by Christi-

cuting vibrations of a slightly ansen and Kundt dejiends on the

shorter [)eriod, the effect of the change of wave fre(|uency indei)en

latter will be to increase the period
of the former and rice vcr.id " (see
A. S. Percival, ' Optics," 1 899, p. 1 81 ).

dent of the change of wave length
in refracting media.

54

SCIENTIFIC THOUGHT.

3G.
View of the

The latest discussion of this form of the elastic-solid

ether as an theory of light, which was gradually developed from

independent' beginnings in the three countries/ is to be

' elastic
solid.

1 In France and Gernaany, where
even in the middle of the century
the labours of English natural phil-
osophers like Green, M'CuUagh,
Stokes, were only very imperfectly
known, the necessity was equally
felt of studying the interaction of
the ether and ponderable matter.
In France the school of the eminent
"elastician," Barre de St Venant,
produced in M. Boussiuesqtheauthor
of the earliest published attempt to
solve the difficulties which the older
methods of Cauchy had not over-
come. In a lucid review of the state
of physical optics. Saint Venant
himself ('Ann. de Chimie et de
Physique,' 4™^ serie, vol. 25, 1872)
hails with delight the researches of
M. Boussinesq from 1865 onward,
where the idea that the ether in the
interstices of transparent bodies has
different elastic constants is given
up, and the participation of the
ponderable matter in the vibrations
is introduced in its place. "En
effet," he says, " il est bien difficile
de concevoir, d'une part, que Tether
puisse etre agile au sein cl'un corps
dont la densite est probablement
bien sup&ieure ii la sienne, sans
lui communiquer une fraction sens-
ible de sa quantite de mouvement,
et d'autre part, que les ondes ne
soient pas bientot eteintes par cette
participation de la matiere ponder-
able au mouvement s'il n'y a pas
concordance entre les oscillations
imprimees k chaque molecule de
cette matiere et celles de I'ether
qui I'environne." It was the
problem of the continuity at the
interface of reflecting and refracting
substances and the problem of ab-
sorption which the older simple
ether theories could not explain.

In Germany a similar impulse was
given to the study of the inter-
action of elastic systems — as indeed
to many problems of mathematical
physics — by Franz Neumann, who
was the centre of a numerous and
influential school. He taught at
Kcinigsberg together with Richelot
and Bessel. His lectures have been
edited by his pupils. Prof. Karl
Pearson, in his continuation of Tod-
hunter's ' History of the Theory of
Elasticity,' does ample justice to the
labours of Neumann, who, "in his
investigations on photo - elasticity
and the elasticitj- of crystals, breaks
almost untrodden ground, which
both physicists and mathematicians
have hardly j^et exhausted " [loc. cit. ,
vol. ii. 2, p. 183). "Neumann was
among the first (1841, ' Abh. der Ber-
liner Akademie') to attribute disper-
sion to the influence of the ponder-
able particles on the particles of the
ether" (ibid., p. 31). The most
important original contrilmtions of
Neumann's pupils are the researches
of Sellmeier, who had been led by
theoretical considerations in 1866
to expect certain anomalies in the
phenomena of dispersion, such as
were in 1870 actually discovered by
Christiansen, and fully investigated
by Kundt. Surface coloration was
shown to be intimately connected
with the absorptive powers in sub-
stances showing these anomalous
phenomena. A full report on these
and other theories, based upon what
has been termed abroad the "Bessel-
Sellmeier hypothesis " (see Ket-
teler, ' Theoretische Optik,' 1885),
will be found in Prof. Glazebrook's
" Report on Optical Theories,"
Brit. Assoc. Reports, 1885.

KINKTIC OR MECHANICAL VIEW OF XATUKE. 55

found in Lord Kelvin's celebrated lialtinuiie l>.'eture8 ^
where with unhinittMl resourcefulness the methods of '
analogy, analysis, and experiment are employed to solve
or to define the intricate problems of pliysical optics.
Nor is it a merely fortuitous coincidence for the history
of thought that, whilst his mind must have been filled
with the many illustrations and mechanical devices, and
all the wealth of suggestions contained in the Baltimore
Lectures, Lord Kelvin should have delivered the opening
address to the mathematical section of the Ihitish Asso-
ciation, entitled, " Steps towards a Kinetic Theory of
]\Iatter." Following — as did also Clerk Maxwell — on
the lines indicated by Stokes's earlier papers, he has done
much to change our fundamental conceptions as to the
properties of matter, and this in two distinct ways.
The first consisted in breaking down the rigid barriei-s
which popular definitions had set up between the dif-
ferent forms of aggregation — the solid, liquid, and gaseous
states of matter ; whilst the second tended to show how

^ The Baltimore Lectures were
delivered by Lord Kelvin (then Sir
\V. Thomson) after the meeting of
the British A.ssociation at Montreal
in the month of October 1884, at
the Johns Hopkins University, be-
fore a company of physicists. The
final edition of these important and
highly suggestive conferences is in
the press as the fourtli volume of
the collected mathematical and
physical pajiers. The comjjletion
of this publication is eagerly ex-
pected, as containing the most
mature exposition of the elastic-
solid tlieory of light, towards which
the author has in the course of the
last fifteen years made various valu-
able additions. Notably in a paper

dated 1888, published in the ' I'liil-
osophical Magazine,' he has, as it
has been said, " extricated the
elastic theory from the position of
deadlock, according to which the
ether must be botii compressible
and incompressiljle," by showing
that the difficulty can be met, " pro-
vided we either sujjpose the medium
to extend all through boundless
space, or give it a fixed containing
vessel as its boundary." I'mf.
Glazebrook has further worked out
the consequences of this suggestion.
See vols. 26 and 27 of the .'ith series
of the ' Phil. Mag.,' also ^ Nature.'
vol. 40, 1889, i>. 32, and Fletcher,
the ' Optical Indicutrix,' p. (J, ic.

56

SCIENTIFIC THOUGHT.

the supposed static properties of matter could be ex-
plained by different modes of motion, translational,
periodic, or rotational. The mathematical and experi-
mental investigations connected with the theory of
radiations and vibrations had thus an influence ^ on
our general views of the nature of physical processes
whicii far exceeded the aims for which they were origi-
nally undertaken. That a substance so attenuated as the
ether should have the properties of a solid ; that brittle
substances like pitch should flow like liquids, if only
sufficient time were given ; that towards very rapid
impulses gases and liquids might behave as solids — all
these observations resulted in a complete revolution of
our scientific notions as well as of our vocabulary. The
great turning-point, indeed, lay in the kinetic theory of
gases, which about the middle of the century had intro-
duced quite novel considerations by showing how the
dead pressure of gases and vapours could be explained on
the hypothesis of a very rapid but disorderly transla-
tional movement of the smallest particles in every
possible direction. Pressure of gases ha^ang been ex-
plained by a very rapid motion of the minute par-
ticles of matter, heat was mimediately conceived to be
merely a " mode of motion." As no event did more to
spread modern views in the theory of light, and to
popularise modern scientific methods, than Kirchhoff's

^ It has been asserted that the
theory of elasticity received a great
impulse when Fresnel was forced to
make assumptions as to the mode of
vibrations of the ether which were
quite incompatible with the then
accepted laws of the vibrations of

an elastic medium. To this view of
the origin of the modern theory of
elasticity Prof. Karl Pearson takes
exception, as Navier's memoir of
1827 was not suggested by optical
investigations (Todhunter-Pearson,
vol. ii. 2, p. 5).

KINKTIC OR MECHANICAL VIKVV OF NATLRE. 57

and Bunsen's spectrum analysis, so in the closely related
<l(»ctrine of heat, piol)aljly no puhlication di<l niore to
estal)lish a general kinetic view of matter and of natural
phenomena than Tyndall's celebrated treatise, ' Heat as a
Mode of Motion.' In spite of the criticisms which
have been levelled against this expression,^ the lj<jok,
which appeared in 186."'), was to the jjopular nnnd a
revelation ; it was translated into many foreign languages,
ran through many editions, was recommended Ijy thinkers
of the first order, and the title coveted as " manifesting
far and wide through the world one of the gi-eatest
discoveries of modern philosophy." "" It is the popular
herald of the kinetic or mechanical view of nature.

The same great authority who has so generously
referred to Tyndall's treatise — Lord Kelvin — had been
inspired from (juite a different quarter to suggest the
most advanced conception, in tliis line of thought, of
which the human mind has so far been capable : the

as.
Tvndairi

39.
Lor<J
Ki-lvin'8
vcirtex
theory of
matter.

1 Notably by Prof. P. G. Tait ;
see his volume on ' Heat,' p. 350,
also his ' Recent Advances of
Physical Science,' which contains
as an appendix his lecture on
" Force," delivered in Glasgow on
the occasion of the meeting of
the British Association. He says
there : " Heat and kinetic energy
in general are no more modes of
motion than potential energy of
every kind is a vuxle of rest.''
" Heat is not the mere motions,
but the energj' of these motions."
There is no doubt that the terms
force and motion can be used in
very different meanings, and that
the early expounders of the me-
chanical theory of heat have not
been always consistent in the use
of words ; though their ideas, wher-
ever they appeared in mathematical

expressions, were definite enough.
A good deal of vagueness has ac-
cordingly crept into popular text-
books and into philosophical treat-
ises, and criticisms such ivs those
of Prof. Tait have been useful in
helping us towards clearer con-
ceptions. We shall come across
more of these instances in the next
chapter when dealing with the
gradual evolution of the conception
of energy.

- See Lord Kelvin's abstract of
lecture, "Elasticity viewed as
possil)iy a Mode of Motion," 1881;
'Popular Lectures,' &c., vol. i. p.
142. "I have always a<lmire<l it"
(viz., Tyndall's title) ; "1 have long
coveted it for elasticity, and now,
by kind permission of its Inventor,
I have borrowed it for this dis-
course."

58

SCIENTIFIC THOUGHT.

40.
Helniholtzs
investiga-
tions.

vortex theory of matter. As this is one of the most
remarkable instances of the fruitful reaction of abstract
mathematical reasoning on the progress of physical re-
search, it will be useful to consider for a moment by
what gradual steps this novel idea was evolved or
suggested. The immediate occasion which led to it was
the publication, in 1858, by Helmholtz of a purely
mathematical investigation of some peculiar forms of
lluid motion.-^ About a hundred years before Helmholtz
published his memoir, Euler had laid the foundation of
theoretical hydrodynamics — i.e., of the theory of the
motion of fluids. In doing so, it was necessary to define

^ Helmholtz's memoir, " Ueber
Integrale der hydrodj'Dami.schen
Gleichungen welche den Wirbel-
bewegungeu entsprechen," appeared
in the 55th volume of Crelle's
' Journal f iir die reine uud ange-
wandte Mathematik. ' It was trans-
lated into English by Prof. Tait in
the ' Philosophical Magazine ' for
1867. Helmholtz's occupation with
the subject had originated in the
acoustical researches which he was
carrying on at the time. These
necessitated an analysis of the
more complicated conditions which
the motion of incompressible and
elastic fluids presents in actual
experience. The hydrodynamical
equations had been solved under
certain simplifying assumptions.
Discontinuity of motion and in-
ternal friction had been left out
of considei'ation. Helmholtz's re-
searches led him to the study of
these more complicated phenomena ;
and he successfully applied the
mathematical methods which had
proved useful in other branches of
physical science for the solution of
these problems. Notably in the
paper on whirling motion, he came

I upon very remarkable and unex-
I pected results, which ten years later
! led in this country to the novel
speculations of Lord Kelvin. It is
interesting to note how at that
time researches in England or Ger-
many could for many years remain
unnoticed in the other country.
The result was that the same prob-
lems were frequently taken up in
ignorance of the fact that they had
been treated before. See Hicks's
" Report on Hydrodynamics," 'Brit.
Assoc. Reports,' 1881-82. Especially
the labours of Stokes seem to have
been little known to German
writers, who usually started from
the better-known French researches.
Stokes had anticipated some of
Helmholtz's results referring to
whirling and discontinuous motion
of fluids. About the middle of the
century the periodical " Fort.schritte
der Physik " was .started by the
" Physikalische Gesellschaft " of
Berlin. Helmholtz himself contrib-
uted several valuable reports on
acoustical subjects. See the
' Wissenschaf tliche Abhandlungen,'
vol. i. passim.

KINETIC OR MECHANICAL VIEW OF NATCRE, 59

mathematically what is nifaiit l>v a lluid. The chief
property of a tluid, as compared with a soliil body, is
the perfect mobility of its parts, the absence of rigidity.
Tluis there were two possible kinds of Huids — those
which retained their bidk or volume, whilst ottering no
resistance to change of shape, and those whicii tried to
expand, and could be compressed by means of external
forces. These latter were called gases. In dealing wiib
the former, incompressibility had to l)e defined mathe-
matically, as also perfect mobility. These properties
constitute what is called a perfect fluid. Sucii perfect
tluids do not exist in nature ; Imt the methud of
reasoning was to begin with an ideal, simple case, and
approach the explanation of natural phenomena by a
process of correction, introducing more and more com-
plications. The phenomena of the How of liquids,
practically by far the most important, could be studied
to a great extent by means of the simplest form of the
hydrodynamical conception, and up to I he middle of the
century such problems, as well as those of the propa-
gation of small displacements under the action of external
forces, — notably the motion of waves,— formed the prin-
cipal problems whicli were treated mathematically. The
idea of the friction of fluids, also called viscosity, had been
excluded in the definition of a fluid, inasmuch as friction
opposed the notion of perfect mobility of the parts, which
was the mathematical definition of a fluid. Now it is a
matter of experience that in all liquids wiib which we
are acquainted friction can produce rotational moliou,
such as whirls and eddies ; it was also found that other
forces, such as magnetic forces, are, under cerl^un con-

60 SCIENTIFIC THOUGHT.

clitions, able to produce these rotations. It was therefore
of interest to study the nature of rotational or whirling
motion, if such could exist in a perfect liquid, and to see
what would be likely to happen to these whirls. Though
it might be ditticult to understand how in a perfect liquid
rotation of any portion could be produced, calculation
misfht determine what would be the nature and fate of
such whirls, if they did exist. The problem was a
purely mathematical one. Can a rotational motion, a
whirl, exist in a perfect fluid, as defined by the mathe-
matical conception ? If it can, what are the properties of
such whirls, and what becomes of them ? Helmholtz
fiolved these questions in his now celebrated treatise,
showing that whirls (called by English waiters vortices)
can exist, but only under certain conditions, such as
can be experimentally represented by smoke-rings issuing
from an orifice ; that, if they existed in a perfect liquid,
they would be indestructible and would possess a motion
of their own, giving them a special individual character
as to permanence and movement. The treatise, like the
problem, was a purely mathematical one,^ and in the
mind of the celebrated author was probably connected
more with the problem of the formation of drops, and
with that of the friction or viscosity of fluids, which
he attacked subsequently, than with the nature of
matter. In this country vortex motion had already
been studied by natural philosophers with very different
ends in view.

It was known that solid bodies which are in a rapid

' It revealed incidentally the analogy of hydrodynamical and electrical
phenomena.

KINETIC OR MEC'HANKAl- VIKW OK NA'iritK. 61

rotary motion acquire i)roperties which they do not
possess otherwise — viz., rigidity — i.r., reaction against
change of shape (the stifiness of a travelhng rope thrcjwn
off' a pulley is a familiar illustration); stability — i.r., re-
action against change of position and motion, as in a sjiin-
ning-top or a bicycle ; elasticity — i.e., tendency to revert to
the same position, if violently disturbed. 'I'he gyroscope^
had been invented in 1852 by Foucault, and used by
him and other physicists in France and Germany to
illustrate the rotation of the earth. It was nr)w shown
that portions of a perfect Huid- — i.e., of a liody which
possesses neither rigidity, nor stal)ility, nor elasticity
— when in a state of rapid rotational motion, acquire
these gyrostatic properties ; that whirling portions can-
not be naturalh' created, but that if once in existence
they preserve their identity, being permanently differ-
entiated from the surrounding ffuid, which may be at rest
or in the state of ffow. These differentiated portions of
the liquid were called by Helmholtz vortex filaments ;
he showed that in a lit^uid without a boundary they
must run back into themselves, foniiing rings which
might be knotted and linked together in many ways.

^ A much older invention was j of this work, and through the

that of Bohnenberger (1817), known inexhaustible wealth of esj)eri-

by his name. The name "gyro- mental illustrations contained in

scope " was introduced by Fou- I many of Lord Kelvin's addresses

cault ; and that of " gyrostat," as j (see ' Popular Lectures and Ad-

defining an apparatus which ac-
quires stability through rotational
(whirling or gyrating) motion, was
used first by Lord Kelvin. An
extensive treatment of the subject
is to be found in the first part
of Thomson and Tait's ' Natural
Pliilosophy' C^nd ed.), i)p. SH-il.'i.
It is mainly through tlie influence

dresses,' vol. i. i)p. 143 ■'«/'/., 218
S(jq. ; iii. 165 .^'jq., 245), that gj'ro-
static and vortex motion has l>ecome
in this countrj" a favourite study of
matiiematicians and natural j>hil-
o.sophers, and forms an iuiiH)rtant
feature in almost every recent
attempt t<> de.'icril>e the proi>ertie»
of matter and ether.

62

SCIENTIFIC THOUGHT.

42. It does not seem that Helmholtz's speculations were

Influence of

Helmholtz's much taken up abroad ; in this country, however, they

speculations ^ ' "^ ' ^

in England. fg|| ^^^ ^^^.^ fruitful soil : ^ they led first of all to

^ It is a remarkable fact that the
country which produced the great
theory that finally destroyed the
older vortex theory of Descartes,
was the one in wliich, a century
after Newton, the modern views on
vortex-motion were first and almost
exclusively developed. Notably
the scientific atmosphere in which
Thomson and Tait moved was, inter
alia, charged with the bold ideas
and the suggestive nomenclature of
Macquorn Rankine. He owes his
permanent place in the history of
science to being side by side with
Lord Kelvin and Clausius, one of the
threefoundersof theoretical thermo-
dynamics. But he was in addition
to this perhaps the earliest and
purest representative of the kinetic
or mechanical view of natural
phenomena, and of the scientific
tendency or habit — derived from his
profession as an engineer — of con-
structing for everj' phenomenon to
be explained a mechanical model.
In a succession of memoirs beginning
in 1850, Rankine put forward his
theory of ' ' molecular vortices,' '
' ' which assumes that each atom of
matter consists of a nucleus or
central point enveloped by an
elastic atmosphere" ('Scientific
Papers of Macquorn Rankine,' ed.
Miller, Loudon, 1881, p. 17). Clerk
Maxwell in 1878 wrote of Rankine's
theory: "Whatever he imagined
about molecular vortices was so
clearly imaged in his mind's ej'e
that he, as a practical engineer,
could see how it would work. How-
ever intricate. therefore, the
machinery might be which he
imagined to exist in the minute
parts of bodies, there was no danger
of his going on to explain natural
phenomena by any mode of action

of this machinery which was not
consistent with the general laws of
mechanism. Hence, though the
construction and distribution of his
vortices may seem to us as compli-
cated and arbitrary as the Cartesian
system, his final deductions are
simple, necessary, and consistent
with facts. Certain phenomena were
to be explained. Rankine set himself
to imagine the mechanism by which
they might be produced. Being an
accomplished engineer, he succeeded
in specifying a particular arrange-
ment of mechanism competent to
do the work." Maxwell goes on to
say : "As long as the training of
the naturalist enables him to trace
the action only of particular
material systems, without giving
him the power of dealing with the
general properties of all such
systems, he must proceed by the
method .so often described in
histories of science — ■ he must
imagine model after model of hypo-
thetical apparatus, till he finds one
which will do the required work.
. . . The theory of molecular
vortices was distinguished from
other theories which attribute
motion to bodies apparently at rest,
by the further assumption that this
motion is like that of very small
vortices, each whirling about its
own axis " (Clei-k Maxwell in
' Nature,' 1878 ; ' Scientific Papers,'
vol. ii. p. 662, &c. ; and Prof.
Tait's memoir of Rankine in the
' Collected Papers,' p. xxix). In the
most recent attempt to reconcile
the two fundamental ideas with-
out which we do not seem to be
able to proceed in a description of
natural phenomena — viz., that
space is a plenum, filled bj' a con-
tinuous something, and that matter

KINETIC OR MECHANICAL VIEW (iF NATIHF:. 63

many experiiiiental contrivanceB, by which tlie it-
iiiaikable phenomena known as " ^yrostatic " — ix.,
the stiible properties of liodies in rapid rotary motion '
— could be studied, as also to the development of tlie
theory of knots and linkage." In llie resourceful brain

(and electricity) is atomic (discrete,
grained), Dr Larnior has traced
the modern vortex theory further
back beyond Raukine to James
MiicCuilagh, who in his ' Essay
towards a Dynamical Theory of
Crystalline Reflexion and Refrac-
tion'(Trans. Irish Academy, 1839),
"arrived at a type of elasticity (of
the ether) which was win illy rota-
tional, . . . somewhat after the
manner that a spinning flywheel
resists any angular deflection of its
axis " (p. 26 of his Adams prize
essay, ' -Ether and Matter,' 1900).
" Rankine, never timid in his specu-
lations, expounded I\IacCullagh's an-
alytical scheme soundly and clearly,
in full contrast with the elastic
properties of matter, as represent-
ing a uniform medium or plenum
endowed with ordinary inertia, but
with elasticitj' of purely rotational
type" (iV)id.,p. 77 ; cf. p. 73) ; but
he also remarks that "up to the
period of Lord Kelvin's vortex
atoms . . . the earlier theories . . .
could only have l)een hypothetical
speculations " (p. 25 note).

1 Helmholtz himself did not give
many practical illustrations of his
remarkable theories. Such were
first given by W. B. Rogers (' Amer.
Journ. of Science ' (2), vol. 26, p.
246) in I8.08, without knowledge of
Helmholtz's theoretical investiga-
tions. In this country such illusti-a-
tions have become quite favourite
popular lecture experiments (see
Sir Rob. S. Ball's memoir). Smoke-
rings, solid and liquid gyrostats, and
a host of similar contrivances, have
impressed on us the hidden re-
sources of whirling motion. Prof.

Tait, in his ' Recent Advances of
Physical Science' (3rd ed., 18S."), p.
296), states that experiments on
smoke-rings which he performed,
suggested to Lord Kelvin the
vortex theory of matter. Tlie
various papers of the latter have,
so far, not been collected in a con-
venient form. The earliest is con-
tained in the ' Proceedings of the
Royal Society of Edinburgh,' Feb-
ruary 1867. Then followed a
memoir in the ' Transactions ' (April
1867) on vortex statics (Proc.
R. S. E., December 1875) ; " Vibra-
tions of a Columnar Vortex " (Proc,
March 1880). Prof. Hicks, and
especially Prof. J. J. Thomson
(Trans. R. Soc, 1884 ; 1881), have
contributed to the theory, and the
latter, in his Adams prize essay for
1882, has further tested the concep-
tion in its application to chemical
statics. See Hicks, ' Recent Pro-
gress in Hydrodynamics ' (Brit.
Assoc. Rep., 1881, p. 63, kc), and
J. J. Thomson ' On the ilotion of
Vortex Rings' (1883, p. 114, kc.)

- The creator of this branch of
purely positional geometry is doubt-
less Johann Benedict Listing, who
was led to his researches by some
suggestions of Gauss. Gauss refers
to the subject in connection with his
unpublislied researches into electro-
dvnamics (1833, posthumously pub-
lished in ' Werke,' vol. v. p." 605).
Listing called this branch of
geometry " Topologie " (cf. Listing,
' Vorstudien zur 'rojiologie,' Giit-
tingen, 1847). In the meantime
Riemann had been (1851) led in his
mathematical representation of
functions on tlie surface uiUcd

64

SCIENTIFIC THOUGHT.

of Lord Kelvin this theory led to the conception that
in an all-pervading, boundless fluid, such as physicists
imagined for the purposes of the theory of light, dif-
ferentiated portions might exist in the form of whirling
rings (vortex rings), which would possess most of the
properties of ponderable matter — identity and perman-
ence of quantity of substance, stability, rigidity, elasticity.
43. It was indeed soon found that although eminently sug-

Difficulties

of the vortex gestive in this way, and pointing in the direction of a
general kinetic theory of natural phenomena, the vortex
ring theory presented two fundamental difficulties. How
does whirling matter acquire weight, and how does it
acquire immensely increased inertia ? In the explana-
tion of these two properties the progress has been small,
— if indeed any glimpse at all has as yet been got.^
But by suggesting numberless experiments through which
our knowledge of things natural has been enormously in-
creased, by placing before the minds of mathematicians
a great number of problems of practical importance and
physical interest, and generally by familiarising the minds
of philosophers with an ultimate kinetic explanation of
nature,^ the vortex -atom theory has marked an epoch in

after him, to distinguish between
singly, doubly, triply, &c., con-
nected surfaces ('Werke, ' 1876,
pp. 18, 88, 448). These studies,
which for a long time were looked
upon merely as curiosa or- of purely
abstract interest, were indepen-
dently taken up in the practical
interest of tlie vortes,-atom theory
by Prof. Taitin 1876 (" On Knots,"
Trans. Roy. Soc. Edinb., 1877, vol.
28, p. 145, &c. ), and continued in
1884-85. To him we owe a con-
venient notation and vocabulary.
For the history of the subject and

further developments, see Diu-
geldey, ' Topologische Studien,'
Leipzig, 1890.

^ See Clerk Maxwell's article
"Atom" in the 9th ed. of the
' Ency. Brit.,' reprinted in 'Scien-
tific Papers,' vol. ii., and the account
given there of Le Sage's theory.

'■^ See Dr Larmor's Address to
Section A of the Brit. Assoc, at
Bradford in 1890 (Report, p. 625) :
" The vortex-atom theory has been
a main source of physical suggestion,
because it presents, on a simple
basis, a dynamical picture of an

KINETIC OR MECHANICAL VIEW UF NATL'KE, 65

the history of thought. As tlie study of stiible motion
or dynamical equilibrium, it has joined hands with the
kinetic theory of gases — i.e., the study of the motion of
a swarm of bodies in rectihnear motion, and with the
mechanical theory of lieat — i.e., of irregular intinitesimal
motion of any kind ; and it has certainly, through the
remarkable results gained by Professor J. .1. Thomson,
afforded a clue to tlie explanation of chemical linkage,
showing how it conies about that stability of chemical
compounds is dependent on, and limited to, a small
number of combinations or linkages.^ The mathematiciil
difficulties in the way of progress are enormous, sufKcient
to tax the brains of many generations to come, l)Ut as it

ideal material system, atomically
constitatcd, which could go on
automatically without extraneous
support. The value of such a
picture may be held to lie, not in
any supposition that this is the
mechanism of the actual world laid
bare, but in the vivid illustration it
affords of the fundamental postulate
of physical science, that mechanical
phenomena are not parts of a
sclienie too involved for us to
explore, but rather present them-
selves in definite and consistent
correlations, which we are able to
disentangle and apprehend with
continually increasing precision."

^ See his essay on the " Motion of
Vortex Rings": "Let us suppose
that the atoms of the different
chemical elements are m.ade up of
vortex rings all of the same strength,
but that some of these elements
consist of only one of these rings,
others of two of the rings linked
together, or else of a continuous
curve with two loops, others of
three, and so on. Our investigation
shows that no element can consist

VOL. If.

of more than six of these rings if
they are arranged in the .sym-
metrical way there described " (p.
119). "Each vortex ring in the
atom would correspond to a unit of
affinity in the chemical theoiy of
quanlivalence. If we regard the
vortex rings in those atoms con-
sisting of more vortex rings than
one as linked together in the most
symmetrical way, then no element
could have an atom consisting of
more than six vortex rings at the
most, so that no single atom would
be capable of uniting with more
than six atoms of another element
so as to form a stable conijiound.
This agrees witli chemical facts,
as Lothar Meyer in his ' Moderne
Theorien der Chemie,' 4th ed., p.
196, states that no compound con-
sisting of more than six atoms of
one element combined with only
one of another is known to exist in
the gaseous state, and that a
gaseous comjjound of tungsten,
consisting of si.x atoms of chlorine
united to one of tungsten, does
exist" (p. 120).

E

66

SCIENTIFIC THOUGHT.

44.

Modem
view of
electrical

has been remarked, " the glory of surmounting them would

be unique." ^

The vortex-atom theory is the most advanced chapter
in the kinetic theory of matter, the most exalted glimpse
into the mechanical view of nature. Though suggested
by Helmholtz, it has, as already stated, been limited
almost exclusively to this covmtry. If science still
shows international differences and patriotic predilections,
this affords one of the few remaining examples. Another
step first taken in this country, the last and most im-
portant contribution to the science of physical motion,
the greatest support of the kinetic or mechanical view
of nature, has, in union with the undulatory theory of
light, been now all but universally accepted in the
scientific world: I refer to the modern view of electric
phenomena, which for a long time was supported by the

phenomena: solitary labours and genius of Faraday

Faraday

His great discoveries of magneto-electricity, of induc-
tion, of the electrification of light, to which I have had
repeated occasion to refer, made his name familiar to
the whole scientific world ; but the processes of reasoning
by which he arrived at them, or to which in his mind
they gave rise, were ignored or not understood." Whilst

^ Tait, in ' Recent Advances of
Phj'sical Science,' p. 302, and Clerk
Maxwell, in article " Atom " (' En-
cy. Brit.,' 9th ed., or 'Col-
lected Scientific Papers,' vol. ii. p.
472).

- See Helmlioltz's ' Faraday Lec-
ture,' delivered before the Chemical
Society on April 5, 1881, reprinted
in his ' Vortriigeund Reden,' vol. ii.
p. 275, &c. "Since the mathe-
matical interpretation of Faraday's
theorems by Clerk Maxwell has

been given, we see indeed how
sharply defined the conceptions are
and how consistent the reasoning
which lay concealed in Faraday's
words, which to his contemporaries
appeared so indefinite and obscure ;
and it is in the highest degree re-
markable to see how a large number
of comprehensive theorems, the
proof of which taxes the highest
powers of mathematical analysis,
were found by him without the u.se
of a single mathematical formula,

KINETIC OR MECHANICAL VIEW OF NATURE. 67

Continental philosophers, following Coulomb, tried to put
into mathematical language the action at measurable dis-
tances of magnetic masses and elements of electrical
circuits,^ Faraday fastened upon tlie pecuUar lines in
which iron tilings arranged themselves in the neighbour-

by a kind of intuition with iu.slinc-
tive certiiinty. I would not de-
preciate Faraday's contemporaries
because they did not see this. I
know myself too well how often I
sat hopeless, gazing at one of his
descriptions of lines of force with
their numbers and tension, or look-
ing for the meaning of statements
where the galvanic current is re-
garded as an axis of force and much
the like" (p. 277). Rosenberger
tells us that it may be in part attrib-
uted to the displeasure and annoy-
ance with which foreign philoso-
phers received l<araday's theoretical
views, that Poggendortf, who printed
Faraday's earlier memoirs in extenso
in his ' Annalen,' only gave a short
abstract of the later series. See
Rosenberger, ' Die moderne Ent-
wickelung der elektrischen Princi-
pien,' Leipzig, 1898, p. 105.

' These researches, of which the
fourth chapter of this work gave
some account, and which culminated
in Weber's well-known law of electro-
dynamic action of electrical particles
at a distance, absorbed almo^^t ex-
clusively the attention of natural
philosophers abroad. Mathema-
ticians of the highest rank, such
as Laplace, Gauss, and Riemann,
worked at the subject. It is, how-
ever, interesting to note that Gauss,
with that remarkable instinct for
physical adaptation of mathematical
ideas which characterised also the
magnetic researches which he
carried on between 1830 and 1840,
refrained from the development of
a mathematical theory of electro-
dynamic action for reasons which
he later explained to Weber. When

the latter prepared for publication
that elaborate series of exact mea-
surements which, irrespective of the
theory attached to them, formed
the foundation of modern electrical
science and of the correlation of the
phenomena of magnetism, of elec-
tricity at rest and in motion, of
induction and of diamagnetism,
Gauss wrote as follows under date
19th March 1845: "The subject
belongs to those investigations
which occupied me very extensively
about ten years ago (especially
1834-36). . . . Perhaps I may be
able to think myself again into these
matters, which have now become so
foreign to me. ... I should no
doubt have long ago published my
researches ; but at the time when
I broke them off, that was want-
ing which 1 then considered to
be the very keystone — nil actum
reputans si quid superesset agen-
dum— namely, the deduction of the
additional forces (which have to be
added on to the mutual action of
particles of electricity at rest, if
they are in relative motion) from
action, not instantaneous, but
(like that of light) projjagated in
time. With this I could not suc-
ceed at the moment, but so far
as I can remember I left the subject
not entirely without hope that this
might later be possible; yet, if I re-
member aright, with the subject-
ive conviction that it would previ-
ously be necessary to form for one-
self a workable representation (cine
construirbarc Vorstcl/uiig) of the
manner in which the jn-opagatiou
takes place " ((iauss, ' Werke,' vol.
v. p. 627, &c.)

68

SCIENTIFIC THOUGHT.

45.

" Line
force.

of

hood of the poles of magnets ; ^ inquired into the nature
and condition of the region — afterwards termed the " field "
— which surrounded magnetised and electrified bodies ;
invented the term " electrotonic state" and " dielectric" " to
describe the part which the surrounding medium played
in the so-called actions at a distance ; and conceived it to
be in a state of tension, which he further described by
filling it with so-called " lines of force." The region or
" field " ^ of magnetic and electric action, filled with
these curved lines of force, possessing definite direc-
tion and frequency, gave him a clear mental repre-
sentation of the direction and intensity of magnetic and
electric forces at any point in space in the neighbour-
hood of magnets or of electric currents. For Faraday,
the lines of force in the magnetic field, from being
originally merely a convenient geometrical device,* ac-

^ " By magnetic curve.s 1 mean
the lines of magnetic forces, how-
ever modified by the juxtaposition
of poles, which would be depicted
by iron filings, or those to which
a very small magnetic needle would
form a tangent" (Faraday, 'Ex-
perimental Researches on Elec-
tricity,' 1st series, November 1831,
No. 114 note). " When an electrical
current is passed through a wire, that
wire is surrounded at every part by
magnetic curves, diminishing in
intensity according to their distance
from the wire. . . . These curves,
although different in form, are per-
fectly analogous to those existing
between two contrary magnetic
poles opposed to each other" (ibid.,
2nd series, January 1832, No. 232).

^ The term "electrotonic state"
was introduced in 1831 to describe
the condition of matter in the
neighbourhood of electric bodies.
" It is probable that what will affect

a conductor will affect an insulator
also, producing, perhaps, what may
deserve the term of the electro-
tonic state" (ibid.. No. 1661,
1838), " the intervening particles
assuming for the time more or less
of a peculiar condition, which
(though with a very imperfect idea)
I have several times expressed bj'
the term electrotonic state" (ibid.,
No. 1729). "I use the word 'di-
electric ' to express that substance
through or across which the electric
forces are acting " (December 1838,
ibid., No. 1168, note).

■* The term " magnetic field "
seems to have been used for the
first time in the year 1845 (see
' Exp. Res.,' No. 2252, vol. iii. p. 30).

* November 1837: "I use the
term line of inductive force merely
as a temporary conventional mode
of expressing the direction of the
power in cases of induction. . . .
The power, instead of being like

KINETIC OK MECHANICAL VIEW OF NATL Ut. 09

([uired gradually a physical* signiHcance, for he had
very early couviriced himself of the fact, known already

that of gravity, which causes
particles to act on each otlier
through straight lines, ... is more
analogous to that of a series of mag-
netic needles. . . . So that in wliat-
ever way I view it, and with great
suspicion of the influence of favourite
notions over myself, I cannot per-
ceive how the ordinary theory . . .
can be a correct representation cf
that great natural principle of elec-
trical action" ('Exp. Res.,' No.
r2:}l ). "1 have used tlie phrases lines
of inductive force and curved linesoi
force in a general sense only. . . .
All I am anxious about at present
is, that a more particular meaning
should not be attached to the ex-
pressions used tlian I contemplate "
(ibid., No. 1304). And after hav-
ing referred to the agreement of his
results with those of Poisson, ar-
rived at by starting from " a very
different mode of action," and with
the experimental results of Snow
Harris, he concludes by .saying,
" I put forth mj' particular view
with doubt and fear, lest it should
not bear the test of general examina-
tion," &c. (No. 1300).

^ It took more than ten j'ears
before the purely geometrical or
conventional use of the term " lines
of force " ripened into a pliysical
conception. The latter is definitely
expounded in a i)apcr in the ' Philos.
Magazine' for June 1852. We can
compare this gradual development
of a symbolical into a physical
theorj' with the gradual develop-
ment of the atomic theory ; atoms
and molecules becoming a physical
necessity to chemists long after
they had been used simply as a
convenient representation of the
laws of equivalence and of the fixed
proportions of combination (see
vol. i. of this work, chap, v., p.
432, &c.) Faraday, during the

years 1810 to 18o0, la»j<)uretl at two
great problemn : the one he iiolve<i
brilliantly and in tlie direction he
anticipated ; the otlier remains a
problem to this day. The first
refers to the action of magnetic on
the dielectric. The dielectric, the
space which Continental philo-
sophers considered as a vacuum no
far as magnetic and electrical i.henu-
mena are concerned, had Ijeen filled
by Young and Fresnel with the
luminifennis ether. Faraday sus-
pected that this luminiferous ether
cannot be insensible U) magnetic
action, and he .sought in the exi>eri-
mental proof of the action of mag-
nets on rays of light in the sur-
rounding space a support for his
view of the part which the dielectric
plays in the transmission of electric
and magnetic action. After many
ineffectual attemjjts to prove this,
he could at last (November 1845)
announce his results to the Royal
Society iis follows: "These inef-
fectual exertions . . . could not
remove my strong jiersuasion de-
rived from philo3oi)hical considera-
tions ; and therefore I recently
resumed the inquiry by exf>erinient
in a most strict and searching
manner, and have at last succeeded
in magnetising and electrifijing a
ray of light, and in illumiiuitiixg a
magnetic line of force. . . . Em-
ploying a ray of light, we can tell,
by the eye, the direction of the
magnetic lines througli a body ; and
by the alteration of the ray and it*
optical effect on the eye, can sec
tlie course of the lines just as we
can see the course of a thread of
glass or any other trans|)arent sub-
stance, rendereil visible bv the
light " (' Exp. Res.,' vol. iii., N.'). 2148
and note). The second problem
which Faraday attjicked was to
prove a similar "connection l>e-

70

SCIENTIFIC THOUGHT.

to Cavendish, that in the case of electric attraction and
repulsion, the nature of the intervening medium was of
importance : it played a part in the electric phenomena
in the same way as in the propagation of light and heat
the intervening medium played a definite part. This
part had been entirely overlooked by Continental philos-
ophers, who worked on the hypothesis of an immediate
action at a distance, based upon the analogy of gravi-
tation. Their researches, carried on by methods similar
to those invented by Laplace and his school for the cal-
culation of the combined effect of gravitational forces at
various points in space, entirely ignored the question how
such effects were brought about. As time did not seem
to enter as an appreciable factor, the investigation of the
mechanism by which action at a distance was communi-
cated was set aside as unnecessary or impossible : the
astronomical view of the phenomena sufficed. For
Faraday, the intervening medium, which — as in the com-
munication of light and heat — took an active part, the
question of its nature and mode of action was very
important ; he accordingly first of all gave it a name.
As in optics the term luminiferous ether had been
recently revived, and had become familiar through
Young and Fresnel, so through Faraday were intro-
duced the terms " dielectric " and " magnetic field,"
as the carriers of ejectric and magnetic action ; and
though for a long time used only by himself, they

tween gravity and electricity." On
the failure of this attempt he fully
reported in his Bakerian Lecture,
November 1850 ('Exp. Res.,' vol.
iii. p. 161). But the former results
were sufHcient to ripen gradually

in his mind the idea of the physical
nature of the lines of force, which
he expounded with increasing pre-
cision from 1851 onward. (See
' Exp. Res.,' 28th series, vol. iii. p.
328 ; also pp. 402, 438.)

KINETIC OR MECHANICAL VIEW OF NATURE. 71

liave been the means of keeping l>efore the minds of
natural philosophers the question h«iw these actions
are mechanically communicated, a problem which lay
outside of the astronomical view of tlie phenomena.
To Faraday himself the analogy between the phenomena
of these actions meant also a real physical relation
or even identity, a supposition which he followed up
with unwearying patience and all the experimental
resources of his inventive mind, till lie succeeded in
showing by experiment that magnets in the neighbour-
ho(jd of transparent substances which ]ia\e a polarising
effect on rays of light possessed the jiroperty of altering
the direction in which the jjolarised rays show their
laterality. Faraday's conception of " lines of force "
filling all space and explaining electric and magnetic
action, radiation, and possibly also gravitation, was
elaborated during the years 1830 to ISoO. An opinion
then prevailed that his discoveries stood in opposition to
the views elaborated and experimentally verified by
Continental philosophers. The first who showed the 46.

Devplop-

analogy and threw out a hint how the two views could imntofthe

^^ conception

be brought into harmony was William Thomson (Lord ^J^"^
Kelvin). As early as 1842,^ when scarcely eighteen

^ " On the uniform motion of [ heat in certain perfectly defined

Heat in homogeneous solid bodies, circumstances. With developments

and its connexion with the niathe- and apijlications contained in a

matical theory of Electricity," subsequent paper (1845), they con-

' Cambridge Mathematical Jour- '. stitute a full tlieory of the cliar-

nal,' February 1842. The following acteristics of lines of force, which

note is attached to the reprint in have been so admirably investigated

the ' Philosophical Magazine ' of experimentally by Faraday, and

1854 : " The general conclusions complete the analogy with the

established show that the laws of theory of the conduction of iieat,

distribution of electric or magnetic of which such terms as 'conduct-

force in any case whatever must be
identical with the laws of distri-
bution of the lines of motion of

ing power of lines of force ' (' Exp.
Re8.,'Noa. 2797-2802) involve the
idea. "

72

SCIENTIFIC THOUGHT.

years old, but already acquainted with English experi-
mental and French mathematical researches, he pointed
out how phenomena of flow — i.e., of motion — could be
mathematically grasped by a formula quite similar to
that of the distribution of masses at rest and appar-
ently governed by attractive forces at a distance. For
instance, the distribution of temperature at various dis-
tinct points in a space in which a flow of heat from an
origin had brought about a stationary condition (the
equilibrium being dynamical, not statical), was mathe-
matically expressed by a formula identical with that
which, according to Poisson and others, gave the dis-
tribution of electrical or attracting masses. Now we
know that in the former case the equilibrium is main-
tained by a flow across the intervening space, which takes
time. This suggests, therefore, the possibility of ex-
plaining the so-called statical effects of attracting or
repelling masses kinetically by a process of flow or motion
going on in the intervening medium, a notion to which
Faraday clung tenaciously. In 1845 Thomson reverted
to this subject, and after harmonising the two views,
concluded by stating that the latter " method of establish-
ing the mathematical theory would be even more simple
if possible than that of Coulomb." ^

^ " On the Mathematical Theory
of Electricity in Equilibrium,"
1845. See ' Reprint of Papers on
Electrostatics and Magnetism,' 2nd
ed. , p. 29. A study of these mathe-
matical researches of Lord Kelvin,
beginning early in the 'forties and
extending over more than twenty
years, is of special historical in-
terest, as showing the gradual
growth of a physical out of a purely

mathematical theory : most of the
conceptions which have since be-
come general through Maxwell's
electro-magnetic theory, as it has
been developed and popularised
by subsequent writers (notably
Prof. Poynting, Prof. Oliver Lodge,
and Mr Oliver Heaviside), being
already contained in Thomson's
papers as mathematical notions.
Thomson is throughout careful to

KINETIC OR MECHANICAL VIEW OF NATUUE. 73

This suggestion was not carried out for some time,
and then not l>y Thomson himself, but, at his instiga-
tion, by Clerk Maxwell. In the meantime, however,
Tiiomson added another step to the one already taken, by
bringing recent discoveries of Faraday, as well as his

point uut how the elementary ex-
perimental data referring to elec-
trical charges, as well as to mag-
netic bodies, can be mathematically
expressed equally well by the con-
ceptions of Cf)ulomb and Poisson
ami by those of conducti(^n and How,
which are more in conformity with
Faraday's physical ideas : neither
of the mathematical analogies, of
attraction at a distance or of con-
duction through an intervening
medium, being sufficient for a
physical theory. These papers con-
tain further the record of the
gradual growth in the author's
mind of the kinetic out of the
statical view of natural phenomena.
Thomson was the first (18.51) to
introduce the terms "field" and
"lines of force"' into mathemati-
cal literature, adopting them from
Faraday. They have since become
indispensable not only to the electri-
cian but likewise to the mathema-
tician ; forming, as it were, a unify-
ing term for apparently distant
regions of physical phenomena, and
being introduced as fundamental
notions at the beginning of dynami-
cal treatises. See, for instance, the
article by M. Abraham entitled
" Geometrische Grundbegrifre," in
the second part of the fourth volume
of the ' Encyclopildie der mathe-
matischen Wissenschaften,' Leipzig,
Teubner, 190L Independently and
quite unknown to Faraday, or to
each other, two eminent mathe-
maticians. Sir W. K. Hamilton at
Dublin and Herrmann Grassmann
at Stettin, were elaborating, be-
tween 1835 and 1845, the geo-
metrical conceptions and vocabulary

wliiL-h are required in the repre-
sentation of "directed" quantities.
Their exijositions have since become
much simplified, and now font),
under the title of " vector an-
alysis," an indispensable geometrical
instrument. Tlie gradual evolution
of the kinetic view of jiliyiiical
phenomena (which here concerns us
most) in the memoirs of Thomson
is most remarkable. Inter alia, he
made a communication in 1847 to
the British As.'-ociation at Oxford,
in whicli he dealt with the phe-
nomena of terrestrial magnetism,
stating that "it becomes an in-
teresting question whether mere
electric currents could produce the
actual j(hen(jmena observed. Am-
pere's electro-magnetic theory leads
us to an affirmative answer which
must be regarded as merely theor-
etical ; for it is absolutely impossible
to conceive of the currents which he
descriljes round the molecules of
matter as having a physical exist-
ence " (Reprint, 2nd cd., p. 469).
On this pas.sage he himself remark-*
in 1872 : " From twenty to twenty-
five years ago, I had no belief
in the reality of this [AmJ>^re's]
theory ; but I did not then know
that motion is the very es.sence of
what has hitherto been called
matter. At the 1847 meeting of
the British Association in Oxfortl
I learned from Joule tlie dynamical
theory of heat, and was forced to
abandon at once many, and gi-adu-
aliy from year to year all other,
statical preconcci)tions regarding
the ultimate causes of apparently
statical phenomena" (ibid., p. 423
note).

74

SCIENTIFIC THOUGHT.

unique conception of the communication of electric and
magnetic phenomena, into connection with the mathe-
matical theory which had been founded and worked out
by Poisson and Green. Without attempting to give
a physical explanation of Faraday's lines of force, he
showed how they could be utilised in calculating the
complicated action of magnetic push -and -pull forces;
suggested that the newly discovered property called dia-
magnetism, in virtue of which bodies in the neighbour-
hood of powerful magnets appeared to be repelled, not
attracted, could be explained as a differential ^ effect of

1 It was in the year 1845 that
Faraday, after having discovered
the "magnetisation of light," and
made visible the " magnetic lines
of force" ('Exp. Res.,' Nos. 2146-
2242), entered upon that remark-
able series of experiments and
speculations which led him to the
discovery of diamagnetism and to
the assertion of the " magnetic con-
dition of all matter" (ibid., Nos.
2243, &c.) In 1847 Thomson wrote :
" According to Mr Faraday's recent
researches it appears that there are
a great many substances susceptible
of magnetic induction, of such a
kind that for them the value of the
coefficient i is negative. These he
calls diamagnetic substances, and
in describing the remarkable re-
sults to which his experiments
conducted him with reference to
induction in diamagnetic matter,
he says, ' All the phenomena re-
solve themselves into this, that a
portion of such matter, When under
magnetic action, tends to move
from stronger to weaker places or
points of force.' This is entirely
in accordance with the result ob-
tained above ; and it appears that
the law of all the phenomena of
induction discovered by Faraday
with reference to diamagnetics may
be expressed in the same terms as

in the case of ordinary magnetic
induction, by merely supposing
the coefficient i to have a nega-
tive value " (Reprint, p. 502). In
the Reprint (1854) of his early
papers (1842) on the corresponding
problems of magnetism and heat
(Reprint, p. 18) he added a note to
the effect that the "same demon-
stration is applicable to the in-
fluence of a piece of soft iron, or
other paramagnetic, or to the re-
verse influence of a diamagnetic
on the magnetic force in any
locality near a magnet in which it
can be placed, and shows that the
lines of magnetic force will be
altered by it pi-ecisely as the lines
of motion of heat in corresponding
thermal circumstances would be
altei-ed by introducing a body of
greater or less conducting power of
heat. Hence we see how strict
is the foundation for an analogy on
which the conducting power of a
magnetic medium for lines of force
may be spoken of, and we have a
perfect explanation of the con-
densing action of a paramagnetic,
and the repulsive eSect of a dia-
magnetic upon the lines of force of
a magnetic field, which have been
described by Faraday " (Reprint,
p. 33 note ; cf . Faraday, ' Exp.
Res.,' Nos. 2807, 2808).

KINETIC OR MECHANICAL VIEW OF NATURE. 75

the magnetic actions which liclong to all Kubstances ;
introduced the term magnetic " permealjilily " ' as de-
scriptive of the degree in which various substances
acquire magnetic properties and conduct the lines of
magnetic force in the neighbourhood of powerful mag-
nets ; and finally demonstrated how, if these properties
were considered as having different degrees in the dif-
ferent axes of crystals, in analogy with the dillerent
elasticities which they exhibited, the consequence would
be a turning effect which would explain the changed
optical properties of crystals under the influence of

magnetic action.

Tn these investigations the ideas of

' Tliis property was afterward.s
termed " permeabifity " by Thom-
son (Reprint, p. 489, 1872). The
general rule of magnetic action can
then be expressed by saying that
" by virtue of differential action a
body may behave paramagnetically
or diamagnetically according as it
is j)laced in a less or a more perme-
able medium than itself " (Clirystal
in article " Magnetism," ' Ency.
Brit.,' 9th ed., vol. xv. p. 248).

- "On Ihe Theory of Magnetic
Induction in Crystalline and Non-
crystalline Substances " ( ' Philos.
Mag.,' March 18.57 ; also Reprint,
2nd ed., p. 471, <&c.) Poisson had
alreadj' foreseen the mathematical
possibility of wliat Faraday termed
magne- (correctly magneto-) crys-
tallic action, but " ce cas singulier
ne s'ctant pas encore prdsente h.
I'observation, nous I'exclurons de
nos recherches " (" Mumoire sur la
Thcorie du Magndt.isme," ' Mem. de
I'Institut, Paris, 1826,' quoted by
Thomson, Reprint, p. 484). .Stimu-
lated by the discoveries of Faraday,
Pliicker at Bonn, during the extra-
ordinary interval wliicli separated
the second from tlie first jjcriod of
his original geometrical speculations
(see vol. i. ]>. 242 of this work), de-

voted himself to the study of the
electric and magnetic jirnjierties of
givses and crystals, and in 1847
commenced that remarkalile series
of physical memoirs through which
he became the fellow-worker, if not
the rival, of Faradaj-. One of hia
first discoveries wa.s the action of
magnets on crystals, published in
1847 (Pogg. Ann., or Pliicker's
' Physicalische Abhandlungen,' ed.
Pockels, Leij)zig, 1896, p. 6, &c.),
which supplied to Thomson "the
verj' circumstance the observation
of which wa.s wanting to induce
Poisson to enter ujion a full treat-
ment of the subject, and made the
working out of a mathematical
theory of magnetic induction . . .
independently of any hyjwthesis
. . . ujion a purely exjierimental
foundation . . . imjwrtant " (Tliom-
son, loc. cit., p. 471). Pliicker was
an original thinker, and mainly a
self-taught geniu.-s, imjierfectly ac-
quainted with the labours of liis
contemi)oraries or predecessors.
Thi.s has been noted i>y his biog-
raphers as much in liis geometrical
as in his physical researches (.see
tlic memoirs of Cleb.sch and of Prof.
Riecke, jncfixed to the two volumes
of the'Gesammclte Abliandlungen ').

76

SCIENTIFIC THOUGHT.

47.
Clerk
Maxwell.

Faraday are used merely for the sake of describing and
calculating in the simplest manner phenomena which
had been experimentally discovered : no attempt was
made to explain physically how these actions come
about. In fact, under the hands of Thomson the con-
ceptions of Faraday were formulated as Dalton's atomic
theory had been elaborated by chemists in the first half
of the century, for the purpose of symbolically represent-
ing and calculating observed phenomena.

But the " lines of force " of Faraday were not to remain
a mere symbolical representation, any more than Dalton's
atoms were to remain merely counters of a chemical arith-
metic. Both theories were to be raised to the rank of
physical theories. What the kinetic theory of gases did
for the atomic theory was done for Faraday's symbolism
by the researches of Clerk Maxwell. And as the fact
that the molecules of matter could be really counted,
and their distances and velocities measured, gave life and
actual meaning to the atomic view of natural phenomena,

In his early geometrical researches
he worked in ignorance of the re-
markable ' Traite ' of Poncelet,
which had been published in 1822
{loc. cit., vol. i. p. 594, &c.) : even
the writings of his countryman
Mobius were unknown to him.
Still more extraordinary was his
comparative unacquaintance with
the electrical measurements and
theories which dominated German
research when he commenced his
physical labours, and which eman-
ated from the school of Gauss and
Weber. But he was equally ignor-
ant of the purely mathematical
theories of Poisson and Thomson,
which, as he himself candidly con-
fessed, might have saved him

from important errors {loc. cit., vol.
ii. p. 460), and which were later
made more widely known in Ger-
many by the excellent treatise of
his pupil Beer ( ' Einleitung in die
Elektrostatik,' &c., Braunschweig,
1869), posthumously edited by
Plucker himself. The fact that
Pliicker was not influenced by the
spirit of Weber's researches prob-
ably made him more appreciative of
Faraday's purely physical methods.
In such names as Beer, Clebsch,
Klein, Fessel, Geissler, and Hittorf,
Pliicker counts an illustrious array
of pupils and fellow-workers. See
Clebsch's characteristic of Plucker,
loc. cit., vol. i. p. xii, &c

KINETIC OR MECHANICAL VIEW OF NATURE. 77

SO the rays of electric and magnetic force seen by Faraday
ill tlie abstraction of bis intuitive mind became a reality
for every experimentalist when Hertz in 1888 actually
showed the wonderful action of electric waves at a dis-
tance. Atoms and lines of force have become a practical
— shall I say a popular ? — reality, whereas they were once
only the convenient method of a single original mind for
gathering together aiul unifying in thought a bewildering
mass of observed phenomena, or at most capable of being
utilised for a mathematical description and calculation of
actual effects.

For a (juarter of a century after Faraday had conceived
the notion of looking upon electric and magnetic
phenomena as depending on a property belonging to
all matter, and pervading all space, like radiation and
gravity, the only natural ])hilosopher wlio to any extent
entered into his ideas was Thomson. Even Tyndall, who
came more than any other prominent physicist under
Faraday's immediate and personal inlluence, and contrib-
uted largely to our knowledge of the new phenomena
discovered by his great master, does not seem to have
assimilated his scientific language and reasoning. It
required a mathematical mind really to grasp and put
into form Faraday's notions. Encouraged by Thomson,
and soon after the publication of 'i1ioins(ni's mathe-
luatical theory of magnetism, (Terk jMaxwell devoted
himself to a theoretical study of electricity and allicil
subjects, a field wliich Thomson bail tlicii ahnost mon-
opohsed in this country.^ The first of Maxwell's revolu-

' See Professor Glazebrook's little "Century Science Scries." 1901.
book on ' James Clerk Maxwell and On page 42 a letter of Maxwell i6
Modern Pliysics,' published in tlie (juoted, in which he speaks of

78

SCIENTIFIC THOUGHT.

48.
His series
of works
on the
theory of
electricity.

tionaiy series of works, ' On Faraday's Lines of Force,'
was published in December 1855. The series was
completed by the appearance in 1873 of his great work
on ' Electricity and Magnetism,' which has formed the
centre of a large literature to which all the scientific
schools of Europe and America have contributed. Histori-
cally, Maxwell brought together two distinct and very
fruitful lines of reasoning, due to Faraday and Thomson.^
He was impressed with the desideratum of every physical
theory bearing on any large class of phenomena — viz.,
that it must be mathematical and physical at the same
time. His own theory had to embrace and unite all the
purely arithmetical and geometrical regularities which
had been discovered, and which at that time were
known to describe correctly the facts of electric, mag-

" poaching upon Thomson's electri-
cal preserves." In the preface to the
treatise on electricity and magnet-
ism, he refers to the apparent dis-
crepancy between the views of
Faraday and the mathematicians,
and he states that he had arrived
at " the conviction that this dis-
crepancy did not arise from either
party being wrong. I was first
convinced of this," he proceeds, " by
Sir William Thomson, to whose
advice and assistance, as well as to
his published papers, I owe most of
what I have learned on the subject.
^ In a different reference we may
say that Maxwell's theory was pre-
pared by three independent lines of
research, starting respectively in
France, Germany, and England : (1)
The investigation of the actions at
a distance of electrified and mag-
netised bodies, and of electric
currents, which found mathemati-
cal expression in the formula of
Coulomb and Ampere. The full

significance and capabilities of the
formula) of electrostatic and mag-
netic action had been demonstrated
by Thomson, who especially showed
that these relations were not
necessarily confined to the physical
theory which had been elaborated
on the Continent, but that, mutatis
mutandis, they lent themselves
equally well to the physical ideas of
Faraday. (2) The exact measure-
ments of magnetic, electro-dynamic,
and galvanic action started bj' Ohm
and Gauss in Germany, and much
extended by Weber. (3) The idea
of physical lines of force, filling
space and representing action
through contiguous particles, not
at a distance, elaborated by Fara-
day. These tliree lines of research
were brought together in the
theory of Maxwell, which in the
beginning professed to be only a
mathematical but ended by being a
physical theory.

KINETIC OK MECHANICAL VIEW OF NATLllK. 79

iietic, and galvanic phenomena, such as Coulomb's electro-
static and magnetic laws, Ampere's electro-dynamic and
electro-magnetic formulie, and Ohm's anil Faraiiay's laws
referring to galvanic currents, and many othei-s. It
liad also to give an intelligible representation of t!ie
elementary actions of which these complicated plienom-
ena are made np. In mder to arrive at the latter, the
method usually employed is to look for anabjgies in
other provinces of science where the desired uniticatiun
has already I'cen brought about. The great natural
philosophers of the French school who had so success-
fully accomplished the most extensive unification yet
attempted in any large branch of knowledge — tlie uni-
fication of physical astronomy under Newton's gravita-
tion formula — had tried to follow up this analogy in
Dther realms of research, and had developed what I
called in a former chapter tlie astronomical view of
natural phenomena. Ampere, and notably "Weber, had
extended this analogy so as to embrace electric and
magnetic phenomena. There was, however, another
analogy which was more familiar to the great experi-
mentahsts in this country, notal)ly to Faraday — namely,
the analogy of those various phenomena which depend
on processes of emanation, of a gradual spreading out,
of a How or conduction: tliose plieiumiena where the
factor of time comes in, and where an apparently sta-
tionary condition is brought about by a mode of motion,
or what has been termed a " dynamic equilibrium."
Thomson, starting from Fourier's mathematical analysis
of sucli processes, had been led to sec bow far-reaching
this analogy is, and bad latterly (1852) extemied it to

80

SCIENTIFIC THOUGHT.

49.

His con-
ception of
"tubes of
force."

embrace the processes of the flow of heat, of electricity,
magnetic and diamagnetic, and of Huid motion. " He
called attention to the remarkable resemblance which
the diagrams of flow bore to those which Mr Faraday
had recently shown at the Eoyal Institution to illus-
trate his views regarding the action of ferro-magnetics
and diamagnetics in influencing the field of force in
which they are placed, and justified and illustrated the
expression ' conducting power for the lines of force ' by
referring to rigorous mathematical analogies presented
by the theory of heat." ^

This view, which Thomson had merely shadowed forth,
was more fully worked out by Maxwell in 1855 and
1861. His methods ^ were " generally those suggested by
the processes of reasoning which are found in the re-
searches of Faraday, and which, though they had l^een
interpreted mathematically by Prof. Thomson and others,
are very generally supposed to be of an indefinite and
unmathematical character when compared with those
employed by the professed mathematicians." The first
addition which he introduced, by which he made Fara-
day's " lines of force " mathematically more definite, was
to change them into " tubes of force," which represented
not only the direction of force at every point of space,
but also — according to their sectional dimensions — the
intensity of the force. These tubes were supposed to be

^ Abstracts of two communica-
tions to the British Association at
Belfast in 1852, " On certain Mag-
netic Curves : with Applications to
Problems in the Theories of Heat,
Electricity, and Fluid Motion "
(Reprint of Papers, &c. , p. 519, &c.)

- James Clerk Maxwell " On
Faraday's Lines of Force," ' Trans-
actions of the Cambridge Philo-
sophical Society,' 1855. See 'Col-
lected Scientific Papers,' vol. i. p.
157.

KINETIC Oil MECHANICAL VIEW UF NATURE. 81

filled with a moving tiuid, and the velocity of the How —
inversely proportional to the sectional area of the tuljes
— represented the intensity of the force at any point in
space. He also showed how very much simpler the con-
ception becomes, if the law of tlie acting forces is the
experimentally established law of the inverse square of
the distance.

This thought of " referring to the purely geometrical
idea of the motion of an imaginary tluid " ^ was tlie
beginning of the now universally adopted view of a
very large class of plienomena, and it was at the same
time a great step in the development of tlie kinetic
or mechanical view of natural processes. These lines or
tubes of force,"^ with which all space surrounding magnets
or electrified bodies was supposed to be filled, enal)led
Maxwell further to give a definite representation of that

peculiar state of matter of which Faradav had very so.
^ ^ J "Electro-

early formed an indefinite conception, and wliich he oj'jj^'t^r'*

called the " electrotonic state." Thomson had already

in 1847 ^ shown how the ideas of Faraday, who as early

^ How little ]\laxwell originally
intended to give a physical theory
is seen from the concluding sen-
tences of the introduction to his
first paper {!oc. cit., vol. i. p. 159) :
" By referring everything to the
purely geometrical idea of the
motion of an imaginary fluid, I
hope to attain generality and pre-
cision, and to avoid the dangers
arising from a premature theory
professing to explain the cause of
the phenomena. If the results of
mere speculation which I have
collected are found to be of any
use to experimental philosophers,
in arranging and interpreting their
results, they will have served their

VOL. II.

purpose, and a mature theory, in
which physical facts will be physi-
cally explained, will be formed by
those who by interrogating Nature
herself can obtain tlie only true
solution of the (luestions which the
mathematical theory suggests."

-' Faraday had already in 1852
spoken of shells and tubes of force,
and invented the term sphondyloid
to denote the portion of space en-
closed between such shells of force
('Exp. Kes.,' vol. iii.. No. 3271).

2 In 1847 ('Cambr. and Dubl.
Math. Journal,' lepriiited in ' Matli.
and Phys. Pai>ers,' vol. i. p. 76)
Thomson wrote tlmt Faraday's
theory of electrostatic inductii>n

82

SCIENTIFIC THOUGHT.

as 1831 conceived this peculiar condition of matter to
be equivalent to a state of strain, could be represented
by the mechanical analogy of the strains existing in an
elastic solid. He had distinguished three distinct forms
of this elastic strain, and had identified these three
forms severally with electrostatic, magnetic, and galvanic
forces. He had not given a physical explanation of the
origin of these forces, but had merely used the " mathe-
matical analogies of the two problems (the electrical and
the elastic) to assist the imagination in the study of
both." ^ Maxwell now took a further step and pro-
ceeded to give a physical or mechanical description of the
nature of this state of stress, of the electrotonic state of
matter. With this object in view he conceives of a
medium which is capable of exerting force on material
bodies by being itself strained, and exhibiting the

" suggests the idea that there may
be a problem in the theory of
elastic solids corresponding to every
problem connected with the distri-
bution of electricity on conductors,
or with the forces of attraction and
repulsion exercised by electrified
bodies. The clue to a similar re-
presentation of magnetic and gal-
vanic forces is afforded by Mr
Faraday's recent discovery of the
affection, with reference to polarised
light, of transparent solids sub-
jected to magnetic or electro-
magnetic forces."

^ Quoted from Maxwell's paper
" On Physical Lines of Force," in
the 'Philos. Mag.,' 1861 (see ' Coll.
Papers,' vol. i. p. 453), in which
Maxwell applies Rankine's concep-
tion of molecular vortices to the
representation of magnetic pheno-
mena. He refers to his earlier paper
(1855) on (geometrical) " lines of

force" in which he had "shown
the geometrical significance of the
electrotonic state," and had used
" mechanical illustrations to assist
the imagination, but not to ac-
count for the phenomena." " I
now," he says, "propose to examine
magnetic phenomena from a me-
chanical point of view, and to
determine what tensions in, or
motions of, a medium are capable
of producing the mechanical pheno-
mena observed. If by the same
hypothesis we can connect the
phenomena of magnetic attraction
with electro-magnetic phenomena,
and with those of induced cur-
rents, we shall have found a theory
which, if not true, can only be
proved to be erroneous by experi-
ments which will greatly enlarge
our knowledge of this part of
physics" (ibid., p. 452).

KINETIC OR MECHANICAL VIEW OF NATUHP:. 83

phenomena of tension and pressure (magnetic uctiun)
as also of motion of its parts (electro-magnetic action).
Now in a medium whicli is so constituted — i.e., which
possesses elastic mobility of its parts — we know that
by a whirling or vortex motion phenomena of pressure
and tension can be produced in certain parts, and the
questions accordingly presented tliemselves to Maxwell,
How Ijy such tension and pressure in certain parts of the
medium can magnetic phenomena be represented ? and
How can the vortices communicate motion to, or receive
motion from, the interlying movable particles of the
medium ? He succeeded in working out a very complete
model of such a medium, representing Ijy its mechanical
motions both magnetic and electro-magnetic phenomena.
Especially was he successful in visualising Faraday's
lines or tubes of force, and endowing them with me-
chanically measurable forces. Maxwell admits that " his
conception . . . may appear somewhat awkward. 1
do not," he says, " bring it forward as a mode of con-
nection existing in nature. ... It is, however, a mode
of connection which is mechanically conceivable and
easily investigated ; ... so that I venture to say that
any one who understands the provisional and temporary
character of this hypothesis will find liimself rather
helped than hindered by it in his search after the true
interpretation of the phenomena." ^

1 ' Collected Papers,' vol. i. p. 486.
At the end of his paper on physical
lines of force. Maxwell touches on
the philosoiihical question, " how
much evidence the explanation of
phenomena lends to the cr^dihility
of a theory, or how far we ought to

regard a coincidence in the mathe-
matical expression of two seUs i>f
phenomena as an indication tlwt
these phenomena are of the 8umc
kind. We know that partial co-
incidences of tliis kind have l>efn
discovered ; and the fact that ihcy

84

SCIENTIFIC THOUGHT.

51.

Corre-
spondence
between
velocities
of light
and of
electricity.

The idea of a medium of extreme rarity, pervading all
space and interpenetrating all matter, capable also of the
elastic reactions of a solid body, was not repugnant to
physicists at the time when Maxwell wrote. Though
violently opposed forty years earlier when proposed by
Fresnel and Young, it had gradually, through the de-
velopment of optical theories, become a well-recognised
instrument of scientific thought. In such a medium a
disturbance or displacement is propagated with a certain
velocity dependent on its elastic nature — the so-called
constants of density and rigidity. Now, looking upon a
charge of electricity not as a material something — an
imponderable — but as a displacement of the medium,
the question arose. Does the velocity with which such a
displacement travels compare at all with the known
velocities of other elastic disturbances, such as light is
conceived to be ? It was known to electricians that
an amount or charge of electricity can be either station-
ary (called statical electricity) or in motion (called
an electric current) ; and Weber and Kohlrausch had in
1856 actually measured the number of units of statical
electricity which must flow through an electric circuit in
order to produce the known mechanical effect of a unit
of electric current. The quantity which they found, and
which corresponded to a velocity, was of the same order
as the velocity with which the elastic disturbance which
we call light is known to travel. Maxwell was the first

are only partial is proved by the
divergence of the laws of the two
sets of phenomena in other respects.
We may chance to find, in the
higher parts of physics, instances of

more complete coincidence which
may require much investigation to
detect their ultimate divergence "

(p. 188).

KINETIC OR MECHANICAL VIEW uF NATURE. 85

,02.
Elastic di«-

to see the physical signiticance of this correspondence.*
" I have deduced the relation between the statical ami
dynamical measures of electricity, and have shown by a
comparison of the electro-magnetic experiments of .MM.
Kohlrausch and Weber willi the velocity of light as
found by M. Fizeau, that the elasticity of the magnetic
medium in air is the same as that of the luminiferous
medium, if these two coexistent, coextensive, and equally
elastic media are not rather one medium." -

After having pointed out this remarkable correspond-
ence and other analogies between electrical and optical
properties which could be verified by experiment, Max-
well seems to have felt satisfied tliat a dynamical or turtai.cea

" of tnt; same

kinetic explanation of electric and magnetic phenomena 'nedium.
based upon rotary and translational motions and elastic
strains in the magnetic field was quite possiljle. The
detailed descriptions given in his earlier papers he looked
upon merely as crude mechanical devices by which some
of the known effects of magnets and currents could be
described. The valuable result was, that the electro-
magnetic field could 1)6 looked upon as a mechanical
system ; that the observed actions at a distance could
be conceived as communicated through this mechanical
system in definite measurable time ; and that certain
analogies had been pointed out as existing between

^ ' Philos. Mag.,' January and Feb-
ruary, 1862 ; ' Coll. Papers' vol. i.
p. 492.

- Cf. ' Coll. Papers,' vol. i. p. r.OO :
" The velocity of transvense undula-
tion.s in our hypothetical medium,
calculated from the electro-magnetic
experiments of MM. Kohlrausch and

Weber, agree.s so exactly with the
velocity of light calculated from the
optical experiment,s of M. Fizeau,
that we can scarcely avoid the in-
ference that light consists in the
transverse undulation.s of the .sjime
medium which is the cause of electric
and magnetic phenomena."

86 SCIENTIFIC THOUGHT.

optical, electrical, and magnetic phenomena, which by
carefully devised experiments might be verified and
extended.

Through Maxwell, following on Faraday and Thomson,
the treatment of electric and magnetic phenomena had
thus entered on a similar stage to that which the
treatment of optical phenomena had attained lialf a
century earlier through Young and Fresnel. A kinetic
or mechanical view, more or less precise and definite, had
been propounded ; a considerable number of facts had
been brought into connection, into line and order ; the
direction which experimental research must take had
been indicated ; and finally a correspondence had been
established between two great groups of phenomena, those
of electricity and magnetism on the one side, those of
light on the other. It might have been expected that
Maxwell would now take the same course as that taken
by Fresnel about the year 1820, and perfect his views
by giving his theory of molecular vortices greater pre-
cision and definiteness — i.e., by perfecting the electro-
magnetic model, as Fresnel and others perfected in their
time the system of vibrations by which they visualised
the processes of light. This is not the method which
Maxwell adopted.^ In his later and more important

^ The progress of Maxwell's reason- i formulation of Faraday's concep-
ing is clearly marked in the three | tion, much in the spirit of Thorn

memoirs, belonging respectively to
the years 18.^5, 1861, and 1864, of
which the last appeared in the
' Transactions ' of the Royal So-
ciety, and which are reprinted in
the first volume of the ' Collected
Scientific Papers.' The first memoir
on " Faraday's Lines of Force " ad-
heres strictly to the mathematical

son's many expositions. The second,
on "Physical Lines of Force," fol-
lows Faraday in the attempt to take
the original symbol in real earnest
as a physical arrangement, and de-
vises, or applies for that purpose,
the theory of molecular vortices.
The third memoir, which is by far
the most important and original,

KINETIC OR MECHANICAL VIEW OF NATURE. 87

writings he adopted a different and more general process
of reasoning. If electrical and magnetic as well as
optical phenomena are produced by the motions of the
parts of a medium possessed of certain mechanical pro-
jjcrties, this medium represents a mechanical system, and
must therefore be subject to the general laws which
regulate all mechanical systems. These general laws are
laid down in dynamics, where it is shown that a complete 'jucnces

•^ '■ on Uie line*

knowledge of the behaviour of such a system can be ^[g"^'"?
reduced to the knowledge of the distribution in it of a
quantity called Energy.

I intend in the next chapter to trace historically the

ConM-

drops this somewhat crude device,
as well as the older theory of par-
ticles acting at a distfince, with
forces which, according to Weber,
depend on their velocities, and starts
from " the conception of a compli-
cated mechanism ca])able of a vast
variety of motion, but at the same
time so connected that the motion
of one part depends ... on
the motion of other parts, these
motions being communicated by
forces arising from the relative dis-
placement of the connected parts, in
virtue of their elasticity " (Papers,
vol. i. p. 533). He further says :
" I have on a former occasion at-
tempted to describe a particular
kind of motion and a particular
kind of strain, so arranged as to
account for the j)henomena. In
the pre.sent paj)er I avoid any hy-
pothesis of thiii kind ; and in using
such words as electric momentum
and electric elasticity in reference
to the known phenomena of the in-
duction of currents and tiie j)()lar-
isation of dielectrics, I wish merely
to direct the mind of the reader to
mechanical phenomena which will
-assist him in understanding the

electrical ones. All such phrases
in the present paper are to hf. con-
sidered a-s illustrative, not as ex-
planatory. In speaking of the
energy of the field, however, I
wish to be understood literally. All
energy is the same as mechanical
energy, whether it exists in the
form of motion or in that (jf elas-
ticitj% or in any other form. The
energy in electromagnetic phe-
nomena is mechanical energy. The
only question is, Where does it
reside ? On the old theories it
resides in the electrified bodies,
conducting circuits, and magnets,
in the form of an unknown quality
called potential energy, or the power
of producing certain effects at a
distance. On our theory it resides
in the electro-magnetic field, in tlie
space surrounding the electrified
and magnetic bodies, as well as in
those bodies themselves, and is in
two different forms, which may be
described without liypothesis as
magnetic polarisation and electric
polarisation, or, according to a very
probable hypothesis, jis tlie motion
and tlie strain of one and the same
medium " (p. 563).

88 SCIENTIFIC THOUGHT.

growth of this conception as apphed not only to the
energy of visible and measurable mechanical motion, but
to all other forces of nature which have in the course of
the century not only been measured in terms of this
one quantity, but also represented with more or less
success as dependent on the energy of specific forms of
motion, be this rotatory or vibratory or translational
motion, regular and periodic or irregular and disorderly
motion. It is clear that such a general abstract view as
Maxwell (first among natural philosophers) took of a
special problem was only possible after it had been
shown how all physical and chemical actions and effects
can be reduced to a common measure. The influence of
the development of these views on the kinetic view of
nature has been very great. The first and most natural
effect of measuring all forces of nature in terms of the
energy of motion is to strengthen the kinetic view of
natural phenomena. This, however, is not the only view
which is possible, or which has been taken, as I shall
endeavour to show more fully hereafter.

The influence of Maxwell's ideas on scientific — nay,
even on popular — thought has been very considerable.
The main conception around which research, both mathe-
matical and experimental, has moved during the last
twenty years is the conception of light as an electro-
magnetic phenomenon. This view has been much sup-
ported and extended by the experiments of Heinrich
Hertz, who by ingenious contrivances succeeded in
actually exhibiting electro - magnetic waves, and in
showing how they differ from light waves merely in
length and period, and agree with them so far as

KINETIC OK MECHANICAL VIKW uK NATURE. 89

reflexion and refraction and other properties are con-
cerned. Luminous waves are now considered !)>- many
physicists to be merely electro-magnetic waves of short
wave length and great frequency, such as the organ of
vision is capable of perceiving in the form of light.
The electric and magnetic medium is identical with the
luminiferous ether, postulated by Young and Fresnel,
and rays of light are merely an electric uiid magnetic
disturbance propagated as a periodic or wave motion.

These discoveries and theories have gone a long m.

. . Destructive

wav to destroy the older astronomical view or natural .met ut

•' '' the new

phenomena, which explained many effects by the action [};^;"J^jJ^°"
at a distance of particles of ponderable or imponderable "lewT'
matter. The firm conviction has taken hold of the
modern scientific intellect or imagination that space is a
plenum tilled with a continuous medium, and that the
undoubted atomic nature of ponderable matter may be
owino- merely to a specific and unmoditiable form of
motion with such properties as Lord Kelvin has shown
to belong to vortex lilaments. The ditticulty still re-
mains how to explain the phenomenon of gravitation as
well as the increased amount of inertia or mass which
belongs to all ponderable matter as compared with that
material substance which we call ether.

The reason why Maxwell abandoned his earlier
schemes, in which he tried to construct a mechanical
model of the electro-magnetic field, is not quite clear.^
The idea has, however, been taken up by others, and
elaborate descriptions have been attempted, by whifh the

1 A suggestion regarding this is given by Dr J. Laruior in ' .Etiier and
Matter,' p. 28.

90

SCIENTIFIC THOUGHT.

processes going on in the neighbourhood of electrically
charged bodies, of electric currents, of magnets and
diamagnets, can be visualised.^ For didactic purposes
such elaborate models may prove to be of great value,
though as a true mechanical basis of a physical theory of
natural processes they have to be received with caution.
None of those physicists who have expended their ingen-
uity in devising these contrivances seem to attach more
than a symbolic or ideal value to them : they have, how-
ever, the desired effect of producing on the mind of the
learner, of the practical inventor, or of a popular
audience a strong conviction that all physical phenomena
can be described as processes of motion, and that the
ultimate solution of the problem of natural philosophy is
to be found in a kinetic or mechanical view of pheno-
mena. Physics and chemistry are, according to this

^ Such illustrations may be found
in Dr Oliver Lodge's 'Modern
Views of Electricity,' a book which
has had a large circulation and has
helped to diffuse correct and practi-
cally useful ideas on electric and
magnetic problems and phenomena.
There is a danger of such mechani-
cal illustrations becoming too rigid
and of their being taken too literally ;
still, for the purposes of practical
application and handling it is indis-
pensable to possess some mechanical
mode of representation and con-
struction by which actual problems
can be readily solved. The success
of Dr Lodge's attempt both in this
country and on the Continent,
especially in Germany, proves suf-
ficiently that it meets a much -felt
want. See inter alia Prof. Rosen -
berger's five lectures, ' Die moderne
Entwickelung der elektrischen Prin-
cipien,' Leipzig, 1898, p. 133. A

great authority abroad, Prof. Lud-
wig Boltzmann, has made use of a
peculiar kind of mechanical motion,
investigated by Helmholtz, to il-
lustrate electrical phenomena. The
characteristic of such motion —
which is termed cyclic — is this,
" that in the place of every particle
which changes its position, an equal
and equally moving particle enters,
so that the condition of the system
during the motion is nowise al-
tered " ( ' Vorlesungen fiber Max-
well's Theorie,' Leipzig, 1891 and
1893, vol. i. p. 14). Cycles can be
" coupled," &c. The general dyna-
mical relations of such cyclic
systems are investigated, and by
introducing the necessary restric-
tions, based upon experimental
facts, and suitable hypotheses —
facts and hypotheses being clearly
distinguished — the general equa-
tions of Maxwell are arrived at.

KINETIC OR MECHANICAL VIEW OF NATURK. 91

view, destined to become idtiinately merely chaptei-s in
dynamics as the doctrine of mechanical motion.

A similar reluctance to look upon the vibrations of the
luminiferous ether merely as a convenient symbolism, as a
crude method of visualising molecular processes, which in
reality we cannot picture to ourselves, does not seem to
have troubled the minds of the great propounders of the
undulatory theory of light — i.e., of tlie elastic sohd
theory, as it is now termed in contradistinction to the
electro-magnetic theory propounded by Maxwell. The
greatest living exponent of the former view. Lord Kelvin,
who in his Baltimore Lectures grappled witli tlie dilli-
culties which still beset that view — falling back on the
principle of optical consonance and resonance, suggested
by Professor Stokes to explain some of the interactions of
the ether and ponderable matter : upon the theory of free
and forced vibrations, suggested by Bessel and Sellmeier ;
and on liis own fruitful suggestion of the vortex atom
to explain some of the properties of ponderable atoms
moving in the continuum which fills all space — expresses .'.r..

• 1 1 • Lord Kelvin

himself very dehnitely on this point. " We must not <"' *•"?

•^ "^ ^ vibrations

listen to any suggestion that we may look upon the "f the ether,
luminiferous ether as an ideal way of putting the thing.
A real matter between us and the remoter stars I believe
there is, and that light consists of real motions of that
matter, motions just such as are described by Fresnel and
Young, motions in the way of transverse vibrations. If
I knew what the magnetic theory of light is, I might be
able to think of it in relation to the fundamental
principles of the wave theory of light, liut it seems to
me rather a backward step from an absolutely definite

92 SCIENTIFIC THOUGHT.

mechanical notion that is put before us by Fresnel and
his followers, to take up the so-called electro-magnetic
theory of light in the way it has been taken up by several
writers of late."

But whilst, no doubt, the train of reasoning started by
Maxwell, and developed by his followers, has somewhat
destroyed the simplicity and directness which the older
vibratory theory of light and the kinetic theory of gases
had brought into our mechanical views of natural
phenomena, the subsequent experimental proof of the
existence of electric waves by Hertz has done much
popularly to strengthen that view. The discovery of
other kinds of rays, by Lenard, Eontgen, and others, has
likewise tended in the same direction, though their exact
nature is still a subject of much conjecture.

Nor can it be denied that the practical usefulness
also of these lately discovered forms of radiation has
tended in the same direction ; as has, all through the
last thirty years, the enormous development of electrical
industry in its many branches. Up to the beginning
of the nineteenth century the principal electric and
magnetic phenomena known were what we term stat-
ical ; the study of these centred in the conception of
electric and magnetic charges concentrated on or in
conductors and acting at a distance. The practical
interest was limited to mariners' compasses and light-
ning-conductors. The discovery of the galvanic current,
and still more its applications by Davy to the decom-
position of the most refractory chemical compounds,
introduced an entirely new class of phenomena. Con-
tinental science, in Coulomb, Ampere, and Weber, first

KINETIC OR MECHANICAL VIEW OF NATCKE. 93

developed the line of reasoning and research suggested
Ijy statical phenomena and applied this to dynamical
phenomena. Faraday, folhjwing Davy, approached the
subject from the point of view of the chemist. It was
soon suspected, and latterly proved by actual measure-
ments, that the quantities whicli come into play in
statical charges, and even in a violent thunderstorm, are
small compared with those of a steady electrical current.
The phenomena of electricity in motion became of in-
finitely more practical importance than those of elec-
trical equilibrium or of static tension. The views of
Faraday, Thomson, and Maxwell, which Hehaholtz,
educated thoui^h he was in the continental methods,
adopted and introduced into German scientific literature,
lent themselves, as he recognised, more successfully and
directly to the solution of the problems which applied
science forced upon theorists.

Something, indeed, has been lost by this fundamental
change which has come over modern reasoning in
electrical matters. This has been most clearly and 56.

Indefinite-

pointedly expressed by M. Poincard, the eminent French nessorthe
mathematician, who has done so much to illumine [Y"^'^!^'"^
physical and mechanical problems from the side of pure
mathematics. " Maxwell," he says, " does not give a
mechanical explanation of electricity and magnetism ; he
confines himself to the proof that such an explanation is
possible." Accordingly, those who were brought up in the
traditions of the school of Laplace and Caucliy feel dis-
mayed at the indetiniteness whicli adheres to the exposi-
tions of Maxwell's latest and greatest work. "A groat
French philosopher," M. Poincar^ proceeds, " one of those

94 SCIENTIFIC THOUGHT.

who have most completely fathomed Maxwell's work,
said to me once, ' I understand everything in the book
except what is meant by an electrically charged body.' "
Professor Glazebrook tells us : " We cannot find in the
' Electricity ' an answer to the question, What is an
electric charge ? Maxwell did not pretend to know, and
the attempt to give too great definiteness to his views
on this point is apt to lead to a misconception of what
those views were. . . . Still, in order to grasp Maxwell's
theory, this knowledge is not necessary."

Nevertheless, Maxwell's followers in this country and
abroad are not satisfied to leave those points which are
obscure or indefinite in his theory unilluminated. I have
already referred to the valuable practical illustrations of
Lodge. What has been done in a more systematic
manner on the Continent and at home I shall briefly
refer to at the end of the next chapter. We may call it
a revival of the atomic view of electricity.

95

CHAPTER VII.

ON THE PHYSICAL VIEW OF NATURE.

I HAVE already remarked that none of the three great i.

T • 1-1 p ■ Rccapitula-

generahsations which we have so far reviewed have been t'on.
creations of the pliilosophers of the nineteenth century.
Their first enunciation belongs to antiquity, though they
have only witliin the last three hundred years been ex-
pressed in sufficiently precise terms to permit of practical
measurements and mathematical deductions. The first
step towards a scientifically comprehensive employment
of the familiar l)ut vague terms of attraction, of atoms,
and of undulations came, as we have seen, in each
case from some solitary thinker of this country : from
Newton, from Dalton, from Thomas Young. The system-
atic elaboration belongs to the combined scientific exer-
tions of all the civilised nations of the world. In books
on astronomy, physics, and chemistry, up to the middle of
the century, we can hardly find any theoretical exposi-
tions which are not based upon one or more of these
three ideas. Indeed they govern the entire science of
inanimate nature during the first half of the century.
None of these three principles, however, appeared suf-

96 ^ SCIENTIFIC THOUGHT.

ficient to cover the whole field. The law of gravitation
embraced cosmical and some molar phenomena, but led to
vagueness when applied to molecular actions. The atomic
theory led to a complete systematisation of chemical com-
pounds, but afforded no clue to the mysteries of chemical
affinity. And the kinetic or mechanical theories of light,
of electricity, and magnetism, led rather to a new dualism,
the division of science into sciences of matter and of the

2. ether. The unification of scientific thought which was

Insuffici-
ency of the gained by any of these three views, the astronomical, the

astronoini- o ^ ./ '

and kinetic ^tomic, and the mechanical, was thus only partial. A
views. more general term had to be found under which the

different terms could be comprised, which would give a
still higher generalisation, a more complete unification
of knowledge. One of the principal performances of
the second half of the nineteenth century has been to
find this more general term, and to trace its all-pervad-
ing existence on a cosmical, a molar, and a molecular
scale. It will be the object of this chapter to complete
the survey of those sciences which deal with lifeless
nature by tracing the growth and development of this

3. greatest of all exact generalisations — the conception of

The concep- <=■ o

tion of energy.

energy. °''

The complex of ideas and the manifold courses of
reasoning which are centred in this conception form
such an intricate network, the interests involved are so
great, the suggestions which led up to it so numerous,
the consequences which resulted for science and practice
so far-reaching, that the historian has no little difficulty
in laying bare the many lines of thought which appa-
rently cross and re -cross each other. Accordingly the

ON THE PHYSICAL VIEW OF NATUKK.

07

history of this sul»ject has been written from various
points of view/ and angry controversies^ as to priority

■ Tlie histories are mostly in Ger-
man. I give the titles of the more
inipurtiint. Foremost stiinil the
writings of Prof. Ernst Mach — viz.,
' Die Geschichte uml die Wurzel
(les Satzes von der Erhaltung der
Arbeit' (Prag, 1872), incorporated
ill the author's ' Poj)ular Scientific
Lectures,' translate<l l>y Thomas
J. M'Cormack, Chicago, 1894 ;
and the same authfir's ' Die Me-
clianik in ilircr Entwickelung, his-
torisch-kritisch dargestellt ' (Leip-
zig, 1883, 2nd ed., 1889, also trans-
lated by M'Cormack, London and
Chicago, 1893). The philosoi)hical
faculty of the University of Got-
tingen has twice (in 1869 and in 1884)
made the principles of dynamics
the subject of a prize competition,
presumably both times at the in-
stigation of the late celebrated
Professor Wilhelm Weber. The
first competition led to the i)ublica-
tion of E. Duhring's ' Kritische Ge-
schichte der allgemeinen Principien
der Mechanik ' (Leipzig, 1872;
re))ublished, with much contro-
versial matter, in 1876 and 1887) ;
the second to the publication of
Prof. Max Planck's ' Das Piincip
der Erhaltung der Energie ' (Leip-
zig, 1887). In the same year as
the last book there appeared ' Die
Lehre von der Energie,' by Dr Georg
Helm (Leipzig, 1887), and lately
his very complete work, ' Die
Energetik, nach ihrer geschicht-
lichen Entwickelung ' (Leipzig,
1898).

- The controversy turned mainly
on the question of the claims of
Dr Julius Pobert Mayer of Heil-
bronn. Tiie experimental work of
Joule in England and the theoreti-
cal work of Helmholtz in Germany
were published in ignorance of the
writings of Mayer. I']v('ii tlie earlier
important papers of William Thom-

VOL. II.

son (Lord Kelvin) and Rudolph
Clausius appeared Ijefore the name
of Mayer was generally known.
The question then arose to what
extent the publications of Mayer
really anticipated the discoveries
and theories of Joule, Helmholtz,
Thomson, and Clausius. It can
hardly be held that they influenced
them. The whole of the evidence
as to the former point is con-
tained in a very complete publica-
tion by Prof. Jacob J. Weyrauch,
" Kleinere Schriften und Hriefe
von Robert Mayer " (Stuttgart,
1892), which forms a supplement
to the edition by the same author
of Robert Mayer's ' Schriften,' en-
titled "Die Mechanik der Wiirme "
(Stuttgart, 3rd ed., 1893). Both
books contain very careful and ex-
haustive notes. Whoever desires
to settle the question of Mayer's
claims, which, however, will always
depend much on individual opinion,
will find all the documentary evi-
dence collected in these interesting
volumes. A further controversy
arose later as to the discovery and
enunciation of the second law of
thermodynamics, the great doc-
trine of the "Dissipation of En-
ergy. " This controver.sy arose over
the publication of the late Prof.
P. G. Tait's 'Sketch of Thermo-
dynamics ' in 1868, which is an
amplification of two articles by
the same author in the ' North
British Review ' of 1864. The con-
troversy, which referred mainly to
R. Clausius's share in the enuncia-
tion of the second law, can 1)6
studied in Tait's little volume (1st
ed., 1868 ; 2nd ed., 1877), in vols.
43 and 44 of the 4th scries of
the ' Phil. Mag.,' in his ' Recent
Advances in Physical Science '
(esjjecially the pieface to the 3rd
edition, 1885), and in the 2nd

G

98 SCIENTIFIC THOUGHT.

of discovery and as to the real points at issue have'
arisen. The history of thought only takes note of these
in so far as they are indications of what was of real
(not of personal) interest in the process, and are thus
a measure of the value which was inherent in its
development.

None of the different views or theories with which the
earlier generations of philosophers during the century
operated seemed sufficient to give an insight into the
real essence, the (pvaig, of natural phenomena. Neither
the astronomical nor the atomic nor the kinetic view
was all-embracing. On the Continent, both in France
and in Germany, the sciences were rigidly marked off
from one another, the connecting links were few and
ill defined, and speculations as to the general forces and
agencies of nature were left to metaphysicians and treated
with suspicion. In England alone the name of natural
philosophy still obtained, and in the absence of separate
schools of science, such as existed abroad, suggested,,
at least to the self-taught amateur or to the practical
man, the existence of a uniting bond between all natural
studies. It is significant that the term under which we
now comprise, and by which we measure, all natural
agencies, the term Energy, was first distinctly used in this
The term scusc by Dr Thomas Young in his lectures on Natural
Yoi^ng. Philosophy,^ a course which, be it noted, also embraced

edition of the 2nd vol. of Clausius, Energy may be applied, with great

' Die mechanische Wiirmetheorie ' , propriet}', to the product of the

(Braunschweig, 1879), p. 324, &c. ' mass or weight of a body into the

In the labyrinth of these eontro- i square of the number expressing

versies I have found Helm a fair its velocity. . . . This product has

and conscientious guide. been denominated the living force

^ Vol. i. p. 59 of the edition of i (the vis viva), . . . and some have

Kelland. Young says : " The term I considered it as the true measure

ON THK PHYSICAL VIKW OF NATl'l'.K.

99

Chemical Science, tliough for merely external reasons
this was summarily handled. iL is equally significant
that the first valuable suggestions as to the connection of
the various sciences, and the practical or common measure
of the various agencies, came from practical or professional
persons who took an outside and general view of physical
and chemical processes and their application in arts and
medicine. Young himself was a medical man, as were
liobert Mayer and Hehuholtz after him. Practical men
such as Watt felt the necessity of measuring not so much
forces (in the Newtonian sense) as the action of forces,
and introduced the term power, and the quantity called 5.

. Watt intro^

horse-power ^ to measure the capacity of an engme for 'luces the
doing work. Newton had already measured this action" "po**-""""

of the quantity of motion ; but
although this opinion has been very
universally rejected, yet the force
thus estimated well deserves a
distinct denomination." See also
p. 172.

' The cjuantity called horse-
power was introduced by Boulton
and Watt to measure the power of
the engines they built and sold at
Soho towards the end of the eigh-
teenth century. They caused ex-
periments to be made with thestrong
liorses used in the breweries in Lon-
don, and from the result of these
trials they assigned 33,000 lb., raised
one foot per minute, as the value of
one horse-power. Dr Young in his
' Lectures ' has the following state-
ment : "A steam-engine of the
best construction, with a 30 -inch
cylinder, has the force of forty
liorses ; and since it acts without
intermission, will perform the work
of 120 horses or of 600 men, each
square inch of the piston being
nearly equivalent to a laljourer"
(vol. i. p. 103).

- See the Scholium to the "■ Axio-

mata sive Leges Motus," p. 25 of
the first edition of the ' Princi[)ia,'
in which the " Agentis Actio " is
measured " ex ejus vi et velocitJite
conjunctim." Thomson and Tait
(' Natural Philosopiiy,' 1886, part i.
p. 250 S'lq., and Tail, 'Dynamics,'
1895, p. 181) have drawn attention
to tlie fact tiiat this passage of the
'Principia' contains imjilicitly the
modern notion of energy, and the
principle of the conservation of
energy. The continental historians
named above are inclined to give
Huygens credit for having first
made explicit use of the idea of tlie
conservation of the ([uautity now
termed energy, and they trace the
further elucidation of it to the
BernouUis, es])ecially John Ber-
noulli, who repeatedly speaks of the
" conservatio virium vivaruin," ami
"urges that where vis viva dis-
appears, tlie power to do work
{fucultas agendi) is not lost, but is
oidy changed into some other
form" ('Opera,' 1742, vol. iii. pp.
239 and 243, quoted by Planck, /or.
cit., p. U»).

100

SCIENTIFIC THOUGHT.

of a force by the product of the force (itself measured by
the velocity of a moving mass) and the velocity or space
per unit of time through which it pushes or pulls a
moving body, and Leibniz ^ had suggested the term vis
viva to distinguish it from the vis mortua, the force
or pressure itself. But the first clear and consistent
fixing of the terminology which has since been universally
adopted is to be found — not in the ' Mecanique analy-
tique ' of Lagrange (that classical work on theoretical
mechanics), but in the ' Mecanique industrielle ' of
Poncelet (1829).^ He introduced the term "mechanical

•" Leibniz's occupation with dyn-
amics began with his publication of
two theses in 1672, which he dedi-
cated respectively to the Academy
of Sciences in Paris and to the
Royal Society. In distinction from
the writings of Huygens and
Newton, where precise definitions
take the place of metaphysical
discussions, Leibniz's tracts — ex-
cept in the comparatively rare cases
where he confines himself to mathe-
matical formulae — are vitiated, like
those of Descartes, by philosophical
speculations. Thus, though emi-
nently suggestive, they contributed
little to the clearing up of ideas.
Influenced by Huygens and by
Newton, he opposed in 1686 the
ideas of Descartes on the measure
of force, and has the merit of
having introduced the term vis
viva in 1695, and of having started
the celebrated discussion on the
measure of force which was- carried
on during fifty -seven years on the
Continent, and onlj- settled by
D'Alembert in his ' Traits de Dyn-
amique' (1743) by stricter defini-
tions. An excellent account of the
questions involved, and of the
gradual clearing up of ideas, will
be found in Prof. Mach's historical
treatise on dynamics referred to

above. See the English translation
by M'Cormack, p. 272, &c. It is
there shown that one of the great
defects of Descartes' and Leibniz's
dynamical writings was the want
of a clear definition of mass or
inertia ; also that this conception
follows more simply from Newton's
definition of force than from Huy-
gens' conception of work (ibid.,
p. ^251).

- By the side of, and sometimes
in opposition to the purely analytical
school headed by Lagrange, Laplace,
and later by Cauchy, there grew
up in Paris the school of practical
mathematicians which taught the
application of theory to practice,
to problems of artillery, engineer-
ing, and architecture. They created
modern geometrj", and to a great
extent modern mechanics. Monge,
Coulomb, the elder Carnot, Pon-
celet, Coriolis, were their leaders :
Navier, Lame, Charles, de Saint
Venant, followed, and combined
their more synthetic methods with
the analytical methods of the
former school. Through Monge,
Carnot, Navier, and Poncelet,
geometry and dynamics were led
into those channels which have
since been so successfully followed
in all applied work. To them

ON THE PHYSICAL VIEW UF NATLRK.

lul

work " for the definite quantity which liad Ijefure him
been variously designated as power, effect, action, &c.,
and he distinctly states that the inertia of matter trans-
forms work into vis viva and vis viva into work. He
also measures this quantity " work " (luilc in the luudcrn
fashion — by the " kilogrammetre," which gives the same
conception as the foot-pound, only in a dillerent measure.
Long before the terminology thus in\'ented and fixed
by Watt, Young, and I'oncelet had been accepted by
scientific writers, a change in the current notions on
the forces of nature had been gradually ljr(night abinit
from quite a ditterent quarter. Uninfluenced by tiie
theoretical views which were developed and firmly held

mathematics was not merely the
science of magnitude, but quite as
much that of position, of design
and perspective, of mechanical
work and effect. They introduced
a whole series of new and i)ractical
ideas, drawn from their own appli-
cations, and created a new vocab-
ulary. They worked hand in hand
with physicists and chemists, some
of whom had little taste for the
extremely abstract and analytical
methods of the school of Laplace
and Cauchy. Poncelet's original
geometrical work, which will oc-
cupy us in a later chapter, led him
into many controversies. It was,
however, greatly appreciated in
Germany and later in England.
His influence on German applied
mechanics has been quite as great
as that on geometry ; and the great
text-books of mechanics by Weiss-
bach, Redtenbacher, Ruhlmanii.aiid
others, are as much indebted to
Poncelet and other French models
as the German text-books on mathe-
matics, physics, antl chemistry were
for a long time to the well-known
works of Biot, Pouillet, Cauchy,

Francccur, Lame, Regnault, and
others. The influence of Ponce-
let on practical mechanics, and
especially in the fixing of an ade-
(juate terminology, can therefore
be studied equally well in French
and in German historical writingB.
Among the former I may mention
especially the ' lOxposd de la .Situa-
tion de la Mecanique appliqu(5e
par Combes, Phillips et Collignou,'
Paris, 18ti7, and among tiie latter,
notably the above-mentioned writ-
ings of Helm, who traces the
growth of the conception of me-
chanical work in Freiicii writings,
and its influence on (ierman thought
(' Knergetik,' j). 12, &c.) See also
Diihring, loc. cit., p. 471, &c. I may
also refer to Heuu's Report ('Jaiires-
bericht der deutscheu Matheniat-
iker-Vereinigung,' vol. ix. part 2,
1901), where the sciences comprised
in "Mechanics" are distinguished
according as they are astronomical
(Laplace, Poincar^), physical (Eng-
lish mathematical jjiiysios, Kirch-
hoff, Hclniholtz, Hertz), geometrical
(Poinsot, Charles, Pall), or tet-hni-
cal (Watt, Poncelet, Rankine).

102

SCIENTIFIC THOUGHT.

by the school of which Laplace was the most distin-
guished representative, natural philosophers like Black,^
Eumford, and Davy had approached the study of those
phenomena where heat and chendcal change are the
prominent features. The phenomena wdiich they
studied experimentally can be comprehended under the
head of the disappearance and appearance of heat as
measured by the thermometer, or as recognisable
directly by our sensation of heat. Black accounted
for the disappearance of heat by the doctrine of latent
heat, and measured this by the capacity ^ for heat, or
the specific heat of different substances. Eumford
made exact measurements of the heat generated by
friction, and showed that Black's doctrine of latent
heat did not account for it. Both Black and Eum-
ford were led to science from the side of practical in-
terests. Black, like Young after him, was a physician.
Eumford was all through his life occupied with the

1 Joseph Black (1728-99), one of
the founders of chemistry, and a
prominent figure in that illustrious
circle of philosophers who, during
the second half of the eighteenth
century, made the literature and
science of Scotland renowned over
the whole world, published very
little, being mostly known througli
his teaching and his pupils. His
name is, even to the present day,
rarely to be found in French books ;
whereas in Germany, mainlj' owing
to the historical writings of Herr-
mann Kopp, and quite recently of
Prof. E. Mach, his great merit and
originality have been fully recog-
nised. See Kopp, ' Geschichte der
Chemie,' vol. i. p. 226, &c.; 'Die Ent-
wickelungder Chemie,' 1873, pp. 57,
&c., 88, &c. ; E. Mach, ' Die Prin-
cipien der Wiirmelehre,' 1896, p.

156, &c. Black, who as early as
1755 had shown that carbonic acid
gas could disappear as a gas and
become "fixed," showed later
that heat could disappear as tem-
perature and become " latent."
By himself, indeed, the former
important discovery was not inter-
preted against the then i-eiguing
phlogistic theory, nor was the latter
used to upset the material theory
of heat. Now, however, both dis-
coveries are cornerstones in the
history of science.

^ According to Dr Young (' Lec-
tures,' new ed., p. 499), the term
" capacity " is due to Dr Irvine,
who, as well as Dr Crawford, was
much influenced by Black's lec-
tures. These were first published
in 1802 by Robison, three years
after the author's death.

ON THE PHYSICAL VIEW OF NATUKE. 103

practical application of scieutiHc knowledge. lilack's
experiments and measurements contributed largely to
fix the difference between temperature and ([uantity
tif heat ; he demonstrated clearly that heat may
disappear in the form of temperature and exist
as latent heat, ihal is, licat not discoverable by
the thermometer. He, however, adhered to the view
that heat was a material substance, whicli, tliough
it mi^ht become latent, did n(jt disappear as such.
Itumford^ was the first who definitely went a step further
and suggested the convertibility of heat and mechanical
work. It was not the disappearance of heat but its
appearance when mechanical work was performed whicli
attracted his attention. After eliminating all the
sources from which the heat produced during the bor-
ing of cannon could have been derived, he comes to the
conclusion that " it appears to be extremely ditticult,
if not quite impossible, to form any distinct idea of
anything capable of Ijeing excited and communicated
in the manner the heat was excited and communicated
in those experiments, except it be motion." Uavy,
who, like lUack, approached science in tlie interests of
the medical man, comes to the conclusion in his firet
published papers, from experiments on the generation

^ Count Rumford's "Inquiiy con-
cerning the Source of the Heat

republislied in America and trans-
lated into several foreign lan-

which is excited by Friction" was | guages. See Uuinford's 'Works,'

published in a later edition of his London, 1876, vol. i. p. 48'2,

'Ussays.' The experiments with and vol. ii. p. 471. In 1804

the boring of cannon were cairied Count Rumford imblished, in lii.s

on at Munich in 1796 and 17f>7 ; ' Meiuoires sur la Clialcur ' [VuriA,

the substance of the essay was an. 13), a " Historical Review oi

read before the Roval Society in j the Various Experiments on Heat "

Januarv 1798. The*' Essays ' were | (' Works,' vol. iii. pp. 138-240).

104

SCIENTIFIC THOUGHT.

of heat by friction and percussion, that heat is not
matter, but " may be defined a peculiar " motion, prob-
ably a vibration,^ of the corpuscles of bodies tending
to separate them, Eumford's and Davy's memoirs
referred to belong to the last years of the eighteenth
century. Dr Young, in his celebrated lectures on natural
philosophy, discussing the experiments of Rumford and
Davy came to the conclusion " that heat is a quality,
and that this quality can only be motion." He refers
to Newton's view " that heat consists in a minute
vibratory motion of the particles of bodies," and to
his own undulatory theory of light. This analogy
with light seems to have for a long time served to
unify the speculations - of those who were inclined to

^ See his " Essay on Heat, Light,
and the Combinations of Light,"
which appeared in Beddoes' ' Con-
tributions to Physical and Medical
Knowledge,' 1799. This essay
Davy soon after condemned as " in-
fant chemical speculations," from
which he turned away to ex-
perimental work, remarking that
chemical knowledge was yet too
incomplete to allow of generalisa-
tions, and that the "fii'st step
will be the decomposition of those
bodies which are at present un-
decompounded." This was written
in 1799. In 1800 (30th March)
Volta's invention of the " pile "
was communicated to the Royal
Society, and on the 30th April of
that year the first pile Was con-
structed in this country. See the
first and second volumes of Davy's
' Collected AVorks,' London, 1839.
Davy's first publication on voltaic
electricity appeared in the Septem-
ber number of 'Nicholson's Journal.'
Though the speculations of Davy
on heat and light, in which heat

is conceived to be motion and light
(strangely) to be material, were dis-
carded by him, they attracted the
attention of Franklin and of Count
Rumford. Davy states that his
experiments on the generation of
heat "were made long before the
publication of Count Rumford's
ingenious paper on the heat pro-
duced by friction" {loc. cit., vol.
ii. p. 117). In spite of his own
refusal to follow up the lines of
thought suggested by them, they
were probably the cause of Davy's
appointment as lecturer on chem-
istry at the Royal Institution : see
vol. i. p. 83 ; also Memoir of Count
Rumford ('AVorks,' vol. i. p. 417),
and Paris's 'Life of Davy,' vol. i.
p. 112, &c. Tait, in 'Recent Ad-
vances,' gives a full account of
Rumford's and of Davy's work.

-' See 'Young's Lectures,' 51 and
52. In the second edition, pub-
lished by Kelland forty years after
the Lectures were delivered, the
editor makes the following signifi-
cant remark : " The theory of heat

ON THE PHYSICAL VIEW (JF NATIKK. 105

embrace a mechanical or kinetic view of the nature
of heat. Joule, as stated above/ was the first who
emancipated himself from it.

But whilst these suggestions that heat may te re- 8.

1 • 1 • ComrUition

garded as somehow connected witli motion remained offoreai.
mostly vague ami undeveloped, they tended to impress
upon the scientiiic mind the interchangeability — or, as
it was called, the correlation of the different forces of
nature ; and the idea seems to have forced itself in-
dependently on many minds, through the study of very
different groups of natural phenomena. In Germany
we may look upon Liebig as the centre of a great 9.

Licbig.

scientific movement which tried l)y means of chemistry
to bring the realms of organic and animated exist-
ence under the treatment of exact methods. Xot
(jiily were the methods of organic analysis perfected
l)y him and his school, and many compounds inves-
tigated which appeared to be specially the bearera of
the living process ; but he was also among the first to
study the economy of li\ing organisms, the circulation
of matter, and the play of the varied processes by
which life is maintained. Among these processes, the
phenomenon of animal heat, its origin, and the part it
plays in the living organism attracted special attention,

may be said to rest where it did whiih was shown to have the same

at the time the.se Lectures were properties of refle.\ion, refraction,

written. The facts which have and polarisation as Hght possessetl.

just been mentioned clearly point The analogy of this form of heat

out its undulatory character" (p. with liglit threw into oblivion

50(5). Between the years 1835 and the beginnings of a more general

184.') theoretical ideas on the nature mechanical theory of heat, which

of heat were entirely dominated i — as we shall see further on — had

by the remarkable discoveries of | been laid by Sadi Carnot iu

Melloni, Baden-Powell, Forbes, and 1824.

others referring to radiant heat, ' ' See vol. i. of this work, ji. 434.

106 SCIENTIFIC THOUGHT.

By his work on organic chemistry, by his many con-
troversies, such as that on fermentation, by his popular
letters on chemistry, and especially by his great intlu-
ence as a teacher, Liebig himself did much to bring
about an alliance of the separate sciences and a connec-
tion between practical pursuits and abstract research, and
to draw attention to the interdependence of the various
10. forces of nature. Only second in influence was Johannes

JohnMuller. _ ''

Mliller of Berlin. Among the many expressions which
took their origin in the circle of studies suggested
by these influences, we may select three as giving
increasingly clear emphasis to the point now under
consideration — viz., the correlation of all the physical
forces of nature. These expressions are those of the
convertibility of forces, of the existence of a common
measure of force, and of the conservation implying
the perdurability of a certain quantity — now termed
Energy — of which all phenomena are merely a partial
exhibition. They are connected with the names of
Karl Friedrich Mohr, Julius Eobert Mayer, and Her-
mann Helmholtz.

Were it my object merely to write the history of
science, I should probably follow the example of some
historians ^ and omit altogether the first of these names
in the present connection. But as my object is to write
the history of scientific thought, I feel bound to give a

^ Mach, iu his recent very lucid
and valuable work, ' Die Priiici-
pien der Wiirmelehre,' Leipzig,
1896, does not mention Mohr. On
the other side, Helm (' Die Ener-
getik,' 1898, p. 9) mentions Mohr
and likewise Planck ('Das Priucip
der Erhaltung der Energie,' 1887,

p. 21). Tait's first edition of
'Recent Advances,' 1874, does not
contain Mohr's name. The third
edition gives a full account of
Mohr's early papers (pp. .51 and
60, &c.) See also the appreciative
article on K. F. Mohr in the ' Ency.
Brit.'

ON THK PHYSICAL VIKW OF NATIIIK

10'

foremost place to the short memoir of F. ^lohr entitled n.
"On the Nature of Heat," which appeared in 1<S:;7 in
an obscure scientific periodical published at ^'ienna. The
publication of it remained unknown, even to the author
himself, and was certainly unappreciated by the scientific
world for more than thirty years.^

' The story of Mohr's memoir is
curious, not to say romantic. His
original paper, ' Ueber die Natur
<ler Wiirme,' was offered to Pog-
gendorf and refused, as were the
later memoii'.s of Mayer and Hehn-
holtz. A dread of inlroducing
speculative matter into the ' An-
naleu ' prevented likewi.-^e — as I
related above (p. 66, note 2) — the
appreciation of much of Faraday's
later work. He then sent the ^lS.
to Baumgartner, in Vienna, who —
always interested in theoretical
jihysics — printed it in a periodical
(' Zeitschrift fiir Physik ') of which
he and von Holger were joint-
editors. He did not inform the
autliur of this. Mohr was a re-
markably original thinker, in whose
mind important ideas rose at times
to extraordinary clearness, but who,
like many original thinkers, did not
always appreciate his own itleas at
their true value, and accordingly
treated them with neglect, and did
not consistently develop them. In
the present instance he contented
himself with inserting an abstract
in the ' Annalen der Piiarmacie '
(vol. xxiv. p. 141), of which he was
then joint - editor, together with
Liebig and Merck. He made no
further inquiries as to the fate of
his larger memoir, and, in con-
versation with friends up to the
j'ear 1860, as also in his 'Mechan-
ische Theorie der chemischen
Aftinitat' (Braunschweig, 1868, p.
4l>), used to deplore the loss of a
document which, more fully than
the short paf>er in the 'Annalen der

Pharmacie,' would have establislied
his priority in the clear enunciation
of a remarkable principle wliich
fifteen years later received general
recognition. The matter would
probably have rested there had it
not been that Tyudall, in the year
1862, in a celebrated lecture before
the Royal Institution, commenced
that long series of historical and
controversial jtublications in which
many persons, includhig himself,
Joule, Tait, d tiding, Helmholtz,
Akin, Bohn, Diihring, Zollner,
and others took part, and in
which, among several claims prior
to or contemporary with Mayer's,
those also of Mohr received due
recognition. It seems to have
been especially l)r Akin who drew
attention to Mohr's claims, and
searched in the forgotten volumes
of the Austrian periodical for the
original memoir, which, unknown to
the author himself, had been in-
scribed on p. 419 of the fifth volume.
This discovery he announced to
Mohr himself after having already,
in November 1864 ('Phil. MagV
4th series, vol. xxviii. p. 474 \
given several extracts, among which
is the one quoted by me in tlie
text. Mohr published, in 1869, a
sequel to the above-mentioned book,
entitled ' Allgemeine Theorie der
Bewegung und Kraft,' in which lie
refers to Dr Akins discovery, and
reprints the original menu>ir in
full. Since that time his name has
figured in many historical uccount.s
as one of tlie pioneers in the de-
velopment of the energy - coucep-

108

SCIENTIFIC THOUGHT.

12.
Mayer.

It forms, therefore, no link in the actual development
of the energy-conception ; but it is a significant evidence of
the direction in which the ideas of natural philosophers
were then moving, and of the high degree of clearness
to which they rose in individual instances. When we
read the following words : " Besides the known fifty-four
chemical elements there exists in nature only one agent
more, and this is called ' Kraft ' ; it can under suitable
conditions appear as motion, cohesion, electricity, light,
heat, and magnetism," it seems difficult, even after the
lapse of two generations, to alter anything in this clear
and simple enunciation of the law of the conservation
of energy. It has indeed been stated that " unless
some still earlier author should be discovered, there
can be no doubt that Mohr is to be recognised as the
first to enunciate in its generality what we now call
' conservation of energy.' " ^ At the same time, the
case shows how little, at the beginning of a scientific
movement, purely abstract statements are capable of
really guiding research into fruitful channels. There is
with Mohr no attempt to establish or apply an actual
measure ^ of the amount of energy appearing in the
various instances which he mentioned. This further
step was taken five years later by J. E. Mayer, who
can claim to be the first ^ to have ventured on a

tion ; his merit being variously
appraised according to the purely
scientific, the philosophical, or the
more practical standpoint taken up
by various critics. See, inter alia,
P. G. Tait's ' Recent Advances,' 3rd
ed., p. 60, &c. ; also the correspon-
dence of Mohr and Mayer in the
latter's ' Kleiners Schrifteu uud

Briefe,' ed. Wayrauch, p. 407,
&c.

1 See the article on K. F. Mohr
in the ' Ency. Brit.,' 9th ed.

- See on this point Weyrauch, in
Mayer's ' Kleinere Schriften,' p. 408.

^ Helm (' Energetik,' p. 34) begins
the list of undoubted determina-
tions of the heat-equivalent with

ON THE PHYSICAL VIEW OF NATLKE.

109

numerical estimate as between mechanical energj' on
the one side, and the amount of one of the imponder-
ables— i.r., heat as measured by the thermometer — (jn
the other. Although his methods were not free from
objection/ while his arguments were mixed uj. with

Mayer, 1S42. His deteriuiiiaiiuii
is contained in his first paper, pub-
lished, a^ was Mohrs, in Liebig's
'Annalen' (vol. xlii.. May), with
the title " Bemerkungen iiber die
Krtif te der unbelebten Natur." The
experiments performed by Rumford
in 179S were made the basis of a
calculation of the heat equivalent,
i.e., of the weight which can be
lifted one foot if the heat required
to raise a pound of water 1° be con-
verted into work against gravita-
tion, and the figure turns out to
be 1034 lb. its compared with 772
lb. given by Joule himself (' Phil.
Trans.,' 1850 ; ' Joule's Papers,' vol.
L p. 299). The earlier computations
of Seguin, based upon the work done
by the expansion of steam, were
referred to bv Joule, TvndaU, and
Tait in 1862 and 1864 (' PhiL Mag.,'
4th series, vols, xsiv.aud xxviii.),aud
shown to lead to figures further off
the mark than those of Mayer. In
the course of this later controversy
it became for the first time gen-
erally known that A. Colding, an
engineer in Copenhagen, had a
little later than Mayer (1843), and
almost simultaneously with Joule,
given a determination of the equiva-
lent based upon friction of metals,
which was lower than Mayer's. He
accordingly now figures as second
in Helm's list. One of Joule's
earliest experiments with heat,
"evolved by the passage of water
through narrow tubes," gave the
equivalent as 770, very near the
figure, viz., 772, finally settled on
as correct in 18.50.

' The reasoning of Mayer is not
completely contained in his first

paper, which subsetjuently, on a
suggestion of Joule's, appeared
in translation in the ' Phil. Mag.'
(4th series, vol. xxiv. pp. 123, and
371 sqq.) The assumption (calletl
by Thomson in 1851 " Mayer's
hypothesis," see ' Math, and Phys.
Papers,' vol. i. p. 213) that "the
work spent in the compression of
a gas ... is exactly the mechani-
cal equivalent of the . . . heat
evolved," which Joule did nut think
it right to accept without satisfying
himself by experiments (see ' Phil.
Mag.,' 4th series, vol. xxiv. p. 122),
was based by Mayer on an almost
forgotten experiment of Gay
Lussac's in the year 1807, as is evi-
dent from his subsequent pajjer,
published in 1845 (reprint in
' Mechanik der War me,' ed. Wey-
rauch, 1893, p. 53), and still more
from his correspondence with Baur
previous to his first publication
(ibid., p. 20, and ' Maver's Briefe,'
p. 130, September 184 i). The sub-
ject was exhaustively investigated
by Thomson and Joule in a joint-
memoir on " the thermal effects of
fluids in motion," 1852 (reprinted
both in Joule's and Li>rd Kelvin's
Scientific Papers), when it was
shown that for air Mayer's hy-
pothesis was approximately, but
not absolutely, correct. So long,
therefore, as the history of Mayer's
rciisoning was not conij'letely
known, it appeared as if he bad
by a kind of accident hit upon an
approximately correct figure. See
Tait, 'Recent Advances' (3rd e<l.,
p. 53 ; but also Helm, ' Euergetik,'
p. 24, and Mach, ' Warmelehre,'
p. 249).

110

SCIENTIFIC THOUGHT.

13.

Joule.

philosophical speculations which tended to prevent
their ready acceptance, it cannot be denied that, as
a first approximation, " his equivalent " was sufficiently
near the truth to be practically useful.

But neither the happy generalisation of Mohr, which
was lost or forgotten, nor the numerical estimate of
Mayer, which remained unnoticed, succeeded in impress-
ing contemporary philosophers with the importance of
the subject. This was done almost at the same date,
though quite independently, by the persistent and per-
severing experiments and measurements of James Pres-
cott Joule, who laboured unnoticed and practically
without support from 1841 to 1847, when he had
the good fortune of gaining the attention and friend-
ship of William Thomson (Lord Kelvin).-^

^ Joule not only defined more
clearly the different data and con-
ditions on which the correctness of
the result must depend, but had
also at his command a much greater
wealth of novel experimental facts,
brought together by his own re-
sourceful mind. Thus from 1843
to 1850 he published no fewer than
ten series of experiments, approxi-
mating from widely differing results
to the true figure. See Helm's list
(' Energetik,' p. 34). After he had
laboured for more than five years
his work was, in 1847, at the meeting
of the British Association in Oxford,
still almost unknown. He himself
reports as follows in 1885 ('Joint
Scientific Papers,' 1887, p. 215) :
" It was in the year 1843 that I
read a paper ' On the Calorific
Effects of Magneto- Electricity and
the Mechanical Value of Heat ' to
the Chemical Section of the British
Association at Cork. With the ex-
ception of some eminent men . . .

the subject did not excite much
general attention ; so that when I
brought it forward again at the
meeting in 1847 the chairman sug-
gested that, as the business of the
section pressed, I should not read
any paper, but confine myself to a
short verbal description of my ex-
periments. This I endeavoured to
do, and discussion not being in-
vited, the communication would
have passed without comment if a
young man had not risen in the
section, and by his intelligent ob-
servations created a lively interest
in the new theory. The young man
was William Thomson, who had two
years previously passed the Univer-
sity of Cambridge with the highest
honour, and is now probably the
foremost scientific authority of the
age." See also Lord Kelvin's ac-
count of the meeting in 1847 in
' Popular Lectures and Addresses '
(London, 1894, vol. ii. p. 556, &c.)

ON THE PHYSICAL VIEW OF NATIKE. Ill

A pupil of Daltou, Joule was early drawn into the
circle of ideas and iii\estigations winch are contained in
Faraday's experimental researches. With much ampler
means, and possibly also with a greater hne for accurate
quantitative measurements, than P'araday possessed, he
grasped the great importance of the law of electrolytic
equivalence as affording the means of accurately measur-
ing chemical processes, and of giving definite expression
to the vaguer ideas supported by Faraday and othei-s
that force was indestructible, and that the different
forces of nature w^ere mutually convertible. These
ideas had received popular circulation and current ex-
pression in Grove's celebrated lectures on the " Corre-
lation of riiysieal Forces" in 1842 and 1843. Joule,
in whose mind they seem to liave existed as axioms,
set himself to devise accurate instruments and methods
by which the convertibility of different forces, their
" mechanical duty," could be measured, and their equiv-
alence put into figures. The first numbers which Joule
found differed considerably,-^ so that the conclusion
arrived at that the mechanical duty or " value " of a
degree of heat is a constant quantity could only have
been drawn by one who had a strong a priori^ con-

^ For details see Helm, ' Ener- A predisposition to believe that
getik,' p. 3-t ; also vol. i. p. 265, j some quantity besides matter could
note, of the present work. Joule's | not be lost or created, but onlj*
equivalent varied from 742 to 890
fuot-pounds, and was finally fixed
at 772 in 1850, this figure being
correct to h per cent (Joule's
'Scientific Papers,' p. 328).

- Philosophical considerations arc
mixed up with all the early enun-
ciations of the principle of the in-
destructibility of force, or energy as
it was later more clearly termed.

preserved and transformed, existed
in the mitids of ^lohr, iSeguin,
Mayer, Colding, Joule, Hirn, antl
has been traced variously back to
the wiitings of earlier thinkei-s,
such as Montgolfier, Faraday, Davy,
Oersted, Leibniz, &c. Prof. Mach
('Wiirmelehre,' p. 238, &e.) dis-
cusses this jioint fully. The prin-
ciple gradually became firudy

112

SCIENTIFIC THOUGHT.

14.

Helmholtz.

viction in that direction. The experimental result did
not satisfy Helmholtz, who, about the same time, was
led to consider the origin of animal heat in living
organisms, a problem with which Liebig ^ had been
greatly occupied for several years. Without himself
devising or instituting new experiments, or attempting
any determination of the equivalent as others — notably
Colding and Holtzmann — were doing, Helmholtz, in
1847, undertook a theoretical investigation which has
since become classical — a corner-stone in the philosophy
of the subject. He first of all gave the principle in-
volved a correct mathematical expression, showed how it
could be considered as an extension of the theorem known
in abstract dynamics as the conservation of the vis viva
of a mechanical system, attempted to define the nature of
forces, in the Newtonian sense, which would be subject to
the new principle, and brought it into logical connection
with the axiom laid down and used by French philos-
ophers, that perpetual motion is an impossibility. After
clearing the ground so far as abstract dynamics is con-
cerned and giving the necessary definitions, sharply dis-
tinguishing between acting (living) forces and mere
tensions (dead forces), Helmholtz proceeds to draw all

established according as strict
definitions, experimental proofs
and figures, and mathematical
formulffi took the place 'of vague
speculations. Joule did the experi-
mental, Helmholtz the mathema-
tical, part of the work ; but it is
interesting to see how little the
latter without the former was able
to impress contemporary German
writers with the value of the prin-
ciple which he established. He

himself even did not for a long
time develop the line of reasoning
which he had begun.

^ See Helmholtz, ' Bericht iiber
die Theorie der phj'siologischen
Warmeerscheinungen,' 1845, re-
printed in ' Wissenschaftliche Ab-
handlungen,' vol. i. No. 1, also
on Joule's early experiments in
' Ueber die Erhaltung der Kraft,'
ibid., vol. i. p. 33.

ON THK PHYSICAL VIEW OF NATURE. 113

other forces of nature into his consideration, showing, in
the case of the phenomena of heat, electricity, i^alvanism,
and magnetic induction, how the dillerent agencies can
be brought into comparison with mechanical ones by
measuring the work they perform ; refers to tlie attempts
to hx the mechanical value of heat ; concludes in each
case that no observed phenomena — not even the pro-
cesses in h\ing organisms — stand in contradiction with
the principle announced, and ends with the words : " I
think in the foregoing I have proved that the above-
mentioned law does not go against any hitherto known
facts of natural science, but is supported by a large
number of them in a striking manner. I liave tried
to enumerate as completely as possible what con-
sequences result from the combination of other known
laws of nature, and how they require to be con-
firmed by further experiments. The aim of this
investigation, and what must excuse me likewise for
its liypothetical sections, was to ex[)lain to natural
philosophers the theoretical, practical, and heuristic im-
portance of the law, the complete verification of which
may well be looked upon as one of the main problems
of physical science in the near future." ^ The reasons
why this valuable document attracted little attention at
the time and was set aside, as were the earlier contribu-
tions of Mohr and ]\Iayer, by the central organ of ex-
perimental physics abroad, are interesting from a
historical point of view. The first and main reason
seems to have been that none of the three original and
independent expressions contained any new experimental

^ 'Gesammelte Abhandlungen,' vol. i. j). (57.
VOL. J J. "

114

SCIENTIFIC THOUGHT.

facts,^ and that the then reigning school of natural philos-
ophers in Germany discouraged theoretical deductions, as
possibly leading back to the fatal " philosophy of nature,"
out of which they had only just escaped. Men of the
intellectual eminence of Liebig, through whose labours an
enormous mass of new facts had been accumulated, and
who desired to see the more hidden processes of organic
life subjected likewise to rigorous measurements, showed
indeed a certain appreciation of the attempted defini-
tions of Mohr and Mayer, struggling as he and
they alike were under the still existing confusion in
the fundamental conceptions.^ And these were not

1 See Mohr, ' Allgemeine Theorie
der Bewegung unci der Kraft,' p.
82, kc. Poggendorf did not reply
to Mayer's repeated communica-
tions and did not return the MS. ;
the fact that he received it was first
established by ZoUner, who in 1877
recovered the MS. from Poggeu-
dorf's heirs (Mayer's ' Schrifteu und
Briefe,' ed. Weyrauch, p. 100), and
gave a facsimile of it in his
' Wissenschaftliche Abhandlungen '
(Leipzig, vol. iv., 1881, p. 672).
Helmholtz, who in 1847 had no
knowledge of Mayer's writings, did
full justice to his claims in his
address, ' Ueber die Wechselwirk-
ung der Naturkrafte ' (1854), and
vindicated them against Tait's
criticisms in a letter published by
the latter in his ' Sketch of Ther-
modj-namics' (Edinburgh, 1868);
see Helmholtz, ' Wissenschaftliche
Abhandlungen,' vol. i. p. 71, &c.
Helmholtz closes his later com-
ments on the subject (' Yortriige
und Reden,' vol. i., 3rd ed., 1884, p.
74) with the following significant
remark : " The best ideas run the
risk of remaining barren, if not
accompanied by that energy which
lasts till the convincing proof of

their correctness has been given."
This explains the neglect of Mohr
and Mayer, and why in England
the interest in the energy ideas
only became general after Joule's,
Thomson's, and Rankine's labours,
as Helmholtz himself remarks in
1854 ('Vortrhge,' &c., p. 39).

^ Helmholtz ("Ueber Mayers
Prioritiit," ' Yortriige,' vol. i. p. 69)
says: "That the [i.e. Mayers] dis-
sertation contained really important
ideas, that it did not belong to the
wide - ranging literature of vague
suggestions, such as are annually
served up by badly informed ama-
teurs, could at best only be noticed
by a reader who had already turned
over in his mind similar reflections,
and who could recognise them
under the somewhat strange vocabu-
lary of the author. Liebig, who, in
the same year in which Mayer's
dissertation appeared, published his
book on animal chemistry, in which
he fully discussed the question as to
the origin of animal heat, was per-
haps such a reader, and was there-
fore willing to insert the article
in his annals." The same remark
would refer equallj' to Mohr's
earlier essay. It is now known

ON THE PHYSICAL VIEW OF NATTKE.

IL

sutlicieully cleared up in ^luhr's sliurt aper^u, which dfyes
not attempt to distinguish between the two ditVerent
meanings of tlie word force, nor in the earlier papei-s
of Mayer, wliu, however, in later writings shows a clear
appreciation of the dilhculty. In Helmholtz's menujii-s
the desired clearness was only attained by mathenuitical
reasoning, which in his age and country was accessible
to but few naturalists. The second and probably the
fundamental obstacle in the way of a just recogni-
tion of the new truth lu}' in the fatal use of the term
" force " in two distinct meanings. Popularly tlie ditti-
culty has only been removed l>y the creation of a new
vocabulary, and dates from the introduction of the term
" work " by Clausius in 1850, and of the term " energy "
by William Thomson, who adopted it from Young in the ^^f '"'"""
year 1852. The confusion which had been kept up by '^'""'"''"
employing the word " force " to mean not only pressure
or dead force (in the Newtonian sense) but also acting
force {vis viva in the Leibnizian sense), and with this
confusion the whole meaning of the great controversies
which raged for many years between the Cartesians
and Leibnizians on the correct measure of force, was
then removed, and a grammatical and logical founda-

15.
Work"anil
energy "
introluced

from Mayer's published correspond-
ence that some remarks of Liel)ig
himself, which appeared early in
1842, induced him to send him his
first paper in order " not to lose the
right of j)riurity " (letter to Gries-
inger, fiili-Gth December 184"2, in
' Schriften and Briefe,' ed. Wey-
rauch, p. 190). Mayer there says :
" Liebig wrote to me, inter alia:
' As to what force, cause, and
effect are, there exist in general

such confused notions that an
easily understood explanation must
be considered to V)e of real value.'
One would accordingly tliink tliat
he himself considers himself quite
above this general confusion ; that
this is ni>t so, 1 could see surti-
ciently from his ' phenomena of
motion in the animal organism '
(Liebig, 'Die organische Chemie,
&c.; 1842, p. 183, &c.)"

116 SCIENTIFIC THOUGHT.

tion secured on which a new generation could enter
at once into the possession of correcter dynamical and
physical views. It is now being recognised more and
more that the word " force " applies only to a mathe-
matical abstraction, whereas the word " energy " or
" power to perform work " applies to a real quantity ;
and there are not wanting suggestions that the former
should be altogether banished from scientific text-books,
and that the latter denotes not merely a property of
matter, but that it is after matter the only real thing
or substance in the material world.^

This radical change in the fundamental notions which
underlie all physical reasoning was not brought about,
however, till the vaguer views expounded by Mayer in
Germany, and the exact measurements of Joule in England,
had been united by the independent labours of Thomson
and Clausius, whose earliest researches (also carried on
independently of each other) had been suggested by the

^ The late Prof. P. G. Tait has methods and systems which ia-
on various occasions expressed volve the idea of force, there is the
himself in this sense. See his leaven of artificiality. The true
lecture on "Force," delivered be- : foundations of the subject, ba.sed
fore the British Association. Glas- < entirely on experiments of the
gow, in 1876, and reprinted in most extensive kind, are to be
'Recent Advances,' 3rd ed., also found in the inertia of matter, and
the closing paragraphs of his article the conservation and transfor-
" Mechanics," in the 9th ed. of the , mation of energy. With the help
'Ency. Brit.,' reprinted as ' Dy- of kinematical ideas, it is easy to
namics,' 1895, where he says (p. base the whole science of dynamics
356) : " The only other known I on these principles ; and there is
thing in the physical univer.se, ; no necessity for the introduction of
which is conserved in the same j the word ' force,' nor of the sense-
sense as matter is conserved, is j suggested ideas on which it was
energy. Hence we naturally con- ' originally based." We must, how-
sider energy as the other objective ever, in that ca.se extend the con-
reality in the physical universe, ception of matter to embrace also
and look to it for information as to the ether (see Tait, ' Properties of
the true nature of what we call Matter,' p. 5, 2nd ed.)
force;" and (p. 361): "In all

ON THE PHYSICAL VIEW UF NATURE. 117

still earlier writings of Sadi Carnot and (Jlapevnjn in m.

Sadi C'arnot.

France. Thomson's interest in the 8u]>ject dates from
the middle of the 'forties. He was then occupied with
finding a method for measuring heat on the ab.solute
scale. Mohr, Mayer, and Helmholtz all approached the
thermo-dynamical problem in the medical or physiological
interest. Trained in the school of Liebig and Johannes
Midler, they were led to study the economics of organic
processes and the mechanism of the physiological pheno-
mena of animal heat, of motion, and of nutrition. Sadi
Carnot, as after him Clapeyron in France and Joule in
^Manchester, approached the thermo-dynamical problem
from the side of practical interests, created by the intro-
duction and universal application of steam in the useful
arts. The great change worked by the steam-engine,
especially in England, the utilisation of coal and iron-
stone, the foundation of England's growing industrial
wealth, seemed to Sadi Carnot to be concentrated in the
problem of the motive power of heat ; as to Liebig, the
key which would unlock the mysteries of vegetable
growth, of animal nutrition, and of human labour, with
their economic, industrial, and political aspects, lay in
the problem of combustion. As in the domain of electri-
cal science, so in that of thermotics, the first thing to
do was to arrive at a correct method of measuring heat
as distinguished from temperature. It was a problem of
applied mathematics. About the same time Gauss had
established the system of absolute measurement from a
universal point of view, and he and Weber had applied
it to magnetic and electrical plienomena. Thomson
set himself to do the same thing in thermotics, and

118

SCIENTIFIC THOUGHT.

he found in the ideas expounded by Poncelet, Sadi
Carnot, and Clapeyron, the means of accomplishing the
object. We now see how there lay, in the fundamental
problem of thermo-dynamics, the unifying idea of sciences
hitherto far apart and working on independent lines and
with independent standards of measurement, speaking, as
it were, separate languages. And what was the new idea
which lay concealed in Sadi Carnot's forgotten pamphlet ? ^
In Carnot's original memoir it appears as an axiom at
the beginning of his reflections. " The production of
motion," he says, " in steam-engines is always accompanied
by a circumstance on which we must fix our attention.
This circumstance is the re-establishment of equilibrium,
or level, in the caloric — that is to say, its passage from
one body where the temperature is more or less elevated.

^ The story of Sadi Carnot's
memoir is not less curious than that
of Mohr's first paper. It was first
given by Lord Kelvin in his earliest
article, "On an Absolute Thermo-
metric Scale" (1848), reprinted in
' Math, and Phys. Papers,' vol. i.
p. 100), and "An Account of Car-
not's Theory" (1849, ibid., p. 113).
He had in 1845 searched in vain for
the ' Puissance motrice du Feu ' in
all the bookshops of Paris. In 1848
he obtained a copy from Levpis
Gordon in Glasgow. It was known
to him before through Clapeyron 's
memoir in the 14th vol. of the
' Journal de I'Ecole polytechnique '
(1834). Sadi Carnot published his
memoir as a pamphlet in 1824. It
has since been republished by his
brother, Hippolyte Carnot (' Reflex-
ions sur la Puissance motrice du
Feu et sur les Machines propres h,
d^velopper cette Puissance,' Paris,
Gauthier- Villars, 1878), with im-
portant posthumous papers, from
which, inter alia, it is evident that

Carnot, before he died, had aban-
doned the material theory of heat,
and actually, by an unknown pro-
cess, calculated the mechanical
equivalent of heat as 360 kilogram-
metres. As in several other cases,
so also in that of Sadi Carnot, the
line of reasoning initiated by La-
place, and brilliantly developed by
his school, militated against the
acceptance of the dynamical as
opposed to the material conception
of the phenomena of heat ; and
M. Bertin, in his "Rapport sur le
Progres de la Thermodynamique en
France" ('Recueil de Rapports,'
&c., p. 5) could write in 1867 : "II
faut bien I'avouer, parceque c'est la
v&-ite : nous sommes restfe long-
temps, je ne dis pas rebelles, mais
Strangers aux nouvelles idees : elles
nous sont restfes trop longtemps
inconnues, et encore aujourd'hui,
on peut regretter qu'elles n'occupent
pas une place plus considerable dans
notre euseignement scientifique."

ON THE PHYSICAL VIEW OF NATURE. 119

to another where it is lower, . . . The production of
moving force is therefore due in steam-engines, not to a
real consumption of caloric, Ijut to a transference from a
hot body to a cold body." ^

If it is the object of physical science to describe the
processes of nature completely and in the simplest
language, we have here an instance of a description of
a very general property in very simple language, and in
terms which reduce it to a measurable quantity. With-
out this, progress is impossible. It is not likely, how-
ever, that Carnot saw the full significance of his simple i:.

Camot

statement, how in it he had introduced into physical and introduces

' ^ "^ the idea of

mathematical science the great question of the avail- abjl'^y'..
ability of the forces of nature, as Mohr and ]\Iayer in
(Germany, and Faraday and Grove in England, somewhat
later, dwelt on the correlation or interchangeability of
those forces. The two ideas were separately developed.
When they came together in one mind, when Thomson
fully realised the importance and meaning of Ijoth
— as he undoubtedly did earlier than any other
natural philosopher — he at once established the great
doctrine of the dissipation, also called degradation or is.

. Tliomson iii-

depreciation, of energy, Jnit it required some modih- tr.Kiuctsihe
cation of Carnot's enunciation of this general property '^'pation."
before it could be put into its modern form. This
modification was preparing itself in Carnot's own mind,
as his papers, posthumously puljlished, have revealed
to US.2 What required to be modified was the word

1 Carnot, ' Puissance motrice,' ed. 187S, p. <J0) : " Loi^iiu'une

ed. 1878, pp. 5 and 6. liypothose ne suffit plus a I'explica-

* His notebook contained the fol- tion des phc^uom^ne8, elle doit etre

lowing entry {'Puissance motrice,' abandonnoe. C'est le aw oil ee

120

SCIENTIFIC THOUGHT.

19.
Fourier.

caloric. Carnot was brought up under the influence of
the school that looked upon heat as an imponderable
substance which might hide itself — might become latent
— but could not be created or destroyed. This was
the view of Black, of Laplace, of Fourier ; it was not the
view of Cavendish, of Davy, of Eumford. The views
of the former were embodied in great treatises, and con-
sistently worked out with much collateral extension of
physical and mathematical knowledge ; the views of the
latter were expressed in detached experiments and in
casual reflections. Fourier^ had just (1822) given to
the world his epoch-making work, the ' Th^orie ana-
lytique de la Chaleur,' in which he had stated that " the
properties of heat form a special order of phenomena
which are not to be explained by principles of motion
and equilibrium ; " ^ and again, " There exists a very

trouve I'hypothese par laquelle on
considere le calorique comme une
matiere, comme un fluide subtil."
Again (p. 92) : " La chaleur est le re-
sultat d'un mouvement. Alors il est
tout simple qu'elle puisse se produire
par la consommation de puissance
motrice et qu'elle puisse produire
cette puissance. Tous les autres
ph^nomenes . . . pourraient s'expli-
quer dans cette hypothese : mais il
serait difficile de dire pourquoi, dans
le ddveloppement de la puissance
motrice par la chaleur, un corps
froid est necessaire, pourquoi, en
consommant la chaleur d'un 'corps
^chauffe, on ne pent pas produire
du mouvement." And (pp. 93 and
94) : " Lorsque Ton fait naitre de la
puissance motrice, par le passage de
la chaleur du corps A au corps B, la
quantite de cette chaleur qui arrive
k B, cette quantite est-elle la
meme, quel que soit le corps em-

ploj-^ Ji realiser la puissance motrice ?
Y aurait-il moyen de consommer
plus de chaleur a la production de
la puissance motrice et d'en faire
arriver moins au corps B ? Pourrait-
on meme la consommer tout entiere
sans en faire arriver au corps B ?
Si cela ^tait possible, on pourrait
creer de la puissance motrice sans
consommation de combustible et
par simple destruction de la chaleur
des corps." And (p. 94): "La
chaleur n'est autre chose que la
puissance motrice, ou plutot que le
mouvement qui a change de forme.
C'est un movement dans les par-
ticules des corps."

■' On the tardy reception and
recognition of Fourier's work see
vol. i. p. 241, note, of this work.

'^ ' Theorie analytique de la
Chaleur,' 1822: ' Discours prd-
liminaire,' p. iii.

ON THE PHYSICAL VIKW OF NATL'KE. 1 1' 1

extensive class of phenomena which are not produced
by mechanical forces, but which result solely from the
presence and accumulation of heat. This part of natural
philosophy cannot be brought under dynamical theories ;
it has principles peculiar to itself, and is based ui^m
a method similar to that of the (^ther exact sciences.^
. . . The dilatations, indeed, caused by the repulsive
force of heat, the observation of which dilatations serves
as a measure of temperature, are dynamical effects ; but
it is not these dilatations which we calculate when we
investigate the laws of the ])ropagation of heat." " He
proceeds to Imild up this new science "upon a very
small nvmiber of simple facts, of which the causes are
unknown, but which are gathered by observation and
confinned by experiments," ^ and he thus arrives at
certain general relations, expressed in the form of equa-
tions, which are different from, though analogous to, and
not less rigorous than, the general equations of dynamics.
One of the great experimental facts upon which Fourier
bases his theory of the propagation (i.e., the conduction
and radiation) of heat is this, that all motion of heat
depends on differences of temperature. He examines
how differences of temperature are equalised and de-
duces the law of the flow of heat."^ Although he does

'Fourier, ' Theorie analytique,' | zig, 1896), pp. 78, &c'., 116 sq/j.
p. 13. '^ Ibid., p. 14. I Every studeut of pliy.sic.s should

•* Ibid., pp. xi, 18, 39. read the chapters referring to this

* I cannot here omit to jxtint out
how elegantly Prof. Mach has trans-
lated into the language of common-
sense the whole process of Fourier
for establi.shing the fundamental

subject. The mathematical for-
mulie will thus l)ecome living to
him ; but he will also see how
necessary the abstract mathematical
expression of common-sen.se cou-

equation of the theory. See his ' ceptions is in order to avoid false
'Priucipien der Warmelehre' (Leip- | reasoning.

20.
His influ-
ence on
Carnot.

122 SCIENTIFIC THOUGHT.

not find it necessary to enter npon any theory of the
nature of heat, the analogy with the flow of water from
higher to lower levels would naturally present itself.
For his purpose this analogy had no importance. For
the purposes of Sadi Carnot, who noticed that upon
the difference of temperature depended not only the
flow of heat, but also the work it might eventually
do, the same analogy seemed all-important. " We may,"
he says, "justly compare the motive power of heat with
that of a fall of water : both have a maximum which
cannot be exceeded. The motive power of a fall of
water depends upon its height and the quantity of the
liquid ; the motive power of heat likewise depends on
the quantity of caloric employed and on what we will
take the liberty of calling the height of its drop — that
is, the difference of temperature of the bodies between
which the exchange of caloric has taken place." ^ In
this analogy two further assumptions seem to be im-
plied : First, that the work capable of being done is in
direct proportion to the difference of levels of height
or of temperature ; secondly, that the quantities with
which we operate, of water or of caloric, remain the
same, before and after the fall. Neither of these
inferences is necessary ; neither is permissible. Carnot
does not adopt the first inference,^ but he does adopt
the second,^ though he significantly remarks that the

^ ' Puissance motrice du feu,'
eel. 1878, p. 15.

"^ " Dans la chute d'eau, la puis-
sance motrice est rigoureusement
proportionelle h, la difference de
niveau entre le reservoir supdrieur
et le reservoir inferieur. Dans la
chute du calorique, la puissance

motrice augmente sans doute avec
la dift'drence de temperature entre
le corps chaud et le corps froid ;
mais nous ignorons si elle est
proportionelle k cette difference "
(ibid., p. 15 ; compare also pp.
38, 39).

^ " La production de la puissance

ON THE PHYSICAL VIEW OF NATL'RE.

l:i3

foundations on which the theory of heat rests retiuire
careful examination.^ Further thought evidently led
him to douht the correctness of tlie second assumption.
It is the first point to which Thomson, more than
twenty years after, directs his attention. He conceives
the idea of measuring temperature hy such a scale that
for an equal drop in the scale — i.e., Ijy letting down heat
by an equal number of degrees on the new scale — equal
amounts of work shall be done.^ The speculations of 8adi
Carnot remained unnoticed for a long time. Ten years 21.
later Clapeyron reverted to the subject, and itut the f.'rapiiicai

■■^ *' . . method.

reflections of Carnot into graphical form and into mathe-
matical language. He introduced the conception, based
on Carnot's theory, of the ratio of heat transferred from
a higher to a lower level of temperature to the maxi-
mum of work obtainable, — a quantity independent of
the substance employed, — and he called this fixed ratio

Carnot's function. It was

motrice est . . . due . . . uon h
uue consommation rdelle du cal-
orique, uiais a son transport d'un
corps chaud h un corps froid, c'est-
ii-dire iV son retablissement d'equi-
libre " (ibid., p. 6).

^ " Au reste, pour le dire en
passant, les principaux fondenients
sur lesquelles repose la thot)rie de
la chaleur auraient besoin de I'ex-
anieu le j)lus attentif. Plusieurs
faits d'exporieuce paraissent ii peu
pr6s inexplicables dans I'dtat actuel
de cette th^orie" (ibid., p. 20,
note). " La loi fondamentale que
nous avions en vue . . . est assise
sur la thc'orie de la chaleur telle
(ju'on la conc;oit aujourd'hui, et il
faut I'avouer, cette base ne nous
parait pas d'uue solidite indbran-
lable" (p. 50). As stated above
(p. 118, note), Carnot emancipated

through his paper that

himself from the conventional or
material view of the nature of
heat. See the appendix to the
edition of 1878.

- See 'Cambridge Piiilosophical
Society Proceedings,' June 1848 ;
reprinted in Thomson's (Lord Kel-
vin's) ' Matli. and Phvs. Papers,'
vol. i. p. 100.

^ Beiioit I'ierre Emile Clai>eyron
was an engineer. In 1834 he puV)-
lished, in tlie fourteenth cahier of
the 'Journal de I'Ecole Poly tech-
nique,' his " Mcmoire sur la Puis-
sance motrice de la Chaleur." It
was througli a translation of tliis
paper in 'Taylor's ScientiKc Mem-
oirs' that Thomson lieard about
Carnot's earlier work, and tlirough
a translation in Poggendorf's 'An-
nalen' (1843) that Helmlioltz be-
came acquainted witli the subject.

124

SCIENTIFIC THOUGHT.

Helmholtz in Germany, and Thomson in England, heard
about Sadi Carnot himself. Sadi Carnot, so much earlier
and so unlike Mayer, had nevertheless one point in
common with him. This point seems to have given
a common anchorage to all those thinkers who, in the
course of a generation, gradually lifted the theory of heat
and energy out of twilight into clear thought. Sadi
Carnot, Mayer, Joule, Helmholtz, Thomson, all express
or imply the same idea — viz., the impossibility of a

In one form or other this seems

22.
Perpetual
motion . .

impossible, perpetual motion.^

^ The conception of a "perpet-
ual motion," or, as it is termed
abroad, of a " perpetuum mobile,"
and that of its impossibility,
have been changed and more
clearly defined in the course of
the hundred years which followed
the decision of the Paris Academy
of Sciences in 1775 not to receive
in future any scheme of perpetual
motion. Into the same class of
axiomatic impossibilities were also
thrown the "squaring of the
circle" and the "trisection of the
angle." Helmholtz (appendix to
his Lecture on ' Die Wechselwirk-
ung der Naturkraf te, ' 1853, dated
1883) remarks that the proof of
the impossibility did not then
exist, and that the resolution was
therefore based merely on the
experience of past failures. The
doctrine of Energy, the arithmet-
ical discoveries of Gauss, and the
elegant researches of Hermite and
Lindemann, have thrown much
light on these celebrated prob-
lems. In the last chapter of
this volume I shall revert to the
two latter ; as to the first, the
"perpetual motion," what follows
may tend to clear the popular
conceptions. Tait has correctly
remarked that "perpetual motion
is simply a statement of Newton's

first law of Motion " ( ' Recent
Advances,' 3rd ed., p. 74). He
might have added that it took
probably as much ingenuity on
the part of Galileo to arrive at the
principle of inertia — viz., that "all
motion is perpetual until force in-
terferes to alter and modify it " — as
it took to formulate correctly the
other principle that such a per-
petual motion is of no use, because
you cannot do any work with it,
except by using it up or anni-
hilating it. In the beginning of
the nineteenth century the im-
possibility of a mechanical device
for the so-called perpetual motion
was universally admitted, though
— as Rosenberger (' Geschichte der
Physik,' vol. iii. p. 229, note)
remarks — this was not also ex-
tended to physical processes, it
being taught that the processes of
nature represented a ' ' perpetual
cycle which uninterruptedly re-
newed itself." In fact, the truth
was beginning to dawn that if
motive power or energy could not
be obtained out of nothing neither
could it be destroyed. Carnot in
1824, and Mayer in 1842, both take
it as an axiom that power cannot
be created ; Mohr in 1837, and
Joule in 1843 and 1845, are equally
convinced that power cannot be

ON THE PHYSICAL VIEW OF NATURE.

125

to be an axiom with them, but even this apparently
simple article of faitli in natural philosophy meant
somethini; diflerent to different thinkers accordin<: to
the greater or less clearness of their physical concep-
tions. Helmholtz, in his celebrated memoir of 1847,
conceives all natural processes to be ultimately re-
ducible to purely mechanical processes, and in doing
so he sees that a well-known law in mechanics, the
conservation of the vis viva, must have a meaning for
all natural forces. This he proceeds to develop. Others,
like Faraday, Mohr, Grove, have a silent conviction that
besides ponderable matter there is some other quantity
in nature which is indestructible and cannot be created,
but only changed and transferred ; they frequently call it
force, and thus entangle themselves or their readers in

destroyed. Under the influence
of Oersted's pliilosophy Colding
expresses similar ideas in 1843
(see ' Phil. Mag.,' 4th series, vol.
xxvii. p. 58). In fact, during the
fifth decade of the century the
three conceptions of the impossi-
bility of creating power, its inde-
structibility, and the converti-
bility of its different forms, were
more and more clearly enunciated.
They were at last expressed in
the formula of the " conservation
of energy.'' It was Tiiomson (Lord
Kelvin) who then — in 1852 — first
clearly recognised that the old phan-
tom of a perpetual motion was
turning up again in a new form.
(See his Essay on " Dissijiation of
Energy " in the ' Fortnightly Re-
view,' March 1892, reprinted in
' Popular Lectures and Addresses,'
vol. ii. p. 452.) Ever since Thom-
son's essay of 1852 naturalists
and philosophers may be said to
be tj-ying to formulate in the
simplest terms the great [)i'inciple

of nature, that though energy is
never lost, it becomes — for our
practical purposes — unavailable.
Prof. Ostwald has expressed this
by reviving the terminology of
the perpetual motion. " It is not
generally recognised that the
principle of perpetual motion has
two sides. On the one side . . .
perpetual motion could be realised
if one could create energy. . . .
The expression of the impossi-
bility of doing this is the first law
of Energetics. ... A perpetual
motion could, however, on the
other side be attained if it were
possible to induce the large store
of energy at rest to enter into
transformations. . . . This might
be termed a perpetual motion of
the second kind." The impossi-
bility of this Ostwald terms the
second princi|)le of Energetics
('Allgemeine Cliemie,' vol. ii.
part 1, p. 172 ; cf. Helm,
'Energetik,' p. 304).

126

SCIENTIFIC THOUGHT.

that confusion which the indefinite use of the word had
caused, especially among Continental writers. One of
the first practical applications of this idea as referred
to the motive power of heat in Carnot's sense was made
23. by "William and James Thomson in 1849. They had

Application

by William both fully realised that lowering of temperature might

and James '' r> l id

Thomson, ^q accompanicd by the doing of work by heat, and
that elevation of heat to a higher temperature meant
expense of work. If, therefore, work could be done by
heat without lowering the temperature, there was an
apparent gain of motive power without corresponding
expenditure. It was known that water at freezing
temperature expanded in becoming ice : it was capable
of doing work, frequently very destructive work, with-
out a lowering of temperature. In order to convert
water into ice of the same temperature, heat must be
abstracted. Here, then, was a case of a possible trans-
ference of heat without fall of temperature, and the
creation or gain of great power to do work ; but, ac-
cording to Carnot's principle, equality of temperature
implied an absence of expenditure of work. So here
was a case of gain without expenditure of power sim-
ply by a transference of heat at freezing-point. James
Thomson ^ saw the solution of the paradox. If water

^ The reasoning of James Thom-
son, based again upon the impossi-
bihty of a perpetual motion, is given
in the following passage of his com-
munication to the Royal Society of
Edinburgh, dated January 2, 1849
(reprinted in his brother. Lord Kel-
vin's, ' Math, and Phys. Papers,'
vol. i. p. 156) : " Some time ago my
brother. Prof. William Thomson,
pointed out to me a curious conclu-

sion to which he had been led by
reasoning on principles similar to
those developed by Carnot with ref-
erence to the motive power of heat.
It was that water at the freezing-
point may be converted into ice by
a process solely mechanical, and yet
without the final expenditure of any
mechanical work. This at first ap-
peared to me to involve an impossi-
bility, because water expands while

ox THE PHYSICAL VIKW OF XATURK.

in expanding by freezing is made lu du wuik, it over-
comes pressure ; it has to freeze under pressure. The
temperature of water freezing under pressure must lie
lower than that of water freezing under ordinary con-
ditions.^ Knowing the mechanical duty of a degree of
temperature and the work of the expansion of ice, he
could calculate how much the freezing-point of water
must be lowered by pressure. In 1850 his brother
William Thomson verified this theoretical prediction by
actual experiment." It is well known how Helmholtz
in 1865 made use of this theoretically predicted and
practically verified phenomenon in liis celebrated glacier
theory.^ Both James and AVilliam Thomson, when
they drew the conclusions from Carnot's theory, still
adhered to the doctrine of the entire conservation of
heat.^ But William Thomson, who was equally ac-

freezing ; and therefore it seemed
to follow that if a quantity of it
were merely enclosed in a vessel
with a movable piston and frozen,
the motion of the piston conse-
quent on the expansion being re-
sisted by pressure, mechanical work
would be given out without any
corresponding expenditure ; or, in
other words, a perpetual source of
mechanical work, commonly called
a perpetual motion, would be pos-
sible. . . . To avoid the absurdity
of .supposing that mechanical work
could be got out of nothing, it
occurred to me that it is necessary
further tocoiiclude that the freezing-
point becomes lower as the pressure
to which the water is subjected is
increased."

^ " The mechanical pressure pro-
motes— as is generally the case with
the alternate action of different
forces in nature — euch a change,
viz., melting of ice, as is favourable

to the effect of its own action "
(Helmholtz, ' Vorthige und Reden,'
vol. i. p. 217).

- ' Proceedings of the Roy. Soc.
of Edinburgh,' January 1850, re-
printed in 'Math, and Phj's. Papers,'
vol. i. p. 165.

■* Helmholtz, loc. cit., p. 215 377.,
where also the jdienomenon dis-
covered and called " regelation of
ice," by Faraday, is similarly ex-
plained.

■* It is important to notice this,
as the formula with which we are
now familiar, that the mechanical
work gained meant consumption of
heat, wiis not available at tiiat time.
This is significantly pointed out by
Helm ('Energetik,' p. 69). The
reasoning was accordingly more
difficult and refined. James Thom-
son, however, had at the time some
misgivings on the tlion jirevalcnt
view, and in a footnote he refers to
the " j)ossibility of the absolute for-

128

SCIENTIFIC THOUGHT.

24.
The two
laws of
thermo-
dynamics.

quainted with Carnot's ideas and with Joule's work,
increasingly felt the necessity of reconciling both views
in one consistent view. So did Clansius independently
at Ziirich. The result was the doctrine of the " con-
servation of energy," — not of heat, as Carnot had it, —
and the embodiment of the two correct ideas contained
independently in Carnot's and Joule's work in the two
well-known laws of thermo-dynamics ^ — viz., the con-
servation, equivalence, and convertibihty of energy, as

mation or destruction of heat as an
equivalent for the destruction or
formation of other agencies, such as
mechanical work " ( ' Math, and
Phys. Papers,' vol. i. p. 161, note).
The acceptance of the doctrine of
the convertibility of heat and
mechanical work — implying the
conservation of energy in place of
the conservation of heat, as Carnot
had it — seems to have taken place
in Lord Kelvin's mind immediately
after his paper referred to ahove in
consequence of a paper by Rankine
" On the Mechanical Action of
Heat " (Roy. Soc. Edinburgh, Feb.
1850), as is shown by his letter to
Joule, dated October 1850 {loc. cit.,
vol. i. p. 170). He there refers also
to a memoir by Clausius in Poggen-
dorf's ' Annalen ' of April and May
of the same year as adopting
" Joule's axiom instead of Carnot's "
(ibid., p. 173).

^ The reconciliation of Joule's
dynamical theorj' of heat with Car-
not's doctrine, and the necessary
modification of the latter, is con-
tained in Lord Kelvin's classical
memoir, " On the Dynamical
Theory of Heat," in the ' Trans, of
the Roy. Soc. of Edinburgh,' March
1851 ('Math, and Phys. Papers,'
vol. i. p. 173 sqq.) In the intro-
duction, Davy, Mayer, Joule, and
notably Liebig, are mentioned as
earlier supporters of the doctrine of

the convertibility of heat into me-
chanical effect, Rankine and Clau-
sius as the latest contributors (p.
176). The first and celebrated
enunciation of the second law by
Thomson is given at the very be-
ginning (p. 179), and in the sequel
the denial of it is shown to mean
the possibility of a perpetual mo-
tion. A little farther on Thomson
refers to Clausius in the words :
" The merit of first establislung the
proposition upon correct principles
is entirely due to Clausius, who
published his demonstration of it
in the month of May last year "
(1850). It has on the other side
been admitted by Clausius (' Die
mechanische Wiirmetheorie,' 2te
Aufl., 1876, vol. i. p. 358) that
Thomson's independent develop-
ment of the second law, though
published later, is conducted from
a more general point of view,
whereas his own treatment was
purely mathematical and confined
to special cases. The most general
and philosophical expression of the
new principle was given by Thom-
son in his celebrated communication
to the Roval Society of Edinburgh,
April 19," 1852, "On a Universal
Tendency in Nature to the Dissipa-
tion of Mechanical Energy " (re-
printed in ' Math, and Phys.
Papers,' vol. i. p. 511).

ON THE PHYSICAL VIEW OF NATURE. 129

expressed in the first law, and the doctrine of the avail-
ability of energy as expressed in ihe second law. U was
Thomson who first clearly saw that the axitjni of the
impossibility of a perpetual motion would l)e infringed if
the first law of thermo-dynamics — the indestructibility of
energy — was accepted without the second. P'or practical
use, for doing work, it is not sufficient that energy be not
lost ; it must be available — get-at-aljle. Energy may Ije
in a condition in w'hich it is useless — hidden away — and
to liring it forth again may either be for us impossible
(if it be dissipated), or may require an expenditure of
work — i.e., of energy — to do so. The second law puts
into mathematical language another very inqxjrtant and
very striking property of the processes in nature. Let
us dwell on this a moment.

The doctrine of the preservation of energy, of the
equivalence of the different forms of energy, tended to
put all the forms of energy on the same level. If they
be convertible, they appear to be of the same value.
If in doing work, energy was not consumed but only
changed, it stood to reason that it might be changed
back again, so that tlie work could be d(jne over again.
In other words, if all processes are purely mechanical
processes — modes of motion — a supposition which very
early forced itself with more or less clearness on the
pioneers of the science of energy, they must be reversible :
it must 1)0 possible to turn them round again, to undo
what has been done, or to do what has been undone.
Now the common-sense view of nature tells us at once
that this is impossible ; but it does not seem to have
struck the earlier propounders of the doctrine of the

VOL. IL I

130 SCIENTIFIC THOUGHT.

equivalence and correlation of forces, such as Faraday,,
Mohr, Mayer, Grove — not even Joule and Helmholtz —
that if neither matter nor power is lost, the phenomena
of loss and waste in nature and in human life remain
unexplained. The only mind to whom this problem
presented itself was Sadi Carnot, and it presented itself
to him in an extreme form ; for he started with the
idea that even heat itself in doing work was not lost
or destroyed, but handed over from the hotter body
(the boiler of the steam-engine) to the colder body (the
condenser of the steam-engine). We now know that
this view was not correct — that the whole heat is not
handed over, but always only a portion of the heat. But,,
with this exaggerated view in his mind, he tried to explain
the phenomena of loss and waste, and he conceived that
the explanation lay in the lowering of the temperature.
" It would be difficult to say why " — though he had
assumed it as an axiom that — " in the development of
motive power by heat, a cold body should be necessary,
why in consuming the heat of a heated body we cannot
produce motion." ^ Heat at high temperature is of more-
value for doing work than the same amount of heat at

^ The words quoted are taken
from cue of the fragments published
in the year 1878 by H. Carnot from
the posthumous MSS. of his brother,
Sadi Carnot. In this fragment he
approaches the modern conception
that heat is the result of motion :
he sees that all other phenomena
can be explained by this hypothesis ;
but he pauses after having stated
the difficulty quoted above in the
text, and reverts, after some
further queries, to the same diffi-

culty in the words, ' ' Can one con-
sume the heat entirely without
letting any arrive at the body B
[viz., from a body A] ? If this were
possible, one could create motive
power without consumption of fuel,
and simply by the destruction of
the heat of bodies" ('Puissance
motrice, &c. ,' ed. 1878, pp. 92 and
94). It is interesting to see how
nearly these reflections approach to
those made more than twenty years
later by Thomson.

ON THK PHYSICAL VIKW UK .NATCKK. 131

low temperature. By doing work, as also by conduction,
and radiation with absorption, this inequality of tempera-
ture is spent, i.e., lost. Clausius and Thomson alone
seem to have grasped the value of this conception. The
difficulty was to put it into mathematical language —
into calculable terms. Each did tiiis independently.
Thomson, more than any other thinker, put the problem
into common-sense language, brought the subject home
to the practical reason ; at the same time he put it into
mathematical language, allowing the conceptions of waste ^
and of value and of availability (or usefulness) of energy
to be scientifically — that is, measurably — defined. In
1851 he put the axiom upon which Carnot's reasoning
is based (without knowing the words of Carnot quoted
above) into the following words : ^ "It is impossible by
means of inanimate material agency to derive mechanical
effect from any portion of matter by cooling it below
the temperature of the coldest of the surrounding objects."
He saw at once, when adopting Joule's doctrine of the
convertibility of heat and mechanical work, that, if all
processes in the world l)e reduced to those of a perfect

' The term "wasted," as distiu-
guished from "annihilated," is first
introduced in Part 1 of the "Dyn-
amical Theory of Heat," 18.51, p.
189 of 'Math, and Phys. Papers,'
vol. i. ; and in the following year,
in a paper read before the Royal
Society of Edinburgh on the 19th of
April, entitled, " On a Universal
Tendency in Nature to the Dissipa-
tion of Mechanical Energy," the
8uV)ject is brought home to the
general understanding by a succes-
sioa of short theses referring to

the dissipation and possible limited ' eternal death.

restoration of energy (' Papers,' vol.
i. p. 511, &c. )

■■^ 'Math, and Phys. Papers,' vol.
i. pp. 179, 511. Helndioltz ('Vor-
triige und Reden,' vol. i. p. 43) said
in 1854 : " In any case we must
admire the acumen of Thomson,
who could read between the letters
of a mathematical equation, for
some time known, which spoke
only of heat, volume, and press-
ure of bodies, c<inclusi()iis which
tlireaten the universe, thuugh in-
deed only in infinite time, with

132 SCIENTIFIC THOUGHT.

mechanism, they will have this property of a perfect

machine, namely, that it can work backward as well as

25. forward. It is against all reason and common-sense

Summary

statement to carrv out this idea in its integrity and completeness.

of Thomson "^ o J c ^

KeTvIn) " "^^^ essence of Joule's discovery is the subjection of
physical phenomena to dynamical law. If, then, the
motion of every particle of matter in the universe were
precisely reversed at any instant, the course of nature
would be simply reversed for ever after. The bursting
bubble of foam at the foot of a waterfall would reunite
and descend into the water ; the thermal motions would
reconcentrate their energy and throw the mass up the
fall in drops, re-forming into a close column of ascending
water. Heat which had been generated by the friction
of solids and dissipated by conduction and radiation with
absorption, would come again to the place of contact and
throw the moving body back against the force to which
it had previously yielded. Boulders would recover from
the mud the materials required to rebuild them into
their previous jagged forms, and would become re-united
to the mountain - peak from which they had formerly
broken away. And also, if the materialistic hypothesis
of life were true, living creatures would grow backwards
with conscious knowledge of the future, but with no
memory of the past, and would become again unborn.
But the real phenomena of Hfe infinitely transcend
human science ; and speculation regarding consequences
of their imagined reversal is utterly unprofitable. Far
otherwise, however, is it in respect to the reversal of the
motions of matter uninfluenced by life, a very elementary
consideration of which leads to the full explanation of

ON THE PHYSICAL VIEW OF NATURE.

133

the theory of dissipation of energy." ^ Whilst Clausiius in
Germany and Thomson in England were busy reconciling
the truths contained in Carnot's older researches with the
new conceptions firmly established by Joule's cla.ssical
measurements, putting both into mathematical and into
popular language, correcting our mathematical fornmlie as
well as our vocabulary, other applications of the new
ideas assisted in procuring for them general recognition Ranw^ine.
and acceptance. Ifankine- in England, Zeuner^ in Cler- uirn*''*"

26.

^ Lord Kelvin, in a paper read
before the Royal Society of Edin-
burgh, 2i)d February 1874, on "The
Kinetic Theory of the I)is.si])ation
of Energj' "" (' Proceedings,' vol. viii.
p. 32.") ii'i'i. ) See ahso hi.s article in
the ' Fortnightly Review' for Mai'ch
1892, reprinted in ' Popular Lec-
tures and Addresses,' vol. ii. p.
449 .S77.

- The earliest formal treatise on
thermo - dynaniics wa.s Macquorn
Rankine's article on " The Mechani-
cal Action of Heat" in Nichol'.s
'Cyclopaedia' for the year 18.')5.
The part he took in the develop-
ment of the new science was prac-
tical and at the same time highly
speculative. His papers on tem-
perature and elasticity of steam
and other vapours, on the expan-
sion of liquids by heat, and on
the mechanical action of heat, of
dates 1849 and 1850 (see ' Miscellan-
eous Scientific Papers,' ed. Millar,
1881, pp. 1, 16, 234), entitle him
to be considered as one of the
first — if not the first (see his claim
to priority in a letter in Poggen-
dorf's 'Annalen,' p. 81, IS.'JO)— to
reconcile Carnot's di.scovery with
the mechanical view. His investi-
gations were peculiar, combining
practical ai)[)lication8 of great value
and important predictions (see
Tait's memoir prefaced to Ran-
kine's ' Papers,' p. xxi.x) with daring

speculation ; his deduction.s Inking
founded on iiis theory of molecular
vortices. Tiiough he exerted in
this country a great influence on
the early workers in thermo-dyn-
amics, his theories were scarcely
relished in (Jermany (see Helm-
holtz's criticism of Rankine's
methods in 1853, quoted by Helm,
' Energetik,' p. 114), where Claus-
ius's independent and simultaneous
researches on the same subject had
meanwjiile usurped attention. But
Rankine's ' Manual of Applied
Mechanics' (1857), his 'Manual of
the Steam-engine and other Prime
Motors' (18.')9), were the first books
of practical application in which,
through a happy nomenclature
and an extensive use of gra])iiical
methods (Watt's indicator diagram
and Carnot's cycle), the new ideas
were introduced to a wider circle.
See Helm's estimate of Rankine's
work in 'Energetik,' p. 116 .•(77.

•* Somewhat later than Rankine
in this country, Zeuner in Switzer-
land and Germany, following upon
Clausius's theoretical memoirs, in-
troduced the mechanical treatment
of practical heat - problems. His
' r.rund/.iige dcr mechanischen
Warmetheorie ' (1860) was to many
a revelation. Aj)peuring about the
time when the German meciianical
and chemical industries were start-
ing upon a new development.

134

SCIENTIFIC THOUGHT.

many, and Hirn^ in France, studied the most important
of all machines then in use, the steam-engine, in the light
of the new discoveries. It became possible to define
clearly what was meant by the efficiency of an engine,
and to distinguish between those losses of the energy of
heat or temperature which were dependent on the use of
steam as the working substance, and therefore inherent
and unavoidable, and those losses which depended upon
the mechanism and upon the carrying out of the process
employed. The older teachings contained in treatises
written before a knowledge, or even an idea, of the

largely based upon the scientific
training afforded in the excellent
chemical laboratories and poly-
technic schools of Germany, it
assisted in giving to German in-
dustrial enterprise that scientific
character which was at first ridi-
culed and has latterly been ex-
tolled in unbounded measure, and
which — combined with the organis-
ing ability inherited from English
ancestry — seems to be one of the
distinctive features of the great
industrial progress of America.
First among writers on the Contin-
ent Zeuner gave such a connected
exposition of the principles de-
veloped by Clausius, Thomson, and
Rankine as met the requirements
of practical engineers ; attached to
them applications referring to the
steam-engine ; criticised the views
adopted by Watt and later writers,
notably de Pambour, with reference
to the behaviour of saturated va-
pour in the steam-cylinder during
expansion and compression ; and
largely prepared the way for the
great improvements in steam, air,
and refrigerating engines which
have been brought out on the Con-
tinent by those trained in his
school. Through Clausius, Zeuner,

and others, Dingler's * Poly-
technic Journal ' became the
organ by which the many discus-
sions on the new mechanical theory,
and notably the second law of ther-
mo - dynamics, gradually forced
themselves upon the attention of
practical men.

^ Equally important were the
labours of Adolph Hiru (1815-90).
He was a self-made man who had
grown up in the midst of the im-
portant textile industry of Alsace.
With a naturally inquiring dis-
position he combined the scientific
and artistic accomplishments for
the manifestation of which the
chemical and mechanical products
of that country have long been
renowned. He approached some
of the great theoretical problems
connected with practical engin-
eering, such as those of heat,
steam, lubrication, and superheat-
ing, by a long series of carefully
planned experiments. A very in-
teresting account by several authors
is given in a publication by Faudel
and Schwoerer (' G. A. Hirn, sa Vie,
sa Famille, ses Travaux,' Paris,
1893). Hirn, like Rankine, was not
only an engineer, but also an artist
and a philosopher.

ox THE niYSICAL VIKW OF NATrUK.

135

mechanical value and the availability of heat ekist-ed,
had to be largely altered, and corrected notions laid
down, fre(juently as a result of prolonged discussion.^
As an example, I may refer to the controversy between
Him and Zeuner as to the cause of the grciit discrepancy
between the theoretical and practical figures referring to
the work in the steam-cylinder, the so-called " Water or
Iron " controversy.^

lint whilst it must be admitted that the corrected
views regarding the nature of heat — the preservation

' The best account of the prac-
tical bearings of the mechanical
theories of Kankine and Clausius
is to be found in Prof. Unwin's
" Forrest Lecture," delivered "ind
May 189."), before the Institute of
Civil Engineers, and published in
the ' Electrician,' vol. xxxv. p. 46
srjfj. and p. 77 S77. He there refers
to the great discrepancy between
the "rational" and the "experi-
mental " theories, and to Hirn's ex-
periments and practical results,
notably with the " steam - jacket,"
and his introduction of "super-
heating" in 1855. " Xo doubt
the rational theory altogether
underrated the enormous facility
of heat-exchange, which arises out
of the contact between a conduct-
ing cylinder-wall and a vapour in a
condition of the greatest instability,
and liable to condense or evaporate
on the slightest change of thermal
condition" (p. 50). The several con-
troversies through which Clnusius
ilefended and gradually elucidated
the somewhat obscure statement
which he gave of the so-called
second law of thermo-dynamics may
be studied with advantage in the
"2nd edition of his collected Memoirs
(' Die mechanische Wiirmetheorie,'
Braunschweig, vol. i., 1876), where
his replies to criticisms of Holtz-

maim, Decher, Zeuner, R<inkine,
Wand, and Tait are most instruc-
tive. A good account is also given
in Baynes's ' Lessons on Thermo-
dynamics,' Oxford, 1878, p. 103

- See Prof. Unwin, loc. cit., p.
79. "On the ajipearance of Isher-
wood's researches in 1863, the dis-
crepancy between the rational
theory and the results of experi-
ment were recognised by liankine
and others. But the conditions of
the steam - cylinder conden.-^ation
are so complex that for a long time
the more theoretical writers prac-
tically ignored both Hirn's and
Isherwocxl's results. Zeuner per-
hajjs had jiushed the rational theory
to the furthest limit of detail, and
with the greatest insight into prac-
tical conditions. But it was not
till 1881 that he began to explicitly
admit the largeness and importance
of the condensing action of the
cylinder. Zeuner then was disposed
to attribute initial condeu.-iation to
the presence of a permanent and
not inconsiderable mass of water
in the clearance space of the engine.
... In o])oning a discu.s.sion with
Hirn in 1881, Zeuner wrote that if
the presence of water in the dejir-
ance space waa conceded, the
Alsiitian calculations would be

136 SCIENTIFIC THOUGHT.

and waste (degradation) of energy, have hardly resulted
in those practical achievements and improvements ^ which
in other departments of applied science, notably in
chemistry and electricity, have followed upon new dis-
coveries, the influence of these new conceptions on
scientific thought and method themselves has been
enormous. Next to the conceptions introduced by
Darwin into the descriptive sciences, no scientific ideas
have reacted so powerfully on general thought as the
ideas of energy. A new vocabulary had to be created ;
the older text-books, even where they dealt with known
subjects in perfectly correct ways, had to be rewritten ;
well-known and approved theories had to be revised and
restated in correcter terms, and problems which had
lain dormant for ages to be attacked by newly in-
vented methods. I propose in the rest of this chapter

greatly shaken. . . . There thus \ the behaviour of steam in the
arose a rather angry controversy j cylinder at all calculable were so
which has been summed up in the far wide of the mark, — that a
question, ' Is it water or iron ? ' general consensus seems to prevail
I do not know that this controversy j among theoretical engineers that
has been as yet completely decided." progress depends less upon an
See also Peabodj-, ' Thermo- immediate application of thermo-
dynamics of the Steam - Engine,' dynamic principles, than upon a
4th ed., New York, 1900, p. 301 careful analysis — ^^guided bj" theory
sqq. — of elaborate tests upon the
^ This explains how it comes various types of engines now in
about that theoretical thermo- use. Such experiments are ac-
dynamics is still regarded with cordingly — following the example
suspicion, not to say aversion, by of Hirn — being carried out in
many engineers of the old school, i many scientific establishments in
whose knowledge is principally this country, on the Continent
baied upon experience derived from of Europe, and notably in the
the steam-engine. The first theo- : United States of America, and are
retical treatment of the steam- elaborately recorded in many
engine by Rankine in England, [ modern publications. See Pea-
and Zeuner in Germany, exhib- j body, ' Thermo - dynamics of the
ited such enormous discrepancies ' Steam - engine,' 4th ed., preface,
between theory and practice ; ; and chaps, xiii. and xiv. ; Ewiug,
the simplifying assumptions which ' 'The Steam-Engine,' 1894, p. 31.
were introduced in order to make

ox THK I'llVslCAI, VIKW OF NATURE. loT

to glance suimmirily at these revoliitiuns in ilif duiuuin
of scientific thought which the physical view, Ijy re-
garding nature as the playground of the transformations
of energy, has brought about. What I have just in-
dicated will suffice to bring some order into the account
I propose to give. There are four distinct directiims in "^•^"^
which we have to look. Firstly, there is the clearer
definition of the new ideas laid down in the new vocab-
ulary of scientific and popular language during the
second half of the century. Seamdly, there is the
revision and recasting of the whole body of ])hysical
and chemical knowledge in the light of the new insight
which had been attained. Thirdly, there is the criticism
of existing theories from the new points of view ; and
lastly, there are the fresh departures which these novel
ideas have suggested.

The first definite use of the new conceptions of power
and work, and of a scale of mechanical value, were con-
tained in the writings of Poncelet and Sadi Carnot in
France during the first quarter of the century. The
first philosophical generalisations were given by j\Iohr
and Mayer ; the first mathematical treatment was given
by Helmholtz ; the first satisfactory experimental verifica-
tion by Joule, during the second quarter of the century.
The practical elaboration of the whole system following
upon Joule's and Kegnault's experiments belongs, through
Thomson and Eankine in this country, and through
Clausius in Germany, to the third quarter of the century.
Students in our age entering on the study of mechanical,
physical, chemical, and even physiological processes, reap
the benefit of these labours by at once grasping the

138 SCIENTIFIC THOUGHT.

underlying unity and correspondence of all natural phe-
nomena, inasmuch as they all depend on the trans-
formation of a quantity, termed energy, which is in
many cases measurable in its Lest-known form — i.e., as
energy of motion — and, where this is not possible, in
the form of heat.

Helmholtz had already, in 1847, summarily reviewed
the whole field, beginning with a restatement of the
fundamental formula; of dynamics in the light of the
new principle, and ending with a reference to the trans-
formation of energy in living vegetable and animal
organisms. The key to his explanations is to be found
in the introduction of a term to denote what becomes
of energy if it ceases to exist as energy of motion or as
a velocity, when it is changed to energy of mere position.
To this end he introduces the idea of stress or tension,
h^olte'on The conception is already contained in older books on
mechanics as latent force (Carnot),^ and the purely
mathematical treatment of dynamics by Lagrange and
Hamilton had prepared the ground by showing how all
dynamical problems could be reduced to the knowledge
of two quantities, the vis viva and the force function.

gether with Monge, one of the
founders of modern geometry, of
which more in a subsequent chapter.
He introduced the principle of the

28.
Helm-

1 L. N. M. Carnot (1753-1823),
usually termed the great Carnot,
father of Sadi Carnot, member of the
Directory, War Minister, and one

of the most celebrated generals of i ' Correlation des Figures de Geo-
France, has a name • in science ! m^trie' (Paris, 1801). His books

through his ' Essai sur les Machines
en gdn^ral ' (Dijon, 1784), his ' Prin-
cipes fondamentaux de I'Equilibre
et du Mouveraent' (Paris, 1803), as
well as through his ' R(^flexions sur
la Metaphysique du Calcul infi-
nitesimal' (Paris, 1797) and his
' Th^orie des Transversales ' (Paris,
1806), by which he became, to-

were translated in Germany, where
they had a great influence. On his
connection with the history of the
conception of energy, see Bohn in
'Phil. Mag.,' iv. 300, vol. xxix. ;
also Helm, ' Euergetik,' p. 13 ; and
the Eloge by Arago of the year
1837.

ON THE PHYSICAT. VIEW OF NATURE.

I.S9

The exposition of Helmhollz, liDwever, does nol seem to
have been understood or accepted. The general recog-
nition of the relation of active and latent forces dates
rather from Thomson's and liankine's writint's in 18;")!
and the following years. Thomson uses the term
"mechanical energy" (later, from 1851, intrinsic
energy, or simply energy), and considers this quantity
to be a measure of the store of power to do work
which a material system possesses ; ^ and Itankine,'
early in 1858, introduces and defines the terms actual
(or sensible) energy and potential (or latent) energy, 29.
which are at once adopted by Thomson^ in the place tiai' and

^ "^ '^ "actual'

of the terms dynamical and statical energy, which he t-nerKy.

^ The memoir of Thomson in
which he introduces the physical
conception of the quantity "energy"
in the place of a merely mathema-
tical symbol used by Clausius, and
inaugurates the terminology of
modern physics, is contained in
the ' Transactions of the Royal
Society of Edinburgh,' vol. xx..
Part 3 (read December 15, 1851,
and reprinted in ' Math, and Phys.
Papers,' vol. i. p. 222), as an ap-
pendix to the great paper "On the
Dynamical Theory of Heat, with
Numerical Results deduced from
Mr Joule's Equivalent of a Thermal
Unit, and M. Regnault's Observa-
tions on Steam" (Trans. Kdinb.
Soc, March 1851 : reprinted in
'Phil. Mag.,' 1852, and '.Math,
and Phy.s. Pajiers,' vol. i. p. 174
tqq. ; see especially p. 186, note).
The term energy had indeed been
used by Thomson already in 1849
as a synonym for mechanical effect,
but he had not then accepted
the dynamical theory. He merely
puts the question in a footnote to
his exposition of Cariiot's theory :
" When thermal agency is . . .

spent, what becomes i>f the
meclianical etiect which it might
produce ? Nothing can be lost in
the operations of nature — no energy
can be destroyed " (' Papers,' vol. i.
p. 118, 1849).

• In a paper read before the
Philosophiciil Society of Gln-sgow,
January 5, 1853, reprinted in
'Miscellaneous Scientific Papers,'
ed. Millar, p. 203 sf/r/. See also
Rankine's note, dated 1864, in the
28tii vol. of the 4th series of the
' Phil. Mag.,' p. 404.

•* See the Proceedings of the
Glasgow Philos. Soc, January
1853, reprinted with additions
from Nichol's ' Cyclopa-dia ' (1860)
in ' Math, and Phys. Papers,' vol.
i. p. 521. In this j)a])er Thomson
also introduces the term '" electrical
capacity" of a conductor. Thom-
son subsequently introduced the
word " kinetic " in place of " actual "
energy. See also Thomson's Lec-
ture before the Royal Institution,
February '29, 1856, rojirinted in
' Math, and I'iiys. PajK-r.t,' vol. ii. p.
182, and ' Pojiular lectures,' vol.
ii. p. 418, especially the note U) p.

140

SCIENTIFIC THOUGHT.

had employed before. How little these ideas, which
have now been introduced into elementary text-books
as the very alphabet of physical knowledge, commended
themselves in that age, except to a few intellects that
had been occupied for many years trying to fix precise
terms which should be capable of mathematical defini-
tion, and at the same time correspond to common-sense
experience, is evident, inter multa alia, from the criti-
cism by Sir John Herschel in 1866,^ Here it is
maintained that the use of the term " potential energy "
" is unfortunate, inasmuch as it goes to substitute a

425. A very complete and careful
historical account of the gradual
invention and crystallisation of the
vocabulary of the energy concep-
tion is given by Helm, ' Die Lehre
von der Energie,' Leipzig, 1887, p.
36 sqq.

^ The passage quoted appears in
an article " On the Origin of Force,"
by Sir John Herschel, in the first
volume of the ' F'ortnightly Re-
view,' 1865, p. 439. The article is
well worth reading for those who
wish to realise the enormous benefit
which has been rendered to science
by banishing the indefinite use of
the word force and by introducing
the term energy, restricting the use
of force to the meaning attached to
it by Newton. Sir John Herschel
still speaks of the ' ' conservation of
force " (as did likewise Helmholtz,
who, however, very early introduces
the term Arbeitskraft, power to do
work, thus removing all ambiguity).
Rankine replied to Herschel's criti-
cism in a paper read before the
Glasgow Philosophical Societj^ 23rd
January 1867 (reprinted in 'Mis-
cell. Scient. Papers,' p. 229 sqq.)
He there states that the quantity
itself occurs as a mathematical sj-m-
bol in Newton's ' Principia ' (prop.
39), but till recently had received

no appropriate name. He closes his
remarks by the still more import-
ant reflection : " One of the chief
objects of mathematical physics is
to ascertain, by the help of experi-
ment and observation, what phy-
sical quantities or functions are
'conserved.'" As such he enum-
erates mass, resultant momentum,
resultant angular momentum,
total energy, thermo-dynamic func-
tion. Whilst this physical problem
was being defined by Rankine,
Cayley, Sylvester, and Hermite
were working at the corresponding
problem in pure mathematics to
decide what properties or quanti-
ties remain unaltered {i.e., in-
variant), if an arrangement of
several algebraical symbols is sub-
jected to algebraical operations.
It is the modern doctrine of " in-
variants." This doctrine has led to
an enormous extension and simpli-
fication of the theory of mathema-
tical forms or quantics. It is the
key to all mathematical tactics, and
prepares a useful instrument for
the application of mathematics to
physical problems. See Major Mac-
Mahon's Address to the Mathema-
tical Section of the British Associa-
tion, Glasgow, 1891.

ON THE PHYSICAL VIKW OF NAT(-RK. 141

truism for a j^reat tlyiuiiuical fact " ; an admission
which would mean that it brings common-sense and
precise mathematical expression into close proximity
and harmony, or describes a very general jihenomenon
completely and in the simplest way.

In order to become generally recognised as the
simple alphabet of scientific language, the new ideas
had to be made the foundation of the whole structure
of physical and cliemical knowledge, theoretical as well
as experimental ; the elements and axioms had to l>e
restated so as at once to express the new view and to
open out the enlarged aspect which had been prepared.
The different departments of mechanics, pliysics, and
chemistry had to l)e elaborated and co-ordinated ac-
cording to a uniform design. Helmholtz had indeed,
as early as 1847, roughly sketched the plan of the
work, but occupied as he was during the twenty fol-
lowing years mainly with another much-neglected field,
the analysis of the phenomena of sensation, he did not
return to his original thesis till many years later, when
he made an application of fundamental importance.

Meanwhile the important task of rebuilding the edifice
of the physical sciences, and establishing on a large scale
that which I term the physical view of nature, fell
almost exclusively into the hands of what we may call
the Scotch school of natural philosophy — James and 30.

-,, , . T « '1 1 ^'"^ Scotch

William Thomson, Macquorn Kankme, -James LlerksciuHji.
IMaxwell, P. G. Tait, and Balfour Stewart, in this country ;
whilst Clausius abroad worked almost alone. IJankine
and James Thomson very early (1855) conceived the
idea of a general science called " Energetics " or " the

142 SCIENTIFIC THOUGHT.

abstract theory of physical phenomena in general." ^
It is only in our day, after the lapse of a quarter of
a century, that these ideas have been taken up by
others, and that the plan begins to be realised. The
reasons why at the time it was abandoned were
manifold.

To begin with, it was soon found, notably by Joule,
Helmholtz, and William Thomson, that the new prin-
ciple of the conservation of energy, if applied to various
other phenomena outside of the narrower field of ther-
motics, led to a co-ordination and comprehension of
them which was then quite unexpected : opening out
new aspects, disclosing unknown properties, and sug-
gesting innumerable experiments. As instances I may
refer to the thermo-elastic and thermo-electric pheno-
mena of bodies, which very early occupied the atten-
tion of the founders of the theory of energy. The
discharge of the Leyden-jar, the generation of electric
currents in the voltaic cell, the heat of electrolysis,
the actions of permanent magnets and those between

^ In a paper read before the to find a general rule for the trans-
Philosophical Society of Glasgow, , formation of energy (' Lehre von
May 1855, entitled "Outlines of ] der Energie,' 1887, p. 63). That
the Science of Energetics," and re- ] such a general rule can in the
printed in 'Miscellaneous Papers,' ; present state of our knowledge

be established on purely energetic
principles is upheld by some (Ost-
wald. Helm) and disputed by

ed. Millar, p. 209 sqq. See for the

above definition p. 228. James

Thomson's contribution is to be

found in a paper on '* Crystalliza- others (see especiallj' Planck,

tion and Liquefaction," read before " Thermodynamik,' 1897, p. 71

the Royal Society, December 5, | sqq.), who state their conviction

1861, in which he establishes and
gives examples of the application
of "a general physico-mechanical
principle or axiom," which indi-

that the " energj'-principle clearly
does not suiBce for the definition
of natural processes." The whole
discussion merges into a philos-

cates when a " substance or system i ophical question, of which more
will pass into the changed state." later on.
As Helm says, it is a first attempt

ON THE PHYSICAL VIEW OF NATIKE. 143

electric curreuls and nuignet.s, tlie pheiiomeiui of dia-
magnetisia, Ampere's theory ami \Vel)er's ImhIs of
electric measurement, Seebeck's production of electric
currents by heating in a non-li(»mogeneous conductor,
the remarkable phenomena known by the name of
Peltier, the electro -dynamic properties of metals, the
thermo- elastic properties of matter, were all studied
in the light of the new principle, the conservation
and transformation of energy. Another very import-
ant problem presented itself, vi/., the introduction of
the new ideas into the higher educational literature,
the re -writing of the text -books of science on the
basis of the principle of energy, and especially ihe
development of the fundamental notions in mechanics
in conformity with the more modern views. Here,
then, it became evident that the physical view of
natural phenomena, according to which they are all
instances of the transformation of energy, could l)e
considered and expounded as a further development of
the laws of motion as laid down in Newton's ' Prin-
cipia.' It was especially the third law of motion, in
which Newton stated the equality of action and re-
action, that lent itself to such an interpretation a.s
would at once lead to the wider grasp and deeper
insight into natural processes which the principle of
energy afforded. Accordingly about the year 1860,
when the new ideas on energy had, in the nuntls of
the great pioneers, acquired that importance which
has enabled them to become the basis of a more
and more comprehensive view — the physical view — of
natural phenomena, the necessity was experienced of

144 SCIENTIFIC THOUGHT.

bringing them into harmony and continuity with the
older Newtonian ideas. These had been only imper-
fectly transmitted by the many commentaries and text-
books of the Cambridge school. The same was the
case in the system of Lagrange, in which the whole
of mechanics had been reduced to a mathematical ex-
pression, the physical and experimental foundations
being pushed aside. The ' Principia ' of Newton was
again studied, and re -edited in the unabridged form,
and an interpretation and amplification of the third
law of Motion— so as to embrace the principle of
energy — was made the key to the science of dyn-
amics. Dynamics was not taught after but before
statics. Statics was treated as a special case of the
theory of motion. To make the new position still
more marked, it was proposed to make the term
dynamics the general term which embraces kinetics
and statics as subdivisions, and to reserve the word
" mechanics " for the science of machines. The change
which then took place in the didactic methods can
be seen by comparing the first and second editions of
the well-known treatise by Tait and Steele on ' The
Dynamics of a Particle.' The real compendium of the
new doctrine is the treatise on Natural Philosophy by
31. Thomson and Tait, which has probably done more than

Thomson

and Tait. any other book in this country to lead the mathe-
matical studies at the foremost universities and colleges
into paths more useful for physical and experimental
research. The greatest exponent of the new ideas was
James Clerk Maxwell, to whom is also due the merit
of having applied them for the purpose of testing and

ON THE PHYSICAL VIEW OF NATLUK. l-4o

conlinuinif the worth ul' the tieiisure which lav hidden
in the experimental researches of Faraday. Next to the
handbook of Thomson and Tait, no writings prohahly
have done mr)re — especiall}' outside of England, on the
Continent and in America — than those of Maxwell to
revolutionise the teaching of natural philosophy.

I must now revert to what I said in the last chap-
ter regarding Maxwell's attempt to ijut the ideas of 32.
Faraday on the comnninication of electric and magnetic Maxweii.
phenomena through space into mathematical language —
i.e., into measurable terms. T there related how Max-
well's earliest treatment of the subject was an attempt
to construct a mechanical model of the dielectric that
would be capable of exhibiting and transmitting the pro-
perties of stress — i.e., of tension and pressure — which
the experimental researches of Faraday had partly de-
monstrated and partly suggested. In the sequel, as
was said, he desisted from this attempt, which lias
since been taken up and further elaborated by others,
and resorted to a different train of reasoning. This
line had been suggested by the introduction of the
doctrine of energy into all phy.sieal research. As the
work of scientific chemists was for a long time ex-
clusively governed by the application of the principle
of the constancy of weight or conservation of matter,
so, when once the mathematical expression of the
various forms of energy had been correctly established,
it became possible to arrive at a multitude of relations
of physical quantities merely by a})plying the ])riiu'ij.le
of the constancy of the quantity of energy. In this
way the principle of energy is a kind of regulative
VOL. IL K

14:6 SCIENTIFIC THOUGHT.

principle, one which allows us to deal with the grand
total or outcome — mathematically called the integral —
of physical processes and changes without necessarily
possessing a detailed knowledge of the minute elements
or factors — mathematically called differentials — out of
which they are compounded. Inasmuch as what we
actually observe are always integral effects — -i.e., sum-
mations or aggregates of great numbers of indi^ddual
and unobservable processes — this line of reasoning is
not infrequently very useful, and has been in many
cases applied to arrive at important conclusions. In
fact, it is the analogue in science of the method accord-
ing to which practical men very often succeed in carrying
on extensive business transactions, of which they possess
a merely external though accurate knowledge ; or of the
balance-sheet of an industrial undertaking which exhibits
and guarantees the correct result, though only the profit
and loss account and the ledgers would show how this
result has been arrived at.
33. Faraday had taught us how to look upon any given

Faraday. . . . ^ • -i t ■ -i-i

portion or space m which electric, magnetic, chemical,
and thermal changes were going on as a connected system,
which he termed the electro-magnetic field. He and
others — notably Oersted, Ohm, Weber, Lenz, and Joule
— had shown how the different occurrences in such a
system could be reduced to a common measure, and how
they were observably connected. Maxwell brought all
these phenomena together under the term " energy of
the electro-magnetic field," and set himself to study the
possible forms and changes of this quantity under the
law of the conservation of energy — i.e., as the preser-

ON THE PHYSICAL VIKW OK NATURK. 147

vation of the sum-total of the energy. TIiIh energy
could exist as motion (actual or kinetic energy), Ixiing
either motion of electricity as in the current controlled
by the law of Ohm, or motion of ponderable masses, such
as magnets or electric conductors ; or it might be dis-
sipated energy — i.e., energy apparently lost in the form
of heat — controlled by the law of Joule, or, to complete
the summation, it might be stored-up energy — potential
energy. Faraday's researches had suggested where this
store was : it was in the surrounding space, which must
be considered as capable of being strained or put int(j a
condition of stress, as elastic bodies are capalile of being
strained. Thomson and Tait had shortly before shown
how to submit the properties of elastic systems to cal-
culation in the most general manner, by studying the
modes in which energy, actual and potential, was dis-
tributed in them, whether at rest or in motion. The
way seemed then paved for Maxwell to consider with the
greatest generality the properties of the electro-magnetic
field, reducing them all to mechanical measures. This he
did b}' introducing the generalised conception of a dis-
placement or strain wliich exists in the field, and which
is commimicated as a periodic or vibratory motion with
a velocity dependent on the properties or so-called con-
stants of the medium. It is known how he succeeded in
identifying very completely all the various experimentally
ascertained electric and magnetic phenomena, fixing their
nature and quantities in conformity with experience,
and arriving finally at the suggestion that the velocity of
tlie transmission of the electro-magnetic displacement in
air must l)e the same as that of light, the latter being.

148 SCIENTIFIC THOUGHT.

in fact, an electro-magnetic disturbance of very short
wave length. I also mentioned above how this sug-
gestion received a brilliant confirmation from Hertz when
he succeeded in exhibiting electro-magnetic waves, which
in travelling through space, though not luminous, showed
all the properties peculiar to light waves, such as re-
flexion, refraction, polarisation, &c.

Whilst in this country, during the period from 1850
to 1870, the Scotch school of natural philosophy was
thus occupied in rebuilding the whole edifice of physical
science on the new basis afforded by the energy ideas,
Clausius in Germany worked at the further elaboration
of the dynamical theory of heat, and, as I stated above,
at the kinetic theory of gases, without abandoning the
astronomical view of natural phenomena, which, with its
supposition of forces acting at a distance, still almost
exclusively governed theoretical physics and chemistry
abroad. No one did more to emphasise the difference
between this and Faraday's views than Clerk Maxwell,
who had welded the latter into a consistent scheme by
means of the conception of energy. About the year
1870 Helmholtz again appeared as a leader of scien-
tific thought in this domain, and placed himself at
the head of a movement which by degrees almost
completely swept away the older ideas. It was by him
or at his suggestion that many of the more modern
English works of science were translated ^ and intro-

1 Notably Thomson and Tait's natural philosophers of eminent
* Natural Philosophy, ' and several i rank abroad who broke with the

of Tyndall's well - known more
popular works on ' Sound,' ' Heat,'
and ' Fragments of Science.' Helm-

older habit of exclusiveness which
clung to academic teachers in Ger-
many, and who followed the English

holtz was also one of the first example set by the " Addresses " of

ON THE PHYSICAL VIEW OF NATIKK.

149

duced in (Jermany, and that especially the ideas of
Faraday and Maxwell were popularised, expounded, and
submitted to elaborate tests. These culminated in the
brilliant discoveries of Hertz already referred to.

As in his earlier researches into the connection of the
phenomena of heat and mechanical work, so in these
later ones concerning the electro-dynamic laws, Helm-
holtz seems to have approached his subject primarily in
the interest of physiological ^ science. At that time

34.

HelmholU
on electro-
d/uimicii.

tlie British Association and tlie still
older "Lectures" of the lloyal
Institution. Before his time there
were only rare instimces — notably
those of Bessel, Liebig, and Hum-
boldt— where .scientific thinkers of
the tirst rank condescended to intiu-
ence general opinion and polite
literature by .stej)ping down from
the university chair into the arena
of a popular audience. No other
German scientific thinker has left a
collection ecjual to Hehnholtz's
' Vortriige und Reden,' not even
Bessel, whose ' Popul;ire Vorlesun-
gen liber wissenschaftliche Gegen-
stiinde ' (ed. Schumacher, HamburL',
1848) are too little known. Du
Bois-Reymond's ' Reden ' are a mine
of information on the history of
science, and von Baer's ' Reden '
(Braunschweig, 1886) cont^iin some
excellent and original discourses.

^ Emil du Bois - Reymond, iu
many passages of his reniarkaVde
addresses, an,d latterly in his ap-
preciative Eloge of Helmlu)ltz
(Leipzig, 1897), has preserved the
historical data for a genetic history
of Hehnholtz's electrical researches,
which, beginning in 1851, and cul-
minating in Hertz's brilliant ex-
periments on the " rays of electric
energy " in 1888, completely
changed the aspect of electrical
science in Germany and to a less
degree in France. The older view.

based upon a mathematical develop-
ment of the fundamentiil concep-
tion of Ampere and mainly asso-
ciated with the brilliant name of
Wilhelm Weber, whose very ex-
tensive and accurate mea-sure-
ments largely supplied the material
for the modern theory, is pnic-
tically unknown to electricians in
this country. No English text-book
contains even a reference to a view
which was once dominant abroad,
and which for this reason forms
a very interesting episode in tiie
history of thought. In the fourth
chapter I have referred to this
view as, beside the theory of Bos-
covicli, presenting one of the moat
remarkable apj>lication8 of the as-
tronomical view of nature, which
originated in this country but was
mainly cultivated by the French
school. I must now briefly refer
to the counter-movement, which
in Germany is mainly identified
with the name of Helinholtz. He
may be said to have left the mark
of his genius on the scientific
history of his country as Lonl
Kelvin has done on that of Eng-
land. His collected pajiers sliow us
— and du Bois-Reymond tells us —
how Hehnholtz's interest in elect-
rical problems was connected with
the remarkalfle jjlicnomena of ani-
mal electricity, to the exploration
of which the former devoted Ids

150

SCIENTIFIC THOUGHT.

there existed three different theories which aimed at
finding a general formiila or law that should embrace
all known electro-dynamic phenomena. The two earlier
ones were propounded independently and about the same

life. Du Bois-Reymond was a pupil
of Johannes MuUer. One of the
merits of Miiller's school was to
have made the discoveries of phy-
sics useful for physiology and medi-
cine as the school of Liebig made
those of chemistry. Helmholtz
was trained in the school of Midler,
but he also came largely under
the influence of Franz Neumann
of Konigsberg, the great teacher of
mathematical physics, and of Gauss
and Weber, the originators in Ger-
many of the system of absolute
measurements. It is known that
the interest in electrical phenomena
received a great impetus through
Galvani's and Volta's discoveries.
But as du Bois-Reymond (' Reden,'
vol. ii. p. 389) tells us, the galvanic
pile constructed by Volta withdrew
attention from the phenomena of
animal electricity to the much
more powerful actions of artificial
arrangements of metals and solu-
tions. The study of animal electric-
ity was for a time continued only by
Italian professors, and beyond the
seas by Alexander von Humboldt
in his observations on the torpedo ;
and had to wait till the school
of Miiller, and notably du Bois-
Reymond, approached the subject
methodically with the methods
and ideas of modern science. This
was in the fifth decade of the
century. Modern science in Ger-
many had, however, studied the
properties of the galvanic current
exhaustively only in linear (one
dimensional) and in closed circuits
or conductors. The phenomena of
nervous and muscular electric cur-
rents demanded the study of sud-
den and repeated electrical impulses,
and of the behaviour of currents

in two and three dimensional con-
ductors, and in unclosed conductors
or circuits. Incited by du Bois-
Reymond, Helmholtz undertook to
deduce from the formula; of
Ampere, Neumann, and Weber the
action of electric currents in these
modified conditions. It was then
found that these formula; gave
indefinite results and required to
be modified or amplified. After
many years of thought and research
Helmholtz arrived at a generalisa-
tion which comprehended all the
different existing theories as special
cases. He then — in addition to a
masterly mathematical discussion
— betook himself to devise spe-
cial experiments to decide which
of the three possible expressions of
the general formula came nearest
the truth. A perusal of the me-
moirs contained in the first volume
of his ' Wissenschaftliche Abhand-
lungen ' (pp. 429-8-20) shows how
by gradual and strictly logical steps
he convinced himself of the in-
trinsic correctness of Faraday's con-
ception, which, in addition to the
phenomena in linear conductors or
wires, constaiatly took notice also of
those of the surrounding medium
or space — i.e., of the electro-
magnetic field. Looking back from
our present position on the develop-
ment of the ideas concerning elec-
tricity in motion, we can say that
Continental thinkers tried to gain
a correcter and more complete un-
derstanding by a mathematical,
English science by a phj'sical, ex-
tension of the then existing notions.
Helmholtz in his Faraday Lecture
(1881) showed how both courses,
consistently pursued, lead to the
same result.

ON THE PHYSICAL VIKW <>K NATL'KK.

151

time by Franz Xeuiuuun and Wilhehu Weber; the later
one was the theory of Maxwell Ijased upon the totally
different view which was maintained and gradually
unfolded in the experimental researches of Faraday.
The two former looked to the effects *»f tin; action of
electricity at measurable distances, and has Ijeen Ciilled
the telescopic view ; the latter reduced these to the
action which takes place in contiguous portions of matter
or of space, and has been called the microscopic view.
Helmholtz first of all, by an independent line of reason-
ing, brought the tliree mathematical formulae in which
these different views found expression under one com-
mon formula, of which each appears as a special case,
and then proceeded by theory and experiment to decide
which of the three possible special forms is to be adopted.
As a theoretical test he applied the j^rinciple of the
conservation of energy in a manner in wliicli it had
at that time hardly been used by ContiuenLal thinkers.
His reasoning, which was largely discussed and criti-
cised by eminent philosophers, gave to this principle
the prominence and im])ortance wiiieh it has ever
since maintained in all Continental treatises. It
meant the introduction of the physical view of natural
})henomena.^

^ In England the publiwition of
Thomson and Tait's ' Natural Phil-
osophy ' formed, as stated above
(p. 144), an epoch in the teaching
of the physical sciences, notalily
through the prominence given to
tlie piinciple of tlie conservation
of energy. A similar epoch was
created in Germany, not so much
by Helmholtz's enunciation of the
principle in 1847 as by tlie use he

made of it, in one remarkable in-
stance, in reviewing and criticising
the existing and apparently conflict-
ing theories. As Lavoisier intro-
duced the chemical balance — baf.ed
upon the conservation of matter —
as a test for the coriectness of chem-
ical statements, so Helndioltz used
the princijjle of the conservation of
energy in two distinct forms, an a
test of the validity of electrical

152

SCIENTIFIC THOUGHT.

In the mean time this view had gained great support
by the efforts of quite a different section of scientific
workers, wliose labours had opened out a new and
promising field of research. The new field for a con-
siderable period belonged almost as exclusively to foreign
science as the energy- conception had for twenty years
belonged to this country. Early and for the most
part isolated labourers were Kopp and Hess in Germany,
Eesnault and Berthelot in France, Julius Thomsen in
Copenhagen.^ They (with many younger men) can be

statements. These two forms were
the impossibiHty of a perpetual
motion and the equality of action
and reaction. See his Faraday
Lecture, 1881. Both in the posi-
tions of Thomson and Tait and of
Helmholtz the principle of energy
is, however, like Lavoisier's prin-
ciple, purely a regulative, not a
constructive, principle of scientific
research. It exerts a control and
enables us to check the correctness
of results. Both in chemistry and
physics other principles or methods
are required for extending — not
merely correcting — our knowledge.
Such principles are in the abstract
sciences the formula of gravitation,
the atomic theory, the ether ; in the
natural sciences the morphological
and genetic theories. The whole
domain of physics and chemistry
has been reviewed for teaching pur-
poses from this point of view by
Hans Januschke, ' Das Princip der
Erhaltung der Energie,'' Leipzig,
1897. See p. 14 sqq.

^ Although the history of thought
has more to do with theories than
with the mere discovery of facts,
and with the latter mainly when,
as in exceptional instances, they
change the scientific aspect of phe-
nomena, I think it important to
mention specially the great merit

of Victor Reguault's experimental
researches. How much the progress
of phj'sical and chemical theory is
indebted to his elaborate and ex-
tremely accurate measurements of
many physical constants may be
seen by the perusal of Lord Kel-
vin's earlj' memoirs on the dynami-
cal theory of heat. The several
(so-called) laws of Boyle, Dulong,
and others were subjected by Reg-
uault to exhaustive tests ; the be-
haviour of steam in the steam-
engine formed a subject of
elaborate investigation ; the proof
that chlorine could be substituted
for hydrogen in hydrocarbons sup-
plied a prominent support to the
chemical theories of Laurent. In
general Regnault's work is a model
of accuracy supported by great in-
genuity in the construction of
apparatus and the surmounting
of difficulties. Like Liebig, he was
the master of many pupils who sub-
sequently became eminent. Besides
being professor of chemistry and
physics in Paris, Regnault was
actively connected with the cele-
brated porcelain works of Sevres.
Similar remarks might be made
with reference to the labours of
Hermann Kopj), who v?as for many
years probably the only professor
of physical chemistry in Germany.

ON THE PHYSICAI, VIKW OF NATL'UK. 153

considered as the founders of the modern science of
physical chemistry, which has received an elaborate ex-
position in the great work of Trofesscjr Ostwald. This i . -

cheiQiiitrjr.

work is probably quite as epoch-making in the domain of
chemistry as Thomson ami Tait's 'Natural riiilosophy '
has lieen in tliat of physics.

1 liave already explained how in the development of
chemistry the attention of its great representatives was
almost entirely absorbed in gaining a knowledge of the
different substances with which they had to deal, and
how through preoccupation with the natural history of
matter, its decomposition, analysis and synthesis, and
appropriate classification, the other more scientific ques-
tions regarding the physical agencies which were at
work in chemical processes — constituting the doctrine
of chemical affinity — were almost completely neglected.
This I traced largely to the influence of that powerful
instrument of exact research, the atomic view, which
had been introduced into chemical science through
Lavoisier autl JJalton.^ The pursuit of physical chem-

' It is not an unusual exjjerience pened when the older ])hlogi.ston
to find that the change froui one , theory was disiielled bj- the atomic
theory to another, though an ad- ' theory and all attention was oon-

vance from disproved to more cor-
rect views, is also accompanied by
some loss either in defiiiiteness or
in actual knowledge of facts. The

centrated upon change of weiglit.
The older theory maintained that
when a metal is calcined it loses
something — viz., phlogiston ; tlie

undulatory theory lo.st the definite new theory had proved that it gains

notion of a rectilinear ray of light, something — i.e., weight in the form

which was only regained by pro- of combined oxygen. More recent

longed and difficult analysis ; the knowledge has shown that both

electro-magnetic theory of Maxwell theories are right. It gains weiglit

has not as yet given a clear repre- and loses potential energy, or power

sentation of those electrical charges to do work — i.e., to coMil>ine, giv-

which the older thcoiy of Coulomb ing rise to molecular motion or

and Weber introduced in the form , heat. The phlogiston theory con-

of stationary or moving electrical I tained the correct idea that besides

masses. Something similar hap- ' matter there is sometijiiig else —

154

SCIENTIFIC THOUGHT.

istry, the consideration of chemical as related to other
physical forces, such as gravitation, heat, or electricity,
though it very greatly occupied the pioneers of chemical
science in the early years of the century, — notably
Berthollet and Gay-Lussac in France, Dalton and Davy
in England, Berzelius in Sweden, — fell gradually into
popular disfavour; so much so that even Faraday's
electrolytic law had hardly any influence on the de-
velopment of chemistry.-^ This one-sided direction of
chemical reasoning and observation was still further
promoted by the great practical and technical results
which followed from the atomic conception, the ease
with which processes worked out in the laboratory
could be imitated on a large scale in the factory and
the workshop. It was the increased power over matter
and its manifold transformations which followed im-
mediately in the wake of atomic chemistry that
gave it its interest, notably when through the study
of the carbon compounds — incorrectly termed organic
chemistry — new industries of undreamt-of magnitude
and importance were created, and when through chemical
knowledge the older methods of metallurgy were rapidly
superseded. To the popular mind the result is always
more interesting than the process of research or of
reasoning which leads up to it ; the possession of the
product than the knowledge of the procedure. The

viz., energy. That the correct idea
contained in the phlogistic concep-
tion was not at once given up, but
only gradually lost sight of, is seen
from the fact that Lavoisier's first
table of elements contained 'caloric '
as one of the simple bodies. See

Kopp, ' Entvrickelung der Chemie,'
p. 209.

^ On the causes of this see Helm-
holtz's Faraday Lecture (' Wissen-
schaftliche Abhandlungen,' vol. iii.)
and Ostwald, ' Allgemeine Chemie,'
2nd ed., vol. ii. part 1, p. 530.

ON THE PHYSICAL VIEW OP NATUHE. I.'i5

new substance witli sUiiLling properties — be tliey useful
or only curious and rare — has almost innuediately a
value, whereas the manifold transformations by which
it was discovered, invented, or produced escape general
notice, and are accordingly of secondary interest. This
interest grows in proportion as another factor of ec^ual
commercial importance gradually and slowly asserts
itself, namely, the factor of cost of ])roducti(jn, the 3«.
property through which not only the material itself, "e.«if in
but also the labour bestowed upon it, and the most
intricate transmutations and secret manipulations, gain
a place and definite figure in the ledger of the
accountant. Those of us who entered into practical
life about the beginning of the last generation of the
century know well by experience how then for the first
time was being established the great system of statistics,
of cost of production, which now governs every well-
conducted industry and manufactory, though in general
this department is still but little understood. Now, in
proportion as with progressing civilisation we come more
and more to use artificially prepared products in the
place of natural ones, the cost-figures become more com-
plex : there is not only the raw material and the labour
of getting it, not only the general economy of arrange-
ment and administration by which we save labour and
avoid waste — there is the whole aggregate of changes
and processes, manual, mechanical, and chemical, through .
which the raw material has to pass. These must all
have a common measure 1)y which they possess a iigure
of value in the ledger of the book-keeper, otherwise the
latter r-nuld not ]>ro(luce a statement of cost. Watt,

156 SCIENTIFIC THOUGHT.

when supplanting manual labour on a large scale by the
introduction of his perfected steam-engine, had suggested
the term " horse-power " as the common measure of both ;
and the French mathematicians, who treated mechanics
with a view to practical application, had introduced the
term " work," In the general industries, however, — out-
side of special branches, notably marine engineering, —
these measures were very crudely applied ; they became
unintelligible and meaningless where other agencies —
notably those of chemistry and electricity — had to be
employed. It is only since the terms " power " and
" work " have been enlarged and the more general con-
ception of energy introduced that it has become possible
to measure the new forces or agencies in terms applic-
able to all alike. Practically as well as theoretically
the system of measurement remained imperfect so long
as the energy of chemical combination could not be
measured in the same way as Watt measured the
energy of heat, and as Joule and others taught us
how to measure the energy of an electric current. The
term " energy " has thus become as important a con-
ception for practical as it has been long recognised to
be for purely scientific purposes. If the only power
we use is manual labour or steam power, there exists
a crude way of measuring both by the hands employed
and the weight 'of coal burnt ; but electrical power is
not so exclusively dependent on a personal or material
item, and thus it can only be measured by a system in
which the several items of cost are reduced to a common
term. It is through the wholesale introduction of the
electric current as a practical agent that the thing called

ON THK PHYSICAL VIKW OF NAM KK. Ifj?

" energy " has become a commercial commodily us it hud
liefore become a scientific measure.

That chemical reactions are connected with meciiun-
ical, gravitational, optical, caloric, and electric phenomena
has been known for a long time. Each of these mani-
festations has therefore been studied as attbrding a
measure of the energy of chemical reactions, and these
have in turn been looked upon as results of attrac-
tions, or of mass actions, or of thermal conditions, or
of electrical polarities. We have thus mechanical,
I hermo- chemical, electro -chemical theories of atlinity.
\'aluable discoveries and important suggestions have
also been arrived at by these special researches : we
have the laws of mass-action suggested by Berthollet
and revived in modern times by Guldberg and Waage ;
the all-important electrolytic law of Faraday and the
so-called third law of IJerthelot in therrao-chemistrv ; 37.

Berthclot

further, the important researches of Kopp and Hess, and ost-
Xone of these discoveries, however, seemed really to
grasp the whole subject of chemical reaction, and ac-
cordingly they remained for a long time unknown, or
fell, after a short life, into oblivion and disrepute. It
has been one of the greatest performances of the last
twenty years of the century to have approached the
all-important question, " What is chemical affinity, and
how is it to be measured ? " in a comprehensive spirit,
and to have brought it to the verge of solution. The
merit of having done this belongs the more incon-
testably to l*rof. Wilhelm Ostwald,^ because no one

' Prof. Ostwald's principal woik Chemie,' of which tlie first edition
is the 'Lehrbuch der allgemoiuen ' appeared in two volumes (lAMi)zig,

158

SCIENTIFIC THOUGHT.

has taken such pains as he to gauge the value of
many single and isolated steps that had been taken
before him, and to combine them all through his own
researches into a comprehensive doctrine. The practi-
cal importance of these labours — so long insufficiently
understood — will doubtless in the near future be real-
ised in proportion as the increasing competition of in-
dustry shall emphasise the necessity of studying the eco-
nomics of production : this economy consisting not only
in the absence of waste of matter, but likewise in the
saving of work — i.e., in the absence of waste of energy.^

1885-87) ; the second edition, of
which the first volume appeared
in 1891, is in progress, and will
comprise three volumes. It is
divided into three parts : Stochio-
mctrie, Chemische Energic, and Vcr-
ivandtschuftslchrc. Nothing can
give a better idea of the enormous
development of chemical science
in the nineteenth century than a
glance at those two monuments of
learning and research, Beilstein's
' Organische Chemie ' (Leipzig,
1893-1900, 5 vols., 3rd ed.) and
Ostwald's ' AUgemeine Chemie.'
They form the basis for future
development, as did Leopold
Gmelin's ' Handbuch der Chemie '
for the greater part of the past
century. The first edition of
Gmelin appeared in 1817. See
Kopp's ' Geschichte der Chemie '
(vol. ii. p. 100). Since the publi-
cation of his great text-book, Prof.
Ostwald has done enormous ser-
vice to science by the foundation
jointly witli Prof, van't HolF of the
' Journal fur physicalische Chemie,'
in 1889, and still more by the open-
ing of the first laboratory specially
designed for physical chemistry, in
Leipzig, in the year 1887. But
perhaps the most original and
suggestive work of Ostwald is

his work on the scientific founda-
tions of Analytical Chemistry
(Leipzig, 3rd ed., 1901. Transl.
by G. M'Gowan).

' How recent is the systematic
treatment and general recognition
of physical, theoretical, or general
chemistry can be seen from the
historical sketches which had been
published prior to Ostwald's great
work. Kopp, in his excellent ac-
count of the development of chem-
istry, published in the Munich col-
lection, and frequently referred to
in the fifth chapter of this work
(vol. i. pp. 382, &c. ), has hardly any
occasion to refer to physical chem-
istry up to the year 1870. This
is the more remarkable as Kopp
himself was a solitary ingenious
worker in this isolated province.
A good account of his labours
is contained in Thorpe's ' Essaj's
in Historical Chemistry,' 1894,
J). 299. A later and brilliant
writer on the historical growth
of chemical knowledge, Dr A.
Ladenburg, in his ' Vortriige iiber
die Entwicklungsgeschiclite der
Chemie' (2nd ed., Braunschweig,
1887), condenses all he has to sa^'
regarding this subject into a few
pages in his last lecture. If Ger-
man science is destined to dis-

ox THK I'llYSKJAL VIEW OF NATrKK.

15 'J

Tlie ideas through which unity and L-(jhereiiee have
been introduced into the many diil'ereut trains of reason-
ing whieli were henL upon unnivclhng the myHteries
of chemical attinity came from an unexpected quarter
— from the country whicli, in the early part of our
century, had become, through Jierzelius, the centre of
a great school of chemical research. Vroi. Ustwald,
in his recent historical sketch of the doctrines of
chemical attinity, dates the latest ])eri(jd frum the year
188G,' when Svante Arrhenius j)ul)lislied his t]ie<»ry as
of the chemical solutions decomposeel liy the galvanic
current, the so-called electrolytes. That the reader
may understand what importance belongs to this latest
development of physical chemistry, I must go further

Arrbeiiiuit.

tinguish hert^elf in the wider
spliere of general or physical
chemistry as much as she has
done in the past l>y the extreme
and one-sided culture of organic
or structural chemistry, it will be
largely owing to the influence of
the school of Ostwald and that
of tiie industrial factor mentioned
in the text, which nowadays em-
phasises as nmch the economical
control of chemical reactions as
it (lid formerly the discovery and
preparati(jn of new com|)ouuds.
The ultimate success in the in-
dustrial preparation of artificial
indigo, which was theoretically
l')ng known, is an example well
worth careful attention.

' Prof. Ostwald had himself
about the same time made an
attempt in the second volume of
the first edition of his great work
to unite the rlisjccta mimbnt of
l>hysical chemistry, notably of the
tlieory of affinity, into a .system-
atic whole. This first attempt
may have contributed quite a.s

nmch as the special labours of
others, among whom he mentions
specially Helmholtz, Van't HoB',
Duhem, Planck, and Arrhenius, ti>
create an era in chemistry. 1 1
may also be noted that, like every
other important step in chem-
istry, this latest theoretical piia.se
is characterised by violent contro-
versies. The.se became more pro-
niiunced as Prof. Ostwald intro-
duced into the second eilition of
his work the idea of "energetics"
as a general and sufficient basis
for the whole of physics and
chemistry ; making a very emphatic
j)rotest against the older jihysical
theories, based upon attractions,
atomism, or kinetics, whidi he
stigmatises as mechanical. On
this important controver.sy I shall
have to report at the end of the
])i'csent chajiter, where I shall al.io
give the full literature of the sub-
ject. In the meantime, see also
Ostwald, ' Allgenieine Cheniie,' vol.
ii. part 1, preface, and i>art -, p.
182 .•«/<].

160 SCIENTIFIC THOUGHT.

back in the history of the subject and draw attention
to the gradual change which the nineteenth century
has brought about in our ideas regarding the different
states in which matter is supposed to exist, be it
in motion or in rest : the solid, the liquid, and the
gaseous states.

Not very long ago the impressions of common-sense,
according to which a fundamental difference separates
solid from liquid and liquid from aeriform bodies, per-
meated scientific treatises also. Eigid demarcations
were maintained between hydrostatics and pneumatics,
and likewise between the doctrines of bodies at rest
and such as are in a state of perceptible motion.
One of the most marked changes which the centmy
has witnessed, has been the breaking down of these
older landmarks of science. The state of rest — once
supposed actually to exist — has had to give way to a
state of concealed yet measurable motion, as in the
case of the kinetic theory of gases, which explains dead
pressure by the bombardment of innmnerable particles
darting about. The idea of dynamical equilibrium —
i.e., the maintenance of a state of uniform motion — has
in many cases taken the place of static equilibrium or
rest, as in the doctrine of the flow of heat, the theory
of exchanges of radiation, and the conception that the
rigidity of solids depends upon a peculiar form of whirl-
ing motion — the vortex. Similarly the intermediate or
transition states which lie between the solid and fluid,
the properties of viscosity and of colloidal substances,
and of vapours as marking the transition between
liquids and gases, have attracted more attention in pro-

ON THK PHYSICAL VIKW OF NAILl;K.

lol

portion as experiiULUlul science has tak(Mi the place of
that purely mathematical treatment wliich ul)tained at
the beginning of the century, notably in the Continental
schools, and whirh thought it could exhaust the infinite
variety of natural phenomena by a few easily defined
properties measured by constants. The narrowness of
this view has been gradually overcome by the inlluenco
of the great experimental philosophers in this country,
and the indepemlent development of chemical research
abroad. IJeside Faraday must be especially named Thomas
Graham ^ and Thomas Andrews, whose original experi- 89,

Gnham and

ments did so much to extend and deepen our knowledge Andrews,
of the less obvious properties of matter. Graham car-
ried on, between 1825 and 1850, extensive experiments
on the diffusion of liquids and gases, on absorption, and
on the phenomena of osmosis or gradual filtering of sub-
stances through porous partitions, showing how in liquids
motion and pressure exist similar to that which is now

1 Thomas Graham (1804 - 69),
for many years professor at Uni-
versity College, London, then
Master of the Mint, cultivated the
unexplored regions of physics and
chemistry in an original si)irit and
yet with very himple apparatus,
some of which is still used under
his name. His ingenious labours
attracted the attention of Liebig,
through whose intluence was brought
about the translation of ' The Ele-
ments of Chemistry ' into Ger-
man by Otto. This work in its
subsequent enlarged editions has
formed for sixty years, next to
Gmelin's ' Handbook,' a corner-
stone of chemical literature in
Germany, where Graham's name
ia a hou.sehold word. The dia-
coveries of Graham on the move-

VOL. n.

ment and " miscibility " of gases
led to the well-known law, " that
the diffusion rate of gases is in-
versely as the square root of their
density." From ga.ses he advanced
to the more comi)licated study of
liquids, divided bodies into two
classes, "crystalloids" and "col-
loids," studied the " transpiration "
of gases tlirough fine tul>c.s, and
their "osmosis" or gradual filtering
through porous (and many ap-
parently noil - porous) partitions.
In many directions he anticipated
later discoveries and collecte«l in-
valuable materials for subsecjuent
theories. Inter alia, he establislicd
the existence of '" alcohoLites,"
compounds analogous to " iiydrates,"
and niaiiiUiined the metallic nature
of hydrogen.

162 SCIENTIFIC THOUGHT.

generally attributed to gases. Andrews ^ in the 'sixties
carried on his important experiments on the transition of
bodies from the Hquid to the gaseous state, and came to
the conclusion " that the gaseous and liquid states are
only remote stages of the same condition of matter, and
are capable of passing into one another by a process
of continuous change." ^ He also referred to the " pos-
sible continuity of the liquid and solid states of matter."
Another important step by which our conceptions of
the nature of the liquid condition of matter were con-
siderably enlarged and altered — motion being introduced
where a former view had seen only rest — was taken by
Clausius, who, following Joule and Kronig, had about the
same time given its modern form to the kinetic theory
of gases. "What suggested this step was the pheno-
menon of electrolysis. The older view looked upon the
action of the electric current, which, passing through
substances in a state of fusion or solution, liberated the
constituents out of which they were composed, as an
exertion of a force contrary to the forces of chemical
affinity, by which the chemical constituents were sup-
posed to be held together. In this case energy would
have to be spent in doing work against chemical forces.
It was, however, very soon found that the decomposi-
tion, or — as Sainte Claire Deville first called it^ — the

^ See vol. i. p. 316, note, of this
History.

"^ See ' The Scientific Papers of
Thomas Andrews,' with a Memoir

series of original investigations, first
iu organic then in metallurgical
chemistry, entered upon his re-
markable work in thermal chem-

by Tait and Crum Brown, London, istry at the time when Clausius in

1889, p. 316.

» Sainte Claire Deville (1818-81)
approached chemical research from

Germany was being led from an
entirely different point of view to
the same subject. He introduced

the side of medicine, and after a the term dissociation to denote the

ON THE PHYSICAL VI KW oF NAILKI-:.

I O.J

dissociation of the olectrolyte, was nut tlie conseniienee, «o.
but the Jicconipanyinji; feature or condition, of the exist- '"-"^
ence of an electric current in a sohition. ("hiusiu.s first
expressed tliis distinctly in 1857, and JiL*hnholt/. re-
peated it in 1880. The conception was thus intro-
duced that ill certain (not in all) solutions of chenncal
compounds dissociation nught exist independently of an
electric current, and that the latter, if introduced, only
directed the already dissociated and wandering molecules
(ions), freeing them at the same time of their electric
charges.^ This conception, tliuugli at first violently

breaking-uj) of chemical compounds
not so much through the presence of
other chemical agencies as through
altered physical conditions, such,
notably, as heat, evaporation, and
condensation. " Deville's observa-
tions on dissociation . . . have a
very direct bearing on the kinetic
theory of gases, and it is a fact of
interest in the history of science
that Deville did not recognise the
validity of that theory. Our esti-
mate of the ingenuity, skill, and
patience shown in his experimental
work, and of the genius and sound
judgment which directed his theo-
retical conclusions, is perhaps raised
when we recollect that he was
neither led in the first nor biassed
in the second by ideas derived
from the kinetic theory, and his
hostile, or at least neutral, attitude
towards it gives perhaps greater
value to the evidence that his work
has contributed to its soundness "
(A. Crum Brown, ' Ency. Brit.,'
9th ed., article " Sainte Claire
Deville ").

' I have already mentioned (vol.
i. p. 43.">, note) that Clausius, when
introducing his kinetic theory and
distinguishing between molecules
and atoms, could refer to several
eminent chemists who had inde-

pendently arrived at similar ideas
by quite different ti-ains of reason-
ing. Again, when introducing, in
18f)7, his theory of dis.sociation by
solution, he could refer to similar
anticipations. Williamson had said
already, in 1850 (Liebig's ' Annalen,'
vol. Ixxvii. p. .37), at the meeting
of the British Association in Edin-
burgh : " We are led to the conclu-
sion that in an aggregate of mole-
cules of every compound there
exists a continual exchange of the
elements contained in it. Suppose,
for instance, that a ves.sel with
hydrochloric acid were tilled with
a great number of molecules of the
compound CIH, then the view at
which we have arrived would lead
us to the supposition that everj'
atom of hydrogen does not re-
main in quiet juxta])osition with
an atom of chlorine, with which it
is combined, but that there is a con-
tinual exchange of places with other
hydrogen atoms " (Clausius, ' Me-
cliani.sche Wiirnietheorie,' vol. ii. p.
167, Braunschweig, 1879). For an
illustration of the theory of Ciau-iius
modified to meet more recent con-
ceptions, see (). Lodge's ' Mixleru
Views of Electricity,' 1892, y. 83,
&c.

164 SCIENTIFIC THOUGHT.

attacked by chemists, became gradually better under-
stood and gained ground. The merit of having finally
introduced into our modern notions the idea of the free
mobility of the constituents of electrolytic compounds
41. belongs to W. Hittorf and F. Kohlrausch. The name

Hittorfand i • i i • p •

Kohlrausch. of the latter will be connected in the history or science
with the phenomenon of the " migration of the ions,"
which he has expressed, after ten years of research
(1869-79), in his well-known law. The question was
put and answered, " What becomes of the energy of the
electric current ? " It was found that electrolytic conduc-
tion increased with dilution and temperature — two agents
which would favour dissociation. The phenomena of
dissociation had, moreover, been studied independently of
the galvanic current. Following in the track of Graham
and Andrews, a number of physicists abroad — notably
van der Waals, Eaoult, and Van't Hoff — had confirmed
and extended the view that bodies in solution resembled
gases, that the osmotic pressure of a liquid resembled
ordinary gas pressure, that the law of Avogadro regard-
ing the number of molecules in a gas could be trans-
ferred to matter in a state of solution, and that the
magnitude of the osmotic pressure in a liquid could be
used as a measure of the number of dissociated — wander-
ing— molecules which are contained in a given volume
of a solution, just as the pressure of a gas would increase
if the number of molecules in a given space were in-
creased through the splitting up of compounds. Apparent
anomalies in the behaviour of gases approaching conden-
sation were explained by the aggregation, and similar
ones in dilute solutions by the dissociation, of molecules.

ON THE PHYSICAL VIEW OF NATURE. 1G5

Tho decisive step was taken in 1887 by Arrhenius/ whu
has the merit of having brought together the two inde-
pendent courses of research and reasoning, and made
them fruitful for each other. He shows - " that the dif-
ference between active and inert molecules consists in
this, that the former are split into tlieir ions, the latter
not. Only the free ions take part in tlie conduction of
electricity and in chemical reactions : this is the rea.son
for the proportionality of the two (Faraday's law). The
ions behave in solution like independent molecules : this
is the reason of the deviation which electrolytic solutions
show from the extended gaseous laws (Van't Hott's dis-
covery)." " What a change has come over our concep-
tions," exclaims Victor ]\Ieyer,^ " if we have to accustom a.

. , Victor

ourselves to see in a dilute solution ot common salt, no Meyor^.n
longer the undecomposed molecules of a salt, but separate ^^^'^^^
atoms of chlorine and sodium. For these revolutionary
innovations we are indebted to the labours of Van't
Hoff, Arrhenius, Ostwald, Planck, Tfeffer, de Vries, but,
so far as experiments go, notably to the splendid re-
searches of Kaoult, wliich for years have been prepar-
ing the way for this miglity theoretical advance."

The year 1887, which brought together these two
fruitful lines of reasoning and research, can also be con-
sidered as the epocli wlien the new science of physical
chemistry was fairly laiiiiclied into existence. The year

1 In a communication to the I Address by Victor Meyer before
Academy of Stockholm of 8th June the German " Naturforscherver

and 9th November 1887.

- Quoted from Ostwald's ' Allge-
meine Chemie,' 2nd ed., vol. ii.
part 1, p. 656.

^ See the highly interesting

sammlung" at Heidelberg in 1S89,
entitled " Chemische IVobleme
der Gegcnwart " (Heidelberg,
1890), p. 32.

166 SCIENTIFIC THOUGHT.

1826 marks the revival of mathematical studies in

Germany through the appearance of Crelle's journal ; so

43. the year 1887 saw the first number of Ostwald and

Ostwald's

journal. Vau't Hoff's ' Zeitschrift flir physicalische Chemie.' From
that period the physical properties of chemical substances,,
so long neglected, or only studied by isolated students,
have received systematic, mathematical, and exact
treatment, guaranteeing something like continuity and
completeness, and leading on to the solution of the great
remaining question. What is chemical affinity ?

The eminent natural philosophers to whom is mainly
due the foundation of this modern science, claim also to
be gradually realising the idea which was suggested ])y
the early representatives of the theory of energy —
notably by Eankine and James Thomson — ^that of a
general doctrine of energy, termed energetics ; and they
hold that this suggestion is only realisable by breaking
with the conventional ideas which the older physical
theories — the astronomical, atomistic, and kinetic views —
have imposed upon our reasoning. They further hold
that the gradual development of chemistry into an exact
science necessarily requires the introduction of this
broader view which they embrace, and that the older
views — useful in their way — only suffice to comprehend
certain restricted groups of natural phenomena, whereas
in chemical changes, where all imaginable natural pro-
cesses seem to come together, a laro-er and more inde-
pendent theory is indispensable. It is interesting to
note how very generally they trace this larger view to
the long unnoticed labours of a natural philosopher in
the New World, Professor Willard Gibbs of Yale.

ON I'UK PFIYSICAL VIKW OF NATl'RK. 1G7

The train of lliuugliL nietliodiciilly and cuinpreheii- «.

* 1 i* 11 1 '/"I'll* Wnl*rd

sively toiloweil out in (fibbss various memoirs had it« o ''»»»•
origin in the early speculations of William Thomson
(Lord Kelvin) and C'lausius, to which 1 ivfcrrt'd above.
Thomson was the first who, in adopting (after much
hesitation) the mechanical view of the phenomena of heat,
the doctrine of the convertibility and equivalence of the
different forms of energy, recognised that, in order to
describe natural phenomena correctly, this view required
a qualification. Tiie change of the different forms of
energy into each other can for the most part take place
only in one direction ; there is a general tendency in
nature towards a degradation or dissipation of energy.
Energy, though not lost, becomes less useful, less avail-
able. The least available form of energy is heat ; and
it is in that form that in all natural changes a por-
tion of energy becomes lost, dissipated, or hidden away.
Thus we have to recognise the difference between
available and unavailable, between useful and useless,
energy. In the seqviel Thomson showed in definite
instances ^ how to calculate the availal)le and tlie un-

^ See ' Math, and Phys. Papers,' in this connection, is applied by liiin

vol. i. No. LIX., 18.02, " On a Uni- to the negative of the idea we most

versal Tendency in Nature to the naturally wish to express. It would

Dissipation of Mechanical Energy" ; only confuse the student if we were

and No. LXIIL, 1853, "On the to endeavour to invent another

Restoration of Mechanical Energy term for our purpose." He then

from an unequally heated Space." proceeds to use the term entropy

In Tait's ' Sketch of Thermodynam- in an altered sense, in whicii it

ics' (1868), we read (p. 100): "It measures the available instead of

is very desirable to have a word to the unavailable energy, creating

express the arai/aljilitij for work of for some time a great confusion

the heat in a given magazine, a and some uiniccessarj' irritJition.

term for that possession the waste See on this the early editic^ns of

of which is called Bisnipation. Un- Clerk Maxwell's excellent ' Theory

fortunately the excellent word civ- of Heat,' and the footnote to p.

<ro/)?/, which C'lausius has introduced 189, 8th ed., and Clausiua, 'Die

168 SCIENTIFIC THOUGHT.

available energy : he introduced the word " motivity," the
conception of a quantity of a "possession the waste of
which is calkd dissipation." Whilst Thomson was thus
putting into scientific language and calculating an im-
portant and obvious property of nature — namely this, that
her processes mainly proceed in a certain definable direc-
tion— Rankine and Clausius were labouring independ-
ently at the mathematical wording, the analytical expres-
sion, of this remarkable discovery. Wherever a change in
a system of various elements, factors, or quantities takes
place mainly in a definite sense or direction, it is presum-
able that there exists a definite quantity which is always
growing or always decreasing. This quantity may not
be directly observable or measurable, as in mechanical
motion velocity or distance is directly measurable ; it
may be hidden — we may have no special sense with
which we can perceive it, as we possess a pressure sense,
a heat sense, a sound and light sense ; nevertheless, it
may be indirectly discoverable, being made up (a func-
tion) of definite observable quantities and factors (such
as heat, temperature, mass, volume, pressure, &c.) Now
Rankine and Clausius found that in all thermal changes

mechanische Warmetheorie,' vol. i.
p. 387, and vol. ii. p. 324 sqq. A
great deal of this confusion would
have been avoided had Tait in 1868
introduced a really new term — viz.,
that suggested later (1876) by
Thomson in a communication to
the Royal Society of Edinburgh,
and more fully explained in a
paper in the ' Phil. Mag. ,' May
1879, the term " Thermo-dynamic
Motivity." W^e should then have
two terms, inasmuch as the "con-

sideration of the energy and
motivity, as two functions of all
the independent variables specify-
ing the condition of a body com-
pletely in respect to tempera-
ture, elasticity, capillary attraction,
electricity, and magnetism, leads
in the simplest and most direct
way to demonstrations of the theo-
rems regarding the thermo-dynamic
properties of matter" {loc. cit.,
'Papers,' vol. i. p. 459).

ON THE PHYSICAL VIEW OF NATURE.

169

or heat processes — and this practically means in all
natural processes — there is such u quantity which is
always on the increase, and which thus measures in
mathematical language the growing loss of available
or useful energy in the world. Ifankine simply called it
the " thermo-dynamic function " : Clausius thought it
important to give it a name which would co-ordinate it
with energy, and he called it entropy : ^ energy which
is turned inside, becomes hidden or locked up. Clausius
thus gave a different wording of Thomson's doctrine of

Entropy.

' Clausius had already in 1854
(Pogg. 'Ann.,' vol. xeiii. p. 481) ar-
rived at the principal consequences
and the final enunciation of what
he termed " the second law of
thermo - dynamics," a law which
refers to the transformation, as the
first refers to tlie conservation, of
energy. He there arrives at similar
conclusions to those put forth by
Tliomson two years earlier. The
word entropy, however, wa.s not in-
troduced by him till 186.5 (Fogg.
' Ann.,' vol. cx.w. p. 390), when he
introduced it with the following
remarks : " I have intentionally
formed the word entropy as much
as possible on the model of that
of energy, for the two cpiantities
which are to be designated by these
two words are in their physical
meaning so intimately related that
a similarity in the terms seemed to
me to be justified." As stated
above (p. 167, note), Lord Kelvin, wlio
worked simultaneously and inde-
pendently at the same subject, laid
more stress upon the direct state-
ment, that in all transformations
of energy we have to distinguish
between the available and tlie toUil
intrinsic energy, and inlroduccil
the terms energy and motivity as

two functions of all the variables
specifying the conditions of a
.system. In liis article on Heat,
contributed to the ' Ency. Brit.,'
9th ed., he gives the mathematical
relation of motivity to entropy
(' Papers,' vol.iii. p. 167). The term
motivity has not become current in
thermo • dynamical treatises, but
the need has been very generally
felt of reserving the word energy in
a restricted sense for available
energy, such energy as can be put
to mechanical use. Wald, in a
very interesting dis.sertiition, ' Die
Energie und ihre Entwerthung '
(Leipzig, 1889), deplores (pp. 43
and 44) the fact that the word
energy has not been re.served to
denote useful, available energy.
" Had the word energy," he says,
" been introduced before tl»e dis-
covery of the first law of thermo-
dynamics, then certainly only me-
chanical energy wouhl have been
termed simply energy." In the
use of tlie word Knift in some
writers, such as Mayer, there
seems occasionally a confusion be-
tween available and total or in-
trinsic energy. See Le Chatelier
in 'Journal de Pliysique," 1894.

lYO SCIENTIFIC THOUGHT.

the universal tendency in nature towards a dissipation
of energy, by saying, " The entropy of the world is
always on the increase."

For about twenty years after these conceptions had
been introduced into scientific language and reasoning,
mathematicians and physicists were mainly occupied
in defining more clearly this hidden quantity, and in
defending what was called the second law of thermo-
dynamics against misconceptions and attacks. In 1875
Lord Eayleigh could still say} " The second law of thermo-
dynamics and the theory of dissipation founded upon it
has been for some years a favourite subject with mathe-
matical physicists, but has not hitherto received full
recognition from engineers and chemists, nor from the
scientific public. And yet the question under what
circumstances it is possible to obtain work from heat
is of the first importance. Merely to know that when
work is done by means of heat, a so-called equivalent of
heat disappears, is a very small part of what it concerns
us to recognise."

Whilst these words correctly describe the general

attitude of the scientific public towards this important

discovery, two men had already made a beginning in

Horstmann. the direction indicated — Horstmann ^ in Germany, and

1 i

Proceedings of the Royal In- ] which began in the year 1869 and

stitution,' vol. vii. p. 386.

- Prof. Ostwald in the historical
section of his ' Verwandtschafts-

were continued in Liebig's ' An-
nalen' in various communications
during the early 'seventies, not

lehre' ('AUg. Chemie,' 2nd ed., without undergoing violent attacks

vol. ii. part 2, p. Ill, &c.), Helm
in 'Energetik' (p. 141, &c.), and
Duhem in his ' Traite de Mecanique
chimique' (1897, vol. i. p. 84, &c. )
all do full justice to the long-un-
recognised labours of Horstmann,

from representatives of the older
conceptions. Ever since James
Thomson's celebrated prediction
(see above, p. 126), physicists
had recognised the importance of
thermo - dynamical considerations,

ON THE PHYSICAL VI KW OF NA'iTHE.

171

Willard Gihlts ^ in America. They seem to have l^een the
first to approach the question of chemical equilihrium,
the result of llie action nf various conflicting cliemical
forces, termeil ailiiiities, from a general comjirehensive
j)oint of view ; recognising that the theory then com-
monly adopted on the Continent — the thermo-chemical
thenry of atlinity — was incorrect <ir incom])lete. This
theory, which had l)een principally ehil)orated by Julius
Thomsen in Copenhagen and l)y Berthelot in l-'iance,
was supi)orted l>y tlie large amount of valuable ex-
perimental research for whicli we are indebted t<^
these two eminent men and their numerous follnwcrs.

whilst chemists pemsted in the ex-
clusive use of atomistic concej)tions,
which, as Horstinann pointed out,
are of no avail in problems of that
nature (see Helm, 'Energetik,' p.
143).

^ More fundamental than the
labours of Hor.«tmann were those of
Gibbs, which began with the year
1874, and were for a long time
buried in the ' Transactions of the
Connecticut Academy." They were
known to Maxwell, but remained
generally unknown, partly owing
to their abstract nature, partly
to the fact that the majority of
Continental chemists wore not
prepared to appreciate the mathe-
matical form in which his exposi-
tions were clothed. Previous to
the study of questions of chemical
equilibrium, Gibbs had successfully
developed an idea of .lames Thom-
son's— viz., the graphical re])resen-
tation of the diti'erent thermo-
dynamic ([uantities in three instead
of merely in two dimensions. Thom-
son had lepresented the projierties
of a body or system by referring
them to volume, pressui-e, and tem-
perature. Gibbs refers them to

volume, energy, and entropy, tlie
former quantities being always de-
finable by the latter, but nut vice
rcrtsa. The advantages of this rep-
resentation were demonstrated to
English students in Maxweirs
' Theory of Heat." In Germany it
was Prof. Ostwald who, by collect-
ing and translating the memoirs
of Gibbs, first made them accessible
to students (' Thermodynamisciie
Studien," von Willard tlibbs. Leipzig,
1892). Subsequently both Ostwald
and Helm have done much to pro-
mote an understanding of Gibbs's
methods. See Ostwald, 'Allg.
Chemie," vol. ii. part 2, p. 114,
&c. ; Helm, ' Grundziige der niathe-
matischen Chemie" (Leipzig, 1S94),
and 'Energetik,' passim. Subse-
quently Gibbs also introduced the
very general and useful term
"phase" to denote tiie different
states in which a substanc-e can
exist. This term denotes not only
such difl'erences as were formerly
called in German Af/i/rrt/atztutUindc,
but likewise conditions of dis-
sociation, allotropic and isomeric
modifications.

1V2 SCIENTIFIC THOUGHT.

It measured chemical reactions by what is termed their
heat - toning, i.e., by the amount of heat developed,
and culminated in the celebrated third law of thermo-
chemistry— viz., that such reactions take place as are
accompanied by the greatest amount of energy liberated
in the form of heat. Now, although this contains an
adequate description of a very large number of reactions
that take place at the temperatures at which we operate
in our laboratories, the rule is by no means universal,
and it required a great amount of ingenuity to ex-
plain away the many exceptions which presented them-
selves. The rule needed to be modified or amplified.
The measurement of the energy of a chemical process by
the heat-toning was not the only instance in which the
thermal side of a phenomenon had been considered a
sufficient means of measuring. In an allied department,
that of electrolysis, Helmholtz had suggested, as early
as 1847, that the electro-motive force of a galvanic cell
may be measured by the heat-toning of the chemical pro-
cesses which produce the current, and for a long time
this was considered to be a correct expression of facts.
In consequence, however, of some discrepancies which
had presented themselves, Helmholtz himself was induced,
abovit 1881, to examine the subject more thoroughly.
He arrived at the conclusion that the heat-toning is not
always a correct measure ; and at the same time he intro-
duced a more adequate and generally applicable method
of measurement. In fact, he arrived at the conception
of available or useful energy for processes which take
place at constant temperature. To this quantity, which
decides in which direction a reaction takes place (tempera-

ON THK PHYSICAL VIEW OF NATl'ItE. ITo

ture reinaiuing constant), lie gave the name of free energy. «'

Ilelmholu'*

He showed that in a state of equilibriiun the free or "'"*
available energy must he a minimum. He also showed
the connection in which the available or free energy
stands to the quantity introduced l)y liankine and
Clausius, the entropy wliich measures the unavailable or
hidden energy. \'>y making chemical changes depend
on the increase or decrease of a definite measurable
quantity a parallel was established between chemical and
mechanical processes, the latter always taking place in
the direction of a decrease of potential energy. Free
energy has thus been appropriately termed Ity M. Duhem
the thermo-dynamic potential.

Helmholtz did not apply this fruitful view to chemical
processes on any extensive scale, but his explanations
have done much to establish that correcter and more
comprehensive way of treating such questions which has
since become general, llorstmann had indeed leil up
to this view, Willard Gibbs had applied it before, and
Lord liayleigh had suggested it.^ The conception of

^ The general use of the concep- and 11), and more definitely ex-
tion of useful or free energy must jilaincd and aijplied to the phy.s-
be dated from the remai'kably lucid ical phenomena of dissociation by
expositions of Helmholtz, though Oibbs (' Thermodynamisclie Stud-
it is now recognised by all who ien,' ed. Ostwald, p. 66, kc. ;
have studied the history of this j ' Amer. Journ. of Sciences and
fertile conception that the physi- t Arts,' 1879) ; and that it is ea-
cal notion of available energy goes i)ecia!ly owing to the labours of
back to Thomson (see Tait, ' Ther- Duliem that the subject has
modynamics,' 1868, p. 100) and received the attention of oliemists.
Maxwell {' Heat,' p. 187, 8th ed. ; M. Duhem, in the introduction to
Duhem, ' Mdamique chimi(|ue,' the work of 1886, gives a very

vol. i. p. 92 ; Le Chatelier in
'Journal de Physique,' 1894, p.
291) ; that the mathematical
formulic were given by Massieu
(quoted by Duhem, ' Le Potential

valuable and lucid historical ex-
position, and subsequently in liis
large work in four volumes ('M<5-
canique chin)i(|ue,' 1897-1900) a
vast number of applications. Kor

Thermodynamique,' 1886, pp. v I the history of thought the imiH.rt-

174

SCIENTIFIC THOUGHT.

48.
Kelvin's
available

energy.

available energy as distinguished from total energy had
been introduced by Lord Kelvin and by Maxwell. This
free energy is measured not only by the heat liberated,
but depends on all the other factors, such as volume and
pressure, the number of chemical substances engaged, and
their physical conditions. The doctrine of energy and the
conception of free energy pointed out a method of co-
ordinatincr all these different factors and reducing them
to a common measure. As Rankine, by the introduction
of the term potential energy, did much to clear the ideas
and guide the reasoning in dynamical science, so Helni-
holtz, by introducing the term free energy, did a great
deal to introduce into chemical science the fruitful con-
ceptions which had been elaborated and appHed in phys-
ical research. The term free or available energy seems
to describe more naturally the characteristic property of
all energy which is useful for doing w^ork, whilst the
opposite term entropy — which measures the unavailable
or hidden energy — refers to a quantity for which we have
no immediate means of perception.^

auce of these somewhat abstruse
expositions lies mainly in two
directions : First, in the recog-
nition of the fact that for the cor-
rect description of natural pheno-
mena and changes the knowledge
of the total energy is as little suf-
ficient as that of the total weight
or mass, but that it -is necessary
to introduce the conception of use-
ful energy, of energy which is free
or available for doing ■work ;
secondly, in the recognition that
the course of chemical changes or
reactions cannot be measured by
attending to one special property,
such as weight, or temperature, or
«utropy, but that it requires the

measurement of a quantity which
comprises all the different agencies
in nature, this quantity being the
energy of the system or substances
in question and its availability. A
third point, which is of more or less
importance according to the general
view adopted, is this, that the ma-
thematical formula8 involved have
exhibited the analogy between
chemical and mechanical processes,
the latter being those which were
earliest and are most easily grasped
by the mind.

^ As Prof. Ostwald has remarked,
it is to a great extent a matter of
taste what particular form one
adopts out of the many in which the

ON THE I'HYSICAL VIEW iJi-' NATL'KE.

175

It was about this time — after experimental research
had been carried on for many years by Julius Thomseu
and Berthelot, after Horstmann had made a lieginning of

second law of therino-dynaiiiics can
be expressed (' Allg. Cheniie,' vol. ii.
part 2, p. 150). In every case it
is simjjly a question how most
conveniently to express and apply
the general jiriiiciplc that heiit
cannot of itself jiass from a colder
to a hotter body, the principle on
which Fourier built hi.s "Theorie
de la Chaleur," and which revealed
itself as the rationale of the ex-
positions of Carnot when in the
middle of the century their hidden
truth emerged from the criticisms
of William Thomson (Lord Kelvin)
and Clausius. Thus already in the
dirt'erent treatment of the same
subject there showed itself the
twofold tendency which reasoning
on physical matters so frequently
exhibits — viz., towards physical
directness and mathematical ele-
gance ; the former leading to prac-
tical a{)plication, the latter to
analytical refinement. Maxwell,
in a review of Tait's ' Ther-
modynamics,' written in 1877
(' Scientific Papers,' vol. ii. p.
666), contrasts the methods of
Clausius and Thomson, and Prof.
Mach ('Warrnelehre,' 1896, p. 300)
has made similar remarks. Of
Thomson the former says, " that
he does not even consecrate a
symbol to denote the entropy,
but he was the first to clearly
dehne the intrinsic energy of a
body, and to him alone are due
the ideas and the definitions of
the available euergj- and the dis-
sipation of energj'. . . . He avoids
the introduction of quantities
which are not capable of ex-
perimental measurement." Since
these criticisms a great deal has
been written to make the second
law of thermo-dynamics and the

concepti(jn of entropy more intellig-
ible. The object here again haii
been twofold : first, to make the
cunceptions useful for the practical
jiurpo.-e of perfecting tlie heat en-
gines (liiinkine, Zeuaer and his
school) and of inve.-^tigating the
conditions of cheuiical equilibrium
(Gibhs, Helmholtz, Duhem) ; next,
to place the second law, which
deals with the transformation of
energy, on an eijually firm foun<la-
tion with the first law, which
deals with the conservation of en-
ergy. There is no doubt tiiat the
jirinciple of tlie consenation of
energy owes a very lari;e part of
its inti-lligiliility to tlie fact that
for purely mechanical i-ystems
it follows from such well-known
dynamical axioms as the laws of
motion. When heat was con-
ceived to have a mechanical
equivalent in mechanical work,
the more general principle of the
conservation of energy seemed
intelligible bj- mechanical con-
ceptions. The second law, how-
ever, introduced a property of
natural processes which is not so
easily understood n)echanically —
viz., that they are not reversible
— and tliis property was shown to
l)e connected witli a sjiecial phys-
ical quantity, for which we have
a sjjccial sense — viz., temjierature.
The problem of making the second
law mechanically intelligible thus
coincides with the jiroblem of
giving a mechanical definition of
temperature. It is not sufficient
t<) call heat a mode (or, more cor-
rectly, the energy) of motion ; we
must ex|iress tcmi>erature, on the
dill'erence of which the usefulneta
of heat depends, in some way by
motion, we must nirivc at a

176

SCIENTIFIC THOUGHT.

introducing thermo-dynamics into chemistry, after W.
Gibbs had shown how to look at chemical energy as a
sum of many forms of energy, and after Helmholtz had
more clearly defined the useful conception of free or
available energy as the measure of chemical reaction —
49. that Prof. Ostwald at length ventured after the lapse of

Ostwald's . •. • 1 • 1 • ,

'Aiigemeine eighty ycars to unite m a comprehensive doctrine the
scattered fragments of our existing knowledge regard-
ing chemical affinity. This he did as a restorer of the
forgotten labours and fame of Berthollet.^ By the

kinetic definition of temperature.
The two principal founders of
thermo-dynamics, Clausius and
Lord Kelvin, did not resort to
kinetic conceptions when estab-
lishing the two laws which deal
with the conservation and trans-
formation of energy : Rankine,
however, connected the subject
with his theory of molecular vor-
tices ; and Clausius, who was one
of the founders of the kinetic
theory of gases, very early at-
tempted to interpret the laws of
the transference of heat by the
help of that theory. So like-
wise did Maxwell, Helmholtz,
Boltzmann, and many others.
Mr Bryan, in a very valuable
report on the " Researches relat-
ing to the Connection of the
Second Law with Dynamical
Principles," has given a critical
summary of these various at-
tempts (see Brit. Assoc. Reports,
1891, p. 85). The three peculiar
forms of motion referred to in
our last chapter — periodic, rota-
tional, and rapid translatioual (dis-
orderly) motion — have been used to
suggest manifold means of trans-
lating thermo-dynamical processes
into kinetic models, explaining,
as Mr Bryan says, " the second
law, about which we know some-

thing, by means of molecules
about which we know much less "
(p. 121). It does not seem that
much more has been gained than
a general presumption that a
mechanical illustration is possible.
To the statistical ideas elaborated
mainly by Maxwell and Boltz-
mann I shall revert when treat-
ing generally of the statistical view
of nature.

1 Prof. Ostwald has himself, in
the Inaugural liecture which he
delivered on the occasion of his
accession to the chair of physical
chemistry at Leipzig, 23rd Nov-
ember 1887, given a very lucid
statement of the principles in-
volved. He goes back to the two
theories of chemical action repre-
sented at the beginning of the
century by Bergmann on the one
side and I5ertliollet on the other.
In place of the conflict of chemical
forces, in which the stronger ob-
tains a complete victory (complete
reactions) — the view of Bergmann —
Berthollet introduces the "mani-
fold play of forces acting to and fro,
the result being that every one gets
its due. The more powerful sub-
stance gets more, the weaker less.
Only in cases where one of the
possible compounds in consequence
of its properties entirely leaves

ON THE PHYSICAL VIKW OF NATriJE.

17'

publication «>!' the second vohnue of his ' Lehrbuch der
allgenieinen Chemie ' a great impetus was given to phys-
ical cheniistiy. Ihe large addition to our knowledge in
this branch, and the consolidation and criticism of re-
seanh wliich it brought about, and to which the second
edition, now appearing, gives ample testimony, mark this
publication as an epoch in modern scientific thouglit. To
tliis development is attached the growth oi the special
view of natural phenomena which Ostwald and some
other Continental thinkers embrace, and which they are
inclined to place in opposition to tlie older views as a
more comprehensive one. The older views they some-
what contemptuously term the materialistic views of
nature — the views, in fact, which 1 have presented
under the headings astronomical, atomic, and mechanical.
As this most recent outcome of what I termed the
physical view of nature refers to fuiulamental concep-
tions and has furnished much matter for discussion

the field of contest, either by falling
down as insoluble or escaijing as
gas, can that complete decomposi-
tion take place which Beigmaiin
held to be the normal result "
('Die Energie und ihre Waud-
lungen,' Leipzig, 1888, p. 20). That
complete reactions were for a long
time studied with predilection was
most natural, esj)ecially as they are
the most useful for practical |)ur-
j^oses ; but the study of moving
cliemical eciuilibrium, depending on
what is now termed mass action and
involving the question of the velocity
of reactions, has in recent times
again asserted itself. Ostwald
dates the revival of this long-
neglected branch of research from
the year 1867, when "two Nor-
wegian chemists, Guldberg and

VOL. n.

Waiige, put the ideas of Berthollet
into precise mathematical form and
subjected the resulting equations to
the test of observation and verifica-
tion " (ibid., p. 21). Ostwald then
shows further how Bergmaun's
theory was simultaneously reviveil
in M. Berthelot's famous third law-
derived from thermo • chemistry.
This in turn had to yield to
the correcter views which date
from Gibbs's studies "on the
equilibria of heterogeneous sub-
stances" (see ' Tliermo<lynami.tche
Studien,' p. 66, 1875 ; also Ostwald,
' Allg. Chemie,' vol. ii. part 2, p.
163, on the reconciliation of Berg-
maun's and BerthoUet'a views ; ami
further, Berthelot in ' Conipte*
Rendus,' 1894, 118).

.M

178 SCIENTIFIC THOUGHT.

abroad, I will try to sum up finally the principal points
in it which are of importance for the history of con-
temporary thought.

Ever since the conception of energy as a quantity
which, like matter, is preserved in all natural processes,
forced itself with more or less clearness upon natural
philosophers, the question has been insistent as to the
number of different forms in which this quantity can
manifest itself ; and some of the earliest propounders of
the doctrine attempted an enumeration of the different
forms, mechanical energy of motion and of attraction
usually heading the list. When that form of energy
which we call heat was subjected to examination, and the
remarkable property formerly called latent heat defined
in the new terminology, the want arose of bringing about
some kind of connection between our ideas of motion and
those of heat, which were shown to be mutually con-
vertible quantities in nature. Before that time sound
and light had already yielded to the kinetic view, and an
enormous increase of our knowledge in acoustics and
optics had followed. Thus we find some of the pioneers of
the physical or energy view of nature— notably Rankine
and Joule in this country, Eedtenbacher and subsequently
Clausius abroad — engaged in translating the properties
of heat into mechanical analogies.^ It was not thought

^ Rosenberger, in his ' Geschichte volumes on ' Die mechanische
der Physik' (vol. iii. p. 550, &c.), , Warmetheorie,' 2nd ed., 1876, &c.).

gives a number of references to
theories mostly forgotten which
were published before and after
the year 1850. Clausius, who
keeps his mechanical theory of
heat quite separate from his kinetic
theory of gases (see the tln-ee

admits, nevertheless, in a paper
published in 1857 (Pogg. 'Ann.,'
vol. c, and ' Mechan. Wiirmetheor.,'
vol. iii. p. 1, &c. ), that "from the
beginning of his researches refer-
ring to heat he had attempted to
account to himself for the internal

ON THE PHYSICAL VIEW OF NATURE.

179

essential, but it was found to be convenient — mainly for
didactic purposes — to elaborate such analogies, explaining
or describing the less known by that which is more
familiar, liegarding the value of such attempts there
have always existed two opinions. I have had occasion
to refer to them when explaining the atomic theory.
There were those who looked upon that theory merely
as a convenient symbolism, and there were those who
looked upon atoms and molecules as really existing
things. The latter view has gained force and importance
through the necessity of more and more elaborating the
atomic hypothesis in order to represent not morely the
chemical constitution of compounds, Ijut likewise tiieir
manifold physical differences, some of which, in fact,
could only be described by geometrical conceptions. T
need only refer to what I said above on the kinetic
theory of gases, and on the property termed chirality
manifested by some chemical substances in solution, as
well as on tlie phenomena of isomerism. In tlie last

state of motion of a hot body, and
that he haxl arrived at a conception
which he had already before his
first publication (in 1850) used for
various investigations and calcu-
lations." He further stiites that
hearing through William Siemens
that Joule had expressed a similar
idea (Manchester Phil. Soc, 1848
and 18.07), and more especially after
the publication of Kronig (18,')6),
he resolved to puV)lish his views.
It is interesting for our present
purpose to see how Clausius, like
Maxwell in a different domain of
re.search, was originally guided by
definite mechanical representations.
It is equally noteworthy that Lord
Kelvin's original researches on the

subject of heat were quite free
from this element, though we
owe to him in other departments
some of the most suggestive kin-
etic illustrations ; and that he ha.s
quite recently offered valuable
criticisms on the attempted me-
chanical interpretation of the second
law of thermo-dynamics (see p. 112
of Bryan's Report, quoted above, p.
176, note). Also the first English
treatise on thermodynamics writ-
ten for didactic jjurj" >ses (Tail's
Sketch, 1868) contains no reference
to molecular theory, and Hirn, one
of the most active workers in the
region of experimental proofs, kept
clear of it.

180 SCIENTIFIC THOUGHT.

chapter, while dealing specially with the kinetic view
of natural phenomena, I had again occasion to refer to
the opinion which has latterly crept into mechanical
explanations — namely, that they are to be looked upon
merely as symbolical, an opinion which did not enter the
minds of the original propounders of the vibratory theory
of sound and light, and which some eminent natural
philosophers to-day strongly oppose. An opposite fate
seems to have befallen the mechanical hypothesis in
chemistry and in physics. Whilst Dalton's atoms were
accepted with hesitation, the further elaboration of the
atomic view has made it almost impossible to resist it
as a physical reahty ; whereas the necessary complica-
tions introduced into Young's undulatory theory in
order to make it cover electro - magnetic phenomena
have given it the appearance of unnaturalness and arti-
ficiality— so much so that Maxwell himself abandoned
the line of reasoning which led him originally to his
fundamental formulae, and contented himself with more
general considerations derived from the conception of
energy.
50. The conceptions which are expressive of the view dealt

"Kinetics" . . -^ ^

and"ener. with in this chapter — the energy ideas — have had a
similar fate. There have been those who have inter-
preted this view to mean that all phenomena in nature
can be translated into the language of mechanics : they
have accordingly been stimulated to invent all manner
of kinetic contrivances by which light, heat, electricity,
and chemical action can be represented. Others have
interpreted the equivalence of all forms of energy to
mean that kinetic energy is only one of the forms in

getics."

ON THE PHYSICAL VIEW OF NATUUE. 181

which this (quantity can appear : they have thus exerted
themselves to lind such general properties as Ijelong
to all tlie forms in which energy presents itself to us.
They look upon energy as a much more general con-
ception than motion, and they think it a mistake to
try to narrow the conception so that it can only mean
the energy of attraction and repulsion (tlie astronomical
view), that between the ultimate particles of matter
(the atomic view), or the energy of various forms of
motion (the kinetic view).

On the purely scientific side the mechanical view has
much to say for itself, and can point to achievements
which recommend it as a fruitful method of progress and
research, and as even more fruitful for the purposes of
instruction. It can claim to give in many instances an
apparently easy account of the common-sense or obvious
properties of bodies, and it gives this accomit in terms
which lend themselves to strict definition, to measure-
ment, calculation, and prediction of phenomena ; it
destroys all \'agueness, and adopts, as it also stimulates,
mathematical, which is the most cogent kind of reasoning.
The kinetic theory of gases and the vibratory theory of
light are notable examples. The ideas of energy and the
remarkable properties of the lowest form of energy —
i.e., of lieat — became gradually clearer and lost their
strangeness as potential energy came to be defined as
energy of position, aA'ailable (or free) energy as the
kinetic energy of regular or orderly, unavailal)le (or
bound) energy as that of irregular or disorderly motion,
and when the strange quantity termed entropy, which
Clausius and IJankine strove in vain to bring home to

182

SCIENTIFIC THOUGHT.

the general scientific intelligence, revealed itself as the
measure of the disorder which prevails in the motion of
the ultimate material elements of a system.^ Faraday's,
lines of force and the whole elaborate imagery invented
and afterwards discarded by Maxwell to describe the
interaction of magnets, electric currents, and charged
bodies, have proved to be most valuable instruments of
thought — a useful scientific shorthand — in the hands of
the teacher, as in those of the practical electrician. And
although the illustrious propounder of the vortex-atom
theory of matter seems latterly to have discouraged the-
use of this kinetic contrivance as not likely to lead
to any great revelations regarding the ultimate constitu-
tion of matter or the nature of the imponderal)les,^ the

^ Helmholtz, in his first memoir
on the thermo-dynamics of chemi-
cal processes (' Sitzungsberichte der
Akaderaie zu Beriin,' 2ud February
1882), after having estabhshed the
formula; for the free energy in iso-
thermal processes without reference
to kinetic hypotheses, concludes his
exposition with the following re-
marks : " We require, finally, an
expression in order to be able to
distinguish clearly what in theoreti-
cal mechanics is termed vis viva or
actual energj' from the work equiva-
lents of heat, which are indeed
mostly to be regarded likewise as
vis viva of invisible molecular mo-
tion. I would suggest that the
former should be called- the vis
viva of orderly motion. I call
orderlj' all motion in which the
compounds of velocity of the
moving masses are difierentiable
functions of the space co-ordinates.
Disorderly motion would then mean
all motion in which the motion of
each particle has no similarity to
that of its neighbours. We have

every reason to believe that heat-
motion is of the latter kind, and one
might in this sense regard entropy
as the measure of disorder. For
our means, which compared with
molecular structure are coarse, only
orderly motion can be freely con-
verted again into other forms of
mechanical work" (' Wissenschaftl.
Abhandl.,' vol. ii. p. 972).

■•^ " I am afraid it is not possible
to explain all the properties of
matter by the vortex-atom theory
alone — that is to say, merely by
motion of an incompressible fluid ;
and I have not found it helpful in
respect to crystalline configurations,
or electrical, chemical, or gravita-
tional forces. . . . We may expect
that the time will come when we
shall understand the nature of an
atom. With great regret I abandon
the idea that a mere configuration
of motion suffices" (Lord Kelvin,
quoted by Prof. S. W. Holman in
' Matter, Energy, Force, and Work,'
New York, 1898, p. 226).

ON THE PHYSICAL VIEW OF NATUKl..

183

foremost intellects are still busy in working this to
them promising vein of reasoning.^

The opponents of the kinetic, mechanical, or material
views of natural phenomena have always existed : in the
early yeare of the century they described their view by
the word " dynamic." At that time it was the atomic
theory they principally objected to. But their criticisms,
though not without use in exposing the limited nature
of all mechanical explanations, failed to yield any fruits,
inasmuch as they moved in vague expressions and did
not lend themselves to that powerful method by which
alone the conquest of nature has been effected, viz., mathe-
matical reasoning, combined with observation.

The more recent critics of the mechanical interpreta- si.

„ , . , , T Ml 1 Criticism of

tion of physical phenomena, among whom 1 will only mechanical

view.

mention Prof. Ostwald of Leipzig, Prof. G. Helm of
Dresden, and Prof. Ernst Mach of Vienna," are fully

^ " With reference to the vortex-
atom tlieory, I do not know of any
phenomenon which is manifestly
incapable of being explained by it ;
and personally I generally endeav-
our (often without success) to
picture to myself some kind of
vortex-ring mechanism to account
for the phenomenon with which I
am dealing. ... I regard the
vortex-atom explanation as tiie goal
at which to aim," &c. (Prof. J. J.
Thomson, quoted ibid.)

^ Prof. Ernst Mach is the earliest
of these writers and had worked on
quite independent lines before the
other two names began to figure in
scientific literature. His criticisms
refer both to metaphysical and
mechanical theories. His position
is original and unique, and his
writings, which are a splendid
example of critical and liistorical

analysis, have been invaluable to
me. His earliest important es-says
date from the year 1872 (' Die
Geschichte und die Wurzel des
Satzes von der Erhaltung der
Arbeit,' and 'Die Ge.stalten der
Fliissigkeiten,' Prag). They are
now generally accessible, having
been collected and translated
(under the title 'Scientific Lec-
tures,' Chicago, 189.=i) by Prof.
T. J. M'Cormack. Hi.s 'Science of
Mechanics' (translated by the same
author from the second German
edition, London and Chicago, 1893)
has, ever since its first ap|>oanince
in 1883, had a great influence in
Germany ; and latterly also in this
country, as may be seen from sucli
works as Prof. Karl Pearsons
'Grammar of Science' (lat ed.,
1892, p. 387\ and noUbly from
Prof. Love's 'Dynamics' (p. 85).

184

SCIENTIFIC THOUGHT.

aware of the importance of mathematical presentation of
their doctrine, and the two former have in fact done
more than any one else to introduce mathematics into
chemistry. But they maintain that their exact treatment
is not arrived at by introducing hypothetical quantities
such as the atomic and other theories are founded upon,
but by contenting themselves with measuring such quan-
tities as are presented directly in observation, such as
energy, mass, pressure, volume, temperature, heat, elec-
tric potential, &c., without reducing them to imaginary
mechanical or kinetic quantities.^ To what extent they

A great many aspects of physical
science which have been more
prominently brought forward by
the modern school of " Ener-
getics " are to be found discussed
in Mach's much earlier writings.
To his valuable 'Principien der
Wiirmelehre ' (Leipzig, 1896) I have
frequently had occasion to refer in
this chapter.

^ In recent discussions and
treatises two distinct tendencies
must be distinguished. First we
have tlie very useful effort to bring
about a correlation of the differ-
ent departments of physics and
chemistry, including their applica-
tions in industry and in physi-
olog)', by the introduction of the
conception of energy and the
principles of its conservation and
transformation. This dates prac-
tically from the publication of
Thomson and Tait's ' Natural
Philosophy. ' The theoretical

foundations of this undertaking
have been very fully discussed,
notably in Germany. I mention
only the valuable series of writ-
ings of Prof. Max Planck, a list
of which is contained at the end
of his ' Thermodynamik ' (Leipzig,
1897). They begin with his prize
essay (' Das Princip der Erhaltung

der Energie,' 1887) and his earlier
dissertation (Munich, 1879) " On
the Second Law." Out of this an-
other endeavour has grown. The
aim is to make the conception
of energy the fundamental notion,
and by following its physical ap-
pearance in its different forms,
to arrive at certain fundamental
relations expressed in equations,
which are to serve as the basis
for calculation, as in conventional
physics the dynamical equations
formed the starting-point for the
various physical theories. In this
more radical scheme the quantity
" energy " was to play a part similar
to that which the quantity " force "
played in Newtonian dynamics.
This method was probably sug-
gested by the novel mode of
treatment invented originally for
heat - problems by Lord Kelvin
and by Clausius, and most strictly
adhered to by the former. The
isolated character of this classical
thermo-dynamics can be got over
either by introducing a kinetic
hypothesis on the nature of heat
or by extending the method of
thermo-dynamics to other physical
provinces. The former was the
most plausible view ; it has its
origin in the writings of Rankine

ON THE PHYSICAL VIEW OF NA'l I l:E.

18;

!iiay succeed in doing this consislenlly seems ul juesenl
uncertain. It has been maintained that the very
elements of all physical measurement, the independ-
ence of the three dimensions in space, necessitates us
to supplement the energy-conception — which by itself
includes no more reference to diroctinn tlian the con-
ception of mass — by an assumption of ;i purely mecliani-
cal nature such as the numljer of degrees of freedom,
and that the much-discussed correlation of all forms of
energy, as it is suggested by W. Gibbs's formuhe, cannot
be usefully carried farther. This correlation ^ has l^een

and Clausius. The latter method
grew out of the gradual aj)|)lication
of thermo- dynamics to chemical
phenomena, where the mechanical
treatment had turned out to be
powerless. This more
scheme of remodelling
of j)hysics, chemistry,
ehanics on the
classical thermo

ambitious
the whole
and me-
model of the
dynamics dates

from the year 1887, when Prof.
Georg Helm published his first
treatise ('Die Lehre von der En-
ergie,' Leipzig) and revived the
word "energetics" invented by
Rankine. Subsequently he pub-
lished his application to chemistry
('Grundziige der mathematischen
Chemie,' Leipzig, 1894), very
much under the influence of
Willard (Jibbs's studies of chem-
ical equilibria and Duhem's elab-
oration of Hehnholtz's conception
of free energy. His last work
('Die Energetik,' Leipzig, 1898)
gives a history of the gradual
purification of the energy concep-
tion from mechanical admixtures,
into which all earlier writers on
the subject except Lord Kelvin
are shown to have lapsed, and
attempts a reconstruction of me-
chanics on "energetic" principles,
<l€fending the author's position

against various criticisms which
had meantime been made.

^ The great generalisation of the
science of energetics referred to in
the text was first explicitly put
forth by Helm in his treatise of
1887. He himself holds that he
there finally brought together sug-
gestions made in various ways by
Zeuner (1866), Mach (1871), Oibbs
(1875), Maxwell (187.''). Von Oettin-
gen (1885), and Popper (1884), and
expressed them in the form of a
general i)rincii)le. The two factors
into which all energy can be sep-
arated are called by various sub-
sequent writers intensity, jiotentiai
level on the one side ; extensity,
capacity, weight, on the other.
In spite of further expositions of
Helm in 1890 the subject did not
attract much attention till Prof.
Ostwald introduced it in a slightly
modified form in the second edition
of his great work on physical chem-
istry (1893), making it tiie foun<la-
tion of the doctrine of affinity.
He had evidently, between the
first and second editions, given up
the mechanical for tiie "ener-
getic " treatment of the subject
(see, inter alia, note 2, p. 114,
of the 2nd edition ; vol. ii. i>. 12).
At the meeting of the German

186

SCIENTIFIC THOUGHT.

placed at the summit of the modern theory of energetics
by Helm and Ostwald, after earlier writers, such as
Zeuner and Mach, had already used it or drawn atten-

"Is'aturforscherversammlung," held
at Vienna in 1894, a committee
was appointed to report in 1895
at Liibeck on the " actual position
of energetics," and the introduc-
tion of the subject was put into
the hands of Dr Helm. His ad-
dress and the discussion which
followed have been given in extract
in the published ' Verhandlungen '
(vol. ii. part 1, p. 28. &c.), and
since continued in ' Wiedemann's
Annalen,' vols. Ivii. et seqq. Simul-
taneously, however, the subject
received a much more fundament-
al or philosophical development
through Prof. Ostwald's general
address at Liibeck with the some-
what polemical title " Die Ueber-
windung des wissenschaftlichen
Materialismus." From that mo-
ment the mechanical view of
nature bore the stigma of ma-
terialism, to which the other
side replied by attaching to the
new or energetic view the stigma
of " metaphysical " (see Planck,
'Wied. Ann.,' vol. Ivii. p. 77) as
being scientifically vague and
useless. It cannot be said that
the whole matter has yet been
fully discussed or fathomed. Prof.
Boltzmann, Prof. Carl Neumann,
and Dr Helm have treated the
questions at stake with much
patience, and have made valuable
approaches to a mutual under-
standing. The various contrib-
utions are most fully discussed
in Helm's latest work, ' Die En-
ergetik ' (Leipzig, 1898). Some of
those who originally assisted in
introducing the energetic treat-
ment have since refused to go the
length of Helm's and Ostwald's final
generalisations, though they prefer
— for the purpose of the treatment

of thermo-dynamical and chemical
problems — the phenomenological
method, admitting at the same
time the usefulness of the atomic
and mechanical hypotheses, though
some do not look upon them as
indispensable. This phenomeno-
logical view, which deals only
with observable and measurable
quantities, in contradistinction to
the atomic and kinetic views,
is largely represented by Prof,
Xemgt (see his ' Theoretical Chem-
istry,' translated by Palmer,
London, 1895, p. 22), and by
Prof. Planck (see his 'Thermo-
dynamik,' Leipzig, 1897), though
the latter considers it merely
provisional, a stepping - stone in
the direction of a mechanical
view (p. V, preface). Prof. Boltz-
mann has summed up the position
from a general point of view in
his address at Munich in 1899.
He there very lucidly defines the
mechanical, energetic, and pheno-
menological positions, admitting
the usefulness of all three, but also
points out the fundamental diffi-
culties into which a one-sided and
exclusive development of any of
them unavoidably leads us. Hav-
ing himself done so much in ap-
plj-ing atomic theories, he con-
cludes by saying that " the
I numerous conquests of the atomic
I doctrine cannot be won by pheno-
I menology or energetics," and main-
tains " that a theoiy which yields
something that is independent
and not to be got in any other
way, for which, moreover, so many
phy.sical, chemical, and crystallo-
graphic facts speak, must not be
combated but further developed "
(' Verhandlungen der Versamm-
lung zu Miinchen,' 1899, p. 121).

ON THE PHYSICAL VIKW OF NATrRE. 187

tion to it. It can be set out in tlie sUitenient that
wherever energy shows itself it appears as composed of
two factors — the intensity and the capacity factoi-s.
These terms, borrowed from the older theories of heat
and electricity, measure the quantity of energy as well as
the direction in which changes of energy take place: the
L^eneral law being that energy, in whatever form it
may appear, tends to go from places of higher to places
of lower potential or intensity.

The characteristic feature of this most recent outcome
of the physical view uf natural phenomena is that it c™*
takes in real earnest the suggestion at which many
natural philosophers have independently arrived, that
energy is a substance quite as much as matter. .This
granted, it seems at least reasonable to some thinkers to
see how far they can get by employing the two con-
ceptions of matter and energy alone without adopting
a third something, the ether, which was introduced at
a time when the idea of the conservation of energy
had not yet been formulated.^

The oDt-

' For an indication of tlie furtlier
development of this point of view I
must refer the reader to tlie chapter
on Photo -chemistry in Prof. Ost-
wald's great work ('Allg. Chemie,'
2nd ed., vol. ii. part 1, p. 1014, &c.)
" lu the interest," he says, "of a
conception of nature which is free
from hypotheses, we must ask
whether the assumption of that
medium, the ether, is unavoidable.
To me it does not .seem to be so.
If we a.sk for the cause of all dis-

energy to be a real thing, indeed
the only real thing in the so-called
outer world, there is no need to
inquire for a carrier of it when we
find it anywhere. This enables us
to look upon radiant energj' as in-
dependently existing in sjiace. A\'e
have found in the gentral law of
intensity — i.e., in the empirical
fact that energy tends to equalise
forced changes of its den.sity in
space — the principle according to
which transmission of energy in

placements of energy in s)>ace space necessarily takes place when

which we can singly observe, we tliere appears aiiywheic an excess."

find that it always consists in differ- From this and other passages of

ences of intensity. . . . The main Prof. Ostwald's writings it seems

point is that, having conceived ; as if ma.s8 likewise wad to lie given-

188

SCIENTIFIC THOUGHT.

53. But whilst the question as to the true method of

Recent

triumphs of physical research is still being ventilated abroad, as it

.atomic view. ^ '' "

has recently begun to be in this country also/ the
mechanical conceptions of atoms and ether have quietly
gained new victories. At the end of the last chapter
I related how, in the hands of Maxwell and his fol-
lowers, the word " electricity " gradually lost its sub-
stantial meaning, so that there remained only the con-
ception of a state of motion or stress in the electro-
magnetic field, it being difficult to assign a definite
sense to the term, an electric charge. That those who
were brought up under the ideas of Coulomb and Weber
would naturally regard this as a defect has also been
noted. Still more had the substantial nature of elec-
tricity been forced upon those who studied the electro-
lytic action of solutions and currents, the wandering of

up as a secondary phenomenon of
£nerg}'. See Boltzmann, loc. eit.,
last note, p. 114, &c. ; also, inter
alia, Dr R. Pauli, ' Der erste und
zweite Hauptsatz,' Berlin, 1896,
preface.

^ The discussions which began in
Germany in the year 1895 at the
meeting at Liibeck, and have, after
being continued at subsequent
meetings, and in the volumes
of the 'Annalen der Physik und
Chemie,' come to a kind of stand-
still by the exhaustive treatise
of Helm on the one side and
by Boltzmann's summing up on
the other, do not seem to have
attracted much attention in this
country. Interest in the subject
was, however, latterly aroused
by two criticisms of the princi-
ples of scientific method coming
from entirely different quarters.
The first, which was of a purely
philosophical character, was con-

tained in Prof. James Ward's ' Gif-
ford Lectures' (1896-98), published
in two volumes with the title
' Naturalism and Agnosticism.'
The other was an Address deliv-
ered by M. Poincare at the
Congress of Physicists in Paris in
1900. In consequence, the subject
of the legitimacy of the various
physical principles, such as action
at a distance, atomism, kinetic and
ether theories, the use of meeliauical
models, and many kindred ques-
tions, have been discussed in the
Addresses of Poynting (1899), Lar-
mor (1900), and Riicker (1901),
before the British Association, with
a very emphatic attestation of the
usefulness and indispensableness of
the atomistic theory regarding the
constitution of matter, and the
view that a continuous ether is
the carrier of all physical actions
through space.

ON THE PHYSICAL VIEW oK NATrRE. 189

the ions, and how, during Llie process, wandering atoms
gave up or lost a definite something — viz., their electrical
charges. It seemed impossible in this cose to do without
an atomic or molecular view of electricity. Accordingly,
Helmlioltz, in his celebrated Faraday Lecture (1881),
after Iiaving traced the gradual displacement of the
Weberian theory of electrical particles acting at a
distance by that of Faraday, feels himself constrained
to say: "I see very well that the assumption of two
imponderable fluids of opposite ([ualities is a rather
complicated and artificial machinery, and that the
mathematical language of Clerk ^Maxwell's theory ex-
presses the laws of the phenomena very simply and
very truly ; . . • but I confess I should really ])e at a
loss to explain . . . what he considers as a quantity
of electricity, and why such a quantity is constant, like
that of a substance." And further on he says : " If we
accept the hypothesis that the elementary substances
are composed of atoms, we cannot avoid concluding
that electricity also ... is divided into definite
elementary portions, which behave like atoms of elec-
tricity."

Besides the phenomena of chenucal decomposition, :>*■

^ '■ Modem

there was another very large and important class of f'cctncai

•JO I researchcj.

phenomena which gradually led up to the conception
of the substantial and atomic nature of electricity.
This province of independent, and for a long time
isolated, research was opened out by the coml)ined
genius of PlUcker and Geissler. It was in tiic year
1857, two years before the announcement of tlie dis-
covery of spectrum analysis, that Pliicker, with the

190

SCIENTIFIC THOUGHT.

aid of the now well-known vacuum tubes of Geissler^
of Bonn, began that long series of experiments on the
discharge of electricity in rarefied gases, on the influence
of magnets upon the course of the luminous rays, and on
the spectra of incandescent gases, which subsequently,
in the hands of Sir WilHam Crookes" in this country,
of Hittorf, Goldstein, Elster and Geitel, and of Giese in
Germany, and of a great number of other natural phil-

1 See the Memoir of Plticker iu
the ' Anualen der Physik und
Chemie' (1857); " Ueber die Ein-
wirkung des Magneten auf die
elektrischen Entladungen in ver-
diinnten Gasen " (reprinted in
' Gesammelte wissenschaftliche Ab-
handlungen,' vol. ii. p. 475, &c.)
Before Pliicker took up the investi-
gation with improved means of
exhaustion (later perfected by the
well-known Sprengel pump), several
French experimentalists — notably
Quet, Gassiot, and Abria — had in-
dependently marked the difference
of the light near the positive and
negative poles, mostly in ignorance
of the observations recorded by
Faraday in his early " Experi-
mental Researches," as far back
as 1838, referring to the " dark
discharge." Lord Kelvin, in his
Presidential Address before the
Royal Society (November 1893), re-
fers to the researches of Faraday,
and to a long list of contributions
to the same subject contained in the
Proceedings and Transactions of
the Royal Society. Except those
of Faraday, they are all later
than Pliicker's earliest papers.
Lord Kelvin himself saj's : " Fifty
years ago it became strongly im-
pressed on my mind that the differ-
ence of quality between vitreous
and resinous electricity, ... es-
sentially ignored as it is in the
mathematical theories . . . with
which I was then much occupied

(and in the whole science of mag-
netic waves as we have it now),
must be studied if we are to learn
anything of the nature of electricity
and its place among the properties
of matter." Cf. the words of Hit-
torf (Pogg. 'Ann.,' vol. cxxxvi. p. 1),
quoted by Rosenberger, ' Geschichte
der Physik,' vol. iii. p. 778.

- The experiments and discov-
eries of Sir \V. Crookes on " Radiant
Matter," beginning with his paper
in the ' Transactions ' in December
1878, and continued in many sub-
sequent communications, as also in
his Address before the Brit. Assoc.
in 1879, especially his theoretical
explanations based upon concep-
tions taken from the kinetic theory
of gases, made a great sensation and
led to much discus.sion in this coun-
try and abroad. The term Radiant
Matter was adopted from Faraday
(see Rosenberger, loc. cit, vol. iii.
p. 779). The corpuscular theory
of light was not indeed revived ;
but in general, after much criticism,
Crookes's views have to a large ex-
tent been adopted ; and if not the
corpuscular theory of light, cer-
tainly that of electricity has been
greatly supported bj' these brilliant
experiments. See J. J. Thomson in
the Princeton Lectures (1898), p.
189 sqq., and Prof. Kaufmann's
Address, delivered at the Hamburg
meeting in September 1901 (trans-
lated in the ' Electrician ' of Nov-
ember 8, 1901).

ON THE PHYSICAL VIKW OF NATUHK. 191

osophers, revealed u huge unay ul' sliange and sUirtling
phenomena, whicli have latterly been brought somewhat
into line and order by the researches of Prof. J. J. Tliom-
son/ of Cambridge. A great many half-forgotten facts
and experiments, wliich did not fit into the regular pro-
gramme of electrical science or practice as it had Ijeen
elaborated by the older doctrine of Couloml) and Weber
on the one side, or by the more modern of Faraday and
Maxwell on the other, were collected and shown to
throw (juite a new light on the processes of radiation
and electrification, and on the relations of the atoms of
ponderable matter to the vacuum, now looked upon as
filled with a continuous substance, viz., the ether. The
older views of the two electricities, brought before
the eye by the celebrated figures of Lichtenberg ; -
many isolated facts connected with the electric spark
and statical electricity, such as were collected by Kiess
seventy years ago, or demonstrated in the hydro-electric
machine of Armstrong ; theories, many times abandoned

' Impressed with tlie importance otiiers as well as of their own by

which attaches to the plienomena in Klster and (Jeitel, will be found in

question for a further development the ' Annalen der Phj'sik' (1889),

of tlie theory of electricity founded i vol. xxxvii. p. 315 sqq.

by Faraday and Maxwell, Prof. J. J. I - Whilst the diHerence.s Vjetween

Thomson, in his ' Researches,' jiub- the discharges from the j)ositive and

lished in 1893 as a sequel to Max- negative terminals, after having

well's great treatise, devoted a for a long time been looked ujion

long cha[)ter to " The Passage of , as isolated curiosities of electrical

Electricity through Oases." His science, were being taken up and

own celebrated contributions to ; studied in connection with the

this subject, after having been . subject here referred to (see J. J.

published in the 'Philosophical Thomson, ' Researches,' p. 172 577. ),

Magazine,' and brought before the Lord Armstrong, during the jwst

Dover meeting of tlie British As- ten years of his long and eventful

sociation in 1899, are now summar- life, carried on a scries of e.\i>eri-

ised in his lectures on "The Dis- ; ments on a large scjilc, and with

chargeof Electricity through Oases" verj- jjowerful si>ccially designed

(1898). A very interesting earlier apf)aratuH, on 'Electrical Discliarge

summary of the researches of in Air and Water ' (ISS.'i).

192

SCIENTIFIC THOUGHT.

and as often revived, like that of Prout/ on the con-
stitution of matter ; the fanciful speculations of Zollner,
based upon the views of Wilhelm Weber, — all these
scattered fragments or glimpses of knowledge promise
at the end of the century to come together into a con-
sistent theory of the nature of electricity as an atomi-
cally - constituted substance which is associated with
particles of ponderable matter, or may even be the
ultimate constituent of such matter itself. When a
large mass of experimental facts and many lines of
special reasoning gradually converge towards a common
view, two things are indispensable in order to weld them
into a consistent whole, viz., a new name or vocab-
ulary and an hypothesis as to the elementary processes
which will allow of a simple construction and subsequent
mathematical calculation of the more complicated phen-
omena of actual experience. In the case before us, both

^ See the concluding chapter of
Prof. J. J. Thomson's ' Discharge of
Electricity through Gases ' (espe-
cially p. 197, &c.), where, after dis-
cussing Goldstein's "ether" theory
and Crookes's " corpuscular " theory
of the nature of the celebrated
cathode rays, he, mainly on the
strength of his own and Lenard's ob-
servations and calculations, inclines
towards the latter theory, conclud-
ing that the carriers of the negative
charges of electricity " are small
compared with ordinary atoms or
molecules, . . . this assumption
being consistent with all we know
about the behaviour of these rays."
"It may," he continues, "appear
at first sight a somewhat startling
assumption in a state more sub-
divided than the ordinary atom ;
but a hypothesis which would in-
volve somewhat similar assumptions

— namely, that the so-called ele-
ments are compounds of some
primordial element — has been put
forward from time to time by"
various chemists. Thus Prout be-
lieved that the elements were all
made up of the atoms of hydrogen,
while Sir Norman Lockyer has ad-
vanced weighty arguments founded
on spectroscopic considerations in
favour of the composite nature
of the so-called elements. With
reference to Front's hypothesis,
if we are to explain the cathode
rays as due to the motion of small
bodies, these bodies must be very
small compared with an atom of
hydrogen, so that on this view the
primordial element cannot be hydro-
gen." See also Sir \V. Crookes's
protyle theory referred to, vol. i.
p. 402, note 2.

ON THE PHYSICAL VIKW OK NAJ ll:i:.

lO.i

The t«-nii

requisites were supplied before the close of the ceuturv,
Here and abroad, the term electron, introduced l»y l)r
.Tohnstone Stoney ^ about ten years ago, has been gener- "eieciruu.
ally accepted to denote the ultimate particle of elec-
tricity, tlie atom of electricity — positive or negative —
of Helmholtz. Mathematical theories have been Wfjrked
out independently abroad by Prof. H. A. Lorentz - of
Leyden, and in this country by Dr Joseph Larmor"^ (;f
Cambridge.'*

^ See 'British Association Report.'
1891, p. r.74, "On the Cause of
Double Lines in Spectra," by G.
Johnstone Stone}' : " The lines of
the spectrum of a gas are due to
some events which occur within
the molecules, and which are able
to affect the ether. These events
may be Hertzian discharges be-
tween molecules that are differ-
ently electrified, or they may be
the moving about of those irre-
movable electric charges, the sup-
position of which offers the simplest
explanation of Faraday's law of
electrolysis. . . . Several consider-
ations suggest that the source of the
spectral lines is to be sought not
in the Hertzian discharges, but
in the carrying about of the
fixed electric clmrges, which, for
convenience, may be called the
electrons."

- Prof. Lorentz's principal writ-
ings are the two memoirs, ' ' La
Theorie dlectromaguetique de
Maxwell et son Application aux
Corps mouvants" (Leyden, 1892),
and " Versuch einer Theorie der
electrischen und optischen Erschei-
nungen in bewegten Korpern "
(Leyden, 189.o). His first labours,
indeed, go back to the year 1880.

•* Dr Larmor's principal publi-
cations are, "A Dynamical Theory of
the Electric and Luminiferous Med-
ium" ('Philos. Transactions," 1894) ;

VOL. II.

Part ii., "Theory of Electrons,"
1895; Part iii., "Relations with
Material Media," 1898 ; and his
Adams Prize Essay, " .i-Ether and
Matter, a Development of the
Dynamical Relations of the .lEther
to Material Systems on the Basis
of the Atomic Constitution of
Matter" (Cambridge, 1900). Dr
Larmor's several shorter pa])er8
and addresses, to which I shall
refer, are very hel[)ful as intro-
ducing one into this novel domain
of science.

■* A little later than Lorentz and
Larmor, Dr Wiechert of Konigs-
berg began (in 1896) a series of
publications on the same subject,
with the aim of making the Max-
welliaii conceptions more definite.
With him, also, the problem narrows
itself down to a reconciliation of
the continuity of the ether with
the atomic nature of ponderable
matter, and of the electrical charges
attached to it. His views, to-
gether with a historicid ana-
lysis of the labours of his great
predecessors. Coulomb, Ampere,
Biot and Savart, Neumann, Far-
aday, Maxwell (including the
formal simplifications introduced
into Maxwell's scheme by 0.
Heaviside, Hertz, and Poynting),
Von Helmh«)ltz, and H. A. Lorentz,
are very concisely set out in a
memorial essay entitled ' Gruud-

N

194 SCIENTIFIC THOUGHT.

56. The theory of Maxwell had not only failed to give a

Difficulties • i> ^ p i

of Maxwell's definite meaning to the conception ot a charge ot eiec-

theory. ° . „

tricity ; it had also, in the general term "dielectric, some-
what obliterated the clear distinction between empty
space and space filled with insulating matter, such as
air. Empty space, i.e., space devoid of matter, was sup-
posed to be filled with some continuous substance, the
ether, which was the seat or bearer of electric and mag-
netic actions, the electro-magnetic field. When the only
clearly known property of this ether, the fact that it
was the carrier of radiation or the luminiferous medium,
was identified with its electro-magnetic nature — light
being conceived to be an electro-magnetic disturbance —
the new theory had to attack the great question of the
relation and interaction of ether and matter, in which
all the remaining problems of physical optics seemed
centred.-^ How was the electro-magnetic theory of light,

lagen der Elektrodyiiamik,' pub- easily explained by the then

lished on the occasion of the un- I current projectile theory of light

veiling at Gcittingen, in 1899, of ' (see above, chap. vi. p. 10, note), has

the monument erected in honour ■ cauised great difficulty to the un-

of Gauss and Wilhelm Weber. It dulatory theory, and even Sir

is interesting to see how, from ap- George Stokes, whose ideas on the

parently quite independent begin- subject have been very generally

nings, and in centres far removed quoted and accepted, would, in his

from each other, the ideas of the Burnett Lectures on Light (1883),

atomic nature of electricitj^ have saj' no more than that " according

almost simultaneously become crys- to the theory of undulations . . .

tallised, and have united them- | it is not inexplicable " (ed. of 1887,

selves with the great experimental ' p. 25). That the electro-dynamic

labours emanating from Pliicker j view of the ether should take up

and Crookes to give rise, at the ' the problem was most natural, and

end of the century, to the modern ! the discussion of it is accordingly

theory of electrons. placed at the opening of Lorentz's

^ One of the most important of memoir of 1895 ; the effect of the

these problems is the question to motion of the earth on optical

what extent the ether takes part phenomena having already been

in the motion of ponderable matter treated by him in 1887. Dr

through it. Astronomical aber- Larmor treats very fully of this

ration, discovered by Bradley, and subject in the first section of his

ON THE PHYSICAL VIEW OF NATURE. 195

or the wave theory of electricity, to deal with the prob-
lem of ether and matter ? In this combined scheme ".
what and where were the electric charges or units ? 'ic ihc

"^ charges ?

On the Continent the labours of Prof. H. A. Lorentz
of I^yden, and the almost simultaneous memoir of Von
Hehnholtz, approached this subject from the side of
certain optical problems, notably the vexed question
whether the luminiferous ether is stagnant, or par-
ticipates in the movements of ponderable matter through
it, and the phenomena of dispersion. These writings
have formed the beginning of a long series of theoretical
and experimental researches, which are by no means
concluded. In this country we must chiefly consult
the many and highly interesting writings of l)r Larmor
for a fundamental discussion of the numerous problems
involved. At the same time we find there a very
thorough criticism, appreciation, and embodiment of the
many scattered suggestions and contributions of English
and Continental thinkers. Dr Larmor starts from a ss.
begnining which is peculiar to him. He niids among iHJsiuon.
the older theoretical discussions of the nature of the
luminiferous ether one ^ which will permit of such an

€6say " On -Ether and Matter," etrate a little deeper into the

and W. Wien has quite recently nature of these building stones

introduced it for discussion at and their mutual action " {loc. cit.,

the " Deutsche Xaturforscherver- p. 56).

«ammlung" (DiisseMorf, 1898, Ber- ' The historical traditions of Dr

icht i. p. 49). On the occasion of Larmor's theory seem to lie in

this discussion, Prof. Lorentz said : what may be called the Dublin

" Ether, ponderable matter, and, school of mathematical physics,

we may say, electricity, are the with the great names of Kownn

building stones out of which we Hamilton (vector analysis), Mac-

•compound the material woild, and Cullagh, and, in recent times, the

if we only knew whether matter, much lamented G. F. Fitzgerald,

in its motion, carries the ether "The form under which tlie

with it or not, a way would have atomic electric theory is intro-

•opened by which we could pen- duced in Dr I^armor'a latest es.say

196

SCIENTIFIC THOUGHT.

elaboration as admits on the one side the Maxwellian
definitions of the propagation of electro-magnetic waves,
and on the other the definition of electrons as per-
manent but movable states of twist or strain, which
form the atoms of electricity, and possibly, in their
aggregate, ponderable matter itself. The history of
thought is mainly interested in this latest and most
comprehensive " theory of the electric and luminiferous
medium," because it is almost entirely based upon that
great advance in physical theory which we owe to
Helmholtz and Lord Kelvin, " the discovery of the
types of permanent motion, which could combine and
interact with each other without losing their individu-
ality, though each of them pervaded the whole field."
This has rendered possible an entirely new mode of
treatment,^ and at least made thinkable the reconciliation
of the two apparently contradictory notions of modern
physics, the continuity and uniformity of the all-
pervading ether and the discontinuity of the embedded
particles of matter and electricity. The history of
thought also takes further note that these latest and
yet unfinished theories revert, after the interval of thirty

originally presented itself . . . in the
course of an inquiry into the
competence of the sether devised
by MacCullagh to serve for elec-
trical purposes as well as optical
ones" Cither and Matter,' p. vi.)
"No attempt was made to ascer-
tain whether MacCullagh's plenum
could, in addition to its vibratory
functions, take up such a state of
permanent strain as would repre-
sent the electrostatic actions be-
tween charged conductors, or such
state of motion as would represent

the electro-dynamic action between
currents. The first hint on this
side of the matter was Fitzgerald's
passing remark in 1880 (' Phil.
Trans.,' "On the Electro-magnetic
Theory of Light"), that Mac-
Cullagh's optical equations ' are
identical with those of the elec-
tro-dynamical theory of optics de-
veloped by Maxwell ' " (p. 78).

^ See Larmor's Address to the
British Association at Bradford
('Keport,' p. 624).

ON THE PHYSICAL VIEW OF NATURE.

10'

years, to the older and apparently abandoned views con-
tained in the writings of Wilhelni Weber, who dealt
with electric particles and tlieir jictions at a distance.
The chasm has been bridged over by such theories as
those of Lorentz and Larmor, and tlie missing link sup-
plied which prevented Gauss ^ from accepting that
theory when it was first comnninieated to him by its
autlior."

' See above, p. 67, note, where
Gauss's letter isquoted ; also Laniior,
loc. cit., and '.-Ether and Matter,' pp.
22, 72 ; ' Philos. Transactions,' vol.
clxxx\-i. (1895), p. 726 ; H. A. Lor-
entz, ' La Theorie ^lectromagndtique
de Maxwell,' 1892, p. 71 : "On voit
done (^ue, dans la nouvelle forme,
la theorie de Maxwell se rapproche
des anciennes idees. On pent
meme, apr^s avoir etabli les for-
niules assez simples . . . regarder
ces formules comme exprimant une
loi fondamentale comparable ii
celles de Weber et de Clausius.
Cependant, ces equations conser-
vent toujours I'empreinte des
principes de Maxwell." Further:
Lorentz, 'Versuch einer Theorie,'
&c. (189.0), p. S : " In general
there lies in the assumptions which
1 make in a certain sense a return
to the older electric theory. The
kernel of Maxwell's vnews is hereby
not lost, Vjut it cannot be denied
that with the assumption of ions
we are not very far removed from
the electrical particles with which
one operated formerly." W'iechert
(' Orundlagen der Electrodynamik,"
p. 108) expresses himself siniilarly.
Lastly, I may refer to Prof. Kauff-
mann's very interesting Address
delivered at Hamburg, Septem-
ber 1891, translated in the 'Elec-
trician' (November 1901, p. 95
sqq.) So we may perhaps say that
as Larmor attaclies himself to the
traditions of the Dublin school,

Lorentz and other continental
representatives of the atomic view
attach themselves to the school of
Gauss and Weber. In pro<jf that
Weber's ideas never died out in the
Gottingen .school, see Riecke's Kloge
of Weber, Gottingen, 1897, p. 27,
and a very significant remark in the
verdict of the philo30i)hical faculty
on Planck's Prize Essay ('Die Erhal-
tung der Energie,' 1887, p. 10).

" It would be unjust to dismiss
this subject, the overwhelming im-
portance of which becomes evident
if we glance at the many contri-
butions which fill the third volume
of the ' Rapports presentcs au Con-
grcs International de Physique'
(Paris, 1900), without stilting that
the atomic theory of electricity nut
only furnishes the very keystone
which Gauss wa.s looking for sev-
enty years ago, but that it has
also stood the test of experimental
verification in the observation by
Zeemann of the effect of magnetism
on the rays of light, an effect
which Faraday souglit for in vain
about the time when Gauss was in
search of the keysUjne of electro-
dynamics. A very concise and
interestitig account of Zeonmnn's
])hen(imenon will be founil in M.
A. Cotton's monograj)!! " Le Phon-
omcne de Zeemann" ("' Scientia,''
Phys. Mathem., Paris, 1899):
"Comment M. Zeemann a-t-il eu
I'iilde d'etudier avec un appareil
de polarisation la lumi{>re t'misc

198

SCIENTIFIC THOUGHT.

59.
Objections
raised by
atomists.

The propounders of this atomic view of electricity
very naturally look with little favour on those other
theories which, under the name of energetics or pheno-
menology, would restrict the method of science to the use
of only such quantities and data as can he actually seen
and directly measured, and which condemn the introduc-
tion of such useful conceptions as the atom, the electron,
and the ether, which cannot be directly seen and can
only be measured by indirect processes ; and there is
no doubt that the century ends with a very emphatic
assertion of the rights and the legitimacy of the atomic
and mechanical views of nature, regarding the energy
principle as a regulative but not, by itself, a constructive
method of research and progress ; for, as Dr Larmor says,
"If a molecular constitution of matter is fundamental,
energy cannot also be so." ^ Nevertheless, though in
many ways opposed, the two views of nature meet at
least in one important point. Both theories have been

dans le champ magu^tique ? Ici
encore, la theorie vint aider I'ex-
perience ; cette fois, c'est h H. A.
Lorentz que Ton est redevable du
resultat obtenu. II est juste de
dire que d'autres considerations,
par exemple celle de Lord Kelvin"
(see Tait, Proc. Royal Soc, Edin-
burgh, 1875-76, p. 118) "auraient
pu, elles aussi, probablenaent con-
duire k cette decouverte de la
polarisation des raies. Mais en
fait, cette decouverte a ete faite
grace h, I'intervention de la theorie
des ' ions ' de H. A. Lorentz. Dans
cette theorie, dit M. Zeemann, on
admet qu'il existe dans tons les
corps de petites masses electris^es,
ou ' ions,' dont les mouvements
constituent tons les phenomenes
electriques ; les vibrations lum-
ineuses seraient des vibrations de
ces ions. L'^tat de Father est

determine entierement par la
charge, la position et le mouve-
ment de ces ions. . . . M. Lorentz
fit remarquer que les bords des
raies elargies devaient etre pol-
arises. L'exp^rience permit a
Zeemann de verifier cette conclu-
sion de Lorentz" (p. 37).

1 ' .Ether and Matter,' p. 286 :
" One efiect of admitting a mole-
cular synthesis of dynamical prin-
ciples ... is to depose the concep-
tion of energy from the fundamental
or absolute status that is sometimes
assigned to it. . . . We can know
nothing about the aggregate or total
energy of the molecules of a ma-
terial system, except that its numeri-
cal value is diminished in a definite
manner when the sj'stem does me-
chanical work or loses heat. The
definite amount of energy that plays
so prominent a part in mechanical

UN THE PHY.SH'AL NIKW i)l- NATl'KK. l'J9

forced to consider anew tlie ultimate principles of all
physical reasoning, notaljly the scope and validity of the
Newtonian laws of motion and of the conceptions of
force and action, of absolute and relative motion, as
defined or implied in the mechanical scheme which is
l)ased upon them. Also with their increasiui; com- «».

" Artllicul

plexity modern dynamical exidanations have undoubt- e'^rarur of
edly, to every impartial observer, acquired a certain llxpuia"''
character of artificiality which su^^gests the question to """"■
what extent all such mechanical schemes are an expres-
sion of actual truths or merely useful illustrations. For
the pursuit of scientific research this question is perhaps
of little importance : a method is a correct one if it
leads to correct results verified by oltservation. Philo-
sophically, as bearing upon the processes, powers, and
limits of human reasoning, the question is all-important.
We are thus led beyond the province of scientific into m.

'' ^ Tlie philo-

that of philosophic thought. In future chapters we shall j^p'''^ p">*>-
frequently ha\e occasion to note this tendency of the
jiurely scientific thought of the century to lead uj* to
philosophical problems. Wherever this is the case a
history of scientific thought may legitimately close one
of its chapters.

and physical theory is really the of iitature as the two conditions
mechanically available energy. ... whicli make generalisations pos-

This energy is definite, but is not,
like matter itself, an entity that is
conserved in unchanging amount.
... It may and usually does di-
minish, in the course of gradual
physical changes."

' The three volumes of the
'Rapports,' ka., mentioned above,
have been significantly prefaced by
a discourse of M. Poincard on the
relations of exi>eriiiiental and ma-
thematical physics, in wliiuh he in-
sists ujion tiic unity and simplicity

sible and useful. With special ref-
erence to modern electrical theories,
such as those of Lorentz and Ijarmor,
which he had aliejuly criticised in
his course on ' Electricit«5 ct Op-
tique' (2nd ed., 1901, p. lul. &c. ),
he discusses the i)i)ssibility <»f ulti-
mate mechanical explanations. Of
these, according to his view, an
" infinity " is always possible. He
asks what is the aim we are follow-
ing— " Ce n'est pas le mo<'anisme,
le vrai, le seul but, c'cit lunito."

200

CHAPTER VIIL

ON THE MORPHOLOGICAL VIEW OF NATURE.

1. The different aspects of nature which I have reviewed
scilnces.""^ in the foregoing chapters, and the various sciences which
have been elaborated by their aid, comprise what may
appropriately be termed the abstract study of natural
objects and phenomena. Though all the methods of
reasoning with which we have so far become acquainted
originated primarily through observation and in the re-
flection over things natural, they have this in common,
that they — for the purpose of examination — remove
their objects out of the position and surroundings which
nature has assigned to them: that they abstract them.
This process of abstraction is either literally a process of
removal from one place to another, from the great work-
and store-house of -nature herself, to the small workroom,
the laboratory of the experimenter ; or — where such re-
moval is not possible — the process is carried on merely in
the realm of contemplation : one or two special properties
are noted and described, whilst a number of collateral data
are for the moment disregarded. In the former case, it
is by a process of actual or physical, in the latter by one

ON THK MOnPHOLOGICAL VIEW OF NATURE. 201

(if purely nu'iiial, aUsLiuctitiu lliat (jur .stiuly l»cgins aud
is prosecuted. One very powerful instrument (jf re-
search, where through size and distance — be they very
great or very small — objects of nature are beyond our
actual reach, is given us in the tliagram and the model.
There we, for the sake of study, picture or imitate on
a reduced or an enlarged scale the movements of the
heavenly bodies which are too large or of the atom.s
which are too small for our actual grip. Now and
again the natural philosopher who thus uses the
abstract methods of experiment, registration, and cal-
culation, is forcibly reminded that he is in danger of
dealing not with natural, but with artificial, things. In-
stances are plentiful where, through the elal)oration of
fanciful theories, the connection with the real world has
been lost and scientific reasoning has been led astray, to
be recalled to a more fruitful path only by the effort of
some original genius living in immediate connnunion
with the actual world.

There is, moreover, in addition to the aspect of con- 2.

Convenience

venience, one very powerful inducement for scientific »»<! useful-

■^ '■ iies.s of the

workers to persevere in their process of abstraction, in ]^^^^"l„
the study of such things and phenomena as can be
handled in the laboratory and the workshop, and studied
by diagram and by model. This is the practical useful-
ness of such researches in the arts and industries. In
these we do actually abstract the possessions of nature
from their proper hiding-places ; we drag the minerals
from the bowels of the earth ; we cut up the timber
of exotic growth into artificial fragments ; we break
up that natural eciuilibrium in which eleclrieal and

202 SCIENTIFIC THOUGHT.

chemical agencies have, for thousands of years, evaded
our discovery and our regard. Having done so, we create
an artificial world of our own making which ministers
to our wants, comforts, pleasures, and supplies that
most inestimable of all commodities of civilisation,
varied and stimulating work for ready hands and active
brains. The wants and creations of artificial life have
thus proved the greatest incentives to that abstract and
artificial treatment of natural objects and processes for
which the chemical and electrical laboratories with the
calculating room of the mathematician on the one side,
and the workshop and factory on the other, have in the
course of the century become so renowned. All this
great activity is — as I have abundantly shown — more
and more governed by the scientific, the exact, or the
mathematical spirit.
3. There is, however, in the human mind an opposite

Interest

opposed to interest which fortunately counteracts to a considerable

the spirit of

abstraction, extcut the onc-sidcd working of the spirit of abstraction
in science and the growing tendency towards artificial-
ity in our practical life. This is the genuine love of
nature, the consciousness that we lose all power if, to
any great extent, we sever or weaken that connection
which ties us to the world as it is — to things real and
natural : it finds- its expression in the ancient legend
of the mighty giant who derived all his strength from
his mother earth and collapsed if severed from her. In
its extreme and purest form this interest probably lies
at the root of all poetry and all art, and it accordingly
governs a great part of the literature and thought of the
century. It will occupy us later on in our historical

ON THE MORPHOLOGICAL VIKW OV NATUltE. 203

survey. At present it interests us only as far as it
asserts itself also in science. In the study of natural
objects we meet with a class of students who are at-
tracted by things as they are : not so much by those
which we artificially prepare in (jur laboratories, as by
the infinite variety of real forms ; not so much ]jy the
geometrical types which allow us to bring them together
under some abstract formula, as Ijy the apparent disorder
;ind di\-ine confusion in which real things are scattered
about in the heavens antl on our globe. It is not the
general equation which in its complete solution contains
all real and many unreal instances merely as special
cases that interests them, Imt the individual examples
themselves. The general laws of motion admit of an
infinity of special cases which may never occur in nature ;
organic chemistry adds daily to the already enormous
array of compounds which do not present themselves in
living organisms. Clearly, besides the abstract sciences,
which profess t(^ introduce us to the general relations
or laws which govern everything that is or can be real,
there must be those sciences which study the actually
existing forms as distinguished from the possible ones,
the " here " and " there," the " where " and " how," of
tilings and processes ; which look upon real things not
as examples of the general and universal, but as alone
possessed of that mysterious something which dis-
tinguishes the real and actual from the ]iossible and
artificial. These sciences are the trul}- descriptive i.

Tlic dc«crip-

sciences, in opposition to the abstract ones. They are tivescieucos.
indeed older than the abstract sciences, and they have,
in the course of the period under re\iow in this work,

204 SCIENTIFIC THOUGHT.

made quite as much progress as the purely abstract
sciences. In a manner, though perhaps hardly as
powerful in their influence on practical pursuits, they
are more popular ; they occupy a larger number of stu-
dents ; and inasmuch as they also comprise the study of
man himself, they have a very profound influence on
our latent opinions, interests, and beliefs — i.e., on our
inner life. It is the object of this and some of the
following chapters to trace concisely the altered ways
and means by which, in the course of the last hundred
years, the study of the actual things and events of nature
has been prosecuted. For those who wrote the history
of the descriptive sciences in the middle of our century,
the arrangement of this vast subject presented little
difficulty. It had been in the main accomplished by
the great naturalists who, during the seventeenth and
eighteenth centuries, laboured to bring the large and
ever increasing number of natural objects into some
supposed system and some professed order, to enumer-
ate them in catalogues or marshal them in museums.
The familiar division of natural things into animals,
vegetables, and minerals had received a general sanction.
Separate sciences, with separate chairs at the univer-
sities, which still survive, attended to the separate
treatment of these subjects. One of the greatest
changes which the present age has witnessed has been
5. the breaking down of the old landmarks and of the

The break-

ing down of stereotyped divisions which existed in the beo-inning and

old land- "^ ^ o o

°^'^^- all throug;li the first half of the centurv.-^

^ This change has also very much
lessened the interest with which
we now regard the solution of a

times, was much discussed— the
classification of the sciences. It
will be seen that of the many prin-

problem which, down to recent ciples of division which have been

ON THE MORPHOLOGICAL VIKW OF NATUKE. 205

It' we try to specify a little iiiuiv closely tiie agencies
iuul interests that were at work in bringing about this
\('ry iiuirked change, which, like every change of the
kind, has been retiected 1)\ the altered vocaVmlary of
our languages, we come upon two distinct influences —

adopted, the present wurk uiily re-
tains that one principle which, in
>iime form or other, appears in
rvery attempt towards classitica-
lion — the difference between the
abstract and the concrete or actual.
The two original philosophical sys-
tems which France and England
in the course of the century
have produced, the positivist phil-
osophy of Conite and the j)hil-
■ i-.)|ihy of evolution of Herbert
Spencer, have both dealt elabor-
ately with the problem of the
1 l,i"iticatiou of the sciences. In
ilii^ they betray their descent from
the philosophy of Bacon and their
[Tactical tendencies. It is mainly
in the interests of teaching that
the division of the sciences is of
importance ; and so here it has
proved to be indispenfcable, but
also, not unfrequently, narrowing
:uul harmful. German philoso-
phers, who have generally been
more influenced by the traditions
ipf Descartes, Spinoza, and Leibniz,
have attached less importance to
the rigid divisions. The result
has been that in Germany, more
tl\an in any other country, those
modern sciences have grown up
which cultivate the borderland
tliat separates the existing well-
niarkcd jirovinces whicii arc; aititi-
ijally kept up by the older chairs
at the universities. Examples of
tliis are the new sciences of jdiysio-
I'l'^'inal psychology and of physical
rlicinistry, both brilliantly and for
tlie tirst time rejiresented at the
university of Leipzig. Tiie two
U'reat conceptions, however, which
have ])robably done more than any
'ithers to break down the old con-
\entional landmarks that kept

the .sciences asunder, the concep-
tion of energj' and the idea of de-
scent, were Hrst prominently )>ut
forward in this country. The
j classical treatise on the division of
j the sciences in the widest sen.se is
' the ' De Augmentis Scientiarum '
of Lord Bacon. An important and
original work on the subject is
Andre Marie Ampere's ' Essai sur la
Philosophie des Sciences, ou Ex-
position analj'titjue d'une ChussiHca-
tion naturelle de toutes les Con-
naissances humaines' (1834). An
analysis of the book is given in
Whewell's ' I'hilosophy of the In-
ductive Sciences,' vol. ii., Book 12.
Ampere's classification, on the
model of that in bot;iny, is sym-
metrical and dichotomous. Aug.
Comte's classification, contained
in the second " Leoon " of the
' Cours de Philosoj)hie positive '
(1830, vol. i.), is termed by its
author "une echelle " or"une hier-
archie encyclop(5dique." Mr Her-
bert Spencer, in an essaj- ' Ou the
Genesis of Science ' (1854), repub-
lished with additions in the third
volume of his ' Essays ' (1874), criti-
cised Comte's attempt to classify the
sciences "serially."' He more than
any other thinker has assisted in
breaking down the older idea, which
was very prominent in many classi-
fications of the great French natur-
alists, the idea of the subordin-
ation of things in nature, of the
" (5chelle des otres," and tiie corres-
ponding conception of an hierarciiy
of the sciences. In the place of
this serial arrangement, a genea-
logical arrangement, uutler the
specific term of evolution, wiv* in-
troduced, and the sciences were
co-ordinated according to their

206 SCIENTIFIC THOUGHT.

one of which has tended enormously to broaden our
view of natural objects and events ; the other to narrow
it down and make it more definite, scientifically ac-
curate, and precise. The former has tended to sweep
away the older landmarks and di\isions as inadequate
to afford us a correct \i.ew of nature ; the latter has
tended to create new di\'isions and definitions, more in
harmony with the lines on which the abstract sciences
of physics and chemistry have been developed, and has
thus brought the actual objects and events of nature
more within the grasp of those exact and mathematical
6. methods which those sciences have perfected. The former

The spirit of . , . , i i ^ i_

exploration, has bccu camcd on in the vast workshop or nature her-
self by those daring and far-seeing travellers who, with
Alexander von Humboldt at theu- head, have attempted
to gain a \iew of natui'e on an extensive scale. For the
sake of the increase of natural knowledge alone, they
visited distant countries where the elemental forces of
nature, undisturbed by the inroads of ci\'ilisation, have
battled and co-operated to produce the magnificent floras
and faunas of the tropics, or where, as in Siberia, the
eternal cold has preserved intact the remains of bygone
periods. Equipped with the instruments and methods of
modern science, they recognised the necessity of studying
the actual formation and stratification of rocks, the geo-
graphical distribution of organic life on the siu'face of the

genesis, the three great divisions | tinctions which I have adopted ;

being the abstract, abstract -con- ' and I remind them again that I

Crete, and concrete sciences. My \ am not writing a history of Science

readers will readily see the j but of Thought, and that all

similarities and the differences divisions of this great subject are,

which exist between this classi- more or less, arbitrary,
fication and the more general dis-

ox THE MORPHOLOGICAL VIEW OF NATrUE. 207

globe, i>v in tlie depths (if the ocean ; of visiting the real
dwelling-places, the habitat of living beingH : thus coun-
teracting and enlarging the narrow and pedantic views
which the older, purely systematic, and lifeless treatment
of natural objects was in danger of fostering. We know
how the germs of two of the greatest generalisations of
science were laid iu llie minds of Mayer and of Darwin
during their visits to distant countries, and how fertile
in natural knowledge of all kinds have been the voyage
of the Challenger and many other similar expeditions,
and with what interest and curiosity scientific and
popular audiences listen to the narrative of such daring
explorers as Fridjof Nansen.

The other and much more concentrated intluence,
which from the opposite side co-operated with the labours
of the great explorers in remodelling the descriptive
sciences and infusing new life and vigour into them,
has been not less marked. There has always existed
one great interest, in which nearly all the descriptive
branches of natural knowledge have found a common
rallying ground and a uniting purpose — namelv, the ".

" The medical

art of healing, the alleviation of human suflering and i"ierest.
the curing of disease. During long ages, when the purely
scientific interest was almost dead, physical and chemical
research was created or kept alive by the physician, the
alchemist, and the apothecary ; medical works like those
of Celsus and Galenus in antiquity ^ have lieen the ency-

' It may also be pointed out l the medical art of his father
that Aristotle was descended from Nicomachus, wlio was the medical
a family of doctors, that — accord- 1 adviser and friend of the Mace-

ing to Zeller (' Philosophie der
Griechen,' vol. ii. , part 2) — the
assumption is warranted " that

donian king, Amyutais, ha<l a
prominent influence on tlie mental
development of his son."

208 SCIENTIFIC THOUGHT.

clopedias of the existing knowledge of nature, and celeb-
rities like Boerhaave, Linneeus, and Haller in more modern
times have been the living centres of all the natural
sciences. The same uniting bond has not been want-
ing in our century, when it has again, as many times
before, manifested its powerful influence, has brought
together researches which were on the point of fall-
ing asunder, and infused new life and interest into the
driest of studies. As I have had occasion to remark
above, the modern school of medicine originated in the
attempt — begun by Lavoisier in France, but carried out
on the largest scale in the chemical and physiological
laboratories of Germany — of making the new discoveries
8. in physical science and chemistry fruitful for medical
science purposcs and the treatment of pathological cases. The

applied to

medicine, discovcry of galvauism gave probably the earliest im-
petus, and was, to the discredit of an exacter treatment,
largely misused in the earlier part of the century, till
Du Bois Eeymond, in the middle of the period, based his
elaborate researches on more correct methods, and created
nearly all the knowledge we now possess of the electrical
currents in the nervous system. Somewhat earlier, Liebig
led the study of the phenomena of animal heat and of
the food relations of the animal and vegetable kingdom ;
the brothers Weber had introduced dynamics into the
theory of the motion of the heart and the limbs ; whilst
Johannes Miiller and his numerous school about the same
time laid the foundations of physiological and pathological
acoustics and optics. Quite independently of these appli-
cations of the mechanical and physical sciences, which led
some over-hastily to imagine that in the doctrine of the

ON THi: MoltPHOLOGICAL VIEW OF NATLKK. 209

organism as a pure machine lay an answer to the great
problems of life and consciousness, Tlieodor Schwann 9

Schwanu.

proclaimed about 1840, on the basis of minute micro-
scopic observation, the essential identity of animal
and vegetable — i.e., of all living — structure, thus taking
probably the greatest ste]) in uniting researches which
had so far been carried uu in a tUsconnected fashi(jn.
Here is the beginning of the modern theory oi the
organic cell — of cellular pathology, antl the actual in-
auguration of modern biology. Twenty years later, the
appearance of Darwin's ' Origin of Species ' urged still 10
further the study of the whole of organic life from a
comprehensive point of view. In addition it led to a
closer union with the sciences of inorganic nature, an
appeal being now made to palteontological and geological
records in proof of the gradual development of all forms
of living as well as of inanimate reality. The studies
of the geologist, which up to then had l)een prosecuted
on independent lines, joined hands not only with those
of the zoologist and botanist, but likewise with the
theory of cosmological genesis of the planetary system,
as proclaimed at the end of the former century by
Laplace in his ' Exposition du Systeme du Monde,' and
fifty years earlier by Kant in his 'Natural History
of the Heavens.' If in the course of our century,
through the combined influence of travel on the one side
and medicine on the other, the history of natural objects
has been united in the larger conception of bicjlogy, this
itself at the close of the century promises to be united
with geology and astro-physics (a science almost entirely
founded on the invention and on the nidations of the

VOL. II. "

210

SCIENTIFIC THOUGHT.

11.
Herbert
Spencer.

12.

Whewell's

divisions

abandoned.

spectroscope), into the still wider conception of a general
science of evolution, as enunciated already forty years
ago in the writings of Herbert Spencer, and in a more
shadowy form by Herder in the eighteenth century, and
by Leibniz in the seventeenth.

Seeing, then, that the treatment of the descriptive
sciences of nature has been so radically changed during
the course of the century, and that the change has been
accompanied by a complete revolution in our modes of
thinking and reasoning on these subjects, the historian of
Thought cannot be content with merely chronicling the
progress of the methods in use in the separate sciences,
such as mineralogy, geology, botany, and zoology, even
with the addition of the more recent sciences of pale-
ontology, physiology, and comparative anatomy. He
might in doing so fairly grasp the history of the descrip-
tive sciences up to the year 1850. It is exactly in this
manner that Whewell, in his ' History of the Inductive
Sciences,' treated this part of his subject. Beyond that
period the old landmarks designated by those names
have disappeared or become of secondary importance.
On the other side, whilst a history of Evolution in
Science might seize on the great characteristic feature
of the more modern research which belongs to the
second half of the century, it would hardly suffice to
sum up the leading ideas of the descriptive branches
of science as they were carried on on independent
lines during the earlier years of our period. Evolu-
tion had then no definite meaning, and Biology was
a disregarded term. We must thus look out for some
more general aspects which belong alike to the earlier

ON THE MORPHOLOGICAL VIEW OF NATURE. 211

and later perioils, and which will enable us to see how
that great change has gradually come al)Out.

All studies that deal witli the actual things and events
by which, on a large and on a minute scale, we are sur-
rounded in nature, are comprised under the term Natural
History. In opposition to Natural Philosophy, which
comprises our abstract knowledge of the possible forms of
motion and the possible combinations of the elements into
which we have so far been able to decompose matter,
Natural History deals only with such forms and combina-
tions as actually exist around us, only with such processes
of change as actually take place in nature. Some of these
forms and changes we may be able to collect in our
museums or imitate in our laboratories, but the forms of
nature cannot in this way be exhausted, nor her pro-
cesses understood. Her forms or things do not exist in
isolation, but always in a certain environment, having a
definite plan, a position in time and space. These sur-
rounding features are as important as the things them-
selves. Besides this, the processes of nature draw on
the great factor of time with a much more liberal hand
than we can permit ourselves to do. Nevertheless, as in 13.

Divisions of

the abstract sciences we deal with things at rest and with uatunu

^ history.

things in motion, so we can appropriately divide our
study of the real and the actual into the attempt to
give some accoimt of the forms and things which
actually exist and continually recur, and the study
(jf the changes which things undergo. In abstract
science the terms statics and dynamics, the doctrines
of rest and nf uiotioii, have been generally introduced,
to distinguish tiie two great aims of study ; some cor-

212

SCIENTIFIC THOUGHT.

responding tenns mar appropriatelv define the twofold
interest which we take in natural objects. The term
morphology^ was introduced early in the century by

^ The term morphologr was in-
troduced bv Goethe to define a series
of researches and studies to which
he was led by his equal interest in
art. nature, and human society.
Returning from Italy, which he de-
scribes as ■■' rich in forms," to Ger-
many, which he tenns in contrast
■• gestaltlos," he reports that three
distinct problems had presented
themselvte. " Wie die b^iinstigte
griechische Nation veriahren um die
ht-ohste Kunst im eigenen National-
kreise zu entwickeln. . . . THe die
Natur gesetzlich zu Werke gehe,
um lebendiges Gebild, als Muster
yiffi kiinstlichen, hervorzubringen.
. . . Wie aus dem Zusammen-
trefien ron Nothwendigkeit und
XNillktir, von Antrieb und Wollen,
von Bewegung und Widerstand ein
drittes hervorgeht . . . die mensch-
liche Gesellschaft." For the pur-
pose of finding an answer to the
second of thee questions, Goethe
collected and observed, read and
speculated, and formed the con-
c-eprion of a general science of or-
ganised beings, termed morpholt^y,
which was not to treat merely of
external figure, but to comprise also
physiology and the study of develop-
ment. It is the first great attempt
to think of nature as a whole, and
to break down the rigid lines which
divided the several natural sciences.
He thus inaugurated the modem
view of nature by introducing the
general science of morphology. His
first literary attempt in this di-
rection was the now celebrated
pamphlet on the 'Metamorphosis
of Plants,' in which he represents
the leaf as the typical formation
from which the other parts of the
plant can be derived. Whether
this derivation is a real proc-ess in

the sense of modem evolution, or a
merely ideal one in the sense of the
earlier archetypal view, Goethe does
not clearly say. This uncertainty
Goethe shares with the whole school
of the •'Xatxirphilosophie, " as Julius
Sachs points out in his ' History of
Botsmy' ^German edition, 1S75,
p. 170). This is not the point to
which I want to draw attention at
present. More important is the
remark which Goethe makes in the
further historical accoiint of the
gradual development of his morpho-
logical ideas. Wolf, the philol<^ist,
pointed out to him that his own
namesake. Casp-ar Friedrich Wolf,
had anticipated Goethe in the at-
tempt to demonstrate the funda-
mental identity of the different
parts of a plant. In the sequel of
his most appreciative analysis of
Wolfs expositions, Goethe charac-
teristically notes that Wolf does
not include in his conception the
*' metamorphosis of animals," or in-
troduces it only as something en-
tirely difiierent. That Goethe's idea
of morpholep as a general science
of the forms and change of forms in
nature is applicable likewise to in-
animate forms — to geological, geo-
grajdiical, and many other forma-
tions, nay. even to rigid things like
crystals, and to such unstable for-
maticms as the pa^ ts of speech and
language — has in the course of the
century been abundantly recog-
nised. It is known how. guided by
the same general interest, Goethe
studied the formations and trans-
formations of animals, rocks, and
clouds, though, according to Zittel
( • Gesch. der Geologie,' 1 599, p. 275\
C. F. Xaumann first used the ex-
pression, " morphology of the svu--
f ace of the earth." in 1 S50. Goethe's

ox THE MORPHOLOGICAL VIEW UF NATURE. 213

one who bjved aliuve all things to watch the works uf
nature in their proper abodes — who combined the poeti-
cal with the scientific interest, — by Goethe. The ttirm
genesis ^ has long been employed to describe the pro-
cesses by which the actual world has come to l>e wiiat
it is. To the statical and dynamical aspects of the
abstract sciences correspond accordingly to some extent
the morphological and genetic aspects of the natural u.
sciences. To some extent only, for in nature, where !i'"iKtnetic«.
everything is subject to continual liow, we ne\ev come
upon a realisation of absolute rest, a pure form, a
rigid type. Eather would I put it in this way : In tlie
perpetual variety of change the morphological \'iew
tries to define those recurring forms or types which
present themselves again and again, towards which all
changes seem to revert ; thus l)ringing some order into

morphological writings have been
for the first time completely edited
and annotated in the three volumes
(6 to 8) of the second division of
his works now being published by
the Goethe-(!esellschaft at Weimar.
The authority whom I approach
nearest in the use I make of the term
morphology is probably Haeckel.
See the first book of his ' Generelle
Morphologieder Organischen Wesen '
(1866, vol. i. pp. 1-108).

' Goethe's morphological studies
were equally directed towards the
formation and the transformation
of living things : morphology was
to him the science of " Bilduug
uiid Umbildung." In the course of
the century the terms morphology
and morphological school have come
to mean more and more that com-
plex of comparative researches
which historically prepared the
genetic, developmental, or evolu-
tionist school of thought, but which

were mainly dominated by the con-
ception of fixed types and forms,
and, though searching for the laws
of modification, did not rise to a
clear enunciation of a theory of
evolution and descent. Goethe him-
self hovered all his life long between
an artistic predilection for the per-
fect form or model and a deeper
philosophical conviction of the con-
tinual flow of things. See a remark
of his (' Werke,' XL, vol. vi. p. 304)
in an aphorism on " genetic treat-
ment " : " Erst bin ich geneigt
mir gewisse Stufen zu denken : weil
aber die Nalur keinen Sprung
macht, bin ich zuletztgenothigt mir
die Folge einer ununterbrochenen
Thiitigkeit als ein Ganzes anzu-
schauen, indem ich das p]inzelne
aufhebe, ohne deu Eindruck zu
zerstoren." See also a remark on
Goethe's undefined position in
Cams, ' Geschichte der Zoologie '
(1872), p. r,90.

214

SCIENTIFIC THOUGHT.

what would otherwise be disorder and confusion. On
the other side, the genetic view deals with the tran-
sition from one form to another in the course of time ;
takes more interest in movement and in the process
and function ; and seeks for their probable laws and
regularities. Without wishing to limit these remarks
to merely organic or living things, the difference be-
tween the morphological and genetic views can be
brought home to the mind by referring to the different
objects of anatomy and physiology.^ This twofold and
very general aim — the desire to know what is, and how
it has come to be — has existed at all times, though fre-
quently obscured by artificial and temporary restrictions.
From this point of view I propose to survey the mental
attitude of the century towards the real things and
events of nature, as distinguished from the artificial or
mathematical forms and processes of our studies and our
laboratories, our calculating and measuring rooms. The

^ Genetic theories have every-
where been prepared and ushered
in by morphological studies. So in
Goethe's time ; so later on, after
Darwin had given a definite law
of descent, and Herbert Spencer
had fixed the vocabulary and ideas
of evolution, this relation is mani-
fested by two great works, the
' Generelle Morphologie der Organ-
ischen Wesen,' by Ernst Haeckel
in Germany (1866), and Francis
M. Balfour's ' Elements of Embry-
ology ' (1874) in England. It is
characteristic that Prof. Haeckel,
in the further development of his
literary activity, dropped the term
morphology, and published the de-
sired new editions of his great work
under two different titles, ' Natur-
liche Schopf ungsgeschichte ' (1868,

2 vols.), and ' Systematische Phylo-
geuie' (1896, 3 vols.) The division
of the great modern biological doc-
trine into morphology and genetics
is in conformity with Mr Herbert
Spencer's treatment in the ' Prin-
ciples of Biology,' vol. ii., published
in 1865, and with the two divisions
of Haeckel's ' Generelle Morpho-
logie,' which treated respectively of
the " science of developed forms "and
the "science of developing forms" —
i.e., of structure and process. I
have chosen such expressions in the
text as will permit of a compre-
hension of inanimate as well as of
animated nature. In 1875 there
were founded simultaneously in
Germany two periodicals, represent-
ing respectively the morphological
and genetic sides of animal biology.

ON THE MORPHOLOGICAL VIKW OF NATURE. 215

present chapter will deal with the innrphohjgical, the
following with the genetic, views of nature.^

Were the real w<irM unly one out of many possible
worlds which the mathematical iniiid can imagine, though
through its complication and intricacy it might .still
far surpass its powers of analysis; were the actual forms
of nature only some of the infinitely possible states of
equilibrium, the events and changes surrounding us in
space and time only a few of the countless condjinations
of motion taught in dynamics ; were the actual course
of things — as mathenuiticians since Laplace have fanci-
fully put it — only one particular solution of the general
differential equations of the world -motion, — then the
two great domains of morphology and genesis would
exhaust the subject and satisfy all the interests by which
natural historv has been created. Unfortunately for the is.

■^ other

pure mathematician, but fortunately for the rest of man- aspects,
kind, notably the poet and the artist, it is not so. An
enormous gulf separates the creations of nature from the
most perfect machine ; and the fact that, with all the
most delicate methods at her command, her most perfect
machines, like the human eye, do not come up to the
demands of the optician,"' shows us that other agencies

' As in abstract mechanics, the
study of the conditions of equili-
brium, i.e., statics, preceded in time
the study of the phenomena of
motion, i.e., dynamics, so in tlie
study of nature the apparently
finished or developed forms at-
tracted attention before their
genesis was inquired into ; and as
the key to statics has in the course
of time been discovered to lie in
dynamics, so the key to an under'

been found to lie in the dynamical
theory of descent or evolution. In
animal biology a separate influence
— the medical interest — led, how-
ever, very early to a studj' of func-
tion and of the processes in the
living organism.

- This refers to a well-known re-
mark of Helmholtz in his popular
lectures on the 'Theory of Light'
(1868), where he enlarges on the
remarkable imperfections of the eye

standing of form and structure has as an optical instrument. His real

216 SCIENTIFIC THOUGHT.

and other interests are at work than we have as yet
been able to grasp. So long as astronomy was content
to observe the orbits and motions of the heavenly l)odies
from a distance, it indeed appeared possible to define
that science as merely " une question d'analyse " ; but in
astronomy even, spectroscopy has brought distant objects
near to us and opened out endless vistas into a purely
descriptive branch of the science, a natural history of
the heavens. Still more so is this the case when we fix
our gaze on the world immediately surrounding us — on
the things and events in which we ourselves take an
active part. Here two phenomena attract our attention
16. — the problem of life, and the problem of consciousness
inind. or mind. The knowledge which we possess, or imagine

we possess, of the latter, which is gained from a purely
introspective point of view, the psychological aspect, I
leave at present quite out of the question. As external
observation through our senses would never have given
it ; as in the map of reality which we call nature, we
have not even succeeded in accurately locating conscious-
ness,—I relegate this large department of Thought to
a different place in this work. At present we have to
do only with the study of nature, the first condition of

object way to dispel the popular
conception that the accuracy and
variety of the performances of the
human eye could be explained bj^
the precision and complexity of its
structure, as if it were an optical
instrument of a degree of perfection
which could not be equalled by any
optician. In the sequel Helmholtz
shows how this admiration of a
wrongly supposed mechanical per-
fection must make room for an
admiration of a different kind, as

" every work of the organic forma-
tive power of nature is for us
inimitable " ; a remark which really
supports the argument in the text
('Vortriige und Reden,' 3. Aufl.
1884, vol. i. p. 240, &c.) It is also
important to note how Helmholtz
traces the imperfections of the eye
to its genesis — i.e., its development
in the embryo. The genetic sup-
plements the purely structural ex-
amination (ibid., p. 255).

ON THE MORPHOLOGICAL VIEW OF NATURE. 217

which is that her phenomena have, or have at some time
had, a definite place and position in space. Here, then,
the phenomena of lower and higlier life and tlie new
creations of human culture, art and industry, open out a
great department of reality which is accessible to external
observation and study. Without committing ourselves
to any theory on the subject, we have in this department
to deal with the phenomena of apparent or real design
and purpose. How has the century dealt with these
phenomena ? The answer to this (question, the history
of nineteenth century thought as directed towards the
phenomena of life and of mind as natural phenomena,
will be dealt with in two further chapters, which will
respectively deal with the vitalistic^ and the psycho-

^ It would have been in some
respects preferable to use the
word " biological " instead of vital-
istic. In fact, in the original draft
of this passage I used the former
term. The reasons which made me
alter it are the following : The
term biology was first used in 1801
by Lamarck in his ' Hydrogdologie.'
" About the same time it occurred
to Treviranus that all those sciences
which deal with living matter are
essentially iind fundamentally one,
and ought to be treated as a whole ;
and in the year 1802 he published
the first volume of what he also
called ' Biologic.' Treviranus's great
merit lies in this, that he worked
out hi;- idea, and wrote the very
remarkable book to which I refer.
It consists of six volumes, and oc-
cupied its author for twenty j'ears
—from 1802 to 1822. That is the
origin of the term ' biologj' ' ; and
that i.s how it has come about that
all clear thinkers and lovers of con-
sistent nomenclature have substi-
tuted for the old confusing name of

' natural history,' which has con-
veyed so many meanings, the term
' biology,' which denotes the whole
of the sciences which de<d with
living things, whether they be ani-
mals or wiiether they be plants."
This extract from Huxley's " Lecture
on the Study of Biology " (South
Kensington, Dec. 1876, reprinted
in ' American Addresses,' &c., 1886,
p. 129, &c.), has induced me to
adopt the term " vitalistic " to
denote those doctrines and chapters
in biology which deal specially with
the principle and phenomena of
life. A very large portion of bi-
ology deals with such phenomena
of living things as can be studied
without any reference to a doctrine
or theory of life in particular, they
being either mere facts of distribu-
tion or that very large and increashig
class of biological processes which
admit of puiciy mechanical, ithysi-
cal, or chemical description and
explanation. The very fact, how-
ever, tiiat tlie ijuestion wiiether the
princijileof life is purely meclianical

218

SCIENTIFIC THOUGHT.

17.
Vitalistic
and psycho-
physical
aspects.

physical views of nature. Thus four distinct chapters,
dealing severally with the morphological, the genetic,
the vitalistic, and the psycho-physical aspects of nature,
will together attempt to describe the manifold and
changing methods of reasoning by which our century
has approached the actual things and events which
surround us.

" Nature does not employ all figures, but only certain
ones of those which are possible : and of these, the deter-
mination is not to be fetched from the brain, or proved
a priori, but obtained by experiments and observations."
These words, set down nearly two centuries ago by a
now forgotten natural philosopher,-"^ express clearly the
object of a study which, towards the end of the eigh-
teenth century, had received definite expression in vari-

or not is not yet decided, makes
it necessary to retain in a history
of Thought a special term com-
prising all speculations which deal
with the purely scientific solution
of that problem. In fact, the ques-
tion what is life is still unanswered.
A fortiori, these remarks refer
also to the question. What is mind
or consciousness ? But the two
chapters referring to these problems
will limit themselves to an historical
exposition of what has been done
to solve them by purely scientific,
i.e., exact, methods. The full name
of the author of the ' Biologie '
was Gottfried Reinhold Treviranus
(1776-18.37) of Bremen. Though
introducing the larger conception
of biology, his own original lab-
ours were mainly in the domain
of zoology. His brother, Ludolf
Christian Treviranus (1779-1864),
devoted himself mainly to botanical

science, and was largely influenced
by the doctrines of the " Natur-
philosophie. " On the former, see
Carus, ' Geschichte der Zoologie '
(Miinchen, 1872), passim: on the
latter, Sachs, ' Geschichte der Bo-
tanik' (ibid., 1875, p. 291).

^ They are quoted by Whewell
('Hist. Indue. Sciences,' 3rd ed. ,
vol. iii. p. 165), from a work en-
titled ' Dissertatio de Salibus '
(1707), by the Italian Professor at
Padua, Dominico Gulielmini (1655-
1710). He was a practical physician
as well as a natural philosopher. He
was the forerunner of Rom^ de Lisle
and Haiiy, inasmuch as he estab-
lished the principle, not then suffi-
ciently appreciated, that the con-
stancy of the angles is characteristic
of all crystals. See Kopp's ' Gesch-
ichte der Chemie,' vol. ii. pp. 83-
404.

ON THE MORPHOLOGICAL VIEW OF NATURE. 219

ous branches of natural science, and which can be best
characterised b}- the term morphology.^ The word was is.

Morphology

first applied only to plants, then also to animals, and <iciiued.
later still to crystals and minerals. The words quoted
above refer to the forms of inanimate nature, to crystals.
In all these cases we have to do with definite individual
objects, which can be removed from their surroundings
and examined in tlie laboratory. There is, however, ncj
reason why a study of the actual forms of nature on
a large scale, such as the physiognomy of landscape, the
configuration of mountains and valleys, the shapes (jf
glaciei-s, the actual distribution of land and water on our
globe, the stratification of rocks, the formation of clouds,
and many other things, should not all be comprised under
the term, the morphological view of nature. And con-
ceived in this larger sense, the study of nature as a whole
and in its separate parts had at the end of the eighteenth
century already made very important progress. In fact,
natural history had, in the course of that century, gradu-
ally emerged from the previous epoch, that of the purely
systematic and classificatory attempts, which aimed at
giving inventories, collecting specimens, and classifying
natural objects, naming, describing, and identifying them.
The interest of the latter was a practical one, frequently

^ In the ' Lei;ons sur les Phdno-
mene.H de la Vie communs aux
Aniiuaux et aux Vdg(5taux,' a
wijrk whicli did so much to break
down the older division of the
sciences which deal with animals
and vegetables separately, Claude
Bernard says (p. 333 of vol. i.,
1885) : " Dans un autre equilibre
cosmique, la morphologic vitale
serait autre. Je pense, en un mot.

qu'il existe virtuellement dans la
nature un nombre infini de formes
vivantes que nous ne connaissons
pas. Ces formes vivantes seraicut
en ijuelque sorte dormantes ou
expectantes. ... II en est ainsi
des corps nouveaux que formeut
les chimistes ; ils ne les crdeut pas,
ils dtaient virtuellement possibles
dans les lois de la nature."

220 SCIENTIFIC THOUGHT.

prompted by the needs of the medical profession, which
studied animals as affording an insight into the analo-
gous structure and functions of the human body ; ^ and
plants, because they largely furnished the materials for
the preparation of medicines. To this must further
be added the practical interests of agriculture, of garden-
ing, and of the artificial culture of flowers and exotic
plants, and the breeding of domestic animals. All
these interests, however stimulating they may have been
and still are, introduce an element of artificiality into
the study of nature. They have all a greater concern
for natural objects, be they beautiful or useful, than
they have for nature itself. From this artificial posi-
tion the true sciences of nature had to emancipate them-
selves by slow degrees and with many efforts. Ever since
the time of Linnaeus, through whose labours the system-
atic attempts received a kind of finality, and even in
his own writings, great discussions were carried on as to
19. the difference between a natural and an artificial order of

Artificial

and natural plauts and animals. " The natural orders,"^ says Linnseus,

systems. . . ,

" teach us the nature of plants, the artificial orders enable
us to recognise plants. The natural orders, without a
key, do not constitute a method ; the method ought to be
available without a master. . . . The habit of a plant
must be secretly consulted. A practised botanist will

^ Referring to Albrecht von
Haller, Victor Carus (' Gesch. d.
Zoologie,' p. 567) says, "Through
the leap which physiology took,
thanks to his labours, zootomical
researches developed in a direction
which brought them into complete
subjection to physiology, with a
neglect of the independent import-
ance which belongs to them. . . .

It diverted attention from the im-
mediate object of zoology, the ex-
planation of animal forms and their
variety, to the more remote problem
— the explanation of the phenomena
of life."

2 Quoted by Whewell ('Hist.,'
vol. iii. p. 268) from the ' Genera
Plantarum' (1764).

ON THE MORPHOLOGICAL VIEW OF NATURE. 221

cUstiiiguish at tlie tiist glance tlie plants of different
([uarteis of the globe, and yet will be at a loss to tell b}-
what mark he detects them. There is, I know not what
look — sinister, obscure, in African plants ; superl> and
elevated in the Asiatic : smootli and cheerful in the
American ; stunted and indurated in the Alpines." ^ The
inventor of the sexual system of plants, which proved to
be such a good " finder " in the hands of the botanist and
herbalist, speaks of the difficulty of the task of discover-
ing the natural orders. " Yet," he says, " I, too, have
laboured at this — have done something, have much still
to do, and shall labour at the object as long as 1 live." "

Linn^eus's artificial system met with little acceptance
in France, where, under the opposite infiuence of Buffbn,'^

20.
Linnii'usand
Buflon.

1 Quoted by Whewell (' Hist.,' vol.
iii. p. 268) from the ' Philosophia
Botaiiica' (1751).

- Ibid., quoted from the ' Chisses
Plantarum ' (1738). Juliuw Sachs,
in his excellent ' History of Botanj* '
(Munich, 1875, transl. from the Ger-
man by H. E. Garnsey, 1890), .says
of Linnaeus, that in his morpho-
logical as well as in his systematic
labours, there existed two unre-
conciled conceptions — a superhcial
one, meant only for practical use,
which found expression in his arti-
ficial sexual system, and a deeper,
scientifically valuable one. " For
practical jjurposes of description he
elaVjorated his nomenclature of the
parts which, however useful, apjjears
nevertheless flat and superficial, as
any deeper foundation through a
comparative study of forms is want-
ing. But alongside of this, there
ai)i)ears in various passages of his
writings the desire for a more pro-
found conception of plant-forms.
What he had to say on this subject
he brought together under the

term ' metamorphosis plantarum ' "
(p. 110 of the German edition).

^ Buffon's great name has a place
in the history of the genetic as well
as of the morphological view of
nature, inasmuch as he looked at
the things of nature as much from
the side of their individual speciality
as from that of their connection
and orderly ariangement in time
and space. And inasmuch as he
" does not only con.sider the form,
but tries to maintain an interest in
the general economj' of the whole
of nature by picturing to us the
homes, the habits and customs, the
instincts, &c., of living things, so
he strove in general to represent
the single phenomena of nature as
existing in intimate connection "
(Carus, ' Gesch. der Zoologie,' p.
523). "As Buflon opposed the ex-
treme systemati.sers, who seeuicd to
think it the end of science, not so
much to know about an object as to
be able to name it, and fit it into
their system, so Daubenton (the
collaborator of Bufton in France)

222

SCIENTIFIC THOUGHT.

the great botanists, from Jussieu to De Candolle, and the
great zoologists, notably Cuvier, made an attempt towards
a freer and more generous and more sympathetic con-
ception of the objects as well as the totality of nature.
These attempts were continued much on the same lines
till well on into the nineteenth century. Buffon's com-
prehensive scheme was premature, but it had a very
great and beneficial influence in popularising and en-
livening the frequently dry and uninteresting pursuits
of the collector and systematiser. Cook's voyages during
the last third of the eighteenth, and Humboldt's travels
at the turn of the two centuries, did much to further a
comprehensive view ; but the great task of the mor-
phologist, like every other scientific work, had to be
solved by special studies in separate departments. It
grew from small beginnings and detached contributions.

One of the most notable of these, and one also which
has all along exerted a great influence on all morpho-
logical studies, is the theory of crystals, both natural and
artificial. I have already had occasion to refer to the
labours of Haiiy^ and his successors. They have led to
a complete mastery of the geometrical forms which
minerals occasionally present in nature, and which sub-
stances assume if allowed to solidify out of the liquid
21. condition. The science of crystallography, now appro-
of°c^sta°s.^ priately termed the " morphology of crystals," " has had

insisted on the study of each animal
as an individual whole. . . . He oc-
cupied himself, therefore, with the
production of a series of admir-
able monographs appended to the
descriptions of Buffon in the ' His-
toire Naturelle ' " (Huxley in the

chapter on Owen's position, &c., in
'Life of Richard Owen,' 1894, vol.
ii. p. 280).

1 See vol. i. p. 116, &c., of this
history.

- See ' The Morphology of Crys-
tals,' by N. Story Maskelyne, 1895.

ON THE MORPHOLOGICAL VIEW OF NATURK. 223

a peculiar fascination as forming the transition from the
abstract science of geometrical forms and statical equili-
brium to tlie study of the actual forms of real things.
Here, if anywhere, it seemed as if we might dis-
cover the link that connects the theoretically calcul-
able with tlie actually existing, the possible with the
real. Accordingly, we find a very general and recur-
ring tendency to carry over the notions of crystal-
lography into other sciences — into the morphology
of plants and animals. The planes and axes of
geometry, and the forces of attraction between particles
of matter, have formed a theme which has been end-
lessly repeated and varied in explaining the elements
and the forms of living matter. IJut whilst these
fanciful analogies^ of organic crystals, of polar distribu-
tion, and the network of tissues, to which are also allied
the spiral theories of leaves and branches in plants and
other geometrical arrangements, have at times attracted
much attention,- and have served to give at least the

1 " Ces comparaisous entre les for analogies, Jul. Sachs, ' Gesch.

formes minerales et les formes d. Botanik,' p. 173, &c.
vivantes ne constituent certaine- - I shall revert to this subject

ment que des analogies fort loin- when speaking of the elder De

taines, et il serait imprudent de Candolle. Here only a passing re-

les exagcrer. II suffit de le.s signal- mark on^ the "spiral theory," which

er. Elles doivent simplement nous was mainly developed by K. F.

faire mieux coucevoir la separation Schimper and Alexander Braun,

theorique de ces deux temps de la after the regular geometrical ar-
creation vitale : la creation ou ! rangement of leaves around their

synthase chiviiqxie, la creation ou
synthase movphologiqiic, qui en fait
8ont confondues par leur simul

stalks had already been nt)ticed in
the eighteenth century by Charles
Bonnet, following Civsalpinus. For

tan^it^, mais qui u'en sont pas about thirty years, from 1830 on-

moins essentiellement distinctes ward, the spiral theory was very

dans leur nature " (Claude Bernard, popular in Germany. In France,

'Le(;on8 sur les Ph^nomfenes de l;i tht> sninewhat related theories of

Vie,' &c., vol. i. p. 296). See also on \ nuufiry of De Candolle, of meta-

the extravagances of such search i uiorphosis of Goethe, and of spiral

224

SCIENTIFIC THOUGHT.

22.
Morphology
on a large
scale.

semblance ^ of an explanation of organic structures and
forms, they have in reality done as little as Boscovich's
centres of force and curves of attraction and repulsion
in mathematical physics to establish a firm basis for
actual research; for nowhere have they been capable of
exact determination such as has been applied to the
angles and figures of crystals.

Simultaneously with the science of crystallography
there came into being the science of minerals on a
larger scale of study, through actual observation in
definite localities of the formation and stratification of
rocks ; of the traces of the influence of the

great

arrangements of Schimper, became
known under the term "Morph-
ologie v(^getale," through Auguste
de Saint Hilaire in his ' Lemons de
Botanique' (1840). To the spiral
theory, although strongly opposed
in course of time by Wilhelm Hof-
meister, one of the founders of the
genetic conception of plant life,
Sachs, the historian of botany,
nevertheless assigns an important
historical influence, " as through
Schimper's theory the morphologic-
ally so important relative position
of the plant organs was for the first
time placed in the foreground of
morphology " {loc. cit., p. 180). See,
however, on this subject the paper
by A. H. Church on " Phyllotaxis "
in vol. i. p. 49 of 'The New
Phytologist,' 1902.

^ The early propounders of the
cellular theory of organic structures
adopted the view that cells were
formed in a surrounding liquid in
the manner of crystals in a mother-
liquor. When it was established
that organic structures grow by
intussusception, not by juxtaposition
and accretion, like crystals, and that
cells multiply by division, the dis-
coveries of Graham, who divided

bodies into crystalloids and colloids,
were utilised for the purpose of
explaining or illustrating organic
processes. On this distinction is
based the celebrated " micellar
theory" of Niigeli, who, in his
' Mechanisch-physiologische Theorie
der Abstammungslehre ' (Miinchen
und Leipzig, 1884), works out a
complete mechanical doctrine of the
constitution and formation of or-
ganic structures. The ideas con-
tained in this elaborate treatise
have been much used in Germany
by various writers, but mostly only
as convenient illustrations. See
0. Hertwig, ' The Cell ' (transl. by
Campbell, 1895), p. 58, &c. The
micellar theory does not seem to
have found much favour in France
or in this country, where a general
opinion prevails which is probably
best represented in the words
of Claude Bernard : " Les pheno-
menes physico-chimiques des etres
vivauts, quoique soumis aux lois
de la physique et de la chimie
gdnerales, ont leurs conditions par-
ticulieres qui ne sont realisdes que 1^,
et dont la chimie pure ne pent ofifrir
qu'une image plus ou moins inexacte"
(' Phen. de la Vie,' &c., vol. ii. p. 487).

ON THE MOKPHOLOGICAL VIEW OF NATURE. 225

agencies of nature, — of water, atmosphere, and of ice
and heat. J^st came the study of the fossil remains
of organic life as the means of fixing the age and the
order of succession of various geological formations.
Werner^ in Germany, Cuvier" in France, Hutton ^ in
Scotland, William Smith * in England, led the way, from
different points of view, towards an actual knowledge and
a possible theory of the existing forms and structures in
and on the crust of our globe. The study of these
subjects, morphology on the largest scale, necessitated
distant travels, the examination of formations in situ
and under diametrically opposite conditions. Its great-
est and unequalled representative was Alexander von
Humboldt,^ who also brought the observations of 23

' <-' Huinbolat.

geographical, geological, and mineralogical facts and
details into connection with the study of climate, of the
weather, of the distribution of plants and animals."

^ See supra, vol. i. p. 283.
- Ibid., p. 125.

3 Ibid., p. 283.

4 Ibid., p. 291.

^ A good account of the grad-
ual development of the plan of
" Cosmos " will be found in
Bruhus's ' Life of A. von Hum-
boldt ' (transl. by Lassell, 1873),
vol. ii. , pas»irii. It is clear that
two great intiuences co - operated
to ripen in Humboldt's mind the
conception of unrolling a great
tableau of the phj'sical world in its
purely material and in its ideal or
jioetical aspects : the influence of
the great scientific movement then
emanating from Paris, and the
not less important influence of
the ideal movement rejiresented
by the names of Herder, Goethe,
and Schelling, which emanated
from the centre of Germany.

VOL. II.

"But, however gi-eatly Humboldt
may be indebted to the inspiring
influence of his contemj)oraries, the
great merit of the work lies in
what he alone has accomplished —
the attempt by means of a com-
prehensive collation of details, and
the institution of the most search-
ing comparisons, to give a scientitic
foundation to the ideal cosmology
of Herder, (Joethe, Schelling, and
their disciples ... In him may
be said to be united the two
schools of philosophy, so brilliantly
represented during the closing years
of the former centurj'. On this
iiccount he was at the same time
exposed to the censure of the
representatives of either system "
(vol. ii. p. 312).

® The third volume of the ' Life
of Humboldt,' in the original
German edition, gives an account

226

SCIENTIFIC THOUGHT.

He may be called the morphologist of nature on the
largest scale : the representation of the grand aspect
of things as exhibited in his ' Cosmos,' and in his earlier
' Ansichten der Natur,' was the leading idea of his hfe
and work. Through him and his friend Karl Eitter
" comparative geography received a treatment worthy of
the subject, showing its connection with the history
of the human race and the advancement of civilisation,
inasmuch as the configviration of the earth is proved to
have been an important element in the dispersion of
nations." ^

But morphology, or the study of forms and struc-
tures, has to be carried on not only on the large, the
gigantic scale, as by Humboldt ; it is quite as im-
portant, and has probably been even more influential,
when directed towards the minute, the imperceptibly
small, which ordinarily quite escapes our notice. If

by various specialists of Hum-
boldt's labours in the sciences of
astronomy, geology, geography, the
distribution of animal and plant life,
meteorology, and other provinces of
research, some of which largely owe
their existence to his initiative. The
study written by Ewald on his
geological work, and that of
Griesbach, on what is termed in
German animal and plant geo-
graphy, are specially interesting.
Unfortunately this most' fascinat-
ing volume has not been brought
out in the English edition. As illus-
trating the comprehensiveness of
Humboldt's view it is well to note
how, before beginning to put to-
gether his materials in the great
tableau which the ' Kosmos ' was
intended to be, he drew two
entirely different pictures of nature
on our globe ; first in the large

work on the New Continent
('Voyage aux Regions equinoxiales
du Nouveau Continent,' in six
parts, published in Paris, 1805 to
1834) and then from an entirely
opposite aspect in his works on
Central Asia ( ' Asie Centrale :
Recherches sur les Chaines et
Montagues et la Climatologie com-
parde,' 3 vols., Paris, 1843). "To
Humboldt the importance of the
Asiatic expedition consisted in its
elevating him above the one-sided
effect of having contemplated
nature exclusively in the New
World, and leading him, so to
speak, to feel experimentally that
the earth, in common with every
other object, is possessed of op-
posite sides" ('Life of Humboldt,'
vol. ii. p. 212).

1 See ' Kosmos,' vol. i. p. 60
(German edition, 1845).

UX THE MORPHOLOGICAL VIEW OF NATURE. 227

the great revolution of ideas which the seventeenth
century witnessed was much assisted by the invention 24.

Mori'hology

of the telescope and founded upon its revelations, the wi a miimu
change of thought during the nineteenth century has
been connected more with the revelations <jf the
microscope. The great movement of ideas started by
Galileo, and continued through Kepler, Newton, and
Laplace, ^^•as accompanied l)y the jierfection of tlie
telescope. The invention of the microscope enabled
Nehemiah Grew and Mal{)ighi to begin half a century
later their embryological studies, and to inaugurate a
line of research which, in our days, through a long series
of oljservations ^ from Amici to Strasburger on the pro-

' These observations begin with
the year 1830, when Amici, to
whom great improvements in the
microscope are due, " traced the
pollen grain from its lighting on
the carpel tip down into the
recesses of the ovule" (Geddes and
Thomson, ' The Evolution of Sex,'
p. 140), and removed all doubts
and uncertainty by his observa-
tions on orchids in 18-15 and 1846.
^' Here he demonstrated the whole
series of processes, from the pollen
dust on the stigma to the for-
mation of the embryo " (Sachs,
'Gesch. d. Botanik,' p. 469).
About the same time (184-3) Martin
Barry " observed the presence of
the sperm within the ovum in the
rabbit ovum" (Geddes and Thom-
son, loc. cit., p. 142). It took, how-
ever, a cjuarter of a century, from
the first discovery of Amici, before
the process of fertilisation described
by him was accepted by embryo-
logists as typical for both plants
and animals. Bischoff, the great
authority in Germany, after con-
firming the entrance of the sperm-
cell into the ovum, maintained by

Barry in 1843, and by Newport
(w'ith frogs) in 1851 and 1853, ex-
presses his "infinite astonishment,"
adding that " Dr Barry is certainly
the first who has seen a sper-
matozoon in the interior of any
ovum, and notablj- in the ovum of
a mammal, and that to him be-
longs the glory of this discovery "
(Theod. Bischort', ' Bestiitigung des
von Dr Newport bei den
Ijatrachiern und Dr Barry bei
den Kaninchen behaupteten Ein-
dringens der Spermatozoiden in
das Ei,' 1854, p. 9). For the
history of scientific thought it is
significant to see how little, even
in the middle of the century, dis-
coveries referring to the phenom-
ena of plant life or structure were
known or utilised by students of
animal life. A mutually fructify-
ing infiuence seems to date like
so many other advances from the
publication, in 1859, of the ' Origin
of Species.' "The distinctively
modern era in the history of
fertilisation dates from about 1875,
when the brilliant researches of
Auerbach, Van Beneden, Biitschli,

228

SCIENTIFIC THOUGHT.

25.
The Micro-
scope.

cess of fecundation in plants, and from Martin Barry to
Hertwig and Fol on that in animals, has been brought
to a temporary climax. The combination of telescope
and microscope in the spectroscope has opened out a
field of research in astronomy of which Laplace had
no conception.

So much has depended, during our century, on the
unravelling and disentangling of the imperceptibly small
(once considered an unworthy occupation), that a short
reference to the history of that optical instrimient to which
we are so greatly indebted may not be out of place.

The gradual perfection of the microscope is as much
indebted to the problems and labours of anatomical
workers during the seventeenth and the nineteenth cen-
turies, as anatomy itself reciprocally has been indebted
to the microscope. Eobert Hooke, in 1660, first gave a
useful form to the compound instrument. Leuwenhoek
perfected the simple microscope ; and during the earlier
part of our century no one did more than Amici in
Modena and Lister in England ^ to start that great suc-

Fol, 0. Hertwig, and others,
showed that one of the essential
phenomena in fertilisation is the
intimate and orderly association
of the sperm-nucleus, of paternal
origin, with the ovum - nucleus,
of maternal origin, the result
being the cleavage or segmentation -
nucleus. The researches of Stras-
burger, De Bary, and others,
established the same result in
regard to plants " (J. A. Thom-
son, ' The Science of Life,' p.
127, 1899).

^ The improvements of Amici
seem to go back to the year 1812,
those of Lister to 1826. The for-
mer is usually considered the in-

ventor of the " immersion " system,
— that of placing a drop of water
between the object or its covering
glass and the objective lens. This
system has lately been improved by
Abbe, who discovered a liquid with
the same refractive index as the glass
of the objective possesses. Accord-
ing to Hogg (' The Microscope,'
15th ed., 1898, p. 10), the immer-
sion system was suggested by Prit-
chard in London before Amici hit
upon it. The necessary modifica-
tions required where the immersion
system is used, seem, however, to
have been first worked out by
the celebrated Paris opticians, MM.
Hartnack and Nachet.

ON THE MORPHOLOGICAL VIEW OF XATURE. 229

cession of iiuproveiuents by whicli enois due to colour
and indistinctness — the chromatic and spherical aberra-
tions— were removed. In the middle of the century
the influence of some eminent Ijotanists, notably of
Hugo von Mohl and Nageli, in perfecting micrometric
processes was considerable ; whilst the last twenty
years have witnessed quite a new departure in the
theory of optical images, in that of microscopic vision,
in the improvement of optical glass, and in the in-
vestigation of the possible limit of the magnifying
powers. The most eminent physical authorities — such
as Stokes and Lord Rayleigh in England, Helmholtz
in Germany — have taken up one or more of these
points ; but the whole subject is associated with
the name of Prof. Ernst Abbe ^ of Jena, who,
through his connection with the well-known firm of
Carl Zeiss, has been able to put into actual practice
many of the suggestions which resulted from his the-
oretical investigations. As the historians of zoology

^ The labours of Abbe go back to
the year 1873. Simultaneously and
independently, Helmholtz attacked
the theory of microscopical vision
and the question of "resolution " —
i.e., of the possible limit to the re-
solving power of any optical arrange-
ment. Airy had attacked the same
subject on purely dioptrical lines.
Helmholtz and Abbe went a step
farther, taking into account the
physical nature of light as a wave-
motion, subject to interference
phenomena, notably those caused
by inflection, where objects with
very fine markings are concerned.
Ablje's methods were for a long
time only imperfectly known. The
publication, however, of his theories

by Czapski ('Theorie der optischen
Instrumente nach Abbe,' Breslau,
1893) made the whole subject better
known, and has been followed by
two masterly papers by Lord Ray-
leigh and Prof. Johnstone Stoney in
the 42nd vol. of the ' Philos. Mag.'
(1896). The latter paper especially
gives several interesting examples
of the use of recent microscopic
appliances and the means of avoid-
ing errors in handling very delicate
and minute objects. It seems that
the instrument caimot any longer
be used without a theoretical know-
ledge of its optical construction,
which enables the observer not only
to see, but also to criticise and to
interpret.

230

SCIENTIFIC THOUGHT.

and botany tell us, the use of the microscope had
made little or no progress ^ during the eighteenth
century : the study of structures and tissues had lost
interest in comparison with the study of the physi-
ological functions of the parts of plants and the organs
of animals, which had been respectively furthered by
2R. Hales in England and by Haller in Germany." Our

Its improve-
ment, century thus found the morphological studies of the

imperceptibly small in a very backward state : it had
to improve the instrument for its research pari passu
with this research itself.^ But it has been truly re-
marked that the increased use of the microscope
necessitated likewise a mental training in the inter-
pretations and delineations of what was observed
through it. " By fortifying the eye with the micro-

^ "So long as, in consequence of
the imperfections of optical instru-
ments, deceptive images existed,
and, for instance, all microscopical
structures appeared as composed of
rows of beads, the explanation of
what was seen stood under the in-
fluence of deceptions, which were
only gradually recognised as such "
(Carus, 'Gesch. d. Zool.,' p. 629).
Compare also what Sachs says
(Gesch. d. Bot.,' p. 241).

^ " The characteristic feature of
that period laj- in this, that the
examination of the finer structure
is always mixed up with reflections
on the functions of elementary
organs, so that anatomy and phy-
siology always support each other,
but also, in consequence of their
imperfect state, do each other in-
jury " (Sachs, loc. cit., p. 240).
Similarly Carus {loc. cit., p. 567),
" Through the progress which phy-
siology made, thanks to Haller's
activity, zootomical investigations

took a direction which brought
them into complete dependence on
physiology, . . . and retarded the
progress of zoology by diverting at-
tention from its primary object —
the exposition of animal forms and
their differences."

' As late as 1827 Aug. Pyrame
de Candolle could still write ('Or-
ganographie v^gdtale,' vol. i. p. 7),
" De nos jours, MM. Mirbel, Link,
Treviranus, Spreugel, Rudolphi,
Kieser, Dutrochet, et Amici out
public des recherches tres d^licates
sur le tissu vegdtal, et les ont ac-
compagnees de figures nombreuses
et soignees ; mais la necessite d'em-
ployer continuellement dans ces
recherches un instrument aussi
difiBcile h, bien manier que Test le
microscope compose, fait que malgr^
I'habilet^ de ces observateurs, I'anat-
omie delicate des veg^taux est encore
. . . d'une incertitude desesperante
pour les amis de la v^ritd. "

ON THE MORPHOLOGICAL VIEW OF NATURE. 231

scope, it became itself a scientific instruiueut wiiich
no longer hurried over its objects in tlighty motion,
but is disciplined by the intellect of the observer and
forced into methodical work." ^ Similarly, no doubt,
the increasing devotion to the pastime of sketching
from life and nature in our days must have the effect
of obliging the eyes of many persons to look stedfastl>'
and carefully at the forms and outlines of things, and
of thus training the artistic faculty.

It is, however, a remarkable fact that one of the
greatest leaders in the morphological study of natural
objects, Bichat, the great observer of membranes and
tissues, despised the microscope, the instrument by
which the sciences he founded were to benefit so
enormously.

The object of morphology, as distinct from that of 27.
classification, can be defined as the attempt to describe, a"J. ciassiti-
and if possible to comprehend and explain, the relative
similarity as well as the graduated differences of form
and structure which natural objects present to our gaze.
Although the study can be conducted on a large as well
as on a small scale, these similarities and differences sooner
made themselves felt in the comparatively smaller objects
of living nature. These can, without apparent loss of
their characteristic appearance and individuality, be col-
lected and brought together, whereas a collection of
minerals, with the exception of crystals and gems, always
presents only fragments, and forces upon us the convic-
tion that they can really be studied only in their habita-
tion, in situ. The same conviction has indeed gradually

1 Sachs, loc. cit., p. 237.

232

SCIENTIFIC THOUGHT.

made its way into botany ; and last of all into zoology.
The herbarium or collection of dead plants was much
sooner superseded by the " jardin des plantes " than the
zoological museimi with its skeletons, stuffed animals, and
specimens in alcohol has been supplanted by any scientific
collection of living animals. Marine stations, which study
plant and animal life m situ, are quite a recent invention.^
The study of the forms of nature or morphology in the
earlier or more limited sense, referred thus more exclu-

^ M. Yves Delage distinguishes
four great periods in the study
of living things. The first, cul-
minating in Linnffius and Buffon,
studies living objects in the great
outlines of their external forms, of
the habits of plants and the cus-
toms of animals. Detailed exam-
ination by dissection is resorted to,
but only as a secondary method and
in order to supplement the intuitive
discovery of natural affinities. Then
comes the second period, that of
Cuvier and his followers, relying
mainly on anatomical dissection.
The third period begins with the
marine stations. "Je ne crains
pas de dire que la fondation des
laboratoires maritimes a marque
une troisieme p^riode et constitud
une nouvelle m^thode aussi im-
portante que les pr&^dentes. Si
I'on songe que plus des trois
quarts des types d'invertebrds
appartiennent au monde de la
mer, que le plus grand nombre ne
pouvaient parvenir dans les cen-
tres scientifiques dans un ^tat
convenable pour I'examen micro-
scopique, si Ton songe que tout
ce qui conceme leurs mccurs et leur
embryogenie ne pent s' etudier loin
de la mer, on comprend I'importance
de ces creations. Faut-il rappeler
que I'introduction de cette mc^thode
est due u H. de Lacaze-Duthiers ?
, . . Aussi la fondation du laVjora-

toire de Roscotf a-t-elle ete le signal
de la creation d'une multitude
d'dtablissements plus ou moins
similaires sur les cotes de tons les
pays" (' L'H(5redit<5 et les grands
problemes de la Biologic,' p. 3).
The fourth period is marked by
microscopic anatomy, and this —
according to M. Delage — has its
home mainly in Germany. "The
study of marine zoology has, since
the publication of the ' Origin of
Species,' been found to require
more complete arrangements in the
form of laboratories and aquaria
than the isolated vacation student
could bring with him to the seaside.
Seaside laboratories have come into
existence : the first was founded in
France by Coste (1859) at Concar-
neau (Brittany) with a practical end
in view — viz., the study of food-
fishes, with an aim to pisciculture.
. . . The largest and Vjest-supported
]:>ecuniarily is that founded at Naples
by Anton Dohrn in 1872; others
exist at Trieste, Villefranche, Cette,
and at New Haven and Beaufort in
the United States ; wliilst a large
laboratory, on a scale to compare
with that at Naples, has been (1888)
opened at Plymouth by the Marine
Biological Association of the United
Kingdom " (Ray Lankester, art.
" Zoology " in ' Encyclop. Brit.,' vol.
xxiv. p. 814).

ON THE MORPHOLOGICAL VIEW OF NATURE. 233

sively to plants and animals, and here the term was first
applied. In order to bring some kind of method into
the perplexing study of living forms, two ways presented
themselves ; and they were consciously or unconsciously
followed by morphologists with more or less success. As
I mentioned above, one of the chief interests which
led to zoological and also to botanical studies was the
medical interest. Animals were dissected and observed,
as affording by analogy an insight into the structure and
processes of the human body. Physiology, the science
which deals with the actions of the different parts
of the animal or human frame, termed from an early
period the functions of the different organs, had made
considerable progress during the eighteenth century. It
was then found convenient to study the whole organism
as an assemblage of different organs or machines, each of
which performs a certain function. Thus we have the
mechanism on which voluntary motion depends, the
mechanism of respiration and of the circulation of the
blood through the body, the mechanism of digestion, the
mechanism of reproduction, and finally, the mechanism
of the nervous system with its specified and localised
optical, auditory, and other organs of sense. All these ^ ^^^^2s
parts or organs could to a great extent be separately H^Hf^
studied and described in their mechanical, chemical, and
electrical actions. These studies had, since the time
of Harvey in England and Haller in Germany, made
great progress. The application of chemistry to the
processes of respiration and digestion, and finally, the
discovery of the galvanic current by Galvani, had given
a great impetus to the physiological study of the different

234 SCIENTIFIC THOUGHT.

organs in living beings, and their functions. In plants,
these organs and functions seemed to be much simpler
and more easily observed than in animals, and Linnasus
had selected the sexual organs, since they were the most
easily distinguishable, as a primary character for his
classification of the vegetable kingdom. Somewhat
later ^ he classifies the animal kingdom according to the
internal structure, and characterises animals for the
purpose of division according to the heart and the blood.
The celebrated dictum, that " minerals grow, plants grow
and live, animals grow, live, and feel," which appeared in
the last edition of the ' Systema Naturae,' places a physio-
lodcal distinction at the base of the classification. This
conception, which has been somewhat modified since
Linnseus's time to meet our altered views, is an obvious
first step towards a description of natural objects. Yet
this no more than the second step, which fastens upon
the organs of reproduction in plants, on the heart and
blood in animals, gives any clue to the comprehension
of the great variety and apparent fixity of forms which
the living world presents to our observation. In fact,
purely morphological considerations were subordinated to
physiological ones, and were brought in only to assist
in the further subdivision of the two great kingdoms.
Linnaeus felt the artificiality of his classification — the
arbitrariness of the characters he selected for the pur-
29. pose of division. But a more natural system could only
stodies.^ be arrived at by an intimate knowledge of and intercourse
with living nature, as well as by a careful comparison of
its hidden forms and organisation — i.e., by a more de-

1 See Carus, ' Geschichte der Zoologie,' p. 503, &c.

ON THE MORPHOLOGICAL VIKW OF NATURE. 235

tailed extenial and internal morphology. Both lines of
study, with their respective methods of observation, re-
search, and reasoning, were ef[ually wanted. The former
was more easily attained with plants, the latter promised
more immediate fruit in dealing with animals. In follow-
ing the former, Bernard de Jussieu became the founder
of modern descriptive botany ; in taking up the latter,
in founding comparative anatomy, Georges Cuvier became
for a long time the leader in zoology.

]>ernard de Jussieu was led to his natural system of
classification, not by any theoretical considerations, but by
the practical task of arranging the plants in the garden
of Trianon, confided to his care by Louis XV., who was a
great lover of botany. He had with him as assistant his
nephew, Ant. Laurent de Jussieu, who in 1789 published
his ' Genera Plantarum,' which is, so far as method goes,
the work of his uncle. " This work produced a verit-
able revolution in botany, for only since its publica-
tion have plants been studied according to the relations
which they exhibit and according to the totality of
their organisation." ^ It was not one special character
or side of their existence, arbitrarily selected by a first
superficial observation, which served as a means of de-
scription ; tlieir different parts or organs were conceived
to be correlated — i.e., dependent on each other and united
to form the totality of their organisation — their various
characters were all taken into account, and looked upon
as subordinated one to the other." From the time of

30.
Jussieu.

' See ' Histoire des Sciences
Naturelles,' par Geo. Cuvier, com-
plot<;e par T. M. de .Saint Agy,
Paris, 1845, vol. v. p. 298.

^ Aug. Pyranie de Candolle
( ' Tiieorie (51dmentaire de la Bo-
tanique,' Paris, 1819, '2iid ed., p.
69) gives the following account of

236

SCIENTIFIC THOUGHT.

31.
Problem of
organisa-
tion.

Jussieu we find introduced into natural science, mainly
for the purposes of classification, the ideas of the correla-
tion of the different parts and the subordination of the
various characters of a plant or an animal. Physiology
and anatomy, hitherto mainly occupied with the study of
the different organs, were henceforth to be occupied with
the problem of organisation, the problem of the unity of
the various characters and organs. Inspired by Jussieu,
De Blainville looked upon the whole development of the
natural sciences as the history of our knowledge of
organisation,^ and De CandoUe, Jussieu's great successor
in botany — the name that in systematic botany ruled
the nineteenth century — wrote an ' Organographie vege-

tale,' a rational description of the

organs

of plants.

the method of the two Jussieus :
" Ce qui characterise la methode
des Jussieu, c'est qu'elle est fondee
8ur la subordination des caracteres.
Sentant le vague des simples
methodes de tatonnement, I'ex-
ageration du principe de com-
paraison uniforme et g^nerale des
organes, ils ont les premiers re-
marque avec soin, que tons les
organes, tous les points de vue
sous lesquels on pent les con-
siderer, n'ont pas un egal degrd
d 'importance, ni de permanence,
que quelques-uns semblent, pour
ainsi dire, dominer les autres ; de
sorte qu'en ^tablissant la classifica-
tion d'abord sur ces organes pr^-
dominans, puis les divisions
secondaires sur ceux qui ont un
moindre degre d'interet, on est
conduit it imiter le plus possible
I'ordre de la nature dans celui de
la classification. Ce principe simple
et peu contestable a ete fecond en
consequences importantes ; et c'est
sous ce point de vue, que I'un des
hommes qui a le plus profoud^-

ment refldchi sur la marche des
sciences et sur le plan general de
la nature, a proclam^, dans une
occasion solennelle, le livre de M.
de Jussieu, 'comme un ouvrage
fondamental, qui fait, dans les
sciences d'observation, une epoque
peut-etre aussi importante que la
chimie de Lavoisier dans les sciences
d'experience. ' " (See Cuvier, ' Rap-
port historique sur les progres des
sciences uaturelles,' Paris, 1810,
p. 305.)

1 See the ' Etude sur la vie et
les travaux de M. Ducrotay de
Blainville,' par Pol. Nicard, Paris,
1890, p. 157 sq.

' See A. Pyr. de CandoUe, ' Or-
ganographie vegetale ou Descrip-
tion raisonnee des Organes des
Plantes,' Paris, 1827, 2 vols.,
especially vol. ii. p. 245, &c.
" The classifications of the scientific
taxonomist are of two kinds. Those
of the one sort are merely handy
reference catalogues. Such are the
' artificial ' systems, useful in their
day and for their particular pur-

ON THE MORPHOLOGICAL VIEW OF NATURE. 237

The problem uf organisuLion was imicli easier in deal-
ing with plants than with animals. In the former there
seems to be only one organ or system of organs definitely
developed and marked off— namely, the organs of fructi-
fication ; and these had accordingly served Linnteus and
his successors as the leading character for their de-
scriptive classification. In animals there are, or seem to
be at least, four or five well-defined and separated sys-
tems of organs. The selection, for the purposes of
classification and morphology, was much more difficult.
Accordingly we find Cuvier, who between the years 32.

. Cuvier.

1^95 and 1817 devoted himself to the morphological
and anatomical study of the animal kingdom, hesitating
in the selection of the leading character according to
which he should classify and arrange it. As I have
had occasion to remark above,^ he finally in 1812
settled on the nervous system as the leading character
governing the figure of an animal organism.^ Before

pose, but of no other value. The
others, known as ' natural ' classi-
fications, are arrangements of ob-
jects according to the sum of their
likenesses and unlikenesses, in re-
spect of certain characters ; in
morphology, therefore, such classi-
fications must have regard only to
matters of form, external and in-
ternal. And natural classification
is of perennial importance, because
the construction of it is the same
thing a,9 the accurate generalisation
of the facts of form, or the estab-
lishment of the emjjirical laws of the
correlation of structure " (Huxley in
'Life of Owen,' vol. ii. p. 28:3).

* See vol. i. p. 130 of this history.

" On the gradual development of
Cuvier's classification see Carus,
' Geschichte der Zoologie,' pp. 602,

612, 614. '^It did not escape
Cuvier that the idea of subordina-
tion is artificial, and that the im-
portance of an organ can only be
fixed by experience — namely,
through the proof of its constancy.
Nevertheless he follows this prin-
ciple, but naturally becomes vacil-
lating. Thus in 1795 he names
the organs of reproduction, to the
action of which the animal owes its
existence, and the organs of cir-
culation, on which depends the
individual preservation of the
animal, as the most important,
whilst in 1812, following the
example of Virey, he declares the
nervous system to be that system
for the maintenance of which the
other systems solely exist " {loc.
cit., p. 602).

238 SCIENTIFIC THOUGHT.

that, he had ah-eady adopted from Lamarck/ whose
many-sided genius has made a lasting impress on the
history of natural science in quite a different direction,
the broad morphological division of the animal kingdom
into animals with or without backbone, uniting under
the former designation the four first classes of Linnaeus.
The more we follow Cuvier in the development of his
classifying attempts, the more we find the form, the
figure, the external and internal structure, urged as the
aspect from which the organisation of living creatures is
to be considered. To him fixity of form is the ever-
recurring character of organised beings as distinguished
from inorganic structures which depend on fixity of
matter." The clearer enunciation of this fixity of form
is accompanied in Cuvier's view by the rejection of an
idea which, before him, had very largely governed the
speculations of naturalists. This idea, by which Charles
Bonnet has been immortalised in natural history, is the
conception of a graduated scale according to which living
creatures can be arranged — viz., the celebrated Echelle des
Etres, coupled with the axiom, " Natura non facit saltus."
This idea Cuvier rejects as untenable, and introduces in
the place of it the conception of distinct plans called
"Types." later " types," ^ according to which living beings are

1 " An indirect inducement for a
more pointed enunciation of the
types of the various classes was
given by Lamarck in 1797 when
he placed the animals with white
blood as ' invertebrates ' in opposi-
tion to those with vertebrae, which
expressions (k vertebres and sans
vertebres) come from him " (ibid.,
p. 612).

(El. iii. p. 156, &c.) and the extracts
from it and from the ' R^gne
animal,' given in the first volume
of this History, p. 129 and notes
passivi.

' According to Carus (' Gesch. d.
Zool.,' p. 615), the term "type,"
which became current later, was
introduced by De Blainville, a philo-
sophical naturalist who held a

" See Cuvier's ' Eloge of Haiiy ' kind of middle position between

ON THE MORPHOLOGICAL VIEW OF NATURE. 239

modelled, and which have always existed. These types
or archetectonic models are capable of certain modifica-
tions, which, however, do not affect the main features of
the plan. The different classes of these main types,
called " embranchements," and designated as l)ackljoned,
molluscous, articulate, and radiated animals, stand near
each other in independence and form no scale.^

The morphological view of nature took a somewhat
different turn in De Candolle, the successor of Jussieu in
botany, who, while greatly indebted to Cuvier, acknow-

34.
De Candolle.

Cuvier and hi.s opponent, GetjfFroy
St Hilaire. In ISltJ Blainville gave
the " principles of a new classifica-
tion of the animal kingdom, in
which, tor the first time, the totality
of structure of animals was used to
characterise larger divisions." He
divides animals first of all into
three sub-kingdoms— symmetrical,
radiate, and those without regular
form. De Blainville seems to have
been an inspiring teacher, whose
ideas became suggestive and fruitful
in many other minds. Nearly the
whole of the third volume of
Comte's ' Philosophie Positive ' is
written under a sense of obligation
to De Blainville, whose ' Cours de
physiologic gL'nerale et comparee '
(1829-32) Comte considers " comme
le type le plus parfait de I'etat le
plus avancd de la biologie actuelle "
(vol. iii. p. 269, Paris, 1838). The
' Philosophie Positive ' was dedi-
cated to Fourier and De Blain-
ville. How the latter also antici-
pated the modern conceptions of
" Stoffwechsel " and " Metabolism "
see Claude Bernard, ' Phenom^nes
de la vie communs aux aniinaux
et aux vegetaux ' (1885, vol. i.
p. 36).

' It is historically interesting to
note that about the time when
Cuvier was gradually defining more

rigidly his four classes, Lamarck
was working at his ' Histoire natur-
elle des Animaux sans vertebres,' of
which the 'Systeme,' &c. (Paris,
1801), can be considered the first
editif)n, the larger work appearing
from 1816 to 1822. With him there
is no mention of a plan or a type.
His classes form a progressive series,
and he was the first to follow the
path from the simple to the more
complex. In opposition to Cuvier,
he thus wrote : " La nature, dans
toutes ses operations, ne pouvant
proceder que graduellement, n'a
pu produire tous les animaux h, la
fois : elle n'a d'abord forme que les
plus sinijiles, et passant de ccux-ci
jusques aux plus composes, elle a
etabli successivement en eux dif-
ferents syst^mes d'organes par-
ticuliers, les a multiplies, en a
augmente de plus en plus IV'nergie,
et les cumulant dans les plus par-
faits, elle a fait exister tous les
animaux connus, avec Torgani-sation
et les facultes que nous leur ob-
servons. Or, elle n'a rien fait
absolument, ou elle a fait ainsi."
('Hist, des Animaux sans vertebres,'
2nd ed., par Deshayes et Milue
Edwards, Bruxelles, 1837, vol. i.
J). 42. Cf. also Carus, loc. cii.,
p. 615.)

240 SCIENTIFIC THOUGHT.

ledges yet another prominent influence in the forma-
tion of his ideas. Cuvier, the zoologist, contemplating
the existing forms of nature from one of the two main
points of view, was impressed with the contrast be-
tween the lifeless and the living, seeing in the latter
stability of form, not of substance, — what we should
now term dynamical equilibrium. To him the vor-
tex is the symbol of life. De Candolle in studying
plants is struck with the underlying regularity and
symmetry of their formation. His views were formed
after very extensive practical occupation with descriptive
botany, which was followed by a lengthy residence in
Paris, where, next to Cuvier, he came greatly under
the influence of the Abbe Haiiy, the founder of
crystallography.^ From the Jussieus he learnt the im-
portance of looking at the " ensemble," the " port et
aspect " (facies, habitus) ; " from them and Cuvier the
value of the principle of the subordination of characters,
and the correlation of parts in the organisation of the
whole.^ But he fastens mostly upon the underlying

1 De Candolle, ' Th^orie ^l^men- j conduit h, quelques-unes des id^es

taire de la Botanique,' 2nd ed., j que j'exposerai dans le livre sui-

Paris, 1819, p. 72 : " Je dois encore i vant." Cf. also ' Organographie

compter, au nombre des causes qui vegetale,' Paris, 1827, vol. ii. p.

ont influe sur I'amelioration des ! 237.

m^thodes botaniques, d'un cot^ les
perfectionnemens importans que la
classification zoologique a recus,
principalement par les travaux
philosophiques de M. Cuvier, trav-
aux qui ont reagi sur quelques
parties de la Botanique elle-meme,
et dont je m'honore d'avoir profits ;
de I'autre, les importans travaux de
M. Haiiy sur les lois de la crystallisa-
tion, et uotamment sur les d&rois-
semens des rangees de mol&ules des
cristaux, lois par lesquelles j'ai et^

2'Theorie ^lementaire, ' p. 89;
also, p. 216.

^ This principle is stated very
clearly by Cuvier in many places —
e.g., in the celebrated " Discours "
prefaced to the ' Recherches sur
les Ossemens Fossiles ' (3rd ed.,
4to, 1825, vol. i. p. 47): "Tout
etre organise forme un ensemble,
un systeme unique et clos, dont les
parties se correspondent mutuelle-
ment, et concourent ii la meme
action definitive par une reaction

ON THE MORPHOLOGICAL VIKW OF NATL'IJK. 241

regulurit}- and syiimietry, and studies the causes which
in the actual visible specimens of ])lant life veil and
cover up this symmetry ; as Haiiy ' had taught us in
crystallography to recognise the primitive forms which
appear changed by the phenomena of decrescence." De
Candolle accordingly enters very fully into the theory
of abortive, degenerate, and -coalesced forms, recurring
asain and again to the statement that the " ciisemUe "
of nature tends to make one think " that all organised 35.

Regularity

Ijeings are ret^ular in their most intimate structure, and a"<i ^

o o .symmetry.

that various and differently combined abortive efforts
produce all the irregularities which strike our glance
and embarrass our combinations." ^ And the morpho-

rt5ciproque. Aucuue de ces parties
ne peut changer sans que les autres
changent aussi ; et par const'quent
chacune d'elles, prise sdparement,
iiidique et donne toutes les autres."

1 Cf. ' Theor. olem.,' p. 116, where
he draws a parallel between the two
methods in crystollography repre-
sented by Rome de I'Lsle and Haiiy
and similar methods in botany. He
reverts to this freiiuently — e.<j.,
' Organographie,' vol. ii. p. 237,
where he says : " Le premier rai-
sonnait comme ceux des botanistes
qui voyaient une feuille ou unc
corolle comme un tout unique,
entaillo sur ses bords par une cause
incounue ; le second m'a servi de
guide lorsque j'ai tentc de montrer
que les decoupures diverses des
organes veg(5taux terraient essenti-
ellement aux modes varies et aux
degres divers de leur agregation."

■^ 'Theorie dlomentaire,' p. 186:
" Les avortemens, les soudures des
parties, leurs degen(5rescences, ne
sont pas plus des suppositions de
desordre ou d'imperfection dans les
etres organises, que les docrois-
semens des molecules ne sont des
desordres dans la cristallisation."

VOL. II.

^ ' Thdorie elementiiire, ' p. 97,
&c. ; also p. 236 : " La vraie science
de i'histoire naturelle g^ndrale con-
siste dans I't-tude de la symctrie
propre u chaque famille, et des
rapports de ces families entr'elles ;
toute la reste n'est qu'un eehafaud-
age plus ou moins industrieux pour
parvenir h ce but. " And 'Organo-
graphie vogotale, vol. i. p. x. :
" L'organographie est la base com-
mune de toutes les parties de la
science des etres organises ; con-
sideree en ce qui tient Ji la symdtrie
lies I'tres, elle est le fou<lement de
toute la theorie des classification.s,
&c." And again, ibid., vol. ii. 239:
" Plus le nombre des etres connus
a augmente, plus on les a etudies
avec soin, plus ou s'est convaincu
de ce principe que j'ai 6t6 le pre-
mier, ou I'un des premiers Ji dnoncer
dans sa g^neralito, qu'il est presque
certain cjue les etres organises sont
symetriques ou reguliers lors qu'on
les considi^re dans leur type, et
que les irregularitcs apjiareutes
des vdgdtaux tiennent ii des pheno-
m6nes constans entre certaines
limites, et susceptiblcs d'exister,
soit separt^meut, soit rouuis, tels

Q

242

SCIENTIFIC THOUGHT.

logical view is still more clearly expressed in the
further analysis of their regularity and symmetry. The
character of the structure is to be found in the ex-
istence or absence, in the relative or absolute position,
number, size, and shape of the different organs,^ whereas
the use or functions of the organs, as well as their
other sensible properties,^ are considered to be, not
the cause, but the consequence, of their structure, and
hence of little importance in the anatomy, and of
none in the classification, of plants, whatever may be
their value from a physiological point of view. " But
symmetry supposes a primitive plan or archetype, and
the proofs of symmetry are those of a general order." ^
" The natural classification of organised beings consists
in appreciating the modifying circumstances, and in ab-
stracting them so as to discover the real symmetrical
type of each group." * Here again De Candolle refers ^ to
the examples of the crystallographer and the astronomer,
who both make abstraction of the disturbing secondary
influences in order to arrive at the primitive form and

que I'avortement ou la degener-
escence de certains organes, leur
soudures entre eux ou avec d'autres,
et leur multiplication d'apres des
lois regulieres."

^ ' Theorie elem.,' p. 147 : " La
sym^trie organique se compose d'un
certain nombre d'^lemens dont les
priucipaux sont : I'existeuce ; la
position relative ou absolue ; le
nombre relatif ou absolu ; la gran-
deur relative ou absolue : la forme ;
I'usage ; la duree ; ... les qualites
sensibles," &c.

- Ibid., p. 170 : " L'usage des
organes est une consequence de
leur structure, et n'en est nulle-
ment la cause, comme certains

ecrivains irr^fl^chis semblent I'in-
diquer ; l'usage, quelle que soit son
importance dans I'etude j)bysiolo-
gique des etres, n'a done eu lui-
meme qu'une mediocre importance
dans I'anatomie, et ne peut en
avoir aucune dans la taxonomie."
... "Ce que je viens de dire de
l'usage des organes, s'applique a
bien plus forte raison encore a leurs
qualites sensibles, qui ne sont que
des consequences plus ou moins
directes de leur structure," &c.

3 Ibid., p. 185. •* Ibid., p. 188.

^ See especially the chapter ' ' De
la Symetrie vdgetale " at the end
of the ' Organographie, ' vol. ii. p.
236 sqq.

ox THE MORPHOLOGICAL VIKW OF NATURE. 243

the true orbit. It follows that " we must study tiiu
different species as constant things," ^ and that this is a
more " dignitied " occupation for a " naturalist than the
accumulation of doubtful cases in favour of the non-
permanence of species." " He agrees with Cuvier in
rejecting the older idea of the " echelle des etres,"^ and
ho praises the sagacity of Linnaeus, who suggests that
the vegetable kingdom resembles a geographical chart,*
— an idea which, in the hands of several French and
German botanists, has become a fruitful conception.

In De Candolle we meet with a repeated accentuation
of the recurring symmetry of form, of the existence of
definite primitive types, in the vegetable kingdom.
Simultaneously witli him there was labouring another
thinker and keen observer of nature, w^ho was primarily
struck by the resemblance exhibited in the different
parts or organs of one and the same plant, and searched
for the type or plan on which they were modelled. He
introduced into the vocabulary of scientific language
the expression " metamorphosis of plants." It was 35.
Goethe the poet who, in 1790, published under this metamor-

pilosis.

title his first contribution to morphological science. In
subsequent publications and essays, covering the last forty

1 " Theorie dlementaire," p. 195.

2 Ibid. Mbid., p. 230.
■• " Linu^ a le premier, avee sa

est tellement juste, tellement
fcconde en consequences utiles,
qu'il est pent - etre convenable

sagacit(5 ordinaire, compard le r^gne d'entrer dans quelques ddtails

vegdtiil a une carte geographique ; ultdrieurs. Je suppose pour un

cette inetaphore, indiquee dans son moment cette carte executce ; les

livre i)ar un seul mot, a etc dd- classes r(5pondent aux parties du

veloppeeensuitepar Giseke, Batscli, monde, les families aux royaumes,

Bernardin de Saint-Pierre, L'Hdr- 1 les tribus aux provinces, les genres

itier, Petit - Tliouars, &c. Et aux cantons et les espdces aux

quoi qu'on ne doive la prendre que 1 villes ou villages," &c. (Thdor.

pour une simple image, cette image | diem., p. 231).

244

SCIENTIFIC THOUGHT.

years of his extraordinary life, he again and again reverts
to the subject, which with him is only one chapter in the
extensive science of morphology, of which he was indeed
the first to form a general conception. G-oethe's ideas
hardly influenced the course of science, but in the history
of thought they form a remarkable anticipation of later
views, and have accordingly been frequently referred to
by contemporary writers, notably by Haeckel and Huxley
in their important works on Morphology and Evolution.
Of the foremost scientific writers, De Candolle was almost
the only one ^ who, during Goethe's lifetime, referred to
his views with approbation ; seeing in his theory of the
metamorphosis of the leaf a truly admirable divination "^
of vegetable organisation. Saint - Hilaire's honourable
mention of Goethe's morphological contributions to zoology
came only just in time to be seen by Goethe himself.^

^ See ' Organograpliie, ' vol. i. p.
551 : " Les parties de chaque rangee
ou de chaque verticille sont sus-
eeptibles de se transformer dans la
nature de la rangee qui la touche
immediatement. Ainsi Ton trouve
des sepales changes en nature
petaloide {Primula calcycanthema),
des petales changes en etamines
{C'apsella Bursa - jmstoris), des
Etamines changees en carpel les
{Magnolia fuscata), ou bien I'in-
verse, savoir : des carpelles changees
en etamines (Euphorbia ■palustris),
des (Etamines changees en petales
(toutes les fleurs doubles), ou les
petales transformes en nature de
calice {Ranunculus abortivus). M.
Goethe a tres-heureusement designe
la premiere de ces series de trans-
formations sous le nom de Metamor-
phose aseendantc ou direete, et la
seconde sous celle de Metamorphose
descendante ou inverse.'^

2 Ibid., vol. ii. p. 243: " C'est

ainsi qu'en voyant la maniere
v($ritablement admirable dont M.
Goethe, quoiqu' habituellement
occupe d'id^es si ditferentes, a
comme devine 1' organisation vege-
tale, on est bien tent^ de croire
qu'il I'a moins invents qu'il n'a
generalise avec genie quelques faits
partiels heureusement choisis."
This was written in 1827.

■^ See Goethe's ' Werke' (W^eimar
edition, Abth. II. Bd. vii.), the
review of " Principes de Philosophic
Zoologique. Discutes en Mars
1830 au sein de I'academie roj'ale
des sciences par M. Geoffroy
Saint-Hilaire, Paris, 1830," especi-
ally p. 181, and dated Sept. 1830.
In 1831 Geofifroy says of the unity
of organisation : " Elle est pre-
sentement acquise au domaiue de
I'esprit humain ; et I'honneur d'un
succes aussi memorable appartieut
b, Goethe." Quoted by Huxley in
'Life of Owen,' vol. ii. p. 291.

ON THE MOIIPIIOLOCKAL VIEW oF NATCRE. 245

What did great haiiu Lo Goethe's correct anticipations
was the fact that in optics he had unsuccessfully com-
bated the generally accepted Newtonian theory of
colours/ and that his morphological glimpses were
taken up by Schelling and his school and incorpor-
ated in the fantastic speculations of the philosophy
of nature. They shared the fate of this and passed
into temporary oblivion.

Tlie idea of the fixity of certain forms in nature, of
the archetectonic modelling of her objects according to
certain archetypes, which Cuvier had put forth as the
result of extensive observation and inductive exam-
ination of living and fossil forms, which in Ue CandoUe
was connected with the conception of geometrical order,
regularity, and symmetry, found in Goethe's mind an 37.

The ideal

artistic sanction. " It is," as the historian of botany type,
lias remarked, " the idealistic conception of nature wliich
looks upon the organic forms as continually recurring

^ A full discussion of Goethe's

theory of colours will be found in
two addresses of Helmholtz : the
first, from the year 1853, was re-
printed in the first volume of
his often - quoted ' Vortriige und
Keden ' ; the second was delivered
nearly forty years later at the
meeting of the Goethe Society at
Weimar, in June 1892. In the
latter Helmholtz :<ignificantly re-
fers to the great revolution which
in the interval hiul come over scien-
tific thought through the general re-
cognition of the principles of energy
and of evolution. Bj- the light of
these we are better able to under-
stand the shadowy but nevertheless
truthful anticipati<jns contained in
Goethe's poetical and scientific
writings. Helmholtz traces the
errors of Goethe's colour - theory

largely to the fact that he worked
with imperfect apparatus and im-
pure colours ; that " he never had
before his eyes perfectly purified
homogeneous - coloured light, and
hence W'Ould not believe in its
existence. On this difficulty,"
Helmholtz continues, "of complete
purification of the simple spectral
colours, a man like Sir D. Brewster
foundered, who was much more
experienced and clever in optical
experimenting than Goethe, and
was equipped with the best in-
struments" (Goethe's ' Vorahnung
kommender naturwissensliaftlicher
Ideen,' by H. von Helmholtz,
Berlin, 1892, p. 30). Cf. also
Helmholtz's Memoir on Brewster's
Analysis of Sunlight, 1852. Re-
printed in Wissenschaftl. Abhandl.,
vol. ii.

246 SCIENTIFIC THOUGHT.

imitations of eternal ideas in the sense of Plato, and
which confounds these abstractions of the mind with
the objective nature of real things." ^ Nevertheless, we
must recognise that through the vague and poetical ex-
positions of Goethe's writings there is to be seen the
fruitful idea of the change, the instability, of forms, as
an equally important side of reality.^ In fact, Goethe
oscillates in his half-formed theories between the ideal
archetypes of Plato and the more recent conceptions of
Darwin and Spencer, as is proved by the vivid, even
passionate, interest which he took in the celebrated
controversy of Cuvier and Saint-Hilaire in the French
Academy of Sciences in the year 1830, — an incident
which carries us into the midst of the ideas with which
the following chapter will be occupied.

Before we take up those entirely different lines of
observation and reasoning, we must note a great ex-
pansion and development of the study of the form of
natural objects — of morphology — in two independent
directions. One of these carried the study of forms
into the larger dimensions of time and space, the past

■• Sachs, ' Geschichte der Botanik,' apprehension was needed to give

p. 181. I these airy nothings a local habit-

^ Of Goethe Huxley says ('Life | ation and a name; to convert

of Owen,' vol. ii. p. 290): "On ' vague suppositions into definite

the face of the matter it is not i hypotheses. And I apprehend that

obvious that the brilliant poet had it was just this service which

less chance of doing good service Goethe rendered by writing his

in natural science than the dullest essays on the intermaxillary bone,

of dissectors and nomenclators. on osteologj' generally, and on the

Indeed there was considerable ; metamorphosis of plants." A very

reason, a hundred years ago, for
thinking that an infusion of the
artistic way of looking at things

full appreciation of Goethe's merit
will be found in all the principal
writings of Ernst Haeckel, notably

might tend to revivify the some- in the fourth chapter of the first

what mummified body of technical ; volume of the ' Natiirliche Schbp-

zoology and botany. Great ideas i fungsgeschichte,' 9th ed., Berlin,

were floating about ; the artistic 1898.

ON THE MOKPHOLOGICAI. \'IK\V OF NAirKK. 247

of history and the morphological changes of the earth ;
the other carried it into those small dimensions where
the unaided eye sees only sameness and repetition, but
where the microscope reveals the liidden structure, the
internal and minute forms, of which living matter is
made up.

I have already pointed out how the great travellers
of the second half of the eighteenth century — Banks,
Pallas, and Humboldt — carried the study of nature
beyond the narrow limits of the museum and the work-
room into the larger area of nature, of the present and
the past world. Camper in Holland, Hunter and Monro
in this country, lUumenbach and Soemmering in (ier-
many, Saussure in Geneva, towards the end of the eigh-
teenth and the beginning of the nineteenth century had
betfun to unite these scattered discoveries and records
into something like order and system. It was again ss.
the great merit of Cuvier to publish a monumental toiogy.

^ Of the labours of other natural-
ists who preceded Cuvier, a very
full account will be found in a post-
humous work of Ducrotay de Blain-
ville, edited by M. Pol Nicard and
entitled ' Cuvier et Geoffroy Saint-
Hilaire' (1890). The author, as is
well known, was for some time a
colleague and collaborator of Cu-
vier, with whom he fell out, partly
from personal reasons, partly owing
to the whole bent of his scientific
researches, which was much more
philosophical than that of Cuvier.
He had a very great appreciation
of Lamarck at a tune when that
speculative naturalist was unknown
or treated with neglect, not to say
with ridicule. The criticisms of De
Blainville on Cuvier must be ttiken
with caution : nevertheless his

works and lectures had a great
influence on the development of
the more philosophical side of nat-
ural science in France, as many al-
lusions of Auguste Comte, Flourens,
Claude Bernard, &c., sufficiently
prove. In the chapter on Palaeont-
ology in the work on Cuvier (p.
380, &c.), De Blainville does full
justice to Camper, Blumenbach,
Soemmering, and other Continental
naturalists, with whose laboui-s
Cuvier, through his German educa-
tion, was better acquainted than
his French colleagues. There is
also a significant remark of his
on the fact that Cuvier was essen-
tially a collector and dissector,
a man of the museum and the
library, not an outdoor naturalist
(!'. 241).

248

SCIENTIFIC THOUGHT.

work on the subject and to found the science of
palaeontology. His researches in this subject were
based upon the collection of fossil remains which had
been begun by Daubenton for the natural history of
Buffon, and which he arranged and largely increased ; on
the collection which Camper had made at Amsterdam;
on descriptions which he procured from all the collectors
of Europe, notably from Blumenbach ; on his excavations
together with Brogniart in the environs of Paris. As
early as 1798 he announced his intention of collecting
everything that was known on fossil remains in a great
tableau — a plan which was not realised till 1812, when
his many separate publications were united in the great
work on the " Ossements fossiles," and was only completed
by the greatly revised and augmented edition of 1821.
This work is important in morphological science, not
only because it contains many accurate and still highly
valued descriptions of " extinct species," but also because,
in its celebrated introduction ^ on the revolutions on the
surface of our globe, it takes a comprehensive view of the
changing aspects which succeeding ages, divided by great
catastrophes characterised by distinct geological formations

^ In this introduction (p. 52 of
vol. i.) there is also to be found the
celebrated passage in which Cuvier
says that by the application of his
principle of the "correlation of
parts " he could, if he only pos-
sessed one well-preserved fragment
of a bone, determine everything as
certainly as if he possessed the whole
animal — a statement on which De
Blainville [loc. cit., p. 417) has some
very pertinent remarks : " Ce ne
sont pas des anatomistes vdritables
comme I'etaient Hunter, Camper,

Pallas, Vicq-d'Azyr, Blumenbach,
Soemmering et Meckel qui se
seraient aiusi avances, et M. G.
Cuvier aurait et^ bien embarasse
lui-meme, si on I'avait pris au mot,
et cependant c'est cette assertion
qui restera formulee dans la bouche
des ignorants,"' &c. Cuvier by this
method determined and classed
more than 150 mammals (loc. cit.,
p. 53). A more favourable view of
Cuvier's work on fossil remains is
taken by Huxley, 'Life of Owen,'
vol. ii. p. 297.

ON THE MORPHOLOGICAL VIEW OF NATURE. 249

ami liy the I'ussil iciuuius ul' exliiiel (jigaiiic creations, pre-
sented on the surface of our earth. " What is certain,"
says Cuvier at the close ^ of this celebrated discourse, "is
that we are now at least in the middle of a fourth
succession of terrestrial animals, and that after the age
of reptiles, after that of the paheotheria, after tliat of
the mastodons, the megatheria, there has come the age
when the human race, supported by some domestic animals,
peaceably rules and cultivates the earth, and that it is only
in the countries formed since this epoch in the recent
alluvial deposits, peat-bogs, and concretions, that we find
in a fossil condition those bones which belong to animals
known and now living." Such is the r^nimd of the ideas
whicli had followed — nay, even tormented'- — (Juvier
during his researches into fossil remains, and which led
hiiu to the conclusion ^ " that it required great events
to bring about the important differences which he recog-
nised " — differences which the slow " inlluence of weather,
or of climate, or of domestication," could not explain,
but which required the violent action of sudden " catas-
trophes," * which frequently " disturbed the life on this
planet by frightful events," ^ " broke off the thread of
operations," ^ " none of the present agencies of nature
sufficing to produce her bygone works." ^

' " Discours sur les revolutions
de la surface du globe et sur les
changemens qu'elles ont produits
dans le n'gne animal," reprinted in
the 3rd ed. of the ' Recherches sur
les osseniens fossiles,' 182.5, vol i.
p. 172.

- " Ces idues m'ont pouisuivi, je
dirai presque tourmento, pendant
que j'ai fait les recherches sur les os
fossiles, dont j'ai donnd depuis peu

au ]iuhlic la collection, recherches
qui u'embrassent qu'une si petite
partie de ces phenomcne.s de I'avant-
dernier Age de la terre, et qui
ce]iendant so lieut h tous les autres
d'une maniOre intiine" (' Discours,'
&c., p. HO).

='Ibid., p. 3. •» Ibid., p. 8.

5 Ibid., p. 9. " Ibid., p. 14.

^ "Ainsi, nous le n'pi-tons, e'est
en vain <iue Ton cherchc, dans les

250 SCIENTIFIC THOUGHT.

39. These words, which embody a conception since appro-

Cuvier's i • i

catastro- priatelv termed " catastrophism, and which picture to

phism. r J jt

the mind's eye a succession of morphological changes of
the entire aspect of our globe, were written at a time
when, in this country especially, through the labours of
Hutton, an entirely opposite view was gradually pre-
paring. With this we shall deal in another chapter.
The Cuvierian conception of epochs in geology harmon-
ised with that of distinct types of organic creation.
These exhibit in space, as those do in time, certain definite
and distinct morphological characters— z.c, certain typical
forms and structures on a vast or a small scale, around
which the features of events and individuals seem to
oscillate, and which permit us scientifically to classify,
describe, and comprehend them. This conception gave
the tone to a long line of researches on the Continent
and in this country in geology as well as in natural
history.

In the study of these typical forms and structures in
which nature repeats herself, reverting again and again
to them, but in every single case departing more or less
from them ; in the study of this order without monotony,
this change without confusion, this variety of forms in

40. which leading features are always recognisable, — the dis-
anaio^es. covcry of analogies played a very prominent part.

Goethe's metamorphosis of plants is based upon the
analogy of their different organs : before he published

forces qui agissent maintenant u la
surface de la terre, des causes suf-
fisantes pour produire les revolu-
tions et les catastrophes dont son
enveloppe nous montre les traces ;

et si Ton veut recourir aux forces ex-
terieures constautes connues jusqu'b,
present, Ton n'y trouve pas plus de
ressources" (ibid., p. 20).

ON THE MORPHOLOGICAL VIEW OF NATURE. 251

this first luorphulogical fnigmeiit he had already — led
by analogy — discovered the intermaxillary bone in the
upper human jaw. Later he and (Iken independently
traced the analogy between the skull and the vertebral
column in vertebrate animals, a view which was taken
up by eminent anatomists, such as Meckel, Spix, and
Geoffroy Saint-Hilaire.^ The tendency which lay in these
attempts, of which the metamorphosis of plants and the
vertebral theory of the skull are only prominent examples,
is one which was naturally provoked by the opposite
tendency which anatomical studies had received through
Linnaeus and Cuvier. Goethe himself gives a clear ex-
planation of its origin. In a remarkable passage in the
history " of his botanical studies, he mentions Shake-
speare, Spinoza, and Linnaeus as the three masters who
had led him to reflect on the great problems of art, of life,
and of nature. Now, he says, the intiuence of Linnaius
lay principally in the opposition which he provoked.

^ A good account of the part
wliich the vertebral theory of the
skull played iu com])arative an-
atomy will be found in Whewell's
History, vol. iii. p. 369, Lc. But
see against this Huxley in ' Life of
Owen' (vol. ii. p. 304): "The hypo-
thesis that the skull consists of
modified vertebra:', advocated by
Goethe and Oken, and the subject
of many elaborate works, was so
little reconcilable with the mode of
its development that, as early as
1842, Vogt threw well - founded
doubts upon it. 'All efforts to in-
terpret the skull in this way,' said
he, 'are vain.' "

'■^ See the \Veimar edition of liis
Scientific Works, vol. ii. The
pa.ssage given in the text is from
an earlier account contained in two
numljers of the ' Morphologische

Hefte' (1817), reprinted loc. cit., p.
389, &c. How Goethe continually
hovered between the theory of
types and that of development is
seen in the following passage (1831,
W. W., vol. vi. p. 120): "Das
Wechselhafte der Pflanzengestal-
ten, dem ich liingst auf .seinem
eigenthiimlichen Gauge gefolgt,
erweckte nun bei mir immermelu"
die Vorstellung : die uns unige-
benden Ptlanzenformen seien nicht
urspriinglich determinirt und fest-
gestellt, ihnen sei viehmehr, bei
einer eigensinnigen, generischen
und specifischcu Hartniickigkeit,
eine gliickliche Mobilitiit und
Biegsamkeit verliehen, um iu so
viele Bedingungen, die iiber dem
Erdkreis auf sie einwirken, sich
zu fiigen und darnach bildeu und
umbildeu zu kijnnen."

252

SCIENTIFIC THOUGHT.

" For as I tried to take up his sharp and suggestive
distinctions, his expressive, useful, but frequently arbi-
trary laws, there arose in me an inner confiiet : what
he tried forcibly to hold asunder, tended according to
the innermost demands of my nature to be united." And
as the process of dividing, classifying, and keeping apart
went on among the successors of Linnaeus, so it must
have produced in many genuine observers of nature a
tendency similar to that which Goethe describes. They
would emphasise the resemblances and analogies of
natural objects and their organs in proportion as the
classijfiers had separated and distinguished them. And
it was just as likely that the artistic mind of Goethe
might succeed in " lifting the veil of nature," as Hum-
boldt ^ put it, when he transmitted to Goethe his
suggestive work on the geography of plants, and as
Huxley" repeated in 1894. Indeed it was the former
who, on the largest scale, Jiad traced those analogies and
correspondences in nature which are so much dearer

- See quotation su^wa, p. 246
note ; also ( ' Life of Owen, vol. ii.
p. 288) : " The cultivator of botany,
who went bej'ond the classification
of ' hay,' became familiar with facts
of the same order. Indeed, flower-
ing plants fairly thrust morpho-
logical ideas upon the observer.
Flowers are the primers of the
morphologist ; those who run may
read in them uniformity of type
amidst endless diversity, single-
ness of plan with complex multi-
plicity of detail. As a musician
might say, every natural group of
flowering plants is a sort of visible
fugue wandering about a central
theme which is never forsaken,
however it may, momentarily,
cease to be apparent."

^ See Goethe's own account (in
Werke, 2 Abth., vol. vi. p. 163):
" Sollte jedoch meine Eitelkeit
einigermasseu gekriinkt sein, dass
man weder bei Blumen, Minern,
noch Knochelchen meiner weiter
gedenken mag, so kann ich mich
an der wohlthatigeu Theilnahme
eines hochst geschiitzten Freuudes
genugsam erholen. Die deutsche
Uebersetzung seiner Ideen zu einer
Geographie der Pflanzen nebst
einem Naturgemiilde der Tropen-
liinder sendet mir Alexander von
Humboldt mit einem schmeichel-
haften Bilde, wodurch er andeutet,
dass es der Poesie wohl auch
gelingen konne den Schleier der
Natur aufzuheben ; und wenn er
es zugesteht, wer wird es leugnen ?"

ON THE MOKPHOLOGICAL VIEW OF NATURE. 253

to the poetical huirI of Goethe, and all other artists,
thau the separations and chissitications of the men of
science. '' It is one of Humboldt's uncontested merits
that he, in order to prove the unity which rules in
the formation of the earth, searched for analogies in
the geological constitution of distant countries. As
we see him pointing out numerous novel coincidences
between the formations of Mexico and Hungary, so
likewise we owe to him suggestive hints for other
similar comparisons." ^ But the man in whose labours
the tendency of thought which was uncritically followed
by Goethe, and magnificently represented in Humboldt,
found the clearest scientific expression, so far as animated
nature is concerned, was liltienne Geoffroy Saint-Hilaire, 41.

Geoffrey

the friend and colleague and then the great rival of s»int-

o '^ Hilaire.

Cuvier." Xo one recognised more clearly the deeper
significance of the great outburst of the two conflicting
ways of viewing nature in the Paris Academy of Sciences
in 1 8 :» 0 than Goethe himself, who in the eighty-first year
of his life was deeply stirred by seeing his favourite ideas
espoused by a scientific authority of the first order.^

' See Julius Ewald in the third great event ? The volcano has come

volume of the ' Leben Hum- to an eruption, everything is in

boldt's ' Vjy Bruhns (German edi- flames, and it is no longer a dis-

tion), p. 184. cus.sion with closed doors.' 'A

- See Huxley in 'Life of Owen.' dreadful affiiir,' I replied. 'But

vol. ii. p. 293. what else could one expect undei-

■* Eckermann in the ' L'onversa- the well-known circumstances and

tions with Goethe ' gives the follow- with such a ministry, but that it

ing remarkable account, under date would end with the expulsion of the

2nd August 1830: " The new.s of Royal Family.'" ' We do not seem

the outbi-eak of the French Revolu- to understand each other, my

tiim arrived to-day, and created friend,' retorted Goethe. ' I am in

e.xcitement everywhere. In the iM'wi-c speaking of tho.se peojile ; I

course of the afternoon I went to am iimcerued with quite different

Goethe. 'Well,' he called out to iliiiiL,'s. I spe.ak of that most im-

me, ' wiiat do you think of this porlant conflict which has come

254

SCIENTIFIC THOUGHT.

Similarly the aged Gauss, twenty-four years later, listened
with emotion when Eiemann, in his celebrated disserta-
tion, touched a string that had been vibrating in the
master's soul for fifty years, unheard or unheeded by
any other thinker.^ We can best understand the two
ways of reasoning in natural objects, which found an
expression in the controversy between Cuvier and Saint-
Hilaire, if we read the account which Goethe himself
subsequently pubHshed in a Berlin periodical : " Cuvier
labours untiringly as a distinguisher, describing accur-
ately what lies before him, and thus attains a command
over a great breadth of facts. Geoffroy Saint-Hilaire,
on the contrary, is silently exercised about the analogies
of living creatures and their mysterious relations." " The
two men had worked as colleagues for thirty-eight years,
Cuvier continuing and defining more clearly the classi-
fying work of Linnseus, who, for example, had thrown
all non-vertebrate animals into one class. This led him

to pass in the Academy between
Cuvier and Geoffroy Saint-Hilaire,
and which is of such importance
to science.' This utterance of
Goethe was so unexpected to me
that I did not know what to say,
and that for some minutes I ex-
perienced a complete cessation of
my thoughts. ' The matter is of
the greatest importance,' continued
Goethe, ' and you have no idea
what I feel concerning the news
of the 19th July. We now have
a mighty ally permanently in
Geoffroy. But I also see from it
how great is the interest of the
scientific world in France in this
matter, as, in spite of tlie frightful
political excitement, the meeting
took place in a crowded house.
What is best is, that the synthetic
treatment of nature, introduced by

GeofiFroy in France, cannot again
go back. ... I have for fifty
years laboured in this cause ; first
alone, then supported, and at last,
to my great delight, excelled by
congenial minds. . . . This event
is for me of incredible value, and
I rejoice rightly over the ultimate
general victory of the cause to
which I have dedicated my life,
and which also is essentially my
own."

^ On this incident see the prefa-
tory notice in Riemann's ' Mathe-
matische Werke,' ed. Weber, Leipzig,
1875, p. 517 ; also the 1.3th chapter
of this volume.

^ Goethe in the ' Berliner Jahr-
biicher fiir Wissenschaftliche Kri-
tik,' vol. ii., 1830, September, re-
printed in Werke II. vol. vii. p. 167
sqq.

ON THE MORPHOLOGICAL VIKW UF NATUKK. 255

tinally in 1817 to establish the four great classes — the
vertebrate, the molluscous, the articulate, and radiated
types — in the animal kingdom. His colleague had con-
tributed much to Cuvier's work, but had been increas-
ingly struck by what lie termed the " unity of organic
composition," which he evermore looked upon as a key ^
to the comprehension of nature : he searched for one
]ilan or type where Cuvier saw four types. In 1818
lie published his principle in a celebrated work with
the title, ' Theorie des Analogies, ou de I'hilosophie
Anatomique.' " It has been correctly stated that he
only gives more precise expression to a truth known
to Aristotle and proclaimed by Buffon, that the mystery
of ort^anisation consists in " unity of plan combined with 42.

'^ ^ iT Cuvier and

variety of composition." Cuvier emphasised and studied Geooroy.
the latter, his colleague the former. For an intimate
knowledge and description of natural objects the work
of distinguishing is all important; for a comprehension
of nature the connection of things, the unity of plan,
the filiation and relations of beings, the mutability of
species, will ever be the more important and fascinating.
The former was a purely scientific, the latter a philo-

' See Goethe's detailed Keport,
loc. cit., W^erke IL vol. vii. p. 173.
A very full account of this cele-
brated controversy is also given in
the i>osthumous work of Ducrotay
de Blaiuville, ' Cuvier et Geuffroy
Saint-Hilaire, Biographies scientif-
iques,' ed. Nicard, Paris, 1890,
pp. 3o7-378, which is specially in-
teresting, because Geotfroj''s ideas
were there traced to Lamarck (p.
351), of whom Goethe takes no
notice. ,

2 See the " Eloge Historique
d'Etienne Geoffrey vSaint-Hilaire,"

par P. Flourens, in the third volume
of his ' Recueil des Eloges,' &c.,
Paris, 1862, pp. 229-281. He quotes,
inter alid, a passage from Vicq-
d'Azyr : " La nature seuible operer
toujours d'aprcs un modele primitif
et g^ndral dont elle ne s'ecarte qu'
b, regret, et dont on rencontre par-
tout des traces. ... On observe
partout ces deu.x charactores (|ue la
nature semble avoir imprimes li tous
lea etres, celui de la coustance dans
le type et celui de la variott^ dans
les modifications," &c. (p. 276).

256

SCIENTIFIC THOUGHT.

sophical, task. Both thinkers were right, but only par-
tially right, as Huxley has clearly shown ; ^ but it was
natural that Cuvier's position should for a long time be
regarded as the stronger ; since he had shown how, by
detailed research, to increase enormously the stock of
actual knowledge about the things of nature ; whereas
the uncritical and only half practical suggestions of
Goethe had undergone in the wild speculations of
SchelHng, Steffens, and Oken a development that fright-
ened off men of exact thought. Cuvier saw the necessity
of crying halt to these vague dreams which he had the
merit of opposing, for the lasting benefit of true science,
with the full force of his great authority.^

As in France and Germany so also in England, the
tendency to distinguish minutely, to describe, to classify,
and in doing so to fill the museums with new specimens.

1 ' Life of Owen,' vol. ii. p. 296 :
"The irony of history is nowhere
more apparent than in science.
Here we see the men over whose
minds the coming events of the
world of biology cast their shadows,
doing their best to spoil their case
in stating it ; while the man who
represented sound scientific method
is doing his best to stay the inevit-
able progress of thought and bolster
up antiquated traditions. The pro-
gress of knowledge during the last
seventy years enables us ,to see that
neither Geoffroy nor Cuvier was
altogether right nor altogether
wrong ; and that they were meant
to hunt in couples instead of pull-
ing against one another."

2 As to Cuvier's own wavering on
the great question of the fixity of
species, see Huxley, loc. cit., p. 294 :
" During the earlier part of his
career, I doubt if Cuvier would
have categorically denied any of

GeofFroy's fundamental theses. And
even in his later years Sir Charles
Lyell, many years ago, gave me
reasons for the opinion that Cuvier
was by no means confident about
the fixity of species. There was
never any lack of the scientific im-
agination about the great anato-
mist ; and the charge of indifference
to general ideas, sometimes brought
against him, is stupidly unjust."
And further, p. 295 : " In later life,
however, Cuvier seems to have be-
come so much disgusted by the
vagaries of the Naturphilosophie
school, and to have been so strongly
impressed by the evil which was
accruing to science from their ex-
ample, that he was provoked into
forsaking his former wise and
judicious critical attitude ; and in
his turn he advocated hypotheses
which were none the better than
those of his opponents."

ON THK MUKI'HOLOGICAL VIKW OF NATUKK. 257

43.
Richard

and Lo discover and uiTunge systeiiuitically unknown
and extinct species, got the upper hand for a long
time. No one has done better work in this large
field than Eichard Owen, who has been termed with
some propriety the British Cnvier. But in following owcil
the lines and filling up the schedules which Cuvier
liad prepared, Owen and other ^ contemporary workers
in the same field have also had the great merit of
bringing the Cuvierian view to the point where it
clearly leads on to another and more comprehensive
view of nature. In the first place, it happened that
in finding and describing the remains of extinct animals,
increasing difficulty was experienced^ in deciding to
which of the great existing groups of animals they
should be assigned. There arose the necessity of in-
terpolating species between groups which we now look
upon as widely separated. The necessity arose of form-
ing the conception of what is now termed the " inter-

' Huxley, loc. cit., p. ;ilO : '• Un-
less it be in the ' Ossenients fossiles,'
I do not know where one is to look
for contributions to paUcontology
more varied, more numerous, and,
on the whole, more accurate, than
those which Owen poured forth in
rapid succession between 1837 and
1888. Yet there was no lack of
strong contemporaries at work in
the same field. De Blainville's
' Ost^ographie ' ; Louis Agassiz's
monumental work on fossil fishes,
achieved under the ])ressure nf
great obstacles and full of bi-illianl
suggestions ; Von Meyer's long series
of wondei-fully accurate memoirs,
with their admirable illustrations
executed by his own hands, all
belong to Owen's generation."

- See on this Carus, ' tleschichte

VOL. IL

der Zoologie,' p. 648, and Huxley,
loc. cit., p. 309, where reference is
made to Owen's memoir "on an ex-
tinct mammal discovered in South
America by Darwin in L833, which
Owen named Taxodon Platensis. It
is worthy of notice that in the title
of this memoir there follow, after
the name of the species, the words
'referal)Ie by its dentition to the
Rodentia, but with affinities to
the Pachydermata and the herbi-
vorous Cetacea ' ; indicating the
imjiortance in the mind of the
writer of the fact that, like Cuvier's
Anoplothcriurii and Palcvothcrium,
Taxodon occupied a position be-
tween groups which, in existing
nature, are now widely separated.
The existence of one more ' inter-
calary ' type was establislied."

B

258

SCIENTIFIC THOUGHT.

44.
Study of
homology.

calary type." Especially through palseontological finds,
the landmarks were gradually removed which separated
the distinct species and groups of organised beings.
It had happened to Cuvier only in single instances
that he had to record resemblances between widely
separated groups. Such resemblances became more and
more frequent and perplexing. In the second place,
Owen had the great merit of giving more definite ex-
pression to the conception of analogies, as developed
principally by the school which Cuvier opposed. In
fact, he revised and brought into general use the term
" homology," which had already been used by French and
German anatomists before him.^ This term signified

^ Great importance has been at-
tached to the term "homology,"
which, to a reader uuiuitiated iu
the complicated and changing vo-
cabulary of the natural sciences,
presents not a little difficulty.
It is a good example of the
classical saying of Goethe, "dass
wo Begriffe fehlen, da stellt ein
Wort zu guter Zeit sich ein." In
the attempt to define the current
term "homology," in seeking for
numerous examples of homologies
as distinguished from analogies, nat-
uralists were led to the recognition
of i-eal, not only of verbal or logical
distinctions. In this respect it is
most instructive to read Owen's
treatise ' On the Archetype and
Homologies of the Vertebrate
Skeleton' (1848), the enlarged re-
print of a Report to the British
Association in 1846. In it he gives
a pretty full history of the term
homology, which in the first half of
the nineteenth century became cur-
rent with special meanings in three
independent sciences. With the
precision of the usage, both in
geometry and chemistry, the vague-

ness of the term as used by nat-
uralists stands in characteristic con-
trast. " The corresponding parts,"
Sir R. Owen there says (p. 5),
" in different animals being made
namesakes, are called technically
' homologues.' The term is used
by logicians as synonymous with
'homonyms,' and by geometricians
as signifying ' the sides of similar
figures which are opposite to equal
and corresponding angles,' or to
parts having the same propor-
tions : it appears to have been
first applied in anatomy by the
philosophical cultivators of that
science in Germany. Geoffroy
Saint - Hilaire says, ' Les organes
des sens sont homologues, comme
s'exprimerait la philosophic Al-
lemande ; c'est-a-dire qu'ils sont
analogues dans leur mode de
develo2323ement, s'il existe veritable-
ment en eux uu meme principe de
formation, una tendance uniforme
li se rep^ter, h. se reproduire de la
meme fagon.'" After remarking
on the looseness of this definition,
Owen proceeds to give his own,
taken from the " Glossary " ap-

ON TUR MORPHOLOGICAL VIP:VV OF NATTRE,

259

correspondence of parts or organs based not so much on
external likeness as on similarity of origin. Ly admit-
ting the latter conception, the idea of origin, the rigidity
■of the purely structural classification was lost. Morpho-
logy became the science, not of fixed, but of flowing
forms and structures. It is remarkable that Owen, in
following up this line of reasoning, was pre-eminently at-
tracted to the oracular writings of Oken, whose influence
his great forerunner Cuvier had combated with all his

pended to tlie first volume of his
' Hunteriaii Lecture.s,' as follows :
" ' Analogue ' — A part or organ in
one animal which has the same
function as another part or organ
in a different animal." " ' Hom-
ologue' — The same organ in dif-
■erent animals under every variety
of form and function." He then
goes on to distinguish " special,"
^' general," and " serial " homology.
For a history of thought the imjwr-
tant point in all these discussions
is that, besides the similarity of
sti'ucture and the sameness of
function, relations and jjoints of
comparison of a different kind
were introduc:ed ; tliat these were,
with more or less clearness, traced
to development ; and that through
this the genetic view, the doctrine
of descent, was prepared by those
who, like Owen, were least ready
to accept it when it ap])eared in a I
■definite form. In the light of this j
new view, of which the ne.\t
chapter will treat, the whole vocab-
ulary of the older morphologists I
required recasting. These older
views, which traced homology t<i
the existence of definite types,
models, or i)atterns possessing a
purely ideal existence, have been
termed Platonic, inasmuch as in
the philosophy of Plato the exist-
•C'uce of a world of ideal forms or

archetypes served to explain what-
ever of order is found in the real
world of separate things. " The
term 'homology,'" says Prof. Itay
Lankester, " belongs to the Platonic
school, but is nevertheless used
without hesitation by those who
reject the views of that school.
Prof. Owen . . . would understand
by ' homologue ' the same firgan
in different animals under every
variety of form and function. . . .
But how can the sameness of an
organ under every variety of form
and function be established or in-
vestigated r This is, and always
has been, the stumbling-block in
the study of homologies without
tlie light of Evolutionism ; for, to
settle this question of sameness,
an ideal ' type ' of a group of
organisms under study had to be
evolved from the human mind,
after study of the comj)onent
members of the group ; and then
it could be assei-ted that organs
might be said to be the ' same '
in two animals which had a
common representation in the
ideal type" {'Annals and Mag.
of Natural History,' 4th series,
vol. vi., 1870. p. 34, &c.) See also
Huxley in ' Life of Owen,' vol. ii.
p. 303, &c. ; and J. Arthur Thom-
son, 'The Science of Life,' p. 32
(1899).

260 SCIENTIFIC THOUGHT.

might, and who " provided him with the subject-matter
of his severest as well as of his most justifiable
sarcasms." ^

The great extension of the morphological or struc-
tural view of nature into distant time and space — into
palaeontology by Cuvier and Owen, into geography by
Humboldt, Eitter, and others — i.e., morphology on an
extensive scale — led to an appreciation of the labours
of a different class of students of nature, namely, those
who — also on a large or a smaller scale — investigated
the agencies which bring about and the laws which
CTovern the change of forms. I have now to mention
the last great contribution to the purely morphological
45. view, I mean the cellular theory, which tended ultimately

The cellular . .

theory. m a Similar direction.

The earlier researches into the minute microscopic
structure of organised beings — such as those of Malpighi
and Grew in the seventeenth century— were conducted
by persons who took an equal interest in animal and
plant life." But this class of research soon fell into
the hands of specialists, with the result that anatomy,
the science of animal structure, and phytotomy, that
of vegetable structure, were conducted on different lines

^ Huxley, 'Life of Owen,' vol. ii. ' sequent researches, of the doctrine

p. 315. of the composition of all organised

- Carus ('Gesch. der Zoologie,' p. ] bodies out of cells, which has given
' 39.5) mentions especially Malpighi to the whole conception of the Hv-
(1628-1694) as an exception, inas- ing creation a definite starting-
much as he conducted his researches ! point, and in the sequel a firm basis
from a purely scientific interest, j for the genetic view." See also on
keeping them free from extraneous ' the same subject, and on the rela-
practical considerations. " In his tion of structural and physiological
anatomy of plants there are laid, researches in the seventeenth and
moreover, the first foundations, eighteenth centuries, Sachs, ' Gesch.
more firmly established by all sub- d. Botanik,' p. 351, &c.

ON THK MORPHOLOGICAL VIEW oK NATURE. 261

ami for dill'ereiiL purposes. Thu fuel that the organisa-
tion of the higher animals, which, for medical reasons, is
more interesting, can be roughly divided into a variety
of separate organs or systems of organs, each of wliicli
can be, to some extent, studied by itself as we study
the parts and workings of a machine, and that for the
physician greater interest attaches to the functions of
these organs, placed anatomy for a long time under the
influence of physiology, which is the science of the per-
formance, not of the structure, of the parts of living crea-
tures. Phytotomy, on the other side, was for a long time
neglected, awaiting the greater perfection of the micro-
scope. Thus it came al)out tliat down to nearly the
middle of the century the morphological study of animals
and that of plants were pursued without much mutual
benefit or regard. The phytotomists of the seventeenth
century had established the fact that plants are built up
of minute parts called variously utricles, bladders, vesicles,
but mostly cells, and which were compared with tlie
structure of the foam of Ijeer or the cells of a honey-
comb.^ Different forms were assigned to these cavities.

'Aug. Pyr. de Caiidolle begins isation des Plautes ' (Harlem, 1812)

his ' Organographie ' (1827) with as the only French book whicli con-

tlie words: "La nature iiitime des tains an account of the phytotoniic

vcgi'taux, vue aux plus forts micro- , reseaiclies cai-ried on by the Ger-

scopes, offre peu de diversitds. Les mans, who, after the lapse of a cen-

plantes les plus disparates par leurs tury, were the first to take uj)

formes extdrieures, se ressemblent I these studies again. In the second

;i I'intc'rieur a un degrd viainieiit chapter l^e Caiidolle says; " Le

extraordinaire," &c. ; and after ti-*su cellulaiio, considers en masse,

going back to the observations of est un tissu membraiieux foi-mc par

Malpighi and Grew, and referring ' un grand nombre de cellules ou de

to the recent ones of Mirbel, Link, i cavites closes de toutes parts ;

Treviranus, Sprengel, Kudolphi rccume de la bicre ou un rayon

Kieser, Dutrochet, and Amici, men- de miel en donnent unc idee gross-

tions Kieser's ' Memoire sur I'Organ- | i6re mai.s assez exacte " (j). 11).

262

SCIENTIFIC THOUGHT.

46.

Hugo von
Mohl.

and it was also recognised that they were frequently
elongated into tubes or joined so as to form larger
vessels. In all these researches and descriptions para-
mount importance was attached to the form and com-
position of the framework of this cellular arrangement,
and only little to its contents. In fact, the historian
of botany^ characterises the period from 1800 to 1840
as that of the study of the cellular framework of plants.
The skeleton, as it were, of plant structure received
primarily the greater attention. In the course of these
researches, which, with a few important exceptions, were
all carried out in Germany, one point was permanently
settled, namely, that " the cell is the one fundamental
element of all vegetable structure." ^ No one did more
to establish this important fact than Hugo von Mohl,
whose name has been somewhat cast into the shade by
the more attractive writings of Schleiden. It was
Schleiden who first brought the new cellular theory
into popular recognition, not without an admixture of
errors, which had to be gradually eliminated in the
various controversies with which his name is connected.

^ See Sachs, loc. cit., p. 276, &c.
This period finds its consummation
in the researches of Hugo von Mohl.
It begins with those of Brisseau
Mirbel, the first French author who
took up this line. His labours were
continued and criticised by a long
list of German naturalists. Sachs
also refers to the erroneous habit
these earlier phytotomists had of
getting their diagrams of what
they saw by the microscope made
by other persons who were sup-
posed to be impartial — a custom
fortunately abandoned by Mohl,
who in his drawings did not give

" undigested copies of the objects
but his own impressions of them "
(p.^281).

- Sachs assigns the final estab-
lishment of this principle to the
year 1831, and considers it as one
of Mohl's achievements, since,
although it had been already
announced by Sprengel and Mirbel,
it had not been sufficiently sup-
ported by observations. Even the
curious but antiquated idea, accord-
ing to which the spiral fibre formed
a fundamental part of plant struc-
ture, survived up to 1830 (p. 323).

ON THE MORPHOLOGICAL VIEW OF NATURE. 263

Soliwanii.

But the highest value for a history of Thought attaches
to this point for a different reason. In it the hjug-
separutetl Hues ^ of botanical and zoological study met
again. Immediately after the appearance of Schleiden's 47.

_ Sclilcideti

epoch-making publication — and partly in consequence of and
it — Theodor Schwann was induced to collect, in 1839,
all the known observations, coming principally from
the scliool of Johannes Miiller, which referred to the
existence and formation of animal cells, and to utilise
them in the enunciation of liis great generalisation,
" that there is one universal principle of development
for the elementary parts of organisms however different,
and that this principle is the formation of cells." ^

' The fourth decade of the cen-
tury was also the period in which
pliysical and (.'lieiiiical methods and
ideas were — notably in France and
Germany — made useful for ana-
tomical and physiological research
in zoology and botany. Sachs,
however, significantly warns us
against the view, which has since
been frequently put forward in an
exaggerated form, that the physi-
ology of jilants consists in nothing
but a])i)lied physics and chemistry
{loc. cit., p. 393, &c. ) That Schwann
himself attached the greatest im-
portance to this point can be seen
from the preface to his jirincipal
work. This appeared in 1839, and
was translated into English by
Henry Smith, and published l)y the
Sydenham Society in 1847 with the
signiticant title, ' Microscopical Re-
searches into the Accordance in the
Structure and Growth of Animals
and Plants. ' The translator has also
attached a rendering of Schleiden's
' Contributions t(j Phylogenesis,'
which a[){)eared Hrst in Part IL of
Miiller's ' Archiv f lir Anatomie und
Physiologic' in 1838, and was also

translated in ' Taylor's Scientific
Memoirs,' vol. ii. part 6.

- Schwann, loc. cit., p. 165. A
little farther on he ;ulds the follow-
ing generalisation, which it is well
to read in the light of more recent
researches: "A structureless sub-
stance is present in the first instance,
which lies either around or in the
interior of cells already existing ;
and cells are formed in it in accord-
ance with certain laws, which cells
become developed in various ways
into the elementary parts of organ-
isms." It is clear that the discovery
of what may be called the morpho-
logical clement or unit of organised
structures in this view meant the
end of pure morphology. The
problem of the explanation of exist-
ing forms was handed over to the
student of development, to the gen-
etic view and conceptinn of nature.
The cellular theory, thus enunci-
ated in its greatest generality by
Scliwann, has formefl a kind of
provisional resting - place in the
study of the forms and changes of
living nature ; as Newton's gravita-
tion formula has served jvs a provi-

264 SCIENTIFIC THOUGHT.

Morphologically the microscopic examination of animal
and vegetable tissues had thus led not to a clearer defini-
tion of the great differences which exist in the forms and
structures of the larger and the full-grown organisms, but
rather to a conviction of their intrinsic and essential
sameness. These differences could not be explained in
the purely morphological manner in which Haiiy had
shown how to trace the difference of crystalline forms
to the shapes and configuration of the " molecules in-
t^grautes." The diversity of forms had to be traced to
4S. processes of growth or development — i.e., the purely

Transition • i i i i i i

to the study morphological examination led on to the developmental

of develop- ■"■ ^

ment. qj. genctic study of organic forms. And this was made

still more evident when the microscopic examination
revealed yet other and more important elements in
the composition of organic structures, elements which
were seemingly quite shapeless or amorphous. The
skeleton, which had so long seemed to contain the key
to the understanding of organic forms, the framework of
the plant structure, the cell-walls and partitions, with
all their geometric figures and arrangements, turned out
to be of quite secondary importance compared with the
cell contents, the substance called in animals by Dujardin
sarcode, and in vegetables by Von Mohl protoplasm, and
with the nucleus or cell-kernel, which had been discovered
by Eobert Brown.^ Accordingly great interest attached

sioual basis for physical astronomy, j cell contents by Dujardin preceded

Both generalisations involve un-
solved problems, with the difference
that the formulation of the cellular
theory is not as precise as that of
gravitation.

^ Both the discovery of the nucleus
by Robert Brown and that of the

the enunciation of the cellular
theory. Brown's discovery was re-
ferred to both by Schleiden and
Schwann. In fact, Brown's re-
searches were much better known
and followed up in Germany than
in England. His papers were trans-

ON THE MORPHOLOGICAL VIEW OF NATUHE. 265

tu these amorphous^ constituents, and chemical investi-
gations as to their composition were added to the previous
microscopic dissection. The purely morphological view

lated into Uerniiin \iy a number of
botanists, and edited in five volumes
between 1825 and 1834 by Nees
von Essenbeck. He did not collect
his original ideas into any great
work or propound a new system of
classification as did Jussieu and De
Candolle, whom he equals in scien-
tific importance ; his valuable geu-
eralisivtions were given occasion-
ally in his numerous monographs,
Sachs considers him more advanced
than the two great rivals just
named, inasmuch as he had an
appreciation of questions of devel-
opment which they lacked (' Gesch.
d. Botanik,' p. 121). Humboldt
called him "' botanicorum facile
princeps," and succeeded in procur-
ing for him, thruugli his influence
with Sir Robert Peel, a pension of
£200 per annum.

' The detinilion of a cell — i.e., of
the morphological or form-element
of organised matter, as consisting
of a membrane, a cell content, a
nucleus, and a nucleolus — stood in
contrast with Felix Dujardin's de-
scription, in 1835, of a living sub-
stance which he met with in his
researches in lower animal life, and
which he had called "sarcode." In
the place of this name — the observa-
tion of Dujardin being little noticed
— Von Mold, after having for a time
accepted the erroneous theory of
Schleiden ami Schwann as to cell-
formation, introduced the term
" protoplasma," which has been re-
tained in science as the name of the
elementary constituent of all living
matter with very varying defini-
tions, acc(jrding to the ditterent
observations of animal or vegetable
organisms and the increasing powers
of the microscope ; this having re-
vealed structures where before only

formless, amorphous substance had
been observed. The history of
these fluctuations of ojnnions and
definitions can be read bcjth in the
older histories (Sachs, Cams) and
the more recent accounts. Among
these numerous e.\|iositions, see
esi>ecially Yves Delage, 'L'HcSrcdite
et les grands jiroblemes de la Bio-
logie,' 1895, p. 19, &c.; O. Hertwig,
'The Cell,' translated from the
(ierman by H. J. Campbell, 1895 ;
and the most recent work by Dr
Val. Hacker, ' Praxis und Theorie
der Zellen und Befruchtungslehre, '
Jena, 1899, p. 10, &c. The cellular
theory has gained enormously in
importance and in popular esteem,
as has also the study of all micro-
organisms, through its application
to medicine and hygiene. In 1847
Rudolph Virchow founded his cele-
brated "cellular jiatiiology," com-
bining the many beginnings of the
cellular theory which had been
laid by others, in his famous axiom
'■ omiiis cellula e cellula. " He gave
up the theory of the free forma-
tion of cells, proclaimed the doctrine
of the genesis of cells — even patho-
logical ones — by cell-division, and
adopted Goodsir's theory of the
uninterrupted filiation of the ele-
ments of all living matter, of tlie
autonomous cells. As in general
biologj', so al.so in cellular path-
ology, the last fifty years have
witnessed gi'cat controversies and
many special theories, one of the
chief difficulties having been to com-
bine the doctrine of the autonomy
or individualitj' of the cells with a
correct view of their filiation and
connected life. In sjiite of tiiese
many changes and modifications, the
name of Schwann still sti\nds at the
opening of every treatise on funda-

266

SCIENTIFIC THOUGHT.

had exhausted itself. The fundamental unity of the
organisation of living beings had been proved ; how was
their actual diversity to be explained ? This evidently
required considerations of a very different kind. What
they were we shall see in the next chapter. The posi-
tion of the morphologist in the middle of the century
had thus become one of considerable perplexity.^ It may
be compared to that of the organic chemist about the
same time. The older ideas, around which, under the
great influence of Cuvier and De Candolle in zoology
and botany, of Werner and Humboldt in geology, the
morphological classification and description of natural
objects had clustered on the Continent, had become
obsolete. The doctrine of definite types, of architec-
tonic models, or of distinct ages of creation, separated
by catastrophic changes, was becoming untenable ; floras
and faunas of entirely different appearance had been
revealed in other countries and climates in the distant
past,^ or in the great newly-discovered realm of living

mental biology, and that of Yirchovv
at the origin of modern pathology,
as the greatest practical application
of the cellular theory. An exceed-
ingly good record of the diffei-ent
and changing views referring to
the cell will be found in the chapter
on " Cell and Protoplasm " in J.
A. Thomson's 'Science, of Life,'
pp. 101-117.

1 " On comprend aisement le
d^couragement de Robin renon9ant
a ^difier son ' Traite d'Anatoniie
generale,' apres avoir teute inutile-
ment, dans sa 'Chimie anatomique,'
de p^netrer le mecanisme des
phenomenes moleculaires s'accom-
plissant dans les corps organises.
La morphologie, pourtant, n'avait
pas dit son dernier mot, et la

barriere bio-chimique ctait nioins
rapprochee que le ne croyaient les
disciples de Comte et de De
Blainville " (Herrmann, article
"Cellule" in 'La Grande Ency-
clo})^die,' vol. is. p. 1060).

■•* Owen, in the very instructive
" General Conclusions " to the third
volume of the ' Anatomy of Verte-
brates ' (1868), clearly points out
how the position of Cuvier has
been made untenable by these
discoveries : " As my observations
and comparisons accumulated, with
parijxtssu tests of observed phenom-
ena of osteogeny, they enforced a
reconsideration of Cuvier's con-
clusions to which I had previously
yielded assent" (p. 188). "Accord-
ingly, these results of extensive,

ON THE MOKPHULOGICAL VIEW OF NATURE. 267

forms only accessible to the microscope. The metamor-
phosis of the different organs in the plant had been sug-
gested by Wolf, and more fully demonstrated by Goethe.
Unity of organisation had Ijcen proclaimed by Saint-
Hilaire and De lUaiuville, and the ultimate identity of
the elementary structure of animals and plants had been
demonstrated by Schleiden and Schwann. How was the
evident relationship of the different types of living beings
to be explained ? It is interesting to note how the very
terms which were then used implied the explanation,
though this was only apparent to one or two natural
philosophers who were then secretly at work. The
word " affinity," which in chemistry has for ages been 49.

■^ ./ o Affinity.

used to denote, without explaining, the mystery of com-
binations and separations of different substances, had
been imported into philosophical anatomy to denote the
deeper structural likeness between animals which at the
first glance appeared to belong to different classes. This
word ordinarily implies blood-relationship, and might have

patient, and unbiassed inductive i which tlicy belonged, I was at

researcli— or, if there were a bias, length led to recognise one cause

it was toward Cuvier — swayed with of extinction as being due to de-

me in rejecting the principle of feat ' in the contest which, as a

direct or miraculous creation, and ' living organised whole, the indi-

in recognising a 'natural law or ' vidual of each species had to

secondary cause as operative in maintain against the surrounding

the j)ro(luction of species in orderly agencies which might militate

succession and progression ' (I'^^-iS) '■ against its existence'" (p. 797).

(p. 789). ... "Each successive parcel . Tlirough this passage, quoted by

of geological trutli has tended to Owen from tlie preface (1866) of

di.ssipate the belief in the un- the same work, a controversy arose,

usually sudden and violent nature it being taken by a reviewer to

f the changes recognisable in the \ prove the admission of the Dar-

earth's surface. In specially direct-
ing my attention to tiiis moot
point, whilst engaged in investiga-
tions of fossil remains, and in the
reconstruction of the species to

winian theory. Tliere followed an
e.xplanation by Owen, rejecting
natural selection and the admitted
contest as explanations of the origin
of species.

268 SCIENTIFIC THOUGHT.

suggested the theory of descent : it was used by those
who most strongly repudiated such a doctrine.^

In the absence of any satisfactory explanation of the
continual recurrence of certain definite forms in nature,
and the presence of an evident relationship and a clear
indication of metamorphosis in single instances, it was
natural that morphologists of the first order, such as
Owen, and other authorities in science, such as Whewell
in England and Alexander Braun in Germany, should
have recourse to older views and vague philosophical
theories. Owen in 1848 spoke of a specific organising
principle which " moulds in subserviency to the exigencies
of the resulting specific forms," argues tliat the know-
ledge of such a being as man must " have existed before
man appeared, for the divine mind which planned the
archetype also foreknew all its modifications," and con-
cludes that we learn from the past history of our globe
that " nature has advanced with slow and stately steps,
guided by the archetypal light, amidst the wreck of
worlds, from the first embodiment of the vertebrate
idea under its old ichthyic vestment until it became
arrayed in the glorious garb of the human form.""^

1 Huxley in ' Life of 11. Owen,' pertie.s of matter, there appears

vol. ii. p. 302. also to be in counter - operation

- See Owen's treatise ' On the ■ during the building up of such
Nature of Limbs,' 1849, pp 85, bodies the polarising force pervad-
86. In the essay ' On the Arche- ing all space, and to the operation
type and Homologies of the Yerte- of which force, or mode of force,
brate Skeleton,' he concludes with the similarity of forms, the rep-
tile following remarks : " Now, be- etition of parts, the signs of the
sides the iSe'a, organising ]irinciple, unity of organisation may be
vital property, or force, which ]iro- mainly ascribed. The Platonic
duces the diversity of form belong- iSia or specific organising principle
ing to living bodies of the same or force would seem to be in an-
materials, which diversity cannot tagonism with the general polar-
be explained by any known pro- ising force, and to sul)due and

ON THE MOKPHOLOCilCAL VIEW OF NATURE. 2G9

Whewell, in various passages of his ' History ' and of his
• I'hilosopliy of the Inductive Sciences,' argues that the
explanation of organic forms is to be found in the study
of the functions which each organ is destined to perform,
and brings morphology back under the guidance of physi-
ology, from which De Candolle and others had only
recently liberated it.^ Alexander Braun, the great German
liotanist, wrote about the same time : " Although the
organism in its growth is subject to physical conditions,
the real causes of its morphological and biological speci-
ality lie, nevertheless, not in these conditions : its laws
Ijelong to a higher grade of development of reality, to a
sphere in which the capacity for spontaneous self-deter-
mination becomes evident." ' Even Johannes ^liiller.

mould it in subserviency to the
exigencies of the resulting specific
form" (p. 172). Huxley attributes
these theoretical views of Owen to
the influence of Lorenz Oken, the
l)rincipal scientific representative
of the school of the " Natur-
philosophie.'" In this respect Owen
left the direction of study initiated
and so successfully followed by
Cuvier. In fact, though opposed
to Darwinism, Owen did not, like
Cuvier, believe in special creation,
as is clearly shown in a passage
frequently quoted, taken from the
conclusion to the third volume of
Owen's great work ' On the An-
atomy of Vertebrates' (1868), p.
807 : " Ho, Vjeing unable to accept
the volitional hypothesis, or that
of impulse from within, or the
.selective force exerted by outward
circumstances, I deem an innate
tendency to deviate from parental
type, operating through ])eriods of
adequate dui-ation, to be the most
{)ri)bable nature, or way of opera-
tion, of the .secondary law, whereby

species have been derived one from
another."

' De Candolle is very clear ou
this point ; he says (' Theorie
<51(5mentaire,' p. 170) : " L'usage des
organes est une con.sdquence de leur
structure, et n'en est nullement la
cause, comme certains ecrivains irre-
flechis semblent I'indiquer ; Tu-sage,
quelque soit son importance dans
I'dtude physiologique des etres, n'a
done en lui-meme qu'une mi^diocre
importance dans I'anatomie, et ne
pent en avoir aucune dans la tax-
onomie ; quelquefois .seulement on
pent s'en servir comme d'un indice
de certaines structures Ji nous en-
core inconnues ; ainsi lorsque je vois
la surface unie d'un pctale suinter
une liqueur, j'en conclus que cette
partie est glandulaire, et je I'assimile
aux nectaires ; mais cette assimila-
tion, bien que reconnue par I'iden-
titi5 de l'usage, est rcellement
otablie sur I'identitc prusumee de
la structure."

- Quoted by Sachs (' Gesch. d.
Botanik,' p. 188).

270

SCIENTIFIC THOUGHT.

who did more than any other naturaUst to base zoology,
anatomy, and physiology on the foundation of the exact
sciences, physics and chemistry, " assumed the existence of
a vital force which, differing from physical and chemical
forces, enters into conflict with them, and which in
organisms acts the part of a supreme regulator of all
phenomena according to a definite plan." ^
50. The insufficiency of a purely morphological description

oftiiemor-' of living bcins's, the unsuccessful search for the morpho-

phological & o '

view. logical elements out of which organisms are built up, as

crystals are formed out of the moUculcs inUgrantes of
Haiiy, led thinkers (up to the middle of the century) to
have recourse to older and vaguer conceptions, which,
under the name of archetypes, formative influences, vital
forces, &c., were destined to help where the purely
mechanical view would not suffice. This dilemma was
appropriately described somewhat later by one who
had— earlier, perhaps, than any other thinker — eman-
cipated himself from the influence of these fanciful
conceptions. Herbert Spencer in his ' Principles of
Biology,' published in 1863, expresses it in the fol-
lowing words : " —

" If we accept the word ' polarity ' as a name for
the force by which inorganic units are aggregated into

1 See Du Bois-Reymond, " Ge-
iliichtuissrede auf Johanues Miiller"
('Reden,' vol. ii. p. 217).

^ The ' Principles of Biology,'
from which this extract is quoted,
appeared in successive instalments,
beginning in January 1863. It is
well to note that this was before the
appearance of Haeckel's ' Generelle
Morphologic,' which bears the date
1866. It does not appear tliat

Spencer lias had any influence on
German .science, though no doubt
many of the conceptions put
forward in the numerous treatises
of German biologists are anticipated
in Spencer's 'Biology,' notably in
his conception of the physiological
units as intermediate between com-
pound chemical molecules and
crystals on the one side, and cells
on the other. In the exhaustive

ON THE MORPHOLOGICAL VIEW OF NATURK. 271

a form peculiar to them, we may apply this word to
the analogous force displayed by organic units, liut
polarity is but a name for something of which we are
ignorant. Nevertheless, in default of another word we
must employ this. ... It will be well to ask what
these units are wliich possess the property of arranging

review of these theories, given by
M. Yves Delage, a very pi'ouiiiient
position is accordingly a-ssigned to
Herbert Sjjencer's biological writ-
ings. In fact, he says ('L'Herddite,'
p. 424 note): "Ici"— i.e., in the
' Principles of Biology ' — " est
montrcSe, pour la premiere fois
€t avec une lucidito parfaite,
Tutilitc de coucevoir des particules
sp^ciales, elements prirnitifs de la
substance vivaute, intermediaries
aux molc'cules et aux cellules. Les
tres nombreux auteurs qui ont
utilise la mome idi-e n'eu out
cr66 que des variantes. Spencer
est le vrai pere de la conceiition
initiale, si fecoude comme on le
verra." And again (ibid., p. 836):
" Brusquement, avec H. Spencer,
on tombe en plein moderue. lei
plus de thiiories vieillottes, plus
de procedes suranni's. . . . Les
phenomenes sont decomposes en
leurs elements avec une puissance
d'abstraction qu'aucun philosophe
n'a depassee, des }>rincipes gener-
aux sont dt'duits qui servent a leur
tour ;i juger, ii interpreter les
phenomenes, h. les ramener a leurs
causes vraies. Comnie resultat de
.-■■< meditations, Spencer nous
otl're les ' Unites physiologiques,'
particules matcrielles toutes iden-
ti'iues dans une rneme espcce
d'etres avec lesquelles il croit
que I'organifime doit pouvoir se
construire de lui-meme, par le seul
jeu de leurs forces moli^culaires.
. . . 11 a . . . ouvert une voie :
sa theorie est un des bras prin-
cipaux du Delta de ce fleuve

qui nous servait de terme de coni-
paraison." The other great arm
of the Delta is Darwin's theory of
Pangenesis, on which see infru,
chapter xii. of this volume. Of
others, such as Erlsberg, Haeckel,
His, Haacke, M. Delage says : '"lis
ont reussi seulenient ii montrer
qu'en substituant aux forces polaires
ties ' Unites physiologiques,' des
formes de mouvenient ou des
proprietes geometriques, on n 'arrive
pas a un meilleur riSsultjit." Prof.
Haeckel in his ' Generelle Mor-
phologie' (1866) has interpolated
a special investigation, as it were,
between the morphology of living
tilings and the corresponding
science of inorganic or purely
physical (such as crystalline and
chemical) sti-uctures and arrange-
ment under the name " Pro-
morphology," investigating with
mucli ingenuity all manner of
symmetrical, axial, radial, &e.,
configurations. J. Arthur Thom-
son ('Science of Life,' p. 34) re-
marks that little attention has
been paid to this subject since,
but, as stated above (p. 223 note),
the systematic treatment of crys-
tallography has all through the
centur}' ap[)eared to biologists as
an enticing and seductive model,
and M. Yves Delage's great work
gives many examples of this tend-
ency— see, c.y., his remarks on the
theories of Haacke, Cope, Niigeli,
Erlsberg, and nianv others, pp.
.304, 315, 424, 441, 451, 459, 475,
495, 502, 593, 743, &c.

272 SCIENTIFIC THOUGHT.

themselves into the special structures of the organism
to which they belong. ... On the one hand, it cannot
be in these proximate chemical compounds composing
organic bodies that this specilic polarity dwells ; . . .
the occurrence of such endlessly varied forms would be
inexplicable. On the other hand, this property cannot
reside in what may be roughly distinguished as the
morpliological units. The germ of every organism is
a microscopic cell, or a structureless blastema which
nevertheless exhibits vital activities. ... If, then, this
organic polarity can be possessed neither by the chemical
51. units nor the morphological units, we must conceive it as
"^h"^sui- possessed by certain intermediate units which we may
umts/' term ipliysiological. . . . We must conclude that in each
case some slight difference of composition in these units
. . . produces a difference in the form which the aggre-
gate of them assumes."

Now, there are only two ways open to the purely
scientific thinker by which he can reach these inter-
mediate structures lying between the mathematical forms
of crystals or the molecular arrangement of atoms, and
the visible but apparently structureless forms of cells and
protoplasm. One of these is the still more advanced
analysis of these microscopic structures by still greater
powers of magnifying instruments ; the other is the
mathematical method of calculating from simple begin-
nings the complex forms of equilibrium which atoms or
molecules are capable of assuming under the action of
known forces. It appears unlikely that the powers of
the microscope can be much further extended ; and the
mathematical calculation of even the simplest configur-

ON THE MORPHOLOGICAL VIEW OF NATURE. 273

atioiis of attracting and repelling centres, or of linked
vortex rings, is already so formidable that much cannot
be expected in that direction. Tliese intermediate units,
vastly more complex than the most complex chemical
molecules, and vastly more minute than the smallest
\ isible grain of protoplasm, must therefore for a long
time to come lie in the region of hypothesis, unattainable
for the eye or the calculus; an indication rather than
a real guide for our scientific researches. Seeing, then,
that the study of forms — the morphological view of
natural objects in the case of organic beings, where to
the naive contemplation of things these forms seemed full
of so much significance, indicative of so much meaning,
])ossessed of so much beauty and striking suggestiveness
— has led to no comprehension of the essence of vital
phenomena, and hardly even afforded a safe criterion for
classification, it is intelligible how the scientific interest 52.

® Change of

has moved away from the consideration of the fixed forms scientific

•' interests.

ami structures to that of the variation and continued
change of these forms. This alteration in tlie scientific
way of looking at the actual forms of nature, goes hand
in hantl with the tendency we had occasion to notice
when dealing with the abstract sciences. Many things
which once seemed at rest, or possessed of very simple
rectilinear motion, have revealed themselves to the mind's
eye as complex states of motion. Colours are exceedingly
minute and rapid but well defined vibrations ; the dead
pressure of gases is the impact of numberless quickly-
moving particles ; and the wonderful properties of the
whirling vortex ring have made us familiar with what
has been termed the dynamical or moving equilibrium, the

VOL. IL 8

274 SCIENTIFIC THOUGHT.

semblance of apparent rest produced by very rapid rotary
motion. Rest and fixity of form seem only to exist j
apparently or for transient moments in the history of
natural events ; and even the finished and recurring struc-
tures of living beings, which appear to our eyes to be
possessed of so much finality and sometimes of so much
finish, owe these qualities only to the comparatively short
space of time during which we are permitted to gaze
at them, and to our ignorance of the slow but endless
changes to which they are nevertheless subject.
53. The period from 1800 to 1860 can be termed the

The morpho-
logical morphological period of natural science. It succeeded

period.

the period of the simpler natural history, which had
been mainly occupied with classification and description
of specimens. During the morphological period the
knowledge of the existing things and forms of nature
was not only largely extended by excursions into distant
lands and periods of history, but forms were also studied
in situ, and the living things visited in their habitats.
A deeper knowledge of the connection and interdepend-
ence of natural things and events was thus gained, and
the relations and resemblances, the analogies and homo-
logies, of the various forms were impressed on the observer.
Besides all this, the microscope revealed the innermost
composition and the ultimate structural sameness of living
matter, adding moreover the knowledge of an enormous
creation which remains hidden to the unarmed eye of
the ordinary observer. The morphological view also took
note of the relatedness and apparent recurrence of definite
forms called types, of the so-called fixity of species and
the succeeding characteristic periods of creation, and

ON THE MORPHOLOGICAL VIEW OF NATURE. 275

sought to explain these morphologically : i.e., it sought
in the abstract study of forms — sometimes geometrical,
sometimes artistic — the key to an understanding of the
recurrence as well as the continued variation of definite
types. The relationship was mostly looked upon as ideal,
not real. How a gradual change came over this view
of nature, how the study of development led on to the
modern phase of natural science which is governed by the
genetic view, I shall try to show in tlie next chapter.

276

CHAPTER IX.

ON THE GENETIC VIEW OF NATURE.

1.
Statics
and dyna-
mics of liv-
ing fonns.

Whilst the great influence of such leaders in scientific
thought as Cuvier, De Candolle, and Humboldt on the
Continent, and of Richard Owen in this country, was
mainly exerted in spreading the morphological view of
nature, describing on a large scale or in minuter detail
the typical recurring forms which natural objects or
natural scenery present to the eye of the unbiassed
observer, another school of naturalists was secretly busy
in following up the changes to which all the things of
nature seem continually subjected. They were as much
impressed with this restless movement of everything as
the others were with the continual recurrence of certain
definite forms — be they geometrical or artistic. The
general ideas which underlay their researches were not
new, — they were probably older and more familiar ^ than

^ Cosmogonies of all sorts abound
in almost every literature, ancient or
modern, whereas Cosmograpliy, ac-
curate, painstaking, and reliable, is
of comparatively recent date. The
first attempt to give a purelj'
descriptive picture of nature as a
whole, beginning with the larger
features of the universe and ascend-

ing through terrestrial, inanimate
and animate, phenomena to the
central and crowning phenomenon
of human life, was A. von Hum-
boldt's 'Kosmos'; and it is interest-
ing to note how averse the author
was to introduce genetic expositions.
In fact, it has been truly remarked
that Humboldt's influence went to

ON THE GENETIC VIEW OF NATURE.

o — ■-'

tlie types and epochs of the other ami <lominant school ;
liut they were difficult to grasp, being not unfrequently
fantastic compromises between Iho legends of religious
tradition and the l)eginnings of scientific thought. For
a long time they evaded the endeavour to put them into

purely lUDipliolugical
and to discourage genetic con-
siderations. Acconlingly the many
beginnings of a scientific account
of the origin and historical develo|>-
ment of the things around us, of
whicli Lyell gave the first fairlj-
accuiate summary in the first
volume of his 'Principles of Geol-
ogy ' (1st ed., 1S30), were hardly
noticed in the 'Kosmos' (vol. i.,
184.5, vol. ii., 1847). None of the
celebrated cosmogonical hypotheses,
which we shall deal with in this
cliapter, — neither tiie 'Protogica'
of Leibniz nor the ' Epoques de la
Nature' of Buffon, neither Kant's
uor Laplace's nebular theory, nor
even tiie brilliant introduction to
the ' Ossemens fossiles ' of Cuvier,
though the latter, and still more
Laplace, must have had a great
personal influence on him, — re-
ceive any adequate attention in
the pages of ' Kosmos. ' They are
rarely referred to, and then only as
works of imaginative value, for
which the true .scientific ground-
work, extensive observation, and
especially the experiences and
results of travel, are wanting.
Humboldt, whose mind was stored
with these rii'hes in an abundance
and variety unequalled before or
since, limited himself to a por-
traiture, to a panoramic and mor-
jiliological, to a structural and
architectonic view of things, with
which he combined a deep sense of
the reaction which the ccntempla-
tion of nature must have on the
artistic facultj'. (See the Intro-
<luction to the second, the most
brilliant, volume of 'Kosmos.')

Genetic theoi-ies were to his mind
premature and foreign to his pur-
pose. " The mysterious and un-
solved problems of development <lo
not belong to the empirical region
of objective observation, to the
description of the developed, the
actual state of nur planet. The
description of the universe, soberly
contined to reality, lemaius averijc
to the obscure beginnings of a
history of organic life, not from
modesty, but from the nature of
its object and its limits" ('Kos-
mos,' vol. i. p. 367). "The world
of forms, I repeat, can in the enum-
eration of space relations only be
pictured as something actual, as
something existing in nature ; not
as a subject of an intellectual pi'ocess
of reasoning on already known causal
connections. . . . They are facts of
nature, resulting from the conflict
of many, to us, unknown conditions
of active push -and - pull forces.
With unsatisfied curiosity we aj)-
proach here the dark I'egion of
develojjment. We have here to do,
in the proper sense of the frequently
misused word, with world-events,
with cosmical processes of im-
measui'able periods. . . . The
present form of things and the
precise numerical determination of
relations has not hitherto succeeded
in leading us to a knowledge of
states traversed, to a clear insight
into the conditions under which
they originated. These comlitions
are not therefore to be termed
accidental, as man calls everything
that he cannot explain genetically "
(vol. iii. p. 431).

278 SCIENTIFIC THOUGHT.

exact language. It is only in the second half of the
nineteenth century that the many independent Hnes of
reasoning, the fragments of the great doctrine of develop-
ment, have been united together, that the search after the
principles or laws which govern the restless change has
been rewarded by a certain number of definite results,
and that what was once vague, fanciful, and legendary
has become a leading idea in all the natural sciences.
As in other instances which we have had occasion to
notice, so also in this case, the appearance of clearer and
more definite ideas has been heralded and helped by a
novel mode of expression, by a new vocabulary. The
2. word " evolution " has in this country done much to
tion." popularise this way of regarding natural objects and

events : abroad, the word has not met with the same
popular acceptance. It was known there and used in
science and literature when it was yet unknown in this
country, and has in consequence not been monopolised in
the same way as in the English language, to denote the
continuous and orderly development of states and forms
of existence.^ Moreover, it has been identified in this

^ On the older and iiKxlern use I geneous rudiment (after-formation),
of the word "evolution" in the Harvey, the expounder of the latter
English language see Huxley's theory against Malpighi, who em-

article in the 9th ed. of the
' Ency. Brit.' It is reprinted in
his collected essays with the title
"Evolution in Biologj-." Accord-
ing to Huxley, the term "evolu-
tion " was introduced in the former
half of the eighteenth century in
opposition to " epigenesis." The two
terms denoted the two theories of
the generation of living things, by
development of pre-formed germs
(pre-formation) or by successive
differentiation of a relatively homo-

braced the former, calls the first
"metamorphosis." Leibniz, Bon-
net, and latterly Haller, were "evolu-
tionists " in the older sense of the
word ; Harvey, C. F. Wolf, and
the modern school of embryologists,
with von Baer as its most eminent
representative, were adherents of
the originally Aristotelian theory
of " epigenesis." " Nevertheless," as
Huxley says, " though the concep-
tions origiuall}' denoted by 'evolu-
tion ' and ' development ' were

ON THE GENETIC VIEW OF NATURE.

279

country with a special philosophical teaching, that of
Mr Herbert Spencer, which, whilst in many points
coinciding with scientific views of development, has
some special and peculiar features which will occupy
us further on in our survey of thought. Havuig sought
therefore for a term which is to comprise all the con-
tributions to scientific thought which deal with the
change and development of natural objects and events,
I propose to use the older word " genesis," and to call
this view " the genetic view of nature " : it is, in general,
the view which seeks to give answer to the (juestion,

'Gi'iiesiH.'

shown to be untenable, tlie words
retained their application to the
process by which the embryos of
living beings gradually make their
appearance ; and the terms ' de-
velopment,' ' Entwickelung,' and
' evolutio ' are now indiscriminately
used for the series of genetic changes
exhibited by living beings, by
writers wlio would emphatically
deny that ' development ' or ' Eut-
wickelung' or 'evolutio,' in the
sense in which these words were
usually employed by Bonnet or by
Haller, ever occurs." The word
evolution has, however, acquired
in the English language, mainly
through the influence of Mr
Spencer's writings, a much wider
sense than evolution in biology
implies : in fact, it takes the place
of the German " Werden," a word
much used in the philosophical
writings influenced by the Hegelian
doctrine, which indeed taught a ■
logical or dialectic devclo])ment of
tilings, as Herbert Spencer and his
school teach a mechanical develop- i
ment. There seem to be given to
UH by observation only two elemen-
tary processes of change, or of
" Werden " (in Greek yiyi'fadat, in
French " devenir," in English "be-

coming," in Latin "fieri," in German
also the synonym " gcschehen ",.
These are, on the one hand, the
process of mechanical motion, and
on the other hand the process
of logical thought : the one being
the movement of external things,
ultimately of atoms, the other the
spontaneous movement of what
Hume called ideas. When the
thinking mind fixes its attention on
the "fieri" rather than the "esse"
of things there are accordingly two
clues available, the mental or the
[)hysical, the logical or the mechan-
ical. Manj' times taken uj) in
earlier ages, both have been con-
sistently applied only in the nine-
teenth century, the latter by Her-
bert Spencer, the former fifty
years earlier by Hegel, whose
philosophy is fundamentally as
nmch a logical as the former is a
mechanical system of evolution.
The narrower meaning of evolution
in h'uAo^y is usually given in
French by the word "transform-
isme," in German by " Entwick-
elungslehre" or " Darwinismus."
See on the general subject Prof.
James Sully's able article on
" Evolution " in the 9th ed. of
the 'Ency. Brit."

280

SCIENTIFIC THOUGHT.

How have things come to be what they are ? What
is their history ^ in time ?

The first great philosopher of modern times who seems

to have approached the question of the genesis of the

objects of nature in the modern scientific spirit was

4. Leibniz, who, in composing his local history of the

Leibniz's

'Protogita.' origin of the Guelphs and the antiquities of Brunswick,
pushed his researches into prehistoric times and made
use of the geological and mineralogical data supplied in
the Harz forest and mountains to arrive at conjectures
as to the past history of the earth. His ideas, based
upon local facts and observations on stratification
and fossil remains, were collected in a famous tract
entitled ' Protogtea,' which during his lifetime was only
known in abstract,^ and was published in 1749, many

•* Although the word '"genesis,"
through its use in the Scriptures,
has acquired the meaning of a nar-
rative of the origin or beginning of
things, this meaning is not neces-
sarily implied in the wf)rd yiyfea-
dai, and the genetic view of nature,
or things in general, may limit it-
self to the study of observable,
actual change, renouncing alto-
gether the question of origins.
The German words, "werden" and
" geschehen," are in this respect less
ambiguous and less ambitious, and
many philosophers may accordingly
prefer "evolution" to "genesis."

'^ On the connection of Leibniz's
genetic studies with his History of
Brunswick, which expanded under
his hands into the ' Annales im-
perii occidentis Brunsvicenses '
(edited by Pertz in the first three
volumes of ' Leibuizens Gesam-
melte Werke,' Hannover, 1843-47,
4 vols.), see the introduction bj'
Scheldt to his complete edition of
the ' Protogsea,' Gottingen, 1749

(reprinted in the second volume of
Dutens' ' Leibnitii Opera Omnia,'
1768) ; the words of Leibniz him-
self in the ' Plan ' of his History
(quoted by Pertz, vol. i. p. xxiii) :
" Prajmittetur his annalibus qua3-
dam dissertatio de antiquissimo
harum regionum statu qui ante
historicos ex naturto vestigiis haberi
potest " ; the address of Ehrenberg,
' Ueber Leibnitzens Methode ' (Ber-
lin, 1845) ; the account in Guhr-
auer's ' Life of Leibniz ' (1846, vol. i.
p. 205, and an interesting note in the
apjaendix). Fontenelle,who knew of
the 'Protoga;a' only by the abstract
(ed. 1693) in the Leipsic 'Acta,'
and from correspondence with Eck-
hardt, Leibniz's executor, says in
his 'Eloge de Leibniz': "II la
[viz., the History] faisait prec^der
par une dissertation sur I'etat de
I'Allemagne, tel qu'il dtait avant
toutes les histoires et qu'on pouvait
le conjecturer par les monuments
naturels qui en etaient restes ; des
coquillages petrifies dans les terres,

ON THE GKNETIC VIEW oK NATURE.

281

years after his death. He conceived that lioth tire and
water ^ had lieen at work in forming the surface of the
earth, ami suggested that simihir examinations of other
localities '" would be required in order to arrive at general
conclusions. Such were subsequently supplied by Werner,
de Saussure, Pallas, Hutton, Cuvier, and William Smith,
before the systematic exploration of the w'hole globe be-
came in the nineteenth century one of the tasks of
geological science. A few years after the publication of
T.eibniz's speculations, which pointed to an accumulation
of local observations as the means of arriving at a history

des pierres oil se trouveiit de.s em-
ineinles de poissons ou de ])liuites
<|ui ne sent point du pays, medailles
iiicoutestables du deluge,'" &c., &c.
How very much Leibniz was — in
this as in niauy other ideas — in ad-
vance of his age can be seen
from his correspondence with the
Ssviss naturahst Scheuchzer of
Ziirich : " Mcrentur Alpes vestrtc,
si quis ahus Europic locus, banc eru-
diti inquilini curani et cieteros
montes utili exemplo pneibunt,
queni admodum magnitudine vinc-
unt. . . . (Jerraanorum nos-
trorum non ea est diligentia quam
vellem : iUique Historias regionum
naturales habemus nullas, cum
Angli Scotique nobis egregiis ex-
etnj)lis pnoiverint " (quoted by
<:ulirauer in the note referred to).
An interesting reference is made in
*5 xvii. of the " Protogiea ' to the
use of the microscope, tlien only
recently invented, and largely used
by Leuwenhoek in connection with
the examination of the formation
and crystiils of the celebrated
" Baumann cave": " Et velim
microscopia ad inquisitionem ad-
hiberi, (juibus tautum prxstitit
s.igax Leuwenhoekii diligentia, ut
«;upe iudigner human;e ignavite,

quie aperire oculos, et in paratam
scientia posse.~sionem ingredi non
diguatur. " A very fair account of
the contents of the ' Protogiea '
is given in W. D. Conybeare's ' Re-
port ou the Progress ... of Geo-
logical Science ' in the first volume
of Brit. Assoc. Reports, p. 366,
&e.

1 ' Protogiea,' § iv. : " Donee
quiescentibus causis atque icquilib-
ratis consistentior emergeret sta-
tus rerum. I'lide jam duplex origo
intelligitur firmorum corporum ;
una, cum ab ignis fusione refriges-
cerent, altera cum reconcrescerent
ex solutione aquarum. Neque igitur
putandum est lapides ex sola esse
fusione. Id enim potissimum de
prima tautum massa ac terra; basi
accipio."

- Ibid, g V. : " H;ec vero utcum-
que cum plausu forte dici possint de
incunabjlis nostri orbis, seminaque
contineant scientiic novic, quam
Geographiam naturalem appelles.
. . . Et licet conspirent vestigia
veteris mundi in priesenti facie
rerum, tamcn rectius omnia detinient
postei'i, ubi curiosilas mortalium eo
processerit, ut per regiones pro-
curreutia soli genera et strata des-
cribunt. "

282

SCIENTIFIC THOUGHT.

5.
Kant's
nebular
theory.

of the earth, another philosopher of the highest rank
took an important step in the direction of the study of
the genesis of things natural, on the largest scale. It
was Immanuel Kant, the philosopher of Konigsberg, who,
stimulated by the perusal of the cosmical theories of
Thomas Wright of Durham,^ applied the principles of
the Newtonian philosophy in a first attempt to trace out
the great stages in the formation of a planetary system.

^ The work of Wright is not so
rare as it is represented to be by
foreign writers, as I picked up two
copies from a second-hand catalogue
several years ago. It is chiefly
interesting as having induced Kant
to venture on his genetic specula-
tions, which appeared anonymously
at Konigsberg in 1855, and for a long
time remained unknown. About
the same time as Kant, the cele-
brated mathematician J. H. Lam-
bert published his ' Cosmological
Letters on the Structure of the
Universe' (Augsburg, 1761), many
ideas in which coincide with the
later expositions of Herschel and
Laplace, which were based on quite
ditferent considerations. The specu-
lations of WVight, Lambert, and
Herschel were what we may call
morphological, whereas it is the
merit of Kant and Laplace to have
built upon the ideas as to the
architecture of the universe a
plausible theory of its genesis. A
full account of Wright's suggestions,
which were accompanied by very
beautiful mezzotint engravings exe-
cuted by himself, is given by Prof.
R. A. Sampson of Durham in the
' Proceedings of the Society of Anti-
quaries ' of Newcastle-upon-Tyne,
vol. vii. p. 99.

Kant's theory has been dealt with
by Helmholtz in his Konigsberg ad-
dress (1854), "Ueber die Wechsel-
wirkung der Naturkriifte" (' Vor-
triige und Reden,' vol. i. ), by Faye

('Sur rOrigine du Monde,' Paris,

1885, 2nd ed.), by C. Wolf (' Les
Hypotheses Cosmogoniques,' Paris,

1886, which contains a translation
of Kant's work), and by G. F.
Becker (Amer. Journal of Science,
1898). It is, however, to be noted
that recent writers on Astronomy
are inclined to speak of the genetic
theories of the universe very mucli
in the same way as Humboldt
treated them in his 'Kosmos,'
wliich professedly excluded the
historical aspect in favour of a
purely descriptive treatment, recog-
nising the many difficulties which
stand in the way of a consistent
elaboration of the "nebular hypo-
thesis." See A. Berry's 'History
of Astronomy' (1898), p. 409; R.
Wolf, ' Handbucli der Astronomic '
(vol. i., 1890), p. 594 ; G. H.
Darwin, 'The Tides' (1898), p.
302 ; also J. Scheiner, ' Der Bau de&
Weltalls' (Leipzig, 1901). On the
additional gi-eat support which
has been given to a genetic con-
ception in general in the second
half of the nineteenth century by
Thermodynamics and Spectrum
Analysis I shall speak later on.
The writings of M. Faye in France,
and of Sir Norman Lockyer in this
country, utilise to the fullest extent
the arguments derivable from these
sources, and mark a great con-
trast to the manner in which cos-
mological questions were treated
by A. von Humboldt.

ON THE GENETIC VIEW OF NATURE.

283

Tlie speculations of Wright liad been purely geometrical.
Tfe had drawn attention to the apparent unity of organ-
isation ill the stellar system, as established by the ac-
cumulation of stars in a certain belt, popularly called
" the milky way." He also suggested that the whole
system was moving in a certain direction. Kant pointed
out the analogy with the solar system, in which, viewed
from the centre, the planetary masses would likewise
appear situated in a narrow belt, moving all iu tlie same
direction. From these data he proceeds to show how,
taking for granted an initial movement and the action of
sravitation, the formation of rint^s like those of Saturn^
can be explained ; further, how these might be broken
up and concentrated in satellites. In fact, he recognised
how, under the influence of gravitation, the solar system
miglit liave been gradually formed out of matter which
was previously scattered through the whole of that space
which the system still occupies. Kant also descended
somewhat further into detail, and proceeded to discuss the
possible retardation of the earth's rotation through tidal
friction.^

' The tract in vvliicli Kant de-
velops his views on this subject was
occasioned by a prize ottered by the
Berlin Academy in 1754 for an answer
to the question whether the time of
revolution of the earth liad suffered
any retardation, and if so, through
what causes? Kant did not com-
pete for the prize, deeming his re-
flections not capable of being suffi-
ciently perfected to deserve to be
submitted. So he simply published
them in a local Konigsberg [laper,
from which they were later re-
jirinted in the collected works,
forming one of the first "f Kent's

publications. At the end of this
tract he announces his " Cosmo-
gonie,' which appeared the follow-
ing year with the title ' Natural
History of the Heavens,' &c. Kant
had the satisfaction of seeing many
of his speculations verified by the
subsequent discoveries of induc-
tive research, notabh- through Sir
William Herschel's observations of
nebulie ; and the German edition of
Herschel's great memoir ' On the
Construction of the Heavens' (' Phil.
Trans.,' 1784), which appeared in
Konigsberg in 1791, by Sommer,
contains an extract from Kant's

284 SCIENTIFIC THOUGHT.

The two lines of speculation, originated by Leibniz
and Kant as to the genesis of things on this earth and
in the universe, mark two distinct ways of approaching
the genetic problem. They were both isolated, and it
was not till well on in the course of our century that
they were again taken up and independently developed
— the one by geologists, the other by physical astronomers.
They remained for a long time without mutual influence ;
till, within the last generation, they were brought to-
gether, their different results deduced, and a reconcilia-
tion attempted. To this I shall revert later on. Forty
6. vears after Kant, Laplace put forward his so-called

Laplace. "^

nebular hypothesis at the end of the popular exposition
which he gave of his mechanical theory of the heavens.
He apparently knew nothing of Kant's attempt, and his
views differ materially from those of Kant, in so much
as he assumes in the rotating nebular mass an attracting
nucleus from which, in the course of condensation through
attraction, the planetary rings and bodies were thrown
off as the centrifugal velocity balanced the attracting
forces. For a long time this sketch of a possible
genesis of the planetary system was paraded in popular

work. The merits of Kant have only
been tardily recognised ; they were
unknown to Laplace, and only
imperfectly known to more recent
authorities, such as Helmholtz and
Lord Kelvin, who were fully pre-
pared to do him justice. Lord
Kelvin, in his Rede Lecture of
1866, refers to Kant as the first
to publish " any definite estimate
of the possible amount of the
diminution of rotatory velocity
experienced by the earth through

tidal friction" ('Pop. Lects. and j Journal of Science,' 1898.
Addr.,' vol. ii. p. 65), and Jin the i

controversj' which took place be-
tween him and Huxley on " Geo-
logical time " the theories of Kant
were frequently referred to. See
his lecture on "Geological Time,"
1868 {loc. cit., p. 10, &c.) ; Huxley
on " Geological Reform," 1869 (re-
printed in ' Lay Sermons,' No. XL)
The best account in the English
language of Kant'.s contributions
to cosmogony will be found in an
article by G. F. Becker in the 5 th
vol., 4th series, of the 'American

ON THE GENETIC VIEW OV NATURE. 285

works on astronomy as an established theory, wliereas
Laplace himself had \n\t it forward with great reserve,
and only as a likely suggestion.^ There is, however, no
(loiilit that it powerfully inlluenced the minds of many
students of nature in the direction of a genetic view of
phenomena.

The attempts referred to so far can ho described as
belontrins to the Komance of Science, i now come to
the more solid contril)utions — to a real genetic theory of
the things of nature. These are not much older than
our century. They belong to two entirely independent
lines of research which were followed up hi England and
on the Continent respectively — the former in palieon-
tology, the latter in embryology. Although they were
carried on quite independently of each other, they had
this in common, that they both resorted to a study of
life — as preserved in geological strata or as now existing
around us — for a guide in comprehending the genesis of
Things on a larger scale.

Tt may be well to remark here that the contemplation
of the phenomena, the forms and the processes exhibited
in the living portion of creation, has not always, and
even not generally, in the course of history led to those
theories which our age is elaborating, and wliidi will in
future times possibly be looked upon as one of its char-

' Laplace himself says : " Je I ' Kosmos,' vol. vi. p. 8). gives u.s

pieseiite cette origine du syst^me
planctaire avec la defiance que doit
inspirer tout ce cjui ii'est point
un resultat de I'observation et du
calcul." The elaborate exposition
of the architecture and system of
the universe contained in A. von
Humboldt's 'Kosmos,' which was
professedly inspired by Laplace (see

little, if anything, about the history
of the universe, professing to be
only a '' W'eltgemiildc " and not a
" Welterkliirung." The time for
genetic theories had not yet come,
and both Kant's and Laplace's cos-
mogonies are only casually referred
to.

286

SCIENTIFIC THOUGHT.

7.
" Cyclical '
▼iew.

acteristic achievements — the genetic view. There is
another view which a superficial glance at organic life,
with its well known phases of birth, culmination, and
decay, has frequently impressed upon the observer ; there
seemed another lesson to learn than that which our age
is trying to master.

That other view can best be termed the " cyclical "
view of things, the doctrine that every thing runs in a
cycle ^ and repeats itself, that all change is periodic and
recurrent, that there is nothing new under the sun.^

1 Mr Thomas Whittaker has given
me various references to the writ-
ings of ancient philosophers which
bear on this subject. He finds the
cyclical or recurrent aspect of the
world-process prominently put for-
ward by the Stoics. Zeller (' Philo-
sophie der Griechen,' vol. iii. I. p.
136, &c., 2ud ed.) says in his
account of the stoical philosophy :
" Out of the original substance the
separate things are developed ac-
cording to an inner law. For in-
asmuch as the first principle, accord-
ing to its definition, is the creative
and formative power, the whole uni-
verse must grow out of it with the
same necessity as the animal or the
plant from the seed. The original
tire — according to the Stoics and
Heraclitus — first changes to ' air ' or
vapour, then to water ; out of this
a portion is precipitated as earth,
another remains water, a third
evaporates as atmospheric air,
which again kindles the fire, and
out of the changing mixture of
these four elements there is formed
— from the earth as centre — the
world. . . . Through this separa-
tion of the elements there arises
the contrast of the active and the
passive principle : the soul of the
world and its body. . . . But as
this conti'ast came in time, so it is
also destined to cease ; the original
substance gradually consumes the

matter, which it segregated out of
itself as its body, till at the end of
this world-period a universal world-
conflagration brings everything back
again to the primaeval condition.
. . . But when everything has thus
returned to the original unity, and
the great world-year has run out,
the formation of a new world begins
again, which is so exactly like the
former one that in it all single
things, persons, and phenomena
return exactly as before ; and in
this wise the history of the world
and the deity . . . moves in an
endless cycle through the same
stages." Zeller, in a note to this
passage, remarks that " the con-
ception of changing world-periods
is frequent in the oldest Greek
philosophy ; the Stoics found it
first in Heraclitus. The further
statement," however, that the suc-
ceeding worlds resemble one another
down to the minutest detail, is to
be found, to my knowledge, before
Zeno only in the Pythagorean school
. . . and is connected with the
doctrine of metemp.sychosis and
the world-year."

^ Mr Whittaker quotes a pass-
age from Aristotle's 'Metaphysics,'
towards the end of the 12th book
(Berlin ed., p. 1074, b. 10-12):
"Kara rh fiKos iroWaKis evprifjL^vrjs
el rh SvvaThv l/catTTTjs Kai Tex^vs
Kal (pi\o<joc(>ias Kai TrdXiy (pOfipofxevuiv.

ON THE GENETIC VIEW OF NATURE.

287

Poets and pliilosophers have repeated this theme in end-
less variations, probably without improving upon the
classical and perfect expression which it has found in
ancient ^ poetry and in the sacred writings. History has
been written with the professed object of gaining, by
analogy, an insight into the drift of modern or future
events, and economic and political theories have been
based upon the likelihood of a recurrence of what has
happened before. Especially has the teaching been
impressed upon us that the universal fate of all develop-
ment is to lead to death and decay, and to make room
for the endless repetition of the same recurring phases

Every art and every kind of philo-
sophy having probably been found
out many times up to the limits
of what is possible and again de-
stroyed ; " and remarks, " This
notion of cycles refers to human
civilisation, not to the universe,
which is one eternal system with
a ti.xed central mass, and with its
outer part in a moving equili-
brium. Empedocles undoubtedly
had a theory of recurrent cycles
in the universe. The four ele-
ments,— which he first brought to-
gether as elements of tiie whole,
early thinkers having tiiken one or
other of them as a first principle
from which the rest are evolved,
— according to Empedocles, are
necessarily aggregated and segre-
gated by the predominance of prin-
cii)les which he calls love {(piKia)
and hate {veiKos). The four periods
are: 1. Predominant love (the
ff<pa7pos), a state of complete aggre-
gation ; 2. decreasing love and in-
creasing hate or strife ; 3. pre-
dominant strife {a.Ku(T/xia, complete
separation of the elements) ; 4. de-
creasing strife and increasing love.
These are cosmic periods. It has
been supjjosed — Zeller takes this
view — tliat we are living in the

fourth cosmic pei'iod, the period
of increasing love."

' The best known passage is that
from the celebrated fourth eclogue
of Virgil, where, after describing the
return of the golden Saturnian age,
the poet continues (vv. 31-36): —

" Pauca taiiieii subenuit j)riseai vestigia

fraudis,
Qiue tentare Tlietini ratibus, quae cingere

imiris
Oppida, quii: jubeaiit telluri iiifindere

sulcos.
Alter eiit tiun Tipliys, et altera qua;

veliat Argo
Dt'lectos licroas : erunt etiam altera bella,
Atqiie ilfiuiii ad Trojam nuignus inittetur

Achilles."

Dugald Stewart (' Philos. Works,'
vol. iii. p. 167) refers to this
with the following quotation from
Clavius's ' Commentary on the
Treatise on the Sphere,' by Joannes
Sacro Bosco : " Hoc intervallo, qui-
dam volunt, omnia qmocunujue in
mundo sunt, eodem ordine esse
reditura, quo nunc cernuntur," and
he also attriliutes this theory of re-
currence to an extreme application
of the mathematical spirit (vol. iv.
p. 207). How tiiis idea of recur-
rent cycles fascinated and haunted
Fr. Nietzsche see Seth's article,
'Contem. Kev.,' vol. 73, p. 734.

288

SCIENTIFIC THOUGHT.

of existence.^ This view was considerably strengthened
by the popular interpretation of the teaching of modern
astronomy, which laid great stress on the periodicity of
the planetary movements, and the stability and inherent
readjustment of the solar system. Also the insight
gained by the first application of chemical knowledge to

' The idea of recurrent, periodic
repetition seems opposed to the
modern idea of progress and de-
velopment as taught by Leibniz
and Herder abroad, by Spencer
in this country ; still it seems
almost impossible in a purely
mechanical system to avoid intro-
ducing the conception of an ulti-
mate recurrence, so long as one
deals with finite space, time, or
number, however great they may
be. The only escape seems to be in
assuming an infinite process or an
immaterial principle which is not
subject to mathematical treatment,
the latter being inherently one of
repetition. It is interesting to note
how Herbert Spencer at the end of
' First Principles ' relapses into the
cyclical conception : " Thus we are
led to the conclusion that the
entire process of things, as dis-
played in the aggregate of the
visible universe, is analogous to the
entire process of things as displayed
in the smallest aggregates. Motion
as well as matter being fixed in
quantit}', it would seem that the
change in the distribution of
matter which motion effects, item-
ing to a limit in whichever direc-
tion it is carried, the indestructible
motion thereupon necessitates a
reverse distribution. Apparently,
the universally coexistent forces of
attraction and repulsion, which
necessitate rhythm in all minor
changes throughout the universe,
also necessitate rhythm in the
totality of changes — alternate eras
of evolution and dissolution. And

thus there is suggested the concep-
tion of a past during which there
have been successive evolutions
analogous to that which is now
going on ; and a future during
which successive other such evolu-
tions may go on — ever the same in
principle but never the same in
concrete result " (' First Prin-
ciples,' 1st ed., p. 536). The other
great system of modern philosophy,
which aims at a reconciliation of
the mechanical and spiritual aspects
— the philosophy of Lotze — though
it dwells less than Spencer's system
on the genetic problem, gives a
different view of cosmic develop-
ment. " The series of cosmic
periods cannot be a number of
phases, in each of which the one
purpc-^e of the universe does in fact
maintain itself : it must rather be
a chain, each link of which is bound
together with every other in the
unity of one plan. The One can
manifest itself in various forms
only when such variety of forms
is necessary for the expression of
its meaning — in a definite order of
succession only when this order
corresponds to a craving for develop-
ment in its nature. As we required
that each section of the worlds
history should present a harmony
of the elements firmly knit through-
out, so we must now require that
the successive order of these sections
shall compoise the unity of an on-
ward advancing melody " (' Micro-
cosmus,' Eng. transl. by Hamilton
and Jones, Book IV. chap. 3).

ON rilK GKNETIC VIKW OF NATURE.

289

physiology and agriculture in the school of I.iebig, and
the first chapters of meteorology, seemetl to favour the
idea that the elements and forces of nature were encracred
in cyclic movements wliich return again and again in the
same fashion. To the same cyclical view the doctrine of
the ti.xity of species, as well as that of the repetition
of various creations, lent further support : lunu-e it con-
tinued up to the middle of our century ' to be fre-

' In Germany Mijleschott's 'Kreis-
lauf des Lcbens,' a jiopular exposi-
tion of the conceptions developed
in the second quarter of the century
through clieniistry and embryology,
represented adetpaately the cyclic
conception of life and development
in a catcliing phrase. Much later
we find — inter multa aim — in
Michael Foster's 'Text-book of
Physiology ' a concise description
of the process in nature which has
always served as a type for the
cyclic conception : " When the
animal kingdom is surveyed from a
broad standpoint it becomes obvious
that the ovum, or its correlative
the spermatozoon, is the goal of an
individual existence ; that life is a
cycle beginning in an ovum and
coming round to an ovum again.
. . . The animal body is in reality a
vehicle for ova ; and after the life
of the parent has become potentially
renewed in the offspring, the body
remains as a cast-off envelope whose
future is but to die." Another
example may be found in .Molir"s
' (ieschichte der Erde,' where the
circulation of different elements in
nature is considered. The concep-
tion of periodic cycles has found
poetical expression in Riickert's
beautiful yujeni, "Chidher," which
is evidently the poetical render-
ing of an Arabian legend quoted
by Lyell (' Principles,' vol. i. p.
31):-

VOL. II.

"Chidlier, the ever youtliful, spake :
I passed a city on my way,
A man in a garden fiuit did break,
I asked how long tlie town here lay?
He spoke, and broke on as before,
' The town sUinds ever on this shore.
And will thns stand (or evermore.'

And wlien five hundred years were gone

I came the same road as anon,

Then not a mark of the lowii I met.

A shepherd on the tlulc did play,

The ealtle leaf and foliage ate.

I asked how long is the town away?

He spake, and i)iped on as before,

'One plant is green when Uie other's o'er.

This is my pasture for evermore.'

And when five hundred years were gone
I can)e the same road as anon.
Then did I lind with waves a lake,
A man the net cast in the bay,
And when he paused from his heavy take,
I asked since wlien the lake here lay"?
He spake, and laughed my question o'er,
' As long as the waves break as of yore
One fishes and fishes on this shore.'

And when five hundred years were gone
I came the same way as anon.
A wooded place I then did see.
And a hermit in a cell did stay ;
He felled with an axe a mighty tree.
I asked since when the wood here lay?
He spake : ' The wood's a shelter for "ever-
more,
I ever lived upon this lloor.
And the trees will grow on as before.'

And when five hundred years were gone

I came the same way as anon.

Hut then I found a city filled

With markets' clamour shrill and gay.

I ask<'d how long is the city built,

Where's wood and sea and shei)herd'splay?

They pondered not my question o'er

But cried : ' So was it long before.

And will go on for evermore.'

And when five hundred years are gone

rU go the same way as anon."

290

SCIENTIFIC THOUGHT.

8.

Supplanted
by genetic
view.

9.

Geology.

quently put forward and popularly accepted. It is
useful then to note that in the course of the second
half of the century we were more and more grow-
ing out of the cyclical and realising the meaning of
the genetic ^ view of things natural. We have been
taught in astronomy to inquire into the origin of our
solar or any similar system and the conditions of its
duration, to ask concerning the central heat of the sun
whence it came and how long it will last — a question
unknown to Laplace, — to consider the effects of tidal
friction, to learn that all the movements in nature are
irreversible as distinguished from completely reversible
ones, which only exist in abstraction ; and, finally, we are
met with the doctrine of the immortality of the germ-
plasma, an idea, the meaning and significance of which I
shall have to explain later on. All these novel theories
and views combine to impress upon us the general
significance of the terms " genesis, evolution, develop-
ment," the fact that everything in and around us, in
spite of the seeming recurrence of smaller movements and
phenomena, and of the periodicity of the minuter and
elementary changes, is slowly, continuously, and inevit-
ably tending in a definite direction, which is certainly
not that of a cyclical recurrence.

Leaving aside for a moment these more general views,
which have been clarified in the course of our century,
it is interesting to note how they gradually emerged in

^ Perhaps it would be more
correct to saj- that we were learning
to consider the changes within the
larger cycles, confining ourselves to
the stud)' of one brancli only of the

periodic or cyclical movement of
things around us, that branch which
we are pleased to call the ascending
or progressive branch.

ON THE GExVETiC VIEW OF NATURE. 291

the teachings of the several natural pliilosophers who
initiated the genetic conception of natural phenomena.
One <if llie earliest wIki l»roke with the older and intro-
duced ihc modern metiiods was James Hutton, wlio to-
wards the end of the preceding century led that school in
geology which is called after him, and wliicli violently
opposed the ideas introduced from the Continent. The
controversy culminated in the wrangle of the Neptunists
and Vulcanists, those who looked to the agency of water
and those who upheld that of lire as the principal cause
of geological change. This difference, which at the time
impressed the popular mind, is hardly thai ]>y whicli, in
ii history of scientific thought/ tliis controversy has
become important. Hutton's position is marked rather
hy his opposition to catastrophism, and by his doc-
trine that geological changes, such as the decay and
reproduction of rocks, were going on with the utmost
imiformity, being always in progress. This he opposed
to the Wernerian view, which believed in the existence
of certain " fundamental rocks," which were "triuni])liantly

' The great merits of James I effect in circles in which everything
Hutton, his extensive and original connected with the revolution

geological .studies, his oi)position to
catastrophism, were overlooked
through the theoretical discussions
and the unfortunate title of his
book. Tlie world had grown tired
of ' Theories of the Earth ' and the
<h"scussi(m of fundamental problems.
A spirit of observation had set in ;
the Geological Society was formed,

against Church and State was dis-
tasteful. As Huxley has told us,
Hutton came before his time. To
him belongs the merit of having
initiated the line of research and
reasoning wliich, through the
brilliant labours of Chailes Lyell a
generation later, swept away the
older geology, and prepared tlie way

and theories were for the time dis- ; for the genetic study of nature on a

countenanced. (See vol. i. p. 290,
note 1 , of this ' History.' ) The att.jicks
a,lso of Kirwan and De Luc, which
turned upon the stale argument
that Hutt'iii's ideas were opposed to
the scriptural records, had tiieir

large scale. (See the "Historical
Sketch" in tlie first volume of
Lyell's ' Princi|)les of (^leology,' and
Huxley's address on "Geological
Reform," ISey.)

292

SCIENTIFIC THOUGHT.

10.
Htttton.

appealed to if anybody ventured to doubt the possibility
of our being able to carry back our researches to the
creation of the present order of things." ^ Hutton
destroyed these characters, which were considered by
many as sacred, and declared that in the economy of the
world he could find " no traces of a beginning nor signs
of an end." And yet, as Lyell has shown, his principles
were only imperfectly carried through, for though he
maintained that " the strata which now compose our
continents have once been beneath the sea, and were
formed out of the waste of pre-existing continents," ^ he
imagined that when the decay of old continents had
furnished the material for new ones these were upheaved
by violent and paroxysmal convulsions. He therefore
required " alternate periods of general disturbance and
repose, and such he believed had been and would for
ever be the courses of nature." ^ A strange mixture of
the genetic and cyclical views of natural phenomena !
Professor Huxley '^ has explained these seeming incon-
sistencies in the theory of Hutton, whom, together with
Sir Charles Lyell, he has described as having founded
the " uniformitarian " school of geology, by the influence
which the discoveries of physical astronomy, brought
out at that time by Laplace and his contemporaries,
had upon Hutton. Thus Hutton writes : " From seeing
revolutions of the planets, it is concluded that there
is a system by which they are intended to continue
those revolutions. But if the succession of worlds

'•■ See Lyell, 'Principles,' Srd ed.,
vol. i. pp. 90, 91.

' Ibid., p. 89. 3 Lyell, p. 92.

^ Huxley, on " Geological Re-

form," quotes largely from Hutton's
'Theory of the Earth' f 1758) and
Playfair's ' Ilustrations of the Hut-
tonian Theory ' (1802).

Lyell.

ON THE GENETIC VIEW OE NATURE. 293

is established in tlie system cf nature, it is in vain
to look for anything higher in the origin of the earth.
The result, therefore, of this physical inquiry is, that
we find no vestige of a beginning, no prospect of an
end." The lieginnings of the genetic view of geolog-
ica] phenomena, which in Iluttun were still mingled with
eatastrophism, were further developed ])y Sir Charles
Lyell in his celebrated ' Principles of (xeology.' When u.
lie entered upon his geological researches, which were
conducted during his very extensive travels all over
Europe, a new element had already been introduced
into science, of which neither Hutton nor Werner liad
been able to a\'ail themselves extensively. This was the
identification of geological strata according to the fossil
remains which were contained in them, — a realisation
of the plan of work already dimly foreshadowed in
Leibniz's ' Protogica,' but nevertheless accepted even by
Humboldt as only a doubtful indication.^ This valuable
brancli of geological science had been started by AA^illiam
Smith ill his 'Tabular View of the British Strata' in
1790, and further elaborated in his geological map of
Kngland (1815), which was the fruit of his own un-
aided labours, " for he had explored the whole countrv

' 'I'lu' Wernerian school ;ire gen-
erally accused of having neglected
the historical record afforded by
fossil remains, and Humboldt, in
his ' Essaj- on the Superposition of
Rocks in both Hemispheres' (182-3),
says (Eng. transl., j). 52): "In
the present age naturalists are no
longer satisfied with vague and
uncertain notions, and they have
sagaciously observed that the great-
est number of those fossils, buried
in different formations, are not

specifically the same ; that many
species wliich they have been enabled
to examine with precision vary with
the superposed rocks. . . . Ought
we to conclude from this assem-
blage of facts that all the forma-
tions are cliaracteri.sed by particular
species ? that the fossil shells nf the
chalk, of the muschclkalk, of the
Jura limestone, and of the Alpine
limestone, all differ from each other ?
This would be, in my opinion, to
carry the induction much too far."

294 SCIENTIFIC THOUGHT.

on foot without the guidance of previous observers or
the aid of fellow - labourers," ^ and "had thus singly-
effected for the whole of England what many celebrated
mineralogists had only accomplished for a small part of
Germany in the course of half a century." ^ Simultane-
ously with Smith in England, Cuvier and Brongniart were
exploring the Paris basin. Thus the three different
nations of Europe with whom I am mainly concerned
in this work furthered independently the main divisions
of geological inquiry. " The systematic study of what
may be called mineralogical geology had its origin in
Germany, where Werner first described with precision
the mineral character of rocks ; the classification of the
secondary formations belongs to England, where the
labours of Smith were steadily directed to these ob-
jects ; the foundation of the third branch, that relating
to the tertiary formation, was laid in France by the
splendid work of Cuvier and Brongniart." ^ To these
words of Lyell we can now add that the theoretical
explanations were first suggested, and the correct line
of reasoning on this accumulated evidence initiated, by
Sir Charles Lyell himself.

The key to the doctrines of Lyell was the study of
existing causes — the attempt to show how the slow
agencies which we now see at work in nature around
us are sufficient to explain the successive changes *

^ Lyell, ' Principles,' vol. i. p.
101.

^ An expression of cl'Aubuisson,
quoted by Dr Fitton, ' Phil. Mag.,'
vols. i. and ii., also " Edin. Rev.,'
Feb. 1818.

^ See Lyell, loc. cit., p. 100.

only by carefully considering the
combined action of all the causes of
change now in operation, whether
in the animate or inanimate world,
that we can hope to explain such
complicated ap]>earances as are ex-
hibited in the general arrangement

* Id. ibid., vol. iii. p. 273 : " It is • of mineral masses."

ON THE GENETIC VIEW OF NATURE. 295

which the recognisable strata of the earth's crust
with their fossil remains indicate as having occurred
in former ages. It was an attempt to " reconcile the
former and the present state of nature." ^ This was
to break with the idea of great and general convulsions,
to which the Continental school resorted in their ex-
planations, and it also meant upsetting the vague notions
which set a limit to the time '^ which should be allowed
for the operations of natural causes. It is possible to
admit that in both directions, in their uniformitarian
explanation and in their geological time-reckoning, the
new school frequently went too far, the indications
of actual catastrophes and paroxysmal convulsions being
to many observers quite unmistakable. On the other
side, the arguments based upon physical astronomy,
mechanics, and thermodynamics, which aftbrd an inde-
pendent basis for geological time -reckoning, were not
yet elaborated,^ or were deemed too crude * to be of
value ; and for a good while geologists were permitted

^ Lyell, vol. i. p. 114. elementary matter of the earth
- Id. ibid., p. 241: "When difR- may have been first iu a gaseous
culties ari.se in interpreting the j state, resembling those nebula-
monuments of the past, I deem it j which we behold in the heavens,
more consistent with philo.^ophical , and which are of dimension.-, so

caution to refer them to our present
ignorance of all the existing agents,
or all their possible effects in an
indefinite lapse of time, than to
causes formerly in operation but
which have ceased to act."

* See Lyell, vol. i. p. 1.54, &c.,

vast tiiat some of them would fill
the orbits of the remotest planets
of our system. . . . Without
dwelling on such speculaiions
which can never have any direct
bearing on geology," &c.

* See Lyell, vol. i. p. 206, whei-e

also vol. ii. p. 274: "It has long he refers to "astronomical t•au^es
been a favourite conjecture that of fluctuations in climate," and to

the whole of our planet was origin-
ally in a state of igneous fu.sion, and
that the central parts still retain a

the calculations of Sir J. Herschel
and the fa<^t that "this matter
still under discussion," and that

great portion of tiieir primitive | "Mil. Fourier and Herschel iiave
heat. Some have imaginetl witii , arrived at very different opinions."
the late Sir W. Herschel that the i

296

SCIENTIFIC THOUGHT.

Embryol-
ogy.

to draw indefinitely on the great bank of time/ just as in
former ages they had been quickly brought to book by
existing prejudices.^

Wliilst these contributions to the genetic view of
nature on the large scale were being independently
worked out, the sciences which deal with the minute
and hidden phenomena of organic growth had made great
progress in the same direction. Here a definite scheme
of development was quite evident to the most casual
observer. In these sciences indeed we have to do with
what is called in the German language " the history of
development " 'par excellence, a term which is inadequately
rendered by " Embryology " in French and English. For
it is an error which has frequently and for long periods
obscured the correcter view to assume that the chang;es
and processes which characterise the development of
embryonic or germ life are essentially different from
those which exist in the larger and more complex adult
organism. The abohtion of the fundamental distinction
between the processes of embryonic and of adult or f ull-

1 Lyell, vol. iii. p. 358 : " Cou-
fiiied notions in regard to the
quantitj' of past time have tended
more than any other prepossessions
to retard the progress of geology,
. . . and until we habituate our-
selves to contemplate the possibility
of an indefinite lapse of ages having
been comprised within each of the
more modern periods of the earth's
history, we shall be in danger of
forming most erroneous views in
geology."

- One of the first to attack the
uniformitarian doctrine in geology
and to applj' the principles of
modern physical science to geolog-

ical and cosmical questions in this
country was Lord Kelvin. His
influence belongs, however, mainly
to the post-Darwinian period, and
begins with his celebrated memoir
' On the Secular Cooling of the
Earth' (Edin. Trans., 1862, re-
printed in the 3rd vol. of ' Math,
and Phys. Papers,' p. 295). See
also the 2nd vol. of his ' Popular
Lectures and Addresses.' Accord-
ing to the introductory statement
in the former paper his doubts
regarding the uniformitarian teach-
ing began as early as 1844. I shall
refer to these speculations at the
end of this chapter.

ON THK (JENKTIC VIKW OF XA'ICRE. 297

giowu life, the unification of thought on these niattere, is
quite as important in the history of science as tlie abolition
of the supposed fundamental difference between animal
and vegetable growth or between normal and abnormal (or
pathological) development. The reduction of all these
seemingly so different changes to the one great problem
of cellular structure, cellular growth, and cellular division
marks one of the greatest achievements of our century.
" Our position with regard to the cell is similar to that
of investigators towards the whole animal or vegetable
body a hundred years ago, before the discovery of the
cell theory."^

Anticipations of this generalisation, of the condensation
of the whole problem of animal and vegetable embryology,
of generation, growth, and organic development in the
formula, " omnis cellula ex cellula," have indeed existed
since the time of Harvey, who, in addition to the great
discovery of the circulation of the blood, laid down the
thesis, " omnp vivuni ex ovo." " Th(> further correct

' See O. Hertwig, " Thy Cell, " important of the organs of the

' Outlines of General Anatomy and i adult, nor by sudden nietamor-

Physiology.' Transl. by Campbell, phosis of a formative substance

1895, p. 11. I into a miniature of the \vhole,

- One of the best expositions of ' which subsequently grows, but by

Harvey's idea.s is to be found in epigenesis, or successive diffeientia-

Huxley's article on " Evolution in tion of a relatively homogeneous

Biologj'" in tlie ninth edition of rudiment into the parts and struc-

the ' Encyclop;cdia Britannica.' He
there also refers to Aristotle's
opinions. " One of Harvey's prime
objects is to defend and establish,

tures which are characteristic of
the adult." In the sequel of his
exposition, after maintaining epi-
genesis or after-formation against

on the basis of direct observation, i evolution in the older sense or pre-

the (jpinion already held by Aris- , formation, Huxley, however, makes

totle, that in the higher animals [ a passing remark that " though the

at any rate the formation of the doctrine of epigenesis, as uiulerstood

new organism by the process of I by Harvey, has definitely triumphed

generation takes place, not sud- over the doctrine of evolution, . . .

denly by simultaneous accretion of it is not impossible that, when the

rudiments of all, or of the must analysis of the jirocess of develop-

298

SCIENTIFIC THOUGHT.

13.

Epigenesis
and evolu-
tion.

14.

C. F. Wolff.

generalisation which he ventured to put forward, that
growth and development of the germ or embryo con-
sisted in the addition or formation of new parts and
structures through division or differentiation, was, how-
ever, obscured and cast into the shade by the opposite
doctrine, termed evolution, according to which every
form or particle of organisation was minutely pre-formed
in an invisible germ, and growth consisted merely in a
process of enlargement, as a particle of " dry gelatine
may be swelled up by the intussusception of water."
The supporters of this doctrine, to which the celebrated
names of Leibniz, Boerhaave, Haller, and Bonnet belonged,
seemed unable to conceive of any force in nature which
was capable of producing organisation, and were thus
compelled to accept in some form or other the doctrine
of the pre-existence of germs, a theory which has in
modern times been revived under an altered form.

The real foundation of scientific embryology, of the
study of the genesis of vegetable and animal organisms,
is now pretty unanimously ^ traced to Caspar Friedrich
Wolff, whose ' Theoria generationis ' appeared in 1759.
His observations refer alike to plant and to animal life,
and his distinct object was to refute the theory of evolu-

meut is carried still further, and
the origin of the molecular com-
ponents of the physically gross,
though sensibly minute, bodies
which we term germs is traced,
the theory of development will ap-
proach more nearly to metamor-
phosis than to epigenesis. . . . The
process, which in its superficial
aspect is epigenesis, appears in
essence to be evolution in the
modified sense adopted in Bonnet's

later writings ; and development is
merely the expansion of a potential
organism or original pre-formation
according to fixed laws."

^ See J. A. Thomson, loc. cit. , p.
121. Yves Delage, ' L'H^rddit^,'
p. 357, note ; and especiallly O.
Hertwig, ' The Biological Problem
of To-day,' transl. by P. C. Mitchell
(Heinemann's Scientific Handbooks,
1896), p. 4, &c.

ON THE GENETIC VIEW OF NATURE.

299

tion and replace it by the correcter doctrine of epigenesis
— i.e., of repeated or after-formation. I Taller^ thought
very highly of this attack on liis own view, hut was
not convinced by it : and although in botany Wolfi's
views on the cellular structure of plants were adopted
in France by Mirbel, and those on metamorphosis were
unknowingly reproduced ]»y Goethe, his influence on em-
bryology dates actually only from the year 1812, when
Meckel translated one of his treatises and thus drew
attention to his great merits. Wolll" tried to refute the
theory of evolution or pre-formation, supplanting it by
that of epigenesis or after -formation, through actual
observations of the development of germs in plants and
animals in definite instances. Tn l)otany his views,
after lying dormant for a long period, led ultimately to
the famous cellular theory of Schleiden and IVlohl. Tn
zoology, shortly after Meckel's republication of his treatise
in 1812, there were published the researches of Pander,
who, in his treatise on the development of the chick,
" gave a fuller and more exact view of the phenomena
less clearly indicated by Wolft*, and laid the foundation
of the views of all sul)sequent embryologists." ^

Pander was a Eussian by l)irth, anil so was his greater pamierana

n K. E. von

contemporary and friend, Karl Ernst \-on l5aer, a man Baer.

' As Prof. J. Ailhur Thomson
says (' Science of Life,' p. V2,Q), " A
.single sentence, ' Es gibt kein
Werden — there is no IJecoming,'
sufficiently iiulicates Haller's posi-
tion."

- .J. A. Thoin.^on in article " Em-
bryolog\'" (' Encv. Brit.,' 9th ed ,
p. 16f.r

=' The work of von Baer (1792-
1876) remained for a long time un-

unrecognised outside

known and

of Cerinany. Huxley made him
known in this country by trans-
lating extracts from his principal
writings for Taylor's ' Scientific
Memoirs' in 18,o3, nearly thirty
years after von Baer had begun the
brilliant .scries of his researches. It
can be said of him that he, even
more than his forermniers, Pander
and Dijllinger, withdrew natural

300

SCIENTIFIC THOUGHT.

who occupies a unique position in the history of natural
science. He introduced the principle and aspect of
development into the midst of those studies which, under
the important but one-sided influence of Cuvier and his
school, were in danger of being confined within the
limits of morphology and comparative anatomy. Through
a long series of most important embryological investiga-
tions, conducted during the years 181 9-1837, he demon-

science from tlie spell under which
it was kept for a long time in the
West of Europe by the great
authority of Cuvier. Geograph-
ically also, von Baer's activity was
centered in Kiinigsberg (where he
was one of a brilliant company who
made the University celebrated) and
St Petersburg. Though a great
admirer of Cuvier, whose biography
he wrote, and an adherent of the
doctrine of animal types, which he
independently arrived at, he intro-
duced three distinct lines of re-
search into his scientific labours, to
all three of which Cuvier was either
foreign or distinctly averse — viz.,
microscopic research, study of em-
bryological development, and the
philosophical spirit of the " Natur-
philosophie." He was not dazzled
by the latter ; but whilst avoiding
its extravagances and premature
generalisations which then flooded
Cerman science, he always appre-
ciated the search for the connection
and unity of all the things of nature
which was characteristic of that
school. Baer stood, historically and
philosophically, in the middle be-
tween the extreme morphological
and genetic views rejiresented
respectively by Cuvier before and
by Darwin after him. Already in
1815, when studying under Dol-
linger at Wiirzburg, he was guided
by the idea that " nature follows in
her creations certain general themes
(types), and that she varies these in
the different species." Von Baer

also combined the geographical and
anthropological interest, so largely
represented by Humboldt and
Ritter, with his morphological
and genetic studies. In fact, it is
doubtful whether in any naturalist
of the very first order the different
interests which the nineteenth
century inherited and created were
more equally and impartially bal-
anced than in him. The embryo-
logical researches of von Baer
stimulated many ardent students in
( Jermany, such as Purkinje, Rathtke,
Bischoff, and it is mainly through
them that this branch of science
was cultivated and made generally
known. The name of the distant or-
iginator thus became .somewhat for-
gotten, so that in French science we
do not find von Baer as frequently
and appreciatively mentioned as he
deserves. Ample information on von
Baer's scientific and personal char-
acter can be found in later publica-
tions : foremost in his ' Auto-
biography,' published in 186.^) ; in
his 'Life,' by Stieda (1877) ; and in
an elaborate work by Professor R.
Stolzle, entitled ' K. E. von Baer
und seine Weltanschauung' (Re-
gensburg, 1897). This work con-
tains very ample and useful refer-
ences and extracts from Baer's
writings and correspondence. Very
important are also von Baer's
miscellaneous writings and essays,
which were published by Vieweg
in Brunswick, in three parts (2nd
ed., 1886).

ON THE OKNKTIC VIKW OF NATUKK. 301

strated in the completest manner the truth of epigenesis.
In fact, he had recognised development as the " sole basis
of zoological classification ; while in France Cuvier and
Geoffrov St Hilaire were emljittering each other's lives
with endless merely anatomical discussions and replica-
tions, and while in Germany the cautious study of nature
was given up for the spinning of Xatur-philosophies and
other hypothetical cobwebs." '

The position which Karl Ernst von Baer occupies in
the liistory of science and thought is in many respects
interesting and unique. He lived early enough in the
century to experience the full influence of Cuvier's
authority, and lived long enough to witness tlie great
change which Darwin's writings brought on in all the
natural sciences ; whereas his great contemporary,
rlohannes JMuller, passed away before the name of
Darwin was known outside of his own country. In
unison with Mliller, and yet in an independent manner,
he effectually liberated German science from the undue
influence of the speculative school. And he lias, prob-
ably more than any other great naturalist, recognised
the importance of the three aspects which a contempla-
tion of natural objects forces u]>()n us: the apparent or
real fixity of certain forms (the morphological view),
the continued and orderly cliange " of these forms (the
genetic view), and the apparent or real existence of a

• Huxley iu Taylor's 'Scientific far as observations now give material

Memoirs,' New Series, p. 176. for inferences, a transformation of

'■^ Very important in this respect certain original forms of animals in

is a lecture delivered by von Baer the succession of generations is very

in 18-34, with the title 'Das all- probable, but only to a limited ex-

gemeinste Gesetz der Natur in aller tent" (p. 60), a view which von

Entwickelung' (reprinted in the Baer maintained to the cn<l against

Brunswick edition, vol. i. p. ;j9 extreme Darwinism (see p. 37).
.^77.) " We must conclude that, so

302 SCIENTIFIC THOUGHT.

design in this process of change (the teleological view).
Though his own researches did so much to give promi-
nence to the genetic view, to the conception of develop-
ment, he retained and elaborated the doctrine of types ;
and though he effectually handled the modern methods
of the mechanical or exact sciences, he realised the full
importance of studying the things and processes of
nature in their actual and living connection,^ and not
merely in the artificial isolation of the laboratory or
the dissecting-room. And he never became an adherent
of the doctrine so prevalent with many of the followers
of Darwin, that the apparent purpose of forms and
processes in organic nature could be mechanically ex-
plained. During the period of his greatest scientific
activity he was little known outside of Kussia and
Germany ; in England, Carpenter and Huxley alone
drew attention to his embryological and genetic studies;
but since the tide of Darwinism has somewhat subsided,
or has ceased to be all-absorbing, it is to the writings
of Baer that many naturalists revert. In fact they
belong to the few books of this class written during
the pre-Darwinian age that bear to be read and re-read
with profit by those who take a philosophical and not
merely a historical interest in the development of
16. natural science. Perhaps the fact that von Baer was

Von Baer's

comprehen- as great in relation to the morphological as he was

sive views. " jr o

in relation to the genetic and the teleological con-
ceptions of natural phenomena prevented him from
producing that revolutionary impression on the minds

^ See the introduction to the geschichte der Thiere' (Konigsbej-g
second part of his ' Entwickelungs- I 1837).

ON THE GENKTIC VIEW OF NATURE. 303

of his contemporaries which Darwin tlid, and for
which he indeed largely ])repared the way. Instead
of opposing the genetic change and development of
the forms of natural objects to their apparent fixity,
he rather reconciled botli views with each other by
maintaining^ "that in order to (jbtain a just insight
into the mutual affinities of animals it is Ijefore all
things necessary to distinguish the different tyijes of
organisation from the different grades of development."
He considered that "' " tlie idea of animal organisation
does not vary at equal intervals, but is realised in
certain principal forms which again break up into
variations of a lower u;rade " : and he ^ " arrived at the
four principal divisions of the animal kingdom estab-
lished by Cuvier." In 1828, in his work on the 'De-
velopment of Animals,' he discusses * " the prevalent
notion that the embryo of higher animals passes through
the permanent forms of the lower animals " — i.e., " the
doctrine of the agreement of individual metamorphosis
with the ideal metamorphosis of the whole animal
kingdom." Von Eaer had himself added greatly ^ to

^ See Huxley's translation, loc. lesults : " It was von Baer who

■c/t., p. 178. first clearly discriminated the great

- Ibid., p. 182. events in a life-hi.^tory ; (a) the

•' Ibid., p. 183. primary jjioeess of egg-cleavage,

* See K. E. von Baer's ' Ueber and the establishment of the

Entwickelungsgeschichte derThiere germinal layers; {b) the gradual

BeobaclitungundReflexi<jn,'Konigs- differentiation of the tissues (hi.s-

berg, 1828. The above extracts togenesis) ; and (c) the blocking

are taken from the fifth scholion : out of the organs (organogenesis),

" Ueber das Verluiltnissder Formen, , and the shape-taking of the entire

die das Individuurii in den versdiie-
denen Stufen seiner Entwickelung
annimmt." See also Huxley's
Translation, loc. cit., pp. 186, 189.
° Prof. J. A. Thomson sum-
marises as follows von Baers own

organism (morphogenesis) (' Science
of Life,' p. 12'SJ. The classical
work of von Baer is dedicated to
his friend Pander, from whom and
DoUingcr he acknowledges iiaving
received the first impulses towards

304 SCIENTIFIC THOUGHT.

the existing knowledge of the early development of
the germs of animals by discovering the ovum in the
body of the mammalia before fructification, and by this
and other discoveries secured his claim to be considered
the greatest embryologist of his own age, and perhaps
of all time. He goes on to examine to what extent the
morphological differences which the animal kingdom ex-
hibits in its various members can be taken as a guide to
the genetic differences in the growth and development of
the higher organisms. He, in fact, tried to ascertain
how far the facts of classification throw a light on the
facts of development, how far the changing embryo of
the higher animal gradually passes through the permanent
forms of the lower animals. He combats the idea that
the classification or morphological arrangement can be
uni-serial — i.e., brought into one continuous line or order.

his researches. He wishes to dis- drew from all this, especially in

tinguish carefully between facts the age of Schelling's 'Natur-phil-

and theory, and is very cautious osophie,' the conclusion that Cuvier

as to the latter, a trait which was not a philosophical mind. To

runs through all his writings. It me it seems that we recognise in it

is also very interesting to see how Cuvier's desire for clearness. He

iu his biography of Cuvier (post- dropped the higher task because

humously published by Stieda) he he found that it would not lead

considers it a merit of that great him to clear views" ('Lebensge-

naturalist not to have indulged schichte Cuvier's von K. E. von Baer,'

in genetic theories. "It is evi- ed. Stieda, 1897, p. 72). English

dent that Cuvier in his youth had readers, to whom the genetic view

als(} a genetic system in view, such has only become familiar since

as Oken afterwards followed up, Darwin or perhaps Lyell, will find

but that he must soon have found with astonishment how in the

out that this task was unattainable writings of Baer, before Lyell and

for him. He abandoned it, and even before the appearance of

sought rather to draw from the Cuvier's final system, genetic ideas

mauifoldness of the formed pro- were thought to be prevalent, and

duct inferences regarding the con- were criticised elaborately and re-

ditions of its genesis. Thus he ceived with the utmost caution

arrived at the teleological concep- even by the great pn^pounders of

tions which he developed on vari- the doctrine of development,
ous occasions. German naturalists

ON THE GENETIC VIEW OK NATUKE. ."05

Animals differ according to the type of organisation tn
which they belong. Thus the " embryo of the vertebrate
animal is from the very first a vertebrate animal, and at
no time agrees witli an invertebrate animal."^ Having,
however, once fixetl the existence of special organic
forms, he asks whether within the limits of such form
no law can be discovered to formulate the development of
the individual. He believes there can," and he f>roceeds
to explain it in terms which for the most part might
appear unaltered in the most modern work on evolution.
He states that the more special type is developed from
the more general, "and that the more different two
animal forms are, so much the further back must tlieir
development be traced to find them similar." Indeetl he
thinks it jirobable that " in tlie condition of tlie actual
germ all embryos which are developed from true ova
agree," and he anticipates the cellular theory of Schwann,
established by observation ten years later, by suggesting
that the simple vesicle is the common fundamental form
" from which all animals are developed, not only idcall}'
but actually and historically." ^ In further examining
the process of development, von Baer introduces the
N'ery suggestive term "* differentiation. " The higher and
lower development of the animal coincides perfectly with
that histological and morphological differentiation which
gradually arises in the course of the development of
the individual." '"' Development, in fact, is the estab-

' Loc. ciL, p. 220; tnuisl., p. 210.

2 Ibid., p. 221.

■> Loc. ciL, p. 224 ; tran.sl., p. 213.
On this anticipation see, however,
von Baer's later explanation in^
' Heden, &c.,' vol. ii. p. 250.

■* The (Jernian term is " Son-
derung," which Huxley lenders bv
the English term " Ditlerentiation."'

'^ Loc. cit., p. 229, 230; tran.sl.,
p. 219.

VOL. II. U

views m

modern

terms.

306 SCIENTIFIC THOUGHT.

lishing of differences, and in reality " the embryo never
passes through the form of any other animal, but only
through the condition of indifference between its own
form and others." And he sums up his reflections by
stating that the " development of an individual of a
certain animal form is determined by two conditions :
first, by a progressive development of the animal by
increasing histological and morphological differentiation ;
secondly, by the metamorphosis of a more general form
into a more special one." ^

In order better to understand the difference which

separates these various reflections, though breathing so

17. much the air of the more modern theory of evolution.

Von Baer's "^ '

from later views, and to prepare for a real comprehension
of the great step taken by Darwin, it will be helpful to
resort to modern nomenclature. None of the terms of
that vocabulary which was invented by Darwin and his
followers to bring home to the popular mind the main
points of his revolutionary doctrine are to be found in
the earlier writings of von Baer. Nevertheless they
are useful in defining the views of the great naturalists
who preceded Darwin. Since we have become familiar
with the idea of the origin and the transmutation of the
different animal and vegetable species, we are accustomed
to apply the genetic view not only to the growth and
development of individual living things in nature, but to
everything else. When von Baer speaks of development,
when he tells us that " the history of development is the
true source of light for the investigation of organised
bodies," he means development in the narrower sense,

1 Loc. cit, p. 231 ,•* transl., p. 220.

ON THE GENETIC VIEW OF NATURE.

307

that which Ilaeckcl has termed " Ontogenesis," the genesis
of the individual being. From this Haeckel distinguishes
" Phylogenesis," the genesis of the phyla, the genera, and
species. Xow, in discussing the relation of the order
which prevails in the natural systems of animals to
the stages of development of individual embryos, von
]^>aer does not seem to have had before his mind the
genesis of one species out of another, a view which he
in fact ridicules ^ after a verv modern fasliiou. He looked

' Lqc. fit., p. 200; transl., p. 187
(1828) : " This idea— viz., that the
higher forms of animals in the single
stages of the devehjpment of the in-
dividual, from its first origin to its
completed development, answer to
the permanent forms of the animal
series — . . . could not fail to be
widely accepted, since it was sup-
ported by a multitude of special
demonstrations. Certain of its ad-
vocates were so zealous that they
no longer spoke of similarity but of
perfect identity, and assumed that
the correspondence had Vieen de-
monstrated in all cases and to the
minutest details. . . . B\' degrees
it became the custom to look upon
the different forms of animals as
developed out of one another, and
then many ajjpeared to forget that
this metamorphosis was after all
only a mode of conceiving the facts.
. . . At length, in sober serious-
ness, and with all due particularity,
we were informed exactly how they
arose from one another. Nothing
could be easier. A fisli, swimming
towards the shore, desires to take
a walk, but finds his fins useless.
Tiiey diminish in breadth for want
of use, and at the same time elon-
gate. Tliis goes on with children
and grandchildren for a few myriads
of years, and at last, who can be
astonished that the tins become

feet ? It is still more natural that
the fish in the meadow, finding no
water, should gape after air, there-
bj', in a like jteriod of time, develop-
ing lungs ; the only difficulty being
that in the meanwhile a few genera-
tions must manage to do without
breathing at all. The long neck of
the heron arose from a habit its
ancestors ac(iuired of stretching out
their necks for the purpose of catch-
ing fish. . . . An immediate conse-
quence of the assumption of this
idea as a natural law was that a
view which had once been very
general, but had subsequently been
pretty gcncially given up, — that of
the universal progression of the
different forms of animals, — gradu-
ally got footing again. ... It
must be confessed that the natural
law being assumed, logical conse-
quence required the admission of
the view in question. There was
then only one road of metamor-
phosis, that of further develop-
ment, either attained in one in-
dividual (inilivi<lual metamor])li()sis)
or througli the different animal
forms (the metamorphosis of tlie
animal kingdom) ; and disea.se was
to be considered as a retrogressive
metamor[)hosis, because universal
metamorjihosis, like a raili-oad,
allows motion backwards oi- for-
wards, but not to one side.''

308 SCIENTIFIC THOUGHT.

upon this order as systematic only, and ideal ; ^ he thinks
merely of arrangement or " taxonomy." We may say
that he deals with phylotaxy (called at that time tax-
onomy), not with phylogenesis. He conceives that onto-
genesis, the historical development of the individual
thing, throws light on the " mutual relations of organ-
ised bodies " ; " he wishes to make ontogenesis helpful
in taxonomy or in phylotaxy. This term did not then
exist, Ijut it is useful in order to enable us to under-
stand the change which came over natural science when
18. the attempts at phylotaxy were succeeded by the schemes

Phylotaxy

aiKi phyio- of phylogenesis, when reasons were established for taking
in real earnest the idea then fancifully ^ put forward that
the natural order of living beings represented the order
in which they had developed out of each other in time.
These reasons did not at that time exist.

A suggestion in this direction had indeed been thrown
out, and an elaborate theory had been published about

scem^sis.

^ lu his later writings vou Baer that of the "fieri" (processes of

notes especially the difference be- change and development). See the

tween a purely ideal and a genetic expositions in the introduction to

or genealogical relationship. See the article on Darwin. He there

' Reden, &c.,' vol. ii. p. 386 (2nd ed. ) , also mentions Meckel and Oken as

-'Entwickelungsgeschichte' i the two principal exponents of the

(1828), p. 231; transL, p. 221. | extreme view then put forward and

' In a later publication of von opposed by himself, that the human

Baer's (see ' Reden, &c.,' 2 Theil, being in its development passes

No. v., "Ueber Dar\Vin's Lehre") through the different higher forms

the aged author trie.s to define more of the animal creation, and he

exactly the part which his early maintains tiiat Johannes Miiller,

writings played in the gradual ' who had in the first edition of his

establishment of a genetic concep- ' ' Physiology ' accejited this view,

tion of natu7-e. If Haller arrived struck it out in the second. He

ultimately at the dictum " es gibt also refers to a passage in a Memoir

kein Wei den," we may say that von of 1859, published just before the

Baer as emphatically asserted the appearance of the ' Origin of

opposite, that "es gibt kein Sein. " Species,' in which he maintains his

In Baer we have progressed from the belief " that formerly organic forms

study of the " esse '" (fixed forms) to i were less rigid."

ON TJ[K OENKTIC VIKW OF NATURE.

309

ten years before von Baer ^ took up " the subject, which
then presented itself as the richest which an anatomist
could take up, the history of development," and twenty
years before his first larger publication on this subject.
Lamarck's "' Philosophic Zoologique ' appeared in 1809.
Though known to von IJaer, it does not seem to have
ever been much appreciated by liim, but it was the
first serious attempt to deal with phylogenesis, as von
Baer's researches were the first consistent studies in
ontogenesis.

It is of interest to inquire into the reasons which
induced Lamarck to form opinions so entirely different
from those which, through the influence and the authoritv
of Cuvier, were then prevalent among naturalists, and to
oppose the idea of variability and of descent to that of

19.

I^iinarck.

' Von Baer himself describes —
usin<; theae words— how in the year
1819 the play of accident or good
fortune " threw this subject into
his hands." Stieda, p. 67.

* Since the interest in the specu-
lations of J. Ba()tiste de Lamarck
(1744 - 1829) has been revived
through tlie writings of Charles
Darwin, the historical antecedents
of his ideas have also been studied,
and his as well as Geoff roy's
tiieories have Ijeen brought into
connection with the views contained
in Butfon's ' Epoques de la Nature.'
See especially the interesting an-
alysis in Edmond Perier's ' La
Philosophie Zoologique avant Dar-
win,' 18S4. " Ainsi surgissont,
poses par Buffon, ce partisan d'abord
si resolu de la fixitc des esp^ces,
tous les probl^mes dont la solution
aura 6t6 sans aucun doute la pensde
dominante de la seconde nioitie de
ce siccle. . . . Et toutes ces
grandes idees que Burton dexine en

quelque sorte, vers lesquelles il est
invinciblement entrainu par la puis-
sante et rigoureuse logique de son
genie, sont prdcisement cellcs qui
coininencent aujourd'hui, appuyees
sur un ensemble imjiosant de re-
cherehes, h. triompher de tous les
scrupules " (p 68). " Trois gi-ands
honimes y vont poursuivre, par des
voies diverses, ru?uvre de Buffon :
Lamarck, Geoffroy St Hilaire, et
Cuvier " (p. 72). For the histori-
cal connections of Lamarck's ideas
see also Huxley's article in the 0th
ed. of the ' Ency. Brit.,' in which he
points to a great change which took
place in Lamarck's views between
1794 and 1809. In fact, the theories
which have given to Lamarck so
distinguished a position in the his-
tory of the genetic view of nature
belong to the latter half of his long
life. I know of no other recent
example <>f so late a development of
(juile original ideas except ])erhaps
the critical philosophy of Kant.

810 SCIENTIFIC THOUGHT.

the fixity and independence of species. And it is equally
interesting to mark the causes which militated against
the more general acceptance of his views, and which
cast the ' Philosophie Zoologique ' into oblivion. To the
first question Lamarck has himself, in the introduction ^
to his great work, furnished us with the means of reply-
ing. He there tells us that when the real study of
natural history began, and each of the different king-
doms of nature received the due attention of naturalists,
animals with a backbone — viz., mammalia, birds, reptiles,
and fishes — received the greater attention.^ Being in
general larger, with parts more developed and more
easily determinable, they, as it were, obtruded them-
selves on the attention of man, for whom they are both
more useful and more formidable. The other large group
of animals, classed together first by Lamarck himself as
" Invertebrates," are mostly very small, with organs and
faculties less developed, and thus much further removed
from man and his interests. Of this by far more numer-
ous class of beings, those called insects had alone at the
end of the former century received considerable atten-
tion, whereas all the others, classed together by Linnaeus
as " worms," formed a kind of chaos, an unknown land.

^ Lauiarck"s later genetic views taining the " pieces justificatives

are contained in the ' Philosophie de ce que j'ai publie dans ma

Zoologique,' which appeared in Philosophie Zoologique." This great

1809, and was republished with a work was republished in 1837 by

biographical notice by Charles Deshayes and Milne - Edwards. I

Martin in 1873. I quote from this quote from this edition, which is

edition. His principal ideas are also in three volumes,
summarised in the introduction to - See 'Philosophie Zoologi(iue,'

his great work, ' Histoire des Discours pr^liminaire, vol. i. p. 29 ;

Animaux sans Vertebres' (1816), also ' Animaux sans VertSbres,"

which in fact he represents as cou- Introduction, vol. i. p. 11.

ox rHK flKNKTIC VIKW DF XATCRK.

311

It was to some extent accidental ' that Lamarck, after
having devoted himself for many years to the exclusive
study of plants, shouUl on the occasion of the foundation
of the different chairs for the natural sciences at the
"Museum" suggested by Lakaual, have allotted to him
the cultivation of this department, unknown to himself as
it was to others, and where even the systematising genius
of Linnseus had abstained from trying to make order.
Thus it came about that Lamarck brought to the study
of the animal world a mind trained in a very different
region of science," and that he approached this study

^ See tlie " Introduction Bio-
graphique," Viy Martins, ' Philos.
Zool. ,' I. xiii. "La Convention
gouvernait la France, Carnot or-
ganisait la victoire. Lakanal entre-
prit (I'organiser les sciences Tiatur-
elles : sur sa ])roposition, le ^luseum
d'histoire naturelle fut cri6. On
avait pu nommer des professeurs
ii toutes les chaires, sauf pour la
zoologie ; mais dans ces temps
d'enthousiasme la France trouvait
des homnies de guerre et des
hornmes de science, partout oil elle
en avait besoin. Etienne Geoffroj'
Saint-Hilaire dtait ag^ de vingt-et-
un ans, il s'occupait de mineralogie
sous la direction d'Haliy. Dauben-
ton lui dit : ' Je prends sur moi la
responsabilitd de votre inexpe-
rience ; j'ai sur vous l'aut(>rit<^ d'un
p6re ; osez entreprendre d'en-
seigner la zoologie, et un jour on
l)uisse dire que vous en avez fait
une science francaise.' Geoffroy
accepte, et se charge des aniniaux
supcrieurs. Lakanal avait coiiipris
qu'un seul professeur ne pouvait
suffire II la tilche de ranger dans
les collections le r6gne animal tout
entier. Oeoffrov devant classer les

vertebres seulement, restaient les
invertdbrcs, h, savoir les insectes, les
moUusques, les vers, les zoophytes,
c'est - <i - dire le chaos, I'incounu.
Lamarck, dit M. Michelet, accepta
I'inconnu ... 11 avait tout ^ ap-
prendre, tout ii crcer dan.^ ce mondo
inexplorc, ou Linno avait pour ainsi
dire renoncc h, introduire I'ordre
mdthodique qu'il avait su si bien
ctablir parmi les animaux supcr-
ieurs." Lamarck was accordingly
about fifty when he undertook this
novel study, which, as Huxley
pointed out, was to work such a
change in his views {loc. cit.)

^ He had written in six months
his ' Flore franeaise,' which was
prefaced by his ' Cli5 dichotomique.'
This was in 1778. "Rousseau
avait mis la botanique h, la
mode ; les gens du monde, les
dames s'en occupaient. Buifon
fit imprimer les trois volumes de
la 'Flore fran(,'aise ' h, I'iiniiriiiierie
royale " {loc. c.lt. p. 11). Lamarck
had also qualified as a naturalist
by extensive travels in many Euro-
pean countries as a companion to
Buffon's son.

312

SCIENTIFIC THOUGHT.

20.
The temi
'•Biology.'

from that side which at the time was the least known,
and probably the least promising : he apjjroached it,
as it were, from below. But this had the consequence
of giving to his original mind in two ways a special
direction. First of all, it enabled him to look at natural
objects from a more general point of view, not as a
zoologist or as a botanist, but as a naturalist and a
biologist — i.e., from the more general view of the pheno-
mena of Life.^ Indeed he himself seems to have been
the first, if not to use, at least to introduce in his
published writings, the term " biology." ^ And secondly,

' ' Philos. Zool..' Discours pre-
lim., p. 31: "Le vrai moyeu de
])arvenir a bien connaitre un objet,
uieine daus se.? plus petits details,
c'est de comtnencer par I'envisager
dans son entier ; par examiner
d'abord, soit sa masse, soit son
etendue, soit I'ensemble des parties
qui le composent ; par rechercher
quelle est sa nature et son origine,
quelles sont ses rapports aveo les
autres objets connus ; en un mot,
par le considerer sous tous les
points de vue qui peuvent nous
eclairer sur toutes les g^neralit^s
i|ui le concernent." P. 32 : " La
n^cessit^ reconnue de bien observer
les objets particuliers a fait naitre
riiabitude de se boruer a la con-
sideration de ces objets et de leurs
plus petits details, de maniere
qu'ils sont devenus, pour la j)lu-
part des naturalistes, le sujet prin-
cipal de I'etude. Ce ne serait
cependant pas une cause reelle de
retard pour les sciences naturelles,
si Ton s'obstinait k ne voir dans les
objets observes que leur forme,
leur dimension, leur parties bk-
ternes, memes les plus petites,
leur couleur, &c., et si ceux qui
se livreut k une pareille etude
dedaignaient de s'elever h, des con-
siderations sup^rieures, comme de

chercher quelle est la nature des
objets dout ils s'occupent quelles
sont les causes des modifications ou
des variations auxquelles ces objets
sont tous assujettis, quels sont les
rapports de ces memes objets entre
eux, et avec tous les autres que
Ton connait," &c.

'•^ Lamarck in his ' Hydrog^o-
logie,' in an appendix (p. 188)
which seems to be a rehear.sal of
his opening lecture of 1801, an-
nounces a work, 'Biologic,' as a
sequel, being the third and last
part of the Terrestrial Physics.
This work was not published, but
was probably comprised in his
' Philosophic Zoologique.' See Prof.
A. S. Packard's excellent work on
Lamarck, ' The Founder of Evolu-
tion, his Life and Work,' London
and New York, 1901. As La-
marck's writings are very scarce
and his teaching only imperfectly
understood, frequently misrepre-
sented, even bj' competent author-
ities, and in popular opinion sur-
rounded by mystery and sometimes
treated with ridicule, the work of
Prof. Packard is most welcome.
It contains copious extracts — un-
fortunately all translated — from
the earlier biological writings and
lectures, which are otherwise al-

ON THE GENETIU VIEW OF NATURE.

8i::5

it intnjducetl hiui to the study of ;iiiiiiial life from that
side where organisation, the phenomena and the organs
of life were the simplest, rudimentary as it were, an<I
unformed. Here the great differences of form, the
morphological differences which the observation of the
higher and more developed creatures force upon our
attention, disappear ; not the marked differences, but
the numerous relations, tlie endless varieties and re-
semblances, seem to command our consideration. These
seem to be much more likely to " make us understand
the beginnings of all organisation as well as the cause
of its complexity and of its development." ^ Now in
descending in the scale of the living objects of nature,
Lamarck was struck by the fact that many of the
phenomena of life which in the higher animals seemed
to originate within were in tlie lower creatures produced

most inaccessible. According to
Huxley (Lecture "On the Studv
of Biology," 1876, and " Evolution
iu Biology," ' Kncy. Brit.,' 9th ed.),
there were .simultaneously three
independent attemjjts to treat the
phenomena ot' organic life as a
whole and in connection, emanat-
ing from Bichat and Lamarck in
France, and from G. R. Treviranus
in Germany. Tiie great but un-
finished work of the latter, witli
the title
phie der
begun in 1796, when the author
was only twenty, but the finst
volume was not published till 1802,
one year after Lamarck's ' Hydro-
gdologie.' Haeckel in his ' Natiir-
liche Schiipf ungs geschichte ' gives
some account of Treviranus' ideas
(Band L Vorlesung 4). Although
so much has been written aliout
"Biology," the deliiiition of the
science is still uncertain. Prof.

Biologic oder Philo.so-
lebenden Natur,' was

Goebel says: "The word Biology
is one of those conceptions of
modei'n times which have not yet
arrived at a generally accepted
limitation. Some understand by
it the whole science of living
things, others only the doctrine
of the phenomena of life iu con-
trast to the purely de.scri])tive
branches "' ( ' Pflanzeubiologische
Schilderuiigen,' Marburg, 1889, vol.
i. p. 1). A\'ith Lamarck biology was
only one division of a general
science of nature, for he says
(' Hydrogdologie,' p. 8): "Toutes
ces considerations partagent natur-
ellement la physique terrestre en
trois parties essentielles, dont la
premiere doit cotnpiendrc la thcorie
de ratmosphere, la Meteorolugie,
la seconde celle de la croute externe
du globe, I'Hydrogeologie ; la troi-
sieme enfin, celle des corps vivants,
la Biologic."

' Philos. Zool. , vol. i. I). 30.

314 SCIENTIFIC THOUGHT.

or excited from outside, and he was thus led to the
conception that nature herself, through the environment,
did a great deal for the lower creatures which in the
gradual development of the higher ones she knew how
to make them do for themselves.^ In fact, the idea is
worked out in the ' Philosophic Zoologique,' that if we
commence the study of living creatures from below, and
from the side of vegetable life, we are inevitably led
to the conviction that the surrounding conditions and
21. influences, the environment, are gradually and slowly

"Environ- . i i i •

ment." modifying the elementary organisms, and through habit
and inheritance '^ developing the higher ones, endowing
them with more specialised organs and more complex
powers and activities.

Lamarck is aware that these ideas sound strange and
novel, and he is quite prepared to admit in the reception
of them by his readers the same inevitable force of habit
which, as it only permits gradual modification of the forms

^ Philos. Zool., ' Avertissement,' un grand nombre d'animaux de-

p. 13 : " Ayant remarque que les | vaient se trouver dans le meme
mouvements des animaux ne sont cas ; eb comme j'avais eu bien des

jamais communiques, mais qu'ils ' occasions de remarquer que, pour

sont toujours excites, je reconnus ' arriver au meme but, la nature
que la nature, obligee d'abord d'em- variait ses moyens, lorsque cela
prunter des milieux environnants ^tait n^cessaire, je n'eus plus de
la jDuissance excitatrice des tnouve- doute a cet egard."
ments vitaux et des actions des "Ibid., p. 13: " Je ])us saisir le

animaux imparfaits, sut, en com- fil qui lie entre elles les causes
posant de plus en plus I'organisa- nombreuses des phenomenes que

tion animale, transporter cette ; nous offre I'orgauisation animale
puissance dans Tinterieur meme de dans ses developpements et sa
ces etres et qu'^ la fin elle parvint diversite, et bientot j'apergus I'im-
h, mettre cette meme puissance h, la portance de ce moyen de la nature,

disposition de I'individu." P. 12 : I qui consiste h, conserver dans les
"Ayant consid^r^ que sans les nouveaux individus reproduits tout
excitations de I'int^rieur, la vie ce que les suites de la vie et des

n'existerait point et ne saurait se | circonstances influentes avait fait

maintenir en activity dans les \ acqu^rir dans I'organisation de ceux

vdg(?taux, je reconnus bientot qu' ' qui leur out transmis I'existence."

ON THK OENKTIC VIEW OF NATURE. 315

of nature, so also opposes a great resistance to any sudden
change of opinion. " I5ut it is better," he says, " that a
truth once perceived sliould struggle a long time to obtain
merited attention than Lliut everything that the ardent
imagination of man produces should be easily accepted." ^
Whereby it may appear to us worthy of note that
Lamarck did not stop to reflect on the existence of those
sudden changes by which such powers as the " ardent
imagination of man " are continually breaking through
the slow action of habit. The doctrine of the mutability
and variability of species, of the influence of the environ-
ment on the habits, and through them and inheritance
on the forms of living creatures, was thus opposed to
the prevalent doctrine of the fixity of species and the
permanence and recurrence of types. Through these
generalisations, and through the larger ^^ew which
Lamarck took of the phenomena of nature and of life,
he stepped outside of that school of natural studies
which was then dominant in his country, and approached
the teaching;s of the German philosophers of nature, such 22.

'=' r 1 Tlie"Natur-

as Schelliny;, Oken, and Steffens, with whom Goethe is pj'i'oso-

o' ' ' pine.

frequently associated, who, rather than limit themselves
to the patient study of detail, indulged in fanciful
theories on the origin of life, the genesis and metamor-
phosis of forms, and the ideal significance of natural
phenomena and processes. A wide gap separated the
speculations of the author of the ' Flore fran^aise,' the
'Histoire des Animaux sans Vertfebres,' and the 'Memoires
sur les Coquilles fossiles des environs de Paris ' from those
of the German school, yet it cannot be dcni(nl tliat in

1 Philos. Zoo)., p. 15.

316 SCIENTIFIC THOUGHT.

many passages of the ' Hydrogeologie,' where he specu-
lated on matters of chemistry, geology, and meteorology
without the necessary foundation of facts, such as he
possessed in botany and zoology, he laid himself open
to the criticism and ridicule ^ of his more cautious
opponents. Thus it happened that the most original con-
tributions to science were forgotten or disregarded for
more than half a century, after which time Lamarckism
became a familiar term in speculative science, denoting
one of the great ideas with which the genetic view of
nature operates — viz., the influence of environment,
adaptation, acquired habits, in the development of living
organisms.
23. In the history of the genetic view of nature, the

Lamarck

^nd von positiou of Lamarck may be regarded as, in a certain
sense, complementary to that of von Baer. Both brought
the study of living forms back to that of their origins
— Lamarck to the study of the lowest forms of animal
creation, the great variety and abundance of which he
was the first to attempt to put into some order ; von
Baer to the study of the embryonic beginnings of the
higher organisms, on which important subject he was
one of the first to throw some light. Though widely

^ See, inter alia, what Cuvier
wrote in his ' Eloge de Lamarck,'
which was read posthumously in

meme paix que la theorie chim-
ique " ; and farther on he touches
on one of the weakest points of all

the Academy by Silvestre, ■26th ■, genetic speculations (p. sxii) : " Le

November 1832 (' Mem. de I'Acad. i temps sans borne qui joue un si

des Sciences,' vol. xiii. p. xx), j grand role dans la religion des

with omissions to tone down its I mages, n'en joue pas un moins

severity : ' ' Quelque int^ret que ces | grand dans toute cette physique

ouvrages excitassent par leurs par- \ de M. de Lamarck, et c'etait sur

ties po.sitives, personne ne crut lui qu'il se reposait pour calmer ses

leur partie systematique assez ' propies doutes et pour repondre

<langereuse pour meriter d'etre ] a toutes les objections de ses

attaquee ; on la laissa dans la ' lecteurs."

ON TIIK GENKTIC VIKW OF NATURE.

317

different in their mental attitude, the two men agreed
in lookinii for tlie advancement of natural science in
an understamling ol' the simpler, unspecified, and un-
dittl'rentiateil forms or stages of existence out of which
they conceived the more complex to have grown or de-
veloped by a process of specialisation or differentiation.
Many other naturalists and philosophers contributed,
partly independently, partly through the influence of
Lamarck's systematic and von Baer's endiryological
labours, to elaborate the same ^•iew and strengthen the
same tendency of thought and research. Nor were
there wanting suggestions as to the ultimate philo-
sophical drift of the line of reasoning. It is doubtful
whether these speculations, like those of Oken in his
' Physio-philosophy,' did not retard rather than promote
the acceptance of the genetic view by scientific thinkers : ^

' On tlie position of Uoetlie and
Oken in the history of the genetic
view, see Carus, ' Geschichte der
Zoologie,' p. 723 ; von Baer,
' Reden und wissenscliaftliche Ab-
handluiigen,' Bd. II. p. '2.')8, «kc.
Both consider Lamarck as the real
originator of a scientific theory of
Descent. Von Baer gives an amus-
ing account of the extent to which,
as early as 18-29, actual genealogical
trees were given in Jacob Kaup's
' Skizziitc Kntwickelungsgeschichte
und naturliches System der Eur-
opaeischen Thierwelt.' Von Baer
sums up his historical account in
the following words (p. 26-1): "In
general 1 believe that at that time,
when the succession of different
animals and plants in the history of
the earth — and generally from im-
perfect to more perfect organisms
— occupied the thoughts of natural-
ists, and when, at the same time,
tlie study of development of single

I organisms had taken a new start,
I the notion of their 'I'ransformation
I was pretty generally accepted.'"
The view expiessed here by von
Baer would probably have to
be limited to German naturalists at
that date. It must, however, bo ad-
mitted that the fairest exposition
and criticism of the arguments of
Lamarck at that earlj* date is prob-
abh' to be found in Lyell's ' Prin-
ciples of Geology' (vol. ii. Bk. III.
chap. i. to iv. ) He there also con-
siders the arguments derived from
embryology as contained in the re-
searches of Thiedemann, confirmed
by Serres ('Anatomic Compareo du
Cerveau,' 1824), and comes linally
to the result that— 1. "There is a
capacity in all species to accommo-
date them-selves." 2. " Tliat the
mutations thus superinduced are
governed by constant laws." 3.
That " some acquired jieculiarities
of form, structure, and instinct are

318

SCIENTIFIC THOUGHT.

24.
Tlie
' Vestiges. '

they belong, therefore, more to the history of philo-
sophical than to that of scientific thought. There is,
however, one instance of which it is necessary to take
a passing notice.

In the year 1844 a book appeared which in nine
years, up to 1853, ran through nine large editions. It
was anonymous,^ and bore

trau.smissible to the offspring." i.
That " indefinite divergence " from
the original type is "prevented."
5. That " tiie intermixture of dis-
tinct species is guarded against by
the aversion of the individuals com-
posing them to sexual union." 6.
That "it appears that species have
a real existence in nature, and that
each was endowed, at the time of
its creation, with the attributes
and organisation by which it is
now distinguished." Tlie reviewers
of Lyell's work — such as Whewell
{'Quarterly,' vol. xlvii. p. 113) —
treat Lamarck with much less
gravity than Lyell himself, who
evidently had studied the ' Philoso-
phic Zoologique ' carefully and with
much interest ; which, I am afraid,
was not the case with many others
who then and long after only quoted
certain extreme passages and ex-
amples which had lieen spread in
general literature in a garbled
fashion. Contrast in this respect
what Lyell wrote to G. Mantell in
1827 (' Life of Lyell,' vol. i. p. 168),
wliere he admits having " devoured
Lamarck with pleasure," and though
disagreeing with him, admits that
it is impossible to say " what
changes species may really under-
go," with the remarks of Charles
Darwin — otherwise so careful and
moderate — when lie talks of " La-
marck nonsense " (" Darwin's Life
and Letters,' p. 23) and his " verit-
able rubbish" (p. 29), and attrib-
utes to him statements which such
a careful student of his writings as

tlie title ' Vestiges of the

Prof. Packard has been unable to
trace (see his work on ' Lamarck,'
1901, p. 74). One would be in-
clined to agree with Darwin that
such absurdities have done the sub-
ject more harm than gt)od, but to
attribute them rather to garbled
paraphrases and quotations by La-
marck'scritics (see Darwin to Hooker,
18.53, 'Life,' vol. ii. p. 39) than to
Lamarck himself. More than thirty
years after the publication of the
' Principles,' when, in consequence
of the appearance of the ' Origin of
Species,' the subject of Transmuta-
tion was much discussed, Lj'ell
wrote to Darwin that he had re-
read Lamarck, and admitted that,
" remembering when his book was
written, he felt he had done him
[Lamarck] injustice" ('Life, &c. ,
of Sir Charles Lyell,' 1881, vol. ii.
p. 365). In the same letter Lyell
states that forty years ago (1823)
Provost, a pupil of Cuvier's, told
him his conviction " that Cuvier
thought species not real, but that
science could not advance without
assuming that thej^ were so."

^ Tlie anonymity of the work was
long maintained, and though, after
various guesses as to the author-
ship— attributing it, e.g., to Lyell or
Darwin— had been made, it was gen-
erally believed that Robert Cham-
bers (1802-1871) was the author,
this was not jjublicly admitted till
Alex. Ireland — the last survivor of
the few friends to whom the secret
was committed — published (1884)
the twelfth edition of the book,

ON 'I'lIK (jenktk; vikw of natuke.

.S 1 9

Natural History of Creation.' This book cuuLaiiied a very
clear and popularly intelligible statement of the genetic
or development hypothesis as applied to cosmic, geolog-
ical, and organic phenomena. The importance of the
book did not lie in its own original L(intri])utions, but in
the great controversy Nvhich it occasioned. In this con-
troversy most of the arguments for and against the

with an introduction, in wliieli he
" tohl for the first time " the "story
of the authorship." It is of interest,
after the hipse of liah" a century, to
read the various — mostly liostile —
criticisms of the book in the reviews
and magazines of the day. The
attacks came from two distinct
sides : from scientific authorities,
who — each in his own specific
branch — -challenged the correctness
of single facts, mostly without in-
quiring whether, in spite of many
misstatements, sufficient evidence
was not after all adduced to prove
the main thesis ; and, secondly,
from both scientific and jiopular
writers, who used the well-known
arguments, that the teaching of the
book was unorthodox, both in a
religious and scientific sense. In
fact, they disjilayed in a great
degree scientific and religious dog-
matism and intolerance, and in some
cases considerable temper. To this
larger section of the critical attacks
belonged the reviews in all the
leading periodicals of the day,
headed by the ' Edinburgh Re-
view ' (Adam Sedgwick), the ' North
British ' (Sir David Brewster), the
'Eclectic,' the 'North American'
(Boweu and Asa Gray), the ' Brit-
ish Quarterly.' Tolerance and a[)-
pieciation were, however, shown
by some of those more recent re-
views which were professedly the
organs of freedom, enlightenment,
and progress, notably the ' Pros-
pective' (E. W. Newman) and the
' Westminster ' in two articles, in

the first of which the genetic view
of the ' Vestiges ' is suggestively
contrasted with the purely descrip-
tive of the ' Kosmos.' Looking at
the whole controveisy, the ' West-
minster Review ' (.\liii. 130) seems,
in the light of history, justified iu
maintaining that, after " having
attentively considered the objec-
tions which have been uiged in
numei'ous able criticisms to the
theory and the arguments of the
author," after noting that " learned
men have discovered that he is less
familiar than they with the pedantry
of science," tliat " they have
triumphed in the detection of slips
of the pen, mistakes in technicali-
ties, and some inaccuracies of fact,"
the conclusion is nevertheless justi-
fied that " these detract but little
from the merit of a work which
may be fairly chaiacterised as the
most skilful generalisation ihat has
yet (1848) apj)eared of the results of
geological, astronomical, aud physi-
ological researches made to bear
ujjon the history of the first and
most momentous of all problems —
the order and plan of creation."
It is known that some scientific
men of first rank, such as Baden
Bowell of O.xford, and the lihysi-
ologist W. B. Carpenter (who,
according to Huxlej', was the only
authoiity in this ('nuiitry ac(|uainted
with the 'Entwickelunnsgeschichte'
of von Baer), distinctly supported
the doctrine of the ' Vestiges ' ; and
Darwin himself, who had studied
the ' Vestiges ' with evident cai-e

influence.

320 ~ SCIENTIFIC THOUGHT.

genetic aspect, which have since become familiar, were
very ably stated by scientific as well as by popular
writers. Earlier anticipations of the genetic view were
recalled, the historical s^ketch given in Lyell's ' Prin-
ciples ' was supplemented by reference to many great and
many forgotten authorities, who in more or less distinct
terms had given expression to their belief in a gradual
development of the existing forms and phenomena of
nature out of simpler beginnings, which they described
with more or less precision. It cannot be denied that
the enormous literature which accumulated during the
ten years following the publication of this book unsettled
Po uiar ^^^® popular mind in this country, and prepared it for a
really able, dispassionate, and exhaustive exposition of
the whole subject, and especially of the crucial problem
to which it was narrowed down, the question regard-
ing the fixity or variability, the historical origin and
development or the sudden creation and persistence, of
animal and vegetable species. The genesis of the cosmos
as suggested by Laplace, the geological history of our
earth as worked out by Lyell, the fact of organic growth
and development as given by embryology, seemed clear

(see ' Life of Darwin," V(j1. i. p. 833), : in tlius preparing the ground for
gave probably the fairest verdict on j the reception of analogous views "
tiie book in the historical preface i ('Origin of Species,' 6th ed., 1872

to the later editions of his own
great work, where he saj's : " The
■work, from its powerful and bril-
liant style, though displaying in the
earlier editions little accurate know-
ledge and a great want of scientific
caution, immediately had a very
wide circulation. In my opinion, it
has done excellent service in this
country in calling attention to the
subject, in removing i^rejudice, and

p. xvii). In a history of European
thought it is well to mention that
the ' Vestiges ' had no influence on
the Continent, for rea.sons partially
stated in the text. A little later,
however, a similar " scandale " (as
the ' Grande Encyclopedie ' has it-
art. "R.Chambers and L. Biichner")
arose in Germany on the publication
of ' Kraft und Stofif.'

ON THK GENKTIC VIEW oK NATURE.

321

and plausible enough, but tliere remained the last strong-
hold of the older view, the existence of definite forms of
animal and vegetable life. Were these to be merely classi-
tied and reduced to separate types, as the morphological
view was contented to reduce them, or was the growing
evidence of variability to be interpreted in favour of a
gradual development of the higher out of the lower and
simpler forms of life ? Above all, how was the highest
type of all, man himself, to be regarded in such a com-
prehensive scheme of development ? In Germany many st;.

'^ '^ . Genetic view

great naturalists^ were quite prepared for a consistent '" 9';.""""^

^ x r r and trance.

genetic or developmental view of nature ; in France at
that time the question was not agitated at all, the sug-
gestive writings of Lamarck and St Hilaire having been

^ This does not refer to the
earher writings of Goethe, Oken,
Treviranus, and others, whose
merits, since the appearance of
the 'Origin of Species,' have been
variou.sly estimated by Huxley in
England and by Haeckel in Ger-
many : tlieir speculations had, with
the generalisations of the ' Natur-
philosophie,' been swept away by
the inductive school represented in
botany at that time by von Mohl,
Nageli, and Hofineister; in zoology
by the einbryological school with
von Baer at its head. Of W. Hof-
meister (1824-1877), whose labours
begin about ten years before the
appearance of Darwin's great work,
Julius Sachs says : " The results of
his ' Comparative Researches' (1849
and 1851) were magnificent beyond
all that ha.s been achieved before or
since in the domain of descriptive
botany, . . . the conception of what
was meant by the development of
a plant was completely changed,
. . . the reader was presented with

VOL. 11.

a picture of the genetic connection
between cryptogams and phanero-
gams which could not be reconciled
with the then reigning belief in the
constancy of species. . . . When,
eight years after Hofmeister's
'Comparative Researches,' Dar-
win's theory of descent appeared,
tiie affinities of the large divisions
of the plant-world lay so openly, so
deeply founded, and so clearly be-
fore the ej'es of students of nature,
that that theory had only to recog-
nise what had been made evident
in this line by genetic morph-
ology " (' Ge.sch. d. Botanik,' p. '215,
&c. ) In another direction Nageli,
by his mechanical theory of " the
growth and internal structure of
organisms," which he reduces to
" physical, chemical, and mechanical
processes" (1860), fell in with Dar-
win's attempt to " reduce the earlier
purely formal consideration of or-
ganic structures to a causal (genetic)
view" (ibid., p. 373).

322

SCIENTIFIC THOUGHT.

entirely overruled by the authority of Cuvier.^ In
England, where geology and natural history were always
popular pursuits, the question was one of more than
scientific interest : it was one which had been appropri-
ated by general literature,'' and the larger bearings of

^ Huxley describes the position
of France and Germany to the doc-
trine of descent as follows: "In
France the influence of Elie de
Beaumont and of Floureus, to say
nothing of the ill-will of other
powerful members of the Institute,
produced for a long time the effect
of a conspiracy of silence. . . .
Germany took time to consider ;
Bronn produced a . . . translation
of the ' Origin ' . . . ; but I do not
call to mind that any scientific
notability declared himself publicly
in 1860. None of us dreamed that
in the course of a few years the
strength (and perliaps, I may add,
the weakness) of ' Darwiuismus '
would have its most extensive and
most brilliant illustrations in the
land of learning. If a foreigner
may presume to speculate on the
cause of this curious interval of
silence, I fancy it was that one
moiety of the German biologists
were orthodox at any price and the
other moiety as distinctly hetero-
dox. The latter were evolutionists
d priori alreadj'," kc. (' Life of Dar-
win,' vol. ii. p. 186). The two men
abroad to whose opinion English
biologists of that day would prob-
ably attach the greatest value were
Karl Ernst von Baer and Milne-
Edwards. The former " wrote to
Huxley in August 1860, expressing
his general assent to evolutionist
views" {loc. cit., p. 186, note). It
was von Baer from whom Huxley
admits to Leuckart that he learnt
the "value of development as the
criterion of morphological views"
(' Life of Huxley,' vol. i. p. 163). Von
Baer later ou qualified his adher-

ence, admitting development only
within the regions of the different
types which he had established (see
the second volume of his collected
papers). The opinions of the great
contemporary French zoologist,
Henri Milne-Edwards (1800-1SS5),
are fully given in the last chapter of
his very interesting ' Rapport sur
les progres recents des Sciences
zoologiques en France' (1867),
where he also refers to the writings
of Isidore Geoffroy Saint-Hilaire,
who in France continued to some
extent the line of research and
reasoning which, through his father,
Etienne Geoffroy, and Lamarck,
dates back to Buffon, Bonnet, and
other philosophical naturalists, of
whom, under the name of " Trans-
formistes," M. Edmond Perier has
given a connected account in his
very valuable historical work, ' La
Philosophic zoologique avant Dar-
win " (1884). Milne -Edwards re-
mained to the end unconvinced by
the arguments of Darwin. He had
already in 1853 set forth his ideas
referring to the general problems of
zoology, and he repeated them in
1867 (loc. cit., p. 432 sqq.) It is,
however, well to note that ever
since 1827 [loc. cit., p. 453, note) he
had contributed largely to the
furtherance of the genetic view by
his principle that progress in nature
depends on division of labour. In
his subsequent writings he dwells
with much success on this principle
of the " division of physiological
labour." (See Spencer, 'Biology,'
voh i. p. 160.)

'■^ About ten years after the con-
troversy about the ' Vestiges ' had

ON THE GENETIC VIEW OF NATURE.

323

which liad been fullv dcuionstiaLed to the educated and
reading public. There lias always existed in this country
a class of literature which is almost entirely wanting, or
has died out, on tlie Coiitinenl. The value of this class
of literature has been difTerently gauged, but it never-

tilled the columns of the foremost
British periuilicivls, we lincl in
Germany a similar agitation origin-
ating through the publication of
several works whicli have since
been generally considered as the
purest expression of Materialism.
The controversy begins in 1852
with tlie publication of Rudolf
Wagner's ' Physiological Letters,'
Moleschott's ' Kreislauf des Le-
bens,' and Carl Vogt's ' Bilder aus
dem Thierleben ' ; it came to its
height, after the appearance (in
18.5.5) of L. Biichner's 'Kraft und
Stoff,' and occupied the meeting of
scientific and medical men which
was held in Giittingen in 1854.
The subject belongs essentially to
the history of philosophical thought,
and can be studied in the very fair
and exhaustive ' History of Materi-
alism ' written by F. A. Lange, with
a distinctly' idealistic tendency
(English translation, three vols., by
Thomas, 1880). I mention the sub-
ject in this connection, because in
Germany and England attempts
were made about the same time to
found a general philosophy of life
ui>nn the teachings of science. This
had b<_'en done about two generations
earlier in France by the " Sensu-
alistes " and the " Ideologues." For
a French public neither the English
nor the German controver.sy pre-
sented any essentially new feature,
or disclosed any novel aigument.
The older orthodox conceptions had
been abandoned very largely in
France in the eighteenth century,
and at once replaced by concep-
tions derived from science. In
'Germany a similar movement took

l>lace, likewise during the eight-
eenth century ; but, instead of
exact science, it was the prevailing
idealistic philosophy wiiich was
apjiealed to for the purpose of
gaining new foundations, and
science only came in when the
speculative restoration was gener-
ally considered to have failed. In
England, which had really supplied
the beginnings both for the French
sensualistic philosophy thiough
Locke, and for German criticism
through Locke and Hume, the
older orthodox foundations were
not materially shaken before the
middle of the nineteenth cen-
tury. Tiie author of the ' Ve.s-
tiges ' distinctly ai)peals to science,
though, in a religious spirit, de-
siring to make it helpful for a
general philosophical, and not
merely an industrial, jiurjiose.
Again, the English movement,
which really culminated in Herbert
Spencer, differs from the German,
being more influenced by biological
conceptions, whereas in Germany
the extreme system of Biichner
took ])urely mechanical, though
ill-defined, ideas — force and matter
— as the shibboleth. It is signif-
icant, as showing the great general
importance of Darwinism, that
through it both the controversy
over the ' Vestiges ' in England
and that over ' Materialismus ' in
Germany were soon cast into
oblivion, though they had both to
some extent prepared the way (see
Lange, ' Gesch. des Mat.,' p. 570,
Ausg. 1867; and Haeckel, 'Schop-
fungsgeschichte,' vol. i. p. 98, 9
.\utl.)

324 SCIENTIFIC THOUGHT.

theless forms an important feature in the development of

English thought, if not also of English science. It is

27. the apologetic literature, those works which deal with

Apologetic

literature in what liave bccu termed the " Evidences." In the absence

England.

of any scientific theology based upon accurate historical
research and philosophical criticism, such as has existed
with many good and some evil results since the end of
the eighteenth century in Germany, the need was felt
for defending or interpreting those answers to the great
problems of Nature, Man, and Life, which seemed bound
up with the Christian belief, or suggested by the sacred
writings. The teaching of science had not become, as in
France, a purely secular occupation ; instruction was not
separated from education ; apologetics had not become
doubtful through the bad faith and duplicities of cynica
like Voltaire, nor ridiculous through the puerilities of
shallow writers such as Campe in Germany. Many
serious minds were occupied with the growing dis-
crepancies between scientific and popular religious teach-
ing, and believing they could discern the drift of the
former, they made various more or less successful
attempts to effect a reconciliation between the moving
and developing conceptions of scientific thought and the
fixed and unalterable ideals of religious belief. Such
attempts must be doomed to failure, or at best they
offer an individual solution, interesting only if it
happens to be the inspiration of a poet or if it repre-
sents the creed of one of the few great and soaring
intellects which appear once or twice in a century.
The conviction is gradually gaining ground that scientific
and religious thought emanate from two separate centres.

ON THE GENETIC VIEW OF NATURE.

325

that although they ineviLably come into frequent con-
tact, tlie study of their independent origin and history
and their different psychological method is more valuable
than a temporary and meiely ephemeral compromise of
their respective doctrines. Happily this country has
produced many great and a few thinkers of the first
order, in whom the greatest that scientific thought
has achieved was in harmony with a truly religious
spirit. Tn contemplating these illustrious examples,
and bowing before their greatness, the popular mind
will probably find its conviction of the possibility of
an ultimate reconciliation of both aspects more strength-
ened than by leaning on the doubtful support of a
voluminous apologetic literature, which proposes to give
general proofs where only individual faith can decide.

I deemed it appropriate to offer these few remarks
on the whole of the voluminous literature ^ from Butler

^ The largest and best known
type of publication in this class of
literature, which is jjractically un-
known on the Continent, but which
belongs to our jioriod, is found in
the Bridgewater Treatises " On the
Power, Wisdom, and Goodness of
God, as manifested in the Creation."
The circumstances under which
this series was published are .-^et
forth in the ])reliminai\v notice to
the first treatise. The Earl of
Bridgewater, heir to the title and
fortune of Francis Egerton, thii'd
Eai'l of Bridgewater, who con-
.structed from the plans of James
Brindley, and in accordance with the
idea of liis fatiior, Lord Chancelhir
Egerton, the tirst of the large canals
in England, from his coal mines at
Worsley to Manchester and Liver-
pool, left in his will to the Royal
Society tl»e sum of £8000, which.

witli its accruing interest, was to
be paid to the person or persons
selected by the President and ap-
pointed to write and ])ublish one
thousand copies of a wurk with the
above title, — " illustrating sucli
work by all reasonable arguments,
as, for instance, the variety and
foi'ination of God's creatures iu
the animal, vegetable, and mineral
kingdoms ; the effect of digestion,
and thereby of conversion ; the
construction of the hand of man,
and an infinite variety of other
arguments ; as also by discoveries,
ancient and modern, in arts, sciences,
and the whole extent of literature."
The series contained works by such
foremost men of science as Sir
Charles Bell, AVilliam Whewell,
William IVout. and William Buck-
land.

o

26 SCIENTIFIC THOUGHT.

to Drummond whilst I was dealing with the ' Vestiges,'
because the latter is probably the last example of that
class of books in which purely scientific thinkers took
any great interest. Similar publications which have
since appeared have made no impression on the course
of scientific thought, though they may have won a
place in the popular literature of their day. To bring
about that complete separation and independence of
the scientific and the religious arguments in this country
which has been recognised during the whole of the
nineteenth century on the Continent, two books have
probably contributed more than any others : Dean
28. Mansel's Lectures,^ ' On the Limits of Eelis;ious ThouQ-ht,'

Manseland ® '^^

Darwin. through its Unanswerable logic : and Darwin's ' Origin of
Species,' through treating fearlessly a scientific argu-
ment which was based upon observation and expanded
by legitimate inference without any reference to the
ulterior consequences which might be drawn from it.
It required some courage to attack a problem l)eset
with such difficulties and which had become hackneyed

^ It is a remarkable coincidence,
showing the general tendencies of
English thought about the middle

previously, belong to a different
section of this ' History.' We shall
there see that in the negative por-

of the century, that Dean Mansel's | tion of this analysis lie also the

" Bampton Lectures " appeared
just a year before the ' Origin of
Species.' The argument of the

germs of the ideas put forward by
Herbert Spencer and Huxley under
the well - known terms of the

Lectures "On the Limits of Re- I " Unknowable" and "Agnosticism,"

ligious Thought " was that which
was elaborated by Sir William
Hamilton on the lines of Kant's
' Critique of Pure Reason ' in his
celebrated article in the ' Edinburgh
Review ' on the " Philosophy of the
Unconditioned." A further ap-
preciation of this line of reasoning,
which had its beginning in Hume's
sceptical writings a hundred years

and there is no doubt that both
Hamilton and Mansel had a con-
siderable influence in forming
Huxley's attitude in this respect.
He .says, in 1863 ('Life,' vol. i. p.
242) : " I believe in Hamilton,
Mansel, and Herbert Spencer so
long as they are destructive, and
I laugh at their beards as soon as
they try to spin their own cobwebs.'

ON THK (JENETKJ VIKW f»K NATURE.

327

had always
which iiiisht

Ihrougli periodical and popuhir literature. Others who.
Ijefore Darwin, treated similar controversial subjects,
such us Whewell, liabbage, Herschel, Lyell, Baden
Powell, and the author of the ' Vestiges,
taken into account the possible inferences
be drawn from their seientitic statements, and had often-
times toned thcni down sf) as not to offend existing
opinions.^ Darwin thought it more modest and more
becoming for an independent scientific thinker to state
his side of the question completely and simply, without
presuming to attack or to support a view of things
which lay outside of the dominion and the powers of
science. And this is not the least of the many reasons
why his work has created an era, especially in this

^ The position adopted by several
of the eminent forerunners of Dar-
win is interestingly analysed by
Huxley in the chaj)ter on the " Re-
ception of the ' OrigMi of Species ' "
contributed to the .second volume
of the ' Tjife and Letters of Charles
Darwin.' Of Lj^el!, who had come
nearest to the doctrine of unbroken
descent of species, Huxley sa3-s
(vol. ii. p. 193): "I see no reason
to doubt that if Sir Charles Lyell
could have avoided tlie inevitable
corollary of the pithecoid origin of
man — for which to the end of his
life he entertained a profound
antipatliy- — he would have advo-
cated the efliciency of causes now
in o])eratioii to bring about the
condition of the organic world, as
stoutly as he championed that
doctrine in reference to inorganic
nature." And Lvell himself wrote
to Darwin in 1S63 (' Life of Lyell,'
vol. ii. p. IBG.'J) : "I rcmemlier that
it wa.s the conclusion lie [Lamarck]
came to about man tiiat fortified
me thirty years ago against the
great impression wliich his argu-

ments at first made on my mind."
Treviranus, the author of the
' Biologie,' the contemporary of
Lamarck, was quite conf.isteiit in
his views of descent and mutabil-
ity, for he declares against catas-
trophism, believes in the evolution
of higher .species from the zoophytes,
and even in that of a higher species
than man (see ' Biologie,' vol. ii.
p. 225, kc.) Neither in German}'
nor in France, at the beginning of
the century, did those prejudices
exist which in 1S59 prevented even
Darwin frcjm developing to the full
the consequences of his main thesis.
This was done in his later works.
See his letter to A. R. Wallace,
22nd Dec. 18.57 ('Life,' vol. ii. p.
109): "You ask whether I shall
discu.ss 'man.' I think I shall
avoid the whole subject, as so sur-
rounded witli prejudices ; tliough 1
fully admit that it is the higliest
and most inteiesting problem for
the naturalist. My work, on which
I have now been at work more or
less for twenty j'ears, will not fix
or settle anything."

view

328 SCIENTIFIC THOUGHT.

country, not only in the region of scientific, but quite
as much in that of philosophical, thought.
29. So far as the purely scientific aspect is concerned, the

Truiiiii)h of r J £■ >

^^p^^senetic ' Origin of Species ' firmly established the genetic or
developmental in the place of the morphological view, or
the earlier purely systematic and classificatory treatment
of the objects and processes of nature ; and it is interest-
ing to note how the period from the publication of the
' Vestiges ' to that of the ' Origin of Species,' the fifteen
years from 1844 to 1859, was also the period during
which Humboldt published his 'Kosmos' — the r6sum6
of the labours of a lifetime. This was the consumma-
tion of that aspect of nature which I have termed the
purely morphological one, and which in his mind was
expanded to the panoramic view : the attempt to unroll
before his readers a picture or panorama of the whole
world as the scientific mind was then able to see it.
Nature appeared mapped out in bold and characteristic
lines and colours, without allowing the questions of past
history or future development, — the origin, life, and
fate of the cosmos, — to present itself at all. The fact
that this latter question was professedly excluded as
foreign, or premature, is probably the reason why the
book attracted so little attention in this country, where
a new manner of treating all the problems of natural
science was being inaugurated ; but it is interesting to
learn from Darwin that his whole life was influenced ^

' See ' Life and Letters of Charles I duction to the Study of Natui-al

Darwin,' vol. i. p. 25 : " During my I Philosophy,' stirred up in me a

last year at Cambridge I read with burning zeal to add even the most

care and profound interest Hum- humble contribution to the noble

bold t's ' Personal Narrative.' This structure of natural science. No

work, and Sir J. Herschel's 'Intro- ! one or a dozen other books influ-

ON THE GENETIC VIEW OF NATLKK.

329

and his studies directed by reading and re - reading
Humboldt's ' Personal Narrative.' The ' Kosmos ' of
Humboldt closed the older, the ' Origin of Species '
of Darwin opened the new, epoch of natural science :
the former was retrospective, the latter prospective.
Both works owe their origin to a visit to the same
portion of the globe, to a study of the subtropical scenery
and life of South America — Humboldt having visited
the inland, Darwin specially the maritime and island
scenery.^ It is further of interest to note how the

30.
Huiiiboldt's
' Kiisrtios '
.iiid the
' Origin of
Sjitcies.'

enced me nearly so much as these
two. 1 copied out from Humboldt
long pas.sages about Tenerifie," &c.
Also vol. i. p. 337 : " I never
forget that my whole course of life
is due to having read and re-read
as a youth Humboldt's ' Personal
Narrative.'"

' Besides Darwin and Lyell, to
whom, of British naturalists as rep-
resenting the genetic view in the
middle of the century, I have so far
confined my remarks, there were
at that time two other eminent nicn
working in the same direction. The
views of these two were likewise
much influenced by travel and by
the study of plant and animal life
in distant countries. I refer to Sir
J. D. Hooker and Mr A. Russel
Wallace. The important part which
these men played in the gradual
conception and birth of the ideas
which were for the first time com-
prehensively set forth in the ' Origin
of Species ' is lucidly and imparti-
ally told by Hu.xley in the well-
known chapter which he con-
tributed to the second volume of
the ' Life and Letters of Charles
Darwin,' edited by his son, Professor
Francis Darwin, in 1887. Few
episodes in the history of thought
have been treated with greater
mastery. Few botanists liave

j)ossessed a greater })ersonal know-
ledge of different and gieatly vary-
ing floras than Sir J. D. Hooker,
who succeeded to the position and
labours of his father. Sir W. J.
Hooker, at Kew. After having
accompanied Captain Ross on his
Antarctic expedition for the dis-
covery of the South magnetic pole,
he became best known by his
'Himalayan Journal' (1854). It
was in constant correspondence and
intercourse with Hooker that Dar-
win, from 1844 to 18.')9, wrote his
first great work. The important
original contributions of Mr Wal-
lace are well known, and the story
how his paper, " On the Tendency
of Varieties to depait indefinitely
from the Original Type," reached
Darwin when he had got half
through the larger work which he
was tiien writing, how this coinci-
dence hastened the publication of
the two ])apers by Wallace and
Darwin, which "contained exactly
the same theory," in the 'Journal
of the Limiiuan Society ' (Zoology,
vol. iii. p. 45), has been told by
Lyell and Hooker (ibid., letter to
the secretary), and by Darwin him-
self (Autobiography, in ' Life,' &c. ,
vol. i. p. 84). No mystery lies
upon the history of the first enun-
ciation of the doctrine of natural

330

SCIENTIFIC THOUGHT.

same year which witnessed the appearance of the work
of Darwin was also that of the invention of Spectrum
Analysis, that great instrument by which astronomy,
doomed by the purely mathematical treatment to be-
come simply " une question d'analyse," was once more
enrolled among the natural sciences ; the means being
supplied for that natural history of the heavens which is
now one of the most progressive and fascinating branches
of science. The reader who has realised from the fore-
going exposition how the genetic view of nature was
anticipated by earlier writers on cosmology, such as
Leibniz and Laplace, how it obtained in geology through
Hutton and Lyell, how it became dominant in embryo-
logy through von Baer, and how the morphological
treatment broke dow^n through the recognition of the
variability of species and the impossibility of deiining
clearly the landmarks of zoological and botanical classi-
fication, will readily understand the importance and
timeliness ^ of Darwin's work, which proposed to deal

selection, no national or personal
jealousies obscure the issues which
were then at stake ; neither of the
two great naturalists has ever put
forward aiij' complaint that the
other has not fairly and generously
dealt with his own merit. Since
the death of Darwin Mr Wallace
has written the well-known book
which, under the title of ' Darwin-
ism ' (London, 1889), gave to many
readers the first comprehensive
account of the celebrated theory
which is generously identified with
the sole name of only one of its
original propounders.

^ Both propounders of the theory
of natural selection have in their
subsequent writings referred to
those who prepared the way be-

fore them, and Mr Wallace has
taken special pains to explain why
a doctrine which was so well pre-
pared, and even anticipated, had
not been more distinctly accepted
before the ap[>earance of the ' Origin
of Species' ('' Darwinism," chap, i.) :
" Notwithstanding the vast know-
ledge and ingenious reasoning of
Lamarck, and the more general
exposition of the subject by the
author of the ' Vestiges of Creation,'
the first step had not been taken
towards a satisfactory explanation
of the derivation of any one species
from any other. Such eminent
naturalists as Geoffroy St Hilaire,
Dean Herbert, Professor Grant,
von Buch, and some others, had
expressed their belief that species

ON THK GENETIC VIKW oK NATL'HK. 331

specially with the actual tact and the luiictiuii uf vaiia- 3i.

'■ '' "Varia-

tion ill the domain of living beings. He pushed the ^io"-"

problem of variation and variability into llie foreground,

and discussed one of its inaiii features — \\z., its possible

etlect and results. Since his time the eye of every

botanist, every zoologist, and every einl )ryologist has

l)een directed towards the varialjility, transition, and

genesis of forms, to their history rather than to their

portraiture, whereas before him it was mostly attracted

by their seeming fixity and recurrence. Variations have

been studied on the large and on tlio minute scale in

geological strata at home ami abroad, and the vexed

question has been raised as to their causes and laws, —

Darwin having been mainly occupied with their existence

and operation, the results which they brought aV)0ut, the

gradual alterations of the forms of living things. On

this side he tells us that he found an important clue

through reading a book which had appeared at the very

end of the eighteenth century, Alallhus's ' Essay on the

Principle of Population.' ^

arose as .simple varieties, and tliat | 1798, and in the enlarged and much

the species of each genus were all | improved form in which it is now

descended from a common ancestor ; I known in 1803. Darwin seems to

but none of them ><ave a clue as to ' have come upon it accidentally. In

the law or the method by which
the change had been effected. This
was still ' the great mystery ' " (p.
6). " Darwin, by his discovery of
the law of natural selection and his
demonstration of the great principle
of tlie preservation of useful varia-
tions in the struggle for life, lias
not only thrown a Hood of light on
the process of development of the
whole organic world, but also estab-
lished a firm foundation for all
futui-e studj- of nature " (p. 9).

his Autobiography (' Life,' vol. i.
p. 83) he writes : " In October 1 838
— that is, fifteen months after I had
begun my systematic iuquirj- — I
happened to read for amusement
' Malthus on Population,' and being
well prepared to apjireciate the
struggle for existence which every-
where goes on, from lonij-continued
observation of the hat>its of animals
and plants, it at once struck me
that under these circumstances
favourable variations would tend

This essay apjieared first in ' to be preserved, and unfavourable

332 SCIENTIFIC THOUGHT.

32. The ideas and reflections contained in this celebrated

Malthus.

essay, which has played a prominent part in the philo-
sophical literature of economics, could not have occurred
to any one who had studied human society or nature
merely in individual specimens or isolated cases ; for
they referred not so much to the natural history of a
single being, as to the peculiar relations and complica-
tions which arise in a community or society of beings,
some of these being applicable quite as much to animal
and plant life as to the life of men. In fact, it was a
chapter in the science of bionomics. Malthus, Darwin,
and Wallace were not " laboratory naturalists, to whom
the peculiarities and distinction of species, as such, their
distribution and their affinities, have little interest as
compared with the problems of histology and embryo-
logy, of physiology and morphology." ^ The problem of
population, whether it refers to man or other living
creatures, is one that will force itself upon those who
study nature and mankind on the large, on the outdoor,
scale, not as does the collector or dissector of specimens.
How has the face of the earth been peopled l)y plants,
animals, and human beings ? What are the forces which

ones to be destroyed. The result book on Population came into his

of this would be the formation of hands, the idea of natural selection

new species. Here, then, I had j came into his mind (' Schopfungs-

at last got a theory by which to ; gesch.,' chap. vi. ) In the first

work," &c. Prof. Haeckel, in his j paper which Darwin published in

'History of Creation,' has dwelt i the 'Journal of the Linnican

e.xhaustively on this connection of j Society' ("Letter to Asa Gray,"

Darwin with Malthus, quoting a vol. iii. p. .51), he uses the term

letter of Darwin's to him, dated 8th ■ "Natural Selection," and refers in

October 1864, in which he says that I the abstract which he there gives

for years he could not comprehend
how any form should be so emi-
nently adapted to its special con-
ditions of life, but that when
through good fortune Malthus's

to Malthus; whereas Wallace (ibid,
p. 56) introduces the term " Struggle
for Existence."

^ Quoted from Wallace, ' Dar-
winism,' preface, p. vi.

ON THE GKNETIC VIEW OF NATURE. 333

ensure the multiplicatiun, what are those which clieck
the increase, of popuhition ? As all living things are
dependent on each other, forming tlie great household or
economy of nature or the smaller one of human society,
a certain adjustment must exist hy which a definite place
and part are allotted to every individual and to every
class of individuals. Malthus had studied the problem
from a political point of view. Here it was felt to be
of human and social importance, but his principle was
applicable to all living creatures. For everywhere, even
in the remotest and only recently discovered countries,
we see at work the luxuriant and productive powers of
nature on the one side, on the other side the many
difticulties and obstacles by which they are forcibly and
automatically kept in check, resulting in the ever-recur-
ring spectacle of a " struggle for existence." The more :«.

"Struggle

we penetrate into the hidden and remoter provinces of for exist-
nature, into the luxuriant " fauna and flora " of tropical
regions, or realise the enormous population among the
lower forms of life, the more the conviction forces itself
upon us that the apparent equilibrium is only maintained
by the phenomenon of " crowding out " on a scale com-
pared with which the spectacle unfolded by Malthus in
his special application to human societies is quite a minia-
ture display. This process of " crowding out " must have
been at work during the untold ages which modern
geology has made known to us, and the effects of it
must indeed have been extraordinary, and well worthy
of study. That living beings, if left to their natural
instincts, multiply at an enormous rate, and would,
except for certain automatic checks, in a very short time

euce.

334

SCIENTIFIC THOUGHT.

34.
OuMoor

shidies.

people the whole habitable portion of the globe, is a
fact which has only been realised since Malthus, and,
on a much larger and more general scale, Darwin and
Wallace have drawn attention to it/ This being
generally admitted, the questions arise : What are these
automatic checks, and what results do they produce ?
It is evidently quite a new line of reasoning, unknown
to former naturalists, or only sporadically and fragment-
arily pursued by them ; but it introduces us at once
into nature itself, away from the class-room and the
museum, where we hear of the forces and laws of nature
in their abstract mathematical development, or where we
behold specimens arranged peacefully and lifelessly side by
side. We are face to face with the fierce and continuous
conflict which is unceasingly going on around us, and
realise the endless changes which it must be producing.

Among the many influences which the Darwinian
view has had in opposite directions on the thought of
our age, none is greater or more fundamental than
this, that whereas before Darwin naturalists stepped

^ On the publication of the
' Origin of Species,' Darwin re-
ceived many letters pointing out
earlier anticipations of his views.
The more important of these — bear-
ing upon descent and change — have
been referred to in tlie present
chapter. The special principle of
natural selection seems to have
been already foreseen by Dr Wells
in 1813, and published in his
famous ' Two Essaj's upon Dew and
Single Vision' in 1818. "In this
paper he distinctly recognises the
principle of natural selection, and
this is the first recognition which
has been indicated" ('Origin of

Species,' historical sketch to later
editions). Another anticipation was
that of Patrick Matthew in 1831, in
his work on ' Naval Timber and
Arboriculture.' " Unfortunately
the view was given very briefly iu
scattered passages in an appendix
to a work on a different subject, so
that it remained unnoticed until
Mr Matthew himself drew atten-
tion to it in the ' Gardeners'
Chronicle' on April 7, 1860. , . .
He clearly saw the full force of the
principle of natural selection "
{loc. cit., p. xvi). Neither of
these writings was known to
Darwin in 1859.

ON THE GENETIC VIKW OF NATUliK.

!35

out of doors only from curiosity, and in searcli (jf new
specimens, prompted by the love of travel and adven-
ture, or as companions to commercial and colonising ex-
peditions, they are now forced to do so, because one of
the greatest agencies in nature — " the struggle for ex-
istence " — can only be studied in nature herself. Before
Darwin the study of nature was artificial ; through his
influence it has become natural. From the point of
view of the history of thought, this is surely a much
greater result than any of the several theories or special
arguments which are connected \\ith liis name. These
are indeed numerous, each making, as it were, a dis-
tinctly new departure in scientific reasoning, character-
ised by that unmistakable sign ' of all that is really
novel in the realm of thought, the creation of a new
vocabulary of distinct terms and phrases. A'arieties
were known to liotanists before Dai'win, but whd studied
" variation " and " variability " ? or who spoke of the
" divergence of character " ? Breeders of stock and
pigeon -fanciers knew what "selection" meant, but the

' The late Hewett Cottrell
Watson, authur of the ' Cj'bele
Britannica" — one of a most valuable
series of works on the topography
and goograi)hical distribution of
the plants of the British Islands —
wrote to Darwin shortly after the
publication of the ' Origin of
Species,' 2l8t November 1859 :
" 1 am tempted to write you the
first impressions, not doubting that
they will, in the main, be the
permanent impressions. Your lead-
ing idea will assuredly become
recognised as an established truth
in science — i.e., 'Natural Selection.'
It has the characteristics of all
great natural truths, clarifying

what was obscure, simplifying what
was intricate, adding greatly to
previous knowledge. You arc the
gi-eatest revolutionist in natural
history of this century, if not of
all centuries. . . . Now these
novel views are brought fairly be-
fore the scientific public, it seems
truly remarkable how so many of
them could have failed to see their
right road sooner. How could >Sir
C. Lyell, for instance, for thirty
years read, write, and think on the
subject of species and their succes-
sion, and yet constantly look down
the wrong road?" ('Life of Dar-
win,' vol. i. p. 352, and vol. ii. p.
226.)

336 SCIENTIFIC THOUGHT.

35. terms " natural selection " and " sexual selection " ap-

" Natural

selection" pearcd for the first time in Darwin's writings. The

and "sexual -^ °

selection." " struggle for existence," and the resulting " survival of
the fittest " individuals, represent definite processes always
going on consciously or unconsciously in nature and in
human society ; nor is it less significant that many other
phrases have been coined, by which the same idea has been
made useful in other domains of research. " Hybrids,"
" mongrels," " rudimentary organs," and " monstrous "
developments, which in earlier times were subjects of
mere curiosity, have been raised to scientific importance
as indicative of the concealed and mysterious agencies
by which natural forms are altered or maintained, and
natural processes encouraged or checked. " Environ-
ment " and " adaptation " open out great vistas of in-
quiry, whilst nearly all those different lines of search
and of reasoning have latterly become centred in the
great problem of " heredity " — the central question of
biological science. In addition to these, the older
terms of the naturalists and anatomists have received
new interpretations. It has been shown by Darwin
himself how the vague endeavours of system -makers,
since Linnaeus, after a " natural " as distinguished from

36. a merely " artificial system of classification " of living

Meaning of

natural bcings, implied " something more " than mere resem-
*'°°- blance, and that this something more is " propinquity

of descent — the only known cause of the similarity
of organic beings — it being the bond, hidden by various
degrees of modification, which is partially revealed to
us by our classifications." ^ In the light afforded by

^ ' Origin of Species,' 1st ed., p. 413.

ON THM GENETIC VIEW OF NATURE.

337

this idea, the whole work of classiHcation has since
Darwin's time heen taken up anew ; and though it is
prohably premature to fix upon any elaborate scheme
as likely to aflbrd a correct view of the main lines
of descent in the two great realms of animal and
plant life, single pedigrees, such as those of the rhino-
ceros and the horse, have, with the assistance of the
geological record, been successfully worked out, the
missing links having unexpectedly turned up.^

In addition to this great service of directing the
glance of the naturalist outside, and of helping to over-
come the bewildering effects which the aspect of nature
must produce on every one who is not prepared for
research by some definite aim and a distinct habit of
reasoning, the Darwinian spirit has further proved its
usefulness by the great increase of our knowledge of
the things and phononicna of nature which has taken

' " It is certain that, before
the tlieory of descent was accepted
or even discussed, genealogical trees
were used to represent possible
relationships among human races,
or possible affinities among animals.
It was used as a ' graphic ' way of
expressing classification, and was
true just in jiroportion as the
classification was true. The nat-
uralist traveller, Peter Pallas, was
one of the first to use it to express
affinities among animals, though
it is possible he .saw a deeper
meaning in his symbol. But when
tiie theory of descent took hold
on men's minds, the genealogical
tree became more than a graphic
register of affinities, — it was used
to express the suppijsed facts of
descent. To Ernst Haeckel be-
longs the credit, or, as some critics
would say, the responsibility, of

VI lb. ir.

introducing the use of genealogical
trees into zoology and l)otany.
In his ' Generelle Morphologie
(186(3) and in his ' .Sclii)i)fungs-
geschichte' (1868, 9th ed. 1S97),
he displayed numerous genealogical
trees designed to show the descent
of various stock.s and types of ani-
mals and plants. There can be
no doubt that in so doing he
focu.ssed the idea of descent into
vividness, and, by the very definite-
ness of the notation, forced natural-
ists to a criticism of the reality
of the supposed lines of descent.
Prof. Ij. von (Jraff.says of Haeckel's
' Stainmljilume,' ' There is due to
them the immortal credit of having
given the first impetus to the
grand revolution in the animal
morphology of the last decades ' "
(J. A. Thomson, ' The Science of
Life," 1899, p. 15).

338

SCIENTIFIC THOUGHT.

place since the publication of Darwin's works, by the
industry of friend and foe, with the object of prov-
ing or of disproving and modifying Darwin's theories.
Whole chapters, such as those referring to the fer-
37. tilisation of plants through insects, to the part which

Fertilisation ^

of plants and colour plavs in the world of Howers or in the plumage

'Mimicry. ± ^ i o

of birds and in the wings of butterflies and moths,
have been added to our handbooks of natural history ; ^

■* Two remarkable instances may
be aientioned. It was known to
Christ. Conrad Sprengel that many
tiowers aie " dichogamous " — i.e.,
that though the organs for self-
fertilisation exist in the same flower,
nevertheless, because of a want of
timekeeping or for other reasons,
polHnation is done by crossing,
wherein the visits of insects are in-
strumental through elaborate exist-
ing arrangements. " Variously col-
oured spots serve as honey-guides
and pathfinders to the exploring
insects, hairs protect tlie nectar
from rain and yet offer no obstacle
to dc'iiirable visitors, other arrange-
ments secure that the insects are
dusted with pollen " (J. A. Thom-
son, 'The Science of Life,' p. 192).
Sprengel published his observations
in a remarkable book (1793) with
the title ' The Secret of Nature
discovered in the Structure and
Fertilisation of Flowers. ' Such
was the enthusiasm of this true
naturalist, that he, " after being
ejected from the rectorate of Span-
dau for neglecting his flock in
favour of Howers, settled down to
a frugal life in Berlin, and gave
lessons in languages and botany.
The commonest j)lant became new
by what he had to say about it ;
a hair, a spot, gave him oppor-
tunity for questions, ideas, investi-
gations" (ibid., p. 191). Sachs
('Gesch.,' p. 449) considers Spren-
gel's little work to contain "the

first attempt to explain the genesis
of organic forms out of definite
relations to their environment."'
For sixty years this biouomical
classic was forgotten. Darwin in
1841 heard of it through Robert
Brown, who, according to Dr Gray
('Nature,' 1874, p. 80), "in coni-
mon with the rest of the world,
looked on Sprengel's ideas as fan-
tastic." The book impressed Dar-
win, who in 1837 had written in
his notebook : " Do not plants
which have male and female organs
together, yet receive influence from
other plants J " as being " full of
truth." (See ' Life of Darwin,' vol.
i. p. 90 ; vol. iii. p. 257.) The other
important research which has been
much stimulated by the two great
propounders of Darwinism, is the
Btudy of tlie meaning of colours
in plants and animals and the allied
subject of "Mimicry." "It is
the wonderful individuality of the
colours of animals and plants that
attracts our attention — the fact
that the colours are localised in
definite patterns, sometimes in
accordance with structural char-
acters, sometimes altogether in-
dependent of them, while often
differing in the most striking
and fantastic manner in allied
species. We are thus compelled to
look upon colour not merely as a
physical but also as a biological
characteristic, which has been dif-
ferentiated and specialised by

ON THE OENETIC VIEW OF NATURE. 339

the older division of zoology and botany having to a
large extent been removed by a study of the inter-
dependence of the many forms of living things and
their connection with peculiarities of climate and soil.
The Darwinian attitude to the study of natural objects
has also introduced 'into the natural sciences the exact
spirit of research, — accurate measurements, together with
elaborate countings, being resorted to in order to decide
the range of variability of species, the rate of increase
in numbers, and the proportion of the surviving to the
lost or wasted specimens. A large amount of statistical
information ^ has tlius Ijeen accumulated, and natural
history is becoming to some extent an exact science.
That it will ever Ije so to a very large extent is doubt-
ful : it is one of the great merits of Darwin that he has
introduced a special method into the sciences of nature —
ihe method of a judicious balancing of evidence. He ss.
was fully " aware that scarcely a single point was dis- method,
cussed in his works on which facts cannot be adduced,
often apparently leading to conclusions directly opposite
to those at which he arrived, and that a fair result can be
obtained only by fully stating and l»alancing the facts

natural selection, and must, there- served as one of the most valuable

fore, find its explanation in tlie illu.strations and proofs of the
jjrinciple uf adaptation or utility " ' theory of natural selection. The

(Wallace, 'Darwinism,' p. 189). whole matter is admirably ex-

Tlie term "Mimicry" was first pounded by Mr Wallace in his

introduced by H. \V. Bates in his long article in the ' Westminster

paper on " Mimetic Butterflies," Review,' July 1867, reprinted in

road befoie the Linnwan Soc, Nov.
l>tjl, and hailed by Darwin ('Life,'

his ' Contributions to the Theory
of Natural Selection ' (1870, pp. 45-

vol. ii. p. 'i'j'2) as "one of the most ] 129), and again in 'Darwinism,

remarkable and admirable pa])ers " j ^ On the development ><{ sUitis-

he ever read. Tiie .'subject had | tical methods in the service of the

been passed over in the first editions i theory of evolution, see chap. xii.

of the ' Origin,' but was introduced below,
in later edition-^, and has always

340 SCIENTIFIC THOUGHT.

and arguments on both sides of each question." ^ It is
quite a different process of investigation and method of
thought from tliat which the abstract sciences use, where
every agency is first considered in its isolated action and
mathematically calculated, and a complex effect is rightly
looked upon as merely the resultant of specific, well-
defined forces, compounded according to rigid dynamical
formulre. That the whole of nature, as well as all
observable phenomena, are in reality only the result of
such a composition of definite simple actions, and can be
studied as such, may be quite correct ; but that this
method, however useful in isolated cases, and especially
however fruitful in the application to artificial mechanisms,
will never lead to a just comprehension of any large
cluster of phenomena, or to an appreciation of the totality
of things which surround us, must be evident to any one
who at once appreciates the rigidity and universality of
mathematical calculations, and sees how soon they fail to
become of practical use when we attempt to attack any
complex problem through them. Now, all processes in
nature herself, as distinguished from the laboratory, are
eminently complex, and far transcend the powers and
grasp of the mathematical calculus, so far as the human
mind is able to employ it. In fact, the outdoor
naturalist must attack the problem of nature and life
by quite a different method : he must, like a judge, con-
front and appreciate the evidence of many witnesses
who are speaking on all sides to him, and he must,
with an open and unbiassed mind, judiciously combine
such evidence in the sentences which he passes or the

^ ' Origin of Species,' 1st ed., p. 2.

ON THE GENETIC VIEW OF NATURE.

341

generalisations which he attempts. Absohite mathe-
matical certainty is almost unknown in such cases : they
can only Ite made out willi mnif! or less clearness and
probability.

It seems to me that the new phase into which scientific 39.

•11 11-1 p Darwin aii<l

thought has entered, mainly through the mnuence of xpw-ton
Darwin, has not been sufficiently appreciated by those of
his critics who have compared his methods with those of
earlier philosophers and naturalists. Darwin has l)een
called by some tlie Xewton of tlie natural sciences,^ and
again by others his method has l)een unfavourably con-
trasted with that of Xewton and C'uvier.^ Some of these

* It is in many instances only
a fa^on dc parlcr. Maxwell simi-
larly called Ampl-re the Newton of
Electrodynamics ; and Young has
been called the Newton of Optics.
Mr Wallace saj-s ('Darwinism,' p.
9) : " We claim for Darwin that he
is the Newton of natural hi.story,
and that, just so surely as that the
discovery and demonstration by
Newton of the law of gravitation
established order in place of chaos,
and laid a sure foundation for all
future study of the starry heavens,
80 surely has Darwin, by his dis-
covery of tlie law of natural selec-
tion and his demonstration of the
great ])rinciple of the preservation
of useful variations in the struggle
for life, not only thrown a flood of
light on the process of development
of the whole organic world, but also
established a firm foundation for all
future study of nature."

'" The most important publica-
tion of this kind is the late Pro-
fessor Albert Wigand's %v(jrk, in
three volumes, ' Der Darwinismus
uiid die Naturforschung Newton's
und Cuvier's ' (Braunschweig, 1874-
1877). The author significantly
classes Humboldt also among those

who belong to that period and
school of research which has — un-
fortunateh', in his opinion — been
superseded bj' the modern genetic
treatment (see vol. iii. p. 14). It is
not likely that a perusal of these
volumes will, in the mind of the
reader, change the current of
thought which is now, even more
than twenty-five years ago, running
in genetic lines, nor will it do any-
thing towards diminishing the sense
of importance which attaches to
this modern movement. Never-
theless, the book is valuable as
giving a very complete resume of
what was said " pro and con " Dar-
winism during the first tifteen ye.ars
of its existence. It is interesting
to see what a small part French
scientific opinion jilayed during that
period as to the tlieoi'ies of descent
and mutability of species, which had
both their origin and their first gi'eat
exponents in France. The book
does not appear to have had much
influence in its time, but more
recently the criticisms of Wigand,
von Baer, and other writers seem
to receive greater attention since
the central biological jjroblems have
been pushed into the foreground. Of

342

SCIENTIFIC THOUGHT.

comparisons refer to the law of " natural selection,"
which is placed in parallel with Newton's law of
" universal gravity." Now, although " natural selec-
tion," the automatic process which ensures the survival
of the fittest and the extinction of the less adaptive
members in a crowd of living beings, is a definite
formula which allows us to understand and clearly
define one of the nlany factors which are at work in
the development, in the genesis and growth, of living
beings, it is only one. It is not a prime mover or force,
like the force of gravity ; it is a check upon the over-
luxuriance of other existing forces of production and
development. These are only very imperfectly known ;
whereas Newton not only discovered the " law of gravita-
tion," but also the correct expression for the general and
all-pervading laws of motion which obtain, even where
gravitation or any similar force ceases to be a valid con-
ception. Again, Newton's greatness does not rest on
the " law of gravitation " alone, but much more on the
general foundations of dynamics and natural philosophy
which he has laid. So also Darwin's greatness is not
limited to the formula of " natural selection," but
depends on the novel conception which he has intro-
duced into the study of nature on the large scale and as
a whole, viewing it as a scene of conflict and ceaseless
development. From this time dates the study of nature
as a whole ^ in contradistinction to that of natural

this I shall treat in the next chap-
ter. See also the various writings
of Hans Driesch, such as 'Analyt-
ische Theorie der organischen Ent-
wicklung' (Leipzig, 1894); 'Die
Biologic als selbstiindige Grund-

wissenschaft (1893), especially p. 7
of the latter.

' Though this was prepared, as
Darwin himself points out, by A.
von Humboldt.

UN JHK OKNKTIC VIEW OF NATl^RE.

34:^

" 1

problems.

objects and processes. The general laws which obtain
in this great field, and wliit-h would correspond to
Xewton's laws of motion — the laws of variation and of
heredity — have not yet been discovered ; but it is again
Darwin more than any other naturalist wlio has called
attention to these prime movers in the living universe.
He has pushed into the foreground the two great problems *o.

, Unsolved

of " variation " and " beriMlity

' Darwin in his subsequent writ-
ings urged another important prob- |
leui, to which he had ah'eady in his
first and greatest work drawn pass-
ing attention. This is the agency
of "sexual selection." It occupies
by far the larger portion of his
third great work, wliich appeared
in 1871 with the title ' The Descent
of Man and Selection in Relation to
Sex.' In the introduction he says,
" During many years it lias seemed
to me highly probable that sexual
selection has played an important
part in differentiating the races of
man ; but in my ' Origin of Species '
I contented myself by merely allud-
ing to this belief. When 1 came
to apply this view to man, I found
it indispensable to treat the whole
subject in full detail. Professor
Haeckel is the sole autlior who,
since the publication of the ' Origin,'
has discu.ssed in his various works,
in a very able manner, the subject
of sexual selection, and has seen its
full importance." The problem of
".sexual selection" is introduced in
the ' Origin ' (p. 87) in the following
words : " Inasmucli as i)eculiaritips
often appear under domestication
in one sex, and become hereditarily
attached to that sex, the same fact
probably occurs under nature ; and
if so, natural selection will be able
to modify one sex in its functional
relations to the otlier sex, or in
relation to wholly different iiabits
of life in the two sexes, as is some-

times the case with insects. And
this leads me to say a few words
on what I call Sexual Selection.
This depends not on a struggle for
existence, but on a struggle be-
tween the males for possession of
the females : the result is not
death to the unsuccessful com-
petitor, but few or no offspring.
Sexual selection is thus less rigor-
ous than natural selection." A
great deal has been written about
sexual selection, and in general it
maj' be said that the question be-
longs to quite a different category
from that of natui-al selection.
Some of the foremost champions of
the latter doctrine, notabl}' Mr
Wallace, reject sexual selection as
unnecessary in tlie whole scheme.
The characteristic feature of natural
selection is this, that it is a purely
automatic process, dependent on
overcrowding, whereas in sexual
selection it becomes much more
difficult to see how the process
works automatically. Nowadays
the question of natural selection
is hardly any longer doubtful ; it
is a fact. As to sexual selec-
tion, the statistical proofs that
there is a superabundance from
which to choose are still wanting.
To understand sexual selection,
or even to define it, we need
to form some conception of the
reason and origin of sexual differ-
entiation, and this cannot be ar-
rived at without a theory of life

344

SCIENTIFIC THOUGHT.

And, besides this, it is well to remember that Newton
was condemned by some of his contemporaries on the
basis of the philosophy of Bacon ; Fresnel and Young
were condemned on the ground of Bacon and Newton
combined. In like manner the novel line of reasoning
adopted or largely cultivated by Darwin has been
attacked as being opposed to Bacon, Newton, and other
great thinkers before him. In all these cases it is the
results, and not the theory, of the process of reasoning
which have justified its continued employment. Without
attempting to elaborate the parallel too minutely, we
may say that as Newton created Natural Philosophy
and took one Inilliant step in fixing for all time one of
the great laws of the material universe, so Darwin has
founded the study of nature as distinguished from that
of the objects and processes of nature, and has enunciated
one of the great factors which obtain in the living
portion of nature : through him a history of nature, the
genetic view of nature on a large scale as distinguished
from the older natural history, has for the first time
become conceivable. The word history indeed suggests
other analogies. Political history, what we ordinarily
term history proper, has in the course of our century
undergone changes and developments similar to those in
the history of nature. Confined once to a casual, un-
methodical, uncritical, and incomplete record of isolated

which rests ou something more
than the two purely statistical or
numerical facts of overcrowding
and of variation — i.e., the fact that
no two individuals are absolutely
alike. The importance of the
phenomenon of sex in the economy
of living nature has been studied,

and given rise to many theories.
A very good account of these will
be found in P. Geddes and J. A.
Thomson, 'The Evolution of Sex,'
1889. In the following chapter,
where I deal with the various
attempts to define " Life," I shall
revert to this subject.

ON THE GENETIC VIEW OF NATURE.

345

events or biographies, it lias Iteen gradually united and
organised as a whole, largely through the same judicial
sifting of manifold ovidenec and clalioration of critical
methods of research. Of this 1 hope to treat in a
different portion of this work : here 1 only wish to
diaw attention to the enlarged aspect, which in both
instances has, through the same process of development, 41.
come over our studies. When once we rise from the on a large

scale.

contemplation and examination of details and single facts,
and grasp the connection and economy of the whole as
a subject worthy of special attention, we involuntarily in-
troduce two new elements into our research — the element
of conjecture and the element of speculation. The former
is needed to fill up the many gaps which we find in the
actual records when we wish to string them together into
a united and intelligible whole ; the latter is the inquiry
into the general principles which underlie any and every
development of the kind we have in view. The creation
l)y Darwin of the science and history of nature, as dis-
tinguished from the science and history of natural ob-
jects and single processes, has been accompanied and
strengthened by the appearance of conjectural and specu-
lative attempts ; just as the cultivation of the science
of general history has gone hand in hand with, and
has been supported by, the brilliant results of philo-
logical conjecture and the philosophy of history.^ Of

' In an el()i|Ueiit passage Professor
Parker coiiipaies the work of the
naturalist of to-day with tliat of
the pliih)logist. This passage occurs
in his Memoir on the Fowl (18ti8),
and is (juoted in his book ' On tlie
Morphology of the Skull ' (by Parker
and Bettany, London, 1877, p. 362):

" Whilst at work I seemed to my-
self to iuive been endeavouring to
decipher a palimpsest, and one not
erased and written upon again just
once but five or six times over.
Having erased, as it were, the
characters of the culminating type
— those of the gaudy Indian bird

346

SCIExNTIFIC THOUGHT.

these I shall treat elsewhere. It may be a question
capable of very opposite answers whether the philosophy
of history, such as it has been offered in the brilliant

42. generalisations of Kant, Herder, Hegel, and Buckle, has

Philosophi-

caitheories. really aided the science of history proper; whereas no
question can arise as to the indispensable service that
has been rendered to historians by the criticism and
conjectural emendation of texts and other monuments
of antiquity. With Darwinism the matter stands dif-
ferently : no person who peruses the great and increasing
literature of the subject can deny the enormous assist-
ance which the philosophical ideas of evolution have
rendered to the cause of Darwinism — how the latter,
when it appeared, found ready made, though then only
slightly appreciated, the philosophical canons and terms
which were so well fitted to its systematic enunciation

43. and literary mise en scdne. This was the independent
Spencer. work of Mr Herbert Spencer.^ The other well-known

— I seemed to Vie among the sombre
grou.se ; and then, towards incuba-
tion, the characters of the sand-
grouse and hemipod stood out be-
fore me. Rubbing these away in
my downward work, the form of
the tinamou looked me in tlie face ;
then the aberrant ostricli seemed to
be described in large archaic char-
acters ; a little while and these
faded into what could just be read
off as pertaining to the sea-turtle ;
whilst underlying the whole the
fish in its simplest myxinoid form
could be traced in morphological
hieroglyphics. "

' The part and position which
belongs to Mr Herbert Spencer in
the history of evolution as a scien-
tific doctrine has not yet received
due attention or adequate recogni-

tion. There is, however, no doubt
that the principal features of the
genetic view of natural phenomena
were clearly before his mind as
early as 1852, when he wrote his
short essay on " The Development
Hypothesis " in ' The Leader,' re-
published in the first volume of his
' Collected Essays. ' It has been
pointed out by Romanes (' Darwin
and After Darwin,' vol. i. p. 257)
that though the attempts towards
a genetic conception of organic
nature were numerous, if not
abundant, before Darwin, yet this
view only broke through and be-
came dominant on the appearance
of the theory of natural selection.
He says : " If we may estimate the
importance of an idea by the change
of thought which it eflfects, this-

ON THE GENETIC VIEW OF NATURE.

347

name which is so frequently associated with Darwin,
especially in Germany, is that of Professor Haeckel,
whose ' Generelle Morphologic ' and ' History of Creation '
have done much to introduce the spirit of Darwinism
into German literature. These works also represent the

44.

Haeckel.

idea of natural .selection is unques-
tionably the most iinpoi-Uuit idea
that has ever been conceived by the
niiud of man. Yet the wonder is
that it should not have been hit
upon long before ; " and after re-
ferring to the forgotten antici-
pations of WelLs and Matthew,
Romanes proceeds : " Still more
remarkable is the fact that Mr
Herbert Spencer — notwithstand-
ing his great powers of abstract
thought and his great devotion of
those powers to the theory of evo-
lution, when as yet this theory was
scorned by science — should have
missed what now appears so ob-
vious an idea." In this connection
it is interesting to note how those
general canons of evolutionary
thought which were established by
Spencer before the publicjilion of
the ' Origin ' were brought into
general recognition by scientific
men only when the definite mathe-
matical or statistical formula of
natural selection was announced,
and that, after the lapse of a whole
generation, it is not this precise
formula but the general conception
of evolution wdiich, according to
many of the foremost naturalists,
will obtain ; the part which natural
selection i>la}'s being uncertain and
variously estimated by the many
adherents of the theory of evolu-
tion. See, inter alia, the article on
'• Evolution in Biology " by Huxley
in the ' Ency. Brit.,' 9th ed., vol.
viii. p. 7.51: "How far natural
selection suffices for the production
of species remains to be seen. Few
can doubt that, if not the whole

cause, it is a very important factor
in that operation. . . . The im-
portance of natural selection will
not be impaired even if further
inquiries should prove that varia-
bility is definite and is determined
in certain directions rather than in
others by conditions inherent in
that which varies."' See also the
Address of Lord Salisbuiy at the
meeting of the Brit. Assoc, at Ox-
ford iu 1894, and the subsequent
remarks of Huxley in .seconding the
vote of thanks ('Life of Huxley,''
vol. ii. p. 378) : " The essence of
this great work (the ' Origin of
Species') may be stated summarily
thus : it affirms tlie mutability of
species and the descent of living,
forms, separated liy differences of
more than varietal value, from one-
stock. . . . And yet it is also true
that if all the conceptions promul-
gated in the 'Origin of Species'
which are peculiarly Darwinian
were swept away, the theory of
the evolution of animals and plants
would not be in the slightest degree
shaken." In fact, the general prin-
ciples of mechanical evolution, as
first systematised by Mr Spencer,
received recognition only through a
definite formula, but may, after all,
survive that special doctrine. It
is further very evident how the
parallel with Newton's formula of
gravitation entirely breaks down if
we look at matters in this light :
every subsequent discovery having
only tended to confirm that special
mathematical relation, and proved
the all-important part it plays in
nature.

348

SCIENTIFIC THOUGHT.

first brilliant attempt to fill up conjecturally the broken
lines of development and descent as the Darwinian con-
ception of living nature postulates them.^ As a first
and daring approximation, they deserve to .have assigned
to them a prominent place in the history of the scien-
tific thought of our age. In elaborating his pedi-
grees, Professor Haeckel has taken up and more clearly
defined the analogy between the development of the
■embryo in the higher organisms and the supposed transi-
tion from lower to higher forms which is found in the
classification of the genera or species of animals and
plants. He has termed this analogy the great law of
biogenesis, of the development of life in the individual
(to 6v), and the species or tribe (to cjjvXov), expressed
also as the parallelism of ontogenesis and phylogenesis.
Long before Darwin and the appearance of the theory of
descent this analogy - was pointed out in a restricted

^ The later editions of the ' Origin
of Species ' contain the following
reference to Haeckel (6th ed., p.
381) : " Prof. Haeckel, in his ' Gen-
erelle Morphologic,' and in other
works, has brought his great know-
ledge and abilities to bear on what
he calls phylogeny, or the lines of
descent of all organic beings. In
drawing up the several series he
trusts chiefly to embryological char-
acters, but receives aid from homo-
logous and rudimentary organs, as
well as from the successive periods
at which the various forms of life
are believed to have first appeared
in our geological formations. He
has thus boldly made a great be-
ginning, and shows us how classi-
fication will in the future • be
treated." And Huxley (art. " Evo-
lution," p. 752) says: "Whatever
hesitation may not unfrequently

be felt by less daring minds in
following Haeckel in many of his
.speculations, liis attempt to sys-
tematise the doctrine of evolution,
and to exhibit its influence as the
central thought of modern biology,
cannot fail to have a far-reaching
influence on the progress of
science."

^ As to the early anticipations of
this so-called "law of biogenesis,"
they are given with more or less
completeness by many modern
writers, such as Huxley in his
article on Evolution (1878, ' Ency.
Brit.'), P. Geddes (ibid., art. "Re-
production "), Yves Delage (' L'Her-
ddite,' &c., p. 159), J. A. Thomson
('The Science of Life,' p. 133, &c.)
The most important earlier state-
ment is that quoted by Huxley
from Meckel's ' Entwurf einer Dar-
stellung der zwischen dem Embryo-

ON TIIK fJENKTIC VIEW OF NATURE.

349

sense liy Meckel, mui iUa-i, jukI Series. It h.as some-
times been termed von liaer's law, tlmuiih mui IJaer
very carefully guarded himst'll' against many ]»o])ular
versions of the analogy, appl} iug it only wiihin the
limits of the fonr great groups or plans of organisation
into which he divided the animal kingdom.^ In his

zustande der hiilieren Thioro uud
dem permaneiiten der niederen
stattfindenden Parallele ' (1811):
"There i.-* no good phyt^iologist who
has not been struck by tlie observa-
tion that the original form of all
organisms is one and the same, and
that out of this one form all, the
lowest as well as the highest, are
developed in such a manner that
the latter pass through tlie per-
manent forms of the formei- as
transitory stages. Aristotle, Hal-
ler, Harvey, Kielmeyer, Autenrieth,
and many others, have either made
this observation incidentally, or,
especially the latter, have drawn
particular attention to it, and
drawn therefrom results of per-
manent importance for physiology'. '"
Louis Agassiz, in his celebrated
"Essay on Classification" (1859),
though rejecting the doctrine of
descent, "insisted, nevertheless, on
the correspondence between stages
in embryonic development and the
grades of differentiation expressed
in the classification of living and
extinct animals " (Thomson, ' The
Science of Life,' j). 134).

^ " A careful examination of von
Baer's ' laws ' shows that he did
not accept the recapitulation with-
out many saving clauses. He be-
lieved in it much less than many
a modern embryologist, such as F.
M. Halfour or A. Milnes Marshall '"
(Thomson, j). 133). Before the
puljlication of Haeckel's ' Generelle
Morphologic ' the naturalist who
seems to have most clearly ex-
pressed the recapitulation theory

was Fritz Midler, who in 1864
published his famous tract ' P'iir
Darwin,' which appeared in 1868
in an English translation by Dallas,
with the title 'Facts and Argu-
ments for Darwin.' The work of
Fritz Jlilller, who for many years
lived in the Brazils, isolated and
secluded, and devoted to scientific
observation, was welcomed by Dar-
win as one of the first and greatest
supports to his doctrine : the
author was singled out by him as
the "prince of observers," and
frequently referred to in the latei-
editions of the 'Origin of Species."
Delage considers him to have first
expressed the fundamental bio-
genetic law (' L'Heredite,' pp. ITjO,
469), and this is in agj-eement with
Haeckel's own declaration in the
13tli chapter of the ' Historj' of
Cieation.' It is, however, well to
mention that the recapitulation
theory has found little favour w ith
botanists ; that Haeckel himself
admits that the parallelism be-
tween ontogenesis and phylogenesis
is general and not exact ; that there
is a tendency to abbreviation ; that
recent adaptations (called by him
" kainogenetic ') may mask more
ancient ("palingenetic '") features,
&c. See J. A. Thomson, 'The
Science of Life,' p. 13.'). Ziegler,
in his recent excellent leview of
the ' Present Position of the Doc-
trine of De.xcent ' (Jena, 1902, p. 12),
admits that the theory of paral-
lelism has " perhaps not realised
all the expectations " which were
cherished thirty years ago.

350 SCIENTIFIC THOUGHT.

time also no attempt was made to bring phytogenesis
— the genesis of plant-life — into line and order with
zoogenesis, the genetic arrangement of animals. It is
Haeckel's undoubted merit to have attempted for the
first time to carry out this general scheme on a large
scale, and by means of detailed pedigrees, beginning
with the undefined organisms in which as yet the
peculiar characters of animal- and plant -life do not
appear to be differentiated, and ascending in two great
trunks into the vegetable and animal kingdom, and
thence through many ramifications into the several
classes, families, genera, species, and varieties of living
things, to construct the supposed real natural system
for which systematists had been unconsciously searching
since the age of Eay and Linnaeus. For the purpose of
elaborating this great scheme he employs not only the
great law of heredity, according to which ancestral
characters are reproduced in development, but also the
older law of adaptation to the existing environment, as
45. pointed out by Lamarck. Haeckel, in fact, combines the

Combines

Darwin and vicws of Darwiu and Lamarck, which other naturalists

Lamarck.

are more or less inclined to keep apart, whence has
arisen the well-known division into the two great schools
of. the neo-Darwinians and neo-Lamarckians.^ Though

^ Natural selection being an ad-
mitted fact among living things,
like gravitatiiin in the physical
universe, three distinct f)roblems
arise : First, how far does it reach ?
the scope of the principle. The
^^ubsequent writings of Darwin were
mainly occupied with this question,
though — as we shall see later — he
also ventured upon an important

suggestion as to the underlying
problem of inheritance. Secondly,
the fact or principle itself requires
to be traced to deeper-lying causes.
We may say natural selection is a
vera causa, but not a pi-ima cmisa :
it is a true but not a prime cause.
The investigations regarding " varia-
tion " and " heredity " work along
this line of research, and form the

ON THK fiKNKTKJ VIKW oK NATTRE.

351

Haeckel's work is, as he hiinsell' admits, highly con-
jectural,^ it has done much to extend and po})ulahse the

whole domain of moderu post-
Darwinian biology. The {)roblem
is far from being solved, though it
is perhaps nearer a solution than
the question as to the cause of
gravitation. Thirdly, there is the
ambitious attempt to construct a
general philosophy of life by means
of the new principle, or some modi-
fication or amplihcation of it. After
>.'ewt(jn had discovered universal
giaviuition, the attempt was made
by Boscovich and the French school
of mathematical jihysics to use the
idea of attraction at a distance as a
general [)hysical theory. Of those
who, before or after Darwin, at-
tempted the more ambitious task,
we may take Herbert Spencer, Ernst
Haeckel, and Niigeli as three dis-
tinct representatives. They, how-
ever, agree in one point — viz., in
considering natural selection to be
insufficient, and in admitting other
agencies, which are largely drawn
from the suggestive writings of
Lamarck. The section of these
philoso])hical writers who consider
Lamarck's principles to be more
fundamental than Darwin's, and
who are laigely repiesented by
American naturalists (notably E.
T>. Cope and A. Hyatt), are called
111 ' i-Lamarckians. The best account
of their views will be found in the
last chapter of Profes.sor Packard's
})ook, ' Lamarck, the Founder of
Evolution' (1901). The following
passage quoted there (p. 391) from
a much earlier memoir (1877) gives
a very clear account of the reason-
ing of this school : " Darwin's
phra.se, ' natural selection,' or Her-
bert Sjiencer's term, ' survival of
the fittest,' expresses simply the
final result, while the process of
the origination of the new forms

which have survived, or been
selected by nature, is to be ex-
plained by the action of the physi-
cal environments of the animals,
cou{)led with inheritance - force.
The |)hrase8 quoted have Vieen mis-
used to sUite the cause, when they
simply express the result of the
action of a chain of causes which
we may, with Herbert Spencer,
call the 'environment' of the
organism undergoing modification :
and therefore a form oi Lamarck-
ianism, greatl}' modified by recent
scientific discoveries, seems to meet
most of the (lifiticulties which arise
in accounting for the origination of
species and higher groujis of organ-
isms." It is also well to note that
Mr Wallace, though not a Lamarck-
ian, considers the principle of nat-
ural selection insufficient especi-
allj' to explain the higher develop-
ments of mental life. (See 'Dar-
winism,' p. 463, &c.)

' " It is evident that our ' phyl-
ogeny ' is and remains an edifice
of hypotheses in the same way as
her sister, historical geology. For
she tries to gain a connected view
of the course and causes of events
long past, the direct invest igati<jn
of which is impossible. Neither
observation nor experiment can
give us direct information regard-
ing the endless processes of change
through which the existing animal-
and plant -forms have emerged out
of lengthy ancesti'al stages. . . .
The empirical documents of our
history of descent will always
remain lai-gely incomplete, however
much through continued discoveries
our region of knowledge of individ-
ual things may increase." (Haeckel,
* Systematische Phylogenie,' 1894,
vol. i. preface, ]). vi.)

352

SCIENTIFIC THOUGHT.

46.
Philosoph-
ical prob-
lems.

47.
Problem of
life.

genetic view of nature, drawing likewise into this circle
of ideas the great departments of anthropology and
geography ; in fact, it amounts to rewriting the ' Kosmos '
of Humboldt on genetic instead of on purely descriptive
lines. But in perusing these and similar writings of
modern times, we feel on the one side that we are
gradually getting out of the depths of science, not only
into the domain of conjecture, without which a know-
ledge of the past cannot be gained, but also into the
regions of philosophical thought, which proceeds on
other lines than those prescribed to science, and which
will claim our attention in a special portion of this
work. On the other side, in using so confidently the
ideas of descent and adaptation, we feel that we are
appealing to two great empirical facts, the facts of
heredity and of variation of living things, on which the
genetic view of nature, when applied to the living
portion of creation, rests, but which are scarcely even
defined in clear terms, much less explained. In fact,
we are face to face with the problem and definition of
life itself. Neither the morphological nor the genetic
view of nature is limited to the living world, although
both views originated there, and were from thence ex-
tended to the larger domain of inorganic and cosmical
phenomena. Into these larger views which try to
grasp the forms of nature in their apparent rest or in
their endless change and history, the phenomena of
life have been fitted by the help of three definite con-
ceptions— the conception of the cell as the morpho-
logical basis or unit of all life, and the two concep-
tions of inheritance and variation, by which living

ON THK GENETIC VIEW OF NATUKE.

353

t'orias are partiall}' nuiintained and cuiiLiuuou.sly altered.^
These three conceptions deserve and have received special
attention by a class of students who, since the begin-
ning of the nineteenth century, have termed themselves
biologists. On what lines of reasoning their studies
liave been conducted, and to what general results they
iiave led, I propose to discuss in the following chapter,
which might be appropriately entitled the " Biological
view of Nature " in the narrower sense of the term.
In order to distinguish the studies which I shall have
to deal with in that chapter from those which have
occupied us in this and the last chapter, which deal
largely but not exclusively with li\ing things, I have
preferred to give to it the title, " On the Vitalistic -

^ To these — according to some
naturalists — might be added the
factor of adaptation, so prominent-
ly put forward by Lamarck and
his followers. But adaptation is
one of the causes of variation, as
natural selection is a consequence.
The latter is a physical necessity
wherever overcrowding exists ;
whereas the scope of adaptation,
which is an undeniable fact so far
as individuals are concerned, is,
so far as it regards inheritance —
i.e., the development of the race —
a much controverted question. It
comes under the larger problem
of the influence of enviionment,
and will occupy us again in later
chapters. Among the most valu-
able contributions to this subject
are Mr Herbert Spencer's articles
on the " Factors of Organic Evolu-
tion," published in the 'Nineteenth
Century ' in 1886, and separately,
with additions, in 1887. In these
essays he also shows how Darwin
himself in his later writings in-
cludes the influence of environ-
ment as an important factor in

VOL. 11.

development. (See p. 29 xqq. of
the reprint.)

- As the two terms " biological "
and " vitalistic " might, according
to their etymology, mean the same
thing, it may he appropriate to
offer some explanation of the
reasons which have induced me
to adopt the latter term for the
purpose indicated in the text.
Biology means the science of life.
This can only be studied in living
things. Living things, however,
are formed entirely of the same
elementary substances as we find in
inorganic or not living things, and
are very lai-gely formed through the
same chemical and physical pro-
cesses as we tind among the latter.
And as our scientific — i.e., exact,
accurate, and useful — knowledge
has all begun with the study of
inorganic phenomena, it is natural
that biologi.sts should have attacked
the problems of living nature from
the side of the similarity or same-
ness which they presented when
compared with lifeless nature.
The main progress in physiology

Z

354

SCIENTIFIC THOUGHT.

view of Nature." Clearly both the morphological and
the genetic views of nature remain incomplete unless
they embrace the forms and the processes of life. It
is the problem from which both started and to which
both lead. They, as it were, presuppose its possible
solution. Let us see what has been done in the course
of our century to effect it.

Before we do this it is well to draw attention to
the great strengthening which the genetic or develop-
mental view of natiu-e has received, since the time of
Darwin, from other quarters — notably from that of
general physics and chemistry in their application to
geology and astrophysics.-^

and medicine during the last hun-
dred years has come from that
quarter. This large class of studies
can be carried ou without facing
the problem of life at all ; and thus
it happens that we may have a very
large biological literature in which
the word life hardly occurs, and
in which we seek in vain for a
definition of life. "We must, there-
fore, have a term which singles out
from the enormous mass of bio-
logical literature that smaller por-
tion which professedly deals with
those properties and phenomena
which are peculiar to the living as
distinguished from the lifeless crea-
tion. I have chosen for this purpose
the term vitalistic ; but I may
not« that in using it I do not limit
myself to that class of thinkers
who are usually termed " Vitalists,"
because they are led to, or start
with the assumption of, a special
vital principle. Even those who,
in studying the phenomena of life,
arrive at or start from the denial of
.such a principle are included under
the vitalistic view, just as Kant is
rightly termed a metaphysician

although the outcome of his phil-
osophj' may be considered to be
the destruction of metaphysics in
the sense which was current in
his age.

^ A general scheme of evolution,
or of development as it was more
frequently termed, which would
embrace equally cosmical and ter-
restrial processes, the lifeless and
living world, was clearly before the
mind of Schelliug and his followers,
notably Oken and Steffens. The
vagueness and extravagancies of
this school brought the idea into
discredit, and the remedy applied
by Hegel, to put a logical process in
the place of fantastic suggestions,
ruined it utterly in the eyes of the
cultivators of exact research. Only
very few of the great students of
organic development, but among
them the greatest, von Baer, re-
tained a just appreciation of the
great aims of Schelling. The study
of development abroad was almost
entirely limited to embryology. In
other sciences the "statical" aspect
ruled supreme. In the face of this
somewhat retrograde movement

ON THE GENETIC VIEW OF NATURE.

355

In the second chapter ul' this vuhnue, which treated of 48.

Oi'iiftic view

the ijhysical view of nature, and developed the various »tr.iiKih-

i '' ' '^ fiail by

ideas wliich chister arouiul the term " energy," I sliowed {.'J.'J^'l^t^'"'
how, in the middle oi the century, through the intro-
duction of these ideas, a new clue w^as gained wherewith
to penetrate the connection of natural phenomena in
time and space. Before that time the conservation of
matter, the rule that matter can neither be lost ncjr
created, guided research by trying to account for the
apparent loss or gain of matter whenever and wherever
changes take yjlace in the material world. The science
of chemistry with its instrument the balance was built
on the foundation of this axiom. When, through the
labom's of ]\Iayer, Helmholtz, and Joule, the further
axiom became established that, besides matter, there
exists in the material universe a second quantity (or
substance) termed " energy," which, like matter, can Ijc
changed, but which, like matter, can neither be created
nor annihilated, the questions began to be asked, " If we

abroad, the merit of Mr Spencer
in urging the '" dynamical " aspect
long before the ' Origin of Species '
put forward a delinite niedianical
agency is so much greater, and he
himself says {' Factors of Organic
Evolution,' p. 5) : " Of the few
. . . who, espousing the belief in
a continuous evolution, had to ac-
count for this evolution, it must be
said that though the cause assigned
(viz., the modification of structures
resulting from modification of func-
tions) was a true cause, ... it
left unexplained the greater i)art
of the facts. Having been myself
one of these few, I look back with
surprise at the way in which the
facts which were congruous with
tlic espoused view monopolised con-

sciousness and kept out the facts
which wei'c incongruous with it —
conspicuous though many of them
were." Mr Spencer was also
probably the first who defined in
mechanical terms, applicable to
cosmical, lifeless, and living pheno-
mena alike, the process of develop-
ment, adopting the term evolution.
This fitting of the process of or-
ganic development into tlie general
formula of evolution, and the sub-
sequent announcement by Darwin
of the mechanical agency of over-
crow<ling and selection, has had
the effect of strengthening im-
mensely the genetic view of nature,
but also of obscuring and pushing
into the background the special
prol)lcm of life.

356 SCIENTIFIC THOUGHT.

receive energy, where does it come from ? if we lose
energy, where does it go to ? " It was recognised that
the great store of energy on which we at present depend
is the heat of the sun, which is partly used or wasted by
daily radiation, partly stored in the separated energies
of chemical substances, such as were produced by the
agency of solar heat in bygone ages ; the deposits of
coal in the bowels of the earth being a prominent
and important example. Where does the heat of the
sun come from, and how is it maintained ? These were
some of the questions which began to be asked. The
genesis of the cosmos, as suggested by Laplace and fanci-
fully elaborated by popular writers, had taken note only
of the matter in the sun and in the planetary system,
and had disregarded the heat ^ or energy which the sun
supplied, and on which the historical changes on the sur-
face of our globe have almost entirely depended. " But
physical laws are for our mental vision," as Helmholtz
says, " like telescopes which penetrate into the farthest
night of the past and the future." "" Shortly before the
pioneers of the mechanical theory of heat published their

1 "When Playfair (in his ' Illus-
trations of the Huttonian Theory')
spoke of the planetary bodies as
being perpetual in their motion,
did it not occur to him to ask,
What about the sun's heat ? Is
the sun a miraculous body ordered
to give out heat and to shine for
ever ? " (Lord Kelvin in 1868, " On
Geological Time," ' Popular Lec-
tures and Addresses,' vol. ii. p. 45.)
" The old nebular hypothesis sup-
poses the solar system and other
similar systems thi'ough the uni-
verse which we see at a distance as
stars to have originated in the con-

densation of fiery nebulous matter.
This hypothesis was invented be-
fore the discovery of thermodyna-
mics, or the nebulae would not have
been supposed to be fiery ; and the
idea seems never to have occurred
to any of its inventors or early
supporters that the matter, the
condensation of which they sup-
posed to constitute the sun and
stars, could have been other than
fiery in the beginning" (id., 1871,
ibid., vol. i. p. 184).

'' See ' Vortriige und lleden,' 3
Aufl., vol. i. p. 57.

ON THE GENETIC VIEW OF NATURE. 357

first theoretical and experimental essays, experiments had
already been made by Sir Joliii Herschel at the Cape,
and independently by PouilluL in France, with the object
of incasurinL!; the annual expenditure of heat by the 49.

",„,., .1 Til.- heat of

sun. They had found it to be an enormous quantity, tii.hun.
Tliey represented it popularly by the thickness of a crust
of ice on the surface of the earth, which the heat radiated
annually by the sun would be able to melt, and they
frtund this to be about -SO metres or 100 feet. Mayer
was the th'st who seems to have put the question
ilefinitely : How is this enormous expenditure of heat
defrayed, which would, if not in some way compensated,
have residted, even in historical times, in a great lower-
ing of the temperature of the sun, and hence also of that
on the surface of our globe, such as is contradicted by all
historical evidence ? The answer which j\Iayer gave to
this question was based upon an application of his con-
ception of the equivalence of heat and the energy of
mechanical motion. As the sun, according to the cos-
nioLronic liypothesis " of Laplace, was originally formed by

' These measurements were made ' si(l(5raiit le grand nombre que

in 1837, and very nearly agreed. nous voyons, comme bolides ou

The resulting figures Ci\n, of course, otoiles tombantes, uous ne pouvons

only be considered as rough ap- pas doubter qu'a tout moment des

proximations : they have been con- myriades d'astoroides semblables a

siderably increased bj' more recent une grele epaisse se jettent dans

observations. See A. Berry, ' A j tous les sens sur le soleil ou ils

Short History of Astronomy,' p. perdent la force vive de leur mouve-

397. I raent" (Mayer's ' Schriften und

- It does not appear that Mayer I Briefe,' p. 264) ; and M. Faye re-

brfiught his " meteoric" hypothesis marks that the fact that Mayer's

of the generation and maintenance ideas are opposed to Laplace's theory

of the heat of the sun into conncc- ] of the origin of the solar system

tion with the nebular hypothesis of j explains how it came about that

Kant and Laplace. In fact, in hi.s ' his theories were never reported on

first mention of it in his com- or explicitly mentioned. Leverrier

munication to the Paris Academy also seems to have ridiculed the

in 1810 he says simply: "En con- ' meteoric hypothesis, according to

358

SCIENTIFIC THOUGHT.

the gathering up of cosmical matter which, under the
force of gravitation, was in rapid motion — so the heat of
the sun originated through the conversion of the energy
of this arrested motion into heat. This process of gather-
ing up of cosmical or meteoric matter is still going on,
and it makes up for the loss or expenditure of solar heat
through radiation. Helmholtz, in the sequel of his
investigation into the conservation of energy, likewise
takes up this problem, and while admitting to some
extent Mayer's theory,^ shows that even without the
accession of cosmical matter, the mere contraction through
gravitation of the gaseous substances of the sun would
result in a continual production of heat. His calcula-
tions show that the amount of this contraction, resulting
in a diminution of the sun's apparent diameter, would not
be great enough to be perceptible during historic ages.
The theory of Helmholtz has in general been accepted as

which the sun's heat was kept up
by breakfasting anil dining on
meteorites. (See Wolf, ' Handbuch
der Astronouiie,' vol. ii. p. 433. ) It
is on the other side equally interest-
ing to see how Herbert Spencer, for
whom the nebular hypothesis was
a principal example of cosmic
evolution, failed to avail himself
of the strengthening support it re-
ceived through thermodynamics (see
' Essays,' vol. i., " On the Nebular
Hypothesis," 18.58). Had Mayer
brought his ideas into connection
with I^aplace's cosmogony, he prob-
ably would have hit upon the
correcter version, the contraction
theorj', which it was reserved for
Helmholtz to propound in 18.'>4.

^ The subject was about the same
time taken up by William Thomson
(Lord Kelvin), fii'st in a paper " On

the Mechanical Energies of the
Solar System " (Trans. Edin. Roy.
Soc, 1854), and continued in a
series of papers and addresses,
reprinted in his mathematical, &c.,
papers (vol. ii. ) in the 1st volume
of his ' Popular Addresses,' and in
an appendix to Thomson and Tait's
'Natural Philosophy.' He shows
that the form of the meteoric theory
propounded by Mayer, and inde-
pendently by Waterston (Brit.
Assoc, 1853), is as little able to
explain the maintenance of the
sun's heat through known historic
ages as the chemical theory of com-
bustion, which was alreadj- aban-
doned by Mayer in 1846, and finally
adopts Helmholtz's foi lu of the
meteoric theorj' as the most likely.
('Pop. Lect.,' vol. i. p. 365, &c. ; p.
373, &c.)

ON THE GENETIC VIEW OF NATURE. 359

a valid explanation of Lho maintenance of solar heat. In
fact, " as to the sun, we can now go both l)ack wards and
forwards in his liistory upon the principles of Newton
and Joule." ^

But further means for tcstin'T the correctness of these so.

Spectrum

tlieories were afforded by the invention, in 1859, of AnaiybU
Spectrum Analysis. It was found that the composition
of the light of luminous bodies, as revealed Ijy prismatic
scattering in the spectrum, enabled us to tell a good deal
about the nature of the body itself from which the light
emanated. We can tell whether the body is shining
with its own or with reflected light, what are the con-
stituents of the incandescent body, whether it is an
incandescent solid or an incandescent gas ; also whether
tlie body is in motion or not. The nebular hypothesis
supposed that the planetary system owed its origin to
incandescent, perhaps gaseous, matter, which, through the
force of attraction, was collected in different centres : the
tliscoveries of thermodynamics and of spectroscopy have
enabled us to expand and correct some of the assump-
tions of this theory, and to add new features to its
minuter elaboration. It is not necessary that the matter
which was originally scattered through space and was
ofathered into attracting centres should be itself incan-
descent or gaseous ; it may have been cold and solid like
dust ; rising in temperature and becoming incandescent
only througli the conversion of arrested motion into heat,
which again was maintained for some time through acces-
sion of new matter or progressive shrinkage, but which
must in a calculable time be radiated away, leaving a

1 Lonl Kelvin, loc. cit., vol. ii. p. 131.

360

SCIENTIFIC THOUGHT.

51.
Genesis of
the cosmos
- Fays and
Lockyer.

cold, heavy, lifeless, and lightless body behind.^ The
action of attractive power would sometimes reveal the
existence of cold bodies, with specific gravity much in
excess of our earth, as in the case of the satellite of
Sirius, and the spectroscope would reveal clusters of
stars or nebulte in the various stages of development,
such as the nebular hypothesis suggested as making up
the genetic process of our planetary system. Much
uncertainty and much conjecture must of course exist
in these chapters of science, which those who are in
full possession of the accumulated and yet very im-
perfect facts may venture to elaborate in a more or
less plausible or fanciful manner. Such attempts to
write the history of the universe have been made in
an original fashion by M. Faye in France " and Sir
Norman Lockyer ^ in this country. They have tried

' See Helmholtz, ' Vortriige und
Reden,' vol. ii., 3rd ed., p. 88, &c.

- ' Sur rOrigine du Monde,' 2nd
ed., Paris, 1S85. The author,
finding the celebrated cosmogonic
hypothesis of Laplace in "full
contradiction" with the actual
state of science, takes up an original
theory of Descartes, that of vortices,
in order to characterise not the
actual, but the initial, stage of the
solar system (see Preface) : " Autre-
fois, je veux dire il y a une vingt-
aiue d'ann^es, on avait les coud^es
franches pour imagiuer un sj'steme
cosraogonique : il suffisait de I'ac-
commoder aux notions contem-
poraiues d'Astronomie solaire et
de m(5canique celeste. II n'en est
plus de meme aujourd'hui, car la
thermodynamique assigne h, notre
Soleil une provision limitee de
chaleur, 1' Analyse spectrale nous
revile la constitution intime des
astres les plus ^loignes, et la paM-

ontologie nous fait renionter a des
epoques oil il n'y avait, sur notre
globe, ni saisons, ni climats."

* Whereas M. Faye has ingen-
iously modified the original and
older nebular hypothesis so as to
account for the anomalies in the
movement of some of the members
of our planetarj"^ system, which
were unknown or unexplained in
Laplace's time, and has tried to
account for the phenomena of loss
and supply of heat which thermody-
namical theory and palseontologieal
records reveal. Sir Norman Lockyer
has during more than thirty years
been occupied with the elaboration
of a special theory which tries to
harmonise the revelations of the
spectroscope as to the chemical
constitution of the sun and other
stars with the more recent develop-
ments of the atomic theory as
suggested by chemical and electrical
phenomena observed in our labora-

ON THE GENETIC VIEW OF NATURE.

361

to do what Professor Haeckel has done in the more re-
stricted field of the history of the living creation. Whilst
these attempts are by inany scioiititif authorities con-

tories. His speculations, based
upon liis own oltservations as well
as those of many other Eurojiean
and American authorities, such as
Seec'hi, Dumas, Kayser and llunge,
Kutherford, Rowland, Vouiig, and,
ahovo all, of Sir W. Crookes and
the late Professor Preston,— all of
which, as well as many others, he
generously quotes, — were given in
three works 'The Chemistry of the
Sun' (1887), 'The Meteoritic Hy-
jiothesis' (1890), and 'The Suii's
Place in Nature' (1897). He has
latterly collected the whole evidence
in a brilliant and fascinating volume
entitled ' Inorganic Evolution as
studied by Spectrum Analysis'
(1900). The central idea contained
in these books, and elaborated with
increasing detail and clearness, was
suggested as eaily as 1873, when
Sir N. Lockyer pointed out "that
many of the difficulties would
vanish it it were conceded that
the ' atoms ' of the chemist were
broken up or dissociated into finer
forms by the high temperatures
emploj-ed in the new method of
investigation " (' Inorg. Evol.,' p.
73). This " dissociation " hypothe-
sis has been much criticised, and
can only be firmly established by
patient and prolonged research in
that borderland which unites
chemistry and astronomy. As the
author says: "The chemist has
little interest in an appeal to
celestial phenomena, and astrono-
mers do not generally concern
themselves with chemistry. The
region investigated by the chemist
is a low temperature region,
dominated by nionatomic and poly-
atomic molecules. The region I
have chiefly investigated is a high
temperature region, in which mer-

cury gives us the same phenomena
as manganese. In short, the
' changes with which spectrum analy-
sis has to do take place at a far
higher temperature level than that
employed in ordinary chemical
work." It is well to note that
during and since the time when
the dissociation hyiiuthesis was first
prominently put forward researches
conducted on entirely different
lines have led to similar views —
i.e., to a further elaboration of
the atomic hypothesis. M. Berthe-
Idt wrote in 1880: " L'etude ap-
profondie des propridtcs physiques
et chimiques des masses clcmen-
taires, qui constituent nos corps
simi)les actuels, tend chaque jour
d'avantage Ji les assimiler, non ;i
des atomes indivisibles, liomogenes
et susceptibles d'eprcmver scule-
ment des mouvements d'eusemble
. . . il est difficile d'imaginer un
mot et une notion plus contraires
k 1 'observation ; mais ii des edifices
fort comjilexes, doues d'une archi-
tecture spociticiue et animcs de
mouvements intestius tres varies "
(quoted in 'Inorg. Evol.,' p. 28).
The first chemical confirmation of
the dissociation hypothesis came
in 1883 through 'the "beautiful
researches on the rare earth Yttria,
contained in Sir Wm. Crookes's
Bakerian Lecture to the Royal
Society. " In the lectures he gave
a sketch of the train of reasoning
by which he had been led to the
oj)ini<)n that . . . this stable mole-
cular group had been (by a process
termed ' fractionation ') split up into
its constituents" (ibid., p. llti) ; and
already, in 1879. Sir Wna. Crookes
had provisionally accepted the
"dissociation" hypothesis (p. 74).
Anomalies also in the periodic

362

SCIENTIFIC THOUGHT.

sidered to be prematvire/ they have contributed much to
impress on the thought of our age the genetic or
developmental view on a large as well as on a minute
scale.

law of Meudeleef were explained
by utilising this hypothesis (p. 165\
and in the sequel other authorities,
such as Brodie and Rydberg, ex-
pressed themselves in the same
sense (p. 164). These, and quite
recently the electrical researches
of Prof. J. J. Thomson (referred
to supra, p. 192), support the view,
originally suggested in a cruder
form by Prout, that what we call
elements are really compounds or
aggregations or complexes, built up
" from similar particles associated
with the presence of electricity "
('Inorg. Evol.,' pp. 167, 190; also
J. J. Thomson, ' Discharge of Elec-
tricity through Gases,' p. 198 sqq.)
^ It would be unfair not to state
that many works on astronomy are
still written in which all genetic
hypotheses are left out, the " stat-
ical " view being still the pre-
dominant one. Especially in Ger-
many, it seems as if " inorganic
evolution" is not very popular;
though a large amount of the best
work in spectrum analysis of the
stars has been done there by H. C.
Vogel, Kayser and Runge, Scheiner,
and many others. Dr Scheiner, in
his valuable work (translated with
the title ' A Treatise on Astro-
nomical Spectroscopy,' by Prof.
Frost of Dartmouth College, U.S.A.,
1894), has some important criti-
cisms on hypotheses and solar
theories (see Preface, and the dis-
cussion of the Meteoritic Hypothesis
in the German edition, Part II.
chap. i. ) In his ' Bau des Weltalls '
(Leipzig, 1901) genetic views are
not discussed. The older very
valuable works of R. Wolf (' Gesch.
d. Astronomic,' 1877, 'Handbuch
der Astrouomie, 2 vols., 1890-92)

give only slight attention to
" genetics," and consider even the
"statics" of the universe though a
possible yet a difficult problem (see
the last-named work, §§ 298, 299).
The latest and excellent ' History
of Astronomy,' by Mr A. Berry
(1898), is likewise reticent about
the evolution of the universe, ad-
mitting only a general, fairly well-
founded presumption in favour of
a modified nebular hypothesis (p.
409). It would, therefore, be
doubtful whether a history of
science should, at the end of the
nineteenth century, give much room
to these modern genetic theories in
astronomy. It is different with a
history of scientific thought. How-
ever premature and venturesome
it may appear to purists in science
to elaborate such hypotheses, there
is no doubt that the genetic argu-
ments and lines of reasoning have
got a firm hold of many great
thinkers in the physics of the
universe as well as in biology, and
that the genetic view of nature
in general has received very strong
support from the sevei-al trains
of reasoning and the rapidly in-
creasing revelations of spectrum
analysis of cosmical and terrestrial
objects, as set forth in Sir N.
Lockyer's interesting volumes.
Already thirty years ago Lord
Kelvin said of the spectroscope :
"It is not merely the chemistry
of sun and stars, as first suggested,
that is subjected to analysis by the
spectroscope. Their whole laws of
being are now subjects of direct
investigation ; and already we have
glimpses of their evolutional history
through the stupendous power of
this most subtle and delicate test.

ON THE GENETIC VIEW OF NATURE.

363

It is intelligible that these different lines in the
genetic view of nature — the different trains of reason-
ing which, in the course of our century, have started
independently in astronomy, in geology, and in natural 52.
history — should, as they develop and expand, come into lofeT and

•' 'J I X ' geophysics.

contact, and in the event either support or invalidate
each other. The former was the case when the geological
record, the discoveries of palaeontology, were brought in
to throw light on the history and development of species ;
the stories of nature, as written from the point of view
of the embryologist, the systematic zoologist and botanist,
and the pakeontologist, seemed more and more to confirm
and support each other. The same cannot be said if we
write the history of our earth from the point of view of
the geological record on the one side and from that of
the purely physical data afforded by thermodynamics
on the other. Lord Kelvin has shown ^ that the untold

We liarl only solar and stellar
ciieiiiistry ; we now have solar and
stellar i)hysiology" (Presid. Address,
Brit. Assoc, 1871. See 'Popular
Lectures and Addresses," vol. ii. p.
ISO).

' The literature of the subject
begins with Lord Kelvin's Address
to the Geological Society of Glas-
gow, February 27, 1868, which had
been preceded by a paper read be-
fore the Royal Society of Edinburgh
in 1865, briefly refuting the " Doc-
trine of Uniformity in Geology."
The address began with the words ;
" A great reform in geological
9[)eculation seems now to have be- !
come neces.sary," and in the sequel
stated : " It is quite certain that a
great mistake has been made — that
British popular geology at the pre- '
sent time is in direct opposition
to the principles of natural philo- i

sophy." These papers are reprinted
in the 2nd vol. of ' Popular Lec-
tures and Addresses' (see pp. 10
and 44). The attack was taken
up by Huxley in his Address to
the Geological Society for 1869,
reprinted in 'Lay Sermons,' &c.,
1891, p. 198. In a rejoinder to
this, delivered in the same 3-ear
at Glasgow {Inc. cit., p. 73), Lord
Kelvin shows how the current
geology was in the habit of look-
ing upon geological time as " an
element to which we can set no
Ijounds in the jiast any more than
we know of its limits in the future"
(quoted from Page's ' Te.\t-book '),
that Darwin's arguments themselves
involve an almost unlimited dura-
tion of the conditions admitting of
the operation of natural selection,
since, in his view, " in all jirobability
a far longer period than 300 million

364

SCIENTIFIC THOUGHT.

53.
Dissipation
of energy.

ages with which geologists, since the time of Lyell, have
been accustomed to reckon, are not supported by our
present knowledge of the periods during which the so-
called secular cooling of the earth has been going for-
ward— the period which has elapsed since the " consis-
tentior status " of Leibniz set in. He has thus put
before natural philosophers a problem — the reconcilia-
tion of the geological and the thermophysical record —
in which the genetic view of nature must be greatly
interested. But even more important than all this is
the doctrine of the dissipation of energy, referred to in
the second chapter of this volume — a doctrine of which

years has elapsed since the latter
part of the secondary period"
(' Origin of Species,' 1st ed., p. 287).
He shows that Button and the uni-
forniitarians were misled l:>y a be-
lief in the so-called stability of the
solar system, which took no notice
of the effect of tidal friction, nor
of the phenomena of radiation and
cooling in the past, .still less of the
law of dissipation of energy, and
maintains that the modern ideas of
evolution are in a sense a return to
the older conceptions of Leibniz,
Newton, and other more recent
geologists (loc. cit, p. 111). Since
the subject was thus brought
prominently forward, astr(jnomers,
physicists, and geologists have not
only — as Huxley expected them to
do (see ' American Addresses,' 1886,
p. 93) — adduced arguments in order
to arrive at an apjiroximate idea
how long the earth may have been
able to maintain organic life, but
biologi.sts have been induced to re-
vise the postulates of the extreme
— almost infinite — slowness, and of
the uniform continuitj' of organic
changes, originally contained in the
Darwinian theory. The influence
of these researches upon biological

and genetic reasoning has been to
emphasise the sudden changes, the
ruptures in the continuity of de-
velopment. In England the great
work of Mr William Bateson
(' Materials for the Study of Varia-
tions,' 1894) has familiarised us
with the idea of " Discontinuity "
in the origin of species. On the
Continent the rapid or even sud-
den appearance of variations is not
a new idea, though the oiiginal
suggestion of Maupertuis (1748;,
which was taken up and elaborated
by Geoffrey St Hilaire (see Yves
Delage, ' L'Heredite, p. 291), was
forgotten. In quite recent yeais
the reconciliation of the " persist-
ence of species " with their " varia-
bility," and of the "geological"
with the " biological " recoids. has
been much furthered bj' the tiieory
of " Mutation " of the celebrated
Dutch botanist de Vries. His view
is that " every species has its be-
ginning and its end ; it behaves in
this way like an individual." He re-
fers to the experiments on heredity
and crossing of butterflies of Stand-
fuss, who has been led to maintain
the existence of sudden or ' ' ex-
plosive " transformations ; and he

ON THE GENETIC VIEW OF NATURE.

3G5

the mechanical and cosmical importance was clearly fore-
seen by Lord Kelvin in 1852, but which is hardly
assimilated yet by scientific, much less Ijy popular,
thought.

The two doctrines of tlie conservation of matter and
of energy would lead to the idea that nature is a kind
of perpettitim mobile, nothing in the way of matter or
energy being lost ; and that such a reversal of her pro-
cesses is possible as we are accustomed to deal with in
purely mechanical contrivances. But a closer examina-
tion of the processes of nature, as distinguished from
those of artificial machines, revealed the fact that,

speaks of " periods of mutation " —
i.e., of rapid change of species, of
which he gives various instances.
He concludes that " as many steps
as the organisation has taken since
the beginning, so many periods of
' inut<\tion ' must have existed."
He considers the vital processes to
be built up out of "units." "Of
such units there are probably in
the higlier plants several thousands,
and tiieir ancestors must have run
through as many periods of muta-
tation." He concludes with the
following words: "Although such
calculations are naturally exposed
to much criticism, they neverthe-
less lead on very different roads to
identical results. Lord Kelvin,
who a few years ago collected and
examined criticiilly the various data
referring to this subject, arrives at
the conclusion that provisionally,
and with all reservations, the dura-
tion of life on the earth can be
placed at '2-4 millions of years. We
accordingly tiike this figure for our
biochronic equation. And as we
can with great proy)ability estimate
the number of elementary pro-
perties in one of the higher plants

at some thousands, it follows tliat
the interval of time between two
periods of mutation must have
lasted several thousands of years."
(See de Vries's Address to the (Ger-
man Assoc, of Science at Hamburg
in 1891, ' Verhandelungen,' &c-., ]>.
202, &c. ; also Lord Kelvin (Phil.
Mag. (5.) 47, p. 66). Mr Wallace
has, from an entirely diflerent point
of view, been led to the conclusion
that " certiiin detinite portions of
man's intellectual and moral nature
could not have been develo])ed by
variation and natural selection alone,
and that, therefore, some other in-
fluence, law, or agency is required
to account for them." This would
account for an a{)parent, though
perhaps not an actual, bi'oak in the
continuity of all natural processes,
which, in the dictum nutura non
facit saltum, has received a very
general expression and acceptance.
This dictum — supported by the
authority of Leibniz — is, however,
by some modern thinkers de-
nounced as a scholastic and anti-
quated aphorism. (See Yves
Delage, ' L'Hert^dit^,' &c., p. 266.)

3H6 SCIENTIFIC THOUGHT.

though matter and energy be mdestructible, the succes-
sion of phenomena, the changes and processes which we
call the genesis or history of things, are dependent on the
condition in which energy exists ; it being a general
tendency for energy not to be lost, but to become un-
available ; change and action, the life of things every-
where, depending on an equalisation of existing differ-
ences, say of level or temperature, or quicker and
slower motions. This great property of natural, as dis-
tinguished from purely mechanical, processes, explains
the fact that the processes of nature are irreversible,
that the clock cannot be turned back, that everything
moves in a certain direction. Various attempts have
been made to explain mechanically this remarkable
property of all natural processes, which seems to lead
us to the conception of a definite beginning and to
shadow forth a possible end — the interval, which con-
tains the life or history of nature, being occupied with
the slow but inevitable running down or degradation
of the great store of energy from an active to an in-
active or unavailable condition.
54. This doctrine of the degradation or dissipation of

Mystery of

the actual energy leads us one step farther towards an understand-

processes of ""^ ■•■

ing, or at least a description, of the processes of nature,
but also of their mystery. It lias been urged that, as
we always only deal with a small portion of existing
things, we have no right to apply conceptions which are
based upon a restricted observation to the totality of
things in the universe. For instance, we know nothing
of what becomes of the energy radiated away into empty
space. This is a reflection we should always bear in

nature.

ON THE GENETIC VIEW UF NATURE. :^G7

niind. We have also bcuii iciuiiKlcd that the theories of
ihe so-called stability of the planetary system which
were propounded in the earlier years of our century,
and which have found their way into popular treatises
on astronomy, are only approximations. (Jn the other
side, we have daily before our eyes the ever -recurring
instances of the building up and running down of natural
forces in smaller systems. Tliese we term organisms, the
living things of nature. It is from and through them
tiiat we first learnt to iook ui)ou tlie whole of nature
as having a history and a life. lmpercepti])ly we have
been led to study life, the genesis of things, on the large
scale and in the abstract, and in doing so have lost sight
of the life which goes on around and near us. ImiUi tlie
morphological and genetic views of nature started wilii a
liiological interest, but have gradually lost sight of it.
It is time to come back to it and to see what real
jirogress has been made during our century in the study
III life itself — the truly biological view of nature. This
will be the oliject of the next chapter.

368

CHAPTER X.

ON THE VITALISTIC VIEW OF NATURE.

In the foregoing chapters, where I have treated of the
several distinct aspects of nature which have become
helpful in science, I have always used the word nature
in its widest sense as comprising everything which is
revealed to us by our external senses, directly or in-
directly.

The title of the present chapter may suggest to some
of my readers that I am now narrowing down the mean-
ing of the word, — the vitalistic view of nature being
possible only where life is present. The astronomer
might say. Life is only known to exist in an infini-
tesimally small portion of the universe, on the surface
of our planet. This infinitesimal area has nevertheless
for us the greatest importance, inasmuch as all that
we know of the larger outlying world is only won by
inference from observations made in this restricted por-
tion. Independently of this, the conception of life itself
has always fluctuated between the two extremes of con-
sidering it as a universal property of all matter, or on
the other hand as quite a casual and accidental occur-
rence attached to conditions which, from a wider point of

ON THE VITALISTIC VIEW OF NATURE.

369

Between these i-

The cnsmi-

view, are extremely rare unci exceptional

two views, the cosmical and the terrestrial, the wider ' ^"^ »'"/ Mj«

' t(!rreslnal

and the narrower views of life, biological theories have ^'
tluctuated even in our century, and are still fluctuating.

' One of tlie foremost upliolders
of the wider coiic-ei>tion of anima-
tion as a universal property of all
matter is the celebrated German
naturalist, Prof. Ernst Haeckel of
Jena. See, inter alia, his Address
"Uel)erdie heutige Eiitwickeluiigs-
lehre im Verhiiltnis.se zur Gesanimt-
wi.ssen.seiiaft," 1876, reprinted in
' Gesammelte popuUire Vortriige,'
&c., part ii., Bonn, 1879, p. 119 :
"The recent controversies regard-
ing the properties of the Atoms,
which we must acce])! in some form
or other as the ultimate elemen-
tary factors of all physical and
chemical processes, seem to be most
easily settled by the assumption
that these smallest particles of mass,
as centres of force, possess a per-
manent soul, that every atom is
endowed with sensation and mo-
tion," &c., p. 109 : " Arriving at
this extreme psychological con-
sequence of our monistic doctrine
of development, we attach ourselves
to tho.-e ancient conce[jtions as to
the animation of all matter which,
in the philosophy of Democritus,
Spinoza, Bruno, Leibniz, Schopen-
hauer, have already found varied
expression." Tlie cosmical origin
of life has also been put forward by
surh authorities as Hclndioltz and
Lord Kelvin, as long ago as 1871.
(See Helmholtz's lecture " On the
Origin of the Planetary System,"
' Popul. Vortriige,' &c. , vol. ii. p.
91, and Lord Kelvin's celebrated
addres.s to the lirit. Assoc, at Edin-
burgh in 1871, reprinted in ' Pt)p.
Lects.,' &c., vol. ii. p. 199, &c.)
This theory of "Panspermia," of
the cosmical or ubiquitous nature of
the germs of life, has also been pro-
po.sed by biologists such as H. E.

vor,. IL

Kichter (1865), and luis been more
fully elaborated by ]*rof. W. Preyer
since the year 1880: it has received
further support in the genetic
theories of the chemical elements
and compounds put forward by
him in 1891 (' Die organischen
Elemente und ihre Stellung im
System,' Wiesbaden), and in 1893
('Das genetische System der cliem-
ischeu Elemente,' Berlin). Of the
fourteen elements which are
common to organic substances, he
says (p. 49) "that they belong to
the oldest elements"; that "they
admit of more varied relations,"
and " agree with the assumption
that, before being condensed as at
present on the surface of the earth,
they formed at higher tempera-
tures more stable protoplasms
which might be in other places the
carriers of life " ; and he has no
doubt " that there existed before
the present terrestrial phytoplasma
and zoojjlasma another plasma,
which ultimately came from the
sun " (p. 50). In fact, Prof. Preyer
asks whether, instead of living
being evolved from dead matter,
the latter is not rather a product
of the former. See also the refer-
ence to organic evolution as a
cosmical process in Sii- N. Lockyer's
' Inorganic Evolution ' (1900, p.
168). In many of the writings of
the celebrated German physicist
and philosopher, Gustav Theod.
Fechner, the fact is empliasi>ed
that we never see the organic de-
veloped out of the inorganic, but
that everywliere the living gener-
ates not only the living but more
frequently the inanimate. See
Lasswitz, ' G. T. Fechner,' Stutt-
gart, 1896, p. 130, &c.

2 A

370

SCIENTIFIC THOUGHT.

Vagaieness

of biological mocleni

theories.

living

No theory of the nature and origin of life has gained
universal acceptance : the very alphabet of biology, or
the science of life, has still to be written. We fancy
we possess some knowledge of certain forms or processes
which are common to all living matter, but the descrip-
tion of these has to be kept in the most general, not to
say the vaguest, terms : quite unlike the rudiments of
other scientific theories which deal with mathematically
defined conceptions expressed in distinct language and
formulae.

For instance, if we take one of the best founded of
biological theories — the cellular theory ^ of
matter — we notice that the pretty definite
description which the early supporters of this theory —
Schleiden and Schwann — gave of this morphological
unit of vegetable and animal structvire has been dis-
placed by much vaguer descriptions. Schleiden and

^ The history of tlie cellular
theory has been written from vari-
ous points of view in all the three
languages. I give the titles of a
few out of the great abundance
of excellent treatises. Foremost
stands the work of Prof. Oscar
Hertwig of Berlin, ' The Cell :
Outlines of General Anatomy and
Physiology.' English transl. by
Campbell (1895). Then there is
the more recent book by Prof.
Valentin Hiicker of Freiburg,
' Praxis und Theorie der Zel-
len- und Befruchtungslehre ' (Jena,
1899). In the French language
we have the great compendium of
biological theories by M. Yves
Delage, ' La Structure du Proto-
plasma et les Theories sur I'Hdr-
edite,' &c. (Paris, 1895). In English
we have the valuable treatise of
Prof. E. B. Wilson, 'The Cell

in Development and Inheritance '
(1896), and the excellent little work
of Pnif. James Arthur Thomson,
'The Science of Life' (1899). Of
high importance are also the older
works of the great master and
brilliant expositor in biological
science, Claude Bernard, notably
his celebiated lectures entitled
" Lecons sur les Phenomenes de la
vie communs au.x animaux et aux
v(5g(5taux" (1878 and 1879), which
every j'^i'^^-'^ophical student of
biology should read, as well as his
excellent posthumously published
little work, ' La science experi-
mentale,' 1890. Of him M. Dumas
says that he has " epuisd ses forces ii
I'etude du grand mystere de la vie,
sans pretendre a pen^trer toutefois
sou origine et son essence" ('Sci.
Exper.,' p. 6).

ON THE VITALISTIC VIEW OF NATURE.

371

Schwann detined the cell as " a small vesicle with a
tirm membrane enclosing Huid content." ^ i>ut the
cellular theory was gradually replaced by the proto-
plasmic theory of ]Max Schultze, the distinct membrane
was found to be frequently absent, and there only
remained " a small mass of protoplasm endowed with
the attributes of life." The cell, which had once been
compared to a crystal, became a \ery complicated and
indefinite thing : it became, in the conception of
biologists, an " organism." "" Further, the nucleus or
kernel to which Schleiden attached great importance
in his cellular theory was, for a while, quite lost sight
of — it being for a long time held that there exist non-
nucleated cells. Elaborate theories, such as that of
Haeckel,^ were founded upon this view, till in more

' O. Hertwig, ' Tlie Cell,' p. 5 n.

- Treatises on the subject uow
usually begin with an apology, the
word cell being considered mislead-
ing. Til us Hertwig says (foe. cit.,
p. 8), "It is evident that the term
'cell' is incorrect. Thar, it has,
nevertheless, been letained may be
partly ascribed to a kind of loyalty
to the vigorous combatants who
conquered the whole field of his-
tology under tlie banner of the
cell-theory, and partly to the cir-
cumstance that the discoveries
which brought about the new
reform were only made by degrees,
and were not geuerally accepted at
a time when, in consequence of its
having been used for several de-
cades, the woixl cell had taken
firm root in the literature of the
subject."

•' " Since, in consequence of the
inadequacy of former methods, no
nuclei had been discovered in many
of the lower organisms, the exist-
ence of two kinds of elementary

cells was assumed — ^ more simple
ones, consisting only of a mass of
protoplasm, and more complex ones,
which had developed in their in-
terior a special organ, the nucleus.
The former were called cytodes by
Haeckel (1866), to the simplest
solitary forms of which he gave the
name of Monera ; the latter he
called celluUe, or cytes. But since
then the aspect of the question
has been considerably changed.
Thanks to the improvements in
optical instruments and in staining
methods, the existence of organisms
without nuclei is now much ques-
tioned." (Hertwig, 'The Cell,' p.
54. See also Hacker, p. 239.) On
the other side ^l. Delage says
(' L'Herodite,' p. 37), " Apros avoir
decouvert un noyau chez la plupart
des moneres et des cytodes et
meme chez les Bacteries, on a, par
une induction ii mon sens un peu
hative, nii; I'existence d'orgauismes
sans noyau."

372

SCIENTIFIC THOUGHT.

recent times, owing to improvements in the microscope,
the existence of organisms without nuclei has become
doubtful. To complicate matters still more, to the
nucleus have been added the nucleolus, the vacuoles, the
central or pole corpuscles of the cell, &c. It is quite
evident from this short reference to the changes which
the definition of the morphological unit of living matter
has undergone, that no complete and accurate descrip-
tion lending itself to measurement and calculation could
be based upon it. The conception, useful as it may
l)e, has therefore not permitted of predictions, such as
mechanical, physical, and even chemical science, abound
in. " Has one ever," says Delage, " in a single instance
biifty of pre- clivined in advance the least of those structures which

diction.

the microscope has unveiled ? Has one divined the
transverse striation of muscles, the cilia of vibratile
epithelia, the prolongations of nerve-cells, the action
of the retina or the arcades of Corti, the chromosomes
of the nucleus, the centrosome of the cytoplasma ? " ^
Or, to take an example not from the morphology but
from the physiology of organic cellular bodies. It is a
very general and a very useful property of cells that
they readily absorb substances ; in fact, this property
is one of the most valuable aids in microscopic exam-

3.
Impossi

1 ' L'Heredite,' &c., p. 746.
Prof. Weismann, in his celebrated
' Es:?ays upon Heredity ' (Engl,
tracsl. by Poulton, &c., p. 2.55),
claims for the theory of descent
that " it has rendered possible the
prediction of facts, not indeed with
the absolute certainty of calcula-
tion, but still with a high degree of
probability. It has been predicted
that man, who, in the adult state,

only possesses twelve pairs of ribs,
would be found to have thirteen or
fourteen in the embryonic state ;
it has been predicted tliat, at this
early period of his existence, he
would possess the insignificant
remnant of a very small bone in
the wrist, the so-called os centralc,
which must have existed in the
adult condition of his extremely
remote ancestors."

ON Till-: VITALISTIC VIEW oF NATURE.

373

ination, insomuch as the diHeieiit behaviour of different
parts of the cellular b(jdy towards organic staining
solutions reveals to the observer dilTerences of structure
otherwise indistinguishable. Yet Professor Pfeffer/ wIid
has studied the absorbing powers of cellular substances
with much care, states that these cannot in the least
be foretfjM, but can only be determined empirically;
nor is the fact that cells require some substances
fur their life, while others are harmful, sufficient to
enable us to predict that either will l)e absorbed or
rejected. Again, hybridisation has Ijeen much studied
by gardeners and breeders, and also, since the time
of Darwin, by naturalists ; nevertheless, the result of
cross-fertilisation of individuals l^elonging " to different
families or species, or even only to different varieties,"
cannot be theoretically foretold, but " can only be dis-
covered by means of experiment." "'

This ignorance in which we are still placed as to the
forms as well as functions of living matter, has been a
subject of much comment by biologists all through the

1 See W. Pfeffer, ' Ueber Auf-
nahiue von Anilinfarbeii in lebende
Zellen.' Unterriuchungon aus dem
botaiiisclien Institul zu Tiibingen.
(juuted by Hertwig, 'The Cell,' p.
136.

- Hertwig, 'The Cell.' p. 310.
Annther point, .strongly urged by
Claude Hernard, is, that a knowledge
of structure in living beings — i.e.,
anatomical kno\vle<lge — in no wise
sutfices to explain the functions, does
not lead to phj'siological knowledge.
See ' La Science Expuriinentale,' p.
10.5, " L'impuissiince de I'anatoinie a
nous apprendre les fonctions organ-
iques devient surtout cvidente <lans
les ca.s particuliers ou elle est

roduite a elle - nieme. Pour le>:
organes sur les usage-s desquels
la physiologic exporinientale n'a
encore rien dit, I'anatomie reste
absolument uiuette. Cest ce qui
a lieu par exeniple jiour la rate,
les capsules surrenales, le corps
thyroide, &c., tous organes dont
nous connaissons parfuitement, la
te.xture anatomique, uiais dont
nous ignorons conipletement les
fonctions. De mcnie, quaud sur
un animal on dccouvre un tissu
nouveiiu et sans analogue dans
d'auti'es organismes, I'anatomie est
incapable d'en devoiler les pro-
prictcs vitales."

374 SCIENTIFIC THOUGHT.

century, nor can it be stated that uniformity of opinion
exists even yet as to the cause of this ignorance. The
enormous progress which has been made in our know-
ledge of the different properties of living things has
had an effect on the minds of those searchers to whom
we are mostly indebted for it, similar to that produced
on a wanderer who ascends an unexplored and distant
peak. Ever and anon, after scaling the eminence just
before him, he beholds a new and greater one rising
into view, which he contemplates with mixed feelings
of discouragement and of eager desire for advance.
But whereas our wanderer must know that the very
greatest height or distance is none the less a measurable
and attainable quantity, what hope has the biologist to
encourage him on his way ? No other — as it appears to
some — than the assurance that he is all the time ex-
ploring an unknown country, whereas the final achieve-
ment is impossible to him through the inaccessibiHty
of the position or the limitation of his own powers.
Others, indeed, from time to time have not taken this
despondent view, but, elated by the triumphs which
every new step has afforded them, have persistently
maintained that some day the last step will be taken
and the central peak really gained.
4. The history of biological thought, as distinguished

Oscillation "^ *= o ' o

th'uiiT''^' from biological knowledge, presents us with the spec-
tacle of a repeated oscillation between these two ex-
treme views : on the one side the continually recurring
conviction that the problem of life is insoluble, and,
on the other, the assertion that it is soluble, though

ON THK VITALISTIC VIEW OF NATURE. 375

it is admittedly as yet unsolved. Biological know-
ledge itself has progressed on the same lines as chem-
ical, physical, and mechanical knowledge ; it registers
the progressive conquest of new regions of phenomena
exhibited by living matter through the methods which
have been discovered in the abstract sciences : but it has
generally been felt that this knowledge does not ex-
haust the subject ; that there is some principle involved
which we know not ; and that we cannot think about
the living portion of creation without consciously or un-
consciously admitting the existence of this principle.
The unknown — nay, possiblv, the unknowable — element 5.

■^ ^ " . . The un-

or factor must be admitted to exist, and it involuntarily known
governs our reflections on that which we know. To
show the diflference between reflections on biological and
on other phenomena, which, though equally unknown,
yet do not contain an admittedly unknown factor, it
may be useful to refer to the scientific way of deal-
ing with meteorological phenomena. The science of
meteorology is probably as young as that of biology,
if not younger. Prediction of the weather is probably
even more uncertain than the prognosis of a physician
at the bedside of a patient suffering from a malignant
disease. Yet no one would suggest that there is a
special meteorological principle involved, as in the case
of the phenomena of life and death there is a special
biological principle. We are quite satisfied that purely
mechanical and physical and possibly chemical pro-
cesses make up the whole of the weather problem,
and that the difficulty of the latter is simply one of

376

SCIENTIFIC THOUGHT.

complexity and intricacy. A similar -^ attitude has in
the course of our century frequently been taken up
with regard to the problem of life, but it has always

We are still told that " in

been abandoned again."

^ See, for instaDce, what Huxley,
who, in his earlier writings, might
be termed a vitalist (cf. his ad-
dress "On the Educational Value
of the Natural History Sciences,"
1854, and his own criticism thereof
in the preface, dd. 1870, in 'Lay
Sermons and Addresses'), says in
his article "Biology," 1875, in the
'Ency. Brit.,' vol. iii. p. 681: "A
mass of living protoplasm is simply
a molecular machine of great com-
plexity, the total results of the
working of which, or its vital
phenomena, depend — on the one
hand, upon its construction, and
on the other, upon the energy
supplied to it ; and to speak of
' vitality ' as anything but the
name of a series of operations, is
as if one should talk of the ' hor-
ologity' of a clock." Similarly
Claude Bernard, in his ' Lemons sur
les ph(^nomenes de la vie,' &c., vol.
i. p. 379, says: " Eu un mot, le
phenomene vital est pre-^tabli
dans sa forme, non dans son ap-
parition. . . . La nature est in-
tentionelle dans son but, mais
aveugle dans I'execution." Both
Huxley's comparison of an organism
with a clock and the quotation
from Claude Bernard suggest a
parallel between the dictum of
Archimedes : " Sos not ttoC (ttw Kal
Thy K6(TfjLov KivTjcrw," and a possible
one of a biologist: "Give me an
organism, and I will explain its
action mechanically." In another
place Claude Bernard says {loc. cit.,
ii. p. 524) : " L'element ultime du
phenomene est physique ; I'arrange-
ment est vital."

- Examples of this could be
multiplied indefinitely. I take
one from an entirely different

field. Prof. Kerner von Marilaun,
the celebrated botanist, says ('The
Natural History of Plants,' transl.
by Dr Oliver, 1894, voL i. p. 52) :
" In former times a special force
was assumed — the force of life.
More recently, when many i)hen-
omeua of plant life had been suc-
cessfully reduced to simple chemical
and mechanical processes, this vital
force was derided and effaced from
the list of natural agencies. But
by what name shall we now desig-
nate that force in nature which is
liable to perish wliilst the proto-
plasm suffers no physical alteration,
and in the absence of any extrinsic
cause ; and which yet, so long as
it is not extinct, causes the proto-
plasm to move, to inclose itself, to
assimilate certain kinds of fresh
matter coming within the sphere
of its activity and to reject others,
and which, when in full action,
makes the protoplasm adapt its
movements under external stim-
ulation to existing conditions in
the manner which is most ex-
pedient ? This force in nature is
not electricity nor magnetism ; it
is not identical with any other
natural force, for it manifests a
series of characteristic effects which
differ from those of all other forms
of energy. Therefore I do not
hesitate again to designate as vital
force this natural agency, not to
be identified with any other, whose
immediate instrument is the proto-
plasm, and whose peculiar effect
we call life." Another example
is that of Prof. Virchow, to whom
we are indebted for the great rev-
olution which the application of
the novel conceptions of the cell-
ular theory has worked in the

ON THE VITALISTIC VIEW OF NATDRE. 377

accepting a mechanical conception," we must not " fall
into the very common mistake of trying to explain vital
processes as being duo directly {>> mechanical causes."
It has Ijoeu (piite as impossible to banish the word
life from the biological vocabulary as it has been to
banish the word " ought " from the ethical, liiological
knowledge has become purely chemical, physical, and
mechanical, but not so biological thought. The question
" What is life ? " still haunts us. Let us see what posi-
tion the foremost representatives of modern biological
research have taken up to this question. We find that
they can be <li\id('d intd Iwo classes.

First, there arc those who have studied the pheno- «■

^ T}ie purely

mena of living matter solely by the means which the f^lf^J.^""^
advancing sciences of dynamics, physics, and chemistry
have placed at their command. To them liiology is an
ai)plied science. The question " AVhat is life ? " is, ac-
cording to their view of method, only to be solved by
degrees, by l)ringing the forms and processes manifested
in the living world more and more under the sway
of observation, measurement, and possibly calculation.
The central problem as to the essence of life and the

aspect.

field of pathology. After hiiviiig
assisted in b.inishing the older
vitalism, he, to the dismay of
many of his own school, reintro-
duced the conceptiun of a vital
jjrinciple in a well-known review
entitled " Old and New Vital-
ism," in his own journal (vol.
ix. {). 20). " Indeed, the living
body consists, so far as we know,
of substances of the same kind
as we find in 'lifeless nature,' and
these substances have not only
no other properties and powers in

the living body, but they do not
even lose any of them. . . . Never-
theless, we cannot see how the
phenomena of life can be under-
stood simply as an assemblage of
the natural forces inherent in those
substances : rather do I consider it
necessary to distinguish as an es-
sential factor of life an impressed
derived force in addition to the
molecular forces. I see no ob-
jection to designating this force by
the old name of vital force."

378

SCIENTIFIC THOUGHT.

consensus of many mechanical, physical, and chemical
processes in the living organism does exist, but it can
only be answered by attacking it from all sides and
reducing it to ever narrower issues. The stronghold in
which life is intrenched is to be conquered by surround-
ing it on all sides by the attacking forces of dynamics,
physics, and chemistry. It will have to yield some day,
though that day may be far off. The number of those
who treat biology in this way has increased very much
ever since Descartes,^ and still more Lavoisier, applied

^ The claims of Descartes to be
considered as one of the founders
of modern physiology are put for-
ward by Huxley in several of his
addresses, notably in that of ' On
Descartes' Discours,' &c. , 1870
('Lay Sermons,' &c., p. 279); and
in that on ' The Connection of the
Biological Sciences with Medicine,'
1881 ('Science and Culture,' p.
32.5). In the latter address he says :
" Now the essence of modern, as
constrasted with ancient, physio-
logical science, appears to me to
lie in its antagonism to animistic
hypotheses and animistic phrase-
ology. It offers physical explana-
tions of vital phenomena, or frankly
confesses that it has none to offer.
And, so far as I know, the first
person who gave expression to this
modern view of physiology, who
was bold enough to enunciate the
proposition that vital phenomena,
like all the other phenomena of the
physical world, are, in ultimate
analysis, resolvable into matter and
motion, was Ren^ Descartes. . . .
And as the course of his specula-
tions led him to establish an
absolute distinction of nature be-
tween the material and the mental
worlds, he was logically compelled
to seek for the explanation of the
phenomena of the material world

within itself" (p. 335). It is in-
teresting to contrast with this
announcement of the banishment
of the animistic aspect from modern
physiology what Prof. Bunge says
in the introductory chapter to his
well-known ' Text-book on Physio-
logical and Pathological Chemistry '
(Engl, transl. by Woolridge, 1890) :
"The mj'stery of life lies hidden in
activity. But the idea of action
has come to us, not as the result of
sensory perception, but from self-
observation, from the observation
of the will as it occurs in our
consciousness, and as it manifests
itself to our internal sense " (p. 7).
" Physiological inquiry must com-
mence with the study of the most
complicated organism, that of man.
Apart from the requirements of
practical medicine, this is justified
by the following reason, which leads
us back to the starting-point of our
remarks : that in researches upon
the human organism we are not
limited to our physical senses, but
also possess the advantage afforded
by the ' internal sense ' or self-
observation" (p. 11). " The essence
of vitalism does not lie in being
content with a term and abandon-
ing reflection, but in adopting the
only right path of obtaining know-
ledge, which is possible, in starting

ON THE VITALISTIC VIKW OF NATURE. 37l*

tilt' purely scientific or exact method to the study of
the organism.

But biology is not only a subject of purely scientific 7.
interest. There is a second and larger class of students ""'''«''"=•
— those wlio study liiology as the basis of the art of
healing, the medical profession. To them the question
of life and death, of the normal or abnormal co-opera-
tion of many processes in tlie preservation of liealth
or the phenomena of disease, is of prime interest : the
knowledge of the mechanical, physical, and chemical
properties and reactions of living matter, of the con-
struction of the organs and their functions, is only the
means to an cml. Before the time of Lavoisier, with the
solitary exception of Descartes, biology was studied only
l)y medical men ; indeed to them both the existence and
the progress of the science were entirely due. For them
the paramount questions must always be, " What is life ?
What is its origin ? What is death ? What are its
causes ? What is disease ? " To this class of students we
are indebted for again and again l)ringing forward and try-
ing to answer these fundamental, these central questions.^

By the other, the smaller yet increasing class of purely
scientific biologists, we are being continually told that
these questions are premature or metaphysical," and

from what we know, tlie internal
world, to explain wliat we do not
know, the external world " (p. 12).
' See, for example, the two very
interesting and suggestive addresses
by Prof. Ed. von llindHeisch of
Wiirzburg, ' Arztliche Philoso-
phie' (Wiirzburg, 1888), and ' Neo-
Vitalisinus ' (Verhandl. d. ,Ges.
deutscher Naturforscher und Arzte
zu Liibeck, 1895, vol. i. \>. 111).

- See Claude Bernard, ' La Science
Expdriinentale,' 3""' ed., p. 211 :
" La vie est I'idce directrice ou la
force evolutive de I'l'tre ; . . . niais
I'erreur serait de croire que cette
force niotaphj'sique est active h la
fa(;on d'une force physique. . . .
La force mdtai)hysi(iue evolutive i)ar
laquelle nous pouvons caractt^riser
la vie e.st inutile h. la science,
parce qu'<?tant en dehoi"3 des forces

380 SCIENTIFIC THOUGHT.

that the answer which we may give to them is of no
scientific importance and of no scientific value. The
question, " What is electricity ? What is the ether ? "
cannot yet be answered ; nevertheless the sciences which
deal with the properties of the ether or of electrical
bodies are advancing daily. So also — we are told —
does the science of biology progress, even though we
leave the question " What is life ? " unanswered. This
would be a tenable position if the living organism were
like an electrical or an optical apparatus, constructed by
man himself with the modicum of knowledge which he
possesses. But the living organism, the eye that can
see or the nervous system that is in action, or even the
smallest " autonomous " cell, visible only with the micro-
scope, are each an apparatus constructed by nature with
the employment of all the intricate agencies which are
at her command. In dealing with such an apparatus,
we are again and again tempted to ask, " What is life ?
On what does the normal and healthy co-operation of
all parts in the living organism depend ? In what does
it consist ? " Fragmentary knowledge may be well
enough so far as it goes, but every medical practitioner
must painfully feel it to be altogether insufficient.
Where practical interests are involved we cannot in-
definitely postpone our answers. Science can wait and

physiques elle ne peut exercer
aucune iufluence sur elles. II faut
done ici separer le monde meta-
physique du monde physique phe-
nomenal qui lui sert de base, mais
qui n'a rien h lui emprunter. . . .
En rcsum^, si nous pouvons definir
la vie ii I'aide d'une conception

pas moins vrai que les forces me-
caniques, physiques, et chimiques,
sont seules les agents effectifs de
I'organisme vivant, et que la physio-
logiste ne peut avoir k tenir compte
que de leur action. Nous dirons
avec Descartes : on pense m^ta-
physiquement, mais on vit et on

metaphysique sp^ciale, il n'en reste agit physiquement."

ON THE VITALISTIC VIEW OF NATURE.

381

content itself with the known and the knowable. Prac-
tice is placed face to face willi tlio unknown and tlie
unknowable.^ Thus the question will auain and again
be asked, "What is life?" And for the benefit or
injury of mankind theories will exist which profess to
handle this delicate problem successfully, even as
weather-prophets will always exist though the necessary
knowledge for accurate prediction is still wanting.

One of the first in time and eminence in the course of
the nineteenth century to whom we are indebted, not

8.
Practice
ur^'cs the
quuKliun :
Wlial U
Life?

9.
Bichat.

' See what Tlieod. Bischoti', one
of the first and foremost German
anatomisttj of the new school, says
in his Eloge of Liebig (Miinchen,
1874), p. 60. " Inorganic science is
not any way induced and is nmch
less obliged to forsake the road
from the known to the unknown.
But what would have been the
result, what would still be the
result, if, in all our researches into
organised nature, and yet nioi-e in
all our actions which have refer-
ence to our state of health or ill-
health, we had proceeded, or were
now to proceed, only from data
firmly established as to cause and
Connection '( Could we then so much
a.s take a morsel into our mouths
or treat a cold otlierwise than with
fear and trembling ? Physiologists
and doctors have surcl^' always been
ready to proceed according to the
methods of exact science so far as
this was developed. But so long as
this gave but a stone instead of
bread, acceptance could n(Jt be
thougiit of ; necessity compelled
us to m.ake some attempt towai-ds
the solution of questions, to invent
some language in order to gain an
understanding ; and through this
fi-e([uently an erroneous ])ri>cedure
has arisen which outlives the means
for its correction." "Physiology,"

says Du Bois-Reymond (Eloge of
Joh. Miiller, ' Reden,' vol. ii. p.
19!>), " is the only science in which
one is obliged to speak about things
which one does not know. Chem-
istrv need not treat of unknown
compounds, nor physics of undis-
covered forces ; botany and zoology
do not miiid what kind of animals
may still move about unknown
among unknown vegetation in un-
explored regions. But in physi-
ology, even if we confine ourselves
to man, a definite number of things
is given which must be dealt with.
The spleen, the thyroid gland, the
thymus, the suprarenal capsules ;
many parts of the brain, ganglia,
nerves, the labyrinth of the ear — all
these are there, and nmst, accoidiiig
to the customary view, be there for
something. Manifold suppositions
as to the functions of these parts,
seemingly supported or invalidated
b}' pathological experience, have
put in the place of absolute dark-
ness a twilight which is richer in
delusions though not in certainty.
The e.\ pounder of our science is
obliged to lead his pupils through
this twilight on an anxious ])ath,
and then meet in return with that
discouragement which really is
owing to the suV)ject itself."

382 SCIENTIFIC THOUGHT.

indeed for the name, but for 'the modern science and
direction of biology, was Xavier Bichat, who during the
short period of his remarkable career (1771 to 1802)
remodelled biological studies. He approached the sub-
ject from the side of medicine and in a philosophical
spirit. In 1800 there appeared two treatises, one
on the membranes and tissues, and another entitled
" Eecherches physiologiques sur la vie et la mort."
These by their titles already reveal the twofold aspect
of biological science which drew the attention of Bichat
and his school. First, the attempt to reform biological
and medical knowledge by a close anatomical examination
of organic tissues in their normal and diseased states, for
the purpose of which he, within a very short time, ex-
amined six hundred corpses. The fuller account of his
researches is given in the four volumes of the ' Anatomie
Gen^rale ' (1801) and in the posthumous five volumes
of the ' Anatomie Descriptive,' completed by some of
his numerous pupils and followers after his death. In
these works Bichat created the science of histology
without resorting to the microscope, which was to do
such good service in the hands of those who came
after him, and without that application of physical and
chemical principles which during his time (notably
by Lavoisier and his school) had been applied with
much success in the theory of animal combustion and
in the foundation of another new science — that of
organic chemistry. The reasons which inclined Bichat
to distrust the microscope were the delusive nature of
the revelations of the imperfect instruments then in use.
They disappeared when, in the course of the next thirty

ON THE VITALISTIC VIKVV OF NATUliE. 383

years, the instrument was gradually improved. The
reasons which prevented Bichat from treating biology
as an application of pliysics and chemistry lay deeper,
and were rooted in the second great idea which governed
him and his school — his " Vitalism." As stated above, lo.
those who have studied the phenomena of life can be vitalism,
divided into two classes. There are those who have
been struck by the resemblance of the processes and
phenomena in living matter with those in dead or
unorganised matter : their attention has been directed
more and more to establishing a paralleHsm between
organic and inorganic nature, and they have fre-
quently ended in the conviction tliat their parallelism
warrants us in asserting their ultimate identity. There
have been others who have lieen impressed with the
essential and fundamental difference between organic
and inorganic processes and phenomena. To them, all
attempts to reduce the living process to a mechanism
seem to have failed, and however much they have ap-
preciated the insight gained Ijy the other class of
students, they have deemed it equally important to
emphasise the essential difference — the independence,
originality, and incommensurability of the phenomena of
life. The latter can be called Vitalists in the broadest
sense of the term. Bichat belonged to them. As the
former class of students have frequently arrived at the
thesis that organic and inorganic processes are ulliin-
ately identical, so the latter have frequently arrived
at the thesis that they are fundamentally opposed and
antagonistic. Bichat gives expression to this view in n.

° O 1 Hisdctlni-

his celebrated definition of life, as the totality of those ti'^""i'ife.

384

SCIENTIFIC THOUGHT.

functions which resist death. He adopts, on the one
side, the method of looking for the explanation of the
phenomena of matter in the properties of matter. In
the introduction to the ' Anatomie Generale,' he says : ^
" The connection of the properties as causes with the
phenomena as effects is an axiom which has become
almost tiresome to repeat nowadays in physics and
chemistry : if my book establishes an analogous axiom
in the physiological sciences, it will have fulfilled its
purpose." But being convinced of the essential difference
of the object with which the physiologist is concerned,

1 Claude Bernard (1813-78), from
whose various writings the passages
of Bichat are mostly taken, has very
fully analysed the theoretical views
of his eminent predecessor. The
following books belong to the best,
in substance and notably in style,
that have been written on the sub-
ject : ' La Science Experimeutale,'
3"'« ed., 1890 ; especially : ' Defini-
tion de la vie,' p. 119, kc. ; ' Lecons
sur les Phenomenes de la vie com-
muns aux animaux et aux v^ge-
taux,' 1878, especiallj' vol. i. p. 57,
&c. ; ' Rapport sur les progres et
la raarche de la Physiologie gdnerale
en France,' 1867. Inti-oduetion.
Although- Bichat was a vitalist, he
took a tii'st and important step in
the direction of getting out of the
vitalistic conceptions which he in-
herited from Haller, and which had
assumed a special form in the
Montpellier school. Through his
foundation of physiological research
upon an anatomical study uf tissues,
he localised the ])robleui of physi-
ology. Had he proceeded further
on the lines he himself started, he
would have thrown off, like his
successors, notably Magendie, the
hypothetical distinction between
physical, chemical, and vital pro-
perties, and become a pure ex-

perimentalist. The founder of this
purely experimental school in
France was Magendie (1783-1855).
It is interesting to note that prior
to Magendie in France, Charles
Bell in London had led up to
experimental physiology in Eng-
land by his famous distinction be-
tween sensory and motor nerves
(1811). But, according to Claude
Bernard, this anatomical distinction
required experimental verification
in a living animal. Magendie
furnished this in 182"2, and, together
with this corner-stone of modern
physiologj', laid the foundations of
the art of vivisection, with all its
wonderful discoveries and its dis-
favour in certain quarters. There
is no doubt that for many years
Paris became, through this in-
novation, the centre of medical
teaching on the Continent. As to
the distinctive merits of Bell and
Magendie, see Claude Bernard's
exhaustive examination (' Physiol,
gen.,' p. 11, &c. ), but also Du Bois-
Keymoud's Eloge of Johannes
Miiller ( ' Reden,' vol. ii. p. 176,
&c. ) According to him the
"Thesis " of Bell was not generally
considered to be proved till after
Midler's experiments in 1831.

ON THE VITALISTIC VIEW OF NATURE.

385

he does not advance to the position that the same
method will lead to parallel results. " There are," he
says, " in nature two classes of things, two classes of
properties, two classes of sciences. Beings (things) are
organic or inorganic, their properties are vital or non-
vital, the sciences are physical or physiological." He
did not anticipate that a faithful examination of the
properties of organised matter, of membranes and tissues
— which should not be limited to lifeless corpses — would
more and more reveal that their properties, the forces
acting on and in them, could be analysed into the
same forces as those we find in the inorganic world.^

^ According to Claude Bernard
('Physiol, gen.,' p. 5, &c.), three
things were wanting at the be-
ginning of the nineteenth century
to place physiology on a sjitisfactory
basis. The first — anatomical know-
ledge of the structure of living
matter — \va.s brilliantly established
by Bichat. But Bichat was not a
physiologist : he neglected the
second requisite, the study of the
continual conflict Vietween the liv-
ing organism and the mechanical
influences of the ''milieux," the
environment. "II faudra" — says
Bernard — " tenir compte de deux
ordres de conditions : 1°, des con-
ditions anatomiques de la matiore
organisee qui domient la nature
ou la forme des phcnomi^nes
physiologiques ; 2°, des conditions
physico ■ chimiques ambiantes qui
ddterrainent et reglent les mani-
festations vitales." A third im-
pulse was wanted in phy .biology :
" il fallait la ramener (lefinitive-
ment ^ la mcthode des sciences
expdrimentales ; il fallait la jwusser
avec vigueur dans la direction des
experiences sur les organismes
vivants, afin de la dctourner de la

VOL. II.

voie des hypotheses et des explica-
tions prcmaturees dans laquelle
elle s'etait si souvent egaree.
Un grand physiologiste francais,
Magendie, mon maitre, est venu,
au commencement de ce siecle,
exercer cette action gendrale sur
la science physiologique, en mcme
temps qu'il I'enrichissait par ses
propres decouvertes. Magendie fut
eleve dans I'ecole anatomique de
Paris, mais il n'otait point dispose
a suivre les successeurs de Bichat
dans leurs explications hypothe-
tiques. Doud d'un esprit prt^cis
et penetrant, sceptique et in-
dependant, il fut lie de bonne
heure avec Laplace, ([ui le patronna.
Par cette influence il se trouva
encore fortifid dans son auti{)athie
iunee pour les explications physi-
ologiques dans lesquelles on ne
se payait que de mots. Puis,
par une tendance spontande de
reaction qui, Ji cette dpoque, fut
trcs utile ii la physiologic, il
s'arreta Ji I'expcrimentation em-
pirique, c'est-il-dire au rdsultat
brut de I'expdrience considdrde en
dehors de toute interprdt;ition et
de tout raisonnement."

2 B

386 SCIENTIFIC THOUGHT.

Bichat, as Claude Bernard has told iis,^ thus clearly and
eloquently found the expression or " formula for the
fleeting ideas of his age. All the ideas of his con-
temporaries regarding life, all their attempts to define
it, are, in a way, only the echo and paraphrase of his
doctrine." We find it repeated by surgeons like Pelletan,
who practised in the Hotel Dieu, and by great naturalists
like Cuvier, who founded comparative anatomy. To both
of these life was a contest, a struggle, as it is at the end
of the century to the Darwinians ; but it was a struggle
of the living forces against the dead, whereas nowadays
it is the struggle of the living for supremacy amongst
each other or a process of adaptation to external condi-
12. tions. Whilst there is this great difference between

Vitalism ami _ _

Darwinism, thcsc two views characterising respectively the begin-
ning and the end of our century, they have one point
in common — they both emphasise the unrest, the con-
tinued change, the extreme mobility which distinguishes
Hving matter. But even this distinction has ceased
during the course of the century to impress us so
much as it did Bichat ; since the stability of the solar
system proclaimed by Laplace has ceased to charm
astronomers, and the dictum of ancient science has
been refuted : " materiam cceli esse inalterabilem." ^

' ' La Science Experimentale,'
p. 164.

- Claude Bernard {loc. cit., p.
172, &c.) dwells on this point with
great eloquence. " Aujourd'hui
I'esprit des astronomes est familiar-
ise avec I'idee d'une mobilite et
d'une evolution continuelle du
monde sidoral. Les astres n'ont
pas toujours existe, dit M. Faye ;
ils ont eu une periode de for-

mation ; ils auront pareillement
une pi^riode de declin, suivie d'une
extinction finale. . . . Les as-
tronomes, avant de connaiti-e les
lois des mouvements des corps
celestes, avaient imagine de i puis-
sances, des forces siderales, comma
les physiologistes reconnaissaient
des forces et des puissances vitales.
Kepler lui - meme admettait un
esprit recteur sideral par I'influence

ON THE VITALISTIC VIEW OF NATURE.

387

inorganic
in that
century.

After the age of IJichat, and largely through his
influence, — i.e., through the cultivation of anatomical
researches, — the pendulum swung in the direction of
proving more and more the parallelism of organic and
processes. It reached its maximum swing
direction about the secon<l third of the
Since then it appears to have again returned
in the opposite direction. Let us follow this movement
somewhat more closely, and see liow the stronghold in
which the innermost secret of life is intrenched has
been attacked from all sides Ijy all the processes and
methods of the mechanical, physical, and chemical
sciences, and how it has persistently refused to sur-
render.^ There was a time when the leading repre-

Uuquel \es plaiiotes suiveut dans
I'espace des courbe.s savantes saus
heurter les astres qui fournissent
•d'autres carricres, sails troubler
rhannouie reglee par le diviii
geoiiiotre." Another j)ri)pei-ty which
was once thouglit pecuHar to and
cliaracteristic of Hving organisms,
that of regeneration after mutila-
tion, of "redintegration," is now
known to exist also in lifeless struc-
tures: " M. Pasteur a signalo des f aits
<le cicatrisation, de redintegration
cristalline, (\\ii mdritent toute notre
attention. . . . Ces faits . . . se
rapproclient conipletement de ceu.K
que presentent les etres vivants
lorsqu'on leur fait une plaie plus
ou moins profonde"^(ibid., p. 173).
^ Bischoff, in his Eloge of Liebig,
who remained all his life a vitalist,
says (p. 57) : "We must, indeed, as
in the exact sciences, guard against
letting a mere word step in as an
explanation, wherever our insight
into the conditioning causes has
been insufficient, as was indeed re-
peatedly dune formerly, when a
Word was considered to be a sufH-

cient reason. We must consider it
to be the continual duty of organic
science to wage, as it were, a con-
stant war against thi> oi-ganic force,
and to dispute its territory where-
soever possible. If, for example, a
talent like his succeeds in deducing
many morphological traits of the
higher animal organisms from the
mechanical conditions of growth in
the embryo, &c., we shall grate-
fully accejit the proof ; but we
must all the while not forget to
ask the further question, by whom
these mechanical conditions have
been brought together. If it be
further true that the cells of the
embryo perform the most extra-
ordinary wanderings, in order to
arrange tliemselves into the various
tissues and organs of the animal
body, we shall welcome this as a
very interesting and remaikalile
phenomenon in the obscure region
of development ; but we have re-
ceived uo light on the question who
acts as guide to the wandering cells.
Similarly, if chemistry should some
day succeed in forming albumen ar-

388

SCIENTIFIC THOUGHT.

13.

The extreme
■vitalism.

sentatives of the medical profession considered it
unworthy and degrading to treat the human frame
as a mechanism, and to approach it by the methods
used in other sciences. " For the vitalist physician,"
says Hehnholtz,^ " the essential part of the vital pro-
cesses did not depend on natural forces which act
according to fixed laws. What these could do ap-
peared of secondary importance, and a study of them
hardly worth the trouble. He thought to be face to
face with something soul-like," — the anima of Stahl,
the vital force of the vitalists, — " which had to be met
by a thinker, a philosopher, a man of spirit. . . . Aus-
cultation and percussion were practised in the hos-
pitals," but I have heard it said that these were crude

tificially, we shall probablj' be able
to date from that day an entirely
new period in natural science, but
this artificial production of albumen
will never be feasible through the
simple affinities of the elements,
but only by producing a new
arrangement in organic substances
already formed by the plant. We
shall gratefully receive all such
increase of our knowledge : we do
not require wonders and belief in
miracles for the vital force, but
only a name for the effects of
which we do not know the
causes. . . . Neither the ancient
primpeval ooze nor the modern
Bathybius, neither the remote
monads nor the recent monera,
neither protoplasm, nor nucleus
and cell and their development,
confessedly so simple and easily
understood up to self - conscious
man, give us the smallest clue
to the forces at work and their
origin. This induces us to ascribe
them to a force, regarding the
essence of which we indeed know

no more than we know of any
cause that cannot be further an-
alysed. But we admit in doing
so the imperfection of our know-
ledge, and do not deceive others
by suggesting that mechanical
science could solve the secret of
organised nature."

^ 'Vortriige und Reden,' vol. ii.
p. 179.

- Chr. Fried. Nasse (1778-1851),
since 1822 professor at Bonn,
where, together with Walther,
Joh. Miiller, and others, he cul-
tivated the physiological method
in medicine, " was, as it seems,
the first German doctor in whose
clinical institute physical diagnosis
was introduced. From 1820 on-
ward percussion was practised ;
since 1821 the stethoscope was
regarded as an indispensable in-
strument " (Haeser, ' Geschichte
der Medizin,' .3rd ed., Jena, 1881,
p. 912). "The thermometer was
first used extensively at the bed-
side by James Currie (1756-1805).
His ' Medical Reports on the effect

ox THE VITALISTIC VIEW OF NATUKE.

!89

mechanical devices which a physician witli a clear
mental vision did not require : moreover, the patient
would thereby be degraded and treated as a machine.
Feeling of the pulse was the most direct method of
ascertaining tlie reactive power of the vital forces, and
was delicately practised as the most important process.
Elderly practitioners considered counting with a second-
watch as hardly good taste : taking the temperature
was not thought of. As to the eye-mirror, a highly
celebrated surgical colleague told me he would never
use the instrument, it being dangerous to throw brilliant
light into suffering eyes : another declared the mirror
might do well for oculists with poor sight ; he himself
possessed very good eyes and did not need it. ... A
celebrated professor of physiology had an argument with
his colleague in physics regarding tlie images in the
eye. The professor of physics invited him of physiology
to come and see the experiment. This was indignantly
refused : a physiologist should have nothing to do with
experiments, which might do well enough for a physicist."
The first great attack upon the organic system of u.

Attack from

forces, upon the citadel of life, was made by chemistry, ti'csideof
and was led by Lavoisier and the great school of chemists
which continued his work. It consisted in the applica-
tion of the theory of combustion, in which oxygen played
such an important part, to the processes of respiration,

chemistry.

of water, cold and warm, as a
remedy in fever and otlier disease.--,'
Loudon, 1797, "contains observa-
tions on the variations of the
body-temjjerature. . . . But these
attempts had little success. Not
till the middle of the nineteenth

century was the importance of
medical thermometry recognised,
first through the classical work
of von Biirensprung (1851), tlien
through that of Trauhe, but
mainly through Wuuderlich "
(ibid., p. 930).

390 SCIENTIFIC THOUGHT.

nutrition, and the generation of animal heat.^ Already in
1783 Lavoisier and Laplace had presented a memoir to
the Paris Academy of Sciences, in which they attributed
the generation of animal heat mainly to a process of
combustion which took place by the conversion of oxy-
gen into fixed air during the process of respiration.
Lavoisier continued his researches on these and other
similar physiological processes, such as perspiration,
along with Seguin. They presented a joint memoir
on the subject in 1790. It is also known, through
the posthumous publication of Lavoisier's scientific
papers in 1862, long after Liebig had brought out his
series of researches on this matter, that the former had
entertained very correct views on the economy of organic
life as it exists in the balance of the animal and veo;e-
table creations. After Lavoisier, the application of the
new science of chemistry to questions of the individual
and collective life of organisms was extended in a series

^ The two great discoveries of ] de riiomme ' (]798), by .1. P. T.

oxygen and of the electric cur- ! Baumes of Montpellier, against

rent at the close of the eighteenth which Fourcroy aimed his ciiticisnis

century were not long in being in a letter to Humboldt. On these

applied to the reform of medical extravagances see Haeser, ' Ge-

doctrine. In both instances exag- j schichte der Medicin,' vol. ii. p.

gerated theories were not wanting. | 737, &c. ; also I)r A. Hirsch,

Fourcroy, himself a medical student I ' Gesch. d. medicin. Wissenschaften

by profession and one of the most
ardent followers and promoters of
the new chemistiy, who, moreover,
edited a journal with the title ' La
medecine eclairee par les sciences

in Deutschland ' (Miinchen, 1893,
p. .567). There is no doubt that
opposition to this one-sided ap-
plication of some chemical or
])hysical theory, or of some special

physiques'(1790-92), found itnever- [ therapeutic method, which might

theless necessary to give warning ' be valuable to a limited and re-

against the premature introduction , stricted degree, partly accounted

into medical teaching of the new ! for the fact that the more thinking

ideas of chemistry. Of this many
instances existed, both in France

members of the pi-ofession clung
to the notion of a vital force or

and Germany, such as the 'Essai \ principle, as yet undefined but
d'un systeme chimique de la science 1 nevertheless existent.

ON THK VITALISTIC VIKW UF NATURK. 391

of very valuable but unconnected researches in all the
(litlerent countries where chemistry was cultivated.
Priestley, in England, hiul noticed ilu' purifying effect
of plants on air ; De Saussure, in a series of remarkable
experiments, carried on in the last years of the eighteenth
century at Geneva, established the fact that in sunlight
plants increase the quantity of cailnm and other con-
stituents in their tissues. Ingenhousz in Holland and
Senebier in France had shown that in the presence of
sunlight bubbles of oxygen gas are given off by plants
when plunged under water, and had traced this oxygen
to its source, the carbonic acid in the atmosphere. Sir
Humphry Davy had applied chemistry to agriculture ;
and, much later, (Jerman physiologists like Tiedemann
and Johannes ^Midler had recognised the necessity of
explaining the processes in the living body chemically.
All these labours, however, were detached, and their
value was little known. It was therefore a very timely
proposal which issued from the British Association in
1839, that a report on the present state of organic
chemistry should 1)6 drawn up. For this task no less
a person than Justus Liebig was selected.^ The event

1 The sources of information on
Liebig'.^ great work in revolutionis-
ing the science of life tViiough his
application of organic chemistry to
agriculture and i>hysiology are nu-
merous. In particular there are
two aclilresses by Vogel and von
Bischoff, delivered in the Munich
Academy in 1874, Hof mann's " Fara-
dav" lecture, delivered in the Royal

Liebig, his Life and Work." Bis-
ohofTs address contains a very full
discussion of Liebig's vitalistic sym-
])athies. His great influence was
established as much by his sjjecial
scientific discoveries as by his
method of teaching, — by his early
attempts to popularise science and
make it an educational power
through his well-known ' Familiar

Institution in 187.'>, and a very j Letters.' He was in this respect a

able sunnnary, drawn mainly from i pioneer, as aftei- liiin Hehuholtz and

these sources by Mr W. A. Shen- [ Du Bois-Reyniond were pioneers in

stone, in Cassell's 'Century Science' spreading scientific ideas by means

Series (189:")), entitled ".Justus von of ]inpular lectures and addresses.

392

SCIENTIFIC THOUGHT.

marks an epoch equally in the science of organic chemistry
proper and in the life-work of Liebig. The necessity
of collecting and systematising the scattered labours
of chemists and physiologists in this department was
simultaneously felt in France, where Liebig's friend and
rival, Dumas, published his ' Essai de Statique chimique
des ^tres organises ' as a conclusion to his course of

Liebig broke through the barriers
which in his age separated science
in Germany from general culture,
and the university professor from
the man of the world. From France
he learnt the merit of a clear style,
and from England the higher art of
popularisation. His fame did not
grow slowly and surely like that of
Helmholtz, spreading almost imper-
ceptibly from narrower into ever
wider circles : he took the world
by surprise, and stirred up every-
where inquiry, opposition, and con-
troversy. He ventured on great
and sweeping generalisations and on
daring experiments and prophecies,
with the result that in the final
establishment of truth his oppon-
ents had frequently as great a share
as himself. Notable instances are
his so - called " mineral theory "
of manuring and his theory of fer-
mentation. Through the former
the great division which separated
the processes in the living from
those which obtained in the inani-
mate (mineral) world was broken
down ; and through the latter the
modern notions of the ubiquity and
continuity of life were to a large
extent established, as will be seen
in the sequel of this chapter. The
correct notions which he enter-
tained as to the necessity of the
mineral ingredients (phosphoric
acid, lime, potash, &c.) in plant-
manures, which he started in op-
position to the older " humus " or
" vegetable mould " theory, was on
the point of being refuted by his

insistence on making his chemical
fertilisers insoluble, ignorant as he
then was of the absorbing and re-
taining function of mould ; but, a
generation after, the prevailing pre-
dilection for soluble manures was
again much modified by the intro-
duction of the " Thomas slag," and
the enormous improvements in the
process of extreme pulverisation.
Prof. Vogel in his above-mentioned
address gives many extracts from
Liebig's writings, referring to the
final and corrected expression of
the chemical theory of fertilisation.
These are so characteristic of
Liebig's habit of thought and his
whole mental attitude, that I tran-
scribe them: "When I knew the
reason why my fertilisers would not
act, I felt like a man who had re-
ceived a new life, for through this
all processes of agriculture were
explained, and now that the law
is known and lies clearly before
our eyes, there remains only the
wonder that we did not see it long
ago : but the human mind is a
queer thing, — what does not fit into
the circle of ideas once given, does
not exist for it. ... I had sinned
against the wisdom of the Creator,
and for this had received merited
punishment. I wanted to improve
His work, and in my blindness I
thought that in the wonderful
chain of laws which bind life to
the surface of the earth, one link
was missing which I, a helpless
worm, could supply" {loc. cit., p.
34).

ON THE VITALISTIC VIEW OF NATURE.

393

chemistry at the Medical School of Paris in 1841.
AVilh him was associated Boussingault, the man who,
next to Liebig, did most for the elaboration of the true
principles of agricultural chemistry.

To Liebig, organic chemistry did not mean the chemis-
try of the carbon compounds as it is defined nowadays,
and has largely become since Dumas himself introduced
into science the fruitful method and idea of substitution.
This idea extended the facilities of the laboratory chemist
enormously,^ but also marks the altered view which has 15.

Cliange in

since taken hold of organic chemistry, the alliance with organic

'=' •' chemistry.

arts and industries rather than with an understanding
of the economy and the phenomena of living organisms.
From the moment of that alliance dates the division
of organic chemistry into the two great branches of
the chemistry of carbon compounds and the chemistry

' It is well known that organic
cliemistry during Liebig'.s lifetime
outgrew the canons and tiie circle of
ideas in which he moved, and that
he complained of not being able to
undeistand the pajjers in his own
] periodical, the 'Annalen,' &c.
Liebig originally opposed Dumas'
ideas on substitution, but in the
end admitted himself defeated,
wlien, through Hofmann, he became
convinced " that the character of a
chemical substance does not depend
so much as he had supposed on the
nature of its constituent atoms,
and depends very largely also on
the manner in whicii these atoms are
arranged. Some years afterwards,
at a dinner given by the French
chemists to chemical visitors to the
F-xliibition of 18i)7, LieV)ig made his
defeat on tliis occasion tlie source of
a happy retort to Dumas, who had
asked him why of late years he had
devoted himself exclusively to agri-

cultural chemistry. " I have with-
drawn from organic chemistry," said
Liebig, " for with the theoi-y of
substitution as a foundation, the
edifice of chemical science may be
built up by workmen : masters are
no longer needed" (Shenstone, 'J.
von Liebig,' 1895, \i. 61). Already,
in 1838, Liebig and Wohlei-, in their
investigation on uric acid and its
derivatives, prophetically suggested
the twofold development which
organic chemistrj' was destined to
take : " From these researches the
philosophy of chemistry must draw
the conclusion that the synthesis
of all organic compounds wiiich
are not orytinised must be looked
upon not merelj' as probable, but as
certain of ultimate achievement "
('Annalen,' &c., vol. xxvi. ]>. 'J4'J).
In fact, we have now a chemistry
of organic and one of organised
substances.

394 SCIENTIFIC THOUGHT.

of organised nature. From this organic chemistry of
the modern school Liebig turned away — continuing to
lead research in the older and less fashionable direc-
tion. This choice is explained by the peculiarity of
his great mind, which, while investigating details, never
lost sight of the organic whole of natural processes,
and which allowed itself many a flight of imagina-
tion into unexplored regions. In fact, if we review the
16. work of Liebig from the side of the history of thought

Influence of

Liebig. rather than from that of science, we must assign to
it a very great and lasting influence. He was prob-
ably the first man of science who conceived the two-
fold meaning which belongs to the words, life and
organism, a meaning which was known and appreciated
by practical men, but which had, at that time, hardly
received scientific recognition.^ Life is not only defined,
as Bichat put it, by the contrast with death ; it is just as
much defined by the idea of co-operation or solidarity :
life is not only the property of individual beings, but
also of the collection or society of several individuals in
a larger organism. As such, political economy had con-
ceived it long before Liebig's time, but Liebig was prob-
ably the first scientific thinker who studied the economy
of nature, who fully realised the interdependence of
animal and plant life, and tried to reduce this larger life
of living things to scientific data and laws. Through
him and his school two terms have become current in
scientific and popular literature which, especially in the

1 The idea of the dependence of I Lamarck (see p. 314 s«^ra) ; but the

living things on the environment, philosophical ideas of that great

on the " milieu," was indeed fully j thinker were then unknown and

recognised and emphasised by i disregarded.

ON THK VTTALISTIC VIKW OF NATUKK. 395

(ieiiuaii tongue, have cliaiacU'i-iscd the new ideas Llieii
introduced into science, and have brought them home
to the intelligence of the educated classes. These two
terms have only heen inadequately rendered^ in any
other modei-n languaue : thev are the words " Stoff- n.
wechsel " and " Kreislauf des Lebens." The former de- Z'^^r^'^-^.
notes the continual change of matter connected with u-bcnti-
maintenance of form in all living things ; the latter
denotes the continual interchange which exists between
tlie separate members and the different provinces of the
living creation, the circulation of living matter and living
processes. Liebig looked u})()u nature on the large and
on the small scale as an economy, as a household, and
he applied himself to study the conditions of its exist-
ence, of its normal and abnormal states. Through
Liebig chemistry entered into close alliance with politi-
cal economy, or, as it is termed abroad, national economics.
We shall see immediately how the progress of science
has, in the further course of the century, tended to
emphasise this twofold aspect and define it more clearly:
how the individual organism, the bearer of life, lias been
traced to smaller and smaller dimensions and units, and
how, correspondingly, life as we see it on the larger scale
has more and more revealed itself as consisting in co-
operation, in the collective action of societies made up
of individuals. We have on the one side the doctrine
of the " Autonomy of the Cell," so elociuentlv proclaimed is.

■^ . "Autonoiiiy

by ProfcssoT- Yin'1u)w : nn the otiier side the doctrine of oftueCeii."

' We shall see farther on Ikjw
the word " Metabolism," with its
two suborclinate terms " A lui hol-

ism"' and *' Catabolism," is eveu
more expressive than the German
term " Stotf wechsel."

396

SCIENTIFIC THOUGHT,

" Division of the "Physiological Division of Labour," the happy ex-

Physiologi- , i • j. tt

cai Labour." pression invented by the great trench zoologist, Menri
Milne-Edwards,

Whilst Liebig was working at the great problems of
the economy of life, and making chemistry subservient
to the interests of agriculture, physiology, and pathology,
another influence was exerted — mainly in Germany — on
the study of the processes which take place in the living
organism. This influence had its source in an application
of the principles of dynamics and the more modern teach-
ings of physics.-^ It emanated from two distinct centres —
from Leipzig, where the brothers Weber '^ taught how to

^ In many passages of his inter-
esting and brilliant "Addresses"
Du Bois-Reymond has dwelt on
the great revolution which came
over physiological studies about the
middle of the centurj-, characteris-
ing it as a special German achieve-
ment. Claude Bernard has given
us an interesting account of a
corresponding, but not identical,
change of ideas in the great medical
schools of Paris. Quite recently Sir
Michael Foster has created in this
country an interest in the history
of medicine, notably of physiology,
and has on various occasions given
us masterly summaries of the results
of his historical research. I may
refer specially to his very lucid and
fascinating monograph on Claude
Bernard (London, 1899, in Fisher
Unwin's ' Masters of Medicine '
Series). Another authority in
modern physiology, Prof. M'Ken-
drick of Glasgow, has treated in a
companion volume of Helmholtz,
dwelling mainly on his physiological
labours, based upon his brilliant
application of physics and mathe-
matics. The two monographs ex-
hibit very clearly two distinct in-
fluences which have been at work

in remodelling the science of phy-
siology and the conceptions of the
phenomena of life.

- Regarding the position and in-
fluence of the three brothers Weber,
I may refer to former passages of this
history (vol. i. p. 196; vol. ii. chap. vi.
2xissim). The greatest of the three
— Ernst Heinrich Weber (1795-1878)
— occupies a unique position in the
development of the " science of life "
in Germany. He seems never to
have come under the influence of
the then prevalent " jAilosophy of
nature," and he had accordingly,
unlike Liebig and Johannes Midler,
nothing to unlearn. See on this
point Du Bois-Reymond's Eloge of
Miiller in ' Reden ' (vol. ii. p. 216),
also Ludwig's Eloge of Weber (Leip-
zig, 1878, p. 10). Weber represents
in the purest form the influence
which physics, based upon experi-
ment and measurement, had upon
the development of the study of
organic form and function, as Liebig
represents in the purest form the
influence of chemical research and
reasoning. In this respect Liebig
was more nearly related to the
Paris school, Weber to the Berlin
school, which he greatly influenced.

ON THE VITALISTIC VIEW OF NATURE. 397

apply strict experimental research, combined with actual
measurements, to pliysical, organic, and psychical pheno-
mena, which had so far escaped all exact treatment ;
and from Berlin, where in the person, and still more in
the school, of Johannes iMiiller, the great and complex i9.

_ Johannes

phenomenon of life in the higher organisms was analysed muirt.
into various mechanical and physical processes, each
connected with some well-defined organ which was more
and more recognised as possessing tlie properties of a
physical apparatus. A great deal of the work of the
numerous members of this school consisted in unravel-
ling with the microscope the structure of sucli organic
apparatus, and studying its action by physical measure-
ments and experiments. As examples and models of
this kind of work we have Du Bois-Reymond's 'Re-
searches in Animal Electricity' (1848), and Helmholtz's
'Physiological Optics ' (1867, second edition, much en-
larged, 1896), and 'Physiological Acoustics' (1862).
In the course of these labours it was found that the
older ideas of " Stoti'wechsel," and the conception of
the circulation of matter as it was taught in the school
of Liebig, required to be corrected and extended. I have
referred in an earlier chapter ^ to the interesting circum-
stances under which our modern notions of the conserva-
tion of energy first dawned independently upon Mayer
and Helmlioltz whilst studying the phenomena of heat
in the animal organism. In the school of Liebig we
meet with an occasional attempt to extend the idea
of " Stofiwechsel," the exchange of material or of
elementary matter in the living body of animals and

' See supra, ch.ip. vii.

398 SCIENTIFIC THOUGHT.

plants, so as to embrace likewise the imponderables —
heat, light, electricity, &c. We find Mohr treating of
heat and animal energy as substances which must be
counted among the elements or prime materials known
to chemists — just as the French chemists of Lavoi-
sier's school enumerated the imponderable along with
the ponderable elements of nature : even Liebig's first
edition of the ' Chemical Letters ' is not quite averse to
such an interpretation. The ideas on this matter were,
however, vague, and needed defining. When ]\Iayer
.attempted a first step in this direction, Liebig did not
see the value of it. The subject was only cleared up
when Helmholtz, in 1847, showed that all so-called
living forces were the different manifestations of a
■certain quantity of power to do work — later termed
energy — and that this power could show itself in
actual change and motion, or be stored up in tensions
in the system, later called " potential energy." After
this, " Stoffwechsel " appeared not only as an exchange
of material, but also as a change in the form of energy,
whereby potential or latent energy could be accumulated
in the organism and let loose, as the latent power of
an explosive substance is let loose by the pulling of a
trigger.

One of the immediate consequences of these varied
researches — all tending to show how the conception
formerly established in chemistry, physics, and dynamics
could be utilised in the description of the phenomena
of living matter, how the complex phenomenon of life
could be split up into a number of separate chemical
and physical processes, which could be imitated in

ON THE VITALISTIC VIEW OF NATURE. 399

tlic laboratory, and how tlie living organism could
be analysed into a complex of separate apparatus or
machines, acting on intelligible mechanical ami i)hysical
principles — was a radical change of the conception of
vital force and tlic vital i)iinci])le. It ceased in the . „ ^o-

' ' Innueiicc of

opinion of many to be opposed to other non-living forces, g^r^"^"'
as it was with Bichat ; according to otlieis it was non-
existent, or at all events useless ; others again reduced
it to a purely regulative function, or e\'en a meie
idea. A popular })hilosophy founded upon the unknown
principle of matter, and tlic c(|ually unknown and
even less clear princi])le of force, pronmlgated the
notion that science had succeeded in banishing all
spiritual entities, and was able to explain everything on
purely mechanical principles. Vitalism and animism 21.

^ •' ^ ^ Mechanism.

were at an end ; there only remained mechanism and
materialism. It is well to note that none of the great
men to whom we are indebted for the real extension of
our knowledge of Inological phemonena favo\ucd or
embraced this view. The reasons which ke^tt tlunn
from drawing what seemed to some the inevitable con-
sequences of their discoveries were manifold.

As I stated before, there are two ways of approaching
the problems of nature, and two interests by which our
researches can be guided. The one is the abstract
mathematical method, which begins with the sunplest
definable and measurable elementary processes, and tries
to i nutate the complicated phenomena of nature by more
and more intricate combinations of these elemeiitaiv pro-
cesses. The other is the more concrete method inspired
by practical interests. The mechanical, i)hysical, and

400 SCIENTIFIC THOUGHT.

chemical methods of analysis and synthesis follow the
former way, and they generally arrive at satisfactory
explanations of isolated parts of the actually existing
phenomena, or of special and simple cases. Notably,
they create the artificial world of manufactured things,
such as instruments, machines, chemical and mechanical
compounds. They may at times make it appear as if
this process of putting together, continued indefinitely,
would ultimately reach the real things which we behold
in inorganic, organised, and even in animated nature.
At all events no other way, it might seem, is open to
science, and the only thing that delays our progress
is the bewildering intricacy and complexity of things
natural. At the beginning of our century, when,
through Laplace and his school, many seemingly com-
plicated phenomena of nature, notably those of physical
astronomy, yielded to the processes of analysis just de-
scribed, there seemed for the moment a possibility of
building up a complete philosophy of nature on such
a groundwork. Laplace himself indulged in a fre-
quently quoted prophetic vision of this kind. When, in
the middle of the century, some molecular phenomena,
notably those of light, had likewise yielded to the
calculus, and when correcter views as to the nature of
forces had further brought another and different world of
phenomena into a calculable form, it seemed likely that
even the mysterious processes of living organisms might
be subjected to similar reasoning. It seemed time to
abandon the familiar conception of a special vital force,
and to hand over physiological problems likewise to the
physicist, the chemist, and the microscopist. A regular

ON THE vitalistk; view of nature.

401

crusade was accoidingly started in Gerinany by philoso-
phers, as well as by naturalists and biologists, against the
vitalists — those who believed in a special principle of life ;
and an impression was createil in the minds of thinking
outsiders that a purely mechanical explanation of life and
mind was finally decided on, and within possible reach.
Among those who assisted in bringing about this im-
pression, I need only single out two names — those of ^yfn*^ond
Hermann Lotze,^ the philosopher of Gottingen, and of

22.
Lotze and
Vu Bois-

1 Tlie position wliich Lotze oc-
cupies in tiie history of the con-
ceptions of life or of vitalism is
peculiar. If we read works deal-
ing specially with the history of
medicine, such as those of Haeser
or Hirscli, we do not come across
the name of Lotze at all, and it is
only in quite recent times, fifty
years after the appearance of Lotze's
writings dealing with vitalism, that
experts in physiology have re-
verted to his discus.sion of the
subject. See notably the follow-
ing : \. Rauber, " Formbildung und
Formsttirung in der Entwickelung
von Wirbelthieren " (' Morphol.
Jahrbuch,' Band vi.), 1880. 2.
Wilhelm Roux, " Einleitung zu den
Beitriigen zur Entwickelungsme-
chanik des Embryo," 188f) (re-
printed in ' Gesammelte Abhand-
lungeu,' vol. ii. p. 11, Leipzig,
1895). 3. 0. Hertwig, 'Zeit und
Streitfragen zur Biologie' (Heft 2,
Jena, 1897), pp. 2.3-29. 4. Carl
Hauptmann, 'Die Metaphysik in
der modenien Physiologic ' (Jena,
1894), p. 3. These and many other
recent references go back to Lotze's
article, " Leben und Lebenskraft,"
in Rud. Wagner's ' Handworterbuch
der I'hysiologie,' 1842 ; and to his
larger publications, 'Allgemeine
Pathologic undTherapie als median -
ische Naturwissenschaften ' (Leip-
zig, 1842), an<l 'Allgemeine Physi-

VOL. II.

olugie des Kbrperlichen Lebens '
(Leipzig, 18G7). The reasons why
Lotze's expositions were so little
regarded at the time were prob-
ably twofold. He taught that
the phenomena of life consti-
tuted a mechanical problem. This
was enough to dismiss in the
eyes of many empirical naturalists
the further, but not easily com-
prehended, statement of Lotze that
life was not merely a mechanical
problem. The definition and solu-
tion of the second part of the
problem was much more difiicult,
and Lotze delayed his expositions
on this side of the question for
ten years, when he published his
' Meclicinische Psychologic oder
Physiologic der Seele ' (18r>2),
which contained a metaphysical
introduction apparently little in
harmony with the supposed purely
mechanical or even materialistic
standpoint of his earlier writ-
ings. In the meantime several
important works had appeared
which carried out in wider or
narrower regions the purely me-
chanical or inductive and experi-
mental treatment, and quite revolu-
tionised physiological and medical
studies. I need only mention such
works as Jacob Henle's ' Allgemeine
Anatomic' (1840), and his ' Hand-
buch der rationellen Pathologic '
(1846-53). Henle, as von Kulliker

2 C

402

SCIENTIFIC THOUGHT.

Du Bois-Eeymond, the eminent physiologist of Berhn.
The former owed much of his scientific training to the
school of Ernst Heinrich Weber in Leipzig, the latter
to that of Johannes Mliller in Berlin. Both agreed
in denouncing the conception of a vital force — as it
was then called — as illogical, and moreover as scienti-
fically useless. But whilst Lotze distinctly stated that
his criticisms on this subject were only addressed to
scientific thinkers, and promised a further philosophical

says, "correctly saw that the work
of Bichat had to be remodelled ou
the foundations laid by Schleiden
and Schwann," an undertaking in
which von KoUiker himself laboured
with the greatest success. But
above all must be mentioned the
appearance of Rud. Virchow's
'Cellular Pathology' (1858, Engl,
transl. by Chance, 1860), "in which
he himself explains that he does
not give a system but a general
biological principle,"' and in so
doing lays the foundation for the
entire exact treatment of patho-
logical cases. It is, however, well
to note that Yirchow does not
regard life as a purely mechanical
problem. The works of such
authorities as Henle and Virchow
give as much or as little jihilosophy
and discussion of general principles
as physiologists of the exact school
required for about thirty years.
Those masters, indeed, had them-
selves grappled with the philo-
sophical problem, and had arrived
at a formulation which sufficed to
lead research into fruitful paths
for a new generation of experts
who themselves were not philo-
sophically educated. The term
vital force disappeared, and in the
specialist medical literature of a
lengthy period even life itself was
hardly any longer discussed. Thus
a firm basis was laid on which

mechanics, physics, and chemistry
could be usefully applied. A similar
silence as to general problems
reigns in the great school which
for two centuries built on the
principles laid down bj' Newton
in natural philosophy. Similarly
in chemistry, the foundations laid
by the atomic theory sufficed for
the greater portion of the century
following its enunciation. We
have seen in earlier chapters of
this work how, even in these
much more firmly established me-
chanical sciences, our century has
witnessed before its end discus-
sions again arising as to funda-
mental questions and leading prin-
ciples. A similar fate has come
over biological science, and with
it a renewed interest in the writ-
ings which stand at the entrance of
that epoch which was so rich in
the unravelling of definite and
special problems. Authorities like
Prof. 0. Hertwig warn us now of
that " other extreme which sees
in vital processes nothing but
chemico - physical and mechanical
problems, and thinks it finds the
true science of nature only in so
far as it is possible to reduce
phenomena to the motions of
attracting and repelling atoms,
and to submit them to calculation "
('Die Lehre vom Organismus, ' an
Address, Jena, 1899, p. 8).

ox THE VITALISTIC VIEW OF NATURE.

403

investigation of the question, J )ii Jluis-Reyniuiul ^ gave
the impression, in his earliest deliverance, that the

' Du Bois-lleyiiiDiitl's jjosilion in
the vitiilistic controversy is inter-
esting and instructive, inasmuch
jis he considerably modified his
opinions in coui-se of time. His
first dehverance on the subject is
to Ije found in the preface to his
celebrated ' Untei'suchungen iiber
Thierische Elektrititiit ' (March
1848). This discussion of the
subject followed soon after the
deliverances of men like Bcr/.elius
(1839), Schwami (1839), Schleideu
(184'2), Lotze (1842), on the same
subject, which are stated to have
been " ineffectual. " After the
lapse of twenty -four years Du
Bois - Reymond approached the
subject again in his celebrated
address at the German Association
of Sciences at Leipzig, 1872, en-
titled " Ueber die Grenzen des
Naturerkeunens." This deliverance
created a great sensation : the
jiainjihlet ajjjieared in many
editions and translations, and
only in this country failed to
get adequately noticed. A further
explanation of the views ex-
])Ounded in it was given by the
author (1880) in an oration at
the meeting held annually in
honour of Ijcibniz in the Berlin
Academy on the 8th of July. It
bears the characteri.stic title " Die
sieben Weltr;ithsel." These docu-
ments together contain the author's
" j)hilosophical creed," which ends
ill "Pyrrhonism," out of which
there seems no escape exce))t
through "Supernaturalism," which,
however, begins where science
ends. (See note 1 to the last-
mentioned address.) All three
documents are reprinted in the
two volumes of ' ]{eden ' (Leipsic,
1886-87), from which I quote. lu
the interval of a quarter of a cen-
tury which lay between the first and

second deliverance great changes
had come ovei- scientific thought.
The mechanical view, which had
been jiut forward in an extreme
form in 1S48, when it was projihe-
sied that " phy.-iology, giving up its
particularistic interest, would dis-
appear in the great united estate
of natural pliilosophy, would be
entirely dissolved in organic
physics and chemistry " (vol. ii. p.
23), had had time and opportunity
to show its power and its limits.
It had gained through gr(!ater
facility of application (such as
Ludwig's automatic curve - plot-
ting), through the larger con-
cepti(Hi of " StofFwechsel " as
denoting " metabolism " of matter
and energy. The author himself
had introduced a new definition
of life as a '• dynamical equi-
libriuTU " in the place of older
descriptions (vol. ii. p. 25) ; and,
above all, Darwin had shown the
possibility of a mechanical exjilan-
ation of so-called "final causes"
in nature. The author himself
was one of that great school,
emanating from Johannes Midler,
but now represented by the still
greater Helmholtz, which had
pushed the mechanical or exact
treatment to its furthest limits,
to the analysis of the phenomena
of the nervous system in its high-
est activity, those of sensation
and perception. It is therefore
highly significant that, instead of
confirming the earlier dictum, that
the exact treatment would halt
only at the most advanced point —
viz., the manifestation of '"free
will,"' — the aulhoi- is now forced to
admit that not only is the " origin "
of all motion quite obscure, but
likewise the lowest forms of
animation or con.sciousness are
not to be exi)lained mechanically,

404 SCIENTIFIC THOUGHT.

question was definitely settled and the road quite
clear for research. To those — and they comprised the
second class of thinkers referred to above — who were
unwilling or unable to follow Lotze and Du Bois-
Eeymond into the details of their criticism of the
illogical conception of force as employed in the term
" vital force," but who looked at the great facts of
economy, design, and recurrent order which are exhibited
in the living creation, these criticisms had little that
was convincing. If the term " vital force " was illogical,
some other term such as " vital principle " might be
substituted. The enormous difference between the
phenomena of living and of dead matter remained and
impressed itself on them. Liebig, and many naturalists
in France and Germany, had approached the study of
nature from the practical side. Their methods were not
mathematical but rather experimental, and very fre-
quently not limited to the laboratory and dissecting-room,
but carried out in the workshop of nature itself. In
spite of his successful attempts to establish clearer views
regarding the economic processes of living nature and
the application of chemical analysis, Liebig ^ to the end

the mystery which attaches to i be studied liy every one who desires
all beginnings as well as to the to be at home in the ancient and

great transitions in the ascending
scale of natural phenomena being
further emphasised and forcibly
driven home in the last - named

modern literature of the f^ubject.
The position of the author has
been many times criticised. See,
inter (dill, Kaufmann, ' Die Meta-

address, which, as has been said, | physik in der modernen Biologic '

bears the title "The Seven Enig- ! (Jena, lS9i], passim.

mas. " The three deliverances of Du i ^ Lord Kelvin in his essay " On the

Bois-Reymond, together with the | Dissipation of Energy " (reprinted

copious notes and references which
he gives in the latest reprint,
serve as a very good and lucid
exposition of the inherent diffi-

in ' Popular Lectures,' &c., vol. iii.
p. 464) has the following interesting
note: "The influence of animal or
vegetable life on matter is infinitely

cuities of the problem, and should . beyond the range of any scientific

ON THE VITALTSTIC VIEW UK NATLKE. 405
(if his life never satisfied himself that the phenomena of , ^.23.

'■ I-icbigH

life can he mechanically explained: he remained, in the viuiiHin.
face of much criticism, a Vitalist. So did WiJhler in
Germany — so diil most of the eminent physiologists in
France and in England. The crusade against Vitalism,
which was started in Germany, seems to have had little
influence on them. In 1854, six years after Du Bois-
Eeymond's essay on Vital Force, and twelve years after
that of Lotze, Huxley ^ couhl still, in the first of his
' Lay Sermons ' " On the educational value of the natural
history sciences," express opinions on the difference be-
tween living and not-living bodies which were distinctly
vitalistic, maintaining, much in the same way as Liebig
did in the later editions of his chemical letters, that "the
phenomena of life are dependent neither on physical nor
on chemical, but on vital forces"; and if, in 1870, he
could himself state that he had long since grown out
of this view, it is interesting to discover what were
the arguments which brought about this remarkable
change. I will at once state what seems to me to be
the great influence which combated Vitalism in this
country, which greatly strengthened the anti-vitalistic or
mechanical views in Germany, but which, as little as the
mathematical and philosophical criticism of Lotze and
Du Bois-lieymond, ever took real hold of biological thought

iu(iuiry hitherto entered ou. About
twenty - five years ago I asked
Liebig if lie believed that a leaf or
■.i Hower could be formed or could
grow by chemical forcea. He
answered, I would more readily
believe that a book on chemistry
or on botany could grow out of
dead matter by chemical processes."
' The address referred to wa.-^ re-

printed in 1870 in the well-known
volume, entitled ' Lay Sermons,
Addresses, and Reviews,' with a
" prefatory letter "" to Tyndall,
in wliich the following passage
occurs : " The oldest essay oi the
whole contains a view of the nature
of the ditiereuees between living
and not-living bodies, out of which
I have long since grown."

406

SCIENTIFIC THOUGHT.

24.
Darwin.

in France, where a modified kind of vitalism still pre-
vails.^ It is the far-reachincj influence of the reasonine
which sprang out of Darwin's theory of descent.

^ The older ideas of vital forces
have in all the three countries been
combated by authorities of the very
first order, but, characteristically,
in a very different manner — • the
phenomena of living bodies having
been attacked from different sides.
In Germany the mechanico-physical
school was for a time the dominant
one. In France the dominant school
was the so-called experimental, also
termed the vivisectional, school,
founded by Magendie. Between
these two extreme positions, both
ecjually opposed to the older
vitalism, there stood in the middle,
with a less strongly pronounced
antagonism to earlier conceptions,
those who, like Liebig in Germany,
Dumas and Boussingault in France,
approached the phenomena of life
mainly by the methods and reason-
ing of the new science of chemistry.
This school had a profoundly modify-
ing influence on the extreme views of
the experimental school in France.
It made itself felt mainlj' tlirough
Claude Bernard. In Germany this
influence was felt later, after that of
Darwinism had somewhat subsided.
In England it was the doctrine of
descent pure and simple which com-
bated the older vitalism : the ques-
tion became one of origins, and vital-
ism, as such, could be temporarily
ignored. The facts of variation,
overcrowding, natural selection, and
inheritance, presented such a mass
of materia], waiting to be sifted and
arranged by exact methods, that
the problem of the essence of life
and its beginnings was set aside.
Accordingly, the attempts both of
Darwin and Huxley to grapple with
the central and final problem of
vitalism are verj' few ; the latter
only repeating what had been said

long before him by thinkers of a
very different school. The question
was not answered, because, for the
progress of the sciences and for their
successful application in medicine,
it did not require to be answered.
It became a purely philosophical
question, and the only English
writer of authority who seriously
grappled with it was Mr Herbert
Spencer in his ' Principles of
Biology.' Darwin in 1863 wrote to
Hooker (' Life,' vol. iii. p. 18) : " It
is mere rubbish thinking at present
of the origin of life ; one might as
well think of the origin of matter."
Huxley, in a letter from the year
1884 (' Life,' vol. ii. p. 67), compares
life with a whirlpool, a favourite
simile of Cuvier's (see supra, vol. i.
p. 129), but is doubtful as to compar-
ing it with a machine. M. Delage
names Chevreul ('Considerations
gendrales sur I'analyse organique et
ses applications,' 1824): "Ha eu le
merite d'ecrire que la Force vitale
n'explique rien, qu'elle aurait besoin
elle-meme d'etre expliquce avant de
pretendre expliquer autre chose, et
que les phenomfenes de la vie ont
leur cause directe dans les priucipes
imra^diats constitutifs de la matiere
organisce. II n'etablit cependant
sur cette donnde une theorie de la
vie, car il conclut, au contraire,
que, eut-on ramene les phenomenes
vitaux II leurs causes prochaines et
aux forces qui rdgissent la matiere
inorganique, on ne serait pas encore
en etat de com prendre comment
I'etre organist en se reproduisant
repete avec une Constance si re-
marquable les caracteres de son
espece." Even Francois Magendie,
the great founder of the purely
experimental school of physiology,
says of Bichat's celebrated ' Recher-

1

ON THE VITALISTIC VIEW OF NATURE. 407

In order to enable my readers to comprehend clearly
the great change which has come over biological thought
through Darwin's writings and reasonings, I must now
introduce an idea which I have so far intentionally
avoided in discussing the various scientific views of
nature. This is the idea of final causes, the apparent
existence of a purpose (in German Zivcck), or an end
(in German Ziel) in all processes of nature, but pre-
eminently in those of the living portion of creation. In
all writings prior to Darwin a great deal is made of
final causes in nature, of the teleology of living processes.
The phenomena of life seemed safely intrenched in the
citadel of final causes : no mechanism could explain
them away. The very fact that organisms were com-
pared with machines, admitted the existence of a definite
end and purpose ; for it is the peculiarity of every
humanly constructed machine or instrument that it
serves a definite purpose which, in the mind of the
inventor or maker, suggested the peculiar arrangement or
organisation which we behold. The criticisms of Lotze ^

ches,' &c. : " Les esprits sdvbres et say tliat Lotze, though ceasing to

amis des progrfes des sciences ... be a vitalist, remained an animist.

ont regrettc que I'auteur o))po.sat Discarding vital force, he retained

sans cesse la vie aux lois physiques, the couce|)tion of a soul in a

comme si les etres vivans n'etaient manner which drew upon him the

pas de corps, avant d'etre des vdgd- ridicule of those wIkjui, like Carl

taux ou des animaux " ("avertisse- Vogt, he had converted to pure

ment " to the 4th ed. of Bichat's materialism. This has had the

' Recherches,' &c., 1822). consequence, that in more recent

' The lengthy discussions of Lotze times his whole philosophy has

contained in the writings quoted been stigmatised as dualistic, and

above are not easy to understand, that he has been accused of having

and it is not surprising that, be- halted halfway. His real meaning

yond the elimination of the con- j can be gathered more easily from

ception of vital force as useless to '. his later and more mature writ-

the purely scientific student, his ' ings : for his contcm)ioraries it

real meaning was at the time not must have remained to a great

grasped at all. In fact, we may extent enigmatical. See Kauf-

408

SCIENTIFIC THOUGHT.

and Du Bois-Eeymond ^ did not do away with this very
evident property of living things, but only maintained

mann {' Die Metaphysik iu der
Physiologie,' 1894, p. 7): '^How-
ever convincingly Lotze destroyed
the conception of a vital force, he
had no desire to criticise in a sim-
ilarly destructive manner the prin-
ciple of a soul, though both have
grown up in the same climate, in
the fertile country where sub-
stances blossom, &c. . . . And
although he emphatically, and in
many ways, urged that all organism
is a definite form and arrangement
of mechanism, he nevertheless
accorded to the principle of in-
herent disturbances (soul, will) a
partial control over the functions
of the animal body," &c. Accord-
ingly this view set only the physi-
ology of plant-life quite free for a
purely mechanical treatment, which
it received — after the suggestive
beginnings made by Schleiden —
mainly at the hands of Julius
Sachs, from whose ' Lectures on
Plant Physiology' (1887) Kauf-
mann gives the following very char-
acteristic extract : " The organism
is only a machine put together
out of different parts ; ... in a
machine, even if only made by
human hands, there lies the result
of deepest and most careful thought,
and of high intelligence, so far as
its structure is concerned," &c. (p.
623).

^ The two great facts which stare
every unbiassed student of nature
in the widest sense in the face,
and which always upset a purely
mechanical view, are Purpose and
"Will. Lotze recognises both, and
in all his writings never forgets or
ignores them. Naturalists, who
for the nonce are deeply interested
and fully absorbed in the analysis
of some definite organ, or some
special chemical power in the
organism, may usefully ignore

these two facts, of which the first
only intrudes itself if we rise to a
general, a comprehensive aspect ;
the second is a result of individual
experience. Nor did Du Bois-
Reymond ignore these facts. It
is interesting to see how he deals
with them in his earlier and later
writings. In the earlier period
he eliminates the problem of free
will as not a scientific problem
at all, and gets over the question
of purpose bj' a reference to the
evident existence of purpose in in-
animate nature also, — an idea which
really comes ultimately back to an
assumj)tion of a general animation
of the whole of nature, such as
has been maintained by many phil-
osophers and naturalists iu very
various forms. See, for instance,
the further remarks of Julius Sachs
in the passage quoted above. But
there is no doubt that this method
of viewing the teleology of nature did
not really satisfy Du Bois-Reymond,
for in the reprint of his paper on vital
force he refers to it as superficial
(' Reden,' vol. ii. p. 26), having in
the meantime adopted the explana-
tion of Darwin, whose " highest
title to glory " will, " so long as
philosophy of nature exists," be
this, that he to " some extent
allayed the agony of the intellect
that ponders over the problems of
existence" ('Reden,' vol. i. p. 216).
In 1887 he holds that what he
wrote as late as 1859, before the
appearance of the ' Origin of
Species', — for instance his cele-
brated Eloge of Johannes Miiller —
is antiquated, though it still gives a
valuable picture of the " tormenting
confusion of those who could not
free themselves from the emban-ass-
ing fetters of the fixity of species,
the incompleteness of the paheonto-
logical records, and, more than all,

ON THK VITALl.STIC VIEW UF NATCRK.

409

lliat this end or purpose was attnined ]>y iiuroly
luechuiiical processes, that no new force, called vital
force, need be assumed to exist, tliat it was the adequate
and sole object of science to disclose the mechanism by
which the various ends of life were attained. The very
idea of life, the vitalistic element or factor, was chased
away beyond the region of the knowal>le, and remained
merely an idea in the realm of thought, as it was for
Descartes and Leibniz, and as it has remained, up to
recent times, for von Baer and for Claude Bernard, and
for all those who do not accept the Darwinian explana- Lotzeand
tion. For Lotze, Du Bois-Eeymoud, and Claude Bernard ^ uemard.

of fiual causes ; in one word, of all
pre-Darwinian Darwinians " (vol. ii,
p. 299).

' Du Bois-Reymoncl (' Redeu,' vol.
ii. p. 557) claims that the greater
partof the progress in modern phj'si-
ology belongs to Germany, in spite
of the great talent and originality
of Claude Bernard. He thus de-
scribes the different position of
the three countries : " One branch
of physiology especially emanated
from Germany — general physics
of muscle and nerves. Whereas in
England experimental physiologj-
lay fallow, while it moved in France
in vivisection and zoochemistry,
being held down in both countries
by vitalism, German science was
the first to advance to the in-
vestigation of the surviving organs,
especially of the frog, looking
upon them as apparatus built up
by nature, extremely complicated,
yet conceivably only machines."
This was spoken in 1880. Since
that time a certain change has
come over physiological reasoning,
notably even in the very centre of
the physico - chemical school at
Herlin. In 1899 Prof. 0. Hertwig
warns us of the other extreme.

opposed to the older vitalism,
"which would lead us to a one-
sided and equally inadequate con-
ception of the vital j)rocess . . .
which would see in it merely a
chemico - physical and mechanical
problem, and would recognise the
genuine science of nature only so
far as it is possible to reduce
phenomena to motions, . . . and
to subject them to mathematical
calculation " ( ' Die Lehre vom
Oi'ganisnms,' an Address, Jena,
p. 8). How far Du Bois-Keymond
in later j'ears modified his earlier
notions, we can to some extent
see from his published addresses.
We know that the French school,
with Claude Bernard as its most
illustrious represent<vtive, never fell
into the mistake of looking at the
living organism as a physico-chemi-
cal machine, and we may be inclined
to attribute this lo a large extent
to those experiments on the living
organism which were first institut-
ed by Magendie, which, under the
hands of Claude Bernard, led to
the discovery of the action of the
pancreatic juice, of the glycogenic
function of the liver, of vaso- motor
nerves, and of the etiects of poisons :

410

SCIENTIFIC THOUGHT.

purpose exists in nature, notably in living nature ; it
is its very characteristic, its definition — the very " quid
proprium " of life,^ but it is useless as a scientific concep-
tion. It remains a problem for the philosopher, but the

all of them epoch - making dis-
coveries which revolutionised
physiological science, and which it
is difficult to conceive of as having
been made without vivisectional
methods. We have also a remark
from the pen of the late Prof. Georg
Wiedemann, that Helmholtz him-
self, that greatest master in the
line of mechanico-physical reason-
ing on the processes and organs
of the higher senses and the nerv-
ous system, foresaw the necessity
of resorting for further progress
to vivisectional research, to which
he had a personal dislike. (See
Wiedemann's Introduction to the
third volume of Helmholtz's
' Wissenschaf tliche Abhandlungen, '
p. xxiv.)

1 In many passages of his later
writings Claude Bernard has dealt
with the definition of life : most
fully in the posthumously pub-
lished volume entitled ' La Science
Experimentale ' (3rd ed., 1890).
He there arrives at the final state-
ments (p. 207) : "Je pense, quant
h moi . . . que les phenomenes
chimiques dans I'organisme sont
executes par des agents ou des
precedes speciaux ; mais cela
ne change rien li la nature pure-
ment chimique des phenomenes,
&c. . . . Les agents des phenom-
enes chimiques dans les corps
vivants ne se bornent pas ti pro-
duire des syntheses chimiques, . . .
mais ils les organisent. . . . Parmi
ces agents . . . le plus puissant et
le plus merveilleux est sans con-
tredit I'ceuf, la cellule primordiale
qui contient le germe, principe
organisateur de tout le corps.
Nous n'assistons pas h la creation
de I'ojuf ex nihilo, il vient des

parents, et I'origine de sa virtualite
Evolutive nous est cachee. ... II
y a comme un dessin vital qui trace
le plan de chaque etre et de chaque
organe ; ... ils semblent dirigds
par quelque condition invisible dans
la route qu'ils suivent, dans I'ordre
qui les enchaine. . . . C'est cette
puissance ou propriete evolutive que
nous nous bornons h. dnoncer ici qui
seule constituerait le quid pi-oj)rium
de la vie, car il est clair que cette
propriety evolutive de I'cEuf, qui
produira un mammif^re, un oiseau
ou un poisson, n'est ni de la
physique, ni de la chimie. . . .
En disant que la vie est I'idee
directrice ou la force evolutive dc
Vetre, nous exprimons simplement
I'idee d'une unite dans la succession
de tous les changements morpholo-
giques et chimiques accomplis par
le germe depuis I'origine jusqu'a la
fin de la vie. ... La force
metaphysique Evolutive par laquelle
nous pouvons caracteriser la vie est
inutile h, la science, parce qu'etant
en dehors des forces phj'siques elle
ne pent exercer jaucune influence
sur elles. II faut done ici separer
le monde m(^taphysique du monde
phj'sique phdnom(5nal qui lui sert
de base mais qui n'a rien Ji lui
emprunter. Leibniz a exprime
cette delimitation dans les paroles :
' Le corps se ddveloppe mdcanique-
ment, et les lois mecaniques ne sont
jamais violees dans les mouvements
naturels ; tout se fait dans les ames
comme s'il n'y avait pas de corps,
et tout se fait dans le corps, comme
s'il n'y avait pas d'ames. "... Nous
dirons avec Descartes : on pense
metaphysiqtiement mais on vit et
on agit physiquement."

ON TUK VTTAT.TSTIC VIKW OF NATURK. 411

uaLuialist may neglect it, or at best can only use it as an
" heuristic " help, as an indication where to look for tlie
special mechanical contrivances ^Yhicll he is trying to
unravel. It seems to me that the position which such
thinkers take up towards the objects or individuals of
living nature is similar to tliat of a mathematical student
who clearly comprehends the solution of an algebraical
problem, but who himself would be unable to find it.
He may all his life remain in this attitude without being
able to find any solution himself : he has got complete
hold uf the mechanism, but not of the idea, of mathe-
matical reasoning. The student of nature could thus
hope eventually to understand the mechanism of life, but
the idea is beyond his comprehension. This can be ex-
pressed by saying : the mechanism of life is ultimately
comprehensible, though highly intricate ; the idea of life
is transcendental, incomprehensible. Let us not trouble
ourselves about the manner in which life first originated,
but let us study the mechanical processes by which it is
maintained, by which its various ends are accomplished.
Let us study the mechanism of the clock, though this
may not tell us the story of its maker nor the process
of its manufacture. Those who cling to the conception
of a vital force or principle would probably not even
admit as much as this. It is doubtful whether Liebiu
to the end, whether Huxley in his earlier period, and
l)u Bois-Eeymond in his later writings, would have
admitted even this position.

We are now prepared tu understand the novel position 26.

. . Iiarwinism

which the Darwinian conception of natural processes "'"' ''"ai

^ causes.

introduced so far as the teleology of nature is concerned,

412 SCIENTIFIC THOUGHT.

— how it dealt with final causes, with the apparent exist-
ence of a purpose, an end in the processes of nature,
notably of the living organism.

It must here be remembered that the question how
living things come to exhibit traces of design and pur-
pose has really nothing to do with the nature and pro-
cesses of life : it is not necessarily a biological question.
Every machine show^s the same marks of design, but is
not therefore alive. The influence of Darwin's principle
of natural selection, of overcrowding and consequent
struggle for existence and survival of the fittest speci-
mens, has therefore not been in the direction of explain-
ing any of the vital processes which are at work in the
individual organism. It is at best merely a statistical
relation, a peculiar phenomenon occurring only in a large
or congested group of living and self-multiplying beings :
it presupposes the facts of reproduction, heredity, and
variation ; it does not explain them. Hence I dealt
with Darwin's ideas in the last chapter, and did not
introduce them under the present heading of Biological
Thought. As we shall see later on, Darwin did re-
cognise the necessity of attempting also a biological
explanation.

The possibility of explaining the marks of design as
merely apparent depends on the conception of the genetic
process acting on a large, a gigantic scale : individual
things put forth ever new developments by which they
eventually overtop their neighbours, ultimately advanc-
ing to such a degree of excellence and individual per-
fection that to an outside beholder the few surviving
specimens give the impression of having been origin-

0\ THE VITALISTIC VIEW OF NATrPJ-;. 413

ally designed. In fact, they (jnly exist because those
numberless indiNiiluals which could not grow in a suffi-
cient degree perished in the struggle. Onl\' Ukjsc in-
dividual specimens survived in whom, in one or a few
directions, something specially excellent was produced
at the expense of development in other directions. In
the mass, the crowd are sacrificed — i.e., automatically
crushed, in favour of the few : in the individual, one
special growth is automatically pursued at the expense
of a general l)ut less enduring — i.e., self-assertive — de-
velopment. The end — the seeming purpose — is pro-
duced in the process of production, it being merely
something more enduring — i.e., something Ijetter. It
conveys the impression to an outside beholder of having
been consciously set at the term of the process of devel-
opment ; in reality it was produced simultaneously. The
mountain peak which towers above its neighbours, and
gives a distinctive rounding off and finish to a landscape,
may be conceived as having been Ijuilt up by the selective
action of the natural artist who brought together the best
materials and placed them in their most enduring posi-
tions : in reality it owes its existence only to one out of
the numberless throes of nature which happened to take
place with stronger materials and in more stable forms
of arrangement and grouping, or it is due to the denuda-
tion of the strata surrounding it. The end and purpose 27.

° -^ "Natural

of any natural development is that which it can itself Jf4",j^(_'
automatically produce and endow with most distinctive "P"'"Po«e-"
and enduring characters, for this only survi\es at the
expense of weaker productions : there is a natural result
in development, but there need not be a purpose. The

414

SCIENTIFIC THOUGHT.

contemplation of the result may permit us to trace
backward the process by which it was brought about ;
but we are not warranted in assuming that it existed
independently, like the plan of a building or the purpose
of an instrument. In the place of a growth according to
a prearranged plan, Darwin put the conception of an
automatic adjustment called " natural selection " ; in the
place of a conscious end or purpose he put the concep-
tion of a mere result, a product, the " surviving fittest." ^
The development and proof of Darwin's ideas gave a
new impetus to biological research, as it did also to the
science of the history and economy of nature. The fact
that the phenomenon of selection, or rather of automatic
crowding out, presupposes intimate relations and contact
of every living thing with numberless other similar and
dissimilar beings, led naturalists into the open air, to

^ A very full appreciation of the
great chanf^e that has come over
the sciences of nature through the
influence of Darwin will be found
in the various wiitings and ad-
dresses of Prof. Haeckel, ncjtablj'
in his address to the German As-
sociation in 1877 at Munich, " Ueber
Entwickelungslehre " (repj-inted in
' Gesaminelte popuUire Vtjrtrage,'
vol. ii. ]). 97). A more critical exam-
ination, referring specially to the
central biological problems, is the
address by Du Bois-Reymond, de-
livered in 1876 in the Berlin Acad-
emy, and reprinted in ' Heden,' vol.
i. p. 21], with valuable literary
notes. He there discusses how far
the principle of natural selection,
in addition to the general doctrine
of descent, has been adopted or op-
posed, and refers to the outstand-
ing difficulties. " One of the great-
est difficulties,"' he .says (p. 226),
" presents itself in phj'siology in the

so-called regenerative power, and —
what is allied to it — the natural
power of healing : this may now be
seen in the healing of wounds, in
tlie delimitation and compensation
of morbid processes, or, at tlie
farthest end of the series, in the
re -formation of an entire fresh-
water polyp out of one of the two
halves into which it had been
divided. This artifice could surely
not have been learnt by natural
selection, and here it ajjpeai's im-
possible to avoid the assumption of
formative laws acting for a pur-
p<i.se. The}' do not become moi-e
intelligible by the fact that the
regeneration of mutilated crystals,
observed by Pasteur and others,
points to similar proce.sses in inani-
mate nature. Also the ability of
organisms to perfect themselves by
exercise has not found sufficient
appreciation with regard to natural
selection."

ON THE VITALLSTIC VIEW OF NATURE. 415

outdoor research, into the arena of real life. On this
I dwelt in the last chapter. Ideas of a cognate kind
had already emanated from other schools, such as that
of Liebig, — the circulation of life in the different pro-
vinces of nature, the interdependence of dillerent species
of living things. Isolated investigations, like those of
Gartner and Sprengel, of Iluber and Lubbock, on insect
life, or of bacteriologists like Pasteur and Boussingault
on fermentation and fertilisation, received a fitting place
as important chapters in the economics of nature. The ss.

Oi'K'anisation

problem of life became twofold — the life of the com- andiudivid-

■^ nation.

munity and the life of the individual : organisation and
individuation. Two great (juestions presented them-
selves : What is an individual ? what is a society of
individuals 1 Physiologists were from of old accustomed
to ask the former ; economists like Rousseau and Adam
Smith had asked the latter question. Both now became
questions for the biologist. Physiology and economics
joined hands. In isolated instances, as in those of Liebig
and von Baer, these two interests had already been united.
The real meaning and reason of this union now Ijecame
clear to every one : it revealed itself as founded on the
two characteristic features of life— individuality and co-
operation. With the exception of the strong emphasis so.

, X • 1 ■ • 1 Biology and

put l)y Liebig on tfie latter side of natural, notably loonomics.
organic processes, biologists before Darwin liad mainly
studied the phenomena of individual life. In two special
directions — in embryology and in the cellular theory —
they had made great progress. 1 have already treated
of these advances in their bearing ujton morphology, the
study of forms, and upon genesis, the study of change

416 SCIENTIFIC THOUGHT.

and development. Let us see how they affected biology
proper — the study of life.

The early propounders of the cellular theory were
evidently much influenced by the then existing theories
which explained the constitution of inorganic chemical
substances by atoms and by the processes of crystal-
lisation. The progress of science, however, was in the
direction of showing more and more that these borrowed
conceptions are quite inadequate. Eeasoning or thinking
on organised matter is quite different from that which
refers to unorganised substance. Chemists and physicists
deal with atoms as imaginary units, which form the ideal
groundwork for constant arithmetical proportions or for
the action of calculable mechanical forces measured
by observable movements. Biologists, whether dealing
with plants or animals, approach the cells which they
regard as the units of living matter with the micro-
scope— an instrument which, till quite recently, has only
been sparingly used in chemical research. The units
of the chemist far transcend our powers of vision ; the
units of the biologist are to some extent accessible to
our senses. All organisms have been found to be
analysable by the aid of the microscope into similar
morphological constituents called cells, which present
very similar forms and functions. This has had the
advantage of permitting the phenomena of life to be
analysed into a few fundamental processes common to
all living things ; the great diversity of the larger
organisms, and the more conspicuous phenomena of life,
being conceived as put together in various ways out of
these elementary units, which exhibit in varying degrees

ON TllK VITALISTIC VIKW OF NATIKb:. 417

of intensity the living processes common to all. Just
so a state or human society is made up of a large
numl)er of individuals, all having the same human
nature, who carry on the different functions peculiar
to each with varying degrees of efficiency. The concep- 3o.

^. . , „ , . -^ '- The cellular

tion or the cell as the unit or type of all living H'wry.
matter, and the further discovery that there exist uni-
cellular beings which are not essentially different from
the constituent living elements of the most complicated
organisms, has brought physiological research to a focus.
The difficulties in the study of biological phenomena
have vanished as those of the organic chemist did on
the introduction of the conception of valency, of the
saturating powers of chemical substances. Accordingly,
if we compare a text-book of these subjects written in
the middle of the century with one Ijelonging to the
latter part of it, we find an enormous difference of
treatment. It is instructive to contrast the introduction
given in Johannes ]\Iiiller's ' Elements of Physiology '
and that of Professor Michael Foster's ' Text-book.' The
former represents the most advanced knowledge obtain-
able at the end of the thirties — the latter that of a
generation later. The former contains a lengthy intro-
duction on general physiology — the latter a short one
on the physiological properties of a living amoeba,^ a

' Already, in 1835, K. E. vou
Baer pointed out how tlie study
of one small animal can revolution-
ise our entire reasoning. " Ninety
years ago a naturalist discovers
the hydropolyp, an insignificant
slimy animal, not larger than a
peppercorn, and how, without
head, sense-organs, muscles, nerves,
blood, and sexual organs it never-

theless is nourished, grows, feels,
moves, and multiplies, — how it can
even be divided, each part form-
ing a whole : he observes it with
much wonder for nine years with
untiring perseverance. At that
time many would, no doubt, con-
sider such an occupation childisii
and unworthy, yet these diligent
observations have slowlv but ma-

VOL. II. 2 D

418 SCIENTIFIC THOUGHT.

unicellular organism which is taken as a type, a model
of all the phenomena of life. The former consists of
philosophical and abstract generalisations, gathered from
many sources ; it treats of life in general, of the vital
force, of the difference between animal and plant life,
&c. : the latter sums up the whole matter of the treatise
under a few heads, taken from the life of the simplest
liviuCT thino;. The generalisation has become an actual
observable example. This transition from the abstract
to the concrete, from the idea to the thing itself, is owing
mainly to those definite conceptions which in Mliller's
time were being slowly elaborated : these were the cellular
theory, the larger conception of " Stoffwechsel " as con-
tained in the term " metabolism," and the conception
of " differentiation of tissue " connected with division
of labour. The two former are already very clearly
foreshadowed in Theodor Schwann's microscopical re-
searches ; the latter takes us back to K. E. von Baer's
embryological researches, to which the Darwinian idea
of a struggle for existence, and the consequent tendency
to one-sided development of form and function, have
given an additional importance. Of the first and third
of these definite modern conceptions I have treated
above. The cell is the morphological unit of living
matter. The process of differentiation was recognised

terially iuflueuced phj'siology, the polyp that have changed the former

basis of medicine, and hence also aspect of things, and that the trans-

the latter ; and it is incalculable formation of the general views of

what many of those here present life has altered the theory of sensa-

have gained through such influence , tiou, circulation, &c., very materi-

in days of sickness or may still gain. ally, and is still active" ("Blicke

Whoever carefully studies the de- ; auf die Eutwickelung der Wissen-

velopment of physiologj', will be schaft," au address, reprinted in

convinced that it is mainly Trem- i ' Reden,' vol. i. p. 109).

bly's observations of the hydro- |

ox THE VITAL18TIC VIEW OF NATUKK.

419

ill the examination of dead embryos in various stages
of development, and the idea of the division of labour
is one ilowing from the premises of the Darwinian
theory — the facts of variability and overcrowding. The
second conception, that of " metabolism," touches im-
mediately upon the processes of life, and demands;
special treatment in the present chapter which deals
with biological Thought.

The conception of a continuous exchange or circulation
of matter and of energy in every living organism, and
the study of this elementary i\pi(;d form of the living
process in the morphological unit of all living or-
ganisms, in the cell, seems to have originated with
Theodor Schwann,^ and is laid down in his ' ]\Iicro- 3i.

Scinvaun

scopical liesearches,' published in 18."! 9. On it is based
the whole simplitication and unification of biological
thought which distinguishes the second from the first
half of our century. The study of the cell — its

' On the change whieli came
over general ]>hysiulogy about 1S40,
and the pai-t he himself played,
Theodor Schwann has expressed
himself in a letter addressed to
Du Bois-lleymond, which is given
in the notes to the latter's Eloge
of Miiller, reprinted in the second
volume of his 'Reden,' pp. 143-334.
It forms one of the most im-
portant historical documents. The
Eloge itself should be read together
with Claude Bernard's 'liapport,'
&c., mentioned above (p. 3S4 n.),
which gives the historj- of the great
change from a more exclusively
Frencli point of view. In the
letter mentioned above, from wliicli
also the ([uotations given in the
text arc taken, Schwann claims

that the first instance in whicli
an "evidently vital phenomenon
was submitted to mathematical,
numerical" rule, was his measure-
ment of the carrying power of
a muscle in relation to its con-
traction in 1836. The purelj'
physical view of vital phenomena
exhibited in this example was not
adopted by Miiller. nor yet the
(juickly following general principle
of the cellular theory. Schwann
refers to the tliird section of his
' Microscopical Researches,' in
which he discards " vitalism," but
ailinits in man ("on account of
his freedom") an immaterial prin-
ciple, and claims that this assump-
tion divides him distinctly from the
materialists.

420 SCIENTIFIC THOUGHT.

formation, growth, division, and maintenance of form
amidst change of matter and alternation of function —
constitutes the " prolegomena " of physiology, and a com-
parison of Prof. 0. Hertwig's recent publication on the
" cell " with the introduction to Johannes Mliller's ' Phys-
iology ' marks well the change of ideas which half a
century has produced. And we must so much the more
admire the clear anticipation of Schwann, as he was not
in possession of the fvill conception of energy in its
two interchangeable forms of kinetic and potential
energy, which was developed in the course of the two
decades following his publication. Schwann not only
conceived the cell to be the morphological unit of all
living matter, but he also saw that " cell formation
must be the general principle of organic development,
and that there can be only one such principle." In
the third section of his ' Microscopical Eesearches ' he
founds on this " his theory of organisms, and rejects
distinctly therein all teleological explanations based upon
a vital force acting according to final purposes." He
thus showed " that the only essential property of all
living matter — viz., growth — is not inaccessible to a
physical explanation," and he did this at a time " when
Liebig had not yet taught physiologists the chemical
changes which take place in living tissues." These ideas
were only partially adopted by Johannes Miiller and
other leading physiologists of the day. Schwann's view
could only be consistently elaborated in proportion as
Circulation to the older conception of a " Stoffwechsel " (a chem-
andmergy. ic^l proccss) there was added that of a " Kraft "- or

ON THK VITALISTIC VIEW OF NATURE. 421

" Energie-wechsel " ^ (a physical process). Bio-cheiuistiy
had to be supplemented by bio-physics. With a clear
anticipation of the correcter and fuller view, Schwann
introduced the Greek term " metabole." It is the merit
of Prof. ]\Iichael Foster to have domiciled this useful
and all-comprising technical term in English physiological

' Du Bois-Reymoiul (' Reden,'
vol. ii. J). 220) mentions this as tlie
tliird imjiortant gain which phys-
iological science had to register
since the appearance of Miiller's
hook ; the first and second being
tlie cellular theory and the mech-
aiiico-physical method, both largely
i)\ving to Schwann. This was
written just before the great
intluenee of Darwin began to be
felt. In the ideas introduced by
Helmholtz, which clarified the con-
cejition of force, he sees the "key
which opens a comprehension of
the ' Stotfweclisel ' in plants and
animals." The term " Stott'-
wechsel," also "Stoffumsatz," or
simply " Umsatz," has been quite
familiar in German physiological
literature during the whole of the
century. I cannot find any gener-
ally accepted term in English liter-
ature before the introduction of
Schwann's term " metabolic phen-
omena,"' which, I believe, was first
adopted by Sir M. Foster, and
is now cjuite domiciled in English
text-books and translations. The
passage in Schwann's ' Microscop-
ical Researches ' is as follows
(' Sydenham Society's Translation,'
p. 193): "The phenomena attend-
ing the formation of cells may be
arranged in two natural groups :
first, those which relate to the
combination of the molecules to
form a cell, and which may be
denominated the plantic jjheiiom-
ena of the cells ; secondly, those

which result from chemical changes,
either in the component particles
of the cell itself or in the sur-
rounding cytoblastema, and which
may be called lactabolic phenomena
(rh ij.tTaQo\iK6v, imjilyiug that
which is liable to occasion or to
suffer change)." It will be seen
later on that tiie term metabolism
is a peculiarly happy one, as it
lends itself by a slight change in
the prefix to denote the twofold
process of building up and of run-
ning or falling down, which con-
stitutes the changes peculiar to
protoplasm as the constituent
element of all organised substance.
It is, accordingly, somewhat sur-
prising that the term has found
so little favour abroad. In France,
where this twofold movement has
long ago been recognised as one
of the characters of the living
process, the terms " composition
et decomposition " (de Blainville),
" organisation et desorgaiiisation "
(Claude Bernard), "assimilation et
desassimilation," have been variously
adopted (see Claude Bernard, 'Phon-
omenes de la vie,' vol. i. p. 36,
&c.) M. Yves Delage (' L 'Herodito,'
p. 53) says : " Les Anglais ont sub-
stitucS it ces expressions si signi-
ficatives : nutrition, assijuilatidn,
dSxassimilation, une terminologie
qui a dil leur paraitre bien belle,
car ils I'ont tous adopt(5e avec
un empressement remaniuable ;
c'est celle de mctabolisme," &c.

422 SCIENTIFIC THOUGHT.

literature, to have placed it at the entrance of his text-
book of physiology, and thus to have given the student
a somewhat more detailed description of the elementary
functions of living matter than was afforded by the older
term " vortex," employed by Cuvier.
33. These merits of Schwann, which attach more to the

"Metabol-
ism." conception of " metabolism " than to that of the cell,

are not reduced by our having to state that the latter
conception has been entirely changed since his time.
The cell of to-day is not the cell as Schwann conceived
it. Of the pretty clearly defined structure or organ-
isation of that biologist, with its wall (membrane),
its kernel (nucleus), and its fluid contents (cell sap),
nothing; has remained but the cell contents, termed
protoplasm by von Mohl ; and the living process can no
longer be considered as the function of a well-defined
organ or machine. It is rather the fundamental property
of an almost homogeneous substance, the mass of proto-
plasm, in which the kernel is the only recognisable
differentiated portion. The immediate eft'ect of this de-
structive analysis of the early conception of the cell was
to destroy the idea that the living processes carried on in
any special cell or organ are a result of its organisation,
as the function of an apparatus is dependent upon the
arrangement and combination of its parts. It has pro-
moted the view that — for our understanding at least —
the first thing to learn is the nature of the processes
themselves. We have to look upon the visible structure
of special cells and organs merely as " mechanical con-
trivances, serving only to modify in special ways the
results of the exercise of these fundamental activities.

ON THK VITALISTIC VIKW OF NATrilK.

423

ami in no sense determining their initial develup-
ment. ^

It seems, iht-n, that we can date back to Schwann's
' Kesearches ' the ori;_i;in ni two distinct courses of Thought
which in tlie second half of our century obtain in
biological science. The first we may call the morpho-
logical or structural school of biology. It is based on
the theory of the cell or some modified conception, ami analysis of
attempts to explain ihe fundamental processes which I,°|:',^^J,ts.

34.
StniPtural

go on m

liying organisms from the structure of the

elementary parts. As the UKJst minute particles of

' See Sir Michael Foster's excel-
lent article on " General Physiologj- "
in the 19th vol. of the ' Eucy. Brit.,'
9th ed., p. ['2. In this connection
a passage from an early review of
Hu.sley's, "On the CeU Tlieory,"
has been frequently quoted, ac-
cording to which cells maj' be
" no more the producers of the
vital phenomena than the shells
scattered in rjrderly lines along tiie
sea beach are the instruments by
which the gravitative force of the
moon acts upon the ocean. Like
these the cells mark only where the
vital tides have been and iiow tliey
have acted" (IS.'iS, in the 'Brit,
and Fit. .Med. Chirurg. Review,'
reprinted in the first volume of
'Scientific Memoirs,' p. 277). Ac-
cording to this view, which has
been further developed in more
recent times, the cells would be
" imlications," not instruments, of
the vital phenomena, which "are not
necessarily preceded bj' organisa-
tion, nor are in any way the result
or efi'ect of formed parts, the
faculty of manifesting them re-
siding in the matter of which living
bodies are com|)osed, as such— or,
to use the language of tiie day,
the ' vital forces ' are molecular

forces." It is interesting to quote
together witii this i)assage fi'ora
Huxley, what was said forty years
later by an eminent living jihysio-
logist. Prof. Max \'erwoi-n of Jena :
'■ Tlie fact has been established that
a fundamental contrast between
living organisms and inorganic
bodies does not exist. In contra-
distinction to all inorganic nature,
however, organ i.-^ms are character-
ised solely by the possession of
certain highly complex chemical
compounds, especially proteids "
(' General Phvsiologv,' tran.-,!. by
F. S. Lee, 1899, i." li'ti). "'We
can summarise our con.--i<lei'atii>ns
and give simple expression to the
problem of all physiology. The life-
process consints in the metabolism
of proteids. If this Ise true, all
physiological research is an experi-
ment in this field : it consists in
following the metabolism of proteids
into its details, and recognising the
various vital phenomena as an ex-
pression of this metabolism which
must result from it with the same
inevitable necessity as the pheno-
mena of itioi'ganic nature result
from the chemical and physical
changes of inorganic bodies" (ibid.,
p. 136).

424 SCIENTIFIC THOUGHT.

living matter, revealed by the most powerful microscope
aided by all the elaborate processes of staining, still
appear to be endowed with the fundamental properties
of life, such as irritability, contractility, and metabolism,
i.e., change in form and chemical constitution, the
object of this line of research, viz., the investigation
of th-e initial structure of the elements of living matter,
can only be reached by indirect means or by conjecture.
Structural chemistry and stereo-chemistry proceed by
similar methods of investigation, and have succeeded
by means of the atomic, molecular, and kinetic theories
of matter in bringing order and unity into a very large
portion of our knowledge of chemical combinations. The
morphological or structural biologist pictures to himself
very much more complicated arrangements of molecules
than the carbon tetrahedron of van 't Hoff or the benzine
ring of Kekule, yet formed on similar principles ; and
by continuing in his mind these combinations which,
as they become more complex, also become more \m-
stable, he arrives ultimately at a very complex and
continually changing chemical structure, which he imag-
ines might be the beginning of the living process, the
element of organisation. This conception, so far as I
can find, was first introduced into biological literature
by Herbert Spencer. He has termed this element
of living matter " the physiological unit." The con-
ception has been varied in endless ways by many sub-
sequent biologists, all of whom have invented special
names for these elementary units of life out of which
they hope to put together the many observable proto-
plasmic and cellular tissues of the plant and animal

ON THE VITALISTIC VIEW OF NATURE. 425

organism as Haiiy attempted to build up crystals out
of his " jhuIccuIl's inlegrantes." The most elaborate an-
alysis of this conception is put forward in the ' ]\licellar
Theory ' of the celebrated botanist Niigeli, which in
Germany has found favour with many eminent Ijio-
logists as a provisional programme of the various
problems involved. It is clear that the conception of
the physiological unit opens out two distinct lines of
research. We can approach it on the one side by
artificially producing in the chemical laboratory more
and more of those chemically stable compounds which
we find in the living organism. After Wijhler had 35.

Synthesis ol

produced urea artificially in 1828, the number of «""Kanic

•^ "^ substances.

these artificial .syntheses greatly increased, and we are
specially indebted to M. Berthelot for having shown
how all the simpler chemical compounds contained in
the organism can be put together by inorganic processes.
Some of the more complex substances have likewise
subsequently yielded to this synthetic method. " It is
possible," we are told, " that after a time our know-
ledge of chemistry may have advanced sufficiently to
enable us to produce albuminous bodies artificially by
synthesis." ^ " We are already able artificially to build
up, atom for atom, out of their elements a series of
organic compounds, some of a very complicated char-
acter. We no longer doubt that all the rest, even
the most complex, will be thus produced ; it is only
a question of time." " Jjut the ways in which the

' See 0. Hertwig, 'The Cell,' p. Chemistry,' trausl. by Wociki ridge,
16. p. 313.

2

See G. Bunge, ' Physiological

426

SCIENTIFIC THOUGHT.

chemist puts together these substances in the laboratory
are rarely the methods adopted by nature in the
living organism, and in many cases the product itself,
though apparently the same, is yet essentially different.^

^ This touches on a very im-
portant point, which is much
emphasised in all the best modern
treatises on the subject. Claude
Bernard in all his writings insisted
on the fundamental difference be-
tween the processes going on in the
organism and those that go on in
the laboratory of the organic chem-
ist, though the two produce fre-
quently the same apparent result.
" Si les forces que I'ctre vivaut met
en jeu dans ses manifestations vitales
ne lui appartiennent pas et rentrent
toutes dans les lois de la physico-
chimie generale, les instruments et
les procedes h I'aide desquels il les
fait apparaitre lui sont certainement
speciaux. En effet, I'organisme
manifeste ses phenomcnes pliysico-
chimiques ou mecaniques a I'aide
des elements histologiques cellu-
laires, epitheliaux, musculaires, ner-
veux, &c. II emploie done de pro-
c(5des, c"est-k-dire des outils organ-
iques qui n'appartiennent qu'a lui.
C'est pourquoi le cliimiste, qui peut
refaire, dans son laboratoire, les
produits de la nature vivante, ue
saurait jamais imiter ses procedes,
parce qui il ne peut pas creer les in-
struments organiques elementaires
qui les executent. Cela revient a
dire que tons les appareils des etres
organises out une morphologie qui
leur est pro pre " ('Rapport,' &c.,
1867, p. 135). Quite recently
Bunge [loc. cit., p. 313) has said,
" All our artificial sj'ntheses can
only be achieved by the application
of forces and agents which can never
play a part in vital processes, such
as extreme pressure, high tempera-
ture, concentrated mineral acids,
free chlorine — factors which are
immediately fatal to the living

cell. ... It follows that the animal
body has command of ways and
means of a totally different char-
acter, by which the same object is
gained." A very interesting specu-
lation, referring specially to this
point, was put forward by the
eminent physiologist, Prof. E.
Pfliiger of Bonn, in the year 1875.
It is fully discussed in Verworn's
frequently quoted work on General
Physiology (pp. 304, 311, 482).
The theory is based upon the le-
markable part which the compound
radicle cyanogen seems to play in
the organism. Pfliiger starts from
the fundamental characteristics of
the substance called proteid, with
which life is inseparably con-
nected. Proteid is known to exist
in a stable form in food-stuffs, for
instance in egg albumen. But this
is not the same as the proteid con-
tained in living matter. In the
latter it is not stable, but is being
continually decomposed. The de-
composition was found to be due
to the ox J' gen that occurs in the
living proteid molecule. This oxy-
gen, which is intramolecular, being
continually received from outside
by respiration, transforms the more
stable molecule into an unstable
labile molecule. In further follow-
ing the clue afforded by this pro-
perty, and comparing the decom-
position products of living proteid
with those obtained by artificial
oxidation of dead proteid, Pfliiger
is led to the conclusion that the
presence of the radicle cyanogen in
the living proteid will explain the
difference. " In the formation of
cell-substance — i.e., of living proteid
— out of food proteid, a change of
the latter takes place, the atoms of

ON THE VITALISTIC VIEW OF XATCRK

427

AnoLliL'i- way of iii([uii}' is b< ;autl}'.^e the existing
organic tissues still further by microscopic and chemical
methods, in order to tiud out how they are built up.
As the result of such inquiries we have a framework
theory of protoplasm, a foam theory, a filament theory,
a granular theory ; antl the attempt has been made to
define liviiit;- protoplasm as a colony of still smaller
structural units termed " bioblasts." By this twofold
method — by synthesis and by analysis — the biologist may
attempt to approach the physiological unit, the seat and
stronghold of the vital process.^

nitrogen entering into a cyanogen-
like relation with the atoms of
carbon, probaljly with the absorp-
tion of considerable lieat." Cj'ano-
gen being a radicle possessing a
great quantity of internal enei'gy,
the addition of it to the living
molecule " introduces into the living
matter energetic internal motion."
The interest which attaches to the
theory lies in this, that it allows us
to form some conception how living
matter originated. This problem is
identified with the problem. How
does cyanogen arise ? This we
know is formed at an incandescent
heat. •' Accordingly, nothing is
clearer than the possibility of the
formation of cyanogen compounds
when the earth was wholly or par-
tially in a tiery or heated state. . . .
If, now, we consider the inuneasur-
ably long time during which the
cooling of the earth's surface
dragged slowly along, cyanogen,
and the conijjounds that contain
cyanogen and hydrocarbon sub-
stances, hail time and o])portun-
ity to indulge extensively tlieir
great tendency towards transfor-
mation, . . . and to pa.ss over, with
the aid of oxygen, and later of
water aiid salts, into that self-
destructive proteid, living matter.

. . . The first proteid to arise was
living matter, endowed in all its
radicles with the property of
vigorously attracting similar con-
stituents, adding them chemically
to its molecule, and thus growing
ad infinitum." This theory is in-
teresting, as it is, so far as I know,
the only attempt to reconcile the
existence of living matter with the
fact of the high temperature which
once existed on the earth.

1 A description of these several
theories on the structure of proto-
plasm, among which the mici'llar
theory of Nageli, the foam theory
of Biitschli, and the *' bioblasts "
of Altmann, have been elaborately
developed, will be found in Prof.
0. Hertwig's work on ' The Cell '
(Engl, transl., p. 19, &c.), as also
in ^I. Yves Delage's great work,
'L'Horcditc' (pp. 299-310). Ver-
worn (foe. cit., \<. 87) draws special
attention to the "alveolar" or
' ' foam " theoiy, which, built upon
investigations of Prof. (,>uincke,
has "comj)letely claritied our ideas
u[)on the real nature of the proto-
plasmic structures so much ob-
serveil. . . . As a result of these
recent investigations the following
picture can be formed of the tiner
morphological structure of proto-

428

SCIENTIFIC THOUGHT.

36.
The

" physical '
method.

There is, however, a second way open to the student
of the phenomena of hfe, and this may be termed
the " physical method," as opposed to the " structural."
Thus chemists and physicists first establish the general
laws of motion and change in dynamics and energetics,
and subsequently apply them to special problems, such
as those of physical astronomy or the chemistry of
electrolysis and solution. Similarly the physiologist
may study the processes common to all living matter,
and look upon the action of a definite cell, tissue, or
organ merely as an application of these general processes.
From this point of view structural biology, like struc-
tural chemistry, only furnishes illustrations, not an ex-
planation, of the vital processes : the special structure
or organ is a result of the process or function —
not its cause. As Prof. Michael Foster says, " We may
throw overboard altogether all conceptions of life as
the outcome of organisation, as the mechanical result
of structural conditions, and attempt to put physi-
ology on the same footing as physics and chemistry,
and regard all vital phenomena as the complex pro-
ducts of certain fundamental properties exliibited by
matter, which, either from its intrinsic nature or from

plasm. Protoplasm consists of a
ground mass in many cases com-
pletely homogeneous, in most cases
very finely foam-like or honej'comb-
like, in which lies embedded a
greater or less quantity of very
various solid elements or granules.
In the foam -like protoplasm the
granules always lie at the corners
and angles where the foam-vacuoles
come together, never in the liquid
of the bubbles themselves." Some
physiologists think that none of

the descriptions of protoplasmic
architecture help us much, and
" hold to the fundamental principle
that living matter acts by virtue of
its structure, provided the term
structure be used in a sense which
carries it beyond the limits of ana-
tomical investigation — i.e., beyond
the knowledge which can be at-
tained either by the scalpel or the
microscope " (Burdon Sanderson,
'Address,' Brit. Assoc, 1889, p.
607).

ON THE VITALISTIC VIEW OF NATURE.

429

37.
Properties

its existing in peculiar conditions, is known as living
matter." ^

Thus, instead of trying to penetrate to the physio-

' J o 1 L J Properties

logical units and construct them through a process of oftheiiving

o o i iiUDstance.

imagination, this latter class of biological thinkers con-
fine themselves to the task of describing in the simplest
manner and as completely as possible the various proper-
ties of the livincr substance — i.e., its functions." And

1 'Ency. Brit.,' article " Phy.si-
ology," vol. xix. p. 12. See also an
address delivered by Prof. Burdon
Sanderson at the meeting of the Brit.
Assoc, at Newcastle in 1889 ('Re-
port,' p. 604) : " During the last ten
or fifteen years histology has carried
her methods of research to such a
degree of jierfection that further
improvement scarcely seems pos-
sible. As compared with these
subtle refinements, the ' minute
anatomy ' of thirty years ago seems
coarse — the skill for which we once
took credit seems but clumsiness.
Notwithstanding, the problems of
the future from their very nature
lie as completely out of reach of the
one as the other. It is by different
methods of investigation that our
better -equipjied successors must
gain insight of those vital processes
of which even the ultimate results
of microscoi)ical analj'sis will ever
be as they are now, only the out-
ward and visible signs" (p. 608).

^ As Prof. Iiurdon Sanderson puts
it in his ' Address,' it is a reversion
to a position which is not new in
the history of physiology. " The
departure from the traditions of
our science which this change of
direction seems to imi>Iy is indeed
more apparent than real. In tracing
the history of some of the greatest
advances, we find that the recogni-
tion of function has preceded the
knowledge of structure. Haller'.s
discovery of irritability was known

and bore fruit long before anything
was known of the structure of
muscle " (p. 607). " . . .In nmch
more recent times the investigation
of the function of gland-cells, which
has been carried on with such re-
markable results by Prof. Heiden-
hain in Germany, and with equal
success by Mr Langley in this
country, has led to the discovery
of the structural changes which
they undergo in passing from the
state of repose to that of activit}' ;
nor could I mention a better ex-
ample than that afforded by Dr
Gaskell's recent and very important
discover}- of the anatomical difier-
ence between cerebro-spinal nerves
of different functions" (ibid.) What
has to a great extent worked this im-
portant change in the methods and
reasoning in ])hysiology is the re-
cognition of "plurality of function
with unity of structure," a princijile
urged strongly bj- the experimental
school of medicine, with Claude
Bernard as its greatest representa-
tive. Notably this was tlie effect of
his "demonstration that the liver
had other things to do in the animal
economy besides secreting bile.
This, at one blow, destroyed the
then dominant conception that the
animal body was to be regarded as
a bundle of organs, each with its
approjtriate function — a concejition
which did much to narrow inquiry,
since when a suitable function had
once been assigned to au organ

430 SCIENTIFIC THOUGHT.

38 here we meet first of all with the great fact that a living
ment. thing cannot be conceived to exist alone : it is dependent

upon its environment, and upon other living things of
similar, never quite identical, and mostly very different
nature. As a consequence of the conception which
guided Lamarck in contemplating the living world—
especially the crowd of living things which before
him had remained unobserved — the influence of en-
vironment plays a greater and greater part in the
study of every form of life. The further funda-
mental property of all living matter — that it absorbs
through intussusception other matter which surrounds
it, that it grows and multiplies by division, casting
oh' some portions of its own substance as useful
secretions or cumbrous and useless excretions — has the
twofold result that every living thing modifies its own
surroundings and that it creates a society of its like which,
through an automatic process of crowding-out, exercises
a kind of selection among its members, they being forced
to accommodate themselves to circumstances and to each
other. ^ The process suggested by Darwin as the rationale

there seemed no need for further in- of the experimental as distinguished

vestigation. Physiologj", expounded I fromtheanatomical method, namely,

as it often was at that time in tlie \ that it deals with the organism

light of such a conception, was apt i whilst it is alive, see the conclud-

to leave in the mind of the hearer ' ing remarks in Sir M. Foster's

the view that what remained to be
done consisted chiefly in determin
ing the use of organs such as the
spleen, to which as j-et uo definite

article on " General Physiology " in
the ' Ency. Brit.,' vol. xix.

^ The relations of living things
to each other and to their environ-

function had been allotted. The | ment admit of being contemplated

discovery of the glycogenic function
of the liver struck a heavy blow at
the whole theory of functions."
(Sir M. Foster in ' Claude Bernard,'
p. 90.) On the necessary condition

in two waj's, which may be best
distinguished by a reference to
human society, exhibiting as it does
the two phenomena of co-oi^eration
and of competition. The former

ON THE VITALISTIC VIEW UF NATURE. 4ol

of variation and development is more and more coming
to Le recognised as an inevitable property of all growing

and iiiultiplyinu; living things. So far as Uie intluence on
the envinninient, the medium in which it lives, is con-
cerned, we owe to the great French biologist, Claude
Bernard, the helpful conception of the inner medium,^ as

is based upon haniiony, tlie latter
upon conflict. Tiie former aspect
i.s more particularly eiuphasi.sed by
the French school of Lamarck, de
Blaiiiville, and Claude Bernard ;
the latter more by tlie English
.school of Malthus and Darwin ;
each starting ai)parentlj' without
any reference to the other. Claude
Bernard in particular says (' Phuno-
uione-s de la vie,' vol. i. p. 67) : " Pour
nous la vie resulte d'un conflit,
d'une relation etroite et harmon-
ique entre les conditions extcrieures
et la constitution pre-etablie de
I'organisme. Ce n'est point par
une lutte contre les conditions
cosmiques que I'organisme se dd-
veloppe et se maintient ; c'est,
tout au contraire, par une adapta-
tion, uu accord avec celles-ci. . . .
L'otre vivant ne constitue pas une
exception a la grande harmonic
naturelle qui fait que les choses
s'adaptent les unes aux autres ; il
ne rompt aucuu accord ; il n'est en
contradiction ni en lutte avec les
forces cosmiques generales ; bien
loin de l:i, il fait partie du concert
universel des choses, et la vie de
I'aninial, par exemple, n'est qu'un
fragment de la vie totale de I'uni-
vers."

^ Although the biology of Claude
Bernard does not contain the
principle of descent and evolution
which so powerfully iniluenced the
contemporary writings of Englisji
and German naturalists, one is
uevertheles.s reminded of the ideas
of Lamarck in reading the second

of his lectures on the ' Phenomena
of Life' (vol. i. pp. 65-124).
Lamarck had expressed the idea
that in the graduated scale of
living things we recognise an in-
creasing inile]iendence with regard
to the external environment. (See
supra, chap. vii. p. 315.) Claude
Bernard says (p. 67) : " Le mode
des relations entre I'ctre vivant et
les conditions cosmiques ambiantes
nous i)ermet de cunsidcier trois
formes de la vie, suivant qu'elle est
dans une dependance tout ii fait
dtroite des conditimis extcrieures,
dans une dependance moindre, ou
dans une indepeudance relative. Ces
trois formes de la vie sont : 1°, La
vie lattnte ; vie non manifestce.
2°, La vie osrillitntc / vie a manifes-
tations vai'iables et dcpendantes du
milieu extdrieur. 3°, La vie coit-
stantc ; vie K manifestations libres
et inddpendantes du milieu ex-
tdrieur." Examples of the " vie
latente " are to be found in the
vegetable and animal creation alike.
Grains of seed, desiccated animals,
germs, eggs, fei-ment.s, yeast, &c.,
are examples. All vegetables Vjelong
to the class of the vie oscillante, also
among animals all inveitebrates,
and among the vertebiates those
with cold blood. These depend on
cosmic conditions, the cold of
winter, and tlie reviving heat of
summer, &c. The higher animals
with warm blood whose tempera-
ture is constant are not in the
same way subject to the influence
of the external medium. They

432

SCIENTIFIC THOUGHT.

39.
The

" internal
medium."

it were the inner atmosphere which any large assembly
of living units must necessarily create for itself. All
larger organisms are complex societies of living units
which depend not only on the external but also on the
internal medium which bathes them. It was one of
Claude Bernard's happiest generalisations to look upon
the blood, not as a living tissue but as a means of com-
munication of the living tissues of the organism, as an
internal medium which bears the same relation to the
constituent tissues that the external medium, the
atmosphere, does to the whole body.

One of the principal functions of this artificial medium
or atmosphere which the larger organisms possess, create
and maintain for themselves during their life, is to
enable a particular elementary substance to get access
to every living cell or tissue of the organism. This
substance is oxygen, without which the continuance
of life in the higher organisms seems impossible.
That life is a process of combustion is accordingly a

possess " un milieu intericur per-
fectionue " (p. 104). But they
begin their existence as beings
with an oscillating life when they
are in the form of eggs. Of the vie
constante ou lihre Claude Bernard
says : " Je crois avoir le premier
insiste sur cette idee qu'il y a pour
I'animal reellement deux milieuxj;
un milieu exterieiir dans lequel est
place I'organisme, et un milieu
intcrieur dans lequel vivent les
Elements des tissus. L'existence
de I'etre se passe, non pas dans le
milieu exterieur, air atmospherique
pour I'etre aerien, eau douce ou
sal^e pour le.s animaux aquatiques,
mais dans le milieu liquidc in-
tcrieur forme par le liquide

organique circulant qui entoure et
baigne tou.s les elements auatom-
iques des tissus ; c'est la lymphe
ou le plasma, la partie liquide du
sang qui chez les animaux superieurs,
penetre les tissus et constitue
I'ensemble de tous les liquides in-
terstitials, expression de toutes les
nutritions locales, source et con-
fluent de tous les echanges ele-
mentaires. Un organisme complexe
doit etre consider^ comme une
rdunion d'etrcs simples qui sont
les elements anatomiques et qui
vivent dans le milieu liquide in-
terieur. La fixitd du milieu in-
terieur est la condition de la vie
libre indepcndante " (p. 113).

ON THE VITALI8T1C VIEW UF NATLKE. 433

definition which has been put forth in vari(ni.s ways
ever since Lavoisier's time, when he and Laplace tried
to explain the existence of animal heat in this manner.
The progress of science in the course of the century
wliich followed Lavoisier has more and more confirmed
the importance of the role which oxygen plays, Init lias
also shown how very complex are the products of
oxygenation in tlie living organism, — how the living
processes are indeed chemical processes, but are quite
different from those of the chemical laboratory. As
Claude Bernard says, " The chemistry of the laljoratory
is carried on liy means of reagents and apparatus
which the chemist has prepared, and the cliemistry
of the li\ing being is carried on by means of reagents
and apparatus which the organism has prepared." ^
One of the great performances of living matter is
the production, another is the storing up and distri-
bution, of oxygen. But though we know that the
chlorophyll - containing cells of green plants, under
the intiuence of sunlight, are able to decompose that
very inert body, carbonic acid, breathed out by both
animals and plants, into free oxygen and carljon, allow-
ing the carbon to be retained or utilised in the form
of more or less complex carbohydrates, and though

' See especially the extensive ex-
planations in the ' Itapport sur les
progros de la Physiul. gen.' (1867,
p. 133 »qq.): "Les phenomenes
physico-chiniiciues qui se passent
dans les corps vivants sent exacte-
ineut les monies, ([uant a leur nature,
i|uant aux lois qui les rogissent et
(|uant a leurs produits, (|ue ceux
(jui so passent dans les corps bruts ;
ce qui diffijre, ce sunt seulenient les | vivant" (p. 2'22)

VOL. II. 1> E

procddes et les ajipareils h, I'aide des-
(juels ils sont manifestos. ... II
est doja jjrouve qu'un gi-and nombre
de phenomenes qui s'accomplissent
dans les corps vivants peuvent etre
reproduits artificiellement, en de-
hors de I'organisme, dans le monde
mineral. Mais ee que Ton ne j)eut
jias rej)roduire, ce sont les procodds
et les outils spociaux de I'organisme

434 SCIENTIFIC THOUGHT.

we also know that the red blood corpuscles in verte-
brate animals convey oxygen in a concentrated form ^
through all the organs, giving it up wherever it may
be wanted, the real chemical process concerned in the
action of chlorophyll is not cleared up ; ^ and " no one
has been able hitherto to explain, by a reference to
physical laws, the active functions of the heart and
muscular wall," by which the circulation of the blood
is effected.^

In the explanation of many physiological phenomena
no idea has proved more fruitful than the con-
ception of natural selection, introduced by Darwin to
explain the growing diversity and the purposeful-
ness of organisms. Coupled with the cellular theory,
which looks upon every living organism as a society
of self-accommodating individual units or cells, forced
by circumstances into differentiation of form and into
divided labour or function, it relieved biologists of that
spectre of vitalism which still survived after Lotze
and Du Bois-Eeymond had placed the creative and
formative influence outside of the mechanism — as the
watchmaker lives outside of the watch, which exhibits
only mechanical contrivances. That which puzzles the
spectator of the watch, as it does the spectator of every

1 See Buuge, ' Physiological
Chemistry,' p. 275.

- " Iron play.s an important part in
vegetable life : we know that chlo-
rophyll granules cannot be formed
without it. If plants are allowed
to grow in nutritive solutions free
from iron, the leaves are colourless,
but become green as soon as an
iron salt is added to the fluid in
which the roots are immersed. It

is even sufficient merely to brush
the suiface of the colourless leaf
with a solution of an iron salt to
cause the ajjpearance of the green
colour in the part thus i>ainted.
Chlorophyll itself contains no iron,
and we do not know in what way
the iron is concerned in its produc-
tion " (Bunge, loc. cit., p. 2.5). See
also Hertwig, 'The Cell,' p. 1.53.
•* Bunge, }). 7 ; cf. also p. 275.

ON THE VITALISTIC VIEW OF NATLKE.

435

ort^^anism, is the apparent design and purpose, without
which neither could be conceived to have been formed.^
Here, then, tlie idea that it was a process of natural
choice, of automatic adjustment, which produced the
apparent end and purpose at the niDUient when the
structure itself was produced, came as a great relief.^
It explained how it comes about that nature, even
with unloaded dice, so often — yet not always — throws
doublets. It permitted naturalists and physiologists
to use purpose and final cause, not as an explana-
tion, but as an indication where to look for causal —
that is, for mechanical — connections. Accordingly the
first systematic attempt to use natural selectinu in
the explanation of the adjustment of the internal
parts of an organism, which is due to Prof. A\"ilhelm

1 "The main problem which the
organic world offers for our solu-
tion i.s the purposefulness seen in
organisms. That species are from
time to time transformed into new
ones might perhayjs be understood
by means of an internal trans-
forming force, but that they are
so changed as to become better
adapted to the new conditions
under wliich they have to live is
left entirely unintelligible" (Weis-
mann on Niigeli's " Mechanisch-
Physiologische Theorie der Ab-
staramungslehre " in ' Essays upon
Heredity,' Engl, transl. , p. 257).

- See Du Bois-Reymond's Ad-
dress, " Darwin versus Galiani "
('Reden,' vol. i. p. 211, <fec.) :
" Here is the knot, here the great
difficulty that tortures the intellect
which would understand the world.
Whoever does not i)lace all activity
wholesale under the sway of E\<i-
curean cliance, whoever gives only
hi.> little finger to teleology, will
inevitably arrive at Paley's dis-

40.
Xatiiral
selection
witliin the
organism.

carded ' Natural Theology, ' and so
much the more necessarily, the more
clearly he thinks and the more in-
dependent his judgment. . . . The
physiologist may define his science
as the doctrine of the ciianges
which take ]ilace in organisms from
internal causes. . . . No sooner has
he, so to speak, turned his back on
himself than he discovers himself
talking again of functions, ])er-
formances, actions, and i)urposes
of the organs. The i)ossibility,
ever so distant, of banishing from
nature its seeming purpose, and
putting a blind necessity everywhere
in the ])lace of final causes, ajijiears
therefore as one of the gi-eatest
advances in the world of thought,
from which a new era will be dated
in the treatment of these problems.
To have somewhat eased the torture
of the intellect which ponders over
the world-problem will, as long as
j)hiloso))hical naturalists exist, be
Charles Darwin's greatest title to
glory" (p. 216).

436

SCIENTIFIC THOUGHT.

Eoux in his work on tlie ' Struggle of the Parts in
the Organism,' was hailed by Darwin as " the most
important book on development that has appeared
for some time." ^ In modern books on physiology the
process of selection is a familiar conception ; but if in
natural history, in the life of plants and insects, there
still remain many extraordinary instances of selection

1 The work appeared in 1880,
and is referred to by Darwin in

letter to Romanes ( ' Life and
Letters,' vol. iii. p. 244 ; 16th
April 1881), where he suggests
also a similar consideration of
plant life and structure. It
has been republished in Roux's
' Gesammelte Abhandlungen zur
Entwickelungsmechanik der Organ-
ismen ' (Leipzig, 1895, 2 vols.), with
an interesting preface (vol. i. p.
139, &c. ), and many historical and
critical digressions. It originally
emanated from the earliest school
of Darwinism in Germany, repre-
sented by Haeckel, Gegenbaur, and
Preyer, at Jena. It has been
found very suggestive, and has
been the beginning of a very
large controversial literature in
Germany, in which the funda-
mental problems of biology have
been discussed, and have received
new formulations. The idea of the
struggle of individuals for survival,
suggested by Darwin, is applied by
Roux to the different parts and
organs within the develoi^ing or-
ganism. Du Bois-Reymond almost
contemporaneously published his
brilliant and celebrated address
on "Exercise" ("Ueber die
Uebung," 'Reden,'vol. ii. p. 404).
In England Roux's suggestive treat-
ise does not seem to have been
much noticed, and Prof. Roux
himself attributes this to the in-
adequate notice of the book by
Romanes in ' Nature ' (vol. xxiv.
p. 505), in which his doctrine

was erroneously' compared with
Spencer's ideas of "direct equi-
libration." Prof. J. A. Thomson,
in 'The Science of Life,' refers
to the importance of Roux's work
(pp. 138, 229), and of his ' Archiv
flir Entwickelungsmechanik. ' Roux
has been classed by some of
his critics among the " organi-
cists," a school represented in
France chiefly by Claude Bernard.
The main the.sis of this view
seems to be that the phenomena
of life consist in the play of two
factors— the organisation and the
environment of the living thing.
Roux applies the process of natural
selection and consequent adapta-
tion, which Darwin sees at work
in a crowd of living things, to the
organisation of the individuals
themselves, each of which is a
microcosm, a society of auton-
omous units, say of cells. He
has accordingly gone a step
farther back than the older
" organicists," studying the de-
velopment, the genesis of the
organism on Darwinian lines. M.
Delage accordingly dates from him
a new school of " organicism."
" L'organicisme commence, h, mon
sens, avec Descartes (1642), se
continue avec Bichat, Claude
Bernard, et arrive avec Roux
(1881) 11 une theorie si profonde-
ment modifiee, bien qu'elle derive
du meme principe, qu'elle peut
etre consideree comme toute
moderne" (' L'Heredite, p. 408).

ox THE VlTALIisTlC VIEW Ub' NATUKF:.

437

for which no teleological inechanisiu hiis been invented,
still more are we baiUed by the apparent " autonomy
of th(.' living cell," in consequence of which it is, c.ff.,
" able to select its food, retaining what is useful and
rejecting what is harmful." ^ And what shall we say
of the so-called " w^andering cells, which are actually
sent out by the organism in order to absorb in the
alimentary canal food-stuffs, notably fat, returning with
it into the blood, or to receive into themselves malig-
nant bacteria, making them innocuous by a process of
digestion ? " ^ Xo mechanical physico-chemical explana-
tion of this process is imaginable, and the word
" selection," with which Darwin charmed away so many
mysteries, has revealed new ones in their place.^

' See the very interesting and
frequently quoted address by Prof.
G. E. Kiud%iscli (Wiirzburg, 1888),
entitled ' Arztliche Philusophie,'
p. 13.
- Rindfleisch, loc. cit., p. l.'n
■' Inthisconnectiou it is interesting
to refer to a discussion which was
raised by the suggestive address of
Prof. F. R. Japp, entitled, "Stereo-
cheuiLstry and Vitalism" ('Brit.
Assoc. Report,' 1898, p. 813). It
refers to the discovery by Pasteur
of " chirality " in solutions of
certain crystallised organic salts,
on which I reported in vol. i.
p. 450. "Pasteur regarded the
formation of asyumietric organic
compounds as the special pre-
rogative of the living organism.
Most of the substances of which
the animal and vegetable tissues
are built up — the proteids, cell-
ulose— are asynnnetric organic
compounds." Now, in his ex-
periments on fermentation Pasteur
found that " the asymmetric living
organism selected for its nutri-

ment that particular asymmetric
form " out of a mixture of two
euantiomorphous compounds held
in solution — " which suited its
needs — and left the opposite form
either wholly or, for the most
I)art, untouched" (p. 817). Prof.
Japp proceeds to consider the
opinion then formed by Pasteur,
" that compounds exhibiting optical
activity have never been obtained
without the intervention of life "
(p. 818). This view, to which
Pasteur adhered, and which he
defended against eminent op-
ponents, has been frequently
challenged, and seemed definitely
set a.side by the explanation of
Piof. Emil Fischer of Berlin, and
by Jungfleisch's synthesis of race-
mic acid and its resolution into
dextro- and Itcvo - tartaric acids.
. . . "Consecjuently, the overwhelm-
ing majority of chemists hold that
the foregoing synthesis and separ-
ation of optically active conqiounds
have been effected without the
intervention of life, either directly

438

SCIENTIFIC THOUGHT.

I

41.

Mobility of

living

matter.

Another property of all living matter which has been
seized upon to furnish a definition of life is its extreme
mobility. It has been stated that the great difference
between living and non-living matter is this — that the
former is in a state of movable or dynamical equilib-
rium, whereas the latter tends always to a condition
of rest or of statical equilibrium. This was especially
urged by the late celebrated Du Bois-Eeymond of
Berlin, to whom we owe the greater part of our know-
ledge of the physical and chemical changes exhibited
in the active nervous system. In comparison with
this property of a dynamical equilibrium, explained by
the analogy of a fountain of water or a vortex which
change their substance whilst maintaining their form,
other older distinctions which had been drawn between
organised and unorganised bodies sank into insignificance.^

or indirect! J'." (p. 824). Prof.
Jajip and Prof. Crutn Brown of
Edinburgh are of the opposite
opinion, inasmuch as in the view
of the former " the action of hfe,
which has been excluded during
the previous stages of the pro-
cess, is introduced the moment
the operator begins to pick out
the two enantiomorphs," as was
done by Jungfleisch.

^ Among the okler discussions
of the best way of defining life
which belong to the second
third of the century, we have
in Germany the various writings
of Du Bois - Reymond ('Reden,'
notably vol. ii. p. 25) ; in France
those of Claude Bernard (' Pheno-
menes de la vie,' notably vol. i. y>.
21, &c.) ; in England the 'Biology'
of Mr Herbert Spencer. The two
last-named authors examine with
some care the definitions of earlier
writers. All three should be read

and re-read by any one who desires
to arrive at a clear understanding of
the subject. Du Bois-Reymond's
definition shows the preponderat-
ing influence of the ideas which
governed the Berlin school of
jihysiology, and which centred in
Helmholtz's tract on the Conserva-
tion of Energy. Claude Bernard
defines life by the words " La vie,
c'est la creation." Organisation
and disorganisation are the two
sides of this process, organisation
and environment the two factors.
The doctrine of evolution goes a
step farther back, and attempts to
analyse "organisation." The pro-
cess of creation is to Mr Herbert
Spencer a process of development.
The word creation in the older sense
ceases to have a meaning. Of more
recent date are the discussions of
the subject in the very interesting
work of Carl Hauptmann, 'Die
Metaphysik in der modernen Physio-

ON THK VITALISTIC VIKW OF NATUUK. 439

orgiuusni

are

It is true that not all parts of a higher
subject to this continued change, but those that are not
— such as the skeleton of an animal or the trunk of a
tree — are automatically deposited l)y the living organism
for the purpose of external or internal support, protection,
or communication. They are the permanent mechanism
by which the economy and administration of the society
of living units or cells are kept up. These it has been
possible, in numy instances, to analyse into stable
chemical compounds, which have Ijeen reproduced in

logie ' (Jena, 1894, iieue AuH.),
esj)ecially the last chapter. Still
more recent is tiie very careful
aualy.sis contained in the new
edition of Mr Spencer's 'Biologj','
notably vol. i. p. Ill sqq. The
final conclusion arrived at by these
two latest philosophers has much
in common. Both strive after a
dynamic concejjtion of life ; both
confess that such is at present un-
attainable— a desideratum, not an
achievement. Hauptmann says (p.
386) : " The most primitive life,
from which alone the living world
on this earth can have sprung, can
only be assumed to be a species the
members of which varied in manifold
ways and propagated themselves.
Here we have to do already with
an eminently complex interaction of
elementary processes. . . . We still
absolutely lack every conception of
such a dynamical system. . . .
Likewise the origin of the simplest
living substance is mechanically
quite unknown and uncompre-
hended. . . . The individual forms
of life stand in the midst of a
yet unintelligible higher order of
the material world." Similarly
Mr Spencer [loc. cit., p. 120) :
" We are ol)liged to confess that
life in its essence cannot be con-
ceived in physico-chemical terms.
The required principle of activity.

which we found cannot be repre-
sented as an independent vital
principle, we now find cannot be
represented as a principle iidierent
in living matter. If, by assuming
its inherence, we think the facts
are accounted for, we do but cheat
ourselves with pseudo-ideas. . . .
It needs but to observe how even
simple forms of existence are in
their ultimate nature incompre-
hensible, to see that this most
complex form of existence is in a
sense doubly incomprehensible. . . .
While the phenomena (of life) are
accessible to thought, the implied
noumenon is ina(;cessil)le, ....
only the manifestations come within
the range of our intelligence, while
that which is manifested lies be-
yond it" (p. 122). There seems
ample evidence that under ditler-
ent forms of words Claude Bernard
and Du Bois-Reymond, in his later
writings, arrived at similar con-
clusions. See ' La Science Ex-
perimentale,' j). 210, and "Die
sieben W'eltriithsel "' ('Reden,' vol.
i. p. 381). "The mystery is the
more profound the more it is
brought into contrast with the
exact knowledge we possess of sur-
rounding conditions" (Prof. Burdon
Sanderson, ' Brit. Assoc. Report,'
1889, p. 614).

440 SCIENTIFIC THOUGHT.

the cliemical laboratory by processes which were like
or unlike those going on in the organism itself. But
such stable compounds are not the bearers, they are
merely the collateral j)roclucts, the accompaniments, of
the living process. The artificial production of organic
compounds, beginning with Wohler's production of urea,
and ending with the production of albumen, do not
approach the problem of the production of living matter.
Could the chemist produce protoplasm, it would not be
living ; or were he fortunate enough to hit upon one of
its many metamorphoses, it would die the next moment,
not having the inner structure or the external and
internal environment necessary for its self-conservation
and activity. Nor do we seem to get any nearer the
real secret by analysing more closely the chemical and
physical changes, the metabolism, the rhythmical processes
which constitute this activity. We call it nutrition or
respiration, assimilation and disassimilation, oxidation and
reduction — storing up and letting loose of energy. We
picture to ourselves the building up of more and more
complicated chemical molecules, containing thousands of
atoms, in a temporary and easily disturbed equilibrium,
and the subsequent breaking down again of these complex
structures by gradual decomposition or by sudden explo-
sions due to external stimuli, or by the still more mysteri-
ous directive action of conscious will : we liken them to
the pulling of a trigger, or the gathering up and letting
loose of a destructive avalanche by the motion of a flake of
snow on the top of a peak. We see how this metabolism,
this " Stoff- und Kraft-wechsel," goes on in the smallest
amoeba in rhythmical movements, and how, in higher

Ox\ THE VITALISTIC VIEW UF NATURE.

441

organisms, it is divided into many stages, allocated to
special cells or to (juite distinct classes of beings, some
of which, like plants, take upon tliemselves the first
important steps of the anabolism, so that others — the
animals — may carry it a stage higher, preparing a dis-
charge, or catabolism, which becomes more and more
effective, till it reaches the unique nervous function
which accompanies the highest phenomenon of animal
activity — the mental process. Claude Piernard ^ has
put into classical words the rationale of this i)rocess.
" If, in the language of a mechanic, the vital phenomena
— namely, the construction and destruction of organic
substance — may be compared to the rise and fall of a
weight, then we may say that the rise and fall are
accomplished in all cells, both plant and animal, but
with this difference, that the animal element finds its
weight "' already raised up to a certain level, and that
hence it has to be raised less than it subsequently falls.

' ' Ph(5noniene.s de la vie,' &c. ,
vol. ii. p. 513. It is oue of Claude
Bernard's greatest merits to have
corrected the earlier formula in
which the circulation of matter had
been expressed. Dumas and Bous-
singault had said : '" L'oxygene en-
leve par ies auimaux est restitue
par Ies vegotaux. Les premiers
consomment de I'oxj'geue ; les
seconds produisent de l'oxygene.
Les premiers brulent du carbone ;
les seconds produisent du carbone.
Les premiers exhalent de I'acide
carbonique ; les seconds fixent de
I'acide carbonique." On this pass-
age Claude Bernard has the fol-
lowing comment : " Cette loi qui
sous la forme j)rdcddente ex prime
avec v(5rit<5 le mucanisme d'une des
])lus gnmdcs harmonies do la nature
est une loi cosmique et noii une loi

physiologique. Ajjplicjuc'e ea ph^'-
siologie, elle n'explique pas les
phdnomtnes individuels : elle ex-
prime comment I'ensemble des
animaux et I'ensemble des plantes
se comportent en definitive par
rapport au milieu ambiant. La loi
ctablit la balance autre la sonnue
de tons les phenoniencs de la vie
animale et de la vie vegetale : elle
n'est point I'expression de ce qui
se passe en p.articulier dans un
animal ou une plantc donni's " (p.
512). This false direction, wiiich
had been introduced into physio-
logy a generation earlier, Claude
Bernard corrected by the view that
the circulation of matter takes
place not only between the two
kingdoms of nature but in every
elementai-y organism.
'- Or its potential.

442

SCIENTIFIC THOUGHT.

42.
Anabolism
and Cata-
bolisra.

The reverse occurs in the green plant cells. In a word,
of the two movements, that of descent is preponderant
in the animal, that of ascent in the vegetable." No one
has done greater service to the fixing of our ideas on
this subject than Dr Gaskell when he analysed the
whole process, called " Metabolism " by Professor Michael
Foster after Schwann, into the two complementary pro-
cesses of Anabolism the upward, and Catabolism the
downward, movement — the winding up and running
down of the clock, the preparation and loading of the
explosive and the discharge of the gun.-^

^ The introduction of these terms
is, however, connected with a.
special view — differing somewhat
from that suggested by the f(3rmula
of Claude Bernard — which is now
verj' generally adopted in text-
books of physiology. Prof. Burdon
Sanderson has given a lucid state-
ment of this difference in his
Address, entitled " Elementary
Problems of Physiology," before
the Brit. Assoc, in 1889 ('Report,'
p. 613). He there says: "A char-
acteristic of living process ... is
that it is a constantly recurring
alternation of opposite and comple-
mentary states, that of activity or
discharge, that of rest or restitu-
tion. Is it so or is it not ? In the
minds of most physiologists the
distinction between the phenomena
of discharge and the phenomena
of restitution (Erkolung) is funda-
mental, but beyond this unanimity
ceases. Two distinguished men —
Prof. Hering and Dr Gaskell —
have taken, upon independent
grounds, a different view to the
one above suggested, according to
which life consists not of alterna-
tions between rest and activity,
charge and discharge, loading and
exploding, but between two kinds
of activity, two kinds of explosion,

which differ only in the direction
in which they act, in tlie circum-
stance that they are antagonistic to
each other. Now, when we com-
jjare the two processes of rest . . .
and discharge . . . with each other,
they may further be distinguished
in this respect, that whereas resti-
tution is autonomic, the other .is
occasional — i.e., takes place onlj' at
the suggestion of external influ-
ences. . . . It is in accordance with
the analogy between the alternation
of waking and sleeping of the whole
organism, and the corresponding
alternation of restitution and dis-
charge, of every kind of living
substance, that physiologists by
common consent use the word
stimulus [Reiz), meaning thereby
nothing more than that it is by
external disturbing or interfering
influence of some kind that energies
stored in living material are dis-
charged. Now, if I were to main-
tain that restitution is not auto-
nomic, but determined, as waking is,
by an external stimulus, that it
differed from waking only in the
direction in which the stimulus
acts — i.e., in the tendency towards
construction on the one hand,
towards destruction on the other —
I should fairly and as clearly as-

ON THE VITALISTIC VIEW OF NATLllE. 443

The modern theories of the cell, of metabolism, and
selection, have also greatly influenced and modified our
conceptions concerning the last itnd nmsl imiHirlaiil pro-
perty of all living matter — viz., that it is self-reproductive.
Older text -books on i)liysiology treated of the great -is-
problem of generation — i.e., the origin of a new individual ^''"'-
— as a phenomenon of organised life which stood quite
isolated ; and although the sexual difference in plants
and animals had early led to certain analogies, to similar
terminology, and to vague inferences, the mysterious
phenomena of generation, and especially of sexual genera-
tion, were not brought into line with the general pro-
perties of all living matter till about fifty jjears ago.
Even Johannes Miiller in his great text - book on
Physiology, which takes a much wider view of the sub-
ject than any work before it, treats of the reproduction
of tissues and of generation in (juite separate, seem-
ingly disconnected, parts of his work. Into this un-
certainty only little light was thrown l)y the original
prcjpounders of the Cellular theory, who, misled by the
supposed analogy of cells and crystals, imagined that
cells originated out of the surrounding cell sap, as
crystals solidify out of the solution or mother liquor.
Correcter views were gradually elaborated by botanists.
Mohl emphasised the important part which protoplasm
plays in the formation of cells. Niigeli established the
process of intussusception as against external accretion ;
anatomists like Max Schulze and Briicke joined hands,

pos.sible express the doctrine wliicli
Dr Gaskell and Prof. Hering have
embodied in word.s which have now
become fainiliar to every student.
The words in question — ' anabolism,'

whiclr, being interpreted, means
winding-up, and 'catabolism,' run-
ning down — are the creation of Dr
Gaskell."

444

SCIENTIFIC THOUGHT.

44.

Tlie proto-

lilasiiiic

theory.

and the year 1863 is usually given as that in which
the protoplasmic theory was established. According to
this view protoplasm is the element or unit of all living
substance : it grows through assimilation (intussusception
and excretion), and multiplies {i.e., gives rise to other
living units) by subsequent division. This process was
found to be fundamental : it describes the growth of
the simplest and the most complicated organisms as
beginning alike with a unit cell, which may or may
not grow by division ; it is the formula of growth,
restitution, and generation (whether sexual or asexual) ;
and, what is equally important, it prevails also in patho-
logical cases — i.e., in the formation of diseased tissues.
In fact, the great generalisation which followed Harvey's
celebrated dictum, " omne vivum ex ovo," was put forth
by the late Professor Eudolf Virchow, the eminent
founder of cellular pathology, in his formula, " omnis
cellula e cellula." The formula has in more recent
times been further elaborated on the same lines of
thought in proportion as the importance of the nucleus
or cell kernel has been recognised, or as the granular
structure of protoplasm has been maintained ; leading
to analogous formulae, such as " omnis nucleus e nucleo,"
" onme granulum e granule." These formulae ^ are the

^ See Roux (' Gesammelte Ab-
handlungen,' vol. i. p. 393) : " Un-
interrupted durability is the in-
dispensable condition of all that is
organic, although this does not
involve a distinction from inorganic
processes. This fact is expressed
by the fundamental theses : Omne
vivum ex ovo (Harvey), Omnis
cellula e cellula (Virchow), Omnis
nucleus e nucleo (Flemrning)."

Hauptmann (' Die Metaphysik,'
&c., p. 334) says: "Altmann for-
nmlates for himself in analogy
with these biological princijiles the
further princijale, ' Omne granulum
e granule.' " On Altmann's theory
of the "bioblasts" as elementary
organisms, see Yves Delage,
' L'Hdredite,' p. 498, &c., Hertwig,
' The Cell,' p. 24.

ON THE VITALLSTIC VIEW uF NATCRE. 445

expression of anatomical observations and theories repre-
senting an enormous amount of research, labour, and in-
genuity, but they iuvohc no new line of reasoning, and
they belong, accordingly, more to the history of Science
than to that of Tliought.

The first to attempt a mechanical explanation of the . *■'-.,
process of cellular division was Mr Herbert Spencer,^ LTgrovrth.'^
who, in his 'Principles of Biology' (I860), pointed out
that there exists a limit of growth through assimilation
or intussusception, inasmuch as volume and mass increase
at a greater rate than the surrounding surface through
which communication with the environment is afforded.
A resultant tension brings about an increase of surface
through rupture, and restores the balance between the
contained mass and the surface. In his analysis of this
process of readjustment, Spencer has given mechanical

^ The principle here referred to
s-ometimes goes under the name of
the Leuckart-Spencer principle, it
having heen suggested independ-
ently by Rudolf Leuckart, Herbert
Spencer, and Alexander James. It
requiret), of course, a great many
qualifii'ations. See the ' Principles
of IJiology,' vol. i. part 2, chap. i.
But " it follows from these con-
siderations tliat the cell can never
surpass a certain size ; for if the
disturbance of metaVjolism that
arises because of the increasing
disproportion between the more
superficial and the deeper layers
has reached a certain extent, the
cell can no longer continue living
in its existing form. Thus the
remarkable fact is exiilained very
simply, tliat no cells of constant
form are known that are larger
than a few millimetres in diameter,
and thus we are made to under-
stand why the development of

large

organisms is only possible
by the arrangement of the living
substance into an aggregate of
small cells instead of into a single
cell, for example, of the size of a
man. ... If, therefore, the living
substance of such a cell is not to
perish by growth, at some period in
its growth a correction of this dis-
proportion between mass and sur-
face and of the disturbance of
metabolism conditioned by it must
come in : such a correction is realised
in the reproduction of the cell by
division. The repnjduction of the
cell by division is accordingly to be
considered merely as a lesult of
growth, and the morphologists for
a long time have rightly termed
i-epniduction a continuation of
growtli, ' a growth beyond the
measure of the individual ' " (Ver-
worn, ' General I'hysiology,' Engl,
transl., p. 530, &c.)

446 SCIENTIFIC THOUGHT.

biologists a formula which, like his physiological units,
has helped to give precision and direction to reasoning
on these subjects. But as growth has a natural limit
and leads to division, so reproduction through division
appears to have a limit also. " Only the very lowest
organisms, such as fission fungi, appear to be able to
multiply indefinitely by repeated divisions : for the
greater part of the animal and vegetable kingdoms the
general law may be laid down that, after a period of
increase of mass through cell division, a time arrives
45. when two cells of different origin must fuse together,
of two producing by their coalescence an elementary organism

elements.

which affords the starting-point for a new series of
multiphcations by division." ^ Fertilisation is now
known to be a cellular problem. As such it has been
studied in favourable cases which permitted of direct ob-
servation, and what has been ascertained in those cases
— exhibiting in general the same common features and
phases of development — has by inference under the great
generalisations of the cellular theory been extended to
all living things in which sexual differentiation exists,
be they animals or plants.^ The male and the female

1 Hertwig, ' The Cell,' p. 2.r2.
The process may be looked at as an
instance of tlie cyclical order of
change. " The multiplication of the
elementary organism, anil with it
life itself, resolves itself into a
cyclic process. . . . Such cycles are
termed generation cycles. They
occur in the whole organic king-
dom in the most various forms."
Similarly Sir M. Foster (' Text-book
of Physiology,' 5th ed., p. l.^.")5), as
quoted, supra, p. 289. We may
add that from a still broader stand-
point, which we may call that of

bionomics — in distinction from
biology — the cycle never repeats
itself, but, owing to overcrowding
and selection, something different,
more complex — i.e., externally or
internally better endowed — is pro-
duced. Philosophically we call this
progress.

- There exists no more remark-
able instance of the extension of
natural knowledge by a process of
very incomplete induction than the
gradual linn establishment of the
now universally adopted doctrine of
fertilisation, no more brilliant refu-

ox THE VITALISTIC VIEW UF NATLKP:.

447

elements concerned have both been recognised to be
cells, both have been found to undergo, before what is
termed the stage of maturity, similar preparatory changes.
The changes represent, as it were, the last stages of their
independent existence as living cells. After these
changes have taken place they can only enter into a
new cycle of existence, exhibiting new powers of growth
and division by a process of fusion where each supjilies
what in the other is wanting to start on a new cycle of
life — i.e., of difi'erentiation and development.

Thus the vague theories of former times, which reach
far into the nineteenth century, the speculations of the
Spermatists and the Ovists, have during the last thirty
years, beginning witli Pringsheim's observation in 1869
of the pairing of the swarm-spores of certain algse,

tation of the purely enumerative,
or all-case method. The number
of instances in which the process
of fertilisation, with its various
preparatory stages and its conse-
(juences, can be actually observed
is infinitesimally small compared
to the number of different species
and varieties in which it is end-
lessly repeated on lines which no
biologist doubts to be essentially
the same. M. Yves Delage says :
"C'est une chose remarquable com-
bien certains etres, par des particu-
larites en apparence sans int<5ret
ont facilitc la solution de certains
problemes presque insolubles en
dehors d'eux. L'Ascaris ranjalocc-
phula [tiie round - worm of the
horse, first observed by van Bcne-
den in 1883], par le petit nombre
de ses chromosomes, lea Echino-
dermes [sea urchins, &c.] par la
facilitc avec lafjuelle ils acceptent
la fecondation artificielle, out fait
faire, en di.\ ans, plus de progres

aux questions relatives a la fdconda-
tion que n'ont fait avant ou dcpuis
tous les autres animaux rdunis.
Dans TAscaride, le tcsticule foi-me
un long tube et les diverses phases
de la spermatogencse s'acconqilis-
sent dans les rt%ions diffcrentes de
I'organe : il y a une zone il sper-
matogonies, une zone a si)ermato-
cj'tes en voie d'accroissement, une
zone ou se font les divisions r^-
ductrices et une enfin oil les sper-
matides se transforment en sper-
matozoides" {' L'Heredite,' p. 133).
See on the variety of objects which
have lent themselves to the gradual
unravelling of the processes of cell
division, nuclear division, fusion of
nuclei, cleavage and embryonic de-
velopment, notalily the volume of
Prof. Val. Haeckcr, ' Praxis und
Theorie der Zellen- und Befrucht-
ungslehre' (Jena, 189!>). A very
lucid summary is contained in J.
A. Thomson's ' The Science of Life '
(1899).

448

SCIENTIFIC THOUGHT.

47.
New
problems.

and centring in van Beneden's discovery/ been replaced
by definite conceptions capable of typical description.
This typical process consists in the fusion of certain
parts of the male and female cells, — the nuclei or
kernels playing an important if not the essential part.
Many biologists of the foremost rank, notably in
Germany and France, have contributed to make clearer
the various lines in this typical picture of the most
mysterious process in the physical organism, whilst
every new discovery has brought with it new and
unanswered questions or given a novel aspect to older
problems.

Of these problems, those of heredity and variation
are at present by far the most important. Both
the cellular theory of living matter and the theory
of natural selection, including the principles of
differentiation and of the division of physiological
labour, converge upon these two great facts of
modern biology. The theory of natural selection pre-

^ See last note. " Since the
researches of 0. Hertwig and
others hi 1875, it had been clear
that each parent contributes a
single germ -cell to the foi-mation
of the offspring ; but the masterly
researches of E. van Beneden
(1883) showed that every nucleus
of the offspring may contain nuc-
lear substance derived from each
of the parents, a conclusion which
is visibly demonstrable for a few
of the first steps in cleavage. In
fact, van Beneden to some extent
proved what Huxley had foreseen
when he said, in 1878, 'It is
conceivable, and indeed probable,
that every part of the adult
contains molecules, derived both
from the male and from the

female jjarent ; and that, regarded
as a mass of molecules, the entire
organism may be compared to a
web, of which the warp is derived
from the female, and the woof
from the male'" (J. Arth. Thom-
son, 'The Science of Life,' -p.
129). Another theoretical antic-
ipation is, according to Haecker
(loc. cit.,]}. 133), the "Idioplastna"
of Niigeli : " The heritable sub-
stance, organised, possessing a com-
plex structure, transmitted from
one generation to another," which
was " about the same time identi-
fied by Strassburger, O. Hertwig,
von Kolliker, and W'eismann, with
the chromatin substance of the
nucleus."

UN THE VITALISTIC VIEW UF NATUIiE. 449

supposes the fact of heredity — that is, the transmission
of characters peculiar to the parents (be they acquired
by them or not), antl llie fact of variation, 1ml it does
not explain them. It does not give any intelligil)le
description of the means which nature uses to secure
that continuity of change which is marked on the one
side by a faithfulness to certain typical forms, and on
the otlier by a gradual development. The cellular
theory permits us to comprise, under the general
categories of cell-growth, cell-division, and cell-fusion,
the great facts of the history of all living matter, but
it does not explain hdw tliat apparent sameness of
structure which the ultimate morphological unit, the
cell, presents to our view, develops into that variety
of recurrent forms which make up the wealth and
the order in the world of natural objects. The older
naturalists were divided into two distinct schools : one
believed in pre-formation with development — the older
meaning of " evolution " ; tlie other in after-formation,
or " epigenesis." The former foundered on the difficulty
of explaining or making plausible how all the germs
of hundreds of succeeding generations could be contained
in the first ancestor ; the latter failed to explain how
nature was able to Imild up by mechanical forces out
of unorganised matter a structure resembling the parent
structures. The suggestion of a " nisus formativus,"
which we owe to the celebrated Blumenbach, is only
a definition of tlie ditliculty, nut an explanation.

The three distinct ideas represented by tliesi^ historic
terms occur again in modern biology, though altered to
suit the vast extension of actual knowledge of facts, and

VOL. II. 2 F

450 SCIENTIFIC THOUGHT.

the three great generalisations mentioned above. Out
of the three ideas of pre-formation, after-formation, and
the directive principle, the three generahsations, namely,
the cellular theory, natural selection, and metabolism,
and the enormous number of facts collected by micro-
scopists and naturalists of all kinds, many more or
less ingenious theories of life have been put together.
None of them has obtained, though some have had a
very marked influence on biological science, and even
48. on popular thought. Of these Prof. Weismann's theories

Weismann -^ ^ "

on heredity, of heredity are probably the best known. Without en-
tering upon the enormous array of biological facts which
have been marshalled by supporters and opponents ahke,
it will be of interest to point out the novel aspects
and lines of reasoning which have come into prominence
through the voluminous discussion belonging to this
subject. They were prepared before the appearance of
Weismann's writings by the changed and enlarged con-
ceptions which the discoveries of the middle of the
century introduced concerning the general phenomena
of Life, Death, and Disease. Three distinct convictions
regarding these three main aspects of the Hving portion
of creation have been forced upon the scientific and
popular mind. First, we have the modern doctrine of
the ubiquity of organisms and germs, at least so far
as our planet is concerned : beyond this sphere we
can say that we know no more of the existence
of living matter than past generations. Secondly, we
have the generally recognised doctrine that spontan-
eous generation of living out of not-living matter is
imknown and inconceivable under such conditions as

ON THE VITALISTIC VIEW OF NATURE. 451

we can realise or imagine. And thirdly, hand in hand
with the conviction of this unique but ubiquitous character
of life, the impression of the mutual interdependence of
living creatures has gained ground, and has especially in-
fluenced our ideas of the cause and treatment of disease.

In one of those luminous addresses in which he to.

Biogenesis.

has rivalled the combination of literary witli scientific
clearness characteristic of the French genius, the late
Prof. Huxley has written the history of Biogenesis ^
— i.e., of the theories of the origin of life from
the time of the Italian Eedi down to Pasteur, show-
ing how experiment and theory alternately supported
and contradicted the doctrine that living matter could
be formed out of not -living matter, till the great
French biologist, by his refined experiments, entirely
banished from the provinces of science and practice
the once admitted fact that, after exclusion or destruc-
tion of all living germs, phenomena peculiar to life, such
as fermentation and putrefaction, could be generated.
Those great departments of medical practice, the anti-
septic and aseptic treatment, with their enormous de-
velopment of prophylactic and antitoxic methods, form
the daily and ever-growing argument against abiogenesis

^ In his presidential address to
the British Association in 1870,
reprinted in ' Critiques and Ad-
dresses,' p. 218 s'lq. A very
readable and much earlier deliver-
ance on " The Diffusion of Life "
is that hy K. E. von Baer, before
the Academy of St Petersburg in
1838, reprinted in the first volume
of his 'Reden,' &c., p. 161 sqq.
In the preface of 1864 to tliis
reprint, the illustrious author tell.-

there were probably few naturalists
who "did not consider the gener-
ation without parents of inferior
organisms as proved, or at least
as highly jirobable," and he him-
self would not at that time (1838)
"declare it to be non-existent"
(p. 173). In 1864 he describes the
theory as having almost vanished,
leaving the problem of the first
beginnings of life in the number-
less varieties, even after Darwin's

Ub that between 1810 ancl 1830 I hypothesis, unsolved (p. 177)

452 SCIENTIFIC THOUGHT.

— i.e., the generation of living out of dead or not-living
matter.

But in proportion as abiogenesis or spontaneous
generation has disappeared from our scientific text-
books, life being recognised as a phenomenon between
which and dead matter there exists no intelligible
and no practical transition except that of destruction,
50. the ubiquity of life has forced itself more and more
Theuiqmy^^ our attention. Not long ago, as Huxley^ tells us,
the adherents of spontaneous generation urged as an
argument on their side that if biogenesis be true,
innumerable facts and experiments prove " that the air
must be thick with germs ; and they regarded this as
the height of absurdity. But nature," as Huxley con-
tinues, " occasionally is exceedingly unreasonable, and
Professor Tyndall has proved that ordinary air is no
better than a sort of stirabout of excessively minute
solid particles." It is now, after a generation has passed,
hardly necessary to refer to any special experiments of
Tyndall or of others, when the daily press brings us
records of the number of bilHons of germs contained in
a cubic inch of the atmosphere of large cities, precisely
as it does of the mortality of their population. The
cellular theory of disease has been succeeded and ampli-
fied by the bacillar theory, and no modern scientific fact
has fastened on the popular mind with a stronger hold
than the ubiquity of the micro-organisms, which, with
beneficent or fatal results, assist everywhere — chiefly in
the larger organisms — in the struggle for existence.
It is, moreover, only a logical inference that if living

' Critiques aud Addresses,' p. 233.

1 <

ON THE VITALISTIC VIEW OF NATURE.

453

matter is not being continually formed out of not-living
matter, while it is an undeniable fact that livinir
matter is continually and everywhere passing out of
existence, the preservation of life is dependent upon
an enormous self-overproduction which, combined with
the process of natural selection, secures its permanence
and the development of the highest forms of which it is
capable. The continuity — i.e., the interdependence — of "^i-
all living forms in time and space guarantees the non-ex- ,^'"."'^y ^^

c r o living forms.

tinction of this phenomenon, which, for all that we know,
is of a unique character. The modern scientific and popular
view of life is that it is a unique phenomenon, that it is
a ubiquitous phenomenon, at least within the area of
what we call " our " world, and that it is a continuous
phenomenon. The unique character or singularity of
life has been directly demonstrated by the sameness of
the ultimate units of all living matter, the cells, indirectly
by the refutation of the older theory of spontaneous
generation ; and has been enormously strengthened by the
doctrine of descent, the phenomena of overcrowding, and
the possibility of natural selection. The ubiquity of life —
within certain limits — has been revealed directly by the
microscope, and indirectly by the modern theories of
disease, and of many forms of growth.^ The continuity of

1 There is a striking passage in
Nansen's 'Farthest North,' vol. i.
p. 445, showing the ul)i(iuity of
organic germs : " When the sun's
rays had gained power on the sur-
face of the ice, and melted the
snow, so that pools were formed,
there were soon to be seen at the
bottom of these pools small yellow-
ish brown spots, so small that at
first one hardly noticed them. J )ay

by day they increased in size, and
absorbing, like all dark substances,
the heat of the sun's riiys, they
gradual! J' melted the underlying
ice and formed round cavities often
several inches deep. These brown
spots were . . . algto and diatoms.
. . . I actually found bacteria,^
even these regions are not free
from them."

454

SCIENTIFIC THOUGHT.

52.
'Pan-
genesis.'

life has — as an inevitable corollary — come more and
more into prominence. It has been the subject of
much discussion, as a phenomenon which is felt to
require a mechanical explanation.

The problem of the continuity in time of the forms
and properties of living matter forced itself on the great
propounder of the modern theory of Descent, on Darwin.
He looked upon the principle of "Ee version^ — this power
of calling back to life long-lost characters — as the most
wonderful of all the attributes of inheritance."

At the end of his second great work, ten years after
the appearance of the ' Origin of Species,' he ventured on
a hypothetical explanation, his theory of " Pangenesis,"
" which implies that the whole organisation, in the sense
of every atom or unit, reproduces itself ; hence ovules and
pollen-grains, the fertilised seed or egg, as well as birds,
include and consist of a multitude of germs thrown off
from each separate atom of the organism," ^ This idea,
as the author himself admitted, and as has since fre-
quently been pointed out, was not fmidamentally new : it
had been anticipated by Buffon in his celebrated "organic
molecules," and since Darwin it has been restated and
adapted in various modified forms. It is hardly an ex-
planation, but it is a statement which emphasises the
great fact of modern biology, — the fact Ijrought out by
the cellular theory, that the units of life are not the large
visible organisms which were formerly studied by prefer-
ence, but the innumerable, infinitesimal living beings

^ ' Animals and Plants under
Domestication,' vol. ii. p. 372.
^ 'Animals and Plants under

Domestication,' chap. 27, vol. ii. p.
358.

ON THE VITALISTIC VIEW OF NATURE.

455

called cells which, through growth and reproduction by
division and fusion, maintain life as a continuous unic^ue
phenomenon.

Into this view, which under the special form of
pangenesis has not found much favour, hut wiiich,
nevertheless, in some form or other, forces itself more
and more on our attention, Professor Weismann has
imported a further distinctive feature, not prominently
brought out by Darwin, though it also dates farther
back ^ than the present generation.

^ The history of tlie knowledge
and theory of sex and heredity has
been written in EngHsh by Profs.
Patrick (leddes and J. Arthur
Thomson, in a book entitled ' The
Evolution of Sex ' (1st ed. 1889) ; in
French by M. Yves Delage, in his
much-quoted work, ' La Structure
du Protoplasma et les Theories sur
rH(5redite et les grands problomes
de la Biologie' (1895). The latter
work contains elaborate criticisms,
and finally inclines towards a theory
of life termed in France " Organi-
cisme," the main idea of which is
the assumption of two distinctive
factors in all the phenomena of
living matter — viz., '"Organisation
and Environment." This view,
according to the author, has not
yet gained sufficient strength to
form a definite current of thought
like the three earlier views de-
fined by the terms " Animisme,"
" Evolutionisme," " Micronicrisme."
The first of these centres in the idea
of vital force, the second iu the
older school of evolution ; the last
begins with Buffon, and comprises
tiie modern theory of Evolution with
Spencer, Darwin, Haeckel, Weis-
mann. Of the last M. Dclage
says : " Ce dernier est, pour le
moment, I'ouvrage le j)lus jiarfait
crec pour expliquer rHcrddit^ et

r Evolution. Nous croj'ons avoir

montre (ju'll est bati d'hypoth^ses

fragiles, invraisemblables, et, tout

en rendant justice au talent de

son architecte, nous con.seillons de

I'admirer de loin et de construire

ailleurs" (p. 837). " Organicisme "

is represented by W. Koux, Uriesch,

and 0. Hertwig, and is historically

traced back to Descartes (p. S'.jS),

and to von Baer and Claude Bernard

(p. 720). To the theories of the

others, "les Organicistes opposent

le concours d'une determinatinn

mod(5r^(5 et des forces ambiantes

toujours agissantes, toujours n^ces-

saires, non comnie simple condition

d'activite, mais comme element

essentiel de la determination finale "

(p. 720). As iu this account the

names of Roux, Driesch, and 0.

Hertwig are placed together, it is

well to remark that since that time

the two last-named authorities have

in v.arious polemical publications

signified the divergence of their

fundamental conclusions from the

later attitude which Prof. Roux

has assumed. For those of my

readers who desire to get some

insight into the drift of this most

recent and advanced controversy,

in which questions of principle, of

scientific and philosojihical method,

I alternate with discussions of minute

456

SCIENTIFIC THOUGHT.

Growth by intussusception and assimilation has long
been recognised as the characteristic property of all
living matter, of every living cell. Mechanical causes
suffice to explain the further process of division as a
necessary consequence of continued growth, the forma-
tion of new cells out of existing ones, the process of
reproduction. Only in the lower organisms, however,
does reproduction exist simply as multiplication by
division. In all higher organisms at least, reproduction
by division seems connected with the phenomenon
of death of a portion of the dividing organisms : a
differentiation seems to set in between the new cells,
some gradually losing their power of self-multiplication
by division, and thus being doomed sooner or later
to arrive at the end of their organic existence ; while
others retain this power or regain it by uniting with
others — the process of fusion of male and female elements
— and seem thus to be specially endowed with the work
of reproduction — i.e., the preservation of the continuity of
life. The great morphologist Eichard Owen, about the
middle of the century, in a tract on Parthenogenesis,
remarked that " not all the progeny of the primary
impregnated germ-cell are required for the formation of
the body in all animals : certain of the derivative germ-
cells may remain unchanged and become included in

embryological development, assisted
or disturbed by experiments carried
on in microscopic dimensions, I
recommend, besides the larger works
of Hertwig and Roux already re-
ferred to, the highly suggestive
writings of Hans Driesch, notably
his 'Analytische Theorie der or-
ganischen Entwickelung ' (1894),

and ' Die Biologic als selbstiindige
Grundwissenschaft ' (1893). As a
very helpful inti'oduction to the
original views of this writer, Eng-
lish readers will welcome the con-
cluding chapter of Prof. E. B.
Wilson's book, ' The Cell in Develop-
ment and Inheritance' (1896).

ox THE VITALISTIC VIEW UF NATL'UE. 457

that body, ... so included, any derivative germ-cell or
tlie nucleus of such may commence and repeat the same
processes of growth by imbibition, and of propagation l)y
spontaneous fission as those to which itself owed its
origin." ^ We have here the first enunciation of that , ^3.

" Germ-sub-

idea of a differentiation between the germ-substance and b^^y.gub-*^
the body - substance, between that portion of living '"^*"*^-
matter which is destined to preserve the continuity of
life, and that other portion which, destined to differen-
tiate more and more into the aggregate of living cells,
each bearing a special form and carrying out a special
function in the economv of the higher organisms, is at
the same time doomed In death, gradually losing, as it
does, its power of assimilation, growth, and division — i.e.,
of self-preservation. Prof. Haeckel in 186G, and Dr
Jager in 1877, elaborated the idea further, pointing out
that the " germinal " element or substance was that
portion wliicli in the ])rocess of division is reserved
for the preservation of the species (the ^uAor, hence
termed the phylogenetic portion), whereas the " personal "
element or substance goes to form the body or individual
(tlie ov, hence termed the ontogenetic portion).^

' Darwin quotes this passage in
a historical note to his theory of
" Pangenesis " in the concluding
chapter of his • Animals and Plants
under Domestication' (vol. ii. p.
375). He adds further, "By the
agency of these germ-cells Prof.
Owen accounts for parthenogenesis,
fur propagation by self - division
during successive generations, and
for the repairs of injuries. His
view agrees with mine in the
assumed transmission and multi-
|ilii:atioii of his germ - cells, but
diU'ers fundamentally from mine in

the belief that the primary germ-
cell was formed within the ovarium
of the female, and was fertilised by
the male. My gemmules are sup-
posed to be formed, quite independ-
ently of sexual concourse, by each
separate cell or unit throughout the
body, and to be merely aggregated
within the reproductive organs."

'-' Complete references to the
earlier statements of this theory,
which, tlirougli tlic various writings
of Prof. Weismann (since 1881,
when he read a paper, "On the
Duration of Life," before the

458

SCIENTIFIC THOUGHT.

This provisional statement, which emphasises the now
generally recognised difference between the germ-sub-
stance and the body-substance, requires, however, two
further quahfications in order to embrace the great
characteristic facts of life and death as modern em-
bryology and the phenomenon of descent have unfolded
them.

Only in rare instances can we observe the continuity
of cells — i.e., of those organisms which, so far as our
knowledge goes, form the ultimate units of living matter.
Weismann recognised, as did the great botanist Nageli,
and long before both of these the philosopher Herbert
Spencer, that though in the cell, with its nucleus and
protoplasm, we may have arrived at the last microscop-
ically visible independent units of life, we must — with
the atomic theory in chemistry — assume the existence
of much smaller units in all living matter, compared with
which even the nucleus of the cell is a very complex
aggregate. If the continuity of life is dependent upon
that of an underlying living substance, this substance
must be only an infinitesimal portion of any visible cell
or nucleus. The conception of a continuous germinal
plasma and substaucc lias thus taken refuge in the more refined

body- *=

plasma. conception of a germ-plasma, as distinguished from the
body or somatic plasma : the former is immortal within
the limits of the conditions of organic life, the latter is

54.

Germ-

Naturforscher - versammlung at
Salzburg, reprinted in ' Essaj's upon
Heredity,' tran^^l. by Poulton and
others, Oxford 1889 ; see also the
' Studies in the Theory of Descent,'
transl. by Meldola, 2 vols., 1882,
and the earlier essays of Weismann
mentioned in the preface, p. viii.).

has become both scientifically and
popularly recognised and debated,
are given in Geddes and Thomson,
' The Evolution of Sex,' p. 93 ; also
in M. Delage's great woi-k, p. 349,
&c., and in Wilson, 'The Cell,' p.
295, &c.

ON THE VITALISTIC VIEW OF NATURE. 459

perishable, mortal, doomed, after temporarily serving the
purposes of individual development, to disappear from
the category of living matter.

And secondly, it appears that the germinal substance ^.^ 55.
or germ - plasma, when once differentiated from the j',asni'''^""'
personal substance or body-plasma, cannot, as a ride,
perform unaided the function of continuous preservation
of the species or phylum. In all the higher animals
the germ -substance appears in two distinct seemingly
complementary forms, and only by the fusion of these
does the development of the germ -substance become
possible.

The great ditticulties which stand in the way of
applying these conceptions (which have found an ex-
haustive exposition in Prof. Weismann's ' Essays on
Descent and Heredity ') to the vegetable kingdom have
been pointed out, and have prevented their general
adoption by biologists ; ^ nor have the elaborate modifi-
cations introduced in Prof. Weismann's later writings
tended to make them more acceptable ; the idea, never-
theless, of a fundamental differentiation of the elements
of living matter into germinal and personal has got hold
of the scientific mind at the present day, and cannot be

' On the objections of Prof. Stras-
burger, wlio pc.ints to the fact that
in the Ciise of begonias the frag-
ment of a leaf jilanted in moist sand
can rejiroduce the whole plant ; of

Problem of To-dav,' transl. by P.
C. Mitchell (1896)' p. 40, &c. On
the discovery of Weismann " that
in parthenogenetic ova only one
polar globule is formed, wliile there

Prof. Vines, wIkj shows that whole ; are always two in ova which are

groiq)s of champignons, which propa-
gate annually, are nevertheless rich
in genera and sjiecics, which have
evidently descended from one an-
other, see Yves Delage, ' L'Heredito,'
p. L2^, &c. ; ' Nature,' vol. x. ]). 02 1 ;
also O. Hertwig, ' The Biological

impregnated," and the "moment-
ary " prcsum])tion in favour of his
theory which it afforded, see ' Essays
on Heredity,' i>. 333, &c. ; Geddes
and Thomson, ' Evolution of Sex,'
p. 180, &c. ; and Delage, ' L'Hero-
ditcV p. 151.

460 SCIENTIFIC THOUGHT.

passed over in a history of Thought. Moreover, it has
made itself felt by giving rise to two separate views of
the cause of variation — i.e., of that phenomenon in the
living creation on which the entire modern theory of
descent is founded.

If it be true that the preservation of the species, the
continuity of living forms, is dependent on the germ-
plasma, whereas the somatic plasma, from this point of
view, only serves individual ends and is a receptacle or
temporary dwelling-place for the germs which it trans-
mits but does not create, the experiences of the body, its
changes and development, can have little or no influence
on the hidden germs and their further history. Thus
56. Weismann is led to a denial of the influence of en-

Weismann v.

Lamarck, viroumcut, of habit and acquired characters, except in
those cases where, as in the lower organisms, no dif-
ferentiation has set in between the germinal and the
personal substance. This amounts to a negation of those
modifying influences which Lamarck emphasised, and
which play such a great part in the theories elaborated
by Darwin, Haeckel, and especially by Herbert Spencer.
On the other side, it has led Weismann to lay a much
greater weight upon sexual selection and the effects
of crossing in the process of descent and the pheno-
mena of heredity. But for sexual selection, and the
endless combinations of different germ - plasmas, there
would, according to Weismann, be no variation, and
hence no development of the higher forms of life. The
controversy turns mainly upon the inheritance of acquired
characters, of which indeed no genuine and authenti-

ON THE VITALLSTIC VIEW OF XATUKE. 461

cated case seems to have been established.^ On the other
side the influence of crossing, of the repeated division
and fusion of different germ-plasmas, to which Darwin
in his later writings attached more and more importance,
and on which Weismann rehes exclusively for an ex-
planation of variation and natural selection, is denied
by some biologists to tend in the direction of the
gradual growth of definite characters : they point rather
to the obliterating and diluting influence of such pro-
miscuous fusion, and they maintain that the presence of
an environment which always acts in a constant manner ^
is indispensable.

If we now look back for a moment on the funda-
mental change of ideas which the century has brought
about in the biological aspect of nature, we are bound
truly to halt in astonishment. In no department of
thought have comparatively small beginnings and de-
tailed discoveries, referring to infinitesimally small
phenomena, led to such revolutionary ideas concerning
those phenomena which most intimately affect our
personal interests — the problems of life and death, of
conduct and of health. The whole of this change has
been brought about by introducing and extending those

^ It i.s needless to give special
references, as all the recent works
on the subject, which have been

hercditaires, niais il parait bien
certain qu'elles le sont quekiuefois.
Cela dejiend sans doute (le leur

largely (juoted in this chaj)ter, deal i nature. D'ailleurs on ne sait j)as

with this point. See, however,
Yves Delage, ' L'Hdrc^dito,' p. 196,
for a very complete bibliograjjhy.
He concludes as follows : " II n'est
])a»s deniontro que les modifications
acquises sous I'influence des con-
ditions de vie soient gtindralement

quelle est dans ce rdsultat la part
de la transmission des modifications
somatiques aux cellules gcrminales
et celle de Taction directe des con-
ditions ambiantes sur celles-ci "' (p.
221).

- Hertwig, ' The Cell,' p. 319.

462 SCIENTIFIC THOUGHT.

methods of investigation and reasoning which have
been learnt in the mechanical, physical, and chemical
sciences : the processes of observation, measurement,
and calculation. And yet it may be asked, have we
come nearer an answer to the qviestion, What is Life ?
At one time, for a generation which is passing away,
we apparently had. But a closer scrutiny has convinced
most of us that we have not. The study of life has
indeed been transferred from the higher and more com-
plex forms to the lower, the minuter, and the simpler ;
and now lingers by preference among cells, germs, and
primitive organisms, out of which we have learnt to
consider the higher ones as put together on the prin-
ciples of co-operation, division of labour, and mutual
57. accommodation. The problem " What is Life ? " has

Two aspects

of the in all this sained a twofold aspect. Wherein consists

problem ^ ^

of life. ^Yie peculiarity of the smallest unit of living as com-
pared with not-living matter ? In organisation we are
told, in growth through intussusception, in metabolism ;
but we are far from being able mechanically to describe
these phenomena or processes. The spectre of a vital
principle still lurks behind all our terms.^ On the other

^ If we broadly summarise the
properties peculiar to living things
which the nineteenth century has
dwelt on in an original manner
under the three conceptions of adap-
tation (fitness), selection (natural or
sexual), and organisation (order or
harmony), the question presents it-
self. Is any of these much-used terms
intelligible or definable without
reference to something which is ex-
traneous to the object we treat of,
this reference existing in our own
thinking or contemplating mind,
and, if actually present in natural

objects themselves, then also indi-
cative of the existence of some im-
material principle ? Though this is
manifested in mechanical contriv-
ances which it has left behind with
its signature upon them, it is never-
theless vaguely analogous to the
selective, purposeful, or orderly
jjerformances of a human intellect
The exclusive study of detail on the
one side, the aspect of the whole on
the other, will always induce opposite
answers to this question. In addi-
tion to the literature given in the
notes to this chapter, I may refer

ON THE VITALISTIC VIEW OF NATURE. 463

side, the union ov co-operation of many essentially similar
units in a complicated organism brings out more and
more, as we ascend in the scale of living things, a new
phenomenon, a new kind of unity, that which we term
" individuality," the wealth of an inner self-conscious life,
to which the older school of biologists attached primary
importance. Life accordingly has now for us two sides
— first, the life of the smallest, the most primitive unit
of living matter, say the cell, the amoeba, or, if you will,
the idioblast, the gemmule, the germ-plasma, the physio-
logical unit. Secondly, the life of the complex society of
cells, the higher organism in which the inner world with
all its mental phenomena has become manifest. How-
ls the unity of this higher complex possible ? In what
does it consist ? What can we know of it ? Neither
the physiological nor the psychological unity is in-
telligible to us. An eminent biologist, to whom we
owe the creation of an entire new science, the late
Professor Virchow, the founder of Cellular Pathology,
has told us recently ^ that only since biologists have
ceased to try to understand the unity of life in the
higher organisms, the psychological unity, and have
realised the fact that the unity of life is in the
autonomous cell, has biology in theory and practice
made much progress. Be it so. It seems likely that
the progress of biology depends entirely on the culti-
vation of the mechanical view ; but from another and

to the following tracts which deal I 0. Biitschli, ' Meehaiiismus unci

specially with the problems of I Vitalismus ' (Leipzig, 1901) ; Eugen

mechanism and vitalism. Hans Albrecht, " Vorfragen der Biologic "

Driesch,'Die mathematisch-mechau- (Wiesbaden, 1899).

ische Betrachtung morphologischer ^ In the Hu.\ley Lecture of 1898.
Problenie der Biologie' (Jena, 1891) ;

464 SCIENTIFIC THOUGHT.

equally legitimate aspect, the unity of the complex as
the bearer of all the phenomena of higher or inner life
is equally important. In many ways it is a counter-
part of the other, showing a peculiar continuity of its
own, that continuity which I have made the special
subject of this work. In proportion as the biological
view of nature has become the science of the cell,
another science has grown up which sets itself to study
this higher phenomenon of living matter, the pheno-
menon of mind, directly by the methods of the exact
58. sciences. This is the modern Science of Psycho-physics.

Transition i • p i

to psycho- Even the microscopist and biologist of the most modern

physics.

type are occasionally startled by phenomena akin to
those which commonly are only visible in the highest
organisms. Psychical existence, an inner side to the
external phenomena of motion, has accordingly been
attributed by eminent representatives of the mechanical
view of biological phenomena to the lowest, the most
primitive, unit of living matter. Another school of
science has set itself to study this inner side of liv-
ing organisms in its more perfect, as it were full-
grown, manifestations, and by appealing in addition to
the facts only known by introspection or self-conscious-
ness. With the history of this movement, so far as it
belongs to exact science, I propose to deal in the next
chapter under the general title of the Psycho-physical
View of Nature.

465

CHAPTER XI.

ON THE PSYCHO-PHYSICAL VIEW OF NATURE.

In the three foregoing chapters I have attempted to trace Abstr^t
the development of the different aspects under which our sciences,
knowledge of the real things which surround us, and of
nature as a whole, has been extended in recent times. I
have brought these different aspects which respectively
consider things natural according to their forms, their
genesis, or their life and purpose, under the general name
of the biological as distinguished from the abstract view,
with which I dealt in the four previous chapters. The
abstract view tries to arrive at the general properties of
all things, which it has succeeded in our times in sum-
ming up under the great generalisations of Attraction,
Atomism, Kinetics, and the doctrine of Energy. The
biological view is interested not so much in general
properties as in real specimens — the things, beings, and
phenomena in which we see the general properties ex-
emplified and become real and in their actual union or
totality which we call nature. The abstract sciences
started on their modern career with mathematics, and
progressed through the dcvelopmont and application ^f
VOL. TI. 2 G

Their

466 SCIENTIFIC THOUGHT.

the mathematical methods to the data furnished by
observation and experiment ; the biological or concrete
sciences began with a study of living things, and have
progressed immensely in our times by viewing these not
in isolation, but in their relations to each other and to
the surrounding lifeless world — the so-called environ-
ment. An exact treatment, that to which the term
" scientific " has been pre-eminently applied, seems here
also to depend largely, if not exclusively, on the degree
to which the mathematical processes of numbering and
measuring can be applied, and on the utilisation of the
general results arrived at in the abstract sciences.
2. The method of the abstract sciences is that of building

different up from Small beginnings, by the process of summation

methods.

or integration, intricate complexes which not infrequently
are found to correspond to phenomena of actual experi-
ence. It has at its command the unlimited resolving
powers of the calculus, and the well-established assump-
tion that things natural are made up of numberless
particles entering into innumerable combinations. The
wdiole is thus for the mathematical view the sum of its
parts. The concrete or natural sciences, on the other
hand, start with the ready-made things or creatures of
nature, or on a larger scale with the great order and
economy of our world or the universe, and only descend
into the minutiiK of the observatory, the dissecting-room,
or the laboratory, with the hope of better understanding
the great and complicated objects of their study. The
greatest progress in the abstract sciences has been made
by those minds that could concentrate their atten-
tion on special points, not infrequently expressed in

ON THE PSVCHU-PHYSICAI. VIEW OF NATURE. 467

iiuithematical formulae, and expand their view through
applications : the greatest progress in the natural sciences
has been made by those who started with a large and
comprehensive view of things natural, and gradually
descended into detail. Newton, Lagrange, Fresnel, and
Helmholtz are good examples of the former ; Humljoldt,
von Baer, Claude Bernard, and Darwin of the latter.

Now, it is a frequent experience that in the study
of things natural, through the unavoidable process of
dissection and analysis, the subsequent synthesis or sum-
ming up has not carried the student back to the real
thing from which he started, but to some artificial pro-
duct differing essentially from the natural object. The
real essence of the thing seemed lost when its parts were
examined by themselves or in their apparent aggrega-
tion. A prominent example of this kind is to be found
in the living organism. Theories have accordingly been
formulated which looked upon life as a special prin-
ciple to be superadded to any conceivable aggregation of
mechanical processes, in order to raise them from the
lifeless into the living order of things. The last chapter
dealt with the various biological hypotheses, of which
three are conspicuous : the purely mechanical, according
to which the living organism is merely a very compli-
cated chemical molecule ; the vitalistic, which establishes
an essential difference between the action and constitu-
tion of a living and a lifeless unit of matter ; and an
intermediate view, which looks upon organisms as manu-
factured machines built up according to some plan, de-
sign, or idea, the nature of which can be further inquired
into, but which does not try to throw any additional

468 SCIENTIFIC THOUGHT.

light on the mechanism itself, the working of which,
like that of a clock, can be described on purely mechani-
cal lines and without reference to the idea which preceded
its construction.

According to many prominent naturalists, the evident
design and purpose which characterise so many pheno-
mena of living matter are explained on purely mechan-
ical lines by the inherent or forced teleology of living
things, which through over-production have to submit to
an automatic process of selection or survival. To others
this automatic process does not seem to suffice, and
they assume a principle of progress which acts in a
regulative manner. This vitalistic view is further sup-
ported by taking into account an extensive class of
phenomena which I have, so far, hardly noticed —
the marvellous properties of the higher creations of
the animal world which exhibit the phenomena of
3. consciousness or of an inner experience. That these

Inner ^

experience, phenomena belong to the realm of natural science as
much as any other properties of living things cannot
nowadays be doubted. The division into natural and
mental science can no longer be upheld, or only with
a very different meaning from that which it had for a
bygone age.

It will be my object in this chapter to give an account
of the various and changing aspects which this great
phenomenon of an inner or conscious life has presented
to naturalists — i.e., to those who have approached the
phenomena of Mind from the side of nature, and of the
different lines of research and reasoning along which
they have dealt with it. I shall comprise the whole of

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 4G9

this section of scientific thought under the general term
of Psycho - physics.^ It refers to the borderland or -i.
common ground where physical and mental or psychical phys'C'*-
phenomena meet or interact.

Although the term psycho-physics is quite modern, the
idea of a special science dealing with the relations of
mind and body, or of the physical and mental life of the
human organism, has been promiiR'utly before the scien-
tific world ever since Cabanis published his celebrated
' Eapports du Physique et du JNIoral de I'Homme,' in
which the well-known passage occurs which has been
frequently repeated, modified, and quoted with varying
approval or reproach : ^ "In order to arrive at a correct

^ The term was first u.sed V)y
G. T. Fechner in the well-known
work bearing this title, of which I
shall have more to say in the course
of the ciiapter. This work, deal-
ing mainly with a certain numerical
relation, narrowed the term down
to a special investigation, whereas
the larger problem, the study of
the interaction of mind and body
by the methods of the exact
sciences, was variously designated
as physiological psychology, mental
physiology, psycho - physiology or
physiology of the soul. As there
is a tendency to regard physiology
more and more as the physics of
the living organism, it is evident
that physics is the larger term ; and
in dealing with the relations of the
j)hysical and the psychical in the
widest sense, the term psycho-
physics seems the more appropriate.

- ' (JEuvres completes ' de Cabanis
(1834), vol. iii. p. 159. The simile
ha-s attained a sort of historical
celebrity through tlie drastic ver-
sion which was given to it by Karl
Vogt in his ' Physiologische Briefe '
(1847), p. 206, where, with a

distinct intention of rousing an
tosthetic disapproval, he compares
the function of the brain with the
secretion of bile by the liver and
of urine by the kidnej's. ThLs
dictum, which he repeated in his
controversy with lludolf Wagner,
led in the middle of the century,
as Du Bois-lleymond tells us, to a
kind of systematic championshii) of
the soul, the comparison with the
kidneys Ijeing looked on as a
degrading offence. " Physiology,
however, has no knowledge of such
grades of dignity. As a scientific
problem the secretion of the
kidneys is to her of the same
dignity as the investigation of the
eye or the heart or any other so-
called noble (jrgan." Vogt used
the simile as an illustration of his
purely materialistic view. Lange
(' Hist, of Materialism,' vol. ii.
p. 242) shows that with Cabanis
the dictum is by no means bound
up with such a view, as he really
was a pantheist. The mistake,
says Du Bois-Reymond, does not
lie in the compari.son, but in the
implied suggestion, that psychical

470

SCIENTIFIC THOUGHT.

Cabanis's
simile.

idea of those operations from which thought arises, we
must consider the brain as a particular organ, destined
specially to produce it in the same way as the stomach
and the intestines are there to perform digestion, the
liver to filter the bile, the parotid, maxillary, and sub-
lingual glands to prepare the salivary juice."

The argument which led Cabanis to draw this parallel
between the functions of the brain and those of other
organs of the human body was based upon the philo-
sophy of Locke, which had been domiciled in France by
Condillac and Helvetius. This philosophy, in its popular
version, taught that all our thoughts and ideas were
ultimately made up of sensations.-^ On the other side.

activity could be " explained
through the structure of the brain,
as secretion can be explained from
the structure of a gland " ( ' Reden,'
vol. i. p. 129).

^ Cabanis (1757-1808), in the pre-
face to the 'Rapports,' &c., p. 11,
gives a list of contemporary French
writers who, following in the line
of Locke, to whom " philosophy is
indebted for the greatest and the
most useful impulse," have taken
up different sides of the doctrine.
Of their writings a very clear and
exhaustive analysis will be found
in M. Picavet's ' Les Ideologues,
Essai sur I'histoire des iddes et
des theories scieutifiques, philoso-
phiques, religieuses, kc, en France
depuis 1789' (Paris, 1891). Ca-
banis's own position is very clearly
defined (p. 16) when he says that
" Les operations de I'intelligence et
de la volonte se trouveraient cou-
fondues h, leur origine avec les
autres mouvements vitaux : le prin-
cipe des sciences morales, et par
consequence ces sciences elles-
memes rentreraient dans le domaine
de la physique ; elles ne seraient

plus qu'une branche de I'histoire
naturelle de I'homme : I'art d'y
verifier les observations, d'y tenter
les experiences, et d'en tirer tous les
resultats certains qu'elles peuvent
fournir, ne dillereraient en rien
des moyens qui sont journelle-
ment employes avec la plus entiere
et la plus juste confiance dans les
sciences pratiques dont la certitude
est le moins contestee." This was
written in 1802. M. Picavet says
of Cabanis with much truth :
" Le continuateur d'Hippocrate, de
Descartes et des philosophes du
XVIII™*' siecle, a ^t^ un precurseur
de Lewes et de Preyer, de Schopen-
hauer et de Hartmaiin, comme de
Lamarck, de Darwin et de bien
d'autres peuseurs qui appartien-
nent aux ecoles les plus diflerentes,
et ne soupwnnent quelquefois
meme pas que les idees dont ils
sont partis leurs sont venues in-
directement, mais par des inter-
mediaires authentiques, de I'auteur
des ' Rapports du physique et du
moral'" ('Les Ideologues,' p. 264).
M. Picavet also gives valuable ex-
planations how it came about that

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 471

the physiologists of the eighteenth century, notably
Hallcr, had demonstrated that tlie properties of the prej|,ej, ^
physical organism culminated in those of the nervous li^l'Jr.*"'*
system — irritability and sensibility. The phenomenon
of sensibility, of producing and combining — as it were
digesting — sensations, was thus the function of the brain,
or the central organ of the nervous system, as other pro-
cesses were the functions of other organs or physiological
apparatus. Cabanis was led on from medical ^ studies,
as Locke had been before him, to the study of mental
and moral subjects, and he formed the conception of a
science of Man, or Anthropology," divided into Physio-
logy, the Analysis of Ideas, and JNIorals, which would
ultimately be of as much use for the practical purposes
of education and government as the exact study of other
natural phenomena then cultivated in France for the
purposes of medicine, industry, and material civilisation.
Although it may be admitted that Cabanis created^
physiological psychology, and that he cast far-reaching
glances into the neighbouring departments of animal,

the line of philosophical thought
so clearly indicated by Cabanis
was uot more systematically de-
veloped in France at the time,
and, like many other lines of re-
.search which originated in that
country, had to be re-discovered
fifty years later in other countries.
The question is important, and
may occupy us later on. See,
however, regarding the disfavour
into which the " moral " sciences
fell owing to political reasons, vol.
i. p. 149 of this work.

' Cabanis blames in Condillac and
Helvetius that they knew noth-
ing of physiology. " S'ils eusseut

mieux connu I'economie animale,
le premier aurait-il pu soutenir le
systeme de regalitc des esprits ? le
.second n'aurait-il pas senti que
I'ame, telle qu'il I'euvisage, est une
faculty, mais non pas un otre; et
que, si c'est un etre, h ce titre elle
ne saurait avoir plusieurs des
qualitos (ju'il lui attribue " (ibid.,
p. 66).

- " C'est ce que les .\llemands
appellent I'anthropologie ; et sous
ce titre ils comprennent en efifet
les trois objets principaux dont
nous parlous" (Cabanis, ' CEuvres,'
vol. iii. p. 40).

■' Picavet, loc. cit., p. 292.

472 SCIENTIFIC THOUGHT.

embryological, and morbid psychology, from which he
expected much assistance, his ideas remained vague, as
did those of the contemporary school of the " Ideologues,"
among whom Destutt de Tracy ^ deserves honourable
mention as having conceived the plan of a psychological
treatment of grammar. Their merit lay more in drawing
the plans of the new science of psychology as a natural
science in its largest sense, and of urging its scientific
and exact treatment, than in making a real and fruitful
beginning on special lines.

It is a remarkable fact that the first attempt to
analyse in detail one of the special instances of psycho-
physical interaction came about a hundred years earlier
from that successor of Locke who has always been
counted as the extreme idealistic development of English
7. speculation. Bishop Berkeley's ' Essay towards a New

Berkeley's -^ r J J

I^Theoryof Thcory of A^isiou ' (1709) has been called "the verit-
able historical starting-point of psycho-physical investi-
gation." ^ Although averse to any exact theory of the
universe, deeming it " beneath the dignity of the mind
to affect exactness," ^ and at war with the mathema-

1 Picavet (p. 398) says of Destutt I ^ Dr Edmund Montgomery, iu
de Tracy (1754-1836): "Venu par his very interesting and valuable
les sciences a la philosopbie, D. critical analysis of ' Space and
de Tracy a donne h I'id^ologie un Touch,' three memoirs contained
nom et un caractere positif. S'il | in the tenth volume of the first
a CTU, ^ tort, qu'il pouvait la series of 'Mind' (1885), p. 385.
constituer de toutes pieces, il a •' See ' A Treatise concerning the

fort bien vu que, pour devenir Principles of Human Knowledge,'
une science independante et com- § 109 : " As in reading other
plete, elle devait s'appuyer sur la books, a wise man will choose to

fix his thoughts on the sense and
apply it to use, rather than lay
them out in grammatical remarks
on the language ; so in perusing
the volume of nature it seems
beneath the dignity of the mind
to afifect an exactness in reduc-

Vision.'

physiologie et la pathologie, sur
I'etude des enfants, sur celle des
fous et sur celle des animaux. II
I'a unie intimement h, la grammaire
et k la logique, a la morale et k
I'economie politique, a la legislation
et a la politique."

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 473

ticians/ as Hobbes had been before him, IJerkeley hud a
clear conception of the following definite prol)lem : By
what succession of physical and mental experiences, by
what " organic and vital data," do we become aware of
space and of body or matter ? His answer, which makes
tactile sensations the base, has been advocated and quoted
by English psychologists of the Association school up to
the present day, and forms the text for their various
explanations.

The genesis of space perception was much discussed
in the circle of Locke's friends, Molyneux proposing
the celebrated query "" named after him, and Cheselden
describing at length, in the Philosophical Transactions,
the experiences of an adult blind patient who had
received his sight l)y couching. The eighteenth century
brought other isolated researches of an experimental or
mathematical nature, which may be regarded as the
beginnings of an exact treatment of the relation of psy-

ing each particular phenomenon to
general rules, or showing how it
follows from them. We should
propose to ourselves nobler views,
such as to recreate and exalt
the mind," &c. In the following
paragraph Berkelej- refers to the
' Principia ' as " the best gj-ammar
of the kind " lie was speaking of.

' A very full account of this con-
troversy will be found in a paper
by Prof. Geo. A. Gibson in the
' Proceedings of the Edin. Math.
Soc.,' vol. .xvii.

- The query is given in Locke's
• Essay,' Book II. ch. ix. § 8, as
follows : " Suppose a man born
blind, and now adult, and taught
by his touch to distinguish be-
tween a cube and a spheie of the
.-^ame metiil and nighly of the same
bigness, so as ty tell when he felt

one and the other, which is the
cube and which the sphere. Sup-
pose, then, the cube and sphere
placed on a table, and the blind
man made to see : Query, whether
b}- his sight, before he touched
them, he could now distinguish,
and tell, which is the globe, whicii
is the cube ? To which the acute
and judicious proposer answers,
No." For a full analysis of actual
cases, such as that of Cheselden,
and more recent ones, see Wundt,
' Physiologisehe Psychologic,' vol.
ii. p. 233. That Berkeley was,
however, neither a psycho-physicist
nor a physioloerical psychologist in
the modern sense, is well remarked
by Campbell Frascr in his essay
on Berkeley (Blackwood's " Philos.
Classics," ' Berkeley,' p. 45, &c.)

474 SCIENTIFIC THOUGHT.

chical with physical phenomena. Fechner, the founder
of psycho-physics as an independent doctrine, refers
notably to two ^ such instances. They were contributed
8. by two great mathematicians, Daniel Bernoulli and
and Buier. Leouhard Euler. The former pointed out that the value
which we attach morally to the addition to any material
possession is not measured by the actual magnitude of
such addition, but by the relation it bears to that which
we already possess. The first sovereign earned by a
poor and starving labourer has an almost infinite value
compared with what it has for a person already possessed
of a million. Laplace and Poisson referred to this state-
ment of Bernoulli, and introduced the terms " fortune
physique," " fortune morale," showing that they stand
in a simple mathematical relation. The same relation
was shown by Euler to exist between our estimate
of musical intervals in the harmonic scale and the
difference of the number of vibrations of the strings
which produce the two notes. It was above a cen-
tury before Fechner correlated these isolated remarks
with observations of modern psycho - physics in his
celebrated law, of which more anon.

On the whole, little progress was made during the
eighteenth century in the department of research I am
now dealing with ; but the end of the eighteenth and
the beginning of the following century brought several
important discoveries, some of which were at the time
much over-estimated, whilst others were for a long time
forgotten or overlooked.

The first is the accidental discovery by Galvani in-

1 'Psychophysik,' 1860, vol. ii. p. 548, &c.

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 475

1786, followed, fifteen years after, by Vulta's greater 9.
invention. The late eminent I'rof. Du Bois-Keymond, "Electricity,
in various passages ^ of liis scientific and literary writ-

ings, has told us of the recurrent fascination which the
fata morgana of Electricity has exercised over those
interested in the explanation of the phenomena of
innervation ; how this seductive clue has been, in the

' See vol. ii. i)p. 212, 386, 528 of
Du Boi-s-Rej-moud's 'Redeu,' also
his ' Untersuchungen iiber thier-
ische Electricitiit ' (1848), vol. i.
pp. 30-128. One of the first to
take up in the interests of nervous
physiology the clue which Galvani's
discovery afforded \va.s A. vou
Humboldt, who i)ublished in 1797.
three yeai-s before Volta's discover}',
his valuable " Versuche iiber die
gereizte Muskel- uud Nervenfaser,
nebst Vermuthungen iiber den
chemischen Process des Lebens
in der Thier- und Pflanzenwelt."
A lucid account of Humboldt's
work is given by Prof. Wundt in
the third volume of the German
edition of Bruhns' ' Life of Hum-
boldt," p. 301 sqq. "It is diffi-
cult," he says, '"'to picture to
oneself nowadays the excitement
which the observations of Galvani
produced in the scientific world.
. . . Such experiments had almost
become a general subject of enter-
tainment in cultured circles. . . .
It almost ajjpeared as if what
at that time was looked upon as
the most general projjerty of living
matter, irritability, were by the
experiment of Galvani to be for
the fir.st time unveiled in its real
essence. ... At the time when
Humboldt m.ide his experiments
the contest was still going on
between the followers of Galvani
and Volta." This referred to a
physiological or purely physical
explanation of the phenomenon.

" Barely three years after the
publication of Humboldt's work
the discovery of Volta's pile put
an abrupt end to all theories
which were based upon the phys-
iological origin of galvanic phen-
omena. The brilliant development
of physical galvanism from tliat
moment pushed the j)hysiological
aspect of electricity for a long
time into the background. , . .
Humboldt's work was forgotten "
(p. 310). In the meantime Hum-
boldt had travelled in South Amer-
ica, where he had — inter alia —
observed the " natural electro-
motors which stand in such ex-
traordinary connection with the
nervous .system" of the electrical
eel {(Jymiwtus clcclricus), giving a
thrilling description of a battle
between the horses and the eels
which he witnessed in the waters
of Calabozo. (See Humboldt's
' Personal Nai-rative,' vol. iv. p. 345
sqq. ; also ' Ansichten der Natur,'
vol. i. p. 33.) Interest in the subject
of animal electricity was again re-
vived by Italian pliysiologists about
the year 1835. Nobili, Marianini,
Santi - Luiari, Matt6uoci repeated
and enlarged the expeiiments of
Galvani, and througli the influence
of Humboldt and Johannes Miiller,
the study of the whole subject
was com))rehensivelj' taken uji at
Berlin by Du Bois-Reymond about
1840, and exhaustivelj'' treated in
his great work on the subject (vol,
i. 1848, vol. ii. 1860).

476 SCIENTIFIC THOUGHT.

course of more than a centurj, alternately taken up
with enthusiasm, and abandoned as misleading. At the
turn of the centuries the mania for animal electricity
was at its height. Men like A. von Humboldt took up
the study with eagerness, and sovereigns like Napoleon
offered special prizes, in the hope that here at last the
secret of life and consciousness would be revealed. The
school of the " Naturphilosophie " in Germany seized
upon the suggestion of polarity and polar forces con-
tained in the phenomena of galvanic action, and, sup-
ported by the still more mystical processes of the
so-called animal magnetism which had been exhibited
by Mesmer twenty years earlier, worked up these
vague indications into fanciful theories of vitalism and
animism. This brought the whole line of thought
into discredit, drove away the soberer, more scientific
students of nature, and retarded real progress in the
knowledge of the electric phenomena of the muscular
and nervous system for fully a generation. At length
in the school of Johannes Mliller the subject was again
approached and was put on a firm scientific basis by
Helmholtz, and notably by Du Bois - Eeymond. It
is now known that, as in inorganic, so also in organic
systems, the energy proper to them can appear under
the different forms of mechanical, thermal, electric or
chemical energy, but also that in none of these can be
found pre-eminently the principle of life, still less that
of consciousness.
10. Another important line of research which has had

an equally fluctuating development, being sometimes
enormously exaggerated, to the damage of sound pro-

ON THE PSYCHO-PHYSICAL VIEW OF NATURE.

477

gress, sometimes repudiated and treated with whole-
sale contempt, was that started by (Jail, who from the
year 1805 onward, and latterly in conjunction with
Spurzheim,^ started on an anatomical description of the
brain as the centre of nervous and conscious mental

' Tlie two most prouiineut
teaoliers of phrenoloj^y were Franz
Joseph Call (1758-1828) of Pforz-
heim, and Joli. Christ. Spurzheiiu
(1776-1834) of Trier, the former
an excellent doctor, the latter a
.skilled anatomist. Their influence
was centred in Vienna and Paris.
In England and America phren-
ology dates its pojjularity from
George Combe (1788-1858). The
terra phrenology was suggested by
George Fonster about 1815, ten
years after Gall had started his
' Schiidellehre ' or ' Craniology.'
Of eminent medical authorities,
the great Broussais in France (1772-
1838) and C. G. Carus (1789-1869)
in Germany were both phren-
ologists, the latter attempting to
^ve the doctrine a more scientific
foundation. Though ijhrciiology
was never popular in l"'rance, where
the Academy of Sciences from the
beginning assumed a very sceptical
attitude (see above, vol. i. p. 136
note), the opponents of Gall have
always given him full credit for
his ability, and for the great im-
pulse he gave to anatomical science
of the brain. Flourens, one of the
most formidable critics of the doc-
trine of the special faculties, and
consequently of the separate phren-
ological organs and their location,
nevertlielcss says: "Gall fut un
observateur profond, qui nous a
ouvert, avec g^nie, I'dtude de
I'anatomie et de la {)hysiologie du
cerveau. . . . Je n'oublierai jamais
I'impression que j'eprouvai la
premiere fois que je vis Gall dissd-
(juer un cerveau ; il me semblait
que je n'avais pas encore vu cct or-

gane " (quot. by Langlois, 'Grande
Encyclop.,' vol. xxvi. j). 801). Some-
what earlier than phrenology the
science or art of phj-siognomics,
which was known already and
practised by the ancients, had a
representative in Caspar Lavater
of Ziirich, who, from 1772 onward,
published his ' Physiognoiaische
Fragiuente,' a work which, accom-
panied by engravings by Chodo-
wiecki, created a great sensation
in philosophical, literarj*, and artis-
tic circles, the whole of Europe
being divided into followers and
critics uf Lavater. Among the
latter was the celebrated Lich-
tenberg of Gottingen. Among
scientific men were Camper in
Holland, and later Charles Bell in
England ; the former putting for-
ward the well - known theory of
the "facial angle" as an external
measure of intelligence, the latter
publishing his ' Essay on the Ana-
tomy of Expression' (1806). In
more recent times no less an
authority than Charles Darwin
took up the subject in his work
on the ' Expression of Emotions '
(1872). Shortly before Ph. Piderit
published his ' Wissenschaftliches
System der Mimik und Physiog-
nomik ' (1867) ; Duchesne (lSb'2) his
' Mecanisme de la physionoinie hu-
maine ' ; and more recently the Ital-
ian Mantegazza his ' Physionomie
et I'expression dcs sentiments'
(French transl., 1885). A very
readable essay on the subject will
be found among Prof. Wundt's
'Essays' (1885). See also his
' Physiologische P.sychologie ' (vol.
ii. p. .598, &c., 4tli ed.)

478 SCIENTIFIC THOUGHT.

action. The scholastic notion of the older psychol-
ogists which divided the mental life into different powers
or faculties as the body was dissected into parts and
organs, lent itself to the idea of a localisation of these
faculties or powers in different spheres of the brain,
which Gall by a hasty generalisation maintained to be
distinguishable on the external surface of the skull.
Though these popular and practical applications, which
form the basis of phrenology, were speedily and easily
refuted, having always been regarded with suspicion by
the medical profession, the anatomical labours of Gall
were taken up and continued by others. Opinions
fluctuated between the different views of Flourens, who
insisted upon the unity of the central organ, as did
Herbart in psychology on the unity of the mind ; of
G. H. Lewes, who assigns to the spinal cord together
with the brain an important and initiatory role in
conscious life ; and of Hermann Munk and Friedrich
Goltz, who by carefully devised experiments on living
animals, by electrical irritation, and by systematic re-
moval of parts of the brain, have to some extent suc-
ceeded in delimiting the special " spheres in which the
various sensory nerves deliver their messages, and where
the latter are transformed into conceptions and mentally
stored." -^ Paul Broca had already, about forty years
ago, succeeded in localising the powers of speech.

^ Du Bois-Reymond, ' Reden,' vol.
ii. p. 558 : " Thougli there is, in prin-
ciple, no hoije that the causal
connection between material pro-
cesses in the brain and consciousness
will ever become clear to us, this
does not hinder our penetrating
deeply into a knowledge of those

processes, or prevent such know-
ledge being of the greatest import-
ance and of fascinating interest. As
a first step in this direction there
presents itself naturally to our
understanding the localisation of
the different faculties into which
we naturally and systematically

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 479

Whilst animal electricity and the examination of the
brain were taken np with ardour, over-valued by popular-
isers, and developed into fanciful theories which postponed
for a long time the sober inquiries of science, another very
fruitful vein of reasoning and research was struck early
in the century, but left unexplored for fifty years. Since
then it has been followed with success and profit.

divide nientiil activity. Out of
the desire for such localisation
there sprang up the fundamental
idea of the phrenological follies ;
but, as so often, here also scien-
titic superstition contained a kernel
of truth. In the same cortex
of the brain in which Gall and
Spurzheim located their badly-
chosen thirty-five mental faculties,
Munk now describes the spheres in
■wliich the various sensory nerves
deliver their messages, and where
the latter are transformed into con-
ceptions and stored. Thus, for the
first time in the domain of sensa-
tion and intellection, a local basis
of mental activity has been demon-
strated, as had been done before
by Paul Broca in the domain of
volition, in the localisation of the
faculty of speech." Most modern
jisycho-physicists would probably
accept this statement with slight
modifications ; it is therefoie well
to note that one of the foremost
and most original workers in this
field of research, Prof. Fr. Goltz,
takes a different view of the result
of the experiments of himself and
others. He does not consider
Munk's teachings as the foundation
of a physiology of the brain, but
looks upon them as a system of
error, and " hopes to see the day
when all the beautifully elaborated
modern hypotheses of circumscribed
centres of the cortex will be laid in
the same grave in which Gall's
phrenology rests" (quoted from

Goltz's memoirs, ' Uber die Verrich-
tungen des Grosshirns,' in Pfliiger's
Archiv, bj' Carl Hauptmann, ' Die
Metaphysik in der modernen Bio-
logie' (1804), p. 2-10). Prof. Fer-
rier, whose ' Functions of the
Brain' (2nd ed.) is a standaid
work in the English language, takes
up a less negative position ; yet he
says (p. 23) : " We are still on the
threshold of the inquiry, and it
may be questioned whether the
time has even yet arrived for an
attempt to explain the mechanism
of the brain and its functions. To
thoughtful minds the time may
seem as far off as ever." Prof.
William James of Harvard, in his
excellent 'Principles of Psychology'
(2 vols., 1891), gives, in his first
chapter, a succinct account of the
" localisation-question," which, he
thinks, " stands firm in its main out-
line " (vol. i. p. 162). The standard
work in tlie German language is
Prof. Wundt's ' Physiologische
P.sychologie ' (2 vols., 4th ed.,
1893), which gives in the first divi-
sion (chaps. 4, 5) a very exhaustive
account of the experimental and
theoretical work on localisation.
Prof. Wundt himself takes up a
position lying between the doctrine
of sharp delimitation and that of a
denial of local distinctions (vol. i. p.
159), but admits that the whole
question is still highly contro-
versial, though latterly the appar-
ent diH'erences of opinion have been
nuicii toned down (vol. i. p. 240).

480

SCIENTIFIC THOUGHT.

11.

Dr Young's

colour

theory.

The beginnings of this line of reasoning are to be
found in the writings of Thomas Young, who here, as
in several other directions, " marched far in advance of
his age." ^ During the last decade of the eighteenth
century Young had been occupied with the study of
the phenomena of Light and Colours ; and, being a
student of medicine, he had given equal attention to
the physical phenomena and the physiological sensations
of Light, going back to the beginnings laid in Newton's
writings on these two important branches of Optics."^
I have treated of his epoch-making discoveries in
physical optics in an earlier chapter. As to the physi-
ological problem of colour sensations, he likewise reviewed
Newton's work, and especially took up the remarkable
fact noted by Newton, that it appears possible to refer
the great variety of colour sensations to three primary
elements, out of which the whole wealth of the colour
scale — varying in intensity, tint, and saturation — can
be made up. In two distinct points he made a definite

^ Note, in many passages of
Helmholtz's ' Physiologisohe Optik '
(2ud ed., Braunschweig, 1896), and
his often -quoted ' Vortriige und
Reden,' the high esteem in which
he held the work of Young.

^ A very succinct and exhaust-
ive account of how Young arrived
at his colour theorj' is given in
a paper by A. M. 5layer, of New
Jersej', in the ' Phil. Magazine ' for
1876 (5th series, vol. i. p. 111).
Young first selected red, yellow, and
blue as the three simple colour-
sensations, but later modified his
view in consequence of the experi-
ments of Wollaston between the
years 1802 and 1807. How little
Young's theory was thought of maj^
be seen from the words of Helni-

holtz, quoted by Mayer (p. 114) :
" The theory of colour, with all
these marvellous and complicated
relations, was a riddle which
Goethe in vain attempted to solve ;
nor were we physicists and physiol-
ogists more successful. I include
myself in the number ; for I long
toiled at the task without getting
any nearer mj' object, until at last
I found that a wonderfully simple
solution had been discovered at the
beginning of this century, and had
been in print ever since for any one
to read who chose. This solution
was found out and published by
the same Thomas Young who first
showed the riglit method of arriving
at the interpretation of Egj'ptian
hieroglyphics."

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 481

advance upon Xewton. For the three primary colours
of the older opticians he substituted red, <^reen, and
violet ; and for the remarkable fact that the simple
colours of the rainbow can be compounded out of these
three, he suggested a physiological reason — viz., that the
eye possesses three distinct colour -sensations or three
distinct senses in relation to light, dependent upon some
peculiarity of nervous structure or function. Young
did not elaborate his ideas, Ijut it is clear lliat in llic
short passages in his ' Lectures on Natural riiilusuphy'
and earlier papers, there were contained a ^•ariety of
definite problems and hints which were destined to
lead research for a long time after.

The next great stei) in advance, which has revolu- 12.

° ^ Charles Bell.

tionised and permanently fixed our ideas on the action
of the nervous system, was taken about the year 1810
by Charles 15ell, who discovered the anatomical difference
between the anterior and posterior roots of the nerves
of the spine, and also went a long way towards show-
ing their different functions. The point as regards
functions was established by means of experiments on
living animals by Magendie, and independently Ijy
Johannes Miiller.^ Upon the comljined labours of these
three masters of anatomy and experimental physiology
is based the distinction between sensory and motor
nerves — namely, that the anterior nerves of the s[)ine
are employed to carry the nervous stimulus outward
to the different organs (efferent or motor nerves), the
posterior and better protected nerves serving to carry

' Ou the respective merits of Claude Bernard aud Du Bois-Rey-
Charles Bell, Magendie, and Jo- nioiul, referred to supra, p. 384 of
hannes Miiller, see tlie writings of this volume.

VOL. II. 2 U

482

SCIENTIFIC THOUGHT.

13.

Jliiller's
" specific
energies."

the peripheral stimuli of the senses inward to the
nervous centres (sensory or afferent nerves).

About the same time Johannes Miiller, under the
influence of Goethe's observations on the subjective
colour -sensations and of Kant's doctrine of the innate
forms of perception/ introduced another important dis-
tinction into the theory of the action of the sensory
nervous apparatus. This doctrine is known by the
name of the " specific energies." It has for a long time
governed all physiological reasoning on the subject of
our sense perceptions. In the words of Helmholtz, who
more than any other has lent the great weight of his
authority to an elucidation of this theory, " physiological
experience has found that by the stimulus of any single
sensible nerve -fibre, only such sensations can be pro-

^ The doctrine of the " specific
energies " of the sensory nerves, one
of Joh. Miiller's earliest speculations,
which has governed a large section
of psycho - phj'sical research, at
least in Germany, has gi-own out of
the philosophical discussions in the
' Kritik der reinen Vernunft,' and
the assthetic treatment in Goethe's
' Farbenlehre,' both of which deal
with the subjective element in our
sense-perceptions. In this regard
the reform of physiology in Germany
contrasts with the contemporaneous
reform by Mageudie in France,
whose extreme experimentalism
Miiller even ridiculed. See on the
historical origin of Midler's psycho-
physics, Du Bois-Reymond's excel-
lent "Elogeof MuUer" ('Reden,' vol.
ii. p. 159), also Helmholtz's lecture on
" Goethe's Naturwissenschaftliche
Arbeiten" ('Vortrlige und Reden,'
vol. i. No. 1, 1853), and his address
i)efoi-e the Goethe Society in 1892.
Helmholtz finds the cause which

misled Goethe in his optical exi^eri-
ments to be the same which misled
Brewster — viz., the difficulty of ob-
taining really pure homogeneous
light of any special tint. He woi-ked
with impure light and dull media.
Helmholtz experienced great diffi-
culties in obtaining the neces-
sary purity in his own labours.
Goethe, however, was not alone in
studying with predilection the sub-
jective colour-sensations. Du Bois-
Reymoud mentions Erasmus and
Robert W. Darwin in England, and
Purkinje in Germany, as working
in the same field (loc. cit., p. 160).
Miiller's work is contained princip-
ally in the treatise, ' Zur vergleich-
enden Physiologie des Gesicht-
sinnes des Menschen und der Thiere
nebst einem Yersuche liber die
Bewegungen der Augeu und iiber
den menschlicheu Blick' (1826), and
in his larger work on Physiology.
See also on Goethe's merits Helm-
holtz, ' Physiologische Optik,' p. 249.

ON THE PSYCIIU-I'IIY.SICAL VIKW OF NATURE. 483

(lucecl as belong to the (qualitative — or order — region of
one definite sense, and that every stimulus which can at
all atlect this nerve fibre produces only sensations be-
longing to this tletinite order." ^ This means that, for
instance, any effective stimulus of the optic nerve
apparatus produces only and always the sensation of
light, whereas the same stimulus would in the auditory
nerve apparatus, if effective, produce the sensation of
sound. " The same vibrations of the ether wdiich the
eye perceives as light, the nerves of the skin perceive as
heat. The same vil^rations of air which the latter per-
ceive as a tremor, the ear perceives as a musical sound." "
The (j^uality of our sensations does not depend on the
stimulus but on the ner\ous apparatus.

Helmholtz has said ^ that the law of the specific
energies forms the most important advance which the
physiology of tlie senses has made in recent times, and
has even compared it with the discovery of the law of
gravitation.'* As we shall see immediately, he has him-

^ See Helmholtz, ' Handbucli der uiucli limited to Germany, and there

Physiologischen Optik,' 2te Aufl. , , also almost entirely to what may

1896, p. '2:313. ' be called ]\Iiiller's school, in which

- Helmholtz, ' Vortriige und Re- Helmholtz is the central figure. In

den,' vol. ii. p. 224 ; al^;o ' Physiolo- England tiie doctiine was subjected

gische Optik,' p. 249 : " Miiller's law to a full ciiticism l>y George Henry

of the specific energies marks an I Lewes, an important thinker, whose

advance of the greatest importance, writings contain many original views,

for the entire doctrine of tlie sense- which have in some instances since

perceptions has since become the been inde])endently put forward by

scientific foundation of this doctrine, other authorities. See his ' Physi-

and is, in a certain sense, the em- ology of Common Life " (ISGO.chap.

jjirical e.xposition of the theoretical i 8) ; ' Problems of Life and Mind '

discussion of Kant on the nature I (vol. i. p. 135, 1874) ; ' Revue Philo-

of the intellectual process of the sophique' (Paris, 1870, No. 2);

human mind." Of. also p. 584. ' The Physical Basis of Mind' (1877,

•' ' Vortriige und Reden,' vol. i. p. j). 184). Without knowing of Lewes's

;j78 ; vol. ii. p. 181. ^ criticisms, Prof. Wundt was led to

^ This excessive appreciation of j a criticism of the doctrine from

^Midler's theory is, however, very | the physiological side in the first

484

SCIENTIFIC THOUGHT.

self made a very important application of it, by bringing
it into connection with Young's colour theory. But
before I refer to this, it will be well to note the different
lines of research which were opened out by Mliller's
formula, and how tliey have led in many ways to very
fruitful expansion of natural knowledge. In this respect
it is indeed permissible to compare Mliller's formula with
that of gravitation, which, as we saw above, through
the different ideas which it introduced, helped to guide
research for fully a century. Miiller in the original
statement of his views had made use of the term " specific
energy," and had applied this term to the process or
sense of sight : he spoke of the seeing substance or
apparatus of sight. Now this apparatus is a complicated
one, consisting mainly of three parts — the external or

edition of his great work on Physi-
ological Psychology in 1872. See
the note on p. 332, vol. i., of the
4th German edition (1893). Wundt
says (p. 331): "Historically, the
doctrine ... is to be traced to the
fact that the philosophical founda-
tion of modern science, and especi-
ally of the science of sensation, rests
on Kant. In fact, that doctrine
is nothing else than a physiological
reflexion of Kants attempt to find
the conditions of knowledge which
are given a priori, or, what was
mostly considered to be the same,
subjectively. This is very evident
in the case of the foremost repre-
sentative of that doctrine — viz.,
Johannes Miiller." In opposition to
Miiller and his school, Lewes and
Wundt put forward a view which
has been termed the doctrine of
indifference of the function of the
nervous elements. The difference
between the two views is very clearly
stated in an excellent paper bj' E.

Montgomerj' in the fifth volume of
'Mind' (1880): " According to the
doctrine of functional indifference,
the various equalities — i.e., our well-
known sensations — are merely due
to differences in the stimulating
rhythm, to differences, therefore, of
motion communicated from outside
to the chemically uniform nerve -
substance, and the whole complex
make-up of our consciousness is,
consequentlj', thought to result
from the coexistence and subse-
quent combination of such stim-
ulated motions. According to the
doctrine of specific energies, the
varieties of sensation are due to pre-
existing differences in the sub-
stratum in which they respectively
arise, and all their manifold combin-
ations to higher products are be-
lieved to be realised in materially
higher — i.e., specifically pre - en-
dowed — ranges of nervous sub-
stratum " (p. 4).

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 485

terminal organ, the connecting tibrc or nerve, and the
central or percipient organ situated somewhere in the
brain. How are these different parts of the combined
apparatus anatomically constituted, and what are their
respective physiological functions — in particular, where
does the specific energy reside ? The answer to these
c^uestions as regards not only the process of seeing, but
likewise that going on in other sense organs, involved
an enormous amount of detailed anatomical and physio-
logical, analysing and experimenting work. With this
work many great names are connected — first of all,
Helmholtz, who in liis two great treatises on 'Physio- 14.

' ^ " _ Helmholtz.

logical Optics ' and ' Thysiological Acoustics,' ^ has laid
the foundation of those two psycho -physical sciences
which bring us nearest to an understanding of the inter-
action of mind and body. Like Young before him, for
whom he expresses the greatest admiration, Helmholtz
had approached the study of nature from the side of
medicine : from this he was, l)y the peculiarity of his
genius, driven to mathematicu- physical studies on the
one side, to psychological on the other. The exact
methods of the mathematical, the experimental methods
of the medical sciences ; the mental analysis of Kant
and Fichte, as well as the logical methods of J. S.
Mill, were equally familiar to him. Inventions of his
own, like that of the eye -mirror, or of others, like

^ ' iJic Lchre voii den Toneniii- iiriucij>al contents of tliose two

tindungen ; Physiologische Urund- great treatises, by an authority in

lage fur die Theorie der Alusik,' the same domain of science, will be

1st ed., 1863. ' Handbuch der ' found in chaps, x. to xii. of Prof,

yjhysiologischen Optiii,' 18(57, 2nd j J. G. M'Kemhick's volume in the

ed., much enlarged. A succinct " Mastei-s of Medicine" Series on

and very lucid exposition of tiic H. von Helmlioltz, 1899.

486 SCIENTIFIC THOUGHT.

the stereoscope of Wlieatstone ; pathological cases, like
those of colour-blindness ; a host of ingeniously de-
vised experiments, as well as the gift of an exception-
ally musical ear, — all these factors, and innumerable
others, contributed to the production of these two
monumental works, which form an epoch in the history
of science as well as of philosophy and psychology.
They form the first magnificent examples of the com-
prehensive application of exact methods to phenomena
which had before been treated only fragmentarily, and
where the infiuences of taste, fancy, and belief, the
vagueness of metaphysics and the diificulties of nomen-
clature, had created a confusion which to many must
have appeared hopeless. This confusion of language
and of terms, of objective observations and subjective
fancies, of the data of experience and the prejudices of
theory, Helmholtz has done more than any other thinker
to unravel.

In his two great treatises on the psycho-physics of the
Eye and the Ear, of Vision and of Music, he has drawn
two elaborate and detailed charts, which for a long time
to come will have to be consulted by those who, in the
interests of physics, philosophy, or cesthetics, enter into
these mysterious domains. Many celebrated theories or
definite aspects and lines of reasoning invented by others,
his forerunners or contemporaries, were adopted, but
mostly with important modifications. It may be of use
to enumerate briefly the principal ones, beginning with
the most mathematical and exact and ending with the
more general and metaphysical. In the beginning of the
century Fourier had shown how any forces of motion in

ON THE PSYCHO-PHYSICAL YIE^Y OF NATURE. 487

two dimensions — however coniplieuted or irregular that
motion might appear to be — could be mathematically
represented or calculated by the superposition or addition
of a larger or smaller number of simple periodic motions ;
as it were analysed and dissected into these simple move-
ments, just as any number can be looked upon as made
up by the addition of others — say of prime numbers.
Now, it was also known that sounds were produced by
wave-like tremors of the air set going by the vibrations
of strings or other sounding musical instruments ; further,
that definite musical notes were absorbed or transmitted
by neighbouring sounding bodies according as these were
in or out of tune with the vibrating source of sound.
This is the well-known phenomenon of resonance. Ohm^
had applied Fourier's mathematical analysis to the ex-
planation of the partial notes, the ground tone and the
harmonic overtones (or upper partial tones), of which
musical " sounds are made up. Helmholtz invented a

^ Ceo. S. Ohm, the same to See the introduction to his treatise

wh(jni we are indebted for the on the galvanic current ('Ges.

well-known law which obtains in I Werke,' p. 6'i).

electric currents, published in 1843 - Cagniard de la Tour had in-
a paper in Poggendorfs ' Annalen ' } vented (1819) and Seebeck the
(reprinted in ' Gesammelte Ab- younger had improved (1841) the
liandlungen,' 1892, p. 575), "On first mechanical counter for the
the definition of a tone and the frequencies of musical sounds, the
theory of the sii-en," in which he i siren ; and the latter as well as
applied the mathematical methods Duhamel had studied the corn-
introduced by Fourier in his ' The- position of such sounds out of their
orie analytique de la Chaleur' elements or simple notes. A sug-
(1822) : as he had already done in gestion had been thrown out as to
liis earlier work on the galvanic , the part played by the up])er

current (1827). In fact, Ohm was
one of the first to recognise the

partial tones which accom])anied
the ground tone. Hehnholtz treats

value of Fourier's conceptions in ' first of this subject in a lecture

contradistinction from Laplace's, ' (1857), reprinted in 'Vortriige und

which were bound up with certain Reden,' vol. i. p. 79, dealing with

hypothetical notions as to the "the psychological causes of musi-

niolecular constitution of bodies. I cal harmony."

488

SCIENTIFIC THOUGHT.

15.
"Timbre"
defined.

series of simple but ingenious apparatus by which these
partial notes could be analysed, isolated, and made speci-
ally audible, or by which the ground tone could be
purified, and thus led up to his conception of the human
ear — the different parts of which he analysed anatomic-
ally and acoustically — as a most delicate resonator which
separately absorbed the different elementary periodic
movements that constitute musical sounds, the different
nerve-fibres carrying them separately to the central
organ of perception.^ On the bases of these distinc-
tions, Helmholtz succeeded in giving an accurate defini-
tion " of that property of musical notes termed " timbre "
by the French, " Klangfarbe " by the Germans — that
peculiar colouring or texture which characterises the
same note^ if produced by different instruments. He

^ See ' Die Lehre von den
Tonempfindungen,' 1st ed., 1863,
pp. 92, 95, 97. "The main result
of our description of the ear can
be thus stated, that we have found
that everywhere tlie ends of the
auditory nerve are connected with
special auxiliarj' apparatus, jjartly
elastic, partly solid, which under
the influence of external vibrations
are made to vibrate correspond-
ingly and then probably affect
and agitate the nerve-substance "
(p. 212).

■■^ Helmholtz was the first to give
a positive definition of "timbre."
As he himself says (p. 114), before
him it meant all the peculiarities
of a musical sound which are not
defined by its intensity or its posi-
tion in the scale— -i.e., its " pitch."
Of these he eliminates all such as
are connected with the beginning,
rising, and dying away of sounds,
and deals only with sounds which
are uniformly maintained (p. 116).

^ The terminology of acoustics

and of music has been considerably
changed, especially in this country,
through scientific literature, in
which the work of Helmholtz
forms a kind of epoch. Accord-
ing to Lord Rayleigh ('Sound,'
vol. i. § 22, 1st ed.), the word
" tone " in the English language
has been adopted by Tyudall to
denote a musical sound which
cannot be further resolved. The
word was used before, but in a
general sense, not limited only to
sounds, and where now " tone " is
used in works on acoustics, the
word "note" was more usually
employed. Sir John Herschel
( ' Encyclop. Metrop.,' article
" Sound," 1845) does not con-
sistently use the word " tone "
as an equivalent for the German
"Ton," but makes use of "sound"
or " note " or " tone " promiscu-
ously. Still more uncertain was
the terminology by which to ex-
press the quality of a musical
sound other than loudness and

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 489

entered into an analysis of the processes l»y which vocal
sounds and notes are produced, and showed their im-
portance in musical and linguistic theories. Combined
with all these deductions and applications, which started
from Fourier's mathematical analysis of compound move-
ments, Helmholtz's anatomical dissection of the organ of
hearing leads him to the conclusiDU that there " must
exist in the ear different parts which are set in \il)rati(in
by notes of different pitch, and which have thus a sensa-
tion of these notes." ^ And here he takes up a different
line of reasoning — that suggested by Johannes ]\Iiiller's
theory of the specific sense energies. In his studies
in physiological optics he had already accepted Young's
hypothesis that there exist in the eye three distinct
kinds of nerve - fibres, to which belong distinct modes
of colour -sensation. Something analogous exists in the
ear." " The differences in notes — namely, pitch and le.

Analogy

colour [or character] — are reduced to differences of the between

-" sound and

sensitive nerve-fibres, and for each nerve-fibre there exists *^°^°^''-
only the difference of the intensity of the stimulus."

This brings the action of the sensory nerves into line
with that of motor nerves : everywhere the nerve itself is

pitch, and, to the present clay. Book of Physics,' Sound, p. 69) we
the Euglisli tongue has no equiv- read, " It is convenient to use the
alent for the French " timbre " or term note for an ordinary coni-

the German '' Klangt'arlje." Everett

used tiie word c:haracter, and so

does Lord liayleigh. Dr Young,

in his "Essay on' Music" (1800,

' Miscell. Works,' vol. i. No. 5),

speaks of the tjuality of sound,

sometimes called its tone, register,

colour, or timbre (p. 118). In the

most recent scientific work on

sound in the English language " Ibid., pp. 220, 2"21

(Piiynting and Thomson's 'Text- '

pound sound to which a definite
pitch may be assigned, and the
term tone for each sim})le harmonic
constituent which goes to form it."
There is an important note on the
terminology by Alex. T. l->llis. the
learned translator of Hehiiholt/.'s
'Sensations of Tone ' (187r>. p. 36).
' ' Tonempfinduugen," p. 215.

490

SCIENTIFIC THOUGHT.

indifferent to the stimulus, which it carries in or out like
a telegraph wire ; which, whilst acting in every case in
the same way, may, according to its terminal connection,^
" deliver messages, ring a Ijell, explode a mine, decompose
water, create or move magnets, produce light, &c. The
same with the nerves. The state of irritation is, so far
as the isolated nerve-fibre is concerned, everywhere the
same, but in accordance with the nature of different
parts, be it of the brain or of the external portions
of the body, it produces motion, secretion, increase or
decrease of blood, of heat in different organs, or lastly,
sensations of light, sound," &c.

The physiology of hearing had its brilliant application
in a clearer understanding of the elements of language,
of the formation of the vowel sounds, and in the study of
the development of music — that art which, more than
any other, seems founded on definite rules.^ In analysing

^ ' Tonempfindungen,' p. 222.

^ " From the time wlien Pythag-
oras is said to have discovered the
arrangement of tones in an octave,
by observing that the sounds of the
blacksmith's hammer in the forge
produce a fourth, a fifth, and an
octave, and was then led to obtain
harmonic proportion between the
strings of the heptachord, all who
investigate musical tones know that,
although these are fleeting sensa-
tions, they depend physically on
numerical relations between various
kinds of movements ; but it was
Helmholtz, more than any other
philosopher, who examined the
whole range of the phenomena,
physical as well as physiological,
and whose work will for generations
remain an enduring monument to
his genius" (Prof. M'Kendrick in
the Helmholtz volume of the

"Masters of Medicine" Series, p.
168).

Since the appearance of the last
edition of Helmholtz's great work,
of which there exists an excellent
English edition with valuable notes,
many of the points first investi-
gated by Helmholtz have been taken
up by other experimentalists as well
as by psychologists. The invention
of the i)honograph by Edison in
1877 gave a great impetus to exact
research in the problems of audi-
tion, and various facts and theories
have been advanced confirming or
modifying the views put forward
by Helmholtz. On these see the
last chapter of Lord Rayleigh's
' Treatise on Sound,' 2nd ed., 1894.
On the psychological side see the
2nd volume of Prof. AVundt's
' Phvsiologische Psychologie,' pp.
47-96.

ON THE PSYCHO-PflYSICAL VIEW OF XATFRE. 401

these Heliiilioltz is led into lesthetical and psycholofrical
discussions, clearly distinguishing between such principles
as are inherent in natural, physical, and physi(jlogical
relations, and such others as depend on the inventions of
genius and the gradual changes l)rought aljout by exter-
nal requirements and ingrained by habit and education.^
The physiology of seeing had yet more remarkable
consequences for the history of Thought. We may say
that through Helmholtz's analysis of the formation of
our space perceptions by the eye in connection with the
tactile and muscular senses, psychology and metaphysics
were brought into immediate contact with physics and
physiology. It is here that Helniholtz takes up an ir.

i.-iT/'P ±^ 1 • 1.1 1 Helmholtz

entirely ditJerent, and, previously, isolated line of reason- a"d Kant,
ing, which centres in Kant's theory of space and time as
innate forms of perception — the so-called subjectivity or
ideality of time and space. The studies of this subject"
had been somewhat prepared by the writings of Herbart
and Lotze. The teachings of Kant have had an influence
in the direction indicated through two distinct channels,
— through Johannes Midler's rhvsiology and through
Herbart's Psychology : the latter seems to have had

^ See the closing words of the
13th chapter of Helmholtz's work :
" As the fundaracntal j)riiici|)le for
tlie developeiiieiit of the European
tonal system, we shall assume that
tlie whole mass of tones and the
connection of harmonics must stand
in a close and always distinctly
perceptible relationship to some
arbitrarily selected tonic, and that
the mass of tone which forms tlie
whole composition must be de-
veloped fi-om this tonic, and must
finally return to it. The ancient
world dcvelojicd this pirinciple in

homophonic music, the modern
world in harmonic music. But it
is evident that this is merely an
icsthetical princi])lc, not a natural
law. The correctness of this juin-
ciple cannot be established a priori.
It must be tested by its results.
The origin of such wsthetical i)rin-
ciples should not be ascribed to a
natural necessity. They are the
inventions of genius, as we pre-
viously endeavoured to illustrate
by a reference to the principles of
arcliitectural style."

492 SCIENTIFIC THOUGHT.

little influence over the Berlin school of physiology, but
it has had a considerable influence on several members of
the Leipzig school. In this school Lotze was educated.

Locke had taught, and his followers had accepted, the
doctrine that the so-called secondary qualities of sensible
things, such as colour, sound, hardness, &c., were sub-
jective. Speculative physics had prepared this view by
translating such properties into special forms of aggrega-
tion or periodic motion, leaving only extension and re-
sistance as the primary properties inherent in things.
Kant had gone a step further, and maintained that
space and time were likewise only subjective forms of
our perceiving sense apparatus. Two problems grew out
of this view, which are not clearly stated in Kant's
writings. First, How does the perceiving mind arrive
at the elaborate and systematic space conception which
is peculiar to us human beings ? — i.e., out of what per-
ceptive elements, and by what psychical processes, is it
gradually built up ? Secondly — What is it that locates
our sensations at definite places in space ? There is a
third question which Kant put and answered, that re-
ferring to the nature and validity of the geometrical
axioms. According to his view the axioms of geometry
are innate, expressive of the inborn nature of our space
conceptions ; in fact, the truths of geometry formed in
his view the only instance of knowledge gained not by
experience but a jpriori — before or outside of experience.
18. An entirely independent series of psycho-physical in-

The brothers . . i n t i

Weber. vcstigations was started even before Johannes Mliller,
by Ernst Heinrich Weber of Leipzig, who, with his two
brothers, Wilhelm and Eduard, may be considered as

ON THE PSYCnO-PHYSK'AL VIEW OF NATUIIE. 493

the ceiitie uf Lhc Leipzig schuul ut' Anatomy, I'liysiology,
and riiysics.^ After having been among the first to
import the exact methods of research into physiology,
and having carried on a variety of investigations refer-
ring to physiological optics and acoustics,^ he approached
tlie subjective phenomena of sensation : recording, for
cxani})le, with what degree of accuracy different parts
of the surface of the skin on face, arm, leg, &c., per-
ceive the distance between two points which touch the
skin — say the two points of a pair of compasses ;
recording also the relation of the smallest increase
of any given sensation to the corresponding increase
of stimulus. In the latter series of experiments, he
arrived at what has been termed'' "Weber's I'sycho-
physical law. He did not call it so himself ; he simply
showed by experiment that in a variety of cases the
stimulus had to increase in proportion to its own initial
intensity in order to produce a just perceptible increase
of sensation. These experiments did not attract much 19.

^ Fcchner's

attention till Gustav Theodor Fechner took them up, Psycho-
building upon them his celebrated " Principles of Psycho-
physics." Before referring more in detail to these, I
must mention a third line of reasoning which, as stated
above, had a considerable influence on the Leipzig school
of Psycho - physics, though probably it had as little

1 On the labours of tlie brothers aiiatomicfc et physiologic^,' in

W'eber, see the references given which, in 1831, tliere appeared his

above, vol. i. p. 196, also the present celebrated treatise ''Tastsinn und

volume, p. 31, note. Oeincingefiilil." Job. Midler's 'Ver-

- E. H.Weber i)ublished in 1817, gleicliendc Anatomic des Gesicht-

' Anatoinia comparata nervi sym- sinnes ' appeared in IS'Jti.

pathici ; ' in 1820, ' Ue aure et ■* By Fechner in his ' Elenieute

auditu hominis et animalium ; ' der Psychophysik ' (2 vols., Leipzig,

from 1827 onward, ' Annotationes 1860).

physics.

494 SCIENTIFIC THOUGHT.

influence on E. H. Weber as the earlier philosophy of
nature, to which it formed a pronounced opposition.
20. Herbart was not an experimental philosopher ; never-

Influence of . „ . .

Herbart. thelcss a placc in a history of scientific Thought lielongs
to him. Indeed, his philosophy, like that of Kant, and,
in quite a different way, of Schelling, has had a marked
influence on many thinkers and men of science who have
prepared the ground for an exact treatment of the pheno-
mena of Life and ]\Iind. Among exact psychologists I
need only name Volkmann, Drobisch, Lotze, and in our
time Professor Wundt ^ of Leipzig. It is therefore of
interest to mark the precise point where Herljart's in-
fluence comes in.

Although an exact school of psychology might aim at
studying psychical and psycho-physical phenomena w^ith-
out reference to any general theory of the soul as the
supposed centre and substance of these phenomena,
the existing ideas and theories as to soul and mind
have nevertheless always played a great part in these
researches, just as it has been found impossible to free
biological research altogether from some theory of life.
Older psychologists were consciously or unconsciously
governed by the conception of a number of distinct
mental faculties. Even Kant's philosophy is still
embarrassed by this view, which reigned supreme in
the teaching of his predecessor Wolf. The attempt of

' This is not the place to speak
about the Herbartian school, which
is almost entirely confined to Ger-
many. I have referred to Prof.
Wundt because, in spite of a run-
ning criticism, in the ' Physiologische
Psychologie,' of Herbart's special

doctrines, the author of that im-
portant and comprehensive work
himself declares (Preface to the 1st
ed., 1874) that for the formation
of his own views he is, next to
Kant, most indebted to Herbart.

ON THE rsYCHO-rHYSlCAL VIEW OF NATURE. 495
Heibait, tlierefore, to overthrow the so-called faculty- 21.

His attack

psychoWv, iind to insist on the essential iinilv and "","'«
1 J c^ > J "faculty-

simplicity of the inner life, must have made a great J^gy*^'.'*"''

impression on all who came uniler the intluence of his

philosophy. It did this in two ways.^ It first of

1 Besides Herbart (1776-1841),
whose psychological writings date
from 1813 to 1825, another Oerman
ps^'chologist is usually- mentioned as
having helped to overthrow the older
l'acultj--i)sych()logy. Beueke (179S-
1854), a younger contemporary of
Herbart, conceived of psychology
as a natural science. His principal
work, ' Lehrbuch der Psychologic
als Naturwissenschaft,' appeared
in 1833, and has been several times
republisiied, the fourth edition ap-
pearing in 187 7. Beneke worked
in opposition to Hegel at Berlin,
liis historical forerunners being the
German philosophers, Jacobi, Fries,
and Schleiermacher, as well as the
English philosophy of the so-called
Association - school. An account
of his philosophy does not belong
to a chapter on psycho-physics ex-
cept in as much as he introduced
into the study of the inner life not
indeed the facts and data of jthysical
— i.e., physiological — science, but
the i)hysical method. He was the
purest representative of the psycho-
logy of the "inner sense." Whilst
Herbart based his jjsychology alike
on experience, metaphj-sics, and
matiiematics, Beneke accejjted only
the first, and discarded the latter.
Standing thus outside the all-
powerful school of Hegel and the
increasing influence of Herbart,
Beneke had during his lifetime
only a limited audience, and re-
ceived due attention in a wider
cii-cle, fii'st and priucipally through
Ueberwcg, who was gi-eatly im-
pressed by him. In fact, his
influence was felt in Germany

about the same time as that of
the English and Scottish philo-
sophers. Ueberweg, in his well
known ' History of Philosuphy,'
vol. ii. pp. 281-292 (Engl, transl.
by Morris, 1874), gives a full ac-
count of Beneke. Prof. Erdmann
gives a very full account also in
his excellent ' Grundriss der Ge-
schichte der Philosophic' (3te Aufl.,
1878, vol. ii. pp. 628-641). The fact
that Beneke's method is intro-
spective, brings him not only into
contact with the English school,
but also with French thought,
which has alwaj-s been character-
ised by subtle psychological aiial-
j'sis. This explains the fact that
M. Marion (in the 'Grande Juicyclo-
jjudie ') calls Beneke " un des prin-
cipaux pliilosophes Allemands du
siecle," — a designation which would
hardly be echoed either in Germany
or in England. The best account
of Beneke's position in the de-
velo])ment of psychology extant in
the Englisli language is that of Dr
G. F. Stout, in his article
" Herbart compared with English
Psychologists and with Beueke,"
in the 14th volume of the 1st
series of ' Mind ' (1889). M. Ribot,
in his well-known book on ' ^Modern
German Psychology ' (Engl, transl.
by Baldwin, 1899), does not say
much about Beneke, but his ac-
count of Herbart and his school,
and their j)osition in psycho-physi-
cal thought, is concise and nmch
to the point. Dr Stout's articles
on Herbart in 'Mind' (vols. 13, 14)
are also much to be reconmiended.

496 SCIENTIFIC THOUGHT.

all liberated them from the trammels of an antiquated
and misleading terminology ; and secondly, it impressed
them with the necessity of giving an answer to the
question how the multiplicity of sensations or the flow
of ideas was held together in the unity of an inner
existence. Thus it is a characteristic of all psycho-
physical writers who have come under the influence
of Herbart, that however much they may be occupied
with detailed description of physiological processes, with
the analysis of sensations or the dissection of the data
of experience, they never lose sight of the underlying
mental unity which is the central phenomenon of psy-
chology and of psycho-physics, just as it must be the
central problem of biology to arrive at some definition
of life. Had the investigations of psycho-physical pheno-
mena remained where Weber or even Helmholtz left
them, we should have brilliant chapters on the phenomena
of touch, of seeing, hearing, and other processes where
the outer and inner worlds come into contact, but no
attempt to sum up these brilliant contributions in a
connected view of the inner and higher life — the most
22. remarkable and unique phenomenon in nature. It seems

Unity of

mental life, to me that, in Germany at least, it is through Herbart,
more than through any other thinker, that we have
been preserved from a threatening disintegration of
psychological research. It is the more necessary to
recognise this, as most of those writers who at one
time came greatly under Herbart's influence have found
it necessary, after having become thoroughly saturated
with this one great truth in his philosophy, to abandon
almost the whole of the more detailed expositions con-

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 49 7

taiiied in his woiks.^ Heibait was quite as correct
in his ideal of what psychology should l)e, as he was
unfortunate in the particular manner in which he
elaborated it.

Psychology was tu be fuuiided on experience, meta-
physics, and mathematics. Kant had studied the inner
activity of the mind as it is compounded of sensation,
perception, and apperception ; of understanding, judgment,
and reasoning. In opposition to this Herbart went back
to the position taken up by Locke and Hume, looking at
the inner life of a conscious mental being or soul, not as
a complex of mental faculties, but as a flow of ideas or
perceptions. How is the unity and simplicity of this
mental being preserved in the midst of this continuous
How of ideas ? how is it regained as often as it is in
danger of beimr 1( )st ? His investigations start at the
point where the inquiries of the association school of
psychologists started in England. Having, however, the
mechanics and dynamics of physical forces more proniin-

^ Dr Stout lias fjiven an ac-
count of the Herljartian school
in the 14th volume of 'Mind,' p.
353 !i<iq. He confines himself to
Drobisch, Waitz, and Volkmann,
the psychologists proper. M.
Uibot {lac. cit.) has dwelt more
on the develojjment of the Herbart-
ian school in the direction of an-
thropology and ethnology ; he
mentions specially Waitz, as well
as Lazarus and Steinthal. He
contrasts their work and their
positions with those of the great
anthropologists of the English
school, such as Tylor, Lubbock,
and Herbert Spencer, and notes,
in the German school, the absence
of Darwinian ideas. It is import-
ant to observe that botli in the case

vor,. II.

of Piof. Wundt of Leipsic and of Mr
Spencer in luigland — that is, in the
case (jf the latest outcome of the
Kant-Herbartian philosophy on the
one side and of the Association phil-
osophy in England on the other —
and in each case under the intiuence
of the exact and biological sciences,
philosophy ends in elaborate treat-
ises on Anthropology, which with
Spencer is conceived under the
name of Sociology. Similarly, the
school of Hegel ended in elaborate
historical treatises. Hume turned
fi-om abstract philosophy to politi-
cal economy and history, and
Herder — as we shall see later on
— anticipated much of all this
movement in his History of
Mankind.

2 I

498

SCIENTIFIC THOUGHT.

23.
Jlathe-
niatical
psychology.

ently before his mind than they had, he was tempted
to try how far the conceptions of equilibrium of motion
and of the composition of forces could l^e applied to the
inner play of ideas which chase, oppose, and displace
each other, preserving all the time a kind of dynamical
equilibrium. His elaborate mathematical calculations in
the first part of his greater work on psychology do not
specially refer to the purely intellectual process ; ^ they
refer rather to all inner processes which oppose each
other, which come into conflict, restraining each other in
proportion to their contrast, creating a tendency towards
reversion to former conditions. Such a play of oppos-
ins; forces is to be found Hkewise in the larger field of
human society ; this is accordingly quite as much a case
for the application of those psychical mechanics which
Herbart aimed at establishing.

In a history of scientific Thought, which aims at
showing by what gradual steps the various provinces
of phenomena have been brought under the methods of
exact treatment, the psychology of Herbart has an im-
portant as well as a unique and isolated position. It

^ Herbart himself saj's of his
mathematical chapter, that the re-
.sults thereiu given " do not follow
immediately from the conception
of a thinking being ; but they re-
fer to the mutual arrangements of
any things, in so far as they are
opposed and as they collide, re-
stricting each other in proportion
to their contrast, tending to revert
to the previous condition, the
unrestricted portions being fused
into complex forces. The forces
which are active in society are
doubtless originally psychological
forces. They meet in so far as they

appear in language and in actions
in a common sensual world. In
the latter thej' restrict each other ;
this is the universal spectacle of
conflicting interests and social
frictions. Also the fusion no doubt
exists. . . . We therefore assume
that among men living together
the same conditions appear which

i exist, according to our view, among

I the ideas in one and the same con-
sciousness. We examine the re-

I suit of their mutual restrictive
action" (" Psychologie als Wissen-

: schaft," 'W^erke,' ed. Harteustein,
vol. vi. Y>. 31, &c.)

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 499

led psychologists to consider more closely the conditions
under which a mathematical treatment is at all possible,
and to recognise that exact and accurate measurements
must precede all application of an abstract calculus.
Herbart's ideal was that of a psychical mechanics ; he
opposed ^ the idea of a union of physiology and
psychology. And yet this was just the direction in

' In a very interesting note <at
the end of tlie introduction to tlie
second part of liis larger work on
psychology, Herbart explains his
position with regard to physiological
psychology. It refers to certain
extracts which he makes from
Kudolph's 'Orundriss der Physiol-
ogic,' in which that eminent physi-
ologist referred to Herbart's ' Lehr-
buch der Psychologic.' "It is not
onlj- a metaphysical but also a
logical en-or to confound psycho-
logical and phj'siological research.
Psychological phenomena are not
in space, but space itself, with all
that appears in it, is a psycholog-
ical phenomenon, and, indeed, one
of the first and most difficult facts
for psychology, which, in the treat-
ment of it, would behave very im-
])roperly if it began l)y discussing
the forces iu the nerves ; for the
question is not, where sensations
come from, but how sensations
acquire the form of space. Now, I
maintain fuither, tliat tlie ditl'er-
ence Vietwccn lifeless and living
matter — that is, between physics
and physiology — cannot be under-
stood until we know mind by means
of p.sychologj', for in all the count-
less elements of the organised body
— in plants as well as in animals — •
there is an analogue of mental de-
velopment which cann(jt po.ssibly
be found on the surface of ])hen-
omena. We observe inteinally a
fragment of our own mental exist-
ence. This fragment is developed
into scientific knowledge through

speculative psychology based on
I metaphysics. This knowledge
I meets another equally metaphy-
I sical science, natural philosophj',
with its conception of matter —
that is, of such inattei- as we know
througli chemistry and dynamics.
Then onlj' can the question be put,
how such matter must be con-
stituted, so that its separate ele-
ments are determined, not only
through their original quality, but
also through a development analo-
gous to the mental one,"' &c. The
section closes with the following

characteristic passage

Those

who favour empiricism can learu
from the present state of physi-
ology how much, or rather how
little, mere exjierience can do.
Physiology, as an empirical doc-
trine, has attained a height which
nobody can despise. ]\Ioreover, it
proceeds in the light of modern
physics. Nevertheless, it has
eagerly sucked up, as the sponge
sucks u]) water, that philosophy
of nature which knows nothing,
because it began by construing the
universe a priori. Towards this
error no science has proved so
weak, so little capable of resist-
ance, as physiology. The talk
about life ha^ liecome tlie Dead
Sea in which all spirit of philo-
sophical research is drowned, so
that, if a resurrection is at all to
be hoped for, it must be born anew
in quite unbiassed minds" (' Werke,'
vol. vi. p. 05, &c. )

500

SCIEN'TIFIC THOUGHT.

24.
Lotze's
Physiology
of the soul.

which an exact or scientific treatment of mental phe-
nomena could meet with any success at all. It was in
the schools of physiology, in those of Johannes Miiller
and of Weber, that philosophers had to learn how to
attack the borderland of bodily and mental phenomena.
The first who approached the subject from this point
of view was Hermann Lotze. He was a disciple of
E. H. Weber, and had been led to psychological re-
searches from two independent starting-points : first from
the study of the medical sciences which, under the hands
of his great master, had largely benefited by the ap-
plication of the exact methods of the physical, the
measuring, and calculating sciences, but also from an
entirely opposite quarter.^ " A lively interest in poetry
and art had led him to philosophy." He was attracted
by that great body of ideas which, through the systems
of Fichte, Schelling, and Hegel, had become permanently
domiciled in German culture. In this great realm lie
could move " with some freedom," for it had not be-
come crystallised into a definite system of doctrine ;
exact studies had, moreover, easily convinced him " how
absolutely untenable was the form into which Hegel had
cast that valuable possession."

I

^ The quotations in the text are
taken from Lotze's polemical pam-
phlet, ' Streitschriften ' (Leipzig,
1857), pp. 6, 7. As already men-
tioned (supra, p. 407 note), Lotze had
been misunderstood bj^ his critics,
of whom some represented him as
a materialist, others as a follower of
Herbart. In refuting the latter
charge he explains his position to-
wards the idealistic sj'stems of the
first half of tiie nineteenth century.

He acknowledges two great personal
influences, that of C. H. Weisse,
which, as it were, touches the
kernel of his convictions, and that
of the study of medicine, which,
in his case, was intimately con-
nected with that of the physical
sciences. He admits, as did Her-
bart, having passed through the
magnificent portal of Leibniz's
Monadology to a general arrange-
ment of his philosophical opinions.

ON THE PSYCHO-PHYSICAL VIEW OF NATIKK. 501

We must bear in mind this twofold source of Lotze's
reflections if we want to estimate correctly the value of
his early criticisms regardin;^ the llifii juevalent treat-
ment of such questions as life and mind in the medical
sciences. On the one side he had the object of clear-
ing the way for purely mechanical explanations. We
learnt in an earlier chapter how he was one of those
who successfully chased out of biology the vague idea of
a vital force. And when lie approached the problem
of mind and body, we liinl hiiu insisting on tlie presence
of a psycho-physical mechanism which rules ^ the inter-

' The opinion of Lotze regarding
the relation of soul and body, or
rather of psychical and physical i)he-
noniena, has been stated by him,
variously, as parallelism, occasional-
ism, pre-established harmony, and
was ultimately crystiillised in the
term psycho-physical mechanism.
The question is fully discussed in
the articles, " Leben und Lebens-
kraft," "Instinct," '' Seele und
Seelenleben." which he contributed
to R. Wagner's ' Handworteibuch
der Physiologie.' They are re-
printed in Lotze's 'KleineSchriften,'
ed. D. Peipers, 4 vols. (Leipzig,
1885-91). He there saj-s, "The
conception of a psycho-physical
mechanism can be stated as fol-
lows : As ideas, volitions, and other
mental states cannot be compared
with the quantitative and special
properties of matter, but as, never-
theless, the latter seem to follow
upon the former, it is evident that
two essentially different, totally
(lisj)arate, series of processes, one
bodily and one mental, run par-
allel to each other. In the intensive
quality of a mental process, the
■extensivedefinitenessof the material
jjrocess can never be found ; but if
the one is to call forth the other,

the proportionality between them
must be secured through a connec-
tion which appears to be extrinsic
to both. There must exist general
laws, which ensure that with a
modification (i of the mental sub-
stance a modification b of the bodily
substance shall be connected, and it
is only in consequence of this inde-
pendent rule, and not through its
own power or impulse, that a
change in the soul produces a
corresponding one in the body "
(vol. i. p. 193). Lotze destroyed
the idea of vital force, but he
oidy chased the conception of
the soul bej'ond the limit of the
psycho-physical mechanism, and he
maintains that natural and medical
science have no interest in pursuing
the question lieyond that limit,
" however interesting the further
discussion of this subject may be to
speculative j>sychology" (vol. i. p.
197) — " for it is ((uite indifferent to
medicine, wherein the mysterious
union of body and soul consists, as
this is the constant event which
lies equally at the bottom of all
phenomena. But it is of the
greatest interest to medicine to
know what affections of the soul
are connected in that mysterious

502 SCIENTIFIC THOUGHT.

action of external and internal phenomena, of stimulus
and sensation.
25. There existed indeed another side — that which we

Two sides of

Lotze's may call the philosophical ; it does not at present enter
into the course of our narrative, which deals only with
the extension of scientific or exact thought, and with
mental phenomena and the inner life in so far as they
form a province — perhaps a very restricted province — of
the whole of nature. This province Lotze was among
the first to proclaim distinctly to be one which natural
science had to conquer and to cultivate. He is careful
to explain that it does not cover the whole ground of
psychology, and at the end of his long discourse on the
" soul and its life," which formed an important con-
tribution to the great physiological encyclopaedia pub-
lished in the middle of the century, he clearly marks
out " physiology of the soul as an exposition of the
physical and mechanical conditions to which, according
to our observation, the life of the soul is attached," ^ as
one of the several problems of psychology. It formed a
counterpart to the physiology of the body, of the physical
side of our existence, and was, like it, to become a natural
— i.e., a mechanical — science. Subsequently he collected
the whole of his reflections belonging to these two de-
partments in two treatises on the ' General Physiology
of Bodily Life' (1851), and on ' Medical Psychology' or
'The Physiology of the Soul' (1852).

As little as it now enters into our programme to

manner with what affections of
the body. Unfortunately, medical
science has only too often lost sight

less speculations referring to that
connection itself " (p. 197). Cf. also
' Medicinische Psychologic,' p. 78.

of this its proper pi'oblem over fruit- ^ ' Kleine Werke,' vol. ii. p. 204.

ON THE rSYCHO-PHYSICAL VIEW OF NATUKE. 503

folluw ii[» the phil(js()i)hical reasonings of Lotze beyond
the limit of the psycho-physical mechanism, so little were
these at the time of their appearance heeded liy many of
his readers, some of whom he seems to have converted
to or confirmed in a purely materialistic conception of
the phenomena of the inner or mental world. Lotze had
banished " vital forces " from Ijiology ; why not follow
him, and banish all other higher principles, and revive
— as Carl Vogt did ^ — the dictum of Cabanis about
the analogy between the functions of the brain and
the kidneys ? AVhy should the " anima " of Stahl not
have the same fate as the " vital force " of Bordeu and
Bichat ?

This was a misconception of what Lotze had intended.
He had, indeed, banished" the principle of life as a
factor useless in physiological explanations ; but not the
principle of organisation, which must have presided over
the beginning of all organic forms. This might he
neglected by physiologists, who had nothing to do with
origins but only with existing relations. It was (|uite
different with mental phenomena, which, manifesting
themselves alongside of physical processes, required to be
dealt with and recognised as actually existing and con-
current events.^ Herbart's psychical mechanism might

^ On this, see the account given
in Lange's ' History of Materialism '
(Engl, transl., vol. ii. p. 285) and
Lotze's reference to it in ' Med.
Psychol.,' p. 43.

- " There is no doubt that a
legitimate attack upon ' vital force '
has marked in our days that line of
reasoning, which has by the law of
inertia carried many of our cou-
temporaries far beyond the correct

limit on to a negation of the exist-
ence of a soul" (ibid., p. 41).

•' These various points are very
fully discussed in Lotze's earliest
philoso])hical work, ' Metaphysik '
(Leipzig, 1841), pp. 2.">1, 2.');'), 259 ;
and again in the ' Med. Psychologie '
(1852), p. 78. Referring to tiie
last chapter, in which I dealt with
the development of the theories of
life and organisation, two points

504 SCIENTIFIC THOUGHT.

be an unrealisable ideal in that it dealt with inner
phenomena as unconnected with outer ones : a psycho-
physical mechanism was a nearer approach to a true
description of reality, and could not be narrowed down
to a purely physical occurrence ; moreover, the unity
of mental life was a special property which had to
be recognised and defined.
26. Lotze himself, after formulating the conception of a

physucsof°' psycho-physical mechanism, and utilising the elaborate

vision. . • e

and fundamental expermients and observations of Weber
as illustrations of what was meant, made an important
contribution towards an analysis of a compound physico-
psychical process. He took up the problem which
Berkeley had attacked, of the formation of our space
perception. It had been introduced into German
psychology mainly through Herbart with reference to
the Kantian doctrine that space is a subjective form.
Through Lotze, and subsequently through Helmholtz, it
has been shown to have not only a psychological but
likewise a physiological importance : it is a problem of
psycho-physics.

There exists a peculiar difficulty in bringing home to
the popular mind the fact that a special problem is in-

maj' be noted. First, it is clear i in the ever indistinct manner in

that Lotze was aia " organicist" be- which language operates in forming

fore Claude Bernard and other more j its words, it may form the correctest

recent thinkers mentioned above. conceptions in just as incorrect a

Secondly, it is very evident that manner as the most erroneous ones.

Lotze belongs to the pre- Darwinian What is important is whether the

school of thought. In fact, he does ' conception, formed anyhow, can

not relish the genetic aspect. The ' justify itself "(' Med. Psychol.,' p.

historical beginnings of ideas are I 41). I shall on another occasion

for him no indication of their value I have to refer more fully to this

and correctness. He says on this , marked absence of the historical

point : " The genesis of a concep- i sense in Lotze.
tion is no argument for its validity ;

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 505

volved in the manner in which (jur senses uf sight and
touch combine and arrange simple sensations into the
whole of a well-ordered })erception of space ; for we do
not become able to appreciate the fact of the slow
and gradual growth of this perception, which takes
place in the early days of our infancy, till long after
we have actually gained full possession of it. Some-
thing similar exists wilii regard to language and
thought : we only hear of grammar and logic long
after the main ditiiculties of speech and thinking have
been unconsciously mastered, and if it were not for
the existence of other languages than our own, and
of an erroneous logic as exemplified in errors of cal-
culation and of measurement, it is doubtful whether
grammar and logic would have Ijcen so early developed.
As it is, the physiological problem of the formation of
our space perception was actually first forced upon
naturalists by the observation of pathological cases, such
as the acquisition of sight in later life through couching,
the existence of colour blindness, and a variety of optical
delusions which still serve as indispensable test cases for
the various theories that have been propoimded. Only
when something turns out to be palpably wrong do we
begin to inquire what constitutes the right side of many
things.

Thus the cases of Cheselden and Wardrop and the
colour blindness of Dalton set physiologists thinking
about the genesis of our space and colour perceptions.
A very great impetus — perhaps the most valuable of all 27.

. . c ^ Wlieat-

— was given by Wheatstone s mvention of the stereo- stoiies

_ _ _ _ stereoscope.

scope in 1838 ; an instrument which, as it were through

'06

SCIENTIFIC THOUGHT.

a kind of deception, gave to perfectly flat surfaces the
vivid appearance of depth and distance. And here we
may note, in passing, how it was ahnost entirely left
to foreign thinkers to utilise this remarkable invention
for the benefit of the theory of vision and the science
of psycho - physics ; ^ Whewell having characteristically
omitted this epoch-making fact, as in his well-known
history he omitted to notice many other contemporary
British contributions to science.

Philosophers, who are accustomed to find hidden
problems where ordinary persons only see common-sense,
had already approached the question of the genesis of our
space perception from two definite jDoints of view, which
we may, for the sake of convenience, identify with the
names of Kant and Herbart. The genetic view associ-
ated by the physiologists with the name of Kant, and
supposed to have been prepared by Locke, Berkeley, and
Hume, was this, that what we know of external things
depends upon the peculiarities of our own perceiving

^ Sir Charles Wlieatstone (1802-
1875), to whom several inventions
of equal scientific and practical
interest are clue, invented the
mirror - stereoscope in 1833. A
notice of it was given in Mayo's
' Outlines of Human Physiology,'
but neither its theoretical nor its
practical importance was recognised
till Wheatstone published his paper
in the 'Phil. Trans.' in 1838. He
there refers to Leonardo da Vinci as
having been the only one before him
to notice the difference of binocular
and monocular vision. Since Wheat-
stone's invention became known and
was perfected bj' Brewster, Moser,
and others, and especially since
Helmholtz entered the field with his
extensive and original researches in

optics, it has been found that
ancient as well as more recent
philosophers had a^jproached the
subject very closely ; and many
references are given in the new
edition of the ' Physiologische
Optik ' (1896), p. 840. The inven-
tion of photography about the same
time (1835, by Daguerre, after ex-
tensive and i)rolonged experiments
by himself and Niepce, published in
1839 by Arago), which was of great
imjiortance to optical theory, was
also for some time singularly little
appreciated by theorists. See
Rosenberger, ' Gesch. d. Physik,'
vol. iii. p. 316. See also Helmholtz's
lecture " Ueber das Sehen des
Menschen" (1855).

ON THE PSYCHO-PHVSrCAL VIKW OF NATURE. 507

and tliinkiiig self, on sensatiuns, and (jn their arrange-
luent or orderly presentation. The sensations them- 29.

LocalirtatioB

selves are the suhstance, the sijatial arrangement ".r»ensa.
of them the form, of owy perception of external
things. The question was gradually put more and
more clearly, H(jw we come to localise certain of our
sensations at definite places in the totality of a spatial
arrangement ? Herbart added another important refiec-
tion, which really dated from Leilmiz. Impressed with
the unity of all mental existence, and claiming this as
the characteristic property of our inner life, he asked the
question. How can the oneness or simplicity of this inner
existence, as it were, expand itself without losing its
unity, into the orderly variety of a spatial contemplation ?
For the purpose of an answer to this question he fixed
on the phenomenon of motion. The conception of an
orderly arrangement of sensations or things in space is
gained in great measure by the aid of definite move-
ments of the sensitive organs, which are accompanied
by definite sensations of motion — c.f/., 1 )y muscular
sensations.

The first of these two questions may be expressed in
the words, Given the subjective form of a space percep-
tion, either complete in its geometrical arrangement (the
nativistic hypothesis) or gradually acquired in the early
moments of our conscious life (the empiric hypothesis),
who do we make ourselves familiar with, and at home in,
this form of perception ? And secondly, By what special
properties or local signs do we localise or place each
single sensation in its right and orderly position ? The
first is the prol)Iem of space construction, the second

508

SCIENTIFIC THOUGHT.

29.
Lotze's
"local
signs."

30.
Feclmer.

that of localisation of things in space. Lotze was one of
the first to attempt detailed answers to these questions.
In particular he propounded the theory of " local signs,"
which with certain modifications has been adopted by-
subsequent writers on the subject. The combination
of physiological, optical, and psychological investigations
in Helniholtz's great work on ' Physiological Optics '
has brought deliniteness and mathematical precision
into many of the questions suggested by philosophers
and naturalists before him. Through it and its great
companion, the ' Physiological Acoustics,' psycho-physics
has to a large extent become an exact science.

A great step in the direction of drawing psychical
phenomena into the circle of the exact sciences was taken
independently by Gustav Theodor Fechner ; ^ in fact, it is

1 G. T. Fechner (1S01-1S87) was
a unique figure in German liter-
ature, science, and philosophy.
Beyond his own country he is only
very imperfectly known and appre-
ciated. He was self-taught, and
living all his life somewliat outside
the conventional categories of Ger-
man academic activity, he made
a position for himself which has
only become intelligible to a larger
public through the issue — after
liis death — of Prof. Wundt's ora-
tion, Prof. Kuntze's (his nephew's)
charming biography (1892), and
Prof. Lasswitz's monograph on
Fechner (Stuttgart, 1896), in
which for the first time a co-
herent exposition of his philo-
sophical teaching
Prof. Wundt has
passages of his

chology, and through the second
edition of the ' Psychophysik,' con-
tributed largely to a better under-
standing of Fechner's views and
merits. He descended on both

is attempted,
also, in many
work on psy-

sides from ancestors whose position
was that of highly esteemed Pro-
testant pastors ; he studied medi-
cine like Lotze, and was the friend
and colleague of Lotze's teachers,
Weber and Weisse. In his auto-
biographical i-ecord, communicated
b}' Kuntze, he confesses having be-
come almost an atheist under the
influence of his medical studies,
until he became acquainted with
the jihilosophy of Schelling, Oken,
and StefFens, which dazzled him,
touched the poetical and mystical
side of his' nature, and, though he
hardly understood it, had a lasting
influence on him. The simultan-
eous occupation with the best
scientific literature of the day (he
translated French text-books such
as those of Biot and Thenard, and
verified Ohm's law experimentally),
however, forced upon him the scep-
tical reflection whether, " of all
the beautiful orderlj' connection
of optical phenomena, so clearly
expounded by Biot, anything could 1

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 509

\n him that we are indebted for the term Psycho-physics,
wliich in the present cha})ter ] have used in a more
general sense. Feclmer Wdikcd independently of Lotze
and Hehnholtz on th(> lines of K. H, "Weber. He does
not seem to have been much inlhienced by either Kant
(ir Herbart. In ISGO lie ])ublished his ' Elemente der
Psychophysik,' which was to be an exact treatise on the
relations of " mind and body," founded upon a measure-
ment of psychical quantities.

Herbart's attempt to submit psychical phenomena to
the exact methods of calculation had failed through the
\vant of a measure for psychical ({uantities. Lotze had
siiij:ested the idea of a psycho-physical mechanism —
'.'., a constant and definite connection between inner
and outer phenomena, between sensation and stimulus.
Iv IT. AVeber in his important researches on " Touch and
1 '>odily Feeling " had made a variety of measurements of
-ensations, and shown that in many cases stimuli must
be augmented in proportion to their own original inten-
sity in order to produce e([nal increments of sensation.
These observations lent themselves t(j an easy mathe-
matical generalisation. Feehner was the first to draw

have been fouml out l>y Okeii-
Si-helling's method'"' This mix-
ture or alternation of exact science
.mil specuhition, of faithfuhiess and
loyalty to facts as well as to theory,
)uus through all Foclmer's life,
Work, and writings. Much of his
)"ietry, of his fanciful and para-
il'xical effusions, is meant seriously,
I 1 is really more colierent than it
. p[>eared to his readers, some of
whom knew him only under his
'•udonym of Dr Mi.>es. He lived,
.ught, and worked truly on the
rderland of nature and mind, of I

this world ami another, of science
and poetry, of reality and fiction.
Like Lotze, he wanted the genuinely
historical sense. Like Lotze, too,
he received from others only sug-
gestions which he elaborated in-
dependently in his own original
fashion. As little as Lotze does
he seem ever to have attempted
to realise and understand any other
philosophical system than his own.
To both, the ultimate problem was
capable oidy of a subjective solu-
tion. Cf. vol. i. p. "200.

510 SCIENTIFIC THOUGHT. |

the attention of philosophers to the existence of this re-
lation in a variety of instances, and collected a large
number of facts to prove its general correctness. He
conceived the idea of measuring sensations by their
accompanying stimuli, a mode of measurement based
upon that relation which, under the name of Weber's
law or formula, he introduced as a general psycho-
physical proposition. The intervals in the numerical
scale, the differences in the magnitude of stars, the
facts established by Weber relating to our estimate of
differences of touch, of weight, and of temperature ;
lastly, the relation of " fortune physique " and " fortune
morale," known to Euler and Lagrange, could all be
utilised towards proving the general accuracy, within
certain limits, of the psycho - physical formula. The
work gave rise to many discussions ^ as to the mean- .
ing of the term quantity applied to psychical pheno- |
niena, as to methods of measurement, and as to the
significance to be attached to the new branch of research

^ In addition to the ' Elemente which he was occupied with it."

der Psychophj'sik ' (1860), uf which i (See the obituary oration, reprinted

a second edition appeared in 1890, { in Kuntze's 'Biography,' p. 360.)

the author enlarged, discussed, and The attacks on Fechner came from

defended his special ideas and j many quarters. In the polemi-

theories in three further pubHca- ' cal treatise of 1877 he notices

tions. The year 1877 produced ' In ' iiow the views of his critics —

Sachen der Psychophysik,' tlie year i Hehnholtz, Aubert, Mach, Bern-

1882 the 'Revision der Hauptpunkte
der Psychophysik,' and shortly be-
fore his death (1887) there ap-

stein, Plateau, Delbreuf, Bren-
tano, Hering, Langer — agree as
little among themselves as with

peared, in the ' Philosophische [ his own. He sums up with fine

Studien ' of Prof. Wundt, his last | humour: " The tower of Babel was

contribution, " Ueber die psychi- , not finished, because the builders

schen Maasprincipien und das could not agree how to build it ;

Webersche Gesetz," which Prof. I my psycho-physical structure maj^

Wundt declares to be '' the clearest i remain standing, because the work-

and most complete exposition of I men cannot agree how to iiull it

the problem which he gave in the down " ('In Sachen,' &c., p. 215).

course of the forty years during I

ON THE PSYCHO-PHYSICAL VIEW OF NATUHE. 511

as well as to the interpretation of the Weber- Feehner
law of psycho-physical dependence.

We are indebted to Prof. Wundt of Leipzig for a
complete and exhaustive exauiinatiiju of the new
jirovince of exact science.^ He enlarged its boundaries,

31.

WuiiUt.

' The psycliulogical t-clii)ol, of
which Prof. Wuudt can be con-
-iilered the head or centre, has been
contrasted by M. Kibot, in his

■ I'sychologie Allemande Conlempo-
i.tine' (1st ed., 1879), with tlie
llnglish school, and, in the ex-
position in the text, I have taken
a simihir view. Ifc would, how-
1 \er, be unjust not to note that in
Knglatid, prior to the publication of
I'rof. Wundt's princi[)al writings, a
ii'velojiment of psychology in the

- tme direction had already begun.
I'lie principal representative of this

■ li'velopment is Prof. Alexander
Main (born 1818), whose two great
v'.orks, ' The Senses and the Intel-
i.'ct' (185.^) and 'Tlie Emotions
and the Will ' (1859), appeared even
I'cfore Fechner's ' Psychophj-sik,'
and were characterised by J. S.
-Mill as "an exposition which de-
serves to take rank as the foremost
of its class, and as mai-king the
most advanced jioint which the a
fistcriori psychology has reached,"

I eing " the most genuinely scientific
analytical exposition of the human
mind wliich the a posteriori psy-
' hology has up till this time pro-

■ luced"" ('Edinb. Rev.,' October
1 ^."^9, reprinted in ' Di.ssertations
and Discussions,' vol. iii. pp. 99,
100). Bain carried out what had
been called by Thomas Hrown " the
physical investigation of the mind,"
and was ])robably the first ICnglish
psychologist who enriched the older
associational jisychology by an ex-
tensive use of the teachings of i)hj-si-
ology ; the germ of his theory being
contained in a passage cited by him
from Johannes Miiller : in fact, he

apiircciated the well-known dictum
of the latter, *' psycholof/ux nemo
nisi physiolo!/us.'" Shortly after the
appearance of Prof. Bain's works,
the overmastering intiucnce of the
evolutionist school in England,
headed l>y Mr Spencer and sup-
ported by Darwin, and the jjro-
nounced opposition with which the
IJsycho-physical school started in
Germany, cast somewhat into the
shade the steady develoi)mont, in
this country, of the exact science of
psychology by those who formed the
direct succession to the older, purely
introspective, school of Scottish
thinkers. As I am not, in the ]ires-
ent chapter, treating of iisych(jlogy
and philosophy, but of the attempt
to gain, by the methods of the
exact sciences, a conception of the
phenomena of animation and con-
sciousness, I leave for another oc-
casion the appreciation of the
English school of psychology-. The
members of this scliool considei-ed
physiology as an aid to psychological
research, whereas most of the rep-
resentatives of the modern German
school were, to begin with, physi-
ologists or physicists, and only
became subseiiuently psychologists
or philosophers. Characteristic of
this school are two points : the
op])osition they made from the
start to the existing methods, and
their jiioniinent use, not only of ob-
servation, but of ex])eriment. The
less ostentatious development of
English thought would, no doubt,
have led in tiie end, but for the
reasons given above, to like results.
An ojiposition similar to that so
marked in Geiniany was, howevei-,

512 SCIENTIFIC THOUGHT.

taking in the ground covered by Lotze's medical
psychology as well as by Helmholtz's physiology of
hearing and seeing ; added a large number of measure-
ments of his own, some of them quite original, such as
those referring to the time-sense, many of them in con-
firmation and extension of Fechner's collection of facts ;
invented new methods and new apparatus ; brought the
whole subject into connection with general physiology, as
also with the more exclusively introspective psychology
of the older, notably the English and Scottish, schools;
and pointed to the necessary completion which these in-
vestigations demand from the several neighbouring fields

32. of research. Through his labours " physiological psycho-
physio-
logical logy " as an independent science has for the first time

psychology. ""^ ^

become possible. The influence of his great work on
this subject, as also of his teaching and demonstra-
tions, has been very stimulating. With its place in the
history of philosophical thought I shall have to deal in a
later portion of this history. At present I will merely
refer to the leading ideas and contributions it contains to
our scientific reasoning on the psycho-physical problem.

Wundt approached psychological research from the
side of physiology ; -^ his earlier writings referred to the

taken up in England in single in-
stances— e.g., by G. H. Lewes and
Dr H. Maudsley, the former in
favour of Positivism, the latter on
the foundation of his ' Physiology
and Pathology of ]Mind ' (1st ed.,
1867).

' Tiie researches of Wundt and
the earlier work of Fechner re-
mained practically unknown in
this country up to the time of
the appearance of the periodical
' Mind,' edited by Prof. Croom

Robertson, in 1876, under the
generous patronage of Prof. Bain.
Even Lotze and Herbart were
hardly known in this country.
A similar disregard of English
psychology existed in Germany.
The foremost writers on the his-
tory of modern philosophy, such as
Erdmann and Ueberweg, wrote as
if modern philosophic — including
psychological — thought existed
only in Germany. Even the
singularly imjjartial and unbiassed

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 513

physiology of the senses, to physiology proper, and to
such phenomena of psychical or inner life as can he
traced, not only in man, l)ut also in the brute creation.
He thus seems to have approached psychology with the
true instinct and methods of an exact student of nature.
In the course of years his psycho-physical studies took
more and more the character of an experimental psycho-
logy, and in the latest edition of his great work he
describes it as such, maintaining that the designation of
physiological psychology has rather a historical meaning.^

author of the ' History of Material-
ism,' Albert Lange, does only scant
justice to the labours of the Eng-
lish school, J. S. Mill being, in
fact, the only English philosophical
writer of the middle of the
century who was appreciated in
Germany. The last twenty -five
years have entirely altered this
state of things. French and
American writers, such as M.
Ribot, Prof. M'Cosh, and more
recently Prof. James, treat im-
partially of the rival claims of
German and English thinkers.
' Mind ' has preserved its fairness
in admitting contributions from
opposite sides ; and latterly there
has been started bj' the publishing
house of Froniniann of Stuttgart;
under the editorship of Prof.
Falckenberg, a series of very use-
ful monographs on recent thinkers,
whose voluminous or scattered
writings make it difficult to arrive
at a comprehehsive and just ap-
preciation of the main diift of
their doctrine. Ever since some
provinces of philosophy were con-
quered by exact research, unit}'
of plan has been to a great ex-
tent sacrificed ; the natural science
of mind is becoming split up into
fragments like that of life. Prof.
Lasswitz has given us for the
first time a coherent account of

VOL. II.

Fechner's philosophj', and although
Prof. Wundt had already jiut forth
in his ' System der Philosophie '
(1st ed., 1890) a statement of his
systematic views, the monograph by
Edmund KiJnig (1901) is very help-
ful in fixing the historical position
of Wundt and the genesis of
his doctrine. I refer to these
volumes for a bibliography of
the thinkers discussed.

^ In the introduction to the
' Physiologische Psychologie' (4te
Aufl., vol. i. p. 9) Prof. Wundt
saj's, " The conception of experi-
mental psychology has been ex-
panded beyond its original limits,
as we now comprehend under it
not only those parts of psychologj'
which aie directly accessible to
experiment, but the whole of
psychology ; as it makes a direct
use of the experimental method
wherever this is possible, and an
indirect use in all other instances
through applying the results gained
in the former, and through render-
ing internal observation more acute.
. . . The designation of physio-
logical psychology, which originated
in the peculiar historical anteced-
ents of our science, is one-sided.
. . . The centre of gravity of the
experimental method lies in this,
that it alone makes reliable inner
observation possible."

2 K

514 SCIENTIFIC THOUGHT.

WHiilsl his methods are exact and definite, his aim is,
nevertheless, wide and compreliensive ; for not only is the
animal creation studied as a valuable field for enlarged
psycho -physical research, l)ut also the psychology of
infancy and of human societies (ethnical psychology) are
drawn into the circle of a scientific psychology. At the
same time his exposition is directed towards the totality ^
of the phenomena of life and mind, it being his ultimate
object to arrive at some appropriate conception of the
whole of human existence. In this respect his scientific
labours form a counterpart to those of naturalists like
Humboldt and Darwin, who did so much to direct the
attention of natural science to the whole of nature, her
history and economy. It seems to me that Prof. Wundt
has similarly introduced into the psycho-physical study
of nature the prominent consideration of the mental side
of life in its totality, starting, as Darwin and Humboldt
did, from a large accumulation of detailed observations.

This regard for the whole problem distinguishes
Wundt's waitings from those of other eminent psycho-
physicists, such as Hehnholtz, who deals brilliantly and
exhaustively with certain special problems, or Fechner,
who relegated the discussion of the fundamental ques-
tions to a series of half-poetical treatises, which are full j
of suggestion rather than close scientific reasoning. But

^ ' Physiologische Psj-chologie ' totality of the phenomena of life,

(4te Aufl., vol. i. p. 2) : "Our science and, if possible, to gain in this

has accordinglj' the task, first, to way a comprehensive conception of

investigate those vital phenomena human existence." See also his

which, lying in the middle between essay " Philosophic und Wissen-

outer and inner experience, require schaf t " in a volume of 'Essays'

the sinmltaneous application of both , (Leipzig, 1885), p. 1; also 'Die

methods of observation, outer and ' Aufgaben der experimentellen

inner; and secondly, to throw light Psychologie,' ibid., p. 127, &c.
from the points thus gained on the

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 515

Wuiult differs quite as much from Lotze, who also strove 33.

^ WulKlt,

to arrive at a view of the totaUty of liuman life and its Fecimer,

'' and Lotze

significance. Lotze belonged, in spite of the original compared,
and independent view which he took of the psycho-
physical problem, to the older school of philosophers.
AVundt belongs quite to the modern school.^ Fechner
forms the transition. Lotze begins his psychology, and
even his physiology of the soul, with a lengthy disserta-
tion on the unity of the soul as a special being, just
as Herbart begins his psychology with metaphysics.
This metaphysical introduction, these definitions relating
to the essence of the soul, its unity, and its location, are
absent in the modern psychology. Instead of founding
psychology on experience, metaphysics, and mathematics,
AVundt founds it on experience (including experiment),
physiology, and mathematics. In consequence of this
altered foundation a new problem has arisen, precisely
as a new problem arose for biologists when they dis-
carded vital force as a meaningless and useless encum-
brance. For the older biologists life was the exhibition

"O"

^ See the preface to the second ' the problems. But I quite well uii-

erlition of the ' System der Fhilo-
>ophie' (Leipzig, 1897), p. ix : "I
have always tried to co-operate in
the endeavour to secure for psycho-
logy an independent position as
an empirical science outside of
philosophy, and to see that she
should not lack the support of the
scientific method in so far as this
could be transferred to her. . . .
As I started from natural science

understand that the position may
be different for him who begins with
philosophy and then makes occa-
sional excursions into the regions
of science or| psychologj'." Com-
pare with this what Lotze says in
the Introduction to his ' Streit-
schriften ' (1857), or the following
passage from one of his last essays
('Contemp. Rev.,' January 1880),
" Except in rare cases, a prolonged

and then came to philosophy 1 philosophical labour is nothing else

through occupation with empirical j but the attempt to justify, scientif-

|)syc!iology, it would have appeared ically, a fundamental view of things

to me impossible to philosophise ! which has been adc)pted in early

in any other way than in corre- j life."
spondence with this sequence of

516 SCIENTIFIC THOUGHT.

of vital force. This having been dropped, the question
arose for modern biology, What is life ? We thus find
thinking biologists of the modern, exact school aiming at
a mechanical definition of life. Many answers have been
attempted, such as that it is the action of a very com-
plex chemical molecule, of dynamical equilibrium, of meta-
bolism, of a special form or organisation, &c. Similarly,
when the word soul dropped out of psychology in its
older metaphysical meaning as a separate being or entity,
when it was used to mean only the sum-total of the
inner ur psychical phenomena, a new problem arose for
the psycho-physicist or experimental psychologist. The
problem now was to give some definition of the unity
and unified totality of all inner or mental phenomena.
The older metaphysical psychology, as also for the most
part the so-called empirical psychology, answered this
question by placing the conception of an independent
entity, the soul, person, or self, at the opening of their
discussions. Modern exact psychology cannot do this.
For it the unity of the inner life and its unified totality
has become a problem. This problem Prof. Wundt faces
34. fully and fairly. He asks himself the ciuestion, Wherein

The unity of .

conscious- consists the unity of consciousness, wherein the totality

ness. '' ' •'

of all mental life, individual and collective ? Armed
with the methods of exact research, he tries to extract
from the whole array of mental phenomena an idea of
their essence as distinguished from external or natural
phenomena, and of their collective meaning and signif-
icance. In so doing he enters the domain of philosophy,
and his results belong to the realm of philosophical
thought. When dealing with that large section of my

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 517

subject I shall have to take up Wundt's theories where
I now leave them.

Through the efforts and widespread influence of Prof.
"Wundt, the inner or psychical phenomena have been
drawn into the circle of exact research ; a large portion
of psychology has become natural science. It is quite
consistent with this that some of the disciples of the
modern school should have assumed towards the new
branch of natural science the attitude which has be-
come habitual among those who cultivate other natural
sciences. All these sciences are based upon observation,
aided if possible by experiment ; none of them, however,
has succeeded in rising to the rank of an exact science
without the aid of some generalisation which admitted
of clear expression in a few definite conceptions, being
the more valuable in the degree that it lent itself to
a clothing of mathematical language. In the course of
the last centuries, notably the nineteenth, several of
these fundamental principles — such as the laws of
motion, gravitation, atomism, vibratory motion, the con-
ception of energy, natural selection, metabolism — have
attained in various degrees, some almost perfectly, to
this state of definiteness, and the sciences Ijuilt up
by their aid have accordingly acquired the character
of certainty. Psycho - physics having through Weber,
Lotze, Fechner, and Wundt gradually evolved the notion
of a partial parallelism of physical and psychical pheno-
mena, the conception of a mathematical dependence or
of function could be introduced between the measur-
aljle external processes and the hidden internal events
which we term mental ; the whole of the latter being

518 SCIENTIFIC THOUGHT.

looked upon as concomitant occurrences, as " Begleit-
erscheinungen " or " Epi-phenomena " of the more ac-
cessible though very complex phenomena of the nervous
system and its centres ; whereby it had to be noted,
that whilst the external visible processes exhibit that
continuity in time and space which is characteristic of
all physical phenomena, the epi-phenomena were subject
to discontinuous appearance and disappearance, to sudden
growth and collapse. Having got hold of this partial
formula, which in some cases admits even of a rigorous
mathematical expression, psycho-physics had no pressing
need of investigating its meaning any further, or of in-
quiring into the supposed independent existence or signif-
icance of the " epi-phenomena " as such ; similar general
inquiries into the origin of gravitation, of atoms, of the
essence of energy or inertia, having proved to be of little
or no use in furthering astronomy, chemistry, thermo-
dynamics. It cannot be denied that this is a perfectly
tenable scientific attitude. Such an attitude has notably
been taken up by Dr Hugo Munsterberg, and by what
we may term the Freiburg school of psycho -physics.
Also there is no doubt that throus-h a series of very
cleverly contrived experiments — particularly those re-
ferring to the muscular sense and the time sense — a
good deal of light has been thrown upon such mental
processes as association of ideas, attention, apperception,
and voluntary effort, which have thus been brought
into closer correspondence with changes taking place in
35. the nervous system. In fact, a parallelism of neurosis

Doctrine of

parallelism, and of psychosis has been more and more established.
This doctrine of psycho - physical parallelism, also

ON THE PSYCHO-PHYSICAL VIEW OF XATLKE.

Id

called the conscious automaton theory, is the central
conception in iisychology as a natural science, or, as
I have termed it, of the psycho - physical view (tf
nature. It was ])repared ^ by earlier thinkers, such as
Descartes, and, in a different form, by Spinoza," and Ity
Leibniz's doctrine of pre-established harmony.^ It has
been strengthened by the physiological theory of reflex
action,"* and, independently, by psycho -pliysics in the
narrower sense of the word, as founded by AVeljer and
Fechner. But the possibilities of the automaton theory
were not scientifically tested till towards the end of
the nineteenth century. In this country, two thinkers

' The doctrine of psycho-physical
paralleHsiii and its histoi-ical genesis
is given l)y Huxley in his address
before tlie British Association Meet-
ing at Belfast in 1874, "On the
Hypothesis that Animals are Auto-
mata, and its History," in whicli lie
goes back to Descartes and Charles
Bonnet. A good account of the
theory is also given by Prof. Wra.
James in the .'Jth chapter of his
' Principles of I'sychology ' ; and it
is fully discussed by Prof. James
AVard in his Citibrd lectures,
' Naturalism and Agnosticism,' vol.
ii. pt. iii.

- The passage from Spinoza which
is constantly quoted, and, as Prof.
Ward says, usually in ignorance of
the context, is in ' Kthica,' part ii.
prop. 7 : " Ordo et connexio ide-
arum idem est ac ordo et connexio
rerum."

'Leibniz, as Huxley {loc. cit.)
tells us, also invented the term
" automate spirituel " and appplied
it to man.

* Du Bois - Reymond, in his
"Kloge" of Johannes Miillei", iias
shown that the principle of reflex
action dates back to Descartes,
wlio also introduced the term re-

flex. Next in time cauie Willis
('De motu muscular!,' Amsterdam,
1682). The subject seems to have
been overlooked to such an extent,
(1784) got for a
credit of having
notion of reflex
his work had to

that Prochaska
long time the
established the
action, and even

be rediscovered by Eduard Weber
(1846), after the principle of the
transition of a reaction from the
afferent to the efferent nerves in
the central organs had been prom-
inently put forward bv Legallois
(1811), Marshall Hall ('1835), and
Johannes Miiller (1835). In more
recent times, Prof. Pfliiger's '' Laws
of Keflex Action," and his and (i.
H. Lewes's theory of the jiresence
of consciousness in the si)inal cord,
liave formed the subject of much
discussion and much expeiimental
work. A good historical account
will be found in the 13th Lei'on
of M. Ch. Hichets ' Physiologie
des Muscles et dos Nerfs ' (Paris,
1882), and a discussion of the whole
subject in Prof. Wundt's ' Physi-
ologische Psychologic,' ch. xxi.,
where especially the difference be-
tween automatic and reflex move-
ment is brought out.

520

SCIENTIFIC THOUGHT.

of eminence, Huxley and Clifford/ have made the theory
accessible to the popular understanding, without, however,
taking a comprehensive view of the study of mental
phenomena, inasmuch as they approached the subject
from the side of natural science — the former more from
that of physiology, the latter from that of the mechanical
sciences. Prof. Wundt treats the subject exhaustively
in many passages of his works, notably in the last
chapter of his great w^ork on ' Physiological Psychology,'
in which he broadly defines " the psycho-physical view
as that view which starts from the empirically well-
established thesis, that nothing takes place in our con-
sciovisness which does not find its foundation in definite
physical processes. The simple sensation, the connection

^ Although neither Huxley nor
Clifford added anything new to the
conception of parallelism as con-
tained in the writings of many ear-
lier Continental philosophers, the
fact that they were driven from
their purely scientific positions to
discuss the subject, and were not
psychologists and metaphysicians
by profession, gave their exposi-
tions, which are otherwise as fresh
as they are immature, a peculiar
charm. Being both masters in
style, they at once enriched the
vocabulary with new terms which
have since become classic. The
word "epi-phenomenon," an equiv-
alent for tlie German ' Begleit-
erscheinung,' which is of independ-
ent origin but expresses Huxley's
view, is a real enrichment of
thought. It is also the direct
way to bring home the absurdity
of the whole theory. The things
of nature being first considered
as "phenomena" — i.e., as "ap-
pearing" to some one, — the some
one is next looked upon as a
secondary phenomenon, an epi-

phenomenon. Clifford actually in
liis psychological atomism goes the
length of saying, " Reason, in-
telligence, and volition are pro-
l^erties of a complex which is made
up of elements, themselves not
rational, not intelligent, not con-
scious " fsee ' Mind,' vol. iii. p. 67).
In the physical theory of atoms it
has been truly said that you cannot
get anything out of the atoms that
you have not, to begin witli, put into
them. Clifford's dictum reminds
one of Carlyle's definition of the
object of political economy, which
has to solve the problem, " Given
a community consisting of fools and
knaves, how to produce efficiency
and honesty by their comliined
action ?" Clifford's solution of the
psychological deadlock is the " Mind-
stuff" theory, the theory that all
matter is the phenomenal correlate
of the elements of mind. Clif-
ford's essay " On the Nature of
Things in themselves" is reprinted
in ' Lectures and Essays ' (1879),
vol. ii. p. 71 sqq.

ox THE PSYCHO-PHYSICAL VIKW OF NATURE. 521

of sensations and peicepLions, Liieir associations, linally,
the processes of apperception and volition, are acconi-
])anied by physiological nerve -processes. Other bodily
processes, such as the simple and complex reflex actions,
do not enter directly into consciousness, Itut they
form important auxiliary processes of tlie phenomena of
consciousness."^ It is, accordingly, (|uite consistent,
from a purely scientiiic })oint of ^■ie^v, to test this
central conception of exact psychology, and to refrain
from introducing any purely psychical conceptions so
long as the possibilities of the conception, that mental
phenomena are only concomitant occurrences of changes
which take place in the nervous system and centres,
have not been exhausted. Investigations, with or
without this definite purpose, have been very largely
prosecuted in the course of the nineteenth century, and
have been in part purely anatomical, in part physio-
logical, the latter again either referring to pathological
or to normal cases. Systematic courses of experiments
have been begun at Leipzig and taken up, according to
a well-defined special programme, by I)r Miinsterberg at .%.

Miinster-

Freiburg, wlio in the researches of his laboratory has, berg,
more distinctly than any other philosopher, adopted the
theory as a working hypothesis.^

i ' Physiologisclie Psychologic ' (4
Aufl.), vol. ii. ]). 644.

- The principal writings of Dr
MUn.sterberg, in which his psycho-
jihy.sical researclies are contained,
are: 1, 'Die Willenshandlung,'
Freiburg, 1888; 2, ' lieitnige zur
Experiinentellen Ps}'chol()gie,' 4
parts, 1889-92 ; 3, ' Ueber Aufgaben
und Methodeii der P.-<yciiologie,'
being part 2 of the 'Schriften der

Gesellschaft fiir Psychologi.sdie
Forsehung,' 1891. These writings,
altiiough starting from the position
I)repared by the Leijizig school of
j)sycho-p!iysical reseaicii, are largely
]i()leniiial, and directed against
some of Prof. Wundt's principal
theories. They have received a
considerable amount of attentinn
in Germany and America and in
this country, and also a good clcal

522

SCIENTIFIC THOUGHT.

It can hardly be said that this course of study has
done more than make a start, and even those who are
incHned to consider it a very one-sided attempt are
bound to admit that it has a promising future. Thus
Prof. Wm. James, whose ' Principles of Psychology ' treat
of the subject from many and very different points of
view, refers to these experiments in a characteristic
passage as follows : " Within a few years, what one
may call a microscopic psychology has arisen in Germany,
carried on by experimental methods, asking of course
every moment for introspective data, but eliminating
their uncertainty l^y operating on a large scale and taking
statistical means. . . . Their success has brought into
the field an array of experimental psychologists, bent on
studying the elements of mental life, dissecting them
out from the gross results in which they are embedded,
and, as far as possible, reducing them to quantitative
scales. . . . The mind must submit to a regular siege, in
which minute advantages, gained night and day by the

of opposition. The late editor of
' Mind,' Prof. Croom Robertson,
reported pretty fully upon Miinster-
berg's work in the 15th volume
of the fii-st series of ' Mind,' and
drew especial attention to the
confirmation which certain views
contained in the writings of the
British Associationist school have
received through Dr Miinsterberg's
expositions. Prof. E. B. Titchener
criticised Dr Miinsterberg's ex-
periments and theories somewhat
severely in the 16tli volume of the
first series of 'Mind,' p. 521 sqq.
As the subject is still under dis-
cussion, and as in more recent writ-
ings of Dr Miinsterberg, who is now
professor at Harvard University,
his studies? have shown quite a

different side from that exhibited
by the above-named earlier writ-
ings, it is impossible in this history
to do more than refer to them
as marking a distinct phase in
modern psycho - physical thought.
It does not appear that Prof.
Wundt agrees with much of the
outcome of the important move-
ment he originated ; see his article
in ' Philosophische Studien,' vol. vi.
p. 382, and a very valuable pajDer by
Prof. J. AVard ('Mind,' 2nd series,
vol. ii. p. 54 aqq.), entitled "Modern
Psychology : a Reflexion. " As these
discussions refer more to the philo-
sophical value than to the jaurely
scientific a.spect of psycho-physics,
they would lead us beyond the
regions of purely scientific thought.

ON THE PSYCHO-PHYSICAL NIKW OF NATURE. 523

forces that hem her in, resolve themselves at last into
lier overthrow. There is little of the grand style about
these new prism, pendulum, and chronograph philo-
sophers. They mean Imsiness, not chivalry. What
generous divination and that superiority in virtue which
was thousiht bv Cicero to irive a man the best insight
into nature have failed to do, their spying and scraping,
their deadly tenacity and almost diabolical cunning, will
doul)tless some day bring about. , . . The experimental
method has quite changed the face of the science, so far
as the latter is a record of the mere work done."

Tt is, however, only fair to remark that it has never
been the ol)ject of any science, and can, tlierefore, no
more be the object of exact psychology, to deal with
everything at once, and that psycho-physical science has
quite as much right to postpone the question, AVhat is
mind ? ^ as Inological science has had to postpone, or
even to eliminate, the question, AVhat is life ? P.ut tliis
comparison reveals also the essential difference between
the exact science of life and tlie exact science of mind.
Of life we know only througli the observation of living
l)eings, but of mind we have not only the apparent
knowledge of its unity, which introspection forces upon

1" Sensation, Retentiveness, As- ' shocked at Lange's 9/io« about a psy-
sociation by Contit;uity, — these are j clioh)gy without a soul, but the

to bo our ultimate and sufficient
psychological conceptions : tiic
facts of feeling and conation are
resolved into facts of sensation ;

' modern ' psychology is a psychol-
(jgy without even consciousness.
' Content of consciousness' as much
as you like, but consciousness itself,

and all mind-processes held to lie ci.nsciousness as activity, is not our

not merely conditioned, but ex- affair ; we leave tliat to nietaphy-

plaineil by brain-processes, which sics, say our 'modern' teachers."

they accompany as epi-phenomena (Pi-of. J. Ward, on " Modern P.sy-

or 'Begleit-erscheinungen.' It is chology," 'Mind,' 2nd series, vol. ii.

not 80 long since the world was p. 5.'j).

tion

524 SCIENTIFIC THOUGHT.

US, but we have also a large array of external facts which
have been appropriately defined by the term " the ob-
jective mind." There are, in fact, two properties with
which we are familiar through common-sense and ordin-
ary reflection as belonging specially to the phenomena
of our inner self-conscious life, to the so-called " epi-
phenomena" of the higher organic or nervous systems,
and these properties seem to lie quite beyond the sphere
and the possibilities of the ordinary methods of exact
37. research. The first of these properties is the peculiar

Phenomenon

ofcentraiisa- unity exhibited by the higher forms of organic existence,
and still more evident in the phenomena of mental or
inner life. Instead of unity, it might perhaps be better
to call it centralisation. Now, the more we apply mathe-
matical methods, the more we become aware of the im-
possibility of ever arriving at a comprehensive unity by
adding units or elements together. The sum of atoms or
molecules, however artfully put together, never exhibits
to our reasoning that appearance of concentration which
the higher organisms or our conscious self seem to exhibit.
In this circumstance lies the difficulty of ever arriving at
any really satisfactory definition of life — which definition
eminent physiologists have, as we have seen, felt com-
pelled ultimately to relegate to the realm of the idea.
In the last chapter I showed how modern research into
the phenomena of life has impressed upon our thoughts
the ubiquity, the continuity, and the unique character or
singularity of life, without being able to fix upon any one
satisfactory mechanical definition of life. But as we
ascend in the scale of living things we become aware of
another property : they are centred — i.e., they exhibit a

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 525

si)eci;il kind of unity whicii cannot be detined, a unity
which, even when apparently lost in the periods of nn-
cunsciousness, is able to re-establish itself by the wonder-
ful and indefinable property called " memory " — a centre
whicli can only be very imperfectly localised — a together
which is more than a mathematical sum ; in fact, we rise
to the conception of individuality — that which cannot
be divided and put together again out of its parts.

The second property is still more remarkable. The
world of the " epi-phenonicna," of tlie inner processes
which accompany the highest forms of nervous develop-
UKMits in human beings, is capable of unlimited growth;
and it is capable of this by a process of becoming ex-
ternal : it becomes external, and, as it were, perpetuates ss.

ij.., ,. . 1 ,.,. Extenialisa-

itselr in language, literature, science and art, legislation, tionand

° ° ' ' ° ' growth of

society, and the like. We have no analogue of this in "''"'^■
physical nature, where matter and energy are constant
quantities, and where the growth and multiplication of
living matter is merely a conversion of existing matter
and energy into special altered forms without increase or
decrease in quantity. ]>ut the (iuantity of the inner
thing is continually on the increase ; in fact, this increase
is tlie only thing of interest in the whole world.

Now, no exact scientific treatment of the phenomena
of mind and body, no psycho-physical view of nature, is
complete or satisfactory which passes by and leaves un-
defined these two remarkable properties of the inner life,
of the epi-phenomena of nervous action, of consciousness.
And it seems to me that Prof. Wundt is the only psycho- 30.

Wuiulf.s

physicist who, starting from science and trying to pene- treatment or
trate Ijy scientific methods into the inner or psychic i"'"i''«"'-

526

SCIENTIFIC THOUGHT.

world, has treated the subject comprehensively, and fairly
and fully tried to grapple with these two facts peculiar
to the inner world- — its centralised unity and its capacity
of unlimited growth through a process of externalisation.
He has done so by his philosophical theory of " ap-
perception and will," and of the " growth of mental
values," two conceptions which lead us into the realm
of philosophical thought.-'^

But, before closing this chapter, which deals with the
study of the phenomena of an inner life and the inter-
action of body and mind by the methods of exact research,
it is well to note that long before psychology existed as
a natural science, a large amovmt of knowledge had been
accumulated by a different method. Especially in this
country— ever since the time of Locke — there has existed
a very large and influential school of thinkers who studied
the inner phenomena by what has been appropriately
termed the inner sense ; every observer recording his
own inner experience and leaving it to others, by doing
the same, to confirm or correct his statements. Psy-
chology, carried on through self-observation or by the

^ It would serve no good pur-
pose to string together a list of
quotations from Prof. Wundt's
voluminous writings in which these
two central ideas of his ^jhilosophy
find expression, especially as there
is no one passage to be found in
which his highest abstractions and
final conclusions find an adequate
expression, still less one which could
be conveniently rendered in the
English language. KiJnig has, it
seems to me, done much to make
Wundt's view more easily under-
stood, and I must content myself
at present with referring to his little

volume, notably to the extracts
given on pp. 134, 141, and 167,
which explain more cle.arly the
theory of apperception and will.
On the theory of the " growth
of mental values," see especially
Wundt, ' System der Philosophie '
(2 Aufl., pp. 307, 596), "Mental
life is, extensively and intensively,
governed by a law of growth of
values : extensively, inasmuch as the
multiplicity of mental developments
is always on the increase ; inten-
sively, inasmuch as the values
which appear in these develop-
ments increase in degree" (p. 304).

ON THK PSYCHO-PHYSICAL VIKW OF NATCKE. 527
introspective method, liad grown to large dimensions in 40.

Iiitros]<ec-

Scotland and in England, long Ijefore Herbart and Beneke t'^t methou.
in Germany gave it a similar direction. In fact, most
of the writings of the introspective school in Germany,
which dates from the midille of the centnry, is con-
cerned with the material accumnlated by Ikitish psycho-
logists. And even the psycho -physical method itself
would carry us only a little way if its results and obser-
vations could not continually be checked, supplemented,
antl interpreted l>y what we already know by introspec-
tion. One of the foremost representatives of the Eng-
lish school of psychology has said, and many will agree
with him,^ " In our desire to know ourselves — to frame
some conception of the flow of our feelings and thoughts
— we work at first by introspection purely; and if at a
later stage we find means of extending and improving
our knowledge, introspection is still our main resort — the
Alpha and Omega of psychological inquiry : it is alone
supreme, everything else sul)sidiar\'. Its compass is ten
times all the other methods put together, and fifty times
the utmost range of psycho-physics alone."

A history of Thought must accordingly contain some
account of the view wdiieli our century has taken of the
introspective method and the value of the inner sense as
a means of enlarging our knowledge." This discussion

' See Prof. Bain's e.s.^aj- in ' ^liml,' , states, has been not onlj- to develop

2n(l series, vol. ii. p. 42: "The
respective Spheres and mutual
Helps of Introspection and Psy-

a clearer view of physiological psy-
chology, but also to define more
cleaily the object of psychology

cho-physical E.xperimcnt in Psy- | proper — that is, of the science

cliology." I which deals with the facts revealed

" One result of the modern psycho- | by introspection. When, in the

l)hysiual view, or of the doctrine of middle of the century, the physiol-

liarallelism of physical and mental ogy of the senses attracted the

528

SCIENTIFIC THOUGHT.

will, in a future volume, form one of the appropriate
links which join science to philosophy — which lead us on
from exact to speculative thought. At present I have
to refer to another and very extensive field of research,
into which the natural as well as the speculative
philosopher have been led from opposite sides, and which
especially affords a hopeful prospect for an enlargement
of the psycho-physical view of nature. If the natural
philosopher cannot consistently and fairly enter into the
mysteries of an inner consciousness from which his
opponent — the speculative philosopher- — starts, he may
perhaps do so l^y a roundabout way or a side-door.

As I stated above, the inner world, the psychosis,
which intermittently accompanies the neurosis, the epi-

attention of psychologists in all the
three counti-ies, it became custom-
ary to introduce purely psycholog-
ical treatises by an exiDosition of
the psycho-physical relations, in-
troducing into psychology chapters
from phj^siology. The consequence
of this has been that modern works
on psychology have grown to in-
ordinate length, and frequently ex-
hibit a dual aspect and method.
Quite recently it has therefore been
insisted on that psychology can be
written either from the physio-
logical or from the purely psycho-
logical point of view. A good ex-
ample of the latter is Prof. G. F.
Stout's ' Analytic Psychology ' (2
vols., 1896). "Physiological re-
sults," he says (vol. i. p. 37), "are
likely to be valuable onlj' in pro-
portion as they are controlled and
criticised by psychological analysis.
This holds good apart from con-
sideration of such metaphysical
questions as whether the brain-
process is the sole real agency, and
consciousness a mere function, or
consequence, or epi • phenomenon ;

or whether consciousness is the
reality of which the correlated
brain-process is a phenomenon, or
whether they are two asi>ects of
the same fact. Whatever may be
our attitude to such questions, the
psychologist has still his own work
to do on his own lines ; and for the
sake of physiology itself, so far as
it entertains the hope of throwing
light on the mechanism of brain -
processes, he must attempt to do
it. It is idle to require psj'chol-
ogy to wait for the progress of
physiology. Such a demand is
logically parallel to a demand that
historj' or biography, or the prac-
tical estimate of character and
anticipation of men's actions in
ordinary life, shall come to a stand-
still until they have a sufficient
physiological basis. On this view,
Carlyle should have abstained
from writing his ' French Revol-
ution,' because he did not know
what precise configuration and
motion of brain particles deter-
mined the actions of the mob who
stormed the Bastille."

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 529

phenomenon which lies on tlie other side of Llie phe-
nomenon, is not only characterised by a peculiar unity or
centred connectedness whifli we look for in vain in the
external and physical world; it has also become external 4i.

^ "^ , The"objec-

or objective, it has detached itself from the sul)jective tivemind."
and hidden source from w^hich it sprang, and can be
studied as such in the great creations of language, litera-
ture, society, science, art, and religion. Why not study
its nature and its life in these great and undeniable
manifestations, and instead of beginning at the hidden
source, the unknown and indefinable centre, try to reach
this by beginning at the periphery, measuring out the
great circle and learning what it contains ?

Ancient philosophy, which found its consummation in
the writings of Aristotle, had already begun this work,
and, in establishing the rules of grammar and logic, had
furnished the material for many modern speculations.
"What the ancients had only begun, modern thinkers of
the most opposite schools have been induced to continue
on more methodical lines, and with the more or less
distinct object of learning something definite regarding
that mental life and unity whicli they have, with little
success, tried long enough to reach by various direct
roads, such as introspection, speculation, physiological
and psycho-physical experiment. Accordingly we find
springing up almost simultaneously in the three coun-
tries, ever since the latter part of the eighteenth century,
the study of mankind or of human culture in all its
historical forms. Hume and Adam Smith, Montesquieu,
and the French physiocrats, studied society and tlie great
falnif of industry and commerce; Cabanis and the " Ideo-

Vf)!,. II. 1* L

530 SCIENTIFIC THOUGHT.

logiies " pointed to the importance of the philosophical
study of language and grammar ; the idealistic school in
Germany ended by leading to the study of the objective
mind in history, art, and philosophy ; the school of
Herbart in Waitz, Lazarus, and Steinthal led into
" Volkerpsychologie " and " Sprachwissenschaft " ; and it
is well known how in our days the synthetic philosophy
of Mr Herbert Spencer in England has entered on the
study of sociology on the large scale. We hear on all
sides of natural histories of mankind, of society, of re-
ligion, &c., and they appear either in the modest attire of
the other and older natural histories which we have been
accustomed to, preparing the ground by patient and un-
biassed collection of facts, or they attach themselves to
certain philosophical theories, such as are furnished by
the dialectics of Hegel, or by the evolutionary doctrine of
Darwin and Spencer, in connection with which we shall
meet them in a future section of this work. For it has
been found here, as it had been in the older natural
histories, that the accumulation of facts and materials
was of little use unless some leading idea was at hand
by which it liecame possilile to regulate and arrange
them.

Thus we see how the psycho-physical problem — the
question of the interaction of mind and body, of soul and
nature, of the inner and the outer worlds — is being
attacked from two entirely different sides, — from the
side of the individual and from that of the collective
life of the human being : the mental principle is being
studied in its inner and hidden existence as the unifying
and centralising factor of individual life, or in its ex-

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 531

teinul numifestiitioiis in history, society, science, art,
industry, and religion, — in fact, in the history of culture
and civilisation. If Bishop Berkeley has, with some
propriety, been called " the historical starting-point " of
psycho-physical investigation of the first kind, the im-
portance of that of the second and wider kind is
nowhere more clearly and definitely expressed than —
over a century ago — in the writings of Johann Gott- its study
fried Herder.^ His influence in this direction was very uercier.

* The influence of Herder (17-14-
1803) on German literature and
tliought was fully acknowledged by
his contemjjoraries, as is testified
liy the frequent references to him
in the biographies of nearly all the
eminent men who lived at the end
of the eighteenth and the beginning
of the nineteenth centuries, as also
in the voluminous correspondence
which he carried on with many
eminent contemporaries. Had it
not been for the overjioweiing and
one-sided influence which the criti-
cal, and, later, the transcendental,
schools of thought gained, not-
ably at the German universities,
Herder's ideas would have been
more generally acknowledged as
forming, to a very great extent,
the starting-point of many lines of
researcli which were not exclus-
ively controlled by the ruling
philosophies, and which gradually
and imperceptibly united at a later
date to form the more modern
current of German thought.
Herder was much more allied
with the historical studies refer-
ring alike to nature, literature,
and culture, than with the critical
and metaphysical systems, being
also well acquainted with con-
temporary English thought, as,
inter (tiki, with the curious writ-
ings of Lord Monboddo. Tln-ough
Mfulame de Stai-1, who was in-

timate with Herder, Ids writings
were early known in France,
whereas Carlyle's studies in
German literature, though most
valuable and original in their
way, do not give that prominence
to Herder's writings which they
deserve. In more recent times,
after the indefatigable Diintzer,
through the publication of his
correspondence, had done much
to revive the interest in Her-
der, full justice has Ijeen done
to his great merit bj' Rudolf
Hayni, whose great work, ' Herder
nach seinem Leben und seinen
Werken' (2 vols., Berlin, 1885),
is a i)erfect mine of informa-
tion. The side of Herder's influ-
ence which is not suflicieutly
dwelt on by Haym, but which in-
terests us most at present, — what
we may call his anthropological
view, — had already been exhaust-
ively dealt with by l)r Heinrich
IJoehmer in his little - known
' Geschichte der Entwickelung der
Naturwissenschaftlichen Weltan-
schauung in Deut-ichland ' ((lotlia,
187'i), who especially draws at-
tention to the ])sycho-pliysical ideas
of Herder. It has been truly said
that there is hardly any modern
idea which has found widespread
application that cannot be traced
in the writings of Heidor ; but
Herder liad no method, having

532

SCIENTIFIC THOUGHT.

great, and would have been greater had he not lived at
a thne when the study of the human mind by the purely
introspective or speculative methods had absorbed all
philosophical interest in England and Germany. His
opposition to the (abstract) subjective philosophy of
Kant and Fichte made him unpopular ; he was only
half understood at the time ; and only towards the end
of our century have his ideas been recognised as con-
taining the clear conception of psycho-physics on the
large scale — i.e., of the natural history of humanity, the
genesis and evolution of the objective mind.

Herder was a pupil of Kant during his pre-critical
period. He was still more influenced by great
naturalists like Haller, Buffon, Camper, Sommering,
Forster, and Blumenbach, wlio through physiology, com-
parative anatomy, and ethnology, attempted to bring the
study of the human race and its mental development into
connection with that of the brute creation, of the
surrounding plant-life, of the characteristics of climate
and soil, and of the great natural features of sky and
landscape. He did not believe that we could study
the great forces of nature and mind from inside or in
the abstract — he desired to follow Haller's physiology, to
complete and continue it into psychology. Irritability,-'

characteristically maintained that
method is frequently only a con-
vention, and he was deficient in
critical acumen. The German mind
had to go through the severe dis-
cipline of the school of mathemati-
cal and critical thought, and to
amass an enormous volume of ex-
perimental and historical know-
ledge, before the brilliant concejition
of Herder in his great work ' Ideen

zur Geschichte der Menschheit ' (4
pts., 1784-87) could be partially re-
alised by A. von Humboldt in his
'Kosmos' (1841-59), and by Lotze
in his ' Microcosmus ' (1856-64).
See especially the preface to the
latter.

* See above, p. 471, on a similar
development of Haller's teaching
through Cabanis in France some-
what later in time.

ox THE PSYCHO-PHYSICAL VIEW OF NATURE. 533

tlie higliest pliysical phenomenon of matter, was to Ije
the starting-point of this psychology. In an early
essay on understanding and sensation (1778) he wrote:
" According to my thinking there is no psychology
possible which is not at every step detinite physiology.
Haller's physiological work once raised to psychology,
and, like Pygmalion's statue, enlivened with mind, we
shall be able to say something aliout Thought and
Sensation." ^

But this psycho-physiological view was not limited to
the study of the individual : it widened out and em-
Ijraced the whole of mankind ; nature on a large scale
had to be observed ; historical records had to be collected
on all sides ; origins had to be studied and the elementary
forces followed up in the beginnings of poetry, art, and
religion. Materials were gathered everywhere from his-
torians, chroniclers, travellers, primitive records, and the
" voices of the peoples." All this was to furnish the
materials for a " History of Mankind." " In many

' " Voin Erkemion uiid Emp-
tiiuleii (ler nien.schlichen Seele "
(1778), in the 9th vol. of the
Works of Herder (' Abtheilung
y.ur Philo.sophie uiid Geschichte,'
1828). To give an idea of Herder's
anticipation of modern views, see
J). 10 : •■ We cannot penetrate
deeper into the genesis of sensa-
tion than to tlie reinai-kablc jihen-
onienou called by Haller ' lleiz.'
The irritated fibre contracts and
expands again ; periia])s a 'stamen,'
the first glowing sparklet of sensa-
tion, towards which dead matter
has purified itself by many ste[)S
and stages of mechanism and or-
ganisation."' Many passages could
V)e (juoted from Herder's ' Idecn,'
&c., and other writings, anticijjating

modern Darwinian ideas, such as
those of the struggle for existence,
and even of automatic selection. See
Prof. J. Sully's appreciative article
on Herder in the ' l-'ncyc. Brit.'
(0th ed.), and notably Fr. von
Biirenbach, ' Herder als Vorgiinger
Darwin's' (Berlin, 1877). Hayni
(' Herder,' vol. ii. p. 209) object.s' to
this extreme view of Herder as a
forerunner of Darwin on the ground
that, according to the former, no
animal in its development ever for-
sook that adjustment of organic
forces peculiar to it, nature having
kept each being within the limits
of its type. Accordinglj', Herder's
evolutionism would be moicakinto
that of K. E. von Baer than to
that of Darwin and lliicckcl.

534 SCIENTIFIC THOUGHT.

43. parts," he says/ " my book shows that one cannot as

His 'History ^ ' -^ ' -^

ofMankind.' yet write a philosophy of human history, but that per-
haps one may write it at the end of our century or
of our chihad."

And indeed the whole of our own century has been
busy in carrying out this prophetic programme of
Herder's, consciously as planned by him in Germany —
unconsciously and independently in other countries. As
a counterpart to the introspective labours of Kant and
their followers, a large array of naturalists, historians,
philologists, and ethnologists have in the spirit of Herder
ransacked every corner of the globe and every monument
of history with the distinct object of tracing there the
physical basis and the workings of that inner and hidden
principle which we call the human mind. In doing this,
they or their numerous followers, who belonged to a
generation which knew not Herder, have strayed far away
from the common starting-point, and have frequently lost
themselves in the bewildering details of special research.

44. Above all, in the country to which Herder belonged, a

Separation . . , . ,

of natural Separation set m early m the century between what ha^'e

and mental i xi

sciences. bccu termed the natural and the mental sciences. The
former came more and more under the sway of the
mathematical spirit, which, as I showed in an earlier
chapter, turned the eyes of its votaries away from their
own national scientific literature to that of their neigh-
bours— first to France, latterly to England. The mental
sciences, on the other hand, — history, philology, the social
sciences, — came under the influence of exactly those phil-
osophical ideas which Herder never understood nor assimi-

^ See the preface to the first part of the 'Ideen,' 1784.

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 535

lated : ^ the critical spirit of Kant, and the constructive
canons of his successors, each of these distinct and separate
movements, supplied exactly what was wanting in the
prophetic, not to say dithyrambic, utterances of Herder ;
they supplied coherence and method. Earlier chapters
of this book have shown how the mathematical spirit
has permeated and revolutionised the natural sciences,
and latterly how it has, in the science of psycho-physics,
led philosopliers l)ack to the problem which Herder had
adumbrated at the end of the previous century. A
second large department of my task will consist in
showing how what in Germany are called the mental
sciences have been developed independently of the
natural sciences, liow the studv of the mind as such —

' During the latter part of his
life Herder was occupied to a great
extent witli those jiublications in
which he gave expression to the
opposition which he consistently
maintained to the critical writings
of his master Kant. His two princi-
l)al works referring to this are 'Eine
Metakritik zur Kritik der Heinen
Vernunft' (2 parts, 1799) and 'Kal-
ligone' (1800). Kant had reviewed
the first volume of Herder's greatest
work, tlie ' Ideen,' anonymously,
criticising the absence of logical
acumen and clear definitions, and
also the attempt towards a genetic
as opposed to a critical treatment
of the intellect, the former being
an enterprise "which transcends
the powers of human reason, whe-
ther the latter gropes with physi-
ology as a leader, or attempts to
soar with metaphysics." In the
second part of the ' Ideen ' If erder
had taken up a polemical attitude
to Kant's teacliings, and Kant had
.igain reviewed it, dwelling upon
the uncritical maimer in which
Herder had built up his hypotheses

on unsifted material gatiiered from
all sides. In the ' Metakritik '
Herder, irritated by what he con-
sidered the arrogance of the Kant-
ian school, undertook to put into
systematic form his criticism of
Kant's principal work, following
to a great extent the suggestions
thrown out l)y a mutual friend of
himself and Kant, .lohann Georg
Hamann (1730-80), and falling back
upon the earlier philosophies of
Spinoza and Leiljniz on the one
side, and upon the common-sense
philosophy of the Scottish school on
the other, seeking for a solution
of the problems i-aised by both,
not in abstract reasoning, but in
the realism of the concrete and tlie
historical sciences. In tlie ' Kal-
ligone,' Herder similarly attacks
Kant's rcsthetical philosopliy ('Kri-
tik der Urtheilskraft,' 1790), which
had been enthusiastically received
in Herder's immediate neighbour-
hood by Scliiller. A full account of
these controversies will be found in
the 2nd vol. of Haym's work.

536

SCIENTIFIC THOUGHT.

in its individual and collective existence — has proceeded
when separated from that of nature. This survey will
start with exactly that movement of thought which was
so distasteful to Herder, the critical inquiry of Kant,
and it will follow this up to the point when in our days
a junction has again been attempted, not unlike in spirit
to that dreamt of by Herder, though very much more
accurate and precise in method. There is, moreover, one
special problem where this has been markedly the case ;
one phenomenon stands out pre-eminently ; it belongs
equally to the realm of nature and of mind. After
being independently attacked by philosophers, naturalists,
travellers, philologists, and latterly by physicists, it has
revealed itself as the psycho-physical problem 'par ex-
cellence ; and it is exactly that which Herder himself
45. treated with special attention. This phenomenon is that
of language, of human spccch — the problem of language.-^

^ The problem of language and
the question of its origin inde-
pendently occupied thinkers in the
three countries in the latter half of
the eighteenth century. In France
the followers of Locke, notablj-
Condillac (' Essai sur I'origine des
connaissances humaines,' vol. ii.),
wrote on the subject, while Rousseau
opposed them ('Sur I'inegalitd
parnii les homines,' 1754). In
Germany the Pastor Siissmilch, of
whom I shall have more to say in
the next chapter, wrote an elab-
orate work to prove the divine
origin of language ( ' Beweis dass
der Ursprung der Menschlichen
Sprache Gottlich sei,' Berlin, 1776).
In order to settle the question the
Academy of Berlin offered, in the
year 1769, a prize in the following
terms : " En supposant les hommes
abandonn(5s a leurs facultes natu-

relles, sont-ils en dtat d'inventer
le langage ? et par quels moj^ens
parviendront-ilsd'eux-memesixcette
invention ? " a problem wliich Her-
der characterised as a " truly philo-
sophical one, and one eminently
suited for me." He had already —
following Hamann — thought much
about the subject, and lie proposes,
in his prize essaj-, which was sub-
sequently crowned by the Academy,
" to prove the necessary genesis of
language as a firm philosophical
truth." A short time after Her-
der had written his essay (1771),
there appeared in England, by
James Burnett, Lord Monboddo, a
work ' On the Origin and Progress
of Language' (1773), in which he
refers to the ideas of James Harris
in his work ' Hermes ; or a Philo-
sophical Enquiry concerning Lan-
guage and Universal Grammar'

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 537

In no department of knowledge has the scientific
spirit worked a greater change than in the science of
hmguage. "Witli tlie exception of suggestions by Leibniz,
who clearly saw the necessity of founding the theory of
language on a broader basis than the small number of
classical and modern tongues then current attbrded,
and of some glimpses of a corrector view such as those
contained in the much ridiculed writings of Lord Mon-
boddo, we find, up to the end of the eighteenth century,
hardly any attempt towards a metlKKlieal treatment of
the great problem. Philosophical theories and vague
etymologies, amounting frequently to little more than
punning with words, brought the subject into ridicule.
Herder has the great merit of having uryed the im-
portance of the study of language and literature in
primitive forms ^ as the great gateway into anthropology

(17r)l\ The question attracted con-
siderable attention, partly through
the eccentricities of Lord Mon-
boddo, of which it has been well
said that they appeared more
ridiculous to his own than thej-
would to the present age, partly
through the controversy which
arose shortly after on the publi-
cation of Home Tooke's celebrated
'"ETTfa TTTtpoevTa, oi- the Diversions
of Purley' (1786). Herder was
acquainted with Monboddo's work,
having occasioned a translation of
it to be made and written a i)reface
(1787) ; but he does not seem to
have taken anv notice of Home
Tooke (1736-1812), who, as the
historian of the science of lang-
uage (Theodor Beufey, 'Geschichte
<ler Sprachwissenschaft,' Miinchen,
1869) siiys, would, for his novel
ideas and method, deserve to be
jjut at the entrance of the modern
linguistic epoch, had lie been able

to avail himself of a knowledge of
Sanskrit.

' This refers to the second great-
est work of Herder, his collec-
tion of popular songs, published
under the significant title of
" Voices of the Peoples " (' Stimmen
der Volker in Liedeni,' 1778), a
work which had the greatest in-
fluence on German literature as
w^ell as on modern j^hilological
studies. See Benfey, loc. cit., p.
316, &c. That the publication of
the ' Percy Ballads ' (1765), of Mac-
pherson's ' Ossian.' and of Lowth's
' Lectures on Hebrew Poetry '
(17.'J3), formed a great stimulus to
Herder in his historical and poetical
studies is shown by Haym in many
extracts and passages, also in the
prefaces of Herder him^^elf and of
his editor, .Toil, von Midler (Herder's
■ Werkc' 1828, • Zur .--choncn Liter-
atur und Kunst,' vols. vii. and viii.)

538 SCIENTIFIC THOUGHT.

and the science of humanity. Through his writings
there rose two distinct views both fruitful for thought, the
philosophico- historical and the strictly scientific. His
immediate successors, or rather those who unconsciously
imbibed the spirit of liis writings, took up the former
line. The great development of classical philology in
the school of Wolf, the discovery of Sanskrit and the
new field of oriental philology, for a time threw the
purely scientific aspect into the backgrovmd. Yet at
the same time with Wilhelm von Humboldt and his
philosophical interests in comparative philology, we find
his brother Alexander giving a large share of his
attention to the unknown languages of the New World,
of which he has been called " the scientific discoverer."
46. But the real beginnings of an exact treatment of the

Its exact

treatment, problem of spcech were laid by one who did not come
under the conscious influence of Herder, though he came
under that of Goethe. By Johannes Mliller it was
carried further, and it was completed by some of his
most illustrious pupils and followers — Bonders, Briicke,
Helmholtz, and Czermak of Vienna. Through the
anatomical and physiological labours of these and other
naturalists, joined to the physical analysis of musical
notes and sounds contained in the great work of
Helmholtz on Acoustics, aided by such instnunents as
the laryngoscope or throat-mirror, and the wonderful
inventions of the phonograph and phonautograph, the
organ of speech is now known to be a complicated wind
instrvmient by which pure notes and an almost infinite
variety of nasal, labial, dental, palatal, guttural, and other
sounds can be produced which form the phonetic ele-

ox THE PSYCHO-PHYSICAL VIKW OF NATURE.

139

iiients of s])eeeh. Sinmllaneously the discovery Ity Broca,
ill ISGl, (if the speech centre in tlic lirain marked an
epoch on the physiological side.^ A new science, called
riionetics or Phonology, has sprung up, and is now
universally admitted to have created the modern science
of language." In addition to this physiological and
physical basis, the superstructure of the science of

47.
I'honetics.

' Thi.s localisatiou placeti the
speech centre in "a very circum-
scribed portion of the cerebral
h.emispheres, and more especially
of the left. This portion is situate
on the upper edge of the Sylvian
Fissure, opposite the island of
Keil, and occupies the posterior
half, probably only the posterior
third, of the third frontal convolu-
tion "' (Broca, ' Bulletins de la
Socicte anatomique,' ISGl). The
discovery resulted from the ex-
amination of the brain of patients
who had been afflicted with '"aph-
asia," which is accompanied with
'"a lesion of the posterior half of
the third, left or right, frontal con-
volution, nearly always — nineteen
times out of twenty — of the left
convolution." The phenomenon
of aphakia has ever since been
one of the great psycho-physical
problems bringing together the
most refined and intricate i>hysi-
ological, psychological, and linguis-
tic analyses. To begin with, we
have to distinguish motor aphasia
and sensory aphasia. " Our know-
ledge of this disease has had three
stages : we may talk of the period
of Broca, the period of Wernicke,
and the period of Cliarcot. Wer-
nicke (1874) was the first to dis-
criminate those cases in which the
patient cannot evfti undcrKtand
speech from those in wliich he can
understand, only not talk ; and to
ascribe tlie former condition to
lesion of the temporal lobe. The

condiliou in question is ivord-diaf-
ness, and the disease is auditonj
aphasia. . . . The minuter analy-
sis of the facts in the light of
individual differences constitutes
Charcot's contribution toward?^
clearing up the subject " (James,
' Principles of Psychology,' vol. i.
p. 54).

- In the modern science of lan-
guage we have one among the
many cases where a historical or
philosophical science is becoming
an exact science by attaching itself
to physics and physiology. On
the other side we have the great
movement initiated by Darwin iu
the purely natural sciences, which,
as was shown above, relies on the
historical collection of facts and
the judicious critical sifting of evi-
dence. " It is phonology," says
Prof. Sayce (' Introduction to the
Science of Language,' 2 vols., ISSO,
chap, iv.), " which has created the
modern science of language, and
phonology may therefore be forgiven
if it has claimed more than right-
fully belongs to it or forgotten that
it is but one side and one branch
of the master science itself. . . .
It is when we pass from the out-
ward vesture of speech to the
meaning which it clothes, that the
.science of language becomes a his-
torical one. The inner meaning
of speech is the reflection of the
human mind, and the devek)i>ment
of the luniKui mind must be stud-
ied historicallv."

540

SCIENTIFIC THOUGHT.

language has likewise been stated to be no longer a
historical or a philosophical, but to have become a
physical, science. It is true that, as with other natural
sciences, so also in this case, the morphological, genetic,
and biological aspects can be specially studied ; also
analogies can be drawn between geology and glossology
as to their mode of inductive reasoning. The great
authority who first took up this novel position w^as the
late Prof. August Schleicher of Jena, and the same has
to a great extent been simultaneously adopted by Max
]\Iuller in his celebrated ' Lectures on the Science of
Language.' It is interesting to note that Schleicher
wrote on the ' Morphology of Language ' in the same
year in which the ' Origin of Species ' appeared, and that
he recognised very early the importance of Darwin's
work for the science of language.-^ This became still
more evident on the publication, twelve years later,
of the ' Descent of Man,' and of ' The Expression of the

1 On August Schleicher (1821-
68) see a very valuable article in
the 'Allgemeine Deutsche Bio-
graphic' (vol. xxxi. p. 402 sqq.) by
Johannes Schmidt. Very different
currents of modern thought, such
as we shall in the sequel frequently
have to represent as opposed to
■each other, the study of the classical
and of the modern languages, of
critical and comparative philology,
the historical and the exact spirit,
Hegelianism and Darwinism — i.e.,
logical and mechanical evolution
— the influence of Grimm, Ritschl,
and Bopp, of botany and gram-
mar, combined to generate in this
remarkable man the conception
of linguistic as a natural science
in contradistinction from phil-
ology as a historical science. The

principal works in which he de-
veloped his original view were :
'Die deutsche Sprache ' (1860);
' Compendium der vergleichenden
Grammatik der indogermanischen
Sprachen' (1861); 'Die Darwin'sche
Theorie und dieSprachwissenschaft'
(1863) ; and ' Ueber die Bedeutung
der Sprache fiir die Naturgeschichte
des Menschen ' (1865). Schleicher's
ideas have been taken up in France,
notably by Abel Hovelacque ('La
Linguistique,' 4^'"^' ed., 1857), who
says of him that "he had com-
pletely liberated himself from meta-
physical aspirations" (p. 6). On
the one - sidedness of the purely
jjhysical theorj' of language see
Sayce, ' Introd. to the Science of
Language ' (1880), vol. i. p. 76,
&c.

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 541

Emotions in Man and Animals ' a year after. Tiiese
\vritings did more than any others to impress upon
jihilosophers the genetic or historical view, the existence
of an unln'oken chain or transititjn from the lower to the
liigher and the liigliest forms of animal structures, and
culminated in the well-known expression of Darwin, that
' in a series of forms graduating insensibly from some
ape-like creature to man as he now exists, it would he
impossible to fix at any definite jjoint when the term
* man ' ought to be used." ^ This dictum has been the
theme on which endless variations have been played
down to the present day — Prof. Ernest Haeckel's address
to tlie Congress of Zoology at Cambridge in 1898 being
the latest summary of tlie physical aspect of the proldem.
But the problem has also a psycho-physical side, and this
aspect is concentrated in the problem of language. Even
those philologists who, like August Schleicher and I\lax
Miiller, look upon the science of language as a natural
science, bring in at this point tlie accumulated and
weighty evidence of the historical, psychological, ami
})hilosophical researches into the growth and development
of human speech and human thought, as absolutely
negativing the possibility of a gradual transition from the 4S.

Tlie dividing

brute to the Innnan creation. To the latter, language, Hne between

° ° man and

which he considers to l^e the union of definite concepts '^™^'^-
with definite names, is the liubicon which cannot be
crossed," tlie chasm which (li\i<les that ]K)rtion of the

^ 'Descent of Man,' 1st ed., vol.
i. p. 23.'^.

- See :^Iiix Miiller, ' The Science
of Thouf^lit,' piixxim, notably chap.
iv. p. 177, where he (juotes and
maintains his dictum of 1861 ( ' Lec-

tures on the Science of Language,'
vol. i. p. 403) : " Language is our
Rubicon, and no biute will dare to
cross it." Referring to Schleicher,
he says (p. 164) : " Professor
Schleicher, though an enthusiastic

542 SCIENTIFIC THOUGHT.

living creation which is capable of an unlimited develop-
ment and an external realisation of its inner life from
that which has no mental history or development : it is
the point of discontinuity in the physical development.
The study of language in its physical and mental aspects
— i.e., in phonetics and in sematology — affords, accord-
ing to this view, the only means of penetrating from
outside into the inner w^orld of thought : it is the
psycho-physical problem par excellence- — ^the " Science of
Thought."

Inasmuch as in this latest development of psycho-
physics the whole of the accumulated material and
most of the arguments have been drawn from the his-
torical and philological researches of such thinkers as
Schlegel, W. von Humboldt, Bopp, Grimm, and their
followers, who were without exception trained, not in
the mathematical but in the philosophical schools of
Thought which ruled in the earlier part of our century,
the further consideration of their ideas belongs properly
to that portion of this work which will deal specially
with philosophical thought and its application in such
separate branches as are presented, inter alia, by the
historical sciences.

admirer of Darwin, observed ouce language as it was felt by Prof.

jokingl}', but not without a deep Schleicher, who, though a Dar-

irony, ' If a pig were ever to say to winian, was also one of our best

me, " I am a pig," it would ipso \ students of the science of language,

/acio cease to be a pig.' This shows | But those who know best what

how strongly he felt that language j language is, and still more, what

was out of the reach of any animal, it presupposes, cannot, however

I

and constituted the exclusive or

Darwinian thev mav be on other

specific property of man. I do not ! points, ignore the veto which, as

wonder that Darwin and other ! yet, that science enters against the

philosophers belonging to his school last step in Darwin's philosophy."

should not feel the difficulty of I

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 543

It now only remains for me to sum up in a few words 49.

Suiiiiiiary.

the leading conceptions which the psycho-physical view of
nature has forced upon us. In the last chapter I showed
how the study of life has in the course of our century
more and more brought out the conviction that life is a
continuous, a ubiquitous, and a unique phenomenon ;
an exhaustive or even a working definition of life being
so far hardly possible. In this chapter we have learnt,
by following the psycho - i)hysical lines of research, to
distinguish another and peculiar side of the higher forms
of living matter, that which is coinuKmly called the
mental, inner, or self - conscious side. This appeared,
when viewed externally, as a discontinuous epi-pheno-
menon — " eine Begleiterscheinung " — of some very com-
plex physiological processes and anatomical arrangements
of living matter, and as such it exhiljits a property with
which we are otherwise not familiar in the visiltle pheno-
mena of nature — namely, discontinuity. Viewed exter-
nally, the inner phenomena, which we comprise under
the term " mind," appear and disappear, their continuity
being preserved in association with the permanence of
the external substratum or basis to which they are
attached, and internally regained by the indefinable pro-
perty of memory. But inasmuch as we have not only an
external but also an internal knowledge of at least some
of these epi-phenomena, we have had forced upon us an
entirely different view of this inner life, of mind. To
the inner view there exists in self-conscious l)eings a
centre of relatedness — a special kind of unity which we
call individuality or personality ; and this inner unity is
cai)able of being externalised or made objective in llie

544

SCIENTIFIC THOUGHT.

mental life of mankind, language being the great instru-
ment by which this is accomplished. In this external
or objective existence — which, however, is only intel-
ligible to beings which form a part of it — that con-
tinuity is regained which in the existence of every
individual is continually being interrupted and in danger
of being lost. Psycho-physical research reveals to us
the existence of a unity different from that visible in
merely external or physical nature, — a centred unity
which is something else than the sum of parts in a
mathematical whole. Through this process of cen-
tralisation and externalisation there has been formed
in the physical world, or in nature, a new world —
the world of mind, which is continually growing in
contrast to the former, which only changes without
increasing or losing its two constituents, matter and
energy.

This new world within the old one, this creation of
man, forms indeed a portion of nature — it is the micro-
cosm in the macrocosm. It might be investigated by
the usual methods of exact research ; and the science of
anthropology, with its many branches, proposes to study
it in the same way as natural history in modern times
has studied the social life of certain animals, such as
bees, ants, and beavers. Inasmuch, however, as the exact
methods do not lead very far, and have continually to
appeal to the interpretations of psychology, gained by
personal experience and introspective methods,-^ it seems

1 Prof. E. Hering ('Ueber das
Gedjichtniss als eine allgemeine
Funktion der organischen Materie,'
Vienna, 1870) says: "So long as

the physiologist is only a physicist
he stands in a one-sided position
to the organic world. This one-
sidedness is extreme but quite

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 545

more practical to range tlie whole of these researches
within that great realm of thought which starts with a
distinct recognition of conscious individual life as its
source and centre. As such, in fact, these researches
have l^een till quite recently carried on, and the main
lines of their recent development l)elong accordingly to
philosophic as distinguished from scientific or exact
thought.

The three great facts, however, which even the exact _ 5o.

o ' Tlie three

treatment of mental phenomena has impressed upon us [fressed by
— namely, the existence of centralised material systems, phys'cs.
termed " individuals," the discontinuity of their inner
life as viewed from outside, and the phenomenon of its
growing external manifestation — have driven natural
philosophers to form some explanation, or at least to
venture upon a definition of this hidden principle,
which shows itself in the highest forms of living matter,
and which, though discontinuous to the external observer,
acquires in the aggregate of human society a continuous
and ever growing reality and development. Two dis-

legitimate. As the crystal to complex whose external aud in-
the mineralogist, the vibrating ternal movements are causally as
string to the student of acoustics, rigidly connected amongst each
so also the animal, and even man, other, and with the movements
is to the physicist only a piece of of the environment, as the work-
matter. That the animal expcri- ing of a machine is with the
ences pleasure and i)ain— that with revolution of its wheels (p. 4). . . .
the material life of the human Thus the i)hysiologist as physicist,
frame are connected the joys and But he stands behind the scene,
sorrows of a soul and the vivid and while he painfull}' examines
intellectual life of a consciousness ; the mechanism and the busy doings
this cannot change the animal and of the actors behind the drop-
human body for the jihysical scenes, he misses the sense of the
student into anything other than whole which the spectator easily
it is — a material conijilex subject recognises from the front. Could
to the unalterable laws which the physiologist not, for once,
govern also the stone and the cliange his position?" (p. 5.)
substance of tiie plant, a material

VOL. ir. 2 .M

546 SCIENTIFIC THOUGHT.

tinct views have been evolved by modern science on
this matter.

The one emphasises the fact of the discontinuity of
mental — i.e., conscious — life, regards it as an ultimate
fact, as a mystery beyond which we cannot travel. This
idea presents itself in various forms, and has been
notably insisted on — with very varying philosophical
inferences — by Du Bois-Eeymond in Germany, by Mr
A. E. Wallace, and quite recently by the late Prof, St
George Mivart in England.

The other takes refuge in the hypothesis of un-
conscious or subconscious mental life, and again with
very different philosophical inferences assumes that all
physical existence has an inner side which only under
certain favourable conditions rises into the light of self-
knowledge or consciousness. The late W. K. Clifford's
"mind-stuff" theory, as also the speculations of Fechner
and of Prof. Haeckel, are types of this view, which has
been consistently and connectedly elaborated in Hart-
mann's ' Philosophy of the Unconscious.'

These speculations can be summed up under the title
" The Creed of Science," and as such will occupy us later
on in one of the chapters on the Philosophical Thought
of the century.

By many natural philosophers it is felt that the tune

has not yet come to arrive scientifically at any definite

51. conclusions on these last questions. Sufficient facts have

Transition ^

to statistics, not been collected ; or even if collected, they have not
yet been classified and tabulated. This is especially the
case with the vast materials referring to the collective
life of mankind, Leibniz had in his time foretold the

ON THE PSYCHO-PHYSICAL VIEW OF NATURE. 547

necessity of extensive statistical information before build-
ing theories. In one instance, that of language, his
advice was followed with signal success.

But even some of the purely physical sciences, like
meteorology, are still almost entirely limited to statist-
ical information.

Statistics have thus become a very important depart-
ment of knowledge, and before taking leave of the exact
lines of thought, it will be well to note more precisely
the part which these have played in our age, as also the
methods by which they proceed. This will be the
object of the next chapter, which will accordingly deal
with the Statistical View of Nature.

548

CHAPTER XII.

ON THE STATISTICAL VIEW OF NATURE.

I HAVE now treated of the several grand and general
aspects under which the objects of nature can be
scientifically regarded, and have tried to show how
these aspects, not unknown to former ages, have never-
theless, in the course of the nineteenth century, become
more definite, and accordingly more useful, as means for
describing, measuring, and, in many cases, predicting
phenomena. It is true that the two last chapters,
which dealt with the phenomena of Life and Mind,
had to take notice of a principle or of principles which
have hardly yet received any scientific definition at all,
and which in the progress of the sciences which deal
with them have played rather a negative part. It has
been mainly by eliminating the conceptions of life and
1. of mind as special agencies, factors, or entities that the

Life and _

Hnutin^ scientific study of living and conscious beings has pro-
conceptions, gressed ; by showing more and more how an accurate
and useful knowledge of much of their nature and
behaviour can be gained with the aid of the methods
adopted in other scientific inquiries, which we may call
mechanical.

ON THE STATISTICAL VIEW OF NATURE,

.49

Scientific iiUjuiiy in biology and p.sych(.-})liysics has
thus advanced on the lines indicated in the earlier
chapters, where it was shown how several positive
scientific conceptions have been gained, defined, and ap-
plied. These conceptions are all generalisations based
upon definite observable facts of nature, such as attrac-
tion, atomic constitution, motion (rectilinear, periodic,
and rotational), energy, form, and change of form,^ and
they have given rise to great branches of science, con-
taining special methods of thought and reasoning. They
have all shown themselves accessible, in a greater or
less degree, to mathematical treatment, and have con-
sequently been the means of introducing the exact
scientific spirit into large fields of research, into ever

^ The statement in the text is not
strictly correct ; for of the six
definite conceptions mentioned we
really, even in single cases, only
see two exemplified — viz., motion
and form. Neither attraction, nor
the atom, nor energy, nor develop-
ment is, even in single cases,
observable, though, with the excep-
tion of energy, they are very early
and very familiar abstractions.
This remark may suggest that
motion and form are, at least
for the present, the simplest and
most obvious conceptions into
which we can analyse oi- resolve
all external observations, and that
conseijuently kinetics and mor-
phology may be the fundamental
sciences, the first in natural phil-
osophy, the latter in natural his-
tory or biology in the widest sense.
That a kinetic view will gradually
supervene in natural phiUisoph\- is,
I think, generally admitted. It
seems less generally conceded that
morphology will supervene in
biology ; especially as all the rage

is just now for evolution and
development. But as development
must start from something, it is
likely that it will lead back to
morphology. As tending in this
direction I read the expositions of
Lotze, Claude Bernard, and the
" Organicists." Organisation must
mean a certain arrangement, and
arrangement is ultimately the same
as order, structure, or form. It
may mean something more — viz.,
unity or centredness ; but this is
a conception not capable of a purely
mechanical or geometrical defini-
tion ; we know of it only through
introsj)ection. A great deal has
been written on Morphologj' and
Morphogenesis by that very sug-
gestive author, Hans Driesch ; see
a list of his writings, stipra, p. 4ft6
note. I here only refei- to them ;
for, being myself unable clearly to
apprehend his main drift, I hesitate
to quote him as confirming the
argument of this note. The reader
must judge for himself.

550 SCIENTIFIC THOUGHT.

widening circles of phenomena and events. This has
been most decidedly the case with the sciences in which
the law or formula of gravitation has become the lead-
ing principle. As we advanced on the other lines of
thought, marked by the conceptions of atomism, of the
various forms of motion and of energy, this subjection
to precise formulae became less perfect, more com-
plicated and hypothetical, whilst the study of the
typical forms of natural objects, and even more of
their genesis and developments, opened out a field for
much conjecture and fanciful reasoning, amid which
little more than the general outlines of a definite theory
could be established. Lastly, in applying these various
conceptions to the phenomena of the living and self-
conscious creation, we have struck upon the limiting
ideas of life and mind, of which, from a purely external
point of view, little more can be said than that they
indicate to us the existence among natural objects of a
unity of a different kind from that which we can under-
stand mechanically as the sum of many parts. In the
higher forms this unity revealed itself to us through the
analogy of our own inner life as a peculiar kind of
centralisation, discontinuous when viewed from outside,
but possessing, when viewed from another side, a con-
tinuity, connectedness, and capacity of unlimited growth
of its own which is the special object of the psycho-
logical and historical sciences. These characteristics be-
long to the great realm of philosophical as distinguished
from exact scientific thought.

"o'

Results of Before entering on this other great branch of our

a V\ e J" f o f* f"

science. subjcct, wc may well pause for a moment and cast

ox THE STATISTICAL VIKW OF NATURE. 551

a general and unbiassed glance at tlie world outside,
leaving our study, our observatory, our laljoratory, our
dissecting- or our nieasuring-rooni, and ask ourselves
the simple question, By the work carried on in these
various secluded places, in the " sapientum templa
Serena," hov^^ much of the world outside have we really
learnt to comprehend, or even only to describe and
picture to ourselves correctly and completely ? The
answer is hardly encouraging. The first thing we
notice in stepping out of our door is a phenomenon
still as incalculable as it has ever been, and yet bound
up with the enjoyment of our lives and the success
of our work as much as ever — the weather. What do
we know of it which is practically reliable and useful ?
The reply must be, " Next to nothing." Some general
astronomical and some more detailed physical and
chemical relations permit us to describe a few general
meteorological and a few recurring seasonable events, but
scarcely with more practical detail and certainty than the
unscientific ancients or the untaught children of nature
of to-day. We know in general the cause of storms, of
changes of temperature, of the seasons, of rain, hail,
drought, and cold, but we do not know much more of
the exact when and where of these various changes
than did our forefathers. The natural atmosphere and
climate which surround us are still elements of con-
jecture and uncertainty.

Assume, however, that we go a step further, and
having accustomed ourselves to take the weather, good
or bad, as it is, enter into the artificial atmosphere and
surroundings of practical life, of industry, trade, and

552 SCIENTIFIC THOUGHT.

commerce, of politics and society, in which most of us
have to spend the larger portion of the working hours of
our existence. We can again put the question. What do
we know with certainty of the changes and vicissitudes
of this artificial atmosphere which surrounds us ; what
of the chances of a fall or rise in prices, of increased
or lessened demand, of impending labour troubles, of the
risks even of famine, fire, shipwreck, disease, or war ?
Again we may say that in general we know the proxi-
mate causes, natural or artificial, which may bring them
about, but the exact when and where of their occurrence
is so slightly known to us that such knowledge is of little,
if of any, practical value, and proceeds, moreover, where
it exists, more from general good sense and practical
experience than from the discoveries of science. Indeed,
the latter have, through the wonderful applications in
the inventions of arts and crafts, tended to make our
artificial atmosphere more complex, liable to more rapid
and more drastic changes, and accordingly its features
less permanent and less calculable and reliable.
3. Thus, in spite of the wonderful increase of scientific

Uncertainty ■> ■,• r'o • c • • n i

in the con. knowledge and the general diffusion of scientific thought
in the course of the century, uncertainty is still the
main and dominant characteristic of our life in nature
and society ; the atmosphere and climate of each are as
fickle and changeable, as incalculable and unreliable, as
ever. Neither the great law of gravitation nor the
fixed proportions of chemistry, neither the intricate
doctrine of undulations nor the conception of energy,
neither the knowledge of typical forms of nature nor that
of their orderly evolution, has, in the hands of those who

Crete.

ON THE STATISTICAL VIEW OF NATURE. 553

fjovern, regulate, and fashion the practical work of life
and society, become an instrument of personal use and
daily importance. Statesmen, legislators, organisers of
men, captains of industry, contractors, practical engineers,
colonisers, pioneers, and leaders of all kinds are still
mostly ignorant of these scientific ideas. They regard
them from a distance, themselves relying mainly on
common -sense, on personal experience, or on the innate
but indefinable impulses of individual genius ; pro-
fessional, scientific knowledge is only one, and hardly the
most important, of the many agencies with which they
deal and which they have to take into account.

And yet, in spite of this fact that the ordinary routine 4.

r. T e • 1 Scientific

of life IS a very different process from the ways of spirit in

" ^ •' business.

science, we must admit that the scientific spirit very
largely pervades the business of to-day. You cannot
enter any commercial, shipping, or general trading office
without being struck with the number of carefully pre-
pared charts, tables, and statistical registers of all kinds
of curves showing the rise and fall of prices, the produc-
tion and consumption, the stocks and values of metals,
coal, grain, chemicals, cotton, and produce of every kind ;
and in quite recent years, not only material things of all
sorts, but the intangible thing called energy — after
supplanting the older term horse-power — has become the
subject of elaborate tabular and graphical registration.
The streets of even the smaller towns in every civilised
country show, besides the sign-boards of shops, otiices,
and banks, an increasing array of insurance firms, whose
whole business depends on elaborate calculations, based
on long tables of births, deaths, marriages, shipwrecks,

554 SCIENTIFIC THOUGHT.

and other casualties. The daily newspapers bring us
weather charts with isothermic, isobaric, and other lines,
on which they found weather predictions or storm
warnings. vSurely, if counting, measuring, and calculat-
ing are the elementary processes of the scientific method,
it must be admitted that the latter has permeated our
practical life to an enormous extent. Thus the question
can be asked, If the calculating spirit is so general, how
does it come about that in its application to life and
commerce it has led to so much grasp but to so little
certainty ; whereas in science itself it has led to so much
actual and reliable knowledge ? How does its application
in practice differ from that in theory ? The answer to
this question is not far to seek, and it will introduce us to
a special branch of science, to a special form of scientific
thought which again is, if not a creation of the nineteenth
century, yet one of its characteristic developments.

That which everywhere oppresses the practical man
is the great number of things and events which pass
ceaselessly before him, and the flow of which he cannot
arrest. What he requires is the grasp of large numbers.
The successful scientific explorer has always been the man
who could single out some special thing for minute and
detailed investigation, who could retire with one definite
object, with one fixed problem into his study or labor-
atory and there fathom and unravel its intricacies, rising
by induction or divination to some rapid generalisation
which allowed him to establish what is termed a law
or general aspect from which he could view the whole
or a large part of nature. The scientific genius can
" stay the moment fleeting " ; he can say to the object

ON THE STATISTICAL VIKW OF NATURE.

555

of his choice, " Ah, linger still, thou art so fair " ; he
can fix and keep the star in the focus of his telescope,
or protect the delicate fibre and nerve oi a decaying
organism from succumbing to the rapid disintegration
of organic change. The practical man cannot do this ;
he is always and everywhere met by the crowd of facts,
by the relentlessly hurrying stream of events. What
he requires is grasp of numbers, leaving to the pro- 5.

^ o 1 ' o 1 Tlie science

fessional man the knowledge of detail. Thus has arisen of large

" numbers.

the science of large numbers or statistics,^ and the many
methods of which it is possessed. It will form the
subject of the present chapter.

1 Gottfried Aclieinvall (1719-
1772) is commonl}' tcnued the
"father" of statistics. Tiiis, how-
ever, is hardly correct, either in
relation to teaching or to the
practical part of the subject, or even
so far as the name is concerned.
In connection with administration
statistics existed in anti([uity.
They were taught hy the celebrated
professor, Conring, the elder con-
temporary and rival of LeiVjniz,
and the name occurs in the
seventeenth century in the ' Micro-
scopium statisticum, (juo status
imperii Komano - (iermanici rep-
ricsentatur auct. Heleno Politauo '
(1672). By Achenwall and his
successor, Ludwig August Schlozer
(173.')-1809), statistics were treated
in connection with liistory. The
latter says, " Statistics are history
standing still, and history is sta-
tistics put in motion." See on
this subject, Wegele, ' (Jeschichte
der deutschen Hi^toriographie '
(MUnchen, 188.5), ]>. 793 ; also
Iloscher, ' Geschichte der Xational-
Oekonomik ' (ibid., 1874), p. 466.
A very valuable and exhaustive
account of the etymology and

gradual change of meaning of the
words " statist " and statistics will
be found in Dr V. John,
'Geschichte der Statistik,' 1. Theil.
(Stuttgart, 1884), pp. 3-14. He
divides the history of the subject
down to (^uetelet into that of the
" German University Statistics,"
following in the lines of Conring,
Achenwall, and Schliizer, also called
the " Gottingen School," and that
of statistics as an exact, an
enumerative science, which he calls
the modern science of statistics. It
appears that in English also the
two meanings of the word are ex-
em[)lified in the older use of the
term '"statist" by Shakespeare
(" Handet," v. '2.; '' Cymbeline," ii.
4.) and Webster, in which sense it
meant simply "statesman"; and the
modern title 'Statist,' for a statis-
tical and financial periodical. Nor
must we forget that England has in
her • Liber judiciarius sen censualis
Willelmi I., regis Angli;e,' called
' Domesday - book • (1083-86), as
David Hume says, " the most
valuable piece of anticiuity pos-
sessed by any nation " (' Hist, of
England,' chai>. iv.)

556 SCIENTIFIC THOUGHT.

The grasp of large numbers, the methodical array of
figures and the registration of events, would in itself be
of little use were it not for a fundamental assumption
which appeals to common-sense and has been confirmed
by science, though it is hardly anywhere expressly stated
— namely, the belief in a general order, in a recurrent
regularity or a slow but continuous change and orderly
development of the things and events of the world.
Science, in the different aspects which we have so far
passed in review, tries to give a definite expression to
this general Order, to this all-pervading rule and regu-
larity. Statistics and the practical use of them limit
themselves to the bare fact that such order and regular-
ity do exist, though the formula or reason for them
may be unknown or unknowable. It may also be well
to note that this belief in a general order is common to
all schools of thought, be they ancient or modern, pagan
or Christian, religious or scientific, optimist or pessimist.
6. The dictum, " est modus in rebus," is the fundamental

Belief in in • ■> ^ • • ^

general axioiii of all thought and all practice ; and the statistical
view of nature, which merely puts into form and figure
this general axiom or truism, has accordingly been ap-
pealed to as much by those who uphold a divine order
of things as by others who insist on a natural or
mechanical one. In the school of Quetelet, through
whose influence statistical knowledge has been so
greatly furthered in the course of our century, the
regular recurrence of events and the stability of large
numbers has been sometimes used as the basis for a
fatalistic and pessimistic view, whereas nearly a hundred
years before Quetelet, statistics had been elaborated by

order.

ON THE STATISTICAL VIEW OF NATURE. 557

the Pastor Sussinilch in I'lussia, in a celebrated book
bearing the title ' On the Divine Order,' with a tendency
towards optimism, and as a proof of an overruling
Providence.^

Although it is generally admitted by writers on stat-
istics that in the narrower sense of the word they have
existed ever since the existence of governments which re-
quired to know the number of their population, the nat-
ural resources of the country, and its means of subsist-
ence or defence, there is a general opinion current that
what we now call the statistical methods in science and
in practice were introduced, or at least expressly recom-
mended, by Lord Bacon under the name of the " Method
of Instances." This method, which consisted in a kind
of tabulating of numbers of facts referring to any
special sul)ject under investigation, has been criticised

7.
Bacon's
"Method of
Iiistances. "

^ The difference seems to narrow
itself down to thi.«, th<at one class
of writers refers everything to a
physical, the other to a moral,
order. M. Maurice Block, an
eminent writer on statistics, dis-
cusses this question, passing a num-
ber of modern authors under
review in the fifth chapter, § 3,
of his excellent 'Traite tht'oriciue
et pratique de Statistique,' (2""^
ed., Paris, 1886). Referring to
tlie theological statistician, A. von
Oettingen, and comparing him with
Quetelet, he says (p. 146): "Sous
certains rapports, i'oj)inion de M.
le professeur de thcologie Alex-
andre d'QJttingen, pouira paraitre
I'opposee de celle de (Quetelet,
mais elle nous semble en diHc'rer
beaucoup moins que le savant pro-
fesseur ne le croit. . . . Nous
pouvons caractdriser en peu de
mots ce que MM. d'(Eltingen et
Quetelet ont de commun et com-

ment ils different : ils ont de
commun le fond de la science ; ils
constatent I'un et I'autre la r6-
gularite du mouvement des faits ;
ils ne different que par linter-
pretation : (Quetelet voit des lois
naturelles l:i oil JI. le professeur
d'Qilttingen voit des lois morales
institutdes par Dieu. Aussi I'un
uomme-t-il son Hvre Physique
sociale, et I'autre Ethi(iue sociale.
M. d'ffittiiigeu est uu croyant qui
aime h, s'appuyer sur la science.
II dit, page 13 de la premiere
edition : ' Dans les sciences connne
dans la religion, ce que I'homme
invente ne pent etre (jue faux,
tandis que les verites qu'il de-
couvre, sont uniquement des faits
ou des lois qui rayonnent du
Createur.'" The reconciliation of
either physical or moral order with
the existence of freewill is not
a statistical but a philosophical
problem.

558 SCIENTIFIC THOUGHT.

by writers like Whewell, von Liebig, Stanley Jevons,
and many others, and shown to be of very doubtful
value ; the example given by Bacon himself — the re-
search into the nature of heat — being especially un-
fortunate and badly chosen. In spite of this, it
is noteworthy that, up to quite recent times, the
Baconian method is continually referred to, mainly by
writers who are desirous of introducing what they call
the exact methods of research into other sciences
than those of external nature. A good example of this
kind is given by Walter Bagehot, and as it serves to
make an important point more intelligible than a gen-
eral statement would, I will here give it in full. He
speaks of the Enumerative, or, as he calls it, the "All-
case method," and then continues: "A very able Ger-
man writer ^ has said of a great economical topic —
banking — ' I venture to suggest that there is but one
way of arriving at such knowledge and truth, namely,
a thorough investigation of the facts of the case : by
the facts I mean not merely such facts as present
themselves to so-called practical men in the common
routine of business, but the facts which a complete
historical and statistical inquiry would develop. When
such a work shall have been accomplished, German
economists may boast of having restored the principle
of banking — that is to say, of German banking, but
not even then of banking in general. To set forth
principles of banking in general, it will be necessary
to master in the same way the facts of English, Scottish,
French, and American banking — in short, of every

1 Prof. Cohn in ' Fortnightly Review,' Sept. 1873.

ON THE STATISTICAL VIEW OF NATURF:. 559

country where banking exists. . . . The only, but let us
add also the safe, ground of hope for political economy,
is following Bacon's exhortation to recommence afresh
the whole work of economic inquiry. In what condi-
tion would chemistry, physics, geology, zoology Ije, and
other branches of natural science which have yielded
such prodigious results, if their students had been linked
to their chains of deduction from the assumptions and
speculations of the last century ? ' " To this Bagehot
replies : " The method which Mr Colin suggests was
tried in physical science ami failed. And it is very
remarkable that he should not have remembered it as
he speaks of Lord Bacon, for the method which he
suggests is exactly that which Lord Bacon himself
followed, and owing to the mistaken nature of which
he discovered nothing. The investigation into the
nature of heat in the ' Novum Organum ' is exactly such
a collection of facts as Mr Cohn suggests, but nothing
comes of it. As Mr Jevons well says. Lord Bacon's
notion of scientific method was that of a kind of scien-
tific book-keeping. Facts were to 1)0 indiscriminately
gathered from every source and posted in a kind of
ledger, from which would emerge in time a clear balance
of truth. It is difficult to imagine a less likely way of
arriving at discoveries." ^

1 ' The Postulates of English
Political Economy ' (1885), p. 17,
&c. He further remarks : " If we
wait to reason till the ' facts ' are
complete, we shall wait till the
human race has ex])ired. I think
that Mr Cohn, and tliose who think
with him, are too 'bookish ' in this
matter. They mean by liaving all

tlie 'facts' before them, liitving all
the i>rinted facts, all the statistical
tables. But what has been said
of nature is true of commerce.
'Nature,' says Sir Charles Lyell,
' has made it no part of her con-
cern to provide a record of her
operations for the use of men ' ;
nor does trade eitlier — tudy the

560

SCIENTIFIC THOUGHT.

In fact, the eight chapters of this work which have
dealt with the various abstract views from which natural
phenomena have been considered in recent times, form
an elaborate refutation of the so-called Baconian, of the
enumerative or " all case," method. It was the light of
the idea which brought life and order into the " rudis
indigestaque moles " of badly collected facts, and in
many cases even led for the first time to their useful
and intelligent enmneration. But now we come to a
further important question. Allowing that in certain
large but nevertheless secluded spheres of science a few
general ideas have been found to apply and work
wonders of calculation, prediction, and useful applica-
tion, how about those complicated phenomena which
form our natural and social environment, and where so
far no scientific formula has proved powerful or com-
prehensive enough ? Are all these elaborate enumer-
ations and graphical representations in meteorology, in
sociology, commerce, industry, and finance, to which we
have instinctively and increasingly had recourse during
the whole of the century, of no value ? Is no useful

smallest of fractions of actual
transactions is set down so that
investigation can use it. Litera-
ture has been called the ' fragment
of fragments,' and in the same way
statistics are the ' scrap of scraps.'
In real life scarcely any one knows
more than a small part of what his
neighbour is doing, and he scarcely
makes public any of that little, or
of what he does himself. A com-
plete record of commercial facts,
or even of one kind of such facts,
is the completest of dreams. You
might as well hope for an entire
record of human conversation."

Stanley Jevous ( ' Principles of
Science,' Preface, p. vii), says :
" Within the last century a reaction
has been setting in against the
purely empirical procedure of
Francis Bacon, and physicists have
learnt to advocate the use of
hypotheses. I take the extreme
view of holding that Francis
Bacon, although he correctlj- in-
sisted upon constant reference to
experience, had no correct notions
as to the logical method by which,
from particular facts, we educe
laws of nature."

ON THE STATISTICAL VIEW OF NATURE. oGl

result to spring from them ? Had they been conducted
under the influence of no useful general idea, our answer
would indeed have to be in the negative. But if, as 8.

General idea

practice shows, they have been of use, if, in fact, they underlying
prove to be in many cases quite indispensable, we may *''"»•
ask. What is the idea, the abstract thought, which
dominates them ? I will give the answer at once and
then fix the aspect with which the present chapter has
to deal. It is the conception and doctrine of averages. o.

Doctrine of

Although to the general reader nothing may seem to averages,
be simpler than a process of counting and of registration,
the science of statistics, the systematic collection of large
numbers, and the fixing of averages, is comparatively
young : it dates from the beginning of the seventeenth
century, when Sully in France, followed by Eichelieu
and Colbert, had organised what may be called the first
statistical bureau.^ It emanated from the same spirit
which called into existence the Paris Academy of
Sciences. Characteristically for the two other nations
with which we are mainly concerned in this history, the

' M. Bldck (loc. cit., p. 25) says :
" En France Sully avait ddj^ or-
ganise, vers 1602, un cabinet com-
plet dc politique ct de finances, qui
peut I'tre considere comme le
premier bureau de statistique.
Les rapports que Sully demandait
einbrassaient I'armee, la marine,
les finances et un grand nombre
de branches de I'adiuinistration,
et le resultat de ses investigations
se trouve exj)ose dans I'ouvrage
([ui a etd souvent reiniprinn' sous
le titre de ' Memoires de Sully.'
Kichelieu et Colbert se sent (5gale-
inent fait adresser des rapports,
auxqut'ls on a puise, dans ces

VOL. II.

derniers temps, bien des dldments
utiles Ji I'histoire et <\ue la statis-
tique pourrait t?galemeiit utiliser."
The Romans, who in aiiticiuity may
l>e regarded as the forerunners of
the French in administrative ability
and business-like conduct of State
affairs, seem also to have develojjed
an extensive sj-stem of registration.
Tiie ([uestion has been fully treated
by the late Prof. Hildebrand of
.lena in the ' Jahrbuch fiir Nationale
()konomie und Statistik ' (186(5), in
an article entitled '" Die Amtliche
Hevolkerungs-statistik iiu alteu
Rom."

2 N

562

SCIENTIFIC THOUGHT.

10. labour of statistics was taken up in Germany by the

statistics in

France, Ger- Universitics, whcrcas in England it fell to the lot chiefly

many, and ' " •'

Engiami. ^f .^ single pcrson — the celebrated Sir William Petty,
the creator of the term " Political Arithmetic." Thus, as
in science generally, so in statistics, Prance marched
ahead with her systematic and administrative genius ;
Germany followed in the person of Professor Conring,^
who introduced the matter as a subject of university
teaching ; whilst Sir William Petty ^ wrote his essay
with the practical object of disproving an opinion then
much current in England, and which has periodically
cropped up in the writings of journalists at home and
abroad — the threatened decline of the English nation.

1 Hermann Conring (1606-81),
Professor of lledicine and Phil-
osophy at Hehnstildt, lectured on
" Staatskunde, Notitia Rerum Pub-
licarum," from about 1660.

- About the same time when
lectures on '" The Science of the
State " were begun in Germany bv
Conring, Sir William Petty (162:3-
87) in England, one of the founders
of the Royal Society, occupied him-
self for practical reasons with similar
subjects, collecting his views in a
tract called 'Political Arithmetic'
about the j'ear 1677, besides con-
tributing various papers to the
' Philosophical Transactions ' and
publishing several 'Essays' (1681-
86). The 'Political Arithmetic'
would have been printed, but for
the French policy of Charles II., to
whom it was presented in manu-
script. It was not published till
1690, after the author's death, on a
permission "given at the Court
of Whitehall on the seventh day
of November," by Lord Shel-
burne, the son of the author.
In the preface, he characteristic-

ally saj's : " I have thoui^ht fit to
examine the following Persuasions ;
which I find too current in the
world, and too much to have
affected the minds of some, to the
prejudice of all — viz., That the
rents of lands are generally fallen ;
that therefore, and for many other
reasons, the whole hingdom grows
every day poorer and poorer. That
formerlj' it abounded with gold ;
but now, there is a great scarcity,
both of gold and silver. That there
is no trade, nor employment for the
people ; and yet that the land is
under -peopled. That taxes have
been many and great. That Ire-
land and the Plantations in
America, and other additions to
the Crown, are a burden to Eng-
land. That Scotland is of no ad-
vantage. That trade, in general,
doth lamentably decay. That the
Jlollanders are at our heels, in the
race for naval power ; the French
grow too fast upon both ; and appear
so rich and potent, that it is but their
clemency that they do not devour
their neighbours."

ox THE STATISTICAL VIEW OF NATURE.

i63

And as in science, so also in statistics, Germany in time
followed the example of France by introducing organis-
ations similar to that of the " Cabinet complet de poli-
tique et de finances" of Sully. It was notably during
the reign of Frederick the Great that the population
statistics were regularly and systematically collected in
Prussia, this enterprise being greatly stimulated by the
publication of J. P. Slissmilch's ^ ' Treatise on the Divine
Order.' In England — with a notable exception to Ije
mentioned immediately — the line of research opened out
by Sir William Petty was not followed up, and Mac-
CuUoch, when publishing, at the beginning of our cen-

' Johann Peter Siissmilch (1707-
67} published, in the year 1741, a
lx)ok with the following title : ' Die
gottliche Ordnung in den Vehinder-
ungen des menschlichen Geschleclits,
aus der Geburt, dem Tode und der
Fortpflanzung desselben erwiesen
von Johann Peter Siissmilch, Pre-
diger beym hochloblichen Kalck-
sieinischen Regiment. Xebst einer
Vorrede Herrn Christian Wolffens.'
The VxKjk, as well as the author,
was for a long time but little ap-
preciated ; for although the former
was dedicated to Frederick the
(jreat, and must presumably, to
judge from the several editions
which appeared, have been made
use of in the statistical labours of the
Prussian administration, the author.
not having been connected with any
university, had, for a long time,
little influence on the so-called
"university school" of statistics.
In the course of the last fifty years,
all prominent writers on statistics,
such as Wappiius, Roscher, von
Oettingen, Knapp, and V. John, in
Germany, M. Block and others in
France, as also Italian writers on
statistics, have taken increased
interest in the book. Dr V. John

('Geschichte der Statistik,' vol. i.
p. 241, &c.) gives an exhaustive
analysis of the work. He calls the
author "the first statistician in the
modem sense," the precursor of
Quetelet, and says, moreover, "It
is easily explained how the philos-
opher .Siissmilch would vanish into
the background as soon as the con-
ception of the encyclopfcdists, that
only matter in motion exists and
no mind, came to be generally ac-
cepted, and that the politician
Siissmilch should utterly disappear
in the turmoil of the French
Revolution." Von Oettingen, who,
on the other side, agrees in accept-
ing with Siissmilch the existence
<)f a Divine or moral order, says of
the latter, that ' ' he has become,
through his magnificent labours,
the founder of the science which
we now call moral statistics," inas-
much as he, "for the first time,
recognised the intrinsic regularity
in the apparently most accidental
human phenomena and actions, and
trie<l to establish it by inductive
methotls " ('Moralstatistik,' 3rd

ed., 18S2,

21). That he was

known to Herder and appreciated
by him, we saw tupra, p. 5-36 note.

564

SCIENTIFIC THOUGHT.

tury, his ' Statistical Account of the British Empire/
had hardly any similar work to refer to during the
whole of the eighteenth century.

The exception just referred to was " The Tables of
Mortality," which date back to the middle of the six-
teenth century, and in a more regular form to 1603.
11. They were analysed by John Graunt, captain, in 1661,

JohnGraunt • ■, r\-i

and Haiiey. in a tract with the title ' iN atural and Pohtical Obser-
vations upon the Bills of Mortality.' ^ Of Graunt's "
work, M. Maurice Block says that the difficulties of
preparing such a table at that time were so great
that it might wellnigh be considered a performance
of genius. The invention once made, improvement

^ The tract wa« presented to the
Royal Society in 1662, and printed
by order of the lattei- in 1665, the
author becoming a fellow at the re-
quest of the king. V. John gives
a full account of the book, and as
much of the author as he could
collect from the scantj* records
of him which exist (loc. cit., pp. 161-
178). He was born in 1620, was a
man of business, and latterly became
connected with the Gresham College
and with sundry matters pertaining
to the administration of the City.
He died in 1674. In 1676 a new,
sixth, edition of the tract was pub-
lished by Sir W. Petty, whom both
Halley and Evelyn eiToneously
referred to as the author.

- ' Statistique,' p. 19-4. Siissmilch,
a century after Graunt, says that
the material for the determination
of the ' Divine Order ' existed in
the parish registers since the time
of the Reformation. " But who," he
exclaims, " made use of it for this
purpose before Graunt ? The dis-
covery was just as easy as that of
America, but the Columbus was

lacking" (quoted by V. John, loc.
cit,., p. 177). The author, however,
who suggested to Siissmilch the re-
searches which led to the celebrated
' Divine Order,' was not John
Graunt, but Dr William Derham
(1657-1735), an eminent divine and
natural philosopher, who published
in 1713 his ' Physico-Theology ; or
a Demonstration of the Being and
Attributes of God from His Works
of Creation,' a book which ran
through six editions in ten years,
being translated into French and
several times into German. This
book contained, as Siissmilch him-
self says, besides numerous notes, a
collection of the observations of
other English authors on the lists
of births, deaths, and marriages.
On following up the clue given by
it he arrived ultimately at Graunt
and Petty, of whom the former
had, as he says, broken the ice,
whereas Petty had mainly dis-
cussed the influence of the changes
of population in politics (V. John,
' Statistik,' p. 243).

ox THE STATISTICAL VIEW OF NATURE. 565

was easy ; the invention was the ditficulty. The
next great name connected witli Uiis subject was
the astronomer and mathematician Edmund Halley,^
who had before liim, in addition to John Graunt's
work, the figures of birth and mortality during
the five years 1686 to 1691 collected by Kaspar
Neumann for the city of Kreslau, capital of the
province of Silesia. Tables of mortality, based upon
several thousands of life annuities, were prepared in
Holland by order of the Grand Pensioner, John de
Witt, and used in 1671 as the basis for a loan in
the form of annuities." The growing practice of
life insurance, as is well known, attaches a great
interest to these tables of mortality, which have been
slowly perfected in the course of the last hundred
and fifty years ; it having been reserved for the labours

^ For a long time it was not
known how Halley came into
[I. Ksession of Ka.spar Neumann's
lii'.rtality - tables ; but, in recent
times, mainly througli examination
of the local records of the city of
Breslau by Bergius and others, and
notably by the aid of S. Griitzer
(' Edmund Halley und Kaspar
Neumann,' Breslau, 1883), it has
become almost certjiin that Neu-
mann's registers were communi-
cated to the Royal Society by no
less a person than Leibniz, who
corresponded with Neumann on
the one side as well as with the
secretaries of the Royal Society on I
the other. Some of the original
documents have been traced in
the archives of the Society by Dr
Bond and Prof. Burdon Sanderson.
It is well kn(nvn that Leibniz him-
self attached great importance to j
accurate statistical knowledge of \

all kinds, and considered the collec-
tion of such to be one of the main
duties of the various academies
which he planned or founded.

'•' " Le grand pensionnaire de
Hollande, Jean de Witt, se fondant
sur les calculs de probabilites en-
seignds par Chretien Huygens, se
servit, comme elements d'observa-
tion, des n'sultats constatds sur
quelques milliers de rentiers via-
gers. II presenta sa table aux
<5tats gdndraux le 25 avril 1671,
pour servir de base ii un emi)runt
fait sous la forme d'annuites via-
gores. Cette table citee par M. de
Baumhauer, se trouve dans les
registres des dtats de Hollande,
annc'e 1671 " (Block, loc. cit., p.
196). A translation of this docu-
ment ajijieared in 'Contributions
to the History of Insurance' bv F.
Hendriks, ' Ass. Mag.,' vol. ii., 1852.

566

SCIENTIFIC THOUGHT.

of quite recent writers ^ to place the whole matter
upon a thoroughly scientific basis. But it is not these
necessary technical refinements that interest us most
at present ; rather let us take note how the needs of
governments, as well as the uncertainty and risks of
life, have automatically led to the definition and study
of three distinct statistical conceptions, which in our
age govern a very large part of all our practical
12. enterprises. These three conceptions are the proba-

Probability, ^ r i.

co-^opera-^^ bility of future events based upon long series of past
buuon!*'^'^' experiences, the idea of reducing or averaging risks
by " amicable " co-operation, and the " equitable " dis-
tribution of the burdens of such co-operation according
to the individual units who co-operate."^ It will at

^ It is generally admitted that
Prof. G. F. Knapp created a kind
of era in the more rigorous mathe-
matical treatment of the subject
by his various publications, dating
from the year 1868 with his tract
' Ueber die Ermittelung der Sterb-
lichkeit aus den Aufzeichnungen
der Bevolkerungs -statistik.' M.
Block {loc.cit., p. 232) says: " Ce
livre a fait une veritaVjle sensation
parmi les hommes speciaux ; noii
que I'auteur ait apporte beaucoup
de uouvelles pierres a I'edifice, mais
il a donn^ h, ces pierres une ordou-
nance, une disposition qui les con-
stituent un monument." In the
year 1874 he published his ' Theorie
des Bevolkerungswechsels. ' Manj-
other writers have followed in the
new track, among whom I will only
mention Becker, Zeuner, and Lexis.
The graphical method is largely
employed by these authors, amongst
whom Zeuner resorts to a repre-
sentation in three dimensions with
some very elegant results. See his
' Abhandlungen zur mathematischen

Statistik' (Leipzig, 1869). A his-
torical and critical review of these
and older writings is given in the
last - named woik of Knapp, p.
5'3, &c. See also Prof. Lexis's
' Einleitung in die Theorie der
Bevi ilkerungs-statistik ' (Strasburg,
1875).

^ This is not the place to dis-
cuss the social and moral aspects
of co-operation, which by future
historians will possibly be looked
upon as one of the very few novel
political ideas which our century
lias evolved or at least elaborated
in a practical form ; the older co-
operative attempts, such as were
made under the influence of the
ideals of the great Revolution by
Fourier, Saint Simon, and Babeuf
in France, and by Robert Owen in
this country, not having contained
the elements of permanent success.
These elements seem to belong
almost exclusively to the line of
development started by the "Roch-
dale Pioneers."

ON THE STATISTICAL VIKW OF NATURK. 567

once be seen how all arrangements which are based
upon these three conceptions — viz., probability, co-
operation, and equitable distribution — lead us away
from the study of individual cases to that of totals
and averages ; how they merge the interests of single
persons and the peculiarities of single cases in those
of the aggregate of a large number and the properties
of the average event or the " mean " man. Their
value and success depend on the consideration and
participation of large numbers, and they have accord-
ingly only arisen during the latter days which have
witnessed the steady growth of modern populations
and the bewildering complication of modern business.
The moral or social aspect which has simultaneously
been evolved during our period does not for the
moment concern us. We are concerned at present
only with the fact that statistics as the science of
large numbers and of averages has been increasingly
drawn into use. In fact, we might call our century
— in distinction from former centuries — the statistical
century.

The necessity of having recourse to elaborate countings,
to registrations of births, deaths, and marriages, to lists
of exports and imports, to records of consumption and pro-
duction of food-stuffs and many other items, forced upon
those who were entrusted with the gathering and using of
these data the observation that all such knowledge is in-
complete and inaccurate. Owing to the variability, within
certain limits, of recurring events and the errors of count-
ing and registration, we have to content ourselves always
with approximation instead of certainty. Error bulks

568

SCIENTIFIC THOUGHT.

13.

The Science
of Chances.

very largely in all statistics, and vitiates them ; and as
regards coming events, our minds are in a state of ex-
pectation rather than of assurance. But events can be
more or less probable, errors can be greater or smaller,
cumulative or compensatory, and our expectations may
be well- or ill-founded. And so there has arisen the
science of Probabilities and of Chances, and the Theory
of Error, two subjects intimately interwoven. The
former arose in the seventeenth century out of the
frivolous or vicious practice of betting and gambling,^
whilst the latter was founded when astronomical observa-
tions accumulated, and the question presented itself how
to combine them so as to arrive at the most reliable
result. The greatest mathematicians and philosophers,
such as Pascal, Huygens, and Leibniz, the BernouUis, De
Moivre, Laplace, Gauss and Poisson, have bestowed much
thought on the subject,^ which has nevertheless been very
differently judged — praised beyond measure by some, and
ridiculed by others ; sometimes pronounced to be merely
common-sense put in figures, and then again wrapped up

^ See supra, vol. i. p. 120 sqq.

- In addition to tlie references
given in vol. i., the following are of
importance. The history of the
Theory of Probabilities, as stated
above, has been written by Isaac
Todhunter. This history brings
the subject down to the writings
of Laplace, whose two works
mentioned in the text still re-
main the two standard works
on the science. In quite recent
times the history has been written
and brought up to date by Prof.
Emanuel Czuber in his ' Entwick-
elung der Wahrscheinlichkeits-
Theorie und ihre Anwendungen,'

contained in the seventh volume
of the ' Jahresbericht der Deut-
schen Mathematiker Vereinigung'
(Leipzig, 1899). The latter work is
written on a different principle from
that of Todhunter. Whereas Tod-
hunter deals in separate chapters
with the work of the foremost
mathematicians on this subject,
Prof. Czuber gives an independent
historical and critical analysis of the
different developments of the
theory and its applications. Quite
recently the same author has pub-
lished an independent treatise on
the subject (Leipzig, 1902).

ON THE STATISTICAL VIEW OF NATURP:. 509

in appalling niystei}.' There is, however, no doubt that
the Theory of Probability increasingly pervades scientific
as well as statistical work in our age, and that in the

' In spite of the encomium on
the theory of jtrobabilities ((uoted
in vol. i. J), l'2-i, Sir John Herschel
gave onl}' a quahfied adherence to
one of its principal applications
(see ' Brit. Ah.soc. Rep.,' vol. i. p.
16.")). The two foremo.st adverse
critics of the theory were Augu.ste
Comte in France and John Stuart
Mill in England. In the second
volume of the ' Philosophic Posi-
tive' (Ist ed., 1835, p. 371) the
former explains why he omitted
to deal with so im])ortant a sub-
ject in his mathematical ])hiloso]ihy.
" Le calcul de.s probabilit<Ss ne me
.semble avoir 6t6 rcellement, pour
ses illustres iuventeurs, qu'un te.\te
commode h, d'ingunieux et difficiles
problcmes numeriques, qui n'en con-
servent pas moins toute leur valeur
abstraite, comme les theories ana-
lytiques dont il a etc ensuite I'occa-
sion, ou, si Ton veut, I'origine.
Quant li la conception philoso-
jjhique sur laquelle repose une telle
doctrine, je la crois radicalement
fausse et susceptible de conduire
aux plus absurdes consequences.
Je ne parle pas seulement de
I'application ovidemment illusoire
qu'on a souvent tent<5 d'en faire
au pretendu perfectionnment des
.sciences sociales : ces essais, neces-
sairement chimuriques, seront car-
acteriscs dans la dernicre partie de
cet ouvrage " : and in the fourth
volume (1839, p. 512), "La seule
aberration de ce genre . . . c'est
la vaine pretention d'un grand
nomlire de gcomctres a rendre
positives les etudes sociales d'aprcs
une subordination chim(?rique ^
I'illusoire thdorie mathematique
des chances. . . . (^uehiue gros-
siere que soit dvidemment une
telle illusion, elle etait neanmoins

essentiellement excusable, quand
I'esprit eminemment philosojjhique
de I'illustre Jaccjues Bernoulli
con(;ut, le premier, cette pensee
g(5n(5rale, dont la production, h. une
telle dpoque, constituait reellement
le prt-cieux et irrecusable symptome
du besoin premature pour ce temps,
mais ()ui n'y pouvait ctre dprouvd
nieme ainsi (jue par une intelligence
vraiment sujidrieure. " John Stuart
Mill, in the .second volume of his
' Logic,' has devoted a whole chapter
to the sul)ject, in which he corrects
a .statement made by him in the
first edition of his book, attributing
a " fundamental fallacy " to the
arguments of Laplace and other
mathematicians, but nevertheless
takes an unfavourable view of the
usefulness of the calculus. In
more recent times the subject has
been exhaustively treated from a
logical point of view by Mr John
Venn in his work, 'The Logic of
Chance' (3rd ed., London, 1888),
and by Stanley Jevons in ' The
Principles of Science' (vol. i. ch. x.)
The doubts with which Mill, and
still more Comte, regarded the
subject, .seem to have been dis-
pelled in works on Logic ; and the
increa.sing use to which the methods
for the correction of error have
been put in manv' branches of
science have convinced mathema-
ticians of its apjilicability. The
ninth edition of the ' Ency. Brit.'
contains an excellent article on
" Probabilities " by M. W. Crofton.
Among the clearest and .safest
guides in this intricate subject
must be counted the late Prof.
Augustus de Morgan, whose pro-
found treatise in the ' Ency.
Metrop.' (vol. ii.), as well as his
' Essay on Probabilities ' (London,

570

SCIENTIFIC THOUGHT.

course of the last hundred years much has been done to
make it more easily understood.

James Bernoulli had already in his celebrated book
which bears the title, ' De arte conjectandi,' promised
to show the application of the mathematical doctrine
of probability to political, moral, and economical sub-
jects,^ but the fourth and last part of the book which
was to give this, remained unfinished. It was left to
his successors, notably to Daniel Bernoulli, to take up
this side of the question. But the first practical states-
condoixjet. man who — as we are told by Condorcet ^ — held the

1838), still rank with the be.st
that has been written. Stanley
Jevons sums up his opinion in the
words : " This theory appears to me
the noblest creation of the human
intellect, and it passes my concep-
tion how two men possessing such
high intelligence as Auguste Comte
and J. S. Mill could have been
found depreciating it, or even
vainly attempting to question its
validity. To eulogise the theory
is as needless as to eulogise reason
itself " (' Principles of Science,' vol.
i. p. 227).

^ James Bernoulli (1654-1705)
was the eldest of the celebrated
family of mathematicians. Daniel,
his nephew, lived half a century
later (1700-82). The 'Ars Con-
jectandi ' was published posthum-
ously in 1713 by Nicholas, another
nephew of the author. In a letter
to Leibniz the author says : " Ab-
solvi jam maximam libri jiartem,
sed deest adhue pnecipua, qua
artis conjectandi principia etiam
ad civilia, moral ia, et ceconomica
appHcare doceo." Daniel Bernoulli,
as we saw above (voL i., chap. v. p.
434), was the father of the kinetic
theory of gases, of which more
hereafter.' He was also the first
to make a distinction between

mathematical and moral expecta-
tion,— a difl'ereuce which led
Laplace to distinguish between
"fortune physique" and "fortune'
morale," to which reference was
made in connection with Fechner's
psycho-physical measurements.

- ' Essai sur I'application de
r Analyse h la Probabilite des D(5-
cisions, Rendues a la plurality
des voix ' (Paris, 1785) : " Uu
grand homme, dont je regretterai
toujours les le9ons, les exemples,
et surtout I'amitie, etait persuade
que les verites des sciences morales
et politiques, sont suscejjtibles de
la meme certitude que celles qui
formeut le systeme des .sciences
physiques, et meme que les
branches de ces sciences qui, comme
I'astronomie, paroissent approcher
de la certitude mathematique.
Cette opinion lui dtait chere, parce
qu'elle conduit h, I'esperance con-
solante que I'espece humaine fera
ndcessairement des progres vers le
bonheur et la perfection, comme
ell'i en a fait dans la connois-
sance de la vorite." It is evident
from this extract that Condorcet
(1743-94) thought that his friend
Turgot shared his own well-known
opinions as to the unlimited per-
fectibility of the human race.

ON THE STATISTICAL VIEW OF NATURE,

571

view that morals and politics might derive the same
henefit from the science of calculation as the physical
sciences had already experienced, seems to have been
Turgot. To show the importance of this view, Con-
dorcet wrote his much quoted hut little read essay on
the application of analysis to decisions based on the
plurality of votes. Tn his fiitroductioii tlie author
laments that his friend, on whose suggestions he had
commenced his work, did not live to see it finished/ It
would have been interesting to know whether so emi-
nent a practical philosopher as Turgot is considered to
have been, would have been encouraged by his friend's
specimen of political algebra, or whether he would have
held the opinion of Mill, who saw in tliese " appli-
cations of the calculus of probabilities . . . the real
opprobrium of mathematics." "

^ {Loc. cit., p. i.) "Si riiumanite
n'eut pas eu le mallieur, longtemps
irreparable, de le ])er<lre trop tot,
cet ouvrage eut etu muiu-s impar-
fait: cclairo par ses conseils, jaurois
vu mieux ou plus loin, et j'aurois
avauce avec plus de confiance des
principes qui auroieut (5to les sieus.
Prive d'un tel guide, il ne nie reste
qu'ii fairo h sa memoire I'liommage
de mon travail, en faisant tous rues
efforts ])our le rendre moins indigne
de I'amitid dont il m'houoroit. "

- There is no doubt tliat the
writings of Condorcet, through the
useless accumulation of forniuUc
with very little substance behind
them, contributed to bring the
whole theory into discredit. An-
other still moie eminent contem-
porary mathematician, D'Alembert,
after having occupied himself at
considerable length with problems
in prtjbabilities, formed an un-
favourable opinion of the usefulness

of the calculus. Gouraud (quoted
by Todhunter, p. 293) says : '■ (^uaut
au reste des malhematiciens, ce ne
fut (jue par le silence ou le dedain
qu'il rcpondit aux doutes que
d'Alembert s'ctait permis d'cmettre.
Mi5pris injuste et malhabile oh tout
le monde avait ii perdre et qu'une
posterite moins pr^venue ne devait
point sanctiouner." It is interest-
ing to note that Laplace, in hi.s
historical account at the end of his
' Essai Philosophique,' does not
refer either to Condorcet or to
D'Alembert. J. S. Mill ('Logic,'
vol. ii. p. 66) says : " It is obvious,
too, that even when the proba-
bilities are derived from observation
and expei-iment, a very slight
improvement in the data, by better
observations, or by taking into
fuller consideration the s]>ecial
circumstiinces of the case, is of more
use than the most elaborate appli-
cation of the calculus to jjrobabil-

»72

SCIENTIFIC THOUGHT.

15.

Laplace.

So far as the formal part of the subject was con-
cerned, it was left to Laplace to place it on the founda-
tion upon which it has ever since rested. He brought
together the ideas of his predecessors, notably of
De Moivre, the two Bernoullis, Sterling, Bayes, and
Lagrange, as well as his own extensive researches, in
his great analytical theory of Probability, which ap-
peared in 1812, and, with several additions and an
elaborate introduction, in two subsequent editions during
his lifetime. This work has been justly considered a
monument of human genius, and stands worthily beside
the great ' Mecanique Celeste ' of its author. The

ities founded on the data in their
previous state of inferiority. The
neglect of this obvious reflection
has given rise to misapplications of
the calculus of probabilities which
have made it the real opprobrium
of mathematics. It is sufficient to
refer to the applications made of it
to the credibility of witnesses, and
to the correctness of the verdicts of
juries." I have already referred to
the position which Comte took up.
De Morgan, with his usual clearness
and wisdom, at the end of his
"Theory of Probabilities" ('Ency.
Metrop.,' vol. ii. p. 470), whilst re-
ducing to a very narrow province
these applications of the calculus of
probabilities, says : " There are cir-
cumstances connected with the
mathemathical theory of independ-
ent evidence which it maj" be useful
to examine. In this, as in several
other preceding investigations, it is
not so much our wish to deduce
and impose results, as to inquire
whether these results really coincide
with the methods of judging which
our reason, unassisted by exact
comparison, has already made us
adopt. The use of the process is,
that both our theory and our pre-

conceptions thus either assist or
destroy each other : in the former
case we feel able to trust this
science for further directions ; in
the latter, a useful new inquiry is
opened. For when we consider the
very imposing character of the first
principles of the science of proba-
bilities, and the mathematical
necessity which connects those
simple first principles with their
results, we feel convinced that,
even on the supposition that the
main conclusions of the present
treatise are altogether fallacious,
there must arise a necessity for
investigating the reason why a
methodical treatment of certain
notions should lead to results in-
consistent with the vuxjue applica-
tion of them on which we are ac-
customed to rely. For it must not
be imagined that opposition to the
principles laid down in this treatise
is always conducted on other
principles : on the contrary, it
frequently happens that it is only
a result of themselves obtained
without calculation, which is ar-
rayed against arithmetical deduc-
tion."

ON THE STATISTICAL VIKW OF NATL'KK. 573

labours of inatheinaticiau.s since Lapluix- in the field of
probabilities have consisted mainly in commentaries on
and simplifications of his expositions, and in a j^reat
improvement in the formal methods, due mostly to
English workers.^ At present we are not interested
in the purely mathematical side of the subject, which
for some minds has a great fascination, but rather in
the ([uesti<in : To what extent have the anticipations of
yuch men as Condorcet, Turgot, and Laplace, as to the
practical value of these researches, been realised ? in how
far hsixe they proved to be " the happiest supplement
to the ignorance and weakness of the human mind " ? ^
This idea, though ridiculed by some, has as often cropped

^ The iirobleiiis suErgested by the
calculu.s of probabilities gave rise,
collaterallj-, to several important
mathematical (leveloj)inent.s, not-
ably the oombinatorial analysis,
the calculus of finite differences,
and, in tlie hands of Laplace, the
theory of generating function and
the recurrent series. A large part
of Laplace's great work is taken
up with this purelj' mathematical
device. It has in more recent
times been supplanted, especially
under the hands of English mathe-
maticians, by the calculus of oper-
ations, of which the germ is to be
found, according to Laplace, in a
suggestion of Leibniz (see ' Essai
Philusophique sur les Probabili-
tes,' p. 65).

- " La theorie des probabilitus
n'est, au fond, ijue le bon sens
reduit au calcul : elle fait apprdcier
avec exactitude ce ijue les esprits
justes sentent par une sorte d'in-
stinct, sans (ju'ils puissent souvent
s'en rendre c()mi)tc. Elle ne laisse
rien d'arbitraire dans le choix des
opinions et des partis a prendre,
toutes les fois que I'on peut, ii son

moyen, di'terminer le choix le plus
avantageux. Par la, elle devient
le supplement le plus heureux ii
r ignorance et ii la faiblesse de
I'esprit humain. Si Ton considere
les niethodes analytiques aux-
quelles cette thcorie a doune
naissance, la vc'ritd des principes
qui lui servent de base, la logicjue
tine et delicate qu'exige leur emploi
dans la solution des problcmes, les
dtablissemens d'utiliti' publicjue qui
s'appuient sur elle, et lextension
qu'elle a revue et qu"elle peut
recevoir encore, par son application
aux questions les plus importantes
de la Philosophic naturelle et des
sciences morales ; si Ton observe
ensuite que dans les choses memes
qui ne j)euvent elre soumises au
calcul, elle donne les aper^us les
plus surs qui puissent nous guider
dans nos jugemens, et qu'elle ap-
preud a se garantir des illusions
qui souvent nous egarent, on verra
qu'il n'est point de science plus
digue de nos mcilitations, et qu'il
soit plus utile de faire entrer
dans le syatome de Tinstruction
publique" {foe. cit., p. 273 ct neq.)

574

SCIENTIFIC THOUGHT.

16.
Four ap-
plications.

17.

Theory of
Error.

up again in the course of the century, and is at present
occupying the attention of distinguished thinkers. It
will be interesting to give some account of these prac-
tical applications.

Of these, four notably attract our attention. First,
the theory of error, prominently associated with the
name of Gauss. Secondly, the writings of Adolphe
Quetelet, and the great impetus given by him to
statistical research. Thirdly, the peculiar development
of the Atomic theory known as the Kinetic theory
of gases, which gave to many scientific investigations
what Clerk - Maxwell termed the statistical, in oppo-
sition to the historical or descriptive, character. Lastly,
the Darwinian ideas which deal with the great and
increasing numbers of living things, and the changes
inherent in their growth and development. These
have led to statistical enumerations and registrations
which, beginning with ]\Ir Francis Galton's researches
into the phenomena of heredity, are at the present
moment being continued on special lines by Prof. Karl
Pearson.

That Error is subject to law, or, to express it mathe-
matically, to regularity, is a reflection which forced itself
upon the attention of thinkers who occupied themselves
with the doctrine of chances, and of statisticians who
collected registers of large numbers of events. Let
special known sources of error be eliminated or allowed
for in every instance, there still remains a very large,
practically an infinite, number of unknown sources of
error which — where we have to do with simple magni-
tude— may increase or reduce our result by mutually

ON THE STATISTICAL VIEW OF NATURE. 575

destroying or augmenting each other. Tlie repeated
measurement of a physical quantity, of the position of a
fixed star ; the arrangement of the bullet marks on a
target ; the grouping of the impressions made on the
sand by a stone let fall vertically from the same point
at a considerable height ; even tlie countings by a large
number of skilled persons of the same number or the
estimates of the same distance or height of an object, of
the weight of a heap of materials : all these statements
will show a certain regularity around the mean number
which we consider to be the most probable or correct
one. Small errors will be more frequent than large ones ;
very large ones will be practically absent ; and the mean
will be the result of a mutual destruction or compensa-
tion of many small sources of error acting both ways.
Mathematicians, from tlie time of Lagrange and
Bernoidli, have tried to put into a mathematical
formula this regularity in the distribution of error;
and, since Laplace and Gauss approached the subject
from different points of view, they have arrived at
a definite analytical expression ^ for the distribution
of errors of increasing magnitude around a fictitious
centre or mean which is considered in every instance
to be the most probable quantity. Practical trials
on a very large scale have been made by Bessel,
Encke, Quetelet, Faye, and others, and they have in
every case yielded a satisfactory approximation to the
figure given 1)y the theoretical formula ; so tliat at
present little doubt as to its usefidness exists in the
minds of those who employ it for the purposes of

' This is tlie well-known "curve of Error."

576

SCIENTIFIC THOUGHT.

18.
Method of
Least
Squares.
Gauss.

elaborate calculations in astronomy, geodesy, and in
various physical and statistical researches.

Bound up with the theory of Error is the celebrated
method of least Squares, first used by Gauss in 1795,
published by Legendre in 1805 in his memoir ' On a
New Method of Determining the Orbit of a Comet,' and
elaborately discussed by Laplace, Gauss, and many sub-
sequent writers to this day.^ It may be looked upon
as an extension or generalisation of the common-sense

' In addition to the references
given in the notes to pp. 120 and
183 of vol. i., I can now recommend
two excellent summary accounts
of the history and theory of the
method of least squares — the one
in Prof. Czuber's ' Bericht,' quoted
above (pp. 150 to 224) ; the other
in Prof. Edgeworth's article on
"The Law of Error" in the Sup-
plement to the last edition of
the ' Encj'. Brit.' (vol. xxviii.,
1902, p. 280, &c.) Prof. Cleve-
land Abbe, in a " historical note
on the method of least squares "
('American Journal of Mathe-
matics,' 1871), has drawn attention
to the fact, that already in 1808
Prof. R. Adrain of New Brunswick
had arrived at an expression for the
law of error identical with the
formula now generally accepted,
without knowing of Gauss's and
Legeudre's researches. See a paper
by Prof. Glaisher in the 39th vol.,
p. 75, of the ' Transactions of the
Royal Astronomical Society.' The
logical and mathematical assump-
tions upon which the method is
based have been submitted to re-
peated and very searching criti-
cisms, many rigid proofs having
been attempted, and every sub-
sequent writer having, seemingly,
succeeded in discovering flaws in
the logic of his predecessors. In
connection with another subject,

I may have occasion to point
out how nearly all complicated
logical arguments have shown
similar weakness, and how, in many
cases, the conviction of the correct-
ness or usefulness of the argument
comes back to the self-evidence of
some common - sense assumption,
which cannot be proved, though it
may be universally accepted. Manj'
analysts have tried to prove the
correctness of the everyday process
of taking the arithmetical mean,
but have failed. Prof. Czuber says,
inter alia (loc. cit., p. 159): "The
fact that Gauss, in his first demon-
stration of the method of least
squares, conceded to the arithmeti-
cal mean a definite theoretical
value, has been the occasion for a
long series of investigations concern-
ing the subject, which frequently
showed the great acumen of their
authors. The purpose aimed at —
viz., to show that the arithmetical
mean is the only result which ought
to be selected as possessing cogent
necessity, hereby giving a firm
support to the intended proofs, has
not been attained, because it cannot
be attained. Nevertheless, these
investigations have their worth be-
cause they aiford clear insight into
the nature of all average values and
into the position which the arith-
metical average occupies among
them."

ON THE STATISTICAL VIEW OF NATURE. 577

method of taking the arithmetical mean in determining
what figure to accept in a number of slightly differing
computations. Where more than one quantity is to be
determined — for instance, where from a series of oljser-
vations dotted on a chart the continuous curve which
marks the course of a planet or comet is to be deduced
— the simple method of averaging cannot be applied.
Every set of three complete observations suffices, as
Gauss has shown, to determine the elements or con-
stants of an elliptical orbit. IJut astronomers try to
get as many observations as possible, and none of these
is a repetition of the same observation — as, for in-
stance, are the repeated weighings of a substance in
chemistry, of the measurings of a length in surveying,
or the counting of a number in statistics : on the con-
trary, each is the independent ascertainment of definite
positions in a moving object. It is clear that the
method of averaging must be more general than the
common-sense method of taking the arithmetical mean,
but must — where the latter is applicable — coincide
with it. It has been shown that the following rule
answers this purpose. Fix the average constants or
elements so that the sum of the squares of the differ-
ences between the observed and calculated positions is a
minimum. In mathematical language this results in the
algebraical determination of the constants in an ec^uation.

Whereas the labours of Gauss and the school of
astronomers which he headed in Germany were mostly
occupied in the mathematical proof of this rule, and
in its applications in astronomical and geodetic com-
putations, the doctrine of probabilities acquired a larger

VOL. II. 2 0

578 SCIENTIFIC THOUGHT.

meaning and attracted much popular attention in France
19- and Belgium through the dominating influence of Lap-

Laplace. fe o o r

lace. He had not only collected in his abstract and
very difficult ' Analytical Theory of Probabilities ' all
that himself and others had done in this line of research,
but he had in a similar manner to that adopted in his
' Celestial Mechanics ' tried to bring the substance of
the theory home to the non-mathematical student in
his ' Essai Philosophique sur les Probabilites.'

The analytical formulae of probabilities can, he main-
tained, " be regarded as the necessary complement of the
sciences which are founded on a mass of observations
which are subject to error. They are indeed indispens-
able for solving a large number of questions in the
natural and moral sciences. The regular causes of
events are mostly either unknown or too complicated to
be submitted to calculation : frequently also their effect
is disturbed by accidental and irregular causes, but it
always remains impressed on the events produced by
all these causes, and it brings about changes which
a long series of observations can determine. The
analysis of probabilities shows these modifications : it
assigns the probability of their causes, and it indicates
the means of increasing their probability more and
more." ^ Then, referring to the phenomena of the
weather, Laplace proceeds : " Moreover, the succession
of historical events similarly shows us the constant
action of the great moral principles in the midst of
the diverse passions and interests which agitate society
in every direction. It is remarkable how a science

^ 'Essai Philosophique,' p. 271.

ON THE STATISTICAL VIEW OF NATURE. 579

wliicli began with the consideration of play has risen
to the most important ol)jects of human knowledge."

In 1823, soon after the appearance of the works of
Laplace and other French writers, this application of
the theory of probabilities was taken up by Adolphe
Quetelet, who collected his researches in his cele-
brated work, ' Sur I'Homme et le I)c\eloppement de ses
Facultes, ou Essai de Physique sociale.' ^ Quetelet

20.
Quetelet.

^ In addition to this work, which
was published at Brussels in 1836
in two small volumes, and which
Quetelet (1796-1874) describes as
a ' resume de tous mes travaux
anterieurs sur la stalistique,'
he published, besides a great
number of memoirs, a series
of ' Lettres sur la Th(5orie des
Probabilites' (begun in 1837, pub.
1845, Eng. trans, by O. G. Downes,
1849), and as a continuation of
the former work in 1848, ' Du
Systome social et des Lois qui le
regissent.' Less known than those
of Quetelet, but about the same
time, and independently, there ap-
peared in France the writings of
A. M. Guerry, beginning with the
publication in 1829 — in collabora-
tion with A. Balbi — of ' Statisticjue
comparde, et I'dtat de I'instruc-
tion et du nombre des crimes,'
and in 1833, 'Essai sur la sta-
tistique morale de la France.'
The term "'moral statistics" ap-
pears here for the first time.
Quetelet was the inventor of the
term " Social Physics." Guerry
employed graphical methods, and
published in 1864 ' Statistiijue
morale de I'Angleterre comparde
avec la statistique morale de la
France.' M. Block ('Statistique,'
p. 43) attributes to Guerry and
Charles Dujiin the general intro-
duction of the gi-aphical method
in statistics ; geometrical represent-
ations having been adopted at the

end of the eighteenth century by
Wm. Playfair in England, and,
before him, bj' Crome, professor
at Giessen, in 1782, and tabular
synoptical statements going back
to the Danish writer J. P.
Anchersen, in his ' Descrijitio
Statuum Cultiorum in Tabulis '
(Cojjenhagen and Leipzig, 1741) ;
see V. John, ' Geschichte der
Statistik,' p. 88. Referring to
Guen-y, V. John (p. 367) says:
" (,!uetelet is incontestably to be
regarded as the founder of the
new science (viz., moral statistics),
for the rival works of the
French lawyer Guerry ajipeared
only partly before (,>uetelet's, and
are excelled by the latter in the
use made of the material. In-
dependently of this formal dif-
ference, the two authors have
quite different conceptions of the
new science. (Juerry regards its
object as consisting mainly in col-
lecting data in order to gain an
opinion of the moral status of a
country. Thus he looked upon
moral statistics as auxiliary to the
history of civilisation. <i>uetelet
went beyond this, inasmuch as he
was the first to inquire into the
cause of the moral level of a
population, and in as much as in
his criminal statistics of Belgium,
1833, he had already given ex-
pression to the fundamentvl idea,
' Society bears the germs of crime
in itself.' "'

580

SCIENTIFIC THOUGHT.

21.
The " mean
man.'

was astronomer-royal of Belgium and the founder of
the Observatory at Brussels. Having opened his career
by some memoirs on geometrical subjects, he directed
his attention to questions of meteorology and statis-
tics, which he was probably the first to extend
into the region not only of the physical but also
of the moral attributes of man, studying the phe-
nomena of crime, suicide, and disease as revealed by
the cruninal courts in France, the Netherlands, and
other covmtries.

Subsequently it was mainly through his influence that
a series of international statistical congresses was held
in the principal cities of Europe, and a greater uniformity
in the methods of research and registration attempted
and partially attained.

Quetelet's statistical inquiries centre in the conception
of the average or mean man who, in a very geometrical
fashion, is looked upon as an analogue of the centre of
gravity^ of a body, being the mean around which the
social elements oscillate. " If one tries," he says, " to

^ Quetelet defines the object of
his work as follows ( ' Sur 1' Homme,'
vol. i. p. 21): "L'objet de cet
ouvrage est d'etudier, dans leurs
efifets, les causes, soit naturelles,
soit perturbatrices qui agissent sur
le developpement de I'liomme ; de
chercher ii mesurer I'influence de
ces causes, et le mode d'apres lequel
elles se modifient mutuellement.
Je n'ai point en vue de faire une
theorie de I'homme, mais seulement
de constater les faits et les ph^nom-
enes qui le concernent, et d'essayer
de saisir, par I'observation, les lois
qui Kent ces phenomenes ensemble.
L'homme que je considere ici est,

dans la soci^td, I'analogue du centre
de gi'avite dans les corps ; il est la
moyenne autour de laquelle oscillent
les elemens sociaux : ce sera, si Ton
veut, un etre fictif pour qui toutes
les choses se passeront conforme-
ment aux resultats moyens obtenus
pour la societe. Si I'on cherche ii
etablir, en quelque sorte, les bases
d'une physique sociale, c'est lui
qu'on doit eonsiderer, sans s'arreter
aux cas particuliers ni aux anom-
alies, et sans rechercher si tel in-
dividu peat prendre un developpe-
ment plus ou moins grand daus
I'une de ses facultes."

ON THE STATISTICAL VIEW OF NATURE. 581

establish in some way the foundation of Social Thysics,
it is the mean man whom one must consider without
stopping at particular and anomalous cases and without
investigating whether some individual can take a de-
velopment more or less great in one of his faculties.^
. . . After having considered man at different epochs
and among different peoples, after having successively
determined the different elements of his physical and
moral condition, . . . we shall be able to fix the laws
to which he has been subjected in different nations
since their birth — that is to say, we shall be able to
follow the course of the centres of gravity of every part
of the system." "' In an astronomical fashion Quetelet
speaks of the perturbing forces and variations, and of
the " stability of the social system," ^ and compares the
new science of society to the mechanics of the Heavens.*
The influence of Laplace and his school is evident in
every page of Quetelet's work. Whilst speaking of the
" variability of tlie human type and the mean man
among different peoples and in different centuries," he

' ' Sur rHonujie,' vol. i. p. 22.

- Ibid., p. 23.

3 Ibid., p. 26.

•* Vol. ii. J). 338. Quetelet speaks of
the annual and diurnal j)eriods, and
continues : " Les causes n-gulieres
et ptriodiqucs, qui dependent ou de
la pdriode annuelle ou de la pcriode
diurne, exercent sur la societe des
effets plus prononce.s et qui varient
dans des liinites jilus larges, (jue
les effetH combines non piriodiques,
produits annuellement par le con-
cours de toutes les autres causes
qui agissent sur la societe ; en
d'autres ternies, le systi;me social,
dans sa maniere d'etre, parait etre

plus dissemblable a lui - niOme
pendant le cours d'une annee ou
nienie pendant resi)ace d'un jour,
que i)en<lant deux annees con-
secutives, si Ton a t'gard ii I'ac-
croissenient de la jiopulation. La
pdriode diurne semble exercer une
influence un pen plus prononcee
que la ])(iriode animelle, du moins
en ce ijui concerne les naissauces.
La pdriode annuelle produit des
effets j)lus sensibles dans les
campagncs que dans les vil!cs, et
il parait en etre de meme des
causes en gentTal qui tendent
Ji modifier les faits relatifs Ji
rhonmie."

582

SCIENTIFIC THOUGHT.

anticipates discussions which came fifty years later.^
His aim is to arrive at a precise knowledge of things
hitherto vaguely known and merely sketched by artists
and literary persons ; but he evidently looks beyond the
study of the average man to that of individual departures,
as of special interest to the physician,^ for instance,
in the case of disease, and he significantly recommends
what he calls the " study of maxima." ^ He regards the
" mean man in the circumstances in which he is placed
as the type of all that is beautiful and all that is

1 Vol. ii. p. 270 : " Les ancieiLs
ont represente avec un art iiifini
I'homme physique et moral, tel
qu'il existaic alors ; et la plupart
des niodernes, frappes de la perfec-
tion de leurs ouvrages, ont cru
qu'ils n'avaient rien de mieux a
faire que de les imiter servilement ;
ils n'ont pas compris que le type
avait chang^ ; et que, tout en les
iuaitant pour la perfection de I'art,
ils avaient une autre nature a
etudier. De la, ce cri universel,
' Qui nous delivrera de.s Grecs et des
Romains ! ' De Ik cette scission
violente entre les classiques et les
romantiques ; de la enfin, le besoin
d'avoir une litterature qui fut verit-
ablement I'exprcssion de la societe.
Cette grande revolution s'est ac-
coniplie, et elle fournit la preuve la
plus irrecusable de la variabilite du
type humain ou de rhomme moyen
chez les difFerens peuples et dans
les difFerens siecles." It is inter-
esting to see from this quotation
that the opposition to a one-sided
classical education emanated at
that time from the romantic move-
ment, whereas in our days it is the
scientific movement which forms the
opposition.

^ Vol. ii. p. 281: "Comme dans
le plus grand nombre de cas, le
malade ne peut presenter aucune

observation satisfaisante faite sur
sa propre personne, ni aucune des
elemens qui lui sont particuliers,
le medecin se trouve force de la
ramener h, I'echelle commune, et de
I'assimiler h, I'homme moyeu ; ce
qui au fond semble presenter le
moins de difEcultes et d'iucon-
veniens ; mais peut causer aussi de
graves meprises dans quelques cir-
constances ; car c'est encore le cas
de faire observer ici que les lois
gen^rales relatives aux masses sont
essentiellement fausses etant ap-
pliquees h des individus : ce qui
ne veut pas dire cependant qu'on
ne peut les consulter avec fruit : et
les ecarts sont toujours consider-
ables."

3 Vol. ii. p. 284 : " II ne faut pas
confondre les lois de developpement
de I'homme moyen a telle ou telle
epoque, avec les lois de developpe-
ment de I'humanite. Elles n'ont
en general (jue peu de rapjjort entre
elles : ainsi je serais tres dispose a
croire que les lois de developpement
de I'homme moyen restent a peu
pres les memes aux diffdrens siecles,
et qu'elles ne varient que par la
grandeur des maxiriui. Or, ce sont
justement ces maxima, relatifs ii
I'homme develoj^pe, qui donnent,
dans chaque siecle, la mesure du
developpement de Thumanite."

ON THE STATISTICAL VIEW (»K NATDRE. 583

good." ^ And further, " one of the principal tilings
accomplished by civilisation is to draw closer and
closer the limits within which the different elements
oscillate which are characteristic of man."^

There was, however, another idea besides that of
the mean man which followed in the course of this
mathematical or astronomical treatment of social
statistics — namely, the seeming negation of the scope
of freewill and of moral responsibility, which seemed
inconsistent with the regularity of the statistical rec-
ords. In his treatise, ' Sur I'Homme,' Quetelet had
drawn attention to the regular recurrence of crime
— of the tendency to crime — as one of the most
remarkable features in society ; which, through its
physical and moral constitution, " prepares crime, the
guilty being only the instrument which carries it

' Vol. ii. p. 287: "J'ai dit prc-
cedemment que I'houmie inoyeii de
cha(jue epoque reprcsente le tj'pe du
developpeinent de rhumanite pour
cette opoque ; j'ai dit encore que
rhomme iiioyen utait toujours tel
que le couiportaient et qu'exi-
geaient le.s temps et le.s lieux ; que
ses quaiito.s se developpaient daus
un juste equilibre, dans une par-
faite harmonie, egaleinent eloiguee
de.s exci'.s et de.s defectuosites de
toute e.s{)oce ; de sorte que, dans
le.-j circonstances oil il se trouve, on
doit le considorer coninie le type de
tout ce qui est beau, dc tout ce qui
eat bien." P. 289 : " Uu individu
qui n5sunierait en lui-merae, ;i une
ejOTque donnee, toutes les qualites
de riiomine moyen, representerait
Il la fois tout ce tju'il y a de grand,
de beau et de bien."

- Vol. ii. p. 342 : " Un des prin-
cii)aux faits de la civili.-iation est de
resserrer, de plus en jjIus, les liiaites

22.
Social Htat-
isticB and
freewill.

dans lesquelles oscilleiit les ditferena
elemens relatifs a riioninie. Plus
les luiuieres se rdpandent, plus les
ecarts de la moyeune vout en
ditninuant ; plus, par consequent,
nous tendons a nous rapprocher de
ce i[ui est beau et de ce qui est
bien. La perfectibilitc de I'espece
humaiue rosulte comnie une conse-
quence uecessaire de toutes uos
recherches. Les defectuosites, les
monstruositt5s disparaissent de plus
en plus au physiijue ; la frociuence
et la graviti5 des maladies se
trouvent combattues avec plus
d 'a vantage par les progrts des
sciences m«$dicales ; les qualit(58
morales de I'honime n'eprouvent
pas de perfeetionnemens moiiis
sensibles ; et plus nous avancerons,
moins les grands bouleversemens
politiques et les guerrea, ces fleaux
de rhumanite, seront iv craindre
dana leurs effets et dans leurs
consequences."

584

SCIENTIFIC THOUGHT.

23.
Buckle,

out '; society, as it were, exacting a certain proportion
of crime, as it does of suicide, poverty, physical and
mental disease, for the maintenance of its equilibrium
and as an " alarming " " tribute to its stability. The
extreme consequences which seemed to flow from this
doctrine were not drawn by Quetelet, who believed in a
gradual though slow development of human society, and
in moral as well as physical causes and influences. They
were drawn, however, by what we may term the mathe-
matical school of social philosophers, who relied greatly
upon the figures collected by Quetelet and confirmed by
others. In this country the statistical labours of Quetelet
were made known by Sir John Herschel in a brilliant
article ^ in the ' Edinburgh Review ' on the " Translation
of Quetelet's Letters to Prince Albert on the Theory of
Probabilities." They do not seem to have been regarded
as detrimental to the moral aspect of human history till
Henry Thomas Buckle, in his celebrated ' History of
Civilisation,' ^ made use of Quetelet's statistics in sup-

^ ' Sur I'Homme,' vol. ii. p. 241.

2 Cf. vol. ii. p. 262 ; also
'Systeme Social' (1848), p. 9.5,
and the ' M^moire sur la Statistique
Morale' (1848).

3 Vol. xcii. p. 18.

* The ' History of Civilisation,'
vol. i., appeared in 1857, and was
very soon translated in Germany,
lunning in a short time through
five editions. There the statistical
theories of Quetelet had not made
that impression which they made
in some other countries. This is
explained by the fact that the
philosophy of Kant, to which
Buckle himself referred in a long
passage in his "Introduction," had
long before Quetelet accustomed

thinkers to abandon the popular
conception of freewill, which sees
in it merely the absence of causal
determinateness, in favour of the
causal connection of so-called free
actions with the motives and the
moral character. The subject has
been very fully discussed by F. A.
Lange in his well-known ' History
of Materialism ' (Eng. trans, by
Thomas, vol. iii. p. 196, &c.)
Lange refers to a remark of the
well - known political economist,
Prof. Adolph Wagner, who, in his
work ' Die Gesetzmiissigkeit in den
scheinbar willkiihrlichen mensch-
lichen Handlungen ' (Hamburg,
1864, p. xiii, &c. ), mentions the
fact that Quetelet's writings had

ON THE STATISTICAL VIEW OF NATURE. 585

port of one of his favourite theses — viz., that the
course of historical progress depends on the combined
action of the external physical surroundings and of
the intellectual side of liunian nature. Apart from
intellectual modifications the moral side is a con-
stant. In the course of the discussions following
the appearance of Buckle's History, especially in Ger-
many, it was conclusively shown that statistical
figures prove neither one view nor the other : indeed,
one of the most complete and exhaustive treatises
on moral statistics comes from the orthodox pen of
Alexander von Oettingen, a Professor of Theology, just
as we saw that the first great work on political arith-
metic in Germany came from the pastor Slissinilch
a century earlier. Philosophical writers like Lotze ^

facts of life, while the German
philosophy, despite its clearness as
to the nullity of the old doctrine
of freewill, still always prefers to
direct its view inwards upon the
facts of consciousness."

^ Lotze's deliverances on this
subject will be found in the third
chapter of the seventh book of
the ' Microcosmus ' (Eng. trans, by
Hamilton and Jones, vol. ii. p. 200,
&c. ), and also in the ' Logik ' of
1874 (Book II. chap. 8). In the
former passage he says : " The dis-
like with which we hear of laws
of jisychic life, whilst we do not
hesitate to regard bodily life as
subordinate to its own laws, arises
partly because we require too
much from our own freedom of
will, partly Ijecause we let our-
selves be too nmch imposed upon
by those laws. If we do not lind
ourselves involved in tlie declared
struggle between freedom and
necessity, we are by uo means
averse to regarding the actions of

not received the attention merited :
"This reproach does not quite
hit the right point. . . . Wagner
might, in fact, have been led by
Buckle ... to see that German
philosophy in the doctrine of the
freedom of the will has for once
an advantage which permits it to re-
gard these new studies with equan-
imity ; for Buckle supjiorts himself
above all upon Kant, adducing his
testimony for the empirical neces-
sity of human actions, and leaving
aside the transcendental theory of
freedom. Although all that ma-
terialism can draw from moral
statistics . . . for the practical
value of a materialistic tendency
of the age as against idealism has
thus been conceded by Kant, it
is by no means indifferent whether
moral statistics, and, as we may
put it, the wliole of statistics, is
placed in the foreground of an-
thropological study or not ; for
moral statistics direct the view
outwards upon the real measurable

586

SCIENTIFIC THOUGHT.

24.
Criticism of
pretension
of statistics.

and Drobisch^ have long ago reduced to their proper
measure the pretensions of statistics, and it is now
generally admitted that in the sciences dealing with
human nature and society, as in those which inves-
tigate purely physical phenomena, observations, figures,
and measurements rarely if ever suffice to establish a
valid generalisation ; but that, if such be suggested by
other processes of thought, notably through attentive re-
flection on, and analysis of, single and accessible cases,
statistics supply the indispensable material by which

men as determined by circum-
stances : in fact, all expectation of
good from education and all the
work of history are based upon
the conviction that the will may
be influenced by growth of insight,
by ennoblement of feeling, and by
improvement of the external con-
ditions of life. On the other side,
a consideration of freedom itself
would teach us that the very
notion is repugnant to common-
sense if it does not include sus-
ceptibility to the worth of motives,
and that the freedom of willing
can by no means signify absolute
capacity of carrying out what is
willed." And, further, he remarks
on " the extreme overhastiness
with which the statistical myth
has been built up from deductions
which cannot be relied upon. We
have yet to obtain from exacter
investigations the true material
for more trustworthy conclusions
— material whicli should take the
place of the statistical myth above
referred to."

^ Before Lotze, and as early as
1849, M. W. Drobisch, the Her-
bartian, had reviewed Quetelet's
Memoir, 'Sur la Statistique morale,'
&c. ; and later (1867), after the
publication of A. Wagner's work, he
came back to the subject in an im-

portant tract, ' Die moralische Stat-
istik und die menschliche Willens-
freiheit,' which should be read by
every one who desires to form just
views on the subject. " In all
such facts," says Drobisch, "there
are reflected not natural laws pure
and simple, to which man must
submit as to destiny, but at the
same time the moral conditions of
society, which are determined by
the mighty influences of family
life, of the school, the Church,
of legislation, and are, therefore,
quite capable of improvement by
the will of man " (Zeitsch. fiir
exacte Philos.,' vol. iv. p. 329).
After all that has been said by
Quetelet, Buckle, and others, the
words of Schiller (' Wallenstein's
Tod,' ii. 3) still remain the best
statement of the problem : —

" Des Mensclieu Thaten uml Gedankeii,

wisst !
Sind uiclit wie Meeres blind bewegte

Wellen.
Die inure Welt, sein Microcosmus, ist
Der tiefe Schacht, aus deni sie ewig

quellen.
Sie sind notliwendig, wie des Baumes

Fniclit ;
Sie kann der Zufall gaukelnd nicht

verwandeln,
Habicli des Mensclien Kern erst unter-

sucht,
So weiss ich audi sein WoUen und seiu

Handeln."

ON THE STATISTICAL VIEW OF NATURE. 587

these generalisations can be tested, elevated to the rank
of leading canons of thought and research, and in rare
cases to that of the expression of a law of nature. So
far, therefore, as the complicated phenomena presented
in meteorology, agriculture, and economics are concerned,
. the suggestions leading to so-called laws have in every
case been got elsewhere — from astronomy, chemistry,
psychology, history, &c. ; and the work of science has
subsequently consisted largely in gathering the necessary
statistical materials by which to prove, amplify, curtail,
or refute them. In many cases it has been found that
even elaborate series of observations had not been per-
formed in such a manner ^ as would permit of the
necessary inferences being drawn from them. Similarly
biologists after Darwin have had to rearrange the collec-
tions made by those who came before the epoch marked
by that great name.

^ This refers as much to statist-
ical figures as to the knowledge
accumulated in many of the natural
sciences. Especially it refers to the
statistical material upon which
Quetelet based his st;irtling and
epix-h-making assertions : theearlier
critics had, as V. John observes
(' Geschichte der St;itistik,' p. 364),
dealt with the deductions whicii
(Quetelet had drawn, without deal-
ing witii the empirical material
itself. It was therefore of great
importance that Prof. Kchnisch of
Gottingen for the first time sub-
mitted the figui'es themselves to a
searching analysis. He did this
in the years 1875-76, in his articles
in the ' Zeitschrift fiir I'hilosophie
und Philosophische Kritik,' through
which it became evident that the
inferences were, as Lotze had
already suggested, to sny the least.

premature. " In the memoir ' Sur
le Penchant au Crime' (1831), only
four years, and in the work ' Sur
THomme,' only six years (1826-31)
of the 'compte general,' furnished
the data upon which the astound-
ing regularity with which crime
repeats itself was maintained " (V.
John, p. 365). Rehnisch adds many
other examples of the extreme in-
completeness of the recoids upon
which the theory of (Quetelet is
built up. More recent labours
have therefore been to a large
extent directed towards gathering
inoie complete statistical data, as
well as towards improving the
mathematical methods themselves
to which not only these but also
the population and mortality
statistics have been submitted, for
the purpose of arriving at average
figures.

588 SCIENTIFIC THOUGHT.

With the scientific treatment of the phenomena of
human society, the name of Adolphe Quetelet will
always be associated ; yet the mathematical or exact
school was not the only one which in the course of
the first half of the century had approached the subject.
25. Notably in Germany, under the ruling influence of

Historical '' '' *^

criticism, philosophical, historical, and critical studies, a school
of research had grown up calling itself the his-
torical. If the centre of gravity of the mathematical
view lies in the conception of a certain uniformity
and stability of social phenomena, the other school
looked more to historical changes and developments,
opposing the doctrine of the movement or of the
dynamics to that of the statics of society. Its in-
spiration came from a different quarter, and will
occupy us in a later portion of this work. For the
moment it suffices to remark how here also, in the
study of economics and social phenomena, the develop-
mental or genetic view has gradually dispelled the
earlier search for recurrent forms and regularities,
which we may term the morphological aspect : the
physiology has succeeded the anatomy of society.

But statistical methods, with the accompanying doc-
trines of probability and averages and the theory of
error, have not only been extensively and usefully
employed where large numbers of similar facts and
events crowd in upon our observation, and, as it were,
overwhelm us by their multitudes, as in astronomy,
meteorology, economics, and political arithmetic : they
have also shown themselves applicable by what we
may term the inverse method. Quetelet, when deal-

ON THE STATISTICAL VIEW OF NATCRE. 589

iug with lonj;- columns of Imiuaii statistics, felt a
relief in studying the average or mean man. Is it
not possible that in many instances what nature and
experience show us is only the average itself — our
senses and our intellect being too coarse to penetrate
to the numberless individual cases out of which the
sum or the average is made up ? May not even the
simplest phenomenon or thing in nature be in fact 20.

Application

an aggregate, a total, and its apparent behaviour and 'i pi'y^'cs.
properties merely a collective effect ? Both the kinetic
and the atomic view of natural objects and phenomena
seem to favour this way of regarding things, — the
former showing us in many cases motion and unrest
where at the first glance we saw only rest, and the
latter dissolving apparently continuous and homogene-
ous structures into crowds or assemblages of many
particles.

Thus the apparently steady pressure of gases is now
known to be in reality the violent bombardment of
the wall of the containing vessel by their mole-
cules ; and the most homogeneous and transparent
crystal is revealed, by its optical properties, as an
assemblage of very minute particles, held together by
forces which may be overcome by mechanical or
chemical agencies. Regarded from this point of view,
our knowledge of natural objects is merely statistical :
it deals with aggregates ; it is a collective knowledge.
And if we further consider that the sameness of the
numberless constituent particles is by no means proved,
this collective knowledge turns out to be merely con-
cerned witli averages : it is statistical, not individual,

590 SCIENTIFIC THOUGHT.

information that we seem to possess ; it resembles the
knowledge which an economist may possess of the
statistics of a society or of the properties of the
" mean " man. If such be the case, the theory of
large numbers and the calculus of probabilities must
be applicable and useful in dealing with those
phenomena which, through their minuteness and great
nimiber, elude our detailed examination.

The first to introduce this conception of treat-
ing a very large assemblage of moving things by the
method of averages was Joule,^ who, adopting Daniel
Bernoulli's conception, calculated the average velocity
which a particle of hydrogen gas must possess in
order to explain the total effect which shows itself
as a definite gas pressure at a definite temperature.
His result was that this average speed must be 6055
feet per second in order to be equal to the pressure
of one atmosphere at the zero temperature of the
Centigrade scale. The speed of the particles, however,
cannot be assumed to be equal, owing to continual
encounters ; and we are indebted to Clausius and
27. Clerk-Maxwell for introducing the more refined statis-

Clausius

and Clerk tical mctliods of the theory of probabilities. They
calculated the mean free path, and showed that
former calculations of the average speed were in the
main correct. The kinetic theory of gases afforded an
opportimity of brilliantly applying the conceptions of
averages or means and of the differences of frequencies
as the measure of the probability of certain occurrences.
In this case — as was first shown by Joule's figures — we

^ See stipra, vol. i. p. 434, and vol. ii. p. 110.

ON THE STATISTICAL VIEW OF NATURE. 591

have to do with billions and trillions of particles, moving
with velocities varying from zero to many thousands
of miles per second : we have therefore to do with
numbers which practically mean infinity — that is to
say, we have to do with that condition of things
where alone the laws of probability become strictly
correct.^

In this case, any deductions which can be made as to
the average condition or collective behaviour of an in-
finitely large assemblage of particles, whose individual
members move about with infinitely varying velocities
at infinitely varying speeds in infinitely varying direc-
tions, must be realised in the well - known laws of
gaseous bodies referring to pressure, volume, expansion,
molecular structure, and heat, assuming the latter to be
merely the sensible effect on our nerves of very numer-
ous impingements of infinitesimally small particles. It
is one of the greatest triumphs of the mathematical
methods applied in one of the most difficult instances,
that the average behaviour and collective properties of

J P. G. Tait ('Heat,' 1884, p. has its course changed. He thus
•355) says : " It is to Clausius that explains also the slowness of diffu-
we are indebted for the earliest i sion of ga.ses, and their very small
approach to an adequate treatment ' conductivity of heat. Clerk-Max-
of this question. He was the first well shortly afterwards improved
to take into account the collisions the theory by introducing, also from
between the particles, and to show the statistical point of view, the
that these did not alter the pre- consideration of the variety of
viously obtained results. He has speed at which the different par-
also the great credit of introducing tides are moving ; Clausius having
the statistical methods of the expressly limited his investigations
theory of probabilities, and of thus by assuming for simplicity that all
giving at least approximate ideas as move with equal speed. Clerk-
to the probable length of the nwin Maxwell explained gaseous friction,
free path — i.e., the average distance and gave a more definite determina-
travelled over by a i)article before tion of the length of the mean free
it imjjinges on another, and thus path."

592

SCIENTIFIC THOUGHT.

28.

Mathe-
matical rep-
resentation
of experi-
mental laws,

such moving crowds turn out to be exactly those laws
which Boyle, Charles, Gay-Lussac, Dalton, and Avogadro
had found out by direct experiments with gaseous bodies.
James Clerk - Max well was the first to recognise the
great importance of the statistical methods, and to
apply them in an exhaustive manner.^ And we witness
here the same spectacle which presented itself in the
history of the theory of probabilities. Problems which
are to be solved by the mere application of a few rules
dictated by common-sense and an exercise of common
logic, present in their complexity such a multitude
of traps, snares, and pitfalls, that it required the suc-
cessive application of the highest intellects to free the
reasoning from insidious errors, and put the results on

\/

^ The mauner in which Joule
dealt with the problem of a large
crowd of moving particles in his
memoir of 1851 was not strictly
statistical, inasmuch as he dealt
with an average velocitj' of the
molecules, and assumed that all the
molecules of a gas moved with the
same velocity. Clausius, in his
memoir of 1857, made use of as-
sumptions which were more in
conformity with nature : he had.
accordingly, to employ the calculus
of probabilities. Clerk - Maxwell's
occupation with the subject dates
from the year 1859, when he read
his paper, " Illustrations of the
Dynamic Theory of Gases," Part I.
(published in the ' Phil. Mag.,' 4th
series, vol. xix. p. 19, reprinted in
'Scientific Papers,' vol. i.) He
showed that " the velocities are
distributed among the particles
according to the same law as errors
are distributed among the observa-
tions in the theory of the method
of least squares. The velocities
range from 0 to <x, but the number

of those having great velocities is
comparatively small." If we leave
out Joule's imperfect attempt to
employ the statistical method, one
of the first applications of the
method of averages to a physi-
cal problem is to be found in
Sir G. G. Stokes's paper "On
the Composition of Streams of
Polarised Light from different
Sources" ('Camb. Phil. Trans.,'
1853), where he shows "what
will be the average effect of a very
great number of special sources
of light : thus giving one of the
earliest illustrations of the use,
in physics, of the statistical methods
of probabilities. . . . From this
point of view the uniformity of
optical phenomena becomes quite
analogous to the statistical species
of uniformity, which is now found
to account for the behaviour of the
practically infinite group of particles
forming a cubic inch of gas " (P. G.
Tait, 'Light,' 2nd ed., 1889, p.
237).

ON THE STATISTICAL VIEW OF NATURE. 593

undisputed and indisputable bases.^ In proportion a8
this has been done the calculated results have proved
to be in closer and closer accord with observed facts. 1
will here mention only one of the latest achievements
in this line of research and reasoning. Assuming — as
the atomic and kinetic theories do — that all external
phenomena of bodies can be reduced to the collective
or mean effect of a practically infinite variety of tur-
bulent movements of a very large number of particles, it
must be possible to give a mechanical explanation of
that remarkable property of all phenomena of nature, 29.

■^ Irreversi-

tirst noticed by Lord Kelvin, that they are essentially |^^'|*yj|''
irreversible — i.e., that, with very rare exceptions, they i"'"<=e-''«es.
take place in a certain direction which we may define as
an equalisation of existing diflterences of level, tempera-
ture, electric pressure, and similar inequalities. In order
to fix this remarkable property of all natural phenomena,
physicists found themselves obliged to introduce, along- •
side of energy and mass (which are both assumed to
conserve or maintain their total quantity), a third some-
thing which is the measure of the degree in which an
existing distribution of mass and energy can be con-
sidered to be capable of external, visible, finite activity

^ Those who are interested in 'Mathematical Appendix,' ]>. 17 ;

seeing how difficult it is to link and the great number of memoirs

together the common-sense argu- , referred to on p. 60 of that book,

ments of the theory of probabilities , Nevertheless Tait speaks of the still

in a consistent chain of unimpeach-
able logic, should read the report
on the various attempts to prove

remaining difficulties in the kinetic

theory of gases as having been

' greatly enhanced by an apparently

Clerk-Maxwell's law (mentioned in ; unwarranted application of the

the foregoing note) contained in I theory of probabilities on whicli

Prof. 0. E. Meyer's ' Kinetische I the stiitistical method is based."

Thoorie der Gase' (2nd ed., Breslau, ('Properties of Matter,' •2nd ed.,

1899), esiiecially p. 46, ic, and 1 1890, p. 291.)

VOL. II. 2 P

594

SCIENTIFIC THOUGHT.

30.
Lord
Kelvin.

— i.e., of its availability to do work.-^ The infinitesimally
small motions of an immense crowd may be exerted in
such a way as to total up to a finite movement per-
ceptible to our senses and accessible to our handling, or
they may so mutually annul each other as to present in
their finite sum and aggregate the appearance of rest and
inaction, however turbulent their behaviour might appear
to an observer gifted with powers of perception millions
of times more delicate than ours. Lord Kelvin intro-
duced the conception of the availability of energy,^
Clausius that of entropy (or energy which is hidden
away), to measure this condition of any natural system.
Has the statistical view any conception to put at the
base of this remarkable property of natural phenomena ?
It has, and we must assign to Clerk - Maxwell ^ the

\/

^ See supra, chap. vii. p. 128,
&c.

- Or of " motivity " {i.e.,
" energy for motive power "),
this being "the possession, the
waste of which is called dissi-
pation." See supra, chap, vii.,
p. 168 ; also Thomson (Lord
Kelvin), 'Popular Addresses,' vol.
i. p. 141.

■* The contributions of Clerk-
Maxwell to this topic are notably
two, independently of the larger
view which he took of statistical,
as compared with historical, know-
ledge, of which I treat farther on
in this chapter. First, in the con-
cluding remarks of his treatise on
the 'Theory of Heat' ("On the
Limitation of the Second Law of
Thermodynamics") he introduced
his famous conception of a " sort-
ing demon," the meaning of which
fanciful device was, to impress upon
the student of the dynamical theory
of heat, first the fact that the

loss of availability of the energy of
molecular motion is owing to the
coarseness of our senses ; and second,
that the restoration of differences
of temperature, or of availability
of energy, is simply a matter of
arrangement or order, not of an
increase of the intrinsic energy
of the system. The subject has
been frequently referred to, notably
by Lord Kelvin, who says (" On the
Sorting Demon of Clerk-Maxwell,"
Royal Institution, February 1879.
Reprinted in ' Popular Lectures
and Addresses,' vol. i. p. 1.37, &c. ) :
" Dissipation of energy follows in
nature from the fortuitous con-
course of atoms. The lost motivity
is essentially not restorable other-
wise than by an agency dealing
with individual atoms ; and the
mode of dealing with the atoms
to restore motivity is essentially a
process of assortment, sending this
way all of one kind or class, that
way all of another kind or class "

ON THE STATISTICAL VIEW OF NATURE.

i95

credit of having first indicated, and lo I'rof. Boltzniann ^
— aided by many otlier eminent natural pliilosopliers
— that of having definitely established, this higlily
suggestive explanation or illustration. The doctrine
of chances, to which artifice the statistical view of

(p. 139). "The conception of the
' sorting demon ' is merely mechan-
ical, and is of great value in purely
physical science. It was not in-
vented to help us to deal with
questions regarding the influence
of life and mind on the motions
of matter, questions essentially be-
yond the range of mere dynauiics"
(p. 1-41). The other contribution
througli which Clerk - Maxwell's
name has become celebrated in this
connection is to be ftjund in the
so-called Maxwell -15oltzmann law
of the distribution of kinetic energy
in a mass of moving particles.
The discussion of the subject
dates from the first memoir of
Clerk-Maxwell, quoted above ; and,
after Prof. Boltzmann had tre;ited
of the siime subject in 1868,
and Mr Watson in 1876, Clerk-
Maxwell returned to it in a paper
' ' On Energy in a System of
Material Points" ('Camb. Phil.
Soc.,' vol. xii.) In the year 1894
Prof. Bryan presented the 2nd
part of his Report on " Our
Knowledge of Thermodynamics "
('Brit. Assoc. Rep.,' 1894, p. 64,
&c. ), in which he gives an account
of all the different investigations
referring to this subject, up to
that date. This was followed by
a long discussion of the subject
in the pages of ' Nature ' (vol. li. ),
in which Messrs Bryan, Boltzmann,
Burbury, Culverwell, Larmor, and
H. W. Watson took part, and
which gave Prof. P.olt/mann the
opportunity of giving a hnal ex-
pression of his opinion (p. 415).

' Prof. Bolizmann's investiga-
tions connected witli tlie second

law of thermodynamics and the
kinetic theoi-y of gases cover the
last thirty - five years. He has
succeeded in putting the whole
problem more and more into a
strictly accurate, <i.s also into a
popularly intelligible, form. Un-
fortunately his vciy numerous con-
tributions lire scattered in various
periodical jiublications, and have
not yet appeared in a collected
edition. Most of them apjieared in
the Proceedings and Transactions
of the Vienna Academy, among
which the Atklress delivered on
the 29 th May 1886 can be
specially recommended. Since
then, and after the correspondence
in ' Nature ' referred to in the
last note, he has jjublished his
lectures ' Vorlesuugen iiber Gas-
Theorie' (2 vols., Leipzig, 1896-98).
He there (vol. ii. p. 260, note)
gives a list of the most important
literature on the subject, and also
a general summary regarding the
application of the theory of prob-
abilities to the distribution of the
kinetic energy of a crowd of
moving particles. In this con-
nection he also deals with the
consequences of the atomic hy-
pothesis, the irreversibility of all
natural pnjcesses, and the applica-
tion of tiie second law to the
history of the universe. He there
says (p. 253) : " The fact that
the closed system of a finite
number of molecules, if it had
originally an orderly condition, and
has then la])sed into a disorderly
one, must finally, after the lapse
of an inconceivably long i)eriod,
assume again orderly conditions, is

596

SCIENTIFIC THOUGHT,

phenomena reduces us, distinguishes between probable
and improbable events or arrangements of a crowd
of elements — i.e., between such as are of an average
and such as are of an exceptional character. Any
highly improbable arrangement — though possible — will
be followed by a gradual settling down to more prob-
able or average arrangements. And as in nature you
are forced to introduce the conception of availability, so
in the calculus of chances you can introduce a certain
mathematical quantity which is the measure of the proba-
bility. The more improbable, i.e., exceptional, the begin-

not a refutation, but a confirmation,
of our theory. But one must not
consider the matter thus : as if
two gases . . . which were initially
unmixed, then became mixed, after
a few days again unmixed, then
again mixed, &c. We find, rather,
that . . . only after a period
which, even compared with 10 10 ^"
years, is enormously great, a per-
ceptible unmixing would take place.
That this is practically equivalent
to never, we see, if we consider
that in this period there would
be, according to the laws of prob-
ability, many years in which, by
mere chance, all the inhabitants of
a large city would, on the same
day, commit suicide, or fire break
out in all its buildings ; whereas
the insurance companies are in so
good an agreement with facts that
they do not consider such cases at
all. If even a much smaller im-
probability were not practically
identical with imi)ossibility, nobody
could rely upon tlie present daj'
being followed by night and the
latter again by day. " And further
(p. 255) : " If we, therefore, repre-
sent the world under the figure of
an enormously large mechanical
system, composed of enormously

numerous atoms, which started
from a very perfectly ordered
condition, and exist still mainly
in an orderly condition, we arrive
at consequences which actually
stand in perfect harmony with
observed facts"; and (p. 258),
" That in nature the transition
from a probable to an improbable
condition does not happen as fre-
quently as the reverse, can be ex-
plained by the assumption of a
very improbable initial state of the
whole surrounding universe, in
consequence of which any arbitrary
system of interacting bodies is, in
general, in an improbable condition
to begin with. But one might
say, that here and there the
transition from probable to im-
probable conditions must, after
all, be observable. . . . From the
numbers regarding the inconceiv-
ably great rarity of a transition
from probable to improbable con-
ditions, happening in observable
dimensions and during an ob-
servable period, it is explained
how such a process within what
we, cosmologically, call a single
world, or, specially, our world, is
so extremely rare that any exjjeri-
ence of it is excluded."

ON THE STATISTICAL VIEW OF NATURE. 5 97

ning yoii choose, the greater your distance from the
average or most probable condition into wliich, in the
long-run, things must settle down ; the more play for
the equalising and levelling down of coming events.
The world — or at least that part of the world accessible
to our observation, and the playground of our activity —
shows a large amount of available energy, or, expressed
in a purely statistical manner, it started from a highly
improbable condition, and it is descending or running
down into a more probable or average condition. The si.

^ ^ "Avail-

doctrine of availability or of its reverse, of entropy ^^'^^^.y^j^ f^
— i.e., of the loss of availability — turns out to be a Probability,
theorem of probabilities ; and the refined mathematical
researches of Prof. Boltzmann and others show that
these two conceptions can be made to cover each other.
Moreover, we can bring home to the popular under-
standing the difference between the exceptional con-
dition, with its large amount of available energy, and
the average condition, with its large amount of self-
destructive and wasted energy (or entropy), by the
simile of order and disorder. For every arrangement of
a crowd of things or beings which is orderly, there are
innumerable arrangements which are disorderly ; every
one knows how easily the orderly arrangement lapses
into disorder, and nobody expects by mere haphazard
or chance movements to produce order out of disorder.
There are thousands of ways by which a stone can fall
from the peak of a mountain to the lower levels, but
only one direction which would take it up again to the
top. A tree has been suggested as the picture of the
course that natural movements take : for the one position

598 SCIENTIFIC THOUGHT.

in the trunk, where all branches and all roots meet,
there are in both directions numberless ways of rami-
fication or dissipation into the twigs or the root-fibres.
The statistical view measures the chances of an orderly
arrangement compared with disorder, of a commanding
unique position compared with the average or mean
position, by saying the odds are infinity to one against
it. The orderly exceptional position and arrangement
of a crowd does not possess more actual energy, but its
energy is directed, arranged, it has become available —
get-at-able.
32. And what is it that changes disorder into order ? It

"Selection"

as conceived ig a proccss of sclection. Maxwell imagined a sorting

by Maxwell. ^ o &

demon endowed with powers of perceiving and dividing
the immeasurably small movements of a gaseous body —
i.e., of a crowd of particles in turbulent to and fro move-
ment. Such a being could, by mere selection and
separation of the slow and fast moving particles, bring
order into disorder, converting the unavailable energy
into available energy. It would be a process of mere
sifting and arranging, such as is apparently carried out
in the living creation and by organic structures.-^ And
Maxwell went a step further, and conceived the idea

^ See supra, chap. x. p. 4-37, note, The mflueuce of animal or vegetable

life on matter is infinitely beyond
the range of anj' scientific inquiry
hitherto entered on. Its power of
directing the motions of moving
particles, in the demonstrated daily
miracle of our human free-will, and
in the growth of generation after
generation of plants from a single
seed, are infinitely different from
anj' possible result of the fortuitous
concourse of atoms."

where the selective action of certain
organisms is referred to in connec-
tion with Prof. Japp's Address to
the Brit. Assoc, in 1898. Lord Kel-
vin says ("On the Dissipation of
Energy," 1892, 'Popular Lectures
and Addresses,' vol. ii. p. 463, &c. ) :
" It is conceivable that animal life
might have the attribute of using
the heat of surrounding matter, at
its natural temperature, as a source
of energy for mechanical effect. . . .

ON THE STATISTICAL VIEW OE NATURE. 599

that, after all, the whole of our knowledge of natural
phenomena and natural things may be only statistical,
not historical or individual. " In dealing," he says,^
"with masses of matter, while we do not perceive the
individual molecules, we are compelled to adopt the
statistical method of calculation, and to abandon the
strict dynamical method in which we follow every
motion by the calculus. It would be interesting to
inquire how far those ideas about the nature and the
methods of science wdiich have l)een derived from
examples of scientific investigation in which the
dynamical method is followed, are applicable to our
actual knowledge of concrete things, which, as we have
seen, is of an essentially statistical nature, l)ecause no
one has yet discovered any practical method of tracing
the path of a molecule, or of identifying it at different
times." And elsewhere ^ he says : " The statistical
method of investigating social questions has Laplace
for its most scientific and Buckle for its most popular

^ 'Theory of Heat,' 8th ed., p. I rather that of a steersman of a

329. vessel — not to produce, but to

- ' Life of Clerk - Maxwell by regulate and direct, the animal

Campbell and Garnett.' Chap. xiv. powers." He then speaks of the

contains a paper with the title, I '• powerful effect on the world of

Does the progress of Physical
Science tend to give any advantage
to the opinion of Necessity (or
Determinism) over that of the

thought" which the developments
of molecular science are likely to
have, considering the "most im-
portiint effect on our way of think-

Contiiigency of Events and the ' ing to be that it forces on our

Freedom of the Will?" In it (p.
435) there occurs the following
passage : '" The doctrine of the
conservation of energy, when ap-
plied to living beings, leads to the

attention the distinction between
two kinds of knowledge, which
we may call for ctmvenience the
Dynamical and Sbitistical." The
paper from which the extracts in

conclusion that the soul of an the text are taken is dated 1873.

animal is not, like the mainspring
of a watch, the motive power of
the body, but that its function is

Clerk-Maxwell was then forty-one
years of age.

600 SCIENTIFIC THOUGHT.

expounder. Persons are grouped according to some
characteristic, and the number of persons forming the
group is set down under that characteristic. This is
the raw material from which the statist endeavours
to deduce general theorems in sociology. Other
students of human nature proceed on a different
plan. They observe individual men, ascertain their
history, analyse their motives, and compare their ex-
pectation of what they will do with their actual con-
duct. . . . However imperfect this study of man may
be in practice, it is evidently the only perfect method in
principle. ... If we betake ourselves to the statistical
method, we do so confessing that we are unable to
follow the details of each individual case, and expecting
that the effects of widespread causes, though very differ-
ent in each individual, will produce an average result on
the whole nation, from the study of which we may
estimate the character and propensities of an imaginary
being called the Mean Man. Now, if the molecular
theory of the constitution of bodies is true, all our
33. knowledge of matter is of a statistical kind. A con-

Statistieal . i i /. i i i • i- m

knowledge stitucut molcculc 01 a body has properties very different
from those of the body to which it belongs. The
smallest portion of a body which we can discern con-
sists of a vast number of molecules, and all we can
learn about the group of molecules is statistical in-
formation. . . . Hence those uniformities which we ob-
serve in our experiments with quantities of matter con-
taining millions of millions of molecules are uniformities
of the same kind as those explained by Laplace and
wondered at by Buckle, arising from the slumping to-

of nature.

ON THE STATISTICAL VIEW OF NATURE. COl

gether of multitudes of cases, eacli of whicli is by no
means uniform with the others. . . . Much liglit may
be thrown on some of these questions by the consider-
ation of stabihty and instabihty. When the state of
things is such that an infinitely small variation of the
present state will alter only by an infinitely small
quantity the state at some future time, the condition
of the system, whether at rest or in motion, is said to be
stable ; but when an infinitely small variation in the
present state may bring about a finite difference in the
state of the system in a finite time, the condition of the
system is said to be unstable. It is manifest that the
existence of unstable conditions renders impossible the
prediction of future events, if our knowledge of the
present*state is only approximate and not accurate. It
has been well pointed out by Prof. Balfour Stewart that
physical stability is the characteristic of those systems
from the contemplation of which determinists draw their
arguments, and physical instability that of those living
bodies, and moral instability ^ that of those developable
souls which furnish to consciousness the conviction of
free-will." "

' There is an awkward misprint
in the first edition of 'The Life,'
which i.-i corrected in the second
edition.

- Clerk - Maxwell frequently re-
verts to this subject. In an article
on " Molecules," contributed to the
ninth edition of the ' Ency. Brit.'
(reprinted in ' Scientific Pajters,'
vol. ii.), he contrasts historical and
statistical knowledge as follows (p.
373) : " The modern atoinists have
ado[)ted a method which is, I
believe, new in the department of

mathematical physics, though it
has long been in use in the section
of statistics. When the working
members of Section F (of the Brit.
Assoc.) get hold of a report of the
census, or any other document con-
taining the numerical data of
economic and social science, they
begin by distributing the whole
population into groujis according to
age, income-tax, education, religious
belief, or criminal convictions. The
number of individuals is far too
great to allow of their tracing the

602

SCIENTIFIC THOQGHT.

The conceptions involved in the atomic and kinetic
views of natural processes, and the statistical manner of
dealing with these crowds of moving particles, have thus
introduced into natural philosophy two distinct and novel
considerations not known to former ages : first, the con-
sideration that our knowledge of things and phenomena
in nature is not historical, but that it is that of the
mean or average and of the total effects produced by an
immensely large number of singly imperceptible events
upon our senses which are too coarse to receive or deal
with individual occurrences ; secondly, the consideration
that our knowledge is not purely mechanical, inasmuch

history of each separately, so that,
in order to reduce their labour
within human limits, they concen-
trate their attention on a small
number of artificial groups. The
varying number of individuals in
each group, and not the varying
state of each individual, is the
primary datum from which they
work. This, of course, is not the
only method of studying human
nature. We may observe the eon-
duct of individual men and compare
it with that conduct which their
previous character and their present
circumstances, according to the best
existing theory, would lead us to
expect. Those who practise this
method endeavour to improve their
knowledge of the elements of
human nature in much the same
way as an astronomer corrects the
elements of a planet by comparing
its actual position with that de-
duced from the received elements.
The study of human nature by
parents and schoolmasters, by his-
torians and statesmen, is, there-
fore, to be distinguished from that
carried on by registrars and tabu-
lators, and by those statesmen who
put their faith in figures. The one

may be called the historical and
the other the statistical method.
The equations of dj-namics com-
pletely express the laws of the
historical method as applied to
matter, but the application of these
equations implies a perfect know-
ledge of all the data. But the
smallest portion of matter which
we can subject to experiment con-
sists of millions of molecules, not
one of which ever becomes sensible
to us. We cannot, therefore, ascer-
tain the actual motion of any one
of these molecules ; so that we are
obliged to abandon the strict his-
torical method of dealing with large
groups of molecules. The data of
the statistical method, as applied to
molecular science, are the sums of
large numbers of molecular quan-
tities. In studying the relations
between quantities of this kind, we
meet with a new kind of regularity,
the regularity of averages, which
we can depend upon quite suffi-
ciently for all practical purposes,
but which can make no claim to
that character of absolute precision
which belongs to the laws of
abstract dynamics."

ox THE STATISTICAL VIEW OF NATUKE. GO.i

as l)esides the i>urt'l}' luecluiuical luoveiuents uud their
summation, it must contain a reference to the nature of
our own faculties — a principle which indicates to what
extent the elementary movements come under our control
or escape it. There must be a principle which measures
the availability and usefulness — for our powers — of natural
processes, marking of!" what is orderly for our senses and
accessible to our powers, from what is disorderly and in-
accessible. This principle the founders of the science of
Thermodynamics — liankine, Clausius, and Thomson — had
empirically established : Thomson haA'ing foreseen its
far-reaching importance in the economy of nature and
the applications of industry. The statistical view of 34.

As opposed

natural phenomena forced upon us by atomism and to historical

*- L */ ana laeciian-

kinetics has shown us that it is not a purely me- ledge."""''
chanical^ principle. It is one belonging to the theory
of averages and probability. The scientific view of
nature is thus, as Clerk-Maxwell says, neither purel}'
historical nor purely mechanical — it is statistical."

To this view of the scientific treatment of natural
phenomena Clerk-Maxwell has attached a further con-

^ Clerk-Maxwell, m a review of commercial and the technical

Tait's "Thermodynamics" (' Scien- chiefs. As regularity is in many

tific Papers,' vol. ii. p. 670) : "The i instances the condition of success,

truth of the second law is therefore ' any Ijreak of its routine is care-

a statistical, not a mathematical, fully examined and criticised. In

truth, fur it depends on the fact such cases the technical man will

tbit the bodies we deiil with consist i look to the proximate mechanical

of millions of molecules, and that
we never can get hold of single
molecules."

" Any one who has had occasion

causes for an e.Kplanation, whereas
the commercial man, unable to
reflect on the technical and mechani-
cal conditions of tlie special case.

to observe the internal work of any , will always refer to his statistics of

large industrial or manufacturing the past as a guide in judging the

organisation, will have noticed the immediate difficulty that is before

twofold way in which important I him.
occurrences are looked at bv the '

604 SCIENTIFIC THOUGHT.

sideration, which is interesting inasmuch as it shows
that that which I called above the inverse method of
statistics does not involve ideas identical with those
which the direct method — as applied in ordinary
economic and social statistics — involves. In the direct
processes of statistics, which we may class under the
all-case or enumerative method, we rise, from a large
number of individual facts and data which are all
different, to the conception of certain uniform averages,
to recurring, or continuously and slowly changing, totals,
such as we handle daily in sciences like meteorology,
in moral, economic, and industrial statistics. The
averages are nowhere represented by the individuals,
and the regularity of the totals does not appear in
dealing with single instances, or with such restricted
numbers as come under the personal control of any
of us ; hence the general uselessness of statistics in
handling individual cases or predicting special occur-
rences. But the statistical view of natural phenomena,
as applied to the atomic constitution of bodies, leads
us ultimately to the conception that the smallest con-
stituents of matter, the atoms, exhibit a regularity and
recurrent uniformity of structure which reminded Sir
John Herschel of manufactured articles. The attempt
to reduce the somewhat numerous types of these ulti-
mate elements to purely geometrical configurations of
the homogeneous elements of one substance has indeed
failed, though it is being continually revived. But
allowing that there exist some sixty or seventy distinct
forms of matter or atomic structures, these structures
seem to be alike and stable wherever we meet with

ON THE STATISTICAL VIEW OF NATUKK. 605

them ; our observations ranging over very large distances
ill space and time, from the particles immediately before
u.s in artificial flames to the vibrations of atoms of distant
stars, which must have taken millions of years to reach
us. " I do not think," says Clerk-Maxwell,^ " that the
perfect identity which we observe between dilierent por-
tions of the same kind of matter can be explained on the
statistical principle of the stability of the averages of
large numbers of quantities, each of which may differ
from the mean. . . . For if the molecules of some sub-
stance, such as hydrogen, were of sensibly greater mass
than others, we have the means of producing a separation
between molecules of different masses, and in this way
we should be able to produce two kinds of hydrogen,
one of which would be somewhat denser than the other.
As this cannot be done, we must admit that the equality
which we assert to exist between the molecules of hydro-

' ' Theory of Heat,' p. 329, &c. rlesign, it is replied that those varia-
Cf. also many passages in the i tions which are not conducive to

articles on "Atom," "Molecule,"
"Constitution of Bodies," &c., re-
printed in the second volume of
' .Scientific Papers ' ; inter alia, p

the growth and multiplication of
living beings tend to their destiuc-
tion, and to the removal thereby of
the evidence of any adjustment not

483 : " ]5ut the equalitj' of the i beneficial. The constitution of an
constants of the molecules is a fact i atom, however, is such as to render

of a very difi'erent order. It arises
from a particular distribution of

it, so far as we can judge, independ-
ent of all the dangers arising from

matter, a cuUocution, to use the ex- I the struggle for existence. Plaus-
])ression of Dr Chalmers, of things \ ible reasons may, no doubt, be as-
which we have no difficulty in signed for l)elieving that if the
imagining to have been arianged constants had varied from atom to
otherwise. But man}' of the atom through any sensible range,
ordinary instances of collocation are the bodies formed by aggregates of
adjustments of constants, which are ■ such atoms would not have been so
not only arbitrary in their own well fitted for the construction of
nature, l)ut in which variations the world as the bodies which
actually occur ; and when it is , actually exist. But us we have
pointed out that these adjustments I no experience of bodies formeil of
are beneficial to living beings, and | such variable atoms, this must re-
are therefore instances of benevolent ' main a bare conjecture."

606

SCIENTIFIC THOUGHT.

gen applies to each individual molecule, and not merely
to the average of groups of millions of molecules."
And Clerk-Maxwell goes on to show how the fact that
the molecules ^ " all fall into a limited number of classes
or species with no intermediate links ... to connect
one species with another by miiform gradation, produces
that kind of speculation with which we have become so
familiar under the name of theories of evolution, it being
quite inapplicable to the case of the molecules. The
individuals of each species " of molecules are like tuning-
forks all tuned to concert pitch, or like watches regulated
to solar time." ^

1 'Theory of Heat,' p. 330.

2 Ibid., p. 331.

^ The passages quoted from Clerk-
Maxwell's writings, and the infer-
ences drawn by liim. were criticised
by Clifford in a lecture delivered
in 1874 with the title, "The
First and the Last Catastrophe.
A Criticism of some recent Specula-
tions about the Duration of the
Universe" (reprinted in 'Lectures
and Essays,' vol. i. p. 191 sqq.) ; and,
quite recently. Prof. Ward has, in
his Gifford lectures, reviewed both
Maxwell's and Clifford's arguments
('Naturalism and Agnosticism,' vol.
i. p. 99, &c. ) As Prof. Ward says,
the ideas of Herschel and Clerk-
Maxwell " are far more due to theo-
logical zeal than to the bare logic of
the facts." It is, therefore, out of
place to discuss here the philosophi-
cal consequences of the ideas of the
immutability or of the gradual
evolution of the ultimate elements
of matter. In a former chapter
(see pp. 360 sqq. and 369, note, of
this volume) I referred to the
theories of the evolution of the
different chemical elements as
they have been put forward by
various scientific authorities. The

intei-est which attaches to the pas-
sages quoted from Clerk-Maxwell
is, that in them, for the first time,
an instance was given of the
application of statistical methods
in the domain of abstract science.
The reader may gather from a
perusal of the writings mentioned
above, as also of the present
and foregoing chapters of this
history, that there is an inherent
contradiction (or as Kant would
say, antinomy) between the logi-
cal methods and the highest ob-
jects of scientific reasoning. The
methods all tend in the direction
of reducing existing differences in
the things and phenomena of natui'e
to a small number of data which
are easily grasped and calculated,
whereas the observation of things
natural forces increasingly upon us
the existence of ever greater differ-
ences, changes, and varieties. The
question presents itself, Is it likely
that a process the principle of which
is unification and simplification, will
ever lead to a comprehension of
that which increasingly reveals
itself to be infinitely complex and
varying ? Dr Larmor has some
remarks which bear on this subject

ON THE STATISTICAL VIEW OF NATURE. 607

The progress of modern science has, however, given 35.

SariieneBii

a great impetus to the development of statistical or ""J vari-
enumerative methods, and notably to the graphical
registration of these results, through the importance
whicli the phenomena of variation attained in all theories
of evolution, and chiefly in those based upon natural
selection. Quetelet had already pointed to the study of
the maxima of the possible deviations from the mean and
average, as of special interest and value. Xevertheless,
the centre of gravity of the aspect unfolded in the
writings of Quetelet and his followers was the idea of
miiformity and average sameness. The conception of
change and development did not fit naturally and logi-
cally into their scheme.^ It was not till after the

C-Etlier and Matter,' j). 288):
" Tlie processes by which our con-
ception of the uniformity of Nat-
ure is obtained essentially involve
averaging of effects, and lose their
eflScacy long before the individual
molecule is reached. Mechanical
deterniinateness thus need not in-
volve molecular determinateness ;
then why should either of them
involve determination in the en-
tirely distinct province of vital
activity .• . . . Every vital process
may conceivably be correlated with
a mechanical process, as to its pro-
gress, just to that extent to which
it is possible experimentally to
follow it, without lending any
countenance to a theory that would
place its initiation under the control
of any such system of mechanical
relations. In other terms, there is
room for com])lete mechanical co-
ordination of all the functions of an
organism, treated as an existing
material system, without requiring
any admission that similar prin-
ciples are supreme in the more

remote and infinitely couiidex
phenomena concerned in giowth
and decay of structure."

^ A fate overtook the theories and
writings of Quetelet and Buckle
similar to that which I had occasion
to notice above in referring to the
great work of A. von Humboldt.
Through the influence of the evolu-
tionist movement, prepared by
Lamarck, von Baer, Spencer, and
others, centring in Darwin, the
statical or morphological view had
in every department of science to
give way to the kinetic or genetic
view. This explains why some
names, once celebrated, like Hum-
boldt and Buckle, sank rajiidly
into oblivion. Grant Allen, in
his somewhat one-sided but spirited
monograph on Darwin (' English
Worthies,' 1888), ha.s drawn atten-
tion to this. I give here the
striking ))assage, reserving for the
sequel of this work the liberty to
differ in detail from much in it
that is too drastically expressed :
"There is no dej)artment of human

608

SCIENTIFIC THOUGHT.

36.
Darwin.

publication of the ' Origin of Species ' that the phenomena
of variation — i.e., of deviation from the existing type
or average — forced themselves upon naturalists and
statisticians as requiring to be specially observed, de-
scribed, and accounted for. Since that time a new
branch of science has sprung up, unknown before even
by name — the study of variation in nature. This, as we
have seen in a former chapter, is one of the great and
important aspects of nature brought prominently before
the thinking naturalist by Darwin's and Wallace's dis-
coveries, and strongly urged forward by the independent
arguments of Mr Herbert Spencer. It involves the
great problems of Inheritance and Adaptation. What
are the facts, and what the causes of variation, of the
moving and propelling principle in natural selection and
evolution ? The latter is a physiological problem — the
former is one of statistics.

thought or human action which
evolutionism leaves exactly where
it stood before the advent of the
Darwinian conception. In nothing
is this fact more conspicuously seen
than in the immediate obsolescence
(so to speak) of all the statical
pre-Darwinian philosophies which
ignored development, as soon as
ever the new progressive evolu-
tionary theories had fairly burst
upon an astonished world. Dog-
matic Comte was left forthwith to
his little band of devoted adherents ;
shadowy Hegel was relegated with
a bow to the cool shades of the
common-rooms of Oxford ; Buckle
was exploded like an inflated wind-
bag ; even Mill himself, — magnum
et venerabile nomen, — with all his
mighty steam - hammer force of
logical directness, was felt instinct-
ively to be lacking in full appreci-

ation of the dynamic and kinetic
element in universal nature.
Spencer and Hartmann, Haeckel
and Clifford, had the field to them-
selves for the establishment of their
essentially evolutionary systems.
Great thinkers of the elder genera-
tion, like Bain and Lyell, felt bound
to remodel their earlier conceptions
by the light of the new Darwinian
hypotheses. Those who failed by
congenital constitution to do so,
like Carlyle and Carpenter, were,
philosophically speaking, left hope-
lessly behind and utterly extin-
guished. Those who only half
succeeded in thus reading them-
selves into the new ideas, like
Lewes and Max Muller, lost gi-ound
immediately before the eager on-
slaught of their younger com-
petitors" {loc. cit., p. 197).

ON THE STATISTICAL VIKW OF XATURp]. 609

The first who seems to have fully grasped the Dar-
winian problem from this point of view is Mr Francis
Galton/ who in a series of papers, and notably in his 37.
well-known works on 'Hereditary Genius ' (1869) and
on ' Inheritance' (1889), made a beginning in the statis-
tical treatment of the phenomena of Variation. The
novel point of view which was thus introduced into
natural science was perhaps somewhat obscured by its
immediate application to a most ditticult and unic^ue
problem, which can hardly be discussed without im-
porting what may be called a sentimental bias. This
was the question of the connection through descent
of those rare occurrences in human nature which we
term genius. Mental phenomena had been almost
entirely passed over^ by Darwin. The residts which
Mr Galton arrives at, so far as the phenomena of genius
are concerned, are of minor importance compared with
the general methods which he introduced or suggested
for dealing with statistics of heredity. In these he
combined the ideas of Quetelet with that remarkable

^ Mr Francis Galton (born 1822, genius," which was "usually

a grandson of Erasmus Darwin) scouted." He rightly claims "to

had, like his celebrated cousin, be the first to treat the subject in
begun his career as a medical | a statistical manner, to arrive at

student, and then become a well- numerical results, and to introduce

known traveller and explorer. the 'law of deviation from an

Subsecjuently he devoted himself average ' into discussions on
to meteorology, where he drew
attention to the e.Kistence and
theory of anticyclones. His first

heredity" (Preface to 'Hereditary
Genius,' published one j-ear after
Darwin's great work in which was

publication, referring not to physi- jiut forward the hypothesis of

eal Vjut to human statistics, ap- • Pangenesis).

peared in ' Macmillan's Magazine ' - As stated by Darwin himself.

in 186.'), in the shape of two See 'Animals and Plants under

articles on "Hereditary Talent Domestication' (1868), vol. ii. p.

and Character." Here he intro- 353.

duced the " theory of hereditary

VOL. II. 2 Q

610

SCIENTIFIC THOUGHT.

38.
"Pan-
genesiB.'

speculation of Darwin's which he put forward at the
end of his work on ' The Variation of Animals and
Plants under Domestication' (1868) — the theory of
" Pangenesis." " This hypothesis implies that the whole
organisation, in the sense of every separate atom or unit,
reproduces itself. Hence ovules and pollen grains, the
fertilised seed or egg as well as buds, include and consist
of a multitude of germs thrown off from each separate
atom of the organism." ^ These germs he calls gem-
mules, and admits that they agree to some extent with
Buffon's organic molecules, only that neither in these nor
in Spencer's physiological units does it seem clear that
each " independent or autonomous " organic unit, say
each cell, throws off or contributes its free gemmule (or
gemmules), which is capable of reproducing a similar
cell.2

The theory of Pangenesis has not found much favour
with biologists.^ Por their purposes it would be neces-

^ Loc. cit., vol. ii. p. 358.

- " Physiologists agree that the
whole organism consists of a multi-
tude of elemental parts, which are
to a great extent independent of
each other" {loc. cit., vol. ii. p.
368). Darwin then quotes Claude
Bernard (1866) and Virchow (1860)
on the doctrine of the " autonomy' "
of cells : " I assume that the gem-
mules in their dormant state have
a mutual affinity for each other,
leading to their aggregation either
into buds or into the sexual ele-
ments" (p. 374). "Physiologists
maintain, as we have seen, that
each cell, though to a large extent
dependent on others, is likewise, to
a certain extent, independent or
autonomous. I go one small step
farther, and assume that each cell

casts off a free gemmule, which is
capable of reproducing a similar
cell'' (p. 377). "As each unit, or
group of similar units throughout
the bodj', casts off its gemmules,
and as all are contained within the
smallest egg or seed, and within
each spermatozoon or pollen-grain,
their number and minuteness
must be something inconceivable "
(p. 378).

^ Grant Allen dismisses the
whole speculation in the fol-
lowing words : " The volume on
the variation of animals and
plants contained also Darwin's one
solitary contribution to the pure
speculative philosophy of life — his
' Provisional Hypothesis of Pan-
genesis,' by which he strove to
account, on philosophical principles,

ON THE STATISTICAL VIEW ()F NATURE. 611

saiy to define soinewluil more clearly what those units
or gemmules are. This has accordingly been attempted
in several other hypotheses put forward about tlie
same time or somewhat later; each thinker having
elaborated, when so inclined, his own fanciful picture,
following consciously or unconsciously in the line of
Spencer's physiological units. We have in Germany
Niigeli's micellar theory, Haeckel's kinetic hypothesis,
Prof. Weismann's idioplasma theory, and Prof. Ptiiiger's
theory of the compound organic molecule. All these
theories attempt to bring biological phenomena into
closer connection with the firmly established concep-
tions current in physics and chemistry, where atomism
and kinetics have been so successfully used in analysing
and, to a smaller extent, in putting together the com-
plex processes of nature. Of this I treated in former 39.

Lends itself

chapters. But the hypothesis of Darwin is capable of ^ statistical

■■■ -^ ^ A treatment.

another treatment. Wherever we have to deal with a
large, an immense number of single elements or units,
which in their totality form certain phenomena, there

for the general facts of physical put forth expressly to meet the

and mental iieredity. Not to self -same difficulty. But while

mince matters, it was his one Darwin's hypotliesis is rudelj'

conspicuous failure, and is now materialistic, Herbert Sjieucer's

pretty universally admitted as is built up by an acute and
such. Let not the love of the , subtle analytical perception of all

biographer deceive us ; Darwin the analogous facts in universal

was liere attempting a task ultra nature. It is a singular instjince

vires. As already observed, his of a crude and essentially uu-

mind, vast as it was, leaned rather pliilosophic conception endeavour

to the concrete than to the ing to replace a finished and

abstract side : he lacked the delicate philosophical idea " {loc.

distinctively metaphysical and cit., p. 12G). See also many

sjjeculative twist. Strange to say, references to the unfavourable

too. liis abortive theory appeared criticisms of Pangenesis in the

some years later than Herbert tliird volume of the ' Life of

Spencer's magnificent all-sided con- Charles Darwin.'
-cejition of ' Phymological Units,'

612 SCIENTIFIC THOUGHT.

is room for the statistical treatment. This treatment
entirely ignores the definite nature of the component
units, and merely investigates those properties which
depend upon aggregation in large numbers, the average
or mean results, and the chances of deviations or vari-
ations. Now, if organic beings are supposed to be made
up of immeasurably large numbers of units transmitted
to them by inheritance, and capable of self -multiplication,
they must be subject to certain regularities, to regular
deviations or recurrent changes ; and, under the influ-
ence of selection, be it artificial or automatic, to
certain developments which can be studied without a
precise knowledge of the biological, chemical, or physi-
cal nature of these units themselves, or of the mechan-
ism of their movements. Economics, meteorology, the
kinetic theory of gases, deal in this way with complex
phenomena, the exact individual history of which they
are quite incapable of narrating. As in the case of the
kinetic theory of gases we had to translate into statis-
tical language the phenomena of pressure, temperature,
volume, available or hidden energy, &c., so in dealing
statistically with biological phenomena, such as inherit-
ance, on the basis of the theory of Pangenesis, we have
to translate into statistical language such phenomena as
" types, sports of nature, stability, variation and in-
dividuality." " The word man," as ]\Ir Galton says,^
" when rightly understood, becomes a noun of multitude,
because he is composed of millions, perhaps billions, of
cells, each of which possesses in some sort an independ-
ent life, and is parent of other cells. He is a conscious

1 'Hereditary Genius' (1892), pp. 349, 350.

ON THE STATISTICAL VIEW OF NATURE. 613

whole, formed by the joint agencies of ;i host of what
appear to us to be unconscious or barely conscious
elements. . . . The doctrine of Pangenesis gives excellent
materials for mathematical formulas, the constants of
which might be supplied through averages of facts." ^
Mr Galton does " not see any serious difficulty in the
way of mathematicians in framing a compact formula,
based on the theory of Pangenesis, to express the com-
position of organic beings in terms of their inherited
and individual peculiarities, and to give us, after certain
constants had been determined, the means of foretell-
ing the average distribution of characteristics among a
large multitude of offspring whose parentage was
known." ... In short, the theory of Pangenesis brings
all the influences that bear on heredity into a form that
is appropriate for the grasp of mathematical analysis."

Evidently in the mind of Mr Galton the problem of 40.

Problem of

heredity divides itself into two distinct problems ; and Heredity.
he has himself laboured at the solution of both. We
may call the one the " historical " or the " mechanical "
problem, the other the " statistical " problem, following
the distinction which Maxwell drew when dealing; with
the kinetics of gases. The historical problem would
involve a more detailed account of the nature of those
organic units which the theory of Pangenesis, in common
with other similar theories, like those of Buffbn and
Niigeli, assumes, and of the mechanism by which they
unite and are transmitted. If this is impossible, or at
all events highly hypothetical, the actual following up —
by observation and experiment — of the phenomena of

' ^Hereditary Genius' (1892), p. .356. -' Ibia.. p. 358.

614

SCIENTIFIC THOUGHT.

variation in special instances would at least allow us to
accumulate many interesting life-histories of families of
living creatures, and might some day lead to important
generalisations. Mr Galton has himself made an
attempt to modify and further elaborate the hypothesis
of Pangenesis ; ^ and Mr William Bateson has given us.

^ Mr Galton in 1871 advanced
certain objections to the theory
of Pangenesis, based upon experi-
ments made with the transfusion
of blood, and tending to show that
blood cannot be the carrier of the
germs or gemmules. See a paper
read before the Royal Society,
March 30, 1871. Darwin did not
think Pangenesis had "received its
deathblow, though from presenting
so many vulnerable points, its life
is always in jeopardy " (' Life of
Darwin,' vol. iii. p. 195). In 1875 Mr
Galton published an article in the
' Contemporary Review,' vol. xxvii.
p. 80, entitled " A Theory of Hered-
ity," in which he put what may be
termed the atomic theorj^ of life
and its propagation into a form in
which it might serve as a working
formula for statistical research.
It is a mistake to look upon any
such theory as a biological,
mechanical, or historical explana-
tion. For statistical purposes only
the scantiest data need be borrowed
from biology. There is, however,
one very important biological con-
ception which Galton introduced,
which is not contained in Darwin's
"provisional hypothesis, "and which
somewhat later became celebrated
mainly through the writings of
Prof. Weismann. This is the dis-
tinction between the germ-plasma
and the body- plasma, the former
preserving the continuity of life
and inheritance, whereas the latter
forms the character of the indi-
vidual, and is probably sterile. In
fact, Galton, from a purely statis-

tical point of view, anticipated — as
several other naturalists did, from
various other aspects — the theory
of the differentiation of the ger-
minal from the personal portions
or aggregates of life units in the
■' stirp " or sum - total of organic
units of some kind which are to be
found in the newly fertilised ovum.
Prof. J. A. Thomson ('The Science
of Life,' p. 147) gives the following
succinct statement of the concep-
tion of "stirps": " Fir.st. Only
some of the germs within the stirp
attain development in the cells of
the 'body.' It is the dominant
germs which so develop. Second.
The residual germs and their pro-
geny form the sexual elements or
buds. The part of the stirp
developed into the ' body ' is almost
sterile. . . . The continuity is kejit
up by the undeveloped residual
portion. Third. The direct descent
is not between body and body, but
between stirp and stirp. The stirp
of the child may be considered to
have descended directly from a
part of the stirps uf each of its
parents ; but then the personal
structure of the child is no more
than an imperfect representation of
his own stirp, and the personal
structure of each of the parents is
no more than an imperfect repre-
sentation of each of their own
stirps. This is a definite expression
of the notion that the germinal cells
of the offspring are in direct contin-
uity with those of the parents. The
antithesis between the ' soma ' and
the chain of sex-cells is emphasised."

ON THE STATISTICAL VIEW OF NATURE. G15

in iiis ' Muteiiiils for the Study of Variation,' a remark- 41.

MrBateson'i

able specimen of tlie historical treatment of the proljlem. i''storicai

*^ *■ treatment.

But the aspect we are at present specially interested in
is the other one which, in the course of Mr Galton's
studies, has presented itself to him with increasing clear-
ness, namely, the bearing which the general laws of
averages and statistics have on the facts of inheritance.
Thus, in his second main contribution to the suljject,
which appeared in 1889, twenty years after the earlier
work, the statistical problem comes out much more
clearly, and quite separated from the mechanical or the
historical one. The hypothesis of Pangenesis is retained
only as a general scheme which suggested " the idea
though not the phrase of particulate inheritance." It
was felt to be no longer necessary, for the purpose of
the problem, " to embarrass ourselves with any details of
theories of heredity beyond the fact that descent either 42.

, 1 • I. • )> 1 . 1 1 "Particul-

was particulate or acted as 11 it were so. And what ate" descent,
is meant by " particulate " {i.e., " bit by bit ") is illus-
trated in the following expressive manner : " " Many of
the modern buildings in Italy are historically known to
have been built out of the pillaged structures of older
days. Here we may observe a column or a lintel serving
the same purpose for a second time, and perhaps liearing
an inscription that testifies to its origin ; while as to the
other stones, though the mason may have chipped them
here and there and altered their shape a little, few if
any came direct from the quarry." " This simile gives a
rude though true idea of the exact meaning of Particulate
Inlicritance— namely, that each piece of the new structure

^ 'Natural Inheritance,' p. 193. - Iliiil., p. 8.

616 SCIENTIFIC THOUGHT.

is derived from a corresponding piece of some older one,
as a lintel was derived from a lintel, a column from a
column, a piece of wall from a piece of wall. . . . We
appear to be severally built up out of a host of minute
particles of whose nature we know nothing, any one of
which may be derived from any one progenitor, but which
are usually transmitted in aggregates, considerable groups
being derived from the same progenitor. It would seem
that while the embryo is developing itself, the particles
more or less qualified for each new post wait, as it were,
in competition to obtain it. Also that the particle that
succeeds must owe its success partly to accident of posi-
tion and partly to being better qualified than any equally
well-placed competitor to gain a lodgment. Thus the
step-by-step development of the embryo cannot fail to be
influenced by an incalculable number of small and mostly
unknown circumstances." ^

Now, wherever we have to do with a very large
number of unknown elements which combine to produce
a result, we are introduced to those conditions with
which the theory of averages and probability deals. The
curve of error discovered by Laplace and Gauss to
picture the distribution of a large number of observations
around the average or mean position, which is taken as
the most probable or correct one, conies in as a valuable
aid, not in studying the errors of natural growth, but as
the graphical illustration of the deviations or variations
which cluster around what we call the normal, or with
Quetelet the mean, figure. Only the interest is now
attached not so much to specifying and defining the

^ ' Natural Inheritance,' p. 9.

ON THE STATISTICAL VIEW (JF NATURE. Gl7

hommc 'n\oyen as to studying the deviations from this
ideal standard. " How little," says Mr Galton/ " is con-
veyed by the bald statement that the average income of
English families is £100 a-year, compared with what we
should learn if we were told how P^nglish incomes were
distributed." A crowd of data furnish for the astronomer
the material out of which he has to choose the most
probable, the correct figure ; a crowd of observations
furnish for the naturalist the material from which he
has to learn how nature deviates from her types and
exhibits variations which are the factors of change and
development. Thus, under the hands of Mr Galton, the
Law of Error becomes a Law of Distribution, and the
whole machinery of the doctrine of probabilities, " excogi-
tated for the use of astronomers and others who are
concerned with extreme accuracy of measurement, and
without the slightest idea, until the time of Quetelet, that
they might be applicable to human measures," become
the only tools 1)y which an opening can be cut through
the formidable thicket of difficulties that bars the path of
those who pursue ' the science of man.' "

Hence while most people regard statistics as dull,
they become for the naturalist and student of human
nature " full of beauty and interest " ; ^ there is scarcely
anything so apt to impress the imagination as the
wonderful form of cosmic order expressed by the " law
of frequency of error." "It would have been per-
sonified by the Greeks, and deified if they had known
of it."*

' 'Natural InheriUnce,' p. 35. : ^ Ibid., p. 62.
- Ibid., pp. 55, 62. | * Ibid., p. 66.

618

SCIENTIFIC THOUGHT.

43. Every mathematical instrument, when applied to a

Application

of theory of novel purpose for which it was not originally in-
vented, " derives as much benefit in its development
as it confers through being made use of." Thus Mr
Galton's application of the theory of error to the
facts of distribution and variation not only enabled
him to bring method and order into such questions
raised by the Darwinian theory ^ as natural selection,

1 It is perhaps premature to
speak with great confideuce of the
actual results which have been
gained by this novel branch of
scientific inquiry, or of the practical
importance which these results may
have in the future with regard to
some of the great social questions.
Still, in a history of thought it is
of importance to note how, through
Mr Galton's writings, the problem
of Inheritance has acquired quite
a new aspect. This finds expres-
sion in his famous so-called " law
of filial regression," which goes
against " the current belief that
the child tends to resemble its
parents " (p. 104). In fact, all
opinions and theories which had
been propounded before Galton,
either popularly or scientifically,
were based upon a one-sided re-
gard to the more visible portion of
the ancestry — viz., the parents ;
whereas, if any general theory like
that of " pangenesis," or of " stirps,"
or of the " differentiation of the
germ-plasma and the body-plasma"
be made the basis of discussion, the
whole ancestral tree must be con-
sidered to contribute to the for-
mation of the characters of any
individual. In fact, we have be-
fore us not one pair, but an endless
line of pairs which are, as the
terms of a series, connected by the
powers of the number two ; and
it is then easily seen, without

going into refinements (which, how-
ever, in the further elaboration of
the problem, may become very
important), that the first term of
the series, which represents the
parents, contributes only one-half
of the whole, that is, each parent
one quarter. It is also evident, if
each parent only contributes on
the average one quarter, that an
exceptional bias in any direction
communicated by them would be
balanced in the long-run by tlie
opposite action of the remaining
ancestry, and that, contrary to
ordinary belief, inheritance would
operate in the direction of bring-
ing each individual back to the
average of the whole lineage. Mr
Galton first observed this law of
regression to the average by definite
countings with seeds and " a com-
paratively small number of ob-
servations of human .stature" ; and
he remarks that if it was only by
these experiments and observa-
tions that the law of regression had
been established, it could not have
been expected that the truth of
the apparent paradox would be
recognised. When, however, tlie
rule was once expressed, it was
" easily shown that we ought to
expect filial regression, . . . two
different reasons for its occurrence "
existing — " the one connected with
our notions of stability of type, the
other as follows : the child inherits

ON THE STATISTICAL VIEW OF NATURE.

61D

regression, reversion to ancestral types, extinction of
families, effect of bias in marriage, mixtm-e of in-
heritance, latent elements, and generally to prepare
the ground for the combined labours of the naturalist
and tlie statistician ; he was also able to put novel
problems to the mathenuitician.

To miderstand this latter point we must realise the

partly from his parents, partly
from his ancestry. In every pop-
ulation that intermarries freely,
when the genealogy of any man is
traced far backwards, his ancestry
will be found to consist of sucli
varied elements that they are
indistinguishable from a sample
taken at haphazard from the
general i)opulation." As to the
mathematical problem referred to,
it was submitted by Mr Galton in
a definite form to Mr J. D. H.
Dickson, whose solution is given
in the appendix to ' Natural In-
lieritance.' On this solution Mr
Galton lemarks : " The problem
may not be difficult to an ac-
complished mathematician, but I
certainly never felt such a glow
of loyalty and respect towards the
sovereignty and v^'ide sway of
mathematical analysis as when his
answer arrived, conlirming, by i)ure
mathematical reasoning, my vari-
ous and laborious statistical con-
clusions with far more miimteness
than I had dared to hope, because
tiie data ran somewhat roughly,
and I hail to smooth them with
tender caution. ... It is obvious
from this close accord of calcula-
tion with oVjservation, that the law
of Error holds throughout with
sufficient precision to be of real
service, and that the various results
nf my statistics are not casual and
disconnected determinations, but
strictly interdependent" (p. 202).
Another passage indicating how
nmch the inferences from the law

of regression run contrary to
popular opinions on inheritance is
the following: "The law of Re-
gression tells heavily against tlie
full hereditary transmission of any
gift. Only a few out of many
children would be likely to differ
from mediocrit}' so widely as their
mid-parent, and still fewer would
differ as widely a.s the more excep-
tional of the two j)arents. The
more bountifully the parent is
gifted by nature, the more rare
will be his good fortune if he be-
gets a son who is as richly endowed
as himself, and still more so if he
has a son who is endowed yet more
largely. But the law is even-
handed ; it levies an equal succes-
sion - tax on the transmission of
badness as of goodness. If it dis-
courages the extravagant hopes of
a gifted parent that his children
will inherit all his powers, it no
less discountenances extravagant
fears that they will inherit all iiis
weakness and di.sease " (p. 106).
Prof. Karl Peaison ( ' The Grammar
of Science,' '2nd ed., p. 479) says
of the law of ancestral inheritance :
" If Darwinism be the true view
of evolution — i.e., if we are to
describe evolution bj' natural selec-
tion coml)ined with heredity — then
the law which gives us definitely
and concisely the type of the i>ff-
spring in terms of the ancestial
peculiarities, is at once the founda-
tion-stone of biology and the basis
upon which heredity becomes an
exact branch of .science."

620 SCIENTIFIC THOUGHT.

44. great difference which exists between dealing with a

Difference in « t • • mi

application yast number of lifeless and of living units. This

to living and

unllr^ difference becomes evident if we consider that in the
former case the number of units is unalterable and
the units are indestructible ; in the latter the elements
or units are subject to enormous increase and corre-
sponding destruction, generally with a preponderance of
the first. In the kinetic theory of gases we have to
consider, in every finite system, the conservation or
persistence of mass and motion, the two units we
deal with. To these two properties of an immensely
large crowd we have to reduce the various phenomena
of pressure, temperature, volume, available or unavail-
able energy. In the vast crowTl of gemmules which
build up a new organism or regenerate an existing
one, we have to deal with a continual influx or
creation of new units and a continual extinction and
ejection of old or dead ones. Without venturing on
any theory as to how this state of things has come
about, we may see that the mathematics and statistics
of such crowds must be different from those referrino-
to stable, lifeless assemblages. The twofold task
arises of formulating the new problems and solving
them. To the extent that this is possible we shall
be able to deal mathematically with the great prob-
lem of variability ; and for the practical application of
these mathematical formuhe we shall have to collect
long series of facts and data of measurements — the
material which has to be statistically arranged and
sifted, and which is to confirm the conclusions and
test the results which calculation has brought out.

ON THE STATISTICAL VIEW OF NATURE.

G21

Mr Galton found ready, or instituted himself, vari-
ous countings of large numbers, which formed valuable
material for his mathematical schemes, and wliich
confirmed them in a surprising degree. Some very
elaborate series (if measurements of the varying dimen-
sions of individual members in large crowds of animals
were published by Prof. Weldon, whose monograph on
Crabs will always remain an historical document.^ It
was noticed about the same time that the attempt to
bring the measured deviations from the average into
a symmetrical arrangement on the sides of more or
less was impossible, and the fact had to be realised
and mathematically expressed that special influences
tending towards change on the intermixing of different
varieties produced an asymmetrical distribution or fre-
quency : " in fact, nature works with loaded dice, pro-
ducing a bias in certain directions; this is the favour
which, according to Darwin, Wallace, and Lamarck's
ideas, must meet the better fitted individuals and
exact from them a smaller tribute in the inevitable
process of destruction and removal.

We owe it to f'rof. Karl Pearson to have first grasped 45.

Prof. Pe.ir-

clearly and comprehensively the mathematical problem son. The
involved, and to have solved it in a manner useful for ^^^ problem.

^ See the ' Proceedings of the
Royal Society ' since 1890, notably
vol. Ivii., 1895, p. 360 sr/r^.

• " An a.syrametrical frequency
curve may arise from two (|uite
distinct cla.sses of causes. In the
fir.st place the material mea.sured
may be heterogeneous, and may
consist of a mi.xturc of two or
more homogeneous materials. . . .

The second class of frequency
curves arises in the case of homo-
geneous material when the tend-
ency to deviation t)n one side of
the mean is unequal to the tend-
ency to deviation on the other
side"' (Karl Pearson, "On tlie Ma-
tlieuiatical Theory of Evolution,"
'Trans. Hoy. Soc.,' 1895, p. 344).

622

SCIENTIFIC THOUGHT.

biological research.^ He has thus put into the hands of
naturalists an instrument wherewith to describe graphi-
cally the observed facts of variation and other allied

^ A considerable literature has
already accumulated iu this novel
branch of exact inquiry. The
complete list of it is given in a
pamphlet by Georg Duncker, en-
titled 'Die Methode der Variations-
statistik' (Leipzig, 1899). From
this list (p. 60) it will be seen that
one of the earliest workers in the
field of biological statistics was
the botanist F. Ludwig, whose
' Abschnitte der Mathematischen
Botanik ' have appeared in various
periodicals abroad since the year
1883. The philosopher, however,
to whom we are most indebted for
the mathematical foundations of the
whole theory, is, as noted above.
Prof. Karl Pearson, whose " Con-
tributions to the Mathematical
Theory of Evolution " have been
appearing since the year 1893 in
the Trans, of the Royal Society.
Very helpful abstracts of these
contributions, covering a large
field of mathematical theory, and
containing elaborate discussions of
many of the terms recently in-
troduced into biological science,
such as regression, reversion, in-
heritance, panmixia, selection, &c. ,
will be found in the Proceedings of
the Royal Society (1893, onwards).
Also in his collected essays, 'The
Chances of Death and other Studies
in Evolution ' (2 vols., 1897); and,
lastly, iu the later chapters of the
second edition of his ' Grammar of
Science' (1890). From the latter it
will be seen what far-reaching infer-
ences may eventually be drawn
from the quantitative treatment
and mathematical discussion of
biological data ; notably the results
so far gained "lead us to consider
variation as a permanent attribute
of living forms, which can hardly

have been substantially modified
since the beginnings of life. In the
same manner we find heredity in-
timately associated with variation
in the individual, and not differing
very substantially as we pass from
one character to a second, or from
one to another form of life. We
conclude that variation and inherit-
ance rather precede than follow
evolution ; they are, at present, one
fundamental mystery of the vital
unit" (p. 502). Prof. Pearson,
whose training was that of a
mathematician and a lawyer, ap-
proached the problems of Ijiology
from the exact point of view, and
it is interesting to see how, in many
ways, he comes to results similar to
those arrived at by one of the other
great representatives of modern
biological research, Mr Wm. Bate-
son. See his ' Materials for the
Study of Variation, treated with
especial regard to the discontinuity
in the Origin of Species ' (1894). If
I understand him rightly, his re-
searches have led him to the con-
clusion that variation cannot be
the work of natural selection, since
he lias given " such evidence as to
certain selected forms of varia-
tions " as to afford " a presumption
that the discontinuity of which
species is an expression has its
origin, not in the environment, nor
in any phenomenon of adaptation,
but in the intrinsic nature of
organisms themselves, manifested
in the original discontinuity of
variations" (p. 567). This "dis-
poses, once and for all, of the
attempt to interpret all perfection
and definiteness of form as the
work of selection. ... It suggests,
in brief, that the discontinuity of
species results from the discontinu-

ON THE STATISTICAL VIEW OF NATURE,

G23

phenomena, such as correlation, heredity, regression and
panmixia, and he has shown how to analyse tliese graphi-
cal tracings so as to indicate the several possible elements
out of which they are compounded, representing separate
agencies which are at work in nature. The mathemati-
cal inventions of Fourier had similarly enabled physicists
to analyse the complicated periodicity of tidal curves
into their elements, and, under the hands of Ohm and
Helmholtz, to resolve the harmonies of music.

We have here arrived at the last stage of the devel-
opment of tlie statistical view of nature. It has been
variously judged l)y biologists according to the special
views they take of their problems, and also according

ity of variation " (p. 568). Mr Bate-
son expects great assistance from
the statistical methods. '"There
is," lie says, "no common shell or
butterfly of whose variations some-
thing would not be learnt, were
some hundreds of the same species
collected from a few places and
statistically examined in respect of
some varying character. Any one
can take part in this class of work,
though few do" (p. 574). Not-
withstanding the general resem-
blance noted above between the
ideas of ^Ir Bateson and of Prof.
Pearson, they differ so much in
detail as to be led to confess
that they do not understand one
another's languages. Cf. W. Bate-
son, " Heredity, Differentiation, and
other Concei)tions of Biology,"
'Roy. Soc. Proc.,' vol. Ixix. pp.
193-205; K. Pearson, "On the
Fundamental Conceptions of Biol-
ogy," ' Biometrika,' vol. i. pp. 320-
344. Prof. Pearson's view is that,
for the working out of the theoiy
of evolution, " biological conceptions
can be accurately dethied, and so
defined measured with quantita-

tive exactness" {loc. cit., p. 324).
Mr Bateson, on the other hand,
regards them as to some extent
out of the reach of mathematical
definition and measurement. "Dis-
continuous variation" in Mr Bate-
son's special sense — by which we
niaj- perhaps understand great as
distinguished from small but num-
erous deviations from the average
— Prof. Pearson regards as "statis-
tically negligible for the purpose
of vital statistics" (pp. 33-3, 334).
He, in fact, holds closer to Dar-
winism as understood by Darwin,
who never looked with much
favour on Huxle\'"s view, for ex-
ample, that "sports," as distin-
guished from the sum of small
differences in individuals, might
furnish an ap[)reciable part of the
materials for natural selection.
Mr Bateson's view found favour
with Huxley, as may be observett
in the ' Life and Letters.' On the
novelty and value of Prof. Pearson's
methods, see ealso the Address by
Prof. Weldon to the Zoological
Section of tiie British A.s.sociation
in 1898.

624 SCIENTIFIC THOUGHT.

to the degree in which they appreciate and are able to
grasp mathematical methods. The subject is still under
discussion, and will belong to the History of Thought of
a coming age. It is enough to have indicated the latest
lines of reasoning which our century has marked out,
and to notice how they form a new and remarkable
instance of the growth and diffusion of the exact or
mathematical spirit in a department of research hitherto
almost untouched by it, prepared though it has been for
such treatment by one among whose great endowments
a grasp of mathematical reasoning hardly formed a dis-
tinctive feature. In former chapters I have had occasion
to show how Charles Darwin introduced into the science
of nature two novel points of view — the genetic view
and the process of judicial sifting of evidence. We may
now add that he has indirectly, more than directly,
furthered quite as much the statistical view of natural
phenomena through which we have learned to find and
trace law and order in great realms of phenomena and
events usually supposed to be governed by what is
termed blind chance. The study of this blind chance
in theory and practice is one of the greatest scientific
performances of the nineteenth century.
46. But whilst acknowledging the great importance which

statistical ... p ^ • i •

knowledge tlic Statistical treatment of phenomena has acquired in

one-sided.

our age, and the value of the statistical view of many
large departments of natural processes which escape
almost every other mode of dealing with them, we
must not forget that it is essentially one-sided.

Clerk-Maxwell has suggestively opposed it alike to the
mechanical and the historical views, of which the former

ON THE STATISTICAL VIEW OF NATURE. 025

tries to describe the general mechanism u/uler which,
the hitter the indiviihuil steps and incidents hj/ whicli,
special events or phenomena proceed and are character-
ised. Pearlier chapters of this narrative attempted to
give an account of the former, whilst the essentially
historical treatment belongs to another portion of the
work. The word history has generally been reserved for
records which deal with those events in which human
consciousness has played a large, if not an overwhelming,
part, and has been able to assist the observer by its own
accounts and representations. What should we know of
Iniman life and himian interests without them, and how
helpless— in spite of minutest observation — do we still
appear to be in understanding the life of the brute
and mute creation, even of the domestic animals, our
daily friends and companions ? But if history, as opposed
to statistics, really seems only possible where the living
voice or the surviving narrative of those who have de-
parted helps us to a true understanding of its incidents
and its meaning, it also imposes upon us the task of sift-
ing its value and trustworthiness critically. Mathe-
matics, logic, and statistics may do something to exclude
the actually impossible or the highly improbable from
a vast mass of material; but more delicate criteria are
requireil in dealing with the accumulated testimony of
bygone ages. With an unerring instinct of what, in
addition to mathematical measurements, may be required
in order to accomplish this task, the nineteenth century
has not only nursed the scientific spirit and cultivated
its methods, but with equal diligence and originality
those other methods which lie at the foundation of
VOL. II. 1' i:

626

SCIENTIFIC THOUGHT.

47.
Critical
methods.

philosophical

thought

the methods of

48.
The instru-
ment of
exact re-
search.

all recent
criticism.

And yet, before taking leave of science and entering
on a comprehensive appreciation of the workings of
the Critical Spirit with which all our thought seems
to be permeated, I owe to my readers the attempt
to answer one remaining question. If it be true,
as the foregoing narrative has abundantly insisted,
that through the increasing application of mathematical
methods of measuring and calculating, our thought has
become truly scientific and our knowledge accurate and
useful for describing and predicting phenomena, as also
for manifold practical applications, we may be curious to
know whether the refined instrument, mathematical
thought itself, has been subject to such change and
development as has been undergone by the various
branches of science to which it has been applied. In
fact, we have to ask the question, How has mathe-
matical thought itself fared in the course of the nine-
teenth century ? The concluding chapter of the present
volume will try to give a reply to this question.

62'

CHAPTER XIII.

ON THE DEVELOPMENT OF MATHEMATICAL THOUGHT DURING
THE NINETEENTH CENTURY.

In venturino; upon the last and most abstract portion of i.

^ ^ ^ History of

the great domain of Scientific Thought of the century, it thought.
may be well to remind the reader that it is not a history
of science but a history of tliought that I am writing.
When dealing in the foregoing chapters with mani-
fold discoveries, drawn promiscuously from the various
natural sciences, I have done so only to show how the
scientific mind has, in the course of the period, come
to regard the things of nature from dillerent points of
view, and to think and reason on them differently.
Such changes have frequently been l)roug]it about by
the discovery of novel facts, but this alone has not
generally sufficed to mark also a cliange in the manner
of reasoning on and thinking about them. The increase
in the number of natural species, of the chemical ele-
ments or of the smaller planets, luis not necessarily
made us think differently about tliese things in them-
selves : tlie theory and point of view may change without
any change in the oliject towards which they are directed,

628

SCIENTIFIC THOUGHT.

for they mark more the attitude of the beholder than
the things which he regards. It is true that a very
small addition to our actual knowledge of facts, like the
sudden appearance of some characteristic feature in a
landscape, may sometimes entirely alter the whole aspect,
induce us to abandon our accustomed views, and call up
suddenly an unforeseen train of ideas ; in such a case,
perhaps, this insignificant discovery becomes historically
interesting, although it is mainly by the altered trains
of thought which it has evoked that it has become
important to us.
2. The difference of scientific knowledge and scientific

Difference

between thought is thus owiug to the two factors which are

thought and » O

knowledge, involvcd— the facts of science or nature on the one side
and the scientifically thinking mind on the other. Xow
it might appear as if this difference vanished when we
approach the abstract science of mathematics, or at least
that of number ; for in numbering and counting we
have really only to do with a process of thought, and it
would seem as if the science of number were itself the
science of thought, or at least a portion of it. In fact,
the question arises, Is there any difference between
mathematical science and mathematical thought ? Some
considerations might induce us to think that there is
not. On the other side, I shall try to show in this
chapter that there is, and that the development of
mathematics during our period has brought this out
very clearly and prominently.
Popular There is an opinion current among many thinking

re^rding* pcrsous who have not occupied themselves with mathe-

mathe- ^ .

matics. matical science, though they may be very efficient in

DEVELOPMENT OF MATHEMATICAL THOUGHT. 629

calculating and measuring, that tlieie is really nothing
new in niatheniatics, that two and two always make
four, that the sum of the angles in a triangle always
make two right angles, and that all progress in mathe-
matics is merely a question of intricacy, a never-ending
process of increased complication liy whicli you can
puzzle even the cleverest calculator. To them the his-
tory of mathematics would Ije something analogous to
the history of games like whist or chess, the resources and
complications of which seem to be inexhaustible. So they
think ^ that the intricacies and refinements of elementary
and higher mathematics will supply endless material for
training the minds of schoolboys or trying the ingenuity

' "Some people have been found
to regard all niatheniatics, after the
47th proposition of Euclid, as a
sort of morbid secretion, to be
compared only with the pearl said
to be generated in the diseased
oj'sler, or, as I ha%'e heard it de-
scribed, ' une excroissance maladive
de I'esprit humain.' Others find
its justification, its raison d'etre, in
its being either the torch-bearer
leading the way, or the handmaiden
liolding up the train of Physical
Science ; and a very clever writer
in a recent magazine article ex-
presses his doubts whether it is, in
itself, a more serious i)ursuit, or
more worthy of interesting an in-
tellectual human being, than the
study of chess problems or Chinese
puzzles. What is it to us, they
say, if the three angles of a triangle
are equal to two right angles, or if
every even number is, or may be,
the sum of two i)rimes, or if every
equation of an odd degree nmst
have a real root ? How dull, stale,
Hat, and unprotitable are such and
such like announcements ! Much
more interesting to read an account

of a marriage in high life, or the
details of an international boat-
race. But this is like judging of
architecture from being shown some
bricks and mortar, or even a quar-
ried stone of a public building, or of
painting from the colours mixed on
the palette, or of music by listening
to tl.e thin and screech sounds pro-
duced by a bow passed haphazard
over the strings of a violin. The
world of ideas which it discloses or
illuminates, the contemplation of
divine beauty and order which it
induces, the harmonious connexion
of its j)arts, the infinite hierarchy
and absolute evi<lence of the truths
with which it is concerned, these,
and such like, are the surest grounds
of the title of mathematics to
human regard, and would remain
unimpeached and unimpaired wore
the plan of the universe unrolled
like a map at our feet, and the
mind of man qualified to take in
the whole scheme of creation at a
glance" (Prof. J. J. Sylvester,
Add less before Brit. Assoc, see
'Report,' 1869, p. 7).

630

SCIENTIFIC THOUGHT.

4.
Use of
mathe-
matics.

of senate-house examiners and examinees, without for a
moment considering the question whether mathematical
thought as distinguished from mathematical problems is
capable of and has undergone any radical and funda-
mental change or development.

Closely aUied with this is the further question as to
the use of mathematics. Two extreme views have always
existed on this point.^ To some, mathematics is only a
measuring and calculating instrument,^ and their interest

^ Of the two greatest mathemati-
ciaus of modern times, Newton and
Gauss, the former can be considered
as a representative of the first, the
latter of the second class ; neither of
them was exclusively so, and New-
ton's inventions in the pure science
of mathematics were probably equal
to Gauss's work in applied mathe-
matics. Newton's reluctance to
publish the method of fluxions in-
vented and used by him may per-
haps be attributed to the fact that
he was not satisfied with the logical
foundations of the calculus ; and
Gauss is known to have abandoned
his electro-dynamic speculations, as
he could not find a satisfactory
physical basis (see stipra, p. 67).
Others who were not troubled by
similar logical or practical scruples
stepped in and did the work, to the
great benefit of scientific progress.
Newton's greatest work, the ' Prin-
cipia,' laid the foundation of mathe-
matical physics ; Gauss's greatest
work, the ' Disquisitiones Arith-
meticfo,' that of higher arithmetic
as distinguished from algebra.
Both works, written in the syn-
thetic style of the ancients, are
difficult, if not deterrent, in their
form, neither of them leading the
reader by easy steps to the
results. It took twenty or more
years before either of these works
received due recognition ; neither

found favour at once before that
great tribunal of mathematical
thought, the Paris Academj- of
Sciences. Newton's early reputa-
tion was established by other
researches and inventions, notably
in optics ; Gauss became known
through his theoretical rediscovery
of Ceres, the first of the minor
planets (see above, vol. i. p. 182).
The country of Newton is still pre-
eminent for its culture of mathe-
matical physics, that of Gauss for
the most abstract work in mathe-
matics. Not to speak of living
authorities, I need only mention
Stokes and Clerk-Maxwell on the
one side, Grassmann, Weierstrass,
and Georg Cantor on the other.

^ Huxley said : " Mathematics
may be compared to a mill of
exquisite workmanship which grinds
you stuff of any degree of fineness :
but, nevertheless, what you get out
depends on what you put in ; and
as the grandest mill in the world
will not extract wheat-flour from
peas-cods, so pages of formulaj will
not get a definite result out of
loose data " ; and on another occa-
sion he said that mathematics "is
that study which knows nothing of
observation, nothing of induction,
nothing of expeiiment, nothing of
causation." The former statement
was endorsed by Lord Kelvin
('Pop. Lectures,' &c., vol. ii. p.

DKVELOPMENT OF MATHEMATICAL THOUGHT. 631

ceases as soon as discussions arise which cannot benefit
those who use the instrument for the purposes of
application in mechanics, astronomy, physics, statistics,
and other sciences. At the other extreme we have
those who are animated exclusively by the love of pure
science. To them pure mathematics, with the theory of
numbers ^ at the head, is the one real and genuine
science, and the applications have only an interest in
so far as they contain or suggest problems in pure
mathematics. They are mainly occupied wiLli examin-
ing and strengthening the foimdations of mathematical
reasoning and purifying its methods, inventing rigorous
proofs, and testing the validity and range of applicability
of current conceptions. We may say that the former
are led by practical, the latter by philosophical, interests,
and these latter may be either logical or ontological,"

102) ; the latter was energetically-
repudiated by Sylvester in his
famous Address to tiie first section
of the British Assoc, at Exeter
(1869, ' Report,' &c., p. 1, &c.)

^ Gauss considered mathematics
to be " the (^ueen of the Sciences,
and arithmetic the (^ueen of Mathe-
matics. She frequently conde-
scends to do service for astronomy
and other natural sciences, but to
her belongs, under all circum-
stances, the foremost place" (see
' Gauss zum (lediichtniss,' by Sar-
torius von Waltershausen, Leipzig,
1856, p. 79). Cayley's presidential
Address to the Britisli Association,
1883, has been frequently quoted :
"Mathematics connect themselves
on one side with common life and
the physical sciences ; on the otiier
side with philosophy in regard to
our notions of space and time and
the questions which have arisen as
to the universality and necessity of

the truths of mathematics, and the
foundation of our knowledge of
them. I would remark liere that
the connection (if it exists) of
arithmetic and algebra with tlie
notion of time is far less obviou.s
than that of geometry with the
notion of space" ('Mathematical
Papers,' vol. xi. j). 130). In addi-
tion to founding higher arith-
metic. Gauss occupied himself with
the foundations of geometry, and,
as he expected much from the
development of the theory of num-
bers, so he placed " great hopes on
the cultivation of the f/roinefriit
sitim, in which he saw large unde-
veloped trivcts which could not be
concjuered by the existing calculus "
(Sartorius, loc. cit., p. 88).

' To this mitrht be added the
psychological interest wliich at-
taches to matliematical concep-
tions. The late Prof. Paul Du
Bois - Reymond occupied liimself

632

SCIENTIFIC THOUGHT.

Twofold
interest
in mathe-
matics.

inasmuch as number and form are considered to be
the highest categories of human thought, or likewise as
the ultimate elements of all reality. These two interests
existed already in antiquity,^ as the word " geometry "

much with the question. See the
following works : ' Die AUgeraeine
Functionentheorie,' part i., Tiib-
ingen, 1882; ' Ueber die Gruud-
lagen der Erkenntniss in den ex-
acten "Wissenschaften,' Tubingen,
1890; and his paper "Ueber die
Paradoxien des Infiuitiircalciils "
('Mathematische Annalen,' vol. ix.
p. 149). In addition to the two
main interests which attach to
mathematical research, and which
I distinguish as the practical and
the philosophical, a third point of
view has sprung up iu modern
times which can be called the
purely logical. It proposes to
treat any special development of
mathematical research with the
aid of a definite, logically con-
nected complex of ideas, and not
to be satisfied to solve definite
problems with the help of any
methods which may casually pre-
sent themselves, however ingenious
they may be. In this way the
gi-eat geometrician, Jacob Steiner,
e.g., refused the assistance of ana-
lysis in the solution of geometrical
problems, conceiving geometry as
a complete organism which should
Solve its problems by its own
means. This view has been much
.strengthened by the development
in modern times of the theory of
Groups ; a group of operations
being ^defined as a sequence of such
operations as alwaj^s lead back
again to operations of the same
kind. Mathematical rigorists in
this sense would look upon the
use of mixed methods or opera-
tions not belonging to the same
group with that kind of disfavour
with which we should regard an

essaj'ist who could not express his
ideas in pure English, but was
obliged to import foreign words
and expressions. It is interesting
to see that the country which has
offended most by the importation
of foreign words — namely, Ger-
many— is that in which this purism
in mathematical taste has found
the most definite expression. (See,
inter alia, Prof. Friedrich Engel's
Inaugural Lecture, " Der Gesch-
mack ill der neueren Mathematik,"
Leipzig, 1890, as also Prof. F.
Klein's suggestive tract, ' Ver-
gleichende Betrachtungen iiber
neuere Geometrische Forschungen,'
Erlangen, 1872.)

■* The literature of this subject
is considerable. I confine myself
to two works. The late eminent
mathematician, Hermann Hankel,
of whom more in the sequel of
this chapter, besides showing much
originalitj' in the higher branches
of the science, took great interest
in its philosophical foundations
and historical beginnings. In 1870
he published a small but highly
interesting volume, ' Zur Ge-
schichte der Mathematik in Alter-
thum und Mittelalter' (Leipzig,
Teubner). We have, besides, the
great work of Prof. Moritz Cantor,
' Vorlesungen iiber Geschichte der
Mathematik,' in three large volumes
(Leipzig, Teubner). It brings the
history down to 1758. Referring
to the two interests which led to
mathematical investigations, Hankel
says (p. 88) : " From the moment
that Greek philosophers begin to
attract our attention through their
mathematical researches, the as-
pect which mathematics present

DEVELOPMENT OF MATHEMATICAL THOUGHT. G38

and the well-known references to mathematical ideas
in the schools of Pythagoras and Plato indicate. An
ancient fragment ^ which enumerates briefly the Grecian
mathematicians, says of Pythagoras, " He changed the oc-
cupation with this branch of knowledge into a real science,
inasmuch as he contemplated its foundation from a
higher point of view, and investigated the theorems
less materially and more intellectually ; " - and of Plato
it says that " He filled his writings with mathematical
discussions, showing everywhere how much of geometry
attaches itself to philosophy." ^

This twofold connection of mathematical with other
pursuits has, after the lapse of many centuries, come
prominently forward again in the nineteenth century.
We have already had to record a powerful stimulus to
mathematical thought in almost every chapter in which
we dealt with the fruitful ideas which governed scientific
work, and we have now no less to draw attention to the
philosophical treatment which has been bestowed upon
the foundations of science and the inroad of niatheraati-

chaiiges radically. Whilst among
the earlier civilised nations we only
meet with routine and practice,
with empirical rules which served
practical purposes in an isolated
manner, tlie Grecian mind on the
other side recognised, from the
first moment when it became
acquainted with this matter, that
it contained something which tran-
scended all those practical ends,
but which was worthy of special
attention, and which could be ex-
pressed in a general form, be-
ing, in fact, an object of science.
This is the high merit of the Greek
mathematicians ; nor need one fear

that this merit should be dimin-
ished by admitting tiiat they bor-
rowed the new material from the
ancient Egyptian civilisation."

' The fragment referred to is
preserved by Proclus, and is given
in full in Cantor's work (vol. i. p.
124 s<iq.) He calls it an ancient
catalogue of mathematicians. It
is generally attiibuted to Eudemus
of Rliodes, who belonged to the
peripatetic school of philosophy,
and was the author of seveial his-
torical treatises on geometry and
astronomy (Cantor, vol. i. p. 108).

- I'antor, vol. i. p. 137.

^ Ibid., p. 213.

634

SCIENTIFIC THOUGHT.

6.

Origin of
mathe-
matics.

cal into philosophical thought ; ^ so much so that this
closing chapter on the development of mathematical
thought forms a fitting link with the next great depart-
ment of our subject — the Philosophy of the Century.

We are told that mathematics among the Greeks had
its origin in the Geometry invented by the ancient
Egyptians for practical surveying purposes. The first
mathematical problems arose in the practice of men-
suration. Modern mathematical thought received in
an analogous manner its greatest stimulus through the
Uranometry of Kepler, Newton, and Laplace : through
the mechanics and the survey of the heavens new
methods for solving astronomical problems were in-
vented in the seventeenth and eighteenth centuries,
and the nineteenth century can be said to have at-
tempted to perform towards this new body of doctrine
the same task that Euclid, three hundred years before
the Christian era, performed towards the then existing
mathematics. As Proclus tells us, " putting together
the elements, arranging much from Eudoxus, furnishing
much from Thesetetus, he, moreover, subjected to rigorous
proofs what had been negligently demonstrated by his
predecessors." " What one man, so far as we know, did
for the Grecian science, a number of great thinkers in

^ Thus, for instance, the recent
investigations and theories of the
" manifold," as they have been
set forth by Prof. Georg Cantor
of Halle, constitute, as it were,
a new chapter in mathematical
science, whereas they were for-
merly a subject merely of philoso-
phical interest. See a remark to
this effect by B. Kerry at the end
of his very interesting article on

Cantor's doctrine in the 9th
vol. of Avenarius's ' Zeitschrift
f iir wissenschaftliche Philosophic '
(1885), p. 231, where he refers to
Kant's comparison of philosophy
to a Hecuba " tot generis natisque
potens."

'^ Quoted by Cantor, vol. i. p.
247. See also Hankel, loc. cit.,
p. 381 sqq.

DEVELOPMENT OF MATHEMATICAL THOUGHT. 635

our century, among whom I only mention Gauss, Cauchy,
and Weieistrass, attempted to do for the new science
which was created during the two preceding centuries.
As Prof, Klein says, " We are living in a critical period,
similar to that of Euclid." ^

^ See ' The Evanston Colloquium,
Lectures on Mathematics delivered
in August and September 1893,' by
Felix Klein, notably Lecture vi.
In this lecture Prof. Klein ex]>lains
his view (to which he had given
utterance in his address before the
Congress of Mathematics at Chicago:
' Papers published by the American
Mathematical Society.' vol. i. p.
133. New York, 1896) on the
relation of pure mathematics to
applied science. This view is based
upon the distinction between what
he calls the " naive and the refined
intuition."' . . . " It is the latter
that we find in Euclid ; he carefully
develops his system on the basis of
well - formulated axioms, is fully
conscious of the necessity of exact
proofs, clearly distinguishes be-
tween the commensurable and the
incommensurable, and so forth. . . .
The naive intuition, on the other
hand, was especially active during
the period of the genesis of the
differential and integral calculus.
Thus we see that Newton assumes
without hesitation the existence, in
everj- ca.se, of a velocity in a mov-
ing point, without troubling himself
with the inquiry whether there
might not be continuous functions
having no derivative."

In the opinion of Prof. Klein
'■ the root of the matter lies in the
fact that the naive intuition is not
exact, while the refined intuition is
not properly intuition at all, but
arises through the logical develop-
ment from axioms considered as
perfectly exact."

In the sequel Prof. Klein shows
that the naive intuition imports

into the elementary conceptions
elements which are left out in the
purely logical development, and that
this again leads to conclusions which
are nut capable of being verified by
intuition, no mental image being
possible. Thus, for instance, the
abstract geometry of Lobatchev.sky
and Kiemann led Beltrami to the
logical conception of the pseudo-
sjdiere of which we cannot form
any mental image. Similar views
to those of Prof. Klein have been
latterly expressed by H. Poincar^
in his suggestive volume ' La
Science et I'Hypoth^se ' (Paris,
1893). He there says (p. 90) :
"... L'exp(5rience joue un role
indispensable dans la gencse de la
geometric ; mais ce serait une
erreur d'en conclure que la geo-
metric est une science experi-
mentale, meme en partie. . . . La
g(5ometrie ue serait que I'etude de.*
mouvements des solides ; mais elle
ne s'occupe pas en realite des solides
naturels, elle a pour objet certains
solides ideaux, absolument invari-
ables, qui n'en sont qu'une image
simplifiee et bien lointaine. . . . Ce
qui est I'objet de la gcomclrie c'est
I'etude d'un ' groupe ' particulier ;
mais le concept gdndral de groupe
preexiste dans notre esprit au
moins en puissance. . . . Seule-
ment, parmi tons les groupes
jiossibles, il faut choisir celui qui
sera pour ain.^i dire I'dtalon autiuel
nous rapporterons les phenomenes
naturels." This distinction be-
tween tiie matliematics of intuition
and the mathematics of logic has
also been forced upon us from quite
a different quarter. The complica-

636

SCIENTIFIC THOUGHT.

Gauss.

8.
Cauchy.

It is right to place the name of Gauss at the head, for
his investigations regarding several fundamental and
critical questions in arithmetic and geometry date from
the last years of the eighteenth century, long before
Cauchy's influence made itself felt. This is now abund-
antly clear through the publication of Gauss's works, and
from much of his correspondence with personal friends,
notably with the astronomer Bessel. We can now
understand how those who knew him regarded him as
a kind of mathematical oracle to whom " nothing in
theory existed that he had not looked at from all sides," ^
and who anticipated in his own mind the development
which mathematical thought was to take for a long
time after him. And yet it was not to him primarily
that the great change was due which came over mathe-
matical reasoning during the first half of the century.
Gauss was not a great teacher. In fact, there existed
in the first quarter of the period only one great training
school in advanced mathematics, and that was Paris.
There it was that Augustin Cauchy — first as lecturer.

tiou of modern mathematics and
the refinement of the modern
theories have brought about the
desire "to create an abridged
system of mathematics adapted to
the needs of the apphed sciences,
without passing through the whole
realm of abstract mathematics"
(Klein, loc. cit., p. 48). In this
country Prof. Perry has made a
beginning by publishing his well-
known work, ' Calculus for En-
gineers,' which has been welcomed
by Prof. Klein in Germany, and
which has led to an extensive
correspondence in the pages of
' Nature ' ; it being recognised by
many that a quicker road must be

made from the elements to the
higher applications of mathematics
in the natural sciences than the
present school sj'stem, beginning
with Euclid, admits of. The
separation of the logical and prac-
tical treatment of any science, as
likewise the independent develop-
ment in Germany of the poly-
technic school alongside of the uni-
versitj", has, however, its dangers,
as is recognised by Prof. Klein
(' Chicago Mathematical Papers,' p.
136).

^ See Bessel's letter to Gauss,
27th December 1810, in ' Brief-
wechsel zvvischen G. and B., Leipzig,
1880, p. 132.

DEVELOPMENT OF MATHEMATICAL THOUGHT. 637

then as professor — exerted his great influence in the
famous lilcole Polytechnique, in the Sorbonne, in the
ColleKe de France.^ In contrast with Gauss — who was
self-contained, proud, and unapproachable, whose finished
and perfect mathematical tracts were, even to those who
worshipped him, an abomination," owing to their unin-
telligible and novel enunciation, who hated lecturing
— Cauchy possessed the enthusiasm and patience of
the teacher,^ spent hours with liis pupils, and pub-
lished his lectures on the foundations of the Calculus
for the benefit of the rising mathematical generation.
Thus lie has the merit of having created a new school
of mathematical thought — not only in France but also
al)road, where the greatest intellects, such as that of
Abel,* expressed themselves indebted to him for hav-
ing ])ointed out the only right road of progress. Tt
will he useful to define somewhat more closely wherein
this new school differed from that preceding it, which
culminated in the great names of Euler, Lagrange, and
Laplace.

The great development of modern as compared with
ancient mathematics may be stated as consisting in the in-

^ See Valson, ' La Vie et les genie des Euler, des Lagrange, des

Travaux du Baron Cauchy,' Paris, Laplace, des Gauss, des Jacobi,

1868, vol. i. p. 60 sqq. I'aniour de I'enseignement portd

^ " On disait que sa manicre jusqu'Ji I'enthousinsnie, une rare

d'exposer etait niauvaise, ou encoie bonte, une siniplicite, une chaleur

qu'il faisait comuie le renard, qui de c(Kur qu'il a conservees jusqu'h

efface avec sa ([ueue les traces de ses la fin de sa vie " (Combes, quoted

pas sur le sable. Crelle dit, selon by Valson, vol. i. p. 63).
Al)el, ([ue tout ce qu'ecrit Gauss * See Bjerknes, 'N.-H. Abel,' p.

n'est qu'abomination (Griiuel), car j 48 sqt). ; p. 300. Cauehy's ' Cours

c'est si obscur qu'il est pres(iue d'Aiialyse' ajipcared in 1821 : the

impossible d'y rien comprendre " ' Kdsume des lei;ons sur le caitul

(Bjerknes, ' Niels Henrik Abe!,' infinitesimal,' to which .\bel refers

Trad, fram/aise, Paris, 188."), p. 92). in a letter to Holmboe, dated 1826,

■* " C'est que Cauchy alliait au appeared in 1823.

638 SCIENTIFIC THOUGHT.

troduction of algebra or general arithmetic, in the applica-
tion of this to geometry and dynamics, and in the invention
of the infinitesimal methods, through which the rigorous
theorems of the older geometricians which referred to the
simpler figures — such as straight lines, circles, spheres,
cones, &c. — became applicable to the infinite variety of
curves and surfaces in which the objects and phenomena
of .nature present themselves to our observation. Logic-
ally speaking, it was a grand process of generalisation,
based mostly on inference and induction, sometimes
9. merely on intuition.^ Such a rirocess of generalisation

Processor '' i o

generaiisa- j^as a twofold cffect on tlic progrcss of science.

The first and more prominent result was the greatly
increased power of dealing with special problems which
the generalised method affords, and the largely increased
field of research which it opened out. We may say that
the century which followed the inventions of Descartes,
Newton, and Leibniz, was mainly occupied in exploring
the new field which had been disclosed, in formulating
and solving the numberless problems which presented
themselves on all sides ; also, where complete and
rigorous solutions seemed unattainable, in inventing
methods of approximation which were useful for prac-
tical purposes. In this direction so much had to be done,
so much work lay ready to hand, that the second and
apparently less practical effect of the new generalisations
receded for a time into the background. We may term

^ " On se reportait incousciem- ; claire et rigoureuse, mais par une

nient au niodele qui nous est I sorte d'intuition et d'obscur in-

fourni par les fonctions considerees stinct" (Pnincarc, " L'ujuvre math,

en mecanique et on rejetait tout | de Weierstrass," ' Acta Mathema-

ce qui s'ecartait de ce modele ; on ! tica,' vol. xxii. p. 4).

u'otait pas guide par une d(5finition •

DEVELOPMENT OF MATHEMATICAL THOUGHT.

639

this second and more hidden line of research the logical
side of the new development. It corresponds to the work
which Euclid performed in ancient geometry, the framing
of clear dehnitions and of unambiguous axioms ; pro-
ceeding from these by rigorous reasoning to the theorems
of the new science.^ But the translation of geometrical
and mechanical conceptions into those of generalised
arithmetic or algebra brought with it a logical problem
of quite a novel kind which has given to modern mathe-
matics quite a new aspect. This new problem is the re-
translation of algebraical — i.e., of general — formuhe into
geometrical conceptions — the geometrical construction of
algebraical expressions. It is the inverse operation of
the former. Tu tliis inversion of any given operation operations,
lies the soul and principle of all mathematical progress,
both in theory and in application." The invention of

10.
Inverse

' lleferring sixjcially to the
defiDition of a " function " or
mathematical dependence, a con-
ception introduced l»y Kuler, but
not rigorou.sly defined by him,
M. Poincare sayw, loc. cit. : " Au
cr)mmenceraent du sifecle, I'idde
de fonction etait une notion Ji
la fois trop restreinte et trop
vague. . . . Cette definition, il
fallait la donner : car I'analyse ne
jjouvait qu'ii ce prix actjuerir la
parfaite rigueur. " In its generality
tliid task wa« performed in the
last third of the century by
Weierstrass, but tlie necessity of
this criticism of the formulic in-
vented by modern mathematics
dates from the api)earance of
Cauchy's ' Momoire sur la thdorie
dcs intcgiales ddfinies' of 1814,
which Legcndre reported on in this
sense, but which wxh not published
till 182f).

- The operations referred to are
generally of two kinds : first, there
is the operation of translating
geometrical relations, intuitively
given, int<5 algebraical relations;
and, secondly, the operation of
extending algebraical relations by
going forward or backward in the
order of numbers, usually given
by indices. In each ca.se the
new relations arrived at reijuire
to be interpreted, and thi.s inter-
pretation leads nearly always to
an extension of knowledge or to
novel conceptions. A simjde ex-
ample of the first kind presents
itself in the geometrical construc-
tion of the higher powers of
quantity. Having agreed to ilefine
by a tiie length of a line, by a^
an area, what is the meaning of
n^ n* . . . a" ? Can any geomet-
rical meaning be attaoiied to these
symbols ? An example of the

640

SCIENTIFIC THOUGHT.

the seventeenth century afforded two grand occasions
for such progress, and the creation through it of novel
mathematical ideas. The translation of geometrical con-

second class i.s the following :
having defined the symbols
dy d-y d"y

dx dx^ ' ' ' rfa;"'
an operation suggests itself in the
inverse order, the indices or their
reciprocals (inversions) being taken
negatively. Can any meaning be
attached to these latter symbols ?
Further, if the operation denoted
by going on from one of these
symbols to the next is known and
feasible, how can the inverse oper-
ation be carried out ? In the first
class of problems we proceed from
an intuitively given order to a
purely hjgical order, and have in
the sequel to go back from the
purely logical order to an intuitive
order of ideas. In the second
case, having followed a certain
logical order, we desire to know
what the inversion of this order will
produce and how it can be carried
out. The view that the direct and
indirect processes of thought form
the basis of all mathematical
reasoning, and an alternation of
the two the principle of progress,
has been for the first time con-
sistently expounded by Hermann
Hankel in his ' Theorie der Com-
plexen Zahlen - Systeme,' Leipzig,
1867. But it had already been
insisted on by George Peacock in
his " Report," &c., contained in
the 3rd vol. of the ' Reports of
the Brit. Assoc.,' 183.3, where he
says (p. 223) : " There are two
distinct processes in Algebra, the
direct and the inverse, presenting
geneially very different degrees of
difficulty. In the first case, we
proceed from defined operations,
and by various processes of de-
monstrative reasoning we arrive
at results which are general in

form though particular in value,
and which are subsequently gen-
eralised in value likewise ; in the
second, we commence fi-om the
general result, and we are either
required to discover from its form
and composition some equivalent
result, or, if defined operations
have produced it, to discover the
primitive quantity from which those
operations have commenced. Of
all these processes we have alreadj-
given examples, and nearly the
whole business of analysis will
consist in their discussion and
development, under the infinitely
varied forms in which they will
present themselves."

It is extraordinary how little in-
fluence this verj' interesting, com-
prehensive, and up-to-date re-
port on Continental mathematics,
including the works of Gauss,
Cauchy, and Abel, seems to have
had on the development of English
mathematics. But the latter have
through an independent movement
— viz., the invention of the
Calculus of Operations — led on
to the radical change which has
taken place in recent mathematical
thought. This change, which can
be explained by saying that the
science of Magnitude must be
preceded by the doctrine of Forms
or Relations, and that the science
of Magnitude is only a special
application of the science of Forms,
was independently prepared by
Hermann Grassmann, of whom
Hankel says {loc. cit., p. 16) : "The
idea of a doctrine of Forms which
should precede a doctrine of Mag-
nitude, and of considering the
latter from the point of view
of the former, . . . remained of
little value for the development

DEVELOPMENT OF MATHEMATICAL THOUGHT. G41

ceptions into algebraical language suggested the inverse
operation of interpreting algebraical terms by geometrical
conceptions, and led to an enormous extension of geo-
metrical knowledge.^ Further, the infinitesimal methods
through which curves and curved surfaces were conceived
as being made up of an infinite number of infinitesimally
small, straight — i.e., measurable — lines, led to the in-
verse problem; given any algebraical operations which
obtain only in infinitesimally small dimensions — i.e., at
the limit — lutw do they sum iip to finite quantities and

of mathematics, so long as it
was only used to prove tlieorems
which besides being already known,
were sufficiently though merely
empirically proved. It was H.
Grassmann who took up this idea
for the first time in a truly
philosophical spirit and treated
it from a comprehensive point
of view." Hankel also refers
to Peacock as well as to De
Morgan, whose writings, however,
he was insufficiently accjuainted
with (ibid., p. 15). In quite
recent times Mr A. N. Whitehead
has conceived " mathematics in
the widest signification to be the
development of all tj'pes of formal,
necessary, deductive reasoning,"
and has given a first instalment
of this development in his ' Treatise
on Universal Algebra' (vol. i.,
Cambridge, 1898). See the preface
to this work (pp. 6, 7).

^ A good example of the use of
the alternating employment of the
intuitive (inductive) and the log-
ical (deductive) methods is to be
found in the modern doctrine of
curves. The invention of Descartes,
by which a curve was represented
by an equation, led to the intro-
duction of the conception of the
" degree " or " order " of a curve
and its geometrical equivalent ;

VOL. n.

whereas the geometrical concep-
tion of the tangent to a curve led
to tiie distinction of curves ac-
cording to their "class," which
was not immediately evident from
the equation of the curve but
which led to other analytical
methods of representation where
the tangential properties of curves
became more evident. A third
method of studying curves was
introduced by Pliicker (1832), who
started from "the singularities"
which curves present, defined
them, and established his well-
known ecjuations. A further study
of these " singularities " led to the
notion of the "genus"' or "de-
ficiency " (Cayley) of a curve. The
gradual development of these and
further ideas relating to curves is
concisely given in <an article by
Cayley on " Curve " in the 6th vol.
of the ' Kncyclopicdia Britannica,'
reprinted in Cayley's collected
papers, vol. xi. This article fur-
nishes also a good example of the
historical treatment of a ])urely
mathematit-al subject by showing,
not so much the ])rogress of mathe-
matical knowledge of special things,
as the development of the manner
in which such things are looked at
— i.e., of malheinatical thought.

2 s

642

SCIENTIFIC THOUGHT.

figures ? What are the properties of these finite figures
as inferred from the properties of their infinitesimally
small parts ? The infinitesimal methods evidently corre-
sponded with the atomistic view of natural objects,
according to which the great variety of observable
phenomena, the endlessly complicated properties of
natural objects, could be reduced to a small number
of conceivable properties and relations of their smallest
parts, and could then be made intelUgible and calculable.
The general reader who is unacquainted with the
numberless problems and intricate operations of higher
mathematics can scarcely realise how in these few words
lie really hidden the great questions of all the modern
sciences of number and measurement ; the trained mathe-
matical student will recognise in a process of inversion
not only the rationale of such extensive doctrines as the
integral calculus, the calculus of variations, the doctrine
of series, the methods of approximation and interpolation,
but also the application of analysis to geometry, the
theory of curves of higher order, the solution of equations,
&c. All these various branches were diligently cultivated
by the great mathematicians of the eighteenth century,
mostly, however, with the object of solving definite
problems which were suggested by the applied sciences,^

1 In general it can be stated that
the impetus given to mathematical
research by the problems set by
the applied sciences has been im-
measurably greater than that which
can be traced to the abstract treat-
ment of any purely mathematical
subject. We have a good example
of this at the beginning of the
nineteenth century in the gi'eat
work of Laplace as summed up,

for the most j)art, in the 'Me-
canique Celeste ' and the ' Theorie
des Probabilites,' which contain
the beginnings and the develop-
ment of a great number of purely
mathematical theories suggested
by problems in astronomy, physics,
aud statistics. On the other side
we have at the same time the so-
called "Combinational School " in
Germanj', whose members and

DEVELOPMENT OF MATHEMATICAL THOUGHT.

043

notably astronomy — not infrequently also as objects of
mere curiosity without any practical purpose whatever.
In the latter part of the eighteenth century the need
was felt of putting the new science into a compre-
hensive system. The attempts to do this — notably the
great text-books of Leonhard Euler in Germany and of
Lacroix in France — revealed how uncertain were the
foundations and how paradoxical some of the apparent
conclusions of the reasoning which, in the hands of the
great inventors and masters, had led to such remarkable
results.

As in other cases which we dealt with in former
chapters of this work, so also in the present instance we
may find a guide through the labyrinth of modern mathe-
matical thought in the terms of language around which
cluster the more recent doctrines. Two terms present n-

Modem

themselves which were rare or altogether absent in older Jj^^j'ly'g'^jf
treatises : these terms are the " complex quantity " and [uougTi.
the " continuous." To these we can add a third term
which we meet with (m every page of the writings of
mathematicians since Newton and Leibniz, but which has
only very recently been subjected to careful analysis and
rigorous definition, — the term " infinite." Accordingly we
may say that the range of mathematical thought during

their labours are almost forgotten,
although in their elaborate treat-
ises there are to be found many
formul;!.' which had to be redis-
covered when, fifty years later,
the general theory of forms and
substitutions began to be sye-
teinatically developed, and proved
to be an indispensable instrument
in dealing with many advanced
mathematical i)roblems. See on

the latter subject an article by
Major MacMahon on " Combin-
ational Analysis" ('Proc, London
Math. Soc. .' vol. xxviii. p. 5, &c. ),
as also the chapters on this subject
and on "Determinants" in tlie
first vol. of the ' Encyclopiidie der
Mathematischeu W'issenschaften '
(Leipzig, 1898). Also, /»i<'.'r a/i«, a
note by J. Muii' in 'Nature,' vol.
Ixvii., 1903, 11. .")l-2.

644

SCIENTIFIC THOUGHT.

12.

Complex
quantities.

13.
The con-
tinuous.

14.

The infinite.

the last hundred years has grown in proportion to the
methodical study and stricter definition of the notions of
the complex quantity, of the continuous, and of the infinite.
And these conceptions indicate three important logical
developments which characterise modern mathematical
reasoning. The conception of the complex quantity or
the complex unit introduces us to the possible extension
of our system of counting and measuring, retaining or
modifying, the fundamental rules on which it is based.
The conception of the continuous and its opposite, the
discontinuous, introduces us to the difference of numbers
and quantity, numbers forming a discontinuous series,
whilst we conceive all natural changes to be made up of
gradual — i.e., of imperceptibly small — changes, called by
Newton fluxions. The discussion, therefore, of the con-
tinuous leads us ultimately to the question how our
system of counting can be made useful for dealing with
continuously variable quantities — the processes of nature.
The conception of the infinite underlies not only the
infinitesimal methods properly so called, but also all the
methods of approximation by which — in the absence of
rigorous methods — mathematical, notably astronomical,
calculations are carried out.

Problems involving one or more of these concep-
tions presented themselves in large number to the
analysts of the eighteenth century : there were notably
two great doctrines in which they continually occur —
the general solution of equations,^ and the theory of

^ A.S it may not be immediately
evident how the ideas of continuity
have to do with the general solution
of equations, I refer to the first

publication by Gauss, in 1799, con-
taining a proof of the fundamental
theorem of algebra, and its republi-
cation fifty years later (see Gauss,

DEVELOPMENT OF MATHEMATICAL THOUGHT. G4 5

infinite series. The solution of an equation being called
finding its roots, it was for a long time assumed that
every equal icui has as many roots as are indicated by
its degree. A proof of this fundamental theorem of
algebra was repeatedly attempted, Ijut was only com-
pleted by Gauss in three remarkable memoirs, which
prove to us how much importance he attached to rigorous
proofs and to solid groundwork of science. The second
great doctrine in which the conceptions of the continuous
and the infinite presented themselves was the expansion
of mathenuitical expressions into series. In arithmetic, 15.

. Doctrine

decimal fractions taken to any number of terms were of series.

"^ Gauss.

quite familiar ; the infinite series presented itself as a
generalisation of this device. A very general formula

' Werke,' vol. iii. pj). 1 aiul 71). .\
very good suiiiiiuiry of this proof
is given liy Hankel ( ' Couiplexe
Zahlen-Systenie,' p. 87). A purely
algebraical deuion.stration of the
same theorem, not involving con-
sidt-rations of continuity and ap-
pruximatifjn.s, was also given by
Gauss in the year 1816, and re-
produced by others, including
George Peacock, in his ' Report,'
(juoted above, p. 297. Hankel
{loc. cit., p. 97) shows to what
extent Gauss's proof supplemented
the siniiiar proofs given by othei-s
before and after.

^ Decimal fractions seem to have
been introduced in the sixteenth
century. Series of other numbers,
formed not according to the decimal
but to the dyadic, duodecimal, or
other sj'stems, were known to the
ancients, and continued in use to
the middle ages. The dyadic sys-
tem wa.s much favoured by Leibniz.
It was also known that every
rational fraction could be de-
veloped into a periodical decimal

fraction. l*i-ominent in the re-
commendation of the use of deci-
mal fractions was the celebrated
Simon Stevin, who, in a tract
entitled ' La Disme ' attached to
his ' Arithmetique ' (1590, trans-
lated into English, 1608), described
the decimal system as " enseignant
facilement expodier par nombres
entiei's sans rompus tons comptes
se rencontrans aux affaires des
hommes." Prof. Cantor ( ' Gesch.
der Math.,' vol. ii. p. 616) says,
" We know to-day that this pre-
diction could really be ventured
on — that indeed decimal fractions
perform what Stevin promised."
At the end of his tract he doubts
the sj)eedy adoption of this device,
connecting with it the suggestion
of the universal adoption of the
decimal system. The best account
of the grail ual introduction of deci-
mal fractions is still to be found iii
George Peacock's ' History of Aiilh-
metic' ( ' Ency. ^tetrop.,' vol. i. p.
439, &c.)

646

SCIENTIFIC THOUGHT.

of this kind was given by Brook Taylor, and somewhat
modified by Maclaurin. It embraced all then known and
many new series, and was employed without hesitation
by Euler and other great analysts. In the beginning of
the centur}", Poisson, Gauss, and Abel drew attention to
the necessity of investigating systematically what is
termed the convergency ^ of a series. As a specimen
of this kind of research, Gauss published, in 1812, an
investigation of a series of very great generality and
importance." We can say that through these two isolated
memoirs of Gauss, the first of the three on equations,
published in 1799, and the memoir on the series of
1812, a new and more rigorous treatment of the in-
finite and the continuous as mathematical conceptions
was introduced into analysis, and that in both he showed
the necessity of extending the system of numbering and
measviriug by the conception of the complex quantity.
But it cannot be maintained that Gauss succeeded in
impressing the new line of thought upon the science of

^ A very good account ot the
gradual evolution of the idea of
the convergency of a series will be
found in Dr R. Reiff's ' Geschichte
der unendlichen Reihen" (Tiibin-
gen, 1899, p. 118, &c.) Also in
the preface to Joseph Bertrand's
'Traite de Calcul Differeutiel'
(Paris, 1864, p. xxix, &c.) Accord-
ing to the latter Leibniz seems to
have been the first to demand
definite rules for the convergency
of Infinite Series, for he wrote to
Hermann in 1705 as follows:
" Je ne demande pas que Ton
trouve la valeur d"uue serie quel-
conque sous forme finie ; un tel
probleme surpasserait les forces
des geometres. Je voudrais seule-
ment que Ton trouvat moyen de

decider si la valeur exprimee par
une serie est possible, c'est-a-dire
convergente, et cela sans connaitre
I'origiue de la serie. II est neces-
saire, pour qu'une serie indefinie
represente une quantite finie, que
Ton puisse demontrer sa converg-
ence, et que Ton s'assure qu'en la
prolongeant suflfisamment Terreur
devient aussi petite que I'on veut.''
In spite of this, Leibniz, through
his treatment of the series of
Grandi, l-l + l-l,&c., the sum
of which he declared to be |, seems
to have exerted a baneful influence
on his successors, including Euler
(See Reiff, loc. cit., pp. 118, 158).

- The memoir on the Hypergeo-
metrical series.

DEVELOPMENT OF MATHEMATICAL THOUGHT. G47

mathenuitics in j^eneral. This was done about fifteen or
twenty years after Gauss had begun to puljlish his
isolated memoirs, in a comprehensive treatment of the
subject by Cauchy, who, before 1820, delivered lectures
on Analysis at the J^cole Polytechnique and in (jther lo.

Caucliy's

colleges, and commenced their puldication in 1821. In Anaiy>.is.
this course of lectures the discussion of the notions of the
infinite, of the continuous, of the convergence of series,
and of the extension of our conception of quantity
beyond the ordinary or real quantities of algebra, is
put in the foreground, and the illicit habit of using the
generalisations of algebra without defining the conditions
of their validity severely criticised.^ It is also evident,
from the extensive notes which Cauchy added to the
"cours" of 1821, that he felt the necessity of a revision
of the fundamental notions of algebra. The publication
of 1821 was followed by others on the Calculus, and it
is through these treatises mainly that a new spirit was
infused into general mathematical literature, first in

' The earliest labours of Cauchy cotnme des inductions projires h.

were geonietrical, and he evidently faire pre.-*.sentir quelque fois la

ac([uired through them an insight verite, mais t[ui s'accordent peu

into the contrast between the avec I'exautitude si vantee des

rigour of the older geonietrical sciences niath(5matiques. On doit

and the looseness of the modern meme observer qu'elles tendent a

algebraical methods. In tliis re- faire attribuer aux fcjrmules al-

gard he says : "J'ai cherchc a leur ' gcljriques une i^tendue indctinie,

donner toute la rigueur (|u'on tandis ([ue, dans la rcalitt-, la plu-

exige en goonietrie, de manifcre a part de ces fornmles subsistent

ue jamais recourir aux raisons uniquenient sous certaines condi-

tirees de la goneralite de I'algcbre. titms, et pour certaines valeurs des

Les raisons de cette espece, quoitjue ((uantiti's (ju'elles renferment. Kti

assez communement admises, sur- doteriainant ces conditions et ces

tout dans le passage des series con- valeurs, et en iixant dune maniore

vergenles aux series divergentes, precise le sens des notations dont

et des (luautitos reelles aux ex- ' je me sers, je fais disparaitre toute

presbions iniaginaires ne peuvent 1 incertitude" ('Coura d'Analyse,'

etre consider($s, ce nie senible, que I 1821, Introd., p. ii).

648

SCIENTIFIC THOUGHT.

France, somewhat later also in England and Germany.
In the latter country, the highly original writings of
Abel, and the independent labours of Jacobi, opened out
an entirely new branch of higher mathematics, beginning
with the discovery of the property of double periodicity of
certain functions.^ This extensive and fruitful province of
analysis for a time retarded the revision and extension of
the groundwork of mathematical reasoning which Cauchy
had begun, and upon which Gauss evidently desired to
make the extension of higher mathematics proceed."

^ Before the discovery of the
functions with a double period,
functions with one period were
known : the circular and expon-
ential functions — the former pos-
sessing a real, the latter an imagin-
ary, period. The elliptic functions
turned out to ''share simultaneously
the properties of the circular func-
tions and exponential functions, and
whilst the former were periodical
only for real, the latter only for
imaginary, values of the argument,
the elliptic functions possessed both
kinds of [jeriodicity. " This great
step became clear when it occurred
to Abel and Jacobi independently
to form functions by inversion of
Legendre's elliptic integral of the
first kind. The two fundamental
principles involved in this new
departure were thus the process of
inversion and the use of the imagin-
ary, as a necessary complement to
the real, scale of numbers. The
share which belongs independently
to Abel and Jacobi has been clearlj^
determined since the publication of
the correspondence of Jacobi with
Legendre during the years 1827-32
(reprinted in Jacobi's ' Gesammelte
Werke,' ed. Borchardt, vol. i.,
Berlin, 1881), and of the complete
documents referring to Abel, which
are now accessible in the memorial

volume published in 1902. A very
lucid account is contained in a
pamphlet by Prof. Klinigsberger,
entitled 'Zur Geschichte der Theorie
der Elliptischen Transeendenten
in den Jahren 1826-29' (Leipzig,
1879).

- Of the four great mathema-
ticians who for sixty years did the
principal work in connection with
elliptic functions — viz., Legendre
(1752-1833), Gauss (1777-1855),
Abel (1802-29), and Jacobi (1804-
51), each occupied an independent
position with regard to the subject,
— suggested originally bj^ Euler, and
important for the practical applica-
tions which it promised. Legendre
during fortj' years, from 1786 on-
ward, worked almost alone : he
brought the theory of elliptic in-
tegrals, whicli had occurred origin-
ally in connection with the compu-
tation of an arc of the ellipse, into
a system, and to a point bej'ond
which the then existing methods
seemed to promise no further ad-
vance. This advance was, however,
secured by the labours of Jacobi
through the introduction of the
novel principles referred to in the
last note. Two years before Jacobi's
publication commenced, Abel had
already approached the subject from
an entirely different and much more

DEVELOPxMENT OF MATHEMATICAL THOUGHT. 049

That such a revision had become necessary was seen, 17.

1 1 • i> • 1 • 1 • 1 U'-vision

slowly if lu many quarters, l)ut it tlid not become gener- 'jffu"<ia-
ally recognised till lute in the century, when thinkers of

iiientalfi.

general point of view. " Abel," as
Monsieur L. Sylow says ( ' Memorial
des dtudes d'Abel,' j). 14), "otait
avant tout algebriste. II a dit lui-
mcuie (jue la theorie des equations
(jtaitson sujet favori,cequid'ailleui-s
apparait claireinent dans ses omvre.s.
Dans ses travaux sur les fonctious
elliptiques, le traitenient des di-
verses Equations algdbriques dont
cette theorie abonde est mis forte-
meiit en ovidouce, et dans le premier
de ces travaux, la resolution de ces
equations est meme indiquee comme
etant le sujet principal. Qui plus
est, la theorie des wiuations etait
entre ses mains I'instrument le plus
dfficace. Ce fut ainsi sans aucun
doute la resolution de IV'quation de
division des fonctions elliptiques qui
tout d'abord le couduisit a la theorie
de la transformation. Elle joue
encore un role capitale dans sa de-
monstration du thcoreme dit theo-
rcme d'Abel, et dans les recherehes
gendrales surles integrates des diffcr-
entielles alg(5briques qui se trouvent
dans son dernier memoire le ' Prdcis
d'une Theorie des fonctions ellip-
tiques.' " But whilst Abel certainly
took a much more general view
than either Legendre or Jacobi, both
of whom came to a kind of dead-
lock on the roads they had chosen
(Jacobi, when he attempted to ex-
tend the theory of the periodicity
of functions), it is now quite clear
that Gauss viewed the whole sub-
ject almost thirty ye.ars before Abel
and Jacobi entered the field from a
still more general jMjint of view.
Already, in 1798, when he was only
twenty-one, he must have recognised
the necessity of eidarging and defin-
ing the fundamental concej)tions of
algebra and of functionality or math-
ematical dependence ; and it is very
likely that the magnitude of the

uudeitaking, fur which his astron-
omical labours left him no time,
debarred him from publishing the
important results wliich he had
already attained, and which covered
to a great extent the field cultivated
in the meantime by Abel and

' Jacobi, leaving only the celebrated
theorem of the former (referring to
the algebraical comparison of the
higher non - algebraical functions)
and the discovery of a new
function on the part of Jacobi
(his Theta function) as the two
great additions which we owe to
them in this line of re.search (see
Kiiuigsberger, loc. cit., p. 104).
In this recognition of the funda-

! mental change which mathematical
science demanded, and its bearing
upon these special problems here
referred to. Gauss must have for a
long time stood alone ; for his great
rival (.'aucliy, to whom we are
mainly indebted for taking the first
steps in this direction, did not for
many years apply his fundamental
and novel ideas to the theory of
elliptic functions, which up to the
year 1844, when Hermite entered
the field, were almost exclusively
cultivated by German and Scandi-
navian writers (see R. L. Ellis,
" Report on the recent Progress of
Analysis," Brit. Assoc, 1846 ; re-
printed in ' Mathematical and other
Writings,' p. 311). Nor could it
otherwise be exidained how Cauchy
could keep the manuscript of Abel's
great memoir without ever occupy-
ing himself with it. and thus delay
its publication for fifteen years after
it held been presented to the .\cad-
emy. (See the above - mentioned
corrcs])ondence Ijctween Legendre
and Jacobi, 1829 ; also Sylow, p.
31).

650 SCIENTIFIC THOUGHT.

the highest rank, who for some time had lived apart
in the sechided regions of sublime analysis, descended
again into the region of elementary science, both pure
and applied, where they speedily remodelled the entire
mode of teaching. England possessed very early a writer
of great eminence who represented this tendency, and
whose merits were only partially recognised in his day —
Augustus de Morgan.
18. It will now be necessary to explain more definitely

Extension of ^ r j

otnumbe" wliat is meant by the extension of our conception of
number and quantity through the introduction of com-
plex numbers or complex quantities. This extension
first forced itself on analysts in the theory of equations,
then in the algebraical treatment of trigonometrical
quantities — i.e., in the measurement of angles, or, as
it is now called, of direction in geometry. The first
extension of the conception of number lay in the intro-
duction of negative numbers. These admitted of com-
paratively easy representation arithmetically by counting
backward as well as forward from a given datum ;
practically in the conception of negative possessions,
such as debts, geometrically by the two opposite direc-
tions of any line in space. In algebra, where the simple
operations on quantities are usually preserved in the
result and not lost in the simple numerical value of
the result as in arithmetic, compound quantities were
looked upon as generated by the processes of addition,
resulting in the binomial (of which the polynomial was
an easy extension), and further by the multiplication
with each other of different binomials or polynomials,
through which process expressions of higher order or

DEVELOPMENT OF MATHEMATICAL THOUGHT. 651

degi'ee were arrived at. The forward or direct process
was easy enough, though even here assumptions or arbit-
rary rules were included which escaped notice for a long
time; l)ut the real labour of the analysts only began
with the inverse problem — viz., given any compound
(juantity, similar in structure to those directly produced
by multiplication of binomials, to find the factors or
binomials out of which it can be compounded. Now
it was found that as in the arithmetical process of
division, the invention of fractional quantities ; as in
that of extraction of roots, the irrational quantities
had to be introduced : so in the analysis of compound
algebraical expressions into binomial factors, a new
(quantity or algebraical conception presented itself. It
was easily seen that this analysis could be carried out
in every case only by the introduction of a new unit,
algebraically expressed by the square root of the nega-
tive unity. There was no difficulty in algebraically
indicating the new quantity as we indicate fractions
and irrational quantities ; the difficulty lay in its inter-
pretation as a number. Since the time of Descartes
geometrical representations of algebraical formulic had
become the custom, and it was therefore natural when
once the new, or so-called imaginary, unit was formally
admitted, that a geometrical meaning should be attached
to it.

Out of the scattered beginnings of these researches i9
two definite problems gradually crystallised: the one, ""'*!"'*"''' ^'"i
a purely formal or mechanical one — ^■i/., the geo- i"""*^'*^'"'*-
metrical representation of the extended conception of
quantity, of the complex quantity ; the other, a logical

652

SCIENTIFIC THOUGHT.

or philosophical one — viz., the clearer definition of the
assumptions or principles which underlie arithmetical
and algebraical reasoning. And if algebraical, then also
geometrical reasoning. Both problems seem to have
presented themselves to the youthful mind of Gauss,
as is evident from his correspondence with Bessel ^ and
Schumacher, and from his direct influence on Bolyai,^
Mobius, and Von Staudt, perhaps also indirectly on
Lobatchevsky.'^ It does not, however, appear as if he

' See especially the letters of
Gauss to Bessel, dated November
and December ISll and May 1812
( ' Brief wechsel,' Leipzig, 1880, p.
151 sqq.)

2 Bolyai, the elder (1775-1856),
was a student friend of Gauss in
the) years 1797 to 1799, and kept
up a correspondence with him dur-
ing half a century. Th is correspon -
dence has now been published by
F. Schmidt and P. Stackel, Leipzig,
1899, with a supplement containing
some information about this extra-
ordinary man. His son, Johann
Bolyai (1802-60), is the author of
the celebrated " Appendix, scien-
tiam spatii absolute veram ex-
hibens," which was attached to
his father's ' Tentamen, juven-
tutem ... in elementa matheseos
pura; . . . introducendi,' 1832.
The tract seems to have been
written in 1823. A translation,
with introduction, has been pub-
lished by Dr G. Bruce Halsted
('Neomonic Series,' vol. iii. 4th ed.,
Austin, Texas, 1896). When the
elder Bolyai sent to Gauss in the
year 1831 to 1832 a copy of his
son's tract and of his own work on
Geometrj-, Gauss expressed great
surprise at the contents of the
former. (See his letter of March
6, 1832.) His remarks that the
younger Bolyai had anticipated
some of his own ideas on the

subject, remind one of a similar
remark which he made, Maj' 30,
1828, to Schumacher with refer-
ence to Abel's " Memoir on Elliptic
Functions " in vol. ii. of Crelle's
' Journal ' (see Gauss, ' Werke, ' vol.
iii. p. 495). In both cases he felt
himself relieved from the necessity
of publishing his own results,
though, so far as those referring
to the foundations of geometry are
concerned, it does not appear that
his ideas had arrived at that state
of maturity which the publication
of his posthumous papers has
proved to have been attained in
his treatment of the higher func-
tions. Indeed little or nothing of
prime importance has been found
among his papers referring to the
principles of geometry ; and he
stated to Bolyai that though he
had intended to commit his views
to paper, so that they should not
be lost, he had not intended to
publish anything during his life-
time.

■* It is doubtful whether Gauss's
speculations had any influence on
the younger Bolyai's theory, and
still more so as regards Lobat-
chevsky, whose first tract ap-
peared in the ' Kazan Messenger,'
1829 to 1830, but dates back
probably to 1826. Inasmuch,
however, as the younger Bolyai
must have become acquainted

DEVELOPMENT OF MATHEMATICAL THOUGHT. G53

had airived at any finality in his .speculations, and,
beyond occasional hints which have only subsequently
become intelligilile, the love of finish exhibited in all his
published writings prevented liini from giving to tiic
world the suggestive ideas which evidently formed the
groundwork of his mathematical labours. There is no
doubt that — like Goethe in a very different sphere —
Gauss anticipated individually the developments in the
sphere of mathematical thought down to the end of the
century. The interpretation of the complex quantity
had been given by Wessel, Buee, and Argand ^ in the
early years of the century ; but it remained unnoticed
till it received the sanction of Gauss in a celebrated
memoir referring to the theory of numbers, and iniiil in

through his father with the
speculations of the j'outliful Gauss,
and as Lobatchevsky was a pupil
of another student friend of Oauss
in the person of Prof. Bartels, it is
not unlikely that the interest which
these thinkers took in the subject
can be originally traced to the same
source. (See Dr Halsted's ad-
dress on Lobatchevsky, ' Neomonic
Series,' voh i., 1894). A complete
bibliography of the earlier papers,
referring to the so-called "non-
Euclidean" literature down to
1878, is given by Dr Halstcd in
the first two vols, of the ' Ameri-
can Journal of Mathematics ' : the
most recent publications are those
of the Hon. B. A. W. Russell in
his work, 'The Foundations of
Geometry' (1897) and his ex-
cellent article on " Non-Euclidean
Geometry " in the 28th vol. of the
' Ency. Brit.' See also Klein's litho-
graphed lectures on ' Nicht-Euk-
lidische Geometrie,' Gottingen,
189.3.

' The first somewhat exhaustive
historical statement as to the

geometrical representation of the
complex or imaginary quantity wa.s^
given bj' Hankel in the above-
mentioned work (see above, note,
p. 645), p. 82. He there says, after
discussing the claims of others, —
notably of Gauss, — that Argand in
his 'Essai' of the j-ear 1806 (re-
edited by Hoiiel, 1874) "had so
fully treated of the whole theory
that later nothing essentially new
was added, and that, except a
publication of still earlier date
were found, Argand must be con-
sidered the true founder of the
representation of complex (juan-
tities in the plane." Such an
earlier publication has indeed been
met with in a tract by Caspar
Wessel, which was presented to
the Danish Academy in 1797, and
puljlished in 1799. Having been
overlooked, like Argand's 'Essai,'
it has now been republished at
Copenhagen, 1897, with the title
' Essai sur la representation de la
direction ' (see ' Eucyk. Math.
Wissenschaften,' vol. i. p. 155).

654

SCIENTIFIC THOUGHT.

20.
Quater-
nions.

this country the labours of De Morgan and of Sir William
Eowan Hamilton gave the matter a further and very-
important extension.^ It was also in this country that
the second problem, tlie critical examination of the
principles which underlie the process of legitimate
generalisation of algebra, received distinct attention. To
George Peacock, and to the school of algebraists which
followed him, is due the merit of having brought out
clearly the three fundamental laws of symbolical reason-
ing now generally admitted in text-books on the subject —
the associative, distributive, and commutative principles.
That these principles were to a great extent conventional,
or empirically adopted from ordinary arithmetic, and in
consequence not necessarily indispensable for a consistent
system of symbolical reasoning, has been generally ad-
mitted ever since Sir William Eowan Hamilton, after
ten years of labour, succeeded in establishing a new
calculus — the method of quaternions, in which the com-
mutative principle of multiplication is dropped. This

^ Far more important than
the suggestions or artifices men-
tioned in the foregoing note, and
which since the time of Argand
and Gauss have been variously
modified, is the conception that
our common numbers do not form
a complete system without the
addition of the imaginary unit,
but that with the introduction
of a second unit " uumbei's form
a universe complete in itself, such
that, starting in it, we are never
led out of it. There may very well
be, and perhaps are, numbers in a
more general sense of the term ;
but in order to have to do with
such numbers (if any) we must
.start with them"' (Cajdey in art.
"Equation," ' Ency. Brit.'; 'Coll.

Works,' vol. xi. p. 50.3). There
seems little doubt that this con-
ception was first clearly established
in the mind of Gauss, and that
none of the contemporary writers
can be shown to have had a
similarly clear insight. Since this
has become generallj' recognised —
and we owe this recognition
probably to the independent
labours of Gra'^smann and Rie-
mann — the discussion of the whole
subject has been raised to a much
higher level, as may be seen by
comparing the Report of Peacock,
quoted above, with the discussion
of Hankel [loc. cit.), and still more
with the exhaustive article by Prof.
E. Study in vol. i., 'Encyk. Math.
AViss.,' pp. 147-184.

DEVELOPMENT OF MATHEMATICAL THOUGH'l'. (".55

calculus was shown to l)e of special use in expressing
the relations of spherical trigonometry. Two terms
expressing definite notions special to geometry, by which
science has been enriched and practical application greatly
simplified, are an outcome of this line of research. These
are the terms "vector," to express the iidtion of directed
magnitude — i.e., of direction and magnitude combined as
distinguished from magnitude and position alone ; and
the notion of an " operator " which changes direction and
magnitude as an ordinary multiplier changes magnitude
only.^ It was shown by Argand and others that the

^ ThetiC two notions, wliich have
their origin in the writings of
Hamilton on the one side and the
Calculus of Operations on tiie
other, belong to this country and to
a period during which mathematical
researches were carried on in a frag-
mentary manner, and much out of
cont;ict with the contemporary
mathematics of the Continent.
Both the Calculus of Quaternions
of Hamilton and the Calculus of
Operations were looked upon for a
long time as curiosities (as was also
the Barycentric Calculus of Mobius
in Germany). Gradually, however,
the valuaVjle ideas which were con-
tained in them became recognised
as much from the practical as from
the theoretical jjoint of view. Jn
the former interest the application
of Vector Analysis or the Algebra
of Directed Quantities received a
great impetus when the need was
felt of having' an 'algebra of " i)hy-
sical quantities." This found e.x-
jiression in the writings of Clerk-
Maxwell. (See his ' Treati.se on
Electricity and Magnetism,' vol. i.
J). 8, 2nd ed., as also his paper on
" The Mathematical Classification of
Physical Quantities," 1871. 'Coll.
I'aiiers,' vol. ii. p. 2.'>7.) In the prac-
tical ajjplication of electrical tiieories

these notions have since become in-
disi)ensable, and the subject lia,s re-
ceived increjvsing attenti(jn, notably
in America, which holds a foremost
place in the development of electrical
-science and its application. Mathe-
maticians of the first order, such
as J. Willard Gibbs, have pub-
lisheil te.xt-books on the subject,
whilst other electricians of emin-
ence, such as Mr Oliver Heaviside,
have elaborated sjiecial forms of the
Directional Calculus to serve their
purpose.s. In Dynamics the Dublin
School, represented after the death
of Hamilton by Sir Robert S. Ball
(in his ' Theory of Screws,' 1876),
has had an imjjortant influence in
tlie introduction of novel and more
a])propriate methods whicii have
gradually permeated the general
treatment of the subject. Whilst
there is no doubt that for a long
time the Calculus of Quaternions
was the oidy methodical elaboration
of these novel and useful ideas, it
was overlooked that simultaneously
and quite independently H. Grass-
mann of Stettin (see above, vol. i.
p. 213) had worked out a much more
com])rehensive and fundamental
calculus, of which the method of
quaternions and all the dili'erent
forms of Vector Analysis can l>e

656 SCIENTIFIC THOUGHT.

arithmetic based upon two units instead of one — i.e., the
arithmetic of couples or complex quantities — could be
completely and consistently represented by choosing as
axes whereon the separate units were counted, the two
perpendicular axes of Cartesian geometry. An attempt
to extend this geometrical representation into space led
Hamilton to the invention of his method, Gauss having
very early satisfied himself that within the limits of
ordinary algebra no further extension was necessary or
possible.

The examination into fundamental principles was not

limited in the mind of Gauss to those of algebra : he

early applied himself likewise to those of geometry and

of dynamics. The great French mathematicians, such

21. as Legendre and Lagrange, were also occupied with such

Foundations ® _ o o ' r

of geometry, speculations. They have been carried on all through
the century, but have only towards the end of the
period been brought into connection and shown to be
of importance for the general progress of mathematics.
The secluded, and for a long time unappreciated, labours
of isolated but highly original thinkers have accordingly

considered as merely special in- ' Grassmann's works is being pub-
stances. This has now been abund- ' lished by Teubner. Those who are

antly proved through the writings
of mathematicians in all countries,
among whom I will only mention
Hankel and Dr V. Schlegel in Ger-
many, Clifford, Prof. Henrici, and
latterly Mr Whitehead in England,
Prof. Peano in Italy, and M. Burali
Forti in France. See on the whole
subject, on the fate of Grassmann
and of his great work, V. Schlegel,
' Die Grassmann'sche Ausdehnungs-
lehre,' Leipzig, 1896 ; also, by the
same author, a short biography of
Grassmann (Leipzig, Brockhaus,
1878). A complete edition of

interested in seeing how the notions
underlying the directional calculus
are gradually becoming clarified, and
the terminology and notation settled,
may read with profit the controversy
carried on in the pages of ' Nature,'
vols, xlvii. and xlviii., between Pi'of.
Macfarlane, Willard Gibbs, Mr 0.
Heaviside, Mr A. M'Aulay, and Dr
Knott ; also Dr Larmor's review of
Hay ward's ' Algebra of Coplanar
Vectors' (vol. xlvii. p. 266), and
Sir R. S. Ball's reference to the
' Ausdehnungslehre ' of Grassmana
(vol. xlviii. p. 391, 1893).

DEVELOPMENT OF MATHEMATICAL THOUGHT. 657

received tardy recognition. Such speculations can hi
carried on either as fascinating exercises of mere
ingenuity, or for practical purposes to improve the
refined instruments of mathematical calculation, or in
the philosophical interest of arriving at the fundamental
processes of human thought .ind intuition.^ Many
persons think tliat only the second of these three in-

' Already Euler had remarked on
the different interests that prompted
mathematical research. Referring
to tiie wTitings of Count Fagnano,
he says in the introduction to
the tirst of his memoirs on Elliptic
Integrals (1761, ([Uoted by Brill &
Nuther in ' BerichL der Deutschen
Matheniatiker-Vereinigung,' vol. iii.
p. 206) : " If one looks at mathe-
matical speculations from the point
of view of utility, they can be divided
into two classes : first, those which
are of advantage to ordinary life
and other sciences, and tiie value
of which is accordingly measured by
the amount of that advantage. The
other class comprises speculations
which, without any direct advant-
age, are nevertheless valuable be-
cause they tend to enlarge the
boundaries of analysis and to exer-
cise the powers of the mind. Inas-
much as many researches which
promise to be of great use have to
be given up owing to the inade-
(juacy of analysis, those speculations
are of no little value which i)romise
to extend the province of analysis.
Such seems to be the nature of
observations which are usually made
or found a posteriori, but which
have little or no chance of being
discovered a priori. Having once
been established as correct, methods
more easily present themselves
which lead up to them, and there
is no doubt that thrcjugh the search
for such methods the domain of
analysis may be considerably ex-

VOL. II.

tended." The school of mathema-
ticians headed by Abel and Jacobi
pursued mathematics from purely
scientific interest, and was criti-
cised on this ground bj- eminent
contemporary mathematicians in
France : see a letter of Jacobi to
Legendre, dated July 2, 1830, in
which he refers to a Report of
Poisson on his great work, but
adds : " M. Poisson n'aurait pas
du reproduire dans son rapport
une phrase pcu adroite de feu M.
Fourier oii ce dernier nous fait
des rej)roches, a Abel et h, moi, de
ne pas nous etre occupes de pre-
fdrence du mouvement de la chaleur.
II est vrai que M. Fourier avait
I'opinion ijue le but principal des
mathcmatiques ot^iit I'utilite pub-
lique et lexplication des i)hcno-
menes naturels ; mais un philosophe
comme lui aurait du savoir que le
but uni<iue de la science, c'est
I'honneur de I'esprit Immain et que
sous ce titre, une question de
nombres vaut autant ([u'une (jues-
tion du systemedu monde." In the
sequel he adds : " Je crois entrevoir
que toutes ces transcendantes " (i.e.,
the elliptic and Abelian functions)
"jouissent des jiroprictcs admir-
ables et inattendues auxquclles on
l)eut etre conduit par le theorfcme
d'Abel. . . . J'ai retlcchi aussi de
temps en temps sur une methode
nouvelle de traiter les perturbations
celestas, methode dans laciuelle
doivent entrer les theories nou-
velles des fonctions elliptiques."

2 T

658

SCIENTIFIC THOUGHT.

22.
Descriptive

Geometry.

ducements is likely to prove fruitful for the progress of
science ; they look upon the first as an amusing pastime,
and upon the third as empty and not devoid of danger.
In recognition of the partial correctness of this view, I
will follow up the practical stimulus in its fruitful in-
fluence upon the development of the lines of mathe-
matical research.

This stimulus came in the closing years of the pre-
ceding century through the lectures of Gaspard Monge
at the I^cole Normale, and has become popularly known
through his invention of Descriptive Geometry, the first
modern systematic application of purely graphical methods
in the solution of mathematical problems. As Cauchy
was the founder of the modern school of analysts, so
Monge, together with Carnot, founded the modern school
of geometricians ; Dupin, Poncelet, and Chasles being
among his most illustrious pupils. The aim of this
school was to give to geometrical methods, such as
had been practised by the ancients,^ the same generality
and systematic unity which characterised the analytical
methods introduced by Descartes.

Not long after the introduction of the latter, Leibniz

^ These methods had been
largely used in this country by
Newton, Robert Simson, and
Stewart. They were systematised
by L. N. M. Cai-not. Chasles
(" Discours d'inauguration, &c.,"
1846, 'G(?om^trie Superieure,' p.
Ixxvii) says : " Dans le siecle
dernier, R. Simson et Stewart
donnaient, li I'instar des Anciens,
autant de demonstrations d'une
proposition, que la figure h. laquelle
elle se rapportait presentait de
formes differentes, h, raison des
positions relatives de ses diverses

parties. Carnot s'attacha a prouver
qu'une seule demonstration ap-
pliquee h. un ^tat as.sez general
de la figure devait suftire pour
tous les autres cas ; et il montre
comment, par des changements
de signes de ternies, dans les
formules d^montrees par une
figure, ces foruiules s'appliquaient
il une autre figure ne ditteraut de
la premiere, commes nous I'avons
dit, que par les positions relatives
de certaines parties. C'est ce qu'il
a()pela le ' Principe de correlation
des figures.' "

DEVELOPMENT OF MATHEMATICAL THOUGHT. 659

had foretold ^ the possibility and necessity of such an
independent development of pure geometry, in which the
relations of position in space, as opposed to those of
measure, magnitude, or quantity, would be placed in the
foreground. Projection, as practised in the drawing of
maps, and perspective, as practised in the fine a.nd
descriptive arts, had already re^'ealed a number of
remarkable properties of figures in the plane and in
space. By continuous motion of points or lines, by
artifices like throwing of shadows, by sections of solids
with lines and surfaces, a vast number of problems had
been solved and isolated theorems established. The
method here practised was that of construction, as in
analysis the method was that of calculation with sub-
sequent interpretation. All this purely constructive
work was to be brought together and systematically
combined in a whole. It was evidently a distinct line
of research, based upon intellectual processes other
than the purely analytical method — a line which,
as it seemed to its followers, had been unduly neglected
and pushed into the background. Although Monge
became the founder of this purely descriptive or con-
structive branch of geometry, he was himself equally
great as an analyst ; in fact, the fusion in his mind
of the two methods was the origin of much of his
greatest work. In attempting to carry out more
thoroughly the separation or independent development
of the constructive or descriptive method, his great pupil,

23.

J. V. Poncelet — whilst deprived of all literary resources Poneeiet.

^ See the quotations fi-oni his letters to Huygens and others given
above, vol. i. p. 103 note.

660 SCIENTIFIC THOUGHT.

in the prisons of Kussia — meditated on the real cause of
the power which algebraical analysis possessed, on the
reason why geometry proper was deprived of it, and
what might be done to give it a similar generality. In
pursuing this line of thought he was led to discover the
cause of the existing limitation of purely geometrical
reasoning in its rigidity, inasmuch as it was arrested as
soon as its objects ceased to have a positive or absolute,
that is a physical, existence.-^ Opposed to this limitation
was the freedom of the analytical method, which, operating
with indeterminate symbols, could, by letting them change
gradually, include not only what was explicitly given,
but also that which was merely implied ; not only the
finite, but likewise the infinite ; not only the real, but
likewise the fictitious or imaginary. In order to gain a
similar generality in purely geometrical or descriptive
science, a similar fiexibility would have to be introduced.
Poncelet was thus led to the enunciation of his celebrated
and much - criticised " principle or law of continuity." ^

1 See the " Introduction " to the ' 122, &c. : "Originally the ex-
ist volume of the ' Traite des Pro- | positions referring to the prin-
ciple of continuity were intended
to occupy much greater space. . . .
In consequence of correspondence
with Terquem, Servois, and Brian-
chon, Poncelet desisted from the
publication of it. . . . However
cautiously Poncelet advanced his

pridtes projectives des figures,' pp.
xi, xii. I quote from the 2nd edi-
tion of 1865. The 1st was published
in 1822. The researches date from
1813, the year of Poncelet's im-
prisonment. See " Preface de la
premiere edition."

^ Ibid., Introduction, p. xiv. ; principle " — in the ' Essai sur les
On the principle of continuity \ proprietes projectives des sections
in geometry, see an article in coniques ' (presented to the
vol. xxviii. ' Ency. Brit.' by the i Academy in 1820) — " it never-
Rev. Charles Taylor, and the re- | theless aroused the doubts of
ferences given therein ; also Prof. ] Cauchj^, who in his report on
E. Kotter's Report on the i Poncelet's paper warns against the
" Development of Synthetic Ge- too hasty application of the
ometry " in vol. v. of the i principle. Gergonne accompanied
' Jahresbericht der Deutschen ' the reprint of this report with
Mathematiker Vereinigung,' p. I notes, in which he characterised

DEVELOPMENT OF MATHEMATICAL THOUGHT. 661

Analytical geometry, Ijy substituting an algebraical ex-
pression for a geometrical figure — say a curve, — could
apply to it all the artifices of abstract analysis. By
varying the co-ordinates you can proceed along the whole
extent of the curve and examine its behaviour as it
vanishes into infinity, or discover its singular points at
which there occurs a break of continuity : you can vary
its constants or parameters, and gradually proceed from
one curve to another belonging to the same family, as is
done in grouping together all curves of the second order,
or — as was done in the calculus of variation, invented
by Euler and Lagrange — you can vary the form of the
equation, proceeding from one class of curve to another.
Now clearly all this operating on equations and sym-
bolic expressions was originally abstracted from geom-
etry, including the mechanical conception of motion ; in
particular the ideas which underlie the method of
fluxions were suggested by the motion of a point in
space. The conception of continuous motion in space- —

the principle as a valuable in- j the habit of considering real and

.strument for the discovery of ! imaginary quantities as equally

new truths, whicii nevertheless did ' legitimate led to that principle

not make stringent proofs super- , which, without analytical geometry,

fluous." Cauchy's report seems to | could never have been discovered,

have aroused Poncelet's indignation, j Thus pure geometry was compen-

Hankel ('Elemente der Projectiv- ! sated for the fact that analysis

ischeu Geometrie,' 187.5, p. 9)
says: "This principle, which was
termed by Poncelet the ' Prin-
ciple of Continuity,' inasmuch as

had for a long time absorbed the
exclusive interest of mathemati-
cians ; indeed it was perhaps an
advantage that geometry, for a

it brings the various concrete i time, had to lie fallow." Kotter

cases into connection, could not
be geometrically proved, because
the imaginary could not be
represented. It was rather a
present which pure geometry re-
ceived from analysis, where im-
aginary quantities behave in all
calculations like real ones. Only

continues : " Von Staudt was the
first who succeeded in subjecting
the imaginary elements to the
fundamental theorem of projective
geometry, thus returning to analyt-
ical geometry the present which,
in the hands of geometricians, had
led to the most beautiful results."

662 SCIENTIFIC THOUGHT.

of motion of points, lines, planes — corresponded accord-
ingly to the notion of vai-iability in analysis. The intro-
duction of motion, gradual and continuous, would give
to purely geometrical or descriptive reasoning the same
flexibility which analysis had acquired in the calculus of
fluxions and of variations. Figures would lose their
rigidity and isolation and limited nature and become
movable, related to each other, filling the whole of space
24. instead of a restricted and confined area or region. It

Character

of modem is the peculiarity of the modern as opposed to the older

geometry. j. ^ x x

geometry, never to let figures become motionless or
rigid,^ never to consider them in their isolation, but
always in their mutual relations ; never to have regard
only to a finite portion of a line or surface, but to
conceive of it in its infinite extension. By a reaction
of analysis and geometry on each other, freedom and
generality have been gradually acquired.

But this moving about of figures in space in order
to learn their properties and mutual relations must b&
according to some method ; otherwise it will not lead to
scientific and exact knowledge. Poncelet, in considering
how the two successful methods in geometry — the
Cartesian and the Descriptive — had attained to their
perfection, discovers a general principle which underlies
their proceedings, and which is capable of great extension:
this is the principle of projection."

^ See, inter ulia, what Geiser
says of Jacob Steiner's method in
his pamphlet ' Zur Erinnerung an
Jacob Steiner,' Schaffhausen, 1874,
p. 27.

^ 'Traite des Proprietes pro-
jectives,' voh i. p. xviii : " En
reflechissant attentivement Ji ce

qui fait le principal avantage de
la Geometric descriptive et de la
mdthode des coordonnees, h ce qui
fait que ces branches des Mathe-
matiques offrent le caractere d'une
veritable doctrine, dont les prin-
cipes, peu nombreux, sont li^s et
enchaiiies d'une maniere necessaire

DEVELOPMENT OF MATHEMATICAL THOUGHT.

663

Of this principle of projection, which Poncelet at once 25-
introduces in the more general form as conical or central projection,
projection, two signal applications existed in the treatises
on Conic Sections handed down from antiquity, and in
the practical methods and Eules of Perspective invented
by Lionardo da Vinci and further developed by various
geometricians. The results, which lay scattered in many
books and memoirs, Poncelet collected in a systematic
form, bringing them, by the application of the law of
continuity, under a few general and eminently useful
points of view or principles. By the method of projec-
tion or perspective he " transformed figures which are
very general into others which are particular, and vice
versa." He established the principle of " homology " in
figures, and by showing how figures apparently very
different could be described by the process of projection
from the same original figure, he showed that there
existed a peculiar relation among figures — viz., their
" reciprocity." ^

et par uiie uiarche uniforme, on
ne tarde pas h reconnaitre que cela
tient uuiquement ii I'usage qu'elles
font cle la projection."

' The properties of figures, called
by Poncelet " liomology " and "I'e-
ciprocity," refer to the correspond-
ence of certain elements of one
figure to those of another figure.
In the case of " homology," we
have to do with corresponding
points or corresponding lines— ix.,
with the correspondence of the
same elements. In the case of
"reciprocity," we have to do with
correspondence of points or lines
in the one figure, with lines or
points in the other — i.e., with
the correspondence of different
elements. The idea of placing

figures in an homologous rela-
tion was got by the device of
making two planes, which con-
tained figures in perspective, fall
together into one plane ; upon
which the section of the two orig-
inal jilanes became the " axis,"
and the ej-e-point the " centre "
of homology — all situated in one
and the same plane. Poncelet had
already conceived of the possibil-
ity of reducing the two planes in
Monge's ' Descriptive Geometry,'
which represent the plan and ele-
vation of a figure in one plane,
on which the elevations were
marked by what are now called
" contour lines." The idea of the
correspondence of figures by what
is called " reciprocity " was sug-

664 SCIENTIFIC THOUGHT.

26. By the law of continuity he showed how in pure
continuity, geometry it became necessary to introduce the considera-
tion of points and lines which vanish into infinity or
which become imaginary, establishing by their invisible
elements the continuous transition from one geometric
form to another ; just as in algebra these conceptions
had forced themselves on the attention of analysts.
Ideal elements were thus made use of to lead to the dis-
covery of real properties.

The consideration of lines and points which vanish
or lie at infinity was familiar to students of perspective
from the conception of the " vanishing line " ; but the
inclusion of ideal points and lines was, as Hankel says,
a gift which pure geometry received from analysis,
where imaginary (i.e., ideal or complex) quantities behave

27. in the same way as real ones. "Without the inclusion of

Ideal _ "^

elements, tlicsc ideal or invisible elements the generality or con-
tinuity of purely geometrical reasoning was impossible.
The geometrical reasoning of Monge, Carnot, and
Poncelet was thus largely admixed with algebraical or
analytic elements. It is true that Monge's descriptive
geometry was a purely graphical method, and that

gested to Poncelet by the prop-
erty, known already to De la
Hire ("Sectiones ConicEc," 1685),
that in the plane of a conic
section every point corresponds
to a straight line called its
"polar," that to everj^ straight
line corresponds a point called
its " pole," that the " polars "
corresponding to all the points of
a straight line meet in one and
the same point, and vice versa
that the "poles" corresponding to
all lines going through one and
the same point lie on a straight

line ; the line and point in ques-
tion standing in both cases in the
relation of pole and polar to each
other. Poncelet uses "this trans-
formation of one figure into its
reciprocal polar systematicallj' as a
method for finding new theorems :
to every theorem of geometry
there corresponds in this way
another one which is its ' polar,'
and the whole of geometry was
thus split up into a series of
truths which run parallel and
frequently overlap each other "
(Hankel, loc. cit., p. 20).

DEVELOPMENT OF MATHEMATICAL THOUGHT. 665

Poncelet's method of central projection attacked geometri-
cal problems from a purely constructive point of view.
Nevertheless the frequently expressed oljject of the later
writings of Monge, as well as those of Carnot and
Poncelet, was to introduce into geometrical reasoning
the generality and continuity which analysis possessed,
and this was largely attained by the interpretation of
notions taken over from analysis. Their endeavours
were, however, in the sequel crowned by the discovery
of a purely geometrical property, the understanding of
which has ever since formed the basis of what may be
termed modern geometry.

This remarkable property, which may be regarded
as revealing the very essence of extension in space or
of the " space -manifold," — inasmuch as it brings the
different elements of space into mutual relation, — is the
go-called principle of " duality " or of " reciprocity." The ss.

. , I J Principle ol

principle of duality is now usually defined to mean that duality.
in geometry on the plane or in space, " figures coexist in
pairs, two such coexisting figures having the same genesis
and only differing from one another in the nature of the
generating element." ^ The elements of plane geometry
are the point and the line ; the elements of solid geometry
i are the point and the plane. By interchanging these
I correlative terms, correlative propositions may be written
down referring to plane and to space geometry. In pro-
jective geometry there are two processes which are cor-
; i relative or complementary to each other — the process of
;i projection and the process of section. We can project

^ Cremona, ' Elements of Projective Geometry,' transl. by Leudesdorf.
Oxford, 1885, p. 26.

666

SCIENTIFIC THOUGHT.

29.
Keciprocity,

from a point drawing lines or rays on the plane and in
space, and we can cut these by lines in a plane or by
planes in space. And it can be shown that " if one
geometric form has been derived from another by means
of one of these operations, we can conversely, by means
of the complementary operation, derive the second from
the first." ^

The projective geometry of Poncelet contains the two-
fold origin of the principle of duality in his method of
projection and section, and in his theory of the reciprocity
of certain points and lines in the doctrine of conic sections,
called the theory of reciprocal polars. But the mathe-
matician who first expressed the principle of duality in a
general — though not in the most general — form was
Gergonne, who also recognised that it was not a mere
geometrical device but a general philosophical principle,
destined to impart to geometrical reasoning a great
simplification. He sees in its enunication the dawn of
a new era in geometry.^

1 Cremona, loc. cit., p. 33.

- The priuciple of Duality seeiu.s
to have been first put forward in its
full generalit}' by Gergonne, in-
spired probably by the theory of
Reciprocal Polars (see note, p. 663)
enunciated by Poncelet, who many
j'ears afterwards carried on a vol-
uminous polemic as to the priority
of the discovery. " Gergonne saw
that the ])arallelisni (referred to
above) is not an accidental conse-
quence of the property of conic
sections, but that it constitutes a
fundamental principle which he
termed the 'principle of duality.'
The geometry which is usually
taught, and in which a line is con-
sidered to be generated by the
motion of a point, is opposed by

another- geometry equallj' legiti-
mate in which a point is gener-
ated by the rotation of a line.
Whereas in the first case the line is
the locus of the moving point, in
the latter case the point is the
geometrical intersection of the
rotating line. In this generality
the principle of duality has been in-
corporated into modern geometry "
(Hankel, loc. cil., p. 21). Gergonne
says of the new principle (1827, see
Supplement to vol. ii. 2nd ed. of;
Poncelet's ' Traite,' p. 890) : " II ne
s'agit pas moins que de commencer
pour la geometric, mal connucii
depuis pros de deux mille ans qu'oni
s'en occupe, une ere tou t - h - f aiti
nouvelle ; il s'agit d'en mettre tousH
les anciens traites ii pen pres auj

DEVELOPMENT OF MATHEMATICAL THOUGHT. 667

It must, however, in all fairness be stated that about
the period from 1822 to 18.")0 this great simplification
and unification of geometric science was as it were in the
air — that it had presented itself to various great thinkers
independently, being suggested from different points of
view. The beginnings can no doubt be traced in the
beautiful theorems of older French mathematicians, such
as Pascal and De la Hire, and more generally in the
suggestive methods of i\Ionge and Poncelet ; its first
formal enunciation is in the memoirs of Gergonne : but
the comprehensive use of it — -the rewriting of geometry
from this point of view — was the idea of Jacob Steiner, 3o.

Steiner-

who, in his great but unfinished work on the " Systematic
Development of the Dependence of Geometric Forms "
(ISoO), set himself the great task "of uncovering the
organism by which the most different forms in the world
of space are connected with each other." " There are,"
he says, " a small number of very simple fundamental
relations in which the scheme reveals itself, by which
the whole body of theorems can be logically and easily
developed." " Through it we come, as it were, into pos-
session of the elements which Nature einploys with the
1 greatest economy and in the simplest manner in order to
invest figures with an infinite array of properties."^

rebut, de leur substituer des traites tion aussi iuiperieusement u^ces-
Vune forme tout a fait ditfurente, saire qu'elle a ete jusqu'ici peu

kles traites vraiment philosophiques prevue.

'qui nous montreut eutin cette eten- ^ See the Preface to the ' Sj's-

Idue, receptacle universel de tout ce tematische Entwickelung, &c.,'

qui existe, sous sa veritable physi- i in Jacob Steiner's ' Gesammelte

nnomie, que la mauvaise inethode
•d'enseignement adoptee jusqu'ii ce
ijour ne nous avait pas permis de

Werke ' (ed. Weierstrass), vol. i.
p. 229. " In the beautiful theorem
that a conic section can be gener-

ii-eniarquer ; il s'agit, en un mot, ' ated by the intersection of two
I'operer dans la science une revolu- projective pencils (and the dually

668

SCIENTIFIC THOUGHT.

The labours of Poncelet and Steiner introduced into
geometry a twofold aspect, and accordingly, about the
middle of the century, we read a good deal of the
two kinds of geometry which for some time seemed to
develop independently of each other. The difference
has been defined by the terms " analytic or synthetic,"
" calculative or constructive," " metrical or projective."
The one operated with formulae, the other with figures ;
the one studied the properties of quantity (size, magni-
tude), distances, and angles, the other those of position.

The projective method seemed to alter the magnitude
of lines and angles and retain only some of those of
position and mutual relation, such as contact and inter-
section. The calculating or algeliraical method seemed
to isolate figures and hide their properties of mutual
interdependence and relation.
31. These apparent defects stimulated the representa-

Mutual in- • n i

fluence of tivcs of the two mctliods to investigate more min-

metrical and °

projective utcly their hidden causes and to perfect both. The

geometry. ^ ^

algebraical formula had to be made more pliable, to:
express more naturally and easily geometrical relations ;
the geometrical method had to show itself capable of'
dealing with quantitative problems and of interpreting
geometrically those modern notions of the infinite and
the complex which the analytic aspect had put promi-

correlated theorem referring to
projected ranges), Steinei- recog-
nised the fundamental principle
out of which the innumerable
properties of these remarkable
curves follow, as it were, automat-
ically with playful ea.se. Nothing
is wanted but the combination of
the simplest theorems and a vivid

geometrical imagination capable oi
looking at the same figure from
the mo.st different sides in orderi,
to multiply the number of pro-l
perties of these curves indefl
initely " (Hankel, loc. cit., p.j
26 ; see also Cremona, ' Projectivfjj
Geometry,' p. 119).

DEVELOPMENT OF MATHEMATICAL THOUGHT.

669

nently into the foreground. The latter was done by
the geometric genius of Von Staudt, who succeeded in
giving a purely geometrical interpretation of the imagin-
ary or invisible elements ^ which algebra had introduced,
whilst Steiner astonished the mathematical world by the
fertility of the methods by which he solved the so-
called isoperimetrical problems — i.e., problems referring
to largest or smallest contents contained in a given
perimeter or vice versd, problems for which Euler and
Lagrange had invented a special calculus.^ In spite of

' The geometrical interpretation
of tlie imaginary elements is given
by Von Staudt in a sequel to his
'Geometrie der Lage' (1847), en-
titled ' Beitriige zur Geometrie der
Lage' (1856-60); and after hav-
ing been looked upon for a long
time as a curiosity or a " hair-
splitting abstraction," it has
latterly, through the labours of
Prof. Reye ( ' Geometrie der Lage,'
1866-68) and Prof. Liiroth ( ' Math.
Annalen,' vol. xiii. p. 145), become
more accessible, and is systematic-
ally introduced into many excel-
lent text-books published abroad.
The simplest exposition I am ac-
quainted with is to be found in
the later editions of Dr Fiedler's
German edition of Salmon's ' Conic
Sections ' (6th Aufl., vol. i. p. 23, &c.,
and p. 176, &c. ) In 1875, before
the great c'nange which has brought
unity and connection into many
isolated and fragmentary contribu-
tions had been recognised, Hankel
wrote with regard to Von Staudt's
work, and in comparison with that
of Chasles, as follows: "The work
of Von Staudt, classical in its
originality, is one of those attempts
; to force the manifoldness of nature
I with its thousand threads running
! hither and thither into an abstract
scheme and an artificial system : an
attempt such as is only possible in

our Fatherland, a country of strict
scholastic method, and, we may add,
of scientific pedantry. The French
certainly do as much in the exact
sciences as the Germans, but they
take the instruments wherever
they find them, do not sacrifice
intuitive evidence to a love of
system nor the facility of method
to its purity. In the quiet town
of Erlangen, Von Staudt might well
develop for himself in seclusion
his scientific system, which he
would only now and then explain
at his desk to one or two i^upils.
In Paris, in vivid intercourse with
colleagues and numerous jjupils,
the elaboration of the system
would have been impossible " {loc.
cit, p. 30).

'^ See the lecture delivered by
Steiner in the Berlin Academy,
December 1, 1836, and the two
memoirs on ' Maximum and Min-
imum ' (1841), reprinted in ' Ge-
sammelte Werke,' vol. ii. p. 75
nqq., and 177 sqq., especially the
interesting Introductions to both,
in which he refers to his fore-
runner Lhuilier (1782), deploring
that others had needlessly forsaken
the simple synthetical methods
adopted by him. Some of
Steiner's expositions in these
matters were apparently so easy
that non - mathematical listeners

670

SCIENTIFIC THOUGHT.

these marvellous works of genius, science is probably
indebted for its greatest advances to those mathema-
ticians who, like Pllicker in Germany, Chasles in France,
and Cayley in England, employed the analytic and con-
structive methods alternately and with equal mastery.

It is impossible — and it is not my object — to allot to
each of these original thinkers the special ideas intro-
duced by him into modern science ; but for the purpose

like Johannes Miiller could not
understand how such simple things
could be brought before the
Academy of Sciences, whereas the
great mathematician Diiichlet was
full of praise of the ingenuity of
the method by which problems
were solved which the Calculus
of Variations attacked long after
Steiner, and then only in ways
which the synthetical method had
indicated (see Geiser, ' Zur Erin-
nerung an Jacob Steiner,' p. 28).
It must not be supposed, however,
that Steiner was an extreme purist
so far as geometrical methods were
concerned, for he says himself
" that of the two methods neither
is entitled to exclude the other ;
rather both of them will, for a long
time, have plenty to do in order to
master the subject to some extent,
and then only can an opinion as to
their respective merits be formed "
('Ges. Werke,' vol. ii. p. 180).
An instance of a celebrated prob-
lem being treated alternately by
synthetic and analj'tic methods
is that of the Attraction of
Ellipsoids, in which the Theorem
of Maclaurin had created quite a
sensation. In spite of the ad-
miration which it evoked, both
Legendre and Poisson expressed
the opinion that the resources of
the synthetic method are easily
exhausted. The latter, whilst ad-
mitting "que la synthese ait
d'abord devance I'analyse," never-

theless concludes that "la question
n'a ete enfin rdsolue completement
que par des transformations ana-
lytiques . . . auxquelles la syn-
thase n'aurait pu suppleer." This
expression of opinion was falsified
when Chasles presented to the
Academy, in the year 1837, a
memoir in which, through the
study of confocal surfaces, the
Theory of Maclaurin was synthet-
ically proved in its full generality.
Poinsot, who reported on this
memoir, attached the following re-
marks : " Ce m^moire remarquable
nous offre un nouvel exemple de
r^legauce et de la clarte que la
geometrie pent repandre sur les
questions les plus obscures et les
jjIus difficiles. ... II est certain
qu'on ne doit ndgliger ni I'une ni
I'autre ; elles sont au fond presque
toujours uuies dans nos ouvrages,
et forment ensemble comme I'in-
strument le plus complet de I'esprit
humain. Car notre esprit ne
marche guere qu'h, I'aide des signes
et des images; et quand il cherche
h, pendtrer pour la premiere fois
dans les questions difficiles, il n'a
pas trop de ces deux moyens et
de cette force particuliere qu'il ne
tire souveut que de leur concoura.
C'est ce que tout le monde peut
sentir, et ce qu'on peut recon-
naitre dans le Memoire meme."
(Chasles, ' Rapport sur les progr^
de la geometric,' 1870, p. 105, &c.)

DEVELOPMENT OF MATHEMATICAL THOUGHT. 671

of bringing some order into the tangled web of mathe-
matical speculation, mainly represented by these, I shall
identify the name of Pliicker with the great advance 32.

'' ° Pliicker,

which has taken place in geometry through the change ^l^f^^'
in our ideas as to the elements of space construction and
the generalisation of our ideas of co-ordinates : with
Chasles I shall specially connect the modern habit in
geometry of combining figures in finite space with their
infinitely distant elements, and with Cay ley the application
to geometrical science of the novel and comprehensive
methods of modern algebra. Let us dwell for a moment
on each of these three great departures.

The elements of any science are a very different thing
from the elements of the special object with which that
science is concerned. The elements of chemistry are not
the chemical elements. The latter are, we suppose, 33.

Historical

somethino; existing in nature, something fixed and un- aud logical

t' " ^ foundations

alterable, which science aims at finding out ; the former
are certain conceptions from which we find it convenient
to start in teaching, expounding, and building up the
science of chemistry. The latter are artificial, the former
iare natural. The same remark obtains in geometrical
science. The elements of geometry have an historical,
a practical beginning : the elements of space form a con-

eption which gradually emerges in the progress of geo-
oaetrical science. In every science there is a tendency
bo replace the casual and artificial elements by tlie

latural or real elements, and to build up the historical
traditional body of doctrine anew, using the very
'dements which Nature herself, as it were, employs in

•reducing her actual forms and objects. As the pass-

672 SCIENTIFIC THOUGHT.

age quoted above shows, such an idea must have been
before the mind of Jacob Steiner when he wrote the
' Systematische Entwickelung.' Through Euclid geo-
metricians had learnt to begin with the straight line of
definite — not indefinite — length, the triangle, the circle,
advancing to more complicated figures ; practice had
made geometry a science of mensuration, involving
number ; the convenience of practice in astronomy,
geodesy, and geography had introduced the artifice of
referring points and figures in space to certain arbi-
trarily chosen data — points and lines. The terms " right
ascension " and " dechnation," " altitude " and " azi-
muth," " latitude " and " longitude," led to the co-
ordinates of Descartes and to analytical geometry. In
this older and modern geometry, the beginnings were
arbitrary, and many conceptions were introduced which
were foreign to the object of research. It was through
a slow process that in quite recent times — notably dur-
ing the nineteenth century — mathematicians became
aware how artificial were their methods, and with how
many foreign elements they had encumbered the objects
of their study. To replace the artificial by natural con-
ceptions, and to open the eyes of geometricians to the
advantage of not confining themselves to the point (its.
motion and distances) as the element in their space
construction, no one did more than Julius Pliicker of
Bonn. We have now not only a point - geometry,]
but likewise a line-geometry — i.e., we have a geom-
etry in which the line is the primary element, the
point being the secondary element, defined by the
intersection of two lines. This conception, whichP

DEVELOPMENT OF MATHEMATICAL THOUGHT.

673

can be applied also to geometry in space, the point
being conceived as generating a plane by its motion, or
three planes defining a point by their intersection, leads
us to the same idea of dual correspondence or reciprocity
which Poncelet and Gergonne had arrived at by entirely
different considerations. Pliicker's was an analytical
mind, and with him the principle of duality at once
assumes an analytical form. He saw that the same
equation lent itself to a twofold interpretation, accord-
ingly, as we adopt point co-ordinates or line co-ordinates
— i.e., according as we refer our geometrical figure to the
point or the line as the moving and generating space
element. Through this step the idea of co-ordinates 34.

° Generalised

was generalised, and the dualistic conception of figures ates"''"
in space received an analytical expression. It was
the junction of analytical and descriptive methods on a
higher level, from which an entirely novel and fertile
development of geometry became possible.

Whilst the labours of Pliicker lay in the direction of
making analytical formulae more natural, better adapted
to the expression of geometrical forms and relations, and
of reading out of these remodelled formula? novel geometri-
cal properties, the French school, with Michel Chasles ^

^ In addition to numerous valu-
able memoirs, Chasles published,
among others, two works of para-
mount importance, inasmuch as
they for a long time dominated
purely geometrical research, not
only in France but also in Ger-
many and England, — the 'Aper(;u
historique sur I'origine et le
ddveloppement des methodes en
gfometrie' (1837), and the 'Traite
de geometi'ie superieure ' (1852).
These works, through their bril-

VOL. II,

liant style, not only threw into the
shade for a time the labours of
contemporary German mathema-
ticians, such as Mobius, Steiuer,
Pliicker, and Von Staudt, but also
obscured some of the single dis-
coveries of the author himself.
The ' Aper(;u ' was early trans-
lated into German ; whereas in
this country it was the Dublin
school, notably Townsend and Dr
Salmon, who spread a knowledge
of Chasles's work.

2 u

674 SCIENTIFIC THOUGHT.

as its leader and centre, laboured at the introduc-
tion into pure geometry of those ideas which were
peculiar to the analytical method, and which gave to
that method its unity, generality, and comprehensiveness.
Two ideas presented themselves as requiring to be geo-
metrically dealt with : the infinite and the imaginary —
i.e., the elements of a figure which lie at infinity and those
which are ideal or invisible, which cannot be construed.
It is usually supposed that the consideration in geometry
of imaginary or invisible elements in connection with real
figures in space or on the plane has been imported from
algebra; but the necessity of dealing with tbem must
have presented itself when constructive geometry ceased
to consider isolated figures rigidly fixed, when it adopted
the method of referring figures to each other, of looking
at systems of lines and surfaces, and of moving figures
about or changing them by the processes of projection
and perspective. The analytical manipulations applied
to an equation, which according to some system or other
expressed a geometrical figure, found its counterpart
in projective geometry, where, by perspective methods, —
changing the centre or plane of projection, — certain
elements were made to move away into infinity, or when
a line that cut a circle moved away outside of it, seem-
ingly losing its connection with it. By such devices,
implying continuous motion in space, Poncelet introduced
and defined points, lines, and other space elements at
35. infinity, and brought in the geometrical conception of

Ideal . .

elements, ideal and imaginary elements. " Such definitions," he
says, " have the advantage of applying themselves at
once to all points, lines, and surfaces whatsoever ; they

DEVELOPMENT OF MATHEMATICAL THOOGHT. 675

are, besides, neither indifferent nor useless, they help to
shorten the text and to extend the object of geometrical
conceptions ; lastly, they establish a point of contact, if
not always real, at least imaginary, between figures which
appear — prima vista — to haAe no mutual relation, and
enable us to discover without trouble relations and
properties which are common to them." ^ It was the
principle of geometrical continuity which led Poncelet
to the consideration of infinite and imaginary elements.

As we saw above, the projective methods of Poncelet
had introduced into geometrical reasoning a remark-
able distinction among the properties of figures. In
general it was recognised that, in the methods of
central and parallel projection ur in drawing in per-
spective, certain properties or relations of the parts of
a figure remain unaltered, whereas others change, be-
come contorted or out of shape. Poncelet called the
former projective or descriptive, the latter metrical,
properties. This distinction introduced into all geom-
etry since his time several most important and funda-
mental points of view ; it divided geometrical research
into two branches, which we may term positional
and metrical geometry — the geometry of position and
that of measurement. We know that ancient geometry
started from problems of mensuration : modern geometry
started, with Monge, from problems of representation or
graphical description. It has thus become a habit to
call ancient geometry metrical, modern geometry pro-
jective. This habit has led to an unnecessary separation
of views, but in the further course of development also

^ ' Traite des Propriet^s projectives,' vol. i. p. 28.

676

SCIENTIFIC THOUGHT.

36.
Invariants.

to a unification on a higher level. But the distinc-
tion mentioned above led to another most remarkable
line of thought and research which tends more and
more to govern mathematical doctrine. The methods
of projection are based upon the motion or upon the
transformation of figures. Under such a process some
relations remain unaltered or invariant, others change.
As analytical methods in the hands of Pllicker and
others began to accommodate themselves more closely to
geometrical forms, as an intimate correspondence was
introduced between the figure and the formula, it became
natural to study the unalterable properties of the figure
in the invariant elements of the formula. This is the
origin and meaning of the doctrine of Invariants.^ It
is the great merit of the English school of mathe-
maticians, headed by Boole, Cayley, and Sylvester, both
to have first conceived the idea of a doctrine of invariant

1 '• In anj subject of inquiry
there are certain entities, the
mutual relations of which, under
various conditions, it is desirable to
ascertain. A certain combination
of these entities may be found
to have an unalterable value when
the entities are submitted to cer-
tain processes or are made the
subjects of certain operations.
The theory of invariants in its
widest scientific meaning deter-
mines these combinations, eluci-
dates their properties, and expresses
results when possible in terms of
them. Many of the general prin-
ciples of political science and
economics can be expressed by
means of invariantive relations
connecting the factors which
enter as entities into the special
problems. The great principle of
chemical science which asserts that

when elementary or compound
bodies combine with one another
the total weight of the materials
is unchanged, is another case in
point. Again, in physics, a given
mass of gas under the operation
of varying pressure and tempera-
ture has the well-known invariant,
pressure multiplied by volume and
divided by absolute temperature.
Examples might be multiplied. In
mathematics the entities under ex-
amination may be arithmetical,
algebraical, or geometrical ; the
processes to which they are sub-
jected may be any of those which
are met with in mathematical
work. It is the principle which
is valuable. It is the idea of in-
variance that pervades to-day all
branches of mathematics." (Major
P. A. MacMahon, Address, Brit,
Assoc, 1901, p. 526.)

DEVELOPMENT OF MATHEMATICAL THOUGHT. 677

forms, and to have foreseen its importance and corre-
sponding significance when applied to a great variety of
scientific problems, notably to the projective processes
in geometry. These were known to them mainly
through the classical treatises of Poncelet and Chasles,
the leading ideas of which had Ijeen introduced to
British students by the labours of the Dublin school.^
The investigations referred to mark the junction of
two important lines of mathematical research, which
had been carried on independently in earlier times, or
only united for special purposes or for the solution
of special problems. The history of the progress of
geometry during the nineteenth century has already
shown us the use and interest which belong to two
different aspects of tlie common object, of which the
one relies mainly on processes of measurement, including
number, the other mainly on processes of description, in-

^ The history of the doctrine of
invariants has been written by Dr
Franz Meyer, and is pubhshed in the
first volume of the ' Jahresbericht
der Deutschen Matheuiatiker Ver-
eiuigung' (p. 79 sqq.) The fact that
this formed the first of the several
Reports which the German Mathe-
matical Society has undertaken to
publish, testifies to the great im-
portance which belongs to this
doctrine in the history of recent
mathematics. A concise summary
with copious references is given by
the same author in the first volume
of the ' Encyklopiidie der Math.
Wissenschaften,' p. 320 sqq. How
necessary the form and perfection
of algebraic operations was for the
development of the geometrical
conceptions which are laid down,
e.g., in the works of Pliicker,
can be seen in the work of
Otto Hesse, who introduced ele-

gance and conciseness into many
of the expositions which, for want
of this formal development, ap-
pear cumbrous in the writings of
Pliicker. "The analytical form in
which Pliicker's Researches present
themselves is frequently wanting
in that elegant form to which we
have become accustomed, sjaecially
through Hesse. Pliicker's calcula-
tions frequently bear the stamp of
mere aids for representing geo-
metrical relations. That algebraical
connections possess an interest in
themselves, and require an ade-
quate representation, was realised
only by a generation which habitu-
ally emjiloyed methods that had
been largely devised by Pliicker
himself" (A. Clebsch, ' Zum Ge-
dachtniss an Julius Pliicker,' 1872,
p. 8. See also Gustav Bauer,
' Gediichtnissrede auf Otto Hesse,'
Muucheu, 1882).

678 SCIENTIFIC THOUGHT.

eluding arrangement. The same difference of views can
be established with regard to many other things which
form the objects of other sciences. In geometry this
difference obtrudes itself, as it were, in its naked form.
Thus in all the natural, and even the social, sciences we
have become accustomed to look first at the constituent
elements or parts of things, to count and measure them,
then afterwards to look at their possible arrangement,
or existence together in the actual world of nature or
society. Astronomy, crystallography, chemistry, geology,
the natural history sciences, economics and statistics, the
doctrine of chances, — all furnish, especially in their sys-
tematic development during the last hundred or hundred
and fifty years, examples of the twofold aspect just re-
ferred to. The progress of these sciences, as we have
abimdantly seen, has depended largely upon the application
of mathematical methods. As the analysis into elements
or parts, and the possible synthesis of such elements in
complicated structures, has become everywhere the order of
study, so there must exist in the abstract science of mathe-
matics— i.e., in the framework of our scientific reasoning
— not only the theory of measurement and number, but
also that of combination, form or arrangement, and order.
37. The doctrine of forms in the well - known prob-

Theory of . ... , .

forms. lems of permutations and combmations begms with
modern mathematics in the seventeenth century, and
received scientific recognition mainly in connection
with the doctrine of chances at the hands of James
Bernoulli abroad, and of De Moivre in this country.
The process of multiplication of binomials and poly-
nomials leads to the formation of combinations, and

DEVELOPMENT OF MATHEMATICAL THOUGHT. 679

where the factors are the same, as in Newton's Iji-
noniial theorem, to combinations with permutation ; and
consequently the doctrine of chances and of arrange-
ments in triangular, pyramidal, or other figures is closely
connected with the doctrine of series and algebraical
expressions. In this country the interest in the subject
has been stimulated and kept alive by isolated problems
and puzzles in older popular periodicals, such as the
' Gentleman's Magazine ' and the ' Ladies' Diary ' ; in Ger-
many— as we noticed before — a school of mathematicians
arose who attempted a systematic treatment of the whole
subject, which, owing to its barrenness in practical re-
sults, brought this line of research somewhat into dis-
repute. What was wanted was a problem of real
scientific interest and a method of abbreviation and
condensation. Both were supplied from unexpected ^

^ The theory of arrangement or
of order, also called the " Ars Com-
binatoria," has exerted a great
fascination on some master minds,
as it has also given endless opi)or-
tunities for the practical ingenuity
of smaller talents ; among the
former we must count in the first
place Leibniz, and in recent times
J. J. Sylvester, who conceived the
" sole proper business of mathe-
matics to be the development of
the three germinal ideas — of which
continuity is one, and order and
number the other two" ('Philo-
soi)hical Transactions,' vol. clix. p.
61.3). This idea has been dwelt on
by Major MacMahon in his address
(I5rit. Assoc, 1901, p. 526), whosays :
"The combinatorial analysis may
be described as occupying an ex-
tensive region between the algebras
of discontinuous and continuous
quantity. It is to a certain extent
a science of enumeration, of mea-

surement by means of integers as
opposed to measurement of quan-
tities which vary by infinitesimal
increments. It is also concerned
with arrangements in which differ-
ences of quality and relative position
in one, two, or three dimensions are
factors. Its chief problem is the
formation of connecting roads be-
tween the sciences of discontinu-
ous and continuous quantity. To
enable, on the one hand, the
treatment of quantities which vary
per salturii, either in magnitude
or position, by the methods of the
science of continuously varying
quantity and position, and, on the
other hand, to reduce problems of
continuity to the resources avail-
able for the management of dis-
continuity. These two roads of
research should be regarded as pene-
trating deeply into the domains
which they connect."

680

SCIENTIFIC THOUGHT.

38.
Tlieory of
numbers.

quarters — the one purely theoretical, the other practical.
Accordingly the doctrine of forms and arrangements has
during the last century been developed by mathematicians
in two distinct interests, which only quite lately seem to
approach and assist each other.

The purely abstract or theoretical interest came from
the side of the theory of numbers, a branch of research
which was revived by Legendre in France and by the
youthful genius of Gauss in Germany ; the more practical
one came from the theory of equations, notably in its
application to problems of geometry. The methods by
which these subjects were treated had in the early part
of the nineteenth century undergone a great change.
The older inductive method in both branches — namely,
in the solution of equations and in the investigation of
the properties of numbers — relied mainly on ingenious
devices which were mostly of special, not of general,
vakie. Theorems were found by induction, and had
afterwards to be proved by rigorous logical deduction.
Success depended on the degree of care with which the
mind operated with mathematical symbols, and rested
frequently on the intuition, if not the inspiration, of
genius. Two of the greatest mathematical minds —

stood

greatest
Fermat ^ in France and Newton ^ in England

1 Pierre Fermat (1601-65) pre-
pared au edition of the Treatise of
Diophantus, and his marginal notes
contain many theorems referring
to the properties of numbers which
have been the subject of much
comment and examination by
mathematicians of the first rank
down to the present day. In
letters to contemporaries he re-
ferred to many of these dis-
coveries, and to liis proofs, which
he did not communicate. Some

of these proofs seem not to have
satisfied him, being deficient in
rigour. In spite of the labours of
Euler, Lagrange, Cauchy, Dirich-
let, Kummer, and others, one of
these theorems still awaits proof.
A full account of Fermat's theorems
is given in Cantor's ' Geschichte der
Mathematik,' vol. ii. 2nd ed., p.
773 sqq. Also in W. Rouse
Ball's 'History of Mathematics,'
p. 260 sqq.

- Newton, in his ' Universal

DEVELOPMENT OF MATHEMATICAL THOUGHT. 681

foremost in having with unrivalled fertility propounded
theorems which were as difficult to prove as the
manner in which they had been arrived at was mysteri-
ous. The great analytical genius of Euler, who possessed
unequalled resources in the solution of single problems,
spent much time and power in unravelling the riddles
of Fermat. In the theory of equations the general
solution beyond the fourth degree battled the greatest
thinkers. The time had come when in both branches
a systematic study of the properties had to be at-
tempted. This was done for the theory of numbers by
Gauss, for that of equations by Abel. Every great
step in advance of this kind in mathematics is accom-
panied by, and dependent on, skilful abbreviations, and
an easy algorithm or mathematical language. An as-
semblage of elements held together by the simplest
operations or signs of arithmetic — namely, those of
addition and multiplication — is much easier to deal
with if it can be arranged with some regularity, and
accordingly methods were invented by which algebraical
[expressions or forms were made symmetrical and homo-
geneous ; ^ the latter property signifying that each term

39.
Symmetry.

Arithmetic,' gave an interesting
[theorem by wliich the number of
imaginary roots of an equation can
be determined ; he left no proof,
and the theorem was discussed by
jEuler and many other writers, till
at last Sylvester in 1866 found the
broof of it in a more general
theorem. In more recent times
Jacob Steiner published a great
lumber of theorems referring to
dgebraical curves (see Crelle's
; Journal,' vol. xlvii. ) which have
been compared by Hesse with the
I' riddles of Fermat." Luigi Cre-
nona succeeded at last in proving

them by a general sj^nthetical
method.

1 The introduction of homogene-
ous expressions marks a great
formal advance in algebra and
analj'tical geometry. The first in-
stance of homogeneous co-ordinates
is to be found in Mobius's "Bary-
centric Calculus" (1826), in which
he defined the position of any point
in a plane by reference to three
fundamental points, considering
each point as the centre of gravity
of those points when weighted.
" The idea of co-ordinates appears
here for the first time in a new

682

SCIENTIFIC THOUGHT.

40.
Determin-
ants.

contained the same number of factors. Such forms
could be written down on the pattern or model of
one of their terms by simple methods of exchange or
permutation of the elements. It would then not be
necessary to write down all the terms but only to indicate
them by their elements, these also being abbreviated by
the use of indices. Eows and columns or arrangements
in squares suggested themselves as easy and otherwise
well-known artifices by which great masses of statistics
and figures are marshalled and controlled. Out of these
manifold but simple devices there grew an algebra of
algebra, a symbol for denoting in a very general way
symmetrical and homogeneous algebraical expressions.^
Gauss termed such expressions Determinants : they
turned up in his ' Disquisitiones Arithmeticae ' as they had
done half a century before in Cramer's ' Analyse des lignes
courbes alg^briques.' Just as common fractions can be

garb, which soon led to a more
general conception. The Bary-
centric co-ordinates were the first
instance of homogeneous co-ordin-
ates, . . . and already with Mobius
the advantages become evident
through the symmetry and ele-
gance of his formulaj" (Hankel,
'Project. Geom.,' p. 22).

^ Determinants were first used
by Leibniz for the purpose of
elimination, and described by him
in a letter to the Marquis de
I'Hospital (1693). The importance
of his remarks was not recognised
and the matter was forgotten, to
be rediscovered by Cramer in the
above - named work (1750, p.
657). It is interesting to note
that the same difficulty of the
process of elimination induced
PHicker to resort to geometrical

interpretation of analytical ex-
pressions, and that whilst he "saw
the main advantage of his method
in avoiding algebraical elimination
through a geometrical considera-
tion, Hesse showed how, through
the use of Determinants, algebraical
operations could receive that pliabil-
ity the absence of which was the
reason for Pliicker to discai'd it."
(See the account of Clebsch's work
in 'Math. Ann.,' vol. vii. p. 13.)
Through this invention the com-
binatorial analysis, which, in the
hands of the school in Germany,
had led into a desert, was raised
again into importance. It has be-
come still more important since the |
general theory of forms and of
groups began to play an increasing
jiart in modern analysis.

DEVELOPMENT OF MATHEMATICAL THOUGHT. 683

dealt with as if they were special things having special
properties, though the latter depend only on the pro-
perties of the numbers they are made up of and their
mode of connection ; as powers and siirds are separately
examined ; so the arrangements called determinants can
be subjected to a special treatment, their properties
ascertained, and themselves subjected to the ordinary
operations of arithmetic. This doctrine, which con-
stitutes the beginning and centre of the theory of
algebraical forms or " quantics " and of algebraical
operations or " tactics," was pretty fully worked out
and first introduced into the course of teaching by
Cauchy in France ; then largely adopted by Jacobi in
Germany, where Otto Hesse, trained in the ideas of
Pllicker, first showed its usefulness in his elegant
applications to geometry. In France it was further
developed by Hermite, who, together with Cayley and
Sylvester in England, proclaimed the great importance
of it as an instrument and as a line of mathematical
jthought.^ In the latter countrv the idea of abbrevi-
ating and summarising algebraical operations had become
jquite familiar through another device which has not
found equal favour abroad — namely, the Calculus of

' ^ "For what is the theory of , p, 301) refers to Otto Hesse's

jdeterminants ; It is an algebra ' " problem of reducing a cubic

upon algebra ; a calculus which function of three letters to another

enables us to combine and foretell | consisting only of four terms by

the results of algebraical opera- j linear substitutions — a problem

jbions, in the same way as algebra I which appears to set at defiance all

enables us to dispense with the
performance of the special opera-
tions of arithmetic. All analysis
nust ultimately clothe itself under
:his form." In this connection
Sylvester ('Phil. Mag.,' 1851, ApL,

the processes and artifices of com-
mon algebra," as "perhaps the
most remarkable indirect question
to which the method of determin-
ants has been hitherto applied."

684

SCIEiNTIFlC THOUGHT.

41. Operations, the idea of treating algebraical operations

Calculus of "^ ' o o r

Operations. ai^(j their symbols as quantities, and of subjecting them
to arithmetical treatment separately from the mate-
rial operated on. The genius of Arthur Cayley was
specially fertile in this direction, as was that of
Sylvester in the nomenclature or language of the
doctrine of forms.^ The merit, however, of having
brought together the new ideas which emanated from
the schools of Poncelet and Chasles in France, of Cayley
and Sylvester in England, into a connected doctrine, and
of having given the impetus to the fundamental re-

^ The theory of invariants was
gradually evolved from many inde-
pendent beginnings. In 1864 Syl-
vester wrote ('Phil. Trans.,' p.
579), "As all roads are said to lead
to Rome, so I find, in my own case
at least, that all algebraical in-
quiries, sooner or later, end at the
Capitol of Modern Algebra, over
whose shining portal is inscribed
the Theory of Invariants." About
the same time (1863) Aronhold de-
veloped the principal ideas which
lay at the foundation of the theory
in organic connection and in com-
plete generality, hereby domiciling
in Germany the doctrine which had
previous!}' owed its development
mainly to English, French, and
Italian mathematicians (see Meyer,
'Bericht,' &c., p. 95). The differ-
ent roads which Sylvester refers to
can be traced, first, in the love of
symbolic reasoning of Boole, who
was " one of the most eminent of
those who perceived that the sj'm-
bols of operation could be separated
from those of quantity and treated
as distinct objects of calculation,
his principal characteristic being
perfect confidence in any result
obtained by the treatment of sym-
bols in accordance with their

primary laws and conditions, and
an almost unrivalled skill and
power in tracing out these results "
(Stanley Jevons in article " Boole,"
'Ency. Brit.'); secondly, in the
independent geometrical labours of
Hesse in Germany (whose mathe-
matical training combined Pliicker's
and Jacobi's teaching) and Dr
Salmon in Dublin (who, after
having transplanted Poncelet and
Chasles to British soil, recog-
nised the importance of Cayley 's
and Sylvester's work, and in-
troduced in the later editions of
his text - book modern algebraical
methods) ; thirdly, in the independ-
ent investigations belonging to the
theory of numbers of Eisenstein in
Germany and Hermite in France.
In full generality the subject was
taken up and worked out by Syl-
vester in the ' Cambridge and
Dublin Mathematical Journal '
(1851 - 54), and by Cayley in the
first seven memoirs upon Quantics
(1854-61), which "in their many-
sidedness, together with the ex-
haustive treatment of single cases,
remain to the present day, for the
algebraist as well as for the geo-
metrician, a rich source of dis-
covery" (Meyer, loc, cit., p. 90).

I

DEVELOPMENT OF MATHEMATICAL THOUGHT.

685

modelling of the text-books and school-books of algebra
and geometry in this country and in Germany, belongs
undeniably to Dr Salmon of Dublin.^ The conception of
a form — be this geometrical or algebraic — suggests the
investigation of the change, the recurrence of forms.
How do forms under the process of geometrical or
algebraical manipulation alter or preserve their various
properties ? The processes of projection practised by
Monge, Poncelet, and Chasles in France had already
led to a distinction between descriptive and metrical
properties of geometrical figures. A corresponding ex-
amination of algebraical forms, which are all capable of
geometrical representation or interpretation, would lead
to the extensive and fundamental doctrine of the in-
variants of these forms — i.e., of such arrangements of
the elements as remain absolutely or proportionally un-
altered during the processes of change and combination,
Notably instead of the geometrical process of projection
by central perspective we may employ in our algebraic
jformulai a corresponding process, that which is known as
jlinear substitution. And at the time when it was
that geometrical transformation had its

Irecognised

' Of Dr Salmon, whose ' Les-
ions introductory to the Modern
Higher Algebra ' appeared in 1859
,4th ed., 1855 ; 1st German ed. by
Fiedler, 1863), Meyer says: " Re-
,;oguising how the special results
n this domain gradual!}' acquired
I considerable bulk, we must the
nore gratefully acknowledge the
vork of Salmon — who had already,
n the direction of algebra as well as
I'f geometry, furnished valuable con-
ributions of his own — in under-
aking the labour of collecting the

widely -scattered material in a con-
cise monograph. For the promulga-
tion in Germany we have to thank
Fiedler both for his edition of
Salmon, and for having already
given an independent introduction
to the subject, in which especially lie
made Cayley's applications to pro-
jective geometry generally access-
ible. About the same time (1862)
there appeared likewise an edition
by Brioschi, which gained many ad-
herents for the theory of Invariants
in Italy."

686

SCIENTIFIC THOUGHT.

42.
Principle of
substitu-
tion.

counterpart in the transformation of algebraical forms
by the processes of substitution, these latter had
already been extensively studied for their own sakes in
the theory of algebraical equations, which in the first
quarter of the century had undergone a great develop-
ment under the hands of two brilliant mathematical
talents both lost to science at an early age — the
Norwegian Abel and the Frenchman I^variste Galois.^
Like all algebraical expressions, those termed equa-
tions were originally invented and commanded attention

^ Evariste Galois is held to have
been one of the greatest mathema-
tical geniuses of modern times, who,
if he had lived, might have been a
rival of Abel: he was born in 1811,
and died before he was twenty-one,
in consequence of a duel. For a
long time his writings remained un-
published and unknown, till Liou-
ville published them in the 11th vol.
of his 'Journal' (1846). Liouville
was also the first to recognise the
importance and absolute correctness
of Galois's method, which, when sub-
mitted to the Academy in the year
1831, and reported on bj' Lacroix
and Poisson, had appeared almost
unintelligible. On the eve of his
death Galois addressed a letter to
his friend Auguste Chevalier, which
is a unique document in mathema-
tical literature, forming a kind of
mathematical testament. He de-
sires this letter to be published
in the 'Revue Encyclop^dique,'
referring publicly the "import-
ance," not the " correctness," of his
discoveries to the judgment of
Jacobi and Gauss, and expressing
the hope that some persons would
be found who would take the
trouble to unravel his hieroglyphics.
The first attempt to make Galois's
ideas generally accessible is to be
found in Serret's ' Algebre Superi-
eure' (3rd ed., 1866), but it was

not till after the publication of i
Camille Jordan's ' Theorie des
Substitutions' (1870) that the
short papers of Galois were recog-
nised as containing the germs and i
beginnings of an entirely novel and
comprehensive mathematical theory,
— viz., the " Theory of Groups."
The relation between the writings,
of Abel and Galois is exhaustively',
treated in Prof. Sylow's Paper on^
Abel's work, contained in the ' Me-
morial Volume,' 1892, p. 24. Hei
there .says: " Le merite de Galois
ne consiste pas essentiellement dans
ses propositions, mais dans la gener-
alite de la methode qu'il appliquaj
C'est son admirable theoreme fondan
mental qui a donne a la theorie
des Equations sa forme definitive,
et d'oii est sortie, en outre, la theorie
des groupes generalisee, qui est
d'une si grande importance, on peut
le dire, pour toutes les branches dee
mathematiques, et qui deja, entre
les mains de Jordan, de Klein, de
Lie, de Poincaro et d'autres, a eun
richi la science d'une longue suitt
de decouvertes importantes." Th(
memoirs of Abel and Galois reP
ferring to the Theory of Equations
have been conveniently edited, iu if
German translation, by H. Maserl
1889. See also Cayley's article oil
" Equation " in the ' Ency. Brit., I
§ 32.

DEVELOPMENT OF MATHEMATICAL THOUGHT. 687

as instruments or devices for the solution of definite
problems in arithmetic, geometry, and mechanics. The
solution of the equation — i.e., the expression of the un-
known quantity in terms of the known quantities —
served a practical end. Gradually as such solutions be-
came more and more difficult, owing to the complexity of
the formuke, the doctrine divided itself into two distinct
branches, serving two distinct interests. The first, and
practically the more important one, was to devise methods
by which in every single case the equations which
presented themselves could be solved with sulficient
accuracy or approximation ; this is the doctrine of the
numerical solution of equations. The other more scien-
tific branch looked upon equations as algebraical ar-
rangements of quantities and operations which possessed
definite properties, and proposed to investigate these
properties for their own sake. The question arose,
How many solutions or roots an equation would admit of,
and whether the expression of the unknown quantity in
terms of the known quantities was or was not possible
lij using merely such operations as were indicated by
the equation itself — i.e., the common operations and the
ordinary numbers of arithmetic ? This doctrine of the
general properties of equations received increasing atten-
'tion as it became empirically known that equations 43.

-*• "^ ^ General

beyond the fourth degree could not Ije solved in the 'solution of
most general form.^ Why could they not be solved,

^ Since the researches regard- , toward the development of the
ing the solubility of Equations | theory of groups — the history of

have led on, through Galois and
the French analysts, to the same
line of reasoning as other re-
searches mentioned before — viz. ,

the whole subject has aroused
special interest. The earlier be-
ginnings and the labours of for-
gotten analysts have been un-

688

SCIENTIFIC THOUGHT.

aud what were the conditions — i.e., the special proper-
ties— of an equation which rendered it soluble ^ These
were some of the questions which the great mathe-
maticians, such as Gauss, Abel, and Galois, placed before
themselves during the earlier part of the century. There
are other unsolved problems which the nineteenth cen-
tury inherited from preceding ones, where the same line
of reasoning was adopted — i.e., where the question was
similarly reversed. Instead of trying to solve problems
as yet unsolved, it was proposed to prove their general
insolubility, and to show the reason of this ; also to
define the conditions which make a solution possible.

earthed and placed in their cor-
rect historical perspective. Prof.
Burkhardt of GottiDgen, to whom
we also owe the chapter on this
subject in the first volume of the
'Encvklopadie,' &c., contributed iu
the year 1892 a most interesting
historical paper, " Die Anfange der
Gruppentheorie und Paolo Ruffini "
{'Abhandl. zur Gesch. der Math.,'
6 Heft). In this paper he also
goes back to other earlier analysts,
among them Prof. Waring of Cam-
bridge, who during his lifetime used
to complain that he knew of no one
who read his mathematical tracts.
It appears that during nearly the
last thirty years of the eighteenth
century nothing had been added re-
garding the general theory of equa-
tions, and that Ruffini was the first
to begin a new epoch in the year
1799, with the distinct assertion that
a general solution of algebraic equa-
tions beyond the fourth degree, by
means of radicals, was impossible,
and with an attempt to prove this.
His researches were therefore con-
temporaneous with those of Gauss,
who published his ' Dissertation '
(see note p. 644) in the same year,
and his great arithmetical work

in 1801. Although Gauss seems i
to have arrived at the same con-
clusion, and perhaps even to have i
anticipated much later attempts to
solve the general equation of the fifth
degree by other than algebraical
operations (see Sylow, loc. cit..
16), his published researches rathe
took the hne of the study of a|
definite class of soluble equations^
which were connected with the
celebrated problem of the divisioa
of the circle ; a satisfactory proof of
Ruffini's statement being withheld
till Abel published his c-elebrated
memoir in the year 1825 in the firet
volume of CVelle's' Journal.' With
this memoir the theory of equations
entered a new phase, towards
which the labours of Ruffini we
preparatory. As in so many othe
cases, so also in this, the sola-l
tion of the problem depended up(n|
stricter definitions of what
meant by the solution of an eqna-l
tion, and by "algebraical" and!
other (" transcendental ") functiong|
and operations. We know tl
both Abel and Galois began the
research by futile attempts to fine
a solution of the general equatiocj
of the fifth degree.

DEVELOPMENT OF MATHEMATICAL THOUGHT. 689

In following this altered course of investigation, an
enormous amount of mathematical knowledge was gained,
and problems were solved which had previously never
been thought of. Especially through the theory of equa-
tions the abstract doctrine of algebraical forms was
created and greatly advanced long before it was gener-
ally recognised that it had peculiar importance through
the correspondence or parallelism which existed be-
tween algebraical expressions and geometrical con-
figurations.

Out of these earlier algebraical and later combined al- 44.

, Theory of

gebraical and geometrical investigations, a novel and very groups,
useful point of view has been gradually gained which
represents the most general conception of mathematical
tactics. This centres in the notion of a group of ele-
ments. These elements may be quantities or opera-
tions, so that the theory of Groups embraces not only
the doctrines which deal with quantities but also those
which deal with arrangements and their possible changes.
The older combinatorial analysis dealt mainly with
assemblages of a quantity of separate elements, their
number, their variety : the modern theory of groups
deals rather with the processes and operations by which
different arrangements can be transformed one into the
other. It is an algebra of operations. The methods
of transformation which presented themselves first of
all were the methods known in algebra as substitution.
Accordingly the first comprehensive treatise on the
theory was the ' Treatise on Substitutions,' published in
1870 by M. Camille Jordan. This book forms a land-
mark in modern mathematics ; it brought into a system
VOL. n. 2 X

690

SCIENTIFIC THOUGHT.

the beginnings of the new and comprehensive calculus
of operations which were contained in the writings of
Lagrange, Abel, Cauchy, and Galois, and established the
terminology and the algorithm. A group of substitu-
tions is defined as having the property that each two or
more operations belonging to it and successively applied
can be replaced by another single operation contained in
the same group. Succeeding operations are symbolically
represented by the product of two or more letters. This
product has certain algebraical properties, and in analogy
with common products it has factors, a degree, an index ;
the substitution may be cyclical and symmetric, and may
have many other remarkable properties which the theory ^

1 The "Theory of Groups" has
now grown into a very extensive
doctrine which, according to the late
Prof. Marius Sophus Lie (1842-99),
is destined to occupy a leading and
central position in the mathemati-
cal science of the future. " The
concej^tion of Group and Invariant
was for him not only a methodical
aspect from which he intended to
review the entire older region of
mathematics, but also the element
which was destined to permeate
and unify the whole of mathemati-
cal science " (M. Nother, ' Math.
Ann.,' voh liii. p. 39). But though it
is an undoubted fact that the largest
systematic works on the subject
emanate from that great Norwegian
mathematician, and that his ideas
have won gradual recognition,
especially on the part of prominent
French mathematicians, notably
M. Picard ('Traite d' Analyse,'
1896, vol. iii.) and M. Poincare,
the epoch - making tract which
pushed the novel conception into
the foreground was Prof. F.
Klein's ' Erlangen Programme '
(1872), entitled " Vergleichende I

Betrachtungen iiber neuere geo-
metrische Forschungen. " To those
who read and re-read this short
but weighty treatise, it must in-
deed have been like a revelation,
opening out entirely new avenues
of thought into which mathematical
research has been more and more
guided during the last generation.
The tract, which has now been
translated into all the important
modern languages, remained for a
long time comparatively unnoticed,
and, twenty years after its publica-
tion, was reprinted by the author
in the 4'3rd volume of the ' Math.
Annalen,' with some introductory
remarks which indicate the changes
that had taken place in the in-
terval as regards the scope of the
idea. The main result of the dis-
sertation is this : That, primarily,
for all geometrical investigations,
the characteristic properties of any
manifold (or arrangement) is not
the element out of which it is com-
posed, but the group, the transfor-
mations of which reveal its invarian-
tive properties. There are, accord-
ingly, as many different ways of

DEVELOPMENT OF MATHEMATICAL THOUGHT. 691

of groups investigates. Its immediate application, and
the purpose for which it was elaborated, was the theory
of Equations. Every equation constitutes an arrange-
ment in which a finite number of independent elements,
called constants or coefficients, is presented under a
certain algebraical form. The solution of the equation
means the finding of sucli an arrangement as when
substituted in the equation for the unknown quantity,
will satisfy the equation.

The conception of a group of operations standing in
the defined relations is, however, capable of a great
and fundamental extension into that region of mathe-
matics which deals, not with fixed or constant, but with
variable or flowing quantities ; not with elements which 45.

Continuous

are disconnected or discontinuous, but with such as are and dis-

' continuous

continuous. To understand the development of modern '^^°^vs.
mathematical thought, it is accordingly necessary to go
back somewhat and review the progress which the

studying any manifold (e.g., such as
projective geometry, line geometry,
geometry of reciprocal radii, Lie's
sphere geometry, analysis situs,
&c.) as there are continuous groups
of transformations that can be
established ; and there are as many
invariant theories (see ' Ency. Math.
"\Viss.,' vol.ii. p. 402 ; Nother, loc. cit.,
p. 22). From that date onward the
different kinds of groups have been
defined and systematically studied,
notably by Klein and Lie and their
pupils. In this country, although
many of the relevant ideas were
contained in the writings notably
of Cayley and of Sylvester, the
systematic treatment of the subject
was little attended to before the
publication (1897) of Prof. Burn-

side's ' Theory of Groups of Finite
Order,' and latterly of his article
on the whole Theory of Groups in
the 29th volume of the ' Ency. Brit.'
It has been remarked by those who
have studied most profoundly the
development of the two great
branches of mathematical tactics
— viz., " The Theory of Invariants "
and the " Theory of Groups " — that
the progress of science would have
been more rapid if the English
school had taken more notice of the
general comprehensive treatment
by Lie, and if Lie himself had not
refrained from entering more fully
into the special theories of that
school (see Dr F. Meyer, ' Bericht,'
&c., p. 231).

692

SCIENTIFIC THOUGHT.

conception of the variable ^ has nndergone in the course
of the last hundred years. Here we come upon a
term which was introduced into mathematical language
mainly through the writings of Euler — the term
function. It is used to denote the mathematical
dependence of two or more variable quantities on each

1 To the theory of equations in
algebra there corresponds the
theory of differential equations in
analysis ; and as the theory of
algebraical equations had gradually
emerged in a complete form out of
investigations of special equations,
or sets of equations, so likewise in
analysis a general theory of differ-
ential equations is gradually being
evolved out of the scattere'd and
very extensive investigations of
special differential equations which
presented themselves notably in
the apijlication of analysis to astro-
nomical and physical problems. It
is claimed by those who have
grasped the abstract ideas of
Sophus Lie, that he has taken a
great step forward in the direction
of a general theory of differential
equations, by apjjlying methods
which suggested themselves to him
through the general theory of alge-
braic forms and its C(jnnection with
geometry. Accordingly, the the-
ories of Lie can be termed an
algebraical theory of differential
equations, depending upon trans-
formations analogous to those
which had been established in the
general theory of forms or quantities
of which I treated above. Prof.
Engel, in his obituarj' notice of
Sophus Lie ('Deutsche Math. Ver.,'
vol. viii. p. 35), tells us that in the
year 1869-70, when Lie met Prof.
Klein in Berlin, the former was
occupied with certain partial differ-
ential equations which exhibited,
under certain transformations, in-
variantive properties, and that Klein

then pointed out " that his pro-
cedure had a certain analogy with
the methods of Abel. The sug-
gestion of this analogy became im-
portant for Lie, as he was generally
intent upon following up more
clo.^ely the analogies with the
theory of algebraical equations."
Dr H. F. Bakei-, in his recent article
on Differential Equations in the
'Ency. Brit.' (vol. xxvii. p. 448),
roughly distinguishes two methods
of studying differential equations,
which he names respectively
" transformation theories " and
"function theories," "the former
concerned to reduce the algebraical
relation to the fewest and simjjlest
forms, eventually with the hope of
obtaining explicit expressions of
the dependent in terms of the
independent variables ; the latter
concerned to determine what gen-
eral descriptive relations among
the quantities are involved by the
differential equations, with as little
use of algebraical calculations as
may be possible." For the historj'
of thought and connection of ideas,
it is interesting to learn, through
Prof. Engel, that it was not purely
algebraical work, — such as is rep-
resented by Galois and Jordan,
to which Lie was early intro-
duced by Pi'of. Sylow, — but the
study of Poncelet's and Pliicker's
methods which led Lie to his
original conceptions, and that he
was fond of calling himself a pupil
of Pliicker, whom he had never
seen (Engel, loc. cit., p 34).

I

DEVELOPMENT OF MATHEMATICAL THOUGHT. 693

other. The question arises, What are we to under-
stand under this term ? What is a mathematical
function or dependence ? The question was approached
by the great analysts of the second half of the
eighteenth century. A preliminary answer which served
the requirements of a very wide field of practical
application was given by Fourier at the beginning of
the nineteenth century. Since that time the question
has been independently treated by two schools of
Continental mathematicians. Of these the first was
founded by Cauchy in France, and is mainly represented
by Bernhard Eiemann and his numerous pupils in
Germany ; the other centres in the Berlin school,
headed by Weierstrass, and goes back to the work
of Lagrange.

The interests which have led to this modern branch 46.

Theory of

of mathematical research ^ are various, but we can Functions.

^ The literature suitable for intro-
ducing the student of mathematics
to the modern theory of functions
— which plays in analysis, i.e., the
doctrine of variable quantity, a
part of similar importance to that
which the theory of forms plays in
algebra — is so enormous, the sub-
ject being approached from so
many sides by different writers,
that it seems worth while to refer
to two expositions which may be
read with profit, and which do not
require extensive mathematical
knowledge. First and foremost I
would recommend Cayley's article
on " Functions " in vol. ix. of the
'Ency. Brit.' Then there is the
chapter on " Foundations of the
General Theory of Functions," con-
tained in the 2nd volume of the
German ' Mathematical Encyclo-
pedia,' written by Prof. Prings-

heim. Cayley's article intro-
duces the general theory after
giving a short summary of tlie
more important " known " func-
tions, including those which pre-
sented themselves in the first half
of the nineteenth century, and
whicli I referred to in dealing with
the work of Abel and Gauss (see
note, p. 648). The treatment of
these latter functions, which had
been brought to a certain degree of
perfection by Jacobi, had made it
evident that more general aspects
had to be gained and broader
foundations laid. But ever since
the middle of the eighteenth
century another development of
mathematical ideas had been going
on which started from the solution
of a problem in mathematical
physics — -namely, that of vibrating
strings, which led in the sequel to

694 SCIENTIFIC THOUGHT.

distinguish two which are very prominent, and are
roughly represented by the two schools just referred
to. In the first place, a function can be formally
defined as an assemblage of mathematical symbols,
each of which denotes a definite operation on one
or more quantities. These operations are partly
direct, like addition, multiplication, &c. ; partly indirect
or inverse, like subtraction, division, &c. Now, so far
as the latter are concerned, they are not generally
and necessarily practicable, and the question arises.
When are they practicable, and if they are not, what
meaning can we connect with the mathematical symbol ?
In this way we arrive at definitions for mathematical
functions which cannot immediately be reduced to the
primary operations of arithmetic, but which form special
expressions that become objects of research as to their
properties and as to the relation they bear to those
fundamental operations upon which all our methods of
calculation depend. The inverse operations, represented
by negative, irrational, and imaginary quantities ; further,
the operations of integration in its definition as the in-

a certain finality when Fourier Euler, Daniel Bernoulli, d'Alem-

introduced his well-known series bert, and Lagrange. The above-

and integrals, by which any kind named chapter, written by Prof,

of functionality or mathematical Pringsheim, gives an introduction

dependence, such as physical pro- I to the subject showing the historical

cesses seem to indicate, could be genesis of the conception of function

expressed. The work of Fourier, \ and the various changes it was sub-

which thus gave, as it were, a sort i jected to, and then proceeds to

of preliminary specification under expositions and definitions mostly

which a large number of problems taken from the lectures of Weier-

in physical mathematics could be strass (see p. 8), whereas Cay ley's

attacked and practically solved, , article introduces us to the elements

together with the stricter defini- ' of the general theory of functions

tions introduced by Lejeune Dir- j as they were first laid down by Rie-

ichlet, settled for a time and for i mann in the manner now commonly

practical purposes the lengthy dis- ! accepted,
cussions which had begun with

DEVELOPMENT OF MATHEMATICAL THOUGHT. 695

verse of differentiation, — led early to investigations of
the kind just mentioned. The experience that ordinary
fractions might be expressed by decimal fractions — i.e.,
by finite or infinite series — led to the inverse problem
of finding the smn of such series and many other an-
swerable and apparently unanswerable problems. The
older method of research consisted in treating these
problems when and as they arose : new chapters were
accordingly added to the existing chapters of the
text -books, dealing with special functions or mathe-
matical expressions. It was only towards the end of
the eighteenth century, and at the beginning of the
nineteenth, that Lagrange, Gauss, and Cauchy felt and
proclaimed the necessity of attacking the question gener-
ally and systematically ; the labours of Euler having
accumulated an enormous mass of analytical knowledge,
a great array of useful formulte, and amongst them not
a few paradoxes which demanded special attention. I
have already had occasion to refer to the problem of
the general solution of equations as an instance where,
in the hands of Abel, the tentative and highly ingenious
attempts of earlier analysts were replaced by a method-
ical and general treatment of the whole question. An-
other chapter of higher mathematics, the investigation of
expressions which presented themselves in the problems
of finding the length of the arc of an ellipse, and which
opened the view into the large province of the so-called
higher transcendents, gave Abel further occasion of lay-
ing new foundations and of creating a general theory of
equations or of forms.

But yet another interest operated powerfully in the

696

SCIENTIFIC THOUGHT.

47.
Physical
analogies.

direction of promoting these seemingly abstract re-
searches. Nature herself exhibits to us measurable
and observable quantities in definite mathematical de-
pendence ; ^ the conception of a function is suggested by-
all the processes of nature where we observe natural
phenomena varying according to distance or to time.

1 Nearly all the "known" func-
tions have presented themselves in
the attempt to solve geometrical,
mechanical, or physical problems,
such as finding the length of the
arc of the ellipse (elliptic func-
tions) ; or answering questions in
the theory of attraction (the poten-
tial function and other functions,
such as the functions of Legendre,
Laplace, and Bessel, all comprised
under the general term of "har-
monic functions "). These func-
tions, being of special import-
ance in mathematical physics, were
treated independently before a
general theory of functions was
thought of. Many important pro-
perties were established, and
methods for the numerical evalu-
ation were devised. In the course
of these researches other functions
occurred, such as Euler's "Gam-
ma" function and Jacobi's "Theta"
function, which possessed interest-
ing analytical properties. These
functions, suggested directly or
indirectly by applications of analy-
sis, did not always present them-
selves in a form which indicated
definite analytical processes, such
as processes of integration or the
summation of series. Very fre-
quently thej' presented themselves,
not in an " explicit " but in an
"implicit" form; their properties
being expressed by certain con-
ditions which they had to fulfil.
It then remained a question
whether a definite symbol, indi-
cating a set of analytical operations,
could be found. This arises from

the fact that the solution of most
problems in mechanics and physics
starts from the assumption that,
though the finite observable pheno-
mena of nature are extremely
intricate, they are, nevertheless,
compounded out of comparatively
simple elementary processes, which
take place between the discrete
atoms, or the elementary but con-
tinuous portions of matter. M athe-
matically expi-essed, this means that
the relations in question present
themselves in the form of differen-
tial equations, and that the solution
of them consists in finding func-
tions of finite (observable) quanti-
ties which satisfy the special con-
ditions. A comparatively small
number of differential equations
has thus been found empirically
to embrace very large and appar-
ently widely separated classes of
physical phenomena, suggesting
physical relations between those
phenomena which might otherwise
have remained unnoticed. The
physicist or astronomer thus hands
over his problems to the mathe-
matician, who has either to in-
tegrate the differential equations,
or, where this is not possible, at
least to infer the properties of the
functions which would satisfy them
— in fact, the differential equation
becomes a definition of the function
or mathematical relation. In con-
sequence of this the theory of
differential equations is, as Sophus
Lie has said, by far the most im-
portant branch of mathematics.

DEVELOPMENT OF MATHEMATICAL THOUGHT. 697

The attraction of the heavenly bodies varies with the
distance, the velocity of a falling stone or the cooling
of a hot body varies with the interval of time which
has lapsed or flown. We are now so much accus-
tomed to represent such dependence by curves drawn on
paper, that we hardly realise the great step in advance
towards definiteness and intelligibility that this device
marks in all natural sciences and in many practical
pursuits. But the representation of the natural con-
nections of varying quantities by curves also forms the
connecting link with the other class of researches just
mentioned. Descartes had shown how to represent
algebraical formula? by curves in the plane and in space ;
and at the beginning of the nineteenth century this
method was modified by Gauss and Cauchy so as to
deal also with the extended conception of number
which embraced the imaginary unit. Two questions
arise, Is it possible to represent every arbitrary de-
pendence such as we meet with in the graphical descrip-
tion of natural phenomena by a mathematical formula —
i.e., by a formula denoting several specified mathematical
operations in well-defined connections ? and the inverse
question, Is it possible to represent every well-defined
arrangement of symbols denoting special mathematical
operations graphically by curves in the plane or in
space ? The former question is one of vital importance
in the progress of astronomy, physics, chemistry, and
many other sciences, and has accordingly occupied many
eminent analysts ever since Fourier gave the first ap-
proximative answer in his well-known series : the latter
question can only be answered by much stricter defini-

698 SCIENTIFIC THOUGHT.

tions of all the more advanced and of some even of the
elementary operations which analysts had become accus-
tomed to use without a previous knowledge of the range
of their validity. AH applications of mathematics con-
sist in extending the empirical knowledge which we
possess of a limited number or region of accessible
phenomena into the region of the unknown and inac-
cessible ; and much of the progress of pure analysis con-
sists in inventing definite conceptions, marked by symbols,
of complicated operations ; in ascertaining their proper-
ties as independent objects of research ; and in extending
their meaning beyond the limits they were originally
invented for, — thus opening out new and larger regions
of thought.
48. A brilliant and most suggestive example of this kind of

The

potential, reasoning was afforded by a novel mode of treating a large
class of physical problems by means of the introduction of
a special mathematical function, termed by George Green,
and later by Gauss, the " Potential " or " Potential func-
tion." ^ All the problems of Newtonian attraction were
concentrated in the study of this formula : and when the
experiments of Coulomb and Ampere showed the analogy
that existed between electric and magnetic forces on the

"o'

^ See vol. i. p. 231 of this work. algebraischen Functionen' (Leipzig,

The history of the subject has been
written by Todhunter (' History of
the Theories of Attraction and the
Figure of the Earth,' 2 vols., 1873)

1882, trans, by F. Hardcastle,

Cambridge, 1893) ; Prof. Carl Neu

mann's ' Untersuchungen tiber das

Logarithmische uud Newtouische

;l

for the earlier period down to 1832. Potential' (Leipzig, 1877); Dr

For the later period see Bacharach's ' Burkhardt's ' Memorial Lecture on

'Abriss der Geschichte der Poten- Riemann ' (Gottingen, 1892); and

tialtheorie,' Gottingen, 1883 ; for i jointly with Dr F'ranz Meyer, the

the connection of the theory with ! same author's chapter on " Poten-

Riemann's mathematical methods, tialtheorie " in the 2nd volume

especially Prof. F. Klein's tract, i (p. 464) of the ' Encyclopildie der

' Ueber Riemann's Theorie der Math. Wiss.,' 1900.

DEVELOPMENT OF MATHEMATICAL THOUGHT. 699

one side, and Newtonian forces on the other ; still more
when Fourier, Lame, and Thomson (Lord Kelvin) pointed
to the further analogy which existed between the distri-
bution of temperature in the stationary tiow of heat
and that of statical electricity on a conductor, and ex-
tended the analogy to hydrostatics and hydrodynamics,
— it became evident that nature herself pointed here
to a mathematical dependence of the highest interest
and value. Many eminent thinkers devoted themselves
to the study of this subject, but it was reserved for
Bernhard lliemann to generalise the mode of reasoning
peculiar to these researches into a fundamentally novel
method for the explanation and definition of mathe-
matical function or dependence.^

' Althougli Riemanii's original
method of dealing in a general way
with algebraical functions is here
introduced as a generalisation of
certain ideas suggested by mathe-
matical physics, it was not in this
way tliat they were intioduced to
the mathematical world. This was
done in his very abstract and difficult
memoir, ' Theorie der Abel'schen
Functionen ' (published in 1857
in vol. liv. of Crelle's 'Journal').
In this memoir the connection
which existed with mathematical
physics was not patent, and it
took a long time before his
methods, which seemed to be a
development of Cauchy's earlier
researches, were understood and
fully appreciated. It was only
after he had lectured repeatedly on
the subject, and initiated a num-
ber of younger mathematicians,
who now occupy many of the chairs
at the German universities, tliat
the discoveries and inventions of
Riemann received their deserved
appreciation. Even in his own
lectures on matliematical physics —

notably on partial differential
equations (including harmonics)
and the theory of the potential —
he did not lead up to the funda-
mental ideas which he developed
in his lectures on the theory of
the Abelian functions. Some light
is thrown on tlie subject of the
genesis of Riemann's ideas by his
dissertation written in the year
1851, though even the biographical
notice attached to the 1st edition
of his works (1876) did not deal
with the origins of his theory.
It seems, therefore, correct tO'
date the adequate recognition of
Riemann's work in wider circles from
the publication in 1882 of Prof.
F. Klein's tract mentioned above.
Like seveial other short treatises
of this eminent living mathema-
tician, it must have thrown quite
a new light upon the subject ;
and, like several of his other wiit-
ings, it revealed connections be-
tween regions of thought which to
many students must have appeared
isolated. "Through the treatment
initiated by Klein, the theory of

700

SCIENTIFIC THOUGHT.

49.
Biemann.

The peculiarity of such dependence, as exemplified in
the phenomena of the steady How of heat or of electric
distribution, consisted in this, that if at certain points
or in certain regions of space the thermal or electrical
conditions were defined and known by actual observation,
then the whole distribution in other points and regions
was completely determined. Those boundary conditions
could therefore be regarded as the necessary and sufficient
definition of the whole existing distribution. Translated
into mathematical language, this means that functions
exist which are completely defined l^y boundary values
and singularities — i.e., values at single points. Nature
herself had shown the way to define and calculate
measured relations when through their intricacy they
evaded the grasp of the ordinary operations of algebra.-^
Pliicker had already in geometry (following in the lines
of Xewton), wiien attacking the problem of the infinite
variety of higher curves, suggested the method of classi-
fying them according to their characteristic properties
or singularities. What had been done by geometers
and physicists in isolated cases with the expenditure
of much ingenuity and skill, Kiemann and his school
elevated to the rank of a general method and doctrine.

functions acquires a great degree
of clearness and connectedness,
which is mainly gained by concep-
tions derived from the (physical)
theory of the potential, and thus
exhibits the intimate relationship
of these theories" (Bacharach,
' Geschichte der Potentialtheorie,'
Gottingen, 1883, p. 71).

^ On this subject see Burkhardt's
' Memorial Lecture on Riemann '
(Gottingen, 1892), p. 5, &c.; Bach-
arach {loc. cit.), p. 30, &c. The
latter especially with reference to

the theorem called by Clerk-Maxwell
" Thomson's theorem " ('Cambridge
and Dublin Mathematical Journal,'
1848, or ' Reprint of Papers on
Electro - statics,' &c., p. 139); and
abroad 'Dirichlet's Principle,' after
Riemann (1857). Further, Brill
and Nother's "Bericht" ('Math.
Ver.,' vol. iii. p. 247) ; and lastly,
a very suggestive address by Prof.
Klein (" On Riemann's Influence on
Modern Mathematics") to the meet-
ing of the German Association in
Vienna in 1894 ('Report,' p. 61).

DEVELOPMENT OF MATHEMATICAL THOUGHT. 701

It is a process of generalisation and simplification.
Moreover, Riemann's manner of proceeding brought
with it the gain that he could at once make the
various theorems of the doctrine of the potential useful
for purely mathematical purposes : the equation which
defined the potential in physics became the definition
of a function in mathematics/

^ "One may define Riemann's
developments briefly thus : that,
beginning with certain differential
equations which the functions of
the complex variable satisfy, he is
enabled to ajjply the principles of
the potential theory. His start-
ing-point, accordingly, lies in the
province of mathematical physics "
(Klein, 'Vienna Report,' loc. cit.,
p. 60). By starting with physical
analogies Prof. Klein evades certain
difficulties which the purely mathe-
matical treatment had to encounter.
In the preface to his tract of the
year 1882, quoted above, — in intro-
ducing his method of explaining
Riemann's theory, — he says: "I
have not liesitated to make exactly
these physical conceptions the stai't-
ing-point of my exposition. In-
stead of them, Riemann, as is well
known, makes use in his writ-
ings of Dirichlet's principle. But
I cannot doubt that he started
from those physical pi'oblems, and
only afterwards substituted Dirich-
let's jjrinciple in order to support
the physical evidence by mathe-
matical reast)ning. Whoever under-
stands clearly the surroundings
among which Riemann worked at
Gottingen, whoever follows up Rie-
mann's speculations as they have
been handed down to us, partly
in fragments, will, I think, share
my opinion." And elsewhere
he says : " We regard as a specific
performance of Riemann in this
connection the tendency to give
to the theory of the potential a
fundamental importance for the

whole of mathematics, and further
a series of geometrical construc-
tions or, as I would rather say, of
geometrical inventions" ('Vienna
Report,' p. 61). Klein then refers
to the representation on the so-
called " Riemann surface," which
is historically connected, as Rie-
mann himself points out, with the
problem which Gauss first attacked
in a general way — viz., the repre-
sentation of one surface on another
in such a manner that the smallest
portions of the one surface are
similar to those of the other : a
problem which is of importance in
the drawing of maps, and of which
we possess two well-known examples
in the stereographic projection of
Ptolemy and the projection of
Mercator. This method of repre-
sentation was called by Gauss the
" Conformal Image or Representa-
tion." His investigations on this
matter were suggested by the
Geodetic Survey of the kingdom of
Hanover, with which he was occu-
pied during the years 1818 to 1830.
(See Gauss, 'Werke,' vol. iv., also
his corresp<nidence with Schum-
acher and Bessel. ) A very complete
treatise on this aspect of Riemann's
inventions is that by Dr J. Holtz-
miiller, ' Theorie der Isogonalen
Verwandschaften ' (Leipzig, 1882).
On the historical antecedents of
Riemann's conception, which for
a long time appeared somewhat
strange, not to say artificial, see
Brill and Nother's frequently
quoted " Report " (' Bericht der
Math. Verein.,' vol. iii.), p. 256 sqq.

V02 SCIENTIFIC THOUGHT.

In the investigation of those higher functions which
the purely analytical methods of Abel and his followers
had forced upon the attention of mathematicians, the
methods of Eiemann proved to be eminently useful and
suggestive. But these novel methods themselves had
been imported into the pure science from the side of its
application in physics. The value of such ideas has
always been questioned by another class of thinkers who
aim at building up the edifice of the science by rigorous
logic, without making use of practical devices which could
only be legitimately employed when once their validity
had been thoroughly proved and its limits defined. The
merit of having done this in the whole domain of those
conceptions which, since the age of Descartes, ISTewton,
and Leibniz, had been introduced as it were from the
outside into analysis, belongs to the school of mathe-
maticians headed in Germany by Karl Weierstrass.
50. Eiemann had grown up in the traditions of the school

Weierstrass. ^ .

of mathematical thought which was inspired by Gauss
and Weber in Gottingen. Geometrical representation
and physical application, including the immediate evi-
dence of the senses, formed a large and important factor
in the body of arguments by which scientific discovery
and invention was carried on in that school ; though
Gauss himself made logical rigour the final test of
maturity in all his published writings, abstaining in
many cases from communicating his results when they
had not satisfactorily passed that test in his own mind.
Through this self-imposed restriction he had permitted
important discoveries, which led to large increase of
mathematical knowledge, to be anticipated by others.

!

DEVELOPMENT OF MATHEMATICAL THOUGHT. 703

The cases of Cauchy, Abel, and Jacobi are the best-
known instances. Through their labours an entirely
new field had been prospected and partially cultivated.
It was to this that Weierstrass, the other great leader
in modern theory, was attracted. He made the clear
definition and logical coherence of the novel concep-
tions which it involved his principal ahn. Gauss
had laboured without assistance at similar problems,
making many beginnings which even his colossal intellect
could not adequately develop. Weierstrass early gathered
around him a circle of ardent and receptive pupils and
admirers,^ to whose care and detailed elaboration he

^ The researches of Weierstrass
(1815 to 1897) began somewhat
earlier than those of liiemann, but
only became generally known and
appreciated in their fundamental
originality through his pupils — his
academic influence dating from
the year 1861. Some account of
Weierstrass's activity is given bj^
Emil Lampe in the 6th volume
(1899) of the ' Bericht der Math.
Verein.,' p. 27, &c. The genesis
of his ideas is traced by Brill
and Neither in the Report quoted
in the last note, and by M.
Poincar^ in ' Acta Math.,' vol. xxii.
The former divides his Researches
roughly into two periods, during
the first of which (1848-56) he
dealt with what Cayley would
call " known " functions ; progress
during this period depending not
so much upon fundamentally new
ideas as upon an investigation of
special problems and great analyti-
cal skill. The second period begins
in the year 1869, and is devoted to
nothing less than the building up
of the entire structure of mathe-
matical thought from the very
beginning upon altered definitions,
through which the dilemmas and

paradoxes would be obviated that
had shown themselves ever since
the middle of the eighteenth cen-
tury in consequence of a too
confident application and extension
of conventional ideas suggested
mainl}^ by practical problems. The
elements of this grand edifice are
now largely accepted, not only in
Germany, Ijut also in France, Italy,
and England. In Germany Prof.
0. Stolz, through his works on
General Arithmetic, 2 vols. (1885
and 1886), and the Calculus, 3 vols.
(1893 to 1899), has probably done
more than any other academic
teacher to utilise the new sj'stem
of mathematical thought for the
elementary course of teaching. It
seems of importance to state, how-
ever, that outside of the circle of
Weierstrass's influence, and quite
within the precincts of Riemann's
school, the necessity was felt of
strengthening the foundations on
which research in higher mathe-
matics was carried on, by going
back to the fundamental ideas of
arithmetic. The principal repre-
sentative of this line of research
was Hermann Hankel (1839-73), a
pupil of Riemann's, who, in the

704

SCIENTIFIC THOUGHT.

confided many separate and lengthy investigations. It
was through one of these that a test-case, in which exist-
ing mathematical definitions broke down, was published
in 1872. It forms a kind of era in the history of

middle of the sixties, delivered
lectures at the University of
Leipsic upon " Complex numbers
and their functions," starting in a
characteristic manner with that ex-
tended algebra which Cauchy and
Riemann had used to such good
purpose. The first part of these
lectures was published in 1867.
In the preface Hankel says : " In
the natural sciences we witness in
recent times the distinct tendency
to ascend from the world of em-
pirical detail to the great principles
which govern everything special and
connect it into a whole — i.e., the
desire for a philosophy of nature,
not forced upon us from outside,
but naturally evolved out of the
subject itself. Also in the domain
of mathematics a similar want
seems to make itself generally felt
— a want which has always been
alive in England." Had the author
not been prematurely taken away,
there is no doubt that he would
have still more largely contributed
to the revolution of mathematical
ideas now in progress. As it
is, he made one further import-
ant contribution, of which more
hereafter. In Italy Prof. Ulisse
Dini began to lecture in the year
1871 to 1872 on the theory of
functions, and published his lec-
tures in 1878. A translation was
brought out in German (1892) by
Prof. Liiroth and Mr A. Schepp,
in which many of the modern
developments aie utilised. In
France we owe to M. Jules Tannery
a valuable introduction to the
theory of functions of one variable,
based upon a series of lectures
delivered in the Ecole Normale
in 1883, in which, as he says

(Preface, p. vii), he collected
the labours of Cauchy, Abel, Le-
jeune Dirichlet, Riemann, Ossian
Bonnet, Heine, Weierstrass, and
others ; after which he considers
that nothing essential need be
added in the way of elucidation of
the , foundations of the theory.
M. Emil Borel published in 1898
' Lectures on the Theory of Func-
tions,' the first of a series of
text - books dealing with various
aspects of the theory of functions,
in which he largely refers to the
labours of Weierstrass. Before
Weierstrass's theory had become
known, however, j\l. Meray had al-
ready entered upon an exposition
of the foundations of analysis on
lines which had much analogy with
those adopted by Weierstrass. In
England the late Prof. Clifford had
occupied himself in various memoirs
with the theories of Riemann ; but
we owe the first comprehensive
treatise, embracing the work of
Riemann as well as that of Weier-
strass, to Prof. Forsyth (' Theory
of Functions of a Complex Vari-
able,' Cambridge, 1893). Almost
simultaneously Professors Harkness
and Morley published a ' Treatise on
the Theory of Functions,' and in
1898 an ' Introduction to the
Theory of Analytic Functions,' in
which they in the main adopted the
point of view of Weierstrass. A
very original thinker, whose in-
dependent researches reach back to
the year 1872, and who played an
important part in the investigation
of many obscure points, was the
late Prof. Paul Du Bois-Reymond,
who published in 1882 the first
part of his ' Allgemeine Func-
tionentheorie,' containing the

DEVELOPMENT OF MATHEMATICAL THOUGHT. 705

mathematical thought. Up to that time " one would
have said that a continuous function is essentially cap-
able of being represented by a curve, and that a curve
has always a tangent. Such reasoning has no mathe-
matical value whatever ; it is founded on intuition, or
rather on a visible representation. But such representa-
tion is crude and misleading. We think we can figure
to ourselves a curve without thickness ; but we only
figure a stroke of small thickness. In like manner we
see the tangent as a straight band of small thickness,
and when we say that it touches the curve, we wish
merely to say that these two bands coincide without
crossing. If that is what we call a curve and a tangent,
it is clear that every curve has a tangent ; but this has
nothing to do with the theory of functions. We see to
what error we are led by a foolish confidence in what
we take to be visual evidence. By the discovery of this
striking example Weierstrass has accordingly given us a
useful reminder, and has taught us better to appreciate
the faultless and purely arithmetical methods with which
he more than any one has enriched our science." ^

"metaphysics and theory of the
fundamental conceptions in mathe-
matics : quantity, limit, argument,
and function " (Tubingen). This
work touches the borderland of
mathematics and philosophy, as
does the same author's posthumous
work ' Uber die Grundlagen der
Erkenntniss in den exacten Wissen-
schaften' (Tiibingen, 1890), and will
occupy us in another place.

1 M. Poincare in the ' Acta
Mathematica,' vol. xxii., "L'ceuvre
mathematique de Weierstrass," p.
5. The "test-case" referred to in
the text consisted in the publica-

VOL. II.

tion by Weierstrass (in the year
1872, 'Trans. Berlin Academy,' re-
printed in Weierstrass's ' Math.
Werke,' vol. ii. p. 71) of the proof
of the existence of a continuous
function which nowhere possessed
a definite (finite or infinite) differ-
ential coefficient. This example
cleared up a point brought into
prominence by Riemann in his
posthumously (1867) published
Inaugural Dissertation of 1854
('Werke,' p. '213). The question
had already, following on Rie-
mann's suggestions, been dis-
cussed by Hermann Hankel in a

2 Y

706

SCIENTIFIC THOUGHT.

Before Weierstrass, Caiichy and Eiemann had at-
tempted to define the vague term " function " or
mathematical dependence. Both clung to the graphical
representation so common and so helpful in analysis
since Descartes invented it. We have, of course, in
abstract science, a right to begin with any definition
we choose. Only the definition must be such that it

remarkable tract on "Oscillating
functions," in which he drew
attention to the existence of func-
tions which admit of an integral,
but where the existence of a differ-
ential coefficient remains doubtful.
In fact, it appears that the question
as to the latter had never been
raised ; the only attempt in this
direction being that of Ampere in
1806, which failed (Hankel, p. 7).
Hankel in his original investigation
showed that a continuous curve
might be supposed to be generated
by the motion of a point which
oscillated to and fro, these oscilla-
tions at the limit becoming in-
finitely numerous and infinitely
small : a curve thus generated
would present what he called "a
condensation of singularities " at
every point, but would possess no
definite direction, hence also no
differential coefficient. The argu-
ments and illustrations of Hankel
have been criticised and found fault
with. He nevertheless deserves the
credit of having among the first
attempted "to gain a firm footing
on a slippery road which had only
been rarely trodden" (p. 8). In
this tract (which is reprinted in
'Math. Ann.,' vol. xx.), as well as
in his valuable article on " Limit "
(Ersch und Grubei-, ' Encyk.,' vol.
xc. p. 185, art. "Greuze"), Hankel
did much to establish clearly the
essential point on which depends
the entire modern revolution in
our ideas regarding the foundations

of the so-called infinitesimal cal-
culus ; reverting to the idea of a
" limit," both in the definition of
the derived function (limit of a
ratio) and of the integral (limit of
a sum) as contained in the writings
both of Newton and Leibniz,
but obscured by the method of
" Fluxions " of the former and the
method of " Infinitesimals " of the
latter. Lagrange and Cauchy had
begun this revolution, but it was
not consistently and generally
carried through till the researches
of Riemann, Hankel, Weierstrass,
and others made rigorous defini-
tions necessary and generallj' ac-
cejited. It is, however, well to
note that in this country A. de
Morgan very early expressed clear
views on this subject. Prof. Voss,
in his excellent chapter on the
Differential and Integral Calculus
(' Encyk. Math. Wiss.,' vol. ii. i. p.
54, &c.), calls the later period the
period of the purely arithmetical
examination of infinitesimal con-
ceptions, and says (p. 60), " The
purely arithmetical definition of
the infinitesimal operations which
is characteristic of the present
critical period of mathematics has
shown that most of the theorems
established by older researches,
which aimed at a formal extension
of method, only possess a validity
limited by very definite assump-
tions." Such assumptions were
tacitly made by earlier writers, but
not explicitly stated.

DEVELOPMENT OF MATHEMATICAL THOUGHT. 707

-corresponds with conditions which we meet with in
reahty, say in geometry and physics, otherwise onr
science becomes useless : further, our definitions must be
•consistent, and follow logically from the fundamental
principles of arithmetic, otherwise we run the risk of
sooner or later committing mistakes and encountering
paradoxes. We have two interests to serve : the ex-
tension of our knowledge of functions and the rigorous
proof of our theorems. The methods of Eiemann and 51.

Riemann

'01 Weierstrass are complementary. " By the instrument a>"i

•^ J J Weierstrass

•of Eiemann we see at a glance the general aspect of compared,
things — like a traveller who is examining from the peak
of a mountain the topography of the plain which he is
going to visit, and is finding his bearings. By the in-
struments of Weierstrass analysis will, in due course,
throw light into every corner, and make absolute clear-
ness shine forth." ^- The complementary character of

' Poiucare, loc. cit., p. 7. Simi-
larly Prof. Klein {loc. cit., 'Vienna
Report,' p. 60): "The founder
■of the theory [viz., of functions]
is the great French mathema-
tician Cauchy, but only in Ger-
many has it received that mod-
ern stamp through which it has,
so to speak, been pushed into the
centre of our mathematical con-
victions. This is the result of the
simultaneous exertions of two
workers — Riemann on the one side
and Weierstrass on the other.
Although directed to the same end,
the methods of these two mathe-
maticians are in detail as different
as possible : they almost seem to
contradict each other, which contra-
diction, viewed from a higher aspect,
naturally leads to this — that they
mutually supplement each other.
Weierstrass defines the functions

of a complex variable analytically
by a common formula — viz., the
' Infinite Power Series ' ; in the
sequel he avoids geometrical means
as much as possible, and sees his
specific aim in the rigour of
proof. Riemann, on the other
side, begins with certain differential
equations. The subject then im-
mediately acquires a physical as-
pect. . . . His starting-point lies
in the region of mathematical
physics." We now know from the
biographical notice of Riemann,
attached to his collected works
(1st ed., p. 520), that he was
pressed (in 1856) by his mathe-
matical friends to publish a resume
of his Researches on Abelian func-
tions— " be it ever so crude." The
reason was that Weierstrass was
already at work on the same sub-
ject. In consequence of Riemann's

708

SCIENTIFIC THOUGHT.

the labours of the two great analysts is nowhere better
shown than in the special manner in which Weierstrass
succeeded in strengthening the foundations^ on which
much of Eiemann's work rests.

The labours of the great analysts — Gauss, Cauchy,
Eiemann, and Weierstrass — all tended to increase our

publication Weierstrass withdrew
from the press an extensive memoir
which he had presented in the year
1857 to the BerUn Academy, be-
cause, as he himself says (Weier-
strass, 'Math. Werke,' vol. iv. p. 10) :
"Riemann published a memoir on
the same problem which rested on
entirely different foundations from
mine, and did not immediately
reveal that in its results it agreed
completely with my own. The
proof of this required investigations
which were not quite easy, and took
much time ; after this difficulty
had been removed a radical remod-
elling of my dissertation seemed
necessary," &c., &c. The mutual
influence of Riemann's and W^eier-
strass's work is also referred to by
Weierstrass in a letter to Prof.
Schwarz, dated 1875, in which
he utters what he calls his con-
fession of faith: "The more
I ponder over the principles of
the theory of functions — and I
do this incessantly — the stronger
grows my conviction that it must
be built up on the foundation of
algebraical truths, and that, there-
fore, to employ for the proof of
simple and fundamental algebraical
theorems the ' transcendental,' if I
may say so, is not the correct way,
however enticing privia vista the
considerations may be by which
Riemann has discovered many of
the most important properties of
algebraical functions. It is a mat-
ter of course that every road must
be open to the searcher as long as
he seeks ; it is only a question of

the systematic demonstration "
(Weierstrass, 'Werke,' vol. ii. p,
235).

^ This refers mainly to Weier-
strass's investigation of the principle
called by Riemann "Dirichlet'&
principle," but which had been
stated already with great generality
by Thomson (Lord Kelvin) in the
year 1847. The validity of this
method depended on a certain
minimum theorem. Weierstra.ss-
has shown that the existence of
such a minimum is not evident, and
that the argument used is not con-
clusive. He laid before the Berlin
Academy in the year 1870, a com-
munication giving a test - case tO'
prove that Dirichlet's method was
not generally valid ('W^erke,' vol.
ii. p. 49). "Through this," Prof.
KJein says (loc. cit., p. 67), "a
great part of Riemann's develop-
ments become invalidated. Never-
theless the far - reaching results
which Riemann bases upon the
prineiple are all correct, as was
shown later on exhaustively and
with all rigour by Carl Neumann
and H. A. Schwarz. Indeed we-
must come to the conclusion that
Riemann himself arrived at these
theorems by a phj-sical intuition,
and only afterwards resorted to the
principle referred to in order to
have a consistent mathematical line
of reasoning " {loc. cit., p. 67). See
on this also Poincar^ (loc. cit.,
pp. 10 and 15), who gives other
instances where the work of Weier-
strass supported that of Riemann.

DEVELOPMENT OF MATHEMATICAL THOUGHT. 709

knowledge of the higher mathematical relations, but
also to reveal the uncertainty and absence of rigorous
definition of the foundations of arithmetic and of geo-
metry. Accordingly we find these great thinkers con-
tinvially interrupting their more advanced researches by
examinations of the principles. This feeling of un- 52.

^ ^ ° Bxamiua-

certainty had led, ever since the end of the eighteenth fg^Jj^ations
century, to many isolated attacks and half-philosophical
discussions by various writers in this country and
abroad. Many of them remained long unrecognised ;
such were the suggestive writings of Hamilton, De
Morgan, Peacock in England, Bolzano ^ in Bohemia,

^ The merits of Bernhard Bolzano
(1781-1848) as oue of the earliest
representatives of the critical period
of mathematics were recognised
after a long interval of neglect by
Hankel in his article on " Limit "
mentioned above. This philosophi-
cal mathematician published many
years before Caucliy a tract on the
Binomial Theorem (Prague, 1816),
iu which he gives, in Hankel's
opinion, the first rigid deduction of
various algebraical series. " Bol-
zano's notions as to convergency of
series are eminently clear and
correct, and no fault can be found
with his development of those series
for a real argument (which he
everywhere presupposes) ; in the
preface he gives a pertinent criti-
cism of earlier developments of the
Binomial Theorem, and of the un-
restricted use of infinite series,
which was then common. In fact,
he has everything that can place
him in this respect on the same level
with Cauchy, only not the art pecu-
liar to the French of refining their
ideasandcommunicatingthemin the
most appropriate and taking man-
ner. So it came about that Bolzano
remained unknown and was soon

forgotten ; Cauchy was the happy
one who was praised as a reformer of
the science, and whose elegant writ-
ings were soon widely circulated."
(Hankel, luc. cit., p. 210.) Follow-
ing on this statement of Hankel
and a remark of Prof. H. A.
Schwarz, who looks upon Bolzano
as the inventor of a line of reason-
ing further developed by Weier-
strass ('Journal fiir Mathematik,'
vol. Ixxiv. p. 22, 1872), Prof. 0.
Stolz published in 1881 ('Math.
Ann.,' vol. xviii. p. 255) an account
of the several writings of Bolzano,
beginning in the year 1810, in so far
as they referred to the principles of
the Calculus. " All these writings
are remarkable inasmuch as they
start with an unbiassed and acute
criticism of the contributions of the
older literature" {toe. cit., p. 257).
A posthumous tract by Bolzano,
' Paradoxieen des Unendlichen,'
was republished in 1889 in ' Wis-
senschaftliche Classiker,' vol. ii.,
Berlin (Meyer and Miiller). As
stated above, Hankel was also one
of the first to draw attention to
the originality and importance of
Hermann Grassmanu's work.

710

SCIENTIFIC THOUGHT.

Bolyai in Hungary, Lobatchevski in Kasan, Grassmann
in Stettin. Most of these were unknown to each
other. However, near the beginning of the last third
of the century three distinct publications created a
great stir in the mathematical world, brought many
scattered but cognate lines of reasoning together, and
made them mutually fertile and suggestive. These
three were — first, the publication in 1860 of Gauss's
correspondence with Schumacher, in which two letters
of the former, dated May and July 1831,^ became
known, where he referred to his extensive but un-
written and unfinished speculations on the foundations
of geometry and the theorem which refers to the
sum of the angles in a triangle. The second was the
publication in 1867 of the first and only part of Her-
mann Hankel's " Lectures on the Complex Numbers
and their Functions." '^ The third was the posthumous
publication in the same year of Eiemann's paper, dated
1854,^ " On the Hypotheses which lie at the Foundation
of Geometry." Almost simultaneously there appeared
the first of Helmholtz's two important papers ^ on the

^ See ' Briefwechsel zwischen
Gauss und Schumacher,' ed. Peters,
1860, vol. ii. pp. 260, 268.

^ The small volume contains so
much original and historical matter
that I have on several occasions
refened to it. See above, pp. 645,
653.

^ Riemann, 'Math. Werke,' 1st
ed., p. 254 sqq.

* The first publication of Helm-
holtz was a lecture on " the actual
foundations of geometry," which
he delivered on the 22nd May 1868
to the Medical Society at Heidel-
berg. This communication, which

referred to investigations carried on
for many years, — notably in con-
nection with the theory of the
colour -manifold, — was occasioned
by the publication of Riemann 's
paper in the ' Transactions ' of the
Gottingen Society. He had heard
of this through Schering, to whom
he wrote on the 21st April 1868
before having seen Riemann's
paper : " I have myself been oc-
cupied with the same subject dur-
ing the last two years, in connection
with my researches in physiological
optics. ... I now see, from the
few hints which you give as to the

DEVELOPMENT OF MATHEMATICAL THOUGHT. 711

same subject, through which it became more widely
known and attracted the attention of other than
purely mathematical writers. The small but eminently
suggestive volume of Hankel showed the necessity of
a revision and extension of the fundamental principles
and definitions ^ of general arithmetic and algebra as

result of the investigation, that
Riemanu has arrived at exactly
the same results. My starting-
point was the question, How must
a magnitude of several dimensions
be constituted, if solid bodies are
to move in it everywhere continu-
ously, monodromically, and as freely
as bodies move in real space?" On
receiving from Schering a reply
with a copy of Riemann's paper,
Helmholtz wrote (18th May), "I
enclose a short exposition of that
which in my researches on the same
subject is not covered by Riemann's
work." A fuller paper, with the
title " On the Facts which lie at the
foundation of Geometry," appeared
in the ' Gottinger Nachrichten,'
June 3, 1868. See Helmholtz,
' Wiss. Abhandl.,' vol. ii. pp. 610
and 618, &c. ; also ' H. von Helm-
holtz,' by Leo Koenigsberger (1903),
vol. ii. p. 138, &c. Li another
lecture, " On the origin and mean-
ing of the .\xioms of Geometry "
(1870, reprinted in abstract in
' The Academy,' vol. i. ), as well as
in an article in vol. i. of ' Mind '
(p. 301), he discussed "the philo-
sophical bearing of recent in-
quiries concerning geometrical
axioms and the possibility of
working out analytically other
systems of geometry with other
axioms than Euclid's " (reprinted in
vol. ii. of ' Vortriige und Reden ').

^ In this treatise Hankel intro-
duced into German literature the
three terms "distributive," "asso-
ciative," and "commutative" to
define the three principles which

govern the elementary operations
of arithmetic, and introduced fur-
ther what he calls the principle of
the permanence of formal rules
in the following statement : " If two
forms, expressed in the general
terms of universal arithmetic, are
equal to each other, they are to
remain equal if the symbols cease
to denote simple quantities ; hence
also if the operations receive a
different meaning." Hankel seems
to have been led to his definitions
by a study of French and English
writers, among wliom he mentions
Servois (' Gergonne's Ann.,' v. p. 93,
1814) as having introduced the
terms "distributive" and "com-
mutative," and SirW. R. Hamilton
as having introduced the term
" associative." He further says
(p. 15): "In England, where
investigations into the funda-
mental principles of mathematics
have always been treated with
favour, and where even the great-
est mathematicians have not
shunned the treatment of them
in learned dissertations, we must
name George Peacock of Cambridge
as the one who first recognised
emphatically the need of formal
mathematics. In his interesting
report on certain branches of
analysis, the principle of perma-
nence is laid down, though too
narrowly, and also without the
necessary foundation." Other
writings, of what he terms Pea-
cock's Cambridge school, such as
those of De Morgan, Hankel states
that he had not inspected ; mention-

712

SCIENTIFIC THOUGHT.

53.
Non-
Euclidean
geometry.

an introduction to the advanced theories of Gauss and
Kiemann ; and for this purpose he went back to the
unnoticed labours of Grassmann in Germany, to the
writings of Peacock and De Morgan in England, and
incidentally introduced into Germany the elaborate
algebra of quaternions, invented and practised by
Hamilton twenty years before that time. The papers
of Eiemann and Helmholtz similarly showed the neces-
sity of a thorough investigation of the principles and
foundations of ordinary or Euclidean geometry, and
showed how consistent systems of geometry could be
elaborated on other than Euclidean axioms. Only
from that moment, in fact, did it become generally
recognised that already, a generation before, two in-
dependent treatises on elementary geometry had been
published in which the axiom of parallel lines was
dispensed with and consistent geometrical systems
developed. These were contained — as already stated
— in the ' Kasan Messenger,' under date 1829 and

ing ouly a short paper by Dr F.
Gregorj' on Symbolical Algebra
in the Edinburgh ' Transactions.'
Whilst Hankel was delivering
lectures on these fundamentals,
Weierstrass in Berlin was likewise
in the habit of introducing his
lectures on the Theory of Analytic
Functions by a discussion of the
theory of Complex Numbers. This
introduction was published, with
Weierstrass's permission, in the year
1872 by Dr E. Kossak (in a pro-
gramme of the Friedrichs-Werder
Gymnasium), after lectures de-
livered by Weierstrass in 1865-66.
To what extent Hankel may have
been influenced by Weierstrass's
lectures, which he seems to have
attended after leaving Gottingen,

is uncertain, for in spite of his very
extensive references he does not
mention Weierstrass. In Kossak's
' Elemente der Arithmetik ' the
term " permanence of formal rules "
is not used, but the treatment of
the extended arithmetic is carried
on along the same lines — i.e., not
by an attempt to represent the
complex quantities, but on the
ground of maintaining the rules
which govern the arithmetic of
ordinary numbers. Great im-
portance is also attached to the
principle of inversion as having
shown itself of value in the theory
of elliptic functions, and being not
less valuable in arithmetic. As
stated above (p. 640, note), this prin-
ciple is also insisted on by Peacock.

DEVELOPMENT OF MATHEMATICAL THOUGHT. 713

I80O, the author being Lobatchevski ; and in the
appendix to an Introduction to Geometry, published
by Wolfgang Bolyai at Maros Vasarheli, a town of
Transylvania, the appendix being by the author's son,
Johann Bolyai. The elder Bolyai having been a
friend and correspondent of Gauss, and his speculations
evidently of the same nature as those indicated by the
latter in the above-mentioned correspondence, conjectures
have been made as to which of the two originated the
whole train of thought.^ The independent investiga-
tions of Eiemann and Helmholtz started from a differ-

^ See above, p. 652, note. What
is important from our point of
view in the investigations of both
Riemann and Helmholtz lies in the
following points : First, Neither
Riemann nor Helmholtz refers to
the non - Euclidean geometry of
Lobatchevski or Bolyai. This is
not surprising in the case of
Helmholtz, whose interest was
originally not purely mathematical ;
in fact, we may incidentally re-
mark how, in spite of his profound
mathematical ability, he on various
occasions came into close contact
with mathematical researches of
great originality and importance
without recognising them — e.g.,
the researches of Grassmaun and
Pliicker. As regards Riemann, his
paper was read before Gauss, who
certainly knew all about Bolyai, and
latterly also about Lobatchevski, of
whom he thought so highlj^ that he
proposed him as a foreign member
of the Gbttingen Societj*. Gauss
could therefore easily have pointed
out to Riemann the relations of
his speculations with his own and
those of the other mathematicians
named. Since the publication of
the latest volume of Gauss's works,
it has become evident that Gauss

con-esponded a good deal, and
more than one would have sup-
posed from reading Sartorius's
obituary memoir, on the subject
of non-Euclidean (astral or imag-
inary) geometry, notably with
Gerling ; and that several con-
temporary mathematicians, such as
Schweikart, came very near to
Gauss's own position. Second, al-
though Riemann, and subsequently
also Helmholtz, made use of the
term " manifold " {3fannigfaltig-
keit), it does not appear in the
course of their discussion that they
considered the space-manifold from
any other than a metrical point
of view. In fact, the manifold be-
comes in their treatment a magni-
tude {Grossc). It is true that
Riemann does refer to certain
geometrical relations not con-
nected with magnitude but only
with position, as being of great
importance. These two points
through which the researches of
Riemann and Helmholtz stand in
relation to other, and at the
time isolated, researches, were
dwelt on, the first by Beltrami,
and the second by Cajdey and
Prof. Klein.

714 SCIENTIFIC THOUGHT.

ent origin : both made use of tlie more general con-
ception of an extended magnitude, introduced the
notion of the curvature of space by analogy with
Gauss's measure of curvature of a surface, and tried
to express in algebraical formulae the general and
necessary properties of a magnitude which should form
the foundation of a geometry. The relation of these
algebraical results to those arrived at by the critical
and purely geometrical methods of Lobatchevski and
Bolyai were set out by Beltrami, who showed clearly
that three geometries of two dimensions are possible —
the Euclidean, that of Lobatchevski, where the three
angles of a triangle are less than two right angles,
and a third where they are more. He showed the
analogy of the third with geometry on the sphere,
and suggested the pseudo-sphere as a surface on which
the second could be similarly represented. At the
same time he indicated the generalisation through the
algebraical formula of the conception of dimensions, and
introduced the symbolical term geometry of four or
more dimensions, as Grassmann and Cayley had done
before him.^ Through all these investigations a habit

^ The geometry of non-Euclidean
space, as well as the geometry
of four or more dimensions (both
usually comprised under the term
" non - Euclidean geometry "), can
now boast of an enormous
literature, the enumeration of
which alone would fill many
pages. A complete bibliography
up to the year 1878 is given in
vols. i. and ii. of the American
' Journal of Mathematics ' bj- Prof.
Bruce Halsted, who has done
much to make known to English
readers the original writings of

the pioneers in this subject.
Later publications are referred to
in Dr Victor Schlegel's papers
('Leopoldina,' xxii. , 1886, Nos.
9-18): "Ueber Entwickelung und
Stand der n-dimensionalen Ge-
ometric," &c., &c. In France
Houel published (beginning with the
year 1866) translations of memoii-s
referring to this subject ; in fact,
he was almost the first to draw
attention to this important modem
departure. But it is almost ex-
clusively owing to the various
writings of Prof. Felix Klein that

DEVELOPMENT OF MATHEMATICAL THOUGHT. 715

has been introduced into mathematical writings which
has not a little puzzled outsiders, and even exposed
the logically rigorous deductions of mathematicians to
the ridicule — not to say the contempt — of eminent
philosophical authorities. The complete parallelism or
correspondence of geometrical with algebraical notions
— the possibility of expressing the former with perfect
accuracy by the latter, and of retranslating the latter
into the former, and this in more than one way, accord-
ing to the choice of the space element (point, line,
sphere), led to the habit of using purely geometrical pre-
sentable ideas as names for algebraical relations which
had been generalised by the addition of more than
a limited number of variables. Thus the conception
of curvature, easily defined for a plane curve, and 54.

"^ ^ ^ Curvature

extended by Gauss to surfaces, was, by adding a third cf space,
variable in the algeljraic formula, applied to space.
We are then told that it is necessary to understand
what is meant by the curvature of space, this being a
purely algebraical relation, not really presentable, but
only formed by analogy from the geometrically present-
able relations of geometrv on a surface. In a similar

the different points of origin of this
most recent mathematical specula-
tion, which are to be found in
the mathematical literature of all
the principal nations, have been
put in the true light and brought
into connection. In fact, here,
as in sevei-al other subjects, his
publications, including his litho-
graphed lectures on non-Euclidean
geometry (delivered at Guttingen,
1893-94), serve as the best guide
through the labyrinth and contro-
versies of this intricate subject.
See especially his article "Ueber

die so-genannte nicht-Euclidische
Geometrie" in vol. iv., "Math. Ann.,'
1871. In this paper he connects the
independent researches of Cayley
(following Laguerre, ' Nouv. Ann.
de Math.,' 1853), who in his sixth
memoir on Quantics showed how
metrical geometry can be included
in projective geometry by refer-
ring figures to a fundamental fixed
figure in space called by him the
"Absolute," with the independent
researches of Lobatchevski, Bolyai,
Riemann, and Beltrami.

716

SCIENTIFIC THOUGHT.

way the idea of the dimensions of space was extended,
and four and more dimensions freely spoken of when
really only a limited number is geometrically pres-
entable. In the hands of mathematicians these terms
are useful, and we may discard the criticism of philo-
sophers and laymen as based on misunderstanding.^
The introduction, however, into geometrical work of con-
ceptions such as the infinite, the imaginary, and the
relations of hyperspace, none of which can be directly
imaged, has a psychological significance well worthy
of examination."^ It gives a deep insight into the
resources and working of the mind. We arrive at
the borderland of mathematics and philosophy.

^ The most important philosophi-
cal criticism of the iiou-Euclidean
geometry is that of Lotze, con-
tained in the second book, chap,
ii., of the ' Metaphysik ' (1879, p.
249, &c. ) It must not be forgotten
that Lotze wrote at a time when
tlie novel and startling conceptions
put forward by popular writers on
the subject had been employed in
the interest of a spiritualistic philo-
sophy, to the delusions of which
some even of Lotze's friends had
fallen a prey. This explains the
severity of Lotze's criticisms, which
are of the very same nature as those
he pronounced many years earlier
on similar aberrations (see ' Kleine
Schriften,' vol. iii. p. 329). Those
who are interested in following up
the subject should refer to] the
writings of Friedr. Ztillner as col-
lected in the four vols, of his
' Wissenschaftliche Abhandlungen '
(Leipzig, 1878-81). They belong
to the curiosities of the philosophi-
cal and scientific literature of that
age, but can hardly claim a place in
the history of thought.

"^ See the remark of Cayley in his
Presidential Address (' Coll. Works,'

vol. xi. p. 434) : " The notion,
which is really the fundamental
one (and I cannot too strongly
emphasise the assertion), under-
lying and pervading the whole of
modern analysis and geometry, is
that of imaginary magnitude in
analysis and of imaginary space (or
space as a locvs in quo of imaginary
points and figures) in geometry. I
use in each case the word imaginary
as including real. This has not
been, so far as I am aware, a subject
of philosophical discussion or in-
quiry. As regards the older meta-
physical writers, this would be quite
accounted for by saying that they
knew nothing, and were not bound
to know anything, about it ; but at
present, and considering the prom-
inent position which the notion
occupies — say even that the conclu-
sion were that the notion belongs
to mere technical mathematics or
has reference to nonentities, in
regard to which no science is pos-
sible— still it seems to me that (as
a subject of philosophical discussion)
the notion ought not to be thus
ignored ; it should at least be shown
that there is a right to ignore it. "

DEVELOPMENT OF MATHEMATICAL THOUGHT. 7 17

There exists, moreover, an analogy between the
manner in which these novel and extended ideas have
been historically introduced and the mode of reasoning
which led Sir W. E. Hamilton to the invention of a new
and extended algebra — the algebra of quaternions. This
analogy becomes evident if we study the small volume of
Hermann Hankel, which appeared about the same time
as Riemann's and Beltrami's fundamental geometrical
dissertations.

The extension of Hamilton was only possible by drop-
ping one of the fundamental principles of general arith- conceptions,
nietic, the commutative principle of multiplication, which
is symbolically expressed by saying that a x & is equal to
h y.a. By assuming that « x & is equal to — & x a, Hamil-
ton founded a new general arithmetic on an apparently
paradoxical principle. Similarly Lobatchevski and Bolyai
constructed new geometries by dropping the axiom of
parallel lines. Hankel made clear the significance of the
new algebra, Riemann and Beltrami that of the new geom-
etry. The practical performance anticij)ated and led up
to the theoretical or philosophical exposition of the under-
lying principles. But there was a third instance in
which a new science had been created by abandoning the
conventional way of looking at things. This was the
formation of a consistent body of geometrical teaching
by disregarding the metrical properties and studying
only the positional or projective properties, following
Monge and Poncelet. The two great minds who worked
out this geometry independently of the conception of
number or measurement, giving a purely geometrical
definition of distance and number, were Cayley in Eng-

718

SCIENTIFIC THOUGHT.

56.

Klein's
exposition.

land and Von Staudt in Germany. It was reserved for
Prof. Felix Klein of Gottingen to show how the gener-
alised notions of distance introduced into geometry by
Cay ley and Von Staudt opened out an understanding of
the three geometries of Euclid, of Lobatchevski, and of
Eiemann.^ We have to go back to the purely projective
properties of space to understand these different possi-
bilities. Lobatchevski attacked the problem practically,
Eiemann analytically, Klein geometrically. Through the
labours of Klein the subject has arrived at a certain
finality. And what was still wanting after he had
written his celebrated memoir (which was approved and

^ See the note ou p. 714, above ;
also ' Math. Ann.,' vol. iv. p. 573,
and vol. vi. p. 112. Prof. Klein
— following a usage iu mathe-
matical language — distinguishes
three different geometries, the
hyperbolic, the elliptic, and the
parabolic geometry, corresponding
to the possession by the straight
line at infinity of two real or two
imaginary (that is, none) or two
coincident points. The whole
matter turns upon the fact that,
although metrical relations of
figures are in general changed
by projection, there is one metri-
cal relation — known in geometry
as the " anharaionic ratio" (in
German Doppdve7-hdltniss)— which
in all projective transformations
remains unchanged. As this an-
harmonic ratio of points or lines
can be geometrically constructed
without reference to measure-
ment (Von Staudt, 'Geometrie
der Lage,' 1847 and 1857), a
method is thus found by which,
starting from a purely descriptive
property or relation, distance and
angles — i.e., metrical quantities —
can be defined. Some doubts have

j been expressed whether, starting
from the purely projective pro-
perties of space and building up
geometry in this way (arriving at
the metrical properties by the
construction suggested by Von
Staudt), the ordinary idea of
distance and number is not tacitly
introduced from the beginning.
This may be of philosophical,
but is not of mathematical,
importance, as the main object
in the mathematical treatment is
to gain a starting - point from
which the several possible con-
sistent systems of geometry can
be deduced and taken into view
together. See on this point,
inter alia, Cayley's remarks in
the appendix to vol. ii. of ' Col-
lected Works ' (p. 604 sqq), also
Sir R. S. Ball's paper (quoted
there), and more recently the dis-
cussion on the subject in Mr
Bertrand Russell's ' Essay on the
Foundations of Geometry' (1897,
p. 31, &c. ; p. 117, &c.) See
also the same author's article on
non-Euclidean Geometry in the
supplement of the ' Ency. Brit.,'
vol. xxviii.

DEVELOPJMENT OF MATHEMATICAL THOUGHT. 719

commented on by Cayley) was later on supplied in con-
sequence of a suggestion of his. The researches of
Eiemann, and still more those of Helmholtz, had not
merely a mathematical, they had also a logical and a
psychological, meaning. Space was conceived to he a
threefold - extended manifold. There are other mani-
folds besides space — such, for instance, as the threefold-
extended manifold of colours. Helmholtz came from the
study of this manifold to that of space. Now the
question arises as to the conditions or data which are
necessary and sufficient for the foundations of a science
like geometry. We have seen that the axiom of parallel
lines is not required ; we have also seen that the notion
of distance and number can be generalised. What other
data remain which cannot be dispensed with ? Helm-
holtz had attempted to answer this question. But
neither he nor Eiemann had considered the possibility
of a purely projective geometry. Now it is the merit of
Prof. Klein to have seen that there exists a purely alge-
braical method by which this problem can be attacked.
This is the method of groups referred to above, and 57.

Sophus Lie.

applied by Sophus Lie to assemblages of continuously
variable quantities. Klein was one of the first to recog-
nise the power of this new instrument. He saw that
the space problem was a problem of transformations, the
possible motions in space forming a group with definite
elements (t]ie different freedoms of motion) which were
continuously variable — i.e., in infinitesimal quantities —
and which returned into themselves under certain well-
defined conditions. They possessed, moreover, in the
maintenance of distance the algebraic property of in-

720

SCIENTIFIC THOUGHT.

variance. He also expressed some doubt regarding the
logical consistency of the assumptions of Helmholtz.
Sophus Lie undertook this investigation, and thus
brousht the log-ical side of the labours of Eiemann
and Helmholtz to a final conclusion.^ This is one of
the celebrated instances where the rigorous algebraical
methods have detected flaws in the more intuitional or
purely geometrical process, and extended our knowledge
of hidden possibilities.

But there is yet another branch of the great science
of number, form, and interdependence, the principles
and foundations of which had been handed down from
earlier ages, where the critical and sifting process of the
nineteenth century has led to an expansion and revolu-
tion of our fundamental ideas. Here also, as in so
many other directions, the movement begins with Gauss.
Hitherto I have spoken mainly of algebra or general
arithmetic, of geometry, of the connections of both in the

^ " Lie was early made aware by
Klein and his "program " that the
space problem belonged to the
theory of groups. . . . Ever since
1880 he had been pondering over
these questions ; he published his
views first in 1886 on the occasion
of the Berlin meeting of natural
philosophers. Helmholtz's concep-
tion was itself unconsciously (but
remarkably so, inasmuch as it
dates from 1868) one belonging to
the theory of groups, trying, as it
did, to characterise the groups of
the sixfold infinite motions in
space, which led to the three
geometries, in comparison with all
other groups. He did this by
fixing on the free mobility of rigid
bodies — i.e., on the existence of an
invariant between two points as

the only essential invariant. When
Lie took up this problem in prin-
ciple, as one belonging to the theory
of groups, he recognised that for
our space that part of the axiom of
monodromy was unnecessary which
added periodicity to the free mo-
bility round a fixed axis. . . .
The value of these investigations
lies mainly in this, that they permit
of our fixing for every kind of geo-
metry the most appropriate system
of axioms. . . . And they justly
received in the year 1897 the first
Lobatchevski prize awarded by the
Society of Kasan" (M. Nother,
'Math. Ann.,' vol. liii. p. 38). A
lucid exposition of Lie's work will
be found in Mr B. Russell's ' Essay,'
&c., p. 47 sqq.

DEVELOPMENT OF MATHEMATICAL THOUGHT. 721

theory of forms and functions : there remains the science

of numbers — of number in the abstract and also of the ss.

Theory of

named numbers of ordinary arithmetic. Gauss's earliest numbers.
labours were connected with this branch. Superseding
the work of Fermat, Euler, and Legendre, he produced
that great book with seven seals, the ' Disquisitiones
Arithmetica?.' The seals were only gradually broken.
Lejeune Dirichlet did much in this way : others followed,
notably Prof. Dedekind, who published the lectures of
Dirichlet and added much of his own. The question
may be asked, Have we gained any new ideas about
numbers ?

In this abstract inquiry we can again facilitate our
survey by distinguishing between the practical and the
purely theoretical interests which stimulated it. Look-
ing at the matter as well as the formal treatment by
which it was rendered accessible, we may say Gauss not
only taught us some very remarkable new properties of
numbers^he also invented a new instrument or calculus
for their investigation. Let us consider his work and
that of his followers from these different points of view.

First, then, there were certain definite problems con-
nected with the properties of numbers which had been
handed down from antiquity. Such were the division of
the circle into equal parts by a ready geometrical con-
struction, the duplication of the cube, and the quad-
rature of the circle or the geometrical construction
of the number it} To the latter may be attached the

^ See above, vol. i. p. 181, note.
The student will find much in-
teresting matter referring to these
problems in Prof. Klein's little

volume entitled ' Famous Problems
in Elementary Geometry,' transl.
by Beman and Smith, Boston and
London, 1879. In it is also given

VOL. II. 2 Z

722 SCIENTIFIC THOUGHT.

properties of the number c, the basis of the Napierian or
natural logarithms, this number having been shown by
Euler to stand in a remarkable arithmetical relation to
the number tt — a relation which could be very simply
expressed if one had the courage to make use of the
imaginary unit. As in the instance referred to above,
when I dealt with the problem of the solution of the
higher order of equations, so also in the case of the three
celebrated problems now under review, the reasoning of
the mathematicians of the nineteenth century lay largely
in proving why these problems were insoluble or in
defining those special cases in which they were soluble.
Moreover, the labours of Gauss and the class of mathe-
maticians who followed or read him were dii'ected
towards the defining and fixing of general conceptions,
the study and elaboration of which embraced these single
problems as special cases. Prime numbers had always
been the object of special attention. Division and par-

an account of several mechanical the true septisection of the circle

contrivances for the solution of \ was so close that he could not

transcendental problems, or of those discover, up to the 7th decimal,

where the use of the compass and whether the error was in the direc-

ihe ruler do not suffice. Although , tion of more or less. On carrj-ing

accurate constructions with a ruler , the calculation further, he found the

and compass, or with either alone,
were known to the ancients only in

approximation to be such that a
heptagon stepped round a circle

comparatively small numbers, ap- i equal in size to the equator would
jiroximations, and sometimes very | reach the starting-point within 50
close ones, seem to have been | feet. The inventor or discoverer
known. A very interesting exam- of this method — Rober, an archi-
ple is Rober's construction of the tect of Dresden — supposed that it
regular heptagon, of which we read , was known to the ancient Egj'ptians,
in the correspondence of Sir W. R. and in some form or other con-
Hamilton with De Morgan (Life of I nected with the plans of the temple
Hamilton, by Graves, vol. iii. pp. at Edfu, but on this point I have
141, 5.34). and which was described \ obtained no information. The ques-
by him in the 'Phil. Mag.,' Feb- I tion is not referred to in Prof.
ruary 1864. The approximation to { Cantor's ' History of Mathematics.'
the correctly calculated figure of

DEVELOPxMENT OF MATHEMATICAL THOUGHT. 723

tition of numbers had been studied, and many interesting
formulce had been found by induction, and subsequently
proved — or not proved — by a multitude of ingenious
devices. As in so many other directions of research
so also here, the genius of Gauss gave a great impetus to 59.

' ® 001 Gauss's

progress by the invention of a definite calculus and an *^^"^°'
algorithm. This invention referred to the solution of ™*^^^-
what used to be known as indeterminate equations : to
find two or more numbers — notably integers, which obey
a certain algebraical relation. For one large class of
these problems (which already occupied the ancient
geometers), viz., those of the divisibility of one number
by another (called the modulus) with or without residue.
Gauss invented the conception and notation of a con-
gruence. Two numbers are congruent if when divided
by a certain number they leave the same remainder. " It
will be seen," says Henry Smith, " that the definition of
a congruence involves only one of the most elementary
arithmetical conceptions— that of the divisibility of one
number by another. But it expresses that conception
in a form so suggestive of analysis, so easily available in
calculation and so fertile in new results, that its introduc-
tion into arithmetic has proved a most important contri-
bution to the progress of the science."^ Notably the
analogy with ordinary algebraic equations and the possi-
bility of transferring the properties and treatment of
these was at once evident. It became a subject of

^ See Henry J. S. Smith in his : pp. 38-364). It gives a very lucid
most valuable ' Report on the ; account of the history of this de-
Theory of Numbers' (Brit. Assoc. , | partment of mathematical science
1859-65, six parts. Reprinted in ] up to the year 1863.
' Collected Math. Papers,' vol. i. j

724 SCIENTIFIC THOUGHT.

interest to determine the residues of the powers of
numbers. A number is said to be a quadratic, cubic,
or biquadratic residue of another (prime) numljer (the
modulus) if it is possible to find a square, cube, or bi-
quadratic number which is congruent with the first
number. The theory of congruences was a new calculus :
as such it was, like the theory of determinants or of in-
variants or the general theory of forms, a tactical device
for bringing order and simplicity into a vast region of
very complicated relations. Gauss himself wrote about it
late in life to Schumacher.^ " In general the position as
regards all such new calculi is this — that one cannot
attain by them anything that could not be done without
them : the advantage, however, is, that if such a cal-
culus corresponds to the innermost nature of frequent
wants, every one who assimilates it thoroughly is able —
without the unconscious inspiration of genius which no
one can command — to solve the respective problems,
yes, even to solve them mechanically in complicated
cases where genius itself becomes impotent. So it is
with the invention of algebra generally, so with the
differential calculus, so also — though in more restricted
regions — with Lagrange's calculus of variations, with
my calculus of congruences, and with Mobius's calculus.
Through such conceptions countless problems which
otherwise would remain isolated and require every time
(larger or smaller) efforts of inventive genius, are, as it
were, united into an organic whole." But a new calculus
frequently does more than this. In the course of its

^ See ' Briefwechsel,' &c., vol. iv. p. 147 ; also Gauss's ' Werke,' vol. viii.
p. 298.

DEVELOPMENT OF MATHEMATICAL THOUGHT. 725

application it may lead to a widening of ideas, to an
enlargement of views, to a removing of artificial and con-
ventional barriers of thought. As I stated early in this
chapter, the attempts of Gauss to prove the fundamental
theorem of algebra, that every equation has a root,
suggested to him the necessity of introducing complex
numbers ; the development of the theory of congruences
and of residues — notably of the higher residues — con-
firmed this necessity. In the year 1831, in his memoir
on biquadratic residues, he annovmces it as a matter of
fundamental importance. In the earlier memoir he had
treated this extension of the field of higher arithmetic
.as possible, but had reserved the full exposition. And
before he redeemed this promise the necessity of doing
so had been proved by Abel and Jacobi, who had created
the theory of elliptic functions, showing that the concep-
tion of a periodic function (such as the circular or har-
monic function) could be usefully extended into that
theory, if a double period— a real and an imaginary
■one — were introduced. A simplification similar to that
which this bold step led to in the symbolic represen-
tation of those higher transcendents, had been discovered
by Gauss to exist in the symbolical representation of
the theory of biquadratic residues which only by the
simultaneous use of the imaginary and the real unit
'" presented itself in its true simplicity and beauty." In
this theory it was necessary to introduce not only a posi-
tive and negative, but likewise a lateral system of count-
ing— i.e., to count not only in a line backwards and for-
wards, but also sideways in two directions, as Gauss
showed very plainly in the now familiar manner. At the

726

SCIENTIFIC THOUGHT.

60.
Generalised
conception
of number.

same time a metaphysical question presented itself — viz..
Can such an extension into more than two dimensions be
consistently and profitably carried out ? Gauss had satis-
fied himself that it could not ; ^ but the proof of this
was only given in more recent times by Weierstrass, who
definitely founded the whole discussion of the subject on
the logical principle " that the legitimacy of introducing
a number into arithmetic depends solely on the definition
of such number." And this leads me to another ex-
tension in the region of number suggested by Gauss's
treatment, which has also become fundamental, and, in
the hands of Dirichlet, Kummer, Liouville, Dedekind,
and others, has remodelled the entire science of higher
arithmetic. It is based on the logical process of the

^ A concise history of this sub-
ject is given by Kossak in the
Program referred to above, p.
712, note. Gauss had promised
to answer the question, " Why
the relations between things whicli
have a manifoldness of more than
two dimensions would not admit
of other " (than the ordinary com-
plex numbers introduced by him)
"fundamental quantities being in-
troduced into general arithmetic ? "
He never redeemed his promise.
In consequence of this, several
eminent mathematicians, notably
Hankel, Weierstrass, and Prof.
Dedekind, have attempted to reply
to this question, and to estab-
lish the correctness of the im-
plied thesis according to which
any system of higher complex
numbers becomes superfluous and
useless. Prof. Stolz, in the first
chapter of the second volume of his
'Allgemeine Arithmetik,' gives an
account of these several views,
which do not exactly coincide.
In general, however, the proof
given by Weierstrass, and first

published by Kossak, has been
adopted. This proof is based upon
the condition that the product of
several factors cannot disappear
excejit one of its factors is equal to
zero. "We must, therefore, ex-
elude from general arithmetic com-
plex numbers consisting of three
fundamental elements. This is,,
however, not necessary if the use of
them be limited " by some special
conditions (Kossak, loc. cit., p. 27).
In the course of the further de-
velopment of this matter Weier-
strass arrives at the fundamental
thesis " that the domain of the-
elementary operations in arithmetic
is exhausted by addition and multi-
plication, including the inverse-
operations of subtraction and
division." "There are," says
Weierstrass, "no other funda-
mental operations — at least it is
certain that no example is known
in analysis where, if an analytical
connection exists at all, this cannot
be analysed into and reduced to
those elementary operations" (p..
29).

DEVELOPMENT OF MATHEMATICAL THOUGHT. 727

inversion of operations in the most general manner. In
the direct process we build up algebraical formula} —
called equations or forms — by a combination of addition
and multiplication. We can omit subtraction and
division, as through the use of negative quantities and
fractions these are reduced to the former. Now, given
the most general algebraical equation or form, we can
search out and define the simple factors or forms into
which it can be split up, and these factors and their pro-
ducts we can take to serve as the definition of numbers.
The question then arises. What are the properties of ei.

Process of

numbers thus mversely defined ? and, secondly, Do these '"version.
numbers exhaust or cover the whole extent of number as
it is defined by the uses of practical life ? The answer
to the former question led to the introduction of complex
and subsequently of ideal numbers ; the discovery by
Liouville that the latter is not the case has led to
the conception of transcendental, i.e., non - algebraic,
numbers.

The idea of generalising the conception of number, by
arguing backward from the most general forms into
which ordinary numbers can be cast by the processes of
addition and multiplication, has led to a generalised
theory of numbers. Here, again, the principal object is
the question of the divisibility of such generalised
algebraical numbers and the generalised notion of
prime numbers — i.e., of prime factors into which such
numbers can be divided. Before the general theory
was attempted by Prof. Dedekind, Kronecker, and others,
the necessity of some extension in this direction had
already been discovered by the late Prof. Kummer of

728

SCIENTIFIC THOUGHT.

62.
Kummer's
ideal
numbers.

Berlin when dealing with a special problem. This was
no other than the celebrated problem of the division of
the circle into equal parts, which had been reduced by-
Gauss to an arithmetical question. Gauss had shown
that the accurate geometrical solution of this problem
depended on the solution of certain simple binomial
forms or equations. The study of such forms accord-
ingly became of special interest : it necessitated the
employment of the extended notion of number called by
Gauss that of complex numbers. Now it is one of the
fundamental laws in the theory of ordinary numbers that
every integer can be divided only in one way into prime
numbers. This law was found to break down at a
certain point if complex numbers were admitted. Rum-
mer, however, suggested that the anomaly disappeared if
we introduced along with the numbers he was dealing
with other numbers, which he termed ideal numbers —
i.e., if we considered these complex factors to be divisible
into other prime factors. The law of divisibility was
thus again restored to its supreme position. These
abstract researches led to the introduction of a very
useful conception — the conception not only of generalised
numbers, but also of a system (body, corpus, or region)
of nimibers ; ^ comprising all numbers which, by the

^ The idea of a clo.sed system or
domain of generalised numbers has
revolutionised the theory of num-
bers. Originally the theory of
numbers meant only the theory
of the common integers, excluding
complex numbers. Gauss, in the
introduction to the ' Disquisitiones,'
limits the doctrine in this way.
He excludes also the arithmetical
theories which are implied in

cyclotomy — i.e., the theorj' of the
division of the circle ; stating at
the .same time that the principles
of the latter depend on theories
of higher arithmetic. This con-
nection of algebraical problems
with the theory of numbers be-
came still more evident in the
labours of Gauss's successors —
Jacobi and Lejeune Dirichlet, and
was surprising to them. "The

DEVELOPMENT OF MATHEMATICAL THOUGHT.

V29

ordinary operations of arithmetic, can be formed out of
the units or elements we start with. Thus all rational
integers form a system ; we can compound them, but
also resolve them into their elements. Where we intro-
duce new elements or units we only arrive at cor-
rect laws if we are careful to cover the whole field or
system which is measured by the application of the
fundamental operations of arithmetic. Throughout all
our abstract reasoning it is the fundamental operations
which remain permanent and unaltered, — a rule which,

reason for this connection is now
completely cleared up. The theory
of algebraical numbers and Galois's
' theory of equations ' have their
common root in the general theory
of algebraical systems ; especi-
ally the theory of the system of
algebraical numbers has become
at the same time the most im-
portant province of the theory of
numbers. The merit of having laid
down the first beginnings of this
theory belongs again to Gauss.
He introduced complex numbers,
he formulated and solved the
problem of transferring the
theorems of the ordinarj' theory
of numbers, above all, the pro-
perties of divisibility and the re-
lation of congruence, to these
complex numbers. Through the
systematic and general develop-
ment of this idea,- — based upon the
far - reaching ideas of Kummer,- —
Dedekind and Kronecker suc-
ceeded in establishing the modern
theory of the system of algebraical
numbers " (Prof. Hilbert in the
preface to his " Theorie der Alge-
braischen Zahlkorper, " ' Bericht der
Math. Ver.,' vol. iv. p. 3). In the
further course of his remarks Prof.
Hilbert refers to the intimate con-
nection in which this general or
analytical theory of numbers
stands with other regions of

modern mathematical science, not-
ably the theory of functions. " We
thus see," he says, "how arith-
metic, the queen of mathematical
science, has conquered large do-
mains and has assumed the leader-
ship. That this was not done
earlier and more completely, seems
to me to depend on the fact
that the theory of numbei's has
only in quite recent times arrived
at maturity." He mentions the
spasmodic character which even
under the hands of Gauss the
progress of the science exhibited,
and says that this was characteristic
of the infancy of the science, which
has only in recent times entered
on a certain and continuous de-
velopment through the systematic
construction of the theory in ques-
tion. This systematic treatment
was given for the first time in the
last supplement to Dedekind's edi-
tion of Dirichlet's lectures (1894,
4th ed., p. 134). A very clear
account will also be found in Prof.
H. Weber's ' Lehrbuch der Algebra '
(vol. ii., 1896, p. 487, &c.) He
refers (p. 494) to the different
treatment which the subject has
received at the hands of its two
principal representatives — Prof.
Dedekind (1871 onwards) and Kron-
ecker (1882) — and tries to show
the connection of the two metliods.

'30

SCIENTIFIC THOUGHT.

63.
Modern
algebra.

64.
Algebraical
and trans-
cendental
numbers.

as we saw above, was vaguely foreshadowed by Peacock,
and expressly placed at the head of all mathematical
reasoning by Hermann Hankel. In passing it may also
be observed how the notion of a system of algebraical
numbers, which l^elong together as generated in certain
defined ways, prepares us for the introduction of that
general theory of groups which is destined to bring order
and unity into a very large section of scattered mathe-
matical reasoning. The great importance of this aspect
is clearly and comprehensively brought out in Prof. H.
Weber's Algebra. Nothing could better convince us of
the great change which has come over mathematical
thought in the latter half of the nineteenth century
than a comparison of Prof. Weber's Algebra with stand-
ard works on this subject published a generation earlier.

I have shown how the definition of alg-ebraical
nvmibers has led to an extension and generalisation of
the conception of number. Another question simultane-
ously presented itself, Does this extension cover the
whole field of numbers as we practically use them In
ordinary life ? The reply is in the negative. Practice
is richer than theory. Nor is it difficult to assign
the reason of this. Numbering is a process carried on
in practical life for two distinct purposes, which we
distinguish by the terms counting and measuring. Num-
bering must be made subservient to the purpose of
measuring. Thus difficulties arising out of this use of
numbers for measuring purposes presented themselves
early in the development of geometry in what are called
the incommensurable quantities : taking the side of a
square as ten, what is the number which measures the

DEVELOPMENT OF MATHEMATICAL THOUGHT. 731

diagonal ? Assume that we prolong the side of the square
indefinitely, we have a clear conception of the position
of the numbers 15, 20, 30, &c. ; but what is the exact
number corresponding to the length of the diagonal ?
This led to the invention of irrational numbers : it
became evident that by introducing the square root of
the number 2 we could accurately express the desired
number by an algebraical operation. But there are
other definite measurements in practical geometry which
do not present themselves in the form of straight lines,
such as the circumference of a circle with a given radius.
Can they, like irrational quantities, be expressed by
definite algebraical operations ? Practice had early in-
vented methods for finding such numbers by enclosing
them within narrower and narrower limits ; and an
arithmetical algorithm, the decimal fraction, was in-
vented which expressed the process in a compact and
easily intelligible form. Among these decimal fractions
there were those which were infinite — the first instances
of infinite series — progressing by a clearly defined rule
of succession of terms ; others there were which did not
show a rule of succession that could be easily grasped.
Much time was spent in devising methods for calculat-
ing and writing down, e.g., the decimals of the numbers
TT and c}

It will be seen from this very cursory reference to
the practical elements of mathematical thought how
the ideas or mental factors which we deal with and

' The transcendent nature of the
numbers e and it was first proved
by Hermite and Prof. Lindemann.
The proofs have been gradually

simplified. A lucid statement will
be found in Klein's ' Famous
Problems,' p. 49 sqq.

nieasurins.

732 SCIENTIFIC THOUGHT.

string together in mathematical reasoning are derived
from various and heterogeneous sources. We begin
65. with counting, then we introduce measuring; in both
and " cases we have definite elements or units which may
serve to express order or quantity or both, and we
have definite conventional operations ; then we have
symbols which may denote order or quantity or oper-
ation. With these devices we perform on paper
certain changes, and we get accustomed to use in-
discriminately these heterogeneous conceptions, arith-
metical, geometrical, algebraical — nay, even dynamical, as
when Newton introduced the conception of a fiow or
fluxion. As mathematics is an instrument for the
purpose of solving practical problems, skill in al-
ternately and promiscuously using these incongruous
methods goes a very long way. Geometrical, mechan-
ical evidence helps frequently where pure logic comes
to a standstill, and pure logic must help and correct
where apparent evidence might deceive us. Mathe-
matics and science generally have always progressed
by this alternate use of heterogeneous devices, and
will probably always do so. The straight line of pure
logic has but very meagre resources, and resourcefulness
is the soul of all progress. But though this may be
so in practice, there are two other interests which govern
scientific reasoning. There is the love of consistency and
accuracy, and of clean and transparent, as distinguished
from muddled and scamped, work. The latter leads
inevitably into serious errors and paradoxes, as the
great mathematicians, Gauss, Cauchy, Abel, pointed out
early in the century. Mathematics then frequently

DEVELOPMENT OF MATHEMATICAL THOUGHT.

733

exhibited the slovenliness of a man who talks at the
same time in more than one language, because he is
too negligent to arrange his thoughts clearly. Then
there come in the demands of the teacher who has
to introduce abstract and difficult subjects in a clear,
consistent, and simple manner, taking heed that with
the elements he does not introduce the sources of
future error. The same interest that led in ancient
times to the composition of the Elements of Euclid has
led, in the higher education of the nineteenth century,
beginning with the Ecole Poly technique and ending with
Weierstrass's famous courses of lectures at Berlin, to
a revision and recasting of the whole elementary frame-
work of mathematics. In the mean time the resource-
fulness in applied mathematical thought which ever
since the age of Newton has characterised the in-
dividual research of this country, has opened out new
vistas and afforded much material for critical siftings
and strict definitions. Both qualities were united in
the great mind of Gauss with a regrettable absence of
the love of teaching and the communicative faculty.
Like Newton's ' Principia,' his greatest works will
always remain great storehouses of thought ; while his
unpublished remains might be compared to the Queries
appended to the ' Opticks ' and to the ' Portsmouth
Papers.'

Several eminent mathematicians in France, Germany,
and Italy have been for many years ^ working at the

' The literature of this sub-
ject has been rapidly increasing
since the year 1872, — the ap-
proximate date of the following

publications, which created an
epoch : R. Dedekind, ' Stetigkeit
und irrationale Zahleu ' (Braunsch-
weig, 1872) ; E. Heine, " Die

I

V34

SCIENTIFIC THOUGHT.

clearer enunciation of the fundamental conceptions of
the science, and though the ways in which they
approach the subject are different, a general consensus
seems to be within view as to the elementary definitions.
The main difficulty lies in the introduction into pure
arithmetic of the ideas which are forced upon us when

Elemente der Functionenlehre "
{' Journal fiir Mathematik,' vol.
Ixxiv. p. 172, 1872). This paper
refers both to Weierstrass's and
Cantor's theories ; H. Kossak, in
the pamphlet referred to above
(p. 7i2, note). This contains the
principles of Weierstrass's theory ;
C. H. Meray, ' Nouveau Precis
d' Analyse infinitesimale ' (Paris,
1872). The first comprehensive
publication of Georg Cantor be-
longs to the year 1883, ' Grund-
la^en eiiier allgemeinen Mannig-
faltigkeitslehre ' (Leipzig, Teub-
ner). It was preceded by various
articles in the ' Journal fiir Mathe-
matik,' vol. Ixxvii. p. 257, vol.
Ixxxiv. p. 82, aud| ' Math. Ann.,'
vol. XV. p. 1, in which he had in-
troduced and defined several of the
terms and conceptions that have
since become generally accepted in
writings on this subject. These
earlier publications, by — or refer-
ring to — the pioneers in this new
province of mathematical thought,
were followed by a number of
further expositions by Cantor,
Dedekind, and Weierstrass. The
principal writings of Cantor have
been republished in the ' Acta
Mathematica,' vol. ii. Prof. Dede-
kind published in the year 1888 an
important pamphlet, ' Was sind
und was sollen die Zahlen,' and has
incorporated many of the results of
his researches in his later editions
of Dirichlet's 'Lectures ' ; whilst the
lines of reasoning peculiar to Weier-

strass have become better known
through the writings of his pupils
and the collected edition of his
mathematical works which is now
in progress. A complete biblio-
graphy is given in three important
articles in vol. i. of the German
'Math. Encyc' by Profs. Schu-
bert (p. 1, &c.), Pringsheim (p.
48, &c.), and Schonflies (p. 184,
&c.) Important works, giving a
summary and analysis of these
various researches, now exist in
the mathematical and philosophical
literature of France, Germanj-,
Italy, and England. Like the non-
Euclidean geometry, the subject
has attracted considerable atten-
tion also outside purely mathe-
matical circles. Notably Cantor's
writings have been exhaustively
dealt with from a philosophical
point of view — in Germany by
Walter Brix (Wundt's ' Philoso-
phische Studien,' vol. v. p. 632,
vol. vi. p. 104 and 261), and by
B. Kerry, ' System einer Theorie
der Grenz-begriffe ' (Leipzig und
Wien, 1890) ; in France by M.
Louis Couturat, ' De I'lnfini ma-
thematique' (Paris, 1896); and
latterly in this country by Mr
Bertrand Kussell, ' The Principles
of Mathematics,' vol. i. (Cambridge,
1903). Italian mathematicians have
also dealt largely with the subject,
notably G. Peano, who published
an important work, ' Arithmetices
principia nova methodo exposita '
(Turin, 1889).

DEVELOPMENT OF MATHEMATICAL THOUGHT. 735

we apply the counting process to the needs of geometry
and physics. We are here confronted with notions
which require to be arithmetically defined — the in-
finite and the continuous. The same notions at the
beginning of the century attracted the attention of
eminent analysts like Cauchy. It is now clear, thanks
to the labours of Prof. Georar Cantor of Halle, that 66.

'^ Geor-Can-

for mathematical purposes we must distinguish between Qf''yjg*''*'°''y
the indefinitely great and the actually infinite in the ^'■'^'^'^""'te-
sense of the transfinite. To deal with the actually
infinite, as distinguished from the immeasurably or
indefinitely great, we have to introduce new notions and
a new vocabulary. For instance, in dealing with infinite
aggregates, the proposition that the part is always less
than the whole is not true. Infinities, indeed, differ,
but not according to the idea of greater and smaller, of
more or less, but according to their order, grade, or
power (in German Mdchtigkeit). Two infinities are
equal, or of the same power, if we can bring them into
a one-to-one correspondence. Prof. Cantor has shown
that the extended range of numbers termed algebraic
have tlie same power as the series of ordinary integers —
one, two, three, &c. — because we can establish a one-to-
one correspondence between the two series — i.e., we can
count them. He has further shown that if we suppose
all numbers arranged in a straight line, then in any
portion of this line, however small, there is an infinite
number of points which do not belong to a countable or
enumerable multitude. Thus the continuum of numeri-
cal values is not countable — it belongs to a different

736 SCIENTIFIC THOUGHT.

grade of infinity ; it has a higher, perhaps the second,
power/

In all these, and in many similar investigations, a
conception has gradually emerged which was foreign to
older mathematics, but which plays a great and useful
part in modern mathematical thought. Older mathe-
matics, ever since the introduction of general arithmetic
or algebra, centred in the conception of equality and in
the solution of equations. Everything was reduced to
magnitude. But there are other relations besides those
of magnitude, of more or less. Often in practical pur-
suits, if we cannot find k counterpart or write down
an exact numerical equation, we can gain information
67. by a correspondence. This conception of correspondence

Correspond- . .

ence. plays a great part m modern mathematics. It is the

fundamental notion in the science of order as dis-
tinguished from the science of magnitude. If older
mathematics were mostly dominated by the needs of
mensuration, modern mathematics are dominated by the
conception of order and arrangement. It may be that
this tendency of thought or direction of reasoning goes
hand in hand with the modern discovery in physics,
that the changes in nature depend not only or not so
much on the quantity of mass and energy as on their
distribution or arrangement.

With these reflections w^e touch the limits of mathe-

^ A summary of Prof. Cantor's i the different recent theories set

work is given by Prof. Schonflies
in the ' Eneyklop. Math. Wiss.,'
vol. i. p. 184 sqq. The importance
of accurate definitions and distinc-
tions regarding the infinite and
the continuous is dwelt on and

forth in a very lucid address to the
London Math. Society by Prof.
Hobson, " On the Infinite and In-
finitesimal in Mathematical Analy-
sis," November 1902.

DEVELOPMENT OF MATHEMATICAL THOUGHT. 737

matical thought and enter the region of metaphysics.
Like other lines of reasoning which have occupied us
in former chapters, the exact and rigid definitions and
deductions of arithmetic and geometry lead us up to
that other large department of our subject — philosophic
thought. Many eminent mathematicians of recent years
have noticed this tendency, and have urged the mutual
help which arithmetic and geometry on this side, logic
and psychology on that, may derive from each other.
The names of Helmholtz, Georg Cantor, and Dede-
kind in Germany ; of M. Tannery and M. Poincare in
France ; of Peano and Veronese in Italy, stand prom-
inently forward abroad ; while England can boast of hav-
ing cultivated, much earlier, by the hands of De Morgan
and Boole, a portion at least of this borderland, and of
having in recent years taken up the subject again in
an original and independent manner.^ Cayley, in his
address to the British Association in 1883, has said :
" Mathematics connect themselves on the one side with
common life and the physical sciences ; on the other

^ I refer to the imjjortant but
unfinished works of Mr Wliitehead
on ' Universal Algebra ' (vol. i.,
1898), and of Mr Bertrand Russell
on ' The Principles of Mathematics '
(vol. i., 1903). I must defer a
more detailed appreciation of these
and other writings of this class,
such as those of the late Prof.
Ernst Schroder (' Algebra der
Logik,' 3 vols., 1890-95) and of
Prof. Gottlob Frege (see an
account of his writings in the
appendix to Mr Russell's ' Prin-
ciples '). They belong largely to
a department of philosophical
thought which may be termed

VOL. XL

" the Philosophy of the Exact
Sciences." This deals with two
great questions — the logical found-
ations of scientific reasonmg, and
the general outcome and import-
ance of scientific thought, not for
technical purposes, but in the
great edifice of human thought
which we may term Philosophy.
It deals with what has been
called " the Creed of Science "
and its value. Stanley Jevons
and Prof. Karl Pearson in this
country, Prof. Mach in Germany,
and M. Poincare in France, have
treated the philosophy of science
in one or both of these aspects.

3 A

738 SCIENTIFIC THOUGHT.

side with philosophy in regard to our notions of space
and time, and in the questions which have arisen as
to the universality and necessity of the truths of
mathematics and the foundation of our knowledge of
them"; and he subsequently refers specially to the
" notion which is really the fundamental one under-
lying and pervading the whole of modern analysis and
geometry," meaning the complex magnitude, as deserv-
ing to be specially discussed by philosophers. Be-
ginnings of the philosophical treatment of this and
other questions indeed exist. The questions are still
suh judice, and the historian can merely refer to their
existence and importance.

There is, however, one controversy which has arisen
out of these and similar speculations, and out of the
desire to bring unity and consistency into the funda-
mental notions of elementary as well as higher mathe-
matics, which deserves to be specially mentioned, because
it occupies a prominent place in foreign literature, hav-
ing given rise to a special term, and thus commanding
more general attention. Prof. Klein of Gottingen, under
whose master-hand many abstract and obscure subjects
have become plain and transparent, has prominently
brought the subject before the scientific public in a
68. recent address.^ I refer to the tendency represented

Arithmetis-

ing tendency in its extreme form by the late Prof. Kronecker or

in niathe- "^

matics. Berlin, to reduce all mathematical conceptions to the
fundamental arithmetical operations with integral num-
bers, banishing not only all geometrical and dynamical
conceptions, such as those of continuity and flow, but

^ ' Ueber Arithmetisirung der Mathematik ' (Gbttingen, 1895).

DEVELOPMENT OF MATHEMATICAL THOUGHT. 739

also siich apparently algebraical notions as those of
irrational and complex quantities. This attempt is an
outcome of the school of Weierstrass, which has done
so much to banish vagueness and introduce precision
into modern text-books.

Opposed to this so-called arithmetising ^ tendency is
the equally emphatic view, strongly urged by the late
Prof. Paul Du Bois-Eeymond in his general theory of
Functions, that the separation of the operations of
counting and measuring is impossible, and, if it were
possible (as, since the publication of his work, the fuller
expositions of Kronecker and his followers have tried to
show that it is), would degrade mathematics to a mere
play with symbols.'^ He tries to show that such is philo-
sophically impossible, and finds a support for his view in
the historical genesis of the idea of irrational numbers in
the incommensurable magnitudes of Euclid and ancient
geometry. Prof. Klein in his address favours the
arithmetical tendency as destined to introduce logical

^ The term seems to have been
coined by Ki-onecker. See Prof.
Pringsheira in the ' Encyklop.
Math. Wiss.,' vol. i. p. 58, note 40.
Kronecker' s position is set forth
in Journal fiir Math., vol. ci. pp.
337-355, 1887.

^ "The separation of the con-
ception of number and of the
analytical symbols from the con-
ception of magnitude would reduce
analysis to a mere formal and
literal skeleton. It would degrade
this science, which in truth is a
natural science, although it only
admits the most general properties
of what we perceive into the domain
of its researches ultimately to the
rank of a mere play with symbols,
wherein arbitrary meanings would

be attached to the signs as if they
were the figures on the chessboard
or on playing-cards. However amus-
ing such a play might be, nay,
however useful for analytical pur-
poses the solution would be of the
jjroblem, — to follow up the rules of
the signs which emanated from the
conception of magnitude into their
last formal consequences, — such a
literal mathematics would soon
exhaust itself in fruitless efforts ;
whereas the science which Gauss
called with so much truth the
science of magnitude possesses an
inexhaustible source of new ma-
terial in the ever-increasing field
of actual perceptions," &c., &c.
(' Allgemeine Functionen-Theorie,'
1882, p. 54.)

740

SCIENTIFIC THOUGHT.

precision and consistency into the foundations of mathe-
matics, and everywhere to further the very necessary
process of critical sifting; but he denies that pure
logic can do all, and points to the valuable assistance
and suggestive power of geometrical construction and
representation.^ Most of my readers will no doubt
agree with this view. Indeed the perusal of the fore-
going chapters must have produced on their minds the
conviction that, so far as the advance of science and also
of mathematics is concerned, it largely depends upon
the introduction of different aspects leading to different
courses of reasoning. The unification of all of these
into one consistent and uncontradictory scheme, though
it remains a pious hope and far-off ideal, has not been
the prominent work of the nineteenth century. Eather,
wherever it has been attempted it has had a narrowing
effect, and has resulted in a distinct curtailment of the
great and increasing resources of Scientific Thought.

^ Prof. Klein summarises the
opinion which he holds as to the
present task of mathematical
science as follows : " Whilst I
everywhere demand the fullest
logical elaboration, I at the same
time emphasise that pari passti
with it the intuitive representation
of the subject should be furthered
in every possible manner. Mathe-
matical developments which have
their origin in intuition cannot
count as a firm possession of science
unless they have been reduced to a
strict logical form. On the other
side, the abstract statement of
logical relations cannot satisfy us
until their importance for every

form of representation has been
clearly demonstrated, so that we
recognise the manifold connections
in which the logical scheme stands
to other departments of knowledge
according to the field of application
which we select. I compare mathe-
matical science to a tree which
stretches its roots ever deeper into
the soil, and at the same time
expands its branches freely up-
wards. Are we to consider the
root or the branches as the more
important part ? The botanist will
tell us that the question is wrongly
put, and that the life of an organ-
ism consists in the interaction of
its various parts" {loc. cit., p. 91).

EETROSPECT AND PROSPECT.

In the foregoing chapters I have attempted to set forth
the chief conceptions which are contained in the scien-
tific literature of the nineteenth century. Upon these
the scientific work of that period has been founded or
they are the results to which its scientific reasoning
has led. The most important outcome of the scientific
work of the century does not lie in the region of
thought, but rather in that of practical application ;
and this I have only incidentally referred to. Only
in so far as it has reacted upon scientific thought, sug-
gesting or modifying scientific ideas, has it been necessary
to allude to it.

My readers who have so far accompanied me may be
struck by one feature which indeed is characteristic of
scientific thought. Our survey has presented such
thought as broken up into a series of different aspects ;
and although certain connections between these aspects
have been occasionally pointed out, no attempt has been
made to combine them into one comprehensive or united
view. The reason for this is to be found in the nature
of scientific thought itself, which, proceeding by a def-
inite method, starts from the great variety of phenomena
which surround us in time and space ; the only assump-

742 SCIENTIFIC THOUGHT.

tion which science is obliged to make being the inevitable

one that Nature is intelligible to the human mind, which

1. is the same as saying that we must assume the existence

Order and "^ °

Unity. of some kind of Order.

There exists, indeed, in the human mind a further
demand, which may l^e defined by saying that the con-
ception of order in Nature or of its intelligibility should
not be held merely as a formal iteration, but should be
expressed as a highest Unity by some term which conveys
to our minds something more than the idea of an empty
form. From this demand there have further arisen at
all times various attempts to give expression to the
ideas of unity, of simplicity, and of the significance of
the whole scheme of existence which we call Nature.
Such attempts do not form part of purely scientific
thought. They are speculations for which those prin-
ciples of science that are capable of exact enunciation
do not suffice. They have, indeed, frequently appeared in
the literature of the nineteenth century. But although
there are isolated cases where scientific authorities of the
first order have indulged in them, such authorities have,
as a rule, shown an increasing reluctance to deal with
fundamental questions or with principles which extend
beyond the limits of scientific thought. We have no
examples in the nineteenth century of such intellects as
those of Leibniz or Newton. However different these
two great thinkers of an earlier age may have been, they
had this in common, that for them the scientific and the
religious aspects were not only equally important, but
equally occupied their attention. The characteristic
difference was that Leibniz apparently strove after a

RETROSPECT AND PROSPECT. 743

unification of scientific and religious reasoning, frequently
to the disadvantage of both, whereas Newton kept them
so distinctly apart that his immortal scientific works
can be studied without any reference wliatever to his
theological writings.

The two positions represented by these two great
men — namely, the attempt on the one side to unify
or combine the scientific and the religious aspects, and
on the other to keep them apart or contrast them —
have, indeed, been adopted by many thinkers in the
course of our period ; but an attempt to do justice to
such problems has been more usually considered the
duty of philosophy par excellence. In the rare instances
in which scientific authorities of the first order have
ventured upon a solution of these problems, they have
stepped outside of the limits of scientific reasoning ;
having, as it were, attempted to occupy the more im-
partial if not more elevated position of judges who as-
sign to scientific reasoning its position and its value in
the connected whole of human thought and interests.^

Consistently with the division of thought which
underlies the present history, and which has been
explained in the third part of the Introduction, I
relegate the exposition of such theories to the second 2.

° ^ Philosophi-

part of this work, which deals with philosophical cai prob-
thought. The fact that in the course of the nineteenth
century there have still appeared scientific thinkers who
have not only attacked special scientific problems, but
also the great universal world -problem, may well be

1 Examples of this will be found mond, and of Gustav Theodor
in the writings of Andre Marie Fechner.
Ampere, of Emil Du Bois-Rey-

744 SCIENTIFIC THOUGHT.

noted as a connection, a bond of union, between those
two great realms of systematic thought which, for the
sake of convenience, I have kept apart in this historical
survey.

There are other features in the scientific thought
of the period, as it has become known to us, which
naturally lead up to a different treatment from that
which is peculiar to science. In almost every instance,
in following up the various aspects of scientific thought,
I have had to show how they have brought us to
problems which cannot be solved by the means which
we call scientific or exact; and in many instances I
have shown how the foremost scientific thinkers them-
selves have been led up to inquiries which they have
variously termed philosophical, metaphysical, logical, or
psychological. Such has notably been the case with
the ultimate conceptions of the atomic theory, of the
doctrine of energy, and, still more, with the concep-
tions which underlie the scientific treatment of the
phenomena of life and consciousness. The further we
have advanced from the simple mechanical conceptions
of motion and inertia or mass, into the phenomena
of the actual world of natural objects which exhibit
order, development, purpose, and consciousness, the more
we have been obliged to make use of terms not
capable of being defined by the simple categories of
exact or mathematical thought ; and with whatever
zeal some of the foremost thinkers have in the course
of the century attempted to express these more indefinite
conceptions in terms of mechanical science, they have
only partially succeeded, and have certainly failed in

RETEOSPECT AND PROSPECT. 745

banishing them from the scientific vocabulary. Such
conceptions have always crept in again, proving that
they are indispensable even to the purely scientific
comprehension or description of natural objects, or of
nature as a whole.

It is not surprising, therefore, that an independent
examination of the ultimate conceptions which science
makes use of, or which it evolves, should have been a
task which has occupied some of the greatest intellects
of our period, and that the problem arising from this
should form a fitting transition from the purely scientific
to the philosophical portion of this history.

Now, if we try to characterise in the briefest possible
manner the general problems which scientific thought as
a whole has definitely formulated and placed before the
philosophical thinker, there are two words which stand
out prominently as indicating the two grand and com-
plementary conceptions which either underlie all scien-
tific inquiry or result from it. The first of these has
already been stated. We saw that exact or scientific
thought assumes that there exists in Nature an in-
telligible Order. The closer definition of this order in
the so-called laws of the cosmos has to be ascertained
by experience, and has been the subject of the fore-
going narrative. The subject which remains for phil-
osophical discussion is not any special form of order,
but the fact that any kind of order exists at all, and
that it is accessible to the human intellect. Clearly
this is a question which affects Nature, the object, as
much as the human Intellect, the subject.

But if the idea of Order underlies all scientific thought,

^-

46 SCIENTIFIC THOUGHT.

standing as it were at the entrance of scientific reason-
ing, there is another idea which stands at the end of all
3. scientific thought. This is the idea of Unity in its
luty!"^"' most impressive form as Individuality. It remains over
as an ultimate empirical fact to which scientific reason-
ing advances, of equal importance with order.

These two conceptions of Order and Individuality
likewise govern the two great divisions under which
scientific thought has been studied by us — Physics and
Biology. After reviewing in the first three chapters
the characteristic attitudes taken up by the three lead-
ing nations in scientific thought, I entered upon the
four abstract conceptions — namely, Attraction, Atom-
ism, Kinetics, and Energy — which are capable of strict
mathematical definition, and which form the skeleton
or framework around or in which the sciences of
Astronomy, Dynamics, Physics, and Chemistry have
arranged their various doctrines. They serve together
to define more precisely the conception of the general
order of things, appropriately termed the Cosmos. In
the four chapters following upon these I dealt with
the different conceptions under which a comprehension,
not so much of the general order as of the special events
and things of our world, has been gained. These con-
ceptions, referring to the actual forms, the history, the
life and soul of things natural, have been likewise
dealt with in four chapters. On them the physics
of the universe and of our earth, the sciences dealing
with the organised and animated creations, have been
built up. Beginning with a special kind of order —
namely, that indicated by external figure — these sciences

RETROSPECT AND PROSPECT. 747

have advanced through the study of the changes of figure
to an increasing appreciation of an underlying unity.
In many of the organs of living creatures the unity
seems to lie outside the organs themselves, as the unity
of a machine which exists in the design of the maker
adapting it to a certain purpose ; whereas in the ani-
mated world it seems to be inside the objects of Nature.
The sciences of life have accordingly forced upon us
more and more the conception not only of orderly
arrangement, but also of a unifying principle — that
is. Individuality.

These two conceptions of Order and Individuality are
as little new as are the various conceptions of purely
scientific thought, most of which, as has been shown,
have been handed down to us from earlier times. They
have accordingly been defined and studied by phil-
osophers from antiquity. The various positions which
thinkers have taken up with regard to them during the
nineteenth century have, however, been characteristic
of the age, and have been very largely influenced
by the conceptions of Order and Unity which science
itself has elaborated. In this connection it is of
importance to note that the idea of Order or
arrangement has only within the nineteenth century
met with a comprehensive mathematical treatment ; and,
so far as that of Unity is concerned, it can also be
said that the mathematical sciences have in the course
of the nineteenth century for the first time approached
the analysis of the allied idea of Continuity, which
indeed plays an increasingly important part in many
scientific theories. It may even be held that the

748 SCIENTIFIC THOUGHT.

scientific mind advances from the idea of Order or
arrangement to that of Unity through the idea of
Continuity.

If, however, these highest conceptions had been intro-
duced to us by scientific thought in the form only
of hmiting ideas or highest abstractions, it is doubt-
ful whether the special discussion of them would have
attracted so much attention or occupied so many
minds as has actually been the case. In many in-
stances we found it to be quite sufficient for the pur-
poses of science that fundamental principles should
be dogmatically asserted, and that their usefulness
should be the only proof of their correctness. If
no other interest attached to the conceptions of order
and unity than attaches, for instance, to the ultimate
principles of dynamics, to atomism, or to the axioms
of geometry, the number of persons who take up
these refined studies would probably be exceedingly
small. The reason why the conceptions of order, unity,
and individuality have received so much attention lies
in this, that they have not only a logical meaning as
instruments of thought, but also, as the words them-
Practfcki ^^^^^^ indicate, a practical meaning, being bound up
IStechiugto ^^^^^ ^^^® highest ethical and sesthetical, as well as with
uLlty.''"'^ 01^1' social and religious, interests. The word order means
something more than arrangement when we speak of the
social or moral order ; the word unity is more than an
arithmetical conception when we speak of the unity of
action or of purpose, or the unity of design in art ; the
word individuality acquires a higher meaning in the
term personality. Those thinkers who in the nine-

RETROSPECT AND PROSPECT. 749

teenth century, as well as in former ages, have dealt
exhaustively with these the most abstract and highest
conceptions of which human thought is capable, have
not been, or have only very rarely been, led to their in-
quiries from the side of purely scientific interests ; they
have approached them with a full appreciation of the
great moral and religious interests which lie hidden in
the deeper significance which we attach to the words.
In starting, therefore, on the survey of philosophical
thought, it would be quite inadequate to take scientific
ideas as a suitable introduction. Whatever future ages
may bring, the philosophy of the nineteenth century has
certainly not been exclusively, or even pre-eminently,
scientific or exact. If philosophy has assumed the name
of a science, it has done so in that larger sense of the
word which, as we have seen, is peculiar to the Ger-
man language. In this connection scientific treatment
means simply methodical treatment, whereas there is an
increasing tendency in many circles to identify the word
science with exact mathematical or positive treatment.
The exact treatment of philosophical problems, such as
has been attempted but only very partially carried out
in the systems of Auguste Comte in France and of
Herbert Spencer in England, belongs almost entirely to
a later part of that century, and forms, even then, only
one side of its large philosophical literature. Philo-
sophical thought had a brilliant history in the earlier
part of the century before the ideas of Positivism or
of modern Evolution were much thought of. It will
therefore be necessary in any account of philosophical
thought to ascertain and clearly define the positions

750 SCIENTIFIC THOUGHT.

occupied by the great thinkers who governed and
revolutionised the thought of earlier generations before
the great generalisations of science, notably those con-
nected with the ideas of energy and the theory of descent,
could have had any influence whatever. Though the
latter have acquired in recent times a great, perhaps
an undue, importance, it will only be after becoming
acquainted with an earlier and different phase of philo-
sophic thought that we shall have once more to return
to those conceptions and trains of reasoning which must
be uppermost in the mind of the writer as well as of the
reader of the foregoing chapters.
5. But in starting on the historical account of an en-

Tlie geo-
graphical tirely different realm of thought, I shall not only have

centre of ° "^

thouTt'"'^ to ask my readers to enter into a new circle of ideas,
which for a long time during the course of the nineteenth
century lay entirely outside of that circle of ideas with
which we have become acquainted so far; we shall be
assisted also by finding an entirely different geographical
centre from which these ideas emanated. It has been
repeatedly pointed out that the great volume of scientific
thought with which we have hitherto been occupied,
emanated in the latter part of the eighteenth century
from the French capital ; and in the course of narration
I have had to go back almost in every single instance
to the foundations laid in French scientific literature.
I shall now have to invite my readers to give their
attention to the peculiar features which were charac-
teristic not of French but of German literature at
the end of the eighteenth and the beginning of the
nineteenth century.

RETROSPECT AND PROSPECT. 751

The centre of philosophical thought during the first
half of the nineteenth century lay as much in Germany
as the centre of scientific thought lay, somewhat earlier,
in France. It is true that in both cases, if we trace
the movement a little further back, we come upon the
powerful influences of English thought. Newton can
be considered as marking the beginning of the modern
era of scientific thought; Locke can be looked upon
as having infused into philosophic thought much of
its modern spirit. But though this must be conceded
to a large extent, it must also be admitted that
the scientific thought of the nineteenth century for
a long time received its special colouring through
the influence of the French mathematicians and
naturalists, with Laplace and Cuvier as their most
illustrious representatives ; while philosophical thought
for a long time received its specific colouring from
the idealistic movement which began with Kant and
culminated in Hegel. And although it was again
the specific influence of English thought which in
the latter part of the nineteenth century diverted
alike scientific and philosophical thought from the
channels in which they ran during the first half
of the century, we have only very partially emanci-
pated ourselves from the overwhelming influence which
the conceptions of the idealistic school of German
philosophy have had upon the deeper philosophical
thought of all three nations alike. The features
peculiar to that period are still strongly marked on
the philosophical countenance of the age : neither the
lights nor the shadows thrown by the great lumin-

752 SCIENTIFIC THOUGHT.

aries which appeared on the philosophical horizon of
Germany a century ago have as yet died away.

It will be the object of the second part of this work
to trace in more detail this powerful influence, to define
more clearly wherein it consisted, and to discover to
what extent it still survives or is mingled with other
influences, among which that which we have studied
exclusively in the first part of this history will prove
to have been one of the most important.

INDEX.

Abbe, Ernst, improvements in the
microscope, ii. 228, 229.

Abbe, Prof. Cleveland, method of least
squares, ii. 576.

Abel N. H., memoir by Bjerknes cited,
i. 184 ; investigations of, 185 ; and
Crelle, 186 ; on Gaii.ss, ii. 637 ; his
' Life ' by Bjerknes, ib. ; on Cauchy,
637 ; ou convergency, 646 ; his jjion-
eering work, 648 ; his relation to
Jacobi and Legeudre, ib. ; Sylow's
memorial of, 649 ; his addition the-
orem, 649 ; 657 ; theory of equations,
681, 686, 690, 692, 693, 695, 704, 732.

Abelard, i. 74.

Abraham, M., ' Geometrische Grund-
begriffe,' ii. 73.

Abria, experiments with vacuum tubes,
ii. 190.

Absolute, the, Cayley on, ii. 715.

Abstraction, process of, ii. 201.

Academic culture in France, i. 134.

Academie de Chirurgie, i. 107.

Academic des Sciences, i. 107.

Academie des Sciences morales et pol-
itiques, i. 145,

Academies, provincial, in France, i.
107.

Academy of Saxony founded, i. 100.

Academy of St Petersburg founded,
i. 100.

Academy of Vienna founded, i. 100.

Academy, Paris, organisation and co-
operation of members of, i. 99.

Achenbach, i. 165.

Achenwall, Gottfried, the " father " of
statistics, ii. 555.

Acland, Sir Thomas Dyke, ' Chemistry
of Farming, ' i. 284.

Acoustics, ii. 12, 485.

VOL. II.

Adams discovers Neptune, i. 277 ;
lunar theory, 329.

Adare, Count, i. 106.

Adrain, law of error, ii. 576.

^Etiology, Huxley's definition of, i. 194.

Affinity, chemical, neglect of the study
of, i. 420 ; chemical, ii. 157, 267.

Agassiz on fossil fishes, ii. 257 ; "Essay
on Classification," 349.

Agnosticism, ii. 326.

Airy and Herschel, article in ' En-
cyclopsedia Metropolitana,' i. 236.

Airy, Sir George Biddell, worked in har-
mony with the Analytical Society,
i. 271 ; the discovery of Neptune,
277 ; measurement of an arc of
loarallel, 322 ; calculus of probabili-
ties, 325 ; Tides, 330.

Akin, ii. 107.

Albrecht, Eugen, ' Vorfragen der Bio-
logic,' ii. 463.

Alexander the Great, Napoleon com-
pared with, i. 153.

Alexander VI., Pope, and the Univer-
sity of Aberdeen, i. 268.

Alison, W. P., i. 272.

Allen, Grant, monograph on Darwin
quoted, ii. 607; on "pangenesis,"
610.

Altmann, theory of " bioblasts," ii. 427,

444.
America, influence of, only touched
upon, i. 14; declaration of Independ-
ence, 79.
Amici, embryological studies, ii. 227 ;
improvements in microscope, 228 ;
230, 261.
Ampere, A. M., on electro-magnetism,
i. 92 ; "mechanical theory of gases,"
310 ; 313 ; electric currents, 347, 367 ;

3 B

754

INDEX.

develops astronomical view of na-
ture, 366 ; 368, 370, 371 ; import-
ance of his discoveries, 372 ; chem-
ical discovery of, 408 ; Avogadro's
hypothesis, 427 ; ' Essai siir la Phil-
osophic des Sciences,' ii. 5, 205 ;
requested Fresnel to write his
' Mi-moire sur la Diffraction,' 25 ; sug-
gested transverse vibrations to explain
polarisation of light, 26 ; equation of
wave surface, 42 ; Lord Kelvin on
electro-magnetic theory of, 73 ; re-
ferred to, 78 ; electrical formulse of,
79 ; researches of, 92 ; theory of, 143 ;
193, 698 ; on oscillating functions,
706, 742.
Amyntas, King of Macedonia, ii. 207.
Anabolism, ii. 395, 442.
Analogies, studies of, ii. 250 ; physical,

Klein on, 701.
Analytical Society of Cambridge, i. 271.
Auchersen, J. P., statistics, ii. 579.
Andrews, Thomas, "critical tempera-
ture " of gases, i. 316 ; experimental
work of, ii. 161 ; 'Scientific Papers'
of, 162 ; 164.
Angle, trisection of the, ii. 124.
Angstrom, spectrum analysis, ii. 278.
Anhalt - Dessau, Princess of, letters

from Euler to, ii. 7.
Anharmonic ratio, ii. 718.
Anilin colours, discovery of, i. 92.
'Annales de Chimie et de Physique,'

i. 236, ii. 25, 54.
Anthropology, ii. 497.
Apologetic literature in England, ii.

324.
Appelt, i. 209.

Arago, letter from Young to, i. 230 ;
' Annales de Chimie et de Physique,'
236 ; and Fresnel, 241 ; eloges of,
279 ; his appreciation of the labours
of Fresnel, ii. 21 ; views on " sided-
ness" of rays of light, 24 ; requested
Fresnel to write his ' Memoire sur la
Diffraction,' 25 ; never accepted theory
of transverse vibrations, 26 ; visit to
England, 27, ; property of polarised
light, 28 ; Eloge on Carnot the elder,
138 ; 506.
" Arbeitskraft, " term used by Helm-

holtz, ii. 140.
Archimedes quoted, ii. 376.
Arfvedson, chemist, i. 188.
Argand, geometrical representation of
imaginary quantities, i. 184 ; on im-
aginaries, ii. 653.
Argon discovered, i. 423.
Aristotle, constructive system of, i. 75 ;

his works models of scientific re-
search, 95 ; 120 ; philosophy in
English universities represented by,
254 ; views of Heraclitus, ii. 3 ; 4,
207 ; analogies of nature, 255, 349 ;
grammar and logic, 629.
Arithmetic, fundamental laws of, ii.

654 ; 703.
Arithmetising tendency, Klein and P.
Du Bois-Reymond on, ii. 738 et seq.
Armstrong, Lord, hydro - electric ma-
chine : electrical discharge, ii. 191.
Arnold, Matthew, introduced new words
into English, i. 22 ; on German cul-
ture, 225 ; ' Literary Influence of Aca-
demies,' 298.
AronTiold on invariants, ii. 684.
Arrhenius, Svante, theory of electro-
lytes, ii. 159, 165.
Art, German, not patronised by royalty,

i. 157.
Arundel collection of antiquities, i. 295.
Ascherson, ' Deutscher Universitats-Kal-

ender, i. 161.
Association, British, founded, i. 42.
Astronomical view of nature : cosmical,
molar, and molecular phenomena,
i. 348 ; developed by Ampere and
Weber, 366 ; opposition to, 381 ; in-
sufficiency of, ii. 96.
' Athenffium ' of Schlegel, i. 84.
Athens under Pericles, i. 67 ; the

schools of, 74.
Atom and molecule, i. 432 ; size of,

437.
Atomic theory (see Dalton), i. 385 ; two
aspects of, 415 ; development of, 431 ;
accepted, 437 ; crystallographic laws,
analogy between, 444 ; linkage, 449 ;
defects and insufficiency of, 461 ; ii.
574.
Atomic view of nature, i. 382 ; criti-
cisms of, 455 ; insufficiency of, ii.
96 ; recent triumphs of, 188.
Atomism, ii. 465.
Atoms, geometrical arrangement of, i.

441.
Attraction, ii. 465.
Attraction and repulsion, i. 342.
Attraction of ellipsoids, ii. 670.
Aubuisson, d', ii. 294.
Aucoc, Leon, 'L'Institut de France,' i.

90, 127, 148, 149.
Auerbach, modern era in history of

fertilisation, ii. 227.
Autenrieth, ii. 349.

"Availability," idea of, introduced by
Carnot, ii. 119 ; 597. See also Kelvin,
Lord.

INDEX.

755

Averages, doctrine of, i. 440 ; ii. 561.
Avogadro, "mechanical theory of

gases," i. 310 ; 313 ; law of, 4i5, ii.

165, 592 ; hypothesis of, i. 427 ; 428 ;

hypothesis of, revived by Cauuiz-

zaro, 445.

Babbage, Charles, i. 18 ; ' Decline of
Science in England,' 127 ; history of
his calculating engine, 248 ; educa-
tional movement begun by, 261 ;
formed the Analytical Society, 271 :
criticisms of science in Britain, 233 ;
236 ; Prof. Moll's reply to, ib. ;
English replies to, 238 ; not a univer-
sity man, '^39 ; ii. 2,17.
Babeuf, co-operation, ii. 566.

Baeharach, 14istoryof Potential Theory,
ii. 698 ; on Klein's Tract, 699.

Bacon, Lord, his influence on the
Encyclopedists, i. 34 ; his interpre-
tation of the word "science," 90;
unscientific, 93 ; his philosophical
status, 94, 311 ; and Newton com-
pared, 96 ; influence in new Univer-
sity of Halle, 160 ; 215 ; schemes ol', re-
alised by the 'Encyclopedie,'&c., 250;
appreciated educational work of the
" Order of Jesus," 256 ; Harvey, and
Napier, 282 ; on the study of natural
phenomena, 285 ; 311 ; his philos-
ophy, 385 ; system of philosophy, ii.
205, 344; " method of instances,"
557.

Bacon, Roger, i. 249, 403.

Baconian philosophy, decay of, i. 306.

Badeu-Powell, radiant heat, ii. 105 ;
apologetic writings, 327.

Baer, Karl Ernst von, his opinion on
the Naturphilosophie, i. 207 ; em-
bryologist, ii. 278 ; his labours, 299 ;
quoted, 307, 417 ; Lamarck and, 316 et
seq. ; Huxley on, 322 ; genetic view
in embryology, 330 ; 341 ; law of
biogenesis, 349 ; and Schelling, 354 ;
idea of life, 409 ; embryological re-
searches, 418; on "diffusion of life,"
451; " organicism," 455; 467, 533,
607. ■

Bagehot, Walter, quoted, ii. 558.

Bailie, Matthew, English medical
science, i. 208.

Bailly guillotined, i. 147.

Baily on Greenwich Observatory and
the Rev. J. Flamsteed, i. 98.

Bain, 'The Senses and the Intellect,' ii.
511; 512: on psychology, 527 ; 608.

Baker, H. F., on differential equations,
ii. 692.

Balbi, ii. 579.

Balfour, Francis M., organic mor-
phology, ii. 214 ; 349.

Ball, Sir R. S., 'Gravitation,' i, 320;
memoir of Helmholtz, ii. 63 ; geo-
metrical mechanics, 10 1; his theory
of screws, 655 ; on Grassmann,
656 ; on generalised notion of dis-
tance, 718.

Ball, W. Rouse, 'A History of the
Study of Mathematics at Cambridge,'
i. 275, 321 ; history of mathematics,
ii. 680.

Banks, Sir Joseph, i. 83, 155 ; travels
of, ii. 247.

Barenbach, ' Herder als Vorganger Dar-
wins,' ii. 533.

Biirenspruug, von, medical thermom-
etry, ii. 389.

Bariire, foundation of Ecoles normales
proposed, &c., i. 112.

Barlow, not member of any university,
i. 239.

Barry, Martin, embryological observa-
tions, ii. 227, 228.

Bartels, friend of Gauss, ii. 653.

Barthez, vitalist, i. r26.

Barycentric Calculus of Mtibius, ii.
655, 681.

Basedow, " philanthropinism," i. 166;
educational work of, 256 ; 257 ; was
inspired by Rousseau, 259.

Bates, H. W., "mimicry," ii. 339.

Bateson, William, 'Materials for the
Study of Variations,' ii. 364; study
of variation, 614 ; 622 ; and Karl
Pearson, 6i!3 ; agrees with Huxley
against Darwin, 623.

Bathybius, ii. 3S8.

Bauer, G., on Otto Hesse, Ii. 677.

Baumes, J. P. T., ' Essai d'uu systeme
chimique de la science de I'homme,'
ii. 390.

Baumgartner, i. 44 ; printed Mohr's
' Ueber die Natur der Warme,' ii. 107.

Baumhauer, ii. 565.

Baur, ii. 109.

Bavaria, Elector of, and Count Rum-
ford, i. 248.

Bayes, ii. 572.

Bayle, value of work of, i. 93 ; followed
Newton, 96 ; French medical science,
208.

Bayne, Peter, ' Life and Letters of Hugh
Miller,' i. 2^8.

Beaumont, Elie de, doctrine of descent,
ii. 322.

Becker, G. F., on Kant's theory, ii.
282 ; 284.

756

INDEX.

Becker on mortality statistics, ii. 566.

Becqiierel, E., phenomenon of fluor-
escence, ii. 52.

Bedson, Prof., ' Memorial Lecture ' on
Lothar Meyer, i. 427.

Beer, physics, i. 44 ; ' Einleitung in
die Elektrostatik,' ii. 76.

Bell, Henry, built the "Comet," i. 303.

Bell, John, i. 293.

Bell, Sir Charles, discovery of the two
kinds of nerves, i. 193, 292, 293 ; ii.
481 ; physiological discovery of, 230 ;
and German universities, i. 251 ; of
Edinburgh University, 272 ; Bridge-
water Treatise, ii. 325 ; experimental
physiology, 384 ; ' Anatomy of Ex-
j>ression,' 477.

Bell, Sir Lowthian, phosphorus as fer-
tiliser, i. 93.

Beltrami, the pseudosphere, ii. 635 ;
supplements Riemann's work, 713 ;

717.

Bence Jones, 'Life and Letters of Fara-
day,' i. 246 ; Royal Institution, 246,
248.

Beneden, Van, on fertilisation, ii. 227 ;
discovery of, 448.

Beneke, psychologist, influenced by
school of Fries, i. 209; "faculty-
psychology," ii. 495 ; introspective
method, 527.

Benfey, Theodor, ' Geschichte der
Sprachwissenschaft,' ii. 245, 537.

Beutham, Jeremy, school of, i. 84.

Beutley, Richard, i. 169 ; influence of,
on German thought and literature,
212 ; services to classical learning
and criticism, 222 ; his theories, 251 ;
Newton's philosophy and atheism,
337 ; Newton's letter to, 340.

Bergmaun, i. 117 ; forerunner of Ber-
zelius, 391 ; doctrine of chemical
affinities, 392 ; theory of chemical
affinity, 452 ; chemical theory of, ii.
176.

Berkeley, and Hume, i. 47 ; ' Theory of
Vision,' ii. 472; space perception,
504 ; genetic view, 506 ; psycho-
physical view, 531.

Berlin Academy, language, ii. 536,

Berlin, foundation of University of, i.
38.

Berlin school of mathematicians, ii. 693.

Bernard, Claude, "Association Fran-
9aise," i. 298; on identity of Animal
and Vegetable Morphology, ii. 219 ;
quoted, 223, 410 ; ' Phenomenes de la
Vie ' quoted, 224, 239, 370, 438 ; De
Blainville, 247 ; ' La Science Experi-

mentale ' quoted, 373, 376, 379, 384,
385, 386 ; change of ideas in medical
schools of Paris, 396 ; 406, 409 ;
'Rapport,' 419; "organisation et
desorganisation," 421; 'Rapport'
quoted, 426 ; 429 ; school of, 431 ;
the "internal medium," 432; chem-
istry of the living being, 433 ; school
of " organicists," 436; rationale of
the mental process, 441; 442; "or-
ganicisme," 455, 467, 481, 504, 549 ;
quoted by Darwin, 610.
Bernard, Thomas, associated with Rum-
ford's philanthropic schemes, i. 249.
Bernoulli, Daniel, the theory of prob-
abilities, i. 120, ii. 570 ; i. 135 ; hypo-
thesis of, 314 ; on gravitation, quoted,
351; ' Hydrodynamica ' (the kinetic
theory of gases), 433 ; motion of par-
ticles of gaseous matter, 434 ; on
Euler's theory of the continuity of the
ether, ii. 8 ; psychophysics, 474 ;
572, 590, 694.
Bernoulli, James, took wp the calculus,
i. 101 ; the theory of probabilities,
120 ; ii. 569 ; ' De Arte conjectandi,'
570 ; 572 ; theory of error, 575 ; doc-
trine of chances, 678.
Bernoulli, John, took up the calculus,
i. 101 ; the conservation of energy,
ii. 99.
Bernstorif, Minister von, i. 158.
Berry, A., ' History of Astronomy,' ii.

282, 357, 362.
Berthelot quoted on crystallography, 1.
117; 'La Synthese chimique,' 418;
' Chimie organique fondee sur la Syn-
these,' 454 ; ' La Synthese chimique '
quoted, 455, 457 ; a founder of physi-
cal chemistry, ii. 152; third law in
thermo - chemistry, 157 ; chemical
affinity, 171, 177 ; quoted, 361 ;
chemistry of organic compounds, 425.
Berthollet issued ' Annales de Chimie,'
i. 41 ; ' Essai de Statique chimique,'
83, 116 ; chemistry at the Ecole nor-
male, 112 ; practical discoveries of,
147 ; gunpowder, iron, steel, 148 ;
152, 200 ; chemical saturation, 347 ;
influenced by Laplace, 380 ; chem-
ical equilibrium, 392 ; quoted, 416 ;
heat a material substance, 433 ;
theory of chemical affinity, 452 ; ii.
154 ; law of mass-action, 157 ; (see
Ostwald), 176.
Bertholon quoted, i. 327.
Bertin, M., ' Rapport sur le Progres
de la Thermodynamique en France,'

INDEX.

757

Bertrand, Joseph, quoted, i. 121, 134;
' Calcul des Probabilites,' 324 ; his
' Calcul difl'erentiel ' referred to, ii.
646.

Berzelius, Rej^orts, i. 42 ; chemistry, 44 ;
discoveries published, 83 ; services to
chemistry of, 188 ; biographical, 189 ;
' Jahresbericht,' 190; organic analy-
sis, 190 ; 191 ; influence on German
science, 208 ; mechanical view in bi-
ology, 219 ; 220, 238 ; experimentally
proved Dalton's atomic theory, 245;
and Faraday, 365 ; electrical action
in chemical processes, 366 ; chemical
combinations, 396 ; elaborated Dal-
ton's theory, 399 ; 400 ; disproves
Prout's hypothesis, 402 ; 403 ; electro-
chemical theory, 404 ; organic chem-
istry, 4(17; 409; " radicle " theory,
411 ; death of the binary theory, 412 ;
413, 414 ; atomic theory, 416, 417 ;
426 ; characteristic of hydrogen
atoms, 430 ; theories of chemical
affinity, 452 ; ii. 154 ; chemical re-
search, 159, 403.

Bessel, Friedr. vVilh., services to as-
tronomy of, i. 177 ; corresjiondence
with Gauss, 185, ii. 6.52 ; i. 199 ;
measurements of, 322 ; taught at
Kcinigsberg, with Neumann and Eich-
elot, ii. 54 ; popular work of, 149 ;
on Gauss, 636 ; functions of, 696.

Bessel-Sellmeier hypothesis, ii. 54.

Beuth founded industrial schools in
Prussia, i. 166.

Beverwijck, i. 282.

Bewick, wood engraver, ' British Birds, '
i. 289.

Bichat, works of, i. 83 : not amoug the
academicians, 126 ; biological labours
of, 194, ii. 313 ; i. 195, 2U0 ; morpho-
logical study of natural objects, ii.
231 ; the science of biology, 381 ;
"Vitalism," 383, 384; 386, 387; on
life, 394 ; doctrine of energy, 399 ;
402 ; quoted, 406 ; school of " orgaui-
cism," 436 ; vital force, 503.

Billroth, Prof., ' Lehren und Lernen der
medicinischeu Wissenschaften,' i. 197;
198 ; influence of English science on
medical studies in Germany, 208 ;
quoted on services of Kant to Ger-
man science, 219.

Biogenesis, ii. 451.

Biology a German science, i. 193 ; grew
out of science and philosophy com-
bined, 216 ; essential unity of sciences
of, not yet recognised in Germany,
220 ; British contributions to, 232 ; ii.

208, 312 ; vagueness of theories of,
370 ; oscillation of thought, 374 ;
415.
Biot, experimental physics, 1. 44, 200 ;
fall of stones at I'Aigle, 328 ; his dis-
covery, 431 ; opposed to undulatory
theory of light, ii. 16, 21 ; member
of Commission of Paris Academy of
Sciences competition, 1819, 25 ;
"laterality," 27 ; influenced German
thought, 101 ; 193, 508.

Biran, Maine de, ' Menioire sur I'habi-
tude,' i. 83.

Bischoft', Theod., embryology, ii. 227 ;
300 ; quoted, 381, 387 ; address on
Liebig, 391.

Bjerknes, A., on Abel, i. 184, 185, ii. 637.

Black, Joseph, discovered carbonic acid,
i. 115 ; on latent heat, 229, 399, ii,
102 ; Scottish university professor, i.
272; and Lavoisier, 386, 387; 391,
400 ; formula! of, 4.36 ; biographical,
ii. 102 ; attitude to science that of a
medical man, ln3.

' Blackwood's Edinburgh Magazine '
published, i. 273.

Blair, Hugh, i. 273.

Blennerhasset, Lady, on De Stael, i. 17.

Block, statistics, ii. 557, 563 ; quoted,
561, 566 ; ' Statistique morale,' 579.

Blomstrand, 'Die Chemieder Jetztzeit,'
i. 430.

Blumenbach of Gottingen University,
i. 165, 194, ii. 247; fossil collec-
tions, 248 ; influences Herder, 532.

Bcickh, science for its own sake, i. 211 ;
212 ; classical learning of, 222 ;
' Logos epitaphios ' on Wilhelm von
Humboldt quoted, 263.

Bode's law, i. 422.

Bodenhausen, i. 104.

Bodenstedt, ' Mirza Schafty,' i. 213.

Boehmer, Dr Heinrich, ' Gesch. d.
Entwick. d. Naturwissenschaftlichen
Weltanschauung in Deutschland,' ii.
531.

Boerhaave, i. 144, 175 ; and the medi-
cal schools of Germany, 208 ; 268 ;
atoms and viassulce, 398 ; epigenesis,
ii. 298.

Bohmer, "libertas docendi," i. 164.

Bohn, ii. 107.

Bohnenberger's gyroscopic instrument,
ii. 61.

Boileau referred to by Voltaire, i. 105.

Boltzmann, Ludwig, lectures on Max-
well's theories, i. 251 ; quoted, ii. 90 ;
176, 186, 188, 595; "availability,"
597.

758

INDEX.

Bolyai, i. 161 ; a pupil of Gauss, 181 ;
father and son, and Gauss, ii. 652 ;
710, 713.

Bolzano, Bernhard, on undulatory
theory of light, ii. 10 ; on the infinite
and couvergency, 709 ; and Cauchy
compared, ib.; Stol.^ on, ih.

Boniare, Valmont de, tirst course of
natural history at Paris, i. 106.

Bonald, De, on origin of language, i. 23.

Bond, Dr, ii. 565.

Bonnet, Charles, regular a,rrangement
of leaves, ii. 223 ; ' Echelle des
etres,' 238; "evolutionist," 278;
279 ; epigenesis, 298 ; 322, 519.

Bonnet, Ossian, ii. 704.

Boole, George, neglect of, in England,
i, 247 ; 272 ; and modern school of
mathematics, ii. 676 ; Stanley Jevous
on, 68-4.

Bopp, language, ii. 540, 542.

Borda, i. 113, 148.

Bordeu, vitalist, i. 126 ; vital force, ii.
503. ,

Borel, Emil, his lectures, ii. 704.

Borelli, medicine in alliance with
physics, i. 126.

Boscovich, Roger, theories of molecular
attraction and repulsion, i. 357 ;
metaphysical theorist, 371 ; 416 ; on
the nature of matter, 419 ; applica-
tion of theory of gravitation to mole-
cular physics, ii. 28 ; gravitation as a
general physical theory, 351.

Bossut, i. 107.

Bougainville, pupil of the Ecole nor-
male,i. 112; 113.

Boiiillier, M., quoted, i. 107, 108 ;
'Eloges de Fontenelle,' 135.

Boulton, use of the term "horse-
power," ii. 99.

Boussinesq quoted on transmission of
vibrations of ether to ponderable
bodies, ii. 54.

Boussingault, agricultural chemistry,
ii. 393 ; 406 ; bacteriological work,
415 ; quoted, 441.

Bowen, criticism of ' Vestiges,' ii. 319.

Boyle Lectures, Bentley's, i. 169.

Boyle, Hon. Robert, Newton to, i. 342 ;
and Lavoisier, 386 ; atoms and mass-
idce, 398 ; law of pressures, 425 ;
427 ; law of, 429 ; ii. 592.

Boys, Prof., determination of force of
gravitation, i. 320.

Bradley, i. 158 ; observations of, utilised
by Bessel, 177 ; 238 ; aberration of
light, ii. 10 ; astronomical aberration,
194.

Brandt, Sebastian, i. 163.

Braun, Alex., sjjiral theory, ii. 223 ; 268 ;

quoted, 269.
Bravais, 'Etudes crystallographiques,'

i. 443.
Breal, educationalist, ou Rousseau, i.

259 ; 260.
Brewster, Sir D., 'Life of Newton,'

i. 98, 321, 342 ; experiments of, 230 ;

quoted on foundation of suggested

"British Association," 238; never

adopted theories of Young, 244 ;

Scottish university professor, 272 ;

opposed to undulatory theory of

light, ii. 16 ; letter from Young, 27 ;

theory of undulations, 37 ; experi-
mental work of, 45 ; adherence to

projectile theory, 46 ; observed the

phenomenon of fluorescence, 52 ; 245 ;

criticism of ' Vestiges,' 319 ; 482 ;

stereoscope, 506.
Brianchon, ii. 660.
Bridgewater Treatises, ii. 324.
Briggs, Henry, ' Logarithmorum Chilias

prima,' i. 269.
Bright, i. 272.
Brill and Nother, ' Theory of Functions,'

i. 308 : ' Bericht ' quoted, ii. 657 ;

700, 701.
Brioschi and invariants, ii. 685.
Brisseau, a pioneer of the cellular

theory, ii. 262.
British Association, i. 42, 236 ; founded,

89, 238 ; suggested by Brewster, ib. ;

successful work of, 239 ; Sir Charles

Lyell on, 240 ; reports, ii. 54 ; 55, 58,

73 ; meeting, 163.
' British Quarterly Review ' quoted on

the two older universities, i. 254.
Brix, Walter, ii. 734.
Broca, .speech, ii. 478, 479, .539.
Brockhaus, 'Conversations-Lexicon,' i.

273.
Brodie, ii. 362.
Brongniart (see Cuvier), associated with

Cuvier in palajontological work, i.

139 ; excavations, ii. 248 ; exploration

of Paris basin, 294.
Bronn, translation of ' Origin of

Species,' ii. 322.
Brougham, Lord, unfair criticism of

Young, i. 244; ' Edinburgh Review,'

273; on Dr Young, ii. 9, 19.
Broussais, French medical science, i.

208 ; phrenology, ii. 477.
Brown, Crum, and Tait, Memoir of

Thomas Andrews, ii. 162 ; on Sainte

Claire Deville and "dissociation,"

163 ; 438.

INDEX.

759

Brown, John, i. 126.

Browu, Robert, used the term "cell," i.
195 ; scientific publications of, 230 ;
not member of any university, 238 ;
discovery of the cell nucleus, ii. 264 ;
338.

Brown, Thomas, ' Cause and Effect,' i.
84 ; ii. 511.

Browning, maturer thought of, i. 76.

Briiclce, i. 198 ; protoplasmic theory, ii.
443 ; language, 538.

Bruhns, 'Life of A. von Humboldt,'
i. 238, ii. 225, 253, 475.

Bruno, animation of all matter, ii.
369.

Brunswick, history of, ii. 280.

Bryan, Prof., second law of thermo-
dynamics, ii. 176 ; 595.

Bryce, James, quoted on German uni-
versities, i. 159.

Buache, geography at the Ecole uor-
male, i. 112 ; 113.

Buch, von, on descent, ii. 330.

BUchner, L., materialism, i. 60 ; 'Kraft
uud Stoff,' ii. 320 ; 323.

Buckland, Wm., i. 106; palseontologi-
cal work of, 139 ; ii. 325.

Buckle quoted, i. 114 ; statistical
method, 124 ; philosophy of, ii. 346 ;
statistics, 584, 599 ; 607, 608.

Buee on imaginaries, ii. 653.

Buffon, importance in French literature
of, i. 105 ; 283 ; intiuence of, on the
study of nature, 106 ; at the Jaidin
des Plantes, 107 ; philosoiihical in-
fluence of, 111 ; 113 ; discouraged
views of Linuaius in France, 117;
119, 131 ; natural history of, 126 ;
137, 142; 'Tlieorie de la Terre,'
144 ; 288 ; against Clairault's attempt
to correct gravitation formula, 334;
classification of natural objects, ii.
22,1 ; 232 ; analogies of nature, 255 ;
'Epoques de la Nature,' 277, 309;
322; "organic molecules,' 454, 610;
455 ; influences Herder, 532 ; 613.

Bunge, ' Physiological Chemistry '
quoted, ii. 378, 425, 426, 434.

Bunsen, Baron von, relative merits of
Young and Cliamx)ollion, i. 244 ;
' Egypit's Place in Universal History,'
245.

Bunsen, R. W. von, i. 412 ; ciesium
and rubidium, ii. 49 ; spectrum
analysis, 57.

Burali Forti, ii. 656.

Burbury, ii. 595.

Burckhardt, J. K., calculates orbit of
Ceres, i. 182 ; lunar theory, 329.

Burkhardt, H., on Ruftini, ii. 688 ; on

Riemann, 698, 700.
Burnet, Thomas, i. 283.
Burnett, James. See Lord Monboddo.
Burns, healthy spirit of, i. 78 ; 212,

285.
Burnside, his ' Theory of Groups,' ii.

691.
Butler, philosophy in English universi-
ties represented by, i. 254 ; apologetic

writings of, ii. 325.
Blitschli, on fertilisation, ii. 227 ; foam

theory, 427 ; ' Mechanismus und

Vitalismus,' 463.
Buys Ballot and Boscovich's theory,

i. 359 ; Doppler's principle proved in

acoustics, ii. 49.
Byron, revolutionary spirit of, i. 78.

Cabanis, alliance with medicine, i. 126 ;
127 ; ' Revolutions de la Medecine,'
135 ; 152 ; ' Rapports du Physique
et du Moral de I'Homme,' ii. 469;
his simile, 470, 503 ; science of man,
471 ; language and grammar, 530 ;
532.

CiBsalpinus, arrangement of leaves of
plants, ii. 223.

Cffisar, Napoleon compared with, i. 153.

Ctesium found by Kirchhoff and Bun-
sen, ii. 49.

Cailletet, condensation of piermanent
gases, i. 316.

Caloric, ii. 154.

Calvin, direct influence of, on Scotland,
i. 253 ; educational work of, 255.

'Cambridge Mathematical Journal,' i.
41.

Campbell and Garnett, ' Life of Clerk-
Maxwell,' ii. 599.

Campbell, H. .J., translation of Hert-
wig's 'The Cell,' ii. 265.

Campe, edition of 'Robinson Crusoe,'
i. 256 ; ii. 324.

Camper, ii. 247 ; collection of fossils,
248 ; physiognomy, 477 ; influences
Herder, 532.

Cannizzaro showed the value of Avo-
gadro's hypothesis, i. 427, 445.

Canton, M., history of mathematics, ii.
632 ; quoted, 633 ; 631, 680.

Cantor, G., on theory of probabilities,
i. 122 ; ii. 630 ; a new chapter in
mathematics, 634 ; 734 ; on the trans-
finite, 735, 737.

Capillary action, i. 356.

Carbon tetrahedron, the, i. 450.

Carlyle, influence of, on English style
and language, i. 22 ; first to give

760

INDEX.

specific meaning to the word Thouglit,
26; 'Life of Schiller,' 134; 171;
quoted, ii. 520 ; 528, 531, 608.

Carnot, Hippolyte, Sadi Carnot's ' Puiss-
ance Motrice,' ii. 118; referred to,
130.

Carnot, L. N. M., on correlation, ii.
100, 138, 658 ; Chasles on, ib.

Carnot, Sadi, valuable researches utilised
by Helmholtz, Thomson, and Joule,
i. 201 ; absolute scale of temperature,
315 ; the steam-engine, 331 ; mech-
anical theory of heat, ii. 105 ; prac-
tical character of his labours, 117 ;
' Puissance Motrice ' quoted, 118,
122 ; analogy between flow of water
and of heat, 122 ; heat theories,
123 ; perpetual motion, 124, 126 ;
and Joule, 128 ; dissipation of energy,
130 ; first definite use of new con-
ceptions of power and work, 137 ;
his theory refeiTed to, 139 ; second
law of thermo-dynamics, 175.

Carocher, i. 113.

Carpenter, labours of von Baer, ii. 302 ;
6U8.

Carruthers quoted on Hugh Miller,
i. 288.

Cartesian physical jjhilosophy, i. 433.

Carus, C. J., phrenology, ii. 477.

Cams, Victor, ' Geschichte der Zoologie,'
i. 130, ii. 213 ; comparative anatom-
ist, and the Naturphilosophie, i. 207 ;
' Geschichte der Zoologie ' quoted, ii.
220, 221, 230, 234, 237, 239, 260,
265 ; Goethe, Oken, and the genetic
view, 317.

Cassini, i. 107, 113; astronomical con-
stants, 322 ; the motion of light, ii.
10.

Catabolism, ii. 395, 442.

Cauchy, Augustin, mathematics and
physics, i. 45 ; 188 ; theories of elastic
forces in solid bodies, 360 ; properties
of ether, ii. 31, 33 ; theory of elasticity,
31, 41 ; molecular researches of, 43 ;
analytical method of, 45 ; referred to,
54 ; school of, referred to, 93, 1 00 ;
influenced German thought, 101 ; his
reforming influence, &c., 636 ; and
Gauss, 637 ; Abel on, ib.; Combes on,
ih.; his memoir on definite integrals,
639 ; Legendre on, ib. ; 640 ; his
' Cours d'Analyse ' quoted, 647 ; on
Poncelet's principle, 660; 680, 683,
690; and Eiemann, 693, 695, 697,
704, 706 ; 707, 732.

Cavendish, discovered hydrogen, i. 115 ;
155 ; scientific discoveries of, 229 ;

not member of any university, 238
important papers of, lost, 277
measurement of gravitation, 320
measurements of, 343 ; founded exact
science of electricity, 347 ; discoveries
of, 354 ; researches of, 363 ; and
Lavoisier, 386, 387; 391, 393;
chemical equivalents, 418 ; ii. 70.

Cavendish Society, 1. 43.

Cayley, Arthur, and PlUcker, 1. 242 ;
developed theories of Boole, 247 ;
doctrine of "invariants," ii. 140;
on mathematics, 631; on "Curve,"
' Encyclopffidia Britannica,' 641 ; on
"deficiency," ih.; on extended sys-
tem of numbers, 654 ; 670 ; geometry
and modern algebra, 671 ; 676, 684 ;
his great memoirs on Quantics, 684,
686, 691 ; on functions, 693 ; on
non-metrical relations, 713 ; on the
"Absolute," 715; on the "Imagin-
ary," 716.

Cell, autonomy of, ii. 395.

Cellular theory, i. 194 ; ii. 260, 417 ;
pathology, i. 195.

Celsus, medical works of, ii. 207.

Centralisation, ii. 524.

Century does not inherit all of the
past, i. 56 ; nineteenth, the scientific
century, 89.

Ceres, discovery and rediscovery of, i.
54, 82 ; discovery of, 423.

Challis and the discovery of Neptune,
i. 277.

Chambers, Robert, authorship of 'Ves-
tiges,'ii. 318; 320.

Chambers, Robert and William, publish
their Journal, i. 273.

Chambers's Encyclopedia, " Educa-
tion," i. 257 ; first published, 273.

Champollion, "hieroglyphics," i. 244.

Chances, science of, ii. 668.

Chaptal, practical discoveries of, i. 147.

Charcot, language, ii. 539.

Charles, and Gay - Lussac's law of
temperatures, i. 425, 429.

Charles, Duke of Wiirtemberg, i. 133.

Charles II. built Greenwich Observa-
tory, i. 98 ; ii. 562.

Chasles, Michel, quoted on Monge, i.
114 ; synthetic method of, ii. 100 ;
geometrical mechanics, 101 ; his 'Geo-
metric supevieure' quoted, 592, 658;
670 ; infinitely distant elements, 671 ;
brilliant writings of, 673 ; eclipses
German mathematicians, 673 ; 684,
685.

Chatelet, du, Madame, explained New-
ton to Voltaire, i. 106.

INDEX.

761

Chemical laboratories established, i.

188.
Chemical symbolism, i. 417 ; affinity,
neglect of the study of, 420 ; theory,
Kopp on, 421 ; and physical reason-
ing contrasted, 424 ; affinity, theories
of, 452 ; affinity, ii. 157.
' Chemie, Gehlen's Allgemeines Journal

fiir,' i. 41.
' Chemische Annalen,' Crell's, i. 41.

Chemistry, a French science, i. 114 ;
equivalents, 399 ; organic, 407 ; Lie-
big's definition of, 409 ; substitution,
ib. ; "type" theory, 411 ; uncertainty
about theory in middle of century,
413 ; periodic law, 422 ; structural
and stereo-chemistry, 447 ; change in
definition of, 454 ; ii. 389 ; change in
organic, 393.

Chenier, Marie - Joseph, Report on
French literature, i. 149.

Cherbuliez, E., ' Ueber einige physik-
alische Arbeiten Eulers,' ii. 8 ;
quoted, 46.

Cheselden, space -perception, ii. 473;
505.

Chesterfield's, Lord, Letters, quoted
from, i. 105.

Chevalier, Aug., Galois's letter to, ii.
686.

Chevenix, not member of any university,
i. 238.

Chevreul, ' Recherches sur les Corps
gras d'origine aniniale,' i. 454 ; ii. 406.

'Chimie, Annales de,' issued by Ber-
thollet, i. 41.

"Chirality" discovered by Pasteur, i.
431 ; origin and meaning of the word,
ii. 22 ; 437.

Chladni, ' Akustik,' i. 83; theory of
elasticity, ii. 31.

Chloral discovered by Liebig, i. 93.

Chloroform discovered by Liebig, i. 93.

Christiansen and Kundt, discovery of
anomalous dispersion of wave -motion,
ii. 53, 54.

Christie, not member of any imiversity,
i. 239.

Christison of Edinburgh University, i.
272.

Chronometers, i. 329.

Chrystal, G., PlLicker, and Faraday, i.
242; "John Napier, Baron of Mer-
chiston,' quoted, 269; on David
Gregory, 270; " Magnetism," ii. 75.

Church on the sjairal theory, ii. 224.

Cicero, ii. 523.

"Cinematique," the word introduced
by Ampere, ii. 5.

Circle, squaring of the, ii. 124 ; division
of the, 728.

Clairault followed Newton, i. 96 ; his
' Theorie de la Figure de la Terre,'
99 ; referred to by Voltaire, 106, 107 ;
mathematics made fashionable in
France, 237 ; Laplace and, 319 ;
lunar theory, 329 ; attempt to cor-
rect Newton's law, 334 ; capillary
attraction, 356, 378.

Clapeyron, i. 379 ; suggested earlier re-
searches of Clausius and Thomson, ii.

117 ; Caruot's ' Puissance Motrice,'

118 ; lieat and work, 123 ; biographi-
cal, ih.

Clark, J. W., and T. M'K. Hughes,
' Life and Letters of Adam Sedgwick,'
i. 267.

Clark, Latimer, " Weber " unit, i. 369.

Clarke, Newton's "descriptive and
calculating" philosophy, i. 337; let-
ter to Leibniz on gravitation quoted,
340.

Classics, foreign, superiority in nundjer
and quality of German translations
of, i. 213.

Classification, ii. 231.

Clausius, Rudolf, on atoms, i. 313 ;
"Entropy," 316, ii. 169, 181, 184,
594 ; the kinetic theory of gases, i.
433, ii. 34, 162 ; ' Die niechanische
Warmetheorie,' i. 434, ii. 163, 167 ;
" on the average mean path of a par-
ticle," i. 438 ; theoretical thermo-
dynamics, ii. 62 ; independence of
Mayer's writings, 97; "work" and
"energy," 115 ; unifies the views of
Mayer and the measurements of
Joule, 116; "conservation of en-
ergy," 128 ; "dissipation of energy,"
131 ; labours of, 133, 173 ; researches
of, 133 ; Prof. Uuwin's account of
theories of, 135 ; elaboration of Joule's
and Regnault's experiments, 137 ;
physical view of nature, 141 ; dyna-
mical theory of heat, 148 ; dissoci-
ation, 163; "free energy," 175 ;
heat, 178 ; theory of probabilities,
590 ; thermo-dynamics, 603.

Clavius quoted, ii. 287.

Clebsch, A., on Julius PlUcker, i. 242,
ii. 75, 76, 677.

Clifford, W. K., "axioms of geometry,"
i. 352 ; refiex action, ii. 520 ; " mind-
stutt"" theory, 546; criticism of Clerk-
Maxwell, 606, 608, 656 ; on Riemann,
704.

Cohu, quoted, ii. 559.

Colbert recognised the practical value

762

INDEX.

of science, i. 98 ; 134 ; first statisti-
cal bureau, ii. 5t)l.

Coldiiig, ii. 107, lu9 ; indestructibility
of force. 111, 125 ; heat, 112.

Coleridge imports philosophy of Kant
and Schelling into England, i. 17 ;
healthy spirit of, 78; ' Christabel,'

84 ; influence on metaphysical studies
of, 91 ; lectured at Royal Institution,
249, 264.

College de France, i. 107.

Colh'ge et iScole de Chirurgie, i. 107.

CoUignon (see Combes), ii. 101.

Collins, invention of the calculus by
Leibniz communicated to, i. 101.

Colour, ii. 484 et seq.

Combe, Geo., phrenology, ii. 477.

Combes, Phillips et Collignon, ' Expose
de la Situation de la M^canique ap-
pliquee,' ii. 101 ; quoted by Valson on
Cauchy, 637.

Combinatorial school in Germany, ii.
642 ; analysis, Leibniz, 679 ; Mac-
Mahon on, ib.

Combustion, theory of, i. 389.

Commutative principle, ii. 717.

Compayre, educationalist, on Rousseau,
i. 259, 260.

Complex quantity, ii. 643 ; interpreta-
tion of, 653.

Comte, Auguste, philosophy of, i. 18,
61, ii. 105 ; his three stages of
thought, i. 73 ; positivist theory of,

85 ; 306 ; ' Philosophie Positive,' 307,
308, ii. 37, 239 ; scientific errors of,
i. 310 ; opposed to undulatory theory
of light, ii. 37 ; and De Blainville,
247, 266 ; theory of probabilities, 569,
608 ; 749.

Comtism, failure of, i. 72.

Condamine, La, astronomical constants,
i. 322.

Condillac, 'Essai sur les Origines des
Counaissances humaines,'i. 144; ne-
glect of, by Napoleon, 149 ; his
ignorance of physiology, ii. 471 ;
language, 536.

Condorcet, importance in French litera-
ture of, i. 105 ; quoted, 110 ; educa-
tional work of, 112 ; the theory of
lirobabilities, 120 ; alliance with medi-
cine, 126 ; Academie des Sciences
morales et politiques, 145 ; suicide of,
147 ; neglect of, by Napoleon, 149 ;
distinguishes education and instruc-
tion, 259, 260 ; statistics, ii. 570, 573.

Conflict between the scientific and the
philosophical views, i. 205.

Conformal representation, Gauss and

Riemann on, ii. 700 ; Holtzmiiller

on, 701.
Congruences, theory of, ii. 723 ; calculus

of, 724.
Conrad, Prof., 'The German Universi-
ties for the last Fifty Years,' i. 159 ;

quoted on German universities, 160 ;

'Die Deutschen Universitaten,' 197,

198.
Conring, Hermann, statistics, 1. 121, ii.

555 ; political statistics, 562.
Consciousness, ii. 516.
Conservation of force, i. 218.
Constable, his influence on painting in

France, i. 19.
Constant, Benj., visits Germany with

Mme. de Stael, i. 17.
Continuity, of living forms, ii. 453 ; in

geometry, 660.
Contifiuous, the, ii. 643.
Convention, decree on Academy of, i.

148.
Convergency of series, ii. 646.
Conybeare, W. D., report on the jjro-

gress of geological science, ii. 281.
Cook, Captain, i. 52, 179 ; voyages, ii.

222 ; Von Baer on, 304.
Cooper, Astley, English medical science,

i. 2("i8 ; no connection with the English

universities, 272.
Co-operation, ii. 566.
Cope, E. D., ii. 271 ; neo-Lamarckian,

351.
Copernicus, i. 118 ; precursor of Kepler,

317 ; stimulated star - gazing, 327 ;

astronomical theory of, ii. 13.
Coriolis, St Veuant quoted on, i. 369 ;

practical school of, ii. 100.
Cornu, "Association Frau9aise," i. 298.
Correspondence in mathematics, ii.

736.
' Correspondenz, Monatliche,' Zach's, i.

41.
Corti, arcades of, ii. 372.
Cosmical view, ii. 369.
Cosmos, genesis of the, ii. 360.
Cossar Ewart on Jameson, i. 283.
"Cost" as factor in industry, ii. 155.
Coste, study of food fishes, ii. 232.
Cotes, Roger, ' Aestimatio errorum in

mixta mathesi,' i. 324; "description

and e-xplanation of phenomena," 337 ;

second edition of 'Principia,' 351;

preface to ' Principia ' misleading,

355.
Cotton, M. A., " Le Phenomene de

Zeemann," ii. 197.
Coulomb, measurements of, i. 343,

362, 368, 369 ; founded exact science

INDEX.

763

of electricity, 347 ; torsion balance,
360 ; attraction and repulsion of
electritied bodies, 361 ; 370 ; two-
fluid theory of electricity, ib.;
electro-static formula of, 371 ; Young
and, ii. 30 ; modern view of electrical
phenomena, 67 ; 7- ; referred to, 78,
92 ; laws of, 79 ; practical school of,
100 ; electrical theory of, 153 ; the
atomic view of nature, 188, 191,
193; 698.

Counting and measuring, ii. 732.

Couper, chemical researches of, i. 447.

Courcier, geometrical work of, i. 114.

(Journot, testimony to work of German
universities, i. 225.

Cousin guillotined, i. 147.

Cousin, Victor, testimony to work of
German universities, i. 225.

Couturat, L., ii. 734.

Cowley, Ode on Bacon, i. 96.

Cowper, 'The Task,' i. 285; Letters,
2S6.

Cramer, 'Analyse des lignes courbes,'
&c., ii. 682.

Crawford, Dr, influenced by Black's
lectures, ii. 102.

Crell's 'Chennsche Annalen,' i. 41.

Crelle's ' .Journal liir die reine und
angewandte Mathematik,' i. 41, 186,
ii. 58 ; correspondence with Gauss,
185.

Cremona, i. 188 ; quoted, ii. 665 ;
proves Steiner's theorems, 681.

Critical methods, ii. 626.

Crofton, M. W., "Probabilities," ii.
569.

Crome, Prof., statistics, ii. 579.

Cronsted, inventor of blow-pipe, i. 117.

Crookes, Sir William, quoted on Prout's
hypothesis, i. 403 ; sodium vapour
in the sun's atmosphere, ii. 48 ; ex-
periments and discoveries, 190 ; "cor-
puscular" theory of cathode rays,
192 : (see Sir Norman Lockyer), 361.

Cruveilhier, French medical science, i.
208.

Crystallographic and atomic laws, anal-
ogy between, i. 444.

Crystallography, i. 116, 441.

Crystals, laws of formation of, Haliy's,
i. 117 ; ii. 222.

Cullen, metaphysical leaning in medi-
cine, i. 126 ; 272.

Culverwell, ii. 595.

Curie, geometrical treatment of crystal-
lography, i. 443.

Currie, first use of thermometer at
bedside, ii. 388.

Curtius, Ernst, ' Alterthum und Gegen-
wart,' i. 215; on English archae-
ologists, 294 ; quoted, 295 ; on M. W.
Leake, 296.

Curves, degree, class, genus of, ii. 641.

Cuvier, Georges, scientific report of,
i. 42, 152, 1.54 ; ' Tableau ' and
'Le9ons,' 82; 112; on Priestley as
chemist, 115 ; on Haliy, 118 ; ad-
vance in study of organic life, 119 ;
services of, to practical science, 125 ;
126 ; Eloge of Halle, 127 ; ' Le Regne
animal,' 128 ; quoted, 129, 132, 141,
146, 147, 150, ii. 249 ; makes nervous
system of animals the basis of classi-
fication, i. 130 ; training of, 133 ;
description of the " Karlschule," 134;
the greatest representative of the aca-
demic system, 136 ; first great his-
torian of science, 137 ; quoted on
science and revolution ,138 ; palfeon-
tological work of, 139 ; Eloge of Four-
croy, 140 ; elementary scientific text-
books, 143 ; report of French Insti-
tute, 149 ; educational institutions,
155 ; 163, 171 ; mistrusted specu-
lative spirit in science, 178 ; his
ideas triumph over those of Geoffroy
St Hilaire, 179 ; 200 ; in praise of
French science, 231 ; quoted on
science in England, 235 ; 264 ; and
Brougniart, founders of palaiontology,
291 ; 306 ; depreciated by Comte,
310 ; zoological labours, ii. 222 ;
study of fossil remains, 225 ; ana-
tomical dissection, 232 ; zoological
work, 235 ; morphological and ana-
tomical study of animal life, 237 ;
classifications, 238, 239, 254; fos-
sils, 240; rejects idea of "Echelle
des etres," 243 ; controversy with
Geoft'roy, 246, 253 ; palaeontology,
247 ; "catastrophism," 250, 251 ; and
" theory of analogies," 254 ; the
question of the fixity of species,
256 ; comljats influence of Oken,
259 ; extension of morphological
view, 260, 266 ; influence of, 276 ;
'Ossemens fossiles,' 277 ; exploration
of Paris basin, 294 ; one-sided in-
fluence, of, 300, 301 ; and Buflbn,
309 ; Eloge <le Lamarck, 316; views
of Lamarck and Geoffroy, 320 ; and
Newton, contrasted with Darwin,
341 ; a founder of comparative an-
atomy, 386, 406; "vortex," 422;
751.

"Cyclical" view, ii. 286.

Cyclopaedia, Nichol's, i. 330, ii. 133.

764

INDEX.

Cyclopaedias, i. 273.

Cyriacus of Ancona, archseological
pioneer, i. 295.

Czapski, ' Theorie der optischen lustru-
mente nach Abbe,' ii. 14, 229.

Czermak, language, ii. 538.

Czuber, Emmanuel, theory of probabili-
ties, ii. 568 ; method of least squares,
576.

Dacier, Report on the progress of His-
tory and Classical Literature, i. 149.

Daguerre, photography, ii. 506.

Dahlmann, " theoretical politician," i.
311.

D'Alembert, contributions to the En-
cyclopedic, i. 34, 144 ; his import-
ance in French literature, 105 ;
theory of probabilities, 120 ; 215, 234,
237 ; the cure of smallpox, 284 ; 319 ;
mathematical study of vibrations, ii.
16 ; "measure of force," 'Traite de
Dynamique,' 100 ; statistics, 571 ; on
functions, 694.

Dallas, ii. 349.

Dalton, John, 'New System of Chem-
ical Philosophy,' i. 83 ; atomic theory,
189, 266, 385, 394, 415-417, 419, 425,
426, 428, ii. 180 ; scientific discov-
eries of, i. 229 ; not member of any
university, 238, 272 ; neglect of, in
England, 245 ; arithmetical mind of,
246 ; furnished texts for lectures
in German universities, 251 ; 265 ;
science of meteorology, 286 ; 298,
311, 313 ; heat a material substance,
433 ; formula of, 436 ; analogy be-
tween crystallographic and atomic
laws, 444 ; his atomic theory insuffi-
cient, 451 ; atomic theory referred to,
ii. 19, 20, 37, 95, 153, 154; colour
blindness, 505.

Dannecker educated with Cuvier, i.
133.

Dante, i. 261.

Danton, i. 107.

Darwin, Charles, constructive ideas of,
i. 81 ; eminence of writings of, 105 ;
179 ; letter from Sir Charles Lyell on
British Association, 240; theory of
descent, 201, ii. 321, 406 ; furnished
texts for lectures in German univer-
sities, i. 251, 310 ; ' Cirripedia' mon-
ograph, 283; 'Autobiography,' ih.;
nature - lover, 287 ; and Gilbert
White, 290 ; 297, 312 ; referred to,
ii. 136; value of his visits to distant
countries, 207 ; studies of organic
life, 209 ; law of descent, 214 ; con-

ceptions of, 246 ; and Owen, 267 ;
theory of pangenesis, 271, 454 ; writ-
ings of, 301, 306 ; 309 ; on Lamarck,
318; 'Origin of Species,' 326, 329;
'Life and Letters,' 328; and Mal-
thus, 331 ; ' Origin of Species ' quoted,
336; Bates's "Mimetic Butterflies,"
339 ; and Newton compared, 341
et seq. ; "natural selection," 351,
354 ; 434, 437 ; hybridisation, 373 ;
" final causes," 403 ; 408 ; struggle
for existence, 418 ; 421 ; environ-
ment, 430 ; conflict in nature, 431 ;
435, 436, 451 ; quoted, 457 ; and
Weismann, 460; 467, 470; 'Ex-
pression of Emotions,' 477 ; 511,
514 ; evolution, 530 ; and Herder's
evolutionism, 533 ; language, 540 ;
587, 607 ; variation in nature, 608 ;
on mental phenomena, 609 ; on " pan-
genesis," 610; 621 ; two novel points
of view of, 624.

Darwin, Erasmus, anticipated Lam-
arck, i. 201 ; 285 ; colour sensations,
ii. 482.

Darwin, Francis, ' Life and Letters of
Charles Darwin,' ii. 329.

Darwin, G. H., ' The Tides,' u. 282.

Darwin, Robert W., colour sensation,
ii. 482.

Darwinism, i. 251, ii. 386 ; and final
causes, 411 ; in Germany, 436.

Daubenton at the College de France,
i. 107 ; natural history at the Ecoles
normales, 112 ; 113 ; collection of
fossil remains, ii. 248.

Daunou, Academic des Sciences mor-
ales et politiques, i. 145 ; 152.

Davy, Sir Humphry, electro-chemical
discoveries of, i. 83, 189, 363 ; scien-
tific work of, 229 ; science in Eng-
land, 234 ; not member of any uni-
versity, 238, 272 ; opposed Dalton's
atomic theory, 245, 246 ; studied in
laboratory of Royal Institution, 249,
264 ; educated Faraday, 265 ; un-
connected with Cambridge mathe-
matical school, 266 ; electric action
in chemical processes, 366 ; decom-
position of soda and potash, 391,
404 ; electro - chemical theory, 405,
452 ; salts and acids, 410 ; attitude
to Dalton's theory, 417 ; attitude
towards the atomic theory, 418 ;
428 ; chemical application of elec-
tricity, ii. 92 ; electro-chemistry, 93 ;
heat and chemical change, 102 ; atti-
tude to science that of a medical
man, 103 ; vibratory view of heat,

INDEX.

765

104 ; indestructibility of force, 111 ;
the dynamical theory of heat, 128 ;
154 ; agricultural chemistry, 391,

Dawson, John, i. 267.

De Bary, embryological studies of
plant life, ii. 228.

De Blaiuville, indebtedness of Cuvier
to, i. 130 ; organisation, ii. 236; 239 ;
' Cuvier et Geoflroy Saint Hilaire,'
247, 255; 'Osteographie,' 257; 266;
unity of organisation, 267 ; ' ' com-
2:)Osition et decomposition," 421 ;
school of, 431.

Decade philosophique ridiculed the
fall of meteors, i. 327.

De CandoUe, A. P., botanist, ii. 222;
theories of symmetry, 223 ; ' Organo-
graphie vegetale ' quoted, 230, 236,
261, 265, 266 ; ' Theorie elementaire
de la Botanique ' quoted, 235 ; mor-
phological view, 239 ; quoted, 240,
242, 269 ; regularity and symnietry
in organic nature, 241 ; symmetry of
form, 243 ; appreciation of Goethe's
work, quoted, 244 ; influence of, 276.

Decher (see Clausius), ii. 135.

Decimal fractions, ii. 645, 731.

Dedekind, R., biographical notice of
Riemann, i. 352 ; and Dirichlet, ii.
721 ; 726, 729 ; on irrational num-
bers, 733, 734, 737.

De Gerando, i. 149.

De Haen, i. 208.

Delage, Yves, history of the study of
organic life, ii. 232 ; ' L'Heredite et
les grands problemes de la Biologie,'
265, 364, 371, 372, 444, 4.55, 458, 459 ;
'L'Heredite' quoted, 271, 298, 348,
349, 406, 421, 427, 447, 461 ; structure
of protoplasm, 370; school of " or-
ganicism," 436.

De la Hire, ii. 664, 667.

Delambre, i. 113 ; report of French
Institute, 149 ; quoted on statistical
methods in France, 153.

Delambre and Cuvier, scientific reports
of, i. 42.

Delaunay, lunar theory, i. 329.

De Luc, attacks on Hutton, ii. 291,

Democritus of Abdera, founder of
atomistic theory, i. 385 ; animation
of all matter, ii. 369.

De Moivre, doctrine of chances, ii. 678.

Derand, geometrical work of, i. 114.

Derham,'^Dr Wm., 'Physical Theology,'
ii. 565.

Descartes, constructive system of, i.
75 ; and Bacon, 84 ; 123, 137 ; and
the philosophy of Kant, 222 ; Order

of Jesus, 256 ; Harvey's discovery,
282 ; discovery of reflex action,
292; 'Les Passions de I'Ame,' 293;
311, 313 ; his philosophy and New-
ton's contrasted, 338; qimlitates oc-
cultce, 351 ; Snell's experiments in
deflection of light rays, 356 ; develop-
ment of kinetic view, ii. 6 ; Euler's
opposition to, 8 ; theoretical hydro-
dynamics, 58 ; older vortex theory
and, 62 ; the measure of force, 100 ;
influence on German philosophy, 205 ;
theory of vortices, 360 ; a founder of
modern physiology, 378'; study of
biology, 379, 380 ; idea of life, 409,
410; school of '• organicisme," 436,
455 ; 470, 519, 638, 641, 697.

Descent, theory of, i. 201.

Descriptive geometry, ii. 658 et seq.

Deshayes, history of invertebrates, ii.
239; Lamarck, 310.

Destructive spirit in writings of eigh-
teenth century, i. 78.

Destutt de Tracy, ' Ideologic,' i. 83 ;
alliance with medicine, 126 ; 152 ;
ideologist, ii. 472.

Determinants, ii. 682 ; history of, ib.

Development, study of, ii. 264.

Deville, Sainte Claire, ii. 162.

De Wette, theologian, influenced by
school of Fries, i. 209, 273.

Diamagnetism, ii. 74.

Dickson, J. D. H., quoted byGalton,
ii. 619.

Diderot on the genesis of new words, i.
21 ; his Encyclopedie, 34, 144, 215.

" Dielectric," ii. 68.

Differential equations, general theory
of, ii. 692 ; Sophus Lie on, ib.

"Diffraction," Fresnel's memoir on, ii.
25, 27.

Dilthey, ' Sclileiermacher,' i. 279.

Dingeldey, ' Topologische Studien,' ii.
64.

Dingler's ' Polytechnic Journal,' ii.
134.

Dini, Ulisse, on theory of functions, ii,
704.

Dionis du Sejour, death of, i. 147.

Dirichlet, Lejeune, lectures on mathe-
matical physics, i. 44 ; discourse on
Jacobi, 185 ; quoted, 186, 188, 189 ;
Fourier's series, 241 ; on Steiner, ii.
670 ; 680 ; and Fourier, 694 ; his and
Thomson's principle, 700, 704, 708 ;
721, 726, 728.

Dissociation, ii. 163.

Distribution, ii. 566.

Dobereiner, i. 190.

766

INDEX.

Dohrn, Anton, seaside laboratory
fonnded at Naples, ii. 232.

Dulliuger, Tgnaz, evolutionist, and the
Naturphiiosophie, i. 207; scientific
researches, ii. 299 ; 303.

DoUond, not member of any university,
i. 238 ; astronomical instruments,
322.

Domesday-Book, ii. 555.

Bonders, 'on language, ii. 538.

Donner's rendering of the Greek dram-
atists, i. 213.

Dopider, enunciated the principle of
iUimer's discovery, ii. 10 ; his prin-
ciple of wave-motion, 49.

Dove, meteorology, i. 205.

Downs, 0. G., ii. 579.

Dreyfus-Brisac, testimony to work of
German universities, i. 225.

Driesch, Hans, ii. 342; " organicisme,"
455 ; works of, 456 ; 463, 549.

Drobisch, psychologist, ii. 494, 497 ;
pretensions of statistics, 586.

Drude, P., ii. 38.

Drummond and Edinburgh University,
i. 269.

Drummond, Henry, ii. 326.

Drummond, Thomas, spectrum analysis,
i. 278.

Duality, principle of, in geometry, ii.
665.

Dublin school of mathematicians, i.
274, ii. 673.

Du Bois-Reymond, Emil, on the intro-
duction of new ideas from abroad,
i. 16 ; 45 ; limits of the knowable,
53 ; 106 ; the speculative tendency in
science, 179; 'Reden,' 188, 215, ii.
149 et seq. ; ' Gediichtnissrede auf
Joh. Miiller,' i. 198, 293; voltaic
elettricity, 199 ; quoted, 216, ii.
270, 381, 469, 478 ; mechanical view
of biology, i. 219 ; Bell's doctrine,
293 ; ' Akademie der deutschen
Sprache,' 298 ; ' Ueber die Grenzen des
Natnrerkennens,' 348 ; objections to
Kirchhoff's definition of "mecl,ianics,"
383 ; researches of, ii. 208 ; Eloge of
Johannes Miiller, 384, 419, 482 ;"'391,
revolution in physiological studies,
396 ; ' Researches in Animal Elec-
tricity,' 397 ; 401 ; position in vitalistic
controversy, 403 ; essay on Vital
Force, 405; 408, 409, 411; on the
principle of natural selection, quoted,
414; vitalism, 434; "Darwin versus
Galiani," quoted, 4-35; "Exercise,"
436 ; active nervous system, 438 ;
animal electricity, 475, 476 ; 481 ;

principle of reflex action, 519 ; 546,
743.

Du Bois - Reymond, Paul, services to
scientific reasoning, i. 45 ; 103 ;
' Grundlagen der Erkenntniss in den
exacten Wissenschaften,' 341 ; 377 ;
gravitation " unknowable," 852 ;
kinetic theory of gases, 433 ; works
of, ii. 631, 705 ; theory of functions,
704 ; on arithmetising, 739.

Du Chatelet, Madame, letter from Vol-
taire to, i. 105.

Duchesne, physiognomy, ii. 477.

Duclos, on education, i. 259.

Ducos quoted, i. 109.

Dufay, controversy on electric fluid, i.
362.

Duhamel, mechanics,, i. 44; taught
metallurgy at the Ecole des Mines,
107.

Duhem (see Prof. Ostwald), ii. 159 ;
labours of, Horstmann, 170 ; thermo-
dynamic potential, 173 ; ' Mecanique
chimique,' 173 ; chemical equilibrium,
175.

Diihring, E., ' Kritische Geschichte der
allgemeinen Principiien der Mechauik,'
ii. 97, 101 ; historical and controversial
writings, 107.

Dujardin, Felix, sarcode, ii. 264 ; defini-
tion of a cell, 265.

Dulong and Petit, specific heat of bodies,
i. 428, 429.

Dumas, ' Le9ous sur la Philosophie
chimique,' i. 114 ; revives Front's
hypothesis, 402, 403 ; explanation of
"isomerism," 406; the "radicle"
theory, 409 ; attack on electro-
chemical theory, ib. ; 410; "type"
theory, 411; 413; attitude towards
the atomic theory, 418 ; quoted, 421,
ii. 370, 441; i. 402, 428; spectro-
scopic observations, ii. 361 ; ' Essai
de Statique chimique des Etres
organises,' 392 ; substitution in chem-
istry, 393 ; 406.

Duncker, G., statistics of variation, ii.
622.

Dlintzer, ii. 531.

Dupin, Charles, ii. 579 ; 658.

Dutens, ' Leibnitii Opera Omnia,' ii.
280.

Dutrochet, Bell's theorem, i. 293 ; ii.
230, 261.

Dynamics, ii. 5 ; and statics, 144.

Eckermann quoted, ii. 253.
Ecole centrale des Travaux publics, i.
112.

INDEX.

767

Ecole des Fonts et Chaussees, i. 107.

Ecole normale superieure, i. 112, 113,

, 237.

Ecole polytechnique of Paris, i. 112 ;
used as model for German poly-
technic schools, 166.

Ecole veterinaire d'Alfort, i. 107.

Ecoles de Sante, i. 113 ; founded at
Paris, Strasbourg, and Montpellier,
142.

Economics and biology, ii. 415.

Edgeworth, Prof., " The Law of Error,"
ii. 576.

' Edinburgh Magazine and Review '
issued, i. 273.

' Edinburgh Pieview,' literary criticism
of, i. 84 ; 233 ; quoted, 234, 235, 236;
on English universities, 254 ; 270 ;
first issued, 273 ; Brougham's attack
on Young, ii. 19.

Edison, phonograph, ii. 490.

Education, aud instruction, i. 258 ;
liberal, ideal of, 255.

Educational conflict on discipline, i.
133.

Educational efforts in different countries,
i. 252 et seq. ; in Scotland, 253 ; liter-
ature of Switzerland, ih.

Educational institutions, French, i. 112.

Educational organisations in England,
i. 262.

Edward, Thomas, shoemaker aud zool-
ogist, i. 287.

Edwards, George, 'History of Birds,' i.
287.

Edwards, Milne, ' History of Inverte-
brates,' ii. 239 ; Lamarck, 310 ; Hux-
ley on, 322; "physiological division
of labour," 396.

Ehrenberg, ' Ueber Leibnitzens Meth-
ode,' ii.''280.

Eighteenth century, one of revolution,
i. 77.

Eisenstein, and theory of numbers, ii.
684.

Elasticity, theory of, ii. 30, 40 ; 31 ;
foundation of theory of, 41.

Electrical and magnetic action, i. 344.

Electricity, aud magnetism, ii. 64 et seq.;
velocities of light and, compared, 84 ;
modern researches, 189 ; electric dis-
charges, 195 ; animal, 475.

Electro-dynamics, Wilhelm Weber's law
of, i. 196 ; ii. 149.

Electro-magnetic theory, ii. 64 ; in-
definiteness of, 93 ; 153.

Electro-magnetism, discovery of, i. 92.

Electrolysis, ii. 154 et seq.

Electron, the term, ii. 193.

"Electrotonic " state of matter, ii. 68,
81.

Elizabeth, England under, i. 67.

Elliptic functions, history of, ii. 648
et seq.

Ellis, Alex. T., on terminology of sound,
ii. 489.

Ellis, Robert Leslie, on Bacon, i. 94,
96 ; his report, ii. 649.

Elphinstone, Bishop, started Aberdeen
University, i. 268.

Elster aud Geitel, vacuum tube ex-
periments, ii. 190.

Emanations, law of, i. 344.

Embryology, ii. 296.

Ernpedocles, relation to Galileo and
Newton, i. 313 ; attraction and repul-
sion, 385 ; recurrent cycles, ii. 287.

Encke, "calculus of probabilities," i.
325.

' Encyclopadie der Mathematischen
Wissenschaften,' ii. 73.

Encyclopadie, lectures on, i. 37.

'Encyclopedia Britannica,' article on
Napier, i. 269 ; first published, 273 ;
article on "Agriculture" quoted,
284; article on F. Mohr, ii. 106;
article on Sainte Claire Deville, 163 ;
232, 279, 569.

' Encyclopaedia Metropolitana,' i. 236.

Eucyclop;edia of Ersch and Gruber, i.
35.

Eucyclopjedias, origin of, i. 40.

Encyclopedic treatment of learning,
age of, i. 34, 215 ; view necessary in
philosophy ami history, 203 ; treat-
ment of scientific subjects, 214.

Encyclopiedists followed Newton, i. 96 ;
constructive work of school of, 110 ;
educational influence of, 112.

Energetics, science of, ii. 141 ; 166 ;
kinetics and, 1>^Q.

Energy, conservation of, i. 199, 201 ;
theory of, ii. 87, 96 ; works deal-
ing with, 97 ; dissipation of, 97, 364 ;
the term first used by Young, 98 ;
notion of, contained in Newton's
'Principia,' 99 ; the term introduced
by Thomson, 115; and "Force,"
115 ; availability and dissipation of,
119; doctrine of, 124; revolutions
brought about by idea of, 137 ;
" potential " and "actual," 139, 398 ;
influeuce of doctrine of, 399 ; circu-
lation of, 420 ; 465 ; availability of,
594.

Engel, F., on taste in mathematics, ii.
632 ; on genesis of Lie's ideas, 692.

England, science and philosophy in,

768

INDEX.

during the early part of the century,
i- 75. ^ .

English character, individualism of, i.

279 ; changes during last fifty years,

280 ; love of nature, 284, 286 ; Hankel
on, ii. 704, 711.

Enneper, ' Elliptische Functionen,' i.
18.^ 187.

Entropy, ii. 169 et seq., 181, 594.

Enumeration, ii. 561.

"Environment," ii. 314, 430.

Epicurus, "essential and inherent
gravity," i. 340; natural philosophy
of, ii. 4.

Epigenesis and evolution, ii. 298.

Equations, theory of, Abel, ii. 681 ;
general solution of, 687 et seq.

Equivalents, chemical, i. 399,

Erasmus, i. 163.

Erdmann, misprint in his ' Grundriss
der Geschichte der Philosophic,' i.
50 ; ii. 495, 512.

Erlsberg, ii. 271.

Ernest Augustus, Elector of Hanover,
i. 158.

Ernest II., Duke of Gotha, i. 54, 176;
patron of the astronomer von Zach,
177 ; system of education of, 256.

Error, element of, i. 323 ; theory of, ii.
568, 574.

Ersch and Gruber, Encyclopasdia of, i.
35.

Eschenburg, representative of encyclo-
paedic teaching, i. 38.

Ether, luminiferous, theory of, ii. 18 ;
properties of, 31 ; nature of, 36 ; hy-
pothesis of, 37 ; Sir 0. Lodge on
nature of the, 38 ; nature of, 40
et seq. ; mathematical and experi-
mental investigation of, 44 ; an
"elastic solid," 54; luminiferous,
69, 70.

Etymology, value of, for history of
Thought, 1. 20.

Eucken, R., on philosophical termin-
ology, i. 21,

Euclid preferred in ^England to Le-
gendre, i. 44 ; his works models of
scientitic thought, 95 ; 120, ii. 4 ;
Proclus on, 634 ; Klein on, 635 ; 718,
733.
Eudenms of Rhodes, ii. 633.
Eudo.xus, Proclus on, ii. 634.
Euler, Leonhard, freed analysis from
geometrical fetters, i. 103 ; 135 ;
competed with T. Mayer, 158 ; 163 ;
connection of, with modern science,
175 ; 181, 183, 234 ; analytical
methods of, 271 ; mathematics, 44 ;

819 ; lunar theory, 329 ; Newton's
gravitation formula, 334 ; " Ur-
sache der Gravitation," 341 ; ether
theory of gravitation, 343, 346, 351 ;
unfavoiu'able to Boscovich's theory,
358 ; ii. 7 ; ' Anleitung zur Natur-
lehre,'8; the successor of Huygens,
16, 17 ; studies in elasticity, 30 ;
spectrum analysis, 46 ; psycho-phy-
sics, 474 ; 510, 637 ; introduces con-
ception of "function," 639 ; 643, 646,
648 ; on different mathematical inter-
ests, 657 ; 669, 680, 692, 694, 695,
721.

Evelyn, John (see Arundel collection),
ii. 564.

Everett, "character" in music, ii. 489.

Evohition, ii. 210, 278.

Ewald, on Humboldt's geological work,
ii. 226 ; 253.

Ewing, 'The Steam-Engine,' ii. 136.

Exner, 'Repertorium der Physik,' i.
323.

Exploration, the spirit of, ii. 206 et seq.

Externalisation, ii. 525.

Fabricius of Acquapendente, teacher of
Harvey, i. 282.

Fagnano, Count, Euler on, ii. 657.

Falk, Johannes, follower of Pestalozzi,
i. 258.

Faraday, electrical theories of, i. 199 ;
electrical researches, 201, ii. 86 ;
electrical and other discoveries of, i.
230 ; science in England, 236 ; not
member of any university, 239, 272 ;
and Pllicker, 242 ; neglected in Eng-
land, 246 ; studied in laboratory of
Royal Institution, 249 ; furnished
texts for lectures in German univer-
sities, 251 ; at Royal Institution,
264, ii. 80 ; educated by Davy, i.
265; "lines of force," 266, ii. 68,
182 ; not connected with Cambridge
mathematical school, i. 266 ; neglect
of his writings, 277 ; 279, 297 ; gravi-
tation, 344 ; electricity, 345 ; sym-
bolism, 347 ; nature of matter, 358 ;
discovery of electrical induction, 363 ;
method of measuring the electric
current, 365 ; electrical action in
chemical processes, 366 ; discovery
of magnetic induction, 368, 371 ; his
influence, 380; discovery of "iso-
merism," 406; his attitude towards
the atomic theory, 418 ; 431 ; theory
of chemical affinity, 452 ; researches
of, ii. 35 ; modern view of electrical
phenomena, 66; "magnetisation of

INDEX.

769

light," 74 ; electro-magnetic radiation,
77 ; and Thomson, 78 ; galvanic cur-
rents, 79 ; and Clerk - Maxwell, 80 ;
" electrotonic state" of matter, 81 ;
tubes of force, 83 ; electricity in
motion, 93 ; and Poggendorf, 107 ;
referred to, 111 ; indestructibility of
force, lb. ; correlation and inter-
cbangeability of natural forces, 119 ;
"force," 125; " regelation of ice,"
127 ; indestructibility of force, 130 ;
electricity in space, 145 ; electro-
magnetic field, 146 ; electrolytic law,
154, 157 ; results of experimental
work of, 161 ; law of, 165 ; atomic
view, 189 ; observations of vacuum
tube phenomena, 190 ; 191, 193.

Faudel and Schwoerer, ' Life of Him,'
ii. 134.

Fay, Du, referred to by Voltaire, i.
106.

Faye, ' Sur I'Origiue du Monde,' ii. 282,
357, 360.

Fechner, Gnstav Theodor, ' Elements
of Psycho-physics,' i. 200 ; andBosco-
vich's theory, 359 ; Ohm's law, 365 ;
electrical theory of, 371; 'Atomen-
lehre,' 433 ; ii. 369 ; psycho-physics,
469, 493 ; psychical research, 508 ;
' Psychophysik,' 511 ; 514, 546, 743.

Felbiger, Von, educational work of,
i. 256,

Fellenberg, Von, follower of Pestalozzi,
i. 258.

Fenelon, i. 253.

Fermat, Pierre, the theory of probabil-
ities, i. 120 ; arithmetical discoveries,
181 ; 187 ; his theorems, ii. 680,
721.

Ferrier, functions of the brain, ii. 479.

Fertilisation of plants, ii. 338.

Fertilisers, invention of artificial, i. 92.

Fessel, fellow-worker with Pllicker, ii.
76.

Fichte, I. H., and Lotze, i. 49.

Fichte, J. G., the province of j^hil-
osophy, i. 36 ; influence on academic
teaching, 37, 38 ; idealism of, 60 ;
' Wissenschaftslehre,' 83 ; doctrine of,
170; 'Nature of the Scholar,' 171;
172 ; influenced liy Spinoza, 212 ; edu-
cational significance of his writings,
258 ; 263, 264 ; system of, ii. 500 ; and
Herder, 532.

Fiedler, German translations of Sal-
mon's works, i. 275, ii. 669 ; 685 ;
expounds von Staudt's method, 669.

Fiedler and Salmon, i. 44.
"Field," magnetic, ii. 68.

VOL. II.

Finnie, John, agricultural chemistry, i.

Fischer, Emil, ii. 437.

Fischer, E. G., first table of standard
equivalents, i. 393 ; 398.

Fischer, Kuno, 'Geschichte der neueren
Philosophic,' i. 67.

Fitton, ii. 294.

Fitzgerald, G. F., ii. 193.

Fizeau, velocity of light, ii. 45, 85.

Flamsteed, Newton's correspondence
with, i. 98.

Flemming, ii. 444.

Fletcher, L., 'The Optical Indicatrix,'
ii. 14, 42, 55.

Flourens, ' Histoire des Travaux de
Georges Cuvier,' i. 130, 139; 'Eloges
Historiques,', 1.35 ; and de Blainville,
ii. 247 ; " Eloge " of Geoftroy, 255 ;
doctrine of descent, 322 ; quoted on
Gall, 477 ; phrenology, 478.

Fluorescence, ii. 52.

Fluxions, invention of method of, i.
101; method of, ii. 706.

Pol, on fertilisation, ii. 228.

Fontanes, conversation of Napoleon
with, i. 153.

Fontenelle popularised science, i. 106 ;
literary influence of. 111 ; 123, 134,
135, 142, 144, 279 ; ' Eloge de Leib-
niz ' quoted, ii. 280.

Forlies, Edward, naturalist, i. 283, 288.

Forbes, J. D., i. 272 ; on radiant heat,
ii. 105.

"Force, lines of," ii. 68; Lord Kelvin
on, 71 ; and "energy," 115.

Force, matter and, mathematically de-
fined, i. 334.

Forces, correlation of, ii. 105.

Forms, theory of, ii. 678, 684.

Forster, Georg, Humlroldt's view of
nature, i. 52 ; naturalist, services of,
179 ; the term " phrenology," ii. 477 ;
influences Herder, 532.

Forster, Johann Reinhold, i. 179.

Forsyth, A. R., theory of functions, ii.

704.
'Fortnightly Review,' ii. 558.
' Fortschritte der Physik ' started, ii,
58.

Foster, Sir Michael, 'Text -Book of
Physiology ' quoted, ii. 289, 446 ;
physiology, 3^6; 'Text-Book,' 417;
"Metabolism," 421, 442; "General
Physiology," 423, 430 ; quoted, 428,
Foucault, spectrum analysis, i. 278;
speed of light, ii. 36, 45 ; prismatic
analysis of the voltaic arc, 50 ;
"gyroscope" and "gyrostat," 61.

3 c

770

INDEX.

Foucher, ' Hypothesis Physica,' ii. 5.

Fouiuiatious of science, historical and
logical, ii. 671 ; of mathematics re-
vised by Weierstrass, 703 ; examina-
tion of, 709.

Fourcroy, ' Annales de Chinjie,' i., 41 ;
at the Jardin des Plantes, 107 ; Ecole
des Travaux pnbliques, 112; 113;
services of, to the Republic, 148 ;
criticisms of Baumes's essay, ii. 390.

Fourier, Fr. M. C, and co-operation,
ii. 566.

Fourier, J. B. Jos., i. 187 ; neglected
by Paris Institute, 241 ; ' Tlieorie de
la Chaleur,' 322, ii. 175; theory of
dimensions, i. 323 ; his mathematics
employed by Lord Kelvin, 330 ;
"dynamic equilibrium," ii. 79;
quoted, 120; dedication of 'Phil-
osophic Positive,' 239 ; heat, 487 ;
analysis of periodic phenomena, 6"23 ;
on Jacobi and Abel, 657 ; definition
of function, 693 ; 697, 699.

Fox-Talbot, light, ii. 11.

France, home of scientific thought in
the early part of the century, i. 75.

Francis I.' founded College de France,
i. 107.

Francke, A. H., influence of, at Halle
University, i. 160 ; educational work
of, 256 ; 257.

Francceur's mathematics introduced
into England and Germany, i. 44 ;
influenced German thought, ii. 101.

Frank, i. 208.

Frankland, Sir Edw., chemical re-
searches of, i. 413, 447 ; atomicity of
chemical compounds discovered by,
414.

Franklin, controversy on electric fluid,
i. 362 ; Davy's speculations on heat
and light, ii. 104.

Fraunhofer lines, i. 278 ; theory and
practice of measuring, 322 ; spectro-
scopic observations, ii. 47.

Frederick, Elector, reconstitutes Uni-
versity of Heidelberg, i. 159.

Frederick the Great, popular education,
i. 256 ; population statistics, ii. 563.

Frederick II. of Denmark and Tycho,
i. 157.

Freewill, ii. 583.

Frege, G., ii. 737.

Freind, John, molecular attraction, i.
355.

French, the, masters in science at the
beginning of the century, i. 41.

Fresenius, text-books of, i. 188.

Fresnel, Augustin, neglected by Paris

Institute, i. 241 ; and Young, theories
of, 244 ; dynamical view of light, 370
revival of kinetic view of nature, ii. 8 ;
optical phenomena, 13, 14 ; undula-
tory theory of light, 21, 36 ; views on
"sidedness" of rays of light, 24;
Memoir on Diffraction, 25, 26 ; trans-
verse vibrations, 28 ; elastic theory
of light, 31 ; nature of the ether, 40 ;
theory of elasticity, 41 ; definition of
motion of light, 42 ; theory of light,
43 ; vibrations of the ether, 56 ; the
dielectric and luminiferous ether, 69,
70, 89 ; " elastic medium " in space,
84 ; reference to, 86, 91 ; 344, 467.

Freytag, ' Bilder aus der deutschen
Vergangenheit,' i. 256.

Frezier, geometrical work of, i. 114.

Fries, Jacob, i. 195 ; school of, 208 ;
psychology, ii. 495.

Fritsch, 'Theorie der Newtou'schen
Gravitation,' i. 343.

Frobel, founder of the Kindergarten, i.
258.

Frost, Scheiner's 'Astronomical Spec-
troscopy,' ii. 46 ; 362.

Function, mathematical, introduced by
Euler, ii. 639.

Functions of living substance, ii. 429.

Functions, theory of, ii. 693 et seq.;
two schools, 693 ; non-difterentiable,
Hankel and Weierstrass on, 705 ;
oscillating, 706 ; analytic, 712.

Fundamentals in mathematics, ii. 649
et seq.; geometrical and logical, 651
et seq.; Gauss on, 652.

Galen, i. 293 ; ii. 207.

Galileo, Bacou's indebtedness to, i. 94 ;
mechanical laws of, 317 ; 318 ; stimu-
lated star-gazing, 327 ; formula3 of,
335 ; described phenomena of falling
bodies, 353; 389, 424; 'Sidereus
Nuncius,' discovered the moons of
Jupiter, ii. 10 ; 12 ; inertia, 124 ;
astronomical work of, 227.

Gall, J. F., i. 136 ; extolled by Comte,
310 ; phrenology, ii. 477, 479.

Galle and the discovery of Neptune, i.
277. .

Galois, Evariste, Theory of Equations,
ii. 686 ; his life and works, ib. ; his
letter to Chevalier, ib. ; and theory
of groups, 687 ; 692.

Galton, Francis, on heredity, ii. 574,
612 ; on variation, 609 ; his works,
ib. ; combines Quetelet and Darwin,
ih. ; on statistical treatment, 612 ;
on pangenesis, 614 ; forestalls Weis-

INDEX.

71

mann, ib. ; on "particulate" inheri-
tance, 615 ; on law of distribution,
617 ; on law of regression, 618.

Galvani, discoveries of, i. 363, ii. 150 ;
galvanic current, 233 ; animal elec-
tricity, 474.

"Gamma" function, ii. 696.

Garnett, R., on Georg Forster, 1. 52 :
179.

Garnett, W., and Campbell, 'Life of
Clerk-Maxwell,' ii. 599.

Gartner, investigations of, ii. 415.

Gases, liquefaction of, i. 316 ; the
kinetic theory of, 425, ii. 34 ; i.
433.

Gaskell, Dr, cerebro-spinal nerves, ii.
429; analysis of process of "meta-
bolism," 44"2.

Gassendi taught at the College de
France, i. 107 ; 385.

Gassiot, experiments with vacuum
tubes, ii. 190.

Gatterer of Gottingen University, i.
165.

Gauss, Carl Fr. , i. 44, 45 ; orbit of
Ceres, 54 ; works of, 82 ; and Weber,
the telegraph, 92, 367 ; " Disquisi-
tiones Arithnieticte,' 105, 120, ii. 682;
Lobatchevski and Bolyai, i. 161 ; and
Humboldt, 167 ; and Zach, 177 ;
178 ; mathematical researches, 181 ;
182 ; least squares, 183 ; 184, 185,
188, 189, 191, 2U0, 207, 211 ; "exact
habit of thought," 222 ; 231, 238, 247 ;
measurement of magnetic action, 265 ;
303 ; absolute measurements, 309,
369 ; astronomical work of, 314, 331 ;
measurements of, 322 ; ' Theoria
motus corporum ccelestium,' 324;
calculus of probabilities, 325 ; 352 ;
Coulomb's methods, 36(», 362 ; 365 ;
importance of his work, 384 ; "Top-
ologie," ii. 63 ; researches into elec-
trical phenomena, 67 ; 76 ; electro-
magnetic measurements, 78 ; system
of absolute measurements, 117 ; arith-
metical discoveries of, 124 ; influences
Helmholtz, 150 ; 197, 254 ; science
of chances, 568 ; theory of error, 574 ;
575 ; method of least squares, 576 ;
doctrine of probabilities, 577 ; law
of error, 616 ; and Newton compared,
630 ; rediscovery of Ceres, ib. ;
pioneer of modern mathematics, 636 ;
Bessel on, ib. ; his style criticised by
Abel, 637 ; 640 ; his fundamental
theorem, 644, 688 ; on convergency,
646 ; his work on higher functions,
648 ct seq. ; on fundamentals, 652 ;

his influence on Bolyai, Lobatchevski,
and others, 652 ; anticipates the work
of others, ib. ; compared to Goethe,

653 ; on extended system of numbers,

654 ; reforms theory of numbers, 680
et seq., 720; on determinants, 682;
686, 688, 693, 695, 697, 698 ; on con-
formal images, 701 ; on non-Euclidean
geometry, 710, 713 ; measure of
curvature, 714 ; theory of congru-
ences, 723 ; on mathematical calculi,
724; on bi-quadratic residues, 725;
732 ; not a great teacher, 646, 743.

Gauss and Gerling, ii. 713.

Gauss and Schumacher, correspondence,
ii. 710.

Gauss and Weber, telegraph, i, 92,
367 ; school of, ii. 702.

Gay-Lussac, Memoirs of, 1. 83 ; ' An-
nales de Chymie et de Physique,'
189 ; 190 ; organic analysis, ib. ;
chemical discoveries, 398, 407 ; ex-
periments, 425 ; 426 - 429 ; Fresnel's
' Memoire sur la Ditt'raction,' ii. 25 ;
visit to England, 27 ; experiment in
heat measurement, 109 ; 155, 592.

Geddes and Thomson, 'The Evolu-
tion of Sex,' ii. 227, 454, 458, 459;
sexual selection, 344 ; " Reproduc-
tion," 348.

Gegenbaur, school of Darwinism in
Germany, ii. 436.

Gehlen, ' Allgemeines Journal flir
Chemie,' i. 41.

Geikie, Sir Archd., quoted on Playfair's
' Huttonian Theory of the Earth,' i.
283 ; G. Wilson and, ' Memoir of
E. Forbes,' 288.

Geissler, fellow - worker with Plucker,
ii. 76 ; electrical researches, 189 ;
vacuum tubes, 190.

Geitel (see Elster), ii. 190.

Generalisation, process of, in mathe-
matics, ii. 638 ; 650.

Generalised co-ordinates, Pliicker, ii.
673.

" Genesis," ii. 279.

Genetic view of nature, ii. 276, 290 ;
in Germany and France, 321 ; triumph
of, 328 ; on a large scale, S45 ;
strengthened by physics and chem-
istry, 355.

Genetics, ii. 213.

Genius, latent thought the material of,
i. 8.

' Gentleman's Magazine,' ii. 679.

Geography, historical, i. 294.

Geological Society, i. 290.

Geology, ii. 290.

772

INDEX.

Geometrical axioms, i. 199, 352 ; ii. 649,

et seq.
Geometry, deficiency of organisation
of research in England, i. 243 ; two
schools of, ii. 668.
Geophysics, ii. 363.
George, Duke of Saxony, reconstituted

University of Leipzig, i. 159.
Gergonne, ii. 660 ; Hankel on, 666 ;

673.
Gerhardt, C. F., revives Front's hypoth-
esis, i. 402 : attack on electro-chemical
theory, 409; "type" theory, 411;
413; on the constitution of substances,
419 ; "types," 423 ; Gmelin's system
of equivalents, 426 ; characteristic of
hydrogen atoms, 430.
Gerhardt, C. J., on the invention of the
calculus, i. 101 ; edited Leibniz, 'Phil-
o.sophische Schriften,' ii. 5.
Germ plasma and body plasma, ii. 457,

458 ; plasma, ditt'erentiation of, 459.
German Association, character and de-
cline of, i. 238.
German language, peculiarity of, i. 22.
German universities, i. 226.
Germany leads in the history of thought,

i. 46.
Gervinus on Herder, i. 51 ; connection
of political and literary history, 59 ;
' Georg Forster's Werke,' 179; rela-
tions of philosophy and history, 206 ;
"theoretical politician," 311.
Gesner of Gottingen University, i. 165.
"Gewerbeschulen," i. 166.
Gibbon, i. 47; 'Roman Empire,' 169;
influence of, on German thought and
literature, 212 ; in German univer-
sities, 251.
Gibbs, J. Willard, energetics, ii. 166,
171; "free energy," 173; chemical
equilibrium, 175, 177 ; formulae of,
185 ; on directional calculus, 655 ;
656.
Gibson, George A., "Fourier's series,"

i. 241.
Giese, vacuum-tube experiments, ii.

190.
Gilbert, Sir J. H., agricultural experi-
ments and publications of, i. 284.
Gilbert, Wm., Bacon's indebtedness to,

i. 94.

Glaciers, Helmholtz's theory of, ii. 127.

Glaisher, Prof., quoted on invention of

logarithms, i. 269 ; 321 ; law of error,

ii. 576.

Glazebrook, Prof., 'Report on Optical

Theories,' ii. 54 ; Lord Kelvin's

theory of ether, 55 ; ' James Clerk-

Maxwell and Modern Physics,' 77 ;
indefiniteness of Maxwell's electro-
magnetic theory, 94.
Gmelin, Chr., chemist, i. 188 ; hand-
book of chemistry, 208.
Gmelin, Leopold, ' Handbuch der
Chemie,' i. 43, ii. 158 ; system of
equivalents of, i. 426, 430.
Goebel, Prof., on biology, ii. 313.
Goethe quoted on history, i. 7 ; quoted
on the success of the few, 9 ; made
modern German language, 22 ; atti-
tude of, to national idealism of Ger-
many, 39 ; style of, 51 ; his work,
61 ; influence of, on taste, 67 ;
'Faust,' 76 ; school of, 84 ; Lewes's
Life of, 166 ; 179 ; as a scientist, 180 ;
influenced by the Naturphilosophie,
207 ; 212 ; introduced hexameter into
German poetry, 213; quoted 251, 286,
ii. 3, 254, 258 ; educational signifi-
cance of his writings, i. 258 ; 261 ;
corresjjondence of, 279 ; on Luke
Howard, 286 ; introduction of the
term morphology, ii. 210 ; 213 ;
theory of metamorphosis, 223, 243,
267 ; influence of, 225 ; theories of,
246 ; influence of Linnajus, 252 ; 253 ;
the genetic view, 317, 321 ; subjective
colour sensations, 482 ; foundations
of the study of language, 538.
Goldstein, vacuum-tube experiments,
ii. 190; "ether" theory of cathode
rays, 192.
Goltz, experiments on the brain, ii.

478 ; 479.
Goodsir, cell theory, ii. 265.
Gordon, Lewis, Carnot's 'Puissance

motrice,' ii. 118.
Gottingen, prize essays on principles of

dynamics, ii. 97.
'Gottinger Gelehrte Anzeigen' of

Haller, i. 176.
Gough, John, the blind naturalist, i.

287.
Gourand quoted, ii. 571.
Grrevius, recognition of Bentley, i. 169.
Graff, Prof. L. von, on Haeckel's

'Stammbaume,' ii. 337.
Graham, Thomas, chemistry, i. 44 ;
salts and acids, 410 ; experimental
work of, ii. 161 : 164 ; discoveries of,
224.
Grandi, series of, ii. 646.
Grant, Sir A., ' Story of the University
of Edinburgh,' i. 160, 232, 267, 269,
283 ; on David Gregory, 270 ; on
Bell, '293.
Grant, Prof., natural selection, ii. 330.

INDEX.

773

Grassraann, Hermann, geometry, i. 44 ;
geometrical labours of, neglected in
Germany, 243, 247 ; ' Ausdelinungs-
lehre,' 275 ; mathematical labours
of, ii. 73 ; 630 ; Hankel on his science
of forms, 640 et seq.; his comprehen-
sive calculus, 655 ; gradual apprecia-
tion of his work, 656 ; 710.

Graunt, John, statistics, i. 122 ; "Tables
of Mortality, "ii. 564.

Graves, R. P., 'Life of Sir W. R.
Hamilton ' quoted, i. 106, 289 ; ii.
722.

Gravitation, formula of, i. 319 ; lines of
thouc;ht emanating from it, 321 ; not
an ultimate property of matter, 338 ;
difBculty of measuring directly, 353.

Gray (the poet), i. 285.

Gray quoted on David Robertson, i.
289.

Gray, Asa, criticism of ' Vestiges, ' ii.
3i9 ; 332.

Greard, educationalist, i. 260.

Green, George, important generalisation
in statics and dynamics, i. 230 ; his
"potential function," 231 ; 246, 272,
331 ; important papers lost, 277 ;
properties of ether, ii. 31, 33 ; in-
spired by Cauchy, 43 ; analytical
method of, 45 ; referred to, 54 ; theory
of electric and magnetic phenomena,
74 ; 698.

Gregoire proposed Bureau des Longi-
tudes, i. 113.

Gregory, David, introduced Newtonian
philosophy into the University of
Edinburgh, i. 232 ; Professor of Astro-
nomy, Oxford, 270, 272 ; astronomical
instruments, 322.

Gregory, F., Hankel on, ii. 712.

Gren's 'Journal der Physik,' i. 41.

Grew, Nehemiah, used the term " cell,"
i. 195 ; microscopic investigations in
biology, 283 ; embryological re-
searches, ii. 227 ; microscopical
studies, 260 ; observations of, 261.

Griesbach, "Animal and Plant Geo-
graphy," ii. 226.

Griesinger, Mayer's "right of priority,"
ii. 115.

Grimaldi, polarisation of light, ii. 18.

Grimm, Jacob, 'Ueber Schule, Univer-
sitat, Akademie,' i. 100 ; language, ii.
540, 542.

Groth, 'Pliysikalische Krystallographie, '
i. 443.

Groups, theory of, ii. 632, 686, 687 ;
Burkhardt on, 688 ; 689 et seq, ;
continuous and discontinuous, 691.

Grove, " Correlation of Physical Forces,"

ii. Ill; "force," 125, 130.
Gruber, Ersch and, Encycloijredia of,

i. 35 ; representative of encyclopaedic

teaching, 38.
Guardia quoted, i. 106; 'Histoire de

la Medicine,' 126.
Guerry, A. M., statistics, ii. 579.
Guhrauer, 'Leibniz, eine Biographic,"

i. 158, ii. 280.
Guizot, education, law of, i. 183, 257.
Guldberg, law of mass-action, i". 157 ;

ideas of Berthollet, 177.
Guyton de Morveau, i. 116, 131 ; gun-
powder, iron, steel, 148.
Gyroscope and gyrostat invented, ii. 61.

Haacke, ii. 271.

Hacker, DrVal., 'Praxis und Theorie
der Zellen- und Befruchtungslehre,' ii.
265,370; 371,447.

Haeckel, Ernst, i. 179; 'Generelle
Morphologic der Organischen Wesen,'
ii. 213, 214, 270, 271, 349 ; Goethe's
ideas, 244, 246; "Ontogenesis" and
"Phylogenesis," 307; 'Natiirliche
Schopfungs - Geschichte,' 313, 323;
'History of Creation,' 332; genea-
logical trees, 337 ; sexual selection,
343 ; 347 ; evolution, 348, 455 ; Dar-
win and Lamarck, 350 ; 351, 361 ;
conception of universal animation,
369 ; biological theories of, 371 ; 414 ;
school of Darwinism in Germany,
436; "germinal" element, 457 ; and
Weismann, 460 ; and Herder's evolu-
tionism, 533 ; man and brute, 541 ;
546, 608 ; kinetic hypothesis, 611.

Haeser, 'Geschichte der Mediciu,' i.
126, 308, ii. 388, 390, 401; on
homceopathy, i. 210 ; on Kant, 219.

Hahn, "Cuvier" in 'Grande Encyclo-
pedic,' i. 130.

Hahnemann's homceopathy .i. 210.

Hales, improvements in microscopy, ii,
230.

Hall, Marshall, ii. 519.

Halle, University of, i. 165.

Haller, Albrecht von, i. 163 ; of Gottin-
geu University, 165; connection of,
with modern science, 175 ; ' Gottinger
Gelehrte Anzeigen,' 176; ' Ele-
menta,' 193 ; 194 ; zoological labours
of, ii. 220, 230 ; study of separate
organs, 233; "evolutionist," 278;
279 ; epigenesis, 298 ; 299, 308 ; vital -
istic conceptions, 384 ; discovery of ir-
ritability, 429 ; psycho-physical view,
471 ; influences Herder, 532 ; 533.

774

INDEX.

Hallej-, Edmund, "reciprocal dupli-
cate " ratio, i. 98 ; 270 ; Newton's
'Principia,' 283; orbits of comets,
324 ; calculates return of comet, 327 ;
Newton to, 342 ; pendulum experi-
ments of, 354 ; statistician, ii. 565.
Halsted, 6. B. , on non - Euclidean

geometry, ii. 652 ; 714.
Hamanu, Johann Georg, ii. 535, 536.
Hamilton, Sir W., ' Discussions,' i. 203 ;
'Dugald Stewart's Works,' 359;
" Philosojjhy of the Unconditioned,"
ii. 326.
Hamilton, Sir W, R., used the notation
of Newton, i. 101 ; Life of, quoted
from, 106 ; paper on caustics, 230 ;
important generalisation in statics
and dynamics, 231 ; Dublin Mathe-
matical School, 274 ; originality of,
ib. ; "characteristic function," 316;
theory of optical phenomena, ii. 13,
42 ; mathematical labours of, 73 ;
dynamics, 139; 195; his quaternions,
654 ; 656, 709 ; introduces term
"associative," 711; 722.
Hank, Theodore, suggested idea of the

Royal Society, i. 227.
Hankel, Hermann, generalising aspects
of the sciences, i. 46 ; quoted on
the establishment of analysis as a
science, 103 ; ' Die Entwickelung der
Mathematik,' 175 ; ' Theorie der com-
plexen Zahlensysteme,' 185 ; ii. 710 ;
' Die Elemente der Projectivischen
Geometric, ' i. 188 ; ii. 632 ; on the
two processes of algebra, 640 ; on
Grassmann, ih., 656; on Peacock
and de Morgan, 641 ; on Gauss's
theorem, 645 ; on imaginaries, 653,
664 ; Poncelet's principle, 661 ; on
Gergonne's principle of duality, 666 ;
on Steiner, 668 ; compares von
Staudt with Chasles, 669 ; on Mobius,
682 ; on fundamentals, 703 et seq. ;
on English mathematics, 704, 711 ;
on oscillating functions, 706 ; on
Bolzano and Cauchy, 709 ; principles
of arithmetic, 711 ; on principle of
permanence, 712 ; on quaternions,
ib., 717; 726.

Hanle's ' Magazin,' i. 43.

Hanselmaun, ' K. F. Gauss,' i. 181.

Hansen, lunar theory, i. 329.

Harcourt, Vernon, i. 236.

Harding, discovery of planets, i. 182.

Harkness and Morley, theory of
functions, ii. 704.

Harmonic functions, ii. 696.

Harriot, a forerunner of Bacon, i. 94.

Harris, James, language, ii. 536.

Harris, Snow, referred to by Faraday,
ii. 69.

Harrison, received prize of Board of
Longitude for his chronometers, i.
158 ; astronomical instruments, 322.

Hart, J. M., testimony to work of
German universities, i. 225.

Hartmanu, ii. 470, 60S.

Hartnack and Nachet, improvement in
immersion system, ii. 228.

Harvey, contemporary with Bacon, i.
94 ; discovery of the circulation of
the blood, 193 ; 272 ; contributions
to biology, 282 ; 292 ; study of sep-
arate organs, ii. 233; "metamor-
phosis," 278 ; embryology, 297 ; 349,
444.

Hatchett, not member of any univer-
sity, i. 238.

Haukesbee, Francis, capillary phenom-
ena, i. 346 ; experiments of, 355, 356.

Hauptmann, C, 'Die Metaphysik in der
modernen Physiologic,' ii. 401, 438 ;
quoted, 407, 444.

Hausser, L., i. 59.

Haiiy, Abbe, physics at the Ecole nor-
male, i. 112 ; crystallography of,
116, 117 ; services of, to mineralogy,
118 ; 136 ; created the science of
crystallography, 441 ; labours of, ii.
222 ; founder of crystallography,
240 ; 241 ; crystallography, 264 ;
building up of crystals, 270.

Haym, Rudolf, 'Leben W. v. Hum-
boldts,' i. 38; chief authority on
Herder, 51 ; biographies of Hegel
and others, ■ 279 ; ' Herder nach
seinem Leben und seinen Werken,'
ii. 531, 533, 537.

Hayward, algebra of 'Coplanar Vec-
tors,' ii. 656.

Heat, Tyndall's dynamical theory of,
ii. 57 ; dynamical theory of, 73 ;
Black, Rumford, and Davy, 102 ; the
non-mechanical nature of heat-phen-
omena, 120 et seq. ; and perpetual
motion, 126 et seq. ; of the sun, 357.

Heaviside, Oliver, popularisation of
Maxwell's electro - magnetic theory,
ii. 72 ; 193 ; his directional calculus,
655, 656.

Hecker, .J. J., established " Realschule"
at Berlin, i. 166.

Heeren of Gcittingen University, i. 165 ;
and Ukert, collections of Histories of
all countries, 167.

Hegel, G. W. F., on the province of
philosophy, i. 36 ; treated science

INDEX.

775

from a metaphysical standpoint, 43 ;
philosophy of, intiuenced by Herdei-,
51 ; ridiculed search for new planets,
54 ; on status of philosophy, 60 ;
his definition of philosophy, 61 ; re-
lation of philosopliy to religion, 73 ;
' PhJinomenologie des Geistes,' 83;
spontaneous development of thought,
85; 'Geschichte der Philosophie,'
145 ; 162 ; speculative tendency of,
178 ; philosophy of, 204, ii. 279, 346,
500 ; i. 207, 208 ; encyclopajdic lec-
tures on philosophy, 214 ; benefac-
tions to historical sciences, 215 ;
Schelling's scheme of evolution, ii.
354 ; 495 ; dialectics, 530 ; 60S, 751.

Hegelianism, failure of, i. 72.

Heidenhain, Prof., function of gland-
cells, ii. 429.

Heine, E., ii. 704, 733.

Helm, Dr Georg, 'Die Lehre von der
Energie,' ii. 97, 142, 185, 186; 'Die
Energetik nach ihrer gescliichtlichen
Entwickelung,' 97, 106, 108-111, 125,
127, 133, 138 ; controversies as to
priority of discovery in theory of
energy, 97, 98 ; influence of Poucelet
on practical mechanics, 101 ; heat
nnit, 109 ; labours of Horstmann,
170; methods of W. Gibbs, 171;
criticism of mechanical view, 183 ;
188.

Helmholtz, metaphysical foundations
of geometry and dynamics, i. 45 ;
'Eeden' quoted, 175; on speculative
tendency in science, 179 ; on Goethe
as a naturalist, 180 ; ' Vortrage,' 193 ;
198, 199 ; doctrine of the conserva-
tion of energy, 2')1 ; on the relations
of mathematical and experimental
science, 205 ; ' Wisseuschaftliche
Alihandlungen,' ib. ; 'Vortrage und
Reden ' quoted, 209 ; ' Ueber das
Deiiken in der Medicin,' 210 ; revival
of doctrine of conservation of force,
218 ; on Kant, 219 ; 220 ; ' Journal
fur Mathematik,' 231 ; Fourier's
series, 241 ; "sense perceptions," 243 ;
on Young, 244 ; ' Ueber die Erhaltung
der Kraft,' 265, 309 ; on Faraday's
ideas, 266 ; vortex motion, 313, ii.
35, 60 ; on the gravitation theory, i.
352 ; 375 ; objection against Weber's
law, 376, 377 ; "action at a distance,"
380 ; on the electro-chemical theory,
405 ; investigations of fluid motion, ii.
58; articles on acoustics, ib. ; "vor-
tex filaments," 61 ; influence of his
speculations in England, 62 ; illus-

trations of his theories, 63; suggested
vortex-atom theory, 66 ; ' Faraday
Lecture ' quoted, ib. ; adopted views
of English scientists, 93 ; independ-
ence of Mayer's writings, 97 ; his
work theoretical, 99 ; " physical me-
chanics," 101 ; scientific services of,
106 ; memoirs refused by Poggendorf,
107 ; classical character of his in-
vestigations into the nature of heat,
112; 'Gesammelte Abhandlungen,'
113 ; his recognition of the claims of
Mayer, 114; 117; and Sadi Carnot,
123 ; perpetual motion, 124 ; conser-
vation of energy, 125, 127, 130, 142,
438; "death" of the universe, 131;
mathematical treatment of power and
work, 137 ; on tension, 138 ; 141 ;
energetics, 148 ; electro - dynamics,
149 ; theories of electro-dynamic phen-
omena, 152 ; Faraday Lecture, 154 ;
dissociation, 163 ; thermal measure-
ments, 172; "free energy," 173;
chemical equilibrium, 175 ; quoted,
182 ; atomic view, 189 ; atom of elec-
tricity, 193 ; memoir of, 195 ; ether
theory, 196 ; imperfections of tlie eye
as an optical instrument, 215 ; micro-
scopic work, 229 ; Goethe's theory of
colours, 245 ; Kant's theory, 282 ;
appreciation of Kant, 284 ; "energy,"
355 ; physical laws, 356 ; cosmical
origin of life, 369 ; on vitalism,
388 ; 391 ; 'Physiological Optics,' 397,
480, 508; 'Physiological Acoustics,'
397 ; nature of living forces, 398 ;
403, 421, 467 ; animal magnetism,
476; quoted on "specific energies,"
482 ; optics, 483, 506 ; psycho-physi-
cal science, 485; "Timbre," 488;
aiTangement of tones, 490 ; and Kant,
491 ; psycho - jihysical phenomena,
496 ; space perception, 504 ; " Ueber
das Sehen des Jlenschen," 506 ; hear-
ing and seeing, 512 ; language, 538 ;
on liarmonics, 623 ; on foundations
of geometry, 710 ; letter to Schering,
ih. ; on axioms of geometry, 711 ;
and Riemann on geometry, 713.

Helvetius, ignorance of physiology, ii.
471.

Henle, Jacob, reconstruction of "gen-
eral anatomy," i. 195 ; 198 ; anthro-
pological lectures of, 215; mechanical
views in biology of, 219 ; on demon-
stration of Bell's doctrine, 293 ;
' AUgemeine Auatomie,' ii. 401.

Henrici, ii. 656.

Henry, Dr, not member of any univer-

776

INDEX.

sity, i. 239; 'Life of Daltou,' 246;
on Charles Bell, 292.
Heraclitus of Ephesns, i. 314 ; the
"kinetic theory," 385 ; conception of
eternal motion, ii. 3 ; conception of
changing world-periods, 286.
Herapath, "mechanical theory of

gases," i. 310; 434.
Herbart repudiated by Lotze, i. 49 ;
208 ; educational influence of, in
Germany, 257 ; phrenology, ii. 478 ;
anticipated Helmholtz, 491 ; influ-
ence of his philosophy, 494 ; on
"faculty -psychology," 495; psycho-
logical research, 496 ; mathematical
psychology, 498 ; 500 ; psychical
mechanism of, 504 ; space percep-
tion, 506 ; 507, 512, 515 ; introspec-
tive method, 527; " Volkerpsych-
ologie" and " Sprachwissenschaft,"
530.
Herbert, Dean, natural selection, ii.

330.
Herder, i. 50 ; History of Humanity,
51; 'Ideen,'53; ' Metakritik,' 83 ;
indebtedness to Gibbon, 169 ; 171 ;
cited on Georg Forster, 179 ; scien-
tific ideal of, 211 ; 212 ; Alcaic and
Sapphic metres, 213 ; educational
influence of, in Germany, 257 ; 258 ;
scientific work of, ii. 210 ; influence
of, 225 ; 280 ; philosophy of, 346 ;
psycho-physical view of nature, 531 ;
quoted, 533 ; 'History of Mankind,'
534 ; 538, 563.
Heredity, problem of, ii. 343, 613.
Hering, ii. 442 ; ' Ueber das Gedacht-
niss als eine allgemeine Funktion der
organischen Materie,' 544.
Hermann, Gottfried, indebtedness to
Bentley, i. 169; 162, 172; science
for its own sake, 211 ; 212, 214 ;
classical learning of, 222.
Hermann, Jac, Leibniz's letter to,

quoted, ii. 646.
Hermite, researches of, ii. 124 ; 649 ;
on determinants, 683 ; on transcend-
ent numbers, 731.
Herodotus referred to on division of

History into centuries, i. 13 ; 296.
Herrmann, Cr., quoted, ii. 266.
Herschel, Caroline, discovers her eight

comets, i. 229 ; 285.
Herschel, Sir John, i. 177 ; quoted on
Laplace, 123; astronomical work of,
230 ; introduction of knowledge of
Continental mathematics to Cam-
bridge by, 233 ; science in England,
234 ; 236 ; and Airy, article in ' En-

cyclopedia Metropolitana,' 236 ;
quoted on Fresnel, 241 ; educational
movement jjromoted by, 261 ; ' A
Preliminary Discourse on the Study
of Natural Philosophy,' 263, 306 ;
founded Anal}i;ical Society, 271 ;
spectrum analysis, 278 ; stands on
Bacon's philosophy, 307 ; 376 ; phe-
nomenon of fluorescence observed
by, ii. 52 ; criticism of the term
"potential energy," 140; 295; 'In-
troduction to the Study of Natural
Philosophy,' 328 ; experiments at the
Cape, 357 ; "sound," 488; theory of
probabilities, 569 ; 606.
Herschel, Sir William, ' On the Proper
Motion of the Sun and Solar System,'
i. 176 ; astronomical discoveries of,
229 ; 238, 285 ; discovery of Uranus,
324; 'Observations of Nebulaj,' ii.
283 ; nebular theorv, 295.
Hertwig, 0., 'The Cell,' ii. 224, 265,
297, 370, 371, 373, 420, 427, 444, 461 ;
embryological researches, 228 ; ' The
Biological Problem of To-day,' 298,
459 ; ' Zeit und Streitfragen zur Bi-
ologic,' 401 ; quoted, 409 ; ' The Cell,'
quoted, 425, 446, 448 ; " idioplasma, "
448 ; ' ' organicisme, " 455.
Hertz, H., electric theory, i. 344 ; elec-
trical wave-motion, ii. 77 ; electrical
view of light, 88, 92; "physical
mechanics," 101; electro - magnetic
wave-motion, 148 ; 193.
Hess, a founder of physical chemistry.

ii. 152; 157.
Hesse, Otto, his elegant work, ii. 677 ;
introduces determinants, 682 et seq.;
and invariants, 684.
Hessel, ' Krystallometrie,' i. 443.
Hettner, history of the idea of humanity,
i. 50 ; literary history of the eigh-
teenth century, 59 ; cited on Georg
Forster, 179.
Heun, ' Jahresbericht der deutschen

Mathematiker-Vereinigung,' ii. 101.
Heussler, Hans, on Bacon, i. 94.
Heyne of Gottingen University, i. 165 ;

indebtedness to Bentley, 169.
Hicks, 'Report on Hydrodynamics,' ii.
58 ; contribution to vortex theorv.
63. ■"

Higgins, theory of, i. 398.
Hilbert on algebraic numbers, ii. 729.
Hildebrand, Bruno, statistics, ii. 561.
Hillebrand, Karl, ' Zeiten, Volker, und

Menschen,' quoted, i. 311.
Hippeau, C, ' Public Education during
the Revolution in France,' quoted, i.

INDEX.

777

108 ; 109 ; quotes Condorcet, 111 ;
' L'Instruction publique en France
pendant la Revolution,' 259.

Hippocrates, ii. 470.

Hirn, the steam-engine, i. 331, ii. 133 ;
indestructibility of force, 111 ; con-
troversy with Zeuner, 135 ; 179.

Hirsch, DrA., 'Gesch. d. medicinischen
Wissenschaften in Deutschland,' i.
210, ii. 390, 401.

Hirzel, Sal., i. 167.

His, VV., ii. 271.

Histology, Huxley on, i. 196.

Historians, supposed objectivity of, 1.
7.

Historical geography, i. 294.

History, contemporary, to what extent
possible and valuable, i. 6 ; Goethe
quoted on re-writing of, 7 ; periods
of, 13 ; philosophy of, due to Con-
tinental thinkers, 25 ; periods of,
take their name from some gi-eat
event or movement, 58 ; and science,
relations of, 206.

Hittorf, W., on attraction in chemical
phenomena, i. 380 ; fellow - worker
with Pllicker, ii. 76 ; electrolysis,
164 ; vacuum-tube experiments, 190.

Hobbes, philosophy of, i. 48 ; ' De Cor-
pore ' quoted on Harvey, 282 ; 385, ii.
473.

Hobsou, on the infinite, ii. 736.

Hoff, Prof, van't, i. 431, 450 ; ' Journal
ftir physicalische C'hemie,' ii. 158 ;
(see Ostwald), 159 ; researches of,
164 ; discovery of, 165 ; carbon tetra-
hedron of, 424.

Hoffmann, F., animist, 1. 126.

Hofmaun, A. W. von, on Liebig, i. 18,
188 ; scientific experiments under, 92 ;
chemical researches of, 412; "Fara-
day " lecture, ii. 391 ; 393.

Hofmeister, Wilhelm, the genetic con-
ception of plant life, ii. 224 ; induc-
tive school of, 321.

Hogg, 'The Microscope,' ii. 228.

Holbach, 'Systeme de la Nature,' i.
144.

Holger, von (see Baumgartner), ii. 107.

Holman, Prof. S. W., ' Matter, Energy,
Force, and Work,' ii. 182.

Holtzmann, investigations into nature
of heat, ii. 112; and Clausius, 135.

Holtzmiiller on isogonal relations, ii.
701.

Homer, i. 261, 296.

Homoeopathy, i. 210.

Homogeneous formulae, ii. 681 ; co-
ordinates, Mobius, 681,

Homologj', study of, ii. 258; in geo-
metry, 663.

Hooke, Dr Robert, "reciprocal dupli-
cate " ratio, i. 98 ; used the term
" cell," 195 ; 283, 434 ; referred to by
Young, ii. 18 ; theory of elasticity,
30 ; compound microscope, 228.

Hooker, Sir J. D. (see Darwin), ii. 329 ;
Darwin to, 406.

Hopital, Marquis de 1', adopted the
calculus, i. 101.

' Horen ' of Schiller, i. 84.

Horner, 'Edinburgh Review,' i. 273,

Horsley, edition of " Newton's Works,"
i. 355.

Horstmann, labours of, ii. 170; free
energy, 173.

Houil referred to, ii. 653 ; on non-
Euclidean geometry, 714.

Hovelacque, Abel, ' La Linguistique,'
ii. 540.

Howard, Luke, classification of clouds,
i. 286.

Huber, investigations of, ii. 415.

Huggins, Sir William, light, ii. 11.

Hugo, Prof., of Gottingen, translated
44th chapter of Gibbon's ' Roman
Empire,' i. 169.

Humboldt, A. von, on scientific state
of Paris at the close of the eighteenth
century, i. 17; ' Kosmos,' 51, 53, ii.
277, 284, 328, 329, 532 ; ' Life ' by
Bruhns, i. 207, 253, 263 ; travels in
America, i. 83 ; eminence in scien-
tific literatiire of, 105 ; his influence
as pojiulariser of the study of natural
history, 106 ; 133, 155 ; and Gauss's
scheme for a network of magnetic
observations, 167 ; 171, 175, 176 ;
uninfluenced by speculative spirit in
German science, 178 ; cited on Georg
Forster, 179 ; 183, 190 ; supported
scientific institutions at Berlin, 238 ;
Bell's theorem, 293 ; founded, with
Oken, " Naturforscher - Versamm -
lung," 298; and Gay-Lussac, 425;
popular work of, ii. 149 ; explorations,
206 ; travels, 222, 247 ; morphology,
225, 226 ; 252 ; extension of mor-
phological view, 260 ; and Robert
Brown, 265 ; 266 ; influence of, 276 ;
293, .300; 341, 390, 467; animal
electricity, 475, 476 ; 514, 607.

Humboldt, W. von, creator of Berlin
University, i. 38 ; 203, 206, 212, 253,
263 ; comparative jjhilologv, ii. 538 ;
542.

Hume, David, transition from the logi-
cal to the historical view, i. 46 ;

778

INDEX.

opposed metaphysics, 75 ; influence
of, on German thought and literature,
212 ; sceptical philosophy of, replied
to by Kant, ib. ; and Kant, 219 ; in-
tercourse with French thought, 268 ;
influence of, '273; ii. 279 ; and German
criticism, 323 ; 326 ; psychology, 497 ;
genetic view, 506 ; the study of
mankind, 529 ; quoted, 555.

Hunter, John, English medical science,
i. 208 ; anatomist, 283 ; ii. 247.

Hunter, John and William, no connec-
tion with the English universities, i.
272.

Hutton, James, a follower of Boscovich,
i. 359 ; study of fossil remains, ii.
225 ; Cuvier's "catastrophism," 250 ;
school of geology, 291 ; genetic view
in geology, 330 ; 364 ; and Jameson,
services to the study of natural his-
tory, i. 283 ; 290.

Huxley, T. H., 'Lay Sermons' and
other writings, i. 193, 201 ; quoted,

193, 292, ii.'^252, 256, 257, 348, 376,
405, 448; 'American Addresses,' i.

194, ii. 364 ; on individuality of
English scientists, i. 250 ; ' Science
and Culture,' 282; 'Essay on Geo-
logical Reform,' 283; 'Geological
Reform ' quoted, 291 ; ' Critiques and
Addresses,' 298; 'Life of Charles
Darwin,' 310 ; on Whewell and the
mechanical equivalent of heat, ih. ;
'Scientific Aspects of Positivism,'
310; onComte, 'Lay Sermons' quoted,
ii. 37 ; extract from " Lecture on the
Study of Biology," 217 ; quotation
from 'Life of Richard Owen,' 222;
Goethe's ideas, 244, 246 ; Cuvier's
work, 248 ; quoted on vertebral
theory of the skull, 251 ; on Hum-
boldt, 253; the term "homology,"
259 ; on Cuvier and Oken, 260 ;
268; "Evolution in Biology," 278,
297, 347 ; controversy with Kelvin,
284; on Hutton, 291, 292; and
Von Baer, 299, 302; 305; historical
connection of Lamarck's ideas, 309 ;
"Biology," 313; 321 ; theory of de-
scent in France and Germany, 322 ;
"Agnosticism," 326 ; "Reception of
the 'Origin of Species,'" 327 ; 329 ;
address to the Geological Society,
363; 'On Descartes,' 378; "vital-
ism," 406; 411 ; "On the Cell Theory,"
423 ; history of Biogenesis, 451 ; the
ubiquity of life, 452 ; psycho-physi-
cal parallelism, 519 ; theory of reflex
action, 520.

Huygens, Chr., variation of gravity in
different latitudes, i. 99 ; 103 ; the
theory of probabilities, 120 ; mechan-
ical laws established by, 317 ; New-
ton and, ib. ; formulte of, 335 ;
mechanical explanation of gravita-
tion ; 342, 351 ; phenomena of gravi-
tation, 353 ; 389 ; kinetic view of
nature, ii. 6 ; 8 ; followed by Young,
9 ; the theory of light, 13, 14, 17 ;
periodic wave-motion, 21 ; 'Traite de
la Lumiere,' 22 ; motion of light, 42 ;
conservation of energy, 99, 100 ; on
probability, 565, 568.

Hyatt, A., neo-Lamarckian, ii. 351.

Ideal elements, ii. 664 ; Poncelet on,
674 ; numbers, 727 ; Kummer's, 728.

Ideals of life during nineteenth cen-
tury, i. 32.

Ideas, migration of, i. 29.

Ideologues, Napoleon and the, i. 152 ;
ii. 3'23.

Imaginary, the, Cayley on, ii. 716.

' Index Lectionum ' of Gottingen Uni-
versity, i. 165.

Individualism of English character, i.
279.

Individuality the centre of interest of
the sciences, i. 125 ; ii. 746.

Individuation, ii. 415.

Inductive reasoning in England, i. 103.

Infinite, the, ii. 643, 735 ; Hobson on,
736.

Infinitesimal methods, necessity of de-
veloping, i. 373.

Infinitesimals, method of, ii. 706.

Inheritance, inarticulate, ii. 615.

Inquiry, scientific method of, i. 30.

Institute, French, reports of, i. 149.

Institution, Royal, i. 264.

Interests, human, unity of, i. 33.

Introspective method, ii. 527.

"Invariants," doctrine of, ii. 140, 676 ;
MacMahon on, 676 ; history of, 677 ;
unknown to Pliicker, 677 ; Sylvester
on, 684 ; diflerent methods in, ib.

Inventions, accidental, in sixteenth,
seventeenth, and eighteenth centuries,
i. 91.

Inverse operations, ii. 639, 727.

"Ions, migration of," ii. 164; 198.

Ireland, Alexander, on authorship of
the 'Vestiges,' ii. 318.

Irvine, Dr, the term "capacity" first
used by, ii. 102.

Isenkrahe, C, 'Das Rathsel von der
Schwerkraft,' i. 341, 342, 343, 377 ;
refers to Euler's ether theory, ii. 8.

INDEX.

779

Isherwood, researches of, ii. 135.

Isonierisni, discovery of, ii. 405.

Isomorphism, ii. 444.

Ivory, scientific work of, i. 229 ; well
known among Continental mathema-
ticians, 232 ; not member of any
university, 238 ; maintaiue'i reputa-
tion of British mathematicians, 270.

Jacobi, C. G. I., i. 44 ; ' Werke,' 185 ;
187, 189 ; inJiuence on Helmholtz,
199 ; 200, 205, ii. 637 ; his relation to
Legendre and Abel, 648 ; on deter-
minants, 683, 686 ; Theta function,
696, 728.

Jacobi, F. H., 'Offener Brief an Fichte,'
i. 83 ; 162 ; influenced by Spinoza,
212 ; psychology, ii. 495.

Jaeger, Dr, "gerunnal" element, ii.
457.

' Jahresberichte ' of Berzelius, i. 167.

James, Alex., process of cellular
division, ii. 445.

James, King, charter to Edinburgh
University, i. 268.

James, Prof. W., ' Principles of Psy-
chology,' ii. 479, 513, 519 ; quoted,
522, 539.

Jameson founded Wernerian Society,
i. 118 ; 288.

Janiin, speed of light, ii. 45.

Januschke, Hans, ' Das Princip der
Erhaltung der Energie,' ii. 152.

Japp, Prof., "Stereo -chemistry and
Vitalism," ii. 437; selective action
of certain organisms, 598.

Jardin des Plantes, i. 107.

Jeffrey, ' Edinburgh Review,' i. 273.

Jenner, Edward, no connection with
the English universities, i. 272 ; 284.

Jevons, Stanley, ' Principles of Science,'
i. 37, 308 ; on theory of probabilities,
120 ; 325 ; Bacon's " method of in-
stances," ii. 558, 559 ; ' Principles of
Science ' quoted, 560, 569 ; 737.

Joachim of Brandenburg, founds Uni-
versity of Kouigsberg, i. 159.

John Frederick, Duke of Hanover, i.
158 ; founds University of Jena, 159.

John, v., 'Gesch. d. Statistik,' ii. 555,
587 ; statistics, 563 ; 564 ; quoted, 579.

Jones, Bence, 'The Royal Institution,'
i. 90.

Jordan, Camille, his 'Theorie des
Substitutions,' ii. 686, 692.

Joseph II., i. 256.

Joule, James Prescott, the mechanical
equivalent of heat, i. 93 ; doctrine of
the conservation of energy, 201 ;

"J" or Joule's equivalent of heat,

265 ; and Dalton, ib. ; not connected
with Cambridge Mathematical School,

266 ; not member of any uiuversity,
272 ; determination of the equival-
ent of heat, 309 ; "mechanical theory
of gases," 310; 313; paper on mol-
ecular action, 433 ; calculations of,
434 ; 435, 437 ; ii. Ill ; kinetic
theory of gases, 34, 162 ; dyn-
amical theory of heat, 73 ; inde-
pendence of Mayer's writings, 97 ;
and Tyudall, 107 ; heat unit, 109 ;
scientific work of, 110 et seq. ; a pupil
of Dalton, 111 ; indestructibility of
force, ib. ; revival of interest in the
ideas of "Energy," ll4 ; his measure-
ments utilised by Clausius and Thom-
son, 116 ; practical foundation of his
researches, 117 ; perpetual motion,
124 ; two laws of thermo-dynamics,
128 ; force, 130 ; subjection of physi-
cal phenomena to dynamical laws,
132 ; measurements of, 133 ; and
experiments, 137; "Thermal Unit,"
139 ; conservation of energy, 142 ;
electrical phenomena, 146 ; law of,
147 ; electrical measurements, 156 ;
heat, 178; "energy," 355; statistics
in physics, 590, 592.

Jousse, geometrical work of, i. 114.
Julius of Brunswick founds University

of Helmstadt, i. 160.
Juugfleisch, ii. 437.
Jurin, Dr, experiments in capillary

attraction, i. 356.
Jussieu, Ant. Laurent de, author of

' Genera Plantarum,' ii. 222, 235,

265.
Jussieu, Bernard de, contributions to

the study of natural history, i. 116 ;

119 ; botanical work of, 126 ; referred

to, 265.
Justi, 'Winckelmann,' i. 279,

Kane, his work overlooked, i. 414.

Kant, scientific methods insulBcient by
themselves, i. 36 ; influenced popu-
larity of lectures on "Encyclopiidie,"
37 ; a century before his time, 45 ;
style of, 51 ; decadence of philosophi-
cal thought after, 78 ; radicalism of
thought of, 81 ; ideas of, developed
by Schiller and others, 83 ; Helm-
holtz and the philosophy of, 199 ;
influenced by political movements in
France and America, 203 ; influence
on development of German schools of
medicine, 208 ; 211, 212 ; mathemati-

780

INDEX.

cal and physical sciences affected by,
216 ; infiuence of, on the development
of modern German science, 219 ; and
Hume and Descartes, 222 ; influence
of, on education in Germany, 257 ;
was inspired by Rousseau, 259 ; in-
fluenced by Hume, 273 ; philosophy
of, dispelled Cartesian philosophy in
Germany, 433 ; cosmological genesis
of planetary system, ii. 209 ; nebular
theory, 277, 282 ; late development
of, 309 ; ' Critique of Pure Eeason,'
326 ; philosophical theories, 346 ;
metaphysics, 354; "si^ecific ener-
gies." 482 ; science of sensation, 484 ;
time and space, 491, 492 ; the mind,
497 ; space perception, 506 ; and
Herder, 532, 535; freewill, 584;
634 ; 751.

Kastner of Gottingen University, i.
165.

Kater, scientific work of, i. 230.

Kaufmann, W., Hamburg Address, ii.
190, 197.

Kaup, Jacob, 'Skizzirte Entwickelungs-
geschichte und natiirliches System der
Europaischen Thierwelt,' ii. 317.

Kayser, spectroscopic observations, ii.
361, 362.

Keill, John, molecular attraction, i.
355.

Kekule, chemical researches of, i. 412 ;
' Lehrbuch der organischen Chemie '
quoted, 421, 448 ; explains pheno-
menon of multiple proportions, 447 ;
theory of aromatic compounds, 449 ;
benzine ring, ii. 424.

Kellaud's edition of Young's writings
quoted, ii. 98, 104.

Kelvin, Lord. See Sir William Thom-
son.

Kepler, Bacon's indebtedness to, i. 94 ;
118 ; three laws, 157, 318 ; received
logarithms with enthusiasm, 269 ;
Newton and, 317 ; 374 ; father of
modern astronomy, 386 ; astron-
omical work of, ii. 227 ; 634.

Kerner von Marilaun, ' The Natural
History of Plants ' quoted, ii. 376.

Kerry, B., on G. Cantor and mathe-
matics, ii. 634 ; 734.

Ketteler, ' Theoretische Optik,' ii. 54.

Kielmeyer and the Naturphilosophie,
i. 207 ; ii. 349.

Kieser, D. G., and the Naturphilosophie,
1. 207 ; ii. 230 ; phytotomic researches
in Germany, 261.

ELinetic, view of nature, ii. 3 ; the word
introduced by Ampere, 5 ; revival of

kinetic view in nineteenth century,
7 ; theories, 34 ; theory of gases, ib. ;
view of nature, insufficiency of, 96 ;
the term substituted for "actual,"
139; "kinetics" and "energetics,"
180 ; 465, 574.

Kirchhoff, Gustav, 'Mechanik,' i. 45;
' Vorlesungen iiber Mathematische
Physik,' 231 ; discovery of spectrum
analysis, 277 ; coincidence between
electrical wave - motion and light,
372; Weber's law, 380; definition
of "mechanics," 382; Frauuhofer's
lines, ii. 48 ; ' Gesammelte Abhand-
lungen,' ib. ; caesium and rubidium,
49 ; emission and absorption of light
rays, 50 ; 51 ; spectrum analysis, 56 ;
"physical mechanics," 101.

Kirwan, i. 117, ii. 291.

Klaproth, i. 117 ; forerunner of Berze-
lius, 391 ; 393.

Klein, 'G. Forster in .Mainz,' i. 179.

Klein, Felix, pupil of Pliicker, ii. 76 ;
his geometrical tract, 632 ; on the
period of Euclid, 635; 'Evanston
Colloquium' quoted, ib. ; on abridged
mathematics, 636 ; 686 ; his ' Erlangen
Programme,' 690; and Lie, 691, 692,
718, 720 ; his tract on Riemann's
theory, 698, 699 ; on Riemann's in-
fluence, 700 et seq. ; on Riemann
and Weierstrass, 707 ; on Dirichlet's
principle, 708 ; on non-metrical rela-
tions, 713 ; on non-Euclidean geom-
etry, 715 ; on Cayley and von Staudt,
718 ; on generalised notion of dis-
tance, ib. ; on famous problems, 721,
731 ; on arithmetising tendency, 738, 1

740. I

Klopstock, Alcaic and Sapphic metres
of, i. 213. a

Knapp, statistics, ii. 563, 566. ■

Knott on directional calculus, ii. 656. ■

Knowledge, accumulation of, in nine-
teenth century, i. 28 ; method and
unity of, 29.

Knox, John, creator of Scotch educa-
tional system, i. 253 ; ' First Book of
Discipline,' 255.

Kobell, 'Geschichte der Mineralogie,' i.
117.

Kochly, i. 162; 'Gottfried Hermann,'
169.

Kohlrausch, F., electrolysis, ii. 164.

Kohlrausch, R., electrical measure-
ments, i. 369; ii. 84.

Kolbe, chemical researches of, i. 412 ;
attacks of, on 'Modern Chemistry,'
455.

INDEX.

781

Kolliker, von, quoted, ii. 401; "idio-

plasma," 448.
Konig, Ed., on Wundt, ii. 513.
Kcinig, H., ' G. Forster in Hans und

Welt,' i. 179.
Konigsberger, L., 'Zur Geschichte der

Theorie der elliptischen Transceu-

denten,' i. 185, ii. 648.
Kopke, Rudolf, ' Die Griindung der

Koniglichen-Wilhelms-Universitat zu

Berlin,' i. 263.
Kopp, Hermann, on the reports of

Berzelius, i. 42 ; ' Die Entwiclceluug

der Chemie,' 115, 246, 418, 419, ii. 154 ;

'Geschichte der Chemie,' i. 175, 188,

191, 308 ; quoted on Lavoisier, 386,

387; quoted, 391, 393, 398, 407,

421, 422; electro - chemical theory,

405 ; 408 et seq., 413 ; Avogadro's

hypothesis, 428 ; on J. Black, ii. 102 ;

founded physical chemistry, 153 ; 157.
Kossak, E., on Weierstrass, ii. 712 ; 734.
Kotter, E., on Poncelet's principle of

continuity, ii. 660 ; on von Staudt,

661.
" Kreislauf des Lebens," ii. 395.
Kronecker, ii. 727, 729 ; on arithmetis-

ing, 738.
Kronig, A., ' GrundzUge einer Theorie

der Gase,' i. 433 ; ii. 162 ; 179.
Krug, representative of encyclopaedic

teaching, i. 38.
Kunimer, ii. 680, 726 ; ideal numbers,

728.
Kundt (see Christiansen), ' Die neuere

Entwicklung der Electricitatslehre,'

i. 380.
Kuntze, quoted in reference to the

brothers Weber, i. 197 ; biography of

G. T. Fechner, 200 ; ii. 608.

La Beche, de, palaeontological work of,
i. 139.

Lacepede, i. 119.

Lacroix, geometry, i. 44 ; ' Differential
and, Integral Calculus,' 233; student
at Ecole normale, 237 ; ii. 643, 686.

Ladeuburg, ' Vortriige iiber die Ent-
wicklungsgeschichte der Chemie,' ii.
158.

' Ladies' Diary,' i. 236, 238, ii. 679.

Laennec, French medical science, i. 208.

Lagrange, mechanics, i. 44 ; general
methods of, 45 ; adapts the calculus
to the problems of the 'Principia, '
102; ' Mecanique analytique,' ,105,
ii. 100; mathematics at the "Ecole
normale," i. 112; 113, 148, 181, 200,
233 ; 237 ; analytical methods of,

271; " potential function," 316 ; 319
theories elaborated by Gauss, 331
ii. 5 ; mathematical study of vibra
tions, 16 ; analytical school of, 100
dynamics, 138 ; his system mathe
matical, 144; 467, 510, 572; theory
of error, 575 ; 637 ; on fundamental
questions, 656; 669, 680, 690; and
Weierstrass, 693-695, 706.

Laguerre, ii. 715. ,

Lakanal on the Ecole normale, i. 109,
112; quoted. 111; 113; obtained a
decree from Convention to continue
sittings of the Academy during sus-
pension, 148; " Museum," ii. 311.

Lalande at the College de France, i.
107; 113, 167, 177; Clairault's at-
tempt to alter gravitation formula,
334.

Lamarck, ' Philosophie Zoologique,' i.
S3, ii. 309 et seq.; beginnings of Dar-
winian theory, i. 137 ; temporary
neglect of suggestions of, 179 ;
' Hydrogeologie,' 194; and the
'Origin of Species,' 201; ' Hydro-
geologie ' quoted, ii. 217 ; natural
history of vertebrates, 239 ; 247 ; and
Geoffroy Saint-Hilaire, 255 ; and Von
Baer, 316 et seq.; 321, 322, 327;
natural selection, 330, 351 ; adapta-
tion, 353; "environment," 394; his
.school, 431 ; 460, 470, 607, 621.

Lambert, J. H., i. 175 ; 'Photometry,'
'Pyrometry,' 176 ; 319; cosmological
letters, ii. 282.

Lame, treatises on mathematics and
physics, i. 45 ; theories of, 360 ; 379 ;
synthetic method, ii. 100 ; influenced
German thought, 101.

La Mettrie, ' L'Homme Machine,' i.
144; ' Histoire naturelle de I'Ame,'
lb.; ii. 699.

Landen, scientific services of, i. 229 ;
well known among Continental mathe-
maticians, 232 ; maintained reputa-
tion of British mathematicians, 270.

Lange, F. A., ' History of Materialism,'
i. 145, 385, ii. 323, 513, 584 ; "psy-
chology without a soul," 523.

Langley, function of gland cells, ii.
429.

Language portrays changes of thought,
i. 11 ; conventional, inadequate for
original thought, 12 ; the problem of,
ii. 536.

Lankester, Ray, "Zoology," ii. 232;
the term " homology," 259.

Lapeyronie
Chirurgie,

founded
107.

Academic de

782

INDEX.

Laplace, works of, i. 82, 97 ; Newton's
ideas elaborated by, 96 ; mathematics
at the Ecole normale, 112, 237; 113,
115; crystallography, 116 ; 'Systeme
du Monde,' 119, 319; 'Tbeorie analy-
tiqiie des Probabilite-s,' 120, 325 ; his
own iiopulariser, 122 ; statistics, 124 ;
126; and Cuvier contrasted, 132; 148,
154, 177, 181, 187, 200 ; "exact habit
of thought," 222; potential func-
tion, 231, 316 ; 241 ; Ualton's atomic
theory, 246 ; 264 ; researches of,
281 ; 306, 311 ; ' Mecanique celeste,'
319 ; 358 ; gravitation, 321 ; least
squares, 324; 326; the Tides, 330;
Gauss, 331 ; mathematical expres-
sion of astronomy, 333 ; emanation
theory of light, 344 ; 346 ; mole-
cules, 347 ; gravitation theory, 349 ;
molecular attraction, 354; 'Theorie
de I'Action capillaire,' 355 ; quoted,
356 ; St Veuaut quoted, 359 ; 362 ;
corpuscular theory of light, 370 ;
measurement of electrical action,
371 ; value of Newton's formula, 373 ;
Newton's law, 378 ; astronomical
view of nature, 380 ; opposed to
undulatory theory, ii. 16 ; on New-
ton's emission theory, 17 ; theory of
light, 20 ; opposed undulatory theory
of light, 24 ; on the commission which
crowned Fresnel's 'Memoire sur la
Diflraction,' 25 ; extension of gravita-
tion into molecular physics, 29 ;
theory of capillarity, 33 ; 'researches
into electrical phenomena, 67 ;
methods of, 70 ; school of, referred
to, 93, 100, 101 ; the material and
dynamical conceptions of heat, 118 ;
cosmological genesis of planetary
system, 209; 215; astronomical work
of, 227; 228; nebular theory,
277, 284 ; quoted, 285 ; 290 ; genesis
of the cosmos, 320 ; genetic view
anticipated by, 330 ; theory of, 357 ;
hypothesis of, 360 ; stability of solar
system, 386 ; animal heat, 390, 433 ;
analysis of phenomena of nature,
399 ; 474, 487 ; science of chances,
568 ; 569, 571, 572, 575 ; method of
least square, 576 ; doctrine of prob-
abilities, 578 ; influence of, 581 ;
statistical method in social questions,
599 ; curve of error, 616 ; 634, 637 ;
his ' Mecanique celeste ' and ' Theorie
des Probabilites,' 642; functions of,
696 ; 751.
Larmor, Jos., vortex theory, ii. 63, 64 •
' ^ther and Matter,' 89, 195 ; mathe-

matical theory of electricity, 193 ;
his position, 195 ; 197 ; atomic and
energetic views, 198 ; 595 ; on vectors,
656.
Lasswitz, 'Geschichte der Atomistik,'
i. 433, ii. 5; 'G. T. Fechner,' 369,
508; Fechner's philosophy, 513.
Laurent, revives Front's hypothesis, i.
402 ; attack on electro - chemical
theory, 409; "type theory," 411;
413; quoted, 419; "substitution"
in chemical combination, 429.
Laurillart, Bell's theorem, i. 293,
Lavater, Caspar, ' Physiognomische

Fragmente,' ii. 477.
Lavoisier, i. 114, 147 ; services to
France, 148 ; 170, 188, 200 ; scientific
method of, 306, 365 ; influenced by
Laplace, 380 ; theory of combustion,
386, 393 ; chemical researches, 391 ;
392, 399, 400 ; organic analysis, 407 ;
chemical balance, ii. 152"; atomic
view, 153 ; 379 ; and his school, 382 ;
animal heat, 390, 433 ; chemical ele-
ments, 398.
Lawes, Sir J. B., experiments and pub-
lications in agriculture, i. 284.
Layard, i. 294.
Lazarus, psychologist, ii. 497 ; the

objective mind in history, 530.
Leake, M. W., explorations of, i. 296.
Learning, apparent disintegration of, i.

30.
Least squares, method of, i. 120 ; 183 ;

ii. 576.
Le Bel, the carbon tetrahedron, i. 450.
Leblanc invents soda process, i. 92.
Le Breton, report on Fine Arts, i. 149.
Le Chatelier, ' Journal de Physique,' ii.

169, 173.
Lecoq de Boisbaudran, discovery of

gallium, i. 315, 423.
Legallois, ii. 519.

Legendre reforms geometry, i. 44 ;
' Theorie des Nombres,' 82 ; method
of least squares, 120, 183, ii. 576 ; i.
181 ; ' Traite des Nombres," 182 ;
'Nouvelles methodes pour la deter-
mination des orbites des cometes,' 183 ;
'Traite des fonctions elliptiques,'
185 ; 187 ; potential function, 231 ;
on elliptic integrals, ii. 648 ; his rela-
tion to Abel and Jacobi, ib. ; Konigs-
berger on, ih. ; on foundations of
geometry, 656 ; on svnthetic method,
670; functions of, 696; 721.
Lehmann, ' Molecularphysik ' quoted, 1.

Leibniz, i. 49 ; essay on, by the

INDEX.

783

author, 50 ; on thought, 66 ; or-
gauises scientific eft'ort, 100; "cal-
culus," 101 ; modern analytical spirit
of, 102 ; letter to Huygens on cal-
culus, 103 ; letter to Bodenhausen,
104; 105; 'Schriften,' 122; 137; at
the court of Brunswick, 158 ; the
Uuiversity of Halle, 160 ; encyclo-
paedic view of ' Wissenschaft,' 171;
modern science, 175 ; reaction against
his philosophy, 212 ; notation of,
233 ; 247, 283, 311 ; "energy," 312 ;
337 ; gravitation, 340 ; 358 ; letter to
Foucher, ii. 5 ; Euler's opposition to,
8 ; "vis viva," 100 ; indestructibility
of force, 111 ; inHuences German
philosophy, 205 ; scientific work of,
210; 'Protogfea,' 277, 280, 293;
' ' evolutionist, " 278 ; ' Protogcea '
quoted, 281 ; 288 ; epigenesis, 298 ;
genetic view anticipated by, 330 ;
364, 365 ; animation of all nature,
369 ; 403 ; idea of life, 409 ; monad-
ology, 500 ; 507 ; doctrine of pre-
established harmony, 519 ; (see
Herder), 535 ; the theory of language,
537 ; statistical information, 546 ;
555 ; Neumann's statistical tables,
565 ; science of chances, 568 ; theory
of probabilities, 573 ; 638, 643 ; his
dyadic system, 645 ; on convergency,
646 ; letter to Huygens, 659 ; on
determinants, 682 ; 706 ; science and
religion, 742.

Leitch, ' Miscellaneous Works ' of Dr
Young cited, i. 244.

Lelievre, i. 136.

Lemonnier at the .Jardin des Plantes, i.
107.

Lenard, discoveries of light rays, ii.
92 ; observation of cathode rays,
192.

Lenz, electrical phenomena, ii. 146.

Le Sage, "ultramundane corpuscles,"
i. 342 ; 344 ; quoted on Epicurus,
ii. 4.

Leslie, scientific work of, i. 229, 230 ;
Scotch university professor, 272.

Lessing, moralising style of, i. 51 ; and
Gibbon, 169 ; 171 ; the scientific ideal
of, 211 ; 212.

Leuckart, Rudolf, ii. 322 ; law of limit
of growth, 445.

Leuweuhoek, perfection of simple micro-
scope, ii. 228 ; reference to, 281.

Leverrier and the discovery of Neptune,
i. 277; "Association scientifique,"
298 ; astronomical achievements of,
314 ; meteoric hypothesis, ii. 357.

Lewes, G. H., on Herbert Spencer, i.
48; 'Life of Goethe,' 166; ii. 470;
phrenology, 478 ; "specific energies,"
483 ; 512 ; spinal chord, 519 ; 608.

Lexis, Prof. , ' Die deutsclieu Universi-
tateu,' i. 226 ; statistics, ii. 566.

Lhuilier referred to by Steiner, ii.
669.

Lichtenberg of Gottingen University, 1.
165 ; electricity and the Geissler
tubes, ii. 191 ; physiognomy, 477.

Lichton, John, Louvain University, i.
268.

Lie, Sophus, ii. 686 ; and theory of
groups, 690; and Klein, 691, 692,
718 ; on differential equations, 696 ;
on fundamental problem of geometry,
718 ; 720.

Liebig, J. von, laboratory at Giessen, i.
18; ' Jahresbericht der Chemie,' 42;
works on chemistry, 43 ; chemical
predictions of, 92 ; on Bacon, 93 ;
115 ; 162, 174 ; temporarily in-
fluenced by speculative spirit in
German science, 178 ; establishment
of chemical laboratories, 188 ; quoted,
190 ; his organic analysis, 191 ; and
Wcihler, 192 ; 194 ; metaphysical
leanings of, 196 ; 200 ; influenced by
the JWUurphilosophie, 207 ; freed
under the influence of French science,
208 ; underlying idea in foimding
chemical laboratory, 214; "vital
force," 218 ; Dalton's atomic theory,
246 ; agricultural exi:ieriments, 285 ;
'Familiar Letters on Chemistry'
quoted, 389; discovery of "isomer-
ism," 406; the "radicle" theory,
409 ; the hydrogen and the oxygen
theory of acids, 410 ; 412 ; quoted on
chemical research in England, 414 ;
his attitude towards the atomic
theory, 418 ; .scientific work of, ii.
105; ' Annalen der Pharmacie,' 107,
163, 170 ; Mohr's and Helm's first
papers published, lo9 ; appreciation
of Mohr and Mayer, 114; 'Die
Organische Chemie,' 115 ; organic
chemistry, 117, 391 ; dynamical
theory of he.at, 128 ; popular work of,
149; 152; (see Thos. Graham), 161;
biological studies, 208 ; physiological
processes, 390 ; 393 ; his influence,
394 ; 396 ; attempt to extend the
idea of " Stoffwechsel," 397 ; ' Chemi-
cal Letters,' 398 ; practical study of
nature, 404; "vitalism," 405; 406,
411, 420; Bacon's "method of
instances," 558.

784

INDEX.

Leibisch, ' Physikalische Krystallogra-
phie,' i. 443.

Liebreich, Oscar, discovered action of
chloral, i. 93.

Life and mind, ii. 216 ; what are they ?
462 ; mental, 496.

Life, problem of, ii. 352 ; what is it ?
381 ; Bichat's definition of, 383 ; 394 ;
and mind, .548.

Light, the undulatory theory of, i. 241,
ii. 153 ; i. 229, 236 ; theories of, ii. 8 ;
undulatory and emission theories,
11 ; undulatory theory prepared by
acoustics, 12 ; and sound, mechanical
difl'erence between, 30; speed of, 36 ;
corpuscular theory of, ib. ; speed, 45 ;
magnetisation of (Faraday), 74.

Limits, method of, ii. 706 ; Hankel on,
ih.

Lindemann, researches of, ii. 124 ; on
transcendency of number tt, 731.

Link, ii. 230 ; observations of, 261.

'Linnajan Society, Transactions of,' i.
41.

Linnseus, contributions to study of
natural history, i. 116; beginning of
geometrical crystallography, 117 ; 119 ;
system and nomenclature of, 126; 145;
classification of living beings, 288 ;
system of classification, ii. 220, 221,
232 ; basis of classification of veget-
able and animal kinfjdom, 234 ; first
four classes of, 238 ; 243, 251 ; classifi-
cations, 254, 336 ; 311.

Lionardo da Vinci, rules of perspective,
ii. 663.

Liouville recognised merits of Green's
work, i. 247 ; publishes Galois'
works, ii. 686 ; 726, 727.

Lister, improvements in microscope, ii.
228.

Listing, J. B., 'Vorstudien zur Topo-
logie,' ii. 63.

Literature, French, influence of science
on, i. 104.

Lloyd, Humphrey, experiments in re-
fraction, ii. 43.

Lobatchevsky, Vasiliev on, i. 161 ; ii
635 ; and Gauss, 652 ; pupil of Bar
tels, 653 ; 710, 713, 718.

Locke, David Hume and, i. 47 ; 144 ,
influence of, on German thought and
literature, 212 ; and Kant, 219
school of, 250 ; influence on educa
tional views in England, 253 ; influ-
ence on French philosophy, 273 ; new
line of thought adopted by, 311 ;
sensualistic philosophy, ii. 323 ;
psycho-physical view, 471 ; genesis of

space perception, 473 ; 497 ; genetic
view, 506 ; 516 ; language, 536 ; 751.

Lockyer, Sir Norman, nature of ele-
ments, ii. 192 ; 282 ; genesis of the
cosmos, 360; 'Inorganic Evolution,'
369.

Lodge, Sir 01., "The Second Law of
Thermodynamics," i. 331; 370; on
"action at a distance," 380; on the
ether, ' Modern Views of Electricity,'
ii. 38, 90, 163 ; popularisation of
Maxwell's electro - magnetic theorj^,
73 ; illustrations of Maxwell's theory,
90, 94.

Lommel, Ohm's 'Gesammelte Abhand-
lungen,' i. 365.

Longet, Bell's theorem, i. 293.

Longitude, Board of, i. 113 ; prize
offered by, 158.

Longitudes, Bureau des, i. 113.

Lorentz, H. A., mathematical theories
of electricity, ii. 193 ; 195 ; quoted,
195, 197.

Lorenz, 0., quoted on division of history
into centuries, i. 13 ; ' Die Geschichts-
wissenschaft,' 206.

Loria, Gino, i. 275.

Lotze, Hermann, definition of "reality,"
i. 32 ; contrasted with Herbert Spen-
cer, 48 ; quotation from ' Microcos-
mus,' 52 ; definition of philosophy,
65 ; constructive ideas of, 81 ; and
Fechner, 200; lectures on "encyclo-
pedia" of philosophy, 215 ; mechanical
view in biology of, 219 ; 220 ; phil-
osophy of, ii. 288 ; 401 ; "Leben und
Lebenskraft, " 401 ; 405 ; vitalism and
animism, 407 ; purpose and will, 408,
409 ; vitalism, 434 ; anticipated Helm-
holtz, 491 ; 492 ; influence of Herbart
on, 494 ; physiology of the soul, 500 ;
psycho-physics of vision, 504 ; theory
of "local signs," 508; medical psy-
chology, 512 ; psycho-physics, 517 ;
' Microcosmus,' 532; 549; quoted,
585 ; on non-Euclidean geometry, 716.

Louis XV., i. 107 ; and botany, ii. 235.

Love, A. E. H., 'Dynamics,' ii. 183.

Lowth, 'Lectures on Hebrew Poetry,'
ii. 537.

Lubbock, Sir John, ii. 415 ; anthropol-
ogist, 497.

Lucretius, scientific speculations of, i.
313; the "atomic theory," 385;
quoted, ii. 4.

Ludwig, F., mathematical botany, ii
622.

Ludwig, K. F. W., Eloge of Weber, ii.
396 ; ' ' automatic curve-plotting, " 403.

INDEX.

785

Luminiferous ether, theory of, ii. 18 ;
69, 70.

Lunar theory, i. 329.

Liiroth, on von Staudt, ii. 669 ; and
Shepp, translation of Dini's work,
704.

Luther, educational work of, 1. 255.

Lyell, Sir Chas., i. 229 ; quoted on
British Association, 240 ; ' Travels in
North America,' 263 ; ' Principles of
Geology,' 291, ii. 277, 317; on Cuvier
and the fixity of species, 256 ; 291 ;
" uniformitarian " school of geology,

292 ; beginnings of the genetic view,

293 ; quoted, 296, 559 ; genesis of the
cosmos, 320 ; 327 ; genetic view in
geology, 330 ; 335, 608.

M'Aulay, A., on directional calculus, ii.
656.

Macaulay eulogises Bacon, i. 93.

M'Cormack, Thomas, translation of
Prof. E. Mach's Works, i. 318; ii.
183.

M'Cosh, James, ii. 513.

M'Cullagh, James, i. 274 ; properties of
ether, ii. 31 ; analytical method of, 45 ;
referred to, 54 ; contribution to vortex
theory, 63 ; 195.

MacCulloch, J. R., ' Statistical Account
of the British Empire,' ii. 563.

Macfarlane on directional calculus, ii.
656.

Mach, Prof. Ernst, ' Mechanik in
ihrer Entwickehmg ' quoted, i. 318,
383, ii. 97, 100 ; ' Die Geschichte und
die Wurzel des Satzes von der
Erhaltung der Arbeit,' 97; 'Prin-
cipien der Warmelehre,' 102, 106,
109, 111, 175 ; popularisation of
Fourier's heat theory, 121 ; criticism
of mechanical view, 183 ; 185, 737.

Machiavelli, a model historian, i. 7.

M'Kendrick on Helmholtz, ii. 396, 485;
quoted, 490.

Maclaurin, Colin, tribute by Playfair
to, i. 232 ; ' Treatise on Fluxions,'
&c., 270 ; 272 ; series of, ii. 646 ;
theorem of, 670.

MacMahon, Major, Address to Mathe-
matical Section of British Association,
Glasgow, ii. 140 ; on combinational
analysis, 643 ; 679.

Madrin despaired of Newton's theory of
gravitation, i. 334.

Mageudie, Bell's theorem, i. 293 ; ex-
perimental school of, ii. 384 ; 385 ;
experimental or vivisectional school,
406 ; experiments, 481.

VOL. n.

Magnus, Gustav, chemist, i. 188 ; 205 ;
chemical researches of, 208.

Mairan, referred to by Voltaire, i. 106.

Malpighi used the term "cell," i. 195 ;
embryological work of, ii. 227, 260 ;
(s^ee De Candolle), 261 ; " epigenesis,"
278.

Malthns, 'Principles of Population,' i.
84, ii. 331 et sea.; conflict in nature,
431.

Mains, polarisation of light discovered,
i. S3; introduced the word "polar-
ity," ii. 22; "polarity" acquired by
light by reflexion, 23 ; on polarisa-
tion, ih. ; referred to by Young, 27.

Man, and brute, the dividing line, ii.
541 ; the "mean," 580.

Manchester Literary and Philosophical
Society, i. 265.

Manifold, ii. 713.

Mansel, Dean, 'On the Limits of Re-
ligious Thought,' ii. 326.

Mantegazza, physiognomy, ii. 477.

Mantell, G., ii. 318.

Marat, i. 107.

Maria Theresa, i. 256.

Marine laboratories, ii. 232.

Mariniui, animal electricity, ii. 475.

Marion, ' Grande Encyclopedie ' quoted,
ii. 495.

Mariotte, Boyle's law of pressures, i.
425 ; 427 ; experimental formulae of,
436.

Markgraf, Andreas Sigismund, i. 175.

Martin, Charles, Lamarck's views, ii.
310 ; " Introduction Biographique " of
Lamarck, 311.

Maser, H., edition of Abel and Galois,
ii. 686.

Maskelyne, N., i. 177 ; scientific work
of, 229 ; not member of any uni-
versity, 238 ; measurement of force
of gravitation, 320 ; personal equation
unknown to, .325 ; discoveries of, 354.

Maskelyne, Story, ' The Morphology
of Crystals,' ii. 222.

Mass, weight and, i. 336.

Massieu, mathematical formulae of " free
energy," ii. 173.

Mathematical methods. Continental, in-
troduced into England by Babbage
and others, i. 18.

Mathematical, spirit, i. 314 ; first intro-
duced into science, 317 ; formulae,
focalising effect of, 332 ; definition of
matter and force, 334.

Mathematicians, Kiinigsberg school of,
i. 186 ; ancient, catalogue of, ii. 633.

Mathematics, Continental, methods in,

3 D

786

INDEX.

i. 100; modern changes in conception
of, 221 ; impetus to study of, given
by French Revolution, 237 ; pre-
judices against, ii. 628 ; Sylvester
on, 629, 631 ; use of, 630 ; Huxley
on, ib. ; Lord Kelvin on, ih. ; Gauss
on, 631 ; Cay ley on, ih. ; twofold
interest in, 632 ; origin of, 634 ;
Euler on, 657 ; Abel and Jacobi's
school of, ih.

Mathurin, geometrical work of, i. 114.

Matter and force mathematically de-
fined, i. 334.

Matter, circulation of, ii. 420 ; living,
mobility of, 438.

Matteucci, animal magnetism, ii. 475.

Matthew, Patrick, 'Naval Timber and
Arboriculture,' ii. 334 ; 347.

Maudsley, Dr H., 'Physiology and
Pathology of Mind,' ii. 512.

Maupertuis followed Newton, i. 96 ;
referred to by Voltaire, 105 ; prin-
ciple of least (or stationary) action,
231 ; astronomical constants, 322.

Maury, Alfred, ' Les Academies d'autre-
fois,' i. 90, 99, 105 ; quoted on Vol
taire and scientific progress, 106 ;
quoted, 127, 135, 147, 148; 143;
226.

Mauvein, i. 92,

Maxwell, Transactions of Society of
Agriculture, i. 284.

Maxwell, James Clerk-, on probabilities,
i. 120; 'Science and Freewill,' 124;
his theories followed up in Germany
and France, 251 ; and Faraday's
"lines of force," 266; contributions
to study of natural philosophy, 274 ;
'Heat,' 315, ii. 173; 'Electricity
and Magnetism,' i. 323 ; electric
theory, 344 ; " the astronomical
method," 347 ; ' Action at a Dis-
tance,' 348 ; ' Electrical Researches
of Cavendish,' 363 ; ' Physical Lines
of Force,' 372 ; 'Equilibrium of Elas
tic Solids,' 379 ; Weber's theory, 380
" energy " a substance, 388 ; ' Dynam
ical Evidence of the Molecular Con
stitution of Bodies ' quoted, 424
kinetic theory of gases, 433, ii. 34
the statistical view of nature, i. 438
'Kinetics,' ii. 5; 'Scientific Papers
quoted, 33, 175 ; treatise on elec-
tricity and magnetism, 35 ; followed
on the lines of Stokes, 55 ; quoted on
Rankine's theory of molecular vor-
tice.s, 62; "Atom," 'Encyclopedia
Britannica,' 66 ; electro - magnetic
theory, 73, 153 ; labours of, 76 ;

theory of electricity, 78 ; " tubes of
force," 80 ; electrotonic state of mat-
ter, 81 ; "On Physical Lines of Force,"
82, 83; "elastic medium" in space,
84; "elastic disturbances" of that
medium, 85, 86 ; theory of energy,
87, 88, 89 ; indefiniteness of electro-
magnetic theory, 93 ; physical view
of nature, 141, 144 ; and Faraday's
views, 145 ; electro-magnetic field,
147 ; 148 ; theory of electro-dynam-
ical phenomena, 151 ; ' Theory of
Heat,' 167; Willard Gibbs, 172;
"available energy," 174; 179, 182;
triumphs of atomic view, 188 ; 191,
193 ; difiiculties of his theories, 194 ;
Ampere, 341 ; statistical view, 574,
603 ; theory of probabilities, 590 ;
statistical methods, 592, 593 ;
" Sorting Demon," 594 ; quoted, 605,
606 ; on historical and statistical
methods, 613 ; 624 et seq., 630 ; on
vector analysis, 655.

Mayer, A. M., Young's colour theory,
ii. 480.

Mayer, Julius Robert, i. 218, 265, 309 ;
theory of energy, ii. 97 ; his work
theoretical, 99 ; scientific services of,
106 ; memoirs refused by Poggendorf,
107; measurement of "energy,"
108 ; indestructibility of force. 111 ;
neglect of earlier writings of, 113,
114 ; his views extended and elabor-
ated by Thomson and Clausius, 116 ;
117 ; correlation and interchange-
ability of natural force, 119 ; per-
petual motion, 124 ; the dynamical
theory of heat, 128, 130 ; first phil-
osophical generalisations on power
and work, 137 ; " Kraft," 169 ; 207 ;
"energy," 355; meteoric theory of
the sun's heat, 357, 358 ; conserva-
tion of energy, 397 ; 398.

Mayer, Tobias, Professor of Mathe-
matics and Economics at Gottingen,
i. 158 ; connection of, with modern
science, 175 ; 176 ; method of least
squares, 183 ; astronomical calcula-
tions of, 324 ; lunar theory, 329 ;
368.

Measurements, Weber's fundamental,
i. 368.

Mechain, i. 113.

Mechanical view of nature, ii. 183.

Mechanism, ii. 399.

Meckel, anatomist, ii. 248 ; morphologi-
cal analogies, 250 ; 308 ; quoted by
Huxley, 348: law of "biogenesis,"
349.

INDEX.

787

Medical faculty, &c., in German uni-
versities, i. 197 ; science and phil-
osophy of nature, 209 ; medical
interest, the, ii. 207 ; thermometry,
389.

Medicine, i. 126 ; Austrian school of,
198 ; German schools of, 208 ; influ-
ence of, ii. 379.

Medium, internal, ii. 432.

Melanchthon, and the first Protestant
universities, i. 159 ; educational work
of, 255.

Meldola, R., analytical and synthetical
methods in chemical research, i. 457.

Melloni, radiant heat, ii. 105.

Mendeleeff, D., classification of the
elements, i. 315 ; j^eriodic laws of,
403, 422, 423, 448; ii. 362.

Mental life of mankind, i. 55.

Mentelle, geography at the Ecole
normaie, i. 112.

Mercator, i. 157 ; his projection, ii.
701.

Merck, ' Annalen der Pharmacie,' ii.
107.

Mere, Chevalier de, i. 120.

Merey, C. H., on foundation of anal-
ysis, ii. 704, 734.

Meridian, measurements of arcs of, i.
99.

Merkel, 'Jacob Henle,' i. 215, 293.

Mersenne, original member of Paris
"Academic des Sciences," i. 228.

Mesmer, animal magnetism, ii. 476.

Metabolism, ii. 421, 422, 442.

Metajihysical treatment of science in
Germany, i. 43.

Methods have their day and are dis-
carded, i. 56.

Metrical and projective geometry, ii.
668.

Meusnier, i. 115.

Meyer, E. von, 'History of Chemistry,'
i. 405, 406, 413 ; quoted, 411; memoirs
of, ii. 257.

Meyer, Franz, his history of Invariants,
i. 247, 308 ; ii. 677 ; 684 ; on Lie and
'Tlieory of Groups,' 691 ; on poten-
tial theory, 698.

Meyer, Lothar, classification of chemical
elements, i. 315 ; ' Modern Theories
of Chemistry,' 393 ; periodic laws of,
403, 422, 423 ; 427 ; ' Die Atome und
ihre Eigenschaften,' 429, 445 ; 456 ;
' Moderne Theorien der Chemie,' ii.
65.

Meyer, 0. E., 'Die Kinetische Theorie
der Gase,' i. 434, 435, 437 ; quoted
on Maxwell, 438 ; ii. 593.

Meyer, Victor, on change of chemical
views, ii. 165.

Michaelis of Gottingen University, i.
165.

Michell, apparatus to measure force of
gravitation, i. 320.

' Microcosmus ' of Lotze, i. 52.

Microscope, ii. 228.

Miething, E., ' L. Euler's Lehre vom
Aether,' i. 343, 352, ii. 8.

Mill, John Stuart, leintroduces phil-
osophy of Comte to France, i. 18 ;
' Logic,' 37, ii. 307, 308 ; on theory of
probabilities, i. 120, ii. 569 ; i. 306 ;
' Autoliiography,' 307; opposed to
undulatory theory of light, ii. 37 ; on
A. Bain, 511 ; 513, 571, 608.

Millar, W. J., Rankine's ' Miscellaneous
Scientific Papers,' ii. 133, 139.

Miller, Hugh, stonemason and geologist,
i. 288.

Miller, W. A., spectrum analysis, i.
278 ; ii. 47, 48 ; ' Chemical Physics,'
i. 316.

Milnes-Marshall, ii. 349.

Milton, influence on German thought
and literature, i. 212 ; influence of, on
educational views in Ens^land, 253.

"Mimicry," ii. 338.

Mind, ii. 216, 455 el seq.; the objective,
529 ; 5,48.

Mines, Ecole des, i. 107.

Minnigerode, geometrical treatment of
crystallography, i. 443.

Mirabeau, higher aims of, not realised, i.
112.

Mii-bel, ii. 230 ; observations of, 261 ;
cellular theory, 262.

INIitchell, P. C'ii. 459.

Mitchelson, speed of light, ii. 36.

Mitscherlich, E., i. 174 ; chemist, 188 ;
190 ; discovery of isomorphism, 191,
444 ; services of, to chemistry, 208 ;
Dalton's atomic theory, 246 ; discovers
polymorphism, 446.

Mivart, St George, ii. 546.

Mobility of living matter, ii. 438.

Mcibius, A. F., his geometry, i. 44 ; a
pupil of Gauss, 181, 187; his writings
unknown to Pliicker, ii. 76 ; and
Gauss, 652 ; his barycentric calculus,
655, 724 ; introduces homogeneous
co-ordinates, 681.

Mohl, Hugo von, "protoplasm," i. 309 ;
improvements in micrometric pro-
cesses, ii. 229 ; cellular theorv, '262,
299 ; protoplasm, 264, 265, 422, 443 ;
inductive school of, 321.

Mohr, Karl Friedrich, i. 413 ; scientific

788

INDEX.

work of, ii. 106; "On the Nature
of Heat," 107 ; indestructibility of
force, 111 ; neglect of early writings
of, 113, 114 ; referred to, 117 ; corre-
lation and interchangeability of nat-
ural forces, 119, 124; "force," 125,
130 ; tirst philosophical generalisa-
tions on power and work, 137 ;
'Gesch. der Erde,' 289; heat and
animal energy, 398.

Moivre, De, the theory of probabilities,
i. 120 ; ii. 568 ; 572.

Molar dimensions, special interest at-
tached to, i. 350.

Molecular action, i. 346 ; phenomena,
astronomical view of, 354.

Molecules, internal energy of, i. 436.

Moleschott, materialistic works of, i.
60; LifeofGeorgForster, 179; 'Kreis-
lauf des Lebens,' ii. 289, 323.

Moll, Prof., of Utrecht, favourable
criticism of science in England, i.
236 ; ignorance of foreign languages
in England and France, 237.

Molyneux, space perception, ii. 473.

Monadology, ii. 500.

Monboddo, Lord (James Burnett), ii.
531 ; ' On the Origin and Progress of
Language, ' 536, 537.

Monge, Gaspard, descriptive geometry,
i. 44, ii.,658, 664, 675, 685 ; geometry
at the Ecole normale, i. 112, 237 ;
'Descriptive Geometry,' 114; 115,
147 ; brass and iron cannons, 148 ;
152, 187 ; 306 ; practical school of, ii.
100.

Monro. Alexander, Edinburgh Univer-
sity,' i. 268 ; ii. 247.

Monro, John, at Edinburgh University,
i. 268.

Montagu, Lady Mary W., inoculation,
i. 284.

Montesquieu reflects the thought of the
eighteenth century, i. 61 ; 107 ; study
of human culture, ii. 529.

Montgolfier, indestructibility of force,
ii. 111.

Montgomery, Edmund, ' Space and
Touch,' ii. 472; article in 'Mind'
quoted, 484.

Montmort, Remont de, letter to Brook
Taylor, i. 101 ; original member of
Paris "Academie des Sciences," 228.

Montucla, ' Histoire des Mathema-
tiques ' quoted, i. 114, 307, 334, 358.

' Monumenta Germanise,' i. 167.

Moore, Thomas, on an English charac-
teristic, i. 240.

Morgan, A. de, theory of probabilities,

i. 120 ; calculus of probabilities, 325 ;
essay on probabilities, ii. 569 ; 641,
650, 709, 711.

Morley, John, ' Diderot,' i. 34.

Morphogenesis, ii. 549.

Morphological view of nature, ii. 200 ;
insufficiency of, 270 ; period, 274 ;
structural analysis of elements, 423.

Morphology, ii. 212 ; defined, 219 ; of
crystals, 223 ; on a large scale, 224 ;
on a minute scale, 227 ; and classifi-
cation, 231 ; 549.

Morveau, Guyton de, ' Annales de
Chimie,' i. 41.

Mosander, pupil of Berzelius, i. 188.

Moser, perfection of stereoscope, ii.
506.

Mosheim, " libertas docendi," i. 164.

Motion, atomic and molecular, i. 437 ;
in ancient jihilosophy, ii. 3 ; per-
petual, impossible, 124.

Motivity, thermodynamic, ii, 168, 594.

Muir, Thomas, ii. 643.

Miiller, Fritz, 'Facts and Arguments
for Darwin,' ii. 349.

Miiller, Johannes, physiology at Berlin,
i. 174 ; temporarily influenced by
speculative spirit in German science,
178; 'Handbuch,' 193; 195; meta-
physical leanings of, 196 ; school of,
197, ii. 397, 403 ; i. 198, 200, 201 ;
influenced by the Naturphilosophie,
207 ; freed under influence of French
science, 208 ; 211 ; upheld the method
of historical survey in science, 215 ;
his achievements in physiology, 217 ;
"reflex action," 263; 292; Bell's
theorem, 293, 294 ; scientific re-
searches of, ii. 106 ; 117 ; influences
Du Bois - Reymond and Helmholtz,
150 ; physiological studies, 208 ; the
cellular theory, 263; "vital force,"
269; 301; 'Physiology,' 308, 417,
420, 443, 491; 381, 384; chemical
processes in the living body, 391 ;
396; cellular theory, &c., 418;
animal magnetism, 475, 476 ; 481 ;
"specific energies," 482, 483; 519;
Herder's 'Werke,' 537; study of
language, 538 ; on Steiner, 670.

Miiller, K. 0., i. 215.

Miiller, Max, quoted on definition of
thought, i. 4 ; 'Science of Language,'
23, ii. 540 ; 608.

Miiuchausen, von, founded University
of Gottingen, with "libertas docendi,"
i. 164.

Munk, experiments on the brain, ii,
478 ; 479.

INDEX.

789

Munro, ' Lucretius,' ii. 4.

Mliusterberg, Dr Hugo, psycho-physics,
ii. 518 ; experiments, 521.

Murdoch, W., not member of auy uni-
versity, i. 239.

' Musenalmanaoh ' of Schiller and
Goethe, i. 84.

Museum d'Histoire naturelle, i. 112.

Nageli, C. von, co-editor with Schleiden
of 'Zeitschrift i'iir wissenschaftliche
Botanik,' i. 195 ; mechanical theory
of organic structures, ii. 224 ; per-
fection of micrometric processes, 229
271 ; inductive school of, 321 ; 351
'Micellar Theory,' 425, 427, 611
Weismaun on, 435 ; process of intus
susception, 443; " idioplasma," 448
613.

Nansen, Fridjof, arctic exploration, ii.
207 ; quoted on the ubiquity of
organic germs, 453.

Napier, John, logarithms, i. 94, 269 ;
272, 282.

Napoleon I., relation to science, i. 42;
offered prize for discovery of a process
of manufacturing carbonate of soda,
92 ; 107 ; his influence on science,
149 ; quoted from Thibaudeau, 150 ;
founded Universite Imperiale, 151 ;
favoured mathematical sciences, ih. ;
152 ; his scientific glory derivative,
154 ; statistical methods employed by,
153 ; 206 ; animal magnetism, ii. 476.

Napoleon III., scientific reports, i. 42.

Narboune, i. 151.

Nasse, Chr. Fried., physiological
method in medicine, ii. 388.

Nations, work of the three, compared, i.
298 ; disappearance of national differ-
ences, 305.

Natural history, first public course in
Paris, i. 143.

Naturalistic school in France, i. 75.

Nature, history of, how to be under-
stood, i. 2 ; philosophy of, 204 ;
philosophy of, and medical science,
209 ; English love of, 284 ; statistical
view of, 438 ; kinetic view of, ii. 1 et
seq. ; physical view of, 95 et seq. ; mys-
tery of the actual processes of, 366.

Naturphilosophie of Schellingand Hegel,
i. 178, 207; ii. 315.

Naumann, C. F. , " morphology of the
surface of the earth," ii. 212.

Navier, mecanique moleculaire, i. 359 ;
360, 379 ; theory of elasticity, ii. 31,
41 ; properties of the ether, 33 ; syn-
thetic method, 100.

Nees von Esenbeck, ii. 265.

Neptune, discovery of, i. 277.

Neptunists and Plutonists, i. 283, 290.

Nernst, 'Theoretical Chemistry,' i. 448,
ii. 186.

Neumann, Carl, development of astron-
omical view of nature, i. 366 ; quoted
on provisional character of electrical
formulre, 375 ; ' Die Principien der
Electrodynaniik,' 376 ; ii. 186 ; on
potential, 698 ; and Dirichlct's prin-
ciple, 708.

Neumann, Franz, the elder, mathe-
matical physics, i. 44 ; 199 ; experi-
ments in chemistry of, 429 ; proper-
ties of ether, ii. 31 ; analytical method
of, 45; "elastic" theory of ether,
54 ; influences Helmholtz, 150 ;
theory of electro-dynamic phenom-
ena, 151 ; 193.

Neumann, Kaspar, statistical tables of,
ii. 565.

Newlands, periodic law of, i. 422, 423.

Newport, his discovery, ii. 227.

Newton, value of work of, i. 93 ; cor-
rected the thought of Bacon, 95 ; his
work completed and amplified by
Laplace, 97 ; mathematical reason-
ings of, substantiated, 99 ; invention
of "fluxions," 100; influence on the
popular miud inappreciable, 105; 118,
119, 123 ; contrasted with Cuvier, 132 ;
137 ; Cuvier on the gravitation theory
of, 146 ; Gauss's appreciation of, 181 ;
discoveries of, frequently forestalled
by others, 184 ; ' Principia,' 188, 189,
227, ii. 6 ; pre-eminent as an exact
thinker, i. 222 ; indebtedness of
French science to, 226 ; notation of,
233 ; and Young, 244, ii. 9 ; Flam-
steed's observations, i. 250 ; 267, 279,
282, 311; "energy," 312; 317;
astronomical instruments, 322 ; 323,
325 ; lunar theory, 329 ; 332 ; mathe-
matical expression of astronomy,
333; matter and force, 334; "de-
scription and explanation " of phen-
omena, 337; gravity not "essential
and inherent," 340 ; mechanical
explanation of gravitation, 342 ;
emanation hypothesis of light,
344 ; actio in distans, 345 ; gravita-
tion, 351, 353 ; molecular attrac-
tion, 354 ; Horsley's edition of
his works. 355 ; correspondence
with Cotes on molecular attraction,
lb. ; Hauksbee's experiments, 356 ;
358 ; St Venant on, and Boscovich,
359 ; idea of mass, 362 ; 370, 372,

790

INDEX.

374 ; universality and accuracy of
his law, 377, 380, 382, 384; 385,
389, 394, 424 ; calculation of molar
and cosmical phenomena, 439 ; " me-
chanical cause " of gravitation, ii.
4 ; 5 ; and Huygens, 6 ; method of,
8 ; Euler's opposition to, ih.; insuffi-
ciency of emission theory, 14, 15 ;
suggested both theories of light, 17 ;
recognised ' ' polarity " of light rays,
22 ; general laws of motion, 28 ; for-
mula of attraction, 44 ; referred to,
62 ; and the French school of physi-
cal astronomy, 79 ; scientific terms,
95 ; ' Principia ' and the modem no-
tion of energ}^ 99, 100, 140 ; vibra-
tory view of heat, 104 ; laws of mo-
tion, 143 ; astronomical researches,
227 ; Darwin and, compared, 341
et seq. ; 344 ; universal gravitation,
351 ; 364, 467 ; optics, 480 ; and
Gauss compared, 630 ; 634, 638, 643 ;
his theorem on equations proved by
Sylvester, 681 ; 706, 733 ; science and
religion, 742 ; 751.

Newtonian formula the basis of physi-
cal astronomy, i. 375 ; unique as to
universality and correctness, 377 ; is
it a universal law ? 378.

Newtonianism created by Voltaire, i.
250, 251 ; dispelled Cartesian physi-
cal philosophy in France, 433.

Nichol, John, on Francis Bacon and
his forerunners, i. 94.

Nichol's 'Cyclopsedia,' ii. 133.

Nicholas V., Pope, and the University
of Glasgow, i. 268.

Nicholson and Carlisle, scientific dis-
covery of, i. 229.

' Nicholson's Journal,' i. 41, ii. 104.

Nicol, 'Crystallography,'!. 117.

Nicomachus, ii. 207.

Niebuhr, B. G., his indebtedness to
Gibbon, i. 169 ; 212.

Niebuhr, Karsten, on Tobias Mayer, i.
158.

Niepce, photography, ii. 506.

Nietzsche, idea of recurrent cj'cles, ii.
287.

Nilson, discovery of scandium, i. 423.

Nineteenth century not one of revolu-
tion, i. 77.

Nobili, animal electricity, ii. 475.

Nomenclature, importance of, in
science, i. 131.

Non-Euclidean geometry, ii. 652 et seq.;
Klein on, 653 ; 712, 715 ; Halsted
and Schlegel on, 714 ; criticised by
Lotze, 716.

Nordenskiold, pupil of Berzelius, i.
188.

' North British Review ' quoted on
Scotch educational movement, i. 254.

Norwood, determined length of a de-
gree, i. 97.

Nbther, M., onSophus Lie, ii. 690, 691 ;
and Klein, 720. See Brill.

Number tt, ii, 721 ; and e, transcendent
nature of, 731.

Numbers, theory of, ii. 680 ; revived
by Legendre; and Gauss, ib. ; general-
ised, 726 ; transcendental, 727, 730 ;
corpus of, 728 ; algebraic, 729.

Objective mind, ii. 529.

Observation, insiifficiency of mere, i.
328.

Observatory, Greenwich, built, i. 98i;
Pulkowa, i. 99.

Odling, chemical researches of, i. 414.

Oersted referred to, i. 238 ; discovery
of electro-magnetism, 92, 207, 370,
371 ; discoveries of, 366 ; electric cur-
rents, 367 ; importance of his dis-
coveries, 372 ; indestructibility of
force, ii. Ill, 125 ; electrical phenom-
ena, 146.

Oettingen, von, ii. 185 ; statistician,
557, 562, 585.

O'Connell, Daniel, i. 240.

Ohm, G. S., Fourier's series, i. 241 ;
anticipated by Cavendish, 363 ; ac-
curacy of his law, 365 ; electro-mag-
netic measurements, ii. 78 ; galvanic
currents, 79 ; electrical phenomena,
146 ; law of, 147 ; resonance, 487 ;
508 ; on harmonics, 623.

Oken, originated scientific associations
in Germany, i. 42 ; exponent of the
Naturphiloso2}hie, 207 ; 238 ; ' Ele-
ments of Physio -philosophy,' 283;
founded " Naturforscher - Versamm-
lung," 298 ; anatomical analogies, ii.
251 ; development of Goethe's views,
255 ; influences Owen, 308 ; natural
philosophv, 315 ; the genetic view,
317, 321 ; 'evolution, 354 ; 508.

Olbers, Heinr. Wilh. Mat., rediscovers
Ceres, i. 54, 82 ; astronomical work
of, 176 ; biographical, 177 ; calculates
orbit of Ceres, 182 ; correspondence
with Gauss, 185, 304.

Oldenburg, i. 283.

Oltramare on Abel, i. 187.

Operations, inverse, ii. 639 ; different
kinds of mathematical, 640 ; calculus
of, ib., 655, 684; Hankel on, 640;
Peacock on, ii.

INDEX.

791

Operator, ii. 655.

Oppolzer, Vienna school of medicine, i.
198 ; 208.

Opthalmoscope, Helmholtz's invention
of, i. 200.

Optics, ii. 484.

Order, ii. 556 ; theory of, 678 ; and
unity, 742 et seq.; 745.

Organic substance, first, produced arti-
ficially, i. 92 ; compound, preparation
of, by Wcihler, 191 ; substances, syn-
thesis of, ii. 425.

Organisation, problem of, ii. 236 ; 415.

Organs, study of separate, ii. 233.

Ossian, i. 212.

Ostwald, ' Die Energie und ihre Wand-
lungen,' i. 380; "energy" a sub-
stance, 388 ; on Berthollet's views,
393 ; ' Classiker der exacten Wissen-
schaften,' 427 ; 'Allgemeine Chemie,'
443, ii. 176; 'Allgemeine Chemie'
quoted, i. 444, 445; " Physikalische
Chemie," 457, ii. 158, 160; principle
of energetics, 125, 142 ; physical
chemistry, 153 ; chemical affinity,
157, 159 ; 165 ; memoirs of W. Gibbs,
171 ; second law^ of thermo-dynamics,
175 ; criticism of mechanical view,
183 ; quoted, 187.

Otto, translation into German of Thos.
Graham's ' Elements of Chemistry,
ii. 161.

Owen, Robert, co-operation, ii. 566.

Owen, Sir Richard, i. 42 ; palseontol-
ogical work, ii. 257 ; the term " hom-
ology," 258 ; influenced by Oken,
259 ; extension of morphological
view, 260 ; Cuvier's position unten-
able, 266 ; quoted, 268 ; morphol-
ogical view of nature, 276 ; parthen-
ogenesis, 456.

Packard, A. S., 'Lamarck, his Life and
Work,' ii. 312, 351.

Page, ' Text-Book,' ii. 363.

Paine, Thomas, 'Age of Reason,' i.
84.

Paleontology, science of, created by
Cuvier, i. 131 ; Cuvier's work in, ii.
247 ; 363.

Paley, philosophy in English universi-
ties represented by, i. 254.

Pallas, travels of, ii. 247, 337.

Pambour, de (see Zeuner), ii. 133.

Pander, ii. 299, 303.

Pangenesis, ii. 271, 454, 610 et seq.

Paper duties, i. 237.

Paradoxes in mathematics, ii. 732.

Parallel lines, axiom of, ii. 518, 717.

Paris, the focus of scientific thought, i.
17.

Paris Academy ridiculed the fall of
meteors, i. 327 ; competition on
" Difl'raction," ii. 25.

Paris Institute, i. 226.

Parker, Prof., quoted, ii. 345.

Parmenides, unity of all existence, ii. 3.

Parthenogenesis, ii. 456.

Pascal, Blaise, his contributions to
science beyond those of Bacon, i. 94 ;
the theory of probabilities, 120, ii.
668 ; 667.

Pasteur, discoveries of, i. 431 ; the car-
bon tetrahedron, 451; "redintegra-
tion," ii. 387 ; 414 ; bacteriological
investigations, 415 ; discovery of
" chirality," 437.

Pathology pre - eminently a German
science, i. 216.

Pattison, Mark, meaning of "thought,"
i. 25 ; on Bentley, quoted, 169.

Paulmier, first maps of Greece, i. '295.

Paulsen, F., ' Geschichte des gelehrten
Unterrichts auf den deutschen Schu-
len und Universitiiten,' i. 159, 160,
163, 164, 166 ; on Lotze and Fechner,
200; 'Die deutschen Universitaten,'
214.

Peabody, C. H., 'Thermodynamics of
the Steam -Engine,' ii. 136.

Peacock, G. , i. 18; introduction of
Continental mathematics to Cam-
bridge by, 233 ; ' Life of Dr Young '
quoted, 245, 417, ii. 20, 21, 23,26;
educational movement promoted by,
i. 261 ; and the Analytical Society,
271; Young's 'Miscellaneous Works,'
ii. 9; his "report" quoted, 640,
645 ; referred to by Hankel, 641 ;
his history of arithmetic referred to,
645; 654; 709, 711.

Peano, G., ii. 656, 734, 737.

Pearson, Prof. Karl, i. 398, ii. 30;
Todhunter's 'History of Elasticity,'
33 ; ' History of Elasticity ' quoted,
43 ; quoted on labours of Neumann,
54 ; modern theory of elasticity, 56 ;
' Grammar of Science,' 183 ; phenom-
ena of heredity, 574 ; mathematical
theory of evolution, 621 et seq. ; and
Bateson, 623 ; 737.

Pearson, William, i. 289.

Peel, Sir Robert, ii. 265.

Pelletan, a founder of comparative
anatomy, ii. 386.

Peltier, phenomenon, ii. 143.

Percival, A. S., 'Optics' quoted, ii. 53.

Percy, Ballads, i. 212 ; ii. 537.

792

INDEX.

Purier, Edmond, ' La Philosopliie Zool-

o^que avant Darwin' quoted, ii. 309,

322.
Periodic law of Mendeleeff, i. 315, 422.
Periodicals, scientific, the oldest, i. 41.
Permanence of formal rules, principle

of, Hankel's, ii. 712.
Perrault, i^lan of co-operation proposed

by, i. 99.
Perry, calculus for engineers, ii. 636.
Perthes, C. T., 'Politische Zustande

und Personen in Deutschland zur Zeit

der franzbsischen Herrschaft,' i. 133,

256.
Perthes, Frederick, Memoirs of, i. 39,

279.

Pertz, first editor of ' Monumenta Ger-
manise,' i. 158.

Peschel, 0. F., 'Geschichte der Erd-
kunde,' i. 291.

Pestalozzi, i. 163, 253 ; his educational
influence in Germany, 257 ; began the
purely educational movement, 258 ;
inspired by Rousseau, 259.

Peter the Great, i. 153.

Petermann, geographical establishment
at Gotha, i. 167.

Petit, i. 107.

Petty, Sir William, statistics, i. 122 ;
(see Arundel) collection of relics, 295 ;
' Political Arithmetic,' ii. 562 ; 564.

PfefiFer, W., labours of, ii. 165 ; cellular
substances, 373.

Pfleiderer, E., ' Philosophie des Heraklit
von Ephesus,' ii. 3.

Pflliger, E., "proteid" theory, ii. 426;
" laws of reflex action," 519 ; on com-
pound organic molecule, 611.

Phalaris, Epistles of, Bentley's con-
troversy about the, i. 169.

" Philanthropinism " of Basedow, i. 166.

Philip of Hesse, first Protestant uni-
versity founded by, i. 159.

Phillips. See Combes.

Philosophical faculty, development of,
in German universities, i. 164, 197.

' Philosophical Magazine and Journal of
Sciences,' i. 41, ii. 48, 50, 55, 58, 69,
75, 85, 97, 109 ; on Carnot the elder,
139 ; 480.

Philosophical theories, ii. 346 ; prob-
lems, 352, 743 ; thought, geographical
centre of, 750.

Philosophy, definition of, i. 62, 65 ;
intermediate between science and
religion, 71, 73 ; and science, conflict
between, 205 ; and science, 311.
Phlogiston, i. 388, ii. 153.
Phonetics, ii. 539.

"Phoronomie," ii. 5.

Phrenology, ii. 476.

Phylota.xy and phylogenesis, ii. 308.

Physical and chemical reasoning con-
trasted, i. 424.

Physical view of nature, ii. 95.

"Physical" method, ii. 428.

Physics and statistics, ii. 589.

'Physik, Annalen der,' Gilbert's, i. 41.

'Physik, Journal der,' Gren's, i. 41.

' Physikalische Gesellschaft ' of Berlin,
i. 42.

Physiocrats, so-called, referred to, i.
16 ; ii. 529.

Physiological, units, ii. 272 ; division of
labour, 396 ; psychology, 512.

Physiology pre - eminently a German
science, i. 216.

' Physique, Journal de,' i. 41.

' Physique, Observations sur la,' i. 41.

Phjrtotomy, ii. 260.

Piazzi discovers Ceres, i. 54, 82, 177,
182, 423.

Picard, Ch. E., 'Traite d' Analyse,' ii.
690.

Picard, Jean, calculations of, i. 97 ; as-
tronomical constants, 322 ; " methods
of dealing with astronomical errors of
observation," 324.

Picavet, F., ' Les Ideologues,' i. 149,
152, ii. 470 ; quoted, 472.

Pictet, condensation of permanent gases,
i. 316.

Piderit, Ph. , mimicry and physiognomy,
ii. 477.

Pinel, medical nomenclature of, i. 131.

Pitcairn, medicine in alliance with
mechanics, i. 126.

Plana, lunar theory, i. 329.

Planck, Max, 'Das Princip der Erhal-
tung der Energie,' ii. 97, 99, 106,
197; 'Thermodynamik,' 142, 186;
159 ; labours of, 165 ; works of, 184.

Planta, Martin, the forerunner of
Pestalozzi, i. 258.

Platen, i. 213.

Plato, constructive system of, i. 75 ;
views of Heraclitus, ii. 3 ; 4, 246 ;
archetypes, 259 ; his mathematics,
633.

Playfair, John, scientific work of, i.
229 ; criticisms of, on science in
England, 231 ; review of Laplace's
' Mecanique celeste ' quoted, 232 ;
biographical, ib. ; tribute to Colin
Maclaurin, ib. ; 234 ; quoted, 236 ;
270, 272 ; ' Huttonian Theory of the
Earth,' 283, ii. 292, 356 ; 579.

PlUcker, Julius, geometry, i. 44 ; 187 ;

INDEX.

793

geometrical labours of, neglected in
Germany, 242 ; spectrum analysis,
278 ; researches of, ii. 75 ; electrical
researches, 189; on "singularities of
curves," 641 ; 670 ; new geometry,
671 ; 672 ; deficient in elegance, 677,
682 ; and Sophus Lie, 692 ; on higher
curves, 700.

Plutonists. See Neptunists.

Poggendorf, 'Annalen,' i. 43, ii. 128,
133, 169, 487 ; refused Helmholtz's
'Ueber die Erhaltung der Kraft,' i.
205 ; Dictionary of, silent about Avo-
gadro, 428 ; refused Mohr's ' Ueber
die Natur der Warme,' ii. 107.

Poincare, H., lectures on Maxwell's
theories, i. 251 ; on indefiuiteuess of
electro-magnetic theory, ii. 93 ; as-
tronomical mechanics, 101 ; Paris
Address, 1900, 188 ; discourse of,
199 ; quoted, 635 ; quoted on Weier-
strass, 638 et seq.; 703, 705; on
"function," 639; 686, 690; on Rie-
mann and Weierstrass, 707, 708 ;
737.

Poinsot, ii. 5 ; "geometrical mechanics,"
101 ; on synthetic method, 670.

Poisson, mechanics, i. 44 ; 188, 345 ;
electricity, 347; "mecanique mole-
culaire," 359 ; 360 ; analysis of, 362 ;
370 ; Newton's law, 379 ; Fresnel's
calculations, ii. 25 ; retired from
commission on Fresnel's theory of
transverse vibrations, 26 ; theory of
elasticity, 31, 41 ; 32 ; properties of
ether, 33 ; referred to by Faraday, 69 ;
formula of, 72 ; theory of electric and
magnetic phenomena, 74 ; ' Memoire
sur la Theorie du Magnetisme'
quoted, 75 ; referred to, 76 ; 474 ;
science of chances, 568 ; on conver-
gency, 646 ; on Jacobi, 657 ; on
synthetic method, 670 ; 686.

Polarisation of light, ii. 22.

" Polarity," origin of the word, ii. 22.

Polymorphism, i. 446.

' Polytechnic Journal,' Dingler's, ii.
134.

' Polytechnique, I'Ecole, Journal de,' i.
41.

Poncelet, J. V., mathematics, i. 45 ;
new science of geometry, 114 ; 187 ;
definitions of horse-power and work,
310; 360, ii. 5; 'Traite,' 76, 660;
' Mecanique industrielle,' 100 ; practi-
cal school of, ib.; his influence on
practical mechanics, 101 ; thermotics,
118 ; first definite use of new con-
ceptions of power and work, 137 ;

658 et seq.; his principle of continuity
criticised, 660 ; quoted, 662 ; on
"homology" and "reciprocity,"
663 ; 673 ; on ideal elements, 674 ;
684, 685, 692.
Pond, not member of any university, i.

2iOO.

Poole, ' Index to Periodical Literature,'
i. 40.

Pope, influence of, on German thought
and literature, i. 212.

Popper, Jos., ii. 185.

Positivism, i. 307.

Potential, ii. 698.

Pouillet, Ohm's law, i. 365 ; influenced
German thought, ii. 101 ; heat experi-
ments, 357.

Poulton, Weismaun's Essays, ii. 372.

Power Series, Infinite, ii. 707.

"Power," the term, .introduced by
Watt, ii. 99.

Poynting, Prof., contributions to
Maxwell's electro-magnetic theory, ii.
72; 193; and Thomson's 'Text-book
of Physics,' Sound, 489.

Practical problems, solidarity of, i.
32.

Preston, T., ii. 361.

Prevost, theory of exchanges, ii. 46.

Preyer, Prof. W., theory of "Pans-
permia," ii. 369 ; school of Darwinism
in Germany, 436 ; 470.

Priestley, chemical discoveries of, i. 115 ;
155 ; scientific discoveries of, 229 ;
not member of any university, 238,
272 ; ' History of Optics,' 358, ii. 9 ;
follower of Boscovich, i. 359 ; and
Lavoisier, 386, 387 ; effect of plants
on air, ii. 391.

Prime numbers, ii. 722 et seq.

Pringle-Pattison. See Seth.

Pringsheim, A., on theory of functions,
ii. 693 ; 734, 739.

Pringsheim, N., observations, ii. 447.

Pritchard, "immersion" system in
microscope, ii. 228.

Probability, theory of, i. 118, ii. 566.

Prochaska, "reflex action," i. 292; ii.
519.

Proclus on Greek mathematicians, ii.
634.

Progress, intellectual, two factors of, i.
27.

Projection, method of, ii. 663.

Projective and metrical geometry, ii.

668 ; properties, 717.
Proportions, fixed, rule of, i. 392 ; mul-
tiple, rule of, 398.
' Protogsea ' of Leibniz, ii. 277, 280.

794

INDEX.

Protoplasm, i. 309, ii. 264 ; theory of,

444.
Proust, theory of fixed proportions, i.

393 ; defeated Berthollet's doctrine of

chemical affinity, 394 ; 398, 416.
Prout, organic analysis, i. 190 ; on

hydrogen, 230 ; hypothesis of, 402 ;

theory of nature of elements, ii. 192 ;

Bridgewater Treatise, 325.
Psychology, ii. 465 el seq.; mathemati-
cal, 49S.
Psycho-physical aspect of nature, ii.

218, 465.
Psycho-physics, E. H. Weber's law of,

i. 196 ; 198, ii. 465 et seq., 469; of

vision, 504 ; three facts imi^ressed

by, 545.
Purkinje, founded first physiological

laboratory, i. 18S ; 198, 208 ; follower

of Baer, ii. 300.
Pusey, E. B. , quoted on English and

German writers, i. 261.
Putter of Gotting-en University, i. 165.
Pythagoras, unity of all existence, ii.

3 ; school of, 286 ; the octave, 490 ;

his mathematical ideas, 633.

Quantics and " tactics " in mathematics,
ii. 683.

'Quarterly Review,' literary criticism
of, i. 84 ; 236, 239 ; quoted on educa-
tional matters in England, 255 ; Young
quoted, ii. 20.

Quaternions, ii. 654 ; introduced into
Germany by Hankel, 712 ; 717.

Quatrefages, de, of the "Association
Frangaise," quoted, i. 298.

Quesnay, economic system of, i. 16,
107.

Quet, experiments with vacuum tubes,
ii. 190.

Quetelet, statistics, i. 122, ii. 563, 588 ;
555, 556, 557 : theory of error, 574 ;
theory of probabilities, 579 ; quoted,
580, 581, 587, 607, 609; the "mean
man," 617.

Quincke, foam theory of, ii. 427.

Rademacher, his empiricism in medical
science, i. 210.

Rammelsberg, i. 174.

Ramsay, Prof., discovery of argon, i.
423.

Ramsden, i. 177 ; astronomical instru-
ments, 322.

Rankine, Macquorn, improvement in
steam-engines, i. 93; "thermo-
dynamic function," 316, ii. 169 ; the
steam-engine, i, 331, ii. 133 ; theor-

etical thermo-dynamics, 62 ; mole-
cular vortices, 63, 82 ; technical
mechanics, 101 ; revival of interest in
the ideas of "energy," 114; on the
mechanical equivalent of heat, 128 ;
Prof. Unwin's account of theories of,
135 ; elaboration of Joule's and Reg-
nault's experiments, 137 ; energy,
"potential" and "actual," 139, 140,
174 ; reply to Sir J. Herschel, 139 ;
physical view of nature, 141 ; theory
of energy, 166; 168, 173 ; heat engines,
175 ; mechanical analogies of heat,
178 ; entropy, 169, 180 ; thermo-
dynamics, 603.

Raoult, researches of, ii. 164, 165.

Rathtke, ii. 300.

Ran, A., 'Theorien der modernen
Chemie,' i. 406, 414, 430, 455.

Rauber, ' Formbildung und Form-
storung in der Entwickelung von
Wirbelthieren,' ii. 401.

Ray, John, botanist, i. 282 ; classifica-
tion of living beings, 288.

Rayleigh, Lord, discovery of argon, i,
423 ; quoted, ii. 170 ; " free energy,"
173 ; optical researches, 229 ; 'Sound,'
488, 490.

"Realschule,"i. 166.

Reaumur, referred to by Voltaire, i.
105.

Reciprocity of figures, ii. 663 ; Ger-
gonne on, 666.

Records, contemporary, value of, i. 8.

Redtenbacher, ' Dynamiden System,' i.
433 ; influenced by Poncelet, ii. 101 ;
heat, 178.

Registration, ii. 561.

Regnaud, i. 150.

Regnault, chemistry, i. 44 ; 245 ; in-
vestigated specific heat of chemical
compounds, 429 ; influenced German
thought, ii. 101 ; experimental work
of, 137; "Observations on Steam,"
139 ; a founder of physical chemistry,

Rehnisch, statistics, ii. 587.

'Reid, Thomas, Life and Writings of,'

by Dugald Stewart, i. 84.
Reifi", R., his history of series, ii. 646.
Reiz, indebtedness to Bentley, i. 169.
Renaissance, period of the, i. 67.
Renan, testimony to work of German

universities, i. 225.
Rendu, Ambroise, ' Code Universitairej'

quoted, i. 150. w,n =

Reports, annual, on scientific progress,

i. 42.
Reproduction, ii. 443.

i

INDEX.

795

Repsold, measurements of, i. 322.

Retrospect and prospect, ii. 741 et seq.

Reuchlin, i. 163.

Revett. See Stuart.

Revolution, French, added the modern

practical popularisation of science, i.

145.
Revolutionary theories not practical, i.

79.
Reye, 'Geometric der Lage,' ii. 669.
Ribbeck, 'Friedr. Wilh. Ritschl.,' i.

169, 172.
Ribot, 'Modern German Psychology,'

ii. 495 ; ' Psychologic Allemande

Contemporaine,' 511 ; 513.
Richelieu, his "metallic" interest in

science, i. 105 ; first statistical

bureau, ii. 561.
Richelot at Konigsberg with Neumann

and Bessel, ii. 54.
Richer, astronomical constants, i. 322 ;

pendulum experiments of, 354.
Richet, Ch. , ' Physiologic des Muscles

et des Nerfs,' i. 293, ii. 519.
Richter, J. B., chemical equivalents, i.

189 ; 313 ; theory of fixed proportions,

393 ; 398 ; atomic theory, 416 ; the

"equivalent" of an element, 419.
Richter, W., theory of "Panspermia,"

ii. 369.
Rie,cke, memoir of Pllicker, ii. 75 ;

Eloge of Weber, 197.
Riemann, B., i. 45; ' Hypothesen der

Geometric,' 200 ; Fourier's series,

241 ; celebrated dissertation of, 243 ;

views on ideas of space, 352 ;

' Werke,' ii. 63 ; researches into

electrical phenomena, 67 ; 254, 635 ;

and Cauchy, 693, 699; on Abelian

functions, 699 ; his work, 700 ; his

surface, 701 ; 704, 706 ; and Weier-

strass compared, 707 ; on hypotheses

of geometry, 710; 717, 718.
Riess, frictional electricity, i. 205 ;

statical electricity and the Geissler

tubes, ii. 191.
Rindfleisch, Ed. von, 'Arztliche Phil-

osophie,' ii. 379, 437.
Ritschl, Friedr. Wilh., indebtedness of,

to Bentley, i. 169 ; quoted, 172 ; con-
ducted philological seminaries, 214 ;

language, ii. 540.
Ritter, Karl, comparative geography, ii.

226 ; extension of morphological view,

260 ; 300.
Rober, construction of the heptagon, ii.

722.
Robertson, Groom, calls Hobbes's the

first English system of philosophy, i.

48 ; 282 ; ' Mind,' ii. 512 ; on Mlin-
sterberg's work, 522.

Robertson, David, naturalist, i. 288.

Roberval, referred to by Voltaire,
105 ; taught at the College de France,
107.

Robespierre, i. 107.

Robin, 'Traite d' Anatomic generale,' ii.
266.

Robison, John, on Boscovich's theory,
i. 358, 359 ; publisher of Black's
lectures, ii. 102.

" Rochdale Pioneers," ii. 566.

Rochow, von, educational work of, i.
256.

Rogers, W. G., illustrations of Helm-
holtz's theories, ii. 63.

Rokitansky, Vienna school of medicine,
i. 198, 208.

Roman system of registration, ii. 561.

Romanes, 'Darwin and after Darwin,'
ii. 346 ; 436.

Romanticism, reactionary movement of,
i. 82.

Romberg, medical school of, i. 208.

Rome de I'lsle, contributions to crystal
lography, i. 117, 118, ii. 241.

Romer, Glaus, motion of light, ii. 10.

Romme, Gilbert, quoted, i. 110.

Rontgen, discovery of X rays, ii. 92.

Roscher, ' Gesch. d. National-Oekono-
mik,' ii. 555 ; statistics, 563.

Ruschlaub influenced by the JVatur-
2)hilosophie, i. 207.

Roscoe, Sir H., '.John Dalton,' i. 417.

Rose, H., i. 174 ; the greatest analyt-
ical chemist of the century, 399.

Rose, H. and G., chemists, i. 188.

Rosenberger, 'Geschichte der Physik,'i.
308, 359, 433, ii. 8, 11, 178, 506;
' Die moderne Entwickelung der
elektrischen Principien,' 90 ; physical
nature and "perpetual motion," 124.

Rosenkranz on the encyclopedists, i. 34.

Ross, Sir James, confirms calculations
of Gauss as to south magnetic pole, i.
331.

Rothmann, i. 157.

Rousseau, influence on Herder, i. 50 ;
gospel of Nature, 51 ; and the " Auf-
kliirung " period, 60 ; 107 ; destruc-
tive revolutionary work of, 110 ;
popularised botanising, 127 ; centre
of reaction against school of Voltaire,
Buftbn, &c., 145 ; 163 ; influence of,
on German thought and literature,
212 ; 253, 257 ; valuable side of his
ideas developed outside of France,
259 ; 285, ii. 415 ; language, 536.

1

796

INDEX.

Roux, Wilhelm, ' Entwickelungsmech-
anik des Embryo,' ii. 401 ; ' Struggle
of the Parts in the Organism,' 436 ;
quoted, 444 ; "organicisme," 455.

Rowland, spectroscopic observations,
ii. 361.

Royal Institution founded, i. 89, 264,
ii. 139.

Royal Society of Edinburgh, i. 269.

Royal Society Catalogue of Scientific
Papers, i. 40 ; ' Transactions ' of, 41 ;
founded, 89 ; 227, 228 ; unfavourably
criticised by Babbage, 233 ; favour-
ably criticised by Cuvier, 235 ; by
Prof. Moll of Utrecht, 236 ; ii. 69 ;
Kaspar Neumann's statistical tables,
565.

Rubidium found by Kirchhoff and Bun-
sen, ii. 49.

Riickert, imitation of oriental poetry,
i. 213 ; "Chidher" quoted, ii. 289.

Rudolf II., Emperor, and Tycho, i.
157.

Rudolph, ' Grundriss der Physiologic,'
ii. 499.

Rudolphi, ii. 230, 261.

Ruffini, Paolo, and theory of groups, ii.
688.

Riihlmann influenced by Poncelet, ii.
101.

Rumford, Count (Benjamin Thompson),
mechanical theory of heat, i. 83 ;
155 ; experiments of, 229 ; not mem-
ber of any university, 238 ; 246 ;
founded Royal Institution, 248, 264 ;
the steam-engine, 331 ; the kinetic
view of nature, ii. 7 ; investigations
of the nature of heat, 102 ; " Inquiry
concerning the Source of the Heat
which is excited by Friction," 103;
Davy's speculations on light and
heat, 104 ; experiments utilised by
Helm in his ' Energetik,' 109.

Runge, C, spectroscopic observations,
ii. 361, 362.

Russell, Hon. Bertrand, his writings, ii.
653 ; 718, 720, 734, 737.

Russell, Lord John, Royal Commission
of Inquiry into University Reform, i.
254.
Rutherford, spectroscopic observations,
ii. 361.

Rydberg, ii. 362.

Sabine, magnetic experiments, i. 230.

Sachs, Julius, the effect on biological
science of the discovery of the cell, i.
195; 'Geschichte der Botanik,' 209
ii. 212, 223, 227, 230, 231, 246, 260,

265, 269 ; importance of the spiral
theory, 224 ; cellular theory, 262 ;
of Hofmeister, 321 ; quoted, 338 ;
'Lectures on Plant Physiology,' 408.
Sacro Bosco, Joannes, ii. 287.
Saint-Hilaire, Auguste de, ' ' Morphologic

vegetale," ii. ,224.
Saint-Hilaire, Etienne Geoffroy, germ
of Darwinian theory, i. 137 ; 200 ;
and the "Origin of Species," 201;
and Cuvier, ii. 239 ; appreciation of
Goethe's work, 244 ; controversy with
Cuvier, 246 ; morphological analogies,
251 ; labours of, 253 ; quoted, 258 ;
unity of organisation, 267 ; 301 ; and
Buffon, 309 ; 321, 322 ; natural selec-
tion, 330 ; 364.

Saint-Hilaire, Isidore Geoffroy, ii. 322.

Saint Pierre, ,Bernardin de, taught
morals at the Ecole normale, i. 112.

Saint Simon, co-operation, ii. 566.

Saint - Venant, Barre de, quoted on
Boscovich's theory, i. 359 ; properties
of ether, ii. 33; "elastic solid"
theory of ether, 54 ; synthetic method,
100.

Salisbury, Lord, Oxford Address, ii.
347.

Salmon, George, text-books on geometry
translated by Fiedler, i. 44 ; scientific
work of, and PlUcker, 242 ; Dublin
mathematical school, 275 ; German
edition of his works, ii. 669, 685 ;
introduces Chasles's work, 673 ; great
merit of his text-books, 685 ; Meyer
on, ih. ; Italian edition of his works
by Brioschi, ib.

Sameness and variation, ii. 607.

Sampson, R. A., 'Proceedings of the
Society of Antiquaries,' ii. 282.

Sanderson, Sir J. Burdon, quoted, ii.
428, 429, 439 ; "Elementary Problems
of Physiology " quoted, 442 ; 565.

Sanskrit, discovery of, ii. 538.

Santi-Linari, animal magnetism, ii. 475,

Sarcode, ii. 264.

Sartorius von Waltershausen on Gauss,
i. 181, 183, ii. 631.

Saussure, de, ii. 247 ; experiments, 391.

Sauveur, referred to by Voltaire, i, 105.

Savage tribes, history of, i. 3.

'Savants, Journal des,' i. 41.

Savart, theory of elasticity, ii. 31 ; 193.

Savigny, i. 162; indebtedness of, to
Gibbon, 169.

Sayce, ' Introduction to the Science of
Language ' quoted, ii. 539, 540.

Scaliger, Joseph J., influence of, on
German thought and literature, i.

INDEX.

797

212, 226 ; services to classical learning
and criticism, 222 ; 295.

Scheele, forerunner of Berzelius, i. 391.

Scheidt, edition of ' Protogfea,' ii. 280.

Scheiner, J., 'Astronomical Spectro-
scojiy,' ii. 46, 362 ; quoted, 49 ; ' Der
Ban des\Veltalls,'282.

Schelling, F. W. J. von, on the province
of philosophy, i. 36 ; on position of
philosophy, 38 ; treated science from
a metaphysical standpoint, 43 ; phil-
osophy of, influenced by Herder, 51 ;
philosophical writings of, 83 ; 162 ;
speculative tendency of, 178 ; ' Ideen
zu einer Philosophie der Natur,' 179 ;
philosophy of, 204 ; 207 ; influenced
by Spinoza, 212 ; benefactions to
historical sciences, 215 ; influence of,
ii. 225, 494, 500 ; and Goethe's views,
245, 255; ' Natur-philosophie,' 304,
315 ; evolution, 354 ; 508.

Schenstone, W. A., 'Justus von
Liebig, his Life and Work,' ii. 391,
393.

Schering, E., ' C. F, Gauss und die
Erforschung des Erdmagnetisnuis,' i.
181, 331 ; address on Gauss's cen-
tenary, 304 ; corresi^ondeuce with
Helmholtz, ii. 710 et seq.

Scheuchzer, correspondence with Leibniz
quoted, ii. 281.

Schiller, style of, i. 51 ; writings of,
83, 84 ; educated with Cuvier, 133 ;
"The German Muse" quoted, 157;
Kant's sesthetical philosophy, ii. 535 ;
' Wallenstein's Tod ' quoted, 586.

Schimper, K. F., "spiral theory," ii.
223.

Schlegel, A. W. von, Berlin lectures, i.
84 ; on Georg Forster, 1 79 ; 263 ;
researches of, ii. 542.

Schlegel, Fr., on Goethe's school, i. 84 ;
made Shakespeare familiar to German
readers, 212.

Schlegel, Victor, ' Hermann Grass-
mann,' i. 243 ; on Grassmann, ii.
656 ; on non-Euclidean geometry, 714.

Schleicher, August, ' Morphology of
Language,' ii. 540, 541.

Schleiden, Mathias, cellular theory of,
i. 194, 309, ii. 262, 263, 299 ; i. 200 ;
' Botany as an Inductive Science,'
209; biological discoveries of, 217;
mechanical view in biology, 218 ; 220 ;
refers to Brown'.s discovery, ii. 264 ;
theory of cell formation, 265 ; ulti-
mate identity of structure of animals
and plants, 267 ; definition of a cell,
370 ; 402, 403, 408.

Schleiermacher, F., new era of education
in Germany, i. 38 ; philosophical writ-
ings of, 83 ; religious revival preached
by, 203; scientihc ideal of, 211;
educational significance of his writ-
ings, 258 ; 263 ; psychology, ii. 495.

SchlOmilch, 0., i. 209.

Schlosser, F. Chr., 'History of the
Eighteenth Century,' i. 59.

Schltizer, Ludwig August, of Guttingen
University, i. 165 ; statistics, ii. 555.

Schmidt, F., and P. Stackel publish
Bolyai's correspondence, ii. 652.

Schmidt, Johannes, on August Schlei-
cher, ii. 540.

Schmidt, Karl, ' Geschichte der Pada-
gogik,' i. 166, 256.

Schonflies, A., ii. 734; on G. Cantor's
work, 736.

Schonlein, Lucas, metaphysical lean-
ings of, i. 196 ; 198 ; influenced by
the NaturphUosophie, 207 ; freed
under the influence of French science,
208.

School literature, reform in, i. 44.

School of Oriental Languages in France,
i. 113.

School of philology, modern German, i.
172.

School, polytechnic, German, first es-
tablished at Vienna, i. 166.

Schools, German, i. 166.

Schools of thought in Germany, i. 167.

Schopenhauer, A. , animation of all
nature, ii. 369 ; 470.

Schriider, E., ii. 737.

Schubert, H., ii. 734.

Schultze, Ma.x, protoplasmic theory, ii.
371, 443.

Schumacher, H. C, i. 45; ' Astronom-
ische Nachrichten,' 167 ; correspond-
ence with Gauss, 185, ii. 652 ; letter
from Gauss on telegraph, i. 304.

Schiitte, German translation of Gino
Loria's work on geometry, i. 275.

Schwann, Theodor, extended cell theory
to animals, i. 195 ; 198, 200 ; the head
of the modern physiological school,
217 ; mechanical view in biology,
320; cellular theory, 309, ii. 263;
identity of all living structure, 209 ;
discovery of the nucleus referred to,
264 ; theory of cell formation, 265 ;
ultimate identity of structure of ani-
mals and plants, 267 ; definition of
a cell, 371 ; 402, 403 ; microscopical
researches, 418 ; ' Microscopical Re-
searches,' 419, 420, 423 ; conception
of the cell, 422 ; "Metabolism," 44'2.

798

INDEX.

Schwarz, H. A., on Dirichlet's prin-
ciple, ii. 703 ; Weierstrass's letter to,
ib.; on Bolzano, 709.

Schweikart, ii. 713.

Schwerd, 'Die Beugungserscheinuugen
aus den Fundamentalgesetzen der
Undulationstheorie analytisch ent-
wickelt' (luoted, ii. 26.

Schwoerer (see Faudel), ii. 134.

Science now international, i. 19, 303 ;
and life, 31 ; and poetry, ib.; as
opposed to other thought, 69 ; the
meaning and use of the word, 89, 90 ;
English and Continental notions of,
91 ; schools of, in France, 106 ; schools
of, promoted by Governments of
Revolution, 108 ; during the Revolu-
tion and under the First Empire,
138 ; popularised by France, 142 ;
German, not patronised by royalty,
157 ; and "Wissenschaft," 168 ; and
exact science, 171 ; German, cosmo-
politan, 189 ; in Germany, 202 ; and
philosojihy, conflict between, 205 ; and
history, relations of, 2o6 ; for its own
sake, 211 ; thoroughness of German
men of, 213 ; and teaching, 214 ; and
philosophy, 215, 311 ; organisation
of, abroad, 226 ; English, in the early
part of nineteenth century, 229 ;
alleged decline of, in England, 230 ;
French, praised by Cuvier, 231 ;
English, criticisms of Playfair, ib.;
criticisms of Babbage, 233 ; decline
of, in England, ' Edinburgh Review '
quoted on, 234 ; in England favour-
ably criticised by Cuvier, ib.; by
Prof. Moll of Utrecht, 235; Prof.
Moll on difference between culture of,
in France and England, 237; English,
individual character and practical
tendency of, 251 ; English, peculiar-
ities more marked in early part of
century, 252 ; importance of British
contributions to, 276 ; diffusion of
scientific knowledge on the Continent,
276 ; isolation of English men of
science, 277 ; philosophy of, 306 ;
interests which promote, 326 ; prac-
tical interest in, 328 ; physical, ap-
plied to medicine, ii. 208 ; abstract,
550 ; of large numbers, 555.

Science, exact, reception of, in Ger-
many, i. 175 ; absent from German
universities in the eighteenth cen-
tury, 178.

Sciences, the descriptive, ii. 203 ; na-
tural and mental, separation of the,
534.

Scientific, reasoning, 1. 45 ; periodicals,
180 ; associations, dates of, 227 ; spirit
in the first and second half of the
century, 302 ; ideas, special, 306 ;
antiquity of leading ideas, 312 ;
spirit in business, ii. 553.

Scotch school of natural philosophy,
ii. 141 ; activity of, 148.

Scott, Sir Walter, i. 82 ; romantic school
of, 84 ; ' Edinburgh Review,' 273.

Secchi, spectroscopic observations, ii.
361.

Sedgwick, A., 'A Discourse on the
Studies of the University of Cam-
bridge,' i. 263 ; 267 ; worked in
harmony with Analytical Society,
271 ; criticism of ' Vestiges,' ii. 319.

Seebeck, electricity and heat, i. 363 ;
thermo-electricity, ii. 143 ; the siren,
487.

Seeley, J., ' Life of Stein,' i. 38.

Seguin, heat units, ii. 109 ; indestruc-
tibility of force. 111 ; physiological
processes, 390.

Selborne, White's ' Natural History of,'
i. 2S7.

Selection, "natural" and "sexual," ii.
336 ; natural, within the organism,
435 ; Maxwell's j^rocess of, 598.

Sellmeier, W., anomalous dispersion of
wave-motion, ii. 53 ; researches of,
54.

Seminaries in Germany, i. 214.

Semler, Archdeacon, established the
first " Realschule " at Halle, i. 166.

Sensation, Johannes MUller's law of
specific energies, i. 198 ; Weber's law
of, 200 ; localisation of, ii. 507.

Sense-perception, i. 199.

"Sensualistes,"ii. 323.

Serres, 'Anatomic Comparee du Cer-
veau,' ii. 317; "law of biogenesis,"
349.

Serret, his 'Algebre Superieure,' ii.
686.

Servois, ii. 660, 711.

Seth, A., on Fr. Nietzsche, ii. 287.

Shaftesbury, i. 145.

Shakespeare, infiuence of, in German
thought and literature, i. 212 ; 261,
ii. 251 ; the word "statist," 555.

Shelburne, Lord, quoted, ii. 562.

Shelley, P. B., freshness of individual
thought of, i. 76.

Siemens, Werner, submerged cables, i.
329.

Siemens, William, ii. 179.

Silvius, chemistry in alliance with
medicine, i. 126.

1
I

f

INDEX.

799

"Simplex sigillum veri," i. 401.

Simpson, Sir J. Y., introduced clilor-
otorm, i. 93.

Simson, Robert, Scotch university pro-
fessor, i. 272 ; and Stewart, ii. 658.

Skoda, i. 198, 208.

Sloman on tlie invention of the calculus,
i. 101.

Sniellie, William, 'Edinburgh Magazine
and Review,' i. 273.

Smiles, 'Life of Thomas Edwards,' i.
287.

Smith, Adam, imported ideas from
France, i. 16 ; intercourse with French
thought, 268 ; 272 ; influence of, 273 ;
ii. 415 ; human culture, 529.

Smith, H., translation of Schwann's
principal work, ii. 263 ; on con-
gruence, 723 ; his report, ib.

Smith, Sydney, lectured at Royal In-
stitution, i. 249, 264 ; ' Edinburgh
Review,' 273.

Smith, William, on 'Strata,' i. 230;
father of English geology, 291 ; study
of fossil remains, ii. 225 ; tabular
view of the British strata, 293.

Snell, deflection of rays of light, i.
356.

Societe Philomatique, bulletin of, i.
41.

Society, Royal, i. 227.

Socrates, ethical philosophy of, ii. 4.

Soemmering, ii. 247 ; influences Herder,
532.

Sohnke, L., ' Entwickelung der Theorie
der Krystallstructur,' i. 443.

Sommer, edition of Herschel ' On the
Construction of the Heavens,' ii.
283.

Sophocles, i. 261.

Sound and colour, analogy between, ii.
489.

Sound and light, mechanical difference
between, ii. 30.

South, not member of any university, i.
239.

Southey, 'Thalaba,'i. 84.

Spanheim, recognition of Bentley, i.
169.

Species, changes of, services of Lamarck
and Saint Hilaire to the study of,
debatable, i. 201.

Spectrum analysis, i. 277, ii. 45 et seq.;
clue to, 47 ; 359.

Speculation, meaning and scope of the
term, i. 64.

Spedding, James, i. 282.

Spencer, Herbert, first English system
of philosophy, i. 48 ; on the " Un-

knowable," 53, ii. 326 ; constructive
ideas of, i. 81 ; system of, ii. 205 ;
works of, 210 ; vocabulary and ideas
of evolution, 214 ; conceptions of,
246; 'Principles of Biology ' quoted,
270 ; "physiological units," '272, 424,
610 ; philosophy of, 279, 346 ; ([uoted,
288; 'Biology,' 322, 323, 406, 438;
351; "survival of the fittest," ib.;
"Factors of Organic Evolution," 353 ;
dynamical aspect of science, 355 ;
"On the Nebular Hypothesis," 358;
"direct equilibration," 436; law of
limit of growth, 445 ; theory of evolu-
tion, 455 ; and Weismann, 460 ;
anthropological work, 497 ; 511 ;
study of sociology, 530 ; 607, 608,
749.

Si^iuoza, influence of, on German
thought and literature, i. 212 ; on
German philosophy, ii. 205 ; 251 ;
animation of all matter, 369 ; psycho-
physical parallelism, 519 ; 5-35.

Spix, morphological analogies, ii. 251.

Spon, Jacob, archajologist, i. 295.

Sprengel, Chr. C, ii. 230, 261 ; fer-
tilisation of plants, 338 ; investiga-
tions of, 415.

Spurzheim, Joh. Chr., i. 136 ; phren-
ology, ii. 477, 479.

Squares, metliod of least, ii. 576.

Staid, Mme. de, and German literature,
i. 17 ; 225 ; writings of Herder, ii.
531.

Stiigemann, i. 45.

Stahl, animist (medicine), i. 126 ;
elaborated the phloi^istic theory, 387 ;
"Anima,"ii. 388, 503.

Stair, Earl of, first agricultural or-
ganisation in Scotland, i. 284.

Stas, J. S., measurements of, i. 403.

Statics, ii. 5 ; and dynamics, 144.

Statistical, methods, used largely by
Napoleon, i. 153 ; view of nature,
i. 438, ii. 546, 548 ; application in
physics, 589 ; knowledge of nature,
600.

Statistics, beginning of science of, i.
121 ; ii. 548 et seq. ; in France,
Germany, and England, 562 ; social,
583 ; pretensions of, 586.

Staudt, 0. G. C. von, his geometry, i.
44, 181, 275 ; and Gauss, ii. 652 ; on
imaginary elements, 661 ; 669 ; his
work expounded by Reye, Luroth,
and Fiedler, ib.; and Cayley, 718 ;
Klein on, ib.

Stebbing, Thomas R. R., ' Naturalist
of Cumbrae,' i. 289.

800

INDEX.

StefFens, H., on Paris at the close of the
eighteenth century, i. 17 ; ' Autobio-
graphy,' 39 ; development of Goethe's
views, ii. 256 ; natural philosophy,
315; evolution, 354; 508.

Stein, H. Fr. K. von, attitude of, to
national idealism in Germany, i. 39 ;
quoted on Humboldt, 263.

Steiner, Jacob, geometry, i. 44 ; new
science of geometry, 114 ; 163 ; and
Crelle, 186, 187 ; neglect of, in Ger-
many, 243 ; against analysis, ii. 632 ;
his method, 662 ; Geyser on, ib.; his
great work, 667 ; on isoperimetrical
problems, 669 ; 672 ; his theorems
proved by Cremona, 681.

Steinheil, measurements of, i. 322.

Steinthal, psychologist, ii. 497 ; the
objective mind in history, 530.

Stephen, Leslie, i. 25 ; on liume, 47.

Stephenson, George, the "Racket," i.
303.

Stereo-chemistry, i. 447.

Stevin, Simon, 'La Disme,' ii. 645;
recommends decimal system, ib.

Stewart, Balfour, spectrum analysis, i.
278; "radiant heat," ii. 46; physical
view of nature, 141, 601.

Stewart, Dugald, works of, i. 83 ;
quoted, 359; ii. 287, 601.

Stewart, Matthew, forerunner of Car-
not, ii. 658.

Stieda, L., 'Life' of von Baer, ii.
300.

Stirling, James, ii. 572.

Stirp, theory of the, ii. 614.

"Stoflfwechsel," ii, 395; older ideas
corrected, 397.

Stoics, "cyclical" view of the, ii. 286.

Stokes, Sir G. G., i. 274 ; spectrum analy-
sis, 277, ii. 49 ; properties of ether,
31 ; quoted, 32, 592 ; 33 ; ' Burnett
Lectures on Light ' quoted, 37 ;
"double refraction," 43; lines of
sodium, 47, 48 ; translation of Fou-
cault's and Kirchholf's memoirs, 48 ;
on emission and absorption of light
rays, 50, 51 ; invented the term
fluorescence, 52 ; referred to, 54, 55 ;
on whirling motion, 58 ; on iin-
dulatory theory, 195; optical re-
searches, 229; 630.

Stoll, Max., i. '208.

Stolz, 0., ' Grossen und Zahlen,' i. 275 ;
and Weierstrass, ii. 703 ; on Bolzano,
709 ; 726.

Stiilzle, 'K. E. von Baer und seine
Weltanschauung,' ii. 300.

Stoney, Dr Johnstone, introduces the

term "electron," ii. 193; use of
recent microscopic appliances, 229.

Stout, G. F., "Herbart compared with
English Psychologists and with
Beneke," ii, 495, 497; 'Analytic
Psychology, ' 528.

Stow, Normal School at Glasgow, i.
257.

Strasburger, E., embryological studies
of, ii. 227 ; "idioplasma," 448 ; 459.

"Struggle for Existence," ii. 332, 333.

Struve on methods of the astronomers
of Greenwich Observatory, i. 99.

Stuart, Gilbert, 'Edinburgh Magazine
and Review,' i. 273.

Stuart and Revett, archaeological ex-
plorations of, i. 295.

Study, E., referred to, ii. 654.

Sturm, J. C. Fr,, recognised merits of
Green's work, i. 247 ; appreciated
educational work of the "Order of
Jesus," 256.

Substitution, chemical, i. 409.

Substitution, principle of, in mathe-
matics, ii. 686.

Substitutions, Jordan's treatise on, ii,
686, 689, 692.

Sully, Due de, doctrine of averages,
ii. 561 ; political statistics, 563.

Sully, James, article "Evolution" in
'Encyclopedia Britannica,' ii. 279;
"Herder," 533.

Sun, heat of, ii. 357.

Siissmilch, Pastor, the divine origin of
language, ii. 536 ; ' On the Divine
Order,' 557, 563; political arith-
metic, 585.

Svieten, G, v., i. 208.

Swan, spectrum analysis, i. 278.

Sybel, H. von, 'historische Zeitschrift,'
i. 159.

Sydenham, i. 272.

Sylovv, L., on Abel, ii. 649; on Abel
and Galois, 686.

Sylvester, J. J., developed theories of
Boole, i. 247 ; on mathematics, ii,
629 ; 631 ; on invariants, 676 ; the
proper business of mathematics, 679 ;
proves Newton's theorem, 681 ; on
determinants and Hesse, 683 ; 691,

Symbolism, chemical, i. 417.

Syme of Edinburgh [Jniversity, i. 272.
Symington built the tug "Charlotte

Dun das," i. 303.
Symmetrical formulge, ii. 681.

Tacitus, a model historian, i. 7.
Tait, P. G., 'Sketch of Thermodyn-
amics,' i. 376, ii. 167, 173, 175 ; on

I

INDEX.

801

" action at a distance," i. 380 ; ' Pro-
perties of Matter,' 388, 425 ; "Kinetic
Theory of Gases," 438 ; "kinetics,"
ii. 5; 'Light,' 11, 592; 'Light'
quoted, 13, 36 ; criticism of Tyndall's
theory of heat, 57 ; translation of
Helmholtz's memoir on vortex motion,
58 ; memoir of Rankine, 62 ; ' Recent
Advances of Physical Science,' 63,
106, 108 ; ' On Knots,' 64 ; ' Recent
Advances of Physical Science' quoted,
66; 'Sketch of Thermodynamics,'
controversy regarding, 97 ; ' Dyna-
mics,' 99 ; and Tyndall and others,
107 ; computations of Seguin, 109 ;
quoted on the relative values of the
terms "force" and "energy," 116;
perpetual motion defined, 124 ; pre-
face to Rankine's papers, 133 ; (see
Clausius), 135 ; physical view of
nature, 141 ; ' Heat ' quoted, 591.

Tait and Crum Brown, Memoir of
Thomas Andrews, ii. 162.

Tait and Steele, ' Dynamics of a Par-
ticle,' i. 101, ii. 144.

Tait and Thomson. See Thomson and
Tait.

Tait's ' Edinburgh Magazine ' published,
i. 273.

Talbot, solar spectrum, i. 278.

Talleyrand, public instruction, i. 109 ;
higher aims of, not realised, 112.

Tannery, Jules, his lectures on theory
of functions, ii. 704 ; 737.

Tauchuitz, edition of ancient classics, i.
167.

Taylor, Bayard, ' Faust ' quoted, i. 52.

Taylor, Brook, i. 101.

Taylor, Charles, on continuity, ii.
660.

Taylor, 'Scientific Memoirs,' i. 325, ii.
263 ; series of, 646.

Telegraph, first, i. 92.

Tennyson, mature thought of, i. 76.

Tenon, i. 107.

" Tension," ii. 138.

Terquem, ii. 660.

Terrestrial view, ii. 369.

Teubner, editions of the ancient classics,
i. 167.

Tliewtetus, Proclus on, ii. 634.

Thenard, practical discoveries of, i.
147 ; organic analysis, 190 ; ' Chem-
istry,' 200 ; ii. 508.

Theological faculty in German univer-
sities, ii. 197.

Thermodynamics, ii. 62 ; two laws of,
128.

Thermo-elastic phenomena, ii. 142.

VOL. II.

Thermo-electric phenomena, ii. 142.

Theta function, Jacobi's, ii. 649 ; 696.

Thevenot, original member of Paris
" Academic des Sciences," i. 228.

Thibaud, i. 162.

Thibaudeau quoted, i. 113 ; ' Le Con-
sulat et I'Empire,' 149, 152.

Thiersch, Fr., i. 162 ; conducted philo-
logical seminaries, 214.

Tholuck, ' Das akademische Leben des
n^™ Jahrhunderts,' i. 163.

Thomasius represents spirit of Bacon
and Leibniz at Halle, i. 160.

Thompson, Benjamin. See Count Rum-
ford.

Thomsen, V. L. P., a founder of phys-
ical chemistry, ii. 152 ; chemical
affinity, 171.

Thomson and Tait, ' Natural Phil-
osophy,' i. 45, 101, 274. 316, 318,
376, ii. 61, 99, 144, 1.52, 1.53, 184,
358 ; the term "kinetics," 5 ; referrecl
to, 62, 148 ; influence of, 145.

Thomson, J. A., 'Science of Life,' ii.
228, 271, 337, 338, 348, 349, 370, 436,
447; the term "homology," 259;
" Cell and Protoplasm," 266 ; 298 ;
"embryology," 299; quoted on von
Baer, 303 ; ''Evolution of Sex,' 344 ;
'Science of Life' qiioted, 448, 455,
458; 459; on ".stirps," 614.

Thomson, James, harmonic aualysis, i.
330; heat and "perpetual motion,"
ii. 126 ; prediction, 126, 170; physical
view of nature, 141 ; "Crystallization
and Liquefaction," 142; theory of
energy, 166.

Thomson, J. J., on vortex motion, ii.
63, 65, 183 ; Princeto\vn lectures,
190; 'Researches,' 191; 'Discharge
of Electricity through Gases,' 192;
electrical researches, 362.

Thomson (the poet), i. 285.

Thomson, Prof. Thos., i. 188 ; and Dal-
ton, 245 ; the atomic theory, 425.

Thomson, Wm. (Lord Kelvin), on
chemical laboratories, i. 188 ; and
Helmholtz, 199, ii. 149 ; the conserva-
tion of energy, i. 201, ii. 128, 142;
Fourier's series, i. 241 ; Green's treat-
ise, 246 ; and Joule, 265, 434, ii. 110 ;
Faraday's "lines of force," i. 266, ii.
71 ; referred to, i. 272 ; his work,
274, ii. 133 ; on discovery of spectrum
analysis, i. 277 ; telegraphic connec-
tion with America, i. 303 ; absol-
ute .scale of temperature, 309, 315 ;
"vortices," 312, 313 ; absolute meas-
urements, 323 ; submarine tele-

3 E

802

INDEX.

graphy, 329 ; ' Popular Lectures and
Addresses,' 330, ii. 61 ; improve-
ments in mariner's compass, i. 331 ;
mechanical theory of gravitation,
344 ; Boscovich's theory, 358 ; elec-
trical measurements, 366 ; cohesion
aud capillary attraction, 376 ; on
"capillary attraction" quoted, 425;
"chirality," 432, ii. 22; "On the
Size of Atoms," i. 437; "Steps to-
wards a Kinetic Theory of Matter,"
456; quoted, ii. 39, 182, 184, 190;
sodium, 48 ; wave-motion, 53 ; optics,
55 ; vortex theory, 57, 58, 63 ; on gyro-
stat, fil ; thermodynamics, 62, 603 ;
diamagnetism, 74 ; on "permeability,"
75 ; electro-magnetics, 77 ; Faraday
and Clerk-Maxwell, 78, 79 ; reprints
of papers quoted, 803 ; physical
lines of force, 81 ; electrical re-
searches, 86; "vortex filaments,"
89 ; vibrations of the ether, 91 ; in-
dependence of Mayer's writings, 97 ;
and Mayer's hypothesis, 109; "en-
ergy," 114; "work "and "energy,"
115 ; Mayer, and Joule, 116 ; ab-
solute measurements in thermotics,
117; Carnot's 'Puissance motrice,'
118; dissipation of energy, 119, 131,
132, 364, 598 ; Sadi Carnot's heat
theory, 123 ; perpetual motion, 124-
126 ; experiment, 127 ; Sadi Carnot,
130 ; experiments of Joule and Eeg-
nault,137 ; " potential " and "actual "
energy, 139 ; physical view of nature,
141 ; Kegnault's measurements, 152 ;
167; thermodynamic "motivity,"
168, 169, 594; "free energy," 173;
"available energy," and "entropy,"
174, 594; 175, 179, 184 ; ether theory,
196 ; recognition of Kant, 284 ; 296 ;
"On Geological Time," 356; "Me-
chanical Energies of the Solar Sys-
tem," 358 ; on the spectroscope, 362 ;
Glasgow Address quoted, 363 ; cos-
mical origin of life, 369 ; on the
dissipation of energy, i. 309 ; ii. 52,
404 ; irreversibility of natural pro-
cesses, 593 ; 699 ; his theorem and
Dirichlet, 700 ; 704, 708.

Thomson, William, aud Sir G, G.
Stokes, contributions to mathematical
physics, i. 274 ; and Tait : ' Natural
Philosophy,' ib.

Thorpe, 'Essays in Historical Chem-
istry,' ii. 158.

Thought, the hidden world, i. 1 ; the
only moving principle, 2 ; Max
Miiller on definition of, 4 ; many

meanings of, 5 ; forgotten and unex-
pressed, 8 ; value of contemporary
records of, 10 ; unity of, a product of
the nineteenth century, 16 ; equi-
valents in German and French, 24 ;
conception of, not specifically Eng-
lish, 26 ; definition of, 33 ; not ex-
hausted by science or philosophy,
66 ; unmethodical, 68 ; religious, 69 ;
personal or subjective, 70 ; scientific,
philosophical, and individual, 72 ; of
nineteenth century characterised, 77 ;
constructive, not destructive, 80 ;
exact, historical, and critical habits
of, 222 ; characteristics of higher
mental work in England, 239 ; char-
acteristics of English, 249 ; scientific,
absence of schools of, in England,
250 ; history of, ii. 627 ; not history
of knowledge, 628.

Thouin, agriculture at the Ecole nor-
male, i. 112.

Thucydides, a model historian, i. 7.

Tiedemann, Fr., chemistry of the living
body, ii. 391 ; 317.

Tilloch, 'Philosophical Magazine,' i. 41.

" Timbre," ii. 488.

Tisserand, 'Comptes Rendus,' i. 377;
quoted on Newton's law, 378.

Titchener, E. B., criticism of Miinster-
berg's work, ii. 522.

Titius, Daniel, astronomical formula of,
i. 422.

Tocqueville, A. de, quoted on contem-
porary records, i. 10.

Todhunter, Isaac, his ' Histories,' i.
91 ; ' History of the Theories of
Attraction,' 98, 99, 308, ii. 698 ;
theory of probabilities, i. 120, ii.
568 ; ' History of the Theory of Prob-
ability,' i. 234; 'Life of Whewell,'
236, 262, 306 ; theory of elasticity, ii.
30 ; on Young's style, ib. ; on Eng-
lish science, ib. ; ' History of Elas-
ticity,' 33 ; quoted, 43.

Todhunter and Pearson, ' History of
the Theory of Elasticity,' i. 376, ii. 43,
56.

Tooke, Home, on words, i. 21 ; the
' Diversions of Purley,' ii. 537.

Tour, Cagniard de la, the siren, ii. 487.

Traube, medical thermometry, ii. 389.

Treitschke, ' Deutsche Geschichte,' i.
312

Trembly, ii. 418.

Trench, Archbishop, on words, i. 21.

Treviranus, G. R., 'Biologie,' i. 194;
identity of all sciences of organic
life, ii. 217 ; 230, 261 ; biological

♦

INDEX.

808

researches of, 313 ; genetic view, 321 ;
evolution, 327.

Treviranus, L. C, botanical laboiirs of,
ii. 218.

Truth, the search after, not the end of
knowledge, i. 29.

Tschirnhausen, refeiTed to, i. 101.

Tubingen school of theological criti-
cism, i. 162.

Turgot, founded the Ecole des Fonts et
Chaussees, i. 107 ; neglect of, by-
Napoleon, 149 ; statistics, ii. 571 ;
573.

Turner disproves Prout's hypothesis, i.
402.

Tycho, a forerunner of Bacon, i. 94 ;
of Kepler, 157 ; 317 ; discovered
variable stars, 327.

Tylor, E. B., anthropologist, ii. 497.

Tyndall, John, 'Heat,' ii. 57; and
Faraday, 77 ; on Mohr's and Mayer's,
&c., scientific work, 107 ; computa-
tions of Seguiu, 109 ; his works trans-
lated into German, 148 ; 405 ;
ubiquity of life, 452; "tone," 488.

Type theory in chemistry, i. 411.

Ueberweg and Beneke, ii. 495 ; 512.

Ukert (see Heeren), i. 167.

Ulrich, Duke, reconstituted University

of Tubingen, i. 159.
Units, living and lifeless, ii. 620.
Unity of human interests, terms for, i.

33.
Universities and high schools, relations

of, i. 166.
Universities, Belgian, i. 161.
Universities, British, and others, dates

of, i. 228.
Universities, Danish, i. 161.
Universities, Dutch, their influence on

German culture, i. 160 ; 161.
Universities, English, unique character

of, i. 254.
Universities, German, foundation of, i.

158 ; 162, 197 ; testimonies to the

gi-eat work of, 225.
Universities, Norwegian, i. 161.
Universities, Russian, i. 161.
Universities, Scotch, i. 160, 267, 271.
Universities, Swedish, i. 161.
Universities, Swiss, retarded develop-
ment of, i. 163.
University, Johns Hopkins, Lord

Kelvin's lectures, ii. 55.
University of Athens, i. 161.
University of Geneva, i. 160.
University of Giittingen, i. 164, 165,

175 ; prize essays on dynamics, ii. 97.

University of Halle, i. 165.
University of Kasan, i. 161.
University of Maros Vasarhely, i. 161.
" Unknowable," ii. 326 ; or unknown

factor, 375.
Unwin, W. C., "The Development of

the Experimental Study of Heat-

Engines," i. 331 ; theories of Rankine

and Clausius, ii. 135.

Valenciennes, Bell's theorem, i. 293.

Valency, i. 447.

Valmont de Bomare, i. 143.

Valson, his Life of Cauchy quoted, ii.

637.
Van't Hoff, ' La Chimie dans I'Espace,'

i. 397 ; ' Die Lageruug der Atome im

Raume,' 431 ; the carbon tetrahedron,

450, 451.
Variation, ii. 331, 343 ; discontinuous,

623.
Variations, calculus of, ii. 670.
Varnhagen von Ense quotes Kant, i.

45 ; memoirs of, 279.
Vasiliev, A., Address on Lobatchevsky,

i. 161.
Vauquelin, practical discoveries of, i.

147.
Vector, ii. 655 ; analysis, 73, 655.
Venn, John, 'The Logic of Chance," ii.

569.
Verdet, M., 'CEuvresdeFresnel,' quoted

on Euler, ii. 9 ; referred to, 14 ;

quoted, 25 ; history of undulatory

theory, 26 ; ' ffiuvres de Fresnel,' 26 ;

quoted, 27, 41, 42.
Veronese, G., ii. 737.
Versification, German, catholicity of, i.

213.
Verworn, Max, quoted, ii. 423 ; quoted

on foam theory, 427 ; ' General Physi-
ology ' quoted, 445.
' Vestiges of Creation,' published, ii.

318 ; 323, 327 ; and natural selection,

330.
Vicq d'Azyr, i. 107 ; forerunner of

Cuvier, 147 ; 200 ; pioneer of the

mechanical view in biology, 219 ;

anatomist, ii. 248 ; quoted, 255.
Vieweg, publishers, ii. 300.
Villemain, review of eighteenth -cen-
tury literature, i. 59 ; quoted on

Napoleon's educational projects, 151.
Villers, ' Coup-d'a?il sur les Universites

d'Allemagne,' i. 225.
Vinci, Lionardo da, mathematics and

science, ii. 5 ; vision, 506.
Vines, S. H., ii. 459.
Virchow, Rudolf, "cellular pathology,"

804

INDEX.

i. 195, ii. 265, 376; i. 198, 208
"Autonomy of the Cell," ii. 395
' Cellular Pathology ' quoted, 402
444 ; progress of biology, 463 ; quoted
by Darwin, 610.

Virey, indebtedness of Cuvier to, i.
130 ; importance of nervous system,
ii. 237.

Virgil quoted, ii. 287.

Vischer, Fr. T., i. 162.

Vital force, i. 218.

Vitalism, extreme, ii. 388.

Vitalistic, aspect of nature, ii. 217 ;
353 ; view of nature, 368 ; idea of
Bichat, 383 ; 386.

Vogel, A., address on Liebig, ii. 391.

Vogel, H. C, spectrum analysis of the
stars, ii. 362.

Vogt, Karl, materialistic works of,
i. 60 ; vertebral theory of the skull,
ii. 251 ; ' Bilder aus deni Thierlebeu,'
323; 407; ' Physiologische Briefe,'
469; 503.

Volkmann, W., psychologist, ii. 494,
497.

Volney, history at the Ecole normale,
i. 112.

Volta, electric pile, i. 83, ij. 104 ; dis-
coveries of, i. 363, ii. 150 ; animal
electricity, 475.

Voltaire imported new ideas into France
from England, i. 16 ; century of, 59 ;
reflects the thought of the eighteenth
century, 61 ; an essayist and man of
the world, 93 ; popularised the ideas
of Newton, 96 ; importance in French
literature of, 105 ; on the progress of
the philosophical spirit in France,
ih.; influenced by Newton and
Descartes, 106 ; constructive work
influenced by, 110 ; philosophical and
philanthropic influence of. 111 ; 123 ;
'Siecle de Louis XIV.,' 135; 142;
' Elemens de la Philosophic de New-
ton,'144 ; 'Lettres sur les Anglais,'
ib.; created Newtonianism, 250 ; cor-
respondence of, 279 ; the cure of
smallpo.x, 284 ; quoted on the Car-
tesian and Newtonian philosophies,
340, ii. 324.

Vortex, motion, i. 199, ii. 35 ; earlier
researches, 61 ; filaments, ib.; theory
developed in England, 62 ; ring
theory, difficulties of, 64 ; atom
theorv', Helmholtz and Thomson, 57,
66. ■
Voss, A., on principles of calculus,

quoted, ii. 706.
Voss, J. H., hexameters, i. 213.

Vries, de, labours of, ii. 165; "muta-
tion," 364.

Waage, Guldberg and law of mass-
action, ii. 157 ; ideas of Berthollet,
177.

Waals, von der, researches of, ii. 164.

Wagner, A., on freewill, ii. 584.

Wagner, Pvudolf, ' Physiological Let-
ters,' iL 323; ' Handworterbuch der
Phvsiologie,' 401, 501 ; controversy
with Karl Vogt, 469.

Waitz, psychology, ii. 497, 530.

Wald, F., 'Die Energie und ihre Ent-
werthuiig,' ii. 169.

Wallace, Alfred Russel, i. 179 ; ' Intro-
duction of New Species,' 310 ; ii.
327, 329; 'Darwinism,' 330, 339;
"Struggle for Existence," 332, 333;
Darwin, 341 ; sexual selection, 343 ;
351 ; quoted, 365 ; 546 ; variation in
nature, 608 ; 621.

Wallis, Dr, quoted in 'History of the
Royal Society,' i. 227.

Walther, Ph. von, physiological method
in medicine, ii. 388.

Walton, Izaak, i. 285.

Wand (see Clausius), ii. 135.

Wappaus, statistics, ii. 563.

Ward, James, ' Naturalism and Agnos-
ticism,' ii. 188, 519 ; modem psychol-
ogy', 522, 523 ; quoted, 606.

Ward, T. H., ' Reign of Queen Victoria,'
i. 310.

Wardlaw, Bishop, founded University
of St Andrews, i. 268.

Wardrop, ii. 505.

Waring, Ed., of Cambridge, quoted, i,
234 ; ii. 688.

Wamkonig, Prof., of Liege, translation
of Gibbon's 'Romau Empire,' i.
169.

Waterston, J. J., meteoric theory of
the sun's heat, ii. 358.

Watson, Hewett Cottrell, ' Cybele
Britannica,' ii. 3-35 ; 595.

Watt, James, an inventor with scien-
titic training, i. 91 ; not member of
any university, 238 ; definitions of
horse-power and work, 310 ; use of
term "horse -power," ii. 99, 156;
technical mechanics, 101 ; (see
Zeuner), 134 ; heat measurement, 156.

Wattenbach, W., 'Zum Andenken
Lessings,' i. 169.

Weber Brothers, theory of elasticity, ii.
31 ; biological studies, 208 ; experi-
mental research, 396 ; psycho-physi-
cal investigations, 492.

INDEX.

805

Weber, Eduard, i. 196, 519.

Weber, Ernst Heinrich, i. 196 ; school
of, 200 ; law of sensation, ib. ;
"science of life," ii. 396; 402;
psycho - physical phenomena, 496 ;
60*0 ; psycho-physics of vision, 504 ;
508; "touch and bodily feeling,"
509 ; psycho-physics, 517, 519.

Weber, H., biographical notice of
Wilhelm Weber, i. 304.

Weber, Heinrich, his treatise on algebra,
ii. 729, 730.

Weber, Wilhelm, of Gottingen and
Gauss, telegraph, i. 92 ; quoted,
171, 172, 196, 199, 211; 'Electro-
dynamische Maasbestimnmngen,' 265,
303 : 365 ; absolute measurements,
309, 323, ii. 117 ; perfected Coulomb's
methods, i. 360 ; astronomical view
of nature, 366 ; electrical researches
of, 367, 368, 369 ; quoted, 370, 373 ;
measurements of, 371, ii. 149 ; im-
portance of his labours, i. 384 ; law
of, ii, 67 ; 76 ; electro - magnetic
measurements, 73 ; 79 ; statical and
current electricity, 84 ; theory of, 87 ;
researches, 92 ; 97 ; electric measure-
ments, 143 ; electrical phenomena,
146 ; influences Helmholtz, 150 ;
theory of electro-dynamic phenomena,
151 ; electrical theory of, 153 ; atomic
view of nature, 188 ; Helmholtz
quoted, 189; 191, 192; electric
particles, 197.

Webster, Daniel, the term " statist," ii.
555.

Webster, Thos., palaiontological work
of, i. 139.

Wegele, 'Gesch. d. deutschen Historio-

graphie,' i. 206, ii. 555.
Weidmann, editions of the ancient

classics, i. 167.
Weierstrass, ii. 630 ; Poincare on, 638,
703 ; and Lagrange, 693 ; his theory
of functions, 694 ; his pure analysis,
702 ; genesis of his ideas, 703 ;
Lampe on, ih. ; on non-differentiable
functions, 705 ; 706 ; aud Riemann
compared, 707 ; on Riemann, 708 ;
his letter to Schwarz, ih. ; proves
Gauss's statements, 726 ; 733.
Weight and mass, i. 336.
Weis, Samuel Christian, mentioned by

Verdet, ii. 41.
Weismann, A., ' Essays upon Heredity,'
ii. 372 ; idio plasma theory, 448, 611 ;
on heredity, 450 ; on pangenesis, 455 ;
theory of evolution, ih. ; "On the
Duration of life," 457; 'Essays on

Descent and Heredity,' 459 ; versus
Lamarck, 460.
Weissbach, influenced by Poncelet, ii.
101. '

Weisse, Chr. H., influence on Lotze, ii.
500 ; 508.

Weld, ' History of the Royal Society,' i.
90, 127, 227, 228, 2.S3 ; quoted on the
publication of the 'Principia,' 98.

Weldon, W. F. R., on crabs, ii. 621 ;
on Pearson's methods, 623.

Wells, 'Essay on Dew,' i. 230 ; 'Two
Essays upon Dew and Single Vision,'
ii. 334 ; 347.

Werner, A. G., Freiberg Mining Aca-
demy, i. 17 ; school of geology of,
116 ; Cuvier on, 118 ; 155 ; connection
of, with modern science, 175 ; scien-
tific strife with Hutton, 283j 290;
study of fossil remains, ii. 225 ; 266 ;
and Hutton, 291 ; describes mineral
character of rocks, 294.

Wernicke, language, ii. 539.

Wessel, Caspar, on imagiuaries, ii.
653.

Weyrauch, Jacob J., 'KleinereSchriften
und Briefe von Robert Mayer,' ii, 97,
108.

Wheatstone and Cooke, first telegraph
lines, i. 303.

Wheatstone, Ohm's law, i. 365 ;
quoted. 366 ; stereoscope, ii. 4S6,
505; 506.

Whewell, Wm., on relations of the
sciences, i. 37 ; identification of
thought with philosophy, 62 ; ' Writ-
ings and Correspondence,' 91; crys-
tallography, 117; 236 ; quoted, ib.; his
influence, "261 ; ' History of the In-
ductive Sciences,' 262, 277, 306, 365 ;
270 ; Analytical Society, 271 ; ' His-
tory of the Inductive Sciences '
quoted, 291, 292, ii. 12; influenced
by Kant, i. 307 ; origin and variation
of species, 310 ; Avogadro's hypo-
thesis not mentioned by him, 428 ;
the final establishment ot the undula-
tory theory, ii. 26 ; ' Philosophy of the
Inductive Sciences,' 205 ; his divisions
abandoned, 210 ; quotation from Lin-
njeiis, 220; account of vertebral theory,
251 ; 268 : the study of functions,
269 ; 318 ; Bridgewater Treatise, 325,
327 ; Bacon's "method of instances,"
558.

Whiston, on reluctance of Cambridge
to accept theories of Newton, i. 270.

White, Gilbert, of Selborne, i. 179;
'Natural History of Selborne,' 286;

806

INDEX.

nature lover, 287 ; 288 ; biographical,

289 ; quoted, 290.
Whitehead, A. N., his 'Universal

Algebra,' ii. 641 ; 656, 737.
Whittaker, Thos., on "cyclical" view,

i. 286.
Wichern, .J. H., follower of Pestalozzi,

ii. 258.
Wiechert. E., 'Grundlagen derElektro-

dynamik,' ii. 193, 197.
Wiedemann, Georg, 'Die Electricitat,'

i. 370 ; ' Annalen,' ii. 186 ; on Helm-

holtz, 410.
W'ien, W., electro - dynamic view of

ether, ii. 195.
Wigand, A., Darwin, Newton, and

Cuvier compared, ii. 341.
Wilberforce, William, associated with

Rumford's philanthropic schemes, i.

249.
Will, H., text-books of, i. 188.
William IV. of Hesse, astronomer, i.

1.57.
William the Conqueror, ii. 555.
Williamson, chemical researches of, i.

414 ; quoted, ii. 163.
Willis, "reliex action," i. 292.
Willoughby and Ray, botanical travels

of, i. 283 ; ' Historia Piscium,' 283.
WUson, E. B., 'The Cell in Develop-
ment and Inheritance,' ii. 370, 456,

458.
Wilson, G. (see A. Geikie), i. 288.
Winckelmann, classic style of, i. 51 ;

171 ; founder of archaeology in Ger-
many, 295.
Winkler, discovery of germanium, i.

315, 423.
Winter, W., "astronomical magni-
tudes," i. 323.
" Wissenschaft," meaning and scope of

the word, i. 90, 168 ; evolution of the

idea in German literature, 170 ; 202 ;

combines the exact, historical, and

critical methods of thought, 222 ;

moral value of, 223.
" Wissenschaftslehre " of Fichte, i. 170.
Witt, John de, tables of mortality, ii.

665.
Wohler, his works on chemistry, i. 43 ;

prepares organic substances, 92, 191 ;

ii. 440 ; i. 188 ; 194, 200 ; ^services

to chemistry, 208; "vital force,"

218 ; discovery of " isomerism," 406 ;

412, 414 ; uric acid and its derivatives,

ii. 393 ; vitalist, 405.
Wolf, C, 'Les Hypotheses Cosmog-

oniques,' ii. 282.
Wolf, F. A., indebtedness to Bentley,

i. 169 ; 171 ; philology, 203 ; 212,
214 ; evolved the science of antiquity
from vaguer beginnings, 220 ; classical
learning of, 222 ; educational ideal
differs from that of Pestalozzi, 258 ;
263, 264; ii. 538.

Wolf, R., 'Geschichte der Astronomie,'
i. 54, 157, 167, 171, 177, 277, 328;
'Handbuch der Astronomie,' 319,
324, ii. 282, 358, 362.

Wolff, Caspar Friedrich, used the term
"cell," i. 195; anticipated Goethe,
ii. 212; metamorphosis, 267; "epi-
genesis," 278, 299; 'Theoria genera-
tionis,'298; 494.

Wolff, Christian, philosophy of, i. 212 ;
astronomical formula of, 422 ; ii. 563.

Wollaston, scientific discoveries of, i.
229, 230 ; not member of any uni-
versity, 238 ; contributions to the
atomic theory, 245 ; 272 ; prophecy
of, 397, 450 ; his attitude towards
Dalton's views, 417 ; experiments
supporting undulatory theory of
light, ii. 19, 45 ; Fraunhofer's lines,
47.

Words, new, and new thoughts, i. 23.

Wordsworth, his visit to Germany, i.
17 ; influence of, on taste, 67 ; fresh-
ness of individual thought of, 76 ;
healthy spirit of, 78; 179, 285;
a friend of Wm. Pearson, 289.

Work, the term introduced by Clausius,
ii. 115.

World, outer and inner, how related, i.
5.

Wright, Ed., length of a degree, i. 97.

Wright, Thos., of Durham, cosmical
theories, ii. 282.

Wunderlich, medical thermometry, ii.
389.

Wundt, Wilh., Fechner'swork continued
by, i. 200 ; 220 ; animal electricity,
ii. 475 ; physiognomy, 477 ; ' Physio
logische Psychologic,' 479, 490, 519
520, 521; '"'specitic energies," 483
influence of Herbart, 494 ; 497, 508
510, 512 ; ' System der Philosophie,
513 ; 514, 515 ; consciousness, 516
517 ; psychology, 525 ; 526.

Wurtz, A., quoted, i. 114 ; ' La Theorie
atomique' quoted, 394, 421, 427,
429 ; on Dalton, 398 ; 413.

' Xenien ' of Schiller and Goethe, i. 84.

Young, Dr Thos., the undulatory
theory of light, i. 83, 229, ii. 16,
36 ; light and hieroglyphics, i. 236 ;

i

INDEX.

807

not a member of a university, 238,
272; and Fresnel, 241 ; inadequate
appreciation of, 243, 244, 277 ; 246 ;
lecturer at the Royal Institution,
249, 264 ; recognition of, by Frencli
scientists, 251 ; quoted on universi-
ties, 261 ; not connected with the
Mathematical School of Cambridge,
266 ; 294 ; dynamical view of light,
370 ; revival of kinetic view of nature,
ii. 8 ; Euler's ether theory, 9 ; ' Out-
lines of Experiments and Inquiries
respecting Sound and Light,' 17 ;
quoted, lb., 20 ; interference of light,
18 ; accuracy of Newton's experi-
ments, 19 ; methods of Laplace, 20 ;
"interference," 21; polarisation of
light, 22; rejects projectile theory of
light, ib.; quoted on Malus's discovery
of polarisation of light by reflection,
23 ; 24 ; memoir of, 26 ; ' Works '
quoted, 27 ; transverse vibrations of
light, 28 ; futility of astronomical
view of nature, 28 ; theory of elas-
ticity, 30 ; theory of capillarity, 33 ;
nature of the ether, 40, 43 ; analogy
of optical and acoustical phenomena,
50; " luminiferous ether," 69, 70,
89 ; "elastic medium" in space, 84;
referred to, 86, 91, 95 ; hrst used
the term " energy," 98, 115 ; his work
theoretical, 99 ; value of one horse-
power, 99; 'Lectures,' 102; theory

of heat, 103 et seq.; heat a form of
motion, 104 ; undulatory theory,
180; 341, 344; (see Sir Norman
Lockyer), 361 ; colour theory, 480 ;
'Essay on Music,' 489.

Zach, von, ' Monatliche Correspondenz,'
i. 41 ; 54 ; first international organ
for astronomical observations, 167 ;
astronomical achievements, 176; bio-
graphical, 177; 182; 422.

Zeemann, magnetism and light, ii. 197.

Zeiss, Carl, improvements in the micro-
scope, ii. 229.

Zeller, E., i. 162; 'Philosophie der
Griechen,' ii. 3, 207 ; quoted, 286.

Zeno, unity of all existence, ii. 3 ;
286.

Zeuner, the steam-engine, ii. 133 ; con-
troversy with Hirn, 135 ; (see Claus-
ius), ib. ; heat engines, 175 ; 185 ;
statistics, 566.

Ziegler, 'Doctrine of Descent,' ii. 349.

Zittel, A. von, ' Gesch. der Geologic,' ii.
212.

Zcillner, F., historical and controversial
writings, ii. 107 ; Poggendorf and
Mayer's MS., 114 ; speculations of,
192 ; ' Wissenschaftliche Abhand-
lungen,' 716.

Zschokke, H., educational influence of,
in Germany, i. 257.

Zwingli, educational work of, i. 255.

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