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EUROPEAN THOUGHT IN THE NINETEENTH

CENTUEY

ToioStos ovu fxoL b crvyypacji€v^ earw, . . .

iivO^ iv TOtS ^t/3AtOlS KOL (XTToAlS.

— LUCIAN.

A HISTOEY

OF

EUROPEAN THOUGHT

IN THE

NINETEENTH CENTURY

BY

JOHN THEODOEE MEKZ

VOL. I.

SECOND UNALTERED EDITION

WILLIAM BLACKWOOD AND SONS

EDINBURGH AND LONDON
M C M I V

All Rights reserved

Ms-

7978?::

PEE FACE.

As the plan of this work is fully given in the Introduction,
only a few points, chiefly of a personal character, remain to
be touched on here.

The first refers to the motive which led me to a course
of studies, extending over more than thirty years, of which
this book is the outcome.

The object of the book is philosophical, in the sense now
accepted by many and by divergent schools — i.e., it desires
to contribute something towards a unification of thought.
"When in the beginning of my philosophical studies I be-
came convinced that this is the task of philosophy, I felt
the necessity of making myself acquainted, at first hand,
with the many trains of reasoning by which, in the
separate domains of science, of practical and of individual
thought, such a unification has been partially and success-
fully attempted. Such a survey seemed to me indispens-
able. The possession of a map showing the many lines of
thought which our age has cultivated seemed to me the
first requisite, the basis from which a more complete

VI PREFACE.

unification would have to start. The following pages
contain the result of this survey. Like every survey, it
can claim to be merely an approximation. It gives outlines
which closer scrutiny will have to correct and fill up.

My original intention was to complete this survey in
three volumes, corresponding to the three divisions of the
subject set out in the Introduction.

Some of my friends, who desired that the publication
of the book should not be unduly delayed, considered that
the Introduction and the earlier chapters of the work would
give something intelligible in themselves, and urged the ad-
vantage of smaller volumes. I therefore decided to complete
the first part of the history, which deals with scientific
thought, in two volumes instead of in one.

For the information of my readers, I mention here that
the two last chapters of this volume, which treat of tlie
astronomical and of the atomic views of Nature, will be
followed in the second volume by similar chapters on
the mechanical, the physical, the biological, the statistical,
and the psychophysical views of Nature, and that it is my
intention to close the first part of my subject by an attempt
to trace concisely the development of mathematical thought
in this century.

My thanks are due to many friends who have supported
me with assistance and encouragement.

I consider myself fortunate in having secured for the
revision of the whole volume the invaluable aid of Mr
Thomas Whittaker, B.A., whose profound erudition, know-

PREFACE. Vll

leclse of ancient and modern literature, and oreat editorial
experience, were well known to my late friend Professor
Croom Eobertson, during his successful editorship of the
first series of ' Mind.'

Mr S. Oliver Eoberts, M.A., of the Merchant Taylors'
School, has kindly read over the fourth, and Professor
Phillips Bedson, of the Durham College of Science of this
city, the last, chapter of this volume. The Introduction has
greatly benefited by a thorough revision by my brother-
in-law, Dr Spence Watson, a master of the English language.

I must also thank him and Dr Thomas Hodgkin for
haviniT mven me what I value as much as assistance —
namely, encouragement.

One indeed to whom I am in this respect more indebted,
perhaps, than to any one else — whom to have known has
meant, for many, a revelation of the power of mind and
the reality of spirit — is no more : Ernst Curtius. While
I was writing the last pages of this volume, in which he
took a warm interest, the tidings arrived that he had passed
away. But she who was nearest and dearest to him is
still with us — a true priestess of the higher life, who has
kept burning in the soul of many a youthful friend the
spiritual fire when it was in danger of being quenched by
the growing materialism of our age.

J, THEO. MEPvZ.

The Quarries,
Newcastle-upon-Tyne, November 1896.

COIs^TENTS OF THE FIEST VOLUiME.

INTRODUCTION.

Thought, the hidden world, 1 ; The ouly moving principle, 2 ; History of
Nature, how to be understood, 2 ; Not intelligible without intellect, 2 ;
History of savage tribes, what is it ? 3 ; Two ways in which thought enters
into history, 4 ; Definition of thought impossible, 4 ; Relation of outer
and, inner worlds undefined, 5 ; Many meanings of thought, 5 ; Thought
of the present age, 6 ; Contemporary history, to what extent possible
and valuable, 6 ; Supposed objectivity of historians, 7 ; Value of contem-
porary records, 8 ; Mystery of the life of thought, 8 ; Latent thought the
material for genius, 8 ; Contemporary record of thought more faithful,
10; Events of the immediate past, 10 ; Changes of language, 11 ; Coining
of new words, 12; Object of this work, 13 ; Not a political history, nor a
history of science, literature, and art, 13 ; Influences which have a result
on our inner life, 14 ; Personal knowledge necessary, 14 ; American influ-
ence only touched upon, 14 ; Only French, German, and English thought
treated, 15 ; Unity of thought, a product of this century, 16 ; Voltaire,
16 ; Adam Smith, 16 ; Coleridge and Wordsworth, 17 ; Mme. de Stael,
17 ; Paris the focus of science, 17 ; Babbage, Herschel, and Peacock, 18 ;
Liebig's laboratory, 18; Comte's philosophy, 18 ; Constable's influence in
France, 19 ; Science become international, 19 ; The light which etymology
throws on the history of thought, 20 ; Goethe, 22 ; Peculiarity of the
German language, 22 ; New thought has found new words, 23 ; De Bon-
ald and Max ^Killer, 23 ; Thought, how expressed in French and Ger-
man, 24 ; Philosophy of History, 25 ; Want of precise terms in German
and French, 26 ; Carlvle, 26.

X CONTENTS.

II. The two factors of intellectual progress, 27 ; Object of the book, 28 ;

Nineteenth century, what it has achieved : («) Method of knowledge ; (b)
Unity of knowledge, 29 ; Seaich after truth, 29 ; Method of science, prac
tised by Galileo, &c., defined by Bacon, &c., 30 ; Disintegration of learn-
ing, 30 ; Apparent distance between science and poetry, 31 ; Closer con-
nection between science and life, 31 ; What has nineteenth century done
for the ideals ? 32 ; Deeper conception of the unity of human interests,
33 ; DiSerent terms for expressing this unity, 33 ; Definition of thought,
33 ; Age of encycloppedic treatment of learning, 34 ; Unity of knowledge
gradually lost sight of, 35 ; Lectures on "Encyclopiidie" in Germany, 37;
Encyclopiedias did not fulfil their promise, 39 ; French were masters in
science in beginning of the century, 41 ; Reaction in Germany against
metaphysics, 43 ; Reform in school literature, 44 ; Germany has taken
the lead in studying the life of thought, 46 ; Transition from meta-
physical to historical method, 47 ; Herbert Spencer, 48 ; Lotze, 48 ;
Herder's ' Ideen,' 50 ; Humboldt's ' Kosmos,' 51 ; Lotze's ' Microcosmus,'
52 ; What the mental life of mankind consists of, 55 ; Methods have
their day and cease to be, 56.

III. Necessity of choosing a road, 57 ; No central event in our age, 58 ; Is
history of thought history of philosophy ? 60 ; Goethe's work involves
the deepest thought of the century, 61 ; Philosophy retrospective, 62 ;
Two questions, 63 ; Speculation, 64 ; Philosophy defined, 65 ; Division
of the book, 65 ; Neither science nor philosophy exhausts " thought," 66 ;
Thought also hidden in literature and art, 66 ; Goethe's and Words-
worth's influence, 67 ; Unmethodical thought, 68 ; Summed up in term
"religious thought," 69 ; Science is exact, 69; Subjective interests, 70;
Philosophy intermediate between exact science and religion, 71 ; Three-
fold aspect of thought : scientific, philosophical, individual, 72 ; Difficult
to separate the three aspects, 74 ; French thought centred in science,
75 ; State of philosophj^ in England, 75 ; Goethe's 'Faust' representative
of the thought of the century, 76 ; A period of ferment, 76 ; Caused by
the Revolution, 77; Thought of century partly radical, partly reactionary,
77 ; Byronic school, 78 ; Revolutionary theories, 79 ; Thought to be con-
sidered as a constructive power, 80 ; Darwin, Spencer, and Lotze, 81 ;
Romanticism, 82 ; Scientific thought to be dealt with first, 84 ; Hegel's
docti-ine, 85.

CONTENTS. XI

PART I.— SCIENTIFIC THOUGHT.

Three cliapters on the growth and the diffusion of the scientific spirit
in the first half of the nineteenth century.

CHAPTER I.

THE SCIENTIFIC SPIRIT IN FRANCE.

Our century the scientific century, 89 ; Difference of English and Continental
notions of science, 91 ; Relation of science and life, 92 ; Foreseen by
Bacon, 93 ; Defect in Bacon's philosophy, 94 ; Corrected by Newton, 95 ;
Bacon's and Newton's ideas taken up by French philosophers : Bacon and
Newton compared, 96 ; Laplace's work, 97; French Academy of Sciences,
99 ; Continental methods in mathematics, 100 ; Modern analytical
methods, 102 ; Older synthetical methods, 103 ; Influence of science
on French literature, 104 ; Absence of this influence in England and
Germany, 106 ; Schools of science in Paris, 106 ; Promoted by Govern-
ments of Revolution, 108 ; Condorcet, 110 ; Lakanal, 111 ; Ecole normale,
Ecole polytechnique, 112; Monge's ' Descriptive Geometry,' 114 ; Science
of Chemistry, 114; New mathematical sciences, 116; Crystallography,
116; Theory of probability, 118; Laplace gained his results by dis-
regarding "individuality," 124 ; The centre of interest in the sciences of
life, 125 ; Into this centre Cuvier carried exact research, 128; Cuvier's
training, 133 ; Cuvier the greatest representative of the Academic system,
136 ; Science during the Revolution and First Empire, 138 ; Popular-
isation of science in France, 142 ; Literary and national popularisation,
142 ; Dangers of the former, 143 ; The Revolution added the practical
popularisation, 145; Influence of the first Napoleon on science, 149;
Napoleon favoured the mathematical sciences, 151 ; Discountenanced
contemporary philosophy, 152 ; Used statistical methods, 153 ; Promi-
nence given deservedly to French names by Cuvier, 155.

CHAPTER II.

THE SCIENTIFIC SPIRIT IN GERMANY.

Foundation of German universities, 158 ; Development of the universities by
the people, 159 ; Geographical distribution of the universities, 162 ; Full
development of the German university system, 163 ; Philosophical fac-
ulty, 164 ; University of Gottingen, 164 ; Relation of universities and

xn CONTENTS.

high schools, 166 ; The university a training-school for research, 167 ;
The ideal of Wisscnschaft, 168 ; Developed under the German university
system, 170 ; Reception of exact science in Germany, 174; Science not
yet domiciled during the eighteenth century, 178 ; Scientific periodicals,
180 ; Gauss's mathematical researches, 181 ; Scientific spirit enters the
universities in second quarter of century, 183 ; Jacobi's mathematical
school, 185 ; Chemical laboratories established in 1826 through liebig,
188 ; Cosmopolitan character of German science, 189 ; Liebig's organic
analysis, 191 ; Biology a German science, 193 ; Cellular theory of
Schleiden, 194 ; and Schwann, 195 ; Ernst Heinrich Weber, 196 ; and
Johannes Miiller, 197 ; Psychophysics, 198 ; Spirit of exact research and
Wisxcnschaft, 202 ; Encj'clopredic view necessary in philosophj' and
history, 203 ; Philosophy of Nature, 204 ; Conflict between the scientific
and the philosophical views, 205 ; A. von Humboldt, 206 ; Influence of
Berzelius on German science, 208 ; Philosophy of Nature and medical
science, 209 ; Science for its own sake, 211 ; Bequest of the classical and
philosophical school, 211 ; Completeness and thoroughness of research,
213 ; Combination of research and teaching, 214 ; Combination of science
and philosophy, 215 ; Biology grown out of science and philosophy com-
bined, 216; Du Bois-Reymond on Miiller, 217 ; "Vital force" abandoned,
218 ; Mechanical view in biology, 219 ; Criticism of principles of mathe-
matics, 221 ; The exact, the historical, and the critical habits of thought,
222.

CHAPTER III.

THE SCIENTIFIC SPIRIT IN ENGLAND.

Scientific organisation abroad, 226 ; Similar institutions in Great Britain, 227 ;
English science in the early part of the century, 229 ; Alleged decline of
science in England, 230 ; Criticisms of Playfair, 231 ; Babbage's criti-
cisms, 233 ; Foreign opinions on English science, 235 ; English replies to
Babbage, 238 ; Foundation of the British Association, 238 ; Character-
istics of higher mental work in England, 239 ; Academies and universities
not always impartial, 240 ; Fourier, 241 ; Fresnel, 241 ; Pliicker,
242 ; Grassmann, 243 ; Central organisation wanting in England, 243 ;
Thomas Young, 244 ; Dalton, 245 ; Faraday, 246 ; Green, 246 ; Boole,
247 ; Babbage, 248 ; Characteristics of English thought, 249 ; Absence of
schools of scientific thought, 250 ; Individual character and practical
tendency of English science, 251 ; English peculiarities more pronounced
during earlier part of the century, 252 ; Unique character of English
universities, 254 ; Ideal of "liberal education," 255 ; Union of education
and instruction, 258 ; Educational organisations in England, 262 ; The

CONTENTS. Xlll

Royal Institution, 264 ; Manchester Literal-}- and Philosophical Society,
265 ; John Dawson of Sedbergh, 267 ; The Scotch Universities, 267 ; The
Royal Society of Edinburgh, 269; The 'Edinburgh Review,' 270; The
Analytical Society of Cambridge, 271 ; University life in Scotland, 271 ;
The Dublin Mathematical School, 274 ; Importance of British contribu-
tions to science, 276 ; Diffusion of scientific knowledge on the Continent,
276 ; Isolation of English men of science, 277 ; Individualism of the
English character, 279 ; Changes during the last fifty years, 2S0 ; British
contributions to biology, 282 ; Jenner, 284 ; English love of Nature, 284 ;
Union of individualism and naturalism in England, 286 ; White of Sel-
borne, 288 ; The Geological Society, 290 ; William Smith, 291 ; Charles
Bell, 292 ; Historical geography, 294 ; Martin William Leake, 296 ; Work
of the three nations compared, 298.

CHAPTER IV.

THE ASTRONOMICAL VIEW OF NATURE.

The scientific spirit in the first and second half of the century, 302 ; Science
become international, -303 ; Disappearance of national differences, 305 ;
Special scientific ideas, 306 ; Philosophy of science, 306 ; Whewell's
' History ' and ' Philosophy,' 309 ; Philosophy and science, 311 ; Leading
scientific ideas mostly very ancient, 312 ; Mathematical spirit, 314 ;
When first introduced into science, 317 ; Newton's 'Principia,' 318 ; The
gravitation formula, 319 ; Lines of thought emanating from it, 321 ;
Element of error, 323 ; Laplace and Newton, 326 ; Several interests
which promote science, 326 ; Insufficiency of observation, 328 ; Practical
interest, 328 ; Focalising efi'ect of mathematical formulse, 332 ; Matter
and force mathematically defined, 334 ; Weight and mass, 336 ; Gravi-
tation not an ultimate property of matter, 338 ; Attraction and repulsion,
342 ; Electrical and magnetic action, 344 ; Law of emanations, 344 ;
Molecular action, 346 ; The astronomical view : Cosmical, molar, and
molecular phenomena, 348 ; Special interest attached to molar dimen-
sions, 350 ; Geometrical axioms, 352 ; Difficulty of measuring gravitation
directly, 353 ; Astronomical view of molecular jDhenomena, 354 ; Capil-
lary attraction, 356 ; Boscovich's extension of the Newtonian formula,
357 ; Coulomb's measurements, 360 ; Extended by Gauss and Weber,
360 ; Davy and Faraday, 363 ; Ampere and Weber develop the astro-
nomical view, 366 ; Weber's fundamental measurements, 368 ; Necessity
of developing the infinitesimal methods, 373 ; Newtonian formula the
basis of physical astronomy, 375 ; The Newtonian formula unique as to
universality and accuracy, 377 ; Is it an ultimate law ? 378 ; Laplace's
opinion, 378 ; Opposition to the astronomical view of nature, 381.

XIV CONTENTS.

CHAPTER V.

THE ATOMIC VIEW OF NATURE.

Recapitulation, 382 ; Atomic theory, 385 ; Lavoisier, 386 ; Phlogistic theory,
388 ; Theory of combustion, 389 ; Rule of fixed proportions, 392 ; J.
Benjamin Richter, 393 ; Dalton, 394 ; Berzelius, 396 ; Atomic theory
and gravitation compared, 396 ; WoUaston's prophecy, 397 ; Rule of
multiple proportions, 398; Equivalents, 399; "Simplex sigillum veri,"
401 ; Prout's hypothesis, 402 ; Discovery of Isomerism, 40.o ; Organic
Chemistry, 407 ; Liebig's definition of same, 409 ; Type theory, 411 ;
Uncertainty in chemical theory about middle of century, 413 ; Two
aspects of the atomic theory, 415 ; A convenient symbolism, 417 ;
Neglect of the study of affinity, 420 ; Kopp on chemical theorj' in 1873,
421 ;*The periodic law, 422 ; Difference between chemical and physical
reasoning, 424 ; The kinetic theory of gases, 425 ; Avogadro's hypothesis,
427 ; Neglect of same, 429 ; Development of the atomic view, 431 ;
Pasteur's discovery of "Chirality," 431; Atom and molecule, 432;
Joule's calculations, 434 ; Clausius's first memoir, 435 ; Internal energy
of molecules, 436 ; The atomic theory accepted as a physical theory
about 1860, 437 ; Clerk Maxwell : The statistical view of nature, 438 ;
Doctrine of averages, 440 ; Geometrical arrangement of atoms, 441 ;
Crystallography, 441 ; Analogy between ci^ystallographic and atomic
laws, 444 ; Isomorphism, 444 ; Polymorphism, 446 ; Structural and
stereo-chemistry, 447 ; Valency, 447 ; Atomic linkage, 449 ; The carbon
tetrahedron, 450 ; Defects and insufficiency of the atomic view, 451 ;
Theories of chemical affinity, 452 ; Practical influences, 453 ; Change in
definition of organic chemistry, 454 ; Criticisms of the atomic view, 455.

A HISTORY OF EUEOPEAN THOUGHT
IN THE NINETEENTH CENTURY.

INTEODUCTION.
I.

Behind the panorama of external events and changes i-

^ ° Thought,

which history unfolds before our view there lies the *^^'^,.i^"^'^®"
hidden world of desires and motives, of passions and
energies, which produced or accompanied them ; behind
the busy scenes of Life lie the inner regions of Thought.
Only when facts and events cease to be unconnected,
when they appear to us linked together according to
some design and purpose, leading us back to some
originating cause or forward to some defined end, can
we speak of History in the sense which the word has
acquired in modern language ; and similarly do the
hidden motives, desires, and energies which underlie or
accompany the external events require to be somehow
connected, to present themselves in some order and con-
tinuity, before we are able to grasp and record them.
VOL. I. A

INTRODUCTION.

Thought,
the only
moving
principle.

History of

Nature, how
to be under-
stood.

4.
Not intelli-
gible with-
out intel-
lect.

That which has made facts and events capable of being
chronicled and reviewed, that which underlies and con-
nects them, that which must be reproduced by the his-
torian who unfolds them to us, is the hidden element of
Thought. Thought, and thought alone, be it as a principle
of action or as the medium of after-contemplation, is
capable of arranging and connecting, of combining what
is isolated, of moving that which is stagnant, of propel-
ling that which is stationary. Take away thought, and
monotony becomes the order.

This assertion may seem bold to many, who would look
rather to the grand phenomena of Nature than to the
narrow limits of man's activity. A few remarks will,
however, suffice to show that my proposition is not
opposed to the view which they take. It may be
urged that, independent of human life altogether, the
earth has a history, the planetary system has a develop-
ment, and that, according to modern theories, evolution
is the principle which governs inanimate as well as ani-
mated nature ; that rest and sameness are nowhere to
be found, everywhere change and unrest. But change
and unrest do not necessarily constitute history. Motion
and change would be as monotonous as absolute rest,
were they merely to repeat themselves endlessly, did the
whole movement not produce something more, and w^ere
this something more not greater or better than the
beginning. But greater and better are terms which imply
comparison by a thinking beholder, who attaches to one
thing a greater value than to another, judging by certain
ideal standards, which are not in the objects or process of
nature themselves, but are contained only in his own think-

INTRODUCTION. 3

ing mind. It may be that a mechanical and mindless series
of changes can produce numbers without end, or forms of
countless variety : but this process would deserve the name
of history only if either the transition from unity to mul-
tiplicity, or the production of formal variety, were capable
of being understood by a thinking mind, — if the result
of the process were a matter of some concern, if an
interest were attached to it, if a gain or loss could be
recorded. The pendulum which swings backwards and
forwards in endless monotony, the planet which moves
round the sun in unceasing repetition, the atom of matter
which vibrates in the same path, have for us no interest
beyond the mathematical formulae which govern their
motions, and which permit us mentally to reproduce, i.e.,
to think them. A combination of an infinite number of
these elementary movements would have as little interest,
were it not that out of such a combination there resulted
something novel and unforeseen : something that was
beautiful to behold or useful to possess, something that
was valuable to a thinking mind in a higher or lower
meaning of the word.

But if, even in inanimate nature, the processes of change
acquire an interest, possess a history, only if referred to
a thinking mind which can record, understand, and appre-
ciate them, how much more is this the case when we deal
with human affairs, where man is not only the thinking
beholder but the principal agent ? Here the historic
interest would cease, were the succeeding years and ages
to produce no valuable change, were the rule of existence

5.

and the order of life to repeat themselves in unceasing History of

'- o savage

monotony. The savage tribes of Africa have a history : but iJ'j^f ' ^^^^^

INTEODUCTION.

6.

Two ways
in which
Thought
enters into
History.

Definition
of Thought
impossible.

this history is all known when the order of the day, the
year, at most of a generation, is known. Even the highly
complicated but stagnant life of China would have a short
historical record — many thousands of years taking up no
more space than as many days of modern European history :

" Better fifty years of Europe than a cycle of Cathay."

Thus it is that Thought becomes in two ways a subject
of great interest and importance to the historian. Of
every change in nature or human life we can ask : What
has been its result in the world of thought ? What
gain or loss, what progress, has it worked in the minds
of men, of us the beholders ? Has it increased our
knowledge, enriched our stock of ideas, deepened our
insight, broadened our views and sympathies — in one
word, has it added to our interests ? has it made larger
and fuller our inner life ?

And of every change in human affairs we can ask this
further question : What part has thought, the inner life,
played in this change ? These two questions mark the
task of the historian of Thought.

I do not think it necessary or practicable at this stage
to explain minutely the terms with which we have so
far been dealing. Many a one might be tempted to ask
for a definition of Thought, or for a preciser statement of
the actual relation between Nature, Life, and Thought.^

^ In refusing to define what I
mean by Thought, 1 take up the
opposite position to that occupied
by Prof. Max Miiller in his latest
work, 'The Science of Thought,'
London, 1887, p. 1, where he says :
" I mean by Thought the act of
thinking, and by thinking I mean

no more than combining. I do
not pretend that others have not
the right of using Thought in any
sense which they prefer, provided
only that they will clearly define
it." So far as definition is at all a
part of the work of the historian,
I maintain that it is the result and

INTRODUCTION. 5

Such definitions must be left to the reader himself, if
in course of the perusal of these volumes he finds it
necessary to form abstract theories on these points.
Any definition given now would inevitably involve us in
controversies, which would be embarrassing and con-
fusing. I rely upon the general and undefined sense of
the word Thought, assuming that every one will connect
some intelligible meaning with it, some Ineaning which
will enable him to understand the very general pro-
position with which we started, the existence of an s.

Relation of

inner or hidden world behind the world of external outer and

inner world

events and facts, the continually changing nature of undefined,
this inner world, and the connection and reaction be-
tween the two worlds. Whether in time and in im-
portance the outer or the inner world is the first,
whether within the latter equal value attaches to the
clearer province of Eeason, ■i.e.j defined Thought, to the
obscurer regions of Feeling and Imagination, and to the
unconscious world of Impulse, these are questions which
it is not necessary to answer at present. As it was
enough to point to the existence of the two worlds of
Life and Thought, so it will be enough to notice that |
thought does not mean merely defined, clear, methodical 9.

. . , -Many mean-

thought, but likewise the great region of desire, impulse, mgs of
feeling, and imagination, all of which play, we must
admit, a great part in the inner life of the soul as well '
as in that of the outer world.

outcome of his narrative, the im-
pression which he leaves on the
mind of the reader when he has
perused the work. History is not
mainly a science which proceeds
by analysis ; it is the attempt to

collect and arrange in a living pic-
ture an enormous mass of detail.
Too rigid definitions, like lines
which are too hard and marked,
spoil the total effect.

6 INTHODUCTION.

In this sense of the word we have in the following
treatise to deal with the History of Thought : not, how-
ever, with the history of thought in general, but with
„ 10. that of a defined period, with that of the present age

Thought of r ' f o

the present g^^^^ ^^le age immediately preceding it, — the age, in fact,
to which the writer and his readers belong, of which
they have a personal knowledge and recollection more or
less wide and intimate. It is the latter circumstance
which has made me select this special portion of the
history of thought ; for it is that portion of which, it
seems to me, I and my contemporaries should — if we go
about it in the right way — know most. As every person
is his own best biographer, so it seems to me every age
is, in a certain sense, its own best historian.
11. We know that this has been frequently denied so far

Contempor-
ary history, as external events (that which many persons call history

to what ex- ^ "^ ^ "^

and vaiu-^^*^ ^ar excellence) are concerned. Contemporary writers do
^^^^' not, it is stated, get beyond mere records of events,

records at once one-sided, incomplete, and confusing. It
is indeed necessary to have the records in great number
and variety : because the true and real record can only
be given by him who combines all these many records
into one, who avoids the errors arising from special
points of view, from narrowness of outlook, from indi-
vidual ignorance, blindness, or prejudice. Still, in spite
of such defects, the contemporary records will always
remain the most valuable sources for the future historian
who may succeed in sifting their various testimonies,
combining and utilising them to produce a fuller and
more consistent picture of the bygone age. But while
his work may be only temporarily valuable, theirs is

INTRODUCTION. 7

lasting. It is hardly doubtful that, after hundreds or
thousands of years have passed, the simple, detailed, and
perhaps contradictory, narratives of contemporary wit-
nesses will outlive those more elaborate and artistic
efforts of the historian which are so largely inspired and
coloured by the convictions of another — viz., his own —
age. For as Goethe has remarked : " History must from
time to time be rewritten, not because many new facts
have been discovered, but because new aspects come into
view, because the participant in the progress of an age
is led to standpoints from which the past can be re-
garded and judged in a novel manner." ^

Most of the great historians whom our age has pro-
duced will, centuries hence, probably be more interesting
as exhibiting special methods of research, special views
on political, social, and literary progress, than as faith-
ful and reliable chroniclers of events ; and the objectivity 12.

' '' '' Supposed

on which some of them pride themselves will be looked objectivity

-C^ of nistor-

upon not as freedom from but as unconsciousness on their
part of the preconceived notions which have governed
them. But where the facts recorded and the mind which
records them both belong to the same age, we have a
double testimony regarding that age. The events, and 1
the contemplating mind, supplement each other to form . if
a more complete picture, inasmuch as the matter and the
medium through which it is viewed belong to the same
time. And so it comes to pass that historians like
Thucydides, Tacitus, and Machiavelli are looked upon as

lans.

\

^ ' ilaterialien zur Geschichte der
Farbenlehre,' Werke, 2te Abtheil-
ung, Band 3, p. 239, I quote from

the uew edition, brought out bj^
the German Goethe Society.

8

INTRODUCTION,

13.
Value of
contempor-
ary records,
both of
Facts and
Thought.

14.
Mystery of
the Life of
Thought.

15.

Latent
Thought
the material
for genius.

perfect models in the art of writing history, and the
memoirs of many modern statesmen are more lastingly
valuable than the more elaborate and connected narra-
tives of remote and secluded scholars.

But if the contemporary record of facts will always
have a peculiar value, however incomplete it may be,
still more must this be the case with the contemporary
record of thought ; especially if thought means the whole
of the inner life of an age, not merely that portion wdiich
in the form of defined thought has been incorporated in
the written literature of the age. For a large portion of
this hidden life is known only to those who have taken
part in it. The vague yearnings of thousands who never
succeed either in satisfying or expressing them, the hun-
dreds of failures which never become known, the number-
less desires which live only in the hearts of men or are
painted only in their living features, the uncounted
strivings after solutions of practical problems dictated
by ambition or by want, the many hours spent by
labourers of science in unsuccessful attempts to solve
the riddles of nature, — all these hidden and forgotten
efforts form indeed the bulk of a nation's thought, of
which only a small fraction comes to the surface, or shows
itself in the literature, science, poetry, art, and prac-
tical achievements -of the age. Equally important, though
not equally prominent, this large body of forgotten
thought has nevertheless been that which made the
measure full, which heaped the fuel ready for the
match to kindle ; it constitutes the great propelling force
which, stored up, awaits the time and aid of individual
talent or genius to set it free. Philosophers tell us of

INTRODUCTION. 9

the wastefulness of oi'ganic life, of the thousands of germs
which perish, of the huge volume of seed scattered use-
lessly. A similar fate seems to fall on the larger portion
of intellectual and moral effort ; but here a deeper con-
viction tells us that it is not the sacrifice but the co-
operation of the many which makes the few succeed,
that excellence is the prize of united effort, that many
must run so that one may reach a higher goal. What
other feeling could console those legions of honest workers
who spend their lives in trying to deal with the seem-
ingly unconquerable host of social evils, the apparently
growing vice and misery of large towns, who raise a
cry for oppressed nationalities, or preach against the
curses of war and militarism ? Or what higher and un-
selfish satisfaction could an author derive from spending
half a lifetime in producing a work which in the end
may fall dead-born from the press, if it were not the
conviction that in the cause in which he has failed
another after him may succeed, and that his failure
may be a portion of the silent and hidden efforts that
co-operate towards a useful end ? ^ But who in after-
ages can write the history of this forgotten and hidden
work of a nation ? Whose historical sense is delicate
enough to feel where the pressure was greatest and the
effort longest ere the new life appeared, whose eye pene-
trating and discerning enough to follow up the dim streaks

^ "Sehen wir nun wiihrend un-
seres Lebensganges dasjeuige von
anderen gelestet, wozu wir selbst
.f ruber einen Beruf f iihlten, ihn aber,
mit manchem andern, aufgeben
mussten, daun tritt das schone
Gefiihl eiu, dass die Mensehheit zu-

sammen erst der wahre Mensch ist,
und dass der Einzelne nur froh
und gllicklich sein kann, wenn er
den Mu|tb hat, sich im Ganzen zu
fuhlen." — Goethe, ' Wahrheit und
Dichtung,' 9th Book ; Werke, 27,
277.

10

INTRODUCTION.

16.
Contempor-
ary record
of Thought
more faith-
ful.

17.
Events of
the imme-
diate past.

of twilight, dazzled as he must be by the blaze of the
risen sun ? We who live in the expectation of the light
which is to come, surrounded by the shadows, difficulties,
and obstacles ; we who belong to the army, and are not
leaders, who live in, not after, the fight, — we claim to be
better able to tell the tale of endless hopes and endeav-
ours, of efforts common to many, of the hidden intellec-
tual and moral work of our age.^

How far back we who have lived during the second
half of the present century may extend the period of
which we claim to have a personal knowledge, is a point
of further interest. Certain it is that in our parents and
immediate forefathers we have known the representatives
of a generation which witnessed and laboured in the in-
terests of the great Anti-Slavery, the Eeform, and the Anti-
Corn-Law movements, who experienced the revolutions
worked by the introduction of steam-power and gas, who
took part in the great work of national and popular edu-
cation abroad and in the reform of school-life in England.
They themselves went through the enthusiasm of the
anti-Napoleonic Eevolution in Germany, came under the
influence of Goethe's mature manhood, were fascinated by
the stories from the pen of the Wizard of the North, par-

■* Compare what A. de Tocqueville
says, ffiuv. comp. ,' vol. viii. p. 170 :
" Nous sommes encore ti'oiJ pres des
evenements pour eu connaitre les
details. Cela parait sinpulier, mais
est vrai. Les details ne s'appren-
iient que par les revelations post-
humes, contenues dans les M^-
moires, et sout souvent ignores des
contempoiains. Ce qu'ils savent
mieux que la posterite, c'est le

niouvemeut des esprits, les pas-
sions geuerales du temps, dont ils
senteut encore les derniers fremis-
sements dans leur esjjrit ou dans
leur occur ; c'est le rapport vrai des
prineipaux personnages et des prin-
cipaux faits entre eux. Yoilh ce
que les voisins des temps racontds
apergoivent mieux que ne fait la
posterity. "

INTRODUCTION. 1 1

took of the spirit of the Eomantic School, felt the electrical
touch of Lord Byron's verse, listened to the great orators
of the third French Eevolution, and could tell us of the
now forgotten spell which Xapoleon I. exercised over
millions of reluctant admirers. Most of these fascinations
and interests live only in the narratives of contemporaries
and surviving witnesses, few of whom have succeeded in
perpetuating them with pen or brush, making them intel-
ligible to a future age ; most of them die with the genera-
tion itself. Not only have we listened to their words and
seen in their features the traces of the anxieties they lived
through, in their eyes the reflected enthusiasms and as-
pirations, in their glances and in the trembling of their
voices the last quiverings of bygone passion and joy, — we
have received from them a still more eloquent testimonial,
a more living inheritance. But this we cannot hand
down to our children in the form in which it was given
to us : it has not passed through our hands unaltered.
This inheritance is the language which our parents have
tauo-ht us. Unknowingly they have themselves altered is. -

=> o J ^ Changes

the tongue, the words and sentences, which they received, g^l'^'^jg^^^jj^e;.
depositing in these altered words and modes of speech the |a?ent°to
spirit, the ideas, the thought of their lifetime. These proof o^iie

changing

words and modes of speech they handed to us m our ufeof

^ -^ _ Thought.

infancy, as the mould wherein to shape our minds, as the
shell wherein to envelop our slowly growing thoughts, as
the instrument with which to convey our ideas'. In their
language, in the phrases and catchwords peculiar to them,
we learnt to distinguish what was important and interest-
ing from what was trivial or indifferent, the subjects which

12

INTRODUCTION.

19.
Inadequacy
of conven-
tional
speech for
original
thought.
Coining of
new words.

should occupy our thoughts, the aims we should follow,
the principles and methods which we should make use of.
The bulk and substance of this they indeed inherited them-
selves ; but the finer distinctions of their reasoning, the
delicate shading of their feelings and aspirations, they
added and modified for themselves, modelling for their own
special use the pliable and elastic medium of the mother
tongue. With this finer moulding we have inherited the
spirit of the former generation : predisposing us to certain
phases of thought and placing in our path a difficulty in
acquiring otherwise than by gradual and almost imper-
ceptible degrees the faculty of assimilating new and un-
expected opinions, tastes, and feelings. Many of us adhere
to the special character and phase of thought acquired
in our youth. Some by learning foreign languages, and
living in other countries, gain a facility for understanding
quite different phases of thought : very few among us
develop so much original thought that they burst the
shell of conventional speech, coining new words and ex-
pressions for themselves, embodying in them the fleeting
ideas of their time, the indefinable spirit of their age.
Once expressed, these new terms are rapidly circulated,
and if we look back on the period of a generation, we
note easily the progress and development of opinion and
tastes in the altered terms and style of our language.

Thus it is that the writer, and those of his readers
whose memory carries them back to the middle of the
century, and whose schooling and education embodied the
ideas of a generation before that time, can claim to have
some personal knowledge of the greater portion of the
nineteenth century, of the interests which it created and

INTRODUCTION.

13

the tlioudits which stirred it.-^ It is the object of these 20.

» ^ '' Object of

volumes to fix, if possible, this possession ; to rescue from ^q^^^"''^
oblivion that which appears to me to be our secret prop- xhrnght^
erty ; in the last and dying hour of a remarkable age to dy^ing^cen-*
throw the light upon the fading outlines of its mental
life ; to try to trace them, and with the aid of all possible
information, gained from the written testimonies or the
records of others, to work them into a coherent picture,
which may give those who follow some idea of the
peculiar manner in which our age looked upon the world
and life, how it intellectualised and spiritualised them.
This attempt is therefore not a history of outward politi-
cal changes or of industrial achievements : the former will
probably be better known to our children than they have 21.

•n 1 r> T Not a politi-

been to us : the latter will soon be forgotten as such, or cai history,

nor a history

incorporated in the still greater results of the future, for j^j^g^Jt^fg'
which they will be the preparation. Nor is it a history ^^^■^^^'
of Knowledge and Science, of Literature and Art, which
I purpose to write ; though as these are the outcome of
the inner life, and contain it, so to say, in a crystallised
form, they will always have to be appealed to for the
purpose of verifying the conclusions which we may arrive

^ On the division of History into
centuries see what Du Bois-Rey-
mond says ('Reden,' Leipzig, 1886,
vol. i. p. 519), and the fuller dis-
cussion of the subject by Prof. 0.
Lorenz, ' Die Geschichts - wissen-
schaft ' (Berlin, 1886, p. 279 sqq.)
The latter refers to what the first
historian says (Herodotus, ii. 142 :
KaiTOi Tpn]K6aiai ^iv avSpwi/ yeveal
Swearai /xvpta erfa- yfvfal yap Tpe7s
avSpwi' ^KaThu erea iari). A per-
son born in 1840 can claim to have
a personal knowledge of the last

half, and through his parents and
teachers a knowledge of the first
half, of the century. In this way
it may be said that his personal —
direct or indirect — knowledge ex-
tends over nearly a century. Lor-
enz says correctlj' : " Fiir jeden
einzelnen bildet der Vater und der
Sohn eine greifbare Kette von
Lebensereignissen und Erfahrun-
gen." And that this applies even
more to ideas and opinions, to
Thought, than to events and facts,
is evident.

14

INTRODUCTION.

22.
Where the
interest of
the book
will lie :
in all the
influences
which have
a result on
our inner
life.

23.
The personal
knowledge
and experi-
ence neces-
sary for a
true por-
trayal forms
a limitation
of the ex-
tent of
ground to be
traversed.

24.
American
influence
only
touched
upon.

at. What will interest us most will be the conscious
aims and ends, if such existed, of any political or social
movement, and, where they did not exist, at least the
results to our inner life which have necessarily followed,
the methods by which knowledge was extended or science
applied, the principles which underlay literary composition
and criticism, and the hidden spiritual treasure which
poetry, art, and religious movements aimed at revealing
or communicating ; in fact the question : What part has
the inner world of Thought played in the history of our
century, — what development, what progress, what gain
has been the result of the external events and changes ?
But if personal knowledge and experience are — as it
seems to me — of the greatest importance in an attempt
like this ; if, without having lived the inner life, a record
of it would be either a mere string of names or a criticism
of opinions, not a living picture, — so it is also the factor
which necessarily limits the extent of the ground which
I propose to traverse. Thus I feel obliged in the first
place to limit myself to European Thought. Such a limi-
tation would hardly have been called for a century ago,
because it would have been a matter of course : but the
steady growth and peculiar civilisation of a new and
vigorous people on the other side of the Atlantic force
from me the twofold confession, that there is a large
world of growing importance of which I have no personal
knowledge, and to estimate which I therefore feel un-
qualified and unprepared ; and further, that I am equally
unable to picture to myself the aspect which the whole of
our European culture in its present state may assume to
an outside and far-removed observer who is placed in the

INTRODUCTION. 15

New World. As this New World grows not only in
numbers and national wealth, but also in mental depth,
as it becomes more and more intellectualised and
spiritualised, so it will no doubt experience the desire of
recording its own inner life and culture, emphasising the
peculiarities which distinguish it as a whole from our
civilisation. But the tendencies of this new culture are
to me vague and enigmatical, and I frankly admit that
I am unable to say anything definite on this subject. Con-
vinced as I am that in human affairs all outer life is the
vessel which contains an inner substance, the shell which
envelops a growing kernel, I am, nevertheless, unable in
this case to penetrate to either, and must therefore content
myself with taking notice of this vast new element of
nineteenth - century culture only where it comes into
immediate contact with European thought, which has
indeed been powerfully influenced by it. And of Euro- 25.

r -J J OnlyFrc

pean thought itself I am forced to select likewise only •^*'™*'i' . ,

i- o J and English

the central portion, the thought embodied in French, subj^Jt^of'*"
German, and English Literature. I have to admit that wo'X*^*'^"
Italian, Scandinavian, and Eussian influences are all
around this centre, sometimes penetrating far into it ;
but here again languages unknown and interests foreign
to me have made it impossible to identify myself ever so
superficially with the new life that is contained in them.
I must therefore here also confine myself to very im-
perfect and casual notices, which make no attempt to
do justice to the subject.

The subject before us, then, is European Thought — i.e.,
the thought of France, Germany, and England — during the
greater part of the nineteenth century. Circumscribed as

OnlyFrench,

16

INTRODUCTION.

26.
Unity of
Thought a
product
of this
century.

27.
Voltaire.

28.
Adam
Smith.

this subject is by the limits of time and space which I
have mentioned, it is, nevertheless, still vast, intricate, and
bewildering. And yet it is my intention, throughout the
inquiries which I have to institute and in the various out-
lines and sketches which I have to draw, never to lose
sight of the unity of the whole. This unity, I maintain,
the progress of our age has more and more forced upon
us. It is itself a result of the work of the century. A
hundred years — even fifty years — -ago, it would have been
impossible to speak of European Thought in the manner
in which I do now. For the seventeenth and eighteenth
centuries mark the period in which, owing to the use of
the several vernacular languages of Europe in the place
of the mediasval Latin, thought became nationalised, in
which there grew up first the separate literature and then
the separate thought of the different civilised countries of
Western Europe. Thus it was that in the last century,
and at the beginning of this, people could make journeys
of exploration in the region of thought from one country
to another, bringing home with them new and fresh ideas.
Such journeys of discovery, followed by importation of new
ideas, were those of Voltaire^ to England in 1726, where
he found the philosophy of Newton and Locke, at that
time not known and therefore not popularly appreciated
in France; the journey of Adam Smith in 1765 to France,
where he became acquainted with the economic system of
Quesnay and the opinions of the so-called " physiocrats,"
which formed the starting-point of his own great work,

^ For a most complete collection
of data referring to this subject
see Du Bois-Revmond's address in

the Berlin Academy, 30th January
1868, reprinted in the collection of
his ' Reden,' Leipzig, 1886, vol. i.

INTEODUCTIOTSr.

17

* The Wealth of Nations.' During the last quarter of the
eighteenth century A. G-. Werner raised the Mining
Academy at Freiberg, which had been founded in 1766,
from a mere provincial institution to be one of the great
centres of scientific light in Europe, to which students
from all parts of the world flocked to listen to his eloquent
teaching. Towards the end of the century Wordsworth
and Coleridge went on a trip to Germany, whence the 29.

° ^ "^ ' German

latter brought to England the new philosophy of Kant ^^°yf|J*to
and Schelling. Madame de Stael, in an age when tidings coimdge^^
of a new literary life in Germany had reached French wOTth.°'^ ^'
Society through some of the emigrants of the Eevolution,
set herself reluctantly to learn German,^ convinced that a 30.

German

new phase of thought had appeared there ; and then with |Jj°'^Q|^g^i
Benjamin Constant visited the country itself at the end by°M^™mt
of 1803, and again in 1807. The result of these journeys
of exploration was her work ' De L'Allemagne.' Whilst
Coleridge and ]\Iadame de Stael drew inspiration from
the new life which centred in the Weimar of Goethe and
Schiller, the scientific students of the whole Continent
directed their gaze to Paris, where alone for many de-
cades the modern methods could be learnt, where the
new scientific ideas were, so to speak, collected in a focus. 31.
For more than half a century Paris remained the centre focus of

scientific

of scientific thought, and even English philosophers, who i«ieas-

^ See Lady Blenuerhasset's in-
teresting work on Madame de Stael,
German ed., vol. ii. p. 461 sqq. ;
especially the remarkable passage
quoted there, p. 465, in her letter
to the Baron de Gerando, October
1802: "Ich glaube wie Sie, dass
der menschliche Geist, der zu wan-

VOL. I.

dern scheint, jetzt bei Deutschland
angelangt ist."

- See Bruhns, ' Life of A. v. Hum-
boldt,' translated by Lassell, vol. i.
p. 232 : " Notwithstanding the
sardonic expression of the frantic
judge, ' Nous n'avons pas besoin de
savans,' Paris was yet at the close

B

18

INTRODUCTION.

32.
Continental
mathemati-
cal methods
introduced
into Eng-
land by
Babbage,
Herscliel,
and Pea-
cock.

33.
Liebig's
Laboratory.

34.

Comte's
philosophy
shown to his
own country
by an Eng-
lishman.

since Bacon and Newton had followed their own inde-
pendent line of research, had to discover in the second
decade of the century that Newton's great name was not
a guarantee for the efficiency of his methods, which had
been greatly developed and improved in the hands of
Continental mathematicians. These improved methods
were imported into England by three Cambridge grad-
uates, Herschel, Babbage, and Peacock, who translated
Lacroix's Treatise, and by doing so gave a great impetus
to mathematical research in this country. Fifteen years
later, students from all parts of the world flocked to the
small University town of Giessen in Germany, thence to
take home with them a knowledge of the new science and
methods of Chemistry, taught in the laboratory of Liebig —
methods previously used only in the private and inacces-
sible laboratories of learned investigators.-^ It will be in
the memory of many how the philosophy of Auguste
Comte, published between the years 1830 and 1840,
remained without much influence in his own country,
whereas, mainly through the writings of J. S. Mill and

of the eighteenth century the
metropolis of the exact sciences.
Lalande, in writing to von Zach on
January 26, 1798, remarks : ' The
love of mathematics is daily on
the increase, not only with us but
in the army. The result of this
was unmistakably aj^parent in our
last campaigns. Bonaparte himself
has a mathematical head, and thougli
all who study this science may not
become geometricians like Laplace
and Lagi-ange, or heroes like Bona-
parte, there is yet left an influence
upon the mind which enables them
to accomplish more than they could
possibly have achieved without this
training. Our mathematical schools

are good, and successfully accom-
plish their main object in the
diffusion of mathematical know-
ledge.' " Compare also vol. i. p.
342, referring to 1804. Also vol. ii.
p. 92, referring to the period 1820
to 1830. " Humboldt continued
to regard Paris as the true metro-
polis of Science" (p. 70), and many
other passages. Hee also StefFens,
" Was ich erlebte," vol. x. p. 233,
and what Goethe said to Eckermann
on the contrast of Germany and
Paris in the year 1827.

' See A. W. Hoffmann, 'The
Life - Work of Liebig, ' Faraday
Lectui'e for 1875, p. 8.

INTRODUCTION.

19

35.

Constable's

his school, it became, as it were, a centre of thought, an
embodiment of a circle of modern ideas in this country,
whence it was reimported into France nearly a generation
after its first appearance. Something similar happened
to a once neglected but now renowned English landscape-
painter. Constable, whose pictures when exhibited in
France in 1824 created a profound sensation, and had pjance^^'"^
such an influence on the artists of that country that they
are said to mark an era in landscape-painting there.-^

Such journeys of discovery in the realm of thought and
ideas have now become almost impossible. In the course
of our century Science at least has become international : se.

Science be-

isolated and secluded centres of thought have become comeinter-

" national.

more and more rare. Intercourse, periodicals, and learned
societies with their meetings and reports, proclaim to the
whole world the minutest discoveries and the most recent
developments. ISTational peculiarities still exist, but are
mainly to be sought in those remoter and more hidden
recesses of thought, where the finer shades, the untrans-
latable idioms, of language suggest, rather than clearly
express, a struggling but undefined idea. Thought has its
dawn and twilight, its chiaroscuro as well as its open day ;
but the daylight has grown wider and clearer and more dif-

^ See Walter Armstroug in the
' Xiueteenth Century ' for April
1887; Julius Meyer, ' Geschichte
der modernen franzosischen Mal-
erei,' Leipzig, 1867, Book 7, chap.
2 ; A. Rosenberg, ' Geschichte der
modernen Kunst,' vol. i. p. 63.
Rosenberg thinks the influence of
Constable on French Art is exagger-
ated, and mentions Paul Huet,
whose early pictures date from
1822. But an Englishman, Bon-
iugton, who, however, is claimed as

of the French School, was even
before Huet and Constable. See
also what Delacroix wrote to Th.
Sylvestre in 1858: " Constable est
une des gloires anglaises. C'est un
veritable reformateur, sorti de I'or-
niere des paj^sagistes anciens. Notre
ecole a grandement protite de ses
examples et Gericault etait revenu
tout etourdi de I'un des grands pay-
sages qu'il nous avait envoyes "
(quoted by Emile Michel in 'Grande
Encyclopedic,' art. "Constable").

20

INTRODUCTION.

The light
which Ety-
mology
throws on
history of
Thought,

38.
and on the
migration
of ideas.

fused in the course of our century, and so far as the greater
volume of ideas is concerned, we can speak now of Euro-
pean thought, when at one time we should have had to
distinguish between French, German, and English thought.
Eeserving, therefore, in the meantime the task of investi-
gating what still, within the bounds of this larger inter-
national life, remains peculiar to the thought of each
nation, it is the great body of common European thought
with which I propose at first to deal. How has it grown
to be what it is now, what special contributions have the
several nations made to the general stock, what is at
present our inventory of it, how has it been changed in
course of the century ? But how, it may be asked, are we
to take stock ? how is this inventory to be drawn up ?
There is indeed one very obvious method which presents
itself, though it is not the one which I propose to use
exclusively, or even largely. And yet it seems to me
well worthy of special attention.

Already I have remarked how the changes of thought
are deposited in the altered language and style of the
age. A closer study of the changes which, in the course of
this century, have taken place in the vocabularies as well
as in the styles of the three principal European languages,
would no doubt reveal to a great extent when and how
new ideas have presented themselves, how they have
become jfixed and defined in special words or terms. It
would allow us to trace to a very large extent not only
the growth of the general stock of European thought, but
also the migration of single ideas from one nation to
another. And, lastly, it would exhibit to a great extent
in what peculiar phrases, in what secluded corners, the

INTEODUCTION.

21

individual thought of each of the three nations has found
refuge/ Any one who has attempted to translate from
one of these languages into another, be it prose or be
it lyrical, philosophical, or descriptive poetry, will have
experienced the necessity of studying minutely the
meaning or hidden thought which a word or a phrase
may signify : he will have been led to notice what is
common and what is peculiar to different languages.

^ The only books which treat
of words in the sense mentioned
above, and which have come under
my notice, are Horne Tooke's ' Di-
versions of Parley ' and Archbishop
Trench's little volumes on 'The
Study of W^)rds' and 'English
Past and Present.' So far as the
use of merely philosophical terms
is concerned, I may refer to R.
Eucken, ' Geschichte der philoso-
phischen Terminologie,' Leipzig,
1879. A great deal of material
for a research of this kind may
be found in the large Dictionaries
of Grimm, Littre, and Murray,
though I do not feel sure that the
great change which has come over
language, through the expansion,
deepening, and dififerentiation of
ideas and of thought in our age,
has been specially taken note of.
The plan of Grimm's Dictionarj',
which aims at embracing the Ger-
man language in its development
during three centuries, beginning
with Lutlier and ending with
Goethe (see Wilh. Grimm's " Kleinere
Schriften,' vol. i. p. 508), almost
excludes the period which I am
reviewing.

It is interesting to remember
that Diderot, the first writer who
attempted to collect the great body
of modern Thought and Learning
into an encyclopaedic whole, re-
ferred to Language very much in
the same manner as we do now,
a hundred and fifty years later.

See the article "Encyclopedic,"
where Diderot says that a Dic-
tionary is only an exact collection
of titles, to be filled in bj^ the Ency -
clopffidia ; and further on, p. 639 :
" Si Ton compte les hommes de
g^nie, et qu'on les repande sur
toute la duree des siecles ecoul^s,
il est evident qu'ils seront en petit
nombre dans cliaque nation et pour
chaque siecle, et qu'on n'eu trouvera
presqu'aucun qui nait perfectionne
la langue. Les hommes createurs
portent ce caractere particulier.
Comme ce n'est pas seulement en
feuilletant les productions de leur
contemporains qu'ils rencontrent
les idees qu'ils ont a employer dans
leurs ecrits, mais que c'est tan tot en
descendant profondement en eux-
memes, tantot eu s'elan^ant au
dehors, et portant des regards plus
attentifs et plus penetrans sur les
natures qu'ils environnent, ils sont
obliges, surtout k I'origine des
laugues, d'inventer des signes pour
rendre avec exactitude et avec force
ce qu'ils y decouvrent les premiers.
C'est la chaleur de I'imagination et
la meditation profonde qui enrichis-
sent une langue d'expressions nou-
velles : c'est la justesse de I'esprit
et la sdverite de la dialectique qui
en perfectionneut la syntaxe ; c'est
la commodite des organes de la
parole qui I'adoucit ; c'est la sen-
sibility de Toreille qui la rend har-
monieuse."

22

INTKODUCTION.

39.

Goethe.

40.
Peculiarity
of the
German
Language.

41.
Growth ia
the mean-
ings of
■words.

and the thought which they express. Of Goethe it
may be said that he created to a large extent the
language and style of that which is best in the modern
literature of his country. No such supreme influence
belonging to a single individual can probably be found
in any other German, French, or English writer in our
century, for reasons which are obvious : but the great
French novelists, the German metaphysicians, and the
original poetical minds of modern England have en-
larged and enriched the vocabulary of their respec-
tive languages, and have added a number of useful
and novel modes of expression (tournures, Wendungen).
Carlyle's influence has been great in introducing novel
epithets, borrowed or imported frequently from the
German. Matthew Arnold has laboured in a similar
direction, his models being, besides Goethe and Heine,
mostly French authors, such as Sainte-Beuve and the
introspective school. Germany has been less fortunate
in extending her vernacular vocabulary : the facility
which her language possesses of assimilating foreign words
and using them almost without any alteration has done
much to complicate German style, destroying its sim-
plicity, its graces, the poetical element. It will, however,
probably be found that by far the greatest accession to
the vocabularies — though not to the finer modelling — of
the modern languages has come from the influence of the
sciences on general culture and literature. Well-known
words, long in use, have at the same time through this
influence acquired altered or more specific meanings.

The vaguer word " development " has been supplanted
by " evolution." " Differentiation " has a definite philo-

INTRODUCTION. 23

sophic — not only a mathematical— meaning. The word
" positive " has, besides the logical signification, acquired
at least two meanings which are very specific, and
which it did not possess formerly. " Energy " has,
besides the general meaning, and the philosophical one
which Aristotle assigned to it, acquired a special meaning,
having first in England and then abroad taken the place
of " force " as a more correct and definable term. In
connection with it, " correlation " and " conservation " are
terms of very specific value. The word " fittest " and the
phrase " struggle for existence " mean something different
from what they meant fifty years ago. Then there are 42.
the terms " exact " and " science " themselves, which mean {;^^°"°^^^
something different now from what they meant formerly, "ew words.
And cominw out of the more recent doctrines of the limits
of human and conscious individual knowledge, there are
the words " unconscious," " unknowable," and " agnostic,"
which indicate whole trains of novel thought. It would
indeed be an interesting and useful investigation to follow
up to their origin the many new words and phrases, or
the altered meanings of well-known and familiar words,
in which the three principal European languages abound.
It would be a methodical study of the changes which
thought has undergone.

Nor need such an undertaking be based upon any
particular or one-sided theory as to the connection of
Civilisation, Thought, and Language. This century has 43.
not been wanting in such, from the extreme theory of theory of

o ' '' revealed

De Bonald,^ who saw in Language an immediate Divine and M^al^
revelation, to the most recent and more scientific view sdenceV

Language.
1 De Ronald (1754-1840), 'Legislation primitive,' Paris, 1802.

24 INTRODUCTION.

of Max Mliller, who would absorb philosophy in the
science of Language ^ in the same way as Astronomy has
to many become merely " une question cl'analyse." In a
certain sense we can agree with both of these thinkers.
Without discussing the vexed question of the origin of
Language and Thought, to us as individuals, born in a
civilised and intellectual age, words certainly came earlier
than clear and conscious thought. The easy manner also in
which, through the use of our parents' tongue, we became
introdviced into a complex and bewildering labyrinth of
highly abstract reasoning is little short of a miraculous
revelation. But, as I mentioned above, it is not my
intention to study the development of European thought
during this century by means of a close analysis of the
changes and growth of the three principal languages.
Such an enterprise would demand an amount of lexico-
graphical knowledge possessed only by the authors of
dictionaries like those of Grimm, Littre, and Murray.
But though I am not qualified for such a task, there is one
special point on which I cannot avoid being drawn into
a grammatical discussion. It refers to the word Thought

44. itself. How is the meaning which I and my readers con-
Thought, . .
how ex- j;iect with this word to be expressed in French and Ger-

pressed m -■-

German^"*^^ man ? How are we to translate the word ? The subject we
deal with does not belong to England alone, but as much
to France and to Germany : it must thus have a name in
each of their languages. ISTow I believe that the word
'pensSe expresses in French very nearly the same thing
which we mean in English by thought. It is some-

^ See his ' Science of Thought,' London, 1887, especially pp. 292 and
550.

INTRODUCTION.

25

what more difficult to find a corresponding word in Ger-
man. 1 have for some time hesitated wliether to use the
word Geist or Weltanschauung, two terms frequently used
to express the aggregate of the inner life of an age : but
have finally resolved to use the word Denken, as this word
lends itself to the same contrasts of Life and Action
(Leben und Handeln), denoting the inner world, whereas
the opposite of Geist is ^^Jojf (matter), and Weltanschauung,
though an expressive and untranslatable word, denotes
rather the outcome, the result, of thought than thought
itself. Passing from the word to the subject itself, I find
that the greater definiteness of the term in the English
language is accompanied also by a more abundant litera-
ture of the subject. The larger idea of a Philosophy of 45.

^ ^ '' Philosophy

History is indeed due mainly to Continental thinkers, ofS'story
'' '^ ' due to Con-

especially to Herder, Hegel, Comte, and Guizot, and twnkMs.

Voltaire's ' Siecle de Louis XIV.' will always be the

model of the historical picture of a period. Still it is —

in my opinion — mainly the writings of Carlyle, Buckle,

Draper, Lecky, Leslie Stephen, and, considering its size,

perhaps more than all, Mark Pattison's ' Essay,' -^ which

have fixed in ovir minds the meaning of the word

Thought as the most suitable and comprehensive term

to denote the whole of the inner or hidden Life and

Activity of a period or a nation. I therefore put in a

claim to start with the use of the English word, as

sufficiently familiar to most of my readers, and request

those who may object to the vagueness of the French

^ See 'Essays and Reviews,'
'Tendencies of Religious Thought
in England, 1688-1750,' by Mark
Pattisou ; also Leslie Stephen's

remarks on it in the Preface to
his ' History of English Thought
in the Eighteenth Century.'

26 INTRODUCTION.

and German equivalents to look for a definition of my
intention in the English word " Thought." I am not
aware that French literature possesses any " histoire de
la pensee," either of a longer or shorter period ; I know
of innumerable works in German which cover a similar
field, but they have mostly used the word Weltanschauung,
or expanded the meaning of Thought into the wider sense
of a history of Civilisation {Kulturgeschichte) or narrowed
it to that of Literature, proving — as it seems to me —

46. the real want of a concise term such as the English

Want of °

precise term language uow supplies. And yet, I think I am right

in German o o jr ir ./ ' o

and French. ^^^ sayiug that the conception of Thought, in the sense
in which I am using it, is truly an outcome of interna-

47. tional, not of specifically English progress, and belongs
of Thought mainly to the period of which I am treating,— a period

neverthe- .; j. c jr

cmcriiy ''^'^ characterised, as I have already remarked, by the great

ng I'^h. interchange of ideas, by the breaking down of intellectual

barriers, between the principal European nationalities.

48. It was above all in the mind of Thomas Carlyle, who first

Carlyle the ^

first to give auiong Englishmen made a profound study of the intel-

a special o o x ./

ttiTword*^ lectual agencies which brought about the great change in
Thought. modern Europe, that the conception formed itself of an
intellectual and spiritual organism, underlying and moving
external events. He first gave the peculiar sense to the
word Thought, in which we here employ it, and made it
an object of special study for those who came after him ;
an object, indeed, definable in various ways and to be con-
templated from differing points of view, but yet a some-
thing, a power recognised by every one, and for which no
better word could be invented. No other language has a
word so comprehensive, denoting at once the process and

INTRODUCTION. 27

the result, the parts and the ideal whole, of what is felt
and meant : it commits us to no preconceived theory,
can be used equally by thinkers of the most opposite
views, and lends itself to any specialisation which may
become necessary.

II.

progress.

-Two processes have helped to determine the Intel- ^^^^.^^
lectual progress of mankind. These two processes have [^teuectuai
often been apparently opposed to each other in their
operations ; but in reality neither of them can proceed
very far without calling the other into existence. They
are the extension and the condensation of knowledge.
Curiosity, the demands of practical life, the experiences
of every day, all tend to an enlargement, to an accumula-
tion of knowledge. Such growing knowledge is, however,
€f little avail if it be not readily grasped : the command
of knowledge is as important as its accumulation. The
more extensive the country which we wish to explore, the
more we look out for elevated and commanding points
of view, which permit us at a glance to overlook a wide
landscape measuring the distance behind or the prospect
before us. But, however enticing, these elevated views
are frequently seductive and misleading. They permit us
not only to look backward on the land which we have
explored, giving us a clearer picture of its many features,
of its winding paths, of the position of its separate objects
— these elevated views present to us likewise the regions
which we have not yet explored, and suggest the attempt
to supersede the laborious process of further exploration

28

INTRODUCTION.

2.

Object of
the book.

Nineteenth
century un-
equalled in
accumula-
tion of
knowledge.

by the more delightful venture of filling up the dim out-
lines which we see before us, with analogies of past ex-
perience or creations of our imagination. And even if
we do descend into the plains and continue the minuter
and more laborious search, we cannot rid ourselves of cer-
tain preconceived but frequently misleading ideas which
the superficial glance has impressed on our minds.

The condensation may become an idealisation of know-
ledge. History affords numerous examples of these dif-
ferent stages of progress ; centuries of dull accumulation,
of unmethodical and ill-arranged learning, have been fol-
lowed by short periods of enlightenment, by the trium-
phant shout of sudden discovery or the confident hope of
invention. Patient work and real progress have for a long
time been repressed by the allurements of seductive phan-
toms, which have had to be abandoned after an immense
waste of labour. New prospects have suddenly opened
the view into vast unexplored regions, heights have been
gained from which the whole of human knowledge ap-
peared for the moment condensed into a single truth or
idealised into a vision, and again these delightful achieve-
ments have for a time appeared lost in an all-pervading
discouragement and dismay.

Whether our century has been characterised by any
one or by a succession of several of these varying moods,
is a question which I hope to answer in the sequel. For
the present it is sufficient to note that in both directions —
in that of accumulating and in that of condensing and
idealising knowledge — the efforts of the nineteenth cen-
tury have been many and conspicuous. In the former it
is altogether unparalleled, whereas in the latter it has

INTRODUCTION. 29

probably not equalled the ideal greatness of Greece in
the Periclean age, the brilliancy of the Eenaissance in
Italy, or the great discoveries of the sixteenth and seven-
teenth centuries in France and England. But what our
century has done is this : it has worked out and deposited ^^.^^^^.^^^^
in special terms of language a clearer view of the correct X^^it'has
methods for extending knowledge, and a peculiar concep- f^^'jietifod

tion of its possible unity. At one time — and that not iedge;b.un-

T 1 **y "^ know-

very long ago — the word truth seemed to indicate to the ledge.

seeker not only the right method and road for attaining

knowledge, but also the end, the crown of knowledge.

" Truth, and nothing but truth," seems still to the popular j

mind the right maxim for seeking knowledge — the whole

truth stands before it as the unity of all knowledge, were

it found. I think it is now sufficiently clear to the scien- 5.

"^ Search after

tific inquirer, as well as to the philosopher, that_ love of ^,';'^*^\j^°^f
truth, while it does indeed denote the moral attitude of the oniTtheft-
inquiring mind, is insufficient to define either the path or the mquir-

ingmind.

the end of knowledge. " What is truth ? is still the un- j
solved question. The criteria of truth are still unsettled. '
It would, indeed, be a sorrowful experience, a calamity of
unparalleled magnitude, if ever the moral ideas of truth
and faith should disappear out of the soul of either the
active worker or the inquiring thinker ; but it is with
these as with other treasures of our moral nature, such as
goodness and holiness, beauty and poetry — our knowledge
of them does not begin, nor does it increase, by definition ;
and though in the unthinking years of our childhood we
acquire and appropriate these moral possessions through
the words of our mother-tongue, they rarely gain in depth
or meaning by logical distinctions which we may learn,

30

INTRODUCTION.

Method of

scientific

inquiry.

Practised

first by

Galileo,

Newton, &c.

defined by

Bacon,

Comte,

Mill, &c.

Disintegra-
tion of
learning
only ap-
parent.

or to which we have to submit, in later Hfe. These do-
not touch the essence, though very frequently they may
succeed in destroying the depth, of our convictions.

In the place, then, of the high-sounding but indefinable
search after truth, modern science has put an elaborate
method of inquiry : this method has to be learnt by patient
practice, and not by listening to a description of it. It is
laid down in the works of those modern heroes of science,
, from Galileo and Newton onward, who have practised it
successfully, and from whose writings philosophers from
Bacon to Comte and Mill have — not without misunder-
standing and error — tried to extract the rationale. These
methods will take up a large portion of our attention.
For the moment it is important to note that the result or
aim of scientific inquiry does not dictate the methods, — the
purely scientific inquirer does not know where the path
will lead him : it is sufficient that it be clearly marked.
Modern science defines the method, not the aim, of its
work. It is based upon numbering and calculating — in
short, upon mathematical processes ; and the progress of
science depends as much upon introducing mathematical
notions into subjects which are apparently not mathe-
matical, as upon the extension of mathematical methods
and conceptions themselves. The terms " exact " and "posi-
tive " are current in the Continental and English languages
to denote these methods and their application. Now to
any one who does not stand in the midst of the scientific
work of the age, it might appear as if by merely following
a defined method which is capable of numerous modifica-
tions,— by treading a clear path which in its course leads
us to endless equally defined ramifications, — the scientific

INTRODUCTION. 31

inquirer is losing daily more and more those elevated
views, those points of condensation, those unifying and
idealising aspects on which, as it seems to us, the com-
mand and grasp of knowledge depends. This is indeed
almost inevitable so far as the older ideas are con-
cerned. Unity of knowledge, order and harmony, even
completeness and symmetry, truth and beauty, are indeed
no longer of direct use as canons for the scientific inquirer,
any more than the mysteries once supposed to be inherent
in certain numbers. Though we still live under the
charm of such entities, however much we may try to get rid
of them, it must nevertheless be admitted that the poetical,
philosophical, and religious aspects of things seem to recede s.

Apparent

into an increasing distance from the scientific ; they do not distance

° "^ between

guide scientific search ; it does not receive from them much ^c'ence and

o ^ poetry.

support. Have both sides been losers by this change ?
So far as science is concerned, it can claim to have attained
by it not only a greater formal completeness and certainty
of progress, but also another very important advantage
which was unknown to ancient and medieval research.

This advantage consists in the closer connection be- 9.

Closer con-

tween science and practical life. The same mathematical nection

■*■ between

spirit which governs scientific methods rules also in trade, ^^11'^^^ ^^^
commerce, and industry, and is gradually penetrating into
the professions, such as medicine, law, and administration.
For all these pursuits have either directly to do with
numbers, measures, and weights, with distances of space
and time, or they have found it necessary to introduce
an elaborate system of statistics and averages through
which the irregularity and captiousness of subjective
and individual influences are practically eliminated. The

32 INTRODUCTION.

problems of scientific research have thus enormously in-
creased ; each advance in science increases our command
of certain measurable phenomena in practical life ; each
new development in the latter prepares a new field for
scientific inquiry. The contact between science and life
has become more intimate in the course of our century.
This to a great extent has counterbalanced the tendency
of modern scientific method, which, operating alone, would
have led to endless specialisation ; for it is the peculiarity

10. of all practical problems that they cannot be isolated in

Solidarity of ^ ^ -, x. ■ e t-

all practical ^]^q sauic wav as scientific experiments — that they, m tact,

problems. j i.

force upon us the necessity of looking at a large number
of surrounding and extraneous circumstances, at the total-
ity of life and its interests.^

If our century can claim to have firmly established
exact or positive methods in science and life, and to have
furthered in this way the interests of both, the question

11. \ remains, Has nothing been done to uphold those older,

Whathasthe ° i • i

nineteenth those timc-hallowed ideals of truth, beauty, and wisdom

century

thri/°ais which to former ages seemed to denote the unifying and
""'^''' harmonising principles of science and life ? What has
become of philosophy, art, and religion, which were once
intrusted with the special care of those ideals, charged
- with preventing the falling asunder of the many branches
of knowledge and practice, and expected to save us from
a loss of the belief in the integrity, interdependence, and
co-operation of all human interests ?

1 Science deals with things in the In this distinction lies the value of

abstract, in their isolation, in vacuo. \ Lotze's definition of the reality of

Practical life deals with the same a thing as "a standing in relation,

things in their position in the real viz., to other things, to all things,

world, surrounded by other things. See ' Microcosmus,' book is.

INTRODUCTION. 33

Unless I believed that our age was elaborating a deeper ^ 12.

" o i Deeper con-

and more significant conception of this unity of all human t^f^°'Jty*'
interests, of the inner mental life of man and mankind, fntere'sts!
I do not think I should have deemed it worth while to
write the following volumes : for it is really their main
end and principal object to trace the co-operation of many
agencies in the higher work of our century ; the growing
conviction that all mental efforts combine together to
produce and uphold the ideal possessions of our race ; that
it is not in one special direction nor under one specific
term that this treasure can be cultivated, but that
individuals and peoples in their combined international
life exhibit and perpetuate it.

A number of words have during this century been in- 13.

Dififerent

troduced by various systems of philosophy to denote this terms for

'' '' i. i. ^1 expressing

unity of the inner life of mankind : Hegel's Geist, Comte's *^** """y-
Humanity, Lotze's Microcosm, Spencer's Social Organism,
all refer to special sides and aspects of the same subject.
And it is interesting to note how the great schools of
Idealism in Germany, of Positivism in France, of Evolu-
tion— physical and mental — in England, and — in spite of
their apparently disintegrating tendencies — how the social
changes of the Eevolution and the specialisations of science
have all combined to emphasise this unity of human life
and interests. To show this in detail is the object I have
in view. So far we have not committed ourselves to any
of the many existing theories : the word Thought seems to 14.

•^ ° ^ _ ° Definition of

me to be capable of the widest application, and to denote Thought.
in the most catholic spirit whatever of truth and value
may be contained in the combined aim and endeavour of
VOL. I. c

34

INTRODUCTION.

15.

1750 to 1850.
The age of
encyclopse-
die treat-
ment of
learninsr.

all these modern aspirations. A history of this thought
will be a definition of Thought itself.

Much has been done in the course of this century to
prepare for an undertaking such as the one before me. It
will be well to review shortly this special side of modern
literature. We have indeed passed out of what may be
called the age of encyclopcfidic treatment of learning — the
hundred years from the middle of the last to the middle
of the present century.^ The plan of such an arrangement
of knowledge belongs to an earlier period, the period im-
mediately succeeding the birth of modern science. Lord
Bacon was the father of it, but neither he nor the most
encyclopsedic intellect of modern times, Leibniz, did much
to realise the idea, and it was reserved for the genius and
the labours of Diderot and d'Alembert ^ in France, in the

^ " Encyclopsedia nomeu hodie
frequentius auditur quam alias." —
Gessner iu Gottinger Lections- Kata-
log for 1756.

^ Diderot's " Prospectus" to the
' Encyclopedia ' appeared 1750 ; the
first volume appeared 1751 with the
celebrated " Discours j^r^liminaire "
of d'Alembert and a reprint of the
" Prospectus." The complete title
was ' Encyclop^die ou dictionnaire
raisonne des sciences, des arts et
metiers, par une society de gens de
lettres, mis en ordre et publie par
Diderot et d'Alembert.' The prin-
ciples which guided the editors,
and the object of the work, are ex-
plained, with repeated references to
Lord Bacon, in this introduction,
as well as in the article " Encyclo-
pedic," in the fifth volume (1755),
which was written by Diderot, and
occupied 28 pages. See also Did-
erot's ' Pensees sur I'interpretation
de la Nature,' published anony-
mously in 1754.

Copious details about the history,
the reception, and the influence of
the ' Encyclopedie ' are to be found
in the correspondence and memoirs
of Grimm, d'Alembert, and Vol-
taire, Madame d'Epinay, the Abb^
Morellet, and many others. They
are combined into a concise nari'a-
tive, giving all the important facts,
in Rosenkranz's 'Leben uud Werke
Diderots,' 2 vols., Leipzig, 1866,
and in John Morley's 'Diderot.'

It is interesting to note how the
idea of the unifying and life-giving
influence of thought was as familiar
to Diderot as it is to us : " Si Ton
bannit I'homme ou I'etre -pensant
et contemplateur de dessus la sur-
face de la terre ; ce spectacle path^-
tique et sublime de la nature n'est
plus qu'une sc^ne triste et muette.
L'univers se tait ; le silence et la
nuit s'en emparent. Tout se change
en une vaste solitude, oh. les pheno-
menes inobserves se passent d'une
maniere obscure et sourde. . . .

INTRODUCTION.

35

middle of the eighteenth century, to carry out the plan,
foreshadowed in the ' Novum Organum,' of collecting all
knowledge, which had been accumulated ever since science
had been liberated from the fetters of theology, into one
comprehensive whole. It must, however, be admitted
that whilst the practical end o? these laborious under-
takings, the diffusion of knowledge, has certainly been „ \^-j
greatly furthered, the original idea, that the sum of J.'Xaiif^
human knowledge is an organic whole, has in the exe- I'^encfcio-^'
cution been by degrees entirely lost sight of. The unity workl
of thought and knowledge was indeed referred to in
Diderot's " Prospectus " and d'Alembert's " Discours pr6-
liminaire," and in the introduction to Ersch and G-ruber's
great Encycloppedia,-^ as also in Coleridge's celebrated essay

Voila ce qui nous a determine ii
cherclierdansles facultds principales
de I'homme la division generale a
laquelle nous avons subordonne
notre travail." — Article " Encyclo-
pedie," p. 641.

^ Ersch uud Gruber's ' AUgemeine
Encyclopixdie der Wissenschaften
und Kiinste,' Leipzig, 1818 to 1875,
unfinished, 1,")1 vols. It was founded
by Professor Joliann Samuel Ersch,
librarian at Halle in 1813, assisted
by Hufeland, Gruber, Meier, and
Brockhaus, and contained contri-
butions by the most learned and
eminent Germans of the century.
It is interesting to compare the
plan and principles which guided
the editors, as expounded in the in-
troductions to the first and second
volumes, with the corresponding
dissertations prefixed to the ' Ency-
clopedie ' in France and the ' Ency-
clopaedia Metropolitana' in England.
The unity aimed at by Bacon was
either purelj' formal, securing only
uniformity and completeness of
treatment, or it was that of prac-

tical usefulness —the philosophy of
fruit and progress. The plan adopt-
ed by Diderot and d'Alembert could
hardly attain anything more than
this. Coleridge, nursed in German
philosophy, and deeply impressed
with the fact that there is a higher
view than that of Lord Bacon, and
that such is to be found rather in
writers like Plato and Shakespeare,
uses the word method in a much
wider sense. He was deeply affect-
ed by the spirit of the idealistic
philosophy, which was foreign to
Bacon and unduly despised by him.
In the idealistic systems of the
Continent, beginning with Kant,
the opinion was current that the
methods and treatment of science
alone were insufhcient to close the
circle of knowledge. The truly
encyclopaedic view was only possible
in a scientific investigation speci-
ally carried on for that purpose,
and this was considered to be one
of the main objects of philosophy.
Thus Kant in many passages of his
works, notably vol. ii. pp. 377, 378,

36

INTRODUCTION.

on the science of method prefixed to the ' Encyclopaedia
Metropolitana ' ; but the result has shown, what was not
evident to Lord Bacon, that neither a systematic division
of learning according to some logical principle, nor the his-
torical identity of the beginnings of all branches of know-
ledge, can in the end preserve the real unity and integrity
of thought. The work of the advancement of learning,
if it be once handed over to different sciences and in-
trusted to separate labourers, does not proceed in a cycle
which runs back into itself, but rather in the rings of an
ever-increasing spiral, receding more and more from the
common origin. Such is the impression we get if we
contemplate the unfinished ^ rows of Ersch and Gruber's

613 ; vol. iii. pp. 188, 212 ; vol. v.
p. 312 (Rosenkranz's edition), especi-
ally the two following: "Philos-
ophy is the only science which can
procure for us inner satisfaction,
for she closes the scientific cycle,
and through her only do the scien-
ces receive order and connection. "
And: "Mere ' noAvicrropia' is a
Cyclopean learning which wants one
eye — the eye of Philosophy — and
a Cyclops among mathematicians,
historians, naturalists, ijhilologists,
and linguists, is a scholar who is
great in all these lines, but having
these considers all philosophy as
superfluous." Still, with Kant
Philosophy is not an "instrument
for the extension," but merelj' a
study of "tlie limits of knowledge"' ;
she does not "discover truth,"
but only "prevents error." This
modest definition was given up in
the systems of Fichte, Schelling,
and Hegel, who maintained that a
certain kind of — and this the highest
— knowledge could be attained by
starting from one highest principle
deductively : the all - embracing,
encyclopsedic character of philoso-

phical, speculative knowledge was
increasingly emiDhasised, and this
not only in special lectures on the
subject, as in Fichte's lectures on
" The Nature of the Scholar," in
Schelling's on "The Method of
Academic Study," in Hegel's ' Ency-
clopedia of Philosophy,' but also
in the regeneration and reform of
many older and in the foundation
of new universities and academies
throughout Germany. The great
' Encyclopaedia' of Ersch and Gruber
was planned in a similar spirit, as
the reform of university teaching
and of academic learning. This
reform has been of the greatest im-
portance to the German nation and
to the interests of science and
knowledge. The Encyclopedia, on
the other hand, has remained
incomplete, a huge but abortive
attempt to combine not only the
principles of knowledge, but also
the colossal and growing volume of
it, into a systematic whole.

^ The promoters of it were evi-
dently not sufficiently impressed
with the two very essential con-
ditions which make a work of this

INTRODUCTION.

37

volumes, or if we recognise the fact that the more useful
and popular publications of our day have abandoned the
philosophical introductions and preliminary discourses^
by which the earlier works preserved a semblance of
unity and method, and are contented to be merely useful
dictionaries of reference. The encyclopa3dic treatment of i
knowledge, the execution of Lord Bacon's scheme, has
shown that the extension and application of learning
leads to the disintegration, not to the unification, of i

knowledge and thought

A conviction of this sort is i7.

Lectures on

no doubt the reason why in German universities lectures "E?cycio-

'' padie

on " Encyclopadie " have been abandoned.^ They were 1"^^^^°^^
very general and popular in the earlier years of the "'"^^''^^ '®^-
century, when, under the influence of Kant, Fichte, and

kind useful — viz., that it must be
finished, however imperfect it may
Tae, and that it must be completed
within a limited time, on account of
the revolutions and smaller changes
in thought and knowledge. These
essential conditions were alwaj's be-
fore the mind of Diderot. See his
article " Eucyclopedie," pp. 636-644.
■^ The object of the philosophical
introductions has in course of this
century been much more completely
attained by such works as Mill's
' Logic ' and Jevons's ' Principles of
Science'; whilst the "preliminary
dissertations," such as were con-
tained in the older editions of the
'Encyclopedia Britaunica,' have
been partially superseded by works
like Whewell's ' History ' and his
'Philosophy of the Inductive Sci-
ences,' in which the common origin,
the genesis, the continuous develop-
ment and interdependence of the
different sciences, are traced. The
value in this respect of an under-
taking like that of the Royal Ba-

varian Academy (' Geschichte der
Wissenschaften in Deutschland,'
vol. i., 1864 : it has now reached
22 vols., the science of War signifi-
cantly filling three large volumes,
that of Mathematics one small one)
is much diminished by the title
suggesting that science is a nation-
al, not a cosmopolitan or interna-
tional concern. Fortunately many
of the contributors to this impor-
tant and highly useful publication
have not limited their narratives
to jjurely German science, but have
largely taken notice of non-German
research. Special reports on the
state of any science or branch of
science in a nation have, of course,
quite a different meaning and
value.

- The term is still in use for
courses of lectures giving a gen-
eral and comprehensive view of
special sciences : thus, " Encyclopii-
die des Rechts, der Medicin, der
Philologie, der Philosophie, der
Theologie."

38

INTRODUCTION.

Schleiermacher, university teaching and learning entered
on a new era, in which the idea prevailed that com-
pleteness, universality, and unity of knowledge could be
secured by one and the same arrangement of study .■^ It
was the age when philosophy for the last time had got a
firm hold of all departments of knowledge, and permeated
all scientific pursuits ; ^ when, favoured by political events.

^ On this subject the literature
connected with the foundation of
the University of Berlin in the year
1809 is of special interest. It was
essentially tlie creation of Wilhelm
von Humboldt, though prepared by
Wolf and Beyme in 1807. See
Seeley, ' Life of Stein,' vol. ii. p.
430 sqq. ; Haym, ' Leben W. v.
Humboldts,' p. 270 srjq. The foun-
dation of this university in the year
of Prussia's greatest misery, when
the first gleams of liberty in the
rising of Spain and the success of
Aspern had been extinguished by
the defeat of Wagram, the voting
of £22,500 per annum for the pur-
poses of the new University and
the Academy of Science and Arts,
when a crushing war-tax hung over
the country, when land was depre-
ciated, the necessaries of life at
famine prices, the cuiTcncy of the
country at a large discount, when
every one, from the king to the
lowest subject, was forced into sac-
rifices and economies of every kind,
was an act as heroic as the great
deeds on the battle-field, and as far-
seeing as the measures of Stein and
Scharnhorst. Interesting from our
point of view are the ideas of Fichte
on university teaching and academic
learning, laid down in his ' Dedu-
cirter Plan einer zu Berlin zu errich-
tenden hoheren Lehranstalt,' wiit-
ten at the request of the minister
Beyme in 1807. In it a great deal
is said about encyclopaedic treat-
ment. The question of the position

of philosophy in the encyclopaedic
or academic treatment of knowledge
was easily solved in the Kantian
school, to which most of the above-
mentioned writers belonged. Later
on in the school of Schelling it be-
came more difficult. It was fre-
quently discussed by Schelling him-
self, who was one of those that
initiated the new era in the Academy
of Munich, which was remodelled
in the year 1807. See, inter alia,
Schelling's essay, "Suggestions con-
ceining the Occupation of the Philo-
logico - Philosoi^hical Class " of the
Academy, and especially the follow-
ing remarkable passage ('Werke,'vol.
viii. p. 464): "If, indeed, Philosophy
were denied living contact with real
things, if she were obliged to soar
in transcendent regions without end
and measure, and to rise a hungry
guest from the well-appointed tal)le
of Nature and Art, of History and
Life ; then it would be incompre-
hensible how she could still find so
much support as to be received in
an academy, and it would be much
better if we also followed the path
of other nations, who have lately
said good-bye to all philosophj', and
have thrown themselves, with the
most glowing ardour, upon the ex-
ploration of Nature and Reality in
every direction."

- The principal representatives of
the encyclopedic teaching at the
German universities were Eschen-
burg, Krug, and Gruber. The
latter, in his introduction to the

INTRODUCTION.

39

ideal aims, a generous spirit of self-sacrifice, and a feeling
of one common duty pervaded the German nation, and
foremost in it the teachers and students of the German
universities.^ This spirit, as it produced co - operation
and unity of action, also favoured unity of thought, and
contributed much to the popularity of several philosoph-
ical systems which promised more than they could give, ^ot^fuifij"^
Encycloptedic surveys were then supposed to be more Tppeared^
than the empty shell, the mere skeleton of learning
which they have since proved to be ; they were looked
upon as being able to grasp and convey the living spirit
of knowledge. This phase of thought, which in the
sequel will largely command our attention, has dis-

is.

Encyclo-

to promise.

second volume of Ersch and Gruber's
' Encyclopiidie,' gives a definition
and history of encyclopedic study,
which, according to him, was intro-
duced into the modern (German)
universities together with the philo-
sophical faculty. In the beginning
this was subservient to the three
higher faculties (theology, law, and
medicine), but gradually took the
lead. He argues that only since
university studies have become en-
cyclopajdic can they be considered
as furthering true humanity. He
refers to the gi-eat crisis through
which in the beginning of the cen-
tury literature, science, and arts
were passing (p. li), and mentions
the conflicting principles in the
treatment of mathematics, phj^sics,
history, philosophy, and philology.
See also the ' Vorbericht,' vol. i.
p. vii.

1 Among the mass of literature
dealing with this subject, the
' Memoirs of Frederick Perthes,'
by his son (English translation,
vol. i. chap. xi. sqq.), and Steffens's
'Autobiography ' (' Was ich erlebte,'

Breslau, 1840-44, 10 vols.), give the
most vivid and exhaustive accounts.
Neither Stein, the great statesman,
nor Goethe, the great poet and
thinker of the age, took part in this
alliance of the patriotic and intellec-
tual interests of the German nation.
Stein's attitude to the idealism of
the age is defined by Seeley, ' Life
of Stein ' (vol. i. p. 30, " It is desir-
able to mark that between him
and the literature and philosophy
of his time and country there was
no connection at all"), and is ex-
pressed in a remarkable conversa-
tion which he had with Steftens,
March 1813, at Breslau (quoted by
Seeley, vol. iii. p. 119 ; StefEens, vol.
vii. p. 120 sqq. ) Goethe's position is
defined by his reply to the invitation
to contribute to the 'Deutsches
Museum,' a periodical planned by
the bookseller Perthes. It was to
be a scientific alliance of all the in-
tellect of Germany, and was in time
"to be transformed into a polit-
ical one possessing the strength and
union necessary for vigorous action "
(Perthes' Memoirs, vol. i. p. 167).

40 INTRODUCTION.

appeared ; the second half of our century does not
expect to find the essence of knowledge condensed in
any philosophical formula, any more than it expects to
find the real unity and integrity of thought preserved in
the fragmentary articles of an alphabetical dictionary.
The purpose of the latter is purely practical ; it is a
popular and handy instrument for the diffusion of
knowledge, whilst philosophical divisions are merely
formal, and at best are applicable only to a narrow
and limited sphere of research.^

The age of encyclopaedic representation of learning
and the short period of philosophical formalism seem
both to belong to the past; but the desire of bringing
together what is scattered, of focussing knowledge and
learning, and of realising the organic continuity and unity
of thought and progress, is as great as, perhaps greater
than ever. Neither the shapelessness of a huge dictionary
nor the barrenness of a concise formula will satisfy the

^ It is interesting to observe the i of encycloppcdism has done least for
development and spread of encyclo-
pajdic learning in the three coun-
tries. En cyclopedias in the modern

encyclopaedic learning. This has
now its home in Germany, where
encycloptedic labours have been
sense have their origin, like so many I specialised, and where every science
other modern institutions and ideas, : is represented by some compilation
in England. They were there com- I or annual register aiming at collect-
piled mainly for practical purposes. ing and sj'stematically arranging the

France took up the scheme in a
philosophical spirit, and carried it
as far as it is capable of being
carried under this aspect. At-
tempts to improve and amplify
the plan proved impracticable ; and
when subjected to the vast eru-
dition of Germany, it became evi-

scattered contributions of the whole
world. But it would be ungrateful
not to mention the Royal Society's
catalogue of scientific papers, and
the services which America has ren-
dered in summarising the literary
productions of the English-speaking
nations in such works as Poole's

dent that unity, depth, and breadth I 'Index to Periodical Literature.'

of view could not be maintained, j Without the aid of such laborious

In course of this century the coun- j compilations the present work could

try which produced the classical era ! not liave been undertaken.

INTRODUCTION.

41

deeper conviction that all mental work is living, indi-
vidual, and of endless variety. To stimulate individual
thought, to bring about life and change, is nowadays felt
to be quite as necessary as to insist on method, system,
and order. Prompted by this conviction, the last fifty
years have done much to facilitate intellectual inter-
change, and to record the historical development of all
branches of science.

This object has been promoted in three different ways, j
The French, who in the beginning of the period were the 'pj.gj^J^-^yg^g
masters in science, led the way by founding a series of -n^gf '
periodicals devoted to the development of separate sciences, beginning
Germany followed, and still later England.^ A living tury? '^^'^'

1 The oldest scientific periodical
is the ' Journal des Savants, ' which
was started in 1665 in Paris ; next
to it comes probably Rozier's ' Ob-
servations sur la Physique' (1771),
continued under the title ' Journal
de Physique' (1778, continued with
interruptions from 1794 - 95 till
1823). In opposition to this
journal, which defended the older
phlogistic theories in chemistry,
the ' Annales de Chimie ' were
started in 1789 by Berthollet,
Guyton de Morveau, and Fourcroy,
as an organ of Lavoisier's ideas.
In 1788 the Societe Philomatique
started its ' Bulletin,' and in 1795
the 'Journal de I'Ecole Poly-
technique' started its influential
career. No such periodicals existed
for special sciences at that time in
any other country, if we perhaps
except the ' Transactions of the
Eoyal Linnsean Society,' which
started in 1791. 'Nicholson's
Journal' started in 1797; the
' London, Edinburgh, and Dublin
Philosophical Magazine and Journal
of Sciences ' had its origin in Til-
loch's ' PhilosojDhical Magazine'; but

the first journal devoted specially
to mathematical sciences in England
was probably the ' Cambridge Ma-
thematical Journal,' started in 1839.
In the meantime the number of
scientific journals in France had
grown enormously. In Germany we
have Crell's 'Chemische Annalen'
(1778), Gehlen's ' Allgemeines Jour-
nal fur Chemie' (1803), Gren's
'Journal der Physik' (1790), Gil-
bert's 'Annalen der Physik' (1799),
Zach's 'Monatliche Correspondenz '
(1800), Crelle's 'Journal flir die
reine und augewandte Mathematik '
(1826), and many others, all peri-
odicals of the first importance. The
' Transactions of the Royal Society,'
which of course contain many of
the valuable scientific contributions
of this country, can nevertheless
hardly be looked upon as a reposi-
tory of the work of English mathe-
maticians and physicists of the
period in question, — not even as
much as the Memoirs of the Paris
Academy in France. In Great
Britain a new centre of scientific
and literary work existed during
the latter part of the last century

42

INTRODUCTION.

intercourse between men of science was greatly promoted
by the British Association for the Advancement of Science,
which held its first meeting at York in 1831. Associa-
tions and meetings of this kind had their origin ten years
earlier in Germany through Oken ; ^ but the line in which
Germany has done most is the establishing of and con-
tinuing annual Reports ^ of the progress of the different

in Edinburgh ('Transactions of the
Royal Society of Edinburgh, 'started
in 1788), and somewhat later like-
wise in Dublin (' Transactions of the
Royal Society of Dublin,' started
1799), and Manchester ('Memoirs
of the Manchester Philosophical
Society,' started in 1789). Many
of the first scientific writers of the
age published in these provincial
papers or in separate pamphlets —
the want of a common collecting
centre being very obvious.

^ Alexander v. Humboldt sup-
ported them, and was instrumental
in giving to the Assembly at Berlin
in 18'2S— which he called "The in-
vasion of philosophers" — a special
importance. It was, as he says,
" a noble manifestation of scientific
union in Germany ; it presents the
spectacle of a nation divided in
politics and religion, revealing its
nationality in the realm of intellec-
tual progress." — Bruhns, 'Life of
A. V. Humboldt,' vol. ii. p. 130.
The British Association for the Ad-
vancement of Science was (as Prof.
Owen informs us) at the outset
avowedly organised after the Oken-
ian model. — ' Encyclopaedia Britan-
nica,' art. "Oken."

'■^ The first reports aiming at
giving a statement of the position
of Science were those drawn up by
Delambre and Cuvier at the request
of the Emperor Napoleon I., and
presented in the year ISOS under
the title ' Discours sur les Progres
des Sciences, Lettres, et Arts depuis

1789 jusqu'^ ce jour ' (1808). They
were imitated on a larger scale by
the Emperor Napoleon III., on the
occasion of the great Paris Exhibi-
tion 1867, and have been continued
under the Republic. Of the report
of 1808 Cuvier says, " Ce tableau
historique nous servira desormais
de point de depart et nos rapports
annuels en seront autant de con-
tinuations." He also adds signifi-
cantly, " Dans les relations actives
oil nous nous trouvons avec la
plupart de ceux C|ui cultivent les
sciences, il est bien difficile qu'ils se
fassent en Europe quelques decou-
vertes importantes sans que le
bruit en reteutisse promptement
dans cette enceinte, et nous excite
a des travaux qui s'y rapportent
plus ou moins directement. "

By far the most important work
of reporting and summarising the
results of scientific labour has been
done by Germany. The first publi-
cation of this kind, however, origin-
ated with Berzelius, who from the
year 1821 reported regularly to the
Academy of Stockholm on the pro-
gress of the physical sciences. Of
Berzelius's periodical Kopp says
('Geschichte der Chemie,' vol. i. p.
403), that it "summarises with the
greatest completeness all that had
been done in chemistry since 1820."
This work, which regularly ap-
peared in German translation, was
continued in Liebig's ' Jahresbericht
der Chemie ' (1847). In Berlin the
' Physikalische Gesellschaft ' has

IXTRODUCTION.

43

sciences, in which all scientific researches are — without
regard to nationahty — reviewed, classified, and arranged in
the most complete manner, according to the place which
they occupy in the general development. Invaluable ser-
vice has also been done in England by special Reports or
Addresses, prepared by men of the greatest eminence — fre-
quently at the request of the British Association — in which
the position of special branches of science is explained, the
work of the past summed up, the leading principles clearly
brought out, and the unsolved problems placed promi-
nently before the minds of young and aspiring workers.

In Germany during the first half of the century a 20.
reaction set in against the metaphysical treatment of in Germany

o r J against me-

scientific subjects, which had been exaggerated in the ^^ataienf
schools of Schelling and Hegel. Experimental research, sui^'e'cts.' '^
following mainly the great French and English models,
was next favoured, and through the establishment of
laboratories and observatories, through voyages of dis-
covery and the application of science to the industries,
an enormous amount of detailed and minute knowledge
was accumulated.^ Eor a time — even within the limits

continued to issue regularly since
1845 annual Reports under the title
' Fortschritte der Physik.' But it
was only in 1868 that a similar
annual was started in Berlin having
reference to matliematics, under
the title 'Fortschritte der Mathe-
matik.' A ' Jahresbericht ' on
Zoology has ajjpeared ever since
1879, and one on Botany since 1873.
^ It was the age which conipiled
the great repositories of chemical
knowledge. Such were Gmelin's
' Handbuch der C hemic ' (1st ed.,
1817. Translated into English by

the Cavendish Society, 1848), and
the ' Handworterbuch der reinen
und angewandten Chemie ' (edited
by Liebig jointly with Poggendorf
and Wohler, 1837). The same age
also set gomg and filled the volumes
of Liebig's ' Annalen ' (started by
Hiinle in 1823 under the title
' Magaziu der Pharmacie,' it finally
assumed the title of ' Annalen der
Chemie und Pharmacie ' under Lie-
big's editorship), of Poggeudorf's
' Annalen der Physik und Chemie '
(1824), and the ' Annales de Chimie
et de Physique.'

44

INTRODUCTION.

of exact reasoning — attempts to condense and unify
knowledge were discredited. The result — especially in
Germany — was that in many sciences information be-
came buried in periodicals and in the memoirs of learned
societies: text -books were chiefly written by men of
secondary importance, translated from the French and
English, and frequently on somewhat antiquated lines.'^
The new spirit which began to leaven scientific research in
the middle of the century was confined to a few master
minds, who — frequently almost unknown — marched in
advance of their age. In the course of the last thirty
years this has been entirely changed. The means of
intercourse and communication, referred to above, make
scientific isolation almost impossible ; the necessity has
21. been felt of remodelling the whole of the popular school

Reform in,. tt [> l^ n j_ •

schooiiitera- literature on more modern lines : some or the first m-

ture.

^ The greater part of the higher
German school literature in mathe-
matics and physics was supplied by
the French or modelled on French
ideas — Legendre and Monge in ele-
mentary and descriptive geometry,
Lacroix in the higher branches.
Franccour's course of mathematics
was introduced in England as well
as Germany ; Poisson, and later
Lagrange and Duhamel, became
the models in mechanics, Biot and
Pouillet in experimental physics,
Regnault in chemistry. The only
great popular authorities which
did not belong to France were
Berzelius and Graham in chem-
istry, and Euler in mathematics.
As late as 1860 hardly any text-
book existed in Germany on the
theoretical and mathematical por-
tions of physics. The second
volume of ' Baumgartner ' was
a miserable compilation. Beer's
' Hohere Optik ' was the first im-

portant work of this kind. Ger-
many had indeed not been wanting
in original research, but the new
ideas of Mobius, Steiner, Staudt,
Pliicker, and Grassmann in geom-
etry found no adherents till, mainly
through the translation of Sal-
mon's text-books by Fiedler, a new
spirit came over geometrical teach-
ing. In the meantime Lejeune
Dirichlet, and Neumann the elder,
cultivated in their academical lec-
tures the higher branches of mathe-
matical phj-sics, and educated a
whole generation of mathematicians
and physicists. Through them the
original researches of Gauss and
Jacobi became better known, and
an independent school of German
mathematical thought was estab-
lished. In England the influence
of French science was much more
limited, and to the present day
Euclid is preferred to Legendre's
more elegant methods.

INTRODUCTION.

45

22.
Scientific

tellects in science have condescended to write text-books
of their subjects, by which a great reform has been brought
about in the higher scientific literature.-^ At the same time
— after fifty years of experimental research and accumula-
tion of material — it has become necessary to review the
fundamental principles on which scientific reasoning rests :
a more philosophical, not to say metaphysical, spirit is ^^^e phfio-
manifesting itself within the limits of science.^ In the ^^p'^^'^^^-
abstract, and especially the mathematical, sciences, real
progress depends now mainly upon the discovery of
methods of simplification, on conciseness and elegance
of treatment, and on the discovery of unifying principles
and generalising aspects.^

1 This remark refers mainly to
England and Germany. In France,
as a result of giving lectures at the
Ecole Polytechnique, the Bureau
des Longitudes, the Faculte des
Sciences, &c., the great mathema-
ticians and physicists of the cen-
tury have frequently worked up their
researches in connected treatises.
For such we are indebted to Lame,
Cauchy, Poncelet, and many others.
But the two works which in Eng-
land and Germany created probably
the greatest reform in the teaching
of the principles of natural phil-
osophy were Thomson and Tait's
' Natural Philosophy ' (first sketch,
1863, 1st ed., 1867) and KirchhofT's
' Vorlesungen liber Mechanik' (Leip-
zig, 1877).

- I refer principally to the various
■writings of Helmholtz, following
those of Riemann, and the many
hints thrown out in Gauss's pub-
lished papers, and in his correspond-
ence with Schumacher. Helmholtz
has — of all purely scientific writers
— paid most attention to the meta-
physical foundations of geometry

and dynamics, and has critically
examined the earlier theories of
Kant, jjublished a century ago. It
is interesting in this respect to note
what Kant is reported to have said
to Stiigemann in 1797: "I have
come with my writings a century
too soon ; after a hundred years
people will begin to understand me
rightly, and will then studj^ my
books anew and appreciate them."
(See ' Tagebiicher,' von Varnhagen
von Ense, Leipzig, 1861, vol. i. p.
46.) Next to Helmholtz we are
most indebted to Emil du Bois-
Reymond and his brother Paul.
See Emil's 'Reden' (Leipzig, 1886-
87, 2 vols.), and the posthumous
work of his brother : ' Ueber die
Grundlagen der Erkenntniss in den
exacten Wissenschaften ' (Tubingen,
1890).

•^ An authority on this subject
says : " Generality of aspects and
methods, precision and elegance
of exposition, have, since the time
of Lagrange, become the common
property of those who claim to
be scientific mathematicians. This

46

INTEODUCTION.

23.
Germany
has taken
the lead in
studying
the life of
thought.

All these are merely external signs of the new life, in-
dications of progress and change : the inner reason and
result, the altered ways of thinking which underlie or are
produced by these external changes, will be the object
of closer study hereafter ; they constitute the real sub-
stance of this work. What I draw attention to here,
by way of introduction, are merely fingers on the dial-
plate of a complicated clock-work : their motion and posi-
tion are patent to every one. Later on I shall invite the
reader to remove the outer case, and try with me to under-
stand the delicate working parts and the principle of the
mechanism, the prime mover and the mode of transmission
of motion within. The general curiosity that exists to fol-
low the internal and hidden workings of thought is mani-
fested especially in that country which in modern history
has frequently taken the lead in philosophical reasoning.
It is manifested by the huge and increasing historical
literature of Germany, which is devoted to tracing out
the growth and development of modern science and
thought. In that country history seems for the moment
to have taken the place of metaphysical speculation.
A similar transition from the logical to the historical view
can be traced in English literature in the last century, the

generality is sometimes exaggerated
at the expense of simplicity and
usefulness, and then leads to ab-
struseness and to the enunciation
of theorems which have no special
application ; precision may degen-
erate into an affected brevity which
renders a dissertation more difficult
to read tlian to write ; elegance of
form has in our days almost be-
come the test of the value of a
theorem. Yet in spite of all draw-

backs these conditions of efficient
progress are of the greatest import-
ance, inasmuch as they keep the
scientific matter within those limits
which are intrinsically necessary if
mathematical research is not to lose
itself in minutise or be drowned in
over - abundance." — Hankel, ' Die
Entwickelung der Mathematik in
den letzten Jahrhunderten ' (Tiib-
ingen, 1869).

INTRODUCTION.

47

typical representative of that change being David Hume,
who, starting with the metaphysical problems involved in
Locke's and Berkeley's writings, was from them led on to
the study of moral, political, and economic questions, and
ended by devoting himself to the study of history/ At
the end of his career political and historical writings
were as frequent in English literature as metaphysical ■
and theological writings had been at the beginning. The
causes which have effected the same transition from the ^ 24.

Causes of

metaphysical to the historical mode of treatment in Ger- ^^^j^'^j^j^f^.
many during the present century are similar to those ^IXki^
existing in England in the last century ; but the whole ^^
movement has taken place on a larger scale, penetrates
deeper into the mental life and work of the nation, and
cannot be so easily studied in the writings of any great
representative.

Whilst in Germany historical studies are now foremost,

^ I am quite aware that general-
isations of this kind must be made
and used with great caution. I
therefore refer my readers to Les-
lie Stephen's ' History of English
Thought in the Eighteenth Cen-
tury,' especially to the Introduc-
tion, where the typical position of
Hume is fully discussed, and also
to the last chapter of the second
volume, where he says of Hume
(vol. ii. p. 381, Isted.): "Hume was,
in one sense, far in advance of his
time, and indeed of the average
opinion of the present time. But
the change may in many respects
be described as a revolt from
Hume's opinions, much more than
a development of them. . . . The
histoiy of philosophical and of theo-
logical opinion in England is a his-
tory of gradual decay down to the

revolutionary era." And p. 444 :
" The last half of the century was
pre-eminently historical. As civil-
isation progresses, as records are
better preserved, and a greater
permanence in social organisation
makes men more disposed to look
beyond their immediate surround-
ings, a tendency to historical in-
quiry is naturally awakened. This
cause alone, without the more
philosophical considerations which
might lead a Hume or a Gibbon
to turn from abstract investigations
to historical inquiries, may account
for the growth of antiquarianism in
the latter years." But the mere
statistics of English literature in
the eighteenth century suffice to
prove the decline of argumenta-
tive and the growth of realistic
literature.

48

INTRODUCTION.

25.
Herbert

and have almost dislodged systematic philosophy, England
has for the first time in her history produced a system of
philosophy — that of Mr Herbert Spencer ; and this with
firsTEn"^-^^ the distinct imderstanding that the object of philosophy
has pro- "^^ is the Unification of knowledge.-^ It is a remarkable fact,
system of which will occupy our close attention hereafter, that the
unifying principle in this system is historical, — a process
of development now specially known under the term
Evolution. This system forms in a certain way a con-
trast to the last great system in German philosophy, that
of Hermann Lotze. Whereas in all systems of evolution
the unity of things is historical, and has to be sought in
their common origin, Lotze emphasises the truth that
unity must be a living presence, a principle which ex-
ists in individual things, not merely a link which con-
nects them by proximity in time or space. His object
is to answer the question. How can the human mind
represent to itself such a living unity, in what ideas

26.
Definition
of Lotze's
system.

^ See G. H. Lewes (' Problems
of Life and Mind,' 1st ed., vol. i.
p. 84), who says: "The absence
of a philosophy in England dur-
ing the last two hundred years
has been a serious defect in her
culture. Science she has had,
and poetry and literature, rivalling
when not surpassing those of other
nations. But a philosopliy she has
not had, in spite of jshilosophic
thinkers of epoch - making power.
Hobbes, Locke, Berkeley, Hume,
have produced essays, not systems.
There has been no noteworthy at-
tempt to give a conception of the
world, of man, and of society,
wrought out with systematic har-
monising of principles. There has
not been an effort to systematise
the scattered labours of isolated

thinkers. Mr Herbert Spencer is
now for the first time deliberately
making the attempt to found a
philosophy." And in his 'History
of Philosophy' (3d ed., vol. ii. p.
653) the same author says : " Mr
Spencer alone of British thinkers
has organised a system of philos-
ophy." Croom Robertson would
take exception to this in favour
of Hobbes, " who attemiDted a task
which no other adherent of the
' mechanical philosophy ' conceived
— nothing less than such a univer-
sal construction of human know-
ledge as would bring Society and
Man within the same principles of
scientific explanation as were found
applicable to the world of Nature "
(Ency. Brit., 9th ed. , vol. xii. p.
39).

INTRODUCTION.

49

belonging to human thought can this unity be grasped,
by what words of human speech can it be expressed ?

Both Mr Herbert Spencer's 'System' and Lotze's 'Micro-
cosmus ' are written with the object of establishing the
unity of thought, of preserving the conviction that things
exist and that events happen in some intelligible connec-
tion, and especially that the religious and the scientific
views of the world and life are reconcilable. But whereas
JVir Spencer is content to point to the underlying unity as
the Unknowable, and then betakes himself to the study
and exposition of the manner in which events follow and
things develop, Lotze considers the whole of this part of •
philosophy as merely an introduction to the solution of_;
the real problem. To him a process of development is
merely the outer form in which some real substance pre-
sents itself, a mechanical method by which something of
higher value is accomplished. He admits the all-pervad-
ing rule of such a mechanism, but he urges the necessity
of finding the substance itself, and of gaining a view of
the end and aim which is to be attained by this array of
processes, by this parade of mechanical means, of the in-
terest that attaches to them, and the result which is to be
secured.^ Knowing the mechanism by which a certain
object is accomplished, we may be able to calculate pheno-
mena and events, but to understand^ them requires a

1 The earliest passage in which
Lotze gives us a pretty complete
idea of his philosophical methods
and aims is to be found in his pol-
emical pamphlet against Fichte the
younger ('Streitschriften,' Leipzig,
1857, p. 52 sqq.) He there also
reviews his attitude to the ideal-
istic school of German Philosophy

VOL. L

and to Herbart, whose follower he
refuses to be called {ibid., p. 5 sq.)
It is evident that at that time his
system was not yet definitely set-
tled in his mind (p. 58).

" The difference between calcula-
ting and understanding phenomena
is probably to be traced to Leibniz.
Lotze emphasises this difference.

D

50

INTRODUCTION.

27.
Lotze's re-
lation to
Herder's
' Ideen.'

further knowledge of the worth of the object which is
accomplished, of the result which is gained by the calcu-
lation. It is one thing to be able to trace the mechanical
conditions upon which the accuracy of a clock depends ;
it is another to mark the hour which the clock strikes,
and to note the time which it measures out to us for our
work. Curiosity will lead a child to pry into the former ;
but the latter depends on our appreciation of the objects
of life and the seriousness of our duties.

When Lotze undertook to write the ' Microcosmus,' he
referred to two great works of a kindred tendency. Both
attempted, yet in very different ways, to give a compre-
hensive view of a large field of scattered phenomena, to
take in at a glance the entire scheme of a great world of
facts. The earlier of the two belonged to the last century
and was concerned with history, with the uniting bond of
all human development. For this Herder, in his ' Ideen
zur Philosophic der Geschichte der Menschheit,' had, if not
invented, yet endowed the term Humanity with a specific
pregnancy, meaning by it the unity of all human interests
in their social and historical development — an idea which
since Leibniz has governed German literature.'^ The other

See, inter alia, the closing para-
graph of the first volume of the
'System der Philosophic ' (1st ed.,
Leipzig, 1874). I cannot omit to
notice here the extraordinary and
misleading misprint in Erdmann's
quotation of this passage : see his
valuable ' Geschichte der Philoso-
phie' (3d ed., Berlin, 1878, vol. ii. p.
861), where instead of berechnen, to
calculate, we read bezcichnen, to
designate !

1 The history of this idea has
been written by Hettner in the

last two volumes of his ' Literatur-
geschichte des 18ten Jahrhunderts.'
I quote from the 2d edition,
Braunschweig, 1872. Herder had
inherited the spirit of Leibniz (see,
inter alia, the concluding chapter
of my essay on Leibniz, in Black-
wood's Philosophical Classics, Edin-
burgh, 1884). Herder formed a
kind of centre of thought, inas-
much as he gathered up in his own
mind and writings the influences of
Leibniz, Rousseau, and the Eng-
lish writers of the eighteenth cen-

INTRODUCTION.

51

great work was that of A. v. Humboldt, who in the course 28.

^ Lotze's re-

of a long career, peculiarly favoured by opportunities for ^2'v"Hum.
studying Nature on an extensive scale, and for appreciating ^Kosmos.'
the detail of modern research, of which he was an illustrious
representative, had never lost sight of the all-pervading
unity/ In an elevated style, in which poetry and science

tury, together with classical influ-
ences and new inspirations drawn
from the pojjular song-literature of
all nations. Hettner says (see last
volume but one, p. 7) : " Herder
applied Rousseau's gospel of Nature
to the demands of poetical sense
and creation. Thus he has become
essentially the forerunner of the
new school of poets : the last fetters
of the moralising style by which
even Lessing was still hampered
fell, and through the scientific study
of the beginnings and development
of human culture he became the
founder of a new science of Lan-
guage, Religion, and History, in the
lines of which we are still advanc-
ing." And p. 101 : "Herder does
not belong to the classics of the
style of Winckelmann, Lessing,
Kant, Goethe, and Schiller ; he is
everywliere only suggestive, hardly
anywhere conclusive and final. For
this reason his writings are to some
extent antiquated. Nevertheless
Herder is one of our most im-
portant and influential spiritual
heroes. Herder made so deep an
impression on his age that the
great poetry of Goethe and Schiller,
the so-called Romantic School, the
philosophies of Schelling and Hegel,
cannot be imagined without Herder
as the precursor." The fourth
volume of Gervinus, ' Geschichte
der deutschen Dichtung,' contains
likewise a very important chajater
on Herder. But the great authority
on Herder is R. Hajnn, 'Herder nach
seinem Leben und seinen Werken '
(Berlin, 2 vols., 1880 and 1885).

From the unpublislied literary
notes, correspondences, and diaries
of Herder, which Haym inspected,
it is evident that the great idea of
writing a History of Humanity
originated in Herder's mind as far
back as the year 1769, on a voyage
from Riga to Nantes (on the way
to Paris). His diary closes thus :
" History of the progress and of the
powers of the human mind in the
concurrence of whole ages and
nations — a spirit, a good demon, has
exhorted me to do this. Be that
my life's work. History, work I "

The first attempt to carry out
his great idea was published by
Herder in the year 1774, with the
title : ' Auch eine Philosophic der
Geschichte zur Bildung der Mensch-
heit.' Herder was then in his
thirtietli year. His chief work
appeared ten years later (1784), with
the title ' Ideen zur Geschichte der
Menschheit.' Herder died in 1803.
Goethe's 'Faust,' which is an at-
tempt to deal with the highest
problems of human interest, the
problems of knowledge, evil, sin,
and redemption, as they aj^pear in
the history of a great individual,
not of the race, had its first begin-
nings about tlie same time as Her-
der's ' History of Mankind.' But
the work was not finished till a year
before Goethe's death in 1831.

^ Alex. V. Humboldt, ' Kosmos.
Entwurf einer i^hysischen Welt-
beschreibung,' 1845. Like Her-
der's great work on the ' History of
Humanity ' and Goethe's ' Faust,'
Humboldt's ' Kosmos ' occupied a

52

INTRODUCTION.

29.
Lotze's 'Mi-
crocosnms.'

are happily blended, he essayed in the evening of life to
unroll before the gaze of his readers a picture of the
grand features of nature as his mind had viewed them
from the elevated regions of scientific study, and his eyes
from the heights of Chimborazo.

In the great picture of the world, in the vast changes
of the universe, where is man with his life and his in-
terests ? In the huge Kosmos where is the Microcosmus ?
This question naturally presented itself to the mind of
Lotze. " It is not," he tells us, " the all-embracing ' kos-
mos ' of the universe which we wish to describe again on
the model which has been given to our nation. As the
features of that great world - portrait sink deeper into
general consciousness, so much more vividly will they
lead us back to our own selves, suggesting anew the
question. What significance belongs to man and human
life with its lasting characteristics and the changing

long period in the life of its author.
Goethe's ' Faust ' deals with the in-
dividual problem, Herder's ' Ideen '
with the problem of the race or
mankind, Humboldt's ' Kosmos '
with the same problem as referring
to the world, the universe. In the
I^reface Humboldt confesses " that
the image of his work had stood
before his mind's eye in undefined
outlines for nearly half a century " :
cf. what Goethe says in the dedica-
tion to ' Faust ' (written probably
after 1797) : —

"Again ye come, ye hovering forms; I

find ye
As early to my clouded sight ye shone,"

&c.

— Transl. B. Taylor.

The view of the universe which was
given in Humboldt's ' Kosmos ' was
prepared by his own publication,

' Die Ansichten der Natur' (1808) ;
also by Georg Forster (1754-1794),
who wrote an account of the second
voyage of Captain Cook round the
world, whom he accompanied with
his father. " He conceived of na-
ture as a living whole ; his account
is almost the first example of the
glowing yet faithful description of
natural phenomena, which has since
made the knowledge of them the
common property of the educated
world " (R. Garnett in ' Ency. Brit.,'
art. "Forster"). Humboldt con-
fesses to have received from him
"die lebhaf teste Anregung zu wei-
ten Unternehnmngeu " (' Kosmos,'
vol. i. p. 345, also vol. ii. p. 65, and
especially vol. ii. p. 72, where in-
cidentally also Darwin's narrative
of the " Adventure " and " Beagle "
is mentioned).

INTRODUCTION.

53

course of its history in the great totality of nature ? " ^
And in collecting the answers to this question which
suggest themselves both in and outside of the study,
Lotze professes only to renew the enterprise brilliantly
begun by Herder in his ' Ideen zur Geschichte der
Menschheit.' Both Herder's ' Ideen ' and Humboldt's
' Kosmos ' belong to the age in which philosophy and -
poetry largely influenced science and history. Many may ,
now think it premature or altogether impossible to try
to combine the detailed studies of modern science and
modern history with the comprehensive view demanded
by philosophers and poets, or to grope through the laby-
rinth of external phenomena and events to their under-
lying significance and unity. They may, whilst fully
maintaining the existence of an all - pervading power,
nevertheless relegate it with Mr Spencer to the region
of the Unknowable."-^ Without desiring at present to

^ Microcosnius, 1st ed., Leipzig,
1856, Preface. Hermann Lotze was
born in 1817, and died in 1881.
His first philosophical essay of im-
portance was the ' Metaphysik '
(Leipzig, 1841).

- Herbert Spencer's Philosophy
of the "Unknowable" is laid down
in his Introduction to ' First Prin-
ciples.' I believe the first appear-
ance of the first part of this book
was in 1860, and the first collected
publication in the year 1867. In
defining the region of the Know-
able an opposite course has been
adopted by Emil du Bois-Reymond,
who in a series of addresses and
articles, now collected in two vol-
umes with the title ' Reden ' (Ber-
lin, 1886 and 1887), tried to lead
up to the limits which are fixed
around scientific knowledge. The
purport of his teaching on the

highest " World-problem " is con-
tained in the four words, ignoramus,
ignorabimus, dubitemus, lahoremus.
The first of these addresses, which
are full of brilliant suggestions and
vivid illustrations, furnishing in the
notes especially an invaluable store
of historical references on the sub-
ject of the philosophy of the sci-
ences, was delivered at the forty-
fifth meeting of the German " Na-
turforscher und Aertze," and pub-
lished at Leipzig, August 1872, with
the title ' Die Grenzen des Natur-
erkennens. ' It made a great sensa-
tion, and was translated into several
languages. It was followed some
years later by an address delivered
in the Berlin Academy, 1880, and
published with the title ' Die sieben
Weltriithsel. ' If H. Spencer's phil-
osophy is termed the philosophy
of the Unknowable, Du Bois-Rey-

54 INTRODUCTION.

criticise the weighty considerations which have led them
to a view so modest and resigned, I propose in the
sequel to test within narrower limits, and by what
seems to me a novel method, the validity of the con-
viction that a true understanding of phenomena and
events can be attained only by viewing them in their
interdependence and collective effect. If anything in
the wide expanse of physical and mental life deserves
to be considered as one and indivisible, it is surely
human thought in its various branches and manifesta-
tions. The attempt to trace its origin in the early ages
of civilisation, or to foreshadow the end which it is
slowly approaching, may indeed be impossible ; but of
the age to which we belong, and the literature of
which we have witnessed the growth, we may claim to
possess a deeper knowledge. Astronomers have suc-
ceeded in gaining a view of immense and distant orbits
by minutely observing and tracing merely an insignifi-
cant portion ^ which came within their view. Com-
parative anatomy teaches how from a few surviving
links to construct the whole framework of an organism.
I propose to apply a similar method to the small portion

mond's may be termed the pbilo- ^ of 1802. After the discovery of this
sophy of the Limits of the Know- first of the small planets, but before
able. Both views form a contrast it was known in Germany, Hegel
to Lotzes philosophy. , published his ' Dissertatio philo-

^ The most brilliant example of I sophica de orbitis planetarum,' in
this is the discovery of the planet
Ceres by Piazzi at Palermo in the
New Year's night of 1801 ; the in-
vention of special methods for cal-
culating the orbit of this planet,
wliich had been lost, by Gauss in the
course of 1801; and the rediscovery
of it by Olbers, aided by Gauss's
ephemeris, in the New Year's night

which he ridiculed the search for
new planets, but which Duke Ern-
est of Gotha sent to the astrono-
mer Zach with the superscription,
"Monumentum insaniae sajculi de-
cimi uoni." See R. Wolf, Ge-
schichte der Astronomie, Miinchen,
1877, p. 684 sqq.

INTRODUCTION. 5 5

of mental progress of which I have been able to take
personal notice and of which I have felt the immediate
personal influence. A tracing as concisely as possible
of this comparatively small portion of the course of
European thought may be the first approximation to
more accurate delineations, which themselves will be
the means of gradually gaining a truer idea of the pur-
port and significance that belong to the larger dimen-
sions of the mental life of mankind.

This life does not consist in the accumulated knowledge
of our century, not in the results of scientific inquiry de-
posited in libraries and museums, not in the many schools
for learning and study, not in educational and social re-
forms, least of all in political and economic institutions. ~
These are all external objects, which are capable of being
described or photographed like the external objects of
nature. The mental life of mankind consists in the inner 30.

What tl

processes of reflection, by which these external objects have mental iife
been produced, by which man has been able to add to the '"'
physical creation of nature a new creation of his own, by
which he has been able to change the face of the earth,
and endow the objects of nature with an ideal meaning.
To this end he is always inventing and using methods
which change, suggesting and applying principles which
turn out to be half true or totally fallacious, guessing at
results and aims which have to be abandoned, inventing
theories which are short-lived — in fact, erecting scaffold-
ings with the help of which he raises the structures of
Society, Art, and Science : these remain as the historical
testimonies of his activity ; the scaffoldings are removed as
of merely transient and temporary value ; and yet they

of mankind
consists of.

56

INTRODUCTION.

31.
Methods,
the most
approved,
have their
day, and
ceabc to be.

32.
One century
does not
inherit all
of the past ;
it discards
much.

alone constitute the mental life which interests us. Only
so far as we have taken part in building the scaffolding,
only in so far as we have witnessed the many contrivances
which have been used, only in so far as we have seen the
growth of any structure from small beginnings, from the
first sketch of the architect, can we say that we know
something of the mental life which lies hidden in and
behind those external signs and documents. A closer
study of what we ourselves have witnessed is thus the
only way of attaining some insight into the workings of
the mind — the spiritual life of mankind. We shall pres-
ently find that in science as well as in philosophy every
period starts from certain assumptions and proceeds ac-
cording to certain methods, that certain habits of thought
become general, and certain views become accepted ; but in
the course of one or two generations we find those assump-
tions questioned, those methods criticised, a new habit of
thought introduced, and those general views which seemed
so natural and convenient giving way to new and altered
ones. The whole fabric of society, the whole structure of
science and knowledge, all the applications of art, have to
be remodelled on new principles, and to meet our changed
demands. Few indeed, very few, of the old creations
remain. One or two so-called laws of science that sur-
vive, a few dozen books that are re-edited, half-a-dozen
works of art and one or two great poems, — this is about
all that our century will at its close have preserved as the
living inheritance of its early years : all the others will be
relegated to the growing bulk of historical records. Pos-
sessed of merely monumental interest as documents of a
bygone life, these creations had to be left aside as incap-

INTRODUCTION. 57

able of marking or guiding any longer our onward career.
A few centuries lapse, and posterity will look upon them
as we do on the huge monuments of early Eastern civili-
sation, on the Sphinx in the desert or the Pyramids of
Egypt, wondering by what ingenious contrivances they
were raised, what amount of human work and suffering
they represent, or what idea lived in the minds of those
who planned and placed them where they still remain.

III.

It is the privilege of art to represent at a glance the -^^^J^.^^ ^^
whole of its object, and thus to produce at once a total ^oadf™^^
effect on the mind of the beholder. Closer scrutiny may>i
follow and may show how the various parts support!
the whole, how the uniting idea is revealed in all the
manifold detail of the component elements : still the im-
pression_of the whole remains and supplies the key for
the comprehension of every part. Literature, science, and
history are denied this privilege of presenting their ob-
jects in their entirety, and thus giving from the outset a
commanding view, a leading and abiding impression of the
whole. We have to ask the student to follow us patiently
by an isolated path to the summit : many ways lead to it,
and we may err in the choice of the right and convenient
one. Even if we succeed in reaching the central position,
we may have fatigued the reader on the road or produced
sensations which prevent the unbiassed contemplation of
the whole view when it is presented. With us the whole"] (
is only the sum of its many parts, whereas with the artist
the parts are merely fractions of a united whole. In i

58

INTRODUCTION.

Some peri-
ods of liis-
tory take
their name
from some
great event
or move-
ment.

treating of the thought of the century, even within the
narrow limits which have been prescribed, I am met with
similar difficulties. In the large circumference of the
domain of thought I have to choose a starting-point and
to construct a road which may lead to the central position,
hoping there to gain a comprehensive view of the whole.
Some periods of history are characterised by one great
and central movement which absorbs all active forces
and all intellectual and imaginative power, making
them either subservient to one end and purpose, and
helpful in the elaboration of one idea ; or else forcing
them into opposition, where they testify equally to the
importance of this central movement. Such periods
were, for instance, the long centuries of Jewish history,
the early age of the Christian Church, the period of the
culmination of Papal power, the Preformation, the French
Eevolution. In studying the thought of such ages, we
are not at a loss where to find the leading idea, — we
easily fix the centre of the vortex which draws into its
motion all the existing forces, all genius and all talent.
In an age like that of the Eeformation we can speak of
the Politics of the Preformation, the Eeligion of the Eefor-
mation, the Philosophy, Literature, and Art of the Eefor-
mation, and we are pretty sure to embrace under these
various heads an account of all the mental progress and
to trace all the thought of that age, be it friendly or anta-
3. gonistic. It is evident that no such central event, no such
event in oiir all-absorbiug vortcx of motion, exists in the period which

age.

we have lived through. The uniting bond, if it exists, lies
much deeper ; the problem we have been engaged in solv-
ing, the prize we are fighting for, does not present itself on

INTRODUCTIOX.

59

the surface ; it is not explicitly stated, it must be implied
rather than defined. The great object of our life and
labour has not been clear to us, as it seemed clear to those
who lived during the Eeformation or the Ee volution, other- •,
wise we should not have philosophies of the Unconscious i
and of the Unknowable, and the century would not end |
in asking, Is life worth living ?

Then, again, we find in history long periods of quiet
development, where men's minds seemingly run very much
in the same direction, exhibiting a general tendency of
ideas, the spreading of a defined habit of thought and of
simple methods, the application of a few principles : such
a period was that preceding the French Eevolution, the
greater part of the eighteenth century. It has therefore
been easy to characterise that century : it has been
termed the philosophical century, the century of the
Aufkldrung, the century of Voltaire.^ No such one

^ The first who reviewed the
literature of the eighteenth century
from an international point of view
was Villemaiu, who as early as 1820
was engaged in lecturing at the
Sorbonne before the elite of the
rising literary generation of France
on the literature of the eighteenth
century, taking France as the centre,
and showing the influence of foreign
literature, especially English, as Hke-
wise the reaction of French ideas
abroad. He was too early to recog-
nise the true meaning of the new
spirit which had then already gone
forth from Germany. In this respect
his ' Cours de Litterature fran9aise,'
pubUshed in 1828 and republished in
1864, remains incomplete. Schlosser
next attempted to present in his
' Geschichte des achtzehnten Jahr-
hunderts,' after the manner of
Gibbon, a picture of the combined

political and literary work of the
last century. The first draft of it
appeared in 1824, after Schlosser
had passed two years in Paris, where
no doubt he must have come under
the influence of Villemain. The
work itself began to appear in 1826,
and was finished in 1848. It is
considered to be Schlosser's greatest
work, and had a large circulation.
The connection of political and
literary history was studied by
Gervinus, who with Hiiusser is
usually counted as a pupil of
Schlosser. But the great work
which Villemain had begun and
Schlosser taken up was adequately
carried out by Hettner, who in
his ' Literaturgeschichte des acht-
zehnten Jahrhunderts ' conceived
the whole intellectual movement of
that age as a battle for enlighten-
ment (Kampf der Aufkldrung). The

60

INTRODUCTION.

4.
Is history
of thought
history of

term can be applied to our age, no one name can be
found which carries with it the recognition of all the
many interests which surrovmd us.

It has been suggested by some that the history of
thought is equivalent to the history of philosophy ; that
philosophy? ^j-^g different philosophical systems and theories exhibit
in the abstract the course which ideas have taken in an
age.-^ A history of thought in the nineteenth century
vi^ould thus mean a history of nineteenth century philo-
sophy. There have indeed been plenty of philosophies
and systems during our period, but in spite of their
I great number and variety — ranging from the extreme
idealism of Fichte to the equally extreme materialism
of Biichner ^ — we feel that they do not cover the whole
area of thought. The period in our century which in
England was most barren in philosophy, the first forty
years, produced an entirely new literature and a novel
conception of art, both containing new sources of mental
life, though they have hardly yet found expression in any
philosophical system. Equally barren in speculation was
France during the Eestoration ; yet there, too, was a

latter part of his work deals with
the reaction against Aufkldrung
and " Rationalism " as it began in
England, and was represented on
the Continent by Rousseau and
the earlier ideals of the French
Revolution. Through Rousseau and
the Revolution the growing in-
fluence of the new spirit of English
literature was overpowered and lost
for the Continent. And, as we have
to regret in Villemain his neglect
of the new life of Germany, so we
have to deplore that Hettuer fol-
lowed the developments of Rational-
ism and Aufklarung only in the

form they assumed in Germany,
neglecting to notice the contem-
porary growth of the new life in
English Literature and Art, to
which, in fact, no German historian
has as yet done justice.

1 See especially Hegel's Lectures
on the History of Philosophy in his
collected works, vol. xiii. p. 68 sqq.
(Complete edition, Berlin, 1832.)

" The principal publications of
this school are Vogt, ' Physiologische
Briefe,' 1845-47 ; Moleschott, ' Der
Kreislauf des Lebens,' 1852 ; Biich-
ner, 'Kraft und Stoff,' 1855.

INTRODUCTION.

61

the century.

brilliant era of literature, and the whole of Europe was
illuminated by the light of science which emanated from
Paris during the first third of this century. History of q^^^^^.^
philosophy has little to say about Goethe, though his wiTCsThe
work embodies for us probably the deepest thought of thought of
modern times. Again, the only great and novel system
of philosophy which Trance has produced during this
century is that of Comte, but it has had only small
influence in its own country ; and who would say that
it reflects French thought of the period as Voltaire
and Montesquieu reflected the thought of the last
century ? Hegel himself, who was intent upon tracing
the working of the human mind in the systems of
philosophy, declared that philosophy is the latest fruit f
of civilisation, — that the special idea which governs any ;
period is already dying out when it appears in a system.-^ f

^ The principal passage expound-
ing this idea of Hegel's is to be
found in the introduction to the
course of lectures which he delivered
at Berlin repeatedly during the years
1816 to 1830. See his collected
works, vol. xiii. p. 66 : " Philosophy
makes its appearance at the time
when the mind of a nation has
worked itself out of the indifferent
dulness of the early life of nature,
as well as out of the period of pas-
sionate interest ; inasmuch as the
direction towards detail has spent
itself, the mind transcends its
natural form — it passes on from
practical morals, from the force of
real life to reflection and compre-
hension. The consequence is, that
it attacks this actual form of exist-
ence, these morals, this faith, and
disturbs them ; and with this comes
the period of decay. The further
stage is, that thought tries to collect
itself. One may say, that where a

people has come out of its concrete
forms of life, where distinction and
separation of classes has set in,
where the nation approaches its
fall, where a rupture has taken
place between the inner desires and
the external reality, where the rul-
ing form of religion, &c., &c., does
not satisfy, where the mind shows
indifference towards its living exist-
ence or lingers discontentedly in it,
where moral life is in dissolution —
then only does one philosophise.
The soul takes refuge in the realms
of thought, and in opposition to the
real world it creates a world of ideas.
Philosophy is then the reparation of
the mischief which thought has be-
gun. Philosophy begins with the
decline of a real world : when she
appears with her abstractions, paint-
ing grey in grey, then the freshness
of youth and life is already gone ;
and her reconciliation is not one in
reality, but in an ideal world."

G2 INTRODUCTION.

6. This means that philosophy is retrospective : it sums up,
retrospe. . ^|^ criticises, it does not prefigure the future. The correct-
ness of this proposition may be doubted. We shall have
to deal with it in another place. At present it reminds
us that thought, in the sense in which we take it, cannot
be identified with philosophy, and hence a history of
philosophy in the nineteenth century is not identical
with a history of its thought. There is indeed a sense
in which the word philosophy is sometimes used, when
it approaches more nearly to the meaning of the word
thought, as we intend to use it. Whewell has in this
sense written the philosophy of the inductive sciences,
meaning to trace in that work the processes of thought
which are consciously or unconsciously employed in
scientific research and reasoning, and which lead to
progress in science. Something similar might be at-

When does

thought tempted in regard to art, commerce, politics, government,

mean phil-
osophy? religion, and literature generally. In every case philo-
sophy would simply mean the peculiar way of thinking
and reasoning which is adopted in these various branches
of practical or intellectual life. This is, however, not the
I sense in which the word philosophy is generally used.
\ It generally denotes something more than a statement of
I method or a rationale of ideas and reflections ; it denotes
'' a definite theory, an explanation of a larger or smaller
circle of phenomena. As such it certainly forms a part
of the thought of the century, probably the most in-
teresting and fascinating part ; but it is also that
which is most liable to change, most subject to discus-
sion ; whereas the other more hidden thoughts and reason-
ings form, as it were, the ground upon which all the

INTKODUCTION. 6 3

intellectual, artistic, and practical achievements of the age
rest.

It would thus appear as if an account of the thought of ^^ ^s- .^^^
the century might naturally divide itself into two separate t^g clntufy
investigations. In the first place, we should regard thought twotue"'**'
merely as a means to an end, as the method adopted to ._ '
attain a certain purpose, be it practical or theoretical. It w
would mean the peculiar kind of reasoning which has been
employed in the search for knowledge or in its useful
application. As all reasoning starts from certain assump-
tions, called premisses, or principles, or axioms, and pro-
gresses from these by certain methods, this portion of our
task would divide itself again into a statement of the
principles which underlie, and an account of the methods
which have guided, theoretical and practical reasoning.
But thought does not exist merely for the sake of in-
creasing our knowledge of things and of applying this to
practical purposes. Occupied in this way merely, it re-
"mains fragmentary, incomplete, and not infrequently it
reveals contradictions. Even those who devote themselves
purely to detailed research or to practical work are again
and again compelled to take a wider and deeper view of
things than their special occupation affords. One may
find that the methods which he is using daily become
useless for certain practical purposes he has in view, and
may thus be forced to question the principles which during
half his lifetime he has applied with unquestioning faith
in their validity and usefulness. Another may have met
with such success in the use of a special method of re-
search, that he wishes to apply it to subjects which were
previously handled in a different manner, or elevate it to

64 INTRODUCTION.

the dignity of a general rule of thought. A third may,
accidentally, be interested in two or more pursuits which
are seemingly unconnected, hut which — being brought
side by side in his mind — he feels the wish to unite
and harmonise. A fourth may, at a certain time of life,
grow tired of the drudgery of petty pursuits which never
carry him beyond a very limited sphere of interests : he
is tempted to look beyond this narrow range, and gain
some wider view of other pursuits and interests. Allowing
that ignorance or indifference prevents even the majority
of those whose powers are not exhausted in the struggle
for mere existence from looking much beyond their nar-
row circle, allowing also that many of us live — like chil-
dren— in a blessed trust that the great and important
interests of mankind are under higher and better guidance
than we can understand or control, there still remain a
considerable number of persons who are always on the
look-out for something higher, wider, and better, who are
driven by an undying thirst after real wisdom, or by an
9. inherent restlessness of disposition to inquire into the

Speculation.

deepest foundations and the ultimate ends of the world
and life. Language has coined a word which denotes the
whole of these occupations and endeavours, how various
so ever they may be, and for whatsoever purpose they may
be undertaken. It calls them speculations. The word
also indicates the venturesome and risky nature of these
undertakings. They have existed in all ages and countries
and languages wherever literature has existed, and have
been carried on by the powers of reason or imagination,
in prose, verse, or symbol, sometimes in defined and clear
terms, more often in mystic allegory. Philosophy may be

INTRODUCTION.

65

said to have grown out of these vague and scattered
beginnings by the attempt to conduct them according to
some method, and to unite them into a complete and con-
sistent whole. Philosophy may thus be defined as specula- lo.

^ J "^ ^ Philosophy

tion carried on according to some clear method, and aim- defined,
ing at systematic unity.^ Both science and philosophy
may be called methodical thought, but the word system is
applicable only to the higher and more advanced forms of
philosophic thought which aim at unity and completeness.
We have thus arrived at a second division of our sub-
ject. In the first we have to consider thought merely as
a means to an end ; in the second we have to consider it as
its own object, as a reflection on itself, carried on with the
object of knowing its own origin, its laws, its validity, of
testing its powers, and with the end and aim of gaining
certainty, completeness, and unity. The whole of this jji^jg^o^Qf
great division of thought I shall comprise under the ^^^ ^°°^-

1 This view of the nature and
object of Philosophy agrees with
Lotze's definition (see ' Grundziige
der Logik,' Leipzig, 1883, § 88) :
"The comTnon culture of life and
the separate sciences contain a num-
ber of suppositions the origin of
which is obscure to us, because they
have been very gradually formed
within us through the comparison
of many experiences, or because
they have first become conscious by
means of such experiences, have
then received definite names and be-
come habitual without having been
suVjjected by us to any examina-
tion as to the reason, the sense, and
the extent of their validity. In this
way science and life make use of the
notions of cause and effect, of matter
and force, of means and end, oi free-
dom and necessity, of matter and

VOL. I.

mind, and they frequently entangle
themselves, owing to the above-men-
tioned defect, in contradictions, in-
asmuch as they are unable to fix the
limits of validity of these to some
extent contradictory assumptions.

"Now we may formally define
the task of Philosophy as follows :
that it is an endeavour to import
unity and connectedness into the
scattered directions of cultured
thought, to follow each of these
directions into its assumptions and
into its consequences, to combine
them all together, to remove their
contradictions, and to form out of
them a comprehensive view of the
world ; mainly, however, to subject
those ideas which science and life
regard as principles to a special
scrutiny, in order to determine the
limits of their validity."

E

66

INTRODUCTION.

12.
Neither
science nor
philosopliy
comprises
the whole
meaning of ;
the word
thought.

13.

Thought
also hidden
in the liter-
ature and
art of the
age.

term Philosophy ; and as the first part will deal with
the scientific, so will the second deal with the philo-
sophical thought of our century.

Science has gradually risen out of the mass of accu-
mulated but inaccurate and disorderly knowledge by
the desire of making it accurate, orderly, and useful.
Philosophy has similarly emerged from the great world
of speculative thought by the desire of carrying it
on methodically and for a defined end and purpose.
Nevertheless neither the one nor the other, nor both
together, really exhaust the whole meaning of the word
"Thought"; neither science nor philosophy covers the
whole region of thought. Both are comprised under the
term methodical thought ; but there remains the great
body of immethodical, undefined thought. This is buried
in general literature, in poetry, fiction, and art ; it shows
its practical influence in the artistic, moral, and religious
life of our age. It is a reflection of the knowledge of
science or the light of philosophy, but, like all reflected
light, it not only follows, it also precedes the real and full
light : it is not only the dusk that comes after, it is also
the dawn that comes before the day, it is the twilight
of thought. In it lie hidden the germs of future thought,
the undeveloped beginnings of art, philosophy, and science
yet unknown and undreamt of ; it encloses and surrounds
the innermost recesses of the mind, where all thought had
its origin, and whence it ever and again draws fresh life
and inspiration.^

^ This is originally a Leibnizian
idea. It is laid down in the doctrine
of the petites perceptions, as given

in the introduction to the ' Nou-
veaux Essais,' and referred to in
many passages of Leibniz's various

INTRODUCTION.

67

No account of the thought of our century would be
complete or satisfactory which took no notice of this great
volume of immethodical and unsystematic thought which
lies buried in the general literature and in the art of
the age. Both have shown a vitality, originality, and
versatility which exceed that of any except the few
favoured periods — those of Athens under Pericles, Italy
during the Eenaissance, and England under Elizabeth.
In one of the arts, in music, our age has, according to the
opinion of many competent judges, exceeded in originality
and certainly in productiveness all former ages. In
poetry Goethe and Wordsworth have raised our tastes h

Goethe and

and demands to a higher level, in fiction France and Wordsworth

■^ raised our

England have almost created a new branch of literature, ^^***®®-
whilst the peculiar features of modern English landscape-
painting were unknown to previous centuries. All this,
though produced under no scientific or philosophical rule

writiugs. See ' Nouv. Ess.,' Pre-
face, Leibniz, Philosophische Werke,
ed. Gerhardt, vol. v. p. 48 : —

"Ces petites perceptions sont done
de plus grandeefficace par leur suites
qu'on ne pense. Ce sont elles qui
forinent ce je ne S9ay quoy, ces
gouts, ces images des qualites des
sens, claires dans I'assemblage, mais
confuses dans les parties, ces im-
pressions que des corps environnans
font sur uous, qui enveloppent
I'infini, cette liaison que chaque
estre a avec tout le reste de I'uni-
vers. On peut meme dire qu'eu
consequence de ces petites percep-
tions le present est gros de I'avenir
et charge du passe, que tout est
conspirant {cn'ifji.Trvoia iravTa, comme
disoit Hippocrate) et que dans la
moiudre des substances, des yeux
aussi per9ans que ceux de Dieu

pourraient lire toute la suite des
choses de I'uuivers.

" Quae sint, quae fuerint, quae
mox futura trahantur. . . . C'est
aussi par les perceptions insensibles
que s'explique cette admirable har-
monie preestablie de I'ame et du
corps, et meme de toutes les Mon-
ades ou substances simples, quisup-
plee b, I'influence insoutenable des
uns sur les autres, et qui au juge-
ment de I'auteur du plus beau des
Dictionnaires exalte la grandeur
des perfections divines au del^ de
ce qu'on eu jamais congu."

The importance of this idea of
Leibniz has been dwelt on at length
by Kuno Fischer in his ' Geschichte
der neueren Philosophic,' where he
also traces its influence in the
development of philosophy and
literature in Germany after Leibniz.

68 INTRODUCTION.

and very frequently outside of any school, points to novel
modes of mental conception, to a fund of ideas yet un-
developed or only partially developed into clear thought.
The whole of this productiveness indicates a vast amount
of mental work which, though not yet absorbed by science
or philosophy, belongs nevertheless, according to our
original conception, to the world of thought. The mean-
ing of it may be enigmatical, and the clear expression
which it will some day produce in philosophical and
scientific reasoning may be far distant and unintelligible
15. to us now. Still there it is, this great body of undefined

Unmethodi- ' ° •'

cai thought, thought, this volume of diffused light, the focus and
centre of which is still hidden from us. We feel that in
discussing the thought of the century we cannot pass it
by or neglect it.

It is difficult to find any one term under which we
could comprise this great body of unmethodical, scattered,
and fragmentary thought, — any one word, similar to
science and philosophy, in which we could sum up and
characterise its general meaning and tendency. So far
we have only stated what it is not, what to a large extent
it perhaps never will be — viz., methodical. And yet we
feel that it contains that kind and portion of thought
which touches our deepest interests, our most intimate
concerns, our noblest aspirations. Science becomes more
and more a mere calculation, une question d^ analyse, an
occupation for the laboratory, the workshop, the manu-
factory, and the market ; philosophy savours at its best
too much of the school and lecture-room, runs too much
into systems and categories, it fatigues us with definitions

INTRODUCTION. 69

and abstractions. But neither calculation and measure- le.

Summed

ment, nor definition and abstraction, suffice to exhaust "p *" *•}«

' term reli-

what is to us, in the quiet and serious moments of life, of f^ought.
the deepest concern — viz., our religion. I use the word
here in its original sense, and I propose to sum up in the
term religious thought the whole of the thought contained
in that large volume of literature which does not submit „ ,
to scientific and philosophical treatment, but which never- ^
theless forms so important an outcome of the mental life
of the century.

There are other words more or less current in modern
literature that may serve to throw some light on the
distinction that I am here drawing for the purpose of
affording a preliminary view of the course to be pur-
sued in the following treatise.

Science is said to be exact, positive, and objective, and . i7.

'~~~ oC16uC6 IS

it is opposed to such other thought as is inexact, vague, tf^^J^^PJ^*'
and subjective. Science is said to convey its results or ^^J^*^*'^^-
ideas in defined, direct, and general terms, whereas there
is a large department of literature and thought which
moves in undefined, symbolical, and indirect expressions.
Science professes to rest on clear and precise knowledge,
and is thus opposed to such other realms of thought as
Test on opinion, belief, and faith. It may be well to note
here that these different terms refer either to the method
of treatment or to the matter which is under treatment.
Science alone professes to have a rigid and undisputed
method. Other branches of thought either borrow their
methods from science, or they have fluctuating, not gener-
ally recognised methods, or they refuse to submit to method

70

INTRODUCTION.

18.
Some in-
terests or
objects of
thought are
personal or
subjective.

19.

Agreement
on these
matters
impossible.

altogether. But so far as the matter under treatment is
concerned, a clearer division is possible. Science deals
with all such things or objects of thought as are common
to a great many persons and — under certain circumstances
— are accessible to everybody : it thus claims that its ob-
servations and reasonings can be checked and submitted to
repeated examination and verification ; so that a large por-
tion of them can always be regarded as settled and agreed
upon, and can be taken for granted and used as a secure
foundation by those persons who are themselves unable or
unwilling to go through the process of verification. But
there are a great many things and interests which centre
in the individual mind of each person — which are, in fact,
personal, individual, or subjective. They are to all of us
just as important as the others. They form the real sub-
ject-matter of all that thought which is separated from
science, and in its very nature and aspect opposed to it.
In this great province of thought one person cannot do
the work for many in the same way as is possible in
science. Proof is almost impossible, and agreement refers
always only to a certain number of persons. Doctrines or
theories in this region of thought cannot be accepted and
taken for granted as they are in science, but every person
must go over the same ground for himself before he has
any right to accept or make use of what is given to him.
The real and true character of all this thought is that it
is individual and personal, whereas all scientific thought
— whatever its origin may be — must be general and im-
personal. At the extreme end of thought in one direction
are placed the mathematical sciences, at the extreme end
in the other lies religion. Disagreement in the former is

INTRODUCTION. 71

almost as unknown ^ as agreement in the latter. There
we have an almost universal unity of thought ; here unity
of thought probably never existed ; it is unknown. Popu-
larly we can say that at the one extreme lie knowledge
and certainty, at the other faith and belief. There is,
however, a very large extent of ground between these two
extremes. This is covered by all such intermediate thought
as rests partly on knowledge, partly on faith, where cer-
tainty is largely mingled with belief. This large inter- 20.

/ ° "^ ° => Philosoi.hy

mediate region, where changes and fluctuations are fre- intermecu-

o ' o ate between

quent and rapid, is the proper home of philosophy, which cafsjfi^ce'
occupies itself with the grounds of certainty and belief, ^"^"^ 'ehgion.
the origin of knowledge and faith, and the relations in
which both stand to each other. Were all our thoughts
either purely mathematical — i.e., referring to number,
measurement, and calculation, or purely religious — i.e., ^
referring to our individual concerns and personal convic-
tions,— the need of a continued compromise or mediation
would be unnecessary, the question as to the grounds of
certainty or belief would never arise. But no sooner
do we wish either to apply our strict mathematical no-
tions and processes, or to bring our personal convictions
into practical use, than the two kinds of thought come
into contact, not to say into conflict, and there is need
of some theory according to which this contact may be
regulated, this conflict settled. And as the occasions for
such contact change with the demands of practical life, or

^ It may be doubted whether this the correct measure of force,

is quite correct, looking at the con- ' These controversies, however, re-

troversies whicli have been connec- ferred really to applied, not to pure

ted with many mathematical theo- mathematics, and were settled by

ries — such as the theory of parallel introducing correcter and more

lines, the meaning of infinitesimals, 1 stringent definitions.

72

INTRODUCTION.

21.
Threefold
considera-
tion of
thought :
scientific,
philosophi-
cal, indi-
vidual.

the progress of applied science, these theories must them-
selves change and develop. Now it may be generally
. stated that it is the task of philosophy to take note of
these different ways by which the strict methods of science
are applied and made useful, or by which personal and
individual convictions are brought to bear upon practical
questions which are not only of personal but of general in-
terest and importance. It does not follow that philosophy
must necessarily construct a complete system ; but it is a
natural and frequent occurrence that the occupation with
a great number of detached theories or aspects of thought
generates the desire to bring them into harmony and to
unite them in a connected whole. Thus the enterprise
which was originally purely critical and preparatory, and
undertaken merely as a means to an end, may lead to the
formation of a general and all-embracing view of things
— i.e., to a philosophical system.

From whichever side we approach the matter, we are
thus always led to a threefold consideration of thought,
as scientific, as individual, and as philosophical. An at-
tempt in which any of these three aspects were neglected
could have no value in an account of the thought of our
age. There have indeed been schools of thought which
identified science with philosophy, or which maintained
that no independence belonged to religious, personal, or
individual thought, inasmuch as this was merely of a
derived character. Though such theories may have ex-
erted considerable influence, they have as a whole failed,^

•• This can be said of Hegelian-
ism as well as of Comtism. In the
former it was a favourite doctrine
that philosophy was the higher
wisdom compared with religion and

art. See Hegel, ' Geschichte der
Philosophic ' (Werke, vol. xv. p.
684) : " The highest aim and inter-
est of philosophy is to reconcile
thought, the idea, with reality.

INTRODUCTION.

73

and we find ourselves at the end of a long and critical
period unable to say that any one of the three realms
of thought has gained an undisputed victory over the
others. Science is more than ever that kind of thought
which gives knowledge and certainty. Eeligion is still
the generally recognised abode for those convictions
which refer to our deepest personal interests. And more
than ever do we feel the need of a reconciliation of both
in some theory of life which is neither purely scientific nor
purely individualistic ; and this means that philosophy is
as much needed as ever. Our century has witnessed a
great development of scientific thought, a great revival in
religious interest, religious feeling, and religious activity,
and it is probably richer than any preceding age in
philosophical theories and systems.

I must repeat here what I said above, that it is a
misfortune that in dealing with a complicated subject
we are obliged to divide it, — that we are forced to give
preference to some one aspect, and to choose a special

22.
Philosophy
the media-
tor between
science and
religion.

Philosophy is the veritable theo-
dicy, compared with art and religion
and their sentiments — this recon-
ciliation of the mind, indeed of that
mind wliich has grasped itself in the
freedom and wealth of its reality.
1 1 is easy otherwise to find satisfac-
tion in subordinate regions of intui-
tion and feeling," &c. , &c. Al-
though it is an exaggeration to say
that Hegel desired to absorb or
evaporate religious belief in philo-
sophical knowledge, as his lengthy
explanation (Introduction to the
' History of Philosophy,' Works, vol.
xiii. p. 77 sqq.) sufficiently proves,
there is no doubt that the senti-
ment expressed in the above pas-
sage indicates that philosophy was
coming to the rescue of true reli-

gious belief, which threatened to be
lost in the rationalistic and mystical
schools of the day. And this had
the further consequence that a
scientific occupation with or inter-
est in religious subjects — be it meta-
physical or historical — took the
place of a purely religious interest,
and that many eminent German
theologians became either pure
metaphysicians or merely critics,
the practical side being lost sight of.
It is probably just as incorrect
to accuse Comte of an intention
to destroy true religion because he
preached the well-known doctrine
of the three stages of human
thought — the theological, the meta-
physical, and the scientific or posi-
tive.

74 INTRODUCTION.

point from which to set out. In dealing with the
thought of our age, I have been obliged to divide what
is in reality connected and coherent ; and I am further
forced, in examining more closely its different aspects,
to select one as the most prominent with which to make
a beginning. In reality such a preference does not exist
in my plan. I recognise all the aspects of thought as
equally important, and I feel that I might begin with
any one of the three, and that I should in due course be
23. led on to a consideration of the other two. They are in

Difficult to

separate the their actual historical appearance in the course of our period

three as-

thought ^^ interwoven that they cannot practically be separated.
And it is indeed not difficult to assume various positions
in contemplating the whole subject from which either one
or the other of the three forms of nineteenth century
thought assumes as it were the ascendancy. Thus it
would be undeniable that from a German point of view
the great movement of ideas centred in the first third of
the century in what I have called philosophy. The
number of systems which succeeded each other was
astonishing, the influence they had on literature, science,
and practical life was without precedent, the enthusi-
asm with which students from all parts gathered in the
lecture - rooms of the great metaphysicians was quite
extraordinary, and probably equalled only in the schools
of Athens in antiquity, or in the lecture-room of Abelard
in the middle ages. From this point of view an account
of this great movement — how it grew, flourished, and
died away — would no doubt afford a suitable introduc-
tion to the history of thought in our century. If after
this we were to turn to France and try to fix upon the

INTRODUCTION. 75

most striking intellectual feature of the century, it would 24.

o ^ French

be the equally great and remarkable array of scientific ^'g'X°ed*in
names of the first magnitude. In France during the jf °J^^^ ^;?Jt
early part of the century the foundation of nearly all the century.
modern sciences was laid ; many of them were brought \^
under the rule of a strict mathematical treatment. It
was there that scientific subjects were made so popular,
and clothed with a garment of such elegant diction, that
they have since that time greatly entered into general
consciousness, and have promoted in literature and art
an independent school — the naturalistic. Compared
with this mathematical and naturalistic spirit, philo-
sophy proper has found but a meagre development and
culture in France : the constructive tendency of ideal-
ism has found nourishment for the most part only in
leanings to the older systems of Descartes, Plato, and
Aristotle, or to the foreign ones of Hegel and other
German metaphysicians. Compared with Germany in
philosophy, and with France in science, England during
the early part of the century appears remarkably unpro-
ductive. English science and English philosophy had
flourished in the seventeenth and eighteenth centuries,
and leavened the whole of European thought, but in the
beginning of our period we find neither represented by
any great schools. The great discoveries in science be-
longed to individual names, who frequently stood iso-
lated ; the organisation and protection which science could
boast of in France was then unknown in England ; into , 25^

° state of

popular thought it hardly entered as an element at all. Pj^[h°|°Priy
Metaphysics had not recovered from the blow which nfnetelnth
David Hume had struck, and speculation was confined England!'^

76 INTRODUCTION.

I almost entirely to the novel field of social and economic
problems. But against this there was a young growth
of ideas springing up in the poetic literature of the
nation. It is the freshness of individual thought as
clothed in the poetic language of Shelley and Words-
worth, maturing and deepening in the works of Tennyson
and Browning, which strikes us as the most original phase
of English thought in this century, whether we compare
it with Continental thought of the same period, or with
English thought of the previous age.

26. And lastly, we might be tempted to make the great

Goethe's

'Faust 're- work of the grcatcst mind of the early part of our period,

presenta- '-' «' ^ •■-

thougiit'of Groethe's ' Faust,' the centre and beginning of our survey,
the century, g^^gj^^g j^; out as a Comprehensive embodiment, as the
classical expression of nineteenth - century doubts and
aspirations, leading us — if we try to understand it —
now into the bewildering labyrinth of philosophy, now
into the cheerful expanse of natural science, and again
into the hidden depths of individual life, of religious
faith with its mysteries of sin and redemption.

But from whatsoever point we may start on our journey,

""^ from whatsoever easily reached eminence we may cast a

first eager glance across the wide country which we wish

to explore, there is one feature which impresses itself

27. alike upon our minds from the very beginning. It is not

A period ^ J o o

pose°but'of ^ country of repose and restfulness, of healthy industry

ferment. ^^^^ quict work, of gradual development, of ripening

crops, of sowing or ingathering ; it does not present the

aspect of a happy division of labour, of successful co-

I operation, of peaceful regulation of employment. It looks

more like a land which has lately been disturbed by

INTRODUCTION. 77

great elemental forces, heaved up by an earthquake or
visited by a destructive storm. We see some persons em-
ployed in filling up great breaches and recently made rents,
others trying to lay new foundations ; others again are
fighting for their possession or trying to divide a disputed
territory ; even the peaceful workers are called out to help
in the battle, or disturbed by the complaints of their
neighbours, on whose ground they are trespassing un-
awares, whose foundations they are unconsciously under-
mining. If we inquire into the cause of this unrest and 28.

Cause of it

anxiety, which seems to be a feature common to nearlv seen in the

■^ century of

all the phases of nineteenth-century thought, we must preciding" t.
look back to the age which immediately preceded it. It
is the storm of the revolution which passed over Europe,
and shook to the foundation all political and social in-
stitutions, that has likewise affected our ideas and thoughts
in every direction. The period we refer to has thus not
incorrectly been termed a century of revolution. If in 29.

Nineteenth

Spite of this I decline to consider nineteenth-century century

•' thought

thought as essentially revolutionary, it is because the ^onar'°^"'
work of destruction belongs in its earlier and more
drastic episodes to the preceding age. The beginning
of our period witnesses everywhere the desire to recon-
struct, either by laying new foundations or by reverting
to older forms of thought and life which it tries to
support by new arguments or to enliven by a fresh in-
terest and meaning. We may say that the thought of 30.
the century in its practical bearings is partly radical, this century

° ^ '' ' partly radi-

partly reactionary, — meaning by the former all those cai, partly
constructive attempts which try to go to the root of '"'^■
things and to build up on newly prepared ground ; by

78 INTRODUCTION.

the latter all those endeavours which, clinging to his-
torical institutions and beliefs, aim at finding the truth
and value which are in them, and the peculiar importance
which they may have for the present day. The work of
destruction is indeed still going on ; in the midst of this
constructive or reconstructive work we still witness the

31. workings of the revolutionary spirit. The healthy new

The thought ^ ^ \ •

of Burns, life which Burns, Wordsworth, and Coleridge infused mto

Words- ' ' *=>

coieHd^e'^ English poetry at the beginning of our period was dis-
the^Byronic^ turbcd iu its quict growth by the revolutionary spirit of
the Byronic school. The new thought, which grew up in
Kant's philosophy and the idealistic school, degenerated in
its further development into a shallow materialism and
a hopeless scepticism. But none of these destructive in-
fluences, however passingly interesting they may have
been, seem to have struck out any new line of thought.

32. Whoever wishes to study the arguments by which social

Destructive J o J

spirit in order was subverted and cherished beliefs destroyed will

writings of ''

ceSiuryf^' find them brilliantly and consistently expounded in the
writers of the eighteenth century, from which many
nihilists of our age have drawn their inspiration. This
is not the task which I have in view. It has been per-
formed in our time by many writers of great eminence.
Nor do I intend to describe the courses which governments
and politicians have taken in dealing with the legitimate
demands of the people, such as a hundred years ago found
a memorable expression in the American Declaration of
Independence, and an exaggerated one in the cry of the
French Eevolution. Only to a small extent has the ideal
of that great movement, as it lives in the mind of many
a democratic leader, been realised in our century. In

INTRODUCTION. 79

most European countries the work of national unification
and consolidation, and the struggle for political indepen-
dence, have retarded internal reforms ; nor have theorists
been able to agree in what form of social organisation
liberty and equality could consistently live side by side.
Their teachino- must indeed command special attention 33.

o ^ Revolution-

as one of the many forms of the philosophic thought of ^o^ p'J.acti!^
the age ; but a wide gap separates theory from practical '^^'"
politics, which have been largely occupied with wars and
diplomatic feats, or, when they really dealt with social prob-
lems, have had to be content with awkward compromises
between prejudices and institutions of bygone ages on the
one side, and legitimate demands for freedom on the other, y'

Though much practical thought and much labour have
been spent in achieving even these moderate results, I feel
that they really fall outside of my programme. Wherever
either science or philosophy steps out of the quiet regions
of the study, the lecture-room, and the laboratory, or
wherever religious faith leaves the secret recesses of the
believing soul to solve the problems of life or to perform
the work of the day, the line is crossed which I have felt
obliged to draw around the following sketch. Not that I
do not recognise this borderland, where the spirit subdues
matter, where thought becomes useful, where the idea
attains reality, this field of strife and endeavour, of patient
toil and slow victory, as by far the most important subject
of history, and as that in which our age has probably ex-
celled every earlier period. But an account of this side of
nineteenth-century life could ill afford to limit its view to
the three principal countries of the Old World. For where
are discovery and invention at this moment more at home

80 INTRODUCTION.

than in America; where have political theories, the original
rights of man, the ideas of liberty, equality, and brother-
hood, been more widely put to the test ; where have reli-
gious beliefs entered into closer contact with the work of
the day ; or where in our age has the simple rule of early
Christianity been more successfully put into practice ?
An account of the application of thought taken merely
from our European experience, where half our endeavour
must always be spent in clearing away obstacles, in
removing the d^ris of antiquated institutions, in over-
coming prejudice, or battling with evils which have grown
to uncontrollable magnitude, would give us but a poor
notion of the influence of thought over material circum-
stances, and a very exaggerated one of the inertia of the
34. mechanism of older societies. With the work of the in-

This is not

a history of vcutor, the practical statesman, or the lawgiver, I have thus

iuvention ^ °

cai°^oMcs ' nothing to do at present ; only in cases where practical
problems have immediately reacted upon scientific research,
or where social questions have given rise to special theo-
ries, shall we be compelled to cast a glance outside of the
inner world of thought into which I invite my readers to
retire.

This inner world has, indeed, not been all rest and peace
and quiet development. No age has been so rich in rival
theories, so subversive of old ideas, so destructive of prin-
ciples which stood firm for many ages, as ours. It is not
my intention to emphasise this critical or radical tendency

Thought to more than is necessary. True to the original view which I

be consid- _

ered in its havc already expressed, I intend to look upon thought as

construe- j r ^ sr ^

Inti^dt ^ constructive, not a destructive agency ; on the world of
atutude^ idcas as a positive acquisition, not as a mere counterpart

INTEODUCTION. 81

or shadow of material existence. Though demanding for
its growth an outer stimulus, and unable to proceed very
far without external correctives, I nevertheless maintain
that the human mind in its individual and collective life
encloses an independent source of reality which contact
with outer things and thought in all its various forms
has to reveal, to preserve, and to develop. To what
extent this has been done in our century is the question
I propose to answer. With this object in view I shall
try to gather my observations and my narrative around
the prominent and novel constructive ideas which have
sprung up in the course of the century, not omitting
the great development which the purely formal side of
thought, the method of research, has undergone. Such
constructive ideas are those of energy, its conservation
and dissipation ; the doctrine of averages, statistics, and
probabilities : Darwin's and Spencer's ideas of evolution 36.

Danvin's,

in science and philosophy ; the doctrines of individualism fnd"Lofa '•
and personality, and Lotze's peculiar view of the world fd^t,™*^*'^^
of " values " or " worths." Around these centres of thought
cluster the many critical oppositions, the great contro-
versies of radical or conservative opponents. As regards
these, I shall welcome all radicalism which lays bare the 37.

The right

roots of our ideas, which delves deep into the ground sortofradi-

^ " calism.

of our opinions and principles, or which points out new
methods by which we may test the correctness and con-
sistency of our axioms. As such I consider the spirit
infused by Kant into all modern thought. That other
radicalism, which merely roots up, which destroys with-
out building, which fails to find any ground of certainty,
simply because human thought and observation may after

VOL. I. F

82 INTRODUCTION.

all be a delusion, — this kind of radicalism I shall try to
pass over as meaningless. And equally meaningless
appear to me those opposite conservative tendencies
which merely annul progress, which shut out the day-
light, and preach the doctrine of inertia. But this, again,
will not prevent me from recognising the real gain and
38. interest which belong to some reacJ;ionary movements,

Reactionary ; . ■ i •< i

movement such as lay at the bottom of Komanticism, with its love

of Romanti-'

cism. , of the past, its artistic idealisation of the childhood of
1 mankind, of aspects of life in their infancy and primitive-
* ness, with its study of medisevalism and its more sober
historical tastes. I shall endeavour always to ask what
addition to the great stock of human ideas has resulted ;
what gain we have to register ; convinced that every-
thing that lives must grow, increase, and multiply : and
what can be more living than Thought ?

But although the school of Critical Thought in Kant,
and the Eomantic school as centred in Walter Scott and
the German Eomanticists, are in time almost the first
intellectual phases of the century, they will not in the
beginning command my special attention.^

^ In order to give some idea of the complexity of the different currents
of thought in the first years of the century, I place here a carefully
selected list of dates. They refer to events or publications which mark
epochs or important stages in the history of thought. Of specifically
scientific importance are —

1796. Laplace's 'Exposition du Systeme du Monde.'

1799. (2 vols.) — 1825. Laplace's ' M(?canique celeste.'

1799. Legendre's ' Theorie des Nombres.'

1801. Gauss's ' Disquisitiones ArithmeticcC. '

1801. Piazzi discovers and

1802 Olbers rediscovers the first of the minor planets, "Ceres," being
assisted by Gauss's new methods of calculation, which were
published in extenso in

1809. Gauss's 'Theoria motus corporum cojlestium.'

1798. Cuvier's 'Tableau dlementaire d'Histoire naturelle.*

1800-5. Cuvier's ' Lemons d'Anatomie compar^e.'

INTRODUCTION. 83

Though somewhat later in point of time than they, the
school of exact research seems to have become the more
generally recognised agent in nineteenth-century progress.

1809. Lamarck's ' Philosophie zoologique.'

1799. Volta constructs his first electric pile, and announces this in

1800 to Sir Joseph Banks.

In chemistry the early years of the century brought many of Gay-
Lussac's important Memoirs, in

1801 Humphry Davy publishes the first of his electro-chemical dis-

coveries, and
1802-3 Berzelius publishes his own.
1803. BerthoUet's ' Essai de Statique chimique. '

1810. John Dal ton's ' New Sj'stem of Chemical Philosophy.'

1801. Thomas Young announces to the Royal Society his belief in the

undulatory tlieorj^ of light, which during

1802, 3, and 4 he substantiates further in his papers, and fully expounds

during

1802 and following j-ears in his lectures to the Royal Institution.
1808. Malus announces his discovery of the polarisation of light through

reflection.

1802. Chladni's ' Akustik.'

Count Rumford's papers, which laid the foundation of the mechanical
explanation of heat, belong to the end of the last century, and in

1799 H. Davy publishes his equally important 'Essay on Heat, Light,
&c.'

1800. Bichat's ' Recherches physiologiques.'

1801. Bichat's ' Anatomic genJrale. '

1799-1804. Alexander von Humboldt travels in America, and lays by
his observations the foundation of the sciences of physical
geography and meteorology.

For the history of the philosophical movement of thought the years

1793-1806 witnessed in Germany the great development, expansion, and
criticism of Kant's ideas in the writings of

1793 Schiller, ' Briefe liber iisthetische Erziehung.'

1796. Schiller, ' Uber naive und sentimentalische Dichtung. '

1797. Fichte, ' Wissenschaftslehre.'
1797. Schelling, 'Naturphilosophie.'

1803. Schelling, ' Transcendentaler Idealismus. '

1799. Schleiermacher, ' Reden liber die Religion.'

1800. Schleiermacher, ' Monologen.'
1799. Herder, ' Metakritik.'

1799. Jacobi, ' OfEener Brief an Fichte.'
1806. Hegel, ' Phiinomenologie des Geistes.'
In France —

1804. Destutt de Tracy's 'Iddologie' represents the reigning philo-

sophy, and

1803 Maine de Biran's ' Mdmoire sur I'Habitude' the beginning of the

later reaction against it.
In England —
1792-1827. Dugald Stewart's 'Elements of the Human Mind' and his

84 INTRODUCTION.

To it are due the great changes in every department of
science, of life, and probably also of literature and art,
the great inventions and the great conflicts of our age.
Science has not only very largely influenced our ideas,
it has also by its applications altered the external face
of the world we live in. It is therefore simply a tribute
to the popular view, and a desire to start from some
striking and generally conceded position, if I select the
39. scientific movement of ideas as the first with which

Scientific

progress to I have to deal. How has it spread in the course of

be consid-

ered first. t;he ccutury ? From what beginnings and through what
influences ? What are its principles and methods ? How
have they themselves changed and developed ? What
has it led to ? These are some of the questions which

1803 ' Life and Writings of Thomas Reid ' represent the predominant

Scottish philosophy, and

1804 Thomas Brown, 'Inquiry into the Relation of Cause and Effect,'

the beginnings of the later associationalist school. At the same
period Jeremy Bentham's influence, which cannot be reduced to
special dates, had already acquired Eluropean if not world-wide
importance. His long life (1748-1832) was contemporary with
Goethe's (1749-1832), whose ' Faust' was given to the world in
successive stages between the years 1790 and 1832.

1794. Thomas Paine's 'Age of Reason.'

1798. Malthus's 'Principles of Population.'

Literary criticism started on a new era and extended its influence in

1802 through the 'Edinburgh Review,' and

1808 the 'Quarterly Review' ; in Germany somewhat earlier in

1794 Schiller's 'Horen.'

1797. Schiller and Goethe's " Xenien " in the ' Musenalmanach.'

1798. Schlegel's ' Athensoum.'

1802. A. W. V. Schlegel's Berlin lectures.

The Romantic school of fiction dates in Germany from 1798, when
Frederick Schlegel uses the term for the first time as characteristic of
a new departure in his review of Goethe's ' Wilhelm-Meister ' (' Athentcum,'
vol. i.) A literary movement with frequently similar aims and charac-
teristics is represented in this countrj' by Walter Scott (" Lay of the Last
Minstrel," 1805), Southey ("Thalaba,"1802), and Coleridge (" Christabel,"
1806), and spreads later into France. As the great source of the new
and original poetic inspiration of nineteenth-century poetry we have the
" Lyrical Ballads," 1798, and besides ' Faust,' the other principal works of
Goethe and Schiller (died 1805).

INTKODUCTION. 85

I shall try to answer as concisely as possible. This
selection does not commit me to any theory on the
value of the scientific view as compared with other
aspects. Such theories will have to be dealt with in a
later portion of the work. They have sprung up in the
course of the last hundred years, partly as the inevitable
outcome of scientific progress itself, partly in the educa-
tional world, where a reaction has set in against the
undue importance which former generations attached to
classical learning and training. I need not at present
do more than note these opinions, nor need I define
my position with regard to Comte's celebrated positivist
theory on the advancing stages of the human intellect.
Curiosity and the consensus of popular opinion suffice
for the moment to make me take up the scientific side
of the thought of the age. As we proceed, other directions
and movements will present themselves, and the inter-
dependence of all human interests will reveal and explain ^^
what truth attaches to Hegel's celebrated doctrine of the umloffhe
inherent dialectic of ideas, the spontaneous development deveiop-'^"'^''

meut of
of thought. thought.

A HISTORY OF EUROPEAN THOUGHT IN
THE NINETEENTH CENTURY

PART I.
SCIENTIFIC THOUGHT

89

CHAPTER I.

THE SCIENTIFIC SPIRIT IN FKANCE.
It will be generally admitted that the scientific spirit is i-

^ '' ^ Our century

a prominent feature of the thought of our century as gentu'^^*'^*'
compared with other ages. Some may indeed be in-
clined to look upon science as the main characteristic
of this age. The century may thus be called with some
propriety the scientific century, as the last was called the
philosophical century, or as the sixteenth was termed the
century of the Eeformation and the fifteenth the century
of the Eenaissance. It is therefore natural that we should
begin our study of the thought of the age with an ex-
amination of this side of modern culture.

It is not necessary to define what I mean by science.^

^ The use of the word science
and its adjective scientific has
varied considerably in the English
language. We must wait for Dr
Murray's great work to give us a
history of the word. I venture to
assert that it acquired its present
definite meaning about the time of
the formation of the British Asso-
ciation for the Advancement of
Science (1831). The two other
great organisations which profes-

sedly started for the culture of
what we now call science — viz.,
the Royal Society for the Improve-
ment of Natural Knowledge, and
the Royal Institution — did not use
the word officially in their charter
or title, although it is used fre-
quently in the documents and cor-
respondence connected with the
foundation of the younger, and
occasionally in those referring to
the older Society. The Royal So-

90

SCIENTIFIC THOUGHT.

Schools and colleges of science, triposes, examinations,
and degrees in science, have established a popular mean-
ing which did not exist a hundred years ago, but which
is now well understood. For my purpose it is of some
interest to note that the meaning of the word in French
is somewhat different, and that the word Wissenschuft}

ciety, and sometimeci the Royal
Institution, use the word " philo-
sophy " in formal and official state-
ments of their object. This is in
accordance with older English
usage. What we now universally
call science was not infrequently
termed in the seventeenth century
natural knowledge, and Bacon him-
self translates scienticE by " know-
ledge," by "learning," and some-
times by "sciences." In France,
on the other hand, the word "sci-
ence" seems to have acquired its
present meaning as far back as the
middle of the seventeenth century.
At the time of the foundation of
the "Academie des Sciences," in
1666, the word was used almost in
the same sense — embracing the
same separate departments of know-
ledge— as the word " science" is now
used in this country when we speak
of a college of science. In France,
so far as I am aware, a cultivator
of science has never been called a
philosopher. Science and philos-
ophy have there never been synony-
mous. But science in France has
been made to cover a larger field
of knowledge by such adjectives as
"moral," "social," " political," and
has been narrowed by such other
adjectives as "exact"and "natural,"
in the same way as the word philos-
ophy has been more strictly defined
in the Englisli language by the ad-
jectives "natural," "experimental,"
"moral," "mental," &c. At the
head of the sciences in France stood
"mathematics," at the base of the

new philosophy in England stood
" experiment" and "observation."
■* The word Wissenschaft has a
much wider meaning than science
in the modern sense, and is the
literal translation of the Latin
scientia. It means knowledge in
a systematic form and connected
bj' some method. What the French
call science, the Germans call exacte
Wissenschaft. This includes mathe-
matics and Naturivissenschaf t,\Y\nch
covers the ground covered by the
word " sciences " in English. The
word Wissenschaft plays an import-
ant part in German culture, as we
shall see later on. The modern
term "scientist" is about synony-
mous with the word Naturforscher
in German. The word savant in
French has no synonym in English,
but is about equivalent to the term
Gelehrter in German ; and this,
again, is partially translated by
"scholar" in English. I suppose
"man of science" and "scholar"
together would be about covered by
either savant or Gelehrter. Those
who desire to study the older and
modern, the English and foreign,
uses of the word science and other
kindred terms, should read Bacon's
English writings ; Weld's ' History
of the Royal Society ' (1848, vol. i.);
Bence Jones's ' The Royal Institu-
tion ' (1871); L^on Aucoc's 'L'lnsti-
tut de France ' (Paris, 1889); Alfred
Maury, ' Les Academies d'autrefois'
(vol. i., Paris, 1864) ; and the cor-
respondence in connection with the
foundation of the British Associa-

THE SCIENTIFIC SPIRIT IN FRANCE.

91

notions of
science.

by which science is translated into German, requires a
qualification in order to cover approximately the same
ground. These verbal differences point to differences of ^.^ 2.

o •"• Difference of

thought. Only since Continental ideas and influences cont'iMnte'i
have gained ground in this country has the word science
gradually taken the place of that which used to be
termed natural philosophy or simply philosophy. One
reason why science forms such a prominent feature in
the culture of this age is the fact that only within the
last hundred years has scientific research approached the
more intricate phenomena and the more hidden forces
and conditions which make up and govern our everyday
life. The great inventions of the sixteenth, seventeenth, ]
and eighteenth centuries were made without special
scientific knowledge, and frequently by persons who
possessed skill rather than learning. They greatly in-
fluenced science and promoted knowledge, but they were
brought about more by accident or by the practical re-
quirements of the age than by the power of an unusual
insight acquired by study.'^ But in the course of the last

tion in Dr Whewell's ' Writings and
Correspondence ' by Todhunter (2
vols., London, 1876). I believe the
word philosophy has lost the specific
meaning which it acquired in the
Baconian school, as much through
the influence of French science on
the one side as through that of
metaphysics on the other. The
latter emanated from Scotland, and
from Germany through Coleridge.
It reinstated the word philosophy
in its original sense.

^ Examples are plentiful. Not to
speak of gunpowder and printing,
which came earlier, we have later
nearly all the great improvements

connected with the manufacture of
textiles, the fly-shuttle, the self-
acting mule, the power- loom, the
spinning - roller, invented by men
of little or no scientific education.
The same is the case with the
older metallurgical processes, the
refining of copper and the intro-
duction of cast - iron. Watt was
one of the first who brought a
trained intellect to his mechan-
ical work. The Royal Society was
started with the distinct purpose
of cultivating such knowledge as
has " a tendency to use " ; the
Royal Institution still more so. It
is, however, still doubtful, view-

92

SCIENTIFIC THOUGHT.

hundred years the scientific investigation of chemical and
electric phenomena has taught us to disentangle the
intricate web of the elementary forces of nature, to lay
bare the many interwoven threads, to break up the equili-
brium of actual existence, and to bring within our power
and under our control forces of undreamed-of magnitude.
3. The great inventions of former ages were made in countries

Relation of • i t p • i

science and wlicrc practical life, industry, and commerce were most
"^^- advanced ; but the great inventions of the last fifty years

in chemistry and electricity and the science of heat have
been made in the scientific laboratory : the former were
stimulated by practical wants ; the latter themselves pro-
duced new practical requirements, and created new spheres
of labour, industry, and commerce. Science and know-
ledge have in the course of this century overtaken the
march of practical life in many directions.^ A confused

ing the history of the learned
societies as well as the rare cases in
which highest scientific genius is
allied with practical skill in the
same person, whether the cultiva-
tion of research for its own sake
should not preferably be kept dis-
tinct from its hasty application.
This is the view held by many great
thinkers abroad. In England the
opposite view has frequently im-
peded the progress of pure science.
^ A few examples may suffice.
The discovery by Oersted and Am-
pere of Electromagnetism (1819,
1820) led at once to the idea of
electrical telegraphy : the first tele-
graph over considerable distances
was constructed by Gauss and
Weber (see ' Wilhelm Weber,'
Breslau, 1893, p. 26, &c.) The
artificial preparation of an organic
substance by Wohler in 1 828 led at
once to many attempts at prepar-
ing expensive organic compounds —

especially medical substances — by
chemical synthesis. The occupa-
tion with this problem under A. W.
Hofmann's instructions led Perkin
in 1856 to the discovery of the first
anilin colour (Mauvein, see ' Ber-
ichte der deutschen chemischen
Gesellschaft,' No. 17, p. 3391).
Leblanc's discovery how to make
carbonate of soda from salt, for
which a prize had been offered by
the Paris Academy under Napoleon,
led to the enormous development
of the sulphuric acid industry in
England and on the Continent.
Liebig foretold in 1840 the recovery
of sulphur from the waste of chemi-
cal works and the effect on the
sulphur mines of Sicily, fifty years
before this process was satisfactorily
carried out (see Liebig's familiar
'Letters on Chemistry,' 1st ed., 1843,
pp. 22, 31, &c.) But the greatest
of all industries created in the
laboratory was probably that of

THE SCIENTIFIC SPIRIT IN FEANCE.

93

picture of this latest stage of culture lived in the pro- i. ^

J- <=> ^ Foreseen oy

phetic but essentially unscientific mind of Lord Bacon. Lwd Bacon.
But he did not sutficiently allow for the amount of patient
scientific toil that was needed, nor for the time which the
preparation of the instruments of research would require,
nor for the necessity of destroying existing superstition
and accumulated errors. All that has since been done by
Newton and the great Continental mathematicians in the
former, and by Bayle and Voltaire in the latter sense,
Bacon had hoped to achieve at once by the new philo-
sophy of fruit and progress. Such expectations were
inevitably doomed to disappointment, though posterity
has made amends by all but universally referring to him
as the pioneer of modern thought, — as the herald of a
new era of human civilisation.^

making artificially the fertilising
compounds required in common
agriculture •which followed on the
publication of Liebig's famous work
on ' Chemistry in its applications
to Agriculture and Physiology ' in
1840 (see Hofmann's Faraday
Lecture of 1875, 'The Lifework of
Liebig,' p. 15, &c.) Liebig also
discovered and described in 1832
the properties of chloroform and
chloral, fifteen years before Simpson
introduced the first as an ansesthetic
and twenty years before Oscar
Liebreich discovered the physiolog-
ical action of chloral (ibid., p. 101,
&c.) Sir Lowthian Bell calculated,
many years before the invention
of the so-called basic process of
making steel, the fertilising value
of the phosphorus which was con-
tained in the ironstone of Cleve-
land, and which then made it use-
less for the manufacture of high-
class iron and steel. The great
revolution in the theorv of the

steam-engine embodied in the work
of Macquorn Rankine is to be traced
back to the patient measurements
by Joule of the mechanical equiva-
lent of heat.

^ A great controversy arose on
this subject through the publica-
tion of Liebig's pamphlet in 1862,
entitled, ' Francis Bacon von Veru-
]am und die Methode der Natur-
forschung.' It was directed mostly
against the exaggerated view taken
by Macaulay in his celebrated essay.
The fact is that Bacon, like Vol-
taire after him, was much more
of an essayist and a man of the
world than a patient labourer in
any special field of research ; he
was more of a philosopher in a
worldly sense (what the Germans
call "ein Weltweiser") than a pro-
found thinker. He misunderstood
manj' of the great discoveries of his
age, though he prophetically fore-
saw the great change in the spirit
of inquiry. He did not appreciate

94

SCIENTIFIC THOUGHT.

Defect in

Bacon's

philosophy.

Our age has in many ways inherited the spirit of
Bacon's philosophy ; but it would be a mistake to attri-
bute its great scientific achievements to the exclusive
working of this spirit. Bacon was neither a retired and
patient nor an accurate thinker — the desire to apply and
make his learning useful led him away from the " sapien-
tum templa serena " into the forum of life : in his own
experience, as well as in his writings, he anticipated many
of the dangers which beset modern culture — the love of
premature application, and the haste for practical results
and achievements. Science, which in the hands of patient
and diligent observers ^ had just been rescued from the
sway of empty metaphysical and theological reasoning,

the enormous part which mathe-
matics would play in the develop-
ment of science. In this respect
Descartes was a genius of much
greater originality — his actual con-
tributions to scientific progress, as
well as those of Pascal, being far
beyond those of Bacon ; but they
both retained the metaphysical
habit of thought which has char-
acterised many, if not all, among
the greatest mathematicians. In
modern culture the popularisation
of novel views and ideas has become
so important a factor that writers
like Bacon and Voltaire, who com-
bine the scientific and literary taste,
are of the greatest importance in
the diffusion of new ideas, though
none of their works need be looked
upon as great repositories of re-
search and knowledge. Before Lie-
big wrote his pamphlet, a very im-
partial and temperate estimate of
Bacon's philosophy and its relations
to actual science was published by
Robert Leslie Ellis in his introduc-
tion to the philosophical works of
Lord Bacon (London, 18.57). As

the literature of the subject is so
large, 1 cannot but recommend this
essay as containing one of the best
discussions of it.

^ A very good and concise account
of the achievements of these con-
temporaries and forerunners of Ba-
con—of Tycho (1516-1601), Kepler
(1571-1630), Galileo (1564-1642),
Gilbert (1540-1603), Harriot (1560-
1621), Napier (1550-1617), Harvey
(1578-1656) — is given by John
Niohol in the second volume of his
' Francis Bacon, his Life and Philos-
ophy ' (Edinb., 1889), pp. 86, 254.
In the same volume (p. 193) there
is also a useful summary of Bacon's
real claims to a place among physi-
cists, of his ignorances (p. 196), and
of the reception which his works
met with in England and abroad
(p. 233 to end). Not quite so read-
able, but more complete, is the
little volume of Hans Heussler,
' F. Bacon und seine geschichtliche
Stellung' (Breslau, 1889), with its
flood of references — which exhaust
the subject. See especially p. 160,
&c., on Bacon's anticipations.

THE SCIENTIFIC SPIRIT IN FRANCE. 95

was in danger of falling a prey to hasty generalisation
for the purpose of practical ends. Practical demands
threatened then, as they frequently still do, to stifle for
to force into premature growth the patient thought which
had just begun to germinate in the new light and freedom
of reason. The narrow view had indeed been widened,
and the breadth of the land had been surveyed, but there
was little inclination to deepen the view, or to do more
than search on the surface. The spirit of Bacon's philo-
sophy required a corrective. For a long time to come the
hope of practical application had to be postponed ; the
thinker and student had to retire into solitude, and there
to lay the more permanent foundations of the new re- 6.
search. This was done by Newton for all time. His byNe\\i;on.
reputation spread more slowly than that of the great
High Chancellor; but it rests on a surer foundation,
which baffles every attempt to shake it, and will outlast
all coming changes of thought.

The beginnings of modern scientific thought are thus to
be found in this country. Lord Bacon foretold propheti-
cally the great change which the new philosophy was
destined to work. Newton more patiently drew up the
first simple rules and gave the first brilliant application.
More than the unfinished and wearisome pages of Bacon's
' Novum Organum ' does the ' Principia ' deserve to be
placed on a line with Aristotle and Euclid as a model
work of scientific inquiry.

For a real recognition of the greatness of Newton, as well 7.

. . . , Bacon's and

as for a partial realisation of Bacon s plans, we are, however, Newton's

■^ ideas taken

mainly indebted to the French philosophers of the second '^p^^^j^ j^jj
half of the eighteenth century. Bacon's plan of promoting °^°^^^'^^-

96

SCIENTIFIC THOUGHT.

8.
Bacon and
Newton
compared.

knowledge and research by the co-operation of many was
more thoroughly realised in the old French Academy
than in the Eoyal Society of London : his desire to unite
all knowledge in a collective work underlies the great
productions of Bayle, and still more those of the Ency-
clopaedists. The many problems contained in Newton's
' Principia ' were first treated singly by Clairault and
Maupertuis ; a general knowledge of his view of the
universe was introduced into popular literature by Vol-
taire/ who made use of it as a powerful weapon wherewith
to combat error and superstition, or, as he termed it, " pour
ecraser I'infame " ; but for a full announcement of its
scientific value and its hidden resources we are indebted
to Laplace, whose ' Mecanique celeste ' was the first
comprehensive elaboration of Newton's ideas, and whose
' Systeme du Monde ' became the scientific gospel of a
whole generation of Continental thinkers.

We may look upon Lord Bacon as one who inspects a
large and newly discovered land,^ laying plans for the

' 1 believe Voltaire was the author
of the term Neivtonianisme. The
modesty and truly scientific spirit
of Newton would not have allowed
him to apply such a term to his
work, and it is doubtful whether
Voltaire did not extract from
Newton's ' Philosophia Naturalis ' a
general philosophy which was not
conceived in his spirit.

^ Cowley in his Ode to the Royal

Society : —

" Bacon at last, a mighty man, arose, . . .
And boldly undertook the injur'd pupil's
cause.

. . . led us forth at last,
The barren wilderness he past ;

Did on the very border stand

Of the blest promis'd land ;
And, from the mountain's top of his ex-
alted wit,

Saw it himself, and shew'd us it."

On this Mr Ellis remarks (Bacon's
Works, vol. i. p. 63) : '" Bacon has
been likened to the prophet who,
from Mount Pisgah, surveyed the
Promised Land, but left it for others
to take possession of. Of this happy
image, perhaps part of the felicity
was not perceived by its author.
For though Pisgah was a place of
large prospect, yet still the Prom-
ised Land was a land of definite
extent and known boundaries, and,
moreover, it was certain that after
no long time the chosen people
would be in possession of it all.
And this agrees with what Bacon
promised to himself and to man-
kind from the instauration of the
sciences. ... In this respect, as in
others, the hopes of Francis Bacon

THE SCIENTIFIC SPIEIT IN FRANCE.

97

development of its resources and the gathering of its
riches. But the wealth lies deep down, and is only indi-
cated by the first labours of the early pioneers. Newton,
following these, unites their beginnings into a systematic
exploration, and sinks the main shaft which reaches the
lode of rich ore. He opens out the wealth of the mine
and marks out the work for his followers. But many
difficulties had to be overcome, much united effort and
a vast organisation of labour were required, in order to
develop to the full Newton's scheme, and to raise the
great treasure which he had reached. This was not done
until the end of the last century, when Laplace collected, 9.
arranged, and condensed the work of French and English work,
mathematicians and observers into a picture of the uni-
verse. A variety of circumstances had combined to make
the French capital the place above all others where the
means and materials for the development of the great
work could be most easily procured. Let us glance for
a moment at the different factors in operation during
the eighteenth century which contributed to the great
achievement.

Whilst ISTewton was labouring privately and almost
unassisted ^ at the greatest scientific work produced in

were not destined to be fulfilled.
It is neither to the technical part
of his method, nor to the details of
his view of the nature and progress
of science, that his great fame is
justly owing. His merits are of
another kind. They belong to the
spirit rather than to the positive
precepts of his philosophy."

^ It has been stated that New-
ton, not knowing of Norwood's ap-
proximately correct determination

VOL. I.

of the length of a degree in 1635
(published in his ' Seaman's Prac-
tice' in 1637), but relying on the
old figure of sixty miles for a de-
gree of latitude (confirmed by Ed.
Wright, Cambridge, 1610), was led
away from the right supposition,
which he entertained as far back as
1665, regarding the moon's orbit,
and had to wait for Picard's figures
(ascertained about 1669, published
in F'rance about 1672, and in the

G

98

SCIENTIFIC THOUGHT.

modern times by any single mincl,^ the penetrating and
far-seeing genius of Colbert had already recognised the
important part which science would one day play in
the government of the world, and had secured the ap-
proval of his royal master to the constitution of an Aca-

Philos. Transactions in 1675), by
applying which he determined that
" the moon appeared to be kept in
her orbit purely by the power of
gravity." See Brewster's ' Life of
Newton,' vol. i. p. 290, &c. ; Tod-
hunter's ' History of the Theories of
Attraction,' vol. i. p. 38, &c. This
account is, however, now discredited
(see infra, chap, iv.) For the part
which iJr Hooke and Halley took in
the discover}' of the " reciprocal
duplicate " ratio, see also Brewster,
loc. cit., vol. i. p. 291, &c. During
the writing of the ' Priiicipia ' New-
ton carried on a useful correspond-
ence with Flamsteed, who was then
Astronomer-Roj'al. Howthishappy
co-operation ceased ten years later
can be read at length in Brewster
{loc. cit., vol. i. p. 312 ; vol. ii. p. 164,
&c.) The greatest material assist-
ance which Newton received was
from Halley, who defrayed the ex-
penses of publishing the ' Principia,'
after the Roj'al Society, to which it
was dedicated, had reversed its resol-
ution to defray them (Brewster, vol.
i. p. 305, &c. ) Nevertheless Weld, in
his 'History of the Royal Society,'
says: "Fortunate indeed was it for
.science that such a bodj^ as the Royal
Society existed, to whom Newton
could make his scientific communi-
cations ; otherwise it is very possible
that the ' Principia ' would never
have seen the light." Though one
must lament the difierences be-
tween Flamsteed and Newton, which
prevented the latter from bring-
ing his investigations of the lunar
and planetary theories to a close
(Brewster, vol. i. p. 312), a word of

deep gratitude is due to Flamsteed's
own exertions in the cause of astro-
nomy. After Charles II. had built
the Observatorj'^ in order to have
the places of the fixed stars " anew
observed, examined, and corrected
for the use of his seamen" (Flam-
steed, History of his own I^ife), and
after he had appointed Flamsteed
Astronomer - Royal at a salary of
£100 per annum, the Observatory,
" hurriedly established, was left for
a period of nearly fifteen years
without a single instrument being
furnished by the Government "
(Weld, vol. i. p. 255). The instru-
ments were mostly supplied by
Flamsteed himself orient by others,
and besides, " the king had ordered
that Flamsteed should instruct
monthly two boys from Christ
Church Hospital, which was a great
annoyance to him, and interfered
with his proper avocations " (Baily,
'Account of the Rev. J. Flamsteed').
" Anj' other man would probablj-
have succumbed under the amount
of drudgery appertaining to the
office (earning his salary by labour
harder than thrashing), if indeed,
in the absence of encouragement,
he would have continued in it at
all, aud particularly when the re-
ward was so insignificant" (Weld,
vol. i. p. 256).

1 "And it may be justly said,
that so many and so valuable Phil-
osophical Truths, as are herein dis-
covered and ])ut past dispute, were
never jet owing to' the Capacity
and Industi-y of any one Man "
(Words of Halley, Philos. Transac-
tions, vol. xvL, 1687).

THE SCIENTIFIC SPIRIT IN PRANCE.

99

demy, which was based upon the endowment of research,
and which prompted the co-operation of its members in
organised ^ scientific work. Whilst the Eoyal Society of
London only received a charter, and existed by the en-
trance payments and contributions of its own members,
augmented by private donations, the Paris Academy had, lo.
as far back as 1671, received the funds with which to Academy

' of Sciences.

commence its labours in connection with the survey of
the kingdom and its extensive dependencies. It was these
labours which led to the measurements of the length of
the seconds pendulum, and of the variation of gravity in
different latitudes ; to the explanation of this variation
by Huygens ; to the controversy regarding the figure of
the earth ; to the direct measurements of the arcs of the
meridian in Peru and Lapland ; and, finally, to Clairault's
celebrated work on this subject." It was almost exclu-
sively by these observations that the data were found
with which to substantiate Newton's mathematical reason-
ings : in his own country that fruitful co-operation which

1 " Le roi assurait I'existence des
Academiciens par des pensions et
mettait liberalement a leur disposi-
tion un fonds destine a pourvoir aux
frais de leurs experiences et de leurs
instruments" (Maury, ' Les Acade-
mies d'autrefois,' vol. i. p. 13). Or-
ganisation and co-operatiou are diffi-
cult to obtain in societies founded
on private and voluntary contribu-
tions. In England they scarcely ex-
isted before the foundation of the
British Association, with perhaps
one illustrious exception pointed
out by Struve ( ' Description de I'Ob-
servatoire de Pulkowa,' 4to, Pdters-
bourg, p. 5) : " II y a, dans I'histoire
de I'observatoire de Greenwich, un
point tres remarquable, savoir que

les astronomes ont travaille sur
un nieme plan, depuis I'origine de
I'etablissement jusqu'a I'epoque
actuelle." Organisation and co-
operation were the order in the
Paris Academy from the beginning.
" On y travaillait de concert " ; and,
" Des les premiers mois de 1667,
Perrault proposa un plan de travail
pour la physique, c'est h, dire pour
I'ensemble de I'histoire naturelle"
(Maury, loc. cit., p. 15).

" A full account of these is given
in Todhunter (' Hist, of Theories of
Attraction, &c. ,' vol. i.) Clairault's
book was published in 1743, and had
the title, ' Thdorie de la Figure de
la Terre, tiree des Principes de
I'Hydrostatique, par Clairault.'

100

SCIENTIFIC THOUGHT.

11.

Continental
methods in
mathe-
matics.

can only be secured by an academic organisation and by
endowment of research was wanting. No one since the
time of Bacon had been more impressed with this neces-
sary condition of modern progress than Newton's great
rival, Leibniz,^ much of whose time was spent in pro-
moting academies all over Europe — in Berlin, St Peters-
burg, Dresden, and Vienna — and who had himself been
early attracted to Paris and London by the scientific
fame of their learned societies, though he significantly
pointed out the want of activity and efficiency in the
early history of the Eoyal Society.

There was, moreover, another and independent line
of scientific thought which had centred in Prance,
the development of which came greatly to the aid of
the students of Newton's work. This was the purely
mathematical elaboration of the various infinitesimal
methods of the French and English mathematicians, by
which they were all brought together, simplified, and
united into a calculus with strict rules, a practical nota-
tion, and an easy algorithm. Newton himself had for the
purposes of his great work invented a new and powerful

^ A collection of Leibniz's writ-
ings on this subject will be found
in the 7th volume of M. Foucher de
Careil's edition of Leibniz's Works,
Paris, 1875. Of the projects of
Leibniz, only the Academy of Berlin
came into existence during his life-
time (1700 and 1701) ; the others
were discussed at great length with
the Elector of Saxonj-, with the Em-
peror, and with Peter the Great.
The Academy of St Petersburg was
founded in 1724, eight years after
the death of Leibniz. The Academy
of Vienna did not come into life till

1846, and in the same year that of
Saxony was founded, which has its
seat at Leipsic. Leibniz had the
largest views on academic life and
work : they were to embrace the
historical and philosophical studies
as well as the purely scientific, and
were to stand in relation with the
higher and lower educational in-
stitutions. His ideas are best
realised at Berlin. See Jacob
Grimm's interesting discourse, en-
titled 'Ueber Schule Universitiit
Akademie' (Kleine Schriften, vol,
i. p. 211, &c.)

THE SCIENTIFIC SPIRIT IN FRANCE.

101

instrument, afterwards called " the method of fluxions " ;
but he had not made it generally known before the
invention of Leibniz was published.^ This, though much
later in time, had been perfected and applied by his
friends and followers in a most extensive manner, and
had, in fact, become the recognised mathematical lan-
guage of the Continent. No learned body did more than
the Paris Academicians to perfect (with purely scientific

^ Leibniz seems to have been in
possession of his method as early
as 1675, and communicated it to
Collins in 1677. It was, however,
not published before 1684 iu the
' Acta Eruditorum,' and then jorob-
ably only on account of some writ-
ings of Tschirnhausen trenching on
the same subject. Newton seems
.to have been in i^ossession of his
methods as early as 1665, fully ten
years before Leibniz made use of
his. Immediately after the publi-
cation of Leibniz's paper in 1684,
the differential calculus was taken
up by the Continental mathema-
ticians, especially by James Ber-
noulli (1654-1705) and John Ber-
noulli (1667-1748), and the Mar-
quis de I'Hopital, who published
the first treatise on the new calculus
in 1696. Newton did not publish
any account of his method, though
he must have used it extensively in
arriving at the results contained
in the ' Principia.' Different views
have been expressed on the reasons
which induced Newton to withhold
from publication his new methods,
and the question to what extent
Leibniz owed the first suggestions
of his method to Newton remains
also undecided. Those who take
an interest in the personal question
should refer to the original docu-
ments, the ' Commercium Epistoli-
■cum,' published by the Royal Society
in 1715 ; the pamphlet of Gerhardt,

' Die Erfindung der Differential-
rechnung' (Halle, 1848). An ex-
treme view, unfavourable to Leib-
niz's originality, is taken by Sloman,
' Leibnitzens Anspruch auf die
Erfindung der Differentialrech-
nung ' (Leipzig, 1857) ; but it has
not been generally adopted by those
who have examined into the subject.
As to the superiority of the Conti-
nental notation for practical pur-
poses, this seems to have been
generally admitted at the beginning
of this century, when it was intro-
duced into English mathematical
works. In the school of \V. R.
Hamilton of Dublin the notation
used by Newton acquired a peculiar
importance, and it is still occasion-
ally used in some important works
like Tait and Steele's 'Dynamics
of a Particle,' and Thomson and
Tait's ' Natural Philosophy. ' See
on this Tait's article on Hamilton in
the ' North British Review ' (Sept.
1866). The importance of the
labours of the Continental school,
headed by Leibniz, for the diffusion
of the new methods, is well de-
scribed by Remont de Montmort in
a letter to Brook Taylor, dated 18th
December 1718, and given in the
appendix to Brewster's ' Life of
Newton ' (vol. ii. ij. 511, &c.) Those
who take more interest in the fate
of ideas and the progress of thought
than in personal matters will do
well to read this letter.

102 SCIENTIFIC THOUGHT.

interest) this new calculus, which in the course of the
eighteenth century had in the hands of Lagrange been
adapted to all the purposes and problems contained or
suggested in Newton's ' Principia.'
12. This leads me to a third and yet more important element

Modern "^ -^

method?^ of Scientific thought, which was peculiar to the Continental,
and especially to the French mathematicians, counting
among them Leibniz, who, though a German, was wholly
trained in the French school. This factor is the estab-
lishment of pure mathematics on an independent founda-
tion, and the cultivation of research into the abstract
relations of quantity, without reference either to geomet-
rical or mechanical problems and applications. It is
the modern analytical spirit introduced by the great
French algebraists of the seventeenth century, which
looks upon geometry, mechanics, and astronomy merely
as " questions d'analyse," and makes their solutions de-
pend upon the perfecting of an abstract calculus rather
than on the study of these individual problems them-
selves. Opposed to this spirit of analysis, which in
general seeks the solution of any given question by
looking upon it as a special case of a wider and more
abstract problem, is the method known to the ancients,
_:which never loses sight of the actual application, be it a
figure in geometry or a special arrangement of physical
forces, and is more interested in the peculiarities of the
individual case than in the abstract formula of which it
may be considered an application. This opposite view
regards the calculus and mathematics in general merely
as an instrument, the value of which lies solely in its
application to real physical problems. It is usually

THE SCIENTIFIC SPIRIT IN FRANCE.

103

termed the synthetical method, and has in modern times i3.

. ^ Older syn-

survived principally in England, where inductive reason- ^^l^l^^l
ing, based upon observation of detail, has since the age
of Lord Bacon been most successfully cultivated.^ These
different ways of approaching the same subject will fre-
quently engage my attention in the course of this survey:
the greatest mathematicians of modern times have recog-
nised the importance of both aspects, and the enormous
progress of the science itself has depended, no doubt, on an
alternating employment of them. Leibniz clearly foresaw
this when, in his correspondence with Huygens and others,
he urged the necessity of not abandoning the purely geo-
metrical view, or entirely sacrificing the older for the
modern methods.^ There can, however, be no doubt that

1 See on this point the opinion of
an authority, Hermann Hankel, in
his highly interesting and sugges-
tive lecture, ' Die Entwickelung der
Mathematik in den letzten Jahr-
hunderten ' (Tubingen, 1869, re-
published by P. du Bois-Reymond,
1884). Speaking of the age of
Leibniz he says : "Though on the
Continent mathematicians were not
so conservative as in England, where
a purely geometrical exposition was
considered to be the only one worthy
of mathematics, yet the whole spirit
of that age was directed to the sol-
ution of problems in geometrical
clothing, and the result of the cal-
culus had mostly to be retranslated
into geometrical forms. It is the in-
estimable merit of the great mathe-
matician of Basel, Leonhard Euler,
to have freed the analytical calculus
from all geometrical fetters, and
thus to have established analysis
as an independent science. Analy-
sis places at its entrance the con-
ception of a function, in order to
express the mutual dependence of

two variable quantities. . . . The
abstract theory of functions is the
higher analysis. . . . The concep-
tion of a function has been slowly
and hesitatingly evolved out of spe-
cial and subordinate conceptions.
It was Euler who first established
it, making it the foundation of the
entire analysis, and hereby he in-
augurated a new period in mathe-
matics" (p. 12, &c.)

■^ To Huygens, 16th September
1679 : " Je ne suis pas encor con-
tent de I'Algebre, en ce qu'elle ne
donne ny les plus courtes voyes, ny
les plus belles constructions de G^o-
metrie. . . . Je croy qu'il nous faut
encor une autre analyse proprement
geometrique ou lineaire, qui nous
exprime directement situm, comme
I'Algebre exprime magnitudinem,
Et je croy d'en avoir le moyen,
et qu'on pourroit representer des
figures et mesures des machines et
mouvements en caracteres, comme
I'Algebre represente les nombres
ou grandeurs" (Leibniz, Mathem.
Werke, ed. Gerhardt, vol. ii. p. 19).

104

SCIENTIFIC THOUGHT.

14.
Influence
of science
on French
literature.

the great success which attended Laplace's work, the
elaboration of a system of the universe out of the prin-
ciples of Newton, was largely due to the perfection which
the analytical methods had gained in the hands of his
predecessors, and to the skill with which he himself re-
duced the several problems to purely analytical questions.
But however much exact methods, learned societies,
and regal endowments may do to promote the growth of
the scientific spirit, experience has shown that popular
favour and interest furnish a still more effective stimulus.
Even the most abstract reasonings of the mathematician
require to be brought into some connection with the gen-
eral concerns of mankind, before they can attract talent
from outside, or enter into that healthy action and reaction
which are the soul of all mental progress. In this respect,
also, France during the second half of the eighteenth cen-
tury was far in advance of other countries. No other liter-
ature of that age can be compared with that of France.when
we look at the influence or the expression which modern
scientific views and interests had already attained in it ;
and no other country could at the end of the eighteenth
century boast of such splendid means of scientific instruc-
tion as then existed in Paris. In two important depart-
ments— the popularisation and the teaching of science —
France for a long period led the way.^ A general inter-

To Bodenhausen (about 1690): "I
am of opinion that in the problems
of ordinary Geometry the mcthodus
Veterum has certain advantages
over Analysin Algcbraicam, and I
tliink I have remarked to you that
thei-e remains Rn Analysis geometr ice
propria, toto ccelo ah Algebra diver sa
et in multis longe Algebra compcndio-

sior utiliorque" (ibid., vol. vii. p.
.359). "It is certain that algebra,
by reducing everything a situ ad
solam magnitudinem, hereby very
frequently complicates things very
much " (p. 362).

^ Perhaps it would be more cor-
rect to say that science was fashion-
able than that it was popular in the

THE SCIENTIFIC SPIRIT IN FRANCE.

105

est was thus created in the proceedings and debates of the
Academy, and the discoveries of its ilhistrious members
found their way into the lectures and text-books of the
professors. Whatever eminence German science may have
gained in this century, from a purely literary point of
view, through the works of A. von Humboldt, or English
science through those of Darwin, the history of both
literatures during the eighteenth century can be written
almost without any reference to science at all — so small
was the direct influence of such giants as Newton and
Leibniz on the popular mind. But who could exclude
from a history of the elegant literature of France the
names of Voltaire, of Buffon, of D'Alembert, or of Con-
dorcet ? These form a connecting link between science
and general literature.-^ A study either of English or

eighteenth century in France. But
it became pojjular through the in-
fluence of the great schools of Paris.
Before becoming popular with the
masses it became so in cultivated
and literary circles. The result
has been that science in France
alone has attained to a perfect form
of expression. Whereas in other
countries the great models of origi-
nal research and thought were writ-
ten in the severe style handed down
by the ancients (Newton's ' Prin-
cipia ' and Gauss's ' Disquisitiones
Arithmetics '), the great work of
Lagrange (the ' ilecanique analy-
tique ') is a model of literary style
in the modern sense. Science in our
age has become popular through
its applications. It is the utili-
tarian spirit that has popularised
science in Germany and England.
In France alone science, before com-
ing under the influence of the utili-
tarian, came under that of the lit-
erary spirit. It was the influence of

the academies that brought this
about. See Maury, ' Les Acade-
mies d'autrefois,' vol. i. p. 178, &c.
More than with Richelieu, the in-
terest in science nowadays is un-
fortunately only too often purely
" metallic " (quoted from Lord
Chesterfield's Letters). See also
on the literary as compared with
the modern practical character of
science, Maury, ibid., p. 161.

^ " On erigeait meme en prin-
cipe la n(?cessite pour un philosophe
de ne rester etranger h, aucune
science. ' L'esprit philosophique
fait tant de progres en France de-
puis quarante ans,' ecrivait Voltaire
a madame Du Chatelet, en lui d^-
dlant sa tragedie d'Alzire, ' que si
Boileau vivait encore, lui qui osait
se moquer d'une femme de condi-
tion, parce qu'elle voyait en secret
Roberval et Sauveur, il serait oblig^
de respecter et d'imiter celles qui
profitent publiquement des lumieres
des Maupertuis, des Reaumur, des

106

SCIENTIFIC THOUGHT.

15.
Absence of
this influ-
ence in Eng
land and
Gerraanv.

16.
Schools of
science in
Paris.

of German eighteenth-century literature does not intro-
duce one to the great controversies of science, but a
study of Voltaire leads one into the midst of the pro-
found problems of the Newtonian and Cartesian philo-
sophy, the disputes on the correct measure of force.^
Buffon's influence, also, by spreading a taste for the study
of nature and by making objects of natural history attrac-
tive, was probably much more important than his actual
contributions to the natural sciences themselves.^

For the growth and diffusion of the scientific spirit
itself, the great schools in Paris were even of greater
value than the popular writings of Voltaire and Buffon.
Most of the Academicians were trained in these schools.

Mairan, des Du Fay et des Clairault ;
de tous ces veritables savants qui
n'ont pour objet qu'une science
utile, et qui, en la reudant agreable,
la rendent insensiblement neces-
saire a notre nation. Nous sommes
au temps, j'ose le dire, ou il faut
qu'un poete soit philosophe et ou
une femme peut I'etre hardiment.'
En parlant ainsi, Voltaire ue faisait
qu'exprimer ropiniou de son siecle,
et ambitieux lui-meme de'reunir le
titre de geometre b, celui de poete et
d'historien, il s'etait fait expliquer
par madame Du Chatelet la physique
de Newton" (Maury, ' Les Acad,
d'autrefois,' vol. i. p. 156).

^ See Maury, vol. i. p. 157, &c. ;
and Du Bois-Reymond, " Voltaire
als Naturf orscher " in ' Gesammelte
Reden,' vol. i. p. 1.

^ " Sans I'eloquence de Buffon,
la zoologie serai b demeuree encore
longtemps le privilege d'un petit
nombre ; elle eut laiss^ inditfereuts
ceux que la nature emeut moius que
le charme de la parole. La vieille
education classique avait le tort
de nous laisser tres-ignorants des
choses du monde cree. Buffon com-

muniqua aux sciences le charme des
lettres. La curiosite s'eveilla, et en
1760, Valmont de Bomare put ouv-
rir h, Paris le premier cours d'his-
toire naturelle ; il fut assidument
suivi " (Maury, vol. i. p. 283). A.
von Humboldt had a similar influ-
ence in Berlin seventy years later.
See Du Bois - Reymond, loc. cit.,
vol. i. p. 510. Guardia, ' Histoire
de la Medecine' (Paris, 1884), says
of Buffon, " Fontenelle avait rendu
la science aimable et accessible.
Buffon I'associa a la philosophie et
aux lettres et I'introduisit defini-
tivement dans la society" (p. 384).
What a contrast, when we read in
the ' Life of Sir W. R. Hamilton '
(by R. P. Graves, vol. ii. p. 196)
that Dr Buckland's communica-
tion at the Bristol meeting of the
British Association (1836) "was
apparently the first occasion of
bringing before the public mind in
England the geological doctrine of
the great antiquity of the earth ;
for out of the expressly scientific
circles, very little — you [viz. , Count
Adare] are aware — is known of
what scientific men are about " !

THE SCIENTIFIC SPIRIT IN FRANCE.

107

and many of them taught there for many years.^ It was
with a true insight into the higher intellectual needs of
the nation that the successive Governments of the Eevo-

^ Before the age of the Revolu-
tion, which did so much to pro-
mote higher scientific education,
Paris possessed already manj' great
schools. First in importance was
the College de France, founded in
1530 by Francis I. Gassendi and
Roberval taught there in the
seventeenth century, and about
the middle of the eighteenth cen-
tury science began to be more ex-
tensively represented, Lalande and
Daubenton, occupying chairs. The
College et Ecole de Chirurgie was an
ancient establishment. There was
the Jardin des Plantes, with Buffon,
Lemonnier, Daubenton, and Four-
croy ; the Ecole royale des Mines,
founded in 1783, where Duhamel
taught metallurgy ; the Ecole des
Ponts et Chaussees, founded by
Turgot in 1775. Daubenton, Four-
croy, and Vicq d'Azyr taught in
the Ecole veterinaire d'Alfort,
founded in 1766. Besides the
Academie des Sciences, the Acad^-
mie royale de Chirurgie, founded
by Lapeyronie under Louis XV. in
1731, had a great influence on the
development of anatomy and sur-
gery during the eighteenth century.
Tenon and Petit, as well as Quesiiay
the economist, were amongst its
members, and it kept up a lively
intercourse with anatomists all over
Euroi^e. The Paris academies had
also their representatives and con-
nections in the provinces. Inde-
pendent academies of science were
affiliated with the Academie des Sci-
ences— 1716 at Bordeaux, 1706 at
Montpellier, 1746 at Toulouse, 1766
at Beziers. Before having received
their lettres patentes, which gave
their members certain privileges,
most of these academies had exist-
ed as independent societies. Other

provincial academies, such as Aries
(1668), Nimes (1684), Soissons
(1674), Marseilles (1726), were affili-
ated with the Academie franraise.
Others, such as Caen (1705), Lyons
(1724), Dijon (1740), Rouen (1744),
Amiens and Nancy (1750), Besau-
con (1757), Metz (1760), Clermont
(1780), Orleans (1786), were not
specially affiliated. These dates
show how very much earlier a
literary and scientific organisation
existed in France than in other
countries. The Protestant univer-
sities in Germany formed an or-
ganisation of a difierent kind, with
which I shall deal later on. The
academic system, so early developed
in France, was of great use to the
culture of the sciences. French
science is usually considered to be
almost entirely located in Paris.
M. Bouillier ('L'Institut et les
Academies de Province,' Paris,
1879) has drawn attention to the
great services of this network of
academies. Many of the most emi-
nent writers belonged to these pro-
vincial centres, and worked for
them even after becoming members
of the more celebrated academies.
Montesquieu is connected with Bor-
deaux, Cassini and many eminent
doctors with ilontpellier, Dijon has
the honour of bringing out Rous-
seau, and Toulouse gave prizes to
Bossut and Clairault. Robespierre's
name is connected with the Academy
of Arras, Marat discourses at Rouen
and Lyons on electricity and optics,
and Danton and Bonaparte compete
for the prix Jiaynal at Lyons.
"Mais," says M. Bouillier, "ce qui
nous semble le plus digne de
remarque et d'eloge, ce sont les
ecoles gratuites de dessin, les cours
gratuits de physique, de chimie.

108

SCIENTIFIC THOUGHT.

Promoted
by Govern-
ments of
Revolution.

lution, in the midst of the more pressing problems of
national safety and welfare, betook themselves to the
solution of the great problem of national education and
the instruction of all grades of society. "The Convention,"
says the historian of f)ublic instruction,^ " affords us the
strange and grand spectacle of an assembly, which on the
one side seems to have no other mission than to crush in
the name of public welfare everything that stands in the
way of the triumph of the Eepublican State, and which
can see no other way of attaining this than the most
terrible and cruel of tyrannies ; and which on the other
side devotes itself, with a stoical calm and serenity, form-
ing a surprising contrast to its acts, to the study, the
examination, and the discussion of all the problems in-
volved in public instruction, of all the measures con-
ducive to the progress of science. It had the glory of
creating institutions, some of which were carried away by
the blast of the Eevolution, but among which the most
important still exist for the great honour of France, and
bear proof of the loftiness of her ideas." ^

d'histoire naturelle, d'anatomie,
d'antiquit(5s, fondes par un certain
nombre d'academieset, entre autres,
par Dijon, par Rouen, par Bordeaux,
par Toulouse, par Montpellier, et
dont les professeurs etaient des
membres, non retribues de ces
academies. ... A coinbien de
jeunes talents les academies provin-
ciales n'ont-elles pas donne I'essor,
par leurs recompenses solennelles et
leurs encouragements ? Combien de
leurs laur^ats ne sont pas devenus
des hommes c^lebres ? " (p. 81, &c.)
Besides Bouillier, consult ou these
matters the several articles, " Aca-
demic," "College," " Ecole," in the
' Grande Encyclopedie.'

1 C. Hippeau, 'L'lnstructionpub-
lique en France pendant la Revolu-
tion,' 1*^ serie, preface, p. xix.

"^ It appears nowadays a kind of
paradox that, as M. Hippeau re-
marks, in the very year 1793, when
" the Convention was labouring
with a feverish ardour at the crea-
tion of schools of all degrees," this
same Convention, on a report of the
Committee of Public Instruction,
voted on the 8th of August the
suppression of all the academies of
Paris and the provinces. On this
M. Bouillier (' L'Institut et les Aca-
demies,'p. 95) remarks: "Bientot
il est vrai, les academies devaient
renaitre apres la chute de la

THE SCIENTIFIC SPIRIT IN FRANCE.

109

It was of immense importance to the cause of science
that in many of the discussions of that assembly a
marked preference was shown for the scientific side of
instruction. In this matter, as in many others, the suc-
cessful constructive efforts of the Revolutionary Govern-
ments came from the side of those brought up in the

Montagne et du Comite de salut
public. Nous n'ignorons pas que
c'est encore la Convention qui, prise
d'un tardif remords, la veille seule-
ment du jour ou elle devait faire
placeaunautre gouvernement moins
despotique et moins cruel, decreta
I'organisation de I'lnstitut. Mais
la Convention du 3 brumaire an
iv. n'etait plus celle de 1793 ; c'etait
en realite une autre Convention,
epuree, decimee, renouvelee, animee
d'un tout autre esprit," &e., &c.
The idea of a national Institute for
the advancement of letters, science,
and arts was a very early one (see
' Rapport de Talleyrand Perigord,'
September 1791, Hippeau, p. 102).
The explanation how the same
Government which was labouring at
the problem of a national instruc-
tion, crowned by the higher teaching
and research of an Institute, could
begin by closing the existing acad-
emies and universities, lies in this,
that the aim was to make education
general and learning popular, not
merely fashionable, as it had been.
See, for instance, what Ducos said
on the 18th December 1792: " Les
moeurs d'un peuple corrompu ne
se r^g^nerent point par de legers
adoucissements, mais par de vigour-
euses et brusques institutions. II
faut opter ouvertement entre I'^du-
cation domestique et la liberte ; car
citoyens, tant que par une instruc-
tion commune vous n'aurez pas
rapproche le pauvre du riche, le
faible du puissant ; tant que, pour
me servir des expressions de Plu-
tarque, vous n'aurez pas achemin^ K

une meme trace, et moule sur une
meme forme de vertu tous les
en f ants de la pa trie, c'est en vain
que vos lois proclameront la sainte
egalitd, la Rei^ublique sera tou jours
divisee en deux classes : les citoyens
et les messieurs" (Hippeau, 2'^
s^rie, p. 21). It was because the
academies and colleges supported
"les messieurs" that they were
supiDressed. In the end education
must always begin from above, and
before the people can be taught
you must form their teachers. See
Lakanal's Report on the Ecoles nor-
males, Hippeau, vol. i. p. 408. The
academies and colleges of the eigh-
teenth century were closed in order
to make room for that uniform
system of public instruction de-
scribed by Talleyrand and Condor-
cet, but not without a frequently
expressed admiration for the work
which they had done. See the de-
fence of the academies by Condor-
cet (Hippeau, loc. cit., vol. i. p. 272),
and the tribute to the " Collt^ge de
France," by Gilbert Romme (ibid.,
vol. i. p. 308). The arguments for
radical change are summed up by
that speaker as follows : " L'exist-
ence de ces corps privildgies blesse
tous nos principes republicains,
attaque I'dgalite et la liberte de
penser et nuit aux progres des
arts. Mais si leur organisation est
vicieuse, les Elements en sont bons,
et nous serviront utilement dans
I'organisation nouvelle de I'instruc-
tion publique que vous allez 66-
creter" (p. 309).

110

SCIENTIFIC THOUGHT.

IS.
Coudorcet.

school of Voltaire and the Encyclopaedists, whilst the
work of destruction had been performed by the followers
of Eousseau. No one has expressed himself on the value
of scientific study and knowledge in a clearer or more
far-seeing manner than Condorcet. In his ' Eeport and
Project of a Decree on the General Organisation of Public
Instruction,' which he presented to the National Assembly
in the name of the Committee of Public Instruction,
he says : ^ " Many motives have brought aljout the kind
of preference which is accorded to tlie mathematical and
physical sciences. Firstly, for men who do not devote
themselves to long meditations, who do not fathom any
kind of knowledge — even the elementary study of these
sciences is the surest means of developing their intel-
lectual faculties, of teaching them to reason rightly and
to analyse their ideas." ... It is because in the natural
sciences the ideas are more simple, more rigorously cir-
cumscribed, it is because their language is more perfect,
&c., &c. . . . These sciences offer a remedy for prejudice,
for smallness of mind — a remedy, if not more certain,
at least more universal, than philosophy itself.^ . . . Those

1 It was presented ou the 20tli
and 21st April 179"2. See Hippeau,
le serie, pp. 185-288. It was
printed hy order of the Convention,
Paris, Imprimerie nationale, 1793.

2 Ibid., p. 203.

^ Ibid., p. 204. It is interesting
to see how in all these reports the
exact sciences are placed in the fore-
ground. See, for instance, what
Gilbert Romme says of the teaching
of the proposed instituts : " Les
.sciences mathematiques et phys-
iques, morales et politiques, I'agri-
culture et les arts raecaniques, la
littorature et les beaux-arts, coru-

poseront I'enseignement des insti-
tuts oil Ton pourra suivre, dans
leurs Elements, I'echelle enti&re des
connaissauces humaines" (vol. i. p.
322). " Les lycees seront I'ecole des
gens instruits ; ils embrasseront les
sciences, les arts et les lettres dans
toute leur etendue." One is forcibly
reminded that the most perfect
realisation of this arrangement of
studies is to be found a century
later in the provincial science col-
leges of this country. The prefer-
ence, however, is now given to
science mainly for utilitarian rea-
sons : the difference is shown by

THE SCIENTIFIC SPIRIT IN FRANCE.

Ill

who follow their course, see the coming of an epoch
when the practical usefulness of their application will
reach greater dimensions than were ever hoped for, when
the progress of the physical sciences must produce a
fortunate revolution in the arts. And lastly, we have
yielded to the general tendency of men's minds, which
in Europe seem to incline towards these sciences with
an ever-increasing ardour. . . . Literature has its limits,
the sciences of observation and calculation have none.
Below a certain degree of talent, the taste for literary
occupations produces either ridiculous pride or a mean
jealousy towards such talents as one cannot attain. In
the sciences, on the contrary, it is not with the opinion
of men but with nature that we have to eng-age in a
contest, the triumph of which is nearly always certain,
where every victory predicts a new one." ^

" It is," says Lakanal, in his report on the " Ecoles cen- 19.

Lakanal.

trales, 16th December 1/94, "of great importance for
the nation to assure itself that the mathematical sciences
are cultivated and deepened, for they give the habit
of accuracy : without them astronomy and navigation
have no guide ; architecture, both civil and naval, has
no rule ; the sciences of artillery and of fortification have
no foundation." ^ Gradually, under the pressure of exter-

the importance then attached to
mathematics as a training of the
intellect in precise thinking ; now-
adays it is the meciiauical side that
is favoured, and this is only too
often destructive of the truly scien-
tific and exact spirit.

^ Hippeau, loc. cit., p. 258. Cf.
p. 261 : '■ Hatons - nous . . . de
porter dans les sciences morales la

philosophic et la methode des scien-
ces physiques " (Condorcet).

^ Hippeau, vol. i. p. 432. It is
interesting to see how the study and
teaching of the sciences in course of
the second half of the last century
in France undergo a development.
The literary interest predominates
in Foutenelle. Buffon aud Voltaire
add to it the philosophical and

112

SCIENTIFIC THOUGHT.

nal events, the exigencies of war and the defence of the
country gain the upper hand, and a central establishment
is founded to cultivate and teach the sciences and arts,
" upon which depend the defence of the Eepublic by land
and sea." ^ Few of the higher and philanthropic aims of
the great educational leaders of the early years of the
Revolution — of Mirabeau, of Talleyrand, of Condorcet —
were realised ; little was done for primary education ;
but science can boast of having been worthily represented
and supported in the two great schools which still bear
their original designation, and which can show a record
of celebrated names and magnificent work superior prob-
ably to that of any other similar institution in Europe.
They are the " Ecole normale superieure " and the
male. Ecole " £cole ceutralc dcs Travaux publics," better known by

polytech- , ^

nique. the title " Ecole polytechnique. ' "

, 20.
Ecole nor-

The founders of this

philanthropic, the Encyclopaedists
and Condorcet the educational ; the
events of the Revolution and the
discussions in the Assemblies bring
out more and more the instructive,
the utilitarian, and the economical
aspects. The only creations which
resulted were those in which the
latter aims wei'e predominant.

^ Lakanal, see Hippeau, vol. i.
p. 447.

- To these two great schools must
be added as a third the " Musdum
d'Histoire naturelle," " le plus mag-
nifique etablissement que les scien-
ces aient possede " (Cuvier, "Eloge
de Fourcroj'," part ii. of the ' Eloges
historiques,' p. 44, Strasbourg, 1819).
The foundation of the " Ecole cen-
trale des Travaux publics " was pro-
posed by Barere on the 11th March
1794, and definitely organised on
the report of Fourcroy (Hippeau,
vol. i. p. 446) by a decree of 7th ven-
demiaire, an iv. (name changed to

Ecole polytechnique, 15th fructidor).
The opening of the courses was an-
nounced for the 10th frimaire fol-
lowing (Hippeau, vol. ii. pp. 139, 174,
175). The foundation of the " Ecoles
normales " was proposed by Barere
(13th prairial, an ii.), and decreed on
a report of Lakanal (Hippeau, vol. i.
p. 423) on the 9th brumaire, an iii.
(30th October 1794) (ibid., vol. ii. p.
179). The courses opened on the 1st
pluviose. The work of the school
was distributed as follows : Mathe-
matics, Lagrange and Laplace ;
physics, Haiiy ; descriptive geome-
try, Monge ; natural history, Dau-
benton ; chemistry, Berthollet; agri-
culture, Thouin ; geography, Buache
and Mentelle ; history, Volney ;
morals, Bernardin de St Pierre.
(Hippeau, vol. ii. p. 180, where also
will be found extracts from the
' Moniteur ' of the 9th pluviose on
the opening addresses.) The oldest
pupil was Bougainville, the great

THE SCIENTIFIC SPIRIT IN FRANCE.

113

magnificent institution recognised " that, in spite of the
diversity of applications, mathematics and physics are
the indispensable basis of the studies in view." ^ Though
the first period of the life of the ficole normale only
counted four months,^ we are indebted to it for the

traveller. The Ecole polytechnique
received an allocation of £12,000,
and had 400 pupils to start with.
On the 20th frimaire, an iii., the
Convention, on a report of Thibau-
deau, voted the necessary expenses
for the enlargement of the Museum
d'Histoire naturelle (Hippeau, vol.
ii. p. 19Q),—viz., nearly £8000 for
expenses, and £200 for each of the
professors. The Museum had been
originally destined for the culture
of medicinal plants. Tournefort had
given a great impetus to botanical,
and Buffon, with Daubenton, to
zoological studies. The Convention
added several to the courses regu-
larly held there on natural history,
botany, mineralogy, and general
chemistry. " Ces cours," says Thi-
baudeau, " fournissent 500 leyons
par an, ofPrent I'eosemble le plus
vaste et le plus complet d'enseigne-
ment sur toutes les branches d'his-
toire naturelle dont le plus grand
nombre manquaient totalement h, la
France et dont quelques-unes man-
quent encore a I'Europe, I'applica-
tion immediate de toutes les sciences
naturelles au commerce et aux arts."
Of other scientific and teaching
institutions I must mention the
"Bureau des Longitudes." This
was organised by the Convention
on a discourse by Gregoire, 7th
messidor, an iii. (24th June 1795),
in which lie refers to the British
Board of Longitude and the superi-
ority of the British navy (Hippeau,
vol. ii. p. 219). The appointments to
this bureau were the geometres La-
grange and Laplace, the astronomes
Lalande, Cassini, Mdchain, De-

VOL. I.

lambre, one of whom had to deliver
a course of astronomy, the travellers
Borda, Bougainville, the geographe
Buache, and the artist Carocher.
It had charge of the observatory,
which had already been reorganised
by a decree promoted by Lakanal on
the 31st August 1793 (Hippeau, vol.
ii. p. 76), and published in the ' Con-
naissance des Temps. ' There were,
besides, several military schools and
the medical schools, not to mention
other foundations less connected
with our subject but equally im-
portant, such as the School of
Oriental Languages, established in
the Bibliotheque nationale (ger-
minal,, an iii., Hippeau, vol. ii. p. 215);
the Ecoles de Sante, established
14th frimaire, an iii., on a report of
Fourcroy, in Paris, Strasbourg, and
Montpellier (Hippeau, vol. ii. p. 194.)

1 Ibid., vol. i. p. 450.

" The Ecole normale was closed
on the 30th flordal, an iii., on a-
decree of the Convention dated
the 7th of that month. Danton
explained that the school had not
taken the line which the Conven-
tion had marked out — the courses
in general having offered a direct
teaching of the sciences rather
than an exposition of the methods
which are to be adopted in teaching
(Hippeau, vol. ii. p. 215). It also
seems that the eminent teachers of
this institution had few pupils suffi-
cientlv prepared to follow them.
The Ecole normale was reopened
in the year 1808 under the Empire,
by the same decree of 17th March
which organised the University of
France.

H

114

SCIENTIFIC THOUGHT.

21. foundation of a new branch of science — the ' Descriptive

Monge's

Geomet^"'^ Geometry ' of Monge, which was given to the world
through shorthand notes -"^ from his lectures delivered in
that institution. They form the beginning of the new
science, since developed by Poncelet, Steiner, and others,
and known under the name of " projective geometry." ^

Next to mathematics with its analytical and graphical
application to physics and the arts, the subject most culti-
vated in these higher educational establishments of Paris

22. at the end of the last century was the new science of

Science of

Chemistry, chemistry. With some justice this science has been termed
a French science,^ not so much because even at that time

^ See the account of the origin of
this branch of mathematics in Bris-
son's edition of the ' Geometric de-
scriptive,' Paris, 1847. In the pro-
gramme prefixed to the treatise the
three aspects of the new school —
the national, the practical, and the
educational — are well set forth :
" Pour tirer la nation franraise de
la dependance oil elle a ^te jusqu'k
present de Tiudustrie etrangere, il
faut premierement diriger I'educa-
tion nationale vers la connaissance
des objets cjui exigent de I'exacti-
tude. ... II faut, en second lieu,
rendre populaire laconnaissanced'un
grand uombre de phenomenes natu-
rels. ... La geometric descriptive
est un moyen de rechercher la ver-
ity ; elle offre des exemples perp^-
tuels du passage du connu a I'iucon-
nu ; et parcequ'elle est toujours ap-
pliqu^e a des objets susceptibles de
la plus grande evidence, il est neces-
saire de la faire entrer dans le plan
d'une education nationale." Monge
generalised and placed on a scien-
tific basis the methods used pre-
viously by carpenters and stone-
cutters, and partially dealt with
geometrically by Courcier, Derand,
Mathurin, Jousse, and Frezier. See

Montucla, ' Histoire des Math^ma-
tiques,' vol. iii. p. 15.

'■^ Monge taught also at the Ecole
polytechnique from the beginning.
See the remarks of Chasles ('Rap-
port sur les Progres de la G^o-
m(^trie,' Paris, 1870, p. 2): "L'en-
seignemeut theorique et profond
qui a ete la base de la premiere et
judicieuse organisation de ce grand
etablissement etait eminemment
favorable aux progres de la science,
en meme temps qu'il pr^parait seri-
eusement les eleves a I'entree dans
les dcoles d'application." The au-
thor then refers with regret to the
less scientific tone which had crept
into the studies of that great school
in the course of this century. See
also p. .379.

^ A. Wurtz ('Histoire des Doctrines
chimiques,' Paris, 1868, p. 1) : "La
chimie est une science francaise ;
elle fut constituee par Lavoisier."
Cf . Dumas (' Lecons sur la Philoso-
phie chimique,' Paris, 1837, p. 137).
Buckle ('History of Civilisation,' &c.,
3 vols., vol. ii. p. 366, London, 1866)
says : " That we owe to France the
existence of chemistry as a science
will be admitted by every one who
uses the word science in the sense

THE SCIENTIFIC SPIRIT IN FRANCE.

115

chemistry was not indebted to illustrious foreigners ^ for
some of its most important discoveries, as because the
modern scientific spirit of accurate measurement first took
hold of chemical phenomena on a large scale in the many
important investigations which bear the name of Lavoi-
sier and his followers, through whom the great reform of
modern chemical knowledge and research was permanently
established. It has been significantly pointed out "^ that it
was the union of mathematical with empirical knowledge
which, through men like Laplace, Meusnier, Monge, first

in which alone it ought to be un-
derstood, &c. . . . Until Lavoisier
entered the field there were no gen-
eralisations wide enough to entitle
chemistry to be called a science."
The correctness of this view is fully
and impartially examined by Her-
mann Kopp (' Die Entwickelung der
Chemie in der neueren Zeit,' Mfin-
chen, 1873, p. 89, &c.) He fully
upholds the claims of Lavoisier to
be called the father of modern
chemistry (p. 145). See also what
Liebig says.

^ These were mainly, Black (dis-
covered carbonic acid, called fixed
air, in 1754), Cavendish (discovered
hydrogen or inflammable air in
1767), and Priestley, who between
1771 and 1774 discovered oxy-
gen (dephlogisticated air), nitrogen
(phlogisticated air), and several of
its compounds, among them am-
monia (alkaline air). Of Priestlej'-
it is said by Cuvier that he may
well be considered as one of the
fathers of modern chemistry, "mais
c'est un pere qui ne voulut jamais
reconnaitre sa fille " (' Eloges,' vol. i.
p. 208). Elsewhere (' Rapport his-
torique sur les Progres des Sciences
naturelles,' Paris, 1810, p. 90) Cu-
vier dates the revolution in chem-
istry from the introduction of the
mathematical spirit : " II en est

uue cause encore plus essentielle a
laquelle meme on doit a proprement
parler, et cette theorie nouvelle, et
les decouvertes qui Font fait naitre.
. . . C'est I'esprit mathematique
qui s'est introduit dans la science
et la rigoureuse precision qu'on a
portee dans I'examen de toutes ses
operations. . . . C'est dans le
Traits elementaire de Lavoisier que
I'Europe vit pour la premiere fois
avec etonnement le systeme entier
de la nouvelle chimie," &c.

■^ Kopp, loc. cit., p. 202: "In-
deed, if we look at those who first
worked together with Lavoisier or
in his spirit, we shall find such as
had devoted themselves principally
to mathematics or mathematical
physics, men like Laplace, Meus-
nier, Monge. Among chemists La-
voisier stood for a long time almost
alone in his opinions." This view
is also taken by Cuvier (' Rapport,'
p. 91): "Les nouveaus chimistes
francais . . . out eu a se louer du
concours de quelques-uns de nos
geometres les plus distinguds," &c. ;
and he attributes the next great
step in chemical science to a similar
introduction of a " rigueur toute
mathematique" ('Rapport sur la
Chimie lu a la Seance des 4 Acad.,'
23rd April 1826).

116

SCIENTIFIC THOUGHT.

23.
New mathe-
matical
sciences.

24.

Crystallo-
graphy.

brought about the general recognition of Lavoisier's ideas ;
"whereas the more exclusive representatives of chemistry,
such as Berthollet and Guyton, held aloof for some con-
siderable time. In the earlier syllabus of the lilcole
polytechnique, chemistry was brought into a similar
proximity with the mathematical branches. And Ber-
thollet's ' Statique chimique ' denotes by its title alone
the mathematical spirit in which the work was conceived.
About that time also two new sciences were, if not
invented, at least set on a firm basis, by which the use
of mathematics was very largely extended, and by which
great realms of interesting facts were made accessible to
accurate measurements and exact reasoning. Both these
sciences can be claimed by France as almost exclusively
her own creations. They are the science of crystallo-
graphy and the great theory of probabilities. The former
was the work of the Abbe Haiiy ; the latter formed, next
to the mechanics of the heavens, the main original con-
tribution by which Laplace has perpetuated his name in
the history of science. The theory of the Abbe Haiiy,
who first taught how crystals are built up from small
particles of definite and regular geometrical forms, such as
cubes, pyramids, &c., came to the aid of the mineralogists,
who before him had vainly groped in the dark, searching
for some method by which order and system could be
introduced into the lifeless forms of nature as by the
methods of Linnaeus and Jussieu it had been introduced
into the world of plants and animals. Before Haiiy,.
the doctrines of mineralogy had been either attached to
geology — especially in the celebrated school of Werner,
or latterly, after the great developments in chemistry had

THE SCIENTIFIC SPIRIT IN FRANCE.

117

set in, to chemistry — especially by Bergmann.-^ Haiiy
established the science of minerals on an independent
foimdation by studying and systematising the forms of
their crystallisation ; and he brought the science of min-
eralogy from Sweden and Germany into France, and gave
it an independent position. Thus it came to form a con-
necting-link between the mathematical — i.e., the measur-
ing and calculating — and the purely descriptive sciences.
" Mineralogy, though it is that part of natural science
which deals with the least complicated objects, is never-
theless also that which lends itself least to a rational
classification. The first observers named the minerals
vaguely according to their external appearances and their
use. It was not until the middle of the eighteenth
century that it was attempted to subject them to those
methods which had done service to geology and botany :
the hope existed of establishing among them genera and

^ See an account of the work of
the chemical school, to which Cron-
sted (the inventor of the blow-pipe),
Bergmann, Kirwan, and Klaproth
belonged, in Cuvier's ' Rapport ' (p.
163). Also his "Eloge de Hauy"
(' Eloges histor.,' vol. iii. p. 143, &c.)
The beginnings of geometrical crys-
tallography seem to go back to Lin-
naeus ; but his view was discouraged
in France by BufFon, who disliked
Linnseus's writings. Whewell, who
was himself an authority on crys-
tallography, thinks Rome de I'lsle,
who was not an Academician, had
only scant justice done to him by
Haiiy and his friends (' Hist, of
the Induct. Sciences,' 3rd ed., vol.
iii. p. 176). More recent writers,
such as Kobell (' Geschichte der
Mineralogie,' Miinchen, 1864, p. 73,
&c.) and Nicol (article "Crystal-

lography," ' Ency. Brit.'), have done
him justice. The 'Grande Ency-
clopedie ' thus summarises the work
of Rome de I'lsle : " II mesura
mecaniquement [I'iz., with Caran-
geot's goniometer] les angles et
etablit que ces angles ont toujours
une valeur constante dans une
meme espece mineralogique." That
of Haiiy is summarised in the two
laws : " 1", Tous les elements sem-
blables d'un cristal sont toujours
semblablement et simultanement
modifies (loi de symetrie) ; 2°, toute
facette modifiante intercepte sur
les aretes de la figure primitive
des longueurs proportionelles k des
multiples simples de la longueur
de ces aretes (loi de derivation) "
(Berthelot in 'Grande Encyclojj.,'
vol. xiii. p. 397).

118

SCIENTIFIC THOUGHT.

species, as among organised beings, and it was forgot-
ten that in mineralogy the principle is absent which
had given birth to the idea of species — viz., that of
generation. The principle of individuality, such as it is
conceived in the organic world — vi>:., the unity of action
of different organs which co-operate in the preservation of
the same life — can scarcely be admitted in mineralogy."^
The Abbe Haiiy, by founding the science of minerals
on their regular forms of crystallisation, made mineralogy
" as precise and methodical as astronomy ; in fact, we
can say in one word that he was to Werner^ and Eome
de risle, his predecessors, what Newton had been to
Kepler and Copernicus." ^
r25. From that well-defined province of science which deals

Theory of ^

Probability, j^^ g^ precisc and strict manner with the simple numerical
relations which seem to underlie all forms of movement
in nature, be they on a stupendous or on a minute scale

,^ Cuvier, " Eloge de Haiiy " in
'Eloges historiques,' vol. iii. p. 155.
- The cliaracter of "Werner (1750-
1815) is nowhere better painted
than by Cuvier in his ' ' Eloge de
Werner" {loc. ciL, vol. ii. p. 303, &c.)
" II commence I'epoque la plus re-
marquable de la science de la terre,
et meme Ton pent dire qu'a lui
seul il la remplit. ... II s'est
forme des academies entieres, qui
ont pris son nom " (for instance,
the Edinburgh Wernerian Society,
founded by Jameson, 1808-1859),
" comme si elles eussent voulu in-
voquer son g^nie et s'en faire un
patron d'une espece auparavant in-
connue. Qui ne croirait, h, entendre
parler de succ^s si peu ordinaires,
que ce fut quelqu'un de ces hommes
ardens h. propager leur doctrine,
qui par des ouvrages nombreux et

^loquens, ont subjugue leurs con-
temporains, ou qui se sont procure
des partisans par I'ascendant d'une
grande richesse ou d'une position
^levee dans I'ordre social ? Rien de
tout cela : confine dans une petite
ville de Saxe, sans autorite dans
son pays, il n'avait aucune influence
sur la fortune de ses disciples ; il
n'entretenait point de liaisons avec
des personnes en place : d'un nat-
urel singulierement timide, hesitant
toujours ^ (Scrire, h. peine subsiste-
t-il de lui quelques feuilles d'im-
pression. . . . C'est ainsi qu'en
peu d'ann^es la petite ecole de
Freyberg, destinee seulement, dans
le principe, h former quelques
mineurs pour la Saxe, renouvela
le spectacle des premieres univer-
sites du moyen age," &c., &c.
^ Cuvier, ibid., p. 163.

THE SCIENTIFIC SPIRIT IN FRANCE. 119

— i.e., from the province of mechanics and astronomy —
two different roads lead into those extensive domains in
which, not simplicity and regularity, but endless variety
and complication, seem to be the order and the rule of
Life. Even a century ago the contrast must have been
striking between the ' Principia ' of Newton and the ' Ex-
position du Systeme du Monde ' of Laplace on the one
side, and the great array of volumes of Linnaeus, Bviffon,
Jussieu, Cuvier, and Lacepede on the other ; though these
after all embraced only a small portion of the living forms
of nature which they attempted to classify or to describe.-^
I have pointed out how the new and especially the
French methods of chemistry and crystallography con-
quered a large portion of intermediate ground, subjected
many tangled phenomena to exact treatment, and pushed
the mathematical method far into the dominion of natural
history. It is that other history, not natural, but human
and often unnatural, which presents the opposite extreme
of the great panorama of world-life. It is significant
that almost at the same time that mathematical reason-
ing found its way into natural history, conquering an ex-
tensive province of its vast territory, an entirely different
method was invented with the aim of dealing in a still
more vigorous manner with the phenomena of human
life and society. This was the science of statistics, and

^ Cuvier gives some figures as to Linnrous had counted in 1778 about
the increase of the known species 8000 species of plants. Cuvier in
during his own lifetime. Lacepede 1824 estimates the^ number as

had described about 1200 or 1300

distinct species of fishes ; but when

Cuvier pronounced his Eloge in

1826, the Cabinet du Roi contained

already more than 5000 species animals).

(' Eloges historiques,' vol. iii. p. 317).

50,000 or more (see ' Eloges,' vol. iii.
p. 469, &c., where he also gives some
idea of the numbers of known
species in the diflereut classes of

120

SCIENTIFIC THOUGHT.

connected with it the doctrine of averages and the mathe-
matical theory of probabilities.-^ The same great mind

^ The beginnings of the science
and theory of probabilities are not
subject to controversy, as were
those of the infinitesimal calculus.
Pascal and Fermat about the middle
of the seventeenth century entered
into a correspondence relative to a
question in a game of chance, pro-
pounded by the Chevalier de Mer^,
a noted gambler. They agreed in
their answer, but could not con-
vince their friend, who moreover
made this the occasion of denounc-
ing the results of science and arith-
metic. But this comparatively in-
significant problem — so different
from the great cosmical problems
which led to the invention of the
infinitesimal calculus about the
same time — was the origin of a
series of investigations and discus-
sions in which the greatest mathe-
maticians, such as Huygens, James
and Daniel Bernoulli, De Moivre,
D'Alembert, and Condorcet joined.
Most of them did not escape the
errors and misstatements which
creep in an insidious manner into
the discussion and vitiate the conclu-
sions. In fact, the science advanced
through the influence of those who
depreciated it like D'Alembert, and
those who exaggerated its import-
ance like Condorcet. At length,
under the hands of Laplace, who
defined it as common-sense put into
figures and attributed to it a high
educational value, it assumed a state
wellnigh approaching to that per-
fection which Euclid gave to geo-
metry and Aristotle to logic. Since
the publication of Laplace's cele-
brated ' Theorie analytique des Pro-
babilites' (Paris, 1812) writers on
the subject have found ample oc-
cupation in commenting on the
theorems or recasting the proofs
given in that work, which holds a
similar position to that occupied in

another department of mathematics
by the ' Disquisitiones Arithmetica; '
of Gauss (1801). Up to the pres-
ent day there exist differences of
opinion as to the value of the
science, the two opposite views be-
ing rei^resented in this country by
Mill ('Logic,' 5th ed., vol. ii. p. 62)
and Jevons (' Principles of Science,'
vol. i.), the latter summing up his
opinion as follows : " In spite of its
immense difficulties of application,
and the aspersions which have been
mistakenly cast upon it, the theory
of probabilities is the noblest, as it
will in course of time prove perhaps
the most fruitful, branch of mathe-
matical science. It is the very
guide of life, and hardly can we
take a step or make a decision of
any kind without correctly or in-
correctly making an estimation of
probability" (1st ed., p. 248). A
similar opinion seems to have been
held by James Clerk Maxwell (see
Life by Campbell and Garnett, p.
143), who called the calculus of
probabilities ' ' Mathematics for
practical men. " In this country
A. de Morgan and Todhuuter, the
former in a popular essay in the
' Cabinet Cyclopicdia ' and in a
profound treatise in the ' Encyclo-
pedia Metropolitaua,' the latter in
his well-known History (London
and Cambridge, 1865), have done
a great deal to make this subject
better understood. The applica-
tions of the theory have gradually
increased through numerous mor-
tality and insurance calculations ;
as also in the estimations of error
in astronomical and physical ob-
servations, where the well-known
method of least squares (first em-
ployed bj^ Gauss in 1795, see Gauss,
Werke, vol. vii. p. 242 ; first pub-
lished by Legendre in 1806, and then
proved by Laplace iu his ' Theorie,'

THE SCIENTIFIC SPIEIT IN FEANCE. 121

which elaborated the principles of Newton into a system
of the universe, and attacked the intricate mathematical
problem which this system presented, gave to the world
likewise the first complete treatise on that calculus which
comes into play if we eliminate from the apparently most
arbitrary region of phenomena, that of human life and
history, all regard for final or efficient causes, for provi-
dential design and freewill, for human error, human malice
and benevolence — in fact, all notice of that element which
from another and equally important point of view forms
the subject of greatest interest — the inner life of the in-
dividual. It was proposed, and it has since been carried
out, to look upon human beings and human events not as
things possessed of an inner world of thought and freewill,
but as lifeless units, more uniform and regular than the
balls thrown into the urn at an election, or the counters
in a game of chance. By overstepping with one bound
the great field of human activity, full of so much con-
fusion and so much interest, it was proposed to investi-
gate what knowledge would result from a purely mathe-
matical inspection, in which human beings figured merely
as units and symbols.'^ This attempt, which has since

&c., 1812) is now extensively em-
ployed. Of this branch of mathe-
matics Bertrand says: "Les plus
grands geometres out ccrit sur le
calcul des probabilit^s ; presque
tous ont commis des erreurs : la
cause en est, le plus souvent, au
desir d'appliquer des principes a
des problemes qui par leur nature
echappent a la science." In the
hands of Clerk Maxwell the cal-
culus has acquired an additional
interest and importance through
the distinction which he made be-
tween what he termed the " histori-

cal " and the "statistical method "
of treating phenomena, and the
application of the latter to the
kinetic theory of gases (see Life,
pp. 438, 562). This subject will
occupy our attention in a special
chapter.

1 The beginnings of the science of
statistics belong likewise to the age
that produced the higher mathema-
tics. More extensive "countings"
seem to have been contemporaneous
with more refined calculations. Her-
mann Conring, professor at Helm-
stiidt, a friend of Leibniz (see Leib-

122

SCIENTIFIC THOUGHT.

led to such interesting results, and which has furnished
almost all the knowledge upon which a judicious regula-
tion and government of society depends, was the work of
Laplace, and was produced in an age and in a nation
which seemed to have set at naught all ideas of order and
method in human affairs, which defied all authority and
all tradition, and trusted its fate to the most radical
^ revolution which civilised society ever witnessed.-^

It is curious to read the criticism which the first
Napoleon, that wayward child of the Eevolution, passed
on the author of the mechanics of the heavens and the
theory of probability, Laplace, like so many other men
of science, had been called by the Emperor to assist in
the labours of administration, but, according to his judg-
ment, proved himself a poor administrator, being unable

niz's ' Philosophische Schriften,' ed.
Gerhard t, vol. i. p. 155), lectured
about 1660 on subjects uow com-
prised under the term " Statistics,"
and about the same time John Graunt
of London published ' Natural and
Political Annotations made upon
the Bills of Mortality ' (1666). Sir
William Petty, one of the founders
of the Royal Society, published in
1683 'Five Essays in Political
Arithmetick.' The newly discov-
ered calculus of probabilities in-
duced mathematicians to take an in-
terest in the subject, and to urge the
desirability of gaining data for their
calculations. Many of these turned
upon questions of mortality and
the ravages of diseases, such as the
smallpox. But though undoubt-
edly the fact that during the
French Revolution mathematicians
for the first time had a great in-
fluence in administrative and gov-
ernmental matters contributed
enormously to the introduction of
statistical methods, the great epoch

I in this science is allied with the
I name of the Belgian Quetelet
(1796-1874), of whom more later
on.

^ Cantor (' Historische Notizen
liber die Wahrscheinlichkeitsrech-
nung,' Halle, 1874, p. 6) says:
"The tendency of thought which
prepared the Revolution, and which
is marked by an unsparing and de-
structive critici.sm of the conditions
of society in state and family, could
not dispense with an instrument
which, more than any other, enables
one to subject to general views the
most different factors of civilisation.
It belonged to the favourite ideas of
that age, that the calculus of proba-
bilities should be among the most
important subjects of public in-
struction ; for it was said to be the
calculus of common-sense, through
which alone the influence of hope,
fear, and emotion on our judgment
could be destroyed, and prejudice
and superstition removed from the
decisions of social life."

THE SCIENTIFIC SPIRIT IN FRANCE. 123

to grasp practical issues, and always descending into in-
finitesimals. It is hardly to be doubted now, after the
lapse of a century, that the infinitesimals of Laplace play
a more important part in problems of administration and
government than the ideas of ISTapoleon. Laplace, un-
like some other great scientific thinkers, attached great
value to a popular exposition of the principles of his dis-
coveries. Descartes required a Fontenelle and Newton a
Voltaire to make their ideas accessible and useful to the
mass of students. Laplace was his own Fontenelle and
Voltaire. " Few works," says Sir John Herschel, " have
been more extensively read, or more generally appreciated,
than Laplace's ' Essai philosophique sur les Probabilites,'
and that on the ' Systeme du ]Monde ' by the same author.
It is not, perhaps, too much to say that were all the
literature of Europe to perish, these two essays excepted,
they would suffice to convey to the latest posterity an
impression of the intellectual greatness of the age which
could produce them, surpassing that afforded by all the
monuments antiquity has left us. Previous to the pub-
lication of the ' Essai philosophique,' few, except professed
mathematicians or persons conversant with assurances
and similar commercial risks, possessed any knowledge of
the principles of this calculus, or troubled themselves
about its conclusions, regarding them as merely curious
and perhaps not altogether harmless speculations. Thence-
forward, however, apathy was speedily exchanged for a
lively and increasing desire to know something of a system
of reasoning which for the first time seemed to afford a
handle for some kind of exact inquiry into matters no one
had ever expected to see reduced to calculation, and bear-

124 SCIENTIFIC THOUGHT.

ing on the most important concerns of life. Men began
to hear with surprise, not unminglecl with some vague
hope of ultimate benefit, that not only births, deaths, and
marriages, but the decisions of tribunals, the results of
popular elections, the influence of punishments in check-
ing crime, the comparative value of medical remedies and
different modes of treatment of diseases, the probable
limits of error in numerical results in every department
of physical inquiry, the detection of causes, physical,
social, and moral — nay, even the weight of evidence and
the validity of logical argument- — might come to be sur-
veyed with that lynx-eyed scrutiny of a dispassionate
analysis, which, if not at once leading to the discovery of
positive truth, would at least secure the detection and
proscription of many mischievous and besetting fallacies."
Both ways of approaching the intricate phenomena of
nature and history, that of mechanics dealing with the
general laws of motion and of lifeless masses, and that
of statistics dealing with the arithmetical properties of
large numbers of units, leave out of consideration that
hidden and mysterious phenomenon to which alone is
attached, if not order and method, yet certainly all
that commands interest in the created world : the factor
•26. of life — the existence of individuality. The view which

Laplace

gained his Laplaco took of the universe or of human affairs is an

results by

disregard- attempt to scc how far science and reasoning can go

mg the prin- r "^ o

dividuaiity. whilc disregarding the principle of individuality.-^ The

^ See Clerk Maxwell on ' Science
and Freewill ' (Life by Campbell
and Garnett, p. 438) : "Two kinds
of knowledge, which we may call for
convenience dynamical and statis-
tical. The statistical method of

investigating social questions has
Laplace for its most scientific and
Buckle for its most popular ex-
pounder. Persons are grouped
according to some characteristic,
and the number of persons forming

THE SCIENTIFIC SPIRIT IN FRANCE.

125

method has been most fruitful, and, far from being ex-
hausted, promises undreamt of results in the future. It
was probably more from the desire to keep his view
clear and his method simple, than with any necessarily
sceptical tendency, that when Laplace was questioned by
JSTapoleon how it was that in the great volumes of the
' Mecanique celeste ' the name of God did not appear, he
replied, " Sire, je n'ai pas besoin de cette hypothese."

But French science did not leave that great field of 27.

Individu-

research uncultivated, which is the very playground of ^^^y ^^Jf^
individual life. Its cultivation was the work of that the^dences
other great representative of French science — the con-
temporary of Laplace — Georges Cuvier.^ Linnaeus had

the group is set down under that
characteristic. This is the raw
material from which the statist
endeavours to deduce general theo-
rems in sociology. Other students
of human nature proceed on a dif-
ferent i^lan. They observe indi-
vidual men, ascertain their history,
analyse their motives, and compare
their expectation of what they will
do with their actual conduct. This
may be called the dynamical method
of study as apialied to man. How-
ever imperfect the dynamical study
of man may be in practice, it evi-
dently is the only perfect method
in principle, and its shortcomings
arise from the limitation of our
powers rather than from a faulty
method of procedure. If we be-
take ourselves to the statistical
method, we do so confessing that
we are unable to follow the details
of each individual case, and expect-
ing that the effects of widespread
causes, though very different in each
individual, will produce an average
result on the whole nation, from a
study of which we may estimate
the character and propensities of

an imaginary being called the Mean
Man."

^ It is not necessary here to ex-
plain the reasons which have in-
duced me to confine myself mainly
to the two great names of Laplace
and Cuvier as the great repre-
sentatives of the exact scientific
spirit, as it first asserted its su-
premacy in France, and from there
gradually fought its way all over
Europe. To me it seems that no-
where has this modern scientific
spirit been represented in greater
completeness and greater purity.
This is so much the more remark-
able, as other influences and tempta-
tions were not wanting in that age
and country which might have in-
terfered with the application of
the purely scientific method. The
scientific spirit is in danger of being
contaminated by two interests which
are essentially foreign to it : the
one is the practical, the other the
philosophical. Frequently they are
united ; and when united their influ-
ence on the progress of science has
frequently been disastrous. In no
department of knowledge has this

126

SCIENTIFIC THOUGHT.

begun the work of natural history by inventing a system
of classification and a technical language or nomenclature.
Buffon in his brilliant and elegant portraits had cast around
it the charms of poetry and romance. Jussieu had im-
ported botany from Sweden into France, and in the garden
of Trianon had given a living model of the arrangement
of plants ; botanising had become popular through the

union of the practical and pliilo-
sophical spirit been more marked
than in the medical sciences. Essen-
tially interested as it is in the im-
mediate application of scientific dis-
coveries to the needs of suffering
mankind, we witness in the course
of the seventeenth and eighteenth
centuries a one-sided alliance of the
art of healing with chemistrj'' (Sylvi-
us, 1614-1672), with physics (Borelli,
1608-1679), and with mechanics(Pit-
cairn, 1652-1713), and the reaction
of the animists (Stahl, 1660-1734,
and Hoffmann, 1660-1742), and the
vitalists (Bordeu, 1722-1776, and
Barthez, 1734-1806). A large por-
tion of the history of medicine (see
Haeser, 'Geschichte der Medicin,'
Jena, 1881, vol. ii., and Guardia,
* Histoire de la Medecine,' Paris,
1884) consists in the account of the
opposition to premature generalisa-
tions, adopted from other sciences,
or still more dangerously from meta-
physics. As examples of the meta-
physical tendency we havetheScotch
systems of Cullen and Brown, and
the German ' ' Philosophy of Nature. "
The reasons why philosophy has so
frequently allied itself with medi-
cine, thus preventing the purely
scientific spirit from gaining ad-
mission, ai'e twofold. " Young
men," says Cuvier, " adojit these
theories with enthusiasm, because
they seem to abridge their studies
and to give a thread in an almost
inextricable labyrinth" ('Rapport,'
p. 333). The other reason is that
the art of healing has as much a

psychological as a physical side,
and a philanthropic as much as
a scientific interest. In respect of
this it is well to note that the age
and country which gave to Europe
the great models of purely scientific
research in Laplace and Cuvier was
rich also in great thinkers wlio
applied themselves in a philoso-
phical spirit to the advancement of
scientific and practical medicine, to
the reform of hospitals, to the care
of the insane, to the education of
the deaf and dumb. The whole
school of the ideologues, headed by
Condorcet, Cabanis. and Destutt
de Tracy, was closely allied with
the medical profession. But how-
ever important this side of French
thought may have been, its in-
fluence on the rest of Europe at
that time cannot be compared
with that of the purely scientific
writings belonging to mathematics
and natural science. Such names
as Cabanis and Bichat belong to
a different current of European
thought, which I purposely separate
from the exact or purely scientific.
And this separation is justified his-
torically by the fact that in the
Acaddmie des Sciences for a con-
siderable time medical science was
only meagrely represented, whilst
philosophy during the period of the
suppression of the Academie des
Sciences morales et politiques, from
1803-1832, had no academic re-
presentation at all. The great
name of Bichat is not among the
Academicians, and Cuvier himself

THE SCIENTIFIC SPIRIT IN FRANCE.

127

writings of Eousseau ; gardening and the study of plant-
life had become a royal pastime, and a favourite recrea-
tion for those oppressed with the troubles of the State
or the sorrows of private life. Cuvier, while asking the
reason why other portions of natural history had not
shared the same attention, breaks out into the following
eloquent words : " The study of animals presents diffi-

€xplains the exclusive attitude of
the Academy ,to the medical pro-
fession in his Eloges of Halle, Cor-
visart, and Pinel (' Eloges,' vol. iii. p.
339, &c._) See also Maury (p. 304) :
" Les sciences physiques, chimiques
et naturelles avaient pris une telle
extension dans les travaux de
I'Academie, qu'a la fin du dix-
huitieme siecle, la medecine, qui
n'y avait jamais ete au reste bien
largement representee, fut de plus
en plus releguee a I'arriere plan ;
<;e n'etait plus que de loin en loin
<j[ue les m^decins, les chirurgieus de
la Compagnie, . . . y presentaient
des observations sur des points
medicaux. ... La medecine, qui,
selon la juste observation deCabanis,
tend aux hj'pothcses par la nature
memedu sujetauquelelle s'applique,
n'offrait point assez de Constance
■dans ses principes et d'evidence
dans ses demonstrations pour satis-
faire des esprits qui se detachaient
tous les jours davantage des vieilles
speculations de r(5cole. C'est ce qui
«xplique le peu de faveur qu'elle
rencontrait a I'Academie." To what
extent this rigid demarcation, ac-
cording to vehich " observations
relatives aux dispositions morales
et intellectuelles des individus
n'entrent assurement dans les
attributions d'aucune acaddmie des
sciences " (' Memoires de I'Institut,'
vol. ix. p. 110), was beneficial to
medical science is an important
■question. In the organisation of
the Institute of the 3rd brumaire, an
iv. (25th October 1795), there are

awarded out of 60 members only 6
to medicine and surgery combined,
and in the " nouvelle organisation "
of 3rd pluviose, an xi. (23rd January
1803), there are 6 members out of
63. This section is given as the last,
even after ' ' economic rurale et art
v^terinaire" (see Aucoc, ' L'Institut,'
p. 3, &c.). It is interesting to note
how in contrast to this the medical
profession occupied for a long period
a foremost place in the Royal Society
of London, so much so that fre-
quently opposition was made to the
admission of new members belong-
ing to it (see Weld, ' History of the
Royal Society,' vol. i. chap. 4 ; vol.
ii. p. 153). Of 5336 papers contained
in the ' Philosophical Transactions '
from 1665 to 1848, 1020, the largest
number in any department,belonged
to anatomy, physiology, and medi-
cine (ibid., vol. ii. p. 565). Babbage
complained of the influence of the
Colleges of Physicians and Surgeons
in the Royal Society, as occasionally
filling the pages of the ' Transac-
tions ' with medical papers of verj-
moderate merit ; and also because
the preponderence of the medical
interest introduces into the Society
some of the jealousies of that pro-
fession ('Decline of Science in Eng-
land,' 1830, p. 188). In the founda-
tion of tlie British Association this
union with the medical interest
was dropped ; though the older
" Versammlung deutscher Natur-
forscher und Arzte," after which it
was modelled, established and
maintained that union.

128

SCIENTIFIC THOUGHT.

28.
Into this
centre
Cuvier car-
ried exact
research.

culties which only great zeal can surmount ; we have
to subject them to torments in order to appreciate their
physical powers ; their innermost energies only reveal
themselves to the dissecting-knife — only by living among
corpses can we discover them. Among them we find the
same spectacle as in the world, whatever moralists may
say : they are hardly less wicked or less unhappy than
we are ; the arrogance of the strong, the meanness of
the weak, vile rapacity, short pleasures bought by great
efforts — death brought on by long suffering — that is the
rule among animals as much as among men. With
plants existence is not surrounded by pain — no sad
image tarnishes their splendour before our eyes, nothing
reminds us of our passions, our cares, our misfortunes —
love is there without jealousy, beauty without vanity,
force without tyranny, death without anguish — nothing-
resembles human nature." ^

Into the centre of individual and organised life — the
life of the animal and human creation — Cuvier carried
exact research, grounding it on the science of compara-
tive anatomy.^ At the same time, he marked out as the
principal problem, around which all investigations must
turn, and upon which all classification must depend.

^ 'Eloges historiques,' vol. i. p. 91.

^ Cuvier, in the Introduction to
' Le Regne animal, distribue d'apres
sou organisation, pour servir de base
a I'histoire naturelle des animaux
et d'introduction a I'anatomie com-
par^e' (Paris, 1817), says that for
thirty years he had devoted to com-
parative anatomj' all his time (p.
v), that the first results had ap-
peared in 1795, his 'Lemons d'Ana-
tomie comparee' in 1800 (p. vii),
that he has made anatomy and zool-

ogy march side by side (p. vi). He
compares natural history as a science
with other sciences, stating that
dynamics is become a science almost
entirely of calculation, that chem-
istry is still a science altogether of
experiments, that natural history
will for a long time to come remain
in most of its parts a science of ob-
servation (p. 5) ; he maintains that
geometry is a study of syllogisms,
natural history a study of method
(p. xviii).

THE SCIENTIFIC SPIRIT IN FRANCE.

129

the phenomenon of individual life, that great vortex into
which agencies, processes, and the elements of inorganic
nature are continually drawn, from which they are con-
tinually ejected, preserving not the unity of substance
but, among changing events, the unity of form.^

" It is not," he says, " in the substance that in plants
and animals the identity of the species is manifested, it is
in the form. There are probably not two men, two oaks,
two rose-trees, which have the compound elements of
their bodies in the same proportion — and even these
elements change without end, they circulate rather than
reside in that abstract and figured space which we call
the form ; in a few years probably there is not left one
atom of that which constitutes our body to-day — only the
form is persistent ; the form alone perpetuates in multiply-
ing itself ; transmitted by the mysterious operation which
we call generation to an endless series of individuals, it
will attract successively to itself numberless molecules of
different matter, all of them merely transient." "

^ " La vie est done un tourbillon
plus ou moins rapide, plus ou moins
complique, dont la direction est
constante, et qui entraine toujours
des molecules de memes sortes,
mais oil les molecules individuelles
entrent et d'oii elles sortent con-
tinuellement, de maniere que la
forme du corps vivant lui est plus
essentielle que la maticre" ('Regne
animal,' p. 13, &c.) "II vient
sans cesse des elements du dehors
en dedans : il s'en echappe du de-
dans au dehors : toutes les parties
sent dans un tourbillon coutinuel,
qui est une condition essentielle du
ph^nomene, et que nous ne pouvons
suspendre longtemps sans I'arreter
pour jamais. Les branches les plus
simples de I'histoire naturelle par-

VOL. I.

ticipent dejJi h, cette complication
et h ce mouvement perp^tuel, qui
rendent si difficile I'application des
sciences generales"( 'Rapport,' p. 150,
&c.) " Dans les corps vivans chaque
partie a sa composition propre et
distincte ; aucune de leurs mole-
cules ne reste en place ; toutes
entrent et sortent successivement :
la vie est un tourbillon continue],
dont la direction, toute compliquee
qu'elle est, demeure constante, ainsi
que I'espece des molecules qui y
sont entrainees, mais non les mole-
cules individuelles elles-memes. . . .
Ainsi la forme de ces corps leur est
plus essentielle que leur matiere,"
&c. (ibid., p. 200).

^ ' Eloges historiques, ' vol. iii. p.
156.

130

SCIENTIFIC THOUGHT.

Keeping this unity of form, this aljsorljing vortex of
life, the totality of organisation, always before him,
Cuvier, in surveying the whole region of animated
nature,^ fixes finally for the purposes of classiiication and
division on that system of organs which expresses most
truly the peculiarity of each of the great branches into
which he divides the animal world — namely, the nervous
system." But rather than follow him at present into the

^ " La partie anatomique du prob-
leme general de la vie est resolue
depuis longtemps pour les animaux,
au moins pour ceux d'entre eux qui
nous interessent le plus. Les voies
que les substances y parcourent,
sont connues ; . . . il apercoit
aussi comment ces routes, si com-
pliquees dans I'homme, se simpli-
fient par degres dans les animaux
infdrieurs, et finissent par se reduire
a une spongiosite uniforme. Les
recherches de M. Cuvier — dans les
lemons d'anatomie comparee — ont
acheve d'assigner h, chaque animal
sa place dans la grande echelle des
complications de structure" ('Rap-
port,' p. 202, &c.)

^ It is not my object here to give
an account of the views of Cuvier,
still less of his contributions to
natural history, which — in spite of
the special theories and laws which
he and his followers established (see
especially Flourens, ' Histoire des
Travaux de Georges Cuvier,' S""**
ed., 1858) — remained in his hands
to the last pre-eminently a science
of observation. It has been pointed
out that Cuvier only graduallj' (pro-
bably about 181 2) arrived at the final
principle of division — riz., the ner-
vous system — and that he adopted
it from others (notably Virey and
De Blainville), that before 18"'l2 he
had successively used the organs of
generation (1795), of nutrition, and
of circulation as principles of clas-
sification. In his Report of 1808,

in mentioning his own labours,

he

says: "'M. Cuvier, en etudiant la
physiologic des animaux vertebrt^s,
a trouve dans la quantite respective
de leur respiration, la raison de leur
quantity de mouvemens, et par con-
sequent de I'espcce de ces mouve-
mens. . . . En effet, M. Cuvier,
ayant examine les modifications qu'
eprouveut dans les animaux sans
vertebres les organes de la circula-
tion, de la respiration, et des sensa-
tions, et ayant calcule les resultats
necessaires de ces modifications, en
a deduit une division nouvelle ou
ces animaux sont ranges suivant
leurs veritables rapports" ('Rap-
port,' p. 311, &c.) Compare also
Carus, ' Geschichte der Zoologie,'
Miinchen, 1872, p. 602 ; Flourens,
" Eloge de Cuvier," in his ' Eloges
historiques, ' 3""^ serie, Paris, 1862,
p. 122, &c. : Hahn in the ' Grande
Encyclopedie,'article "Cuvier." See
also the Introduction to the ' Regne
animal,' which proposes to arrange
living beings according to their " or-
ganisation," bj' investigating their
" structure," their " internal as well
as external conformation." Cuvier
here states that no one before had
tried to arrange the classes and
orders according to the ' ' ensemble
de la structure " (p. vi). He is thus
led to the law of the " subordination
des caracteres, . . . ayant soin
d'dtablir toujours la correspond-
ance des formes exterieures et in-
terieures qui, les unes comme les

THE SCIENTIFIC SPIEIT IN FRANCE.

131

details of his natural history, his comparative anatomy,
or his paltfcontology, of which latter sciences he is the
creator, it serves our present purpose better to learn how
he viewed the object of natural science in general — how
he defined its task. As the first step in civilisation was
the creation of a language possessing definite rules, so
the first step in the growth of a science is that taken by
Linnaeus, who was not terrified by this enormous work,
that of giving names, of framing a nomenclature."^ " But,"
says Cuvier, " to name well, you must know well. These

•autres, font partie integrante de
I'essence de chaque animal " (p. xiv).
He opposes former artificial classifi-
cations, such as the principle that
living beings can be arranged " de
maniere a former des etres une
seule ligne" (p. xx). " Un etre
organise est un tout unique, un
•ensemble de parties qui reagissent
les unes sur les autres pour produire
un effet commun. Nulle de ses
parties ne peut done etre modifiee
essentiellement sans que toutes les
autres ne s'en ressentent " (' Eloges,'
vol. ii. p. 279).

^ The formation of a nomencla-
ture or a terminology is one of the
most important steps in the begin-
ning and the progress of science.
•Cuvier refers frequentlj' to this :
"Nos livres saints, a leur debut,
■nous representent le Createur fais-
ant passer ses ouvrages sous les
jeus du premier homme, et lui
ordonnant de leur imposer des
noms. . . . Ces noms, qu'il est
prescrit a 1' homme d'imposer, ne
sont pas des signes incoherens ap-
pliques au hasard a quelques objets
isoMs. Pour qu'ils deviennent re-
guliers et significatifs, ils exigent,
comme il est dit, que les etres aient
passe devant le nomenclateur "
. (' Eloges,' vol. iii. pp. 450, 4.52). No-
where is terminology more import-

ant than in chemistry. "L'un des
moyens qui ont le plus puissamment
contribue a faciliter I'enseignement
de la science en general, et a pre-
l^arer I'adoption universelle de la
theorie nouvelle, c'est la nomen-
clature creee par cette societe de
chimistes francais. . . . Donner aux
elemens des noms simples ; en
deriver, pour les combinaisons, des
noms, qui exprimassent I'espece et
la proportion des elemens qui les
constituent, c'etait ofFrir d'avance
a I'esprit le tableau abrege des re-
sultats de la science, c'etait fournir
a la memoire le moyen de rappeler
par les noms la nature meme des
objets. C'est ce que M. Guyton
de Morveau proposa le premier des
1781, et ce qui fut completement
execute par lui et par ses collegues
en 1787" ('Rapport,' p. 88, &c.) Of.
'Eloges,' vol. iii. pp. 194, 482, 496.
Cuvier ('Eloges,' vol. iii. p. 302)
mentions "cette antipathie pour
les methodes et pour une nomencla-
ture precise a laquelle BuSbn s'est
laisse aller en tant dendroits " ; he
speaks of Pinel "qui avait cherchd
d'abord a former pour les descrip-
tions des maladies un langage pre-
cis, modele sur celui que Linnreus
avait introduit en botanique " (ibid.,
vol. iii. p. 386).

132 SCIENTIFIC THOUGHT.

beings and their parts which are to be known are to be
counted by the million ; it is not enough to know them
singly, for they are submitted to an order, to mutual
relations, which must likewise be appreciated, for it is
according to this order that each has its part to play,
that each disappears at its time, that they reappear simi-
larly made, always in the same proportions, and armed
with the necessary forces and faculties for the main-
tenance of these proportions, and of the whole of this
perpetual vortex. Not only is each being an organism,
the whole universe is one, but many million times more
complicated; and that which the anatomist does for
a single animal — for the microcosm — the naturalist is
to do for the macrocosm, for the universal animal,
for the play of this alarming aggregation of partial
organisms." "^

It was this sustained regard for the value of detailed
research and minute observation, coupled with an equal
appreciation of the unity of all regions of existence,
and all branches of learning, that elevated Cuvier to
the height of the science of his age and his country,
and made him a true exponent of the modern scientific
spirit. The works of Newton and Laplace may contain
more formulae of lasting value, more instruments of per-
manent scientific use — they may, for all time, have traced
a few lines of the enwoven cipher of the all-pervading
mechanism of nature ; it is, however, well to note that he
only who keeps in steadfast view the life rather than the
mechanism of existence, approaches the great secret of
nature, and gauges rightly the value of each component

1 Cuvier, ' Eloges historiques,' vol. iii. p. 453.

THE SCIENTIFIC SPIRIT IN FRANCE.

133

part, or the worth of each human effort.^ In this respect
the nineteenth century knows no greater figure than
Cuvier ; not even Humboldt, great and comprehensive as
was his scientific view. The advantages also of Cuvier's
position as permanent Secretary of the French Academy
of Sciences were exceptional, and well fitted to bring out
his extraordinary talents. We can say that in him science
has become fully conscious of its true methods, its useful-
ness, its most becoming style, its inherent dignity, its past
errors, its present triumphs, the endless career which lies
before it, and the limits which it cannot transgress.

Educated in Germany, at the same school as Schiller 29.

Cuvier's

and Dannecker, imbued by early experience and by training.

■• "C'estlacontinuation dececom-
maudement de voir et de nommer,
par ou s'ouvre la vie de notre espece,
c'est la voie qui devait nous con-
duire soit Ji des contemplations plus
hautes, soit seulement h, des inven-
tions utiles. En effet I'liistoire
naturelle ne fait aucun pas sans
que la physiologie et la philosophie
g^ndrale marchent d'un pas egal,
et sans que la societe recjoive leur
tribut commun " (' Eloges,' vol. iii.
p. 474).

^ Cuvier has himself written an
account of his early life and studies.
It is given by Flourens, ' Eloges,' vol.
i. pp. 167-193. He was born in 1769,
of a Protestant stock, at Mont-
b^liard, the capital of a small prin-
cipality, situated in the Jura, and
then belonging to Wiirtemberg.
The autocratic Duke Charles (1737-
1793) had founded a military acad-
emy in Stuttgart, his capital, where
400 youths were at his expense
housed and educated according to
a strict rule, but under the guid-
ance of enlightened masters, and in
a thoroughly modern spirit. The
institution was a kind of oppo-

sition to the Protestant Church
rule, which had very early spread
a system of popular and compulsory
education throughout the country.
It is a chapter of history well worth
reading. The great problems of
popular education as against higher
instruction, Protestant discipline in
the lower as against militarj' dis-
cipline in the higher schools, the
democratic as against the aristo-
cratic spirit, the independence as
against the State - regulation of
University teaching, were fought
out by the dukes and the Estates
of Wiirtemberg in a prolonged war-
fare, a sample of similar movements
all over Germany, and well told by
Perthes in his ' I'olitische Zustiinde
und Personen in Deutschland zur
Zeit der franzosischen Herrschaft '
(Gotha, 1862, pp. 501-548). Cuvier
evidently saw the better side of the
system, for he entered after the
imperious character of the duke
had been subdued by the victorious
estates. Forced to change his ways,
which he conscientiously did, the
duke laid by for his country, as a
local historian says, " a fund of in-

134

SCIENTIFIC THOUGHT.

personal contact with that spirit of general education
and universal training which then animated the German-
speaking nations of the Continent, thoroughly grounded
in classics and mathematics, with a cosmopolitan know-
ledge of languages and literature, which fitted him to
understand the merits of different nations, he became
the great exponent of that peculiar system of higher
culture which since the time of Colbert the French had
elaborated — the academic system/ The centre of this

telligence and acquisitions by which
we have benefited up to modern
times" (Perthes, p. 510). We know
the other and older side of the
picture from the ' Life of Schiller '
(see, i7ite7' alia, Carlyle, ' Life of
Schiller,' collected works, library
edition, vol. v. p. 258). Cuvier
gives a long description of the " Karl-
schule " : " C'etait un tStablisse-
ment vraiment magnifique. Envi-
ron quatre cents boursiers et pen-
sion naires, loges dans un edifice tel
qu'il n'y en a aucun d'approchant
en Europe (parmi ceux qui sont
consacres h, I'instruction de la jeun-
esse), vetus d'un bel uniforme, con-
duits par des officiers et des sous-
officiers tires des regiments du due,
recevaient des lecons de tout genre
de plus de quatre-vingts maitres ou
professeurs. On a beaucoup parle
de I'esprit de despotisme avec lequel
le due disposait de leurs personnes
et choisissait pour chacun d'eux
I'etat qu'il devait embrasser, et je
crois en effet qu'il en etait ainsi
dans I'origine de I'etablissement ;
mais de mon temps, je n'ai rien
vu de semblable, et ce qui est cer-
tain, c'est que personne ne prdtendit
meme me donner de conseil h, cet
%ard. II y avait cinq facult^s
sup^rieures, droit, mddecine, admin-
istration, militaire et commerce"
(Flourens, loc. cit., p. 171).

^ The first great representative

of this academic sjiirit and culture
was Fontenelle, who, living during
a hundred years, from 1657 to 1757,
was Secretary of the Academie des
Sciences during forty - two years,
from 1699 (the year of the recon-
stitutiou of the Academy) to 1741.
Among his successors were men like
Condorcet, Delambre, Cuvier, and
Arago. Fontenelle gave to scien-
tific subjects a dignified popularity,
separated the departmentsof science
and metaphysics, kept the scientific
interest free from the commercial,
and through his connection with the
Academic francaise did probably
more than any other writer to es-
tablish that superiority of style and
diction for which the great French
men of science are so remarkable and
so superior to those of other coun-
tries. Bertrand, himself a successor
of Fontenelle, says of him : "Pretant
aux travaux de ses confreres la
finesse de ses apergus et la vivacite
ingenieuse de son style, il a su dans
leurs portraits, qui sont des chefs-
d'oeuvre, plus encore que dans I'ana-
lyse de leurs decouvertes, donner
aux plus humbles et aux plus
modestes une ccldbrite imprevue
et durable, et le juste et serieux
hommage qu'il rend au vrai mdrite
fait aimer et respecter tout a la fois
les savants et la science" ('L'Aca-
ddmie des Sciences et les Acadcmi-
ciens,' p. 113). See also Voltaire's

THE SCIENTIFIC SPIRIT IN FRANCE.

135

system was the old Academy of Sciences, which, with
a short interruption during the storm of the Eevolution,
survived,^ and formed the principal feature in the Insti-
tute. Allied with this institution, and directly inspired
by its spirit, were the great schools of natural science, the
great collections of natural objects, latterly also the great
medical institutions of Paris. It professed to protect
scientific studies in a royal and generous manner, at-
tracted talent from outside, rewarded foreign as well as
French research," and tried to keep the scientific spirit
of inquiry, as well as the form in which it found
expression, pure and undefiled.^ It favoured the co-

' Siecle de Louis XIV.' ; Cabanis,
' Revolutions de la Medecine '
(CEuvres, Paris, 1823, vol. i. p. 200) ;
Flourens, 'Eloges historiques,' vol.
iii. p. 31, &c. ; Maury, ' Les Aca-
demies d'autrefois,' vol. i. p., 1.^)3,
163 et passim; Bouillier, 'Eloges
de Fontenelle,' Introduction.

^ " Tandis que tout a ete renou-
vele dans la politique et les moeurs
publiques ... la vie scientifique
et litteraire a sensiblement garde sa
constitution, ... Le College de
France, I'Academie francaise, I'Aca-
demie des Inscriptions et Belles-
lettres, I'Academie des Sciences, la
Bibliotheque imperiale, I'Observa-
toire, le Museum d'Histoire natur-
elle, subsistent encore, comme au
siecle dernier, et dans nos provinces,
une foule d'academies sont d'une
creation anterieure a 1789 " (Maury,
loc. cit., p. 1).

- " Euler fut quatre fois eouronne
pour des questions de physique et
de mathematiques. . . . Daniel
Bernoulli obtint le prix dix fois "
(Maury, , p. 171). Among the cele-
brated Eloges by Fontenelle there
are those of Leibniz, of Peter the
Great, of Newton, of Marsigli, of
Boerhaave ; among those by Con-

dorcet there are those of Haller,
Linnaeus, Hunter, and Euler ; among
Cuvier's there are those of Gilbert,
Priestley, De Saussure, Cavendish,
Pallas, Rumford, Werner, Banks,
and Davy.

^ "Jusqu'^ present," says Fon-
tenelle in 1699, "I'Academie des
Sciences ne prend la nature que
par petites parcelles. Nul systeme
general, de peur de tomber dans
I'inconvenient des systemes preci-
pites dont I'impatience de I'esprit
humain ne s'accommode que trop
bien, et qui, etant une fois etablis,
s'opposent aux verites qui survien-
nent " (quoted by Flourens, 'Eloges,'
vol. iii. p. 19). " L'esprit de I'Acad-
emie des Sciences a done toujours et6
I'esprit d'experience, d'etudedirecte,
d'observation precise, I'amour de la
certitude. D'abord cartesienne, elle
devint ensuite Newtonienne," &c.
(ibid., p. 21). Fontenelle contrasts
the " philosophie ,des mots et celle
des choses,,de I'Ecole et de I'Aca-
demie" ('Eloge de Du Hamel' in
Bouillier, p. 10). " Fontenelle se
plait a multiplier les exemples de
cette incapacite chez les savants de
faire fortune et de ce noble des-
interessement." "Ilaimait mieux

136

SCIENTIFIC THOUGHT.

30.
Cuvier the
greatest
representa-
tive of the
Academic
system.

operation of many minds in rearing the great edifice of
science, and found a place for the minutest research, as
well as a field for the development and sway of great and
governing ideas. Of the best form of this spirit and
system — the Academic — Cuvier was the greatest repre-
sentative. Through several dozen filoges which he pro-
nounced on the decease of a number of the most illus-
trious scientific men of Europe, as well as through
several Eeports, in which he summed up the labours and
progress of his age, and the peculiar features of his period,
he affords to the student of history an insight into that
distinctive phase which scientific thought had entered in
France at the end of the eighteenth century. This he
allows us to contrast with other phases of thought, such
as the philosophical or individual, which obtained in other
ages or countries, and suggests as well as gives the means of
answering the question, to what extent the scientific ideal

etudier que subsister," he said of
one of the Academicians (BouiUier,
pp. ix, xii). Cuvier was very watch-
ful over the Academy in keeping
out the speculative spirit. See
■what he says in the joint Report
on geology with Haiiy and Lelievre
('M(5m. de I'lnstitut,' vol. viii. 1607,
p. 136). " Que doivent done faire
le.s corps savans pour procurer h, une
science aussi interessante et aussi
utile, les accroissemens dont elle est
su.sceptible ? ... lis doiveut tenir
la conduite, qu'ils ont tenue depuis
leur etablissement, \i I'egard de
toutes les autres sciences : encour-
ager de leurs dloges ceux qui con-
statent des faits positifs et garder
un silence absolu sur les systemes
qui se succedent. " Compare with
this what he says about the use of
the principle of "vital force," al-
ways referring to Newton's method

('M^m. de I'lnst.,' vol. vii. p. 77,
&c.), further in his analysis of Gall
and Spurzheim's Memoire ('M^m.
de I'Inst.,' vol. ix. p. 65): "Les
commissaires de la classe . . . ont
donn^ leur assentiment h. presque
toutes les propositions de MM. G.
& S., qui ne dependent que de
I'inspection anatomique, &c. . . .
les commissaires ont cru dgale-
ment de leur devoir de prevenir le
public, qu'il n'y a aucun rapport
direct, aucune liaison necessaire
entre ces decouvertes et le doctrine
enseignee par MM. G. & S., &c. . . .
Toutes ces mati5res sont encore trop
etrangeres aux attributions de la
classe, elles tiennent aux faits sen-
sibles d'une mani6re trop lache,
elles pretent a trop de discussions
vagues, pour qu'un corps tel que
le notre doive s'en occuper" (p.
159).

THE SCIENTIFIC SPIRIT IN FRANCE.

137

of the end of this century agrees with or differs from that
of its beginning. Upholding the Newtonian rather than
the Baconian and Leibnizian standard in the mathemati-
cal and physical sciences/ he has marked that line which
our whole century has contributed to trace out more dis-
tinctly; whilst, as regards the purely natural sciences, his
continued emphasising of the great problem of organisation,
and his later controversy with Geoifroy de Saint-Hilaire,
mark that point in which this century has most distinctly
departed from the prevailing ideas of its early years.^
He also recognised earlier than any other mind of similar
eminence what our century increasingly realises, how,
without a system of condensation, contained in reports,
statistics, and figures, aided by classifications and systems,
the growing bulk of accumulated knowledge becomes

chaotic and unmanageable.^

^ Cuvier was not brought up in
the school of the Eucyclopsedists,
and I cannot find that he attached
the great importance to the writ-
ings of Bacon which that school
commonly did. As to Newton and
Leibniz, he contrasts their methods,
considering them "comme les chefs
et les reprdsentans des deux
methodes oppos^es qui se sont dis-
pute I'empire de la science" ('His-
toire des Sciences naturelles,'
publiee par Magdeleine de Saint-
Agy, Paris, 1841, vol. iii. p. 19,
&c.) See also in his joint Report
with Haiiy and Lelievre on the
Science of Geology ('Mem. de I'ln-
stitut,' 1807, p. 133): "On vit
renaltre dans cette partie de I'his-
toire naturelle la methode systema-
tique de Descartes, que Newton
semblait avoir bannie pour jamais
de toutes les sciences physiques,
. . . et lorsqu'on songe que Leib-
niz et Buflon sont au nombre

des philosophes dont je parle ici,"
&c.

^ A future chapter will deal speci-
ally with this subject. Cuvier, as
is well known, maintained the fixity
of species, and opposed the theories
of St Hilaire and Lamarck, in which
a later generation recognises the
beginnings of the Darwinian doc-
trine of the transmutation of species.
"On est oblige d'admettre certaines
formes, qui se sont perpetuees
depuis I'origine des choses, sans
exceder ces limites ; et tous les
etres appartenans h. I'une de ces
formes constituent ce que I'on
appelle une espece " (' Regne ani-
mal,' vol. i. p. 20).

•* Cuvier was the first great scien-
tific writer who undertook to give
a historical survey of the position
of the different natural sciences,
with a view of ascertaining what
had been achieved and what re-
mained to be done. He did what

138

SCIENTIFIC THOUGHT.

31

On the

Ciivier had also a true historical sense, which enabled
him to trace the connection of science with political
history, with literature, with the fine and useful arts.
And he helps to answer a question which to us is of
sciencedur- paramount interest, How did science fare during the
wfutioifand great cataclysm of the Eevolution ? how under the reac-
Empire! tionary despotism of the First Empire ? Before attempt-
ing to reply to these questions in the light of subse-
quent and general European history, I will select a few
passages from Cuvier which throw light upon these
points : ^ —

" There is always a revolution required in order to
change habits which have become general, and the most
necessary revolutions do not take place without some
circumstance, which is sometimes long delayed. We
have been able to see how in such a case everything
furthers the sciences, even the delays and contrarieties
which they seem to suffer under.

" The events which disturbed the world, and which for
natural science temporarily dried up the sources of its
riches,^ obliged it to return to itself, and to make a new
study of what it possessed, more fruitful than the most

a generation later the British Asso-
ciation undertook to do, and what
in Germany the many "Jahres-
beriehte" do nowadays. See his
"Analyse des Travaux," &c., 'Mem.
de rinstitut,' vol. ix. p. 53, and his
celebrated 'Rapport historique sur
le Progr^s des Sciences naturelles
depuis 1789,' Paris, 1810.

^ ' Eloges historiques,' vol. iii. p.
456, 1824.

■^ This refers to the isolation of
France during the war and the Con-
tinental blockade, which deprived

it of foreign imports and the scien-
tific collections of foreign specimens ;
see also ' Eloges,' vol. i. p. 9; vol. iii.
p. 202 : " Quand la jalousie des
peuples .' nous privait des i^roduits
etrangers, la chimie les faisait eclore
de notre sol." " Le conseil des
mines etabli en 1793, lorsque I'in-
terruption de tout rapport avec
r^tranger fit sentir le besoin de
tirer parti de notre territoire a
donne a ces sortes de recherche.s
une impulsion toute nouvelle "
('Rapport,' p. 178).

THE SCIENTIFIC SPIRIT IN FRANCE.

139

fortunate departures could have been. During this ap-
parent rest, all the different parts of method were deep-
ened ; the interior of natural objects was studied ; even
minerals were dissected and reduced to their mechanical
elements ; a still more intimate analysis was made by a
perfected chemistry ; the earth itself was, during this
interval, if the expression is allowable, dissected by the
geologists ; its depths were sounded ; the order and layers
of rock which form its shell were recognised,^ In the
absence of foreign contributions the interior of the soil
on which we walk became tributary to science. The
beings of which it contains the remains came to light,
and revealed a natural history anterior to that of to-
day, different in its forms, and nevertheless subject to
similar laws, thus giving to these laws a sanction which
no one expected. The botanists did not gather so many
plants in their collections, but with the lens in hand they
demonstrated more and more the intimate structure of
the fruit, the seed, the various relations which connect
the parts of the flower, and the indications which these
relations furnish for a natural division. The most deli-
cate forms of organic tissues were exhibited ; medicine

^ Cuvier refers here to the inves-
tigation of the fossils in the Paris
basin, which he undertook during
the years 1804 to 1808 : " La singu-
larite des animaux dont je decouv-
rais les ossements a Montmartre
me fit desirer de connaitre plus en
detail la composition geologique des
environs de Paris. Mon ami Brong-
niart s'associa a moi pour ce travail ;
nous fimes ensemble et separement
beaucoup de courses. . . . Ces
recherches ont donne une face toute
nouvelle a la geologie, et ont occa-

sionue toutes celles qu'ont faites
ensuite en Angleterre MM. Webster.
Buckland, Labeche et autres "
(Cuvier, "Mem. sur sa Vie" in
Flourens, ' Eloges,' vol. iii. p. 188).
This was the beginning of the
Science of Palseontologj', a term
which Cuvier did not use himself
(Flourens, 'Travaux de Cuvier,' p.
147). See also Cuvier, 'Recherches
sur les Ossemens fossils de Quadru-
pedes,' &c., 1st ed., 1812, 3rd ed.,
1825, in the Introduction.

140 SCIENTIFIC THOUGHT.

and chemistry united their efforts to appreciate in the
minutest detail the action of external elements on the
living organism.^ The different combinations of organs,
or what we call the different classes, the different genera,
were not less studied than general theories. There were
no animals, ever so small, the inner parts of which,
unveiled by anatomy, did not become known as well
as our own. Every organic system was likewise sub-
mitted to a special examination. The brain, marking
the degree of intellectual power ; the teeth, signs of
the nature and energy of the digestive forces ; the bony
system, above all, which is the support of all others,
and which determines the connected forms of animals,
— all these were followed into the smallest species and
into the minutest parts. We see how, after such studies,
there could be no more talk of superficial or artificial
methods. The old natural history had ceased to rule.
It was not that old natural history any more, but a
science full of life and youth, armed with quite novel
ways and means, which beheld the world reopened by
the Peace." ^

In an earlier passage,^ speaking of the reopening of
academies and schools by the Government of the Revolu-

^ Compare with this the ' Rap-
port' of the year 1808, p. 201, &c.
The above remarks refer mainly to
Bichat. " Bichat a donnd a I'ana-
tomie un grand interet, par I'opposi-
tion de structure et de forme qu'il
a developpee, entre les organes de
la vie animale, c'est-a-dire, du senti-
ment et du mouvement, et ceux de
la vie purement v^g^tative. . . .
L'attention particuli^re donn^e par
Bichat au tissu et aux f onctions des
diverses membranes, et I'analogie

qu'il a 6tablie entre celles de parties
tres dloigndes, ont jete aussi des
lumieres nouvelles sur I'anatomie,
principalement dans ses rapports
avec la medecine " ('Rapport,' p.
218).

- This refers to the peace which
concluded the Napoleonic wars, and
re-established the free intercourse
of France with the rest of the world.

^ In the "Eloge of Fourcroy,"
of the year 1811 (' Eloges,' vol. ii.
p. 40, &c.)

THE SCIENTIFIC SPIRIT IN FRANCE.

141

tion, Cuvier remarks : " It was not merely a question of
isolated discoveries, but of institutions, which, in assuring
the conservation of the sciences, would multiply their
progress indefinitely. What was needed was no longer a
simple experimenter, master of his subject and his instru-
ments, it was a man obliged to battle against all kinds of
obstacles, and to benefit his fellow-citizens, mostly in spite
of themselves. The Convention had destroyed academiesT]
colleges, universities ; nobody would have dared to ask '
boldly for their restitution ; but soon the effects of their
suppression showed themselves in the most susceptible
point ; the armies were without doctors and surgeons, |
and these could not be created without schools.-^ But
who would believe that time was required to give courage
enough to call them schools of medicine. Doctor and
surgeon were titles too contrary to equality, apparently
because there is no authority over the patient more neces-
sary than that of the doctor ; therefore the odd term
" schools of health " was used, and there was no question
of either examination or diploma for the students. In
spite of this, a penetrating glance reveals, in the regula-
tions which were carried, the intentions of him (Fourcroy)
who drew them up. The three great schools founded at

1 See ' Eloges,' vol. i. p. 353.
" Cependant les gens qui avaient
fait toutes ces suppressions eurent
promptement lieu de s'apercevoir
que, s'il ^tait a la rigueur superflu
d'apprendre toute autre chose, on
ne pouvait guere se dispenser d'ap-
prendre la medeciue. Toute la
France se precipitait aux fronti^res,
et, apres des prodiges inouis de
ddvouement et de valeur, les defen-
seurs de la patrie ne trouvaient

aucun secours pour leurs blessures
et pour leurs maladies. On com-
men9a done par I'erection des ecoles
de medecine cette lougue suite de
restaurations, que I'etablissement
de I'universite vient de couronner
et de lier en un ensemble aussi
imposant par I'etendue de son plan
que par la vigeur de son organisa-
tion." See also 'Rapport,' &e., p.
360.

142 SCIENTIFIC THOUGHT.

this epoch/ received an abundance of means, of which
up to that time there was no idea in France, and which
still form the finest ornament of the University."

Similar passages might be collected in which Cuvier
enlarges on the influence of war and revolutions, of the
Continental blockade and the isolation of the countrv ; on
the reconstruction of hospitals and the admission of medi-
cal science into the Academy ; on the creation of new
industries ; on the development of the mining and mineral
wealth of the country ; on the scientific value of colonies
and travels, and many other interesting topics. In con-
fining myself more closely to the history of thought and
the growth of the modern scientific spirit, I will make
some reflections which his remarks force upon us.

32. I have noted above how France more than any other

France lias "^

tCn ™her ^ountry worked for the popularisation of science, how her
popuiaHse° politc literature alone during the eighteenth century bears
the strong impress of modern scientific ideas ; no other
country has a Fontenelle, a Voltaire, a Buffon. This
peculiarity must be recognised as a very powerful and
valnal)le stimulus to the growth of the scientific spirit.
It emanates largely, if not exclusively, from the peculiar
position of the old Academy of Science. It must, how-
ever, not be forgotten that it was not a popularisation of
the kind we witness nowadays.

33. The class of literature which in our age spreads broad-

Diffeiencc

between ti>e cast the discovcries or ideas of science : the endless num-

literary and

^oViaris.r' ^-"^^ °^ magazines, reviews, and daily papers ; the small
treatises, the cheap primers, the compact text-books, did

^ They were the three " Ecoles de
Saute" at Paris, Strasbourg, and
Montpellier (see Hippeau, ' L'ln-

tion.

^ They were the three " Ecoles de | struction publique en France,' vol
Sante" at Paris, Strasbourg, and ii. p. 194).

THE SCIENTIFIC SPIKIT IN FRANCE. 143

not tlien exist.^ Science was not a subject of general, still
less of popular, instruction. It was an occupation of the
few, who, privileged by fortune or talent, or gifted with
inordinate perseverance, forced their way into the salons
of society'^ or the rooms of the Academy. The first public
course of natural history was opened in Paris by Valmont
de Bomare in 1760.^ Science still stood far out of the reach
of the practical man or the poor man ; it had not yet
become an element of education or an instrument for
industry. It was a fashionable pursuit, a luxury of the
great, a key that occasionally opened the door of the
palace ; but it was not a thing of immediate use, except
in adding glory and renown to its royal protectors, or
to the rare genius which could make new discoveries.
Almost the only application made of it was in naviga-
tion, and in the construction of instruments connected
therewith. This essentially literary — not national —
popularisation of science had also its great dangers. Daagwsof

Tii6 iiiGrdv

No ideas lend themselves to such easy, but likewise to uterarypop

ularisation.

such shallow, generalisations as those of science. Once
let out of the hand w^hich uses them, in the strict and
cautious manner by which alone they lead to valuable
results, they are apt to work mischief. Because the tool
is so sharp, the object to which it is applied seems to be

I

34. I

^ Cuvier, in his 'Rapport,' &c., p.
361, mentions the elementary works
published by some of the medical
professors at the beginning of the
century, but says also that " En
Allemagne, surtout, ou I'usage des
livres elemeutaires est plus commun
que chez nous, il n'est presque
aucune universite, dont les profes-
seurs n'en aient public d'excel-
leus."

- See Maury, p. 182, &c. Also Cu-
vier, ' Rapport,' vol. ii. p. 427 : " En
France la reputation des ouvrages
d(^pend, pour I'ordinaire, des f emmes
et de quelques gens de lettres, qui
croient pouvoir juger des sciences
positives, parce qu'ils ont combine
quelques idees generales de meta-
physique."

^ See Maury, ' L'ancienne Acad-
emie des Sciences,' p. 283.

144

SCIENTIFIC THOUGHT.

SO easily handled. The correct use of scientific ideas is
only learned by patient training, and should be governed
by the not easily acquired habit of self-restraint. It is
r well known how the fundamental notions of a mechanical
science, let loose into literature by Fontenelle, by D'Alem-
bert, by Condorcet, or absorbed by Voltaire and Diderot,
were expanded into a system of materialistic philosophy
in ' L'Homme Machine,' the ' Systeme de la Nature,' and
other works, the extreme views of which the great scien-
tific thinkers could hardly approve of.^ These hasty but

^ As a great deal of confusion ex-
isted for a long time in European
literature as to the exact succession
in time of the different works which
assisted to spread mechanical views
of the world and of life, I put down
the main dates : —

Fontenelle (1657-1757) published
his Eloges of the great Academi-
cians, in which the principles of
the philosophy of Descartes, Leib-
niz, and Newton were popularly
expounded and discussed, from
1700 onward. His 'Plurality des
Mondes' had appeared already in
1686 ; it had popularised Cartesian
ideas.

Voltaire (1694-1778) published
his ' Elemens de la Philosophie de
Newton' in 1738.

La Mettrie (1709-51) published
his ' Histoire naturelle de lAme'
in 1745, and his 'L'Homme
Machine' in 1748.

DAlembert and Diderot pub-
lished the first volume of the ' En-
cyclopedic' in 1751.

Buffon (1707-88) published, 1749,
his ' Th^orie de la Terre,' being the
first portion of the ' Histoire natur-
elle.'

Holbach (1723 - 89) published
under the name of Mirabaud,
1770, the ' Systfeme de la Nature.'

Of these works, the three which

created the greatest popular sensa-
tion— vis., Voltaire's 'Elemens,'
La Mettrie's ' L' Homme Machine,'
and Holbach's ' Systeme ' — were all
published in Holland. Voltaire,
D'Alembert, and Diderot appear to
have approached philosophical prob-
lems mainly from the position of
Newton's natural philosophy. La
Mettrie from the teachings of the
great Boerhaave, Holbach princi-
pally from a study of chemistry,
it is unnecessary to say that none
of them had the sanction of their
great masters for the applications
they made of principles which had
been established and used for special
scientific purposes. And the same
may be said with reference to the
influence of Locke, which in almost
all the instances mentioned was
combined with that of the great
naturalists. But this does not be-
long to the line of thought in which
we are interested at present. For
the sake of completeness only I
mention that Locke's teachings as
well as Newton's were made popu-
larly known in France by Voltaire's
' Lettres sur les Anglais ' (burnt by
order of the Parliament of Paris in
1734), whereas Condillac's (1714-80)
more systematic treatise, entitled
'Essaisurl'OriginedesConnaissances
humaines,' appeared in 1746. It is

THE SCIENTIFIC SPIRIT IN FRANCE.

145

brilliant generalisations, expressed frequently in the most
perfect language, did no good to the truly scientific cause ;
they did not spread the genuine scientific spirit. Much
of the good done by Fontenelle, by Voltaire, by Buffon,
was spoiled or neutralised by premature and ill-founded
theories. How much, or how little, they contributed
(either directly or by a kind of reactioa. which set in
against them, of which Eousseau may be regarded as the
centre) to bring about the Eevolution is a matter of
much controversy ; certain it is that the Eevolution
broke their sway, and destroyed their immediate influ-
ence.^ To the purely literary the Eevolution added

35.
The Kevolu-
tion added
the modem
practical
popularisa-
tion of
science.

important, in dealing with the ex-
treme materiaHstic writings which
French Hterature produced between
1745 and 1770, to keep distinct the
different origins from which they
started, and the different influences
which combined to produce them :
the mathematical and mechanical
principles borrowed from Newton,
the physiological and medical eman-
ating from Linnaeus and Boerhaave,
and the psychological coming from
Locke and Shaftesbury. Lange, in
his ' History of Materialism ' (transl.
by Thomas, London, 1880, 3 vols.),
was the first to point out clearly the
correct chronology and succession
of these writings (see especially vol.
ii. pp. 49-123), and to dispel the
misconceptions which, since the ap-
pearance of Hegel's ' Geschichte der
Philosophie' in 1833-36, had passed
through nearly all historical works
published in Germany. From his
exhaustive references, it is evident
that the extreme views of La
Mettrie, Diderot, and Holbach can-
not be fathered on any of the great
scientists or philosophers, but were
an attempt to apply scientific prin-
ciples to the solution of philosophi-
cal, ethical, or religious questions,

VOL. I.

frequently for practical and politi-
cal purposes.

^ It would probably be more
correct to say that these daring
attempts to deal with the general
problems of knowing and being,
with the nature of the soul and the
conduct of life, were discarded as
premature, and that the followers
of Condillac and Locke betook them-
selves to a more patient study of
the facts of the inner life, as the
followers of Buffon forsook his bril-
liant generalisations for the more
patient and fruitful study of all
the forms of phj^sical nature. And
in this respect the Government of
the Revolution took a memorable
step when it founded on the 3rd
brumaire, an iv. (25th October
1795), on a Report of Daunou,
based mainly on ideas expounded
by Condorcet, the " Academic des
Sciences morales et politiques." It
was the intention to abandon meta-
physical generalisations, and to com-
bine the scientific and historical
spirit in the study of mental,
moral, and social phenomena, draw-
ing extensively on the assistance of
the medical sciences, or a know-
ledge of human nature in its nor-

K

146

SCIENTIFIC THOUGHT.

something different — viz., the modern practical popular-
isation of science : it established its educational and its
technical importance. Science was to be not an elegant
amusement, or a refined luxury, nor even exclusively
the serious occupation of the rare genius : it was to be
the basis of a national instruction, and the foundation
of the greatness and wealth of the nation. The Memoirs
of the Academy were cleansed of all dangerous general-
isations which might have brought them into touch with
political controversy ; the language was confined to the
measured and concise statement of facts, or to theories
capable of mathematical verification and treatment ; con-
jectural matter was carefully excluded, and a standard of
scientific excellence, both in matter and form, was raised,
to which we still look up with admiration.^ At the same
time, this lofty and dignified spirit enlivened the courses

mal and diseased conditions. This
organisation produced, during its
sliort existence of only seven years,
some memorable works ; but its
position was for various reasons
secondary only : it was eclipsed by
the European renown which the
"Academie des Sciences" possessed,
owing to its historical antecedents
and its brilliant discoveries and the
practical usefulness of its labours.
But the idea of including ethical
and political studies under the term
"Science," due probably to Con-
dorcet, was fixed by this organisa-
tion, and has in the course of the
century acquired increasing influ-
ence. From these beginnings we
shall have to study its career in an-
other portion of the present work.

1 According to Cuvier, " la langue
naturelle de I'Academie des Sci-
ences" is "la langue des chiffres "
(' Eloges,' vol. i. p. 24) ; "I'Acade-
mie a tou jours eu pour principe de

ne se rendre qu'a des calculs ou ii des
experiences positives" (vol. iii. p. 12).
Compare also 'Mem. de I'lnstitut,'
vol. vii. p. 77, where he speaks of
the method of Newton, showing
how little the employment of a
principle like that of " vital force "
in physiology can be compared with
that of gravitation, employed by
Newton to explain the movement
of the heavenly bodies ; again, vol.
viii. p. 139, where he refers to the
great service rendered by the Aca-
demy, "s'il parvenait a diriger les
esprits vers des reeherches positives,
mais longues et pdnibles." And
vol. ix. p. 61 : " On aime toujours
kvoir se multiplier dans les sciences
expdrimentales les moyens simples
d'arriver h, la precision et de se
rapprocher des sciences math^ma-
tiques," and other passages quoted
above, p. 115 and p. 128. See also
his remarks on the Philosojihy of
Nature, 'Rapport,' p. 335.

THE SCIENTIFIC SPIRIT IN FRANCE.

147

of lectures delivered in the great schools by the first men
of the nation, and became, through them, the habit of a
large number of ardent pupils, who were to carry it fur-
ther into more popular teaching, or into the applications
of art and industry.^ The results of both are well known.
We still live, at the end of the century, under their im-
mediate influence. If now we continually appeal to scien-
tific authorities for aid in the solution of practical prob-
lems, it is well to remember that nothing helped more to
raise science to the eminence of a great social power than
the action of the Eevolutionary Government in 1793.'
Whilst it guillotined Lavoisier, Bailly, and Cousin ; drove
Condorcet to suicide, and others like Vicq-d'Azyr and
Dionis du Sejour into premature death ; ^ it had to ap-

^ See Cuvier, " Reflexions sur les
Sciences," 1816, in 'Eloges,' &c.,
vol. i. p. 24, &c. : " Que Ton re-
cherche, ce qu'ont valu a la France
depuis vingt ans les inventions
pratiques derivees des decouvertes
de MM. BerthoUet, Chaptal, Yau-
quelin, Thenard, &c., dans la seule
chimie minerale, dans cette branche
assez bornee des sciences physiques ;
I'extraction de la soude, la fabrica-
tion de I'alun, du sel ammoniac, des
oxydes de plomb, des acides mine-
raux, toutes substances que nous
tirions de I'etranger ; I'epuration
des fers, la cementation de I'acier
et enfin le developpement des arts
qui emploient ces matieres premi-
eres : il est clair que c'est par cen-
taines de millions qu'il faudra cal-
culer." Also, vol. iii. p. 202 : " Les
applications de la science h la pra-
tique avaient fait de M. BerthoUet,
lorsque la guerre de la revolution
dclata, le chimiste le plus connu du
public, apres Lavoisier ; et il etait
presque impossible que Ton ue re-
courut pas h. lui au moment oil la

chimie devint pour la guerre un
auxiliaire de premiere necessite, et
lorsqu'il fallut demander h notre
sol le salpetre, la potasse et jus-
qu'aux matieres colorantes ; qu'il
fallut appi-endre h. faire en quelques
jours toutes les operations des arts.
Chacun se souvient de cette prodi-
gieuse et subite activite qui ctonna
I'Europe, et arracha des Eloges
meme aux ennemis qu'elle arri'ta.
M. BerthoUet et son ami M. Monge
en furent I'ame."

- Vicq-d'Azyr (1748-94), the great
forerunner of Cuvier in the new
science of comparative anatomy,
" au sortir d'une de ces parodies
sinistres decorees du nom de fete
nationale, ^tait saisi d'un mal qui
I'enlevait en quelques instants dans
le delire de la peur. Dionis du
Sejour (1734-94), apres deux anndes
d'efFroi et de misere, ne trouvait
plus assez de force pour gouter lea
temps moins malheureux amenes
par la chute de Robespierre"
(Maurv, ' Les Academies d'autre-
fois,' vol. i. p. .332).

148

SCIENTIFIC THOUGHT.

peal for its most necessary requirements to the society
of scientific authorities, which it professed not to need.
" Everything," says the historian of the Academy,^ " was
wanting for the defence of the country — powder, cannons,
provisions. The arsenals were empty, steel was no longer
imported from abroad, saltpetre came not from India. It
was exactly those men whose labours had been proscribed
who could give to France what she wanted. Fourcroy,
assisted by researches begun by Lavoisier, taught the
methods of extracting and refining saltpetre ; Guyton de
Morveau and Berthollet made known a new method of
manufacturing gunpowder, and studied the making of
iron and steel ; Monge explained the art of casting and
boring cannons of brass for land use, and cast-iron cannons
for the navy. On the 6th of August 1793 the Conven-
tion had again to appeal to the Academy in order to know
what advantage it would be to refine as much as possible
the coins of the Eepublic ? " In the space of a few years
science had become a necessity to society at large.^ In the
Constitution of the regenerated Academies it was placed at
the head, as the most important department of knowledge.

^ Maury, loc. cit., vol. i. p. 329.
See also Blot's ' Essai sur I'Histoire
generale des Sciences pendant la
Revolution francjaise.' Paris, 1803.

^ The last entry in the record of
the "proces-verbaux de I'Academie "
before the suspension was a Report
by Borda, Laplace, and Lagrange,
in answer to a demand of the Con-
vention, dated 19th January 1793,
for advice on the new system of
weights and measures which the
Republic should adopt. And so
necessary had the assistance of men
of science become to the Govern-
ment, that even during the suspen-

sion, which lasted from the 8th
August 1793 till the 22nd August
1795, Lakanal had succeeded in
procuring the following decree from
the Government of the Convention :
" La Convention nationale decr^te
que les membres de la ci-devant
Acad^mie des Sciences continueront
de s'assembler dans le lieu ordinaire
de leurs stances, pour s'occuper
specialement des objets qui leur
auront ete ou pourront leur etre
renvoy^s par la Convention nation-
ale " (Maury, loc. cit., p. 331 ;
Aucoc, 'L'Institut de France,' p.
ccvii, &c. )

THE SCIENTIFIC SPIRIT IN FRANCE.

149

The influence of the first Napoleon on science is natur- 36,

Influence of

ally a matter of as much controversy as his merit in the first

«' «' Napoleon

almost every branch of administration. The reports ^ °^ science.

^ According to a decree of the
Government, dated 13th ventose, an
X. (4th March 1802), the Institute,
then consisting of three classes —
the "Academie des Sciences phy-
siques et mathematiques," the
" Academie des Sciences morales
et politiques," and the " Academie
de Litterature et Beaux-arts" —
was ordered to furnish " un tableau
de I'etat et des progres des sciences,
des lettres et des arts, depuis 1789
jusqu'au l'® vendemiaire an x."
This " tableau " was to be divided
into three parts according to the
three classes of the Institute. These
Reports were to be rej^eated every
five years. The first (and only)
Reports were not presented before
February and March 1808. The
Republican Government had then
been superseded by the Empire, and
by a decree of the 3rd pluviose, an
xi. (23rd January 1803), the Institute
had been reorganised. There were
now four classes : 1. Des Sciences
physiques et mathematiques (corre-
sponding to the old Academie des
Sciences). 2. De la langue et de la
litterature fran^aises (correspond-
ing to the old Academie francaise).
3. D'histoire et de litterature anci-
enne (corresponding to the " Acad-
emie d'Inscriptions et de Belles-
lettres"). 4. Des beaux-arts. "On
supprima la classe des sciences
morales et politiques qui existait
dans I'organisation du 3 brumaire,
an iv. Ce fut un trait caracteris-
tique de la repugnance du premier
Consul pour la discussion des
matieres politiques et leur enseigne-
ment " (Thibaudeau, ' Le Consulat et
I'Empire,' Paris, 1835-37, vol. iii. p.
396). Accordingly there were pre-
pared four, or rather five, Reports,
the first in two parts by Delambre

and Cuvier on the progress of the
Mathematical and Physical Sciences ;
the second by Marie-Joseph Ch^nier
on the progress of Literature ; the
third by Dacier on the progress of
History and Classical Literature ;
the fourth by Le Breton on Fine
Arts. Of these the two Reports of
Delambre and Cuvier gave great
satisfaction, that of Dacier gave less
satisfaction ; Chenier, who himself
admired the eighteenth - century
philosophy, had an embarrassing task
to perform, of which, however, he
acquitted himself worthily (Thibau-
deau, loc.cit., vol. vi. p. 557). The
Report of Chenier has been several
times reprinted. The new science
which was founded by Condillac,
Turgot, Condorcet, and others, and
which aimed at introducing the truly
scientific spirit into psychology, psy-
cho-physical researches, and ques-
tions of society and legislation, re-
ceived no recognition, as it had also
lost its representation in the sus-
pended "Academie des Sciences
morales et politiques." After the
re- establishment of this section of
the Institute in 1832, a royal decree
of 22nd March 1840 ordered a Re-
port on the progress of the Moral
and Political Sciences from 1789 to
1832. The task was so great that
it could not be accomplished before
the Revolution of 1848, and was
therefore abandoned (Aucoc, ' L'ln-
stitut de France,' pp. 62 note, 300).
Some reference to the subject is
contained in the introduction to
Ch^nier's Report, and in the last
chapter of Dacier's, which was
written by De Gerando. The true
history of the new science has been
recently written by F. Picavet,
' Les Ideologues,' Paris, 1891.

150

SCIENTIFIC THOUGHT.

which Delambre and Cuvier drew up at his request,
touching the progress of science during the twenty years
which followed the outbreak of the Ee volution, have
become classical as monuments of the achievements of a
great age,-^ and as examples of the best style in which to
treat such a subject. Written immediately under his eye,
they cannot be considered quite impartial, so far as the tone
is concerned in which they refer to his personal favours
and protection.^ There can, however, be no doubt that
he recognised scientific merit, and drew many eminent
men of science into the service of the Government. The
institutions on which he prided himself so much, — the
Ecole Normale, the Ecole Polytechnique, and the unfin-
ished scheme of a great centralised Institution of Learn-
ing and Education, descending from the heights of the
Institute, through the various branches of the higher and
secondary into a multitude of primary schools, bearing
the name of the " University," — had either existed, or
been planned before him.^

^ Napoleon in discussing at the
council meeting the decree which
ordered the several reports, said to
Regnaud : ' ' Soignez bien cette re-
daction, car elle sera examinee par
les pedagogues de toute I'Europe "
(Thibaudeau, Zoc. cit., vol. ii. p. 496).

- See what Cuvier himself says
on this subject (Memoires, &c., in
Flourens, ' Eloges,' vol. iii. p. 187) :
" Un rapport sur le progres des
sciences devait etre presente aux
consuls en fructidor an xi. . . .
Ou ne fut pret qu'a la fin de 1807 :
ce n'etait plus aux consuls mais h
I'empereur que Ton avait h, pre-
senter le travail. II le recut avec
un grand appareil dans la sdance du
conseil d'Etat. M. Delambre et
moi presentames le notre les pre-

miers ; le 3 fdvr. 1808, accom-
pagnes de Bougainville, president,
et des doyens de toutes les sections.
La ceremonie fut solennelle ; I'em-
pereur fit une belle reponse, qui
est imprimce k la fin du rapport.
Je sus le lendemain, par M. de
Segur et d'autres conseillers d'Etat,
qu'il avait exprime une grande satis-
faction de mon rapport en parti-
culier : ' II m'ajoue comme j'aime h,
I'etre, dit-il.' Cependant je m'etais
borne il I'inviter ti imiter Alexan-
dre et h, faire tourner sa puissance
au profit de I'histoire naturelle."

■^ Regarding the University, see
' Code Universitaire ou Lois, Statuts
et Reglemens de 1' University Royale
de France, mis en ordre par M.
Ambroise Rendu,' Paris, 1835. In

THE SCIENTIFIC SPIRIT IN FRANCE.

151

It will therefore always remain a matter of doubt to
what extent he originated ideas, or merely adopted those
of others before and around him. He favoured the mathe- 37.

Napoleon

matical sciences, and created great prizes for physical, [^^'^henf^ti^^
notably electrical, discoveries, partly because these pursuits '^'^^ sciences,
promised to surround his Government with glory, partly
because he recognised their practical importance for the
purposes of the state and nation ; partly also, because he
himself had had a mathematical training.^ During his

the Introduction we read as follows :
"Bonaparte passait h, Turin. Un
jour qu'il parcourait le palais de
I'Uuiversite fondee en 1771 par
Charles Emmanuel III., il se fit re-
pr^senter les statuts qui regissaient
cette institution. II y vit quelque
chose de grand et de fort qui le
frappa. . . . Tout ce plan
d'education etabli sur la base an-
tique et imperissable de la foi chrd-
tienne, tout cela lui plut, et il en
garda la inemoire jusqu'au sein de
ses triomphes en Italic et en Alle-
magne. Rassasie enfin de gloire
militaire, et songeant aux genera-
tions futures, apres avoir solidement
etabli I'administration civile, apres
avoir releve les autels et promulgue
le Code Napoleon, apres avoir par
dififerentes lois, substitue les Lyc^es
aux Ecoles Centrales, reg^n^re les
Ecoles de Medecine, et cree les
Ecoles de Droit, il voulut fonder
aussi pour la France un systeme
entier d'instruetion et d'education
publique. II se souvenait de I'uni-
versitS de Turin et I'agrandissant
comme tout ce qu'il touchait, dans
la double proportion de son empire
et de son genie, il fit I'Universite
imperiale. "

^ Among many references relat-
ing to this subject, I select one from
Villemain, 'Souvenirs contempor-
ains d'Histoire et de Litterature, '
which in the first volume (9™^ ed.,

Paris, 1874, p. 137) contains, the
description of a visit to the Ecole
Normale in 1812, and a discussion
witii Narbonne, to whom the Em-
peror had fully expressed his aims
regarding education and learn-
ing. " L'Empereur n'est inquiet
que d'une chose dans le monde, les
gens qui parleut, et a leur defaut
les gens qui pensent. ... II
veut, et il me I'a dit vingt fois, que
son regne soit signale par de grands
travaux d'esprit, de grands ouv-
rages litteraires. Etre loue comme
inspirateur de la science et des arts,
etre le chef eclatant d'une epoque
glorieuse pour I'esprit humain, c'est
I'idee qui le flatte le plus; c'est ce
qu'il a cherche par des Prix Decen-
naux. ... II veut (a I'Ecole
Normale) des etudes fortement clas-
siques, I'antiquite et le siecle de
Louis XIV. ; puis quelques Elements
de sciences mathematiques et plus
tard la haute geometric, qui est,
dit-il, le sublime abstrait, comme la
grande poesie, la grande eloquence
est le sublime sensible." Napoleon
said to Narbonne: "J'aime les
sciences mathematiques et phy-
siques ; chacune d'elles, I'algebre,
la chimie, la botanique, est une
belle application partielle de I'esprit
humain ; les lettres, c'est I'esprit
humain lui-meme. . . . Aussi,
j 'ai deux ambitions : elever la France
au plus haut degr^ de la puissance

152

SCIENTIFIC THOUGHT.

38.

campaigns in Italy and Germany, and on his expeditions
to Egypt and the East, he surrounded himself with some
of the greatest scientific authorities, such as Berthollet
and Monge. From political as well as personal motives,
He discoun- hc discountcuanccd the once fashionable sensualistic phil-

tenanced the

contempor- osophy. This philosophy has now fallen to the second

ary repre- l J l l j

piiiiosopiiy.^ rank, though still represented by eminent thinkers, such
as Cabanis, Destutt de Tracy, Daunou and Garat. It
was these thinkers of whom Napoleon sneeringly spoke
under the designation of " Ideologues." ^

After all that has been said by admirers to magnify,
and by opponents to minimise, Napoleon's merits in pro-
moting the cause of science, and in spreading the modern
scientific spirit, I cannot but recognise that he was, amongst
the great heroes and statesmen of his age, the first and
foremost, if not the only one, who seemed thoroughly to
realise the part which science was destined to play in

guerriere et de la conquete affermie,
puis y developper, y exciter tous
les travaux de la pens^e sur une
^chelle qu'on ii'a pas vue depuis
Louis XIV. C'^tait le but de mes
Prix Decennaux qu'on ni'a gates par
de petites intrigues dHdeologues et
de couronuements ridicules, comme
celui du catechisme de Saint-
Lambert."

^ A full account of these authors,
their influence and their aims, will
be found in F. Picavet, 'Les Ideo-
logues, Essai sur I'histoire des iddes
et des theories scientifiques, philo-
sophiques, religieuses, &c., en France
depuis 1789,' Paris, 1891.

Thibaudeau, ' Le Consulat et
I'Empire,' gives many details re-
garding Napoleon's connection with
science, with literature, and with
the growing industries of France.
Among the latter see especially

the great efforts made to supersede
colonial and foreign goods by home
productions. Prizes and encourage-
ments of all sorts were given ;
technical schools and colleges were
established ; exhibitions were pro-
moted. Sheep were imported from
Spain, sugar was made from raisins
and beetroot, saltpetre and soda by
chemical processes, the garance or
madder root and the kermes were to
take the place of cochcnille; the ^^as-
tel the place of the imported indigo.
That an enormous impetus was
thus given to chemistry cannot be
denied. (See Thibaudeau, passim,
and especially vol. v. p. 248, &c.)
See [also Cuvier's 'Rapport,' &c.,
for an account of applications of
science, especially chemistry, pp.
376-386, and Delambre, ' Rapport,'
&c., pp. 326-362.

THE SCIENTIFIC SPIEIT IN FRANCE.

153

the immediate future. This part, as we know, it has
played both Ijy entirely changing the external face of
things, and by running out into endless applications ; and
we have seen the importance of that statistical spirit of
numbering, measuring, and registering, by which alone
a survey of complicated phenomena is possible. Of the 39.

He himself

statistical method jSlapoleon himself made use on an ex- made exten-
sive use of

tensive scale : perhaps he was the first among rulers to ^'li ^^ethod '
do so.^ That the great leader of men has to recognise
not only the inductive philosophy of statistics and aver-
ages, but likewise governing ideas of a different class,
Napoleon was well aware, and his ultimate failure may
be traced to the fact that, however great as a general
and as a calculator, his soul had no room for those high,
religious, and unselfish motives of which he himself said
to Fontanes, that they in the end always decide the fate
of nations.^ Yet he belongs to the small company of
great military figures in history — a company which in-
cludes Alexander the Great, Caesar, and Peter the Great

^ See Delambre, 'Rapport,' &c.,
p. 222. " Depuis le peu de temps
qu'on s'en [i.e., with statistics] oc-
cupe en France, elle y a fait les
plus grands progres, au moyen de
I'attentiou particuliere et des se-
cours que le Gouvernement fran9ois
donne a tous les travaux utiles.
Les prefets des'departemens ont et^
invites a recueillir et k transmettre
au Ministre de I'interieur les
lenseignemens les plus precis sur
toutes les questions qui sont du
ressort de la statistique. "

'^ See ' (Euvres litteraires de
Napolt'on Bonaparte,' vol. iii. p. 5 ;
Conversation avee Fontanes, Saint
Cloud, 19 Sept. 1808: "Fontanes,
savez-vous ce que j'admire le plus
dans le monde ? C'est I'impuis-

sance de la force pour organiser
quelque chose. II n'y a que deux
puissances dans le monde : le sabre
et I'esprit. J'entends par I'esprit
les institutions civiles et religieuses.
A la longue, le sabre est toujours
battu par I'esprit." Also vol. iv.
p. 423 : " Les vraies conquetes, les
seules qui ne donnent aucun re-
gret, sont ceux que Ton fait sur
I'ignorance. L'occupation la plus
honorable comme la plus utile pour
les nations, c'est de contribuer a
Textension des idees humaines. La
vraie puissance de la R^publique
francaise doit consister desormais
a ne pas permettre qu'il existe une
seule idee nouvelle, qui ne lui ap-
partienne. "

154 SCIENTIFIC THOUGHT.

— who have succeeded in permanently inscribing their

names in the annals of science beside those of its true

and great representatives. Some of the glory of Laplace

^. 40. and Cuvier falls upon him. Except for this Napoleon has

His scienti- ■■■ r r

maini°/diri- scarccly a place in the history of thought. In it those
who were Napoleon's servants are rulers and lawgivers ;
it is they who enlighten our century. They, were the first
great exponents of the scientific spirit, nursed under the
influence of the academic system. This was peculiarly
a product of the French mind and culture. It is well
to recall in the words of Cuvier what the scientific spirit
is. At the end of the report w^hich he presented in the
year 1808 he says : ^ " These are the principal physical
discoveries which have lighted up our period, and which
open the century of Napoleon. What hopes do they not
raise ! how much does not the general spirit signify,
which has brought them about, and which promises so
much more for the future ! All those hypotheses, all
those suppositions, more or less ingenious, which had
still so much sway in the first half of the last century,
are now discarded by true men of science : they do not
even procure for their authors a passing renown. Experi-
ments alone, experiments that are precise, made with
weights, measures, and calculation, by ; comparison of all
substances employed and all substances obtained : this
to - day is the only legitimate way of reasoning and
demonstration. Thus, though the natural sciences escape
the application of the calculus, they glory in being subject
to the mathematical spirit, and by the wise course which
they have invariably adopted, they do not expose them-

^ 'Rapport,' &c., p. 389.

THE SCIENTIFIC SPIRIT IN FRANCE.

155

41.
Deserved

Cuvier.

selves to the risk of taking a backward step ; all their
propositions are established with certainty, and become
so many solid foundations for that which remains to be
built." ^

Nor can we look upon the great prominence which
Cuvier gives to French names in the course of his survey prominence

" J given to

as unjust or partial. He was well aware of the contribu- name's by
tions of other nations : no one has spoken in more gen-
erous and correct terms of Priestley and Cavendish, of
Banks and Eumford, of Pallas, Werner, and Humboldt.
We must admit the correctness of the remark, " that
even in those departments where chance has willed that
Frenchmen should not make the principal discoveries,
the manner in which they have received, examined, and
developed them, and followed them out into all their
consequences, places their names next to those of the
real inventors, and gives them in many ways the right
to share in the honour." ^

In the first decades of this century the home of the
scientific spirit was France : for though not born there,
it was nevertheless there nursed into full growth and

vigour.

But it soon set out on its wanderings throucrh

o o

■^ Compare also the " Reflexions
sur la marche actuelle des Sci-
ences,',' being the introduction to
the ' Eloges historiques,' vol. i. p.
1, &c.

- ' Rapport,' p. 391. It is also
remarkable how clearly Cuvier here
announces the defects which the
teaching of science was still labour-
ing under. Whilst he rightly
praises the great Paris institutions,
the medical schools, the mathe-
matical, physical, and polytechnic
establishments, the new schools of

technology and agriculture, as un-
equalled organisations for higher
instruction, he draws attention to
the absence of equally efficient ele-
mentary schools and to the neglect
of those provincial institutions
which before that age had already
done so much to disseminate know-
ledge and learning. At the end of
our century both France and Great
Britain have still only very partially
supplied the wants which Cuvier so
clearly defines in the beginning.

156 SCIENTIFIC THOUGHT.

other lands and nations. At the end of our century —
nay, even during the whole of the second half — we find
this spirit naturalised in Italy, in Germany, in England,
in the north and east of Europe. There is now no science
which can be named pre-eminently after one nation. All
nations have contributed their share to the cosmopolitan
power and influence which science possesses. They have
enlarged and deepened the scientific spirit and widened
its career. Thus far it has been the growth of the
scientific spirit which has occupied us ; we must now
proceed to study its diffusion, and learn to recognise the
peculiar features which Germany and England have on
their part contributed. In doing so, we must turn away
for a moment from the academic system with which we
have been specially occupied.

157

CHAPTER II.

THE SCIEXTIFIC SPIRIT IN GERMANY.

" No Augustan epoch flowered,
No Lorenzo favours showered

Ever German Art upon ;
She was not by glory nourished
And her blossom never flourished

In the rays of Royal sun." ^

Perhaps with more correctness Schiller might, early in
the century, have applied these lines to German science
than to German art. If art and poetry were only slightly
indebted to princely protection, German science was still
less so." Leibniz's scientific labours languished while he

^ Schiller, "Die deutsche Muse."
^ Astronomy was the only science
that enjoyed some little princely
favour. William IV., surnamed
"the Wise," son of Philip the
Magnanimous of Hesse and himself
Elector, was an astronomer of some
note, and stood in intimate re-
lations with Mercator, Tycho, and
other astronomers. In 1561 he
built himself an observatory at
Cassel and appointed Rothmann to
be his "Mathematicus." Frederick
II. of Denmark gave Tycho a
magnificent observatory, called
" Uranienburg," where he laboured

from 1576 to 1597, but which was
subsequently destroyed. Tycho
was then employed by the Emperor
Rudolf II., and inaugurated the
observatory in Prague (1599-1601);
he made Kepler his assistant, and
enabled the latter by the use of his
observations to find and prove his
three celebrated laws (" Astronomia
nova," Prague, 1609 ; " Harmonices
mundi," Linz, 1619; "Tabulaj
Rudolphinaj," 1627). Full details
will be found in Rudolf Wolf,
' Geschichte der Astronomie,' Miin-
chen, 1877, p. 266, &c.

158

SCIENTIFIC THOUGHT.

Foundation
of German
universities.

occupied the position of historiographer and diplomatist
at the Court of Brimswick/ and Tobias Mayer's valuable
observations were only published with the aid of English
money .^ But if the German princes did little or nothing
directly for the development of science, they indirectly

1 Leibniz (1646-1716) entered,
1676, the service of John Frederick,
Duke of Hanover, as librarian and
councillor. The Duke died 1679,
and Ernest Augustus, who in 1692
was made Elector of Hanover, suc-
ceeded him. Leibniz's time was
taken up with diplomatic and legal
researches and negotiations refer-
ring to the position of the House
of Hanover, and the reunion of the
Protestant and Roman Catholic
Churches ; latterly with genealogi-
cal and antiquarian studies refer-
ring to the history of the House of
Brunswick. He wrote the ' Annales
imperii occidentis Brunsvicenses,'
beginning with the year 768, the
date of the accession of Charles the
Great, from whom Leibniz proved
that the House of Brunswick de-
scended through the Italian House
of Este. He carried the history
down to the year 1005, closing a
few days before his death with the
words, " quos ex tenebris eruendos
aliorum diligentia; relinquo." The
work was not printed till 1843,
when G. H. Pertz, the first editor
of the celebrated ' Monumenta
Germanitc' founded by the great
Stein, published it with an elabor-
ate preface. Of the annoyances to
which Leibniz was subjected in the
course of his studies, see an account
in the correspondence with the
Minister von Bernstorff (1705-16),
published by Doebner, Hanover,
1882, introduction. See also Guh-
rauer, ' Leibnitz, eine Biographic,'
2 vols., 2nd ed., Breslau, 1846.
Considering the greatness of
Leibniz in so many different
directions, his motto is note-

worthj'^ : " Didici in mathematicis
ingenio, in natura experimentis, in
legibus divinis humanisque auctori-
tate, in historia testimoniis niteii-
dum esse."

'^ Tobias Mayer (1723-62), born
at Marbach, the birthplace of
Schiller, from 1751 Professor of
Economics and Mathematics at
GiJttingen. To use the words of
Karsten Niebuhr, " Though he
had never seen a big ship, he
taught the English how to deter-
mine the longitude on the open
sea." He competed for the great
prize of £20,000 offered in 1713 by
the Board of Longitude for a method
of determining the longitude at
sea within V' accurately ; smaller
prizes being offered for an accuracy
of §° and 1°. The prize of £5000,
and subsequently of £10,000, was
awarded to Harrison in 1758 and
1764 for his chronometers. Euler
and Mayer laboured in a different
direction at the same subject, bj'
publishing lunar tables and per-
fecting the lunar theory. After
repeated revisions, Mayer sent his
tables, 1755, to London, where they
were submitted to Bradley, who re-
ported favourably on them. After
further corrections, and after also
submitting his theory, Mayer's
widow received, in 1765, £5000,
Euler £3000, and the work was
published, 1770, by order of the
Board of Longitude, under the
title, 'Tabula; motuum solis et
lunte nova; et corrects, auctore
Tob. Mayer : Quibus accedit
methodus longitudinum promota
eodem auctore.'

THE SCIENTIFIC SPIEIT IN GERMANY.

159

Develop-

furthered her cause most powerfully by founding that
great institution of culture, which more than anything
else is characteristic of the German mind, in which it
has found its most perfect expression, and where it can
be most exhaustively studied — the system of the German
universities.

" There is no people," says Mr James Bryce, " which
has given so much thought and pains to the development men* of the

^ o J. i universities

of its university system as the Germans have done — none ^3l
which has profited so much by the services universities
render — none where they play so large a part in the
national life." ^ If it is correct to say that this system
owed its foundation to the German princes, it is equally
true that its development is the work of the German
people.^ It may be doubtful whether, without the

^ See James Bryce's pi-eface to
the English translation of Conrad's
valuable book, ' The German Uni-
versities for the last Fiftj^ Years,'
Glasgow, 1885, p. xiii.

- A great deal has been written
about the German universities.
For the purposes of a History of
Thought, I confine myself to a
reference to the valuable writings
of F. Paulsen, ' Geschichte des
gelehrten Unterrichts auf den
deutschen Schulen und Universi-
taten,'

Leipzig,
essaj's in the
Von Sybel's '
schrift,' 1881.

1885, and two
45th volume of
Historische Zeit-
The succeeding
phases of media3val and modern,
of Roman Catholic and Protestant,
of the thought of the Church, the
Renaissance, the classical and the
modern ideals, are all reflected in
the foundation and reform of the
universities and high schools of
Germany and the surrounding
countries. The Jirst foundations,
in imitation of the universities of

Paris and of Italy, were Prague
1348, Vienna 1365, Heidelberg
1386, Cologne 1388, Erfurt 1392,
Wiirzburg 1402, Leipsic 1409,
Rostock 1419. A second epoch —
under the influence of the human-
istic studies — begins in the middle
of the fifteenth century and adds
eight new foundations — Greifswald
1456, Freiburg 1457, Trier 1457,
Basel 1459, Ingolstadt 1472, Tubin-
gen 1477, Mainz 1477, Wittenberg
1502, Frankfort on the Oder 1506
(Paulsen, ' Geschichte,' p. 14). A
third epoch begins with the Refor-
mation. The first Protestant uni-
versity is Marburg, founded by
Philip of Hesse, 1524. Melanch-
thon's influence is everywhere deci-
sive. Tubingen is reconstituted by
Duke Ulrich 1535 ; Leipsic by Duke
George 1539. Basel, after three
years' suspension, is reopened 1532.
Frankfort on the Oder is reopened
by Joachim of Brandenburg 1537,
who also founds the new University

of Konigsberg

Greifswald is

160

SCIENTIFIC THOUGHT.

individual influence of the former, without the divided
interests of the dismembered empire, without the con-
flicting religious views, the political and personal rivalry
of the many states and sovereigns,^ so many scattered
centres of culture and learning would have sprung so
early into existence ; but it is not doubtful that it is
owing to the common interests of the nation, to the
uniting tie of the same language, the same thought, and
the same aspirations, that these scattered centres have
been in course of time united into a great network," a
vast organisation for the higher intellectual work of the
nation and of mankind. The German nation may pride
itself on possessing at the present moment the most

reconstituted on a Protestant foun-
dation 1539 ; Rostock in 1540-50 ;
Heidelberg by the Elector Frederick
II. in 1544. Jena is founded 1558
by John PVederick, Helmstiidt by
Julius of Brunswick in 1568 ; Gies-
sen followed in 1607 ; Rinteln in
1621; Altdorf in 1662. Of the
greatest influence on German cul-
ture were the Dutch Protestant uni-
versities— Leyden 1575, Franeker
1585, Utrecht 1634, Harderwyk
1648 ; they were for a long time —
as formerly the Italian universities
— the goal of the young scholar's
wanderings (Paulsen, p. 179).
They — as well as Geneva — held a
similar position to the Scotch uni-
versities (see Sir A. Grant, ' Story
of the University of Edinburgh,' vol.
i. pp. 21, 126, 188, 213,229, 233, 263,
274, 283, 297, &c., vol. ii. p. 263).
A fourth epoch begins with the
foundation of Halle 1694, the first
really modern university (Paulsen,
p. 353). The spirit of Bacon and
Leibniz, represented by Thomasius,
is the leading power ; it is not by
any means irreligious, since Francke

(the so-called "pietist") is as im-
portant a factor as Thomasius.
German is substituted for Latin.
Other universities follow the re-
form, thus Konigsberg 1735,
Leipsic, Wittenberg, Helmstiidt,
Kiel, Tiibingen, &c. A fifth epoch
— the evolution of the ideal of
science in the German sense. Wis-
senschaft — begins with the founda-
tion of Gottingen in 1737. Of this
more in the text.

1 Conrad, loc. cit., p. 2 : "There
is scarcely a stronger bond of con-
nection between the various parts
of Germany than that supplied by
the universities, and in no other
respect have the barriers that sep-
arated State fi-om State been so long
broken down. . . . The historical
development cannot be accurately
traced unless the growing extent in
which the south German universities
are attended by students from the
north be kept in view."

■•^ See especially Paulsen's remarks
referring to the foundation of Got-
tingen underGeorge II. (' Geschichte
des gelehrten Unterrichts,' p. 425).

THE SCIENTIFIC SPIRIT IN GERMANY.

161

powerful and best equipped army. But this is only the
creation of the present age. With greater pride it may
boast of having trained in the course of centuries the
largest and most efficient intellectual army, ready at any
moment to take up and carry to a successful issue great
scientific undertakings demanding the intense thought
and labour of a few secluded students, or the combined
efforts of a large number of ready workers. This army
is scattered through the length and breadth of the land,
and even beyond its frontiers in neighbouring countries,
wherever universities and high schools are situated.^ It
is not a stationary power, but is continually on the move
from south to north, from west to east, to and fro, exchang-
ing and recruiting its forces, bringing heterogeneous ele-
ments into close contact, spreading everywhere the seed
of new ideas and discoveries, and preparing new land
for still more extended cultivation.

^ The extent of the German uni-
versity system cannot be estimated
by the twenty universities marked
on the map attached to the trans-
lation of Conrad's book, as these
represent only the existing univer-
sities of the present German empire ;
nor yet by the forty-three univer-
sities given in the appendix, p. 290,
as they contain only some of the
Austrian, but none of the Swiss
universities ; nor even by taking up
Ascherson's valuable ' Deutscher
UniversitJits-Kalender,' which con-
tains the German-speaking univer-
sities— thirty-four in number in
1887 — but of course does not con-
tain the names of those which have
been suppressed. There are also
the universities of Denmark, Nor-
way, and Sweden, which have ex-
changed many important professors
with Germany, and those of Hol-
land in older, of Belgium in modern
VOL. I.

times, which have done the same
thing. The Russian universities
also were largely organised on Ger-
man models, though since the re-
forms of 1863 they aim at a more
national character. Brandis found-
ed the University of Athens on
German lines in 1837. The Russian
University at Kasan , that ' ' ultima
musarum Thule," was founded in
1804, and Gottingen supplied its
first professors. From there and
from the hardly less remote Tran-
sylvanian town, Maros V^sdrhely,
there issued the revolution of our
fundamental notions in geometry,
and there is reason to believe that
both Lobachevsky's and Bolyai's
theories are ultimately connected
with the speculations of Gauss.
See Prof. A. Vasiliev's Address on
Lobach^vsky, translated byHalsted,
p. 5 sqq.

162

SCIENTIFIC THOUGHT.

3.

Geographi-
cal distribu-
tion of the
German uni-
versities.

It is not my intention to dwell on the history of the
German universities, on the gradual growth of the univer-
sity system ; though every stage in that history is interest-
ing and important if we wish to understand the inner work-
ing and usefulness of this great organisation. Neither do
I wish to do more than just mention, as an equally impor-
tant subject, the geography of the German universities ;
how through nearly fifty larger or smaller towns, in the
course of six centuries, learning and higher education have
been spread over the German-speaking countries of Europe.
These figures alone suggest the intricacy of the subject,
the many springs, the continual ebb and flow of the rising
tides of ideas, the many courses of thought, the many
schools of learning, the internal conflicts, the unavoidable
friction, the healthy competition and rivalry, the repub-
lican spirit, the impossibility of any creeping stagnation
of life, the absence of any lengthened tyranny of doctrine,
of an oppressive hierarchy, or of idols of opinion and
belief. I leave it to my readers to indulge in comparisons
easily suggested by these different aspects, to fasten upon
the strong and upon the weak points of this great system
of the German universities.^ What I wish to emphasise

^ The migration of students as
well as of eminent professors from
one university to another is one of
the most important features of
German academic life. Thus we
find the imaginative tendencies of
the southern intellect represented
by Hegel and Schelling in philo-
sophy transplanted into the midst
of the encj-clopsedic and logical
sciences of the North, or into the
centre of industrial Switzerland in
the person of Vischer ; the theo-
logical criticism of the Tubingen
school wandering northward to

Marburg and Berlin in Zeller ; and
the philological criticism of Gott-
fried Herrmann locating itself in
Zurich in his celebrated pupil and
biographer Kochly, and in Bavaria
through Thiersch. Jacobi came from
the lower Rhine to Munich, where
also Liebig formed a centre of mod-
ern scientific celebrities. Savigny
in Berlin and Thibaud in Heidel-
berg represent the historical and
philosophical schools of German
jurisprudence. Vienna for a long
time was the most celebrated Ger-
man training - school of practical

THE SCIENTIFIC SPIRIT IN GERMANY.

163

very strongly here is the existence in the midst of
European life, all through our century, of this vast organ-
isation for intellectual work, this great engine of thought ;
and to assign to it one of the foremost places among the
great agencies with which we shall have to deal.

The beginning of the present century found this great 4.

Full devel-

institution of university education in full swing among all opment of

'' 00 tjig German

the German-speaking nations.'^ The eighteenth century syg^gnf''^^
brought it to that state of perfection in which we have
been accustomed to see it. In the course of that century
it outgrew its earlier and more limited phases of existence,
its period of more restricted usefulness ; it emancipated
itself from Court and personal favouritism, from ecclesias-

medicine and surgerj', whereas Ber-
lin concentrated the great repre-
sentatives of the more recent scien-
tific developments. In the course of
the last hundred years no one uni-
versitj' has been allowed to retain
for any length of time the sujjremacy
in any single branch. The light
has quickly been diffused all f)ver
the country, when once kindled at
one i^oint. How will the future
compare in this respect ?

1 This is not quite the case as
regards Switzerland. The city of
Basel, which before the Reformation
was the seat of much learning, the
names of Sebastian Brandt, Reuch-
lin, and Erasmus being intimately
connected with it, had a university
from 1459. The antagonism to
classical and polite literature which
characterised a large section of the
Reformers (see Paulsen, p. 128 sqq.)
destroyed many flourishing centres
of culture ; amongst them the Uni-
versity of Basel, which was sus-
pended in 1529, when the citj^ ac-
cepted the Reformation, but re-
opened three years later in 1532.

Geneva, though this is outside of the
German-speaking area and presents
a culture quite peculiar to itself,
had an academy from 1559, with
many celebrated professors and
numerous students of theology from
all countries of Eurofie. Lausanne,
Bern, and Ziirich had colleges or high
schools in the seventeenth century.
But down to the nineteenth century
Basel remained the only university
in the Continental sense. The
reasons why Switzerland developed
her university system so late are
discussed in Tholuck, ' Das akade-
mische Leben des IJ*-™ Jahrhun-
derts,' vol. ii. p. 314, &c. , where
also minute information is given on
the several high schools of Switzer-'
land. The question is interesting,
seeing that the greatest in many
branches of science — such as Ber-
noulli, Euler, Haller, Cuvier,
Steiner — have come from Switzer-
land, and that by reason of the
names of Rousseau and Pestalozzi it
has become the centre of modern
ideas on education.

164

SCIENTIFIC THOUGHT.

r

5.

The philo-
sophical
faculty.

The Univer-
sity of Got-
tingen.

tical protection and influence ; it acquired through the
statutes of governments or special foundations larger and
better secured means of subsistence ; it substituted the
vernacular for the Latin tongue. The circle of studies,
though from early times professedly all-embracing, did
not become worthily filled up and cultivated with equal
and impartial care till the fourth faculty, the philoso-
phical faculty, was properly developed. Theology, law,
and medicine conduct their studies for practical ends
and purposes ; the two former especially were frequently
liable to be used merely for the ends of the Church or the
State ; but the philosophical faculty embraces all those
studies which aim at establishing truth, be this defined
as merely formal or as real, as belonging to method or
to knowledge. We can assign a definite date to the
firm establishment of the " libertas philosophandi," and
the professed introduction of the " libertas docendi " in
the university programme ^ — namely, the opening (in
1734) of the University of Gottingen (inaugurated in
1737). " The foundation stone," says Professor Paulsen,
" of the academic constitution is the ' libertas docendi.'
On this point Von Miinchhausen, whom we may call the
real founder of the university, and his two advisers,
Mosheim, the theologian of Helmstadt, and Bohmer, the
jurist of Halle, were agreed. All ' inquisitiones,' so writes
the former, choke the powers ' ingeniorum,' and spoil the
beginnings of a learned society. He advises above all
that the greatest care should be used in the equipment
of the theological faculty. Accordingly Miinchhausen
laid his eye upon men whose teaching led neither to

^ Paulsen, ' Geschichte des gelehrten Unterrichts,' p. 424, &c.

THE SCIENTIFIC SPIRIT IN GERMANY. 165

' Atheismo ' nor ' ISTaturalismo,' who neither attack the
' articulos fundamentales religionis evangelicse,' nor in-
troduce enthusiasm, nor yet evangelical popedom. Like-
wise the jurists received full freedom for teaching and
for the expression of legal opinions, whereas at Halle,
following the common rule, the Prussian interest, at
least in matters of public law, was the measure of
things. At Gottingen the chief stress was laid on
the culture of the essentially modern sciences. In the
foremost rank stood the administrative and historico-
political branches where Putter, Achenbach, Schlozer,
Gatterer, Heeren, gave to the university her world-
wide fame ; the mathematical and scientific branches are
marked by the brilliant names of Haller, Lichtenberg,
Blumenbach, Kastner ; the philological branches by
Gesner, Heyne, Michaelis. The university met the de-
mand for encyclopaedic discourses, Mlinchhausen ar-
ranged in 1756 that a member of each faculty should
deliver a public course on the whole field of the sciences
taught there ; in the philosophical faculty Gesner treated
philologico-historical, Kastner physico-mathematical sub-
jects. An ' Index Lectionum ' of the year 1737 shows
nine professorships : 1. Politics and Morals. 2. History
of Literature. 3. History. 4. Elocution and Poetry.
5. Logic and Metaphysics. 6. Oriental Languages. 7.
Mathematics and Physics. 8. Administrative Sciences ;
to which is added, lastly, a professorship of Philosophy
without special definition." ^

It is evident that, owing to their constitution, as well

^ The original endowment of Gott-
ingen was fixed at 16,000 thalers,
equal to £2400. This was more

than double the endowment of
Halle. (Paulsen, p. 425.)

166

SCIENTIFIC THOUGHT.

Relation of
universities
and high
schools.

as to their number, the German universities were destined
to become the most powerful organisation for the diffusion
of knowledge. Further, they have been in the course of
the present century more closely linked with many hun-
dreds of high schools, and with the growing number of
technical schools.^ For both of these they had to train
the teaching staff, and from the ranks of these they
again largely filled their own chairs. Thus they not
only combined in themselves the spirit of research and
the profession of teaching, but they infused into the
widely scattered teaching staff of many hundreds of

^ The technical schools in Ger-
many and Switzej-land are a crea-
tion of modern times. We can dis-
tinguish three classes. (1) The
" Realschule. " This stands in a
kind of opposition to the ' ' Latin
school." The name (according to
Paulsen, p. 483) occurs first in Halle,
where the archdeacon Semler es-
tablished iu 1706 a mathematical
and mechanical " Realschule." J. J.
Hecker established at Berlin in 1739
an '■' economico- mathematical Real-
schule. " The object of these schools
was to teach " Realia," to introduce
practical lather than learned infor-
mation. A special development was
the " philanthropinism " of Base-
dow, well known even to English
readers from Lewes's Life of Goethe
(see vol. i. p. 276, &c.) (2) A
second class embraces the " Gewer-
beschulen," which may be rendered
"Schools of industry." Karl
Schmidt ('Geschichte der Piida-
gogik,' vol. iv. p. 163) calls Beuth
the founder of them in Prussia,
1817, and gives the school of
Aachen as the first. They form
a kind of bifurcation with the
higher classes of the Gymnasia (or
learned schools). They may be
more specially commercial, agricul-

tural, or military. (3) Out of these
a third class — answering to the
growing demand for the practical
application of the higher mathe-
matical sciences — has grown up,
named polytechnic schools. The
celebrated Ecole Polytechnique of
Paris has been the model. The first
of this class in Germany was estab-
lished at Vienna in 1816. Then
followed Munich, Hanover, Karls-
ruhe, Stuttgart, Niirnberg, Augs-
burg, Darmstadt, Ziirich, Aachen,
latterly also Berlin (Reichsanstalt)
and Brunswick (Carolinum). In
many ways they equal the univer-
sities in the scientific spirit of their
teaching. What is wanting is the
philosophical, the historical, the
en cyclopaedic treatment. In this
respect they form in their best
examples a contrast to the Gotting-
en programme. To many serious-
thinking minds they indicate the
gradual dissipation of the German
ideal of Wissenschaft, the narrowing
down of Wisficnschaft to science in
the English and French meaning of
the word. Their danger lies in the
direction of being contented with
practical usefulness, as the danger
of the German type of university lay
in being contented with erudition.

THE SCIENTIFIC SPIRIT IN GERMANY.

167

schools the same habit — almost absent in other countries
— of looking upon private study and research as a
necessary qualification of the lecturer and teacher. The
educational organisation of the combined universities and
higher schools has thus become an equally powerful
organisation for research, and for increasing knowledge.
Wlierever the progress of learning and^ science requires
a large amount of detailed study inspired by a few lead-
ing ideas, or subservient to some common design and plan,
the German universities and higher schools supply a well-
trained army of workers, standing under the intellectual
generalship of a few great leading minds. Thus it is s.

... The univer-

that no nation m modern times has so many schools of sity a train-

"^ ing-school of

thought and learning as Germany, and none can boast of research.
having started and carried through such a large number
of gigantic enterprises, requiring the co-operation and col-
lective application of a numerous and well-trained staff.^
The university system, in one word, not only teaches
knowledge, but above all it teaches research. This is
its pride and the foundation of its fame. i

^ The editions of the ancient
classics brought out by Tauchnitz,
Weidmann, and Teubner are well
known. The collections of the His-
tories of all countries, begun by
Heeren and Ukert and continued in
this century by the publishing firm
of Salomon Hirzel of Leipsic ; the
' Jahresberichte,' started by Ber-
zelius for chemistry, and now separ-
ately conducted for all the different
sciences ; contain summaries of the
labours of the whole world syste-
matically arranged. There is the
geographical establishment of Peter-
mann at Gotha ; not to speak of
publications specifically national,
such as the 'Monumenta Germanic,'

as other countries possess similar
undertakings. Von Zach was the
first to establish a regular inter-
national organ for astronomical
observations. It was started in
1798, and soon became the "living
organ of astronomy," equally ap-
preciated by Lalande and Gauss.
This " montlily" was soon succeeded
by Schumacher's "weekly," the
' Astronomische Nachrichten.' See
Wolf, ' Geschichte der Astronomic,'
p. 764, &c. Humboldt's and
Gauss's scheme for a network of
magnetic observations all over the
world was taken up by English
men of science.

168 SCIENTIFIC THOUGHT.

It is a useful and interesting task to trace intellectual
developments and habits to their external causes. The
centralisation of the powers and resources of a whole
nation into one capital, as was the case in Eome and in
Paris, may explain the brilliancy of their literatures ; the
more scattered and diffused culture of Greece and of
Germany is likewise reflected in their many schools of
thought and learning ; the insular position of England has
impressed its advantages and disadvantages upon her
history, and has influenced her mental life. These influ-
ences have frequently been pointed out and examined.
The historian of thought has another and more difficult
task to perform. Habits of thought and intellectual
qualities never become the property of a large number of
persons unless they assume a definite form ; through this
they become a marketable article which can be communi-
cated and transmitted, and in which those also can par-
ticipate from whom the deeper motives and higher aims
remain hidden. Every school has its watchword, in which
its leading thought, its ideal, is embodied. The widely
scattered and yet closely connected community of intel-
lectual workers rej)resented by the German university
system, which covers with its network of universities and
high schools the German-speaking countries of Europe,
has during the period of its greatest influence developed
its own special ideal, and it has expressed this in a special
9. word — namely, the word Wissenschaft. Neither the French

The ideal

of ivissen- nor the English application of the word science corre-
sponds to the use or gives the meaning of the word
Wissenschaft. This meaning cannot be defined by any

^ Compare the uotes at the beginning of the last chapter, p. 89, &c.

THE SCIENTIFIC SPIRIT IN GERMANY.

169

single word in the English language. Expressions such
as " student of science " or " science tripos " have a mean-
ing in English, but they would have none if translated
into German. In each case the word Wissenschaft would
require a qualification. An " Academic des Sciences "
could not according to German usage exist separately
beside an " Academic franqaise " or an " Academic des
Inscriptions," for it would include them.^ Scientific
treatment in England means the exact experimental or
mathematical treatment of a subject : no one ever calls
Bentley ^ or Gibbon ^ a great scientific writer, though in

^ The two older academies in
Paris, the " Academic des Sciences "
and the "Academic des Inscriptions
et Belles Lettres," covered very
nearly the same ground as the
modern Berlin "Academic der Wis-
senschaften und Kiinste," which
is divided into two classes, the
" mathcmatisch - naturwissenschaft-
liche " and the " philosophisch-his-
torische Classe," the two sides
being equally comprised under the
term Wissenschaften. A similar
division exists in the learned so-
cieties of Vienna, Leipsic, Munich,
and Giittingen.

2 Richard Bentley (1662-1742),
popularly known in England mainly
through his Boyle Lectures, his
controversy about the Epistles of
Phalaris, and his thirty years' feud
as Master of Trinity College, Cam-
bridge, with the dons of his col-
lege, but hardly known "as the
first, perhaps the only, Englishman
who can be ranked with the great
heroes of classical learning" (Mark
Pattison, ' Ency. Brit.'), was from
the first recognised as a consum-
mate genius by the scholars of Ger-
many, by Graevius and Spanheim,
who welcomed him as " novum
et lucidum Britanniae sidus," as
" splendidissimum Britannite lu-

men." The many beginnings which
he had laid for subsequent critical
research among the ancient classical
authors were taken up abroad by
men like Heyne, Reiz, F. A. Wolf,
Gottfried Hermann, and Fried rich
Ritschl, in whose hands they have
developed into a special sciiool of
philology, counting i^robably over
a hundred representatives, many of
whom have openly avowed their in-
debtedness to Bentley. (See Kochly,
'Gottfried Hermann,' Heidelberg,
1874, pp. 115 sgq., 142, 189. Rib-
beck, 'Friedr. Wilh. Ritschl,' 2
vols., Leipzig, 1879 and 1881, vol.
i. p. 229 ; vol. ii. pp. Ill, 176, &c.,
418, 429.)

^ Gibbon (1737-94) gave a new
impetus to the study of the history
of Roman law through the cele-
brated 44th chapter of his ' Decline
and Fall of the Roman Empire.'
It was translated by Professor
Hugo of Gottingen and Professor
Warnkonig of Liege, and has been
used as the text-book on Civil Law
in some of the foreign universities.
See Smith's edition of Gibbon's
History with the Notes of Milman
and Guizot, chap, xliv., note.
Herder, Savigny, and Niebuhr
stand all under the immediate in-
fluence of Gibbon, and Leasing saw

170

SCIENTIFIC THOUGHT.

r

10.

Has been

developed

under the

German

university

system.

Germany each stands at the head, and forms the begin-
ning, of a definite scientific movement. The distinction
between scientific and philosophical thought which I have
explained in the Introduction would be unintelligible if
science were translated simply by Wissenschaft ; the word
Wissenschaft is not opposed to, but embraces, the word
philosophy : Fichte, whose whole doctrine was, according
to French and English ideas, almost the reverse of scien-
tific, uses the word Wissenschaftslehre to denote and char-
acterise his system.^ In fact the German word for science
has a much wider meaning than science has in French or
English ; it applies alike to all the studies which are
cultivated under the roof of " alma mater " ; it is an
idea specially evolved out of the German university
system, where theology, jurisprudence, medicine, and
the special philosophical studies are all held to be
treated " scientifically," and to form together the universal,
all-embracing edifice of human knowledge.^ Such an

in him kindred tendencies, though
in a different direction (seeWatten-
bach. ' Zuna Andenken Lessing's,'
p. 23).

1 Fichte (1762-1814) begins his
first philosophical work, published
in 1794, with the words, " Philo-
sophy is a science," and he then
proceeds to give to his philosopl)y
the term Wissenschaftslehre, or gen-
eral doctrine or theory of science.
A further definition which he gives
is as follows: "A science has a
systematic form ; all propositions
in it hang together in one single
fundamental proposition, and are
united by it into a whole." It is
evident that whoever approached
Fichte's writings with the ideal of
science, as it was established by
the labours of Lavoisier and the
great French academicians, would

not accept these first sentences of
Fichte's book. He would admit
that the sciences as cultivated by
the great Frenchmen had a unity
of method, the exact method, the
method of observation, measure-
ment, and calculation, but not
necessarily a unity of system, or
a highest all-embracing proposition.
It is evident that science means
to Fichte something more than it
meant to the Academic des Sciences:
it meant Wissenschaft, not merely
methodical, but systematic, unified
knowledge.

- It would be an interesting task
to trace in German literature from
the time of I^eibniz the gradual
evolution of the idea of Wissen-
schaft, to see how the word has
grown in pregnancy and signifi-
cance till it became firmly estab-

THE SCIENTIFIC SPIRIT IN GERMANY.

171

idea, the use of such a term, could only be born and
developed where the different faculties, the various
branches of knowledge, lived habitually, for many ages,
under the same roof, coming into continual contact, and
learning to regard each other as members of one family,
as integral parts of one whole. The German university

Hshed as denoting a moral as much
as an intellectual ideal, which it was
the duty of the German university
to uphold and to realise. Such an
investigation would have to show
how the encyclopfodic view is repre-
sented by Leibniz, how Winckelmann
applied the term to the studies
of antiquity, liow Lessing taught
method and clearness, how Herder
widened and deeiDened the view, ex-
tending it to the elemental forces
as well as to the finished forms of
human culture, how it was finally
raised as the standard of Gern)an
university teaching by F. A. Wolf
and W. von Humboldt, finding an
eloquent exposition in Fichte's lec-
tures on the " Nature of the
Scholar" {' Vorlesungen tiber das
"VVesen des Gelehrten,' Erlangen,
1805), and a practical realisation
in the foundation of the University
of Berlin in 1809, during the period
of Germany's greatest degradation.
The following words of Fiehte
have reverberated in the soul of
many a German scholar to whom
Fichte's philosophy was unknown
or distasteful, and this same spirit
has leavened and united studies
which stand apparently in no con-
nection with each other. ' ' The
scholar " (and specifically the
teacher of scholars) " shows his
respect for science [Wissenschaft]
as such and because it is science,
for science generally as one and
the same divine Idea in all the
various branches and forms in
which it appears." Of one who
mav be seduced into overestimat-

ing his own branch, Fiehte says :
" It becomes evident that he has
never conceived science as One,
that he has not comprehended his
own branch as coming out of this
One, that he thus does not himself
love his branch as science but only as
a trade ; this love of a trade may
otherwise be quite laudable, but in
science it excludes at once from the
name of a scholar. ... In the aca-
demic teacher science is to speak,
not the teacher himself," he is to
speak to " his hearers not as his
hearers but as future servants of
science," he is to represent the dig-
nity of science to coming genera-
tions (Fiehte, W^erke, vol. vi. p.
4-36, &c.) I have myself heard
expressions similar to these from
the mouth of one who represented
what we should now consider the
very opposite phase of nineteenth-
centurj' thought, from one of the
earliest representatives in Germany
of exact research, AVilhelm W^eber
of Gottingen. Driven into a corner
by the questionings of devoted
friends as to his own discoveries
and contributions, which he was
modestly fond of tracing to Gauss,
and unable to deny his own part,
he would warmly exclaim, " But
is it not possible that science
could do something herself ? " Pro-
fessor Adamson has pointed out
('Fiehte,' in " Philos. Classics," p.
79) how the fundamental idea in
these writings of Fiehte has been
made familiar to English readers
through the teaching of England's
greatest modern moralist, Carlyle.

172

SCIENTIFIC THOUGHT.

system has the merit of having elaborated the widest con-
ception of science, of having fixed the highest and most
general scientific standards. Opposed to science is that
which is unscientific, dilettante, popular ; that which is
not a vocation, but a handicraft ; that which grows and
lives outside of the great university system, including in
this the innumerable learned schools which form its base,
and the academy which forms its summit.

What France and England have elaborated and termed

""^^nce"""^ Science, is called in Germany Exact Science ; but it is

actsclenccV' opposcd to the German ideal of science to hold that the

exact method is the only method which deserves to be

called scientific.^

11.

In Fiance

^ This is perhaps not quite cor-
rect. No doubt the term " exact
Sciences " is used frequently during
the last half - century to denote
the mathematical and experimen-
tal sciences ; very much in the
same sense as we see them de-
fined by Cuvier in the beginning
of the century, and described as
the ground covered by the labours
of the "Academic des Sciences."
There exists, however, in Germany
another school of thought, very
influential throughout this cen-
tury, and one that has exerted
a very wide and wholesome influ-
ence, which stands in no connec-
tion whatever with the mathema-
tical sciences, though it applies the
word " exact" to its methods and re-
searches. This is the school which
maintains that the real introduc-
tion to the study of antiquity lies
in a knowledge of the ancient, pre-
eminently the classical, languages,
as exact and precise as any mathe-
matical knowledge could be, and sees
in an acquisition of such precise
knowledge the training necessary
for success in philological and his-

torical research, just as famili-
arity with mathematical formuhe
and measuring instruments has long
been considered quite indispensable
training to success in the natural
sciences. Of this view Gottfried
Hermann may be considered as
a somewhat one - sided, Friedrich
Ritschl as a more profound and
far - seeing, but equally energetic
representative. It is Ritschl who
was the most influential. Without
at present entering into the con-
troversies which existed between
what were termed the ' ' Sprach-
philologen " and the " Sach-philo-
logen," I desire here to refer to
the fact that such very different re-
presentatives of thought as Fichte,
Weber, and Ritschl, than whom no
men could be more dissimilar in
cast of mind, all find their ideal
expressed in the word Wisscnschaft.
I have quoted Fichte, the specu-
lative generaliser, and Weber, the
exact mathematical physicist. I
will add what Ritschl, the critical
philologist, says. He trusted, as
his biographer reports, " in the
indestructible magnetic force of

THE SCIENTIFIC SPIRIT IN GERMANY. l73

Before the methods of exact science were introduced
into Germany under English and French influences, the
Germans possessed many scientific methods. There was
the science of philosophical criticism, established by
Kant; the science of historical criticism, of Biblical
criticism ; the science of philology : all these professed
to have methods as definite, aims as lofty, and a style
as pure, as the exact sciences brought with them.

At present a tendency of thought may exist in Ger-
many, akin to the positive philosophy in France and
England, which aims at introducing the methods of the
natural sciences so as to cover the whole ground of re-
search, and to allow of no other methods. Should it
succeed, it will destroy the essential features of the
German university system, and with it the ideal of
Wissenschaft as it has existed in all the leading minds
of Germany during the last hundred years.

I intend to come back to this subject later on, and
to define more clearly what the German ideal of science
— what Wissenschaft — is. That which we are occupied
with at present is the diffusion of the scientific spirit, in
the narrower sense, as it was firmly established in France
through the great mathematicians and scientists at the

the studies of classical antiquity " ;
he maintained that philology, as
science, not the barren training of
a pedagogic seminary, is the only

the depth of knowledge ; it must,
even in its circumscribed nature,
contain the germs of further mental
development. Such depth, such

right thing for future masters. fructifying power, comes only from
" The good teacher must, even for j science " ( Wissenschaft). See Rib-
teaching purposes, have and know, ' beck, ' Leben Ritschl's,' vol. ii. p

both in quantity and qualitj', more
than he requires for immediate
progress ; the portion he requires
for immediate communication, for
practical teaching purposes, must
be delivered out of the fulness and

277. And as every mode of thought,
if clearly felt and active, finds its
expression in language, so Ritschl
was fond of characterising his scien-
tific method by the word a.Kpij3eia.

174

SCIENTIFIC THOUGHT.

12.

Reception
of Exact
Science in
Germany.

beginning of this century, as it is summed up in their
works and in the Memoirs of the Institute. "WHiat
reception did it find in Germany ? How has it thriven
under the German university system ? These are the
questions which interest us at present.

The general recognition of the purely scientific studies
conducted on a large scale by the French Academy of
Science, as an integral portion of the German university
syllabus, belongs to the beginning of the present century.
During the first forty years of the century complaints
were continually heard that some of the most important
sciences were not worthily represented.^

The eighteenth

^ Oue of the latest instances of
such complaint is to be found in
J. Liebig's paper " On the state f)f
Chemistry in Austria" ('Aimalen
der Pharmacie,' 1838, vol. xxv. p.
339). This was followed by the
highly interesting pamphlet ' On
the state of Chemistrj' in Prussia '
(Braunschweig, 1840). According
to the eminent author, chemistry
was the science which was the latest
to attain a worthy domicile and an
independent footing in the great
universities of Germany. Mathe-
matical physics liad a centre at
Konigsberg, physiology had been
established as an independent sci-
ence at Berlin through the appoint-
n^ent of Johannes Miiller in 1833,
chemistry was still only taught in
Prussia in connection with other
branches of science, with medicine,
with technology, with mineralogy.
There were no chemical laboratories
to be found in Prussia. Men like
Rose, Rammelsberg, Mitscherlich,
received none or only the scantiest
support in their practical courses of
chemistry. It is interesting to note
how Liebig, whilst pointing to the
enormous importance which chem-
istry possesses from an economic

and political point of view by reason
of its working great changes and
revolutions, industrial and other,
insists on the necessity of teach-
ing chemistry scientifically, and not
with an immediate jiractical bias.
In this respect he is as much a
representative of the scientific
spirit in the wider sense as the
great men mentioned in the note
to p. 171. The following passage
(p. 39) may still be read with in-
terest and profit : " I have found
among all who frequent this labora-
tory [Giessen] for teclmical pur-
poses a prominent inclination to
occupy themselves with applied
chemistry. They usually follow
hesitatingly and with some suspi-
cion my advice to leave alone all
this time-absorbing drudgery, and
simply to become acquainted with
the necessary waj's and means of
solving purelj' scientific questions.
By following this advice their minds
learn easilj' and quickly how to find
the best means ; they themselves
adapt them to circumstances and
modify them : all operations, all
analyses, which serve to ascertain
a certain state, which must be
made in order to find the conditions

THE SCIENTIFIC SPIRIT IN GERMANY.

175

century produced in Germany men of great scientific im-
portance ; but their position was irregular and uncertain,
and they undoubtedly do not wholly or exclusively belong
to the history of the university system. Leibniz, Euler,
Haller, Werner, Markgraf, Tobias Mayer, Lambert, and
Humboldt are all intimately connected with the growth of
modern science : their position and sphere of action were
in each case different.^ Leibniz was a courtier, Euler an

for the solution of the problem,
have a definite sense ; each of them
possesses a certain charm which
dispels fatigue, and if the question
is really answered, then they know
the ways and means of attaining
similar ends. I know many who
are now at the head of soda-, vitriol-,
•sugar-factories, of colour- works and
other establishments. Without ever
having had anything to do with them
beforehand, they were in the first
half -hour acquainted with the pro-
cesses, the second already brought
a number of appropriate improve-
ments, &c., &c. " Similarly Helm-
holtz in 1862 ('Redeu,' vol. i. p.
142) : " He who in the cultivation
of the sciences aims at immediate
practical usefulness, may be joretty
sure that he will miss his aim.
Science [ Wissenschaft] can aspire
only to a perfect knowledge and
a complete understanding of the
sway of physical and mental forces.
The individual worker must find
his reward in the joy over new
discoveries, as new victories of
mind over matter, in the sesthe-
tical beauty which an orderly dis-
play of knowledge affords, &c., &c."
How little do our modern colleges
of science correspond with this view
of Wissenschaft !

1 On Leibniz (1646-1716), see p.
158 ; Werner (1750-1817), p. 118 ;
and Tobias Mayer (1723 - 62), p.
158. A. von Humboldt (1769-1859)
is well known to English readers.

Leonhard Euler (1707-83), a native
of Basel, passed the greater part of
his life at St Petersburg as a mem-
ber of the Academy, a i^ortion of
it (1741 - 66) as an Academician
at Berlin. He has been termed
the father of pure mathematics,
inasmuch as he freed mathemati-
cal analysis from geometrical con-
ceptions, established the notion of
function or mathematical depend-
ence, and did much to make the
theory of numbers an independent
branch of science. His memoirs
are said to number nearly a thou-
sand ; his works, if all printed,
would fill 60 to 80 quartos (see
Hankel, ' Die Entwicklung der
Mathematik,' Tiibingen, 1884, p.
12). Andreas Sigismund Markgraf
(1709 - 82) was born and lived at
Berlin, a member of the Academy.
On his various chemical researches
see Kopp, ' Geschichte der Chemie,'
vol. i. p. 208. Albrecht von Haller
(1708-77) was a native of Bern.
He was, next to Leibniz, perhaps
the most encyclopaedic mind of
modern times, equally celebrated
as botanist, physiologist, and poet.
He has been termed the father of
physiology. Brought up under the
celebrated Boerhaave, he accepted
a chair at the newly founded Uni-
versity of Gottingen in 1736, and
taught there for seventeen years
anatomy, botany, medicine, and
surgery.

176 SCIENTIFIC THOUGHT.

academician, Werner the head of a great mining school,
Humboldt a traveller, Markgraf a private gentleman.
Haller, indeed, shone as a great light in the University
of Gottingen, where he did more than any other to place
scientific studies on a level with classical ones, and to
create for them a permanent abode within the pale of
"alma mater." He founded in 1751, in close connection
with the university, the Gottingen Society, which from
1753 published the celebrated ' Gottinger Gelehrte An-
zeigen.' ^ Tobias Mayer and Lambert ^ can hardly be
said to have got much help either from the university,
to which the former belonged, or from the Academy, of
which the latter was a member ; their celebrity rests on
works produced by private and unaided effort. Hum-
boldt also depended upon his personal means and upon
his connection with the Paris Academy, and only attained
late in life, and in the course of the present century, his
eminent position as the head and patron of German
science. Von Zach and Gibers, who together with Tobias
Mayer and Lambert raised German astronomy during the
eighteenth century to the level of English and French
science, stood outside the university system. Von Zach
was indebted to personal connections, and ultimately
to Duke Ernest IL of Gotha, for the position which

1 The ' Gottinger Gelehrte An-
zeigen' had existed since 1739.

2 Joh. Heinrich Lambert (1728-
77), a very extraordinary man, was
a native of Miihlhausen, Alsace,
which then belonged to Switzer-
land. He was received as a mem-
ber of the Berlin Academy, and
associated there with Euler and
Lagrange. He is celebrated through
his 'Photometry' (1760) and 'Pyro-
metry ' (1779), his equation referring

to the orbits of comets, employed
by Gibers in his method for calcu-
lating them (Weimar, 1797, re-
published by Encke, 1847), and his
prophetic prediction of the proper
motion of the sun (in his Cosmolo-
gical Letters, 1761). This motion
was actually calculated by Sir Wil-
liam Herschel in his paper " On the
proper Motion of the Sun and Solar
System" ('Philos. Trans., 1783).

THE SCIENTIFIC SPIRIT IN GERMANY.

177

he held as a kind of corresponding centre of European
astronomy, and as the leader of a large school of German
astronomers of this century.^ Olbers was a practising
physician at Bremen," where he followed astronomical
studies as a recreation, making himself eminent by great
services to science, among them by his method of calcu-
lating the orbit of a comet : as the greatest of his services
he counted the fact of having discovered, trained, and
appreciated the rising genius of Bessel.^

^ Franz Xaver vou Zach (1754-
1832) was a native of Pesth. After
having served in the Austrian artil-
lery, and taken to astronomy as a
favourite study, he spent some time
in Paris and London, and became
acquainted with Lalande, Laplace,
Herschel, Maskelyne, Ramsden, and
others. He was engaged by Duke
Ernest II. of Gotha in 1786 to
erect an observatory on the See-
berg near Gotha. This was com-
pleted in 1791. Here he trained a
number of younger astronomers,
and was the first to establish and
maintain a periodical specially de-
voted to astronomy. It was first
(1798) published under the title
' Geographische Ephemeriden,' then
(1800-13) as 'Monatliche Corres-
pondenz zur Beforderung der Erd-
und Himmelskunde.' Lalande and
Gauss both testified to the use-
fulness of this international pub-
lication, without which Piazzi's
discovery (see p. 182, note 1) would
probably have been lost. See
Wolf, ' Gesch. d. Astronomie,' p.
764.

2 Heinr. Wilh. Mat. Olbers (1758-
1840) was born near Bremen. He
followed astronomy as a private
study. He is mainly known by
his rediscovery of the first of the
smaller planets (see p. 182, note 1),
by his theory, once generally ac-
cepted, of the origin of the smaller

VOL. I.

planets through the disruption of a
primitive large planet, and by his
' Abhandlung iiber die leichteste
und bequemste Metliode die Bahn
eines Cometen aus einigen Beo-
bachtungen zu berechnen ' (1797).
In this work, by using Lambert's
equation, he succeeded in perfecting
the methods of Newton and his suc-
cessors so as actually to calculate
the elements of several comets.
This method is still in general use
(see Wolf, loc. cit., p. 519).

3 Friedr. Wilh. Bessel (1784-1846)
attracted the attention of Olbers by
his mathematical abilities whilstem-
ployed as clerk in a shipping ofiice
at Bremen. If Tobias Mayer's
lunar tables were remunerated and
published with English money,
Germany repaid the debt by the
industry of Bessel, who calculated
and reduced the observations made
by Bradley (1692-1762, Astronomer
Royal from 1742) at Greenwich
during the years 1750 to 1761.
They had been neglected and re-
mained unpublished till 1798, when
Olbers induced Bessel to make
them useful to science. This he
did by calculating from them some
of the most important and funda-
mental data of astronomy. After
many years of labour he brought out
his 'Fundamenta Astronomiac pro
A. 1755 deducta ex observation-
ibus viri incomparabilis James

M

178

SCIENTIFIC THOUGHT.

13.

Science not
yet domi-
ciled at the
German uni-
versities
during the
eighteenth
centurj'.

The general impression we receive from a perusal of
the histories of science and learning in Germany at the
close of the eighteenth century is, that the university
system had, so far as philosophical and classical studies
were concerned, attained almost to the eminence which
it has held during this century, hut that it had not — with
the exception perhaps of Gottingen — received into its pale
the modern spirit of exact research, such as it had been
developed by the great French Academicians. Eminent
students of science lived outside of the universities, belong-
ing wholly or largely to the international Eepublic which
had its centre in Paris, exerting little influence on higher
German education through the universities, and hardly
any on German literature, which had meanwhile ripened
into the age of Classicism. This scattered condition of
German science gave it on the one side a character
which was foreign to the general tendencies of German
thought, since this had come under the excessive in-
fluence of the speculative spirit without that whole-
some check which exact research has always exerted.^

Bradley in specula astronomica
Grenovia3nsi per A. 1750-62 insti-
tutis' (1818). By his determina-
tion (1838-40) of the parallax of the
star 61 Cygni he made the first ac-
curate calculation of the distance of
a fixed star, which he computed at
12 billion astronomical miles.

1 It was the age of the Natur-
2yhilosophie, which, through the in-
fluence of Schelling in the south
and Hegel in the north of Ger-
many, tilled the chairs in the uni-
versities, and penetrated into the
learned societies. This philoso-
phy of nature had the effect of
frequently replacing induction by
speculation, the patient work of

the calculator, the observer, the
experimenter, and the dissector by
general theories, such as, applied
to literary, historical, and poetical
subjects, had acquired a certain
importance, and a semblance of
veracity and usefulness. In France
the whole spirit of the Academy of
Sciences opposed this form of learn-
ing. Cuvier denounced it or re-
garded it with fsuspicion, in Eng-
land it remained unknown, and in
Germany itself individual great
minds opposed it, or did their
work outside of its influence.
Such were notabl}^ A. von Hum-
boldt and Gauss. Younger men,
such as Liebig and Joh. Miiller,

THE SCIENTIFIC SPIRIT IN GERMANY.

179

On the other side, we find in the wide domain of gen-
eral Hterature valuable beginnings and foreshadowings
of later scientific thought, as in Georg Forster -^ and in

came temporarily under its influ-
ence. As regards its harmful
effect on the natural and medical
sciences, the popular addresses of
Helmholtz and Du Bois-Reymond
may be consulted. Its philoso-
phical value will frequently oc-
cupy us in later chapters of this
work. Its period can be approxi-
mately fixed by the publication in
1797 of Schelliug's 'Ideen zu einer
Philosophie der Natur.' The death
of Hegel in 1831, and Humboldt's
Berlin lectures during the years
1827 and 1828, may be considered
as marking approximately the end
of the generation which came
under the one-sided influence of
the Naturphilosophie. We shall
have ample occasion later on to
notice how many valuable leading
ideas connected with this phase
of thought were temporarily aban-
doned and have since come promi-
nently before the scientific world.
The year 1830 marked the victory
of Cuvier's ideas over those of his
great contemi^orary Geoffrey St-
Hilaire in the French Academy,
and with it the temporary defeat
of the valuable suggestions con-
tained in the writings of Lamarck
and Goethe.

^ Georg Forster (1753-94) was one
of those unique men in the history
of literature and science who com-
bine the artistic with the scientific
spirit, promoting equally the inter-
ests of poetry and of exact know-
ledge by a loving study of Nature,
leading to new views of art as well
as to deeper conceptions in science.
He may be classed with White of
Selborne and other naturalists of
England among the small number
of those who quietly and unostenta-
tiously prepared the healthier forms

of Naturalism which permeate the
poetical and scientific thought of our
century, culminating in the great
names of Wordsworth and Goethe,
of Humboldt and Darwin, of Wal-
lace and Haeckel. His life presented
many interesting and some un-
happy episodes ; it introduces us
into the political aspirations of
the early French Revolution, to
which he sacrificed himself. It
has been written by Moleschott, the
naturalist, by Heinrich Konig, the
novelist (' G. Forster in Haus und
Welt,' Leipzig, 1858, 2 vols.), by
Klein {'Georg Forster in Mainz').
Fr. Schlegel ('Charakteristiken und
Kritiken,' vol. i. ), Gervinus (Intro-
duction to the 7th vol. of 'Georg
Forster's Werke'), and Hettner
(' Literatur des 18'*^" Jahrhunderts,'
vol. iii. ) have written appreciative
essays on him. A. von Humboldt
calls him his master (' Kosmos,'
vol. i. p. 345), and Herder (Pre-
face to Georg Forster's translation
of 'Sakuntala') prophesies his last-
ing fame against the opinion of
his less apiDi'eciative contempor-
aries. He has a place in the class-
ical literature both of England and
Germany through his beautiful de-
scription of Caf)tain Cook's second
voyage round the world — his
father, Joh. Reinhold Forster, hav-
ing been selected as the naturalist
on that voyage (London, 1777, 2
vols. 4to), German edition, 1779.
Richard Garnett has said of him :
"His account of Cook's voyage is
almost the first example of the
glowing yet faithful description of
natural phenomena which has since
made a knowledge of them the
common property of the educated
world. ... As an author he stands
very high ; he is almost the first

180

SCIENTIFIC THOUGHT.

14,
Scientific
periodicals

Goethe ; ^ but they could hardl}- be encouraged and de-
veloped sufficiently withovit that strict training which is
acquired through the routine of the class-room, or under
the eye of a recognised authority.

The want of academic union and organisation, and the
scattered situation of the many small centres of learning
and culture in Germany, led, however, to the early de-
velopment of those scientific periodicals which form such
a characteristic feature in German literature. They were
the medium for the exchange of ideas, and the collecting-
ground for researches, in an age when exact science was
not systematically taught at the Universities, and when
such researches otherwise would have run the risk of
being lost in obscurity or oblivion.

At the end of the eighteenth century Germany,

and almost the best of that valu-
able class of writers who have made
science and art familiar by repre-
senting them in their essential
spirit, unencumbered with techni-
cal details" ('Ency. Brit.,' vol. ix.
p. 419). Forster lived in the period
of transition from the thought of
the eighteenth century to that of
the nineteenth, and a study of his
Life, Works, and Correspondence is
a very good introduction to nearly
all the great problems which then,
especially on the Continent, trou-
bled the minds of the greatest men.
If he may be accused of want of
patriotism, he is certainly to be
admired for his freedom from na-
tional narrow-mindedness.

^ It has taken nearly a century
before the real value of Goethe's
scientific ideas has been correctly
gauged. His non- academic sur-
roundings, his unscientific style, his
antagonism to Newton, his mission
as a poet — supposed in those days
to be less realistic than we have

since become accustomed to con-
sider it — all these circumstances
contributed to the result that
Goethe's scientific writings were
not taken au gerieux by the natural-
ists of his age. Then came a period
when men of science began to sift
the wheat from the chaff; but even
they have only tardily recognised
that, more than in special dis-
coveries or suggestions, his great-
ness lies in that general conception
of Nature which was so foreign to
his age, and which nevertheless is
becoming more and more familiar
and necessary to ours. See espe-
cially Helmholtz's valuable essays
on Goethe as naturalist from the
years 1853 and 1892 (' Vortriige,'
vol. i. , and address delivered at the
meeting of the Goethe Society at
Weimar, 1892), and the remark-
able progress of his own views on
this subject contained therein. We
shall have ample opportunity of re-
verting to this subject.

THE SCIENTIFIC SPIRIT IX GERMANY.

181

though not by its universities, was aheady an import-
ant power in the Eepublic of exact science which
then had its centre in Paris. Just at the beginning
of the nineteenth century two events happened which
foreboded for the highest branches of the mathematical
sciences a revival of the glory which in this depart-
ment Kepler and Leibniz had already given to their
country. These two events are both coupled with the
name of Carl Friedrich Gauss. They added greatly 15.
to the reputation of the University of GiJttingen, with mathemati-

*" cal re-

which this remarkable man was connected for half a searches,
century.^ The first was the pulilication of the ' Dis-
quisitiones Arithmeticse ' in Latin in 1801 — a work by
which Gauss placed himself on a level with the great
mathematicians, Euler, Lagrange, and Legendre." The

1 Carl Friedrich Gauss (1777-
1855), a native of Brunswick, called
by Laplace the first mathematician
of Europe, may be considered as
the first and foremost representa-
tive of the modern mathematical
school, of which we shall have to
treat later on. Unlike most of
the great mathematicians of the
Continent, he was self-taught, and
followed in his earliest works quite
independent lines of thought ; re-
sembling in this the great isolated
thinkers of Britain whose ideas take
a generation or more to penetrate
into the test-books of the school.
Gauss had the highest opinion of
the dignity of pure science, and it
almost appears as if, among the
moderns, only Newton had come
up to his ideal. For him alone
he reserves the adjective " sum-
mus," and he adopts his synthetic
and classical methods of exposition,
removing, as has been said, the
scaffoldings by the aid of which he
had erected his monumental works.

Gauss trained few mathematicians ;
but among the few who penetrated
the secret of his ideas are such
original thinkers as the Hungarian
Bolyai (1775-1856), the geometers
Mobius (1790-1868) and Von Staudt
(1798-1867), who all mark quite
independent lines of research. On
Gauss see Sartorius, ' Gauss zum
Gediichtniss,' Leipzig, 1856 ; Han-
selmann, ' K. F. Gauss,' Leipzig,
1878 ; E. Schering, ' C. F. Gauss,'
Gottingen, 1887.

'^ It appears that Gauss, to whom
the arithmetical discoveries of For-
mat and the proofs of Euler, La-
grange, and Legendre remained for
a long time unknown (see his Works,
edited by Schering, vol. i. p. 6 ;
vol. ii. p. 444), had independently,
in his eighteenth year, as a student
at Gottingen, already arrived at a
great number of propositions refer-
ring to the properties of numbers,
and had then also found methods
of geometrically constructing the
regular polygon of seventeen sides.

182

SCIENTIFIC THOUGHT.

second was the invention of a new and shorter method
of calculating the orbit of a planet from a limited number
of contiguous observations.^ This method was communi-

The latter was the first addition
made after 2000 years to the
knowledge of this matter possess-
ed by the ancients. (See ' Disquis.
Arithm.,' sec. 36.5 : " Magnopere
sane est mirandum, quod, quum
jam Euclidis temiioribus circuli
divisibilitas geometrica in tres et
quinque partes nota fuerit, nihil
his inventis intervallo 2000 anno-
rum adjectum sit," &c. ; and his
manuscript note to this passage,
given by Schering, vol. i. p. 176 :
" Circulum in 17 partes divisibilem
esse geometrice, deteximus 1796,
Mart. 30.") It is probably owing
to the independent manner in which
Gauss approached the subject that
he early found the necessity of
treating subjects of higher arith-
metic {i.e., of the theory of num-
bers or " discrete magnitudes " as
distinguished from algebra, which
is the theory of " continuous mag-
nitudes") by an independent me-
thod, for which he invented a
language and an algorithm. He
thus raised this part of mathe-
matics into an independent science,
on which the ' Disquisitiones Arith-
meticse' is the first elaborate and
systematic treatise. Legend re's
'Traite des Nombres' (1799) is a
complete thesaurus of all that was
at that time known and of what
was added by him, but it does not
attempt to establish the science on
a new basis.

^ On the 1st January 1801
Piazzi at Palermo had found a
movable star of 8th magnitude,
RA. 57° 47', ND. 16° 8', which he
announced to Bode at Berlin as a
comet on the 24th January ; but
a few days later he concluded it
must be a planet, and named it
" Ceres Ferdinandea." No one be-

sides Piazzi could find the star, but
several astronomers, Piazzi himself,
Olbers at Bremen, and Burckhardt
at Paris, tried to calculate the orbit
from the observations of the dis-
coverer, which were contained
within only 9 degrees. The at-
tempt to do so under the sup-
position of either a circular or a
parabolic or an elliptic orbit failed,
and OlViers expressed the fear that
with the circular or elliptic ele-
ments which had been published in
Zach's periodical, it might prove
impossible to find the star when
it should again become visible.
Very near the expected time, as
late as the beginning of December,
Gauss commuuicated his elements
to Von Zach, who published them
at once, recommending astronomers
to follow Dr Gauss's figures and
look 6° to 7° more eastward than
the positions of Burckhardt, Piazzi,
and Olbers indicated. And actu-
ally on the 7th December 1801
Zach himself, and on the 1st Janu-
ary 1802 Olbers, succeeded in find-
ing the star, " like a grain of sand
on the sea-shore," very near the
positions calculated by Gauss.
These results, followed soon by
the discovery of other planets by
Olbers and Harding, gave a great
impetus to the study of astronomy.
Gauss's methods were published
Ml extenao in the now celebrated
' Theoria motus corporum cceles-
tium ' in 1809. Two problems are
herein treated in a novel and com-
plete manner. The first was to
calculate by a simple and accurate
method from the necessary number
of observations tlie orbit of a planet
or comet on the assumption of New-
ton's law of gravitation, but with-
out any other special conditions.

THE SCIENTIFIC SPIRIT IN GERMANY. 183

cated to Von Zach in the course of the year 1801, and
enabled him and Olbers to rediscover the first of the
small planets, Ceres, which Piazzi had observed on the
1st of January 1801 at Palermo, and afterwards lost as
it approached the region of the sun's light. Through
this Gauss placed himself on a level with the great
French astronomers Laplace, Lalande, and others. The
new professor of mathematics and director of the obser-
vatory of Gottingen was admitted into the august com-
pany of the Paris academicians, who then ruled, and since
the death of Euler had almost monopolised, the mathe-
matical studies of the world. Although Gauss thus
introduced the higher and abstract branches of exact
science into the programme of a German university,
and established a link between Paris and Germany
in mathematics, as Humboldt had done shortly before
in the natural sciences, fully a quarter of a century
was to elapse before the spirit of exact research, and le.
of the higher mathematics, really began to leaven the spirit enters

the univer-

German universities. It then at length entered the field sitiesjnthe

o second quar-

as a third and equally important agent by the side of the cent^tL-y'!^

This was achieved to perfection,
a proof of the usefulness of the
method being the fact that Gauss
succeeded in finishing in one hour
a calculation which had taken Euler
three days, and Jiad resulted in his
blindness. The second problem
arises from the fact that the num-
ber of observations is always in
excess of the number mathemati-
cally necessary, and that, owing to
the unavoidable inaccuracies, dif-
ferent sets of observations give
slightly different orbits. How are
these to be used so as to give the

most correct average result ? This
involves a question in probabilities.
As early as 1795 Gauss was in pos-
session of the so-called method of
least squares, which occurred to him
so naturally that he susjJected that
Tobias Mayer must have already
known about it. It also occurred
independently to Legendre, who
was the first to publish it, in 1806,
in his ' Nouvelles m^thodes pour la
determination des orbites des co-
metes. ' See Sartorius, ' Gauss zum
Gedachtniss,' p. 41 sqq.

184

SCIENTIFIC THOUGHT.

philosophical and classical spirit. During these twenty-
five years Gauss lived and soared in solitary height — a
name only to the German student, as Euler had been
before him. Probably he was better known to the
younger astronomers whom he trained, and the elder ones
with whom he corresponded. But astronomy was not
then within the pale of the universities. To what extent
the character of Gauss's own genius was the cause of this
it is difficult to say.-^ He himself had not come under
the influence of any great teachers such as Paris then
possessed ; he was self-taught, and had early imbibed
a great admiration for the methods of Euclid, Archimedes,
and Newton ; he wrote in the classical style fitted for all
times, but not for uninitiated beginners." It is certain,

^ Bjerknes, in his most interesting
memoir on Abel, refers frequently
to the awe in which Gauss was held
by younger mathematicians.

" In this Gauss resembled New-
ton. He was therefore, like Newton,
frequently forestalled by others,
who published his new methods
and ideas in an unfinished and frag-
mentary form ; whereby it is not
suggested that these simultaneous
discoveries or inventions vt'ere not
quite indej^endent. Two examples
of this may be added to those given
above. When Gauss published the
'Disquis. Arith.' in 1801, he left
out the last or eighth section, which
was to treat of the residues of the
higher orders. He had already
nearly completed the theory of
biquadratic residues. In dealing
with this subject he had found it
necessary to extend the conception
of number beyond the limits then
in use. If we confine ourselves to
integers, the only extension which
then existed of the notion of number
was in the use of negative numbers.

These were counted on a straight
line backward, as positive (or or-
dinary) numbers were counted for-
ward. Gauss conceived the idea of
counting numbers laterally from the
straight line which represented the
ordinary — positive and negative —
numbers. He called numbers which
were thus located in the plane
" complex numbers," as they had to
be counted bj' the use of two units,
the ordinary unit 1 and a new unit
i. He also showed that this new
unit i stood in such relations to the
ordinarj' unit 1 as were algebraically
defined by the mysterious imagin-
ary symbol ^'-1. The complete
exposition of this new or complex
system of counting was not ex-
plained by Gauss till the year
1831, when he published the
' Theoria residuorum biquadrati-
corum.' In the meantime the
geometrical representation of im-
aginary quantities had been devised
and published by Argand (1806),
but not being employed for such
important researches, it had re-

THE SCIENTIFIC SPIRIT IN GERMANY.

185

however, tliat the spirit of exact and specially mathe-
matical research owed its right of domicile within the
universities to others who came after him, and to cir-
cumstances with which he was hardly connected.

The man to whom Germany owes its first great school
of mathematicians was Jacobi. He was self-taught like ''
Gauss ; but whilst Gauss followed in the footsteps of
Newton and the ancients, Jacobi followed in those of '
Euler, Lagrange, and Laplace. The style and methods '
of these mathematicians, being more suited for didactic I
purposes than the classical style of Euclid, Newton, and
Gauss, was probably more congenial to the mind of
Jacobi, who from his twenty-first year (1825) developed
a great activity as an academic teacher.^ He was first

mained unknown and unnoticed.
See on the history of the subject,
Hankel, ' Theorie der comijlexen
Zahlensysteme,' 1867, pp. 71, 82.
Gauss, through hiding his researches
on this subject so long, lost the
claim to the priority of the inven-
tion, though not of the effectual
use of it. In another instance he
allowed others to appropriate the
merit of cultivating a large new
field which had been familiar to
him many years before. It was
known all through the first half of
the century that Gauss was in pos-
session of valuable discoveries in
what he termed the "new transcen-
dent functions." References in the
' Disquisitiones,' § 335, in his corres-
pondence with Schumacher, Bessel,
Olbers, and Crelle, had made his
friends curious to see the "amplum
opus" which he had promised. It
appears, however, that, independ-
ently of him, Jacobi and Abel
(1802-29) following the investiga-
tions of Legendre (whose labours
began in 1786 and culminated in

his great work ' Traite des fonctions
elliptiques, &c.,' 1825-28, 2 vols,
and 3 supplements), succeeded in
developing the theory very much
on the same lines as Gauss had
taken nearly a generation earlier.
Eminent mathematicians who, since
the publication of Gauss's posthu-
mous papers, have fully investi-
gated the subject, assign to Jacobi
and Abel the undisputed priority
of publishing, but to Gauss that of
discovering, the fundamental pro-
l^erties of the " doubly periodical "
functions. Full details will be
found in the historical introduction
to Enneper's ' Elliptische Func-
tionen,' 2nd ed., Halle, 1890. See
also Gauss's Werke, vol. iii. p. 491-
496 ; Dirichlet's Discourse on Jacobi
in Jacobi's Werke, vol. i. p. 11 ; C.
A. Bjerknes, ' N. H. Abel,' Paris,
1885; Koenigsberger, 'Zur Ges-
chichte der Theorie der elliptischen
Transcendenten,' Leipzig, 1879.

^ Carl Gustav Jacob Jacobi (born
at Potsdam 1804, died at Berlin
1851) was the first great mathe-

186

SCIENTIFIC THOUGHT.

at Berlin, then at Konigsberg; these two universities
having become through him and Bessel the German
teaching centres of the higher mathematics, both pure
and applied. They have up to the present day fully
maintained this pre-eminent position. They were teach-
ing centres in the sense defined above — not only as
regards mathematical knowledge and method, but like-
wise as regards mathematical research. For this pur-
pose— as in the philological sciences — the lecture-room
was not sufficient ; there was also wanted a repository
for the independent and original contributions of the
school. Like the Jficole polytechnique thirty years before
in Paris, the Berlin school of mathematicians started with
an important periodical. This was known as Crelle's
Journal. Together with the Memoirs of the Paris Aca-
demy and the Journal de I'jficole polytechnique, it forms
the principal repository for the higher mathematical work
of the first half of the century.^ It was also through

matical teacher of Germany. Of
him Lejeune Dirichlet says : " It
was not his business to communicate
what was finished and what had
been communicated before ; his
lectures all treated of subjects
which lay outside of the field of
the text -books, and covered only
those parts of science in which he
had himself been creative. With
him this meant that they exhibited
the greatest variety. His lectures
were not remarkable for that kind
of clearness which is character-
istic of intellectual poverty, but for
a clearness of a higher kind. He
tried jirimarily to show the leading
ideas which underlay any theorj',
and whilst he removed everything
that had an artificial appearance,
the solution of problems presented
itself so easily to his hearers that

they could hope to do something
similar. . . . The success of this
unusual method was truly remark-
able. If in Germany the knowledge
of the methods of analysis is now
spread to a degree unknown to
former times, if numerous mathe-
maticians extend the science in
every direction, this gratifying re-
sult is principally owing to Jacobi.
Nearly all have been his pupils,"
&c. (Dirichlet's Discourse in the
Academy of Berlin, 1852, Jacobi's
Werke, vol. i. p. 21.)

^ The two mathematicians on
whom A. L. Crelle (1780-1855) re-
lied mainly for contributions when
he started the ' Journal fiir die
reine und angewandte Mathematik'
in 1826 were Abel and Steiner.
For originality of thought they
stand quite alone. Both extended

THE SCIENTIFIC SPIEIT IN GERMANY.

187

Jacobi, and still more through his contemporary Lejeime
Dirichlet (born 1804 at Diiren, of French extraction,
and trained in Paris under Laplace, Legendre, Fourier,

the field of research which thej-
cultivated by fundamentally new
ideas of such breadth that full}'
half a century was required be-
fore they were thoroughly appreci-
ated by mathematicians. Abel
(a Norwegian by birth) died in
1829 when only twenty - seven
years old, having during the four
years wliich embrace his published
memoirs extended the limits of
algebra and laid the foundations
for a more comprehensive treat-
ment of the higher or transcendent
functions, or forms of mathematical
dependence. Mathematicians be-
fore him had tried to solve algebra-
ically equations beyond the fourth
degree, but had failed. Abel proved
that the problem as then conceived
could not be generally solved. Le-
gendre had through his unaided
labours, extending over thirty
j'ears, established the theory of
elliptic integrals as far as was
possible on the lines then adopted.
Abel — and simultaneously Jacobi —
treated the subject from an entirely
novel point of view, and by doing
so opened out quite a new field of
research, the extent and importance
of which Abel fully recognised when
he presented to the French Acad-
emy his memoir of 1826, in which
he dealt with functions of which
those studied by Legendre and
Jacobi were only special cases.
This memoir, containing Abel's
celebrated theorem, which he had
already discovered in 1825, and
which was published in a brief ar-
ticle in Crelle's Journal in 1829, re-
mained unnoticed, being, as Legen-
dre explained to Jacobi, almost un-
readable. See Enneper, ' EUiptische
Functionen,' 2d ed., p. 192 ; Jacobi's
Werkc, vol. i. p. 439, &c. Abel

has been called the greatest mathe-
matical genius that has yet existed
(Oltramare in ' La grand e Encyclo-
pe'die,' art. "Abel"); his fellow-
worker, Jacob Steiner (1796-1863,
a Swiss by birth), has been termed
the greatest geometrician of modern
times. The progress of analysis
had thrown into the background
purely geometrical researches, al-
though a revival of these had com-
menced in France with Monge and
his followers, and had been further
promoted by Poncelet, as well
as simultaneously by Mobius and
Pliicker in Germany. The labours
of the two latter remained for a
long time unknown and unrecog-
nised. Steiner, who was self-
taught, who disliked the calculus,
and considered it a disgrace that
geometry could not solve her prob-
lems by purely geometrical methods,
undertook to find the common root
and leading principle which con-
nected all the theorems and por-
isms bequeathed to us by ancient
and modern geometry ; he brings
order into the chaos, and shows
how nature with a few elements
and the greatest economy succeeds
in giving to figures in space their
numberless pi-operties. He not
only completed that part of geome-
try which had been treated by the
ancients — the geometry of the line,
the conic sections or curves of the
second order, and the surfaces in
space corresponding to them — but
he also attacked problems which
before him had been solved only by
the calculus, and even succeeded in
carrying his methods beyond the
reach of the calculus of varia-
tions, specially invented to deal
with geometrical questions. Like
Fermat in the theory of numbers,

188

SCIENTIFIC THOUGHT.

Poisson, Cauchy), that the great work of Gauss on the
theory of numbers, which for twenty years had remained
sealed with seven seals, was drawn into current mathe-
matical literature, and became, as Newton's ' Principia '
had become a century earlier, an inexhaustible mine of
wealth for succeeding generations.
18. About the same time the experimental side of exact

Chemical

laboratories rcscarch — the USB of the chemical balance, through which

established "

throu"|h Lavoisier and his followers had done so much to establish
Liebig. chemistry on a firm and independent basis — received a
great impetus by the establishment of the first chemical
Iciboratories within the pale of the universities.-^ In this
direction the greatest influence probably belongs to the
small town of Giessen, where Liebig opened his cele-
brated laboratory in the year 1826. It became the

Steiner in geometry left to his fol-
lowers a large number of theorems
and problems without proofs which
he had solved by his methods ; and
it was only in quite recent times
that the Italian Cremona succeed-
ed in definitely clearing up the
whole of this original and valuable
bequest. See Hankel, ' Die Ele-
mente der pi'ojectivischen Geome-
tric,' chapter i. ; Jacob Steiner,
Werke, vol. ii. p. 495.

^ On Liebig's laboratory see Hof-
mann's Faraday Lecture, p. 8.
Chemical laboratories existed for
teaching purposes before Liebig's
at Giessen. Kopp (' Geschichte der
Chemie,' vol. ii. p. 19) mentions one
at Altorf, which was founded, 1683,
by the council of the city of Niirn-
berg for academic teaching pur-
poses. For the training of the
modern school of chemists no man
did more than Berzelius, in whose
laboratory there were trained Chr.
Gmelin, JVIitscherlich, H. and G.

Rose, Wohler, Magnus, Arfvedson,
Nordenskiold, Mosander, and others.
Sir William Thomson (Lord Kelvin)
in 'Nature,' vol. xxxi. p. 409, men-
tions the beginnings of laboratory-
teaching at Glasgow by Prof.
Thomas Thomson in 1828. But
what was j^robably peculiar to
Liebig's laboratory was the syste-
matic and methodical training, on
a specially devised plan, in quali-
tative, quantitative, and organic
analysis, by which young persons
were introduced to a thorough
knowledge of chemical properties
and manipulations. The guides,
text-books, and tables for analytic
work of Will, Fresenius, and others
were elaborated to meet the
requirements of such methodical
teaching. Almost simultaneously
with Liebig at Giessen, Purkinje at
Breslau laid the foundation for the
first physiological laboratory. See
Du Bois-Reymond, 'Reden,' vol. ii.
p. 367.

THE SCIENTIFIC SPIRIT IN GERMANY. 189

training - school for the greater part of the eminent
chemists outside of Paris, and the model for similar
establishments, and extended its influence over the
world — into England, Scotland, and America. It also
did more than any other institution of that kind for the
development of ready and accurate methods of analysis,
such as are now used in the remotest regions. But it
was significant for German chemistry, and for the cos- 19.

. 11 1 Cosniopoli-

mopolitan character of German science generally, that tan charac-

^ ° "^ ter of Ger-

this brilliant development of experimental research was man science.
stimulated from two independent centres; that German
chemists as little as German mathematicians attached
themselves in a one-sided manner to the Paris school.
In mathematical science the classical style of Gauss,
transmitted from the ancients through ISTewton, com-
bined with the analytical or modern French style of
Jacobi and Dirichlet to give to German research its
character of universality. In a similar manner, when
chemistry again found a domicile in Germany and be-
came an integral portion of the university programme,
it had been trained in two different schools. For there
lived at that time in Sweden the eminent authority Ber-
zelius,^ who divides with Gay-Lussac the glory of being

^ J. Jacob Berzelius (a Swede,
1779-1848), one of the most eminent
and industrious of chemists, had a
great influence on the development
of modern chemistry by the num-
ber as well as by the accuracy of his
experimental determinations, by his
invention of methods and apparatus
for analysis, and by his extensive
proofs of several of the most im-
portant theories. The latter di-
rected the labours and governed the
opinions of many — especially Ger-

man— investigators. It was through
him mainly that Richter's chemi-
cal equivalents and Dalton's atomic
theory were extensively verified and
applied to all parts of the science,
to organic and mineralogical chem-
istry. He also elaborated, in close
connection with Davy's electrical
discoveries, his celebrated electro-
chemical theory, which up to the
year 1840 was very generally ac-
cepted by chemists ; and he assisted
through his repeated expositions

190

SCIENTIFIC THOUGHT.

the master of the great German chemists of the middle
of the century. Mitscherlich at Berlin and Wohler at
Gottingen belonged to the school of the former, whereas
Liebig had the good fortune to be introduced through
Humboldt into Gay-Lussac's laboratory at Paris as the
first pupil/

and criticisms in breaking down the
older oxygen theory of acids in fa-
vour of Davj^'s more general views,
based upon his recognition of chlo-
rine and iodine as elementary bodies.
His handbook of Chemistry, as well
as his ' Jahresbericht ' (from 1820),
probably did more than any other
publications for the diifusion of ac-
curate chemical information.

^ Liebig has himself, in an auto-
biographical memoir published post-
humously, so fully described the
merits of the two schools, and at
the same time given such a vivid
picture of the truly scientific s^Dirit
which animated German universi-
ties at that time, that I am tempt-
ed to give here some extracts. Of
his studies in Paris he says : " What
influenced me most in the French
lectures was their inner truthfulness
and the careful omission of all mere
semblance of explanations : it was
a complete contrast to the German
lectures, in which, through a pre-
ponderance of the deductive pro-
cess, the scientific doctrine had quite
lost its rigid coherence. ... I re-
turned to German}' (1824), where,
through the school of Berzelius,
... a great reform had already
begun in inorganic chemistry. . . .
I always remember with pleasure
the twenty - eight years which I
passed at Giessen : it was, as it were,
a higher ])rovidence which led me
to the small university. At a large
university, or in a larger town, my
powers would have been broken up
and frittered away, and the attain-
ment of the aim which I had in

view would have been much more
difficult, if not impossible ; but at
Giessen all were concentrated in
the work, and this was a passion-
ate enjoyment." " The necessity of
an institute where the pupil could
instruct himself in the chemical art,
by which I understand familiarity
with chemical operations of analysis
and adroitness in the use of appar-
atus, was then in the air, and so it
came about that on the opening of
my laboratory . . . pupils came
to me from all sides. . . . The
greatest difficulty presented itself,
as the numbers increased, in the
practical teaching itself. In order
to teach many at once, an ordered
plan was required and a progres-
sive way of working, which had
to be thought out and tried. . . .
A very short time had sufficed for
the celebrated pupils of the Swedish
master to give to mineral analysis
... an admirable degree of per-
fection. . . . Physical chemistry
. . . had through the discoveries
of Gay-Lussac and Humboldt, . . .
and of Mitscherlich, . . . gained a
solid foundation, and in the chemi-
cal proportions the edifice appeared
to have received its coping-stone.
. . . No organic chemistry . . . then
existed ; Thenard and Gay - Lus-
sac, Berzelius, Prout, Diibereiner,
had indeed laid the foundation of
organic analysis ; but even the
great investigations of Chevreul on
the fatty bodies received for many
years only scant attention. Inor-
ganic chemistry still absorbed too
many, and indeed the best, forces.

THE SCIENTIFIC SPIRIT IN GERMANY.

191

Twenty years after Gauss's great mathematical achieve-
ments, two new discoveries announced to the scientific
world that Germany had again taken a foremost position
in chemistry. These were Mitscherlich's discovery of
isomorphism in 1819/ and Wohler's preparation of an
organic compound from inorganic materials in 1828.^

In 1830 Liebig succeeded in finally establishing that 20.

Liebig's

smiple and accurate method of organic analysis known organic

<-> '' analysis.

by his name. Organic chemistry, in its modern sense,

The direction I had received in
Paris was a different one. ... I
saw very soon that all progress in
organic chemistry depended on its
simplification. . . . The first years
of my residence at Giessen were
almost exclusively devoted to the
improvement of organic analy.«is,
and with the first successes there
began at the small university an
activitj'^ such as the world had not
yet seen. ... A kindly fate had
brought together in Giessen the
most talented youths from all
countries of Europe. . . . Every
one was obhged to find his own
way for himself. . . . We worked
from dawn to the fall of night :
there were no recreations and
pleasures at Giessen. The only
complaints were those of the at-
tendant, who in the evenings, when
he had to cleau, could not get the
workers to leave tlie laboratory."
See 'Deutsche Rundschau,' vol.
Ixvi. pp. 30-39.

1 Eilhard Mitscherlich (1794-
1863), a pupil of Berzelius, dis-
covered in 1819 that in compound
bodies which crystallise in definite
forms certain elements can be re-
placed by others in the proportion
of their chemical equivalence with-
out changing the form of crystallisa-
tion. Such elements are termed
" isomorphous." Berzelius declared

this to be the most important dis-
covery that had been made since
the theory of chemical proportions
had been established.

•^ This synthesis was the prepara-
tion of urea, a Iiighlj^ organic sub-
stance, out of the compounds of
cyanogen, with the examination of
which he and Liebig were then oc-
cupied. " It was the first example
of the fact that an organic sub-
stance could, by chemical methods
alone, be produced out of inor-
ganic materials ; this discovery de-
stroyed the difference which was
then considered to exist between
organic and inorganic bodies — viz.,
that the former could only be
formed under the influence of vege-
table or animal vital forces, where-
as the latter could be artificially
produced" (Kopp, ' Geschichte der
Ghemie,' vol. i. p. 442). It must
here be remarked that this state-
ment is only correct if the sub-
stances, cyanic acid and ammonia,
out of which Wohler produced urea,
are considered to be inorganic ; in-
asmuch as neither of them had then
been produced otherwise than out
of organic substances, the popular
notion on Wohler's important dis-
covery requires this correction. See
Kopp, ' Gesch. der Wissenschaf ten
in I)eutschland, ' vol. x. p. 546.

192

SCIENTIFIC THOUGHT.

may be said to date from these and other simultaneous
labours of Liebig and Wohler.^ But although the pure
sciences, mathematics, physics, and chemistry, advanced
on new lines in the hands of German students, and
although theoretical investigations have always been
favourite pursuits of theirs, as we shall have ample
opportunity to note in the course of our further survey,
the greatest contribution to the progress of science, and
the most brilliant performances of the exact spirit of
research which emanated from Germany during the first
half of this century, lay in a different direction. And it
is hard to believe that the conditions favourable to this
peculiar growth could have been found anywhere else
than in the German universities. The many elements of
thought which meet on that ground, the equal dignity

^ The joint labours of Liebig
(1803-73) and Wohler (1800-82),
which have become of such im-
portance to science, form one of
the most interesting instances of
scientific co-operation between two
men pursuing different lines of
thought and trained in different
schools. See the preface to Hof-
mann's edition of Liebig and Woh-
ler's Correspondence. In Liebig's
autobiographical sketch, quoted
above, he thus enlarges on his re-
lations to Wohler : "It was my
good fortune that, from the be-
ginning of my career at Giessen,
similar inclinations and endeavours
secured me a friend, with whom,
after so many,'years, I am still (be-
tween 1860 and 1870) connected
by ties of the warmest affection.
Whereas in me the tendency pre-
dominated to look for the likenesses
of substances and their combina-
tions, he possessed an incomparable
talent for seeing their differences ;

acuteness of observation was joined
in him to an artistic aptitude and
to a genius for finding new ways
and means of analysis such as few
men possess. The perfection of
our joint researches into uric acid
and the oil of bitter almonds has
been frequently praised ; this is his
work. I cannot sufficiently estimate
the advantage which both my own
and our joint aims derived from my
union with Wohler ; for in them
were combined the peculiarities of
two schools, and the good which
each had, attained its value through
co-operation. Without grudge or
jealousy we pursued our way hand
in hand ; if one required help, the
other was ready. An idea can be
formed of this mutual relation
when I mention that many of the
smaller productions which bear our
names belong to one alone ; they
were charming little presents which
one gave the other " (p. 39).

THE SCIENTIFIC SPIRIT IN GERMANY.

193

which there belongs to pure and to applied science,
the continual contest which exists there between meta-
physical and exact reasoning, and the general ebb and
flow of rival currents of ideas, all seem to have been
necessary to raise to the rank of an exact science those
researches which deal with the phenomena of life and
consciousness in their normal and abnormal forms of ex-
istence. In the hands of German students ^ chemistry 21.

Biology a

and physics, botany and zoology, comparative anatomy German
and morphology, pathology, psychology, and metaphysics,
have laboured from different and unconnected beginnings
to produce that central science which attacks the great
problem of organic life, of individuation, and which studies
the immediate conditions of consciousness. Physiology,
or to use its more comprehensive name, Biology^ may be

science.

^ The two greatest discoveries
in physiology belong to England.
These are Harvey's discovery of the
circulation of the blood in the seven-
teenth century, and Charles Bell's
discovery of the difference of sensory
and motor nerves in the early part
of this century. The two men, how-
ever, who have done most to estab-
lish physiology as an independent
science, whose systematic works
have done most for the student
of physiology, are probably Haller
(see supra, p. 176), whose ' Ele-
menta ' cast into the shade all
older handbooks, and Johannes
Miiller (1801 - 58), whose ' Hand-
buch' (1833-40) was translated
into French and English. See Du
Bois-Reymond, 'Reden,' &c., vol.
ii. pp. 143, &c., 195, 360, who also
points out how in other sciences,
like mathematics, physics, chem-
istry, Germans made use almost
exclusively of translations of French
and English text-books and hand-
books, whereas in physiology they

VOL. I.

furnished for a long period the
systematic treatises for the whole
world (vol. ii. p. 196). Physiology
has therefore with some right been
termed a German science (see
Helmholtz, 'Vortrage, ' &c., vol. i.
pp. 339, 362 ; Du Bois-Reymond,
'Reden,' vol. ii, p. 265). Com-
pare also what Huxley says,
' Critiques and Addresses,' pp. 221,
303. On the connection of physi-
ology with all other sciences see
likewise Helmholtz, loc. cit. ; Du
Bois - Reymond, vol. ii. p. 341 ;
Huxley, ' Lay Sermons,' &c., p.
75 ; ' Science and Culture,' p. 52 :
" A thorough study of human physi-
ology is, in itself, an education
broader and more comprehensive
than much that passes under that
name. There is no side of the in-
tellect which it does not call into
play, no region of human know-
ledge into which either its roots or
its branches do not extend," &c.

^ The word "biology" seems to
have been first used by G. R.

N

194

SCIENTIFIC THOUGHT.

22.
Cellular
theory of
Schleiden

said to be a German science as chemistry has been
named a French science. I have already referred to the
great Haller in the last century, who may be called the
father of physiology ; to Blumenbach, the comparative
anatomist ; and to Liebig and Wohler, who first among
chemists succeeded in producing an organic compound by
the processes of inorganic chemistry. I have now to add
two names, which together mark a great revolution in our
ideas of the structure of organisms, and link together
the two sciences which had treated separately of the
animal and vegetable worlds. About the year 1838
Mathias Schleiden ^ propounded his cellular theory con-

Treviranus (1776-1837), a learned
physician of Bremen, who began to
write his ' Biologie oder Philosophic
der lebenden Natur' in 1796 and
to publish it in 1802 (6 vols., 1802-
22). Lamarck used the word in
his 'Hydrog(^ologie,' 1801. They,
as well as Bichat about the same
time, independently " conceived the
notion of uniting the sciences which
deal with living matter into one
whole, and of dealing with them
as one discipline" (Huxley, on the
study of Biology, 1876, in 'Ameri-
can Addresses,' p. 136, &c.) The
term, though of German origin, has
not found favour in that country,
and after having been used officially
in France and England, makes its
appearance in German only since
the great works of the modern
English School, headed by Darwin,
have gained so much influence in
Germany. In the meantime the
biological sciences had been exten-
sively represented at the German
universities by chairs of physiology,
zoology, botany, &c. According to
Huxley, biology has been "substi-
tuted for the old confusing name
of natural history," and "denotes
the whole of the sciences which

deal with living thing.s, whether
they be animals or whether they
be plants" {loc. cit., p. 138). It
can be divided into three branches
— (1) Morphology, which comprises
the sciences of anatomy, develop-
ment, and classification ; (2) the
science of the distribution of living
beings, present and past ; and (3)
phJ^siology, which deals with the
functions and actions of living
beings, and tries to " deduce the
facts of morphology and of distribu-
tion from the laws of the molecular
forces of matter" (Huxley, 'Lay
Sermons,' &c., p. 83, 1864). To
these three Huxlej' adds ('Ency.
Brit.,' art. "Biology") the infant
science of "etiology," which "has
for its object the ascertainment of
tlie causes of the facts of biology
and the explanation of biological
phenomena, by sliowing that they
constitute particular cases of general
physical laws" (p. 688).

1 Mathias Jacob Schleiden (1804-
81), for some time Professor of
Botany at Jena, was a man of
peculiar ability and disposition,
combining a philosophical mind
with exact knowledge and a gen-
eral literary taste, not frequently

THE SCIENTIFIC SPIRIT IN GERMANY.

195

cerning the structure and growth of plants. About the and

° ^ ^ Schwann.

same time Theodor Schwann extended this theory to
animal organisms. A variety of circumstances combined
to make the announcement of the cellular theory, which
will always be associated with those two names, an epoch
in the history of scientific, indeed of general, thought.

The historian of botany, Julius Sachs, describes the
publication of Schleiden's great work as a burst of day-
hght," and Du Bois-Eeymond says : " In order to measure
the magical progress which it marks, one must have wit-
nessed the rise of the cellular theory, when it suddenly
spread daylight in the darkness of the hidden structure

to be fouud among men of pure
science in Germany. Opposed to
the idealistic philosophy as a fol-
lower of Fries, and on the other side
to the dry systematisation of the
Linnaan school, he was the man at
•once to broaden the scientific view
and to create a popular interest in
the " life of the plant "-world. The
titles of his t>vo best known works
are characteristic, ' Die Botanik als
inductive Wissenschaf t ' (1842-45),
and his short-lived periodical (filled
with the labours of his equally im-
portant co-editor, Niigeli), ' Zeit-
schrift fiir wissenschaftliche Bo-
tanik.'

^ Through the friendship of
Schleiden and Schwann (1810-82,
a pupil of Johannes Miiller and
professor at Louvain), two inde-
pendent courses of research and
scientific thought were brought to-
gether. Schleiden placed the " cell "
— a term used before him by Hooke,
Malpighi, Grew, Wolff, Brown, and
Mirbel — in the forefront of his de-
scription as the element of form
and as the origin of life, or — as we
now express it — as the morphologi-
cal and embryological unit, in the
plant. A similar series of great

names, beginning with Bichat and
leading up to Johannes Miiller,
marks the studies of animal tissues.
Schwann, struck with the analogy
of Schleiden's nucleated cells and
similar structures which he had
observed in the notochord, con-
ceived and verified on a large scale
the idea " that a common principle
of development exists for the most
different elemental parts of the
organism, and that the formation
of cells is this principle."' This is
the beginning of the cellular theory,
wliicli produced at once a recon-
struction of the whole of " general
anatomy" by Jacob Henle (1809-
85), and subsequently the "cellu-
lar pathology " of Rudolph Virchow.
As tlie latter has himself said, he
aims at the establishment of a gen-
eral biological principle, and thus
the discovery of Schleiden and
Schwann is characterised as the
transition from the "historical" to
the "Inological" study of animated
nature.

^ See Julius Sachs, ' Geschichte
der Botanik vom 16 Jahrh. bis
I860,' p. 203, and in many other
passages.

196

SCIENTIFIC THOUGHT.

of animals and plants, where the rays of comparative ana-
tomy and embryology could not reach." ^ This bold gener-
alisation, which had been prepared by a long series of
botanical and morphological researches in and out of Ger-
many, met alternately with applause and criticism ; it gave
rise to a long controversy, and was the starting-point of a
whole line of important discoveries.^ It secured for Ger-
many a long period of supremacy in physiological science.
This supremacy was more than maintained by a great
23. volume of minute investigations, which emanated from

Ernst Heiu. ^

rich Weber the schools, and Centred in the names, of E. H. Weber ^

^ Du Bois-Reymoud, ' Ileden,' vol.
ii. p. 541, &c.

^ " Whatever cavillers may say,
it is certain that liistology before
1838, and histology since then, are
two diiferent sciences — in scope, in
purpose, and in dignity — and the
eminent men to whom we allude
may safely answer all detraction by
a proud Circwnspice." — Huxley in
his valuable paper on "The Cell
Theory" in the ' British and Foreign
Medical Chirurgical Review,' 1853,
vol. xii. p. 290.

•* The three brothers Weber (Ernst
Heinrich, 1795 - 1878 ; Wilhelm,
1804-91; andEduard, 1806-71) may
be looked upon as early representa-
tives of the best form of German
research on the lines now recognised
as the true and fruitful ones in na-
tural science. Born in an age when
other great and more widely known
reformers — such as Liebig, Schon-
lein, and Joh. Miiller — freed them-
selves with difficulty from the pre-
vailing metaphysical systems, they
seem to have at once seized the
true spirit of exact research with-
out relinquishing the broader philo-
sophical and encyclopedic view of
the sciences which they cultivated.
Living far into an age when the
utilitarian spirit became equally

seductive in an opposite direction,
they preserved pure and undefiled
within themselves the German ideal
of Wissenschaft as a pursuit carried
on for its own intrinsic value, not
for any immediate practical object.
Their position, especially that of
the two elder brothers, is in this
respect unique, and may be studied
independently of the scientific ideas
which they represented, and which
will occupy us later on as a chapter
in the history of thought character-
istic of the German mind and the
best type of the university studies.
In three works of classical value —
' Die Welleulehre auf Experimen-
ten begriindet' (E. H. and W.
Weber), 1825 ; 'Die Mechanik der
menschlichen Gehwerkzeuge ' (W.
and E. Weber), 1836; 'Elektro-
dynamische Maasbestimmungen '
(W. Weber), 1846 onward— and in
a great number of special investi-
gations, the method of exact mea-
surement was applied to physical,
physiological, and even mental
phenomena, and the foundation
laid for a mechanical description
and mathematical calculation. The
later generalisations, known as Wil-
helm Weber's law of electro-dyna-
mics and E. H. Weber's law of
psycho-physics, have given rise to

THE SCIENTIFIC SPIRIT IN GERMANY.

197

and Johannes Miiller. The school of the latter especially and Johan-

i . , . „ , . . , , nes Miiller.

has the merit ot having introduced over the whole field
of physiological phenomena exact methods of inquiry,
of having established physiological laboratories all over
Germany similar to Liebig's chemical laboratory at
Giessen, and of having effectually chased away the vague
notions of the older metaphysical school, and diffused the
true scientific spirit. It boasts of having filled the chairs
of medicine, physiology, and anatomy at the German
universities with a long list of eminent teachers who have
spread this true scientific spirit in every branch of the
medical sciences,^ which it has in consequence drawn into

long controversies and fruitful
theories. Their joint labours
cover fully half a century. See
for a sympathetic picture of the
position which the three brothers
Weber held in the learned world
the biography of Fechner by Kuntze,
1892, p. 243: "They were among
the first to raise the study of Nature
among Germans to the eminence
occupied by the philosophers and
discoveries of the Latin races."

^ The medical sciences, represent-
ed by the medical faculty, but also
by those biological sciences which,
like botany, zoologj', anthropology,
&c., belong to the philosophical
faculty, now furnish the largest
number of students to the German
universities. In the beginning of
the century the theological faculty,
which then included the greater
part of those wlio prepared them-
selves for higher teaching, stood
at the head as regards numbers.
Under the influence of the philo-
logico-historical movement, which
grew and culminated in the course
of this century, and the rising tide
of the exact sciences, the philoso-
phical faculty for a time gained

and maintained the upper hand.
Biological — including medical —
studies now command the greatest
attention. In his statistical report
(contained in Lexis, ' Die deutschen
Universitiiten,' Berlin, 1893) Prof.
Conrad gives an interesting table
of the changing numerical pro-
portion in the different faculties
(vol. i. p. 125, &c.) Prof. Billroth
in his admirable treatise, ' Ueber
das Lehren und Lernen der medi-
cinischen Wlssenschaften,' Vienna,
1876, deals with this subject at all
the German universities, including
the Austrian. As Vienna is such
an important centre of medical
studies, the proportion of those
students who cultivate biological
studies would probablj' be still
greater if we were to include the
Austrian universities. I suppose
the figure would be about 40 per
cent of the whole. To Billroth's
treatise I may also refer as con-
firming in relation to these more
modern branches what I said above
of the culture of Wisscnschaft. See
p. 279 and the whole section on the
relation of the biological sciences to
the university, pp. 411-446. It is

198

SCIENTIFIC THOUGHT.

24.
Psycho-
physics.

the circle of the exact or mechanical sciences. But not
only in its far-reaching applications to medical know-
ledge and practice has the movement which centred in
Weber and Miiller shown its strength and importance ; it
has also, from the commencement, extended its influence
in another direction. To it belongs pre-eminently the
cultivation of that borderland which connects the natural
and the mental sciences, Miiller ^ himself began his
career by a study of the mechanism of the perceptions
of the senses. He affirmed the law of specific energies,

interesting to note that Prof. Bill-
roth does not employ the word
biological, but uses the untranslat-
able compound naturwissenschaft-
lich-medicm isch .

1 Johannes Miiller (1801-58) has
been termed the Haller of the
nineteenth century, the Cuvier of
Germany. A very good account
of his work, which forms an im-
portant chapter in the history of
German biology, is contained in Du
Bois-Reymond's ' Gediichtnissrede
auf Joh. Miiller (1858), reprinted
with extensive notes in his ' Reden,'
vol. ii. pp. 143-334. Miiller is there
considered as the last representa-
tive of a dynasty of philosophers
who embraced the whole domain of
"biology," which since has become
divided into various sciences, not-
ably the morphological and the
physiological branches. He thus
stands out as the master of some
of the greatest modern represen-
tatives of natural and medical sci-
ence, such as Schwann and Henle
in anatomy, Briicke, Du Bois-Rey-
mond, and Helmholtz in physiology,
Virchow in pathological anatomy.
He together with Lucas Schonlein
(1793-1864) may be considered as
the founder of the modern Berlin
school of medicine, contemporane-
ous with which is the modern

Austrian school, with the names of
Purkinje, Skoda, Oppolzer, and
Rokitansky. An excellent charac-
terisation of the different positions
and influences, of the cross-currents
of thought, of the original homes
and of the wanderings of the scien-
tific spirit through the many Ger-
man - speaking countries and the
extensive network of German uni-
versities, will be found in Billroth,
loc, cit., pp. 307-366. If we imagine
a similar life as existing all through
the century in other domains of
thought — in philosophy, theolog}',
philology, mathematics, chemistry,
law, and the science of history — we
get a faint idea of the work of the
German universities. In Lexis,
' Die deulschen Universitiiten,' an
attempt has been made to give
such a picture. The picture, how-
ever, suffers by the exclusion of the
Austrian universities, and these —
notably in the medical world — hold
such a very high position that the
record of the united work is some-
what incomplete. The sciences are
also in this record cut up into
many branches, whereas in the
earlier part of the century many of
these were united and represented
by one great name. Such a name
was Johannes Miiller in biology.

THE SCIENTIFIC SPIRIT IN GERMANY.

199

which declares that the differences of the sensations of
light and colour, of sound, of touch, &c., do not depend
upon the mode of irritation, nor even upon the different
structure of the specific nerves, but upon the nature of
the central sense organ. In the school of Mliller the
phenomena of voltaic electricity, which had been so seduc-
tive and misleading to an earlier school of physiologists
not experienced in the methods of exact research, were
again subjected to scientific investigation, and led to
the brilliant researches with which the name of Du Bois-
Eeymond is so intimately connected. He is as ready as
Helmholtz, who in his two great works on physiological
optics and musical acoustics has founded new branches
of science,^ to acknowledge the leadership of Johannes

1 Helmholtz (1821-95), equally
celebrated as physiologist and ma-
thematical philosopher, was edu-
cated under the influence of Jo-
hannes Mliller on the one side, of
Jacobi and the Konigsberg school
of mathematicians (Bessel and Neu-
mann) on the other. If we add to
this that he also made a profound
study of those far-reaching specula-
tions which originated in the phil-
osophy of Kant, we realise how rare
is the combination of ability and
knowledge which he has brought to
bear on the discussion of the most
advanced problems iu physics,
biology, and psychology. In the
sequel I shall have to refer so
frequently to his writings that I
confine myself here to giving the
date of his principal, his epoch-mak-
ing publications : 1847. ' Ueber die
Erhaltungder Kraft'; 1858. 'Ueber
die Integrale der hydrodynamischen
Gleichungen, welche der Wirbel-
bewegung entsprechen ' — both re-
printed in ' Wissenschaftliche Ab-
handlungen,' Leipzig, 1882 and

1883, 2 vols. These two Memoirs
may be considered as corner-stones
of two of the most important mo-
dern theories in physical science,
the "conservation of energy" and
the " theory of vortex motion." In
both, the name of Helmholtz is in-
timately allied with that of William
Thomson (Lord Kelvin). Equally
important and more comprehensive
have been his researches in the
physiology and psychology of sense-
perceptions in his ' Physiologische
Optik,' Leipzig, 1867 ; ' Lehre von
den Tonempfinduugen,' Braunsch-
weig, 1863.

Helmholtz has also contributed
largely to the discussion of two very
important branches of modern spe-
culation^first, the theoretical views
on the nature of electrical pheno-
mena expressed by the opposite
conceptions of Wilhelm Weber in
Germany and Faraday in England ;
second, the origin of geometrical
axioms, especially the axiom refer-
ring to parallel lines. A great
interest in this subject had been

200

SCIENTIFIC THOUGHT.

Mliller. And out of the circle of which E. H. Weber
was the centre, has emanated that work of Fechner,
'Elements of Psycho -physics,' which marks an epoch
in psychology : it is indeed mainly occupied with the ex-
position and application of what is termed Weber's law
of sensation.-^ In the course of the second quarter of the
century, the names of Gauss and Jacobi in mathematics,
of Liebig and Wohler in chemistry, of Schleiden and
Schwann in the science of life, of Mliller and Weber in
physiology, raised German science to the level previ-
ously reached by the French Academicians, by Laplace
and Lagrange, by Lavoisier and Berthollet, by Cuvier
and St - Hilaire, by Vicq - d'Azyr and Bichat. During

created by the posthumous jmbli-
cation of Riemann's celebrated Me-
moir, ' Ueber die Hypotheseii welche
der Geometric zu Grunde lichen,'
Gottingen, 1865. Hehnholtz's in-
vention of the ophthalmoscope in
1851 marks an epoch in ophthal-
mology.

^ GustavTheodor Fechner (1806-
87), professor at the University of
Leipsic, was an extraordinary man.
The wide range of his interests and
his great personal influence are well
described in his biography by Dr
Kuntze, ' G. T. Fechner, Ein
deutsches Gelehrtenleben,' Leipzig,
1892. Together with Lotze he may
be said to have brought about the
reform of German speculative phil-
osojihy, and in relation to this he
will occupy our attention largely
in a later portion of this book. He
belonged to the circle of which E.
H. Weber was the centre, and has
taken an important place in the
history of philosophy and science
by his now celebrated work, ' Ele-
mente der Psychophysik,' 2 vols.,
Leipzig, 1860 ; 2nd ed., 1890. The

object of this work is to establish
" an exact doctrine of the relations
of body and mind," the principal
task being " to fix the measure of
psychical quantities." He says in
the preface : " The empirical law
which forms the principal founda-
tion, was laid down long ago
by difiTerent students in different
branches, and was expressed with
comparative generality mainly by
E. H. Weber, whom I would
call the father of psycho-physics "
(Preface, p. v). In early life
Fechner did much, by his transla-
tions of Biot's ' Physics ' and Thd-
nard's ' Chemistry,' as well as by his
own experimental works, to intro-
duce the French scientific spirit into
German research. His psycho-phy-
sical labours have been continued
by Prof. Wundt ; his importance
as marking a turning - point in
German philosophy is brought out
in Paulsen's ' Einleitung in die
Philosophic,' Berlin, 1890. See
especially Preface, p. viii, and p.
318, where Fechner is placed before
Lotze.

THE SCIENTIFIC SPIRIT IN GERMANY. 201

the second half of the century, the influence of French
thought on German science has been less marked, partly
owing to the independent course which the latter, since
the age of Johannes Mliller, has struck out for herself
in the biological sciences, partly through the more inti-
mate intercourse which has set in between English and
German thought. The three great scientific ideas which
the second half of the century has been establishing — the
law of the conservation of energy, Darwin's theory of
descent, and Faraday's novel conception of electrical
phenomena — have been elaborated mainly by the co-
operation of English and German research, though it
must be admitted that at least one of these developments
dates back to the beginnings laid by French science,^
whilst the views of Faraday are subversive of some of
the fundamental notions to which the works of the great
French mathematicians had given very general currency.
Before we can enter more fully on a review of these more
modern ideas, I must, however, give a picture of the state
of scientific thought in England during the first half of
the century. This will be our subject in the last portion
of the present section.

1 Darwin's theory of descent has
its forerunners in Lamarck and St-
Hilaire, whose merits in this re-
spect are supposed to have been
overlooked owing to the overwhelm-
ing authority of Cuvier. See Hux-
ley, " Origin of Species " in ' Lay
Sermons,' 1891, p. 252; "Evolu-
tion in Biology " in ' Science and
Culture,' 1888," pp. 296, 313. But
■whilst it is true that Lamarck and
St-Hilaire entertained doubts as to

place is entirely due to Darwin,
and without this further step
speculations as to the origin of
species would have remained for a
long time in the vague. Lamarck's
speculations were of no real use to
Darwin, and had besides been anti-
cipated by Erasmus Darwin. On
the other hand, the researches of
Sadi Carnot were of great value in
the hands of Joule, Thomson, and
Hehnlioltz, who may be regarded

the fixity of species, the explana- ! as the founders of the doctrine of
tion of the particular manner in i the conservation of energy
v?hich the change of species takes I

202 SCIENTIFIC THOUGHT.

s irit of ^^^^ ^^ ^^ "^-^ object at present not so much to dwell

and'^jFt^scM-' ^^po^i spccific ideas or doctrines as on the growth, the
schaft. diffusion, and the general character of scientific thought,
as this has been established by the separate contributions
of the three nations in the course of the first half of our
century. I therefore cannot leave the subject of German
science without still more precisely noting the peculiar
character which scientific thought has assumed under
the influence of the German university system. As
we saw before, when the spirit of exact research, mainly
through the influence of the great French mathema-
ticians and physicists, became diffused in Germany,
and entered the pale of the German universities, it was
met there by that peculiar ideal of learning which the
German language terms Wissenschaft. This encounter
did not everywhere produce a favourable reception for
the new school ; but in the end it led, like every con-
troversy, to a firmer establishment of the true princi-
ples of research. The life of the German universities
had in the earlier centuries begun with classical studies ;
it had been reformed under the influence of the theo-
logical and juridical requirements of the Protestant
Governments ; and ultimately it had been entirely re-
newed under the influence of the classical and philo-
sophical studies centred in the fourth or philosophical
faculty. These classical and philosophical studies com-
bined to create the ideal of Wissenschaft, or science, in
the broadest sense of the word. This ideal formed the
central conception in the new scheme of a higher and
general education of the nation ; it accompanied the
great revival in art, poetry, and literature. In the

THE SCIENTIFIC SPIRIT IN GERMANY. 203

philosophy of Kant and Fichte, the republican notions
which led the political movements in America and
France had been reduced to a system and theoretically
proved ; the discipline of a classical education was the
school in which leaders and youths were trained who
marched into the war against the great oppressor. This
ideal of Wissenschaft had thus acquired a practical mean-
ing, an ethical — not to say a religious — significance ; it
was allied to the religious revival preached by Schleier-
macher and a section of the Eomantic school. Of its
value as a principle for guiding research and learn-
ing it had given proof in that great circle of studies
which, since the time of F. A. Wolf and Wilhelm von
Humboldt, was comprised under the name of Pliilology.
Under its influence new universities were beins; founded
and academies remodelled.

Now, it is the peculiarity of all philosophical and
historical studies that they deal with one great subject,
which cannot easily be divided into a number of inde-
pendent parts capable of separate treatment ; since their
interest attaches mainly to the fact that they explore
the workings and manifestations of the human mind in
the past and in the present. These studies are there-
fore forced to keep always in the foreground the idea
of a great unity of action and purpose, to aim at com-
pleteness of view, and to refer all special researches to
general principles and standards. The encyclopaedic view, 26.
in fact, is forced upon all philosophical and historical p»dicview

^ necessary in

sciences. Almost without exception the great masters p^"ios.ophy \

^ o and history. ^

and teachers who lived in the beginning of this century
adhered to this view, and however great in special and

1

204 SCIENTIFIC THOUGHT.

detailed research, measured the importance of their
results according to the light which they were able to
throw upon the questions referring to the whole subject
and its combined life and unity.

It was also natural, seeing that this comprehensive
or philosophical treatment led to such great results in
the historical sciences, that an attempt should have been
made to deal with the phenomena of Nature by a similar
conception. It was not a new or a far-fetched sugges-
tion to regard Nature as the playground of a hidden
intelligence, of an unconscious mind, just as history, lan-
guage, and thought were viewed as the manifestations
of the conscious human mind. After this the further
conception was not remote that both the mind of Nature
and the mind of Man are only two different sides of the
universal or absolute Mind. The philosophy of Schelling
was the first attempt to put this idea into an applicable
form, the system of Hegel the first confident elaboration
of it in its various ramifications and applications. At
the time when the mathematical and physical sciences
were leading the way in France, and gradually forcing
their way into Germany, most of the universities in the
latter country had one or more representatives of that
new and apparently promising school which termed itself
27. the " Philosophy of Nature." The trammels of this school

Phuosopliy

of Nature, had to be shakcu off by those who, as they became
gradually convinced of its barrenness in actual results,
took up the cause of the exact or mathematical sciences
now that they had been cultivated by many isolated
labourers in Germany and in England, and had been

THE SCIENTIFIC SPIRIT IN GERMANY.

205

for the first time connected into a great organisation by
the French Academy of Sciences.

The opposition in which the new school of exact and 28.

Conflict be-

detailed research stood to the representatives of the broad t^^een the

•^ scientific

philosophical view gave rise to a great many currents pHuo^oVi-
of thought; for neither the former nor the latter pre- °''^^'®^^-
sented a united front. Among those who advocated the
exact methods of research there was a section which
clung more exclusively to the empirical side, and culti-
vated the descriptive and experimental sciences ; whereas
others, whom we may call the French school of science,
developed the mathematical methods, not without a cer-
tain ill -disguised contempt for pure empiricism.-^ On
the side of classical and philosophical studies there was
a section which cultivated the historical^ in contradis-

1 On the relations of mathemati-
cal and experimental physics, and
the different opinions which existed
during the first half of the century,
see Helmholtz's popular addresses
in many places, but especially the
discourse on Gustav Magnus (1802-
70), who may be regarded as a re-
presentative of the experimental
school in Germany. In the opin-
ion of this school, which cultivated
the borderland of physics and chem-
istry, of organic and inorganic phe-
nomena, or investigated the less
known phenomena of frictional elec-
tricity (Riess) or the complicated
phenomena of meteorology (Dove),
a danger existed that mathematical
theories and elaborate calculations
might lead to an estrangement from
nature and observation, similar to
that which speculative philosophj'
had created before. Helinholtz him-
self was met by this sentiment when
he published his great memoir,

'Ueber die Erhaltung der Kraft,'
in 1847 ; Poggendorf's physical
periodical would not receive it,
and Jacobi, the mathematician,
was the only one who showed any
interest in it. See Helmholtz,
' Wissenschaftliche Abhandlungen,'
vol. i. p. 73; 'Reden,' vol. ii. p.
46.

- As the philosophy of Schelling
promoted a study of nature, and in
doing so prepared its own downfall,
so the philosophy of Hegel led to a
study of history, and thus to the
proof of the insufficiencj' of its own
generalisations. Many valuable be-
ginnings of historical researcli eman-
ated also from the Romantic school
of literature. In all these instances
philosophical interests led beyond
theabstract logical and metaphysical
treatment into the broad and fertile
plains of actual life, be it that of
nature or of art or of history. But
the true methods of research in

206

SCIENTIFIC THOUGHT.

29.
Alexander
von Hum-
boldt.

tinction to the philosophical view, and another which
elaborated what it termed exclusively the critical meth-
ods/ not without a certain suspicion regarding those who
showed a desire to roam into outlying fields which did
not permit of equally strict discipline and treatment. So
far as this refers to the purely historical sciences, I
shall revert to the subject when I come to treat of the
principles which underlie and guide this line of studies.
At present I am concerned with the growth and dif-
fusion of the exact scientific spirit and its methods.

No one did more to spread the ideas and methods of
French science in Germany than Alexander von Hum-
boldt. He himself had done original scientific work " be-

tliese extensive fields were after-
wards found not so much in philo-
sophical canons as in a love of detail
and observation, and in the exercise
of an unbiassed criticism of facts
and records. For the relations of
philosophy to history in respect of
this, see Wegele, ' Geschichte der
deutschen Historiographie,' Mlin-
chen, 1885, 5th book, p. 975, &c.
Equally impoitant are — Gervinus,
' Gruudziige der Historik,' Leipzig,
1837 ; the ' Nekrolog auf Schlosser,'
Leipzig, 1862, including the whole
literature which it provoked ; and
0. Lorenz, ' Die Geschichtswissen-
schaft,' Berlin, 1886, especially the
first chapter.

^ On the Critical school of phil-
ology, and the wider and narrower
sense in which the aims and meth-
ods of the science of antiquity were
defined, see Bursian, ' Geschichte der
classischen Philologie in Deutsch-
land,' Miinchen und Leipzig, 1883,
p. 665, &c. ; also 0. Ribbeck, ' Fried-
rich Ritschl,' Leipzig, 1879 and
1880. Further, the essays on Bockh,
K. 0. Miiller, and Georg Curtius in
the third volume of Ernst Curtius,

' Alterthum und Gegenwart,' Berlin,
1889 ; and, finally, the chapter on
"Klassische Philologie" by Wila-
mowitz-Mollendorf in Lexis, 'Die
deutschen Universitiiten,' vol. i. p.
457, &c.

- Alexander von Humboldt (1769-
1859)publi3hed in 1797, shortly after
Galvani's great discovery, his ' Ver-
suche liber diegereizte Muskel- und
Nervenfaser.' In the history of sci-
ence his name will live as that of
the man who organised that ' ' scien-
tific conspiracy of nations ' ' which is
peculiar to our centurj-, and with-
out which the study of geography,
meteorology, astronom}', the phe-
nomena of tides and magnetic dis-
turbances— called by him magnetic
storms — could not effectually be
carried on. The fact also that on
his return from his great travels he
became next to Napoleon Bona-
parte the most famous man in
Europe, did more than anj'thing
else to raise the natural sciences in
the popular mind to that eminence
which earlier belonged to polite
literature.

THE SCIENTIFIC SPIRIT IN GERMANY. 207

fore he left Germany for the extensive travels by which
he became celebrated, and through which he founded a
new science — the science that deals with the geographical
distribution of plant-life. Moreover, his absence from his
native country fell within that period during which the
philosophical school, headed by Schelling and Hegel, at-
tained to its greatest power. He was never drawn into its
vortex ; on the contrary, he maintained a lifelong protest
against the spirit of its doctrine at a time when the circle
which surrounded him at Berlin came under its powerful
influence.-^ He led a long line of ardent young workers
both to the right sources of scientific knowledge and
to an ultimate victory over the opposed school of
thought. Though not a profound mathematician him-
self, he appreciated the part which mathematics were
destined to play in science. Among other things, he
protected and encouraged younger mathematical talents,
and tried to draw Gauss from the solitary heights which
he inhabited into the midst of the scientific circles of
the day.^ Then there was the great influence which

^ Cf. p. 178, note 1. It has latterly
become the fashion to say so much
against the mistaken methods of the
Naturphilosophie that it is well to
remember how many men of fore-
most rank in the natural sciences
belonged at one time to this school
or were influenced by it. Foremost
of all stands Oken (1779-1851), the
founder of the German Association

the earliest evolutionists ; D. G.
Kieser (1779 - 1862), a medical
teacher of great influence. More
or less influenced by the teachings
of this school were Goethe (1749-
1832); Karl Ernst von Baer (1792-
1876), whose impartial opinion on
the Naturphiloaopliie as early as
1821 is important. Further, Lie-
big (1803 - 73) ; Johannes Miiller

of Science, and editor of the peri- i (1801-58); Roschlaub (176S-1835)

odical ' Isis.' Further, the compara
tive anatomist Carus (1789-1869) ;
Oersted (1777-1851), the discoverer
of electro-magnetism ; Kielmeyer,
the friend of Cuvier (1765-1844) ;
Ignaz Dollinger (1770-1841), one of

Schonlein (1793-1864), the founder
of what is called the " natural-
history" school of medicine.

- See A. von Humboldt's Life by
Bruhns, translated by Lassell, 1873,
vol. ii. p. 145 sqq.

208

SCIENTIFIC THOUGHT.

30.
Influence of
Berzelius
on German
science.

Berzelius exerted on German science through his teach-
ing and his writings. From him emanated that great
perfection of the purely experimental methods which
in his own hands, as well as in those of Wohler, Mit-
scherlich, Magnus, and others, led to an accumulation
of detailed knowledge in chemistry of unforeseen im-
portance and magnitude. His own annual reports, as
well as Gmelin's celebrated handbook of chemistry, are
monuments of this unparalleled industry.

Others, like Liebig, Johannes Miiller, Lucas Schcinlein,
freed themselves under the influence of French science,^
or by their own deeper insight, from the sway of the
false and misleading philosophy to which they had at
one time listened. A third section started from philo-
sophical premisses, but from premisses opposed to the
doctrines of Schelling and Hegel.
I The school of Fries,^ in which Schleiden was the most

^ English science had an import-
ant but less marked influence on
the development of naturalistic and
medical studies in Germany. So
far as the latter especially are con-
cerned, see Billroth, ' Ueber das
Lehren und Lernen der medici-
nischen Wissenschaften an den
Universitjiten der deutschen Na-
tion,' Wien, 1876, p. 33. He
roughly divides the medical schools
of Germany into two groups, both
descending from Boerhaave : the
one, the modern Berlin school of
Miiller, Schcinlein, Romberg, and
Virchow, through Haller, Reil,
Hufeland, and Roschlaub ; the
other, the modern Vienna school
of Oppolzer, Rokitansky, and Bill-
roth, through Gerhard von Swiet-
en, De Haen, StoU, Frank, Pur-
kinje, and Skoda. Of French
names which had great influence

he gives Broussais, Corvisart, Bayle,
Cruveilhier, and Lacnnec ; of Eng-
lish, John Hunter, Matthew Bailie,
and Astley Cooper. He gives also
the name of Immanuel Kant as
an important influence in the de-
velopment of the German schools of
medicine.

2 Jacob Fries (1773-1843) pro-
fessor at Heidelberg and Jena, led
the critical philosophy of Kant into
the channels of psychology and an-
thropology. During the heyday of
transcendental philosophy, the phil-
osophy of Fries, like that of the
Scotch school, was regarded with
contempt by Hegel, and even by
Herbart, the opponent of Hegel. It
succeeded, however, in the end in
influencing a considerable number
of philosophical minds, who carried
philosophical thought into the in-
ductive sciences. Besides the psy-

THE SCIENTIFIC SPIRIT IN GERMANY.

209

illustrious name, carried on within the pale of the
philosophical school of science itself a successful opposi- i
tion to the philosophy of Nature.^ But whilst much good i
and sound work was done by many who were content
to remain outside of the favoured studies which set the
tone of university culture during the classical and philo-
sophical period of German thought, the great attack
upon the mistaken canons of the philosophy of Nature 31.
came from that science which had probably suffered of Nature^

and medical

more than any other under the baneful influence of science.
hollow theories and empty phraseology.

Helmholtz describes the despair which had taken hold
of thinking minds in the medical profession ^ : " My edu-
cation fell within a period of the development of medi-
cine when among thinking and conscientious minds there
reigned perfect despair. It was not difficult to under-
stand that the older and mostly theorising methods of
treating medical subjects had become absolutely useless.
But with the theories the facts which underlay them
were so indissolubly entangled that these too were mostly
cast overboard. How the science must be newly built up
the example of the other natural sciences had made clear,
but yet the new task stood of giant-height before us. A
beginning was hardly made, and the first beginnings were

chologist Beneke and the theologian
De Wette, these were principally
members of the Jena school, Apelt,
Schloiuilch, and others, who edited
' Abhandlungen der Fries' schen
Schule,' Jena, 1847 ; and foremost
among them Schleiden, the reformer
of botany in Germany. Schleiden's
great work appeared with the title
' Botanik als inducti ve Wissenschaf t. '
It opened with a philosophical in-

VOL. I.

troduction of 131 pages, in which
inductive reasoning is recommended
in opposition at once to the trans-
cendental Naturphilosophie, and to
dry empiricism. See Sachs, ' Ges-
chichte der Botanik,' p. 203, &c.

^ See Schleiden, ' Schelling's und
Hegel's Verhiiltniss zur Naturwis-
senschaft,' Leipzig, 1844.

'•^ See Helmholtz, ' Vortnige und
Reden,' vol. i. p. 361.

0

210

SCIENTIFIC THOUGHT.

often very crude. "We cannot wonder if many honest,
serious, thinking men then turned away in dissatisfaction
from medicine, or if they from principle embraced an
extreme empiricism." -^ " But the right kind of work
brought forth its fruits much sooner than many had
hoped. The introduction of mechanical notions into the
theories of circulation and respiration, a better insight
into the phenomena of heat, the more minutely elabor-
ated physiology of the nerves, speedily produced practical
results of the greatest importance ; the microscopical ex-
amination of parasitic tissues, the stupendous development
of pathological anatomy, led irresistibly from nebulous
theories to real facts." And again ^ : " Whilst in the
investigation of inorganic nature the different nations of
Europe progressed pretty evenly, the recent development
of physiology and medicine belongs pre - eminently to
Germany. The questions regarding the principle of life

^ Of. Helmholtz, ibid., vol. ii.
p. 178, in his discourse "Ueber das
Denken in der Medicin " : " At that
time there were many among the
younger doctors who, in despair
about their science, gave up all
therapeutics, and took to empiri-
cism, such as was then taught by
Eademacher. This on principle
regarded as vain all hope of scien-
tific insight." Not only the ex-
treme empiricism of Rademacher
(1772-1850), but still more the wild
theories of Hahnemann (1755-1843)
found during this age of general
unsettlement many followers. See
on the origin, the principles, and
the spreadj of homoeopathy, Hciser,
' Geschichte der Medicin,' vol. ii. p.
793, &c. Hiiser gives the year 1816
as the date at which Hahnemann's
docti'ines began to be accepted in
wider circles. "It must not be

forgotten that the hej^day of ho-
moeopathy fell in that age when
medicine, especially in Germany,
was in a very deficient state, so
that the accusations raised by
Hahnemann and his adherents did
not apjiear quite unfounded. It is
even to be admitted that homoeo-
pathy has contributed to the re-
action through which in our times
the regeneration of the art of heal-
ing has been brought about, though
this would have taken jalace with-
out Hahnemann " (p. 803). Homoeo-
pathy has no scientific represen-
tative at any of the German
universities, and yet it is admitted
that it " still enjoys a great repu-
tation in some influential circles
among the general public " (Hirsch,
' Gesch. d. mediciuischen Wis.sen-
schaften,' p. 570).

2 Helmholtz, ^oc. cit.,vo\. i. p. 362.

THE SCIENTIFIC SPIRIT IN GERMANY. 211

are closely allied to psychological and ethical questions.
To start with, here also that untiring industry is required
which applies itself to pure science for purely ideal pur-
poses, without immediate prospects of practical usefulness.
And indeed we may glory in the fact that in this German
scholars have always distinguished themselves by their
enthusiastic and self-renouncing diligence, which labours
for inner satisfaction and not for outer success."

This habit of self-renouncing labour, of singleness of 32.

® ° Science for

purpose — in short, the ideal of pure science and its pur- itsownsake.
suit — had been elaborated in many a secluded workshop
of a retired German university mainly under the influence
of the classical and philosophical studies of the end of
the last and the beginning of the present century. It was
held up high and conspicuous by the priests of humanity,
beginning with Lessing, Herder, and Kant, and ending in
Schleiermacher, Hermann, and Bockh, at the head of a
great army of devoted followers, travelling through the
wilderness of national depression, barbarism, and despair
into the promised land of freedom, culture, and hope.
Such an ideal is of priceless worth, and it is this ideal
which the philosophical and classical school of thought
bequeathed during the first half of the century to that
new school of thinkers which was destined to study, in
an equally patient and unselfish spirit, the seemingly less
elevated, but not less mysterious and fascinating, prob-
lems of Nature. Truly Gauss, "Weber, and Johannes
Miiller worthily headed the new army of labourers.

But though the elevated spirit in which scientific work Bequest of

1 ii.1 i.1111 1. s i.i_ the classical

is carried on may be the most valuable bequest or the andphiio-
classical and philosophical to the exact and empirical school.

212 SCIENTIFIC THOUGHT.

school, there were certain more tangible characteristics
of German research, which were carried over from the
older to the modern type of thought. It will be useful
to define these more clearly.

In the course of the second half of the eighteenth
century German literature and German philosophy had
started from the beginnings laid by other nations, and
after mastering and appropriating their achievements,
had set out for a new course and a higher flight. Milton
and Shakespeare ^ in epic and dramatic poetry ; Ossian,
the Percy Ballads, and Burns in song and lyric ; Gibbon
in history ; Joseph Scaliger and Bentley in philology ;
Locke, Hume, and Spinoza in philosophy ; Rousseau in
prose, — all these great names of a later or earlier past
had become familiar watchwords to German poets or
students — to Lessing, Herder, and Goethe, to Schlegel,
F. A. Wolf, and Wilhelm von Humboldt, to Bockh, Her-
mann, and Mebuhr, to Kant, Fichte, and Jacobi, before
they came forward with their own creations. The same
cosmopolitan spirit of looking elsewhere and everywhere
for beginnings, and for co-operation in the united work
of learning ; the same historical taste, the same desire to
glean from all quarters, — characterised the early decades
of the revival of German science. Hence the many
periodicals and annual reports ; hence the fact that the

German readers only through
Goethe and Schlegel. Similarly
the reaction against the school of
Leibniz and Wolff in philosophy
began with Kant's reply to Hume's
sceptical philosophy, whereas the
study of Spinoza influenced Kant's
followers and opponents, Jacobi,
Fichte, and Schelling.

^ These names are not given as
they follow in time, but as they
followed in their influence on Ger-
man thought and literature. Thus
the early representatives of the
German revival were influenced by
Milton and Pope more than by the
greater Shakespeare : epic and di-
dactic pi-eceded dramatic poetry :
Shakespeare was made familiar to

THE SCIENTIFIC SPIRIT IN GERMANY.

213

nation which requires them least ^ possesses the most 34.

Complete-

and the best translations of roreien authors. But the nessand

" thorough-

quality of greatest value for science which springs from "1^^^^^'^'

the cosmopolitan and historical spirit is that of complete- '
ness and thoroughness of research.

Secondly, the German man of science was not only
thorough, but was as little as the German philosopher
or classicist had been, an isolated thinker. He was
neither the member of an academy only, nor a solitary
genius reduced to the resources of his own study. He
lived mostly at a university, surrounded by others, whose
labours came in contact with his own, or who treated the
same subject from a different point of view. He had thus
to define the limits of his science, and to see that no part
of the common field was left uncultivated and unexplored.
His object could not be to produce simply a work of indi-
vidual greatness or of finished artistic merit ; his work
was an integral portion of the one great science ; his

' This must not be misunder-
stood. A knowledge of the master-
pieces of foreign literature was as
necessary to the development of
the German mind as it is to that
of any other nation ; it was and
is more complete there than in any
other country : what I mean is,
that as a knowledge of French and
English has been for a long time
so common among the educated
classes in Germany, translations are
more easily dispensed with there
than in other countries. In spite
of that, German literature abounds
in excellent translations of the
classics of France and England
both in general literature and in
science. It is also interesting to
note that no modern language
has succeeded so well in imitating
foreign and classical metres as the

German, hexameters having become
domiciled in Germany through Voss
and Goethe, the Alcaic and Sapphic
metres through Klopstock and Her-
der, the more complicated stanzas
through Platen, and above all
through Donner's excellent ren-
derings of the Greek dramatists.
Riickert excelled in the imitation
and reproduction of Persian, Indian,
and Ai-abic poetry, and through him
and Friedrich Bodenstedt German
literature has been enriched by
many lines of which it would be
difficult to say whether their home
was in Germany or in the far East,
so perfectly is the spirit and dic-
tion reproduced. The well-known
' Weisheit des Brahmanen ' of
Riickert, and Bodenstedt's 'Mirza
Schaffy ' are examples.

214

SCIENTIFIC THOUGHT.

35.

Combina-
tion of re-
search and
teaching.

labours had to fit in with the general plan, to find a
place in the one great edifice.

Thirdly, the German man of science was a teacher ; he
had to communicate his ideas to younger minds, to make
the principles and methods of research clear, to guarantee,
in his course of lectures, something like completeness,
to give a comprehensive survey ; not to teach " une
science faite," but to draw out original talent in others,
to encourage co-operation in research, to portion out the
common work to the talents which surrounded him, or it
might be to direct the flight of the aspiring genius.^

^ Here the two main objects of
academic teaching are to impart
a knowledge of the right method
in the special science, and to give
a survey of the whole domain
of the science. The two principal
institutions by which these ob-
jects are attained were first set
going in the classical branches of
study, and may be defined by two
terms — the "seminary" and the
lecture on "encyclopffidia." Both
terms are taken from earlier insti-
tutions. The seminary was origin-
ally a training - school for priests
or teachers. Under such masters
of methodical research as F. A.
Wolf and Gottfried Hermann, the
institution acquired a different
character. " The seminaries are
the real nurseries of scientific
research. They were founded, in-
deed, with a different object ; the
first seminaries, the philological
seminaries, which were started
during the last century at Halle
and Gottingen, were or should have
been pedagogic seminaries for the
future masters in the learned
schools. In reality they were —
especially that of F. A. Wolf —
in the first place institutions in
which the art of philological re-
search was taught. This is even

more the case in the philological
seminaries and societies which
during the nineteenth century
have been conducted by G. Her-
mann, Fr. Thiersch, Fr. Kitschl, and
others : they were nurseries of
philologists, not of teachers. And
the same may be said of the num-
erous seminaries which in modern
times have grown up in the other
sciences within the philosoi^hical
faculty, and also in the faculties
of theologj^ and law : they set up
as their aim — with few exceptions
— the training for scientific work
and research, not the utilisation of
knowledge for a practical purpose "
(Paulsen in Lexis, 'Die deutschen
Universitiiten,' vol. i. p. 74, &c.)
The same idea was in the mind of
Liebig when he started the first
chemical laboratory at Giessen (see
supra, p. 188, note). The ency-
clopaedic treatment of every large
subject in a special course of lec-
tures arranged for this purpose
had the object of preventing the
different studies from falling asun-
der or ultimately failing to unite
in the realisation of one great aim.
This great aim of all philological
studies, for instance, was always
held up by men like \Volf, Her-
mann, Bockh, and Ritschl, among

THE SCIENTIFIC SPIRIT IN GERMANY.

215

Lastly, the German man of science was a philosopher. 36.

■^ _ _ _ ir r Combina-

Whatever his aversion might be to special philosophical *'9" ^^ ,

° t: r r science and

doctrines, he had generally come vmder the influence of P^^iiosophy.
some philosophical school, the teaching of which he desired
either to uphold or to combat. Sooner or later, con-
sciously or unconsciously, he had to make clear to him-
self and to his disciples the underlying principles which
he thought the right ones, to defend them against attacks
from others, or to modify them, as progressing research
made it necessary. If the historical sciences had bene-
fited most by the philosophy of Schelling and Hegel,
which attempted to give new and constructive views
on the intellectual and ethical manifestations of the
human or the general soul, the mathematical and phy-

whose favourite lectures were those
on " encyclopEedia " of philology.
Something similar existed, and
exists still, in theology, law, and
what are called " Staatswissen-
schaften." All these terms are
supposed to embrace a variety of
studies which are organically com-
bined in one whole, forming a cycle.
In philosophy proper Hegel, and
later Lotze, delivered well-known
and largely attended lectures under
the title of EncyclopEedia. This is
a remnant of the encyclopaedic or
organic treatment of knowledge
sketched out by Bacon, and pro-
posed as a basis for their celebrated
work by Diderot and D'Alembert
(see ante, p. 35 and note). The
encyclopaedia, as a learned diction-
ary, we have seen, has since become
merely a synopsis. How different
from this was the truly encyclo-
paedic treatment given by men like
Bockh can be seen from his cor-
respondence with K. 0. Mliller,
where he scolds his younger friend
for undertaking to write the article

" Topography of Athens " for " such
a cursed publication as an encyclo-
paedia," whereas he himself was
regularly lecturing on ' ' encyclo-
paedia of philology," in which he
took in earnest the idea of classi-
cal philology as " the historical
science of the life of the ancient
peoples " (see Curtius, ' Alterthum
und Gegenwart,' vol. iii. p. 138, &c.)
Now although the exact sciences
when they became domiciled in the
German universities did not in
general copy this institution, yet
the historical and philosophical
survey, giving method and unity
to a large circle of studies, has been
upheld by many among the fore-
most men of science, especially in
the medical faculty. Of these I
only mention Joh. Miiller (see Du
Bois-Reymond, ' Reden,' vol. ii. pp.
195, 279) and his pupil and follower
Jacob Henle, who in his lectures
on anthropology took a philosophi-
cal survey of the whole subject of
the medical studies (see 'Jacob
Henle' by Merkel, p. 271, &c.)

216

SCIENTIFIC THOUGHT.

37.
Biology
grown out
of science
and philo-
sophy com-
bined.

sical sciences have been most affected by the spirit of
Kant's philosophy, which has ineradicably engrained in
the German mind the necessity of a criticism of the
principles of knowledge. Ever and anon some of the
most brilliant intellects in mathematics and science have
reverted to the same problems, and, on the whole, they
have confirmed the position taken up by Kant a cen-
tury ago.

It was thus under the influence of the exact methods
of experiment and calculation taught by the great French
school in the beginning of the century, and at the same
time through the philosophical spirit peculiar to German
science, that in the middle of the century the different
sciences which deal with the phenomena of life and con-
sciousness were remodelled. The great science of biology,
based upon mechanical principles, was thus created, and
the results gained in it brilliantly applied to the reorgan-
isation of the medical profession. But this great reform
does not belong exclusively to one great name ; it is the
work of a long line of thinkers : nor can I conceive that
the exclusive employment of the methods of exact re-
search would have so effectually brought it about, unaided
by the philosophical, historical, and critical spirit which
formed the peculiar characteristic of German thought
before the exact methods had been generally introduced.
And just because this reform required to be effected from
so many different beginnings, and gradually elaborated
and defended before it became firmly established, do the
modern sciences of physiology and pathology deserve to
be termed pre-eminently German sciences ; for no other

THE SCIENTIFIC SPIRIT IN GERMANY. 217

country possessed the necessary conditions and extensive
organisations, the habits of combined study and patient
co-operation, the large views and the high aims, which
had been acquired at the German universities under the
guidance of the German ideal of Wissenschaft, and under
the sway of the philosophical and classical spirit.

A great authority,^ who as much as any one represents
the modern as distinguished from the earlier views in
biological science, reviewing the different agencies which
have brought about the great change, speaks thus. He
is referring to Johannes Mliller, the father of modern 38.
physiology. " The modern physiological school," he says, Reymond

, on Muller.

" with Schwann at its head, has drawn the conclusions for
which Muller had furnished the premisses. It has herein
been essentially aided by three achievements which Mliller
witnessed at an age when deeply-seated convictions are
not easily abandoned. I mean, first of all, Schleiden and
Schwann's discovery, that bodies of both animals and
plants are composed of structures which develop inde-
pendently, though according to a common principle. This
conception dispelled from the region of plant-life the idea
of a governing entelechy, as Mliller conceived it, and
pointed from afar to the possibility of an explanation of
these processes by means of the general properties of
matter. I refer, secondly, to the more intimate know-
ledge of the action of nerves and muscles, which began
with Schwann's researches, in which he showed how the
force of the muscle changes with its contraction. In-
vestigations which were carried on with all the resources

1 See Du Bois-Reymond, ' Reden,' vol. ii. p. 219, &c.

218 SCIENTIFIC THOUGHT.

of modern physics regarding the phenomena of animal
movements, gradually substituted for the miracles of
the ' vital forces ' a molecular mechanism, complicated,
indeed, and likely to baffle our efforts for a long time to
come, but intelligible, nevertheless, as a mechanism. The
third achievement to which I refer is the revival among
us by Helmholtz and Mayer of the doctrine of the con-
servation of force. This cleared up the conception of
force in general, and in particular supplied the key to a
knowledge of the change of matter in plants and animals.
By this an insight was gained into the truth that the
power with which we move our own limbs (as George
Stephenson did those of his locomotive) is nothing more
than sunlight transformed in the organism of the plant :
that the highly oxygenated excrements of the animal
organism produce this force during their combustion, and
along with it the animal warmth, the Ttvivfxa of the
39. ancients. In the daylight which through such know-

" Vital -^ ° * .

force_' ab.in- ledge penetrated into the chemical mechanism of plants
and animals, the pale spectre of a vital force could no
more be seen. Liebig, indeed, who himself stood up so
firmly for the chemical origin of animal heat and motive
power, still retains an accompanying vital force. But
this contradiction is probably to be traced to the cir-
cumstance that the celebrated chemist came late, and as
it were from outside, to the study of the phenomena of
life. And even Wohler still believes in a vital force, he
who in his time did more than any one to disturb the
vitalistic hypothesis through his artificial production of
urea."

THE SCIENTIFIC SPIRIT IN GERMANY.

219

It was a process of critical sifting similar to that which
Kant ^ applied to our general metaphysical ideas, which
in the middle of the century, through the writings of
Berzelius and Liebig, of Schwann and Schleiden, of Henle,
Lotze, and Du Bois - Eeymond, gradually dispelled the
older confused notions, and firmly established the mech-
anical view in the study of the phenomena of life. But
as we are forced to recognise the substance of much of
Kant's philosophical criticism in the lucid expositions
of Locke and Hume before him, so it has been pointed
out that the words of the eminent French physiologist,
Vicq-d'Azyr, contain the substance of the more modern
ideas on life." It required the co-operation of the exact

40.
Mechanical
view in
biology.

^ The great influence which be-
longs to Kant in the development
of modern German science has been
frequently dwelt on. In more re-
cent times some of the first repre-
sentatives of the medical and bio-
logical sciences have dealt with the
subject, and the opposition which
fifty years ago originated in the ex-
travagances of some of Kant's suc-
cessors, has given way to a renewed
recognition of the just claims of
Kant. We may refer to Du Bois-
Reymond, who, forgetting Lotze,
calls Kant the last philosopher who
took a part in the work of the
naturalist (' Reden,' vol. i. p. 33) ;
to Helmholtz, who in many passages
of his popular addresses refers to
the merits of Kant ('Vortriige und
Reden,' 1884, vol. i. pp. 44, 368 ;
ii. 58, 227, 234, 248, &c.) ; to
Haeser {'Geschichte der Medizin,'
vol. ii. p. 811). I will add to these
the opinion of so great an authority as
Prof. Billroth of Vienna, who, speak-
ing of the two modern schools of
medicine in Germany, says ( 'Lehren

und Lernen der medicinischen Wis-
senschaften,' &c., p. 334): "How-
ever great the degree of independ-
ence may be which the two parallel
schools have attained, thej^ would
hardly have develojDcd so rapidly
without the powerful influence
which came from France and in a
lesser degree from England ; nor yet
without that of Immanuel Kant,
who in his ' Autophysiology of
Reason ' enlightened German minds
regarding their own selves, and
who with his lively imagination
fervently embi-aced natural science."
- The remarkable passage re-
ferred to is quoted by Du Bois-
Reymond ('Reden,' vol. ii. p. 27) :
" Quelqu' etonnantes qu'elles nous
paraissent, ces fonctions {viz., dans
les corps organises) ne sont-elles
pas des efi'ets physiques plus ou
moins composes, dont nous devons
examiner la nature par tous les
moyens que nous fournissent I'ob-
servation et I'experience, et non
leur supposer des principes sur
lesquels I'esprit se repose, et croit

220

SCIENTIFIC THOUGHT.

spirit of research with the critical methods acquired in
the school of philosophy, and the exhaustive survey of
a large array of facts acquired through historical and
classical studies, before the significance of this brilliant
apergu became evident ; before the underlying ideas could
become useful guides of research and progress. " Tantae
molis erat Eomanam condere gentem."

Though the reform of the biological^ sciences, and their
application to pathological inquiries, are probably the
greatest achievement which the methods of exact re-
search, in conjunction with the philosophical spirit, can
boast of in Germany in the centviry, the same habit

avoir tout fait lorsqu'il lui reste
tout a faire." This was said at
the end of the last century, and
fifty years later Du Bois-Reymond
{loc. cit.) could complain that the
truth contained in these words was
not yet generally admitted, in spite
of the labours of Berzelius, Schwann,
Schleiden, and Lotze. Compare
also A. von Humboldt's own con-
fessions on this jioint in his 'An-
sichten der Natur,' vol. ii. p. 309,
&c., edition of 1849.

^ I must remind the reader here
that though I use the word biolo-
gical as denoting the more recent
point of view from which all pheno-
mena of the living world are being
groujjed and comprehended, and
though the word seems to have
been first used by a German, never-
theless the arrangement of studies
at the German universities has
hardly yet recognised the essen-
tial unity of all biological sciences.
They are unfortunately still divided
between the philosophical and the
medical faculties. It is indeed an
anomaly, hardly consistent with
the philosophical and encyclopajdic

character of German research, that
palaiontology, botany, zoology, and
anthropology should belong to the
philosophical, whereas anatomy,
physiology, and pathology are
placed in the medical faculty.
Eminent biologists and anthropo-
logists, such as Schleiden, Lotze,
Helmholtz, and Wundt, have ac-
cordingly belonged to both facul-
ties. To place biological studies
on the right footing would re-
quire a mind similar to that of
F. A. Wolf, who evolved out of
the vaguer idea of humaniora the
clearer notion of a " science of an-
tiquity," and who accordingly was
able to convert the training-school
of teachers, the seminary, into a
nursery of students of antiquity.
Whether a similar reform in the
purely scientific interests of the
"science of life," which is now
mostly cultivated for the benefit
of the medical practitioner, can be
effected in this age, when practical
aims are gradually taking the place
of scientific ideas, is another ques-
tion.

THE SCIENTIFIC SPIRIT IN GERMANY. 221

of thought has shown itself in other fields of research,
and led to similar innovations. I will here only mention
one other line of inquiry, where neither exact nor meta-
physical reasoning alone suffices, but where a combination
of both is essential. I mean the gradual change which, 41.

° ° ^ _ Criticism of

mainly through the writings of German mathematicians, principles

>/ o o 'of matlie-

has come over our fundamental conceptions in the region "i^^'<=s-
of geometry, algebra, and the theory of numbers. This
subject belongs so essentially to the domain of pure
thought that a history of thought seems specially called
upon to take notice of it. Accordingly I intend to devote
a special chapter to it. At present it interests us mainly
because it is an outcome of that peculiar modification
which the exact or scientific spirit of thought underwent
when, introduced by French and English models, it came
in contact with the philosophical and classical ideal of
learning in Germany. I will repeat more clearly and
concisely what I mean. The exact methods of thought,
mainly elaborated in France, and there largely applied,
give to science its accuracy and definiteness. In spite
of this accuracy and definiteness, it is not immediately
clear whether they will lead to completeness of know-
ledge, or whether they may not be misapplied. To
guarantee completeness, to make sure that in the whole
great field no portion has remained untouched and un-
explored, that love of detail, that searching and explor-
ing spirit, is required which is nursed pre-eminently
by historical and classical studies. And to avoid the
abuse of existing methods, there is further required that
critical spirit which inquires into the value of principles

thought.

222 SCIENTIFIC THOUGHT.

and the limit of their usefulness. These three directions

of thought mark three tolerably distinct attitudes of the

human mind. Skill in inventing and in applying new

42. and precise methods — the exact habit or attitude of

The exact,

raf andThe ^hought ; love of detail, and the desire for complete and
habite of exhaustive knowledge — the historical habit or attitude of
thought ; lastly, the desire to become fully alive to the
value of existing methods or principles, which implies a
consciousness of the limited nature of one and every
principle — the critical habit or attitude of thought. The
progress of mathematics and natural science depends pri-
marily on the first ; classical studies depend on the second ;
philosophical reasoning mainly on the last. Each of the
three nations which have led human progress and thought
during the past centuries has probably been possessed
of these three cardinal virtues in equal proportions. For
though Newton stands pre-eminent in the first, we have
Laplace and Gauss and their numerous followers in other
countries ; though the great volume of classical learning
and criticism has emanated from the schools of "Wolf,
Hermann, and Bockh, they themselves point back to
Bentley and Joseph Scaliger ; and even Kant's unrivalled
enterprise was prepared by Hume, and dates back to
Descartes. There need, therefore, be no angry rivalry or
carping jealousy. We may point to the remarkably equal
contributions of the three nations to the general progress
of thought. But a very different and truly legitimate
interest prompts us to note how in the great performances
of each nation, in the literature of each of the three lan-
guages, different factors have been at work — different

THE SCIENTIFIC SPIRIT IN GERMANY. 223

agencies have combined to produce the effect. In this
regard the spectacles presented by French, German, and
Enghsh thought differ. And there seems to me little
doubt that during a considerable portion of this century
the German universities, grown out of theological, legal,
and medical studies, and widening gradually till they
embraced and deepened all three by the philosophical,
the classical, and the exact spirit of research, present that
organisation in which the different elements of thought
are most equally balanced, through which modern know-
ledge and the scientific spirit have been most widely
and successfully diffused, and that the German ideal of 43.
Wissenschaft embraces at once the highest aims of the the German

^ ideal of Wis-

exact, the historical, and the philosophical lines of ^'wc^a/t.
thought.

Nor would it be right to pass from the consideration of
this peculiar feature of nineteenth-century thought, which
is an outcome of the German university system, without
noticing the moral significance which this ideal of Wis- 44.

^ ° Moral value

senschaft acquired, and which marks it as a factor in °4.^f**"'
progress and in culture of much more importance even
than the lasting discoveries in science which it has made,
or the monuments of learning which it has reared. It is
not the political side of this movement which I refer to,
not even pre-eminently the educational, though these are
interesting and important enough to demand special his-
torical treatment. What I should like to point to as the
greatest in this movement is, that it belongs to the few
and rare instances in the history of mankind when we
see a large number of the most highly gifted members of

224 SCIENTIFIC THOUGHT.

a nation following a purely ideal cause, apart from the
inducements which gain or glory may furnish. The pur-
suit of truth and the acquisition of knowledge for its own
sake, as an ennobling and worthy occupation, has during
a large portion of our century been the life-work of pro-
fessors and students alike in the German universities.
In the biographies of many of them we meet with that
self-denial and elevation of spirit which is the true char-
acteristic of every unselfish human effort. In perusing
these records of high aspirations, arising frequently amid
disheartening surroundings, these stories of privations
cheerfully endured, of devotion to an ideal cause, glow-
ing with all the fervour of a religious duty, we gain a
similar impression to that which the contemplation of the
Classical period of Greek art or the early Eenaissance
produces on our mind.

Once at least has science, the pursuit of pure truth and
knowledge, been able to raise a large portion of mankind
out of the lower region of earthly existence into an ideal
atmosphere, and to furnish an additional proof of the
belief that there, and not here below, lies our true home.
I We may perhaps have to admit with regret that this
' phase is passing away under the influence of the utili-
tarian demands of the present day ; we may be forced to
think that another — and, we trust, not a lower — ideal is
held up before our eyes for this and the coming age.
But no really unselfish effort can perish, and whatever the
duty of the future may be, it will have to count among
the greatest bequests of the immediate past that high
and broad ideal of science which the life of the Ger-

THE SCIENTIFIC SPIRIT IN GERMANY.

225

man universities has traced in clear and indestructible
outlines.^

^ The testimonies by illustrious
foreigners to the great work of the
German universities are frequent
and well known, from the time
when Mme. de Stael visited Ger-
many, and her friend Villers wrote
his ' Coup-d'ncil sur les Universit^s
d'Allemagne ' in 1808, through the
writings of Cousin, the verdict of
Renan, of Cournot, of Dreyfus-
Brisac, and of the American, J. M.
»Hart. To these often-repeated ex-
pressions I will add that of the
great apostle of higher culture of
our age, of Matthew Arnold, who
sums up his interesting report on
the German system of higher edu-
cation in these characteristic words :
" What I admire in Germany is,
that while there, too. Industrialism,
that great modern jDower, is making

at Berlin and Leipzig and Elber-
feld most successful and rapid pro-
gress, the idea of Culture, Culture
of the only true sort, is in Germany
a living power also. Petty towns
have a university whose teaching
is famous through Europe ; and
the King of Prussia and Count
Bismarck resist the loss of a great
savant from Prussia as thej' would
resist a political check. If true
culture ever becomes at last a
civilising power in the world, and
is not overlaid by fanaticism, by
industrialism, or by frivolous plea-
sure-seeking, it will be to the faith
and zeal of this homely and much-
ridiculed German people that the
great result will be mainly owing "
('Schools and Universities on the
Continent,' 1868, p. 256).

VOL. I.

226

CHAPTEK III.

THE SCIENTIFIC SPIRIT IN ENGLAND.

1. The history of science in France and Germany during

Scientific •' JO

organisation the first half of the present century is identical with the

abroad. ^ "^

history of two great organisations, the Paris Institute and
the German Universities. It is to them that we owe
nearly all the great scientific work in the two countries :
to the former we owe the foundation of the modern
methods of scientific work during the last period of the
eighteenth and the early years of the nineteenth cen-
tury ; to the latter we owe pre-eminently the diffusion
and widespread application of those methods.^ We now
turn to the country which, in advance of France and Ger-

^ In respect of this I cannot suffi-
ciently i-ecommend M. Maury's
volume on ' L'aucienne Academic
des Sciences,' which is as eloquent
a testimonial to the scientific
labours of eminent Frenchmen
during the eighteenth century as
the companion volume on ' L'an-
cienne Academic des Inscriptions
et Belles Lettres' is a proof of
the absence of philological studies
during that period. The recent
publication of Lexis' work, ' Die
deutschen Universitiiten,' is just
as eloquent a testimonial to the

laboui's of the German universities
during this century. The first im-
pression we get from the perusal of
these two works is that for a long
period France almost monopolised
the exact sciences, just as later,
for a similar period, Germany
almost monopolised classical re-
search, the science of antiquity.
And yet the former was probably
as much indebted to the English-
man Newton as the latter was to
the Frenchman Joseph Scaliger for
the character each acquired during
the two periods I refer to.

THE SCIENTIFIC SPIRIT IN ENGLAND.

227

many, had produced the greatest scientific model of modern
times, a work which has probably done more than any
other purely scientific work to revolutionise our scientific
notions — the ' Principia ' of Newton. In the subsequent
history of the thought of this century, the next chapter
will deal with the part tliat the Newtonian ideas have
played throughout the whole period. We have now to
turn our attention to the state of science in Great Britain
during the period when Paris academicians and German
professors combined to define and carry the spirit of
modern scientific thought into the several mathematical,
physical, and biological branches of research.

Considering that the great scientific institutions of the
Continent — -the Paris Institute, the scientific and medical
schools in Paris, and the German universities — have done
so much for the furtherance of science and the diffusion
of the scientific spirit, it is natural that we should ask,
What have similar institutions done in this country ? 2.

Similar in-

These institutions are, indeed, mostly older than the ftitutions

' ' '' in Great

academies and modern universities of the Continent. Bntam.
The Eoyal Society, if not older than the French Academy^
is certainly older than the Paris Academy of Sciences.^

^ The actual dates are as follows :
The first Academy devoted to the
pursuit of science seems to have
been the " Academia Secretorum
Natunc," founded at Naples in 1560.
Several societies devoted to the cul-
ture of literature and art existed in
Italy, such as the Academy " della
Crusca" (founded at Florence in
1.582). The great French Academy,
devoted exclusively to the study of
the French language, dates from
1629, and received its charter in
1635. The Royal Society, though

not the first scheme of its kind
which was started in this country
— for the establishment of a Royal
Academy was discussed as far back as
1616 — actually started (164.5) in the
private meetings described in ' Dr
Wallis's Account of Some Passages
of his own Life ' (quoted by Weld,
' Hist, of the Royal Societj',' vol. i.
p. 30). These meetings, according to
him, were suggested by a German,
Tlieodore Hank, then resident in
London. The members were " per-
sons inquisitive into natural philo-

228

SCIENTIFIC THOUGHT.

The universities of Oxford, Cambridge, Edinburgh, Dub-
lin, and Glasgow ^ are older than most of the German
universities which have done the great scientific work
of this century. So far as wealth is concerned, no in-
stitution on the Continent could compare with the two
older English universities, and the Eoyal Society had
in the beginning of this century long emerged from the
poverty which characterised her early history during the
lifetime of Newton.^ Let us look at the subject from a

sophy, . . . and particularly of what
hath been called the New Philosophy
or Experimental Philosophy." It
formed a branch at Oxford in 1649,
and received a royal charter in
1662, four years before the "Acad-
emic des Sciences" at Paris — which
had also previously existed as a
private gathering of savants at the
houses of Mersenne, Montmort, and
Thevenot — was formally installed in
the Bibliotheque du Roi. The
" Accademia del Cimento " at Flor-
ence was established in 1657 ; but
it only lasted ten years. Very
irregular were also the life and
labours of the " Academia naturaj
Curiosorum " (later called A.
Ctesarea Leopoldina), founded at
Vienna in 1652. The Accademia
del Cimento printed an important
volume of Transactions in 1666.
The Royal Society published its
first volume in 1665. The first
volume of the 'Journal des Sa-
vants ' is of the same year. Very
complete information will be found
on all foreign Academies in the
' Grande Encyclopddie,' art. " Acad-
(5mie."

^ Although the dates of the foun-
dation of Oxford and Cambridge are
uncertain, they were certainly more
than a century — jjrobably two cen-
turies— older than Prague, the first
German university, founded by the
Emperor Charles IV. in 1347. The

older Scotch universities were found-
ed in the course of the fifteenth
century, about the same time that
Leipsic appears to have had its
origin through a secession from
Prague. The German universities
— Halle, Gottingen — which were
the seat of modern erudition, have
a much later date, as given in chap,
ii. p. 159, above. Edinburgh was
founded at the end of the six-
teenth century, and Trinity Col-
lege, Dublin, about the same time.
Leyden, which exerted a great in-
fluence both on Scotch and German
higher education during the seven-
teenth century, was somewhat older
than Edinburgh.

^ It appears from Weld (' History,'
&e., vol. i. pp. 231, 241, 246, 31 6,462,
473) that the financial position of
the Royal Society was precarious,
and frequently engaged the serious
attention of the Council, during
the whole first hundred j-ears of its
existence ; that as late as 1740 the
whole revenue of the Society was
only £232 per annum. An effort
was then made to get in the large
arrears of subscriptions and other
contributions. In the following
year the income seems to have
exceeded the expenditure by £297.
Weld adds, " It is a painful task to
recoj-d these periodical visitations
of poverty, which threatened the
very existence of the Royal Society;

THE SCIENTIFIC SPIRIT IN ENGLAND. 229

different point of view. England has during the early part 3.

. English

01 the century, m all but the purely mathematical sciences, science in

•^ the early

a greater array of scientific names of the first order than ^entu'*^^
Germany, and nearly as great an array as France. Black,
Herschel, Priestley, Cavendish, Davy, Young, Dalton,
Faraday, Eowan Hamilton, Brewster, Lyell, Charles Bell,
are all identified with one or more novel ideas or definite
branches of research.-^ Great Britain had thus no lack

there is, however, a proportionate
amount of pleasure in witnessing
the triumphant manner in which
the small band of philosophers ex-
tricated their institution from seri-

ous diflficulties, unassisted by Royal
bounty and labouring alone on ac-
count of their love for science "
(vol. i. p. 474).

^ The following are the principal dates referring to the great discoveries
made in this country during the half-century ending 1825 : —

1774. Priestley (1733-1804) discovers oxygen and a variety of other

gases.

1775. Black (1728-99), Memoirs on latent heat.

1775. Maskelyne (1732-1811) measures the Attraction of Mount She-
hallien.

1775. Landen (1719-90) expresses the arc of an hyperbola in terms of
two elliptic arcs.

1778. Benjamin Thompson (Count Rumford, 1753-1814) first experi-
ments on heat by friction.

1781, 13th March, Sir William Herschel (1738-1822) discovers Uranus.

1784. Cavendish (1731-1810) discovers the composition of water.

1786-97. Caroline Herschel (1750-1848) discovers her eight comets.

1798. Cavendish determines the density of the earth.

1799. Davy (1768-1829), essay on heat, light, &c.

1800. Nicholson and Carlisle decompose water with the voltaic pile.

1801. Dalton (1766-1844), theory of evaporation.

1801. Young (1773-1829), first essay on the theory of light and colour.

1802. Dalton, law of expansion of gaseous fluids.

1802. Playfair (1748-1819), ' Illustrations of the Huttonian Theory.'

1802. WoUaston (1766-1829), on Iceland spar, and undulatory theory.

1802-3. 'William Herschel, observations on uebulie and double stars."

1802-3. Young expounds the principle of "Interference."

1803-4. Dalton proposes the atomic theory.

1804. Leslie (1766-1832), experiments on heat.

1804. Wollaston discovers palladium and other kindred metals.

1806. Davy isolates the alkaline metals.

1807. Young introduces the word Energy (lect. i. p. 75).

1809. Ivory (1765-1842), on the attraction of ellipsoids.

1810. Young (in 'Quarterly Review') explains the different refractions

in crystals.
1810. Davy discovers chlorine to be a simple body.

230 SCIENTIFIC THOUGHT.

either of great men of science or of great institutions,

and yet — in spite of these — we read in the course of

4. the first third of the century about the decline of

Alleged de- ''

eiineof science in England. That such could be seriously said

science iii ~ ''

England. ^f ^ country which within fifty years had in astronomy
discovered a new planet (the first addition to the number
known to the ancients), had discovered oxygen, latent
heat, and the decomposition of water, applied the gal-
vanic current for isolating the most refractory metals,
laid the groundwork for the undulatory theory of light,
established the atomic theory, put forth in statics and
dynamics two of the most important modern generalisa-
tions,^ and introduced in the treatment of electric and

1810. Brown (1773-1858) publishes his ' Prodromus Florfc IsTovse Hol-

landife,' &c.

1811. Charles Bell (1774-1842) asserts the difference of sensory and

motor nerves.
1813. Brewster (1781-1868) begins his experiments on refraction and

dispersion.
1813. Davy discovers iodine.

1813. Wollaston pul)lishes his synoptical scale of equivalents.

1814. Wells (1757-1817), essay on dew.

1815. William Smith (1769-1839) publishes his work on 'Strata.'
1815. Brewster gives his law for determining the polarising angle.

1815. Leslie (1766-1832) experiments on radiant heat and temperature

of the earth.

1816. Prout (1785-1850), Memoir on the position of hydrogen.

1817. Young (in a letter to Arago) suggests transverse vibrations of

light.
1819. Kater (1777-1835) measures the length of the seconds-pendulum.
1821. Faraday (1781-1867) discovers the rotation of a coil round a fixed

magnet.
1821. Brown, monographs on botanical subjects.
1821. Sabine (1788-1883) experiments on the dip of the magnetic

needle.
1823. Rowan Hamilton (1805-65) presents his paper on Caustics to

the Irish Academy.

1823. Faraday condenses chlorine and other gases.

1824. Sir J. Hersche] (1792-1871), observations of double stars.

1825. Sir J. Herschel, on the parallax of fixed stars.

■* The two important generalisa-
tions I refer to are contained in :
1. George Green, 'An Essay on

the Application of Mathematical
Analysis to the Theories of Elec-
tricity and Magnetism,' published

THE SCIENTIFIC SPIRIT IN ENGLAND.

231

magnetic phenomena novel conceptions, the vahie of
which other fifty years have hardly sufficed to realise
— is, indeed, an extraordinary fact well worthy of careful
examination. Certainly the language in which Cuvier
with truth congratulates the French nation on the pre-
eminence which it has attained in all branches of science
contrasts strangely with the repeated attacks made in
periodical literature, and in special pamphlets, on the
state of science in England. And these not by persons
ignorant of the great names and signal achievements just
mentioned, but by men of note, occupying all but the
very first places among the scientific men of this country.

It will suffice to give only two out of many examples
of this criticism.

One of the earliest complaints regarding the culture of 5.
higher mathematics in this country will be found in an ofpiayfair.

at Nottiugliam by private subscrip-
tion ia 1828. The term " potential
function," to denote the sum (F)
obtained by adding together the
masses of all the particles of a
system, each divided by its distance
from a given point, or in mathe-

fdm
matical language V= I — , occurs

there for the first time. See
Green's mathematical papers, ed.
Ferrers, 1871, p. 22. The function
had before that time been used by
Legeudre and Laplace, but Green
was the first to give a general
mathematical theory of it. His
essay remained unknown to the
mathematical world, and the prin-
cipal theorems were independently
published by Gauss in his celebrated
essay ' Aljgemeine Lehrstitze iiber
die im verkehrten Verhtiltnisse des
Quadrats der Entfernung wirken-
den Anziehungs- und Abstossungs-
Kriifte,' 1839.

2. W. Rowan Hamilton's memoirs
in the ' Philosophical Transactions '
of 1834 and 1835, preceded by his
theory of systems of rays in the
' Transactions of the Royal Irish
Academy,' 1828. In these papers
is contained his celebrated prin-
ciple of varying action, which is a
development of Maupertuis's prin-
ciple of least — or stationary— ac-
tion. A great deal has been written
on this principle, which is now con-
sidered to be the most general
principle of dynamics, as well for
its mathematical usefulness in cal
culations (see Kirchhofi', ' Vorlesun
gen iiber mathematische Physik,
vol. i. pjj. 28, 29), as from a phy
sical point of view (Helmholtz,
in ' Journal fiir Mathematik,' vol
100). It has gained this import
ance since the conception of energy
or power to do work, has been
placed at the base of the theory
of all physical processes.

232

SCIENTIFIC THOUGHT.

excellent review of Laplace's ' Mecanique celeste ' by
Playfair in the ' Edinburgh Eeview ' of 1808.^ " In the
list of the mathematicians and philosophers to whom the
science of astronomy for the last sixty or seventy years
has been indebted for its improvements, hardly a name
from Great Britain falls to be mentioned.^ . . . Nothing
prevented the mathematicians of England from engaging
in the question of the lunar theory, in which the interests
of navigation were deeply involved, but the consciousness
that in the knowledge of the higher geometry they were
not on a footing with their brethren on the Continent.
This is the conclusion which unavoidably forces itself
upon us. . . . We will venture to say that the number
of those in this island who can read the ' Mecanique
celeste ' with any tolerable facility is small indeed. If
we reckon two or three in London and the military

^ ' Edinburgh Review,' vol. ii. p.
279, &c. John Playfair (1748-1819)
was a native of Forfarshire, and
Professor of Mathematics, and later
of Natural Philosophy, at the Uni-
versity of Edinburgh. " Playfair
was struck with the backwardness
of the English mathematicians in
adopting the results of the Conti-
nental analysts. While they boasted
of Newton, they were unable to
follow him, and the mantle of
Newton had indeed passed over to
France, where it rested ultimately
on the shoulders of Laplace. Play-
fair accordingly set himself to dif-
fuse among his countrymen a know-
ledge of the progress which science
had been making abroad. This he
did in a variety of ways, — by his
articles in the ' Encyclopaedia Brit-
annica, ' by his papers in the Trans-
actions of learned societies, by his
articles in the 'Edinburgh Review,'
and by his class-teaching. As David

Gregory introduced the Newtonian
jihilosophy, so Playfair introduced
the Continental methods into the
studies of the University of Edin-
burgh " (Sir A. Grant, ' The Story
of the University of Edinburgh,'
vol. ii. p. 302).

- Playfair heie excepts hiscountry-
man, Colin Maclaurin (1698-1746),
" in whose time the teaching of
mathematics at Edinburgh reached
a point which it cannot be said to
have yet surpassed " (ibid., vol. ii.
p. 299 ; cf. also vol. i. p. 271, where
a progi-amme published in 1741 is
given of the mathematical and phy-
sical lectures at Edinburgh, which
surpassed probably at that time
the teacliing of any other English
or Continental university). Play-
fair might have excepted also Ivory
and the Englishman Landen, both
of whom were well known among
Continental mathematicians.

THE SCIENTIFIC SPIRIT IN ENGLAND.

233

schools in its vicinity, the same number at each of the
two English universities, and perhaps four in Scotland,
we shall hardly exceed a dozen, and yet we are fully
persuaded that our reckoning is beyond the truth."

The other opinion I am going to quote dates from more 6.

Babbage's

than twenty years later, and is contained in a pamphlet by ciiticisms.
Charles Babbage,^ who with Herschel and Peacock had
done much to introduce at the University of Cambridge
that knowledge of Continental mathematics which, accord-
ing to the Edinburgh Eeviewer, was so much needed. His
'Decline of the State of Science in England' (1830) was
directed mainly against the Eoyal Society, as the review

1 Charles Babbage (1792-1871), a
native of Devonshire, well known
all over Europe through his calcu-
lating machine, was a very remark-
able and original man. He lived
during the age when the appli-
cation of machinery to manufac-
tures, trades, and arts produced
the great reform in the industrial
sj'stem of this countrj^, and his
talents, which might well have
been employed in promoting pure
science, were largely spent in solv-
ing problems of practical interest.
An account of these several pur-
suits and schemes is given in his
' Passages from the Life of a Philo-
sopher,' London, 1864. Of his
analytical machine we shall have
occasion to speak hereafter (see p.
248). Of the beginnings of the
new school of mathematics at Cam-
bridge he gives the following ac-
count (p. 27). Having purchased
for seven guineas a copy of Lacroix's
'Differential and Integral Calculus,'
he went to his puVjlic tutor to ask
the explanation of one of his diffi-
culties. " He listened to my ques-
tion, said it would not be asked in
the Senate House, and was of no

sort of consequence, and advised
me to get up the earlier subjects of
the university studies." Repeated
experience of this kind had the
effect that he acquired a distaste
for the routine studies of the
place, and devoured the "papers
of Euler and other mathemati-
cians scattered through innumer-
able volumes of the Academies of
Petersburg, Berlin, and Paris." He
then perceived "the superior power
of the notation of Leibniz." It
being an age for forming societies
for printing and circulating the
Bible at Cambridge, Babbage con-
ceived the plan of a society for
promoting mathematical analysis,
and to parody one of the many
advertisements he proposed to call
it a society for promoting " the
Principles of pure rf'ism {d being
Leibniz's symbol) in opposition to
the dosage (dots being Newton's
notation) of the university." The
most important result of this move-
ment was the publication in 1816
of a translation of Lacroix's treatise,
and of two volumes of examples in
1820.

234

SCIENTIFIC THOUGHT.

of Playfair was against the English universities.^ " That
science has long been neglected and declining in England
is not an opinion originating with me, but is shared
by many, and has been expressed by higher authority
than mine."^ The author then proceeds to give ex-
tracts from the writings of Davy, Herschel, and others
on this subject, " It cannot," he says, " have escaped
the attention of those who have had opportunities of
examining the state of science in other countries, that

■* Some of the causes of the de-
cline as given by Babbage are in-
teresting, the more so if we remem-
ber that they were written at the
period which marked the culmin-
ation of Wissenschaft in another
country (p. 10) : " The pursuit
of science does not in England
constitute a distinct profession, as
it does in many other countries.
. . . Even men of sound sense and
discernment can scarcely find means
to distinguish between the posses-
sors of knowledge merely elemen-
tary and those whose acquirements
are of the highest order. This
remark applies with peculiar force
to all the more difficult applications
of mathematics ; and the fact is
calculated to check the energies of
those who only look to reputation
in England." In 1794 Professor
Waring of Cambridge wrote : " I
have myself written on most sub-
jects in pure mathematics, and in
these books inserted nearly all the
inventions of the moderns with
which I was acquainted ; . . . but
I never could hear of any reader
in England, out of Cambridge, who
took the pains to read and under-
stand what I liave written ; " and
" he then ])roceeds to console him-
self under this neglect in England
by the honour conferred on him by
d'Alembert, Euler, and Lagrange"

(see Todhunter, ' History of the
Theory of Probability,' p. 453).
Babbage remarks (p. 13) that "in
England the profession of the law
is that which seems to hold out the
strongest attraction to talent," that
science is pursued as a favourite
pastime, and that mathematics "re-
quire such overwhelming attention
that they can only be pursued by
those whose leisure is undisturbed
by other claims." "By a destruc-
tive misapplication of talent we ex-
change a profound philosopher for
but a tolerable lawyer" (p. 37).

- One of the causes given by the
Edinburgh Reviewer of 1822 (vol.
xxxvii. p. 222) is the following :
" In Cambridge there must always
be a great number of men devoted
to scientific pursuits ; but from the
want both of the facilities and the
excitements furnished by such an
association, apt to lose the spirit of
original investigation, — a remark
peculiarly applicable to those young
men who yearly distinguish them-
selves in the favourite studies of
the University, and who, after the
laborious course of discipline by
which thej' have attained the first
object of their ambition, are prone,
if left alone, to become the mere
instruments for enabling others to
pursue the same course."

THE SCIENTIFIC SPIRIT IN ENGLAND. 235

in England, particularly with respect to the more difficult
and abstract sciences, we are much below other nations,
not merely of equal rank, but below several even of
inferior power."

" It is," says the Edinburgh Eeviewer of 1816,^ " cer-
tainly a curious problem with respect to national genius,
whence it arises that the country in Europe most gener-
ally acknowledged to abound in men of strong intellect
and sound judgment should for the last seventy or eighty
years have been inferior to so many of its neighbours in
the cultivation of that science which requires the most
steady and greatest exertions of understanding, and that
this relaxation should immediately follow the period when
the greatest of all mathematical discoveries had been made
in that same country."

It must be said that these opinions, expressed as they v.
were by men of the highest attainments, did not remain opinions on

■^ *= ' English

unchallenged at home or unnoticed abroad. It will be ^'''enee.
interesting to see how they have been met. Let us first
hear what Cuvier says in his I^loge of Sir Joseph Banks
in 1821"' regarding the work of the Eoyal Society during
the period of forty-one years of his presidency : " During
this period, so memorable in the history of the human
mind, English philosophers have taken a part as glorious
as that of any other nation in those labours of the intel-
lect which are common to all civilised peoples : they have
faced the icy regions of both poles ; they have left no
corner unvisited in the two oceans ; they have increased
tenfold the catalogue of the kingdoms of nature ; the

^ ' Edinburgh Review,' 1816, vol. ■ - See Cuvier, ' Eloges historiques,'
xxvii. p. 98. : vol. iii. p. 79.

236

SCIENTIFIC THOUGHT.

heavens have been peopled by them with planets, with
satellites, with vmheard-of phenomena ; they have covmted,
so to speak, the stars of the Milky Way : if chemistry has
assumed a new aspect, the facts which they have furnished
have mainly contributed to this change : inflammable air,
pure air, phlogisticated air, are due to them ; they have
discovered how to decompose water ; new metals in great
number are the outcome of their analysis ; the nature of
the fixed alkalis has been demonstrated by none but
them ; mechanics at their call have worked miracles, and
have placed their country above others in nearly every
line of manufacture." Another foreigner, Professor Moll
of Utrecht, remarked in his reply to Mr Babbage's
pamphlet ^ : "If Mr Herschel and some of his friends

1 The pamphlet was entitled ' On
the alleged Decline of Science in
England.' By a Foreigner. Lon-
don, 1831. It was by Dr Moll of
Utrecht, and was introduced by a
few lines from Faradaj', who, with-
out taking anj^ side in the question,
remarked that " all must allow that
it is an extraordinary circumstance
for English character to be at-
tacked by natives and defended by
foreigners." In the discussion on
the subject bj' this writer, as also
by Eabbage, Herschel, Playfair,
Whewell — pro and con. — a good
many points of importance are
brought out : some of them are
still interesting, others refer to
defects wliich have since been
remedied. I will mention a few
of them. Playfair, in the ' Edin-
burgh Review ' (vol. xxxi. p. 393,
1S19), thinks that the "very ex-
tensive dissemination of general
knowledge, which is so much the
case over the whole of this king-
dom," is against the advancement
of the higher branches of mathe-

matics. This refers probablj^ to
the absence of periodicals devoted
to special sciences, such as the
' Annales de Chimie et de Physique,'
published by Arago and Gay-Lussac
in France. In the absence of these
special organs, memoirs of original
value, which marked an era in
special researches, were scattered
in general literary reviews, as
Young's on Light and Hieroglyphics
in the ' Quarterly,' Herschel's and
Airj''s in the ' Encyclopaedia Metro-
politana ' ; and much good mathe-
matics was buried in the ' Ladies'
Diary ' among poetry of the " worst
taste" and " childish scraps of litera-
ture and philosophy " (' Edin. Rev.,'
vol. ii. p. 282, 1808). Another
point is that " the researches of
English men of science have been
too much insulated from each other
and from what is doing in other
countries " (Whewell to Vernon
Harcourt, 1831 ; see Life by Tod-
hunter, vol. ii. p. 126). The British
Association, which was founded very
much as a result of this agitation,

THE SCIENTIFIC SPIRIT IN ENGLAND.

237

have such a poor opinion of the English scientific journals,
a different judgment is entertained abroad, as is well
proved by the eagerness with which the German journal-
ists seize upon every article issuing from the presses of
their British colleagues. The value which is set in
Germany upon the scientific pursuits of the English,
the rapidity with which translations are made in Germany
of whatever English philosophers of some reputation pub-
lish, shows abundantly that in that country at least, in
docta Germania, a far greater value is set upon the pro-
ductions of English science than is done by Mr Herschel
and his friends." ^

has remedied this defect; and special
periodicals exist now in multitudes ;
but who could say that a third
point has been sufficiently attended
to — viz., "the ignorance of foreign
languages, which prevails both in
England and in France : in Eng-
land the number of those who ac-
quire a smattering of French is
very small, and still smaller is the
number of those who know enough
of German to read a book in
that language without considerable
trouble " (Dr Moll, loc. cit., pp. 7, 8).
A fourth defect existing at that time
is worth mentioning, as we have long
left the age of such di'awbacks ; it
"is the high price in England of
foreign books, in consequence of an
importation duty." The paper
duties were repealed in 1861.

^ Moll, loc. cit., p. 7. Another pas-
sage is of interest, as bearing upon
the difference between the culture of
science in England and in France :
" At the time of the French Revolu-
tion it so happened, by the exer-
tions of d'Alembert, Clairault, Con-
dorcet, and others, that of all
sciences mathematics were the
most fashionable. . . . With this
view the Ecole Normale was

founded, which, though of short
duration, was perhaps of more
utility towards the extension of
mathematical knowledge than all
the universities of Europe together.
It was there that Laplace, La-
grange, and Monge were lecturers,
and men like Lacroix among the
hearers. The study of classics
having been in a great measure
abolished by the French lie volu-
tion, mathematics were studied in
its stead ; and it thus happened
that a number of mathematicians,
unusually great, were scattered
over the soil of France, and every
one thought himself capable de
faire les x, as they themselves
called it, upon any given subject.
But most of these investigations
were all theoretical, and practical
applications were foregone in almost
every instance " (p. 11). " Mechan-
ics in particular do not seem acces-
sible, according to the tenets of the
French school, to any man not well
versed in sublime analysis. . . .
Hence it arises that many have
acquired a profound knowledge of
the higher branches of mathematics,
whilst the more elementary part of
mathematics, which leads to the

238

SCIENTIFIC THOUGHT.

s. The answers to the challenges of Babbage and the

English re-
plies to Edinburgh Reviewer given by English writers theni-

Babbage,&c. *= b J o

selves cannot on the whole be said to be very reassur-
ing. One of them counts the scientific periodicals in
England and in France, but omits to weigh the merit
of their respective contributions. Another points to the
' Ladies' Diary,' in which many curious mathematical
problems, far beyond the mere elements of science, are
often to be met with. A third, whilst in general admit-
ting the correctness of Babbage's strictures, draws attention
to the ' Penny Magazine ' and the ' Cabinet Cyclopedia ' as
counterparts in England of the Pieports of Cuvier and
f. Berzelius abroad. The true position was probably recog-

Foundatioii . . . .

of tiie Brit- nised by the founders of the British Association for the

ls>h Associ- "^

ation. Advancement of Science about 1830,^ who saw that, be-

most useful applications, is far less
diffused in France than in England "
(p. 12). "The principle of the
division of labour [in science] is
more acted upon in France than in
England" (p. 14).

^ The movement, which origi-
nated in the circle to which Bab-
bage belonged, was — as stated
above, p. 42 — to some extent
copied from the German Associa-
tion founded by Oken in 1822. The
latter acquired a kind of EuroiJean
renown througli the exei-tions of
Humboldt in 1828, who succeeded
in attracting a considerable number
of celebrities — such as Gauss, Ber-
zelius, Oerstedt,— who for them-
selves preferred a solitary to a " gre-
garious " mode of science. Babbage
was a guest at this meeting at Ber-
lin, and gave an account of it in an
appendix to the ' Decline of Science.'
A good account of the character
and gradually declining influence
of these German meetings will be
found in Bruhns' ' Life of Hum-

boldt' (vol. ii. p. 127, &c., transla-
tion). They " degenerated after the
usual German fashion into the un-
intellectual form of feasting. " The
British Association for the Advance-
ment of Science, founded shortly
afterwards on the 27th September
1831 at York, was the immediate
outcome of a suggestion thrown
out by Brewster at the end of a
review in the ' Quarterly ' of Bab-
bage's 'Decline of Science.' He
fully endorsed the latter's opinion,
and was even more severe upon the
universities, maintaining " that the
great inventions and discoveries
which have been made in England
during the last century have been
made without the precincts of our
universities. In proof of this we
have only to recall the labours of
Bradley, Dollond, Priestley, Caven-
dish, Maskelyne, Rumford, Watt,
W'ollaston, Young, Davy, and Che-
venix ; and among the living to
mention the names of Dalton, Ivory,
Brown, Hatchett, Pond, Herschel,

THE SCIENTIFIC SPIRIT IN ENGLAND. 239

sides a number of separate societies, "concentration was
needed in one association in order to give more systematic
direction to scientific inquiry, and that the first thing
needed would be to procure reports on the state and the
desiderata of the several branches of science." Babbage,
at the Oxford meeting in 1832, "expressed the general
feeling that meetings should be held in places likely to
bring science into contact with that practical knowledge
on which the wealth of the country depends." There is
also no doubt that in the course of half a century the
British Association has done a very extensive service
to science in the direction of supplying the wants which
its early founders clearly defined, and in bringing about
that concerted action and scientific co-operation which so
highly distinguishes the great academies and universities of
France and Germany.^ It has done so without altogether
destroying that peculiar feature which characterises not lo.

•^ ^ ^ Charactei

only the scientific but all the forms of the higher mental j^^.t'cs of

'' o higher ini

work of this country. In no country has the voice of EngYa^nd.
public criticism been so free to unveil the shortcomings
which attach to all — even the highest — human effort. In
England there has existed for a long time the habit of
promoting advance in every department by the cultiva-

Babbage, Henry, Barlow, South, association of our nobility, clergy,

Faraday, Murdoch, and Cliristie ; gentry, and jihilosophers" (p. 342).

nor need we have any hesitation ^ The British Association has from

in adding that within the last fif- the beginning had two features which

teen years not a single discovery or did not exist in the German su-

invention of prominent interest has ciety — first, the Reports on the

been made in our colleges, and that position of various branches of sci-

there is not one man in all the eight [ ence, delivered by specialists of the

universities of Great Britain who is j highest ability ; and, secondly, the

at present known to be engaged in , Committees, which undertake to

any train of original research " do special work requiring concerted

(' Quarterly Review,' vol. xliii. p. action.

327, 1830). He then suggests "an I

240

SCIENTIFIC THOUGHT.

11.

Academies
and univer-
sities not
always im-
partial.

tion of party spirit, party criticism, and party shibbo-
leths, as the easiest method of enlisting popular favour ^
and individual interest ; for here there exists no central
authority which can create powerful organisations or dis-
burse public means without the distinctly and repeatedly
expressed support of a large section of the people. But
all this must not induce us, in our historical survey,
to dwell on the defects rather than on the excellence of
the British contributions to the growth and the diffusion
of science. Brilliant is undoubtedly the array of British
names which have during the first half of this century
become immortal by scientific labours, and it would be
narrow-minded simply to emphasise the fact that they have
not done so by the same means and through the same
organisations as the Continental nations have established
and perfected. Eor we must not forget that these even,
with all their rightly extolled universality and breadth
of spirit, have sometimes failed to recognise merit or to
encourage genius. In spite of the impartial dealings of
the Institute, on which Cuvier congratulates the French
people, there are several instances in which contribu-
tions of the first order lay unnoticed for many years.

^ Referring to the British Asso-
ciation itself, Charles Lyell wrote
in 1838, after the Newcastle meet-
ing, to Charles Darwin : " Do not
let any papers, whether of saints
or sinners, induce you to join in
running down the British Associa-
tion. I do not mean to insinuate
that you ever did so, but I have
myself often seen its faults in a
strong light, and am aware of what
may be urged against philosophers
turning public orators, &c. But I
am convinced, although it is not
the way I love to spend my own

time, that in this country no im-
portance is attached to any body
of men who do not make occasional
demonstrations of their strength in
public meetings. It is a country
where, as Tom Moore justly com-
plained, a most exaggerated im-
portance is attached to the faculty
of thinking on your legs, and where,
as Dan O'Counell well knows, no-
thing is to be got in the way of hom-
age or influence, or even a fair share
of power, witliout agitation " (' Life,
Letters, and Journals of Sir C. Lyell,'
London, 1881, voL ii. p. 45, &c.)

THE SCIENTIFIC SPIRIT IN ENGLAND.

241

Fourier's great work on the theory of heat, which for the
first time propounded a universal method applicable to
the mathematical treatment of almost every physical
problem, inasmuch as it, so to speak, follows nature into
the marvellous composition of the many movements out
of which all her phenomena are compounded, lay buried
for fourteen years in the archives of the Institute. That
great authority had failed to recognise its paramount
importance.^ Fresnel's first memoir, which estabhshed
on a firm mathematical basis the undulatory theory of
light, was for years left unpublished, whilst the whole
scientific world was anxiously expecting the results of
his inquiries.^ In Germany we have examples of similar

12.
Fourier.

^ Jean Bapt. Jos. Fourier (1768-
1830), of humble origin, in his
celebrated ' Theorie aualytique de
la Chaleur' (Paris, 1822), and in
previous memoirs, carried further
the mathematical treatment of phy-
sical phenomena and introduced
wider conceptions of mathematical
quantities and their dependence —
i.e., of a mathematical "function."
His investigations have led to far-
reaching applications in physical
science (Ohm and Lord Kelvin),
and to profound mathematical theo-
ries (Dirichlet, Riemann, &c.) The
so-called " Fourier " series has thus
a great applied as well as theoreti-
cal interest. Fourier's first memoir
was presented to the Institute in

1807 ; an extract was published in

1808 ; a second memoir was pre-
sented in 1811 and crowned, but
was not printed till 1824, two years
after the great work itself had ap-
peared. On the physical importance
of Fourier's analysis see Helm-
holtz, 'Vortriige und Reden,' vol. i.
p. 101, &c. ; Sir W. Thomson,
Mathematical and Physical Papers,
passim, but especially vol. ii. p. 41,

VOL. L

&c. On the purely mathematical
interest that attaches to the Fou-
rier series see especially Riemann,
' Mathematische Werke,' p. 218,
&c. A very concise summary of
the history of the series is also
given byt George A. Gibson in the
'Proceedings of the Edinburgh
Mathematical Society,' vols. xi. and
xii. We shall revert to this subject
in a subsequent chapter.

2 Augustin Fresnel (1788-1827)
divides with Thomas Young the
merit of having established the
undulatory theory of light on a
firm basis. His first memoir on
Diffraction of Light was presented
to the Academy in 1815, a more
extensive paper in 1818 ; this was
crowned in 1819, but not printed
till 1826. Other papers of his
were mislaid or lost. The delay
in bringing before the world these
important discoveries has been at-
tributed to the opposition of La-
place and his party in the Institute,
which even the influence of Arago
could not overcome. See what Sir
John Herschel says in 1827, refer-
ring to Fresnel's memoir of 1821 on

Q

13.
Fresnel.

242

SCIENTIFIC THOUGHT.

14.
Pliicker.

discouragement and neglect being thrown in the way of
the growth of new ideas. Pliicker of Bonn laboured for
many years on the union of the geometrical and analytical
methods in the treatment of geometry ; but he found so
little appreciation that he abandoned his investigations,
and only resumed them when in after-years a similar line
of thought was independently developed in England.-^

Transverse Vibrations, which the
Academy had recommended to be
printed : " We are sorry to observe
that this recommendation has not
yet been acted upon, and that this
important memoir, to the regret
and disappointment of men of sci-
ence throughout Europe, remains
yet unpubUshed " (' Ency. Metrop.,'
article "Light"). A full account i
of the opposition and difficulties I
which both Young and Fresnel j
had to encounter will be found in
Whewell's ' History of the Induc-
tive Sciences,' vol. ii. In earlier
times R(5aumur seems to have ex-
ercised a similar tyranny in the ,
Academy of Sciences : see Maury,
' Les Academies d'autrefois,' vol. i.
pp. 280, 123; also Huxley, 'Critiques
and Addresses,' 1890, p. 112, &c.

1 Julius PUicker (1801-68), pro-
fessor at Bonn, equally known in
England by his scientific co-opera-
tion with Faraday and by that
with Cayley and Salmon, worked
both in pliysics and geometry on
independent lines. In the latter
especially he brought about that
union of purely geometrical and
algebraic methods which has be-
come so fruitful in the development
of modern geometry and modern
algebra. He had two periods of
original geometrical work. The
first began in 1826 (the year of
the revival of mathematics in Ger-
many), and closed in 1846. His
mathematical researches were little
noticed in his own country, where-
as in France, and still more in

England, his name was well known.
After having published in 1846 a
'System of Geometry,' which con-
tained his former results in a more
methodical form, he dropped his
mathematical researches for twenty
years, during which time he devoted
himself to phj'sical investigations of
great originality. By these, if he
had not been a personal friend, he
might almost have been called a
rival of Faraday (G. Chrystal in
'Ency. Brit.') During a visit to
England in 1864 he was agree-
ably surprised to meet with ap-
preciative interest from English
geometricians, who had independ-
ently worked on the same lines as
he had done twenty years earlier.
He was thus induced to resume his
favourite studies, and to develop an
idea which had already been expres-
sed in his last-named work of 1846.
This led to a new fundamental con-
ception of geometrical forms, in
which not the point but the line
is the element of space. He was
not spared to complete this line-
geometry, but after his death his
pupils found sufficient material to
put his researches into a systematic
form under the title, ' Neue Geo-
metrie des Raumes, gegriindet auf
die Betrachtung der geraden Linie
als Raumelement' (Leipzig, 1868
and 1869). See Clebsch on Julius
Pliicker, Gottingen, 1872. A very
appreciative notice of Pliicker, by
George Chrystal, will be found in
the 9th edition of the ' Encyclope-
dia Britannica. '

THE SCIENTIFIC SPIRIT IN ENGLAND.

243

Grassmann, in his ' Aiisdehnimgslehre,' published in 1844, i5.

Grassmann,

is now generally admitted to have originated quite a novel
way of considering geometrical relations,^ It took twenty
years, however, before he succeeded in attracting any at-
tention, and his great work, of which the first edition had
been sold as waste-paper, was later on reprinted in its
original form — mathematicians having now begun to study
and recognise its intrinsic value. Such cases of neglect
have undoubtedly been much more frequent in England,
where even at the present day no central organisation le.

^ J o Central or-

exists which annually collects and arranges the scattered ^^^^ntf^""?
labours of individual workmen, and where that historical ^°siand.
and encyclopa-dic spirit is wanting which does its utmost
to guarantee completeness and thoroughness of search
and of research. Men of the greatest eminence, pioneers

^ Hermann Grassmann (1809-77)
■was born, lived, and died at Stettin.
He did not succeed till late in life,
and fully thirty years after he had
published his original investigations
in geometry, in gaining for these the
recognition and appreciation which
they deserved. Neither he nor even
Jacob Steiner at Berlin attained to
positions worthy of their ability ;
the latter, in spite of his connec-
tion with other great mathemati-
cians, never filled the chair of an
ordinary professorship, whilst the
former never entered the sphere of
university teaching at all. The
* Ausdehnungslehre,' as a new
branch of mathematics, appeared
in 1844. It is a science of pure
extension, the application of which
to empirical space is geometry.
Similar investigations, in which
space of three dimensions is con-
sidered to be merely a particular case
of pure extension of any number of
dimensions, which are not neces-
sarily determined by the same pro-

perties as our empirical sijace, have
become familiar since the publica-
tion of Riemann's celebrated disser-
tation of 1854 (published in 1867),
and since Helmholtz was led to
similar investigations by consider-
ing the different dimensions or
manifoldnesses of our sense per-
ceptions (see his ' Vortriige und
Reden,' in many passages). Grass-
mann, who at the end of his life
witnessed the growing appreciation
of his ideas, had filled up the in-
terval with entirely different studies,
the translation of the ' Rig-Veda '
(Leipzig, 1876-77), and the compo-
sition of a dictionary to the same
(1872-75). He seems to have been
the only mathematician, besides
Thomas Young, who combined the
ability for exact mathematico-
physical and for philological studies.
Both can complain of having been
very insufficiently appreciated by
their contemporaries. See Victor
Schlegel, ' Hermann Grassmann,'
Leipzig, 1878.

244

SCIENTIFIC THOUGHT.

17.
Thomas
Young.

in their line of thought and discovery, have to the present
day remained popularly unknown to their countrymen,
who have not only neglected but reviled them, allowing
their great discoveries to be taken up as their own by
foreigners. Such was Dr Thomas Young, whom many
educated persons at the present day cannot distinguish
from the author of ' Night Thoughts.' ^ The great founder

1 Thomas Young (1773-1829), a
native of Somensetshire, attained
equal eminence by his discoveries
in connection with the uudulatory
theory of light, in which he was
the first to assert the principle of
interference and that of transverse
vibrations, and by his discovery
of the key to the system of hiero-
glyphics. Of his discoveries and
suggestions some were published in
anonymous review articles (so es-
pecially his hieroglyphical papers) ;
some in his Lectures on Natural
Philosophy, delivered early in the
century at the Royal Institution,
and published 1807 ; some in the
' Transactions of the Royal Society '
(from 1800 onwards) ; and some in
various collective works, especially
the ' Encyclopedia Britannica.' The
remarkable fact that Young, of
whom Helmholtz says (' Vortriige
unci Reden,' vol. i. p. 279) that he
came a generation too soon, re-
mained scientifically unrecognised
and popularly almost unknown to
his countrymen, has been explained
by his unfortunate manner of ex-
pression and the peculiar channels
through which his labours were an-
nounced to the world. His fre-
quently unintelligible style, his ob-
scure and inelegant mathematics,
the habitual incognito which he pre-
served, his modesty in replying to
attacks, and his general want of
method in enunciating his ideas, con-
trast very markedly with the writ-
ings of some of his rivals, especially

in France, where the qualities of
style, method, and elegance were
highly developed, and where recog-
nised organs existed for the pub-
lication of works of genius. The
historian of thought, however, must
not omit to state that several great
names contributed, by the author-
ity they commanded, to oppose
Young's claims to originality and
renown. Lord Brougham, shielded
by the powerful anonymity of
the ' Edinburgh Review,' and osten-
tatiouslj' parading the authority of
Newton, submitted the views of
Young to a ruthless and unfair
criticism, the popular influence of
which Young probably never over-
came. The great authority on op-
tics, Brewster, who has enriched
that science by such a number of
experiments and observations of
the first importance, never really
adopted the theories of Young and
Fresnel. In the other great branch
of research with which Young's
name is now indissolubly connect-
ed, in the science of hierogh'phics,
the authority of Bunsen decided
against Young and for the French-
man Champollion. But this de-
cision, which did so much to ob-
scure the merits of Young, was
founded on an insufficient know-
ledge of the dates of Young's pub-
lications. Since these were collect-
ed by Leitch in the third volume
of the ' Miscellaneous Works ' of Dr
Young (London, 1855), the chrono-
logy of his discoveries, which begin

THE SCIENTIFIC SPIRIT IN ENGLAND.

245

of modern chemistry, who next to Lavoisier did more
than any one else to introduce into this science mathe-
matical ideas, John Dalton, grew old and infirm before
his countrymen sufficiently recognised and honoured him.
Deprived of all but the very meanest apparatus for the
proofs of his theories, and yet able to do what he did,
what might not such a genius have accomplished if he
had possessed the means of a Gay-Lussac or a Eegnault ? ^

18.
Dalton.

in 1814, has been well established.
See Benfey, ' Geschichte der Sprach-
wissenschaf t ' (Miinchen, 1869, p.
729). Bunsen pronounced his ver-
dict in his well - known woi'k,
' Egypt's Place in Universal His-
tory,' published in 1845-57. On the
whole, the words of Peacock, ' Life
of Dr Young' (London, 1855), p.
472, are still correct : " His scien-
tific works were rarely read and
never appreciated by his contem-
poraries, and even now are neither
sufficiently known nor adequately
valued ; whilst if justice was award-
ed more promptly and in more lib-
eral measure by his own countrymen
to his hieroglyphical labours, these
also were singularly unfortunate, as
far as concerned the general diffu-
sion of his fame, by coming finto
collision with adverse claims, which
were most unfairly and unscrupu-
lously urged in his own age, and
not much less so by some distin-
guished writers in very recent
times."

1 John Dalton (1766 - 1844), a
native of Cumberland, spent the
greater part of his life in teaching
elementary mathematics at Man-
chester, first at a college and then
privately. In 1801 he propounded
the law known under the joint name
of Dalton and Gay - Lussac (who
stated it six months later). In the
years immediately following he ela-
borated his atomic theory, which
was to account for the existence of

those definite quantitative relations
between the chemical constituents
of bodies known already to Richter.
It was published in 1805. But the
man who did most to make known
to chemists the ideas of Dalton was
Thomas Thomson (1773-1852), Pro-
fessor of Chemistry at Glasgow, who
in 1807, in the -Srd edition of his
' System of Chemistry,' gave an ac-
count of the atomic theory based
upon communications of Dalton.
Two memoirs published in the
' Philosophical Transactions ' of
1808 — one by Thomson on "Oxalic
Acid," and one by Wollaston on
"Super- Acid and Sub- Acid Salts"
— pointed to the great importance
of the atomic theory, which (Wol-
laston prophetically added) would
not stop short witli the determin-
ation of the relative weights of
elementary atoms, but would have
to be completed by a geometrical
conception of the arrangement of
the elementary particles in all the
three dimensions of solid exten-
sion. The real merit of having ex-
perimentally proved the theory of
Dalton belongs to Berzelius, whereas
Sir Humphry Davy opposed it for
many years after it had been ac-
cepted abroad. Dalton himself by
no means followed the development
which his ideas underwent at the
hands of others. For example, he
opposed Gay-Lussac's law of vol-
umes. He was on the whole more
successful in working out his own

246

SCIENTIFIC THOUGHT.

19.
Faraday.

20.
Green.

Faraday, instead of being backed by a wealthy Academy
and ample assistance, had during all the years when his
great discoveries were being made, to keep alive, with an
income scarcely exceeding a hundred pounds a-year, an
institution which but for him the memory even of such
names as Rumford, Young, and Davy would not have
sufficed to preserve from utter ruin and collapse/ The
author of one of the most suggestive treatises in the
application of mathematics to physical phenomena,
George Green, published it in 1828 at Nottingham by
private subscription. Seventeen years later, William
Thomson (Lord Kelvin) tried in vain to procure a copy

ideas than in comprehending those
of others who, like Berzelius, Mits-
cherlich, Laplace, Liebig, and many
later, contributed to the confirma-
tion of the atomic theory. A good
account of this is given in Henry's
« Life of Dalton ' (1854) and in
Kopp's ' Entwickelung der Chemie
in der neueren Zeit ' (Munchen,
1873).

1 Michael Faraday (1791-1867),
though not a mathematician, intro-
duced into the science of electricity
those ideas which have since been
developed into a mathematical the-
ory approaching in completeness the
mathematics of the undulatory the-
ory of light. What the atomic the-
ory has done for chemistry, Fara-
day's lines of force are now doing for
electrical and magnetic phenomena.
Dalton, though unacquainted with
the higher mathematics of the
French school, had essentially a
mathematical or arithmetical mind.
Faraday's peculiar ideas on the
nature of electrical and magnetic
action, though supported by an ex-
perimental knowledge many times
surpassing in volume and accuracy
that of Dalton, did not find much
appreciation among his contem-

poraries. They were much more
interested in his experimental re-
searches than in his theories. In
France and Italy Faraday's eminence
was recognised early. Already in
1823 he was elected member of the
Academies of Paris and Florence,
almost before any society at home
had received him. "The circum-
stances under which Faraday's work
was done were those of penurj'.
During a great part of the twenty-
six years the Royal Institution was
kept alive by the lectures which
Faraday gave for it. ' We were
living,' as he once said to the
managers, ' on the parings of our
own skin.' He noted even the
expenditure of the farthings in
research and apparatus. He had
no grant from the Royal Society,
and throughout almost the whole
of his time the fixed income which
the Institution could afibrd to give
him was £100 a-year, to which the
Fullerian professorship added nearly
£100 more" (Bence Jones, 'Life and
Letters of Faraday,' London, 1870,
vol. ii. p. 344). See also Bence
Jones, ' The Royal Institution,'
p. 311.

THE SCIENTIFIC SPIRIT IN ENGLAND.

247

of this document, of which he knew by a reference in
another work. At last he got possession of a copy which
had probably during all this time been buried in the
library of a prominent mathematical tutor at Cam-
bridge, with whom he had been in frequent intercourse.
Thomson then took it with him to Paris, where Sturm
and Liouville at once recognised its merits. He then
published it in ' Crelle's Journal,' where it has ever
since been referred to as a fundamental essay on the
so-called potential theory,^ One of the most original
thinkers on mathematics, who introduced a novel prin-
ciple into algebraical science, George Boole, never at- 21,

Boole.

tained to a higher position than that of teacher at a
remote Irish provincial College.^ But perhaps the most
signal example of the want of support which the

^ See note 1 to p. 231 ; also Sir
William Thomson, reprint of papers
on " Electrostatics and Magnet-
ism," 2nd ed., London, 1884, p. 2,
note ; p. 126, note.

^ George Boole (1815-64), a native
of Lincolnshire, was one of the few
great and original mathematicians
who, like Leibniz and Grassmann,
and to some extent Gauss, looked
at the logical as well as the purely
arithmetical side of the language
of symbols. Though his treatises
on 'Differential Equations' (1859)
and on 'Finite Differences ' (I860)
have become well-known text-books,
and his 'Laws of Thought' (1854),
in which he examined the found-
ations of the mathematical theories
of logic and probabilities, remains a
unique work, his principal services
to science lie in the direction of
the "calculus of operations." In
this branch of mathematics, which
is peculiar to England, the sym-
bols indicating an arithmetical op-

eration are separated from those
denoting quantity and treated as
distinct objects of calculation. In
connection with these investiga-
tions, many of which have now
penetrated into ordinary text-
books, Boole was led to examine
the conditions under which and the
forms in which algebraical expres-
sions, whilst undergoing changes
and transformations, remain, never-
theless, unaltered (invariant) (1841).
By introducing this point of view
he has, so to speak, created modern
algebra ; founding the extensive
and fruitful science of "Invari-
ants." Of this we shall treat
later on. I now only refer to the
further development of this sub-
ject in the hands of Cay ley and
Sylvester, and to the valuable
sketch of the history of this branch
of mathematics by Dr F. Mayer in
the first volume of the 'Jahres-
bericht der deutschen Mathemati-
ker-Vereinigung,' Berlin, 1892.

248

SCIENTIFIC THOUGHT.

U2.
Babbage.

wealthiest of nations has shown to scientific genius is
to be found in the history of Babbage's calculating
engine. Yet this machine was approved by all experts
— English and foreign — during the inventor's lifetime ;
and the Eeport of a Commission of the British Asso-
ciation appointed specially to examine into the matter,
concluded by stating that the scheme was perfectly feas-
ible, and might, if carried out, mark an invention as great
probably as that of logarithms.^ Who among us who
has been interested in the promotion of institutions for
higher education has not a story to tell of pecuniary
troubles, continued through many a long year, whilst
the wealth of the country seemed to exert its influence
only in the direction of making the demands on a strug-
gling establishment more formidable, the expenses more
difficult to defray ? "

1 On Babbage see p. 233, note 1.
The history of the " difference en-
gines " and the " analytical engine "
is given by Babbage himself in his
' Passages from the Life of a Phil-
osopher. ' See also Weld, ' History
of the Royal Society,' vol. ii. p.
369, &c.

'^ Like the Royal Society, which
for a century had to struggle
with poverty, the Royal Institu-
tion has a story to tell of want
of funds through a long period of
its early existence. See Bence
Jones, ' The Royal Institution,'
London, 1871, pp. 202, 281. The
Royal Institution was founded by
Benjamin Thompson, Count Rum-
ford (1753-1814), and had origin-
ally not a scientific, hardly even a
higher educational object. The
scheme arose in the mind of its
founder after he had successfully
exerted himself at Munich under
the patronage of the Elector of

Bavaria in foundingindustrial work-
houses, improving the state of the
army, and putting down beggary
and immorality in the capital and
country. His jDrinciple was to
make " vicious and abandoned
people first hapjjy and then virtu-
ous" (p. 31). After leaving Mun-
ich in 1793 and spending two years
in Italy, similarly occupied, he
visited London in 1795 in order to
publish his Essays, which appeared
separately betwen 1796 and 1802.
The first essay contained "a pro-
posal for forming in London by
private subscription an establish-
ment for feeding the poor and giv-
ing them useful employment, . . .
connected with an institution for
introducing and bringing forward
into general use new inventions
and improvements," &c., &c. (p.
44). The first outcome of this was
the formation of a society for en-
couraging industry and promoting

THE SCIENTIFIC SPIRIT IN ENGLAND.

249

But it is hardly the duty of the historian of thought to
record that which belongs more to the impediments of
mental progress than to its promotion, were it not that
in and through these peculiar circumstances the genius
of the nation has developed its main features, its strong
character. These are manifest as much in the depart- 23.

Character-

ment of science as they are in general literature and in i^^c^of

"^ " English

the institutions of practical life. British science through thought.
all the centuries, since the time of Eoger Bacon, and
in spite of the efforts of his illustrious namesake, has[

the welfare of the poor. William
Wilberforce was one of the original
promoters ; Thomas Bernard, the
founder of many other charitable
institutions, one of its most active
members. To a committee of this
Society Count Rumford submitted,
in 1799, his proposals for forming
the Royal Institution, and it was
accordingly founded in February of
that year on j^rivate subscriptions
of fifty guineas each. It was de-
scribed as a " public Institution
for dififusing the knowledge and
facilitating the general introduc-
tion of useful mechanical inven-
tions and improvements, and for
teaching by courses of philosophical
lectures and experiments the appli-
cation of science to the common
purposes of life." In the course of
a very few years the original char-
acter of the Institution entirely
changed, the aim of influencing
directly the condition of the poor
was lost sight of, and little re-
mained besides the result of " bring-
ing science into some degree of
fashion " and "affording a new em-
ploj'ment and amusement to the
higher classes of life." The inter-
est of the Institution for the his-
tory of thought is the fact that in
its laboratory Davy and Faraday

conducted their researches, and that
they, as well as Young, Coleridge,
and Sydney Smith, there delivered
their lectures. And the history of
the Royal Institution is also typical
of the history of other establish-
ments for higher culture in this
country : it has been in its main
features repeated on a larger or
smaller scale in many provincial
societies, and notably in the col-
leges of Manchester, Bii'mingham,
Liverpool, Newcastle, Leeds, Bris-
tol, Nottingham, &c. Started bj-
persons with large but nevertheless
insufficient means, or by subscrip-
tions and endowments of moderate
extent, obliged to gain popularity
and fashionable support in order to
meet their growing expenses, these
institutions have depended mostly
on individual energy for their first
successes, and have all had to pass
through periods of great difficulty,
till in course of years they have
acquired a special character of use-
fulness and defined their peculiar
sphere of action. The absence of
a definite programme and a great
waste of energy and funds over
special departures are not un-
common features of these develop-
ments.

250

SCIENTIFIC THOUGHT.

24.
Absence of
schools of
scientific
thought.

refused to congregate in distinct schools and institutions
or to be localised in definite centres. The Eoyal Society,
the Eoyal Institution, the British Association, and many
other smaller societies, have all more or less started with
the programme of Lord Bacon, and have failed to realise
it : everywhere the schemes of co-operation or organised
scientific research have encountered the opposition of
individual pursuits or of local interests.

Newton could not secure the use of Mamsteed's obser-
vations, which on their part remained uncompleted and
unpublished through the want of appreciation of others.
Great schemes in practical life have been carried out
by the unaided efforts of eminent persons, and great
ideas have been put forward with all the power and
all the resources of individual genius,-^ but no great
master in scientific research in this country can point
to a compact following of pupils — to a school which
undertakes to finish what the master has begun, to carry
his ideas into far regions and outlying fields of research,
or to draw their remoter consequences. Newtonianism
was a creation of Voltaire ; the school of Locke is to be
found in France ; the best realisation of Bacon's schemes
are the Encyclopedic, the French Institute, and the
foreign Academies.^ Dr Young's discoveries in optics

1 See Huxley. ' Lay Sermons,
&c.,' edition of 1891, p. 43 : " Eng-
land can show now, as she has been
able to f-how in every generation
since civilisation spread over the
West, individual men who hold
their own against the world, and
keep alive the old tradition of her
intellectual eminence. But in the
majority of cases these men are
what they are in virtue of their

native intellectual force, and of a
strength of character which will
not recognise impediments. They
are not trained in the courts of
the Temple of Science, but storm
the walls of that edifice in all sorts
of irregular ways, and with much
loss of time and power, in order to
obtain their legitimate positions."
- See above, pp. 34, 95.

THE SCIENTIFIC SPIEIT IN ENGLAND.

251

and hieroglyphics were made known to the learned world
through his French contemporaries. Dalton/ Charles
Bell," Faraday, Darwin, and Maxwell, no less than
Bentley and Gibbon," have furnished the text for lecture-
courses in German universities, and created a whole
literature of pamphlets and scientific memoirs.^ English
societies may sometimes honour and admire, but they do
not support, their great representatives, and these them-
selves often refuse to be tied by exclusive academic
duties, still more by official restrictions. Two charac-
teristics have marked most of them : they have, at all
expense and sacrifice, guarded their individual freedom 25.
of thought, and they have almost always shown a great character

and practi-

desire to combine some application with their abstract caitendency

. ^ ^ of English

researches, to take part in the great practical work of ^"""ce.
the nation. Continental thinkers, whose lives are devoted
to the realisation of some great ideal, complain of the
want of method, of the erratic absence of discipline, which
is peculiar to English genius. The fascination which
practical interests exert in this country appears to them
an absence of full devotedness to purely ideal pursuits.^

^ See above, p. 245, note.

- See above, p. 193, note.

^ See above, p. 169, note.

•* Germany may be said to have
produced Darwinismus in this cen-
tury as France created Newtonian-
isme in the last. Huxley writes
('Life of Darwin,' vol. ii. p. 186) :
" None of us dreamed (in 1860)
that in the course of a few years
the strength (and perhaps I may
add the weakness) of Danoinismus
would have its most extensive and
most brilliant illustrations in the
land of learning." Quite recently
Prof. Boltzmann at Munich, and
M. Poincarc, have published courses

of lectures on Maxwell's electric
theories.

^ What appears irksome to an
English genius — the red tape of
academic restrictions, the barriers
of officialism, and the duties of the
teacher — melted away in the glow
of enthusiasm and love of truth
which animated the great leaders
and founders of university culture
abroad ; as Goethe has told us that
the rigid form of the sonnet melts
in the fervour of the love-song :

" Das AUerstarrste freudig aufzuschmel-

zen
Muss Liebesfeuer allgewaltig gUihen."
— Sonette No. 14.

252 SCIENTIFIC THOUGHT.

The English man of science would reply that it is unsafe
to trust exclusively to the guidance of a pure idea, that
the ideality of German research has frequently been
identical with unreality, and that in no country has so
much time and power been frittered away in following
phantoms, and in systematising empty notions, as in the
Land of the Idea ; but he would as readily admit that
his own country is greatly deficient in such organisations
for combined scientific labour as exist abroad, and that
England possesses no well- trained army of intellectual
workers.
26. These differences between English and Continental

English pe- "

cuiiarities scieucc wcrc most prouounced in the first half of the

more pro- ^

during'^tariy prescut ccutury, when Germany developed her university
cciitiiry. ^^ system, when France clearly defined the exact scientific
methods, and when the encyclopaedic view — peculiar to
the historical and philosophical pursuits of the earlier
years — gradually became dominant in the exact sciences
also. Since then the intercourse of the different nations
has done much to destroy these national peculiarities.
The reform of the universities, in which Germany was
engaged in the early years of the century, did not touch
the English universities before the middle of the century.
In the meantime quite different demands had sprung up
all through the civilised world ; and as nothing repeats
itself in history, it will be impossible to reach in this
country the same broad organisation for purely intellec-
tual work as Germany can rightly boast of during the
period we are dealing with. Some persons doubt whether
it will be maintained in Germany. It appears still more
doubtful whether such an organisation could now be

THE SCIENTIFIC SPIRIT IN ENGLAND.

253

created in the face of the industrial spirit of our age. Ever
since the latter half of the eighteenth century schemes for
a general education of the masses have attracted the
thought and the attention of philanthropists and states-
men in many countries of Europe. But the directions
taken by these educational efforts have been character-
istically different in the different countries, and their suc-
cess, so far as the great masses of the people are con-
cerned, has been very partial indeed. It is true that
during the first thirty years no country possessed such
distinguished schools of science as did France in the great
scientific and medical institutions of her capital. It is
also true that no country equalled Germany in her system
of universities and higher schools, which had come under
the influence of classical learning and philosophical ideals.
England, which at that time took no part in the educa-
tional movements of the Continent,-^ possessed, neverthe-

^ This statement requires two
qualifications. Firstly, both Milton
and Locke have had great influ-
ence in spreading enlightened views
regarding the principles and the
object of education in general —
especially in the direction of en-
larging the idea of education, so as
to make it comprise something more
than merely instruction and pedan-
tic teaching. I cannot find, how-
ever, that in England, either in the
direction of higher university edu-
cation or of a general system of
popular education, their influence
has been very marked. Locke's
influence abroad, through his psy-
chological analysis of the mind, has
been very considerable. Secondly,
in the direction of practical educa-
tion, of the endeavour to reach
large numbers of the people by
educational institutions, we must

look with admiration to the early
work done in Scotland, whicli in
this respect somewhat resembles
Switzerland. The Scotch system of
parochial schools, and their influence
on the education of the people,
has been too little studied abroad,
though rightly extolled at home. It
is true that, with the exception of
Calvin, none of the great Continen-
tal educationalists — such as Fene-
lon, Rousseau, Pestalozzi, or W.
von Humboldt — have had any di-
rect influence on Scotland ; nor has
the educational work of Scotland
produced any great educational
literature like that which Switzer-
land can boast of, and which has
brought the theory of education
so prominently before the world.
But nevertheless there it stands,
this creation of John Knox and
the early Reformers. " Civilised

254

SCIENTIFIC THOUGHT.

27. less, somethincp peculiar in her two great universities.

Unique tj j. o

character of i{, ^as neither the scientific, nor the classical, nor the

English mil- ' '

versities. philosophical spirit exclusively which reigned there; if
any or all of them had ruled, we should not meet with
those repeated complaints that higher mathematics were
absent in Cambridge, that no philological studies were
cultivated in either of the universities, and that philosophy
was represented merely by Aristotle, Butler, Locke, and
Paley/ According to the representatives of the university

Europe has never witnessed a nobler
spectacle than the first Protestants
of Scotland in the assembly of the
nation demanding that from the
funds before abused by a licentious
superstition one - third should be
devoted, not to increase the re-
venue of the Reformed Church, but
to the education, the universal edu-
cation, of the youth in all depart-
ments of instruction, from the high-
est to the lowest" ('North Brit.
Rev.,' 12, p. 483).

^ As to the deficient mathemati-
cal teaching at Cambridge, see jd.
2-3.3, note, &c. The complaints re-
garding the teaching of other sub-
jects are frequent, but belong to a
later date, the middle of the century,
when the Royal Commission of In-
quiry, which was appointed under
the Government of Lord John Rus-
sell on the 31st August 1850 and
expired with the presentation of its
rejjort on the 30th August 1852,
attracted the attention of the pub-
lic to university reform, and gave
rise to a very full discussion of the
whole subject in the various litei'-
ary papers and reviews. The two
older universities are called " cita-
dels of political prejudice and sec-
tarian exclusiveness, instead of be-
ing the temples of liberal arts and
the repositories of science " (' Brit.
Quart. Review,' 1860, July, p. 205).
Theology is stated to be " the last

thing taught at Cambridge " (ibid.,
p. 221) ; ther-e was no professor of
Latin, none of English literature,
of logic and metaphysics, of modern
languages (p. 225). In 1849 Cam-
bridge had no laboratorj' ; the uni-
versities took no part in the legal
training of lawyers (' Edinb. Rev.,'
April 1849, p. 511) ; Oxford afforded
no ti-aining in natural science (ibid.)
Cambridge " sacrificed to the mon-
opoly of a severe geometry every
other exercise and attainment of
the human mind. There was no
theological study, no study of his-
tory, none of moral science, none of
chemistry, none even of experi-
mental philosophy" (ibid., p. 514).
These criticisms were fully justified
by the Reports of the Commissions
published in 1852. See on the teach-
ing of Theology at Cambridge, Re-
port, pp. 89, 102 ; Evidence, pp. 88,
168, 190, 216 : on the teaching of
Latin, Rep. , pp. 98, 102; Evid.,pp.
165, 176, 289 : on the teaching of
English, Evid., pp. 124, 136 : of mo-
dern Languages, Rep., pp. 26, 101;
Evid., pp. 165, 216, 300 : of Law,
Rep., pp. 35, 182 ; Evid., pp. 123,
190 : of Natural Sciences, Evid., p.
115, &c. In 1874 the 'Edinburgh
Review' could point out that during
twenty years, whilst the examination
for the Indian Civil Service had been
thrown open, the English universi-
ties had practically contributed no

THE SCIENTIFIC SPIRIT IN ENGLAND.

255

system, what England did possess was the ideal of a liberal 28.

"^ — Ideal of

education. But none of these three forms of intellectual Liberal Edu-

'. . ... cation.

training — neither the scientific in Paris, nor the classical
in Germany,, still less the liberal in England — touched
the great masses of the people. They all did good work
in their respective lines ; but they left, or would by them-
selves have left, the country in darkness. The begin-
nings of general popular education are to be traced
independently in Switzerland, in Scotland, and in many
of the small States of Grermany.-' The great scientific

candidates to the competition (April
1874, p. 342). " Nothing cabout uni-
versity life was more striking" to
the Edinburgh Reviewer "than the
contrast between the efforts and
the high aims of the few, the
culture and solid result achieved
by them — and the utter uselessness
of it to the many " (p. 354). The
'Quarterly Review' of June 1826,
notes "a growing taste for the
cultivation of physical science as
characteristic of the state of the
public mind in England" (p. 159),
and refers to the " measures which
have been carried into effect
throughout the country with great
harmony of design, although chiefly
by the unassisted exertions of pri-
vate individuals, . . . the recent
establishment of numerous literary
and philosophical institutions in our
metropolis and many of our pro-
vinces" (ibid., p. 154).

^ The great Reformers — Luther,
Melanchthon, Zwingli, and Calvin —
alike took a great interest in educa-
tion, which thej' intended to be uni-
versal and popular. But their suc-
cess, so far as the education of the
people was concerned, remained
everywhere very partial. A real or-
ganisation of primary schools was
not attained. They prepared for
it by introducing the vernacular

languages, the reading of the Bible,
the popular hymns. Their main
efforts lay in the training of good
teachers for church and schools in
the reorganisation of what were
called the Latin schools. In the
course of the sixteenth and seven-
teenth centuries the smaller Protes-
tant States of Germany — especially
Saxony, Wtirtemberg, Brunswick,
the northern cities Hamburg and
Liibeck — received under various
forms what was called " Eine Kir-
chen- uud Schulordnung." Luther's
tract of the year 1524, addressed
to the "burgomasters and coun-
cillors of all towns of the German
land, that thej^ should found and
maintain Christian schools," was
the beginning of this movement.
In Scotland burgh schools, also
grammar (or Latin) schools and
lecture schools, "in which the
children were instructed to read
the vernacular language," existed
long before the Reformation. But
to John Knox is due the scheme
for popular education contained in
the ' First Book of Discipline.' The
parochial schools were started in
many instances bj' voluntary or ec-
clesiastical assessment through the
efforts of the Reformed clergy.
The foundation of the subsequent
system of parochial schools was laid

256

SCIENTIFIC THOUGHT.

schools of France trained the civil and military engin-
eers in that country, and produced text -books for the

in the statute of 1696. It must
not be forgotten, however, that the
"Order of Jesus" (founded 1540),
whose higher educational work has
found so much appreciation from
men like Sturm — the Protestant
educationalist — Lord Bacon, and
Descartes (see the quotations in
Schmidt's ' Geschichte der Padaj^o-
gik,' 4th ed., vol. ii. p. 248), was also
active in the direction of popular
and jOTmary education. In emula-
tion of the Protestant movement,
it had introduced " school regula-
tions" in many Catholic countries,
and even founded a special order
• — the " Patres piarum scholarum "
(1600) — for the education of the
poorer classes (ibid., p. 253). Whe-
ther the statute of 1696 is the ear-
liest official document referring to
popular education and providing the
means of maintaining an adequate
number of schools (one in 1000 of
population) to teach the lower
classes, I cannot say. It appears
that Duke Ernest of Gotha, in the
course of the seventeenth century,
established a general system of
primary education in his terri-
tory which was "quite unique, at
first an object of ridicule, but then
very soon of emulation" (ibid., p.
333). The regulations were cer-
tainly most wise and liberal, and
attendance was made compulsory.
The question of popular education
was taken up on a much larger
scale by Frederick the Great in the
middle of the eighteenth century.
The year 1763, which marks the
end of the Seven Years' War, is
also the year of an edict which
forms the basis of the regulation
of popular education for the whole
monarchy : it establishes village
schools with compulsory attend-
ance. It met with much opposi-
tion, and its ends were only slowly

realised, and only as training-schools,
where a sufficient number of teach-
ers were educated, sprang up, and
as popular school and story-books
were provided. Campe, with his
edition of ' Robinson Crusoe,' marks
an epoch in this direction. In fact,
the cause of universal popular edu-
cation remained in the hands of
private persons, frequently of men
of great insight and organising
ability — such as A. H. Francke
(1663-1727), the indefatigable friend
of the poor and of orphans ; Base-
dow (1723-90), the founder of the
Philanthropin and populariser of
Rousseau's ideas ; Von Rochow
(1734-1805), the friend of the coun-
try - folk and founder of village
schools; Von Felbiger (1724-88),
the adviser of Maria Theresa and
Joseph II., the organiser of the
popular educational system in Aus-
tria (1770-80): or else it was de-
pendent on the casual favour of
enlightened princes and sovereigns.
At length, in the middle of the
eighteenth century, training-schools
for teachers, so-called " seminaries,"
were founded all over Germany. A
beginning had been made bv Duke
Ernest of Gotha (1601-75), but
had been neglected like many
other beginnings. But in the
second half of the eighteenth cen-
tury no less than thirty-three semi-
naries were founded all over Ger-
many, including Austria. For details
on this important and interesting
subject, see the third volume of
Schmidt's ' Geschichte der Piida-
gogik.' Frey tag's 'Bilder aus der
deutschen Vergangenheit ' also con-
tains many interesting details; but
above all I would recommend for
the countries of the west and south
of Germany the valuable researches
of C. T. Perthes contained in his
'Politische Zustiinde und Personen

THE SCIENTIFIC SPIRIT IN ENGLAND.

257

higher scientific training of the whole of Europe ; ^ but
no serious effort was made, during the brilliant days of
the First Empire, to secure for the nation the blessing of
a popular education. This state of things continued
under the Eestoration ; the real beginnings of an or-
ganised primary system are to be found in Guizot's
celebrated law of 183.3. In Germany the influence of
Pestalozzi and Zschokke in the south; of Basedow, Francke,
and the school of Kant and Herder, and, later, of Herbart
in the north, — stimulated many Governments to establish
a system of popular schools for the education of the masses,
and a system of seminaries for the training of a popu-
lar teaching staff. This movement was chiefly carried
on independently of the reform ■ of the universities and
higher schools, over which the ideal of Wissenschaft ex-
ercised a powerful spell. Under the latter were trained
the leaders and higher teachers of the nation, as well as
the members of the learned professions. The educational
influence of this ideal on the more gifted among the
student class was the very highest and best ; but it hardly

in Deutschland zur Zeit der fran-
zosischen Herrschaft,' 2 vols.,Gotha,
1862 and 1869. As unfortunately
this work, with its collection of
interesting and not easily accessible
facts referring to the inner history
of the German people, has no index,
I give the following references :
Compulsory education in Kur Trier
in 1712, vol. i. p. 225 ; in Kurmainz,
1750, vol. i. p. 19 ; popular educa-
tion in Baden, vol. i. p. 411 ; in
Bavaria, vol. i. pp. 436, 467 ; in
Wurtemberg, vol. i. p. 537 ; and the
chapter on Joseph II. 's school re-
form, vol. i. pp. 153-170. The sem-
inary or training-school being thus

VOL. I.

the centre and beginning of na-
tional education in Germany, as it
has also, with a different constitu-
tion, become the centre of scientific
work (see p. 214, note), it is inter-
esting to note that Scotland, so far
advanced in educational work, had
no real training-school for teachers
before Stow started his Normal
School in Glasgow (see ' Cham-
bers's Encyclopedia,' art. "Educa-
tion"), and that the "seminary"
for higher scientific work has to
this day not yet been introduced
into this country.

' See above, p. 44, note.

R

258

SCIENTIFIC THOUGHT.

29.

Union of
education
and instruc-
tion.

reached the multitude of less gifted minds, who always
gave themselves to bread-studies ; and it must necessarily
fail yet more when not only the future teachers and
leaders, but the masses of the nation, flock into the halls of
the universities. Imperceptibly a differentiation has taken
place in Germany between the educational work which
was meant to reach the people at large and the intellectual
instruction of a select few. But it is exactly this differ-
entiation of education and higher instruction which the
champions of a liberal education in England have desired
to avoid. ^ In France, very soon after Eousseau's time, dis-

^ The two developments in Ger-
many start from different centres.
The purely educational movement
began in Switzerland with Pestal-
ozzi (1746-1827). His forerunner
was Martin Planta (1727-1772), his
successors were legion, all over
Europe, including sovereigns, states-
men, and philosoijhers. He created
an enthusiasm for education, which
was to begin at home, not in the
school ; to depend on the influence of
the mother; to be founded on a re-
ligious spirit ; to direct itself to the
development of the body as much as
of the mind ; to rest primarily on ob-
servation and experience, not mainly
on memorj' and learning ; and then
to absoi'b the whole mind and the
entire man, not exclusively the in-
tellect. It was to begin from be-
low, not from above, with the
people, the poor, the unfortunate
and deserted ; on the part of the
teacher it was to be a sacrifice,
an end in itself, not a profession.
The greatest followers of Pestalozzi
were Von Fellenberg (1771-1844),
the founder of Hofwyl and other
industrial schools for poor and de-
serted children among the peasant
population of Switzerland ; Johan-
nes Falk (1760-1826), the founder

of a great number of houses for the
poor and the fallen, of the " So-
ciety of Friends in Need " ; J. H.
Wichern (1808-1881), the founder
of the " Raulie Haus " near Ham-
burg ; lastly, the celebrated Frobel
(1782-1852, a native of Thiiringen),
the founder of the Kindergarten.
The other — not to say opposite —
development was centred in F. A.
Wolf, in whose school the ideal of
Wissenschaft with its enormous in-
fluence on universities and high
schools was elaborated. In the
history of this development, with
which our second chapter dealt,
the name of Pestalozzi does not
occur. The term "pojjular" vi'as
for a time banished as identical
with the liavavaia of the ancient
Greeks. The two movements find
a connecting-link in the extra-acad-
emical, the classical literature of
Germany, notablj' of Herder and
Goethe, to whom we must add
Fichte and Schleiermacher. The
present age is working towards
a fusion of both interests, of the
educational and higher scientific,
the bridging over of tlie gap which
had been left ; it is trying to re-
move the estrangement which ex-
isted in the middle of the century.

THE SCIENTIFIC SPIRIT IN ENGLAND.

259

cussions on educational matters confine themselves to the
ends and means of general or higher instruction ; ^ in

We may say that no educational
•scheme can be permanently satis-
factory that does not regard with
equal favour, aud does not find equal
room for, the two ideals of Pestal-
ozzi and Wolf. It is interesting,
however, to note that neither in
Switzerland nor in Scotland, the
two countries in which popular
education has been longest at
home, do we find a reallj' great
development of the higher institu-
tions and centres of learning ; the
universities in these two countries
have alwaj's stood somewliat in the
relation of higher schools to the
rest of the educational establish-
ments ; but both countries have
produced and reared some of the
greatest geniuses of all time — geni-
uses wlio have given to German
and English literature and science a
fame over the whole world and for
all ages ; they would have sufficed,
had they stayed at home, to form
academies and universities of the
first order.

^ Compare chapter i. pp. 112, 142,
&c. We are indebted to France
for three great educational influ-
ences which have left indelible traces
over the whole domain of European
thought. These proceed from the
Paris University, the model of higher
education ; the great school of Port
Royal, that model of secondary
education ; and the ' Emile ' of
Rousseau, which gave to the edu-
cational aspirations of Basedow, of
Kant, and of Pestalozzi a definite
direction. It has, however, fre-
quently been stated that the val-
uable side of Rousseau's ideas
was developed outside of France.
" C'est une chose remarquable,"
says M. Compayre, "que I'influence
du philosophe de Geneve se soit
surtout exerc^e a I'ctranger, en
Allemagne et en Suisse " (' His-

tou-e critique des Doctrines de
r Education en France,' 5'""^ ed.,
1885, vol. ii. p. 101). "II y avait,
chez Rousseau," says M. Breal,
" un cote genereux et vivifiant :
I'amour de I'humanite et particu-
lierement de I'enfant, la confiance
dans ses facultcs et le respect de son
activity intellectuelle. Cette partie
111, qui etait le germe de vie ddpose
dans les oeuvi-es de Rousseau, nous
I'avons laissee aux etrangers." In
French writers a great deal of dis-
cussion is to be found on the differ-
ence between education and in-
struction. Duclos (1704-72) in his
celebrated ' Considerations sur les
moGurs de ce siecle' (1751), in
the second chapter, which treats of
Education and Prejudice, says : " On
trouve parmi nous beaucoup d'in-
struction et peu d'education. On
y forme des savants, des artistes
de toute espece ; chaque partie des
lettres, des sciences et des arts y
est cultivee avee succes, par des
methodes plus ou moins conven-
ables. Mais on ne s'est pas encore
avise de former des hommes, c'est
a dire, de les elever respectivement
les uns pour les autres, de faire
porter sur une base d'education
gdnerale toutes les instructions par-
ticulieres," &c. When the successive
Governments of the Revolution took
up the question of a national edu-
cation, the formula of Condorcet
quite inevitably became more and
more the leading principle. Con-
dorcet distinguished " instruction "
— i.e., knowledge positive and cer-
tain, truths of fact and calculation
— from " education " — i.e., " politi-
cal and religious belief s. " He gives
the State the power to extend the
former, whilst he denies it the right
to direct and dispense the latter (see
Hippeau ' L'Instruction publique
en France pendant la Revolution,'

260

SCIENTIFIC THOUGHT.

Germany, education and higher instruction present in-
dependent developments ; in England alone the genius
and language of the nation have refused to admit of any
curtailment of the original sense of the word. This con-
tinued to imply a discipline of the character as well as
of the mind, practical as well as intellectual training.
So much has been said in this country and abroad re-
garding the shortcomings of the English universities and
higher schools, that I feel it a duty to point to the posi-
tive gain which this ideal of a liberal education ^ has

ISSl, vol. i. p. xvii ; also Compayre,
loc. cit., vol. ii. p. 280, &c. ) Every
Government which has attempted
to systematise, to ceiitrali&e educa-
tion, has been forced also to secu-
larise it, to reduce it to instruction,
leaving out what many consider the
central problem of education, the
training of the character and the
discipline of the feelings and the
heart. Considering the large organ-
isations which have been developed
in England by the unaided efforts
of working men, such as the trade-
unionsand the co-operative societies,
and looking at the amount of self-
government, self-control, and self-
denial which they demand from
their members, one might be tempt-
ed to say that England is the best
educated, though it may be the
worst taught and the least informed,
of the three nations now under
review.

^ The term "liberal education"
has acquired a peculiar significance
in the history of English culture
and thought. It cannot be trans-
lated into French or German with
any certainty that the real signifi-
cance of the term or the subject
which it denotes is conveyed. It is
interesting to note how each of the
three nations has given to special
words of the once common Latin

language a peculiar pregnancy, de-
noting a peculiar form of thought
or culture which they have especi-
ally elaborated. Thus " science "
in the modern sense is a product of
French thought, Wissenschaft a pro-
duct of German thought. England
has reserved to itself the elabora-
tion of a " liberal education."' I ani
at a loss how to translate it into
French, unless I am permitted to
use simply the word education in
its contrast to instruction and en-
seignemcnt, not as this was defined
by Condorcet, but as it is under-
stood in the writings of modern
French educationalists, such a.s
Greard, Breal, Compayre, and
others. To convey the meaning
of " liberal education " to a Ger-
man, I would revert to the Greek
phrase, the eAfvd^ptos TraiSeia of the
post - classical age. The fact is
that down to the middle of the
century the Germans in discussions
on the work of universities and
high schools always talk of Wissen-
schaft, English writers always talk of
"liberal education." To a German
scholars heart Wissenschaft is dear
beyond anything ; to an English
university man it is " liberal edu-
cation." The former will sacrifice
everything to Wissenschaft ; the
latter will not ])art with "liberal

THE SCIENTIFIC SPIRIT IN ENGLAND.

261

been. For it is the principal object of this work to
attempt to portray the actual progress of thovight, the
valuable contributions of each of the three nations to the

education." In German}', the real
home of the educationalist or Er-
zieher has not been the university ;
the home of the man of science has
not been and is not the universitj'
in England. The German educa-
tionalist can point to a special crea-
tion of his own, the Volksschule.
The English man of science has
no organisation to jjoint to except
it be the select society of a dozen
great names of world-wide fame,
corresponding to the solitary and
unconnected heights of Homer, So-
phocles, Dante, Shakespeare, and
Goethe in literature. To descend,
however, from generalities to the
real thing, 1 give here some ex-
tracts referring to English univer-
sity life, chosen from among hun-
dreds, all variations on the same
theme. Dr Thomas Young, who
knew both German and English
universities, having studied at Got-
tingen and taken his degree at
Cambridge, was not indebted to
any university for his position or
his knowledge ; yet he significantly
defends the English universities
against the criticism of the Edin-
burgh Reviewer : " We do not in-
tend to imply a censure of the
system adopted by our universities ;
. . . for it must be remembered
that the advancement of learning is
by no means the principal object of
an academical institution : the diffu-
sion of a respectable share of in-
struction in literature and in the
sciences among those classes which
hold the highest situations and have
the most extensive influence in the
State is an object of more import-
ance to the public than the dis-
covery of new truths. . . . We
think that we have observed num-
erous instances, both in public life

and in the pursuit of natural know-
ledge, in which great scholars and
great mathematicians have reasoned
less soundly, although more ingeni-
ously, than others, who, being some-
what more completely in the pos-
session of common-sense, . . . were
still far inferior to them in the re-
finements of learning or of science "
('Quarterly Review,' May 1810,
reprinted in Miscellaneous Works,
vol. i. p. '23.5, &c.) I shall now
give a quotation from an entirely
different source, from one who in
his department was equally well
acquainted with German and Eng-
lish thought and life. In 1830 E.
B. Pusey attempted to give his
friend, Prof. Tholuck of Halle, a
sketch of what had been "recently
done in English theology." He
begins by referring to the "prac-
tical character of the nation " and
" the different condition of the uni-
versities," and then continues as
follows : " Few, if any, of our writ-
ings have originated in an abstract
love of investigation : our greatest
and some immortal works have
arisen in some exigencies of the
times. ... A German writes be-
cause he has something to say ; an
Englishman only because it is, or
he thinks it is, needed" ('Life of
Pusey,' vol. i. p. 238). The man
who did most for the widening of
the circle of university studies in
England during the first half of the
century was William Whewell (1794-
1866), whose influence at Cambridge
extended over more than a genera-
tion. In the beginning he assisted
the movement begun by Babbage,
Herschel, and Peacock, and pub-
lished several text -books on me-
chanics and dynamics, in which the
influence of Continental, especially

262

SCIENTIFIC THOUGHT.

30.
Educational
organisa-
tions in
Ensland.

general stock of ideal possessions, not merely to criticise
the shortcomings and failures of separate schools of
thought, or separate sources of mental development.
Only in the aggregate of these different ideals is to be
found the inventory of the intellectual possessions, the
outcome of the higher work of the century.

When the modern scientific methods and their impel-
ling force, the mathematical spirit, made their way from
France to Germany during the first quarter of the century.

French models, can be clearly traced.
Between 1830 and 1850 his influence
exerted itself in two directions,
firstly by the publication of his
' History of the Inductive Sciences '
(3 vols. 1837 ; a second edition ap-
peared in 1847, a third in 1857), and,
secondly, by a series of papers and
pamphlets referring to university
education. As the ideal and defini-
tion of this Whewell adopts the term
" liberal education." The first of
these papers appeared in the 'British
Critic' (No. 17, 1831, "Science of
the English Universities "). Then
followed in 1836 "Thoughts on the
study of Mathematics " ; " Addi-
tional Thoughts," 1836; "On the
Principles of English University
Education " 1837 ; " Of a Liberal
Education in General" (Part 1,
18-15 ; Part 2, 1850 ; Part 3, 1852).
The second part of the little work on
Liberal Education gives a history
of the various changes previous to
1850 through which the University
of Cambridge tried to meet the
growing demands of the times for
a wider and more liberal programme
of higher scientific work. In these
various writings the work of educa-
tion and "original research" (a term
introduced by Whewell— see Tod-
hunter, ' Life of Dr Whewell,' vol. i.
p. 50), the nature of "permanent"
and "progressive" studies at the
universitj', of "university" and

"college" education, of "tutorial"
and "professorial "teaching, are fully
discussed. In the course of thirty
years the university of Cambridge
added to the examinations for ma-
thematical honours the " Classical "
Tripos (1822), the " Moral Sciences "
Tripos and the " Natural Sciences "
Tripos (1848); also a "Board of
Mathematical Studies" (1848). Dr
Whewell's great influence declined
when in 1850 Royal Commissions
were appointed to "inquire into
the state, discipline, studies, and
revenues of the universities of Ox-
ford and Cambridge." He "regarded
the Commission as an unw-arranted
and undesirable intrusion into the
affairs of the university." The
results of this inquiry belong to
the second half of the century.
Although this movement, which
was brought about by many in-
fluences, has somewhat changed the
issues, the central idea which in
England tries to assimilate the
higher work and thought of the
nation is that of education. The
term liberal education, which for
twenty j^ears, from 1830 to 1850,
formed the banner of university
reform, has since somewhat yielded
to "scientific," and more recently
to "technical," education; the in-
fluence of the universities has gone
out in the work of university exten-
sion in the provincial towns ; still

THE SCIENTIFIC SPIRIT IN ENGLAND.

263

they there met with a powerful intellectual organisation,
the German university system, in which classical and philo-
sophical studies had elaborated the ideal of Wissenschaft
— of science in the larger sense of the word. Gradually,
and not without opposition, the exact or mathematical
spirit was received into this system, and has since become
an integral portion of it. In England the older traditions
which clung to the two great universities, and the higher

the whole movement can be de-
fined as an feducational movement.
Whereas in Germany about a gen-
eration earlier the term Wissenschaft
gained the upper hand and governed
the intellectual life of the nation,
purely educational movements being
separated from it, in England the
purely scientific interest has never
gained the upper hand, and can
still complain of having nowhere a
full and complete representation.
Around the writings of Whewell as
a centre may be grouped those of
A. Sedgwick (' A Discourse on the
Studies of the University of Cam-
bridge,' 1S:^;3, f)th ed., 1850); Sir
Wm. Hamilton (articles in the
' Edinburgh Review,' reprinted in
' Discussions on Philosophy, &c.,'
185.3) ; Sir John Herschel ('A Pre-
liminary Discourse on the Study
of Natural Philosophy,' 1831) ;
the criticisms of Lyell (' Travels
in North America,' 1845), and of
the 'Edinburgh,' 'British Quar-
terly,' and 'Westminster' Reviews
(' Edin. Rev.,' Ap. 1849, Jan. 1874,
'Brit. Quart.,' Nov. 1850, 'West.
Rev. ,' Jan. 1855). Whoever desires
to gain an insight into the different,
frequently diametrically opposite,
considerations which moulded and
governed the reconstruction of the
German university system on the
one side, and on the other side
widened in England the older ideas
of university education, should com-

pare the documents relating to the
foundation of the University at
Berlin in the beginning of this cen-
tury (collected by Rudolf Kopke,
' Die Griindung der Koniglichen
Friedrich - Wilhelms -Universitiit zu
Berlin,' Berlin, 1860) with the writ-
ings referred to in this note, and
centering in Whewell's pamphlets
and essays. The personification of
the German scheme was Wilhelm
von Humboldt, of whom Bockh
said in his ' Logos epitaphios ': " He
was a veritable statesman, pene-
trated and led by ideas — a states-
man of a Periclean greatness of
spirit. Philosophy and poetry, elo-
quence, historical, philological, lin-
guistic erudition, were fused in
him into undisturbed harmony and
wonderful symmetry." The re-
forming and revolutionary ideas of
Fichte, the classical ideals of Wolf,
the historical interests of J. Miiller
thehistorian,the literary interests of
Schlegel, the philosophical interests
of Schleiermacher, were combined by
Humboldt into a realisable scheme.
Stein said of him in 1810 : " Prussia
has intrusted the management of
her educational and scientific in-
stitutions to a man possessed of a
remarkable intellect and of great
firmness of character, and who
utilises these qualities in his sphere
of action with glorious loyalty "
(ibid., pp. 61, 62).

264 SCIENTIFIC THOUGHT.

practical interests of a select class which upheld those
traditions, prevented any of the Continental ideals, be
it the philological of F. A. Wolf, or the philosophical of
Fichte, or the scientific of Laplace and Cuvier, from
establishing themselves in the older seats of learning.
And they were, after all, the only organisations for higher
culture which possessed a historical character and con-
tinuity. Around these centres, partly in a friendly, more
frequently in a hostile spirit, other institutions, other
centres of culture and learning, had grown up. Let us
rapidly survey these more recent institutions. It is
hardly necessary again to mention the Eoyal Society,
which was an early offspring of the older universities, a
kind of overflow of the scientific interests from them into
31. the capital. More recent was the Royal Institution, the

The Royal ^ "^ . .

Institution, creation of that extraordinary man, Benjamin Thompson,
Count Eumford. Like the Eoyal Society, it was de-
pendent upon private subscriptions and on the popular
interest created by its lectures. These were very pro-
miscuous, exhibiting no plan or unity. In the early
years Dr Young and Davy lectured there, as well as
Coleridge and Sydney Smith. Later it became the home
of Faraday, and through him, and many other illustrious
lecturers, has done much to spread a taste for natural,
especially experimental, science, in the higher and cul-
tivated classes. It has been a means of diffusing the
scientific taste, more perhaps than the exact scientific
spirit, in the stricter sense of the word. Whilst its
lectures may have kindled in many a young listener the
love of scientific work, the Institution did not fulfil the
early intention of its founder, nor did its laboratory play

THE SCIENTIFIC SPIRIT IN ENGLAND.

265

the part of some of the great laboratories of Paris or of
Germany, in turning out a large number of well-trained
experimentalists. Davy may be said to have educated
Faraday, though he was suspected of having become
jealous of him, and Faraday declared he received only
one valuable suggestion from any member of his audience
during the whole course of his lecturing. It is the
strongly marked individuality of all these great men,
expressed in their persons, their lives, and their works,
rather than the character of the institution itself, which
has given celebrity and historical importance to the Eoyal
Institution. John Dalton's^ position in the Literary and 32.

:Manchester

Philosophical Society of Manchester was similar to that Literary and

'- '' Philosopni-

of Davy and Faraday in the Eoyal Institution ; and as '^^^ society.
Faraday can in some sense be called a pupil of Davy, so
can Prescott Joule "" be termed a pupil of Dalton, whom

^ See note, p. 245.

- James Prescott Joule (1818-
89), a native of Salford, " received
from Daltou his first inducement
to undertake the work of an ori-
ginal scientific investigator." He
was one of the first who tried to
measure electrical action in terms of
the units of well-known mechanical
or chemical changes. His publica-
tions began in 1840. Weber's ' Elec-
trodynamischeMaasbestimmungen,'
that great monument of exact meas-
urement, was published in 1846.
Mayer's first publication, contain-
ing a calculation of the mechanical
equivalent of heat, bears the date
1842. But the great i^ublication of
Gauss, in which he measures mag-
netic action in ordinary mechanical
(or absolute) units, dates from 1832 :
' Intensitas vis magnetics; terrestris
ad mensuram absolutam revocata '
(Comm. Societ., Getting., 1832, &c.)

Joule in 1843 published the first
of his accurate determinations of
what is termed in physical science
" J " or " Joule's equivalent of
heat." He read successively papers
on this subject before the meetings
of the British Association, first at
Cork (1843), giving the constant
" J " as 838, then as 770, then as 890
in 1845 (Brit. Assoc, at Cambridge),
lastly at Oxford (1847) as 781*5.
From this meeting dates the ac-
quaintance and scientific co-opera-
tion of Joule and Thomson (Lord
Kelvin) and the gradual recognition
of the importance of the subject
by other men of science (see Thom-
son's address on Joule, 1893, in
' Popular Lectures and Addresses,'
vol. ii. p. 558 sqq.) Helmholtz's
memoir. " Ueber die Erhaltuug der
Kraft," which was theoretical — as
Joule's were experimental — dates
also from 1847.

266

SCIENTIFIC THOUGHT.

he succeeded as president of the Society. These names
are identified with some of the greatest work in experi-
mental science. Some of them may be said to be identi-
fied with quite original theoretical ideas which have
governed the development of great departments of re-
search ever since. Dalton's atomic theory in chemistry,
however, received a tardy recognition in England, and
was firmly established only by foreign research, while
Faraday's " lines of force " remained a mystery to elec-
tricians,^ till William Thomson and Clerk Maxwell made
them the groundwork of our most recent conceptions.
It is well to note that neither Young, nor Davy, nor
Faraday, nor Dalton, nor Joule belonged to the circle
of Cambridge men, and that probably none of them re-
ceived any inspiration from that official school of English
mathematics.^ In the early years of the century that

^ See Helmholtz on Faraday's
ideas in 'Vortriige und Reden,' vol.
ii. p. 277. " Since the mathemati-
cal interpretation of Faraday's theo-
rems has been given by Clerk Max-
well in methodically elaborated
scieutific formuke, we see, indeed,
how much defiuiteness of conception
and accurate thought were con-
tained in Faraday's words, which
seemed to his contemporaries so
indefinite and obscure. And it is
indeed remarkable in the highest
degree to observe how, by a kind
of intuition, without using a single
formula, he found out a number of
comprehensive theorems, which can
only be strictly proved by the
highest powers of mathematical
analysis. I would not depreciate
Faraday's contemijoraries because
they did not recognise this ; I
know how often I found myself
despairingly staring at his descrip-
tions of lines of force, tlieir number

and tension, or looking for the
meaning of sentences in which the
galvanic current is defined as an
axis of force, and similar things.
A single remarkable discovery can
indeed be brought about by a happy
chance, . . . but it would be against
all rules of probability that a numer-
ous series of the most important
discoveries, such as Faraday pro-
duced, could have had their origin
in conceptions which did not really
contain a correct, though perhaps
deeply hidden, ground of truth."

^ Young resided at Cambridge to-
take liis medical degree on his re-
turn from Gottingen ; but though
his biographer has inserted a chap-
ter on Cambridge in the ' Life of
Young,' and though Young's first
great discovery, that of the inter-
ferences of waves of sound and light,
fell within that period, there is no
evidence that his scientific studies
were promoted by Cambridge in flu-

THE SCIENTIFIC SPIRIT IN ENGLAND.

267

centre had, indeed, to receive aid from a still more
secluded and vmacademie quarter. Undergraduates of
Cambridge used to migrate from the seat of teaching
which has been immortalised by Newton to the remote
Yorkshire village of Sedbergh, where John Dawson,^ one 33.

>^ o > JohnDaw-

of the few British analysts who held their own against 1°" of ^

•^ ° Sedbergh.

the great foreign authorities, taught the higher mathe-
matics for five shillings a-week.

During the latter part of the eighteenth century a
formidable rival to the learning of Oxford and Cambridge
had sprung up in the Scotch universities. These were 34.

^ ° -^ The Scotch

teaching centres, more after the manner of the foreign u^^^er-
universities. They had been started on the model of the
University of Paris or of the older Italian universities ;
some had their origin in the educational movement which,
especially in those countries where the doctrines of Calvin
prevailed, accompanied the Eeformation.^ All through the

sities.

ences; in fact he makes a disparaging
remark regardingBr it ish as compared
with Continental mathematics. See
Peacock's 'Life of Dr Young,' p. 127.
1 John Dawson (1734-1820), the
son of a poor " statesman " of Gars-
dale, tended his father's sheep till
he was twenty. He studied mathe-
matics with innate love and ability,
inventing a system of conic sec-
tions out of his own brain. By
teaching he gained a little money.
In 175(5 he instructed three young
men — of whom Adam Sedgwick's
father was one — before they went
up for their Cambridge studies. He
then became assistant to a surgeon
at Lancaster. Having saved £100
he walked to EdinVjurgh and studied
medicine there. His funds spent,
he returned to Sedbergh, where he
jjractised as a surgeon. When he
had saved a larger sum he proceeded

with this to London. After tak-
ing his degree in 176", he settled
in his native county to practise his
profession and teach the higher
mathematics to Cambridge under-
graduates. They flocked to him
in the summer, and between 1781
and 1794 he numbered eight senior
wranglers among his pupils. Li
1797 and subsequent years he
counted four more. In 1812 he
ceased teaching. He wrote papers
on the " precession " and the lunar
theory, and followed the develop-
ment of higher mathematics on the
Continent. See ' Life and Letters
of Adam Sedgwick,' by J. W.
Clark and T. M'K. Hughes, 1890,
vol. i. p. 61, &c.

- Details referring to the founda-
tion of the Scotch universities are
given by Sir A. Grant in the first
volume of his ' Story of the Univer-

268

SCIENTIFIC THOUGHT.

seventeenth and eighteenth centnries they stood in inti-
mate relations with such Continental centres of study as
Paris, Geneva, and the Dutch universities. Adam Smith
and David Hume were in direct and very intimate inter-
course with French thought, the former having obtained in
France a knowledge of the novel views of the great politi-
cal economists of the pre-revolutionary period. Edinburgh
became in the first half of the last century, under the
influence of John Monro and his son Alexander (1697-
1767), who was a pupil of Boerhaave, a medical school
of great importance, rivalling London in its foreign re-

sity of Edinburgh,' 2 vols., 1884.
Three of them — St Andrews, Glas-
gow, and Aberdeen — were founded
in the century preceding the Re-
formation ; St Andrews about
1411 by BishojD Wardlaw, because
Scotch students had been un-
popular and " molested " at Ox-
ford. The University of Glasgow
was founded in 1450, reference
being made to the University of
Bologna in the Bull of Pope Nicholas
v.; but it has also been observed
that ' ' the customs and technical
phraseology showed an imitation of
the institutes of Louvain, then
and for all the following century
the model university of Noi-thern
Europe, of which a Scotchman,
John Lichton, had been Rector "
(p. 21). Aberdeen was started by
Bishop Elphins tone, who had studied
in Glasgow and Paris, and been pro-
fessor, both there and at Orleans, of
canon and civil law. In the pre-
amble to the Bull of Pope Alexander
VI. the Universities of Paris and
Bologna are referred to (p. 29).
But the universities seem not to
have flourished previous to the Refor-
mation, when they wei-e "purged"
and a new spirit and order infused
into them. St Andrews was to have
four faculties, named as in foreign

universities — Philosophy, Medicine,
Law, and Divinity (p. 63). Glas-
gow and Aberdeen were to have
two faculties, of which the first
was to be Philosophy (or Arts),
the second to comprise Law and
Divinity. The ' Book of Discipline '
contained a verj' complete scheme
of higher graded education ; but
this was only gradually and par-
tially realised ; secondary schools
being wanting, the "colleges" had
to descend to elementary teaching
(p. 67). A jealousy also existed on
the part of those in power regard-
ing the older universities, these
being — as the King of France de-
clared when refusing to grant to
the Academy of Geneva the rights
of a university — hotbeds of heresy
(p. 125). Accordingly the latest
academic creation in Scotland was
the foundation by the "Town
Council and ministers of the city "
of the College of Edinburgh (pp.
99, 121, 127) between the years
1561 and 1578, King James's char-
ter dating from 14th April 1582.
" But it did not, like the older uni-
versities, commence with a blaze
of success and then collapse. It
started from a humble beginning
and steadily expanded into greater
things" (p. 158).

THE SCIENTIFIC SPIRIT IN ENGLAND.

269

putation.^ Edinburgh had also one of the earliest chairs
of chemistry. It grew into an independent centre of ^j^^ ^^j^^j
original scientific work when in 1783 the Eoyal Society Idtoturgh.
of Edinburgh was incorporated. Ever since the founda-
tion of the Scotch universities, mathematics had been
studied independently in Scotland, where John Napier
of Merchiston had at the end of the sixteenth century
invented logarithms. "Whether we consider the great
originality of the idea, the difficulty of carrying it into
effect in the state in which algebraical analysis then was,
or the immense practical and theoretical value of the inven-
tion, we shall have little difficulty in claiming for Napier
the honour of a discovery unsurpassed in brilliancy in
the whole history of mathematics." ^ From that time the

^ "In 1738 the foundation-stone
of that building which was till re-
cently the Royal Infirmary of Edin-
burgh was laid, and a great public
enthusiasm on the subject was mani-
fested. Drummond, the greatest
^dile that has ever governed the
city of Edinburgh, and Monro, were
appointed the Building Committee,
and they paid the workmen with
their own hands. All classes con-
tributed : landowners gave stone ;
merchants gave timber ; farmers
lent their carts for carriage of
materials ; even the masons and
other labourers gave one day's work
out of the month gratis, as it was a
building for the benefit of the poor "
(Sir A. Grant, loc. cit., vol. i. p.
306).

- Quoted by Sir A. Grant [loc.
cit., vol. ii. p. 293) from Chrystal's
unpublished Inaugural Address,
' John Napier, Baron of Merchiston '
(1550-1617). The ' Mirifici Logar-
ithmorum Canonis Descriptio ' ap-
peared in 1614. The 'Logarithmo-
rum ChUias prima ' of Henry Briggs

(1556-1630), professor at Oxford,
contains the first table of com-
mon or decimal logarithms.
Kepler (1571-1630) received the
invention with great enthusiasm as
of immense importance to astro-
nomy. "The more one considers
the condition of science at the time,
and the state of the country in
which the discovery took place,
the more wonderful does the in-
vention of logarithms appear. . . .
It is one of the surprises in the
history of science that logarithms
were invented as an arithmetical
improvement years before their
connection with exponents was
known. It is to be noticed also
that the invention was not the re-
sult of any happy accident. Every-
thing tends to .show that it was
the result of many years of labour
and thought undertaken with this
special object ; Napier succeeded in
devising, by the help of arithmetic
and geometry alone, the one great
simplification of which they were
susceptible — a simplification to

270

SCIENTIFIC THOUGHT.

36.
The 'Edin.
burgh
Review.'

science was cultivated at the different Scotch universities,
which supplied Oxford with a Professor of Astronomy
(preferred to Halley), in the person of David Gregory.
" David Gregory not only introduced the ' Principia ' to
Edinburgh students, but he also brought them to the
notice of Englishmen." ^ The Philosophical (afterwards
called the Eoyal) Society of Edinburgh was much in-
debted to Colin Maclaurin,"^ who almost alone with Landen
and Ivory maintained the reputation of British mathe-
maticians during seventy years, whilst the Continental
school was revolutionising that science. A successor to
Maclaurin in the mathematical chair at Edinburgh, John
Playfair,^ introduced the Continental methods into the
studies of the Scotch universities about the end of the
last century. He was one of the early contributors to
the ' Edinburgh Pieview,' which in politics, literature,
and science inaugurated a new kind of criticism, and led
a powerful attack upon all those traditional forms of
government, taste, and learning which prevented the free
expansion of ideas and the progress of science and prac-
tical interests. Though not always judiciously used, the

which the following two hundred
and eighty years have added no-
thing" (Glaisher in ' Eney. Brit.,'
9th ed., article "Napier").

1 David Gregory (1661-1708) has
" the honour of having been the
first to give public lectures on the
Newtonian philosophy. This he did
in Edinburgh five-andthirty years
before these doctrines were accepted
as part of the public instruction in
the university of their inventor "
(Sir A. Grant and Chrystal, loc.
cit, vol. ii. p. 296). Cambridge
writers, headed by W'^hewell, are
loath to admit any reluctance on

the part of their university in ac-
cepting the Newtonian philosoj^hy,
in spite of Whiston's testimony to
the contrary. See on this Whewell's
' History of the Inductive Sciences,'
3rd ed., vol. ii. p. 149, &c.

■- Colin Maclaurin (1698-1746)
published, 1742, a 'Treatise on
Fluxions,' 2 vols. 4to. In 1740 he
shared with Daniel Bernoulli and
Euler tlie prize of the French Aca-
demy for his 'Essay on the Tides.'

3 John Playfair (1748-1819) was
Professor of Mathematics and tlien
(from 1805) of Natural Philosophy.

THE SCIENTIFIC SPIRIT IN ENGLAND. 271

influence of that review must have been very powerful
in rousing the older English universities out of a state
of stagnation, and especially in stimulating younger minds
in the direction of the long-delayed reform of studies.
An important step in this direction was taken by three 37.

The Analy-

undercjraduates of Cambridge — Herschel, Babbage, and ucai society

° =' ' O ' of Cam-

Peacock — who in 1812 formed the Analytical Society, "^""^se.
with the distinct object of introducing the more modern
and powerful analytical methods developed mainly by
Euler and Lagrange, and deposited in their numerous
Memoirs in the publications of the foreign academies.^
In harmony with them worked Whewell, Airy, and
Sedgwick, who did much to enlarge the programme of
mathematical and scientific studies, though they very
staunchly upheld that the real object of university
education could not be identified with any special
method or school of thought, but was expressed in
the specific ideal peculiar to England, that of a liberal
education.^

The universities of Scotland, unlike those of England, 38.

, p . , . . . , . University

instead of nursing an exclusive spirit, and encouraging life in

*= f ' & to Scotland.

only scanty intercourse between teachers and students of
difierent centres, lived in constant exchange of professors
and ideas — much in the same way as has always been the
custom on a larger scale among German and other Conti-
nental universities. Though this is destructive of that
individual character of the university or the college which

^ See note 1 to p. 233 ; also for
many details Rouse Ball's ' History
of the Study of Mathematics at
Cambridge,' 1889, p. 120, &c.

'^ On Whewell and his writings
•on university education see note

to p. 261. Sir George Biddell
Airy (1801-1891) published in 1826
'Mathematical Tracts' (2nd ed.,
1831) on the lunar and planetary
theories, &c., for the use of students
in the university.

272

SCIENTIFIC THOUGHT.

is so highly prized by many English fellows, it is certainly
more conducive to the progress of studies and of research,
and it is the cause why in the early history of recent
science the universities of Scotland have played so much
more important a part than those of England. Whilst in
England modern science was cultivated outside the pale
of the universities by Priestley, Davy, Wollaston, Young,
Dalton, Faraday, and Joule, to whom we may even add
Green and Boole, all eminent Scotch men of science, such
as Gregory, Simson, Maclaurin, Playfair, Black, Thomson,
Leslie, Brewster, and Forbes, were university professors,
many of whom did not confine their labours to one centre,
but spread the light of their ideas and researches all over
the country.-^ Whilst England has been great in single
names, Scotland has certainly in proportion done more

^ Napier of Merchiston remained
outside the pale of the universities.
At that time the College of Edin-
burgh had no mathematical pro-
fessor ; but Glasgow had, and so
had Aberdeen. James Gregory was
educated at Aberdeen, was then pro-
fessor at St Andrews, and subse-
quently at Edinburgh. Colin Mac-
laurin was educated at Glasgow,
then professor at Aberdeen and at
Edinburgh. Playfair was educated
at St Andrews, and lectured there
before coming to Edinburgh. Leslie
was trained at St Andrews, and was
then professor first of mathematics
and afterwards of natural philosophy
at Edinburgh. Black was educated
at Glasgow and Edinburgh, and
was professor at both universities.
Brewster studied at Edinburgh, and
was subsequently principal of St
Andrews and then of Edinburgh.
Forbes, as student and professor, be-
longs exclusively to Edinburgh, and
so did in earlier times Robert Sim-

son, the great mathematical pro-
fessor. Adam Smith belongs exclu-
sively to Glasgow, though he had
lectured in Edinburgh before he
was appointed professor at Glasgow.
But the contrast between England
and Scotland becomes still more
prominent if we look at the medi-
cal sciences and note the great
array of celebrated professors at
Edinburgh, Cullen, Brown, Gregory,
Alison, Hamilton, Syme, Simpson,
Christison, and Charles Bell, where-
as the equally great names of John
and William Hunter, of Jenuer, of
Astlej^ Coojaer and Bright, have no
connection with the English univer-
sities ; Sydenham was only slightly
connected with Oxford and Cam-
bridge, and even Harvey never
occupied a prominent position at
Oxford. Through situation or con-
stitution the English universities
were unable to open a field of ac-
tivity for these celebrated men.

THE SCIENTIFIC SPIRIT IN ENGLAND.

273

to diffuse modern scientific knowledge. The great pub-
lishing firms of Edinburgh have also for more than a
century done much through Cyclopedias, Reviews, and
Magazines to spread general information of all kinds ; ^
whilst Hume, Adam Smith, and the subsequent Scotch
school of metaphysicians have exerted their influence
during the whole of this century, not only in Great
Britain, but over the whole of Europe." In the more
circumscribed domain of scientific thought a powerful
influence has again been exerted from Scotland as a
centre, and through the larger instrumentality of the
University of Cambridge, on the study of mathematical
and experimental physics, and what we may term the
spirit and method of these sciences. This influence be-

^ The most popular Cyclopfedia,
that of Chambers, had its origin in
Edinburgh in 1 860. It was founded
on the tenth edition of Brockhaus's
'Conversations-Lexicon.' The more
important ' Encyclopsedia Britan-
nica ' was published there also in
1771, 3 vols. ; 2nd ed., 1777. The
' Edinburgh Review ' was estab-
lished in 1802 by Jeffrey, Scott,
Horner, Brougham, and Sydney
Smith ; it was the first successful
"Quarterly," carried on independ-
ently of the booksellers, after
several unsuccessful attempts had
been made in a similar direction by
Adam Smith and Hugh Blair in
1755, and after Gilbert Stuart and
William Smellie had issued from
1773 to 1775 the ' Edinburgh Mag-
azine and Review.' No such peri-
odical ever attained to the circula-
tion of the ' Edinburgh Review,' of
which at one time 20,000 copies
were sold. The first high - class
monthly Magazine was also printed
in Edinburgh by Blackwood in
1817, with Scott, Lockhart, Hogg,

VOL. I.

Maginn, Syme, and John Wilson as
contributors. ' Tait's Edinburgh
Magazine ' was the first shilling
magazine. The brothers William
and Robert Chambers, in 1832,
started the Journal named after
them. They also brought out many
popular works of sterling merit,
mostly written by Robert Cham-
bers, than whom none did more to
introduce a knowledge of nature
into popular reading, and to give a
healthy tone and moral influence
to the cheap literature which has
become such an important factor
in modern culture.

- Whilst Locke exercised the
greatest influence on French phil-
osophy, Kant starts more directly
from Hume. The literature of the
Restoration in France again at-
taches itself to the Scotch meta-
physicians, notably Reid. It is
interesting that both Kant and
the greatest representative of the
French " Ideology," De Tracy, were
of Scotch descent.

S

274 SCIENTIFIC THOUGHT.

longs to the second half of the century, and is centred in
the two names of William Thomson (Lord Kelvin) and
James Clerk Maxwell, who may be said to have jointly
revolutionised natural philosophy. It began with the ap-
pearance of George Stokes's and William Thomson's im-
portant contributions to mathematical physics, and with
the publication of that suggestive and stimulating — but
unfortunately unfinished — work by Thomson and Tait on
Natural Philosophy. It was represented to the fullest
extent in Clerk Maxwell's activity in the Cavendish
Laboratory at Cambridge. But tlie consideration of this
subject belongs to a later chapter of the present work,
and is only mentioned here in connection with the intel-
lectual intercourse and exchange which has existed all
through this century between the invigorating spirit of the
north and the more conservative spirit of the southern
39. portion of the island. Besides Scotland another centre

The Dublin

Mathemati- — the Dublin School — has gained European renown

cal School. • ° ^

through a series of mathematical labours of the highest
importance, some of them of an originality hardly yet
sufficiently recognised. This school is represented by
the names of Eowan Hamilton,^ MacCullagh, Sal-

1 Of Rowan Hamilton's dyuami- maticiaus who, like Gauss, led the

oal "principle of varying action" way into new channels of thought

I have spoken in a note to p. 231. and succeeded in breaking through

William Rowan Hamilton (1805-65) the traditional forms of this science,

cannot with the same certainty as which more than any other is ham-

Kant and De Tracy be claimed as ! pered in its development by trans-

of Scotch descent. Indeed he ! mitted customs and habits of repre-

seems to belong distinctly to Ire- sentation. Thus, after ten years of

land. See Tait's article in the research and thought in connection

' North British Review,' September ' with the representation of extend-

1866, and Perceval Graves's reply in
'Life of W. R. Hamilton' (3 vols.,
1882-89, vol. i. p. 5). He was one

ed algebraical forms by means of
the different directions in space, he
succeeded in establishing the fun-

of the few quite original mathe- i damental principle of his theory of

THE SCIENTIFIC SPIRIT IN ENGLAND.

275

mon ; ^ nor should we forget the suggestive writings of
George Boole.^ The influence of these men originated
outside of Cambridge, and a history of mathematics at
that university does not contain their names,^ though the
ideas of which they have been the bearers have largely
entered into the text-books and the teaching of the Cam-
bridge school.

So far I have mainly dealt with one side only on which
the progress of science depends, namely, the methodical
use of experiment, measurement, and calculation : this

quaternions — comiolex quantities
Avhich are compounded of a purely
algebraical or quantitative element
■and three distinct elements corre-
sponding to the three directions or
dimensions of sjaace. He was the
first to work out this calculus, and
the labour occupied twenty years
of his life. In Hamilton's calculus
of quaternions, distance (or length)
and direction are introduced as they
naturally present themselves when
we deal with geometrical or physical
problems, instead of all quantities
being reduced to lengths, as was
the case in the Cartesian geometry.
Hamilton thus broke through the
•conventionalism of the latter and
showed how the consideration of di-
rections in space forces us to extend
the original operations of arithmetic.
It is interesting to note how simul-
taneously Grassmann (see p. 243,
note 1) iu his ' Ausdehnungslehre '
(1844) and Von Staudt in his ' Geo-
metrie der Lage ' (1847), quite inde-
jiendently worked at similar exten-
sions of our arithmetical and geo-
metrical conceptions, and how sub-
sequently quaternions, in which
Hamilton had seen a powerful me-
thod for solving geometrical and
physical problems, present them-
selves as a special form of the ex-
tended algebra and geometry elabor-

ated from these different beginnings.
Whilst the practical usefulness of
the calculus has been demonstrated
by some extensive applications, as,
for example, to spherical trigono-
metry, the ideas contained in it —
frequently without Hamilton's no-
tation— are gradually finding their
way into text-books, and the strange-
ness which for half a century pre-
vented the labours of Hamilton,
Grassmann, and Von Staudt from
being generally ai^preciated, is dis-
appearing. A popular exposition
of the relation of quaternions to
general arithmetic is given in 0.
Stolz, ' Grossen und Zahlen,' Leip-
zig, Teubner, 1891.

^ The excellent treatises of Sal-
mon on ' Higher Algebra,' ' Higher
Plane Curves,' ' Geometry of Three
Dimensions,' and 'Conic Sections'
have in their German translations
by Fiedler done a great work in
systematising and popularising mo-
dern conceptions in algebra and
geometry. See Giuo Loria's treatise
on the " Principal Theories of Geo-
metrj'" in the German translation
by Schiitte, Leipzig, 1888, p. 25,
&c.

- See p. 247, note 2.

^ See Rouse Ball, ' A History of
the Study of Mathematics at Cam-
bridge,' 1889.

276 SCIENTIFIC THOUGHT.

side had been very largely developed by the great French
naturalists and mathematicians in the beginning of our
period. The change in the higher branches of science
which took place during the first half of the century is
greatly owing to them, and to the later German school,

40. which was much influenced by them. If we compare

Importame ^ -^

of British ^]^g contributious of British science in these branches,

contriDu- ^

sdence! they are indeed inferior in bulk, and still more so in
methodical arrangement ; but among them is a small
number of works of the first order which are embodi-
ments of scientific ideas of the very highest importance.
Introduced into the great edifice of scientific research
which was being planned and erected on the Continent,
they mark the very corner-stones of the building, stand-
ing out in bold and conspicuous prominence. But it is
a fact that no Academy existed in this country which
was zealous in collecting and arranging all the best
labours of scattered philosophers, no university which
was anxious to attract and train promising intellects,
no comprehensive text-books and hand-books, ensuring
right guidance, correctness of knowledge, and complete-
ness of study, no historical and philosophical traditions
guaranteeing that novel contributions should make their
appearance under favourable conditions, or supplying the
most appropriate mise en scdne for new ideas.

41. It is the French Institute, in the earlier years of the

Diffusion of

scientific ccntury, and the German university system, with its

knowledge ■' ' ^ t/ '

contkient. many local ramifications and literary organs, during the
whole of the century, which have done the great work
of systematising and diffusing scientific knowledge, and
of introducing the exact spirit of research. There is

THE SCIENTIFIC SPIRIT IN ENGLAND.

277

of science.

something casual and accidental about the great ideas
which British men of science contributed during the first
half of the century. Each of them chooses an isolated 42.

Isolation of

position, a special form of delivery, frequently a Ian- Englishmen
guage and style of his own. They attach little or no
importance to the labours of others, with which they
are frequently unacquainted."^ Important papers are
lost or buried, as in the case of Cavendish and Green.
Novel ideas are communicated in unintelligible language
and symbols, and accordingly neglected. This was the
case with Dr Young's writings, and to a certain extent
with Faraday's. The greatest discoveries were unduly
postponed through the absence of assistance, as seems to
have been the case with Adams's discovery of Neptune/
perhaps with Stokes's anticipation of spectrum analysis.^

/-

^ This is correct of most of the
great men referred to in the course
of this chapter. Among them, how-
ever. Rowan Hamilton forms an ex-
ception. Though working on quite
original lines, he took a great in-
terest in the labours and sugges-
tions contained in the writings of
his forerunners and contemporaries,
as the historical notices in the pre-
face to his ' Lectures on Quater-
nions ' (1853) prove ; likewise his
correspondence with De Morgan (see
'Lifeof Sir W. R. H.,' vol. iii.)

- The story of the discovery of
Neptune has been frequently told.
The first publication of the ele-
ments of the suspected planet,
which enabled a search to be made,
came from Leverrier to the Paris
Academy of Sciences on the 1st
July and the .31st August 1846.
In consequence of this publication,
Galle at Berlin, requested by Lever-
rier to search in the neighbourhood
of 5 Capricorni, and comparing his
observations made on the same

night on which he received the
request, 23rd September 1846, with
Bremiker's map, actually found the
planet. Subsequently it became
known that Adams of Cambridge
had already communicated his
elements in September and October
1845 to ChaUis and Airy, and that
the former had actually seen the
planet on the 4th and 12th of
August 1846, but — for want of
equally detailed maps — had not
compared the observation and estab-
lished the discovery. See Whewell's
' History of the Inductive Sciences,'
third ed., 1857, vol. ii. p. 460, &c. ;
also Wolf, ' Geschichte der Astro-
nomic,' p. 537, &c.

'^ It appears from a communica-
tion of Sir William Thomson (Lord
Kelvin) to Kirchhoff immediately
after the latter had published in
1859 his explanation of the iden-
tity of the dark lines in the solar
spectrum with the bright lines in
the spectra of coloured flames, that
Stokes, soon after the publication

278

SCIENTIFIC THOUGHT.

What might not these great minds have accomplished had
they attached the same importance to style and form as
most of the great French men of science, or had they been
called upon to teach a number of eager pupils, anxious,
not to take honours and degrees, but to understand and
further elaborate the suggestions of their master, as has
been the custom and tradition in Germany ? The history
of English science during the first half of the century
consists of a series of biographies, or of monographs on
single ideas and points of view. We are struck by the
individual greatness of the minds which produced them,
their originality or the suddenness of their appearance.
An 6loge by the permanent secretary of the Academy has
usually been considered sufficient to satisfy the historian
of science in France ; the life of every great philosopher
in Germany is identical with the history of a phase of
thought or with a school of research ; in England alone
the person of the thinker has nearly always claimed the

by Miller in 1845 and by Foucault
in 1849 of observations relating to
this subject, had suggested in the
course of conversation that there is
a correspondence between emission
and absorption of the same kind of
light by the vibrating molecules of
the same body, according as it is
used as a source or a screen for
light. Had this idea of Stokes's,
which suggested the presence of
sodium in the atmosphere of the
sun, been followed out at the time,
the discovery of spectrum analysis
would have taken place ten years
earlier. Actually, the various pub-
lications, beginning with Fraun-
hofer's description of the dark lines
in the solar spectrum in 1814 and
proceeding through the observa-
tions of Herschel, Talbot, Drum-

mond. Miller, Angstrom, Pliicker,
Swan, and Balfour Stewart on
the absorption and radiation of
heat, found their consummation
when Bunsen and KirchhofF settled
the main point in question — viz.,
"that the bright lines of an in-
candescent gaseous body depend on
the chemical constituents of the
same." Then at length spectrum
analysis became possible. See on
this matter Kirchhoff's own histori-
cal resunie of the year 1862, re-
printed in ' Gesammelte Abhand-
lungen ' (Leipzig, 1882), p. 625,
&c.; also Sir William Thomson's
'Baltimore Lectures,' shorthand
notes, 1884, p. 100, and Stokes's
translation of Kirchhoff's first paper
in 1860 ('Philos. Magazine,' March
1860).

THE SCIENTIFIC SPIRIT IN ENGLAND.

279

greater share of popular attention.^ His mental labours
have preserved an individual character, shutting them
out during his life from common contact, and limiting
their fertilising power, like that of an oasis in the desert,
to a narrow circle of casual visitors. Minds like Newton
and Faraday, full of new life, but modestly content with
deepening and strengthening their secluded vigour, re-
frained from boastful publicity or ostentations parade,
working for all ages rather than for a special school or a
passing generation. It is the individualism of the English 43.

Individual -

character, the self-reliant strength of natural genius, which is™ ^^^^^

_ ° o ' English

comes out most strongly in its great examples of scientific character,
work. In characters of smaller breadth, in intellects of
lesser power, these tendencies show themselves in ways
which we cannot always admire or commend : in the
emulation for place and position, in the competing for

^ Tliis explains the remarkable
richness of English literature in
biographies, containing copious col-
lections of correspondence, and the
almost total absence of such litera-
ture in France, which, on the other
side, is rich in memoirs, written by
statesmen and authors themselves.
As the students of nature have
usually little time for autobio-
graphy, we possess of the long list
of great names in modern French
science hardly any personal records
such as are so plentiful in English
literature. What we miss in many
of these elaborate and frequently
gossiping narratives is a just ap-
preciation of the position of the
subject of the biography in the
history of science, literature, and
thought, a definition of the exact
place and imjjortanee which belongs
to him and his work. This is what
is given in such a masterly and con-
densed form in the better 6loges of

Fontenelle, of Cuvier, of Arago,
and other secretaries of the French
Academies. In Germany biographi-
cal literature is less developed than
in this country, and memoirs are
almost absent — those of Varnhagen
von Ense and of Perthes, among
literary men, being remarkable and
rare exceptions. Similarly the great
correspondence carried on by Goethe
through nearly sixty years is a
unique monument of his genius
and his influence, comparable only
to that of Voltaire during the last
century. R. Haym in his biographies
of Hegel, \Vm. von Humboldt, and
Herder, which combine the bio-
graphical with the historical and
critical elements, has done a great
work, and these books are invalu-
able contributions to the history of
thought. Justi's ' Winckelmann ' is
of equal importance ; but Dilthey's
' Schlciermacher ' is unfortunately
unfinished.

280

SCIENTIFIC THOUGHT.

44.
Changes
during the
last fifty
years.

honours and championships — in all the noble and ignoble
forms of racing, where much energy, which might more
usefully have been merged in co-operative action, is
sacrificed for the sake of individual distinction. But
where the height of genius forbids emulation, where the
towering intellect has distanced all records, this indi-
vidualism has produced single specimens of the greatest
work, examples of the highest moral worth. It is not in
the courses of scientific work alone that we shall have
occasion to mark the peculiarity of British, especially of
English, thought ; but it is interesting to note how even
in this sphere, which more than any other seems to bear
an international and cosmopolitan character, the genius
of the nation strongly asserts itself, baffling every effort
to control it or to lead it into more conventional chan-
nels. The last fifty years have done much to destroy
the peculiarly national customs, the idiosyncrasies of the
different peoples. English institutions have been copied
in France, and German customs introduced into England ;
it has recently been stated that the older type of scientific
amateur which existed in this country is dying out, being
rendered impossible by the more complicated machinery
of science, the manifold conditions on which progress de-
pends. It seems to me doubtful whether this view is
correct. Surely the advance of the highest kind of
thought will always depend upon the unfettered devel-
opment of the individual mind, regardless of established
habits, of existing forms of expression, or of adopted
systems ; just as the diffusion and wholesale application of
single discoveries will depend on a ready and efficient ma-
chinery and organisation ; whilst their influence on gen-

THE SCIENTIFIC SPIRIT IN ENGLAND. 281

eral thought and literature will depend on the cultivation
of a perfect form, of an expressive and elegant style. The
Trench alone in the beginning of the century could boast
of the last ; the Germans have most successfully developed
the second ; whilst England, the country of greatest indi-
vidual freedom, has been the land most favourable to the
growth of genius as well as eccentricity, and has thus pro-
duced a disproportionate number of new ideas and depar-
tures. Nor is it to be desired that the reliance of genius
on itself should be in any way curtailed, as it is impos-
sible to foretell whence the new light will come which is
to illuminate future ages. This individualism of the
English mind presents other accompanying features, and
these are of great interest to the historian of thought.
They manifest themselves in the province of science as
much as in other provinces. We will now study them
more closely ; in the sequel we shall meet with them in
other departments also.

Hitherto our observations on English science have nearly
all referred to only one side of modern scientific work, —
the side on which lie the experimental, measuring, and cal-
culating sciences ; those sciences which abroad are termed
" exact " ; in which mathematical notions and methods,
be it of measurement or of calculation, obtain. But these
sciences cover only one side of reality. We noticed how in
France, during the great scientific epoch, the other side of
nature, that which exhibited and was filled by the pheno-
mena of life, was simultaneously explored with equal
originality and equal success. As Laplace was the great
representative of the one, so Cuvier was the great re-
presentative of the other. We liave also seen how in

282

SCIENTIFIC THOUGHT.

Germany this latter department of research was specially

cultivated, how all the mathematical, experimental, and

philosophical sciences combined to organise the one great

45. science of physiology or biology, with its central and

British con- f J OJ bJ >

tributionsto crowning problem — the problem of consciousness. We

biology. o JT r

also noted how this science worked a great reform in
the whole domain of medical theory and practice. Let
us now return to the question, What has Great Britain
done during the first half of this century in this great
department of scientific thought ? Single great names, like
those of Harvey,-^ marked in former centuries discoveries
in the natural sciences equal to those of Newton in the
mathematical; the name of Eay^ is still preserved in the

1 William Harvey (1578-1657), a
native of Kent, received his medical
education in Italy, especially in
Padua, under Fabricius of Acqua-
pendente. The discovery of the
circulation of the blood belongs to
the year 1616, and is almost con-
temporary with Napier's invention
of logarithms. This discovery is con-
tained in the manuscript of Harvey's
lectures preserved in the British
Museum, but the publication did not
take place till 1628 ('Exercitatio
anatoniica de motu corporis et san-
guinis in animalibus,' published at
Frankfort). Although Harvey was
drawn into long controversies by
his publication of this work, he
had the satisfaction of seeing his
discovery generally recognised. Des-
cartes abroad took Harvey's part in
his letter to Beverwijckin 1637, and
in his ' Discours de la Methode,' pub-
lished in the same year ; and it is
noteworthy that — as has been the
case with many subsequent English
discoveries— the first great acknow-
ledgment came from the Continent,
notably Holland. The acceptance in
France by the faculties of Paris and

Montpellier was less rapid, and in
England it is vrell known that Lord
Bacon took no notice either of
Harvey's discovery or of Napier's
invention. See James Spedding's
preface to the " De interpretatione
Naturae Procemium " in works of
Lord Bacon, vol. iii. p. 507, &c. ; also
Harvey's own opinion on Bacon, ibid.,
p. 515. Hobbes, on the other hand,
" was eager to accept Harvey's revo-
lutionary discovery " (Groom Rob-
ertson, 'Hobbes,' p. 123), and refers
to Harvey in the dedication of the
'De Corpore' (1655) as "the only
man I know that, conquering envy,
hath established a new doctrine in
his lifetime" (ibid., p. 187 u.) On
Harvey's other works, notably on
the work 'DeGeneratione,' see, inter
alia, Huxley, ' Science and Culture,'
1888, p. 333, &c.

^ John Ray, or Rajus, as he is
called abroad (1628-1705), a native
of Essex, was a Cambridge man ;
he, however, gave up his fellowship
in 1662, feeling himself unable to
subscribe to the Act of Uniformity
of 1661. He was one of the first
great classifiers of plants ; he col-

THE SCIENTIFIC SPIRIT IN ENGLAND.

283

Society called after him : in more recent times Hutton
formed a school in geology which was opposed to that of
Werner, emanating from Germany.^ Hunter, the anato-

lected a vast amount of information,
beginning with the neighbourhood
of Cambridge and extending it in
travels over Great Britain and the
Continent with Willoughby. The
' Historia Plantarum ' — describing
18,625 species of plants — appeared
from 1685 to 1704 in 3 vols. The
first volume contains a chapter on
the anatomy and physiology of
plants, which was much extolled
by Cuvier and recommended for
republication. The " Ray Societj-,"
started in 1844 " for the pub-
lication of works on Natural His-
tory," brought out among many
other excellent and celebrated
works (such as Darwin's ' Mono-
graph of the Family Cirripedia'),
Memorials (1844) and Correspond-
ence (1848) of John Ray : it also
translated that eccentric specimen
of the " Naturphilosophie " Oken's
' Elements of Physio - philosophy,'
1847. A contemporary of John Ray
was Nehemiah Grew (1628-1711),
one of the first to make extensive
use of the microscope (invented in
Holland between 1590 and 1600)
for the examination of the anatomy
and physiology of plants. After
Oldenburg he was Secretary of the
Royal Society together with Hooke.
The Society printed his ' Anatomy
of Plants.' About the same time
it seems to have exhausted its
funds in printing Willoughby's
' Historia Piscium,' so that it was
unable to carry out its design of
defraying the cost of printing the
' Principia. ' This was generously
done by Halley. See Weld, ' His-
tory of the Royal Society,' vol. i.
p. 309, &c.

1 Beneath the strife of the Wer-
nerians and Huttonians, or the
Neptunists and Plutonists as they

were termed, the real merits of
Robert Jameson (1774-1854) and
James Hutton (1726 - 97) have
sometimes been overlooked. Both
were ardent naturalists who spent
their lives in observation and study
of nature. They made Edinburgh
for some time the centre of geology
in this country. Jameson was fifty
years Professor of Natural History,
founded the first school of Natural
History in this country (see Cossar
Ewart's address, quoted by Sir A.
Grant, ' Story of the University of
Edinburgh,' vol. ii. p. 444), trained
a number of eminent naturalists,
among whom are Edward Forbes and
Grant [N.B. — The name of Darwin
must be added with caution, see his
'Autobiography,' vol. i. p. 44, &c.),
founded the Edinburgh Museum of
Natural History, which includes the
Huttonian collections, and founded
the W^ernerian and Plinian Societies
of Natural History. James Hutton,
though not a teacher like Jameson,
exerted a great influence through
John Playfair, who popularised his
views in his 'Illustrations of the
Huttonian Theory of the Earth '
(1802). It is termed by Geikie a
"classical contribution to geological
literature." Though the opposition
of Hutton's theoretical views to
those of Werner gave him a great
reputation as a theorist, it is claimed
for him that he first among geolo-
gists disclaimed the intention of
investigating the origin of things,
and thus put an end to the cosmo-
gonies of the eighteenth century.
Such had been promulgated in all
the three countries by the most
illustrious philosophers and natural-
ists, by Burnet, Buffon, and Leibniz.
On Hutton's great merits see es-
pecially Huxley, " Essay on Geolo-

284

SCIENTIFIC THOUGHT.

46.

Jeniier.

47.
English love
of nature.

mist, acquired a world-wide reputation in the latter part
of the eighteenth century.

Many other students of nature could be added to this
list. Perhaps none has acquired greater popular celebrity
than Jenner.^ This he acquired through his extraordinary
discovery, by which he grappled successfully with one of
the most prevalent and distressing epidemics from which
former generations had to suffer. The study of animated
nature, the observation of the sky and the heavens, have
always been favourite occupations of Englishmen. The
love of travels abroad and of the country at home has
favoured a close intercourse with nature. A fickle and
humid climate invited the superior skill of the agriculturist
and the gardener, and rewarded them with heavier crops
and more luxuriant verdure.^

gical Reform" (1869. Reprinted
in 'Lay Sermons and Addresses,'
No. 11). He is there considered
as the first representative of " IJni-
formitarianism " against the older
" Catastrophism. " Unif ormitarian-
ism has been followed by " Evolu-
tionism."

1 Edward Jenner (1749 - 1823),
one of the greatest benefactors of
mankind, spent twenty years on
the farms of Gloucestershire, fol-
lowing the advice of his friend and
master John Hunter, " Don't think,
but try," before he undertook the
first inoculation of cowpox on the
14th of May 1796. About the end
of the century the process of vacci-
nation, which dispelled the older
process of inoculation — introduced
into England by Ladj' Mary W.
Montagu in 1721 — had become
generally known in Europe. The
governments of the Revolution in
France and the Academy of Sci-
ences had at the end of the century
occupied themselves a good deal

The chill of the long winter

with the cure of smallpox, both Vol-
taire and d'Alembert having taken
great interest in the subject.

" The yield of an acre in wheat
is in England about 30 bushels or
one ton of grain ; next comes Bel-
gium, then Germany, then France ;
the average yield in the United
States of America is barely one-half
of that in England. The yield of
an acre in Scotland exceeds slightly
that in England. In Scotland farm-
ing is carried on with much skill
and enterprise, and, in spite of the
severe climate, gardening is prob-
ably further developed there than
in any other country. It appears
that the first voluntary organisa-
tion for the improvement of agri-
culture was the "Society of Im-
provers in the Knowledge of Agri-
culture in Scotland " formed in
1723, of which the Earl of Stair
was one of the leaders. Though it
counted 300 members, it was short-
lived : its ' Select Transactions *
were published by Maxwell in 1743.

THE SCIENTIFIC SPIRIT IN ENGLAND.

285

stimulated active exercise and outdoor sport ; the abun-
dant rains, which fed the many rivulets with a constant
supply of fresh water, suggested the cultivation of that
pastime of which Izaak Walton had left a classical de-
scription, long before Eousseau in France made the love
of nature a fashionable sentiment. Lord Bacon pointed
to the study of natural phenomena as the only source
of knowledge. Evelyn wrote a treatise on forest-trees,
and the old-fashioned English flower-garden is immor-
talised in Bacon's ' Essays,' in the " Winter's Tale," in
Cowper's " Task," and in the works of many other poets.
Through the literature of the eighteenth century there
runs a vein of increasing love and knowledge of natural
objects and natural scenery, beginning in Thomson and
Gray, widening and deepening in Erasmus Darwin and
Cowper, and attaining full vigour and originality in
Burns and Wordsworth, as also in the school of English
landscape-painting. William and Caroline Herschel com-

Next came the Bath and West of
England Society, 1777 ; the High-
land Society, 1784 ; and the Na-
tional Board of Agriculture, 1793.
The ' Farmer's Magazine ' was start-
ed in 1800. About the same time
that Lawes and Gilbert in England
and Liebig in Germany gave such
an impetus to scientific farming
through their experiments and pub-
lications, " Mr John Finnie at Swan-
ston, near Edinburgh, having sug-
gested (1842) to some of his neigh-
bours the desirableness of obtaining
the aid of chemistry to guide far-
mers in many departments of their
business, the hint was promptly
acted upon, and these Mid-Lothian
tenant-farmers had the merit of
originating an Agricultural Chem-
istry Association (the first of its

kind), by which funds were raised,
and an eminent chemist engaged"
(' Ency. Brit.,' article "Agricul-
ture," vol. i. p. 305). There is pro-
bably no country where farming is
such a favourite pursuit of gentle-
men of leisure and wealth as Great
Britain, or where the intelligence
of higher society and of the univer-
sities is so liberally transferred to
the benefit of the country, of its
population, its crops and its live-
stock. Among many examples of
the past and present I mention as
an outcome of this spirit the little
volume by Sir Thomas Dyke Ac-
land, ' On the Chemistry of Farm-
ing' (London; Simpkin & Co.,
1891), and his liberal patronage of
agriculture in the west of England.

286

SCIENTIFIC THOUGHT.

menced the long line of amateur star-gazers of this
country ; Luke Howard's study of clouds drew from the
kindred spirit which lived in the great Goethe a loving
memorial ; ^ and John Dalton was induced by the mists
and fogs of his native lake country to join in the foun-
dation of the modern science of meteorology.

We now discover the reason why the strong individual-
dividuaiism ism of the Encjlish character, which prompted new de-

and natural- *=' ' j. j.

partures and inspired new ideas in science, as it produced
adventures and novel enterprise in life and arts, has not
more frequently led to discouraging failures in the latter,
or to eccentricity and dreaminess in the former ; why it
has, on the whole, alike in practical work and in scientific
study, been rewarded by signal success. The rare genius,
gifted with the power of original thought, who found no
academy ready to call him, no schools where he could be
trained, no university eager to nurse and develop his

48.
Union of in

isni in
England

1 Luke Howard (1772-1864), a
member of the Society of Friends,
was one of the many lovers of nature
and amateur naturalists of this
country in whom new sciences —
like thatof meteorology — are nursed
during their unpretentious infancy.
He himself gave a simple narrative
of his life and doings to the great
Goethe, who, attracted by his at-
tempted classification of clouds
(about 1802, published in his 'Cli-
mate of London'), had addressed
some lines to him, accompanying
them by a statement in verse of
Howard's description of the stratus,
cumulus, cirrus, and nimbus : —

" Er aber, Howard, giebt mit reinem

Sinn
Uns n(M\er Lelire heniiclisten Gewinn :
Was sich nicht halten, nicht erreiclien

Kisst,
Er fasst es an, er halt zuerst es fest ;

Bestimmt das Unbestimmte, scliriinkt es

ein,
Benennt es treffend !— Sey die Ehre Dein !
Wie Streife steigt, .sich ballt, zerflattert,

fallt,
Eriunre dankbar Deiuer sich die Welt."

Goethe subsequently tried to get
some information about Howard's
way of life, ' ' so that I might see
how such a mind is formed, what
opportunities, what circumstances,
have led him into ways of looking
at Natui-e naturally, have taught
him how to devote himself to her, so
as to find her laws and to prescribe
these again toher in anatural human
manner." Li his autobiographical
narrative (reprinted in the last vol-
ume of Goethe's Works) Howaixl
refers to the meteoric phenomena
of 178.3, mentioned also in Cow-
per's Letters (13th June 1788), aud
White's ' History of Selborne.'

THE SCIENTIFIC SPIRIT IN ENGLAND.

287

talent, did not retire into the depths of his own con-
sciousness, or surround himself with the artificial at-
mosphere of erudition. The result of such a process
•can be abundantly traced in other countries and other
literatures. In England the isolation from society and
the solitariness of genius threw him into the arms of
iSTature, and she has in many instances, in science, in
poetry, and in art, rewarded and refreshed him by a
novel inspiration — she has lifted her veil to his loving
•eye and revealed to him one of her secrets. The in-
dividualism of English science has been tempered by
its naturalism. A type of this peculiar form of the
naturalist was Gilbert White, the natural historian of
Selborne.-^

^ A long list might be given of
these retired nature-loving souls,
among -R'hom Charles Darwin will
always rank as the greatest and
most conspicuous. I give here a
few names in addition to those
mentioned in the text.

John Gough of Kendal (1757-
1825) might, according to John
Dalton (see his Life by Henry, pp.
9 and 10), "be deemed a prodigy
in scientific attainments. . . . De-
prived of sight in infancy by the
smallpox, . . . possessing great
powers of mind, he bent them
chiefly to the study of the physical
and mechanical sciences. It was he
who first set the example of keeping
a meteorological journal at Kendal;
... he knew by the touch, taste,
and smell almost every plant within
twenty miles ; he could reason with
astonishing perspicuity on the con-
struction of the eye, the nature of
light and colours, and of optic
glasses," (fee, &c. For about eight
years Dalton and he were intimately
acquainted.

George Edwards (1694-1773) of
Stratford, Essex, was the author of
the ' History of Birds, ' which he
published between 1743 and 1764
in six volumes. He had journej-ed
through France and other countries,
and gave engravings of six hundred
subjects not before delineated by
naturalists.

Still more remarkable was Thomas
Edward (1814-86), the shoemaker
of Banff, who, having been turned
out of three schools for his zoolo-
gical propensities, without friends,
without a single book on natural
history, not knowing the names of
the creatures he found, gained a
knowledge unique in its freshness
and accuracy. At the University
of Aberdeen, where he exhibited
his collections, he was told by the
professors that he came "several
centuries too soon," as they had
then no chair of Natural History.
His life has been written by Smiles,
1876.

Edward Forbes (1815-54) of
Douglas, Isle of Man, a born lover

288

SCIENTIFIC THOUGHT.

49.
White of
Selborue.

Not long after Eay and Linnpeus had attempted the
artificial and logical classification of living beings, and
about the same time that BufFon in France infused into the
literature of his country a somewhat pretentious love of
nature, Gilbert White, in a simpler and more healthy style,
betook himself to describe the aspect that nature presented
when viewed from the quiet home of an English country
parson. He may be said to have represented that other

of nature, "led an unusually full
life, occupied in promoting science
and arousing enthusiasm and awak-
ening intelligence in others. To
almost every department of biology
he rendered much service, especially
by connecting various branches to-
gether and illustrating one by the
other. Though his published works
have been few, his ideas have been
as the grain of mustard-seed in the
parable" ('Dictionary of National
Biography '). After holding various
badly paid oiBces in London and
elsewhere, he succeeded Robert
Jameson as Professor of Natural
History at Edinburgh (see ' Memoir
of E. Forbes,' by G. Wilson and A.
Geikie, 1861).

Hugh Miller (1802-56), the self-
taught stonemason of Cromarty,
combined the soul of an artist with
that of a naturalist. His writings
occupy a place by themselves in
English literature. "The principal
scene of his own investigations was
the Cromarty district, where he
ransacked every wrinkle of the hill-
side, and traced every stratum sawn
through by the watercourse, and
where on the beach at ebb, in in-
durated clay of bluish tint and
great tenacity, belonging to the old
Red Sandstone formation, he dis-
covered and dug out nodules which,
when laid open by a skilful blow of
the hammer, displayed organisms
that had never been seen by the
human eye." In September 1840

there appeared in the ' Witness ' a
series of articles entitled " The Old
Red Sandstone." They formed the
nucleus of a book of this title which
established the reputation of Miller
as an original geologist, as a prac-
tical thinker and fascinating writer.
' My Schools and Schoolmasters ' is a
masterpiece of the English language.
" In an age prodigal of genius, yet
abounding also in extravagance,
glare, and bombast, the self-edu-
cated stonemason wrote with the
calmness and moderation of Addi-
son." " The fossil remains seem in
his glowing pages to live and
flourish, to fly, swim, or gambol, or
to shoot up in vegetative profusion
and splendour, as in the primal
dawn of creation " (Carruthers,
quoted by Peter Bayne in ' The
Life and Letters of Hugh Miller,'
2 vols., 1871).

David Robertson, the naturalist
of Cumbrae in the Firth of Clyde
(born in 1806), was a farm-labourer
till he was twenty -four, then
took to the study of medicine,
and had afterwards for many
years a china and hardware shop
in Jail Square, Glasgow. He
gained a sufficient independence to
be able to retire in 1860 to Great
Cumbrae, where he devoted the
rest of his life to a study of nature.
Especially in " the marine section,
by his own unaided efforts, he
opened up in a remarkable degree
the zoology of the Firth of Clyde.

THE SCIENTIFIC SPIRIT IN ENGLAND.

289

side of natural science, which does not try to comprehend
nature through the artificial arrangement or classification
of a museum, but in those connections, among her own
animate and inanimate objects, which constitute reality,
and are the characteristics of life and development. It
was the real, not the artificial, Jardin des Plantes,
where he and his successors tried to study natural
objects and the habits of living beings.^ Another re-

Many animals, till then accounted
rare, are now known to exist as
common objects, while the annals
of science have received many im-
portant additions of animals alto-
gether new to natural history
records — discoveries which have
caused the Firth of Clyde, and more
particularly the Cumbrae Islands,
to become one of the best explored
and most widelj' known districts
of Britain " (Gray, Secretary of
the Glasgow Natural History So-
ciety, quoted by Thomas R. R.
Stebbing in his ' Naturalist of Cum-
brae,' London, 1891).

William Pearson (1767-1847) of
Borderside, Crosthwaite, near Ken-
dal, was a self-educated yeoman,
who after many years spent in a
bank at Manchester retired to a
small patrimonial estate on the
southern border of Westmorland.
He possessed a choice collection of
books, representing fully the English
poets of all ages, and in translation
the best German authors. " Of
the habits of birds and other native
creatures around him he was a
watchful observer, and he described
them in purest English with a
charm that suggested no disadvan-
tageous comparison with \Vhite of
Selborne " (see Groves, ' Life of
Hamilton,' vol. iii. p. 15). He was
a friend of Wordsworth.

To this list, which could be in-
definitely extended, I might add
another, beginning with Thomas

VOL. I.

Bewick (1753-1828), the reviver of
wood-engraving in England, who
lent his art and life to the delinea-
tion of nature. 'British Birds'
(1797-1804) is a standard work on
the borderland of art and science,
in which manj' other British artists
have, in humbler or more extensive
fields, laboured with so much faith-
fulness and success.

^ The ' Complete Angler ' and the
' Natural History of Selborne,' are
types of a class of literature peculiar
to this country. In these classical
productions we are introduced into
the nursery of English thought, po-
etry— nay, of science itself. These,
as the nation draws ultimately its
wealth from the produce and culture
of the land, on their part receive
valuable ideas from a study of
nature. The purity and origin-
ality of English art and poetry have
their home in the same region.
Gilbert White (1720-93) was born
and lived in the little Hampshire
village of Selborne. He was one of
five brothers, all of whom, in vari-
ous positions and vocations of life,
followed the study of nature in its
minute and local aspects, combining
with it an antiquarian taste. He
may not only be classed with the
naturalists, but belongs also to that
class of writers, peculiar also to Eng-
land, who devote their time to the
compilation of local records, of
county histories, and to the preser-
vation of the relics and memorials

290

SCIENTIFIC THOUGHT.

50.
The Geologi-
cal Society.

action against the theorising methods which had come
over from the Continent led to the formation of the
Geological Society in the year 1807. At that time
the war of the Wernerians and Huttonians, or, as they
were also called, the Neptunists and Plutonists, was rag-
ing in the northern metropolis. The Geological Society
of London was established with a view to " multiply and
record observations, and patiently to await the result at
some future period — that is, its founders resolved to apply
themselves to descriptive geology, thinking the time not
come for that theoretical geology which had then long
fired the controversial ardour of Neptunists and Plu-
tonists." ^ Fifty years after the formation of this society

of country life in bygone centuries.
The series of letters written be-
tween the years 1765 and 1787
containing "the observations of
forty years," and published, 1789,
with the title ' The Natural History
and Antiquities of iSelborne,' had
the object " of laying before the
public his idea of parochial history,
which, he thinks, ought to consist
of natural productions and occur-
rences as well as antiquities." To
him " nature is so full tliat that dis-
trict produces the greatest variety
which is the most examined." He
early insists on the necessity of
monographs in natural history ;
suggests the usefulness of a "full
history of noxious insects " ; gives
in a series of letters a faithful and
minute description of the swallow
tribe as they are found in his
country ; traverses the Downs of
Surrey with a loving eye a hundred
years before they became celebrated
through the greater Darwin ; makes
valuable observations about " earth-
worms," suggesting a monograph
on them ; suggests, in an age which
was governed by the systematising

mania, that " the botanist should
study plants philosophically, should
investigate the laws of vegetation,
should promote their cultivation,
and graft the gardener, the planter,
and the husbandman on the phy-
tologist," as "system should be
subservient to, not the main object
of, pursuit."

1 "The one point the catastro-
phists and the uniformitarians
agreed ui)on when this society was
founded was to ignore it [vi~., geo-
logical speculation]. And you will
find, if you look back into our re-
cords, that our revered fathers in
geology plumed themselves a good
deal upon the practical sense and
wisdom of this proceeding. As a
temporary measure I dt) not pre-
sume to challenge its wisdom ; but
in all organised bodies temporai-y
changes are apt to produce per-
manent effects ; and as time has
slipped by, altering all the condi-
tions vi'hich may have made such
mortification of the scientific flesh
desirable, I think the effect of the
stream of cold water which has
steadily flowed over geological specu-

THE SCIENTIFIC SPIRIT IN ENGLAND.

291

the author from whom I quote, Dr Whewell, in the third
edition of his ' History of the Inductive Sciences,' could
still say that " their task was not yet finished, their mis-
sion not yet accomplished — that they had still much to
do in the way of collecting facts ; and in entering upon
the exact estimation of causes, they have only just thrown
open the door of a vast labyrinth which it may employ
many generations to traverse, but which they must needs
explore before they can penetrate to the Oracular Chamber
of Truth." ^ One of the many individuals in this country
who " had long pursued his own thoughts without aid and smith.
without sympathy " ^ was William Smith. " No literary

51.

William

lation within these walls has beeu
of doubtful beneficeuce " (Huxley
on " Geological Reform," Address
to the Geological Society, 1869 ;
reprinted in ' Lay Sermons,' &c. ,
1891, p. 207.)

^ See Whewell, ' History of the
Inductive Sciences,' 3rd ed., vol. iii.
pp. 428, 518. Lyell, ' Principles of
Geology,' 3rd ed., vol. i. p. 102, &c.

'^ Whewell, loc. cit., vol. iii. p.
427. William Smith (1769-1839),
a native of Oxfordshire, has been
called the Father of English Geo-
logy. He was — like so many other
naturalists of this country — an
amateur in his scientific studies,
which were conducted on the occa-
sions of his elaborate surveys of
Oxfordshire, Warwickshire, and
Somersetshire in connection with
the engineering of several canals.
He initiated in England the science
called on the Continent " Strati-
graphy," observed the successive
layers in the geological structure
of the country, and in 1799 pre-
pared a tabular view of the order
of the strata and their organic re-
mains in the neighbourhood of
Bath. For many years after this

he was occupied in preparing his
Geological Map of England and
Wales, which appeared on the five
miles to the inch scale in 1815 in
fifteen sheets. He was popularly
known as "Stratum Smith," but
remained almost unknown abroad,
as he himself also seems to have
taken little notice of Continental
geology or prevailing theories.
Though he began earlier than Cu-
vier and Bronguiart, they antici-
pated him by publishing in 1811
their mineralogical description of
the Paris Basin, thus becoming the
founders of the science of paleon-
tology (see Peschel, ' Geschichte
der Erdkunde,' Miinchen, 1877, p.
714, &c.) Of the Geological Map
Lyell says ('Principles of Geology,'
vol. i. p. 101) that it "remains a
lasting monument of original talent
and extraordinary perseverance ; for
he had explored the whole country
on foot without the guidance of
previous observers or the aid of
fellow-labourers, and had succeeded
in throwing into natural divisions
the whole complicated series of
British rocks."

292

SCIENTIFIC THOUGHT.

52.
Charles Bell.

cultivation of his youth awoke in him the speculative
love of symmetiy and system ; but a singular clearness
and precision of the classifying power, which he possessed
as a native talent, was exercised and developed by exactly
those geological facts among which his philosophical task
lay. Some of the advances which he made had been
entered upon by others who preceded him ; but of all
this he was ignorant, and perhaps went on more steadily
and eagerly to work out his own ideas from the persuasion
that they were entirely his own." In what he did and
published, beginning with the year 1790, "we see great
vividness of thought and activity of mind unfolding itself
exactly in proportion to the facts with which it had to
deal." '

About the same time that geological studies received a
great impetus in this country from two distinct centres —
the philosophical teaching in the Scotch metropolis, and
the more empirical labours of the Geological Society — a
signal discovery in another line marked a great step in
anatomy and physiology. This was Charles Bell's dis-
covery, in the year 1807, of the difference between sensory
and motor nerves, "doubtless the most important accession
to physiological knowledge since the time of Harvey." ^

1 Whewell, loc. cit, p. 423.

■•* This statement, takeu from Dr
Henry's ' Report of the British As-
sociation,' vol. vi. , and repeated by
Whewell {loc. cit., vol. iii. p. 352),
probably requires a correction, since
Du Bois-Reymond and others have
placed in their true historical posi-
tion the gi'eat merits of Descartes,
who by the discovery of the principle
of " reflex action " " did for the
physiology of motion and sensation
that whicli Harvey had done for

the circulation of the blood, and
opened up that road to the me-
chanical theory of these processes
which has been followed by all his
successors" (Huxley in his address
to the British Association at Bel-
fast, 1874; reprinted in 'Science
and Culture, &c.,' {>. 200, &c.) The
tirst enunciation of the principle of
reflex action had been variously
ascribed to Joh. Midler, Prochaska,
Willis, till Du Bois-Reymond in his
most interesting ' Gediichtnissrede

THE SCIENTIFIC SPIRIT IN ENGLAND.

293

Bell's career was a unique one. He had early severed
his connection with the great medical schools of Edin-
burgh, where his brother taught. He lectured and prac-
tised privately in London, where he gained a considerable
reputation ; but in his case also it was on the Continent
that his greatness was more generally recognised. As in
Dal ton's case, his countrymen were slow to do him justice.^
In France he had so great a name that a celebrated

auf Joh. Miiller' (Berlin Acad.,
1859) showed how the merit uf
enunciating it is due to Descartes,
whose tract on ' Les Passions de
rime ' was published in 1649.
Both Du Bois-Reymondand Huxley
give full extracts from the writings
of Descartes. There seems, however,
to be some doubt to what extent
Descartes substantiated his mechan-
ical view of the action of the ner-
vous system by actual experiments.
Richet in his ' Physiologic des
Muscles et des Nerfs' (Paris, 1882,
p. 505, &c. ) refers to this, and
while giving Descartes his due,
also says that practically from the
time of Galen to Charles Bell no
marked progress had been made
in the knowledge of the nervous
system, and that this belongs al-
most entirely to the nineteenth
century (pp. 502, 507, 514). Huxley,
who takes a much higher view of
the merits of Descartes, says he
was not only a speculator, but also
an observer and dissector (ioc. cit.,
p. 201), and actually places him
at the head of modern physiology
(p. 334, &c.)

1 Charles Bell (1774-1842) was
born at Edinburgh. His elder
brother, John Bell (1763-1820),
who was a lecturer of great repute
in the extra-mural School of Surgery
at Edinburgh, first drew his atten-
tion to the medical profession. It
was only late in life, and after he

had gained his European renown,
that he was appointed to the Chair
of Surgery at the Universit}' of
Edinburgh, whicli had been created
in 1831, and it does not appear
that he was at all sufficiently ap-
preciated in this position : he used
to say, "I seem to walk in a city of
tombs," being unknown in the city
of his birth (see Sir A. Grant,
'University of Edinburgh,' vol. ii.
p. 453). Whilst Charles Bell es-
tablished the difference of sensory
and motor nerves, and dispelled
" the confusion which prevailed up
to that time in the minds of anato-
mists and physiologists regarding
the functions of the various nerves,"
the merit of proving by strict ex-
periment the correctness of Bell's
theorem belongs to Johannes Miiller
(1831), who showed it in the frog,
and to Magendie and Longet, who
succeeded in exhibiting it in warm-
blooded animals. Up to the date
of Miiller's experimental proof no-
body regarded " Bell's doctrine as
more than an ingenious and indeed
plausible, but nevertheless not suf-
ficiently demonstrated, idea " (see
Du Bois-Reymond, ' Reden,' vol. ii.
p. 176, &c. : also Henle's descrip-
tion of the demonstration given by
Miiller in Paris on the 13th Sep-
tember 1831 to Humboldt, Dutro-
chet, Valenciennes, and Laurillart,
in 'Jacob Henle,' by Merkel, 1891,
p. 83).

294 SCIENTIFIC THOUGHT.

anatomical professor, when Bell visited his lecture-room,
dismissed his class with the words, " C'est assez, messieurs,
vous avez vu Charles Bell."

In Germany one of the great achievements of Johannes
Miiller, through which he acquired European celebrity,
was his actual experimental proof of Bell's thesis, with
which he had occupied himself for many years.

Instances might be indefinitely multiplied, showing the
individual greatness, but also the isolation, of English
men of science and their discoveries ; how the latter ema-
nated so frequently from the depths of original genius
in intimate communion with nature ; how they as fre-
quently lacked those social advantages, that organisation
for development, which the great schools and establish-
ments of the Continent all through the century have pos-
sessed in so eminent a degree. Not only in the study
of nature has this individual character of British research
53. shown itself, though it is here most conspicuous. In the

Historical . p n • i n

geography, exploratiou of foreign lands and the monuments of by-
gone civilisations — in the historical branches of research,
we meet with similar pioneer work. Who does not recall
the names of Dr Young and of Layard ? I will mention
only one instance of this kind, where individual ability
joined to fortuitous circumstances laid the foundation of
a new branch of research on the borderland of natural
and political history, the geography of ancient and modern
Greece — the exploration of the land which produced the
most remarkable, and perhaps the most intense, culture
which the world has yet seen. Note what Ernst Curtius ^

^ See his essay in the ' Preupsische I Wetteifer der Nation en in der
Jahrbiicher,' vol. 38, on M. W. ^ Wiederentdeckung der Lander des
Leake, and his discourse, "Der Alterthums" (1880), both reprint-

THE SCIENTIFIC SPIRIT IN ENGLAND,

295

says, — the man to whom we are most indebted for the
systematic historical and artistic study of this remarkable
country; whose mind has better than any other succeeded
in representing to itself the natural and ideal features of
that country and that bygone race, and who has drawn in
his writings a series of pictures, reproducing that past
glory in unequalled perfection. In tracing the begin-
nings of the modern science of archaeology or historical
geography, he assigns to England and Englishmen a fore
most place as pioneers. " In England there was no medi
a;val tradition which suggested expeditions to the East,
nor did there exist any external occasion or public inter-
est, but it was a free and purely human attraction which
led Britons to the classical soil, and private means have
made all the sacrifices that were required in order to
satisfy a craving of the soul.^ .

England became the

ed in that valuable collection, ' Al-
terthum und Gegenwart,' 3 vols.,
Berlin, 1882 and 1889. In the re-
discovery of the countries of ancient
civilisation, Italians made the be-
ginning with Cyriacus of Ancona
(from 1412 to 1442). Then follow
the French — Jacob Spon of Lyons,
a German by birth, being among
the earliest (1675). The generation
that succeeded the age of Scaliger
produced the first maps of Greece
(Paulmier). Then follows England,
where the name of Arundel has ac-
quired a doubtful celebrity through
that wholesale acquisition of an-
cient relics which Mr (afterwards
Sir William) Petty and John Evelyn
carried on in his name in Greece
and Asia Minor. It is interesting
to note here the position that Ger-
many holds in the growing science
of archaeology, of which Winckel-
mann may be considered the foun-
der. " The Germans possessed no

advantages and resources bj' which
they could take part in the con-
test of nations over the rediscovery
of the countrie? of ancient histoiy.
. . . Whilst in Italy it was national
feeling, in France political relations
with the East, in England the love
of collecting and travelling common
among the aristocracy, which estab-
lished the connection of the Old
World with the New, in Germany
it was the workroom of the profes-
sor " (Curtius, loc. cit., vol. ii. p. 229).
^ E. Curtius, loc. cit., vol. ii. p. 226.
" In the year 1742 Stuart and
Revett wandered among the ruins
of Rome, and recognised that in
its relics they beheld only later and
degenerate forms of ancient art.
Six years later they set sail for
Greece. It was, after Cyriacus of
Ancona and Jacob Spon of Lyons,
the third journey of exploration ;
but it was the first in scientific im-
portance" (p. 227).

296 SCIENTIFIC THOUGHT.

treasury of the wonders of the East, and whilst the Con-
tinent was closed to her, her travellers flocked to Hellas,
registering with marvellous patience, watch in hand, on
the back of the slowly marching mule, piece by piece, the
remains of antiquity. . . . The political mission, headed

Martin ^^ Martin William Leake, was as such quite unsuccessful ;

Leake™ ^^r sciencc, it was of priceless value : from the moment
that Leake trod on classic soil the reminiscences of Homer
and Herodotus were kindled, and he saw clearly his life-
work before him. Under the powerful impressions pro-
duced by the great table-land of Asia Minor with the
solitary snow-peak Argaios, deeply moved by the deserted
places, marching over Grecian inscriptions, over sarcophagi
and temple ruins, he felt the irresistible charm of the
attempt to explore and to understand these homes of
ancient culture.^ . . . The scientific result was a lasting
gain for the civilised world, and the travels which he
made from 1805 to 1807 mark an epoch in our know-
ledge of Grecian antiquity." ^

But the labours of the pioneer in science, life, or art,
which form so conspicuous an element of this country's
mental work during the first two-thirds of the century,
must be supplemented and carried further by a great
army of patient and trained explorers. Original ideas
must be cast into an appropriate and elegant form ; new
discoveries must be extended and criticised by strict
methods of research ; erudition and philosophy are re-
quired to guarantee completeness and depth. In the
large domain of the historical sciences these labours of

^ E. Curtius, loc. ciL, p. 307.
-Ibid., p. 312.

THE SCIENTIFIC SPIRIT IN ENGLAND. 297

the school and the study are even more important than
in the exploration of nature, and thus it is not surpris-
ing that in these especially the bulk of the work,
though frequently begun by Englishmen, has been car-
ried on by the great schools and academies of the Con-
tinent. In the regions of exact science, with which we
are at present more immediately concerned, there will
always be a much greater inducement for original minds
to forsake the beaten track, the recognised method or
system.

The genius gifted with a larger field of vision and a
keener glance will always feel the longing to return to
Nature herself, and the practical man will be allured by
the prospects of application of science in the arts and
industries. Both will find their reward ; nor is it likely
that the works of Faraday and Darwin should be the last
illustrious examples of great and far-reaching ideas sprung
from the living intercourse of original genius and nature
without the support of any school ; or that the practical
success of the Atlantic cable will be the last fruit of
the rare combination of highest mathematical genius with
industrial and commercial enterprise. The historian of
thought is forced to admit that such rare combinations
are most likely to spring up amongst a people who have
always opposed the rule of systems and methods, of schools
and academies ; who have nursed and cherished an inti-
mate communion with nature ; and for whom practical
interests and adventures have always preserved an irre-
sistible attraction.

Living in an age when the foundation in England and
in Germany of institutions similar to the Academie Fran-

298

SCIENTIFIC THOUGHT.

65.

Work of
the three
nations
compared.

Qaise has been seriously discussed,^ when the British
Association has been copied abroad,^ and when scientific
men of eminence are joined in conference as to the advis-
ability of founding a professorial university in London,
in imitation of the great University of Berlin, it seems
appropriate to recall the various ways and means by
which, mainly in this century, the exact spirit of re-
search, the mathematical method of investigating nature
and reality, has been established and diffused.

France was the country in which the modern scientific
methods of measurement, calculation, and classification
were first practised on a large scale, reduced to a system,
and employed for the investigation of the whole of nature.
The Academy of Sciences, together with the High Schools
of Science, the Natural History collections, and Medical
Institutions, all in close connection, furnished an organi-
sation of the highest intelligences of the nation, by which

^ See Matthew Arnold's essay on
' The Literary Influence of Acad-
emies,' and Du Bois - Reymond,
' Ueber eine Kaiserhche Akadeinie
der deutschen Sprache,' 1874, re-
printed in ' Reden, &c.,' I^eipzig,
1886, vol. i. p. 141, &c. On the other
side see Huxley in ' Critiques and
Addresses,' ed. of 1890, p. 113, &c.

■^ The British Association, itself
established somewhat on the model
of the German " Naturforscher-
Versanimlung," founded by Oken
and Humboldt (see supra, p. 238)
in the year 1831, has become the
model of the younger " Associa-
tion fran9aise pour I'Avancement
des Sciences," founded in 1872
under the presidency of Claude
Bernard. It held its first public
meeting at Bordeaux in 1874. In
the opening addresses of the presi-
dent, M. de Quatrefages, and the

secretary, M. Cornu, the elder sis-
ter in England is referred to. A
characteristic passage in M. Quatre-
fages' address as regards the results
achieved by the British Association
is the following : " Grace a elle
une partie de la population a ete
transformee. Les fils de ces chas-
seurs de renards, qui, pour se
d^lasser de leurs rudes passetemps,
ne connaissaient que des joies
egalement violentes et materielles,
sont aujourd'hui des botanistes,
des geologues, des physiciens, des
archeulogues " ('Comptes Rendua,'
lere session, p. 40). Following
the resolutions carried in 188.'i,
the French Association amalga-
mated in 1886 with the older "As-
sociation scientifique de France,"
founded by Leverrier in 1864. See
' Compte Rendu de la 16me Ses-
sion,' vol. i. p. 1, &c.

THE SCIENTIFIC SPIRIT IN ENGLAND. 299

a systematic exploration of the heavens and the earth,
the inanimate and the living world, could be undertaken.
At the same time, the methods of measurement and cal-
culation were submitted to closer study ; new sciences
were created by the application of these methods; and
problems were attacked for the first time, with which,
at the end of the century, the scientific world is still
occupied. It was in France also that the discoveries of
the laboratory were first applied so as to contribute to
the revolution of arts and industries. In all its different
expressions — in the production of works of classical per-
fection in substance and in form, in its application to the
problems of life and society, and in its influence on gen-
eral literature — we find the scientific spirit, as we know
it, fully established in France in the beginning of the
century. About three decades later we find this spirit
domiciled in Germany, the study of the exact sciences
having been gradually accepted at the German univer-
sities as an integral part of the university cycle. It there
met the philosophical and classical spirit, which had or-
ganised the German university system and the teaching
of the higher schools, and had revolutionised historical,
especially philological, studies. What might have been
wanting at times in French science, historical complete-
ness and philosophical criticism, was added in Germany.
Germany has in the course of this century not only be-
come the country where the most faithful and exhaustive
record is kept of the scientific labours of the whole world,
but it has also become the country where mainly those
problems have been attacked which lie on the border-
land of natural science and philosophy, the problems of

300 SCIENTIFIC THOUGHT.

life and consciousness. Modern physiology, especially
psychophysics, is claimed as essentially a German science.
Meanwhile England, where the introduction of the
soientific spirit as an established canon of systematic and
methodical research was later than in other countries,
has all through this century, as before, continued to
do pioneer work in many isolated branches of science :
individual, as opposed to corporate effort, has here been
rewarded by a succession of brilliant discoveries, which
have revolutionised practical life or opened out new
views into the hidden recesses of nature. For the
want of organisations of research and teaching, such as
other countries possessed, these ideas of English thinkers
have frequently lain dormant or been elaborated by
foreign talent ; but this want of a recognised system, and
of a standard course of study, has forced original minds
into a closer communion with nature and with life,
whence they have frequently returned to the laboratory
with quite novel revelations. The largest number of
works perfect in form and substance, classical for all
time, belongs probably to France ; the greatest bulk of
scientific work probably to Germany ; but of the new
ideas which during this century have fructified science,
the larger share belongs probably to England. Such
seems to be the impartial verdict of history. During the
second half of the century a process of equalisation has gone
on which has taken away something of the characteristic
peculiarities of earlier times. The great problems of science
and life are now everywhere attacked by similar methods.
Scientific teaching proceeds on similar lines, and ideas and
discoveries are cosmopolitan property. So much more

THE SCIENTIFIC SPIRIT IN ENGLAND. 301

interesting must it be for those who have been born
members of this international repubhc of learning to
trace the way in which this confederation has grown up,
what have been the different national contributions to
its formation, and how the spirit of exact science, once
domiciled only in Paris, has gradually spread into all
countries, and leavened the thought and literature of the
world.

302

CHAPTER IV.

THE ASTRONOMICAL VIEW OF NATURE.

1. So far I have only treated of the scientific spirit, or of
tific spirit the mcthod of exact research, in a general way ; showing

in the first o o o

and second how it was firmly established and developed in France,
century. }^q^ ^|- spj.ga(j j^to Germany, and received there larger
and more systematic application, and how in this country
it gradually and almost imperceptibly grew out of the
older experimental philosophy. This growth, as we have
seen, took place partly under the infiuence of foreign
science, but still more through the individual and un-
aided labours of a small number of native intellects of
the very highest order, to each of whom was for a time
allotted the enunciation of some specially fruitful idea.
The period referred to in this survey was mainly the first
half of our century ; in it were most clearly marked the
characteristic differences between the three great civilisa-
tions of Trance, Germany, and England. A step further
in time would lead into the midst of our own period —
into the age which has largely reaped the benefits of those
earlier labours, both in theory and in practice, fully realis-
ing in many directions the predictions and even the ideals

THE ASTRONOMICAL VIEW OF NATURE. 303

national.

of the pioneers of science. One of these benefits, and
perhaps that which to an external beholder marks the
greatest difference between the first and the second half
of the century, is the greatly increased intercourse which
now exists as compared with the earlier years of our cen-
tury. This intercourse has reacted on the domain of 2.

Science be-
thought, and produced that exchange of ideas which •^o"?<' ^^^r-

promotes more rapid progress. It hardly belongs to the
history of thought to analyse^ the different steps by which
the great change has been brought about. Still, a very
superficial glance will suffice to show how the work of
bringing about an international exchange of ideas has
been very characteristically divided among the three
nations in which we are specially interested. It was not
in the interest of thought, of science, or of literature, but
rather in that of commerce and of industry, that the
modern facilities of intercourse and exchange were in-
vented and introduced.^ We shall therefore expect to

^ The principal dates of the in-
troduction of steam - engines and
telegraphs for facilitating communi-
cation are as follows : —

1802. The tug Charlotte Dundas,
built by Symington, was tried on
the Forth and Clyde Canal.

1812. Henry Bell built tlie Comet
with side paddle-wheels. It ran on
the Clyde as a passenger steamer.

1829. George Stephenson's Rocket
was tried on the Stockton and Dar-
lington Railroad, which had been
begun in 1821. In the year 1829
the Liverpool and Manchester Rail-
way was inaugurated.

1838. The first steamboats, Sirius
and Great Western, crossed the
Atlantic.

1833. A comprehensive system of
railways was planned by the French
and Belgian Governments.

1835. The first German railway
was opened between Niirenberg and
Fiirth. The first electric telegraphs
for public use were almost simul-
taneously constructed in England,
Germany, and the United States —
the first successful line being prob-
ably that constructed by Wheat-
stone and Cooke between 1836 and
1840. The first Atlantic cable was
begun in 1857, and after repeated
failures, which were in the main
corrected by the scientific investi-
gations of William Thomson (Lord
Kelvin), telegiaphic communication
with America was permanently es-
tablished in 1866.

- This remark applies fully to the
railway system, hut scarcely to the
development of the electric tele-
graph, which was first actually used
for scientific purposes by Gauss and

304

SCIESTrFIC THOUGHT.

fin" -" " r'z'-:.'.- .-inly in that conn try in which
TL^T -:^=:cx spheres oi praeiie^ work had grown nn-
It t i~i ::: rl;f.T~ — ^in Great Britain and its esten-
siTc -T tl ti. ;_t- Io Germany, on the other side, with
irs fniiT develof-ed system of learning, we are indebted
mainlv for the : ziT'rie recxirdin^. resisterinz- and analvs-
ing of the scirZTir. : .a : vjts of the whole world. To France

Weier at ^ i.tI :z :_t ^ear S<>jO fees. ... I have devised a

ISSS. ""- - __.-.-.-_— - - -, simple ajrrangeraeiii by wiiioli I can

^is t^--'. -."^e install tlv reverse Lhe liirection of

ree^Kl~ -- - . _ H. the c^^rr^nz. wMct I call a et'tii-

Wcber - . - . " - : '^■Hl- mutator. . . . We kave already

hJia Weber. BresliTi- 1 » i-c . p. i-f . i c. used zhis K-ntrivance for telesrapliiir
"We fead. kfcere * ' - " ^'t after 15S'J esperimenis. ■whioii suc-ceett vary
haA t-eer ei ■witli re- well widi wiole words and short

- ,_-- -_ -_-rnis senteices. ... I am. convinoec

toam. i - ii? thai: by oang suSdeiiuy strong

cjuklMo. " -Lns ooe migiit telesraph instaii-

Hsagaeti--- - "aneoo^y in this manner irc>Ea

nj^ocatau'^ > ' - So- GOTtinaeti to Hanove- or fr'jm

t ii'tn im T>t=..~ .^_ _;!.•__ i-_ r tit Hanover to BrQuea" see Sche--

Wecer to take -' •—- hLz's address c^n the 'jccason of

" - - 7 -. In- Gauss's c-Qitaiary. 'jottingei. 1*77.

l'_~ip: ■■'..'- -t a p, 15. ic. I To Sthmraeher. 6th

-Ttva- Aogueh 1S35. Gaass wrote as lol-
- ' -■- lows : " With a budget of 150
thalers [£22, lOs.j annually for
. - — Oheerrszorj and Magnetic Insti-
tute toeecfaer, really extsiare trials
eaimot of coarse be made. But
ecrald thousands of thaiers be be-
- - r Stowed the^oo^ I ThinV that, for

. _^ i-.i_^T- instance^ elesromaeDede telegraphy
- r years 1 5cS mizht be carried to a psfecdon and

li-. ' - -- to dimensjose a£ wfaieii fmagrrtation

?T^ —- almort starts haekJ" Gazis esti-

mates that fifteen miUkiDS sterling
- :fc»pp^ wire would suffice to reach

_ "t- _ : - 1 t" - " . ■ . - : te antiixjdes, and he says signrfi-

1 - - ' ' - ' lantly. " I do not think it impoe-

r::-: - sTbie to invent a mecfaanian by

' which a despatch could be played

oS almost as meefaanically as a

- - muaeal-boi ji«ns aS a tmie wfaoi

- ir is Qoee fixed on a roOer " (see

' ^Kiefweehsel zw^efasi Gaaoa uitd

SckamadxT.' ed- Peters. voL H. p.

t. . , - . .: 41L*c.}

THE ASTEOXOMICAL NIEW OF XATUKE. 305

we owe the first begiimiiigs of a general and mtranational
STstem of units and measnrements, whiclL like the com-
mon Latin tongue in former centuries, or like the unirersal
lancruages of algebra or of music, enables as to express the
results of scientific research in fommlse intelligible everr-
where and at all tnnes, without laboiicnis translations and
time-absorbing re«luctions.

The effect of these international labours has been to
destrc'T the clearly marked differences of national thoi^it.
At least in the domain of sdenoe the peculiarities of the
French, the German, and the English schcwls are rapidlr
disappearing. The characteristics of national thoo^t
still exist : but in order to find them in the present age
we should have to study the deeper philoso^^iical leasiHi-
iuiTs, the general Kterarure and the artistic efforts of
the three nations. These aspects of the dioi^t of our
c-entury lielong to later portions of this work. I hc^
there to take up many of the threads which I here l»eak
off. as for the present purpose they cannot be profital^
continued. To separate the scientific work of the second
half of the centurv ac-cordins to c-ountries and natims
would lead to unnecessary repetition. The second half of
the c-enrury sees everywhere in the domain of science the
dying out of national restrictions — in every country the
introduction of foreign meth«3ds and foreign models, foreign
institutions and foreign apparatus. The establishment of
an observatory or a laboratory in oor age lays nnder con-
tribution almost every civilised c-ountry in the world, and
the mc-st international of sciences — ^that of electricity —
fixes its units by the names of discoverers of many
c-ountries.

VOL. L r

306

SCIENTIFIC THOUGHT.

4.

Special

scientific

ideas.

5.
Philosophy
of science.

I therefore look upon the spirit of exact research as I

thoroughly domiciled in the leading countries of Europe!

i

during the second half of the century, and intend in the;
sequel to explain more precisely the different views, the'
leading ideas, under which this research is everywhere
conducted. These leading ideas have themselves been,
more clearly brought out and recognised during this^
period.

The narrow spirit of the Baconian philosophy which:
reigned in England, the vagueness of the philosophy of I
nature which reigned in Germany, during the earlier!
decades of the century, have disappeared in favour of the!
more comprehensive and the stricter methods taught by
Lavoisier, by Monge, by Laplace, and by Cuvier in France..
New ideas of extensive bearing have been added, and in:
the light of these the powers and the limits of science
have been more correctly recognised.

To some of my readers well-known names will occur
which might serve as guides to fix these leading ideas,,
under the influence of which the march of science has!
proceeded : Sir John Herschel, Auguste Comte, Johni
Stuart Mill, and Whewell ^ have indeed done much toi

1 Of these writings the earliest is
Sir John Herschel's " Preliminary
Discourse on the Study of Natural
Philosophy," which appeared in
Lardner's ' Cabinet Cyclopedia ' in
1831. Tlie writings" of William
Whewell on the ' History ' and ' Phil-
osojihy of the Inductive Sciences'
were begun about the same time.
They were planned to serve three
distinct objects — to give, Ist, a
philosophical history of astronomy,
mechanics, physics, chemistry, and
botany; 2nd, an analysis of the na-
ture of induction and the rules of

its exercise ; and 3rd, to answer the!
question of applying inductive pro-
cesses to other than material sci-;
ences — as philology, art, politics,]
and morals (see ' William Whewell,''
by I. Todhunter, vol. i. p. 90)..
The 'History' appeared in 1837 in;
three volumes, a second edition iu!
1847, a third in 1857; tlie ' Philo-'
sophy' appeared in 1840 in two'
volumes, a second edition in 1847. j
In the course of its execution the!
original plan was not strictly ad-i
hered to — the scope of the History!
was enlarged considerably, and the.

THE ASTRONOMICAL VIEW OF NATURE. 307

familiarise the unscientific public with the progress of
science and its canons of thought. And it would thus
appear natural to resort to their teaching and their ex-
planations. But this is not the road I propose to follow.
Whewell's ' History of the Inductive Sciences,' being the
first attempt to compass a large subject, will, like
Montucla's earlier ' History of Mathematics,' always re-
main a standard work. It was, however, written at a
time when the tendency of modern scientific thought was

Philosophy was broken up mto
dififerent parts. Herschel stands
mainly on the ground of Bacon's
philosophy, whereas Whewell starts
with the remark that " Bacon only
divined how sciences might be con-
structed," but that '"we can trace
in their history how their construc-
tion has taken place" ; that "tliough
Bacon's general maxims still guide
and animate philosophical inquirers,
yet that his views, in their detail,
have all turned out inapplicable."'
He accordingly aims at a " New
Organ of Bacon, renovated ac-
cording to our advanced intel-
lectual position and office " (Pre-
face to •2nd ed. of the ' Philosophy,'
1847). lu the exposition of his
views Whewell was greatly in flu -
-enced by Kant's philosophy. He
thus searches for the fundamental
ideas which underlie all scientific
reasoning ; for " besides facts, ideas
are an indispensable source of our
knowledge." The historical por-
tions of Whewell's works have met
with great appreciation in England
and Germany even from those who,
like Herschel (see the review in the
'Quarterly,' June 1841) and Mill
(see ' Autobiography,' p. 208), could
not agree with his philosophy.
The latter has been eclipsed by
the bolder speculations of Auguste
Comte, whose 'Philosophie positive'
appeared in six volumes between the

years 1830 and 1842 in France.
Still more than Whewell did Comte
emphasise the necessity of learning
from the exact sciences how to
treat economical and social pro-
blems in a methodical manner.
Instead of the minute and fre-
quently hesitating elaborations of
W'hewell, we find in Comte the
bold generalisation of the three
stages of knowledge — the theologi-
cal, metaphysical, and positive, —
which forms the groundwork of
" Positivism." Of more permanent
value than Whewell's and Comte's
philosophies are the investigations
of J. Stuart Mill, who in his ' Sys-
tem of Logic, Ratiocinative and In-
ductive' (1st ed., 1843), has laid
the foundation for all subsequent
treatises on this subject, and whose
thoroughgoing empiricism is being
more and more adopted by scien-
tific thinkers. Like Whewell and
Comte, to whom he acknowledges
his obligations ('Autobiog.,' pp. 165,
209, &c.), his ultimate object was
to solve the question "how far the
methods by which so many of the
laws of the physical world have
been numbered among truths irre-
vocably acquired and universally as-
sented to, can be made instrumen-
tal to the formation of a similar
body of received doctrine in moral
and political science" (Preface to
Isted.)

308

SCIENTIFIC THOUGHT.

not as clear as it has become since, and the work hu
also been superseded by more detailed labours, espe
cially of German historians.^ The ' Philosophy of the Ie
ductive Sciences,' by the same author, was written wit
the object of doing something towards determining th
nature and conditions of human knowledge, and ha
thus a philosophical rather than a historical object i
view. The same can be said of Mill's ' Logic,' of Comte
' Philosophic positive,' and of more recent works— sue
as Jevons's ' Principles of Science.' They form an in
portant section of the philosophical literature of on
century, and on future occasions I shall frequently hav
to refer to their teaching. At present I am not aboi
to investigate the eternal principles of correct reasoi
ing, and the particular methods adopted, consciously c
unconsciously, by scientific writers of all times. Whs
1 desire to do is, to enumerate and analyse brietiy tli
changing ideas, the general views, under the guidanc
of which scientific work has progressed in the cours
of this century. No doubt the same object was befoi

^ Besides the works on the his-
tory of tlie special sciences con-
tained in the Munich Collection,
' Geschichte der Wissenschaf ten in
Deutschland,' which in many in-
stances is not limited to German
science and learning, there is the
unique ' Geschichte der Chemie,'
by Hermann Kopp (Braunschweig,
4 vols., 1843-47), the 'Geschichte
der Physik,' by Rosenberger (Braun-
schweig, 3 vols., 188-2-90), and
Hiiser's ' Geschichte der Medicin '
(Wien, 1875-82, 3rd ed.) In addi-
tion to the numerous works of Ger-
man specialists, I must mention as of
the first importance and value the
histories by the late Isaac Todhunter

of the ' Theory of Attraction an
Figure of the Earth' (2 vols
1873), the ' Calculus of Variations
(1861), the ' Theory of Probability
(1865), and the 'Theory of Elasti.
ity ' (continued by K. Pearson,
vols, in 3 parts, 1886-93). The
supply the want of a good histor
of modern mathematics, which dot
not exist. Lastly, the " Deut.scli
Mathematiker- Vereinigung " hav
published in their Jahrbuch vali
able histories of special branches c
mathematics — notably the ' Theor
of Invariants ' by Franz Ma^-er, an
the ' Modern Theory of Functions
by Brill and Noether. ,

THE ASTRONOMICAL VIEW OF NATURE. 309

the mind of Whewell when, after writing his his- e.

® W}iewen's

torical work, he attempted in the philosophical sequel ^^^'fpj?,'
to abstract the general ideas which have led scientific ''^ophy.'
research : but it is instructive for our present purpose
to note how, writing about the middle of the century,
he hardly brought out any of those principles which
in the course of its second half have turned out to
be fruitful, and have almost become watchwords of
popular science. In the year 1857, the date of the
publication of the latest editions of Whewell's works,
nothing was poj)ularly known of energy, its conserva-
tion and dissipation, — nothing of the variation of species,
and the evolution of organic forms, — nothing of the
mechanical theory of heat or of that of gases — of
absolute measurements and absolute temperature ; even
the cellular theory seems to have been popular only in
Germany. And yet all the problems denoted by these
now popular terms were then occupying, or had for many
years occupied, the leading thinkers of that period. But
we find no mention of them in Whewell's works.^ So

^ The dates of the birth of these
leading ideas of the second half of
our century are approximately as
follows : —

Absolute measurements were
started by Gauss about 1830, and
the scheme published in 1833 in
his memoir, 'Intensitas vis magne-
ticfe terrestris ad mensuram absolu-
tam revocata.' They were extended
to electrical phenomena by W^eber in
his' Electrodynamische Maasbestim-
mungen,' 1846. The absolute scale
of temperature was introduced by
William Thomson in 1848.

The cellular theory was pro-
pounded by Sclileiden in 1838, and

extended to animal structures by
Schwann in 1839 ; the term "pro-
toplasm ' was introduced by Mohl
in 1846.

The mechanical theory of heat
dates from Mayer's and Joule's de-
terminations of the equivalent of
heat in 1842 and 1843.

The doctrine of the conservation
of energy dates from Helmholtz's
memoir, ' Ueber die Erhaltung der
Kraft,' in 1847; that of dissipation
of energy from William Thomson's
paper " On a Universal Tendency
in Nature to the Dissipation of
Mechanical Energy," 1852 ; it was
prepared by Watt's and Poncelet's

310

SCIENTIFIC THOUGHT.

little was the foremost champion of inductive though
able to discern the tendencies of his age : a warning t(
those who attempt to recognise the aims of contemporar
thought.^ j

It is not, then, to the philosophical writers that I shal
apply in order to trace the leading directions of scientific

definitions of hoise- power and work
(1826), which Whewell does not
mention.

The mechanical theory of gases —
not to mention the older specula-
tions of Daniel Bernoulli — dates
from Avogadro's and Ampere's
hypothesis, published in 1811,
" that all gaseous bodies, under the
same physical conditions, contain
the same number of units," from
Herapath (1821) and Joule (1851).

OnWhewell'sjJOsition with regard
to the question of the origin and
variation of species, then already
ventilated by Lyell, see ' History of
Induct. Sci.^' vol. iii. p. 489, &c.
(3rd ed.), and Huxley's remarks in
the 'Life of Charles Darwin,' vol.
ii. p. 192, &c. Wallace's essay
the Law which has regulated
Introduction of New Species '
published in 1858 along with Dar-
win's preliminary statement of his
views.

We might form a whole catalogue
of scientific terms, some of them
by no means of recent origin,
which are wanting in Whewell's
books, but which now govern scien-
tific progress: such are energy,
work, action and efficiency, absol-
ute measurement, to mention only
physical terms. The general ideas
upon which he himself lays some
stress, such as those of polarity and
symmetry, appear on the other
hand to be vague generalisations,
which have frequently led people
astray.

^ " It is a remarkable evidence of

On
the
was

the greatness of the progress whic
has been effected in our time, tha
even the second edition of th
' History of the Inductive Scieii
ces,' which was published in 184(
contains no allusion to the publi
cation in 1843 of the first of th
series of experiments Vjy which th
mechanical equivalent of heat wa
correctly ascertained. Such a faii
ure on the part of a contemporary
of great acquirements and remark
able intellectual powers, to reai
the signs of the times, is a lesso:
and a warning worthy of bein^
deeply pondered by any one wh
attempts to prognosticate th
course of scientific progress " (Hux
ley in Ward's ' Reign of Queen Vic
toria,' vol. ii. p. 355). The sam
writer has pointed out how Au
guste Comte was still more un
fortunate in his opinions on con
temporary science. " What struc
me was his want of apprehensio:
of the great features of science
his strange mistakes as to th
merits of his scientific contempoi
aries; and his ludicrously erroneou
notions about the part which som
of the scientific doctrines curren
in his time were destined to play ii
the future" ("Scientific Aspects i
Positivism," 'Lay Sermons,' 1891
p. 130). He then goes on to sho^
how Comte treated the undulator
theory with contempt, extolle'
Gall, depreciated Cuvier, and spok
of the " abuse of microscopic in
vestigations " (ibid., p. 134). -

THE ASTRONOMICAL VIEW OF NATURE. 311

thought in our century : their position towards this
thought is indeed instructive, but it is frequently unsafe.
Philosophical reasoning either precedes or succeeds t.

. . Philosophy

the labours of the scientific thinker ; it rarely accom- ^"d science.
panics them. In the history of earlier times, during the \
first centuries of the modern period, we find some of the
foremost philosophers, such as Descartes, Bacon, Leibniz,
occupied in attempting to lay down the correct lines on
which science should proceed, or to find general ideas
which could serve as supreme principles of scientific
truth. It is a rare thing to find that they have succeeded
in either of these attempts. In more modern times,
ever since Locke started on a different track, it has been,
especially in this country, the endeavour of philosophers
to abstract out of the existing volumes of scientific re-
search the leading ideas which have proved so helpful,
and to explain their origin, their bearing, and their value.
Perhaps they have been more successful than their pre-
decessors : it has, however, frequently happened to them,
that whilst they were elaborately analysing some process
of reasoning, or some prevailing scientific principle,
science has meanwhile adopted some entirely different
line, and presented an entirely unexpected development.
In this respect they resemble that school of historical
politicians which in the middle of our century in Ger-
many ^ attempted to read the signs of the times, and to

^ This is the school represented by
the historians Dahlmann and Ger-
vinus. A good account, with a
somewhat severe criticism of the
aims of this school, will be found
in Karl Hillebrand, ' Zeiten, Volker
und Menschen,' vol. ii. pp. 205-290.
" The State and Literature had

grown in Germany alongside of
each other without coming into
contact, the former active, reticent,
modest, the latter declaiming,
noisy, pretentious. It appeared as
if all our life had become intellect-
ual ; Gervinus himself thought so
and blamed us. In reality it was

312 SCIENTIFIC THOUGHT.

prescribe the lines on which the desired unification of the'
nation could be secured. Events took their own course,
and the great statesman who was the central figure of thej
new era of European history may be excused the scornj
with which he has sometimes treated these theoretical]
politicians. \

8. The leading ideas which I select as marking the progressl

Leading . _ ^ & r & ,

scientific of Scientific research in our century have, with few excep-i

ideas mostly '' ^

Indent. tions, hardly been discoveries or inventions of this age.'
Some of them are very old. The ideas of attraction,;
which in the hands of Newton and Laplace have led toj
such remarkable results, are of great age, and were'
familiar to the philosophers of Greece and Eome ; the
same can be said of the atomic theory, which in thei
hands of Dalton became such a powerful instrument.!
The principles of energy and its conservation can be]
traced back to the writings of Newton and Leibniz, audi
even to earlier thinkers. The same may be said of thel
modern ideas on heat, of the molecular theory of gasesj
and even of Lord Kelvin's vortices ; whilst the viewsl
which through Darwin have revolutionised the uaturali
sciences have been traced in the suggestions of much ear-l

i

not so. When the professors turned j thought the German professorsi

their backs on science in order to
turn to politics, they imagined pol-
itics were now only beginning :
with the wonted pride of learning
they saw in the administrative
class only labourers and clei'ks ; for
to them parliaments and freedom

composed the German nation, as|
the French lawyers formed the
French nation ? And indeed pub-
lic opinion in Germany was that of;
the professors. . . . The learned
newspaper writers imagined the,
spirit of the age spake in them ; i

of the press were identical with no wonder that they overestimated*

politics. The mouthpiece of Ger- | the importance of this spirit and of |

many was in the universities, as this so-called public opinion " (ibid., i

that of France was at the bar ; p. 254). See also Treitschke's i

they only heard each other : was ' Deutsche Geschichte,' vol. v. p. ■

it therefore unnatural if they 408, &c.

THE ASTRONOMICAL VIEW OF NATURE. 313

lier writers. Elaborate claims to priority have thus been
set up for persons to whom it is said the credit of modern
discoveries should be given. I do not intend to contribute
to this controversial literature, except by a general remark,
which will explain how it has come to pass that ideas and
principles now recognised as useful instruments of thought
and research have only recently attained this importance,
while they have frequently been the property of many
ages of philosophical thought, and familiar even to the
writers of antiquity. It is the scientific method, the exact
statement, which was wanting, and which raises the vague
guesses of the philosophical or the dreams of the poetic
mind to the rank of definite canons of thought, capable of
precise expression, of mathematical analysis, and of exact
verification. Obscure notions of the attractive and re-
pulsive forces of nature have floated before the minds of
philosophers since the time of Empedocles, but they did
not become useful to science till Galileo and Newton took
the first step to measure the intensity of those forces.
Lucretius's poem introduces to us the early speculations
on the atomic constitution of matter, but the hypotheses
of his school only led to real knowledge of the things of
nature when Dalton, following Lavoisier and Eichter, re-
duced this idea to definite numbers ; still more so when,
through the law of Avogadro and Ampere, and the calcu-
lations of Joule, Clausius, and Thomson, the velocities, the
number, and sizes of atoms became calculable and measur-
able quantities. Descartes, and after him Malebranche,
filled space with vortices which were to explain the con-
stitution of matter and the movements of its parts ; but
the notion was abandoned and ridiculed till Helmholtz

314 SCIENTIFIC THOUGHT.

and Thomson approached the subject with mathematical
analysis and calculated the properties of vortex motion.

Heraclitus proclaimed, six hundred years before the
Christian era, the theory that everything moves or flows ;
but not till this century was the attempt made to work
out the definite hypothesis of Daniel Bernoulli, and
to explain the properties of bodies, apparently at rest —
the pressure of gases, or the phenomena of elasticity —
by assuming a hidden motion of the imperceptible portions
of matter. The same fate of lying dormant for ages at-
9. taches to the suggestive ideas of many thinkers. In every

Mathemati-
cal spirit, case the awakening touch has been the mathematical

spirit, the attempt to count, to measure, or to calculate.
What to the poet or the seer may appear to be the
very death of all his poetry and all his visions— the cold
touch of the calculating mind, — this has proved to be the
spell by which knowledge has been born, by which new
sciences have been created, and hundreds of definite prob- j
lems put before the minds and into the hands of diligent
students. It is the geometrical figure, the dry algebraical
formula, which transforms the vague reasoning of the
philosopher into a tangible and manageable conception ;
which represents, though it does not fully describe, which !
corresponds to, though it does not explain, the things and
processes of nature : this clothes the fruitful, but other-
wise indefinite, ideas in such a form that the strict logical
methods of thought can be applied, that the human mind
can in its inner chamber evolve a train of reasoning the ;
result of which corresponds to the phenomena of the outer
world. By such processes did Gauss and Leverrier suc-
ceed in tracing the lines in the heavens on which invisible

THE ASTRONOMICAL VIEW OF NATURE.

315

stars were speeding through the universe ; without them
these objects of nature would probably never have been
seen, and if seen, they would not have been recognised.
Similar, and still more intricate, reasonings permitted
Mendeleeff ^ to arrange in geometrical order the several
elements or simple substances out of which matter is
compounded, and to point to the vacant places on the
chart, some of which have since been filled up by new
discoveries. Thus it has also been shown that the ranges
of temperature cannot be extended indefinitely in both
directions — viz., those of heat and cold — but that the
latter possesses a zero point, representing the complete
absence of motion.^

^ The periodic arrangement of
the elements, according to which,
with increasing atomic or combining
numbers, the same properties — such
as density, fusibility, optical and
electric qualities, and formation of
oxides, &c. — recur in periods which
are at least approximately fixed, so
that they can be represented by
curves, dates from the year 1869,
when D. MendeleefE and ^othar
Meyer published almost simultane-
ously their classification of the ele-
ments. Newlands seems to have
indicated some of these facts as
early as 1864. Mendeleeff pre-
dicted the properties of a missing
element, found to be those of scan-
dium, which Nilson discovered ten
years later. The same applies to
the two other elements which were
subsequently discovered by Lecocq
de Boisbaudran (1878, gallium) and
"Winkler (1886, germanium), and in
1894 the newly discovered element
argon was found to fill a vacant
place in the plan.

- The zero point of temperature
was originally a purely mathemati-
cal quantity suggested by the for-

mula which gives the expansion of
air in the air thermometer as de-
pendent on the temperature. The
ideal, not realisable, temperature
at which, according to the for-
mula, the volume of air would be
nothing, was fixed by calculation at
459° -13 Fahr. or 272° -85 Centi-
grade. The real physical, not mere-
ly mathematical, meaning of the
absolute scale of temperature with
its zero point was only revealed
when, through Carnot and Thom-
son, it was established that every
degree of temperature has an assign-
able value for doing work, and when
a scale of thermometry was sug-
gested by Thomson (1848) in which
every one degree had the same
dynamical value, 100° in it cor-
responding to the 100° Centigrade
in the air thermometer. It was
then found that the two scales —
that of the air thermometer and
that measuring the dynamical value
of temperature — agreed almost ex-
actly. The number 273° Cent, thus
acquired a physical meaning (see
Clerk Maxwell, ' Heat,' 8th ed.,
pp. 49, 159, and 215). Another

316

SCIENTIFIC THOUGHT.

By drawing curves on paper which correspond to the
thermal properties of various substances, the conditions
have been defined beforehand under which gaseous bodies
like oxygen, hydrogen, nitrogen, or common atmospheric
air can be reduced to liquid and solid bodies, upsetting
the notions of the last generation, which looked upon
these substances as permanent gases/ If the matlie-
matical formula has killed, or failed to grasp, the true
life of nature, that which to the poet and the philosopher
will always be the feature of supremest interest, it has on
the other side given birth to that new life of ideas which
in our reasoning minds serve as the images of things

example of a purely mathematical
quantity which, suggested originally
by a formula, acquired later a physi-
cal meaning, is that of the potential
function, used first by Lagrange as
a simplification in calculating the
forces of a disturbing planet, and
termed by Laplace " a cause de sou
utilite, une veritable decouverte"
('Mdc. eel.,' V. livre xv. chap, i.)
This function, which has the pro-
perty that by a simple differentia-
tion the component of the force in
any direction is found, acquired a
physical meaning as the quantity,
the change of which measures the
work required to move a unit of
matter from one point to another
(see Thomson and Tait, ' Natural
Philosophy,' vol. i. 2, ]). 29). Other
examples of purely mathematical
quantities which reveal physical
properties are Hamilton's " char-
acteristic function " (see Tait,
"Mechanics," ' Ency. Brit.,' 9th
ed., p. 749), Rankine's "Thermo-
dynamic function," called by Clau-
sius " Entropy " (see Maxwell,
'Heat,' pp. 162, 189): it measures
the unavailable energy of a system.
1 Thomas Andrews (1813-85) took
up the experiments begun by Cag-

niard - Latour in 1822, and ex-
plained how it comes about that a
gas remains incondensable however
great the pressure may be, pro-
vided the temperature exceeds
what he termed the " critical tem-
perature,"' which is different for
different pases. He accompanied
his statements, which were first
published in the 3rd edition of
Miller's Chemical Physics, by curves
representing the behaviour of at-
mospheric air and of carbonic acid,
the latter being a condensable gas,
and he suggested in 1872 that the
so-called permanent gases had a
critical point far below the lowest
known temperatures, and that this
was the reason why their lique-
faction had not yet laeen achieved.
Two physicists, Cailletet and Pictet,
took up these suggestions ; after
various trials thej' succeeded inde-
pendently in 1877 in liquefying
several of the permanent gases,
notably oxygen and nitrogen.
These have been followed by all
the other permanent gases, includ-
ing atmospheric air, of which large
quantities can now be prepared in
a liquefied form.

THE ASTRONOMICAL VIEW OF NATURE. 317

natural, and allow us to make them subservient to our
purposes.

Whoever grasps the significance of the change which lo.

° ^ ° ,- & When first

the exact or mathematical treatment of knowledge has introduced

— c5 into science.

worked in our life and thought, will readily place that
name at the entrance of a history of modern thought,
whijchis^ identified with a few simple mathematical for-
mulae, by which ever since his time the progress of science
has been guided. Though belonging to an earlier period,
the full meaning of Newton's work has only been recog-
nised in the course of our century. In fact the New-
tonian philosophy can be said to have governed at least
one entire section of the scientific research of the first
half of this period : only in the second half of the period
have we succeeded in defining more clearly the direction
in which Newton's views require to be extended or modi-
fied. Newton's greatest achievement was to combine the
purely mechanical laws which Galileo and Huygens had
established with the purely physical relations which
Kepler — following Copernicus and Tycho — had discovered
in the planetary motions, and to abstract in so doing
the general formula of universal attraction or gravitation.
Newton looked upon the motion of the moon round the
earth, or the planets round the sun, as examples on a
large scale of the motion of falling bodies — studied by
Galileo — on the surface of the earth. Delayed in the
publication of this simple rule of planetary motion
through the absence of correct measurements, and through
the necessity of inventing a new calculus by which the
mathematical results of the formula could be ascertained,
Newton did not publish his ' Principia ' till 1687. The

318

SCIENTIFIC THOUGHT.

11.

Newton's
' Principia.

work, however, was conceived in the highest philosophic
spirit, inasmuch as the enunciation of the so-called law of
gravitation required the clear expression of the general
laws of motion. In the first and second parts of the
work the discoveries of Galileo and Huygens were ab-
sorbed, generalised, and restated in such terms as have up
to our age been considered sufficient to form the basis for
all purely mechanical reasoning.^ In the latter part the
new rule, corresponding to Kepler's empirical laws, is
represented as the key to a system of the universe. The
great outlines of this system are boldly drawn, and the
working out of it is left as the great bequest of Newton
to his successors. At the end of the eighteenth century,

^ The most recent historian of
the subject is Prof. Ernst Mach of
Prague, whose ' Meehauiii in ihrer
Entwickelung, historisch - kritisch
dargestellt,' 2nd ed., 1889, I cannot
praise too highly. It has been
translated into English by M'Cor-
mack (Chicago and London, 1893).
Referring to Newton, he saj's :
" Newton has with regard to our
subject two great merits. Firstly,
he has greatly enlarged the hori-
zon of mechanical physics through
the discovery of universal gravi-
tation. Further, he has also com-
pleted the enunciation of the prin-
ciples of mechanics as we now ac-
cept them. After him an essen-
tially new principle has not been
established. What after him has
been done in mechanics refers to
the deductive, formal, and mathe-
matical development of mechanics
on the ground of Newton's prin-
ciples" (p. 174). " Newton's prin-
ciples are sufficient without the
introduction of any new principle
to clear up every mechanical prob-
lem which may present itself, be

it one of statics or of dynamics.
If difficulties present themselves,
they are always only mathematical,
formal, not fundamental " (p. 2-39).
" All important mathematical ex-
pressions of modern mechanics were
already found and used in the age
of Galileo and Newton. The spe-
cial names . . . have sometimes
been fixed much later. Still later
came the adoption of uniform
measures, and this process is even
yet incomplete " (p. 252). In this
country it is one of the great mer-
its of Thomson and Tait's ' Nat-
ural , Philosophy ' that they ' ' re-
stored " the teaching of mechanics
and placed it on the original foun-
dations afforded by Newton's laws
of motion, in his own words, as
" every attempt that has been
made to supersede them has ended
in utter failure" (Preface), and,
though they " are only temj^or-
arily the best," there does not
exist, " as yet, anything nearly as
good " (Tait in article " Mechanics,"
' Ency. Brit.,' 9th ed., p. 749).

THE ASTRONOMICAL VIEW OF NATURE. 319

after many able mathematicians and observers had gen-
erally investigated the numberless problems contained in
the ' Principia,' Laplace published his ' Exposition du
Systeme du Monde,' followed in the course of the first
quarter of this century by the ' Mecanique celeste ' ;^ and
at the close of the present century the most learned
astronomer of the age could say that the ' Principia '
still formed the sole foundation of all investigations in
that domain.^

It is interesting to see how in a simple formula the
mathematician is able to condense an almost immeasur-
able volume of thought, bringing the theory and the
observations of past ages to a focus from which new lines
of thought diverge in many directions. Every mathe-

12.

The gravita-
tion for-
mula.

^ The ' Exposition du Systeme
du Monde' appeared, 1796, in 2
vols. 8vo : the first and second
volume of the ' Mecanique celeste,'
1799, 4to; the third, 1802; the
fourth, 1805 ; the last, 182.1. Be-
fore publishing this work, which
has been termed a second edition
of the ' Principia,' Laplace had
himself during thirty years assisted
in dispelling the last doubts as to
the sufficiency of the doctrine of
universal gravitation to explain all
cosmical phenomena ; and he had
especially brought the investiga-
tions of Clairaut, Euler, d'Alem-
bert, Lambert, and Lagrange to a
final result by publishing in suc-
cessive memoirs between 1773 and
1786 the doctrine of "the stability
of the system of the universe,"'
based upon the invariability of the
major axes and the periods of re-
volution of the planetary orbits.
He and his predecessors also ex-
tended the solution of the problem
" to find the orbit of two bodies,
acting under the law of mutual

gravitation," which was given by
Newton in such a way that the
action of one or more third (dis-
turbing) bodies could be taken into
account, dealing thus with the case
of nature, which had in the first
instance presented itself in treating
of the complex motion of the moon.
Laplace himself, who in number-
less passages of his works re-
curs to the discoveries of Newton,
announced the object of the 'Me-
canique celeste ' to be the treat-
ment of astronomy "as a great
problem of mechanics, from which
it was important to banish as much
as possible all empiricism," and to
perfect it so as " to borrow from
observation only the most indis-
pensable data" ('M^c. eel.,' vol. i.
introd. )

- The late Professor Rudolf Wolf
of Zurich, whose ' Haudbuch der
Astronomic, ihrer Geschichte und
Litteratur,' 2 vols., 1890-93, as well
as his earlier ' Geschichte der As-
tronomic,' Miinchen, 1877, 1 warmly
1 recommend.

320

SCIENTIFIC THOUGHT.

matical formula which expresses the existing relations
of natural things acts in a similar way, but probably few,
if any, subsequent discoveries have given scientific minds
so much fruitful work to do as the gravitation formula,
An analysis of it will serve us as a guide through a very
large portion of the scientific work of our period ; it will
serve also as an example of the great service which the
mathematical mode of dealing with conceptions renders tc
the progress of science and of thought.

The so-called law of gravitation states that every twc
portions of matter, placed at a distance from each other
exert on each other an attractive force,^ which depends
on the masses of each, and on their distance from
each other. The attractive force varies in the direct
proportion of the mass of each, and in the in^•ers€
duplicate ratio of the distance. Three distinct lines ol

^ The gravitation formula gives
no indication of the actual or abso-
lute amount of the force in ques-
tion ; it only establishes a relation.
It was fully three - quarters of a
century after the publication of the
' Principia ' that experiments were
suggested in order to determine the
actual magnitude of the force of
gravitation — i.e., the constant c in

the formula /= c

m.m

Michell in

1768 devised an apparatus, em-
ployed later (1797) by Cavendish,
and Maskelyne made measurements
towards the end of the last century.
More and more accurate determin-
ations were made all through the
present century, and latterly by
Prof. Boys. Few i)ersons have an
idea of the extreme feebleness of the
force, which nevertheless, tlirough
the magnitude of the earth, ac-
quires in our daily experience such
formidable proportions. As it is

desirable, in accordance with one oi
the principal scientific tendencies o:
our age, to place the knowledge oi
absolute physical quantities in th(
place of merely relative numbers
I mention here that the force wit!
which two units of matter {i.e., '
grammes) placed at unit distanc<
(i.e., 1 centimetre) apart attraci
each other is such that they woulc
approach each other with a velo
city of nearly 7 hundred millionthi
of a centimetre in the first seconc
of time. As a pound is a mor<
familiar quantity, we may also sa^
that two masses, each containing
415,000 tons of matter, and situ
ated at a distance of one statuti
mile apart, will attract each othe:
with the force of 1 lb. (see Sii
R. S. Ball, 'Ency. Brit.,' 9th ed.
art. "Gravitation"). See also Si
R. S. Ball, 'The Story of th(
Heavens,' p. 106, and Prof. Boy;
in 'Nature,' vol. 50, p. 330, &c.

THE ASTRONOMICAL VIEW OF NATURE.

321

scientific research are involved and opened out by this is.

Lines of

Statement. thought

. emanating

First, There is the purely theoretical task of defining ''■'°'" '*•
clearly what is meant by the different words which are
used, and which in the formula are expressed in algebraic
symbols. What is the definition of force, what of mass,
what of distance ? The ' Principia ' give Newton's defi-
nitions.^

Second, The definitions must be given in such a way
that they express definite measurable quantities ; and in
order to verify and apply the formula, methods must be
devised for measuring these quantities as they occur in
nature, and these measurements must be actually carried
out.^

^ It will be readily admitted that
the definition of force as measured
by change of motion, and the defi-
nition of mass as the quantity of
matter, are definitions involving
some difficulty. As to distance,
it may be thought that this is a
purely mathematical, not a physi-
cal quantity. So it would be if
physical bodies were mathematical
points, such as the planets in a
first approximation may be con-
sidered to be. But in comparing
the attraction of the earth upon
a body at its surface with that on
the moon, the dimensions of the
earth could not he neglected, and
the problem presented itself how
the quantities of mass and distance,
in the case of the earth and the
body on its surface, had to be de-
fined. It appears from a statement
by Prof. Qlaisher (see Rouse Ball,
'History of Mathematics,' p. 297,
&c.) that the publication of the
' Principia,' containing the gravita-
tion formula, was delayed, because
Newton found it difficult to prove
that in a sphere the different parts

VOL. I.

with their different distances from
any point need not be considered
separately, but that a quantity
equal to the whole mass situated
at the centre of the sphere may
be substituted. Laplace showed a
century later that this property of
the sphere exists only for one de-
creasing function of the distance —
viz., that of the inverse duplicate
ratio. It exists likewise for that
function which increases in propor-
tion to the distance, but for none
other (see 'Principia,' 1st ed. , pp.
198, 200; 'Mecanique celeste,' 1st
ed., vol. i. p. 143). Hitherto the
delay in publishing the ' Principia '
was (see Brewster, ' Life of New-
ton,' vol. i. p. 290) always attribut-
ed to the erroneous figure of the
moon's distance from the earth,
with which Newton had been
reckoning, and which did not sat-
isfy the gravitation formula.

- Up to the beginning of this
century the merit of carrying out
accurate measurements of astrono-
mical constants is about equally
divided between France and Eng-

322

SCIENTIFIC THOUGHT.

Third, the formula is a mathematical expression, and, as
such, can be subjected to purely mathematical analysis :
this analysis may refer to purely algebraical processes of

land ; the former country having
supplied the means and organised
many expeditions (under Richer,
Picard, Cassini, La Condamine,
Maupertuis, and others), the latter
having invented and furnished the
greater portion of the delicate in-
struments, through Newton, Greg-
ory, Ramsden, Dollond, Harrison,
and others. The latter was a
matter of personal, the former one
of organised, talent. England did
not take any great part in the re-
peated measurements of the arc of
the meridian till, towards the end
of the eighteenth century (1785-87),
the French astronomer Cassini de
Thury presented to the Royal So-
ciety a memorial on the uncertainty
in the difference of longitude of
Greenwich and Paris, and proposed
that the English and French mathe-
maticians in concert should deter-
mine, by geodetic operations, the
distance measured along an arc of
parallel. This was assented to, and
the late Astronomer Royal (G. B.
Airy) claims that it "may be said
that in this as in other grand ex-
periments, though we began later
than our Continental neighbours,
we conducted our operations with
a degree of accuracy of which, till
that time, no one had dared to
form an idea." Since the begin-
ning of this century Germany has,
through the accurate measurements
of Gauss and Bessel, and through
the famous establishments of Fraun-
hofer, Steinheil,Repsold, and others,
taken a leading position both in the
theory and practice of measuring.
So far as gravitational astronomy
is concerned, the United States of
America seem at the end of this
century to eclipse all previous
performances. But if we owe to

English genius the invention of
logarithms, the sextant, the reflect-
ing and the achromatic telescope,
the theodolite, and the chrono-
meter, we owe to France the idea
of an absolute system of measure-
ments and the first approxima-
tion to it in the metrical system,
which England has been tardy to
adopt. A really absolute unit of
measurement; as the ten-millionth
part of the earth quadrant was in-
tended to be — one which would be
recoverable, if every actually ex-
isting pattern was destroyed — does
not yet indeed exist ; but the
Government of the Revolution laid
the foundation in 1790 of our
present international decimal cen-
tigrade system. It does not ap-
pear that the idea of extending this
system to all other forces and
quantities in nature was then con-
templated. A valuable contribu-
tion towards this desirable object
was made by Fourier, who in his
celebrated 'Thcorie de la Chaleur'
(1822, p. 152, &c.) laid down the
doctrine of the " dimensions " of
physical quantities which had to
be measured and compared with
each other. The first who reduced
the measurement of other than
purely mechanical phenomena to
the standard of mechanical forces
was Gauss (1832). In his investi-
gations referring to the intensity
of magnetic force at dififerent points
of the earth, he found it necessary
to abandon the unit of weight, the
gramme, and to adopt the unit of
mass, inasmuch as the weight of
the unit of mass varied at different
points of the globe. He introduced
the name "absolute" to signify
that this standard is independent
of local or relative influences (see

THE ASTRONOMICAL VIEW OF NATURE. 323

calculation, or to geometrical figures. These geometrical
figures represent on paper, and on a small scale, the
curves or orbits of bodies in space and time, and can
be interpreted as such. Then, as in nature two bodies
or portions of matter are never single gravitating points
occurring alone, but are surrounded by the totality of
existing things, the formula which reduces the action of
gravitation to that of pairs of things, and to the elements
of matter, requires to be extended to more than two — in
fact to an infinity of elements. The infinitesimal calculus
teaches us how to deal with such a progression from finite
numbers and quantities to infinite numbers ; or from rela-
tions which refer to infinitesimal elements to finite meas-
urable quantities. We find very soon that our powers of
calculation reach only a small way, and cover only a small
extent of the ground which observation opens to our eyes.
We are thus forced to deal with the element of error 14.

Element of

which creeps into our calculations ; to be satisfied with error.
approximations ; ^ and instead of certainty, probability is

Gauss, Werke, vol. v. pp. 85, 293,
&c. ) Of Weber's electrodyuamic
measurements I shall speak later ou.
Absolute measurements were used
by William Thomson (Lord Kelvin)
as early as 1851, and owing mainly
to his influence the present system
■was graduall}' established in the
course of the following twenty years
(see William Thomson, ' Popular
Lectures and Addresses,' vol. i. p.
S3, &c.) Fourier's theory of dimen-
sions was first brought prominentlj^
before the scientific and teaching
world by Clerk Maxwell in his trea-
tise on ' Electricity and Magnetism '
(1st ed., vol. i. p. 2). There also
we meet for the first time with
the use of astronomical magnitudes
and relations by which the usual

three units, time, mass, and dis-
tance, can be reduced to two. This
is also lucidly explained by Lord
Kelvin {loc. vit.) It has been fol-
lowed up in detail in two interest-
ing papers by W^. Winter in Exner's
' Repertorium der Physik ' (vol. 21,
p. 775, and vol. 24, p. 471).

1 The history of astronomical cal-
culations since the time of Newton,
\\hen the theoretical basis was once
for all laid, is a history of gradual
approximations. Mathematically a
conic section is sufficiently defined
if the position of the focus (the sun
in our planetary system) and three
positions of the moving star are
known by observation. But it was
a long time before even tolerably
complete methods of observation

324

SCIENTIFIC THOUGHT.

the best we can attain to in our results.^ An entirely
new branch of investigation springs up — viz., the theory
of error, the doctrine of probability, and the investigation

and calculation were invented to
deal practically with the problem.
Up to 1781, when the new planet
Uranus was discovered by Her-
schel, the interest centred mainly
in the determination of the orbits
of comets, which were assumed to
be parabolic. Halley was the first
to calculate these by means of ten-
tative methods given by Newton in
the ' Principia.' After 1781 the ne-
cessity arose of determining closed
orbits, and a first attempt was made
to do so by assuming circular orbits
(neglecting the ellipticity) and ne-
glecting the inclination of the plane
of the orbit to that of the earth.
But in the first year of this century
neither the parabolic nor the circular
figure of the orbits seemed to an-
swer in the case of the new planet
Ceres, nor could the inclination of
the orbit be neglected. It required
all the skill of Gauss to tackle the
entire, unabbreviated problem, and
this was done in his fundamental
work ' Theoria motus corporum
coelestium.' As the 'Principia'
form the foundation of all physical,
so does the ' Theoria motus ' of all
calculating astronomy. A similar
fundamental work which should take
the next important step, solving
generally the problem of the motion
of a body which is attracted from
more than one fixed or movable
centre (the problem of three bodies),
would mark the next great era in
calculating astronomy. Hitherto
this problem has only been treated
under the assumption that the third
attracting body disturbs the real
orbit which has been calculated.
The necessity of solving the prob-
lem of three bodies has made itself
felt in the theory of the moon and
other satellites, which stand under

the influence of the main planet as
well as the sun, and where therefore
the ellipsis of Kepler cannot even
be taken as a first approximation.
And here again the necessity of tak-
ing into account the volume and
the figures of the attracting bodies
still further complicates the prob-
lem. On them depend the preces-
sion of the equinoxes and the ir-
regularity of the precession known
under the name of nutation.

^ According to Wolf (' Handbuch
der Astronomic,' vol. i. p. 128 sqq.)
the merit of having first considered
the best methods of dealing with
errors of observation belongs to
Picard (1670) and Roger Cotes
('Aestimatio errorum in mixta
iiiathesi,' 1722). The former seems
to have first used the apparently so
obvious rule of taking the arith-
metical mean of a number of ob-
servations, the latter introduced
the notion of attributing to each
observation its value or weight.
Cotes accordingly found that the
centre of gravity of a number of
weighted points distributed over a
plane coincided with the position of
greatest probability. Gauss sus-
pected that Tobias Mayer had
already employed modern methods
in his calculation of long series of
observations, and he himself used
what is termed after Legendre the
" method of least squares " as early
as 1795. It was not published till
1806 by Legendre, in his memoir
' Nouvelles methodes pour la deter-
mination des orbites des cometes.'
Gauss published his methods in 1809
in the celebrated 'Theoria motus
corporum coelestium.' This method
of finding the most probable result
when a larger number of equations
is given than unknown quantities

THE ASTRONOMICAL VIEW OF NATURE.

325

of the degree of approximation which we can attain to.
And this does not only refer to the methods of calculation
which we adopt, — is not only a consequence of the limits
of our mathematical powers; this element of error attaches
likewise to our actual observations, to the imperfection of
our senses and of our instruments. The many sources
of mistake and inaccuracy which surround us may either
combine to produce an absolutely useless result, or may
be adroitly adjusted so as very largely to destroy each
other.-^ The arrangement of instruments of observation
and calculation, so as to minimise our errors, is a special
branch of science. Before the time of Newton few minds

is the same as that of finding the
centre of gravity of a number of
weighted points. Tliis centre has
the property that the sum of the
squares of its distances from these
points is a minimum. After the
method had been introduced, La-
place and Gauss independently tried
to prove it by a variety of considera-
tions. These have not always been
accepted as conclusive, though it is
remarkable that very different ways
of attacking the problem all lead to
the same result, and that the rule
is confirmed by actual trials on a
large scale. It has been shown that
the method of least squares in the
case of a series of observations of
one and the same quantity is equal
to taking the arithmetical mean, — a
process which recommends itself to
common-sense, though it is not easy
to prove it mathematically to be the
best. On the whole, the calculus
of probabilities and the so-called
law of error are attempts to put
into figures and mathematical for-
mulaj a few common-sense notions,
and it is interesting to see to what
complicated processes of reasoning
a combination of these simple no-
tions may lead. The literature of

the subject, belonging almost en-
tirely to this century, is very large,
Laplace and Gau:^s heading the list.
Encke has summarised the scattered
discussions of Gauss and Bessel in
his memoir on the subject, reprinted
in Taylor's ' Scientific Memoirs ' and
in the •2nd vol. of Encke "s ' Abhand-
lungen,' Berlin, 1888. De Morgan,
Airy, and Jevons ('Principles of
Science,' vol. i. ) in England have
done much to popularise the sub-
ject, and Bertrand (' Calcul des Pro-
babilit^s,' 1888) has very fully dis-
cussed the principles of the whole
matter and shown up the weak
points. The application of the cal-
culus to statistics will occupj' us in
a future chapter.

^ Not only has every instrument
its constant errors, but even every
observer himself has what is called
a personal equation — i.e., he is sub-
ject to constant errors of obseiva-
tion, dependent on the peculiarity
of his sense organs, or his tem-
perament, &c. This was hardly
recognised at the beginning of this
century, when Maskelj-ne, the As-
tronomer Royal, dismissed an as-
sistant whose observations showed
a constant difference from his own.

326 8CIP]NTIFIC' THOUGHT.

were occupied with the many researches indicated here.
But as the contents of the ' Principia ' became familiar
and intelligible to men of science, a large army of
workers, collected from all sides, had within the tirst
century after its publication accumulated a great mass of

15. research. It is the glory of the old French Academy of

Laplace and .

Newton. Scicnccs, in spite of the opposition to Newton that ruled
there for some time, to have in all earnest taken up hig
great bequest, and to have made such a summary possible
as was given by Laplace in the two works above re-
ferred to. To Laplace belongs also almost exclusively the
merit of having recognised the importance which attaches
in all human science to the existence of error, and of
having founded the theory of probability. The element
of error cannot be eliminated from our observations and
our reasonings : the only true scientific method is to mea-
sure and study it.

The gravitation formula of Newton not only brought
precision and definiteness into scientific work in the three
directions mentioned above — it not only produced strict
definitions of the fundamental notions of dynamics, pro-
moted accurate measurements of physical quantities, and
inaugurated a new literature in pure mathematics ; but it
had, as all other great generalisations have had since, a
very far-reaching influence on scientific thought in other

16. ways. There always have been, and always will be,
^terests scvcral distiuct interests which induce men to study
Science? nature. Some are driven to it by curiosity, or a pure

love of nature. To those who belong to this class the
end of the study of nature is to describe and to portray
the objects which surround us, to see and know them

THE ASTRONOMICAL VIEW OF NATURE. 327

better. It would seem as if to such minds the scientific
formula, the so-called law of nature, must be distasteful,
and probably useless. Nevertheless the scientific view, of
which the mathematical formula is an extreme expres-
sion, has reacted, though not always beneficially, upon
the labours of those who confine themselves to observa-
tion and description ; it has given to their efforts general
interest and encouragement, indicated new directions, and
frequently opened new fields. Thus the new formula of
Copernicus and Galileo gave a great impetus to star-
gazing, which was greatly increased by the almost con-
temporary invention of the telescope. The new theory
required the rotation of the planets, and led to minute
observations of their phases, and to the discovery of the
satellites of Jupiter and the ring of Saturn. Variable
stars were incidentally discovered by Tycho, and the
long-neglected comets received greater attention. Ber-
noulli attempted, and Halley actually carried out, the
calculation of the return of a comet. Still later- — in
fact, not before the end of the eighteenth or the beginning
of the present century — came the turn for reliable obser-
vation of meteors and auroras; for as late as 1790 the
' Decade philosophique,' as well as the Paris Academy and
many learned persons, ridiculed the authentic reports of
the fall of meteors, and Chladni's classical dissertation on
the stone of Pallas.^ It seems as if the purest love of

1 When iu the year 17i<0 the
municipality of Juillac iu Gascony
submitted a report, signed by more
than 300 eyewitnesses, to the Paris
Academy, on a fall of stones which
had there taken place, one of the
editors of the ' Decade philoso-
phique ' remarked that it would be

better to deny such incredible things
than to enter into any explanations.
Bertholon could not help pitying a
community which had such a foolisli
maire, and remarked in the ' Jour-
nal des Sciences utiles ' : " How sad
it is to find a whole municipality
attesting formally by protocol popu-

328

SCIENTIFIC THOUGHT.

17.
Insuffici

nature, the greatest devotion of the observer and the
observation^ collcctor, lead Only a little way in finding out the hidden
paths of natural things or the behaviour of natural ob-
jects ; and however grateful we must be to those pioneers
of knowledge who with unrewarded patience amass the
material for later theorists, it is to the classification of a
Linnaeus, to the arrangements of a Cuvier, to the theories
of a Darwin, to the measurements of a Bradley and a
Herschel, most of all to the formulai of a Newton or a
Gauss, followed by the calculations of their pupils, that
we are indebted for a real grasp, for a comprehensive
knowledge, of great masses of natural phenomena.

Next to the pure love of nature, the desire to apply
natural knowledge, and to make it useful for practical
purposes, has rendered in return great services to science.
The Eoyal Society and the Eoyal Institution had both
from their infancy a large admixture of the practical
spirit. These were founded, more even than the academies
abroad, to a great extent upon the desire to make know-
ledge useful.

The Governments of England and of France promoted

18.
Practical
interest.

lar fables which are only to be pitied !
What can I add to such a protocol ?
The philosophical reader will him-
self suggest what to say when he
reads this authentic proof of an
evidently wrung fact, of a pheno-
menon which is physically impos-
sible" (Wolf, 'Geschichte der Astro-
nomie,' 1877, p. 697 sq.) Chladni
published his essay on the large
mass of iron found by the traveller
Pallas in Siberia in the year 1794,
and, in spite of adverse criticisms,
followed it up by a catalogue and
an atlas of meteoric stones, sug-
gesting that they were of cosmic

origin. Fortunately, a remarkable
fall of stones, accompanied by
meteoric phenomena, took place in
1803 not far from Paris, at I'Aigle
in the department de I'Orne, and
Biot was commissioned by the
Academy to proceed to the dis-
trict and examine the case. In the
' Relation,' &c., which he read before
the Institute, he established the
fact that a meteor exploded in the
district, and that at the same time
a fall of many thousand stones,
weighing about 20 tons, took place
(Biot, ' Melanges scientifiques et
litteraires,' vol. i. p. 15 sqq.)

THE ASTRONOMICAL VIEW OF NATURE.

329

the study of the " mechanics of the heavens " by offering
large prizes for scientific and practical means of deter-
mining the longitude at sea. The lunar theory, which
has occupied the attention of the greatest mathematicians
since I^ewton — of Euler, Clairaut, and Tobias Mayer in
the last century ; of Burckhardt, Plana, and Hansen, of
Delaunay and Adams, in the present century — was an
outcome of this. It still engages the attention of scien-
tific minds, involving as it does all the most delicate
astronomical calculations, whilst for practical nautical
purposes the moon has ceased to be the great timekeeper,
and has since 1763 been replaced by the wonderful
chronometers of Harrison and his successors. A similar
stimulus both to abstract scientific research and to the
perfection of the practical instruments of measurement
was given in this century by the development of sub-
marine telegraphy : in this case both sides of the problem,
the scientific and the practical, were attacked, and carried
to a high degree of perfection by one and the same mind ^ —

1 William Thomson's (Lord Kel-
vin's) investigations and inventions,
which made submarine telegraphy
at long distances commercially prac-
ticable, refer mainly to the over-
coming of the " embarrassment "
occasioned by the property (dis-
covered by Werner Siemens, 1849,
and investigated by Faraday, 1854)
which submerged cables possess
of " retaining a quantity of elec-
tricity in charge along the whole
surface." In 18.54 Thomson made
a full theoretical examination of
this phenomenon, showed how it
depended on the length, the elec-
tric resistance, and the electro-
static capacity of the line, and gave
a mathematical formula, with prac-
tical examples of the retardation of

the signals and the gradual increase
of the strength of the electric cur-
rent at the receiving end of long
submarine cables ("On the Theory
of the Electric Telegraph " and
other papers, reprinted in the 2nd
vol. of ' Math, and Phys. Papers,'
1884). The importance of con-
structing delicate instruments for
registering feeble signals, and of
a method for reducing the time
of single signals, became evident
through these theoretical investi-
gations. The mirror galvanometer
was first used in 1858 on the first
Atlantic cable, and afterwards on
the successful cables of 1865 and
1866. It was followed by the
spark -recorder, which led to the
syphon -recorder (1867-70), which

330

SCIENTIFIC THOUGHT.

an almost unique instance of the combination of abstract
reasoning and practical inventiveness. An almost equally
important problem, having both scientific and practical
interest, arising out of the Newtonian gravitation formula,
is the problem of the tides. Here also the first suggestions
towards a theory were given in the ' Principia,' whereas
the first attempt at a solution is contained in Laplace's
great work. A closer approximation was reached by Sir
W. Thomson in his extensive theoretical and practical use
of Fourier's mathematics.

I shall have frequent opportunity to refer to the bene-
ficial and fructifying influence which practical problems
have exerted on scientific thought ; ^ in fact, in spite of

has since been in use in submarine
telegraphy. The best account of
these discoveries and inventions is
to be found in Lord Kelvin's own
papers, a good summary being given
in his short article in Nichol's
' Cyclopedia,' reprinted as No. 82,
vol. ii. p. 138.

^ How much science owes to the
practical interests of navigation can
be seen by a glance at the subjects
contained in the third volume of
Lord Kelvin's ' Popular Lectures
and Addresses.' The Tides, Deep-
Sea Sounding, Cable-Laying, and
Terrestrial Magnetism all furnish
important practical as well as high-
ly abstract theoretical problems,
the solution of which demands new
instruments and new methods of
calculation. The phenomena of
the tides and those of terrestrial
magnetism are intimately connect-
ed with two of the most refined
mathematical theories which this
century has developed. The for-
mer was first attacked by the so-
called equilibrium theory — the pro-
blem being to find the figure of
equilibrium of a rotating ellipsoid

covered with water under the in-
fluence of various attracting forces.
Laplace, followed by Airy and
Thomson, showed how it is much
more a question of dynamics than
of statics, and that it resolves itself
into the analysis and subsequent
synthesis of a number of jjeriodic
movements, dependent upon the
several periodic changes of the ro-
tation of the earth and the revo-
lutions of the moon round the
earth and the sun. A general
method of dealing mathematically
with the superposition of several
periodic changes had been invented
by Fourier in the early part of this
century, and it was this which,
especially in the hands of Lord
Kelvin and his brother — the late
Prof. James Thomson — led to the
harmonic analysis of tide motion
and the subsequent invention of
tide-predicting apparatus (see the
above volume, p. 177 sqq.) The
observation of the magnetism of
the earth is connected with great
improvements in the theory and
construction of the mariner's com-
pass, suggested and carried out by

THE ASTRONOMICAL VIEW OF NATURE. 331

the great reciprocal influence which science has gained in
the course of this century over practical life, I am still
doubtful whether scientific thought has, at the end of
our century, as yet balanced the debt which it owes to
practical inventors. It is instructive, for instance, to
consider how much, in the hands of Eumford, of Sadi
Carnot, of Hirn, and of Eankine, science has learnt from
the steam-engine, and to reflect whether from all the
theoretical insight gained any really radical improve-
ment of the steam-engine — still one of the most imperfect
machines — has resulted.-^

Lord Kelvin ; and it has in an-
other direction led to remarkable
scientific results in the hands of
Gauss, who Vjetween the years 1830
and 1840 brought the theory al-
most to perfection. Here again
the physical phenomenon required
for its treatment a special mathe-
matical analysis, which Gauss gi-eat-
ly furthered in his ' Allgemeiue
Lehrsiitze in Beziehung auf die im
verkehrten Verhaltnisse des Quad-
rats der Entfernung wirkenden
Anziehungs - und Abstossungs-
Knifte ' (1840). This is a matiiema-
tical investigation of the Newtonian
gravitation-formula. Gauss followed
out the theories of Laplace and La-
grange simultaneously with Green,
whose now celebrated memoir on
the subject remained long unknown
(see supra, pp. 231, 247). The mathe-
matical theory showed that in a
sphere containing a certain amount
of attracting (magnetic) matter an
ideal distribution on the surface of
the sphere can be found which
takes the place of the real but un-
known distribution in the interior,
and that if through observation the
necessary data are supplied, the
magnetic condition of anj' point
on the surface can be foretold with
great approximation. As an ex-

ample, Gauss foretold from the
imperfect data at his command
the position of the south magnetic
pole. In 1840 Capt. Sir James Ross
approached it sufficiently to show
the correctness of the calculation.
The theoretical investigations in
connection with magnetic attrac-
tion and with tidal movements
have remodelled the methods of
observation of the phenomena them-
selves, the older methods having
proved to be in many ways insuf-
ficient. A full account of Gauss's
labours here referred to will be
found in E. Schering, ' C. F. Gauss
und die Erforschung des Erdmag-
netismus,' Gottingen, 1887.

^ I refer in this matter to two
addresses delivered recently — one
by Prof. Unwin ('Electrician,' voL
35, pp. 50 and 79) on "The De-
velopment of the Experimental
Study of Heat - Engines " ; the
other by Prof. Lodge on "The
Second Law of Thermodynamics "
('Electrician,' vol. 35, p. 80 sqq.)
From a perusal of these papers one
gains the impression that science
has been more successful in teach-
ing us why the steam-engine is so
wasteful a machine than in show-
ing how it can be greatly improved.
It is interesting to hear that "al-

332 SCIENTIFIC THOUGHT.

19. The mathematical formula is the point through which

Focalising -^ "

matjiemati. ^^^ ^^^ light gained by science passes in order to be of
cai formula!, ^^gg ^^ practicc ; it is also the point in which all know-
ledge gained by practice, experiment, and observation must
be concentrated before it can be scientifically grasped.
The more distinct and marked the point, the more con-
centrated will be the light coming from it, the more un-
mistakable the insight conveyed. All scientific thought,
from the simple gravitation formula of Newton, through
the more complicated formulae of physics and of chem-
istry, the vaguer so-called laws of organic and animated
nature, down to the uncertain statements of psychology
and the data of our social and historical knowledge, alike
partakes of this characteristic, that it is an attempt to
gather up the scattered rays of light, the diffused know-
ledge, in a focus, from whence it can be again spread out
and analysed, according to the abstract processes of the
thinking mind. But only where this can be done with
mathematical precision and accuracy is the image sharp
and well defined, and the deductions clear and unmis-
takable. As we descend from the mechanical, through
the physical, chemical, and biological, to the mental,
moral, and social sciences, the process of focalisation
becomes less and less perfect, — the sharp point, the

most all the present difference be- provement of the steam-engine to

tween the best steam-engine and
the worst is some 5 or 6 per cent"
(Lodge). Prof. Unwin sums up by
saying: "Since 1845 purely scien-
titic men, scientific experimenters

the exclusion of either of the
others. . . . Representing perhaps
rather the scientific than the prac-
tical interest, I do not think that
the mathematical and plij'sical re-

and practical engineers have all ^ searches of which I have tried to

been engaged in the study of the
steam-engine. I do not believe
that any one of the three can
claim all the credit for the im-

give an account have had no in-
fluence on the practical business of
the engineer."

THE ASTRONOMICAL VIEW OF NATCRE. 333

focus, is replaced by a larger or a smaller circle, the
contours of the image become less and less distinct,
and with the possible light which we gain there is
mingled much darkness, the source of many mistakes
and errors. But the tendency of all scientific thought
is towards clearer and clearer definition ; it lies in the
direction of a more and more extensive use of mathe-
matical measurements, of mathematical formulae.

There is probably no science which has come so per-
fectly under the control of this kind of mathematical ex-
pression as has astronomy since the time of Newton or of
Laplace, and, we may add, there exists probably no mathe-
matical formula which has stood the test of application to
existing phenomena so long and so thoroughly as the
gravitation formula of Newton. It possesses two unique"
properties which no other formula possesses — so far as we
can now see — it is universal ^ and it is accurate.^ These

^ The law of gravitation can be
called the first and most general
physical law or statement of uni-
versal application. The laws of
motion may be called mechanical
or dynamical statements. Both
the law of gravitation and the
laws of motion describe facts, and
have been found by experience ;
but the laws of motion con-
tain no phj'sical constant — i.e.,
no quantity which requires to be
fixed and measured by observa-
tion, and the absolute value of
which has for us at present no
ulterior meaning. The law of gra-
vitation has one physical constant,
the universal gravitation constant
(see p. 320). As it measures what
we call matter, it need not be de-
termined, and its actual determina-
tion, which has been accurately
made only in recent times, has not

in any direction advanced our gen-
eral physical knowledge. For all
practical purposes of physics the
unit of mass is a weight, just as for
all commercial purposes gold is the
standard of value. The astrono-
mical view permits us to go a step
further and express the mass of a
pound of matter in units of time
and space, and the political econo-
mist may seek for a real standard
of value — for instance, an article
of food like wheat. Other funda-
mental physical laws or general
statements involve other physical
constants, as we shall see later on.
^ The accuracy of the so-called
laws of nature, or, more correctly,
of the expressions which science
gives to the laws of nature, is a
very important question. Little is
said on this point in the ordinary
text - books. It is only in very

334

SCIENTIFIC THOUGHT.

20.
Matter and
force matlie-
matically
detined.

two properties of the gravitation formula have been brought
out by a long line of investigations, carried on with the
view of substantiating or of refuting the formula. They
mark the development of whole sciences, the foundation
of quite novel branches of research. I propose briefly to
follow up these developments.

Common-sense has never had any difficulty in knowing
what matter and force are, or in defining them for the
purposes of practical life. But it took thousands of years
to find a definition of these quantities which could serve
as the basis of exact measurement, and permit calcula-
tions of results into which both factors entered in varying

recent jiuVjlications that attention
is sufficiently drawn to the fact
that very few niathematical for-
mula; in physics or chemistry are
more than approximations. The
law of gravitation is one of the few
mathematical expressions which,
besides being universal, have stood
the most rigorous tests as to accur-
acy. A most intere.sting attempt
to prove the inaccuracy of New-
ton's law was made, but speedily
abandoned, bj' Claiiaut, one of
the earliest Newtonians in the old
Academy of Sciences. Clairaut
began about 1743 to study the
lunar theory in the light of New-
ton's system, which Madrin be-
fore him had already despaired
of reconciling with the facts of
observation. When he himself,
on calculating the annual motion
of the moon's ajjogee (or farthest
point in its orbit round the
earth), found only half the value
which observation furnished, he was
tempted in his communication to
the Academy of November 1747 to
suggest that the Newtonian for-
mula might require a correction for
great distances. This suggestion
was followed, as Lalande tells us.

by a veritable scandal in the learned
world. Buffon, for purely meta-
physical reasons, oljjected to this
infringement of the simplicity of
the laws of the universe. The
opponents of Newton's sj'stem had
a short triumph, which however
was speedily reversed when Clair-
aut, putting a greater precision
into his calculations by taking
inequalities into account which he
had previously neglected, explained
to the Academy in Maj' 1749 that
he had succeeded in reconciling the
movement of the moon's apogee
with the law of attraction accord-
ing to the inverse square of the
distance. From that time the
Newtonian theory, to which only
shortly before mathematicians like
Euler had been won over, reigned
supreme. See Lalande in the 4th
volume of Montucla's ' Histoire
des Mathematiques,' p. 67, &c.
Euler's merits in solving many
problems in physical astronomy were
so great that the Academy procur-
ed permission from Louis XV. to
receive him as a sur numeraire, the
eight places granted to external
members being all occupied.

THE ASTRONOMICAL VIEW OF NATURE. 335

quantities and in varying combinations. That a smaller
quantity of matter in motion could produce the same
action as a larger which was moving slowly, or even
apparently at rest, and acted only by what is termed its
dead- weight, was a well-known phenomenon ; but it was
only within the half-century which preceded the publica-
tion of the ' Principia ' that, through the labours of Galileo
and of Huygens, mathematical definitions and simple
formulae were laid down, and generally accepted, which
gave the means of accurately measuring and calculating
the phenomena of moving bodies and the combination of
forces. These labours resulted in a definition of matter
which, translated into the language of our day, says that
matter is that which moves and is capable of resisting
any change of motion. Motion is a measurable quan-
tity. For its measurement we require the measurement
of space and time, and the well-known relation of both
— viz., velocity.

The above formula therefore says that matter is mea-
sured by the resistance it offers to change of motion or
of velocity. And correspondingly force is that which is
capable of producing change of motion, or velocity in
matter, and it is measured by the amount of change it
produces. Given a definite, though unknown, force,
portions of matter — i.e., masses — can be compared by the
resistance they offer to the change of their motion ; the
smaller the change the larger the mass or quantity of
matter. Given a definite, though unknown, quantity of
matter, forces can be measured by the different changes
they produce in the motion — i.e., the velocity — of this
quantity ; they are greater or smaller in the proportion

336 SCIENTIFIC THOUGHT.

of the change of velocity which they produce. One of
the great difficulties which stood in the way of the fixing
of these very simple mathematical relations and defin-
itions was the fact that all matter with which we can
experiment is under the influence of a constant but un-
known force, that which makes it fall if not supported.
It was only by freeing themselves from the effect of this
constant force, or by balancing it, that philosophers
gradually arrived at the conception and definition of
mass, or quantity of matter, as something independent
21. of its weight. It was reserved for Newton to show and

Weight and ®

mass. define the exact relation which weight bears to the other

properties of matter defined and measured by his pre-
decessors. By doing so he added a new definition, a new
means of measuring the quantity of matter or its mass,
showing at the same time to what extent the popular
measure of matter — i.e., its weight — could be accurately
used for scientific purposes. Again, to express it in the
language of our day, Newton showed that matter is not
only that which offers resistance to change of motion,
but also that which causes change of motion in other
portions of matter : it is not only the object on which
force spends itself, it is the seat of this force, and the
degree in which it can change motion in other portions
of matter is proportional to the degree in which it
resists the change of its own motion — in other words,
the gravity or weight of matter is proportional to its mass
or inertia, and is not dependent on any other difference,
whether of size or of quality. This second universal pro-
perty of matter, which brought out more clearly the
reciprocity of all mechanical, and subsequently of all

THE ASTRONOMICAL VIEW OF NATURE.

337

physical actions, is, however, dependent on the mutual
distances of the particles of matter, and can therefore be
altered, but can as little as the existence of matter itself
be removed. This view of Newton's explained or de-
scribed clearly ^ the phenomena of moving and falling

^ The distinction between an ex-
planation and a description of the
facts of nature has been slowly de-
veloped in the course of modern
thought. Probably Leibniz was
the first to insist on it, and to
maintain in the abstract that all
description of nature would be me-
chanical, but that the explanation or
interpretation of nature must be
spiritual. But the first practical
instance of this important distinc-
tion is really to be found in New-
ton's philosophy. In many jaas-
sages of the ' Principia,' and especi-
ally in the ' Optics,' the double view
of the problems of philosophy is
clearly indicated. The principles
of science since the time of Newton
are general facts, established by
experience and put into mathe-
matical language, admitting of con-
stant verification by observation
and by the deductions of the cal-
culus. These principles are not
the ultimate causes, but only a
concise description of some of the
phenomena of nature. These prin-
ciples Newton calls mathematical —
referring to measurable quantities
— and distinguishes them from the
philosophical principles ('Priuc. ,'
1st ed., p. 401). Especially as re-
gards gravitation, Newton explains
many times that he uses this term
not as an explanation, but only as
a mathematical description of the
force with which bodies approach
eacii other, whatever the cause of
this phenomenon may be, which he
leaves others (called with some
irony metaphysicians) to deter-
mine (' Optics,' query 31). That

VOL. L

Newton, besides giving the precise
mathematical principles of all future
dynamical science, indulged also in
further speculations, which he put
into the form of queries and ad-
vanced with hesitation and merely
tentatively, gave his opponents
ample opportunity to attack the
doubtful and uncertain statements
in his philosophj'. Instead of
studying and understanding the
mathematical truths of the ' Prin-
cipia,' they attacked the doctrines
which were fragmentarily put for-
ward in the queries to the ' Optics '
or added in the general scholium
at the end of the second edition of
the 'Principia.' Roger Cotes in
his preface to the second edition
of the ' Principia,' and Clarke in
his correspondence with Leibniz,
pointed out the difference between
Newton's descriptive and calculat-
ing and the older or metaphysical
philosophy. They were, however,
more interested in disproving the
atheistical consequences of which
Newton's philosophy had been ac-
cused than in clearly insisting on
the fundamental difference between
mathematical and metaphysical
principles — i.e., between the exact
and the philosophical views of na-
ture. And in Bentley's Boyle lec-
tures, delivered in 1692 and 1693,
the principles of Newton's philo-
sophy were specially brought for-
ward to refute atheism, an under-
taking which Newton himself sup-
ported in his contemporary corre-
spondence with Bentley, published
half a century later, in 1756.

338

SCIENTIFIC THOUGHT.

masses, not only at a point on the surface of our earth,
where the force of gravity can be considered to be con-
stant, but all through the universe, where it varies with
the distances of the moving masses.

The Newtonian formula of gravitation was not at once
accepted by philosophers as a correct statement of the

It appeared to limit the existence of

22.
Gravitation
not an
ultimate

matten^°^ facts of nature.^

•* The philosophy of Descartes,
which then reigned on the Con-
tinent, seemed in many ways to
hinder the acceptance of Newton's
doctrines. Descartes had taken a
great step in advance in philosophi-
cal teaching ; he had placed mathe-
matics at the head of his doctrine ;
he had opposed the older metaphysi-
cal methods, and he had, through
his application of algebra to geo-
metry, made great progress towards
a mechanical description of phe-
nomena. But he had not separated
the description from the interpre-
tation of nature. Philosophy and
science remained united, the mathe-
matical formula) were only a new
kind of metaphysics, incapable with-
out observation of making any real
advance in the knowledge of nature.
The facts of geometry which are
required for an application of an-
alysis are the well-known axioms of
Euclid. An application of analysis
to dynamics requires a knowledge
of the laws or fundamental jiroper-
ties of motion. These were not
correctly and completely known to
Descartes ; Newton placed them at
the head of his mathematical phil-
osophy of nature. A further appli-
cation to physical phenomena re-
quired a knowledge of some general
physical fact: such was supplied by
Newton in the gravitation formula.
The laws of motion and gravitation
once admitted as facts, there was
plenty to do for mathematics. Not
so with Descartes. In his philoso-

phy the basis of facts was too nar-
row and indefinite, and had to be
supplemented by metaphysical sup-
positions and deductions. The field
for mathematical reasoning not be-
ing sufficiently prepared and wide
enough, Descartes had speedily got
back again into metaphj'sical rea-
soning. In fact the doctrines of
Newton, in which mathematical and
philosophical deductions had for the
first time been successfully separ-
ated, encountered on the Continent
the doctrines of Descartes, in which
mathematical and philosophical de-
ductions were hopelessh' mixed up.
On one point especially the two
views seemed to clash. Descartes
had by metaphysical consideratit>ns
tried to define what matter is.
Newton had postponed the answer
to this question, but had defined
mathematically two properties of
matter — viz., inertia and gravita-
tion. Descartes' metaphysical con-
siderations had led to the conception
that matter and extension were
identical, that space therefore could
not be empty. Newton, occupying
himself not with matter in the ab-
stract, but only with moving observ-
able matter, had established the
general law of gravitation, leaving
it undecided whether the apparent
vacuum existing between visible
bodies was really empty or full.
For the deductions from the law
of gravitation it might in the
first instance be considered empty.
Thus on this question about space

THE ASTRONOMICAL VIEW OF NATUKE. 339

matter to certain changing places in an empty space,
and to attach the forces of nature likewise to this dis-
tribution of matter. This was hardly the intention of
the author himself, who saw in the so - called law of
gravitation not a final explanation, but only a descrip-
tion of the phenomena of nature — notably of the larger
phenomena. That behind the mathematical formula there
may be conditions which are capable of further analysis,
— that the larger or molar phenomena of moving bodies
are made up of their smaller or molecular movements,
was well known to Newton. For before he approached
the great laws of the universe he had been occupied
with investigations which led him into the minutest
phenomena, those of light and colour. To liim, indeed,
are owing some of the observations and methods by
which subsequently the greatest and the smallest meas-
urements of natural objects have been carried out. But
in exact science the deeper philosophical meanings dis-
appear where the strict mathematical deductions point
to definite conceptions, mark certain fixed paths of re-
search, and promise definite results. The eighteenth
century gradually settled down to a wholesale adoption
of the gravitation theory — looked upon space as empty,
upon matter as siibject to a definite though changing
distribution in space, and upon the forces of nature as
attached to certain moving centres, between which only
a mathematical, l)ut no intelligible physical, connection

— whether it was empty or full — i ties of the scholastic philosophy, and

the two doctrines came into conflict. ' a great fight was started against his

That Newton's position was not a views in the Academy of Sciences,

final, but only a provisional one, where Descartes' philosophy reigned

was overlooked ; he was accused of supreme,
introducing again the occult quail-

340

SCIENTIFIC THOUGHT.

could be traced.^ What to some contemporaries of Newton,
and even to Newton himself, seemed an absurdity — that
action could take place at a distance ^ — became through

^ Voltaire, who did not dive very
deep into the teachings of NevFton,
gives a graphic description of the
different opinions then current in
English and French learned circles.
In his ' Lettres sur les Anglais,'
written about the time of the death
of Newton, after having discoursed
on Quakeiism, the Church and
Government, on vaccination, Bacon
and liocke, he devotes four chapters
to the i)liilos()phy of Newton, which
he contrasts with that of Descartes.
" Un Fran^ais qui arrive a Londres
trouve les choses bien changdes en
philosophic, comme dans tout le
reste. II a laisse le monde plein, il
le trouve vide. A Paris on voit
I'univers compose de tourbillons de
matiere subtile, a Londres on ne
voit rien de cela. Chez nous c'est
la jaression de la lune qui cause le
flux de la mer ; chez les Anglais
c'est la mer qui gravite vers la
lune. . . . Chez vos Cart^siens
tout se fait par une impulsion qu'on
ne comprend guere ; chez M. New-
ton cest par une attraction dont on
ne connait pas mieux la cause. . . .
Descartes assure encore que I'eten-
due seule fait la matiere, Newton y
ajoute la solidite " (lettre xiv.)

2 (' You sometimes speak of grav-
ity as essential and inherent to
matter. Pray, do not ascribe that
^ notion to me ; for the cause of grav-
ity is what I do not pretend to
know" (Newton's 2nd letter to Bent-
ley, 17th January 1692-93). " It is
inconceivable that inanimate brute
matter should, without the media-
tion of something else, which is not
material, operate upon and affect
other matter without mutual con-
tact, as it must be, if gravitation,
in the sense of Epicurus, be essential
and inherent in it. And this is one

reason why I desired you would not
ascribe innate gravity to me. That
gravity should be innate, inherent,
and essential to matter, .so that one
body may act upon another at a
distance through a vacuura, without
the mediation of anything else, by
and through which their action and
force may be conveyed from one to
another, is to me so great an ab-
surdity that I believe no man, who
has in philosophical matters a com-
petent faculty of thinking, can ever
fall into it. Gravity must be caused
by an agent acting constantly ac-
cordingto certain laws ; but whether
this agent be material or immaterial,
I have left to the consideration of
my readers " (3rd letter to Bentley,
5th February 1692-93). And in
the fifth answer to Leibniz (pub-
lished after Leibniz's death) Clarke
says : " That the sun attracts the
earth . . . — that is, that the earth
and sun gravitate towards each
other, or tend towards each other,
with a force which is in a direct
proportion of their masses, . . .
and in an inverse duplicate propor-
tion of their distances, and that the
space betwixt them is void — that is,
has nothing in it which sensibly re-
sists the motion of bodies passing
transversely through : all this is
nothing but a phenomenon or actual
matter of fact, found by experience.
That this phenomenon is not pro-
duced sans moycn — that is, without
some cause capable of producing
such an effect — is undoubtedly true.
Philosophers therefore may search
after and discover that cause, if
they can ; be it meclianical or not
mechanical. , . . The phenomenon
itself, the attraction, gravitation, or
tendenc}^ of bodies towards each
other, and the laws or proportions

THE ASTRONOMICAL VIEW OF NATURE. 341

a century of confirming thought, observation, and calcula-
tion an adopted axiom, and the accepted formula of all
physical explanations. For a time, indeed, the exact
formula of gravitation seemed liable to some correction,
but gradually the apparent anomalies disappeared, and
even in our century none of the many attempts to modify
the gravitation formula, to look upon it as merely an ap-
proximation, or to go behind it and find some more general
relation from which it could be deduced, have been gen-
erally useful or acceptable.-^ It still stands there as the
only universally accepted mathematical expression which
corresponds to a general physical property of natural
objects.

Two different lines of thought combined to give the
formula of Newton a still wider importance than its
author primarily intended, or than it has been found
possible to maintain in the course of further inquiry. The
first was the ancient philosophical idea of attraction, which,
without being mathematically defined and practically use-
ful, had nevertheless, from the dawn of Greek speculation

of that tendency, are now suffici- these diflerent attempts will be

eutly known by observations and found in the writings of C. Isen-

experinients. If this or any other krahe, ' Das liathsel von der

learned author can by the laws of , Schwerkraft,' Braunschweig, 1879;

mechanism explain these phenom- i " Euler's Theorie von der Ursache

ena, he will not only not be con- der Gravitation," in 'Zeitschrift fiir

tradicted, but will, moreover, have I Mathematik und Physik,' V(j1. xxvi. ;

the abundant thanks of the learned i ' Ueber die Fernkraft,' Leipzig,

world. But in the meantime, to 1 1889; "Ueber die Zuriickfiihrung

compare gravitation, which is a phe- der Schwere auf Absorption," in

nomenon or actual matter of fact, ' Abhandlungen zur Gescliichte der

with Epicurus' declination of atoms Mathematik,' vol. vi., Leipzig, Teub-

seems to be a very extraordinary ner, 1892. See also as bearing on

method of reasoning" (§§118-124, this subject, Paul du Bois-Reymond,

Leibniz's ' Philosophische Schrif- 'Ueber die Grundlagen der Erkennt-

ten,' by Gerhardt, Berlin, 1890, vol. niss in den exacten Wissenschaft-

vii. p. 439 sq.) en,' Tubingen, 1890.
^ A very complete account of

342

SCIENTIFIC THOUGHT.

and all through ancient and mediaeval philosophy, figured

as one of the occult causes or forces which regulate the

behaviour of living and dead matter. That the force of

23. attraction alone would result in an accumulation of all

Attraction

sion'^*'^"^' iw^tter in one body was of course recognised, and a second
arbitrary and occult force — that of repulsion — was intro-
duced as a counteracting or balancing agent.

In Newton's system of the universe the balancing force
was found to be that of an inherent initial motion which
matter, in consequence of its mass or inertia, maintained
in addition to the motion due to gravitation. If motion
and inertia were able to account for the apparent repul-
sion of bodies at a distance, it might be that they could
also account for their apparent attraction. This idea,
though expressed about the time when the Newtonian
gravitation formula was established, did not meet with
serious attention till far on in our century other lines of
thought led to similar views.^ The phenomena of attrac-

^ Newton himself seems to have
looked for a mechanical explanation
of gravitation. Long before the
publication of the ' Principia ' he
laid before the Royal Society a
paper containing " a hypothesis
explaining the properties of light "
by the assumption of an "jetherial
medium, much of the same consti-
tution with air, but far rarer,
subtiler, and more strongly elastic "
(Letter to Oldenburg, January 25,
1675-76, given in Brewster's ' Me-
moirs of Sir I. Newton,' vol. i.
p. 390 sqq.), which miglit explain
magnetic and electric phenomena,
as well a.s those of gravitation, and
especially light. And in a letter
to Robert Boyle, of 28th February
1678-79 (Brewster, vol. i. p. 409),
he reverts to this subject. Having,

however, in the course of the next
decade found it more useful to work
out the mathematical conclusions
to be drawn from the phenomenon
of gravitation, which was a fact and
not a hypothesis, lie abandoned the
metaphysical part of the subject,
the question how gravitation was
to be explained, "finding" (as Mac-
laurin says in his account of New-
ton's discoveries) " that he was not
able, from experiment and obser-
vation, to give a satisfactory ac-
count of this medium and the
manner of its operation in produc-
ing the chief phenomena of nature."
And in his letter to Boyle, as well
as in a later one to Halley (20th
June 1886, Brewster, vol. i. p. 439),
he carefully distinguishes between
the results of the ' Principia ' and

THE ASTRONOMICAL VIEW OF NATUEE.

343

tion and repulsion at a distance rather received additional
weight and importance when, following Newton's cosmical
measurements, Cavendish and Coulomb, towards the end

the mere framing of hypotheses
and conjectures, for which he pro-
fesses to have little fancy, though
" the heads of some great virtuosos
run much upon hypotheses " ; and
he describes his earlier speculations
as "guesses which I did not rely
on." In fact, the elaboration of
the theorems contained in the
' Principia ' marks the transition
from the metaphysical to the exact
or scientific treatment of natural
phenomena. Before Newton showed
the fai-reaching consequences, the
unexpected grasp of a simple mathe-
matical formula in combining facts
apparently disconnected, no one
could have suspected that such
would be possible, and it is not to
be wondered at that when once
philosophers realised the power of
such formulse, an opposite move-
ment set in through which mathe-
matical processes were extolled at
the expense of experiment and
observation on the one side, and
of philosophical reasoning on the
other. Newton himself never fell
into this error. He knew well the
importance of observation, and he
retained to the end of his life a
great interest in the philosophical
or metaphysical problems which lay
beyond or behind tlie mathemati-
cal statement ; he carefully distin-
guished between the vis r/ravitatis
and the ctnisa gravitatis. Two other
great thinkers, second only to New-
ton himself, took up a similar posi-
tion to the law of gravitation.
Whilst firmly believing in it, they
considered it to be not an ultimate
law of nature, a causa occulta, but
believed that it must be possible to
derive it from some mechanical
properties of matter. The one was
older than Newton. It was Huy-

gens (1629-95) who through his
analysis of centrifugal forces (1673)
had done so much to pave the way
for Newton's own work. In 1690,
after having paid a visit to England
in order to become more intimately
acquainted with Newton's work, he
published at Ley den his ' Discours
sur la Cause de la Pesanteur,' a
treatise which was little noticed at
the time, and in which he is sup-
posed to have revived the vortices
of Descartes. Those who have care-
fully examined it (Fritsch, ' Theorie
der Newton'schen Gravitation,' &c.,
Konigsberg, 1874 ; and Isenkrahe,
' Das Riithsel von der Schwerkraft,'
p. 87, &c.), find that Huygens re-
verted to his conception of a mate-
rial fluid, an ether, such as he had
suggested for the explanation of
optical phenomena, "which sur-
rounds the earth up to very great
distances, which consists of the
minutest particles, which fly about
in the most different ways in . all
directions with tearing velocity " —
an anticipation surelj' of Lesage's
" ultramundane corpuscles." The
other great thinker who, whilst
firmly believing in Newton's law,
sought for a mechanical explanation
of it, was Leonhard Euler (1707-83).
In his ether theoiy, to which he
reverts frequently, he made an
attempt to explain the various
physical agencies, among them
gravitation (1743, in his ' Disser-
tatio de Magnete, ' which received
in 1744 the prize offered bj' the
Paris Academy), by the pressure of
the ether. He admits the difficulty
of the problem, but insists upon the
necessity of finding a mechanical
cause for gravitation. See Isen-
krahe in ' Zeitschrif t fiir Mathe-
matik und Physik,' vol. xxvi. ; but

344 SCIENTIFIC THOUGHT.

24. of the last century, subiected the less universal terrestrial

Electrical •' ' •'

andma-;- plienoinena of magnetic and electric action to exact mea-

netic action, '^ o

surements, finding that a formula corresponding to the
gravitation formula described them with surprising ac-
curacy, with this remarkable difference, that here not only
attractive but also repulsive forces, following the same
mathematical relations as to mass and distance, came into
play. To these confirmatory discoveries must be added
the measurement of the intensity of radiations which
proceed from centres, such as those of light and heat,
made by various philosophers during the latter half of
the last century. Newton, and his great successor La-
place more than a century after him, both favoured the
emission or emanation hypothesis of light, and it was
thus natural to fasten upon the analogy which existed
between the intensity in which radiation, gravitation, and
electric and magnetic action change with the distance

25. from their respective centres. All these agencies came

Law of . „ „ .

emanations, thus Under the general conception of forces emanating
from fixed centres, and spreading through space, in the
proportion of the superficial area of the spheres described
around their centres with increasing radii — i.e., decreasing
or becoming diluted in the ratio of the squares of these
radii or distances. These analogies were indeed recognised
to be very imperfect, inasmuch as light and radiant heat
occupy a measurable time to spread from their centres,
whereas the time occupied by the force of gravitation is

especially Miething, ' L. Euler's self, has again received attention

Lehre vom Aether,' Berlin, 1894. through Faraday's, Maxwell's, and

In the course of this century the : Hertz's electric theories, and \Vm.

mechanical theory of gravitation, ' Thomson (Lord Kelvin) has especi-

including the attempts of Lesage, ally studied the ideas of Lesage.

Euler, Huygens, and Newton him- Of this more later on.

THE ASTRONOMICAL VIEW OF NATURE.

345

either exceedingly small or this force is propagated
instantaneously through the greatest cosmical distances
which come under our notice. Then, again, light and
radiated heat spend themselves as they meet with reflect-
ing or absorbing bodies, whereas gravitation does not
seem to be affected by intervening or screening bodies.^

' It is now known that this

screening effect exists likewise in

magnetic and electric action. In

the formula which expresses the

action at a distance of magnetic,

electrical, and ponderable masses,

. m.m!
VIZ., /=jii ^^ y the older view —

previous to Faraday's researches —
considered m and m' the masses
(ponderable or imponderable), and
the distance r to be variable, fi a
constant, corresponding to the gra-
vitation constant. As stated above,
the gravitation constant is, so far
as we know, a real constant — i.e., it
is not affected by the nature of the
medium which fills the space inter-
vening between m and rn!, the at-
tractive masses. Faraday doubted
this; but leaving gravitation — "as
a relation by some higher quality "
— aside, he directed his efforts to
the testing of the validity of this
view as regards electric and mag-
netic action. He found that ix. is
not a real constant, but dependent
on the nature of the medium and
the objects which intervene be-
tween the magnetic and electric
masses. These researches, which
are probably the first step in the
direction of gaining by observation
some notion of the mechanical
manner in which action at a dis-
tance is brought about, begin with
the year 1837 (see 11th series of
' Experimental Researches in Elec-
tricity,' No. 1252). The result was
that the " specific electric induction
for different bodies " was estab-
lished, contrary to the ideas of

Poisson and others ('Exper. Res.,'
No. 1167), and the word "dielec-
tric " invented to denote the " action
of the contiguous particles of the
insulating medium" (No. 1168).
From this point he was led a
step farther, to "expect that all
polar forces act in the same general
manner" — viz., by contiguous par-
ticles. Faraday, however, is care-
ful to remark that bj' contiguous
particles he means those " which
are next to each other, not that
there is no space between them "
(No. 1665).

In 1838 Faraday was still doubt-
ful whether magnetic action was
similar in this respect to statical
electric action ; but he thought it
probable that it was "communi-
cated by the action of the interven-
ing particles" (No, 1729), and in
pursuing this line of thought, in
spite of many unsuccessful trials,
he at last saw his ideas realised,
discovered the magnetisation of
light, and invented the term " dia-
magnetic" to describe "a body
through which lines of magnetic
force are passing, and which does
not b\' their action assume the
usual magnetic state" (1845, 'Ex-
per. Res.,' No. 2149). At the end
of the 19th series of researches he
says: "In former papers (1838) I
proposed a theory of electrical in-
duction founded on the action of
contiguous particles, . . . and I
then ventured to suggest that prob-
ably . . . magnetic action was also
conveyed onward in a similar man-
ner. At that time I could discover

346

SCIENTIFIC THOUGHT.

26.
Molecular
ftction.

Nevertheless, the fact that gravity, radiation, and
electric and magnetic action appear as central emana-
tions, decreasing with the square of the distance, — two
properties which lend themselves to mathematical and
geometrical representation, — seemed to pave the way for
further generalisations. All forces in nature were put
down as central forces, either attractive or repulsive, and
if not following the Newtonian formula, still dependent on
the distance according to some mathematical expression.
For nearly a century theoretical physics were occupied in
working out the mathematical formulae expressive of these
ideas, and Laplace himself promoted these attempts by the
weight of his great authority. We do not possess the final
views on this point with which the great mathematician
intended to complete the last edition of his ' Exposition
du Systeme du Monde ' ; but some of the later chapters of
this work, treating of gravitation and molecular attraction,
show us clearly in which direction he looked for progress
in theoretical physics.^

no peculiar condition of the inter-
vening or diamagnetic matter ; but
now that we are able to distinguish
such an action ; . . . now that
diamagnetics are shown not to be
inditierent bodies, I feel still more
confidence in . . . asking whether
it may not be by the action of the
contiguous or next succeeding par-
ticles that the magnetic force is
carried onward," &c. (No. 2443).
Faraday also made repeated experi-
ments with the view of determin-
ing how the force of gravitation
is communicated, believing as little
as Newton did in an actio in distant:,
and he was wont to quote New-
ton's words on this matter, referring
also to Euler's ether theory (No.
3305).

^ In the fifth edition of the ' Ex-
position du Sj'st^me du Monde ' La-
place had suppressed these chapters,
and had announced his intention
" to unite the principal results of the
application of analysis to pheno-
mena depending on a molecular
action differing from universal at-
traction " into a special treatise
which should form a sequel to the
' Exposition,' &c. This project was
never carried out (see "avertisse-
ment au sixi^me edition do T Ex-
position ' "). The success which
attended Laplace's attempts to ex-
plain double refraction and aberra-
tion of light (following Newton's
suggestions in the ' Principia ' and
' Optics ') as well as capillary pheno-
mena (following Haukesbee) left no

THE ASTRONOMICAL VIEW OF NATURE.

347

The great prominence given by Laplace to the gravita-
tional explanation of all natural phenomena, the fact that
all the observable movements of the universe, the shape
and size of the moving masses, and the orbits they de-
scribe, as well as many phenomena observable on the
surface of our globe, such as the aberration and refraction
of light, the phenomena of the tides, of atmospheric pres-
sure, and some of the more important molecular properties
of matter, could be perfectly or approximately described,
calculated, and predicted by gravitation or analogous at-
tractions, gave to what we may call — following a hint
of Clerk Maxwell's — the astronomical method ^ of con-

doubt in his mind that such pheno-
mena " are owing to attractive and
repulsive forces between molecule
and molecule" ('Expos.,' 6"'« ed.,
p. 328). He saw in molecular at-
traction the cause of the solidity of
bodies, of chemical affinities, and of
the properties of chemical satura-
tion, which Berthollet had developed
about that time ('Expos.,' p. 360) ;
he thinks it likely that the law of
molecular attraction is the same for
all bodies, and he finally dwells on
the question whether the attraction
of gravity and molecular attraction
could be united under one common
law or expression (p. 363), and
throws out the idea that thus the
phenomena of physics and astro-
nomy might be brought under one
general law, adding, however, signi-
ficant!}', " Mais I'impossibilite de
connaitre les figures des molecules
et leurs distances mutuelles, rend
ces explications vagues et inutiles a
I'avancement des sciences."

^ " Cavendish, Coulomb, and
Poisson, the founders of the exact
sciences of electricity and magnet-
ism, paid no regard to those old
notions of ' magnetic effluvia ' and
' electric atmospheres ' which had

been put forth in the previous
century, but turned their undivided
attention to the determination of
the law of force, according to which
electrified and magnetised bodies
attract or repel each other. In this
way the true laws of these actions
were discovered, and this was done
by men who never doubted that
the action took place at a distance,
without the intervention of any
medium, and who would have re-
garded the discovery of such a
medium as complicating rather
than as explaining the undoubted
phenomena of attraction. . . .
Ampere, by a combination of
mathematical skill with experi-
mental ingenuity, first proved that
two electric currents act on one
another, and then analysed this
action into the resultant of a sj's-
tem of push-and-puU forces be-
tween the elementary parts of
these currents. . . . Whereas the
general course of scientific method
then consisted in the application
of the ideas of mathematics and
astronomy to each new investiga-
tion in turn, Faraday seems to
have had no opportunity of ac-
quiring a technical knowledge of

348

SCIENTIFIC THOUGHT.

27.

Tlie astro-

uomical

view.

Cosmical,

molar, and

molecular

phenomena.

sidering nature a great impetus. As we have seen, it
was entirely an outcome of Newton's great discovery.

It is sometimes useful to distinguish between cosmical,
molar, and molecular phenomena ; it is, however, well to
note that this distinction is a popular or practical, not a
scientific one. The question, in how far pure magnitude
affects the appearance and relations of the parts or ele-
ments of which the universe is composed, is indeed of
great scientific interest, but it has not yet received a
definite answer. In the meantime we can use the term
cosmical for such magnitudes of space, mass, or time as
far transcend our own powers of direct measurement by
the foot-rule, the balance, and the timepiece, and still
more, our powers of direct action : those dimensions com-
pared with which our own homes and actions absolutely
disappear. We will call molar those masses which we
can handle directlv, those dimensions in which we build
our own homes and pass our own lives. And we will
call molecular those sizes and masses which on the other
side are so small that the utmost powers of the micro-
scope and the dividing machine fail to make them directly
visible, still less tangible or manageable for our active
powers. The lines which limit these three regions are
indeed neither fixed nor fixable ; the middle region, which

mathematics, and his knowledge of
astronomy was mainly derived from
books. . . . Thus Faraday was de-
barred from following the course
of thought which had led to the
achievements of the French philo-
sophers, and was obliged to explain
the phenomena to himself by means
of a symbolism which he could un-
derstand, instead of adopting what
had hitherto been the only tongue

of the learned " (Clerk Maxwell,
■'Action at a Distance," 'Proceed-
ings of the Royal Institution,' vol.
vii. Reprinted in ' Scientific Papers,'
Cambridge, 1890, vol. ii. p. 317 S'/.
Cf. also vol. i. p. 156). Du Bois-
Reymond uses the term " astro-
nomical knowledge " in a somewhat
wider sense in his discourse " Ueber
die Grenzen des Naturerkennens "
('Reden,' vol. i. p. 120).

THE ASTRONOMICAL VIEW OF NATURE.

349

we may call our own home, seems to be extending through
improved means of seeing and handling ; still every one
has a vague notion, and science has supported this notion,
that there are certain limits, marking the immeasurably
large and the immeasurably small, which we cannot tran-
scend. Now it is a question of great scientific interest
to what extent mere enlargement, such as the microscope
makes familiar to us, would essentially alter the behaviour
and appearance of things natural. Would the planetary
or stellar systems, reduced in size many million times,
present an aspect similar to the view we here enjoy of the
inanimate matter on the surface of our earth, and would
the molecular structure of microscopic objects, many times
enlarged, differ essentially from that aspect ? Our present
knowledge would lead us to say they would essentially
differ. Certain phenomena or modes of motion seem, so
far as we know, essentially characteristic of the molecular,
others of the molar, others again of the cosmical world.^

' Laplace has made a significant
remark on this point. See ' Ex-
position du Systeme du Monde,'
6 ed., p. 319 sq. : "La loi de la
pesanteur reciproque au earre des
distances . . . est celle de toutes
les emanations qui partent d'un
centre, telle que la lumiere ; il pa-
rait meme que toutes les forces dont
Taction se fait apercevoir h des
distances sensibles, suivent cette
loi : on a reconnu depuis peu, que
les attractions et les repulsions
electriques et magnetiques decrois-
sent en raison du carre des dis-
tances, en sorte que toutes ces
forces ne s'afFaiblissent en se pro-
pageant, que parcequ'elless'etendent
comme la lumiere ; leurs quantites
^tant les memes sur les diverses
surfaces spheriques que Ton peut

imaginer autour de leurs foyers.
Une proprietd remarquable de cette
loi de la nature est que si les
dimensions de tous les corps de cet
univers, leurs distances mutuelles
et leurs vitesses, venaient a aug-
menter ou a diminuer proportion-
ellement ; ils decriraient des courbes
entierement semblables h celles,
qu'ils decrivent, et leurs apparences
seraient exactement les memes; car
les forces, qui les animent, etant le
resultatd'attractionsproportionelles
aux masses divisees par le carre des
distances, elles augmenteraient ou
diminueraient proportionellement
aux dimensions du nouvel univers.
On voit en meme temps, que cette
proprietd ne peut appartenir qu'h
la loi de la nature. Ainsi, les ap-
parences des mouvements de I'uni-

350 SCIENTIFIC THOUGHT.

28. And we cannot but be struck by the fact that only those

Special ...

attaclfed dimensions which we call molar appear to be the abode
diiMnsTons. of living and conscious beings. The cosmical world has,
so far as we know, no inhabitant which can behold it in
the same way as man beholds this planet, and the same
obtains so far as we are acquainted with the molecular
world. So far as our knowledge goes and is likely ever
to reach, a special importance or dignity will therefore
always belong to molar dimensions and masses. The pro-
cess by which we try to picture to ourselves in tracings and
models, constructed in molar dimensions, the behaviour
and appearance of cosmical as w^ell as molecular masses will
always recommend itself, not only as the most practical, but
likewise as the most interesting and plausible, for only by
this procedure do these unreachable worlds become amen-
able to direct observation and to the processes of experi-
ment in the physical laboratory. It seems prima facie
that the wealth of phenomena and the variety of different
kinds of motion decrease as we ascend into the cosmical,
or as we descend into the molecular world, giving way
in the former to essentially uniform, though to many
times multiplied modes of motion, and disappearing in

vers sout iuddpendantes de ses

dimensions absolues, comme elles

]e soiit, du mouvement absolu,

qu'il peut avoir dans I'espace ; et

nous ne pouvous observer et con-

naitre que des rapports." This is

easily seen. For if in the formula

. m.m! ,, ,. . , „

f— , the dimensions be all

a centre like the sun would be
-pr, — -, = A'^-"x— , which is only

K times the acceleration ^. if

71 = 2. In another passage Laplace
repeats the above statement in
slightly different words : " L'uni-

?■" t vers reduit successivement jusqu'au

multiplied by A', we get the new plus petit espace imaginable, otfrir-

formula F=K^-y.'-'f, and the fit touj ours les memes apparences

r" I a ses observateurs (p. 440). Ihat

acceleration of a body moving round | this would not apply to molecular

! attractions or repulsions is evident.

THE ASTKONOMICAL VIEW OF NATURE. 351

the latter in stable and self-repeating averages. Pos-
sessed therefore, as we seem to be, of the greatest wealth
and variety of observations and notions, we may — perhaps
erroneously — conclude that we can grasp the simpler
cosmical and molecular movements and phenomena by
starting from molar, physical, or mechanical models.-^

^ English natui-alists have always
excelled in this Hue of investigation,
whereas foreign scientific literature
has been rich iu purely mathemati-
cal deductions from formula3 which
contained no constmirbarc Vorstel-
lung. And it is interesting to note
that both lines of thought go back
to Newton. Whereas Newton him-
self believed in the possibility of a
mechanical explanation or represen-
tation of the gi-avitation formula,
the second edition of the ' Priu-
cipia ' b}^ Cotes can be looked upon
as sanctioning the view that gravi-
tation is an ultimate quality which
must be accepted as such ; and as
it was the second edition through
which Newton's ideas became large-
ly known on the Continent, it is
not surprising that he was there
accused of reintroducing the quali-
tales occultcB of the older metaphj's-
ics, which Descartes and others had
successfully banished. Clerk Max-
well says (" Action at a Distance,"
'Sclent. Pap.,' vol. ii. p. 316):
" The doctrine of direct action at
a distance cannot claim for its
author the discoverer of universal
gravitation. It was first asserted
by Roger Cotes in his preface to
the ' Principia,' which he edited
during Newton's life. According
to Cotes it is by experience that
we learn that all bodies gravitate.
We do not learn in any other waj'
that they are extended, movable,
or solid. Gravitation, therefore,
has as much right to be considered
an essential property of matter as
extension, mobility, or impenetra-

bility. And when the Newtonian
philosophy gained ground in Europe,
it was the opinion of Cotes rather
than that of Newton that became
most prevalent." In fact, philoso-
phers could be divided into two
classes — those who took the fact
of gravity or the wider idea of a
universal attraction as a beginning,
and drew from this beginning all
the i^ossible mathematical and ex-
perimental consequences which they
could think of ; and those who,
whilst admitting this process as a
legitimate one, thought it neces-
sary to go behind the assumed
beginning and find a still more
hidden mechanical reason fur this
admitted property. To the latter
class belonged Newton himself,
Huygens, Euler, and in modern
times notablj' Faraday and his fol-
lowers ; to the former class be-
longed Daniel Bernoulli, who wrote
to Euler, 4th February 1744, refer-
ring to the ether theorj' of the lat-
ter : " Moreover, T believe both that
the ether is (jravis versus solera and
the air versus terrain, and I cannot
conceal from you that on these
points I am a perfect Newtonian,
and I am surprised that you ad-
here so long to the 'principiis Car-
tesianis ; there is possibly some feel-
ing in the matter. If God has been
able to create an anirnam whose na-
ture is unknown to us. He has also
been able to impress an attractioncm
U7iiversalem materice, though such is
att radio supra captum, whereas the
principia Cartesiatui involve always
something contra captum" (see

352

SCIENTIFIC THOUGHT.

29.
Geometrical
axioms.

I may, in passing, mention here that in the course of
our century certain views have been put forward in pure
mathematics, or rather in geometry, which make it con-
ceivable, if not probable, that our ideas of space might
not apply to immeasurably small or to immeasurably
large dimensions.^ Should the future progress of thought

Miething, ' L. Euler's Lehre voin
Aether,' p. 30). In quite recent
times a similar position has again
been taken up by Paul du Bois-
Reymond in his essay " Ueber die
Unbegreiflichkeit der F'ernkraft,"
ill the ' Xaturwissenschaftliche
Rundschau' (vol. iii. No. 14), and
in his posthumous work, ' Ueber
die Grundlagen der Erkenntniss in
den exacten Wissenschaften ' (Tii-
bingen, 1890), in which he adds
action at a distance as a third
" ignorabimus " or unknowable pro-
blem to the two given in his
brother Emil's address, " Ueber die
Grenzen des Naturerkennens "
(1872, reprinted in 'Reden,' vol.
i. p. 105). On the Continent,
about thirty years ago, the fruit-
lessness of pursuing this problem
seemed generally admitted. Helm-
holtz in 1847 speaks of the initial
assumption "that all actions in na-
ture are to be reduced to attracting
and repelling forces, whose inten-
sitj' depends merely on the distance
of points mutuallj' acting on each
other" {actio in distans), and Du
Bois-Reymond repeats this in 1871
in liis address. But it is significant
that Helmholtz, who (through his
memoir on vortex motion in 1858)
gave such an impetus to the me-
chanical explanations of molecular
forces, modified his views on this
point (see his address on Magnus,
1871, ' Vortriige und Reden,' vol.
ii.) ; accordingly in the reprint of
his memoir of 1847 he has accom-
panied it with .some significant re-
marks on the necessity of that in-
itial assumption (18S1, ' Wissen-

schaftliche Abhandlungen,' vol. i.
p. 68).

^ lliemann was probably the first
to give expression to this line of
thought. His memoir on this sub-
ject, " On the Hypotheses which lie
at the Foundation of Geometry,"
bears the date 1854. It was read
before the Philosophical Faculty of
Gottingen in the presence and at the
request of Gauss, on whom it made
a profound impression (see the bio-
graphical notice on Riemann by
Dedekind, attached to Riemann's
'Gesammelte Werke,' Leipzig, 1876).
The memoir was not published till
after Riemann's death in 1867. In
England the late Prof. Clifford in-
troduced the subject to the Cam-
bridge Philosophical Society in 1 870 :
" The axioms of plane geometry are
true within the limits of experiment
on the surface of a sheet of paper,
and yet we know that the sheet is
really covered with a number of
small ridges and furrows, upon
which these axioms are not true.
Similarly although the axioms of
solid geometry are true within the
limits of experiment for finite por-
tions of our space, yet we have no
reason to conclude that they are
true for verj' small portions ; and
if any help can be got thereby for
the explanation of physical pheno-
mena, we may have reason to con-
clude that they are not true for
very small portions of space " (see
Clifford's ' Mathematical Papers,'
p. 21 . Compare also his lectures
on "The Philosophy of the Pure
Sciences " in ' Lectures and Essays,'
vol. i. p. 295 sqq.)

THE ASTRONOMICAL VIEW OF NATURE. 353

or observation bring forward any indications that the
idea is not only a theoretical possibility, but an actual
reality, then the mode of thought now so successfully
used — viz., that of transferring phenomena belonging to
molar dimensions, and exemplified in the physical labora-
tory, into cosmic or molecular space by a process of en-
larging or of reducing — would become inapplicable.
Mathematics indeed would not fail, but our ordinary
geometry and the physical model and mechanism would
fail : we should probably still be able to calculate,
though not to represent, those phenomena of immeasur-
able dimensions.

As it is, the first great example of calculating and pre-
dicting the phenomena of an unreachable world was
Newton's successful attempt to explain the movements
of the moon, and other cosmical bodies, by using the
phenomena of falling bodies on the surface of the earth
described by Galileo and Huygens ; and he was rewarded 30.

, -^ JO ^ ^ ^ Difficulty of

by the discovery of a universal law of attraction, which measuring

"' "^ giavitation

would probably never have been discovered by experi- directly.
ments carried on within molar dimensions, the mass of
the earth being so immeasurably greater than that of
any molar masses under our control. It quite escapes
our observation that in the action and reaction of the
falling stone the immensity of the earth's mass is com-
pensated by the vanishing distance through which the
earth moves when attracted by the stone. Thus the
astronomical view came to the rescue of physical or molar
experiments, helped to explain them, and indicated the
manner in which cosmical forces could be measured
even on the surface of the earth. The pendulum experi-
VOL. I. z

354

SCIENTIFIC THOUGHT.

ments of Eicher, Halley, and many others, the measure-
ments of the arc of the meridian, and Cavendish's and
Maskelyne's experiments, were some of the direct results
of the discovery.

It was natural that, having explained the cosmical, and
subsequently many terrestrial phenomena, successfully by
the formula of attraction, Newton himself, and still more
Laplace and his school, should have attempted the ex-
planation of molecular phenomena by similar methods.

The astronomical view spread into molar and molecular
physics. Newton himself made use of the notion of
phenomena. |j;LQ]gcuiar attraction ^ — i.e., of attraction existing only at

31.

Astronomi-
cal view of
molecular

^ In the fourteenth section of
the first book of the ' Principia '
Newton is, however, careful to speak
always of "attractio vel impulsus,"
leaving it open to the reader to
form his own opinion whether it is
an action at a distance or a " vis a
tergo," a push. He says also that
the particles of light approaching
solid bodies with a definite velo-
city are bent, "quasi attracti in
eadem {i.e., corpora)." And in the
twenty - third query to the first
Latin edition of the ' Opticks '
(1706) he says : " May not the
small particles of bodies have cer-
tain virtues, powers, or forces by
which they act at some distance,
not only on the rays of light, re-
flecting, refracting, or inflecting
them, but also on each other, pro-
ducing various natural phenomena?
For it is sufficiently known that
bodies mutually act on each other
through the attraction of gravity
and through magnetic and electric
virtue. And these examples show
what is the order and reason of
nature, so that it becomes very
probable that there may be other
attractive forces. For nature is
very similar and agreeing to her-

self. Through what efficient cause
these attractions are brought about
I do not inquire here. What I
here call attraction may well be
produced by an impulse or in some
other way unknown to us. I take
this word attraction here in this
way, that it be understood merely
to mean some universal force with
which bodies try to approach each
other, whatever cause this force
may have to be attributed to. For
from the phenomena of nature it
behoves us first to be taught which
bodies attract each other, and what
are the laws and properties of this
attraction, before we inquire by
what efficient cause this attraction
is brought about. The attraction
of gravity and of the magnetic and
electric virtue extend to sufficiently
large distances, so that they fall
under the notice of the vulgar
senses ; but it may be that there
are others which are contained in
such narrow limits that they have
so far escaped all observation."
And he goes on to speak of the de-
liquescence of some salts and of
chemical combinations of finely
powdered substances. And fur-
ther on in the same query, after

THE ASTRONOMICAL VIEW OF NATURE.

355

very small distances — to explain the refraction and in-
flection of light passing from empty space, or from the

referring to attractive forces acting
only at small distances, he pro-
ceeds: "And as in algebra, when
the positive quantities disappear
and cease, negative quantities be-
gin ; so in mechanics, where attrac-
tion stops, there a repelling force
must come in. But that such a
force exists, seems to follow from
the reflection and inflection of the
rays of light. For the rays are
repelled by bodies in both these
cases, without the immediate con-
tact of the reflecting or inflecting
body. And if all this is so, then
the whole of nature will lie very
simple and similar to herself ; per-
forming all the great motions of
the heavenly bodies by the attrac-
tion of gravity, which exists be-
tween all those bodies, and almost
a.11 the smaller motions of their
particles through some other at-
tracting and repelling force, which
exists mutually between those
particles" (' Optice,' mdccvi., p.
341). The suggestions of Newton
regarding forces of molecular di-
mensions were taken up by other
contemporary writers and experi-
mentalists, and the ' Philosophical
Transactions' during the early
years of the last century contain
several memoirs touching on this
subject, notably by John Keill
(1708), who refers to Newton's
'Opticks,' and enlarges, as does
also John Freind (' Prelectiones
Chymicse '), on the usefulness of the
idea of molecular attraction in ex-
plaining chemical and physiological
phenomena. In the later editions
of the 'Opticks,' evidently in con-
sequence of the elaborate experi-
ments of Hauksbee, Newton enters
more fully into the question of
molecular, especially capillar}', ac-
tion ; and his last query, No. 31, is
quoted by Laplace in his ' Theorie

de I'Action capillaire,' which forms
the supplement to the tenth book
of the 'Mecanique celeste.' I may
here mention that as some confu-
sion exists in the different editions
of the ' Optics ' regarding the num-
bering of the "Queries," it is best
to refer to Horsley's Collected Edi-
tion of the Works of Newton,
where the latest English edition is
reprinted, and all the variations
and additions noted from the first
(English) edition through the sub-
sequent ones. The first edition
breaks oS" with querj' 16 ; the first
Latin one with query 23, and this
was in later editions numbered 31,
a number of new queries being in-
serted, Nos. 18 to 24, referring to
the " j)''ob^bility of a medium more
subtle than air" and the "me-
chanical efficient of gravitj'." This
was added " to show " (Newton's
words in preface dated 16th July
1717) "that I do not take gravity
for an essential property of bodies,
. . . choosing to propose it by way
of a question, because I am not
yet satisfied about it by way of
experiments." We may note that
this was written a few years after
the second edition of the ' Principia '
was published by Cotes, whose
preface did a good deal to occasion
the misunderstanding regarding
Newton's views on gravitation as a
Ijrimary quality of matter. From
his correspondence with Cotes,
edited by Eddleston (1850), we
know that Newton in composing
the "Scholium generale," which is
added to the second and later edi-
tions of the ' Principia,' had in-
tended to say " much more about
the attraction of the small par-
ticles of bodies," but that on second
thoughts he abandoned this inten-
tion (p. 147).

356 SCIENTIFIC THOUGHT.

atmosphere, into or in the neighbourhood of solid bodies.
He conceived light to be a material substance, consisting
of minute particles, propelled in straight lines from the
luminous centres. These small particles, when arriving
at or near the surface of transparent bodies, came under
the influence of an attraction from the substance of such
bodies, and Newton succeeded in showing that for rays
of light which fall on transparent surfaces at an angle,
the path of the ray in the body would be deflected accord-
ing to the rule experimentally determined by Snell, and
published by Descartes. This application of the idea of
attraction, or action at a distance, to very small or mole-
cular dimensions, required a modification of the gravita-
tion formula. The first who took an important step farther
in this direction was Francis Hauksbee. Between the
year 1709 and 1713 he made a series of experiments on
32. what is called capillary action. His experiments were

Capillary r j r

action. discussed by Newton in the later editions of the ' Opticks,'
and followed by those of Dr Jurin in 17 18. Hauksbee,
Newton, Jurin, and subsequent writers, like Clairaut, all
attributed these and similar phenomena to molecular
attractions, and Laplace showed that for the mathematical
treatment of the subject a knowledge of the exact law
(corresponding to the Newtonian law of molar attraction)
was unnecessary, but that it was necessary and sufficient to
assume the existence of an attraction of the molecules of
bodies, which decreases very rapidly as their distances in-
crease, " so as to become insensible at the smallest distances
perceptible by our senses." ^ The phenomena of atmos-

^ See ' Mecaiiique celeste,' vol,
iv. (1805), Supplement, p. 67. See

temps, h determiner les lois d'at-
traction qui representent ces phe-

also p. 2 : " J'ai chercW, il y a long- nom^nes : de nouvelles recherches

THE ASTRONOMICAL VIEW OF NATURE. 357

pheric refraction as well as those of cohesion and adhesion

of bodies — i.e., the attraction of particles of the same or of

different matter under what is commonly called contact or

at distances which we call in science molecular — were thus

submitted to calculation, and the results brought largely

into harmony with experience.^ The problem presented

itself and occupied natural philosophers all through the

last century, whether a more general law of action at a

distance could be found which comprised the phenomena

of molecular as well as of molar attraction.

The most celebrated attempt in this direction is that 33.

of the Jesuit Koger Boscovich, who in 1758 published an ex°ten°sion olr
IT , , . , . , . o the Newton-

elaborate treatise on this subject. lan formula.

m'ont enfin conduit a faire voir
qu'ils sont tous representes par les
memes lois qui satisfont aux phe-
nomeaes de la refraction, c'est-k-dire
par les lois dans lesquelles I'attrac-
tion n'est sensible qu'k des distances
insensibles ; et il en resulte une the-
orie complete de Taction capillaire."
^ The terms insensible and im-
perceptible, which are commonly
used in these discussions, must be
taken with caution. It is now
known that, though not directly
perceptible or sensible, the distance
through which molecular action
takes place is measurable. Plateau
in Belgium (1843 and following
years) and Quincke in Germany
(1868) made experiments on inde-
pendent lines, and came to very
similar results. The distance of
molecular action appears to be about
the twenty thousandth part of a
millimetre. See Clerk Maxwell's
article on Capillary Action in the
9th edition of the ' Ency. Brit.,'
reprinted in ' Scientific Papers,'
vol. ii. ; also Violle's ' Cours de
Physique,' German edition, vol. i. p.
591, &c., and p. 639.

'■^ Roger Joseph Boscovich, of the
Society of Jesus (1711-87), took up
the ideas thrown out by Newton in
the last query to the ' Opticks,' and
published in 1758 at Vienna an
elaborate treatise with the title
' Theoria Philosophise Naturalis re-
dacta ad unicam legem virium in
Natura existentium.' A second
edition was published at Venice in
176-3. His speculations begin with
the year 1745, when he hit upon
his general view that all forces in
nature can be reduced to the action
of indivisible and inextended atoms,
endowed with inertia and with a
mutual force which at vanishing
distances is repulsive, which at in-
sensible distances alternates accord-
ing to some mathematical formula
between repulsion and attraction,
and, finally, at sensible distances
becomes identical with Newton's
force of gravitation. The general
form of the curve which exhibits
this action at a distance is given,
and the algebraical formula dis-
cussed, in the Supplement. But
it was, of course, impossible to
define the law any further. The

358

SCIENTIFIC THOUGHT.

Though many of the views contained in this treatise
were really the same as those embraced by a large school
of Continental mathematicians till far into this century,

whole treatise is really more of a
philosophical than a mathematical
or experimental investigation. A
large portion is taken up in de-
fending his view against possible
objections, and in showing how it
agrees with or differs from the
philosophies of Leibniz and New-
ton. Whilst this treatise represents
in general a view largely held by
Continental philosophers of nature,
it does not contain any new mathe-
matical methods such as the ' Prin-
cipia' contained before and La-
place's 'Mecanique celeste' later, nor
does it contribute any experiments
such as those works likewise con-
tained and suggested to others.
In fact, it is more a metaphysical
than an exact treatise, and as such
has exerted no lasting beneficial
influence on the progress of science.
" The eighteenth century made a
school of science for itself, in which
for the not unnatural dogma of the
earlier schoolmen, ' matter cannot
act where it is not,' was substituted
the most fantastic of paradoxes,
contact does not exist. Boscovich's
theory was the consummation of
the eighteenth- century school of
physical science. This strange idea
took deep root, and from it grew
up a barren tree, exhausting the
soil and overshadowing the whole
field of molecular investigation,
on which so much unavailing
labour was spent by the great
mathematicians of the early part
of our nineteenth century. If
Boscovich's theory no longer cum-
bers the ground, it is because one
true philosopher required more light
for tracing lines of electric force "
(Sir William Thomson's Lecture
before the Royal Institution, May
1860. Reprinted in ' Papers on

Electrostatics and Magnetism,' 2nd
ed., 1884, p. 224). Nevertheless it
is extraordinary to note that Bos-
covich's theory was more popular
among British than among Con-
tinental physicists. In France the
book seems to have been little ap-
preciated, although Boscovich was
well known through his optical and
astronomical researches (see Montu-
cla's ' Histoire des Math^matiques,'
vol. iii. p. 490, vol. iv. p. 188) ; and
his diiferences with d'Alembert were
notorious. But French science was
then occupied less with metaphysi-
cal theories than with mathematical
analysis and experimental research.
In (Tcrmany the book remained
unknown, probablj' because Euler's
authority favoured an opposite
theory. In this country, however,
the theory is often referred to from
the time of Priestley (' History of
Optics') to Faraday ("On the Na-
ture of Matter," ' Phil. Mag.,' 1844,
vol. 24), and more recently Thom-
son (Lord Kelvin). The last has
probably more than any other living
writer of similar eminence referred
to Boscovich, whose theory he con-
siders suggestive, and we are in-
debted to him for the first serious
attempt to establish by actual cal-
culation the real capabilities of the
Boscovich atoms in explaining the
properties of chemical molecules,
their stability and degree of satur-
ation (see the Report of the
British Association at Liverpool,
1896). In Scotland Boscovich's
theory was fully discussed in a
posthumous article on " Corpuscular
Forces " by John Robison, Professor
of Natural Philosophy at Edinburgh,
and published by Brewster in the
1st volume of Robison's 'System of
Mechanical Philosophy' (Edinburgh,

THE ASTRONOMICAL VIEW OF NATURE.

359

the book was almost completely forgotten on the Con-
tinent.^ No real progress has indeed been made in the
explanation of physical phenomena by the application of

1822). His ' Elements of Mechani-
cal Philosophy' (Edinb., 1804) be-
tray, according to Dugald Stewart,
"a strong and avowed leaning to
the theory of Boscovich" (Works
by Hamilton, vol. v. p. 107). The
theory probably found favour,
among other reasons, because it
seemed to give support to the pre-
valent corpuscular theory of light,
which Euler opposed, as he did
simple action at a distance. In
the Scotch school of philosophy,
of which Dugald Stewart was the
most popular exponent, Boscovich
was well known. Stewart refers to
him frequently (Works by Hamilton,
vol. ii. pp. 50, 107, 110, 343; vol.
iii. p. 233 ; vol. v. p. 93 sqq. ; vol.
vii. p. 173 sqq.) He quotes Priest-
ley, Robison, and James Hutton as
followers of Boscovich, whilst his
own adherence is certainly very
qualified, and he makes a very
pertinent remark in his Introduc-
tion to the ' Elements of the Philo-
sophy of the Human Mind' (1792) :
"I cannot help taking this oppor-
tunity of remarking that if physical
inquirers should think of again em-
ploying themselves in speculations
about the nature of matter, instead
of attempting to ascertain its sen-
sible properties and laws (and of
late there seems to be such a ten-
dency among some of the followers
of Boscovich), they will soon involve
themselves in an inextricable laby-
rinth, and the first principles of
physics will be rendered as mys-
terious and chimerical as the pneu-
matology of the schoolmen " (vol.
ii. p. 50). Boscovich seems to have
been fond of tracing mathematical
curves to represent all kinds of pro-
cesses, such as the intellectual ad-
vancement of the age, and he shows

graphically that this was declining
(Dugald Stewart's quotation in his
' Dissertation,' W^orks, vol. i. p. 499).
1 When Fechner published the
first edition of his ' Atomenlehre '
(lsted.,Leipzig,1855; 2nd ed., 1864),
he does not seem to have known of
Boscovich's treatise (see p. 229 of
the 2nd edition), and it was simi-
larly unknown to the Dutch meteor-
ologist Buys Ballot, whose curves
of the attracting and repelling
forces of matter agree almost ex-
actly with those of Boscovich (see
' Fortschritte der Physik,' 1849, p.
1 sqq. ; also Rosenberger's ' Ge-
schichte der Physik,' vol. iii. p. 536
sqq.) In French scientific literature
the treatise of Boscovich is mostly ig-
nored— the ' Grande Encyclopedic '
does not even give its title. In
fact, French science does not con-
sider itself beholden to the cele-
brated Jesuit for what I call the
astronomical view of matter. See
St Venant in ' Comptes Rendus,'
vol. 82, p. 1223: " Plusieurs auteurs,
soit anglais, soit allemands, dans
ses ceuvres qui sont du reste d'une
haute portee, . . . se sont pris a
condamner vivement, sous le nom de
tMorie de Boscovich, non pas son
idee capitale de reduction des atomes
h. des centres d'action de forces,
mais la loi meme, la loi physique
generale des actions fonctions des
distances mutuelles des particules
qui les exercent reciproquement les
unes sur les autres. Et ils attri-
buent ainsi au celebre religieux
I'erreur grave oil sont tombes, sui-
vant eux, Navier, Poisson et nos
autres savants, createurs, il y a un
demi-si^cle, de la mecanique mole-
culaire ou interne. Or cette loi
blamde, cette loi qui a ^te mise en
oeuvre aussi par Laplace, &c., et

360

SCIENTIFIC THOUGHT.

34.
Coulomb's
measure-
ments.

S5.
Extended hy
Gauss and
Weber.

Boscovich's or similar formulae, though the idea of action
at a distance between the minute particles of matter un-
derlies the theories by wliich Poisson, Navier, Cauchy,
Lame, and others calculated the effect of elastic forces in
solid bodies, or the phenomena of light passing through
transparent and crystalline substances. A different school
of physicists, starting from ideas of a different kind, with
which we shall become acquainted hereafter, have shown
that specific notions as to the molecular structure of bodies
are not required in order to deal with the phenomena
referred to. Nevertheless, the idea of action at a distance
governing the movements of immeasurably small, as it
seemingly does those of immeasurably large masses in
nature, received a great support by the development of
two other branches of science, which belong essentially to
the history of the present century.

The sciences of electricity and magnetism can be said
to have originated with Coulomb's accurate measure-
ments with the torsion-balance. With this instrument
he measured the attracting and repelling forces of
bodies, electrified or magnetised, by comparing them
with the mechanical forces required to twist a metallic
wire. In this way he fixed what have ever since his
time been termed the units of electricity or magnetism,
reducing these quantities to the same system of measure-
ment with which we measure the masses or inertia of
moving bodies. His methods were adopted and modi-
fied and greatly perfected by Gauss and Weber — the

prise par Coriolis et Poncelet pour
base de la m^canique physique,
n'est autre que celle de Newton lui-
meme, comme on le voit non seule-

ment dans son grand et principal
ouvrage, mais dans le scholie g^n-
(5ral de sa non moins immortelle
' Optique. ' "

THE ASTRONOMICAL VIEW OF NATURE.

361

former applying them to the measurement of the mag-
netic forces of the earth, the latter to that of the forces
exerted by currents of electricity — i.e., by electricity
which is not at rest but in motion. As I have already
stated, the measurements of Coulomb confirmed the
prevalent notion that action at a distance, varying
inversely as the square of the distance, and directly in
the proportion of the quantities of the acting substance,
was a universal formula or law of nature.^ The idea

■* Coulomb's exact measurements
of the attraction and repulsion at a
distance of electrified bodies and of
magnets were published during the
years 1784 to 1789 in seven memoirs
presented to the Paris Academy of
Sciences. They are conveniently
collected, together with some other
memoirs of Coulomb, Poisson, and
others on kindred subjects, in the
first volume of the ' Collection de
Memoires relatifs a la Physique,'
published in 1884 by the Societe
francaise de Physique. Coulomb
made use of the torsion - balance
and the proof-plane, the actions of
which he carefully examined. He
confirmed the law, which had been
vaguely or approximately expressed
by various writers before him, that
electrified bodies act on each other
with a force which is proportional
to the inverse square of their dis-
tances. This he did by direct
measurements of the repulsion of
small electrified bodies in the tor-
sion-balance (1785, 1st Memoire).
He tlien extended his measure-
ments by an indirect method to
the action of electrified bodies of
larger size and to magnets (2nd
Memoire). He also defined what
is meant by quantity and density
of electricity and magnetism, and
showed how these could be meas-
ured and how the action of elec-
trified bodies and magnets depended

on the more or less of these quan-
tities. Coulomb's researches con-
tain experiments of gieat delicacy.
Although the laws which bear his
name appear so simple when written
down, the phenomena they repre-
sent are most complicated, as in
the case of electricity the effect of
electrical influence, called by Fara-
day induction, and in tlie case of
magnetism the presence of the
earth's magnetism, and the fact
that we have never to do with one
kind of magnetism but always with
two states, destroys all chance of ex-
hibiting experimentally the simple
case represented by the mathemati-
cal formula. It was therefore ne-
cessary to consider this formula as
being merely a convenient descrip-
tion of the elementary action of
supposed isolated quantities of
electricity and magnetism, and by
a process of summation to deduce
mathematically the actual effects
for such cases of interaction as
are actually observable in the la-
boratory. It was especially the
phenomena of the distribution of
electricity on the surface of elec-
trified bodies of simple shape and
the distribution of magnetic forces
in the neighbourhood of magnets
which had to be calculated and
measured. In physical astronomy
a similar course of reasoning and
observation combined had verified

362

SCIENTIFIC THOUGHT.

of mass, which in the Newtonian formula meant merely
the quantity of matter, had indeed to be enlarged, and
to the attracting forces had to be added those of re-
pulsion ; still, though physically the phenomena were
entirely different, the mathematical expression which
ruled the two electric and the two magnetic quantities,
usually termed fluids, looked very much like the New-
tonian gravitation formula : it betrayed philosophers into
thinking they possessed an explanation where really they
had only a measurement and a description.^

Newton's elementary law of gravita-
tion, Laplace as it were summing
up the evidence in his great work.
What Laplace did for Newton was
done by Poisson for Coulomb's ele-
mentary law of electric and mag-
netic action, and on a still larger
scale by Gauss, who worked out
the mathematical theory and ap-
plied it to the case of the magnetic
distribution on the earth's sur-
face. In England, already before
Coulomb's researches were pub-
lished, Cavendish had, likewise by
a combination of experiment and
calculation, established the elemen-
tary formulte and properties of
electrical phenomena. See note to
the following page.

^ The exact measurements of
Coulomb and the mathematical
analysis of Poisson and Gauss
superseded the vaguer discussions
on the nature of electricity and
magnetism which were very fre-
quent before that period, just as
the mathematical principles of
Newton and Laplace drove into
the background the discussion on
the nature and cause of gravity.
Coulomb himself does not profess
to settle the controversy carried on
between the two schools of which
Dufay and Franklin can be con-
sidered as the principal representa-

tives— viz., whether there existed
two electric fluids or only one.
Coulomb judged the rival views
simply as to their usefulness in
describing and measuring phenom-
ena : " Comme ces deux e;s:plications
n'ont qu'un degr^ de probabilite
plus ou moins grand je previens,
pour mettre la theorie ... a
I'abri de toute dispute systematique,
que dans la supposition des deux
fiuides electriques je n'ai d'autre
intention que de presenter avec le
moins d'elcments possibles, les re-
sultats du calcul et de I'experience,
et non d'indiquer les veritables
causes de I'electricitc^ " (' Collection
de Memoires,' vol. i. p. 252). He
had previously, in 1777, rejected
the theory of vortices to explain
magnetic phenomena: "II semble
qu'il resulte de I'experience que ce
ne sont point des tourbillons qui
produisent les difFerents phenom-
enes aimantains, et que, pour les
expliquer, il faut necessairement
recourir a des forces attractives et
repulsives de la nature de celles,
dont on est oblige de se servir pour
expliquer la pesanteur des corps et
la physique cdleste " (vol. i. p. 8).
And in 1789 he is still more
cautious : " Pour dviter toute dis-
cussion, j'avertis . . . que toute
hypothese d'attraction et de rdpul-

THE ASTRONOMICAL VIEW OF NATURE. 363

The extension and confirmation which the Newtonian
attraction formula had thus gained in the minds of
many seemed to be entirely upset by a series of dis-
coveries in which electrical, and subsequently magnetic,
phenomena played an important part. These were, the
discovery of galvanic electricity by Galvani in 1791 and
by Volta in 1800 ; of the physiological and chemical
effects of this form of electricity, especially by Davy
(1806); of the magnetic effect of moving electricity by
Oersted in 1820; of the connection of heat and elec-
tricity by Seebeck in 1822; of induction by Faraday in
1831 — i.e., of the action of electric currents and magnets
in generating other electric currents or magnetic effects
in bodies which are moving in their neighbourhood; and,
finally, of diamagnetism by Faraday in 1845.

Many of the celebrated men with whose names the mod- 36.

... Davy and

ern discoveries m electricity are identified, and amongst Faraday,
them notably Davy and Faraday, were not brought up
in the mathematical school of the Continent,^ in which

sion suivant une loi quelconque ne j humous papers (edited by Max-
doit etre regardee que comme une ' well in 1879 under the title of
formule qui exprime un re.sultat ' The Electrical Researches of the
d'experience " (vol. i. p. 297). Hon. Henry Cavendish') he anti-
^ To these mu.st be added the ' cipated, as Maxwell has shown,
name of Cavendish (1731-1810), i many later investigations of British
whose electrical researches, in ; and Continental writers. He had
which he anticipated many of Cou- ] a clear notion of electrical capacity,
lomb's results, proceeded on en- ■ of potential and of electrical resist-
tirely different lines from those of > ance, he anticipated Ohm's law-

the Continental school. He proved
—in or before 1773 — from the fact
that a small globe' situated in the

i.e., the proportionality between
the electro -motive force and the
current in the same conductor.

hollow of a large electrified globe ; He studied the properties of diel-
and communicating with it showed , ectrics, and " not only anticipated
no signs of electricity, that electric i Faraday's discovery of the specific

attraction and repulsion must be
inversely as the square of the dis-
tance. In his published and post-

inductive capacity of different sub-
stances, but measured its numer-
ical value in several substances "

364

SCIENTIFIC THOUGHT.

the astronomical view of phenomena had been established
and strengthened mainly by a development of the New-
tonian philosophy. They belonged to another school,
which approached that great field of research from the
purely experimental side, — mainly, so far as Da\y was
concerned, from the side of chemistry, which, dealing
with the qualitative, not merely the quantitative, proper-
ties of matter, was at that period almost entirely thrown

(Maxwell's Introduction to the
'Researches,' p. xlix sqq.) Caven-
dish's electrical work seems to have
remained unnoticed abroad. Cu-
vier, who fully appreciates him as
a pioneer in modern chemistry,
does not refer to his electrical
researches, and in Continental
works his name is hardly men-
tioned in connection with elec-
trical science. He, however, clearly
belongs to the same lineage as
Davy and Faraday, whose breadth
of experimental observation some-
what prevented them from fully
assimilating the results of Coulomb
and his school, which moved in
narrower but more precise lines.
If Cavendish was unknown abroad
as an electrician, Coulomb was
little known in England. Whewell,
who did more than any other to
make known the researches of the
mathematical school (see his article
in the ' EncyclopEedia Metropoli-
tana,' 1826, and his British Associ-
ation Report, 183.5), could state in
the first edition of his ' History of
the Inductive Sciences' (1837) that
" the reception of the Coulombian
theory has hitherto not been so
general as might have been reason-
ably expected from its very beauti-
ful accordance with the facts which
it contemplates" (3rd ed., vol. iii.
p. 28). He then refers to the ex-
periments of Snow Harris. These
experiments, as well as those of

Faraday, carried on about the same
time, dealt largely with the proper-
ties of dielectrics and of what we
now call the electric field, a subject
almost entirely neglected by the
mathematical school of that period.
It was not till 1845 that William
Thomson (Lord Kelvin) cleared uj)
the whole subject in a memoir,
" On the Mathematical theory of
Electricity in Equilibrium " (see
'Reprint of Papers,' &c., p. 15).
He there refers to the fact that
" manj' have believed Coulomb's
theory to be overturned by the in-
vestigations " of Snow Harris and
Faraday, and he therefore pro-
poses to show that "all the experi-
ments which they have made hav-
ing direct reference to the distri-
bution of electricity in equilibrium
are in full accordance with the
laws of Coulomb, and must there-
fore be considered as confirming
the theory" (p. 18). He thus
brought together the two inde-
pendent lines of research and
thought, the mathematical and the
experimental, represented by the
school of Gauss and Weber abroad,
and by Faraday in England, and
suggested those further researches
of which Maxwell's ' Treatise on
Electricity and Magnetism ' is the
great exponent. See the preface
to this work, p. xi, &c., 1873 ; also
Maxwell's ' Scientific Papers,' vol.
ii. pp. 258, 302, 304.

THE ASTRONOMICAL VIEW OF NATURE.

365

upon experimental research.^ Chemistry had only just
entered the list of the exact sciences, by the use of the
balance, largely owing to Lavoisier and his followers.

1 Although Faraday's ' Experi-
rneutal Researches iu Electricity '
(1831-52) contain mostly what
chemists would call "qualitative"
investigations and only few exact
"quantitative" measurements —
forming in this respect a very
remarkable contrast to Weber's
' Electrodynamische Maasbestim-
mungen ' (1846-78) — it is important
to remark that one of the methods
for exact measurement of the
electric current — viz., by the chem-
ical decomposition of compounds
— was established by Faraday in
1833 and 1834. He showed that
whenever decomposition took place
the quantities decomposed were in
proportion to the amount of elec-
tricity flowing through the circuit
and in proportion to the chemical
equivalents. Owing to the want of
a clear definition of quantity and
intensity of current, Berzelius op-
posed this view of Faraday's as
illogical, confounding the quan-
tity of substance decomposed with
the force required to set it free.
Clearer definitions and accumu-
lated experience have confirmed
Faraday's law, which is now
looked upon as one of the best es-
tablished general facts of chemical
and electrical science. Somewhat
earlier than Faraday, Georg Simon
Ohm established (1827, 'Die gal-
vanische Kette, mathematisch
bearbeitet') the proportionality of
the quantity of electricity passing
through a circuit with the electro-
motive force in the same conductor,
introduced the notion of electrical
resistance, and showed how this
varies as the length and inversely as
the thickness of the same conductor,
and is different in diSerent con-
ductors. The accuracy of Ohm's

law, though elaborately tested by
Fechner and confirmed by Pouillet,
was frequently doubted; in France
it met with tardy recognition, and
in England some of the most im-
portant researches — such as those of
Faraday — were carried on without
reference to it. In the first edition
of Whewell's History it is not men-
tioned. When the second edition
was published (1847), Ohm had
received the Copley Medal of
the Royal Society (1841), and
Wheatstone had besides in the year
1843 drawn attention to the clear
definitions which Ohm had intro-
duced. The opinion has been ex-
pressed that Ohm found his law by
theoretical considerations based on
analogy with the flow of heat in
conductors, and that he subse-
quently proved it experimentally.
The publication of Ohm's collected
papers by Lommel ('Gesammelte
Abhandlungen,' Leipzig, 1892), how-
ever, disproves this opinion ; as his
experimental measurements had
during 182.5 and 1826 — not without
some initial mistakes — led him to
the well-known expression of the
relations of the different quantities
(see Lomniel's Introduction, p. vii).
Whereas in Germany it was a pure-
ly scientific interest— that, namely,
of subjecting physical phenomena
to mathematical calculation — which
induced Ohm, Gauss, and W^eber
to devise instruments and methods
for exact measurement, it was in
England mainly the practical re-
quirements of telegraphy which
created the desire for clear defini-
tions and exact methods. With
these requirements in view Wheat-
stone invented his instruments and
drew attention to the definitions of
Ohm. See his Bakerian Lecture for

366

SCIENTIFIC THOUGHT.

37.
Ampere and
Weber de-
velop tlie
astrouomi-
cal view.

Yet the great variety, more than the exact measurement
of phenomena, attracted the attention of natural philoso-
phers in this new field. And when through Davy,Berzelius,
and Faraday in different ways the importance of electric
action in chemical processes became established, it was
natural that from this school an entirely different view of
electrical and magnetic phenomena should emanate : we
may term it — in opposition to the astronomical — the phys-
ical view of phenomena. This view, which, as the astron-
omical view had done, found later on its expression in a
mathematical formula, will occupy our attention in a sub-
sequent chapter. It has in the course of the second half
of the century very largely expelled the other and rival
view from the domain of molar and molecular physics.
But the astronomical view, with its largely developed
mathematical apparatus, was not easily defeated : it was
quite able to grapple with even such complicated processes
as the discoveries of Oersted and Faraday had revealed.
In the opinion of many Continental thinkers it won its
greatest laurels when, under the treatment of Ampere in
France and of Neumann and Weber in Germany, the
perplexing interactions of magnets, diamagnets, and

1843 ('Philos. Transactions,' 1843,
p. 303, &c.) : "An energetic source
of light, of heat, of chemical action,
and of mechanical power, we only
require to know the conditions un-
der which its various effects may
be most economically and ener-
getically manifested to enable us
to determine whether the high ex-
pectations formed in many quarters
of some of these applications are
founded on reasonable hope or on
fallacious conjecture." Forty years
later Lord Kelvin, in his address

" On the Electrical Units of Meas-
urement" (1883: see 'Popular
Lectures and Addresses,' vol. i. p.
76), could still speak of the com-
paratively recent date at which
"anj'thing that could be called
electric measurement had come to
be regularly practised in most of the
scientific laboratories of the world,"
wliereas such measurements had
then been for many years " familiar
to the electricians of the submarine
cable factories and testing sta-
tions."

THE ASTRONOMICAL VIEW OF NATURE. 367

electric circuits — the phenomena of electro-magnetism,
diamagnetism, and induction — were all resolved into
elementary processes of attraction and repulsion, and
summed up in a formula which looked like an extension
of the Newtonian gravitation formula, revealing the
mysterious influence of molecular forces.

" Oersted had found that an electric current acts on a
magnetic pole, but that it neither attracts it nor repels it,
but causes it to move round the current. He expressed
this by saying that the electric conflict acts in a revolving
manner. The most obvious deduction from this new fact
was, that the action of the current on the magnet is not
a push-and-pull force, but a rotary force, and accordingly
many minds began to speculate on vortices and streams
of ether, whirling round the current. But Ampere, by a
combination of mathematical skill and experimental in-
genuity, first proved that two electric currents act on one
another, and then analysed this action into the resultant
of a system of push-and-pull forces between the elemen-
tary parts of these currents." ^

Weber in Germany took up the work where Ampere
had left it.^ One of his objects was to combine the

1 Clerk Maxwell " On Action at
a Distance" ('Scientific Papers,'
vol. ii. p. 317).

- Weber's interest was twofold.
The primary object was to put
accurate quantitative data in the
place of merely qualitative descrip-
tions or mere estimates of pheno-
mena. He had then already pub-
lished, together with his brothers
(see supra, p. 196, note 3), two
works in which in a similar way
exact research has taken the place
of inexact description. The first

was his experimental investigation
of wave-motion ('Die Wellenlehre
auf Experimente gegriindet,' 1825),
the other the still more delicate at-
tempt to treat a physiological pheno-
menon, tlie mechanism of the organs
of locomotion, on exact mechanical
principles (1836). This rare gift of
exactness, invaluable at all times,
but almost unique at that time in
Germany, where philosophical vague-
ness was only too common, attract-
ed the notice of Gauss, who brought
Weber to Gottingen in 1830 after

368

SCIENTIFIC THOUGHT.

38.
Weber's fun-
damental
measure-
ments.

different electric phenomena — those of electricity in the
state of rest, called statical effects ; those of electric
currents on each other, the dynamical results ; and those
of electric conductors in a state of motion, the pheno-
mena of induction — in one general and fundamental
formula or law. He had before him Coulomb's electro-
static formula, Ampere's electro-dynamic formula, and a
more general one established by Franz Neumann, which
described and embraced not only the phenomena dis-
covered by Oersted, but also those of moving conductors
discovered by Faraday. It is not necessary here to enter
into the details of the investigations, experimental and
mathematical, by the aid of which Weber succeeded in
establishing his very remarkable and seemingly all-
embracing formula. Two remarks, however, present
themselves, bearing upon the history of thought and the •
value of precise mathematical expressions. The first is,
that as the gravitation formula necessitated a series of
the most careful definitions and measurements of physical
quantities, and the invention of accurate instruments and
methods of measurement, so the first and probably the
most valuable performances of Weber were his ingenious-
apparatus, and the careful measurements by which he

the death of Tobias Mayer. Gauss
introduced Weber to his own exact
measurements of terrestrial magnet-
ism, and from hence Weber's own
line of thought led through the
phenomena of magneto - induction
(discovered by Faraday in 1831)
and terrestrial magneto - induction
(1832) to electro - dynamics, the
science which Ampere had created
in the years 1820 to 1823. In 1846
Weber speaks iu the introduction
to the ' Electro-dynamische Maaa-

bestimmungen' of the endeavour to
determine natural phenomena ac-
cording to number and measure,
expressing surprise that this has
not yet been done in electro-
dynamics, and then proceeds to de-
scribe his "electro-dynamometer,"
an instrument used by him for
many years. With this instrument
he tiien, further, proceeds to con-
firm Ampere's formula for the action
at a distance of the elements of
electric currents.

THE ASTRONOMICAL VIEW OF NATUEE. 369

fixed the elementary conceptions and quantities with
which he operated. All his researches were comprised
under the very significant title " electro-dynamical mea-
surements." As such they remain a great monument
of ingenuity and unparalleled accuracy.-^ The second

^ Gauss had, some years before
Weber commenced his electrical re-
searches, introduced the idea of an
absolute measure of other than
mechanical forces — i.e., following
up the definition of force in the
Newtonian laws of motion, that it
is the cause which brings about a
change of motion, he suggested that
every physical force can be measured
by the velocity it imparts to a mov-
able body of measurable mass, the
quantity of mass being in the same
locality measured by its weight ;
and he applied this to the measure-
ment of magnetic forces. In ap-
plying the same idea to the measure-
ment of electric currents, Weber
came at once upon the circumstance
that the forces exerted by an elec-
tric current can be measured in
two ways — viz. , by the action they
have upon magnets or by that
which they have on other electric
currents. Now by a familiar con-
ception, electricians look upon a
current of electricity as measur-
able by the quantity of electric-
ity which flows through a section
of the circuit in a given unit of
time, this quantity of electricity
being measurable in the same way
as Coulomb measured the action
at a distance of charged bodies.
Should it then be possible to
carry out this latter measurement
of an electric current, a comparison
between the electro-magnetic and
the known electro-static units of
electricity would become possible.
Faraday had already, in 1833 and
1834, made estimates of the numer-
ical relation of the quantity of
electricity in a current, measured

VOL. I.

by its chemical or electro-magnetic
effects, and of the same quantity if
produced by an electrical machine.
These estimates were more than
twenty years later, in 1856, reduced
to accurate measurements by Weber
and Kohlrausch. Through these
measurements, which confirmed the
enormous numbers which are re-
vealed when we compare electricity
at rest and electricity in motion,
Weber finished the series of ac-
curate measurements, reduced to
an absolute or mechanical standard,
which had been begun by Gauss in
1833. It was soon recognised of
what practical importance these
data must be to electricians. Ac-
cordingly the British Association at
their meeting at Manchester in 1861
appointed a committee, on the sug-
gestion and under the presidency
of Sir William Thomson, called the
" British Association Committee of
Electrical Standards." " This com-
mittee worked for nearly ten years
through the whole field of electro-
magnetic and electro-static measure-
ment, until in its final report, pre-
sented to the Exeter meeting in
August 1869, it fairly launched the
absolute system for general use "
(Thomson, 'Popular Lectures and
Addresses,' vol. i. p. 84). In recog-
nition of Weber's great merit in
first introducing this system into
electrical science and practice, the
name " Weber " had been selected
by Latimer Clark for the unit of
current. In the final fixing of the
units in Paris in 1881 other units
than those previously in use were
adopted, and to avoid confusion the
names were somewhat differently

2 A

370

SCIENTIFIC THOUGHT.

point I wish to urge is, how in those days the Newtonian
formula was taken as the great model of a law of nature,
and how the researches of Coulomb, Poisson, Ampere, and
Weber stand in logical connection with the theory of
gravitation. Let us see what Weber himself says on this
subject : ^ " After the general laws of motion had fur-

chosen. This explains the fact,
deplored by Weber's friends and
admirers, that his name has dropt
out of the list of terms now adopted
throughout the civilised world. (See
Wiedemann, ' Die Electricitiit,'
Braunschweig, 1885, vol. iv. p.
906, &c.) Recently Prof. Lodge
has suggested the introduction of
the names of Weber and Gauss to
denote some of the derived units in
the electrical measurements. See
Brit. Assoc. Report, 1895, p. 197 n.
^ Weber's theoretical conception
of the nature of electric action at a
distance is mixed u^) with his exact
measurements of electrical quanti-
ties, though these can be stated
without making use of his theoreti-
cal conceptions. It is the nature
of the absolute system of measure-
ment that it establishes numeri-
cal relations based upon a small
number of original units (space,
time, and mass, or space and time
alone, see note to p. 323 above)
which are universally intelligible.
Whatever, therefore, the theoretical
views may be which led the investi-
gation, in the end these are elim-
inated in the system of original
(primary) and derived (secondary)
units. But Weber's theory com-
mands attention for its own sake
as the furthest stage to which
the gravitational view of phenom-
ena, provisionally introduced by
Newton, has been pushed. It has
been extolled and condemned, ac-
cording to the favour with which
the purely mathematical treatment
of phenomena has been received.

In the school of Laplace this purely
mathematical treatment quite ob-
scured all other views which did
not minister to it. Thus Laplace
remained to the end an adherent of
the emission or corpuscular theory
of light, and opposed the ideas of
Young and Fresnel, who developed
the dynamical view. In order to
make the cosmical view of nature
useful for the explanation of mole-
cular phenomena, two distinct and
definite conceptions, contained in
the gravitation formula, had to be
modified and enlarged. The con-
ception of matter, which in physical
astronomy is limited to gravitational
matter, had to be extended so as to
bring into calculation what was then ,
called imponderable matter, such as
light, heat, and electricity. And
the law of gravitation, which defines
the purely attractive property of
ponderable matter, had to be modi-
fied so as to embrace also the repul-
sive action observable in a certain
class of phenomena. Coulomb had
shown that ponderable matter
chai-ged with electricity followed
the same formula for attraction
and repulsion as gravitating bodies
did : he simply adopted the two-
fluid theory of electric matter.
Poisson developed the mathematics
of fluids, actuated by repelling forces
depending on the inverse square of
the distance. Oersted showed the
action of electric currents on mag-
nets ; and Ampere showed that
magnets can in their action be sup-
planted by electric currents. La-
place very early satisfied himself that

THE ASTRONOMICAL VIEW OF NATURE. 371

nished a foundation, there remained in physics mainly the
investigation of the laws of interaction of bodies ; for
without interaction bodies would for ever remain in that
state of rest or motion in which they happened to be.

these actions of ponderable matter,
in which electricity was flowing,
could be reduced to an action at a
distance proportional to the inverse
square of the elements of the electric
circuits. When Faraday showed
that a current of electricity under
certain conditions induced in con-
ductors in its neighbourhood other
currents, this was explained hy
saying that the electric fluid exerted
not only pondero-motoric but also
electro-motoric action at a distance.
Not only did electrified matter act
on other electrified matter, but
electricity as a fluid acted on elec-
tricity itself. Weber adopted, for
the purpose of putting these ap-
parent actions into mathematical
language, and for finding an ele-
mentary law of the ultimate par-
ticles of electric matter out of
which by summation the observ-
able data might be calculated, the
hypothesis of Fechner, according to
which in an electric current the
two electric fluids were moving
with equal velocity in opposite
directions. It then became evident
— looking at the phenomena dis-
covered by Oersted, Ampere, and
Faraday — that the electro - static
formula of Coulomb required to
be supplemented by an additional
term, if the mutual action was to
be determined not only for the case
of equilibrium and rest, but also for
that of relative motion. The ad-
ditional term, depending on this
relative motion, had to be found.
(See ' Electrodynamische Maasbes-
timmungen,' vol. i. p. 102). From
this starting-point, and with this
definite problem in view, W^eber un-
dertook a series of most valuable
measurements. No doubt can exist

as to the lasting importance of these
measurements. Any theoretical con-
cej^tion which produces in its appli-
cation such results must hold a
prominent place in the history of
scientific thought. And the very
fact that, unlike Boscovich and
other purely metaphj^sical theorists,
Weber undertook to fix by experi-
ment the actual constants or nu-
merical quantities which his ab-
stract formula contained, led to
much enlargement of actual know-
ledge. I will mention only one
of the most interesting points in
his elaborate researches. I stated
above that it took a whole century
after the discovery of the law of
gravitation before the gravitation
constant was approximately fixed,
but that for tlie progress of phy-
sical astronomy this was of little
importance, gravity being a uni-
versal property of matter. Still
such a constant exists, because we
possess another definition of matter
— vi::., inertia or mass. The con-
stant in Coulomb's law cannot be
determined in a similar manner, as
the property of attraction or repul-
sion defines for us ultimately the
numerical quantity of electricity.
We have — so far — no other ultimate
absolute measure of electricity. But
in Weber's law it was the quantities
of electrical matter which acted on
each other not only according to
their distances, but also according
to their relative motion or their
velocities. A second constant thus
entered into his formula, and this
constant established a relation be-
tween electricity at rest and elec-
tricity in motion. This constant
was a velocity, and, if determinable,
it revealed a constant of nature in

372

SCIENTIFIC THOUGHT.

All changes of these states, and all phenomena depen-
dent thereon, are therefore consequences of these inter-
actions. But bodies exert such mutual actions when in
contact as well as from a distance, and it was evident
that a beginning had to be made with the latter in
order to gain a clue for the investigation of the former ;
this being especially needful whenever the spatial rela-
tions of bodies escape observation, as is the case with
bodies which are in contact. And so it has really
happened, inasmuch as a beginning was made by ex-
amining the mutual action of cosmic bodies — i.e., with
the phenomena of gravitation. To this first field of
research — viz., the phenomena of gravitation — there was
then added the investigation of electric and magnetic
interactions, as next to gravitation these are the only
actions which take place from one body to another at
measurable distances, — these actions being themselves
measurable. Now for a long time Newton's doctrine
of gravitation furnished the leading idea for nearly all
theories of electricity and magnetism, till a new clue
was gained through Oersted's and Ampere's discoveries

the form of a velocity. It had
for Weber a theoretical as well
as a practical meaning, for it en-
abled him to effect a connection
between the electro-magnetic and
the electro-static or absolute sj'stem
of measurements. When he suc-
ceeded in measuring this quantity,
it was found that the figure for the
constant, which meant a velocity,
was practically the same as that for
the velocity of the propagation of
light. Weber himself does not seem
to have attached any physical mean-
ing to this coincidence : later he and
Kirchhoff remarked that under cer-

tain conditions an electrical wave-
motion might take place in an
electrical conductor, and that the
velocity of the propagation of this
would coincide with that of light
(see Kirchhoff in ' Annalen der Phy-
sik und Chemie,' 1857 ; and Weber,
' Electrodyn. Maasbest. ,' 1 864). It
was reserved for Clerk Maxwell to
point to the real physical interpre-
tation of Weber's constant. Of
this I shall speak in a later chapter
(see Maxwell's memoir ' On Physical
Lines of Force,' 1862, reprinted in
' Scientific Papers,' voL i.)

THE ASTRONOMICAL VIEW OF NATURE.

373

regarding the equivalence of closed electrical currents
with magnets. This led, first, to the reduction of all
magnetic effects to the action of electrical currents ; and,
secondly, to the enunciation of a fundamental law of the
interaction of two elements of electricity in motion. A
third leading idea was that of reducing the interaction
of all bodies to that of the mutual action of pairs of
bodies. This idea could in general be considered as
well established and confirmed by experience on a large
scale." ^

This leads me to another and a final remark on the
view of natural phenomena, first introduced by New-
ton's gravitation formula, which has been so success-
ful in the calculation of all the movements of cosmic 39.

IT 1 1 • 1 • !• Necessity of

bodies, and which m the eyes of such a great authority developing

, ° theintini-

as Laplace contained the clue to an explanation also of |;^ethods
molar and molecular phenomena.^ This view calculates

^ ' Electrodynamische Maasbes-
timmungen,' 1878, p. 645.

'•^ Although Weber followed the
lines so deeply impressed upon the
whole of Continental thought by
the labours of Laplace and his
school, it does not seem that he
held the same exalted opinion of
the value of any mathematical for-
mula as did Laplace. Though he
looked upon his electro - dynamic
law as well established by experi-
ment and valuable in guiding
further research, he was fully im-
pressed with the fact that all such
formulae are merelj"^ provisional.
Thus he says in the first part of
his researches, written in the year
1846 : " It seems to follow that
the immediate interaction of two
electrical particles does not depend
upon these alone, but also upon the
presence of third bodies. ... It is

conceivable that the forces com-
prised in the discovered funda-
mental law may be partly the
forces which two electrical particles
exert indirectly on each other, and
which therefore depend on the in-
tervening medium. . . . The general
law for the determination of the
acting forces might perhaps be yet
more simply exj^ressed by taking
the intervening medium into ac-
count, than has been possible
without it in the fundamental
law now established. The explora-
tion of the intervening medium,
which might afford an insight into
many other matters, can alone give
an answer to this question. ... A
hope now exists that it will be
possible, in several new ways, to
gain some information as to the
neutral electric fluid which per-
vades everything. Perhaps in

3V4

SCIENTIFIC THOUGHT.

the actions of large masses and complicated systems of
bodies by a process of summation from the interaction of
units placed in the simplest relation — that of two and
two, pushing or pulling each other in a straight line.
Now, in consequence of the great distances at which we
are placed from the heavenly bodies, these appear to us
as mere points, and the observation of their movements,
their orbits, and their periods enabled astronomers like
Kepler, and mathematicians like Newton, to gain by mere
observation and subsequent calculation an idea of the
elementary rule which masses, considered to be concen-
trated in points, follow in their motion in a connected
system. The next step was to see how these elementary
actions would add up in cases where the dimensions of
the moving bodies were not vanishingly small in com-
parison with their distances. The infinitesimal methods,
invented in the age of Newton, and developed by him
and others into a special calculus, came to the aid of
mathematicians, and enabled them to calculate from
elementary data the motions and phenomena of extended
bodies and systems of bodies. These could afterwards
be actually measured, thereby confirming the elementary
formulae and assumptions which had formed the basis of
those calculations. As already remarked, this process

other bodies, which are not con-
ductors, there exist, not currents,
but only vibrations, which may in
future be observed by the methods
indicated above. Further, I need
only point to Faraday's recent dis-
covery of the influence of electric
currents on the vibrations of light,
which makes it probable that the
all-pervading neutral electric medi-
um itself constitutes the all -pervad-

ing ether which contains and pro-
pagates luminous vibrations, or at
least that the two are so intimately
connected that the observation of
luminous vibrations may afford some
information regarding the proper-
ties of the neutral electric medium."
He then refers to Ampere's own
suggestion in this direction. (' Elec
trodynamische Maasbestimmungen,'
Part I., p. 169.)

THE ASTRONOMICAL VIEW OF NATURE.

375

of confirmation occupied a long period, during which it
became more and more satisfactory and complete. In
fact, so great has the coincidence of calculation with
observation turned out to be, in all problems of physical
astronomy, that no astronomer at the end of this century
doubts that the gravitation formula alone will suffice to
explain all anomalies which still exist in great number
in the movements of cosmic bodies — such, for instance,
as the moon.

Moreover, in the whole wide range of physical and
chemical, not to speak of other natural phenomena, there
is probably no instance of a simple mathematical rela-
tion having been applied to so large a field of facts,
found so trustworthy a guide, and been so unfailingly
verified.

And yet the very extent of this field must not blind
us to the fact that for the explanation of molecular ^

40.
The Newton-
ian formula
the basis of
physical
astronomy.

^ This is indeed not to be won-
dered at when we consider that in
all molecular and molar phenomena
such a variety of elements and forces
come into play that it is impossible
to isolate any special quantities as
we do when from the cosmic point
of view we lose sight of everything
except mass, time, and distance —
i.e., the elementary factors of our
system of measurement. In the
phenomena of electricity, for in-
stance, it is merely by a process of
mental abstraction, which has no
counterpart in the ob.servable phe-
nomena, that we speak of electrical
masses, be they one or two ; of
fluids ; of elements of current.s,
which in nature cannot exist alone ;
of velocities of a something which
as yet cannot be clearly defined.
Any mathematical formula can
under such conditions be merely

tentative, and the preciseness of it
must not hide from us the fact that
it is based upon hypothetical rela-
tions and artificial definitions. This
was, for the gain of scientific
thought, very clearly brought out
in the theoretical discussions which
followed upon Helmholtz's critical
examination of Weber's and kindred
formulae, and is well expressed by
Carl Neumann : " Electrical mat-
ters " — if such there be — "never
exists alone, but only in combina-
tion with ponderable matter." Any
law like that of Weber can there-
fore be merely a "particular," not
a "fundamental" or "universal"
law, for it refers merely to a small
portion of the properties, forces,
and relations of electric and pon-
derable matter, leaving others — as,
for instance, those between electric-
ity and heat, electricity and light,

376

SCIENTIFIC THOUGHT.

phenomena, or even for such processes as happen con-
tinually under our eyes and our hands, this universal
law of gravitation has practically done nothing. The
action of gravitation alone between masses which we
can manipulate directly is so weak that it takes the very
finest instruments to detect it at all, and at molecular
distances it is so immeasurably small that it is hardly
conceivable how it can explain the existence of those
enormous forces with which we here have to deal.^ If

&c. — more or less in the dark (see
' Mathematische Aunalen.' vol. xi.
p. 3'A'S). From a philosophical point
of view these discussions, in which
many other eminent leaders of
scientific thought took part, are
of great interest and importance,
as they bear upon the value of
mathematical formuhc in physical
research, upon the definition of
laws of nature, the extent of their
applicability, the correct lines of fut-
ure research, the use of analogies in
the formation of physical theories,
&c. I therefore refer here to the
literature of the subject : Tait,
' Sketch of Thermodynamics ' (1868,
pp. 57, 76) ; Thomson and Tait,
' Natural Philosophy ' (1st ed., p.
311) ; Carl Neumann, ' Die Prin-
cipien der Electrodynamik ' (Tub-
ingen, 1868); Helmholtz in various
memoirs from 1872 onwai-ds, all
collected in ' Wissenschaftliclie Ab-
handlungen' (vol. i. pjj. 545, 636,
774, &c. ) and in ' Vortriige und
Reden' (vol. ii. Faraday Lecture);
Carl Neumann, ' Mathematische
Aunalen ' (vol. xi. p. 318). See
also Riecke on ' Wilhelm AVeber '
(Gottingen, 1892), and Clerk Max-
well, ' Electricity and Magnetism,'
(vol. ii. last chapter) ; ' Elementary
Treatise on Electricity' (p. 51).

^ An interesting speculation as to
whether the Newtonian formula of
gravitation is capable of explaining

cohesion and capillary attraction
will be found in Thomson's (Lord
Kelvin's) paper to the Royal Society
of Edinburgh (1862), and in his lec-
ture before the Royal Institution
(1866) on Capillary Attraction, both
reprinted in the first volume of
' Popular Lectures and Addresses.'
He there shows that if we combine
Newton's law with the assumption
of an ultimate heterogeneousness of
matter, — as is demanded in the so-
called atomic theory used in chem-
istry,— the mass of ultimate por-
tions of matter at vanishing dis-
tances, or what is called in contact,
may give rise to molecular forces of
attraction of any magnitude ; since
the Newtonian attraction depends
on two data — the distance and the
density (or mass) of attracting par-
ticles. He concludes by saying that
"it is satisfactory to find that, so
far as cohesion is concerned, no
other force than that of gravitation
need be assumed " (p. 63). It does
not seem that this view, which was
also held by Sir John Herschel, is
generally adopted by physicists (see
Todhunter and Pearson, ' History
of the Theory of Elasticity,' vol. i.
p. 418, &c. ; vol. ii. art. 1650). An-
other interesting speculation arose
out of the discussion over Weber's
law. One of the objections started
by Helmholtz against Weber's law
was that, under certain conditions,

THE ASTRONOMICAL VIEW OF NATURE.

377

I

for the purpose of discovering the forces which exist in
the universe between cosmic bodies we had been con-
fined to experiments in the laboratory, as we are in all
other departments of physics and chemistry, it is very 41.

^ -^ "^ -' •' TheNewlon-

doubtful whether this universal law of gravitation would ian formula

^ unique as to

ever have been discovered. And yet it stands there as and^accur-*^^
almost the only formula universally applicable to all ^'^^'
matter throughout the visible and tangible universe.

In the foregoing pages I have sometimes spoken of this
great discovery of Newton, on which is based the astron-
omical view of nature, as a formula, sometimes as a law.
A formula is merely the expression in definite terms of
certain relations of measurable quantities. By a law
we are apt to understand something more — viz., the
statement of some fundamental, all-pervading property
of the things of nature, which, so far as we are con-
cerned, is final.^ Whether the human mind is at all

this expression would give an in-
finite value for the force between
electrical particles in motion.
Weber replied that the same argu-
ment could be used against the
gravitation formula, and hinted at
the possibility that a correction
might have to be added to the New-
tonian formula to make it appli-
cable to molecular distances (' Elec-
trodyn. Maasb.,' 1871, p. 60). This
idea was taken up by several Con-
tinental mathematicians (see Isen-
krahe, ' Das Rathsel von der Schwer-
kraft,' p. 33, &c.; Paul du Bois-
Reymond, ' Ueber die Grundlagen
der Erkenntniss,' p. 50 ; Tisserand,
'ComptesRendus,' September 1872).
^ Helmholtz says, referring to
Weber's so-called law: "If we
are to consider Weber's law as an
elementary law, as an expression
of the ultimate cause of the phe-

nomena to which it refers, and not
merely as an approximately correct
expression of facts within narrow
limits, then we must demand that,
if aj^plied to objects of the largest
imaginable dimensions, it should
give results which are physically
possible" (1873, ' Wissenschaf tliche
Abhandlungeu,' vol. i. p. 658). This
sentence raises a philosophical ques-
tion as to the demands which we
can legitimately expect to be satis-
fied by any so-called law of nature
expressible in the symbols of hu-
man thought, be these words or
algebraic signs. I venture to think
that nowadays, and largely in con-
sequence of discussions similar to
those carried on over Weber's law,
physicists do not any longer expect
to find laws of that general and
fundamental character which the
words given above describe.

378

SCIENTIFIC THOUGHT.

42

Is the New-
tonian for-
mula an
ultimate
law?

43.
Laplace's
opinion.

capable of finding out the ultimate properties of things,
is a question which has been answered in opposite
ways. But whatever the answer may be to this philo-
sophical question, the further and more modest ques-
tion can be raised, Does the gravitation formula express
one of those universal facts which we have to accept as
final, beyond or behind which we cannot penetrate ?
Opposite answers have been given to this question. But
it stands very much in the same position in which
Laplace left it when he said : ^ " The extreme difficulty
of the problem referring to the system of the universe
obliges us to have recourse to approximations, which
leave room for the fear that the neglected quantities
may have a sensible infiuence on the results. As soon
as mathematicians by observation became aware of this
influence they returned to their analysis : by rectifying
the same they have always found the cause of the ob-
served anomalies ; they have determined the laws of
these, and frequently they have outrun observation by
discovering irregularities which had not yet been ob-
served. The lunar theory, the theory of Saturn, of
Jupiter and his satellites, offer many examples of this
kind.^ Thus we may say that nature herself has helped
in perfecting the astronomical theories founded upon the

1 Exposition du Systeme du
Monde,' 6th ed., p. 318.

- Tisserand, in discussing the diffi-
culties which still beset the lunar
theory, and after referring to the
"prix Damoiseau" offered by the
Academy of Sciences for an essay
on this subject, says ('Bulletin
astronomique,' 1891, vol. viii. p.
501): "La tlieorie de la lune se

trouve arretee par la difficulte que
nous venons de d^velopper ; dejh,
h I'epoque de Clairaut la gravita-
tion universelle paraissait impuis-
sante Ji expliquer le mouvement
du perigee ; elle triomphera encore
du nouvel obstacle qui se presents
aujourd'hui, mais il reste h. faire une
belle decouverte."

THE ASTRONOMICAL VIEW OF NATURE.

379

principle of universal gravitation. This is, in my opinion,
one of the greatest proofs of the truth of this admirable
principle. As to this principle, is it a primordial law
of nature ? Is it only a general effect of an unknown
cause ? Here the ignorance in which we are as to the
ultimate properties of matter stops us, and removes all
hope that we shall ever be able to answer these questions
in a satisfactory manner."

In the meantime, as I have tried to show, the clue
afforded by this principle has led physicists by strict
analysis, by observation, by cleverly arranged experi-
ments as well as by guesses drawn from analogy, to the
discovery of many unknown phenomena, to the fixing in
mathematical language of interesting relations, and in
general to a large extension of the field of natural know-
ledge. No wonder that a principle which has done, and
is still doing, such valuable service in physical astronomy
should have done much to establish the astronomical
view of nature.^ As one of the latest representatives of
physical science abroad has said, " The present generation

^ This view was concisely put by
Poisson at a time when the corpus-
cular theory of the imponderables
— light, heat, and electricity — still
reigned supreme in the Continental
school: " Toutes les parties de la
matiere sont soumises a deux sortes
d'actions mutuelles. L'une est at-
tractive, ind^pendante de la nature
des corps, proportionnelle du produit
des masses, et en raison inverse du
carre des distances : elle s'etend
indefiniment dans I'espace, et pro-
duit la pesanteur universelle et
tous les phenomenes d'equilibre et
du mouvement qui sont du ressort
de la mecanique celeste. L'autre

est attractive et repulsive ; elle
depend de la nature des particules
et de leur quantity de chaleur ;
son intensity decroit tres rapide-
ment quand la distance augmente,
et devient insensible, des que la
distance a acquis une , grandeur
sensible" ('Journal de I'Ecole poly-
technique,' cahier xx, p. 4, 1831).
See also Clerk Maxwell, ' On the
Equilibrium of Elastic Solids ' (1850,
reprinted in ' Scientific Papers,' vol.
i. p. 30), where a similar assumption
is stated as the basis of the mathe-
matical theories of Navier, Poisson,
Lame, and Clapeyron.

380

SCIENTIFIC THOUGHT.

is still more or less accustomed to think in the manner of
Newton's view of nature, in which the supposition of
forces acting at a distance appears as the most simple
view : we feel it difficult to step out of this circle of
ideas." ^ Nevertheless, the country itself which produced

^ Kundt, ' Die neuere Eutwick-
lung der Electricitiitslehre ' (Berlin,

1891, p. 35). This habit is prob-
ably more marked on the Continent
than in England. In this country
the later developments of Laplace's
astronomical view of nature have
remained unknown except to a few
scientific specialists. Through Fara-
day's influence, and in consequence
of the backwardness which the
English school of science exhibited
early in the century in assimilating
Continental ideas (see p. 232, note),
theoretical views on electricity as
well as on other forms of energy
were formed and taught more in
conformity with experimental ob-
servation. I am not aware that
Weber's theory was expounded in
any English text -book or handbook
before Maxwell referred to it as the
view to which Faraday and he him-
self were opposed. In fact, the
astronomical view of molecular
physics is almost entirely of foreign
growth. In England "action at a
distance " is now stigmatised as a
pernicious heresy (Tait, ' Properties
of Matter,' 2nd ed., 1890, Introduc-
tion) or as unthinkable (0. Lodge,
'Modern Views of Electricity,'

1892, p. 386, &c.) Abroad weighty
authorities have pronounced against
the astronomical view of nature as
final or even helpful in the present
stage of physical and chemical
science. Helmholtz, who was
trained in it, gradually emanci-
pated himself, probably under the
influence of physiological studies ;
so did Kirchhoff, who in his lectures
on Electricity (edited by Planck,
1891) hardly mentions W^eber's law,

though he had previously, in 1857,
based an elaborate and valuable
investigation upon it (' Ueber die
Bewegung der Electricitiit in Driih-
ten,' ' Gesammelte Abhandlungen,'
p. 131, &c.) Still more marked is
the aversion to the attitude or
habit of thought which belongs to
the astronomical view of nature on
the part of those who approached
physical problems from the side of
chemistry. Hittorf (quoted by
Lehmann, ' Molecularphysik,' vol. ii.
p. 456) explains the opposition of
Berzelius to Faraday's electrolytic
law and to his other results from
the fact that they stood in direct
opposition to that view " which at
the end of the last century had
been introduced into chemistry
through the success of Newton's
law in astronomy, and under the
influence of Laplace on Lavoisier
and Berthollet," and sees the im-
portance of his own laborious
researches in the demonstration
" that the mysterious potential
energy cannot in the case of un-
combined chemical substances be
explained by the work of attractive
forces," and " that a confession of
ignorance in such matters is more
conducive to progress than the as-
sertion that everj' process in nature
is essentially a phenomenon of at-
traction in the Newtonian sense."
Of Ostwald's endeavours to liberate
theoretical views in chemistry from
the tyranny of the older hypotheses
I shall have frequent occasion to
speak. His discourse ' Die Energie
und ihre AVandlungen ' (Leipzig,
1888) contains an expression of
opinion similar to those quoted here.

THE ASTRONOMICAL VIEW OF NATUEE. 381

the author of this the astronomical view of nature has ^ 44

Opposition

also been the birthplace of a different manner of regard- n^^'l^*^*'''^"
ing physical phenomena. It will be the object of a future nature!
chapter to trace the origin and growth of what I propose
to call the physical view of nature. We shall then learn
how the germs of this different view can be traced even
in the writings of Newton. But before I take up this
subject I must deal with another and independent way
of regarding nature which very largely supplemented the
astronomical view. If the Newtonian gravitation formula
is the basis and principle of physical astronomy — of our
knowledge of cosmic phenomena — the view I am now
going to explain has been equally useful in building up
another most important science of modern times — the
science of chemistry.

382

CHAPTER V.

THE ATOMIC VIEW OF NATURE.

1.

Recapitula-
tion.

In the last chapter I have shown how, under the influence
of the Newtonian pliilosophy, the ancient but indefinite
ideas of Attraction and Eepulsion acquired a definite
meaning, and how — at least so far as cosmical phenom-
ena are concerned — the Newtonian Gravitation formula
was made the foundation of very successful explanations ^

' I use the word explanation in
conformity with the popularly ac-
cepted meaning of the term. It is,
however, well to remark here that, in
the course of our century and greatly
owing to the influence of the exact
scientific spirit, a change is being
gradually introduced into language,
which will assist in conveying more
correct views as to the objects of
science. In England the meta-
physical interest has been so long
banished from scientific literature,
the part also which experiment and
observation have played has been
so great, that misunderstandings as
to the real objects of .science have
been less frequent than abroad,
especially in Germany, where the
metaphysical or philosophical in-
terest still largely pervades scien-
tific literature, though metaphysics
themselves may be on the decline.
There the definition of the science

of mechanics (now more usually
termed dynamics in this country),
given l)y Kirchhoff in his ' Vorlesun-
gen iiber mathematische I'hysik '
(vol. i. p. 1), has marked quite an
epoch in the philosophy of the ex-
act sciences. This definition is as
follows: "Mechanics is the science
of motion ; we can assign as its
object : to describe completely and
in the simplest manner the motions
which occur in nature." Inas-
much as a large school of natural
philosophers consider that it is the
object of all exact sciences to give
a mechanical explanation of natural
phenomena, it would follow that
the object of all science is to re-
duce the phenomena of nature to
forms of motion, and to describe
these completely and in the simplest
manner. We may feel some re-
luctance in assenting at once to
this definition. Still an analysis of

THE ATOMIC VIEW OF NATURE.

383

I

of nature. Towards the end of the last century, and all
through the present one, this view of things natural, which
I have called the Astronomical view, has exerted a great
fascination over scientific minds : especially in the mathe-
matical schools of France and the Continent it has been
a leading idea in scientific thought. It has been ex-
tended into molar and molecular physics, and has in
these led to some very extraordinary and ingenious
theories. In England, this astronomical view of Nature
has, in the course of the present century, been received

what has been done since Newton
in real science will probably con-
vince us that the definition is safe
and sufficient. It means the an-
alysis of phenomena as to their
appearance in space and their se-
quence in time. Both can, in con-
sequence of the small number of
elementary relations on which
arithmetic, geometry, and dynam-
ics are built up, be reduced to
— or described in — a small num-
ber of elementary terms or concep-
tions, the alphabet of all science.
To show how in every instance the
terms of this alphabet are to be put
together, in order to correspond to
any phenomenon, is all the explana-
tion we can give. Objections have
been raised to KirchhofE's definition
by Du Bois-Reymond (" Gothe und
kein Ende," in ' Reden,' vol. i.
p. 434), inasmuch as it does not
define the difference between the
descriptive (historical) and the ex-
act (mathematical) sciences of na-
ture ; but the difference is really
maintained if we demand a com-
plete description. Natural history
only affords an incomplete descrip-
tion. The only complete descrip-
tion is that afforded by a mathe-
matical formula in which the con-
stants are supplied by observation.
This permits us to calculate those

features or jDhases of phenomena
which are hidden from our obser-
vation in space or in time. An
objection to the view which identi-
fies physics with mechanics, seems
implied in Mach's remarks con-
tained in the last chapter of his
veiy thoughtful book ' Die Me-
chanik in ihrer Eutwickelung '
(Leipzig, 1889). According to his
view, the aim of exact science is
not necessarily to give mechanical
explanations or descriptions of phe-
nomena, inasmuch as temperature,
electric potential, &c., are just as
simple elements of natural phenom-
ena as mass and motion. It seems,
nevertheless, that exact measure-
ments are only possible in the
data of time and space. Assum-
ing that a complete and simple
description — admitting of calcula-
tion— is the aim of all exact science,
it is evident how much and how
little we may expect from science.
We shall not expect to find the
ultimate and final causes, and
science will not teach us to under-
stand nature and life. The search
after ultimate causes may perhaps
be given up as hopeless ; that
after the meaning and significance
of the things of life will never be
abandoned : it is the philosophical
or religious problem.

384 SCIENTIFIC THOUGHT.

with less favour, although it was entirely owing to
Newton's gravitation formula that it ever obtained its
great influence, the labour of Continental men of science
being very largely spent in two directions : first, in draw-
ing the purely mathematical consequences of Newton's
formula — in this they have met with increasing success,
u.nparalleled by that in any other domain of science ;
and secondly, in extending the principle of Newton, by
experiment and analogy, into other departments. In some
of these, very remarkable results have been achieved ; but
nevertheless at the end of the century no extension or
analogue of the Newtonian gravitation formula has been
generally accepted, and it still stands there as almost
the only firmly established mathematical relation, ex-
pressive of a property of all matter, to which the pro-
gress of more than two centuries has added nothing,
from which it has taken nothing away. The value,
however, of all those partial attempts in another direc-
tion has been enormous ; for with the aim of applying,
extending, or modifying a rigorous mathematical for-
mula, those philosophers have carried out a series of
the most exact observations and measurements of physi-
cal quantities, very greatly extended our knowledge of
natural phenomena and their mutual relations, and
founded that general system of physical measurement
which is now universally adopted. The names of Gauss
and Weber stand out prominently as leaders in this
work. I shall have to come back to this point later
on, after I have shown that other views of nature
besides the astronomical have also led up to it, and
placed it in similar prominence.

THE ATOMIC VIEW OF NATURE.

385

2.
Atomic

About a century after the publication of the ' Principia,'
which, by propounding the gravitation formula, raised the
ancient and indefinite notion of Attraction to the rank of
a useful and rigorously defined expression, another favour-
ite theory of the ancient philosophers ^ was similarly ele-
vated to the rank of a leading and useful scientific idea.

Although no mathematical relation equal in value and
definiteness to the gravitation formula marks the intro- theory,
duction of the Atomic theory in Chemistry, it never-
theless owes its success to similar qualities — viz., to the
fact that it led natural philosophers to make definite
measurements, and put exact research in the place of
vague reasoning.

The atomic theory, usually associated with the name
of Dalton, is, however, not nearly as much the historic
property of that great man as gravitation is that of
Newton, for whereas the latter gave the fullest gen-
eralisation that can so far be safely made, the atomic

^ Ancient philosophers have fur-
nished us with three distinct ab-
stractions which have survived, and
which, put into definite mathemati-
cal language, have led exact research
in physics and chemistry in modern
times — the theory of Attraction
and Repulsion, the Atomic Theory,
and the Kinetic Theory, or the
notion that everything is motion.
Of these three theories the second
was most developed in antiquity ;
Lucretius's great poem on the na-
ture of things being really a treatise
on the subject, in which the atomic
view is placed in the centre, the two
other ideas being likewise largely
utilised. The historians of ancient
philosophy trace these abstract or
leading ideas back to the earlier
Greek thinkers. Thus Heraclitus

VOL. I.

of Ephesus is credited with having
first taught that everything is in
motion. Empedocles of Agrigentum
made use of the notions of Attrac-
tion and Repulsion, poetically re-
presented as Love and Hatred, to
explain the action of his elements ;
and Democritus of Abdera is uni-
versally considered to be the true
founder of the atomistic theory,
which was adopted and developed
in the School of Epicurus, and very
fully explained by the Roman poet.
A veiy good analj'sis will be found
in Lange's ' History of Materialism '
(English translation by Thomas, 3
vols.), in which also the historical
connection with modern thought,
especially through Bacon, Gassendi,
and Hobbes, is clearly brought
out,

2 B

386

SCIENTIFIC THOUGHT.

Lavoisier.

theory has been gradually defined and variously modi-
fied in the course of this century, and is still in a some-
what unstable condition. We are also bound to attach
the greatest importance to the preliminary step taken
by Lavoisier, who is even more justly called the father
of modern chemistry than Kepler is called the father
of modern astronomy.

The exact claims of Lavoisier to this important place in
the history of chemistry have been variously stated : -^

^ Continental writers are pretty
unanimous in dating modern chem-
istry from the time of Lavoisier
(1743-1794). In this country there
has been less unanimity, the names
of Black, of Cavendish, of Priestley,
even of Robert Boyle, having occa-
sionally been put forward. The
fact that Lavoisier did not suffi-
ciently acknowledge his indebted-
ness to some of his English con-
temporaries has given occasion in
some quarters to depreciation of his
merits. It cannot be upheld that
he was the first formally to express
the doctrine of the indestructibility
or conservation of matter, as this
idea underlay many experimental
researches before his time ; nor
that he was the first to refer to
the balance as the ultimate test
of chemical facts. The assertion
that he first introduced the idea
of two different kinds of matter,
ponderable and imponderable, is
also questionable, and still more
so his claim to having discovered
oxygen, the comijosition of water
and of atmospheric air, the combus-
tibility of the diamond, and other
special facts. His fame rests upon
a much broader basis, and has
been most clearly investigated and
settled by Hermann Kopp in his
' Entwickelung der Chemie in der
ueueren Zeit ' (Miinchen, 187.3).

In this excellent work the author
somewhat modifies the view he
took in liis earlier ' Geschichte der
Chemie ' (Braunschweig, 1843, espe-
cially vol. i. p. 274, &c.), and sums
up Lavoisier's merit in the follow-
ing words (p. 145): "His contem-
poraries could dispose of the same
inherited and much new material,
but not one of them understood
how to build up out of this material
and his own independent researches
a chemical system, the reception of
which should form the starting-
point for all future improvement
of this science. Lavoisier has the
whole merit of having achieved
this. He added to his own recog-
nition of the correct views the work
of procuring recognition for them
from others. He imparted his own
matured views to those who repre-
sented chemistry at the end of the
last century. . . . We must measure
his greatness not merely by his
own insight but also by the re-
sistance which he had to overcome
in other chemists who clung to
the older theory. These achieve-
ments are great enough not to re-
quire the exaggeration with which
they have occasionally been an-
nounced, and not to be touched by
attempts on tlie other side to mini-
mise them."

THE ATOMIC VIEW OF NATUEE.

387

there is however no difference of opinion on this point,
that since his time, and greatly through his labours, the
quantitative method has been established as the ultimate
test of chemical facts ; the principle of this method being
the rule that in all changes of combination and reaction,
the total weight of the various ingredients — be they ele-
mentary bodies or compounds — remains unchanged. The
science of chemistry was thus established upon an exact,
a mathematical basis. By means of this method Lavoisier,
utilising and analysing the results gained by himself and
others before him, notably those of Priestley, Cavendish,
and Black, succeeded in destroying the older theory of
combustion, the so-called phlogistic theory.-^ From a

^ This result was aunounced in
1777 to the Paris Academy, and
the demonstration completed in a
memoir of 1783. " He closes this
latter memoir with the exiDi-ession,
that his object had been to bring
forward new proofs of his theory
of combustion of 1777, and to
l^rove that Stahl's phlogiston was
something purely imaginary, — that
without it facts could be more
easily and more simply explained
than with it ; he did not expect
that his views would be at once
accepted, . . . time would have
to confirm or to reject the opinions
he had developed, but already he
recognised with satisfaction that un-
prejudiced students of the science,
unbiassed mathematicians and phy-
sicists, believed no longer in phlo-
giston as Stahl viewed it, and that
thejT considered the whole doctrine
more as a hindrance than as a help-
ful scaffolding in erecting the edifice
of science" (Kopp, ' Entwickelung,'
p. 202). This and the further re-
mark of Kopp that it was the
mathematicians who took up La-
voisier's views (see supra, p. 115,

note 2) are significant signs of the
introduction of the mathematical,
the measuring, spirit into chemistrj^.
Few ideas which once exerted so
great and lasting an influence on
science as that of phlogiston, have
so entirely disappeared from our
text-books, and it is interesting to
note that those whose researches
were guided by it were not so far
from grasping a valuable truth
as has been supposed. This theory,
elaborated by Stahl, a contem-
porary of Newton and Leibniz
(1660-1734), was the first attempt
to co-ordinate a great mass of ob-
servations, to bring the phenomena
of chemical change under one com-
mon principle. Phlogiston was
the thing the migration of which
gave rise to chemical change, and
as the most obvious changes were
exhibited in the processes of com-
bustion, " Phlogiston" or " Brenn-
stofF" was the name which sug-
gested itself as most suitable for
this principle. Chemical changes
were not to be measured so much
by the resulting change of weight
as by the readiness with which

388

SCIENTIFIC THOUGHT.

Phlogistic
theory.

scientific point of view, the principal defect in this theory
was, that its explanations could not be subjected to any
strict and exact numerical verification. Whenever an
element enters into our operations which has either no
weight or a negative weight, and thus evades exact de-
termination and control, explanations and observations
become vag-ue and uncertain.

In the time of Lavoisier, and pre-eminently through his
exertions, this vague and unmeasurable principle phlo-
giston was eliminated from the laboratory and the text-
books : quantities took the place of indefinable qualities,
and numerical determinations increased in frequency and
accuracy. The vague phlogistic theory, which contained
a germ of truth, l)ut one which at that time could not be
put into definite terms, had helped to gather up many
valuable facts and observations : these were collected and
restated in a new and precise language. It has been said
that every science must pass through three periods of
development. The first is that of presentiment, or of
faith ; the second is that of sophistry ; and the third is
that of sober research. Liebig states the case somewhat

substances enter into chemical re-
action ; and the mobility or inert-
ness of chemical substances was to
be measured by the presence or ab-
sence of a definite something. A
hundred and fifty years after Stahl,
science had so far advanced, that
besides the change of weight or
mass, the change of the power
of entering into chemical com-
bination could also be measuj-ed,
and the term " potential energy "
was introduced to describe many of
those properties and processes which
Stahl had fastened upon, when he,
as the pioneer, undertook to co-

ordinate chemical phenomena. If
Stahl considered phlogiston to be
a substance, though he did not in-
quire into its mass or ponderable
property, the question might be
put again, whether " energy " is not
to be considered after all as a sub-
stance. Cf. Tait, ' Properties of
Matter' (2nd ed., introduction, es-
pecially p. 5 sqq.) ; 'Recent Ad-
vances of Science,' introduction ;
also Clerk Maxwell, ' Electricity and
Magnetism ' (last chapter) ; Ost-
wald, ' Chemische Energie ' (Leip-
zig, 1893, p. 41).

THE ATOMIC VIEW OF NATURE. 389

more correctly when he says : " To investigate the essence
of a natural phenomenon, three conditions are necessary :
We must first study and know the phenomenon itself,
from all sides ; we must then determine in what relation
it stands to other natural phenomena ; and lastly, when
we have ascertained all these relations, we have to solve
the problem of measuring these relations and the laws of
mutual dependence — that is, of expressing them in num-
bers. In the first period of chemistry, all the powers
of men's minds were devoted to acquiring a knowledge of
the properties of bodies ; it was necessary to discover,
observe, and ascertain their peculiarities. This is the
alchemistical period. The second period embraces the
determination of the mutual relations or connections of
these properties ; this is the period of phlogistic chemistry.
In the third period, in which we now are, we ascertain by
weight and measure and express in numbers the degree
in which the properties of bodies are mutually dependent.
The inductive sciences begin with the substance itself,
then come just ideas, and lastly, mathematics are called
in, and, with the aid of numbers, complete the work." -^

As Galileo, Huygens, and Xewton, by a series of bril-
liant investigations and theories, such as those of the pen-
dulum, the fall of bodies, finally of universal gravitation,
established the usefulness of the mathematical treatment
of physical phenomena, so Lavoisier and his school proved
the correctness and usefulness of their views by the new 5.
theory of combustion, as consisting in the combination of combustion.
a special body or element called oxygen with other bodies

^ 'Familiar Letters on Chemistry,' translated by Blyth, 4th ed., London,
1859, p. 60.

390 SCIENTIFIC THOUGHT.

or elements. A very large field of research — all on the
lines pointed out by the new school — was opened out. But
the age for a further application of mathematical reason-
ing came much more slowly in chemistry than in physical
science.

The latter had at least one great department, in which
a small number of factors, all admitting of mathematical
accuracy— those of distance, mass, and motion — sufficed
to explain the phenomena, at least if viewed from a great
distance. This science is the physics of the heavens, the
science of cosmic phenomena. On this earth — in physical
and still more in chemical phenomena — the matter stood
very differently. Here we have not to deal with a few
measurable quantities only. A large number of elements
or factors, of which only very few can be accurately
measured, combine to make up what we called in the last
chapter molar and molecular phenomena. In the study
of inanimate nature, astronomy — the mechanics of the
heavens — deals with the simplest relations ; chemistry —
the science of the changes which bodies undergo when
being combined or separated — deals with the most com-
plicated side of reality. Physics occupy an intermediate
position, and thus we can also trace in the history of
physical research the twofold influence of the astronomical
method of inquiry on one side, and the chemical on the
other.

But the general rule, that in chemical changes the
weight of all the constituents pu.t together never changes,
was not the only numerical relation which came to the
aid of students of nature, when they, at the end of the last
century, betook themselves to exact measurements and

THE ATOMIC VIEW OF NATURE.

391

determinations. Tliat rule is indeed the foundation of all
work in the laboratory, the principle which decides the
degree of accuracy attained in every analysis, and which
not infrequently is the only method of determining the
presence of some undiscovered constituent.-^ Not long

^ The revolution in chemistry at
the end of the last century manifests
itself in nothing more than in the
various distinct problems, corre-
sponding to different eimrses of
scientific thought and different in-
terests, which have guided chemical
research since that time. The first
definite object was the search after
the real elements, the attempt to
decompose the existing substances
of nature into their ultimate consti-
tuents. This interesting occupa-
tion somewhat pushed into the
background the theoretical investi-
gations regarding the forms of the
combinations of the various ele-
ments into compounds, still more
the study of chemical affinity. A
second definite object was the de-
velopment of the theory of combus-
tion which Lavoisier propounded,
and the confirmation or refutation
of the idea according to which
oxygen occupied almost as import-
ant a position in chemical reactions
as phlogiston had done before. A
third definite object was the develop-
ment of analytical chemistry, the
systematic and methodical use of
the balance. So far as the first
branch of this pursuit was con-
cerned, Lavoisier's catalogue of the
elements was still very incomplete ;
it contained thirty-three members,
including light and heat, and
twenty - three of the substances
which now figure in the list of the
seventy elements enumerated in the
text-books ; the alkalies and earths
were still considered to be simple
bodies. A great addition to our
knowledge in this department came

through Davy's decomposition of
soda and potash. And after his
proof of the elementary nature of
chlorine the oxygen theory of La-
voisier had also to be greatly modi-
fied. "Through a series of most
importaiit investigations, he rose in
the beginning of this century to
such eminence, that he was then
considered to be the first represen-
tative of chemical science. W^ith
great experimental ability he com-
bined a singular freedom from all
the theoretical doctrines which were
recognised in his age " (Kopp, ' Ent-
wickelung der Chemie,' p. 4.51). In
this he resembled Dalton and Fara-
day and other natural philosophers
in this country, on whom theoretical
notions formed in the Continental
schools had little or no influence.
Qualitative analysis was less indebt-
ed to Lavoisier than other branches
of the science were. In fact, it was
more at home in Sweden and Ger-
many, where the interests of miner-
alogy and metallurgy promoted it.
Bergmann and Scheele in Sweden,
Klaproth in Berlin, were the fore-
runners of Berzelius and of the
Berlin school of analysts. In this
country Black and especially Caven-
dish had carried out some important
quantitative determinations, the ac-
curacy of which seems very far be-
hind modern standards (see Kopp,
' Geschichte der Chemie,' vol. ii. p.
70, &e., 1844). It was the introduc-
tion of the notion of chemical equi-
valence, a term used already by
Cavendish, which furnished the
ultimate test for accuracy and re-
volutionised quantitative analysis.

392 SCIENTIFIC THOUGHT,

c. before the age of Lavoisier, another general conception

Rule of fixed '^ ' o r

proportions, had been introduced into chemical research ; this was the
rule of definite proportions — i.e., the fact that substances,
whether simple or compound, combine only in definite
proportions of their weight, and that the numbers marking
these proportions are characteristic of every definite
chemical substance. It took some time, nearly a century,
before this idea, which arose through the examination of
neutral salts and the determination of the quantities of
acids and alkalies which were wanted to effect mutual
saturation, became clear ; before the rule of definite pro-
portions was generally established, becoming a guide for
chemical analysis. It is interesting to note how the
vaguer terms of chemical affinity and elective attraction,
of chemical action, of adhesion and elasticity — mostly
borrowed from other departments of science where they
had definite meanings — gradvially disappeared, when by
the aid of the chemical balance each simple substance
and each definite compound began to be characterised,
and labelled with a fixed number. Nevertheless, even at
the beginning of this century, eminent chemists were still
so much engaged in discussing the rival claims of the old
phlogistic, and the modern theory of combustion, of Ber-
thollet's chemical equilibrium, of the so-called dynamical
and the electro-chemical views of phenomena, that the first
methodical attempt actually to fix these numbers — i.e., to
give a table of chemical equivalents — remained unnoticed.^

' The history of chemistry early
in this century furnishes a good ex-
ample of the sway which theoretical
views exercised over the minds of in-
vestigators. Berthollet, who began
by critically examining Bergmann's

doctrine of chemical affinities, was
evidently much influenced by the
mathematical theory of attraction,
and by the mechanical laws of equi-
librium, which formed so prominent
a subject of investigation in the

THE ATOMIC VIEW OF NATUEE.

393

The merit of having made this attempt belongs to one
who approached chemistry entirely from the mathematical
side, who wrote the first chemical book with a title point-
ing directly to measurements, but who perhaps spoilt his
work by giving way to the fascination which regular
numerical and geometrical arrangements have again and
again exercised over philosophical inquirers. Jeremias 7.

J. Benjamin

Benjamin Eichter — a name possessed of no popular cele- H'ciiter.
brity — published in 1792 to 1794, in three parts, his
" Stoechiometry," or the art of measuring chemical ele-
ments." ^ From his data, Fischer calculated in 1802 the

writings of Laplace and his school.
Chemical affinity was to be co-
ordinated with what he called astro-
nomical attraction ; both were to
be ultimately the same phj-sical
property ; thej- acted difi'erently,
because in the case of gravitation
the dimensions were so large, that
the form, distances, and peculiar
properties of the molecules had no
influence. It was an attempt to
introduce the astronomical view of
matter into molecular physics, and
to base chemistry upon this view.
BerthoUet adhered to the corpus-
cular theory of heat against Rum-
ford, who had just propounded his
opinion that heat is not a consti-
tuent part of bodies ; and he main-
tained that chemical affinity was a
function of the mass of bodies as
was astronomical attraction. The
germ of truth in Berthollet's views,
which were approved by Laplace,
but cast into oblivion under the
influence of Proust and Richter's
theory of fixed proportions, has
in recent times been shown by
Lothar Meyer (' Modern Theories of
Chemistry,' Introduction), and by
Ostwald ('Allgemeine Chemie,' vol.
ii. p. r)57, 1st ed., also ' Die Energie
und ihre \Vandlungen,' Leipzig,

1888, p. 20). If the astronomical
view of molecular phenomena pre-
vented BerthoUet from accepting
Proust's doctrine of fixed proportions
and definite combinations, Richter
injured his own reputation by ad-
hering to the nomenclature of the
phlogiston theory after it had been
discarded by French chemists, and
in Germany after Klaproth's deter-
minations in 1792. The oxj-gea
theory of combustion of Lavoisier
got such a firm hold on the minds
of Continental chemists that the
labours of those who, like Cavendish
in England and Richter in Germany,
put forward important discoveries
in the language and on the principles
of the older theory, were temporarily
forgotten. See Kopp, ' Entwickel-
ung der Chemie,' p. 271, &c.

^ Stoechiometry comes from the
Greek to. crToix«'a, the constituent
parts, and /xfTpuv, to measure.
All Richter's works are connected
with the application of mathematics
to chemistry ; his inaugural disser-
tation, which appeared in 1789,
bearing the title ' de usu matheseos
in chymia' (Kopp, ' Geschichte der
Chemie,' vol. ii. p. 350). " Richter
etait preoccupe de I'idee d'appliquer
les mathematiques a la chimie, et en

394

SCIENTIFIC THOUGHT.

8.

Dalton.

first table of chemical equivalents, taking sulphuric acid
as the standard with the figure 1000.

The conviction that chemical substances combine ac-
cording to fixed and simple proportions gained ground
on the Continent, chiefly during the discussion in which
Proust finally disproved and defeated Berthollet's theory
of chemical affinity ; but it is to Dalton that the doctrine
of fixed and multiple proportions is indebted for a con-
sistent exposition. Dalton based it upon a mental re-
presentation which ever since has been the soul of all
chemical reasoning.

When Newton, from the measurable data of the move-
ments of cosmic bodies, deduced the celebrated gravita-
tion formula, he had to descend to molar — nay, even to
molecular — dimensions, and to express it as a relation
referring to the very elements of matter, before he could
apply it in a useful manner : he had to express it as a
formula which had reference to the smallest portions of
matter. In the same way, the measurements made by

particulier de decouvrir des relations
numcriques eutre les quantites des
corps qui se conibinent. Ses efforts,
dans cette direction, u'ont pas ete
egalement heureux ; car, s'il a re-
connu et dnoncd le premier la loi de
proportionnalite eutre les quantites
de bases qui s'unissent au meme
poids d'acide et entre les quantites
d'acides qui s'unissent au meme
poids de base, fait important et ex-
act, il a cherche a demontrer, d'un
autre cotd, que ces quantites fermai-
ent des series numeriques dont les
termes augmenteut suivant des re-
lations simples, ee qui est errone.
. . . Ces erreurs n'ont pas ecliappd,
saus doute, k I'attention des con-
temporains de Richter et ont con-
tribue h discr^diter ses travaux.

. . . Mais nous n'avons pas a insister
sur ce dernier point. Relevons,
dans i'ccuvre de Richter, les idees
justes et les decouvertes fondamen-
tales qui recommandent d'autant
plus son nom h, I'attention recon-
naissante de la posterity qu'il est
demeure meconnu et presque ignore
de son temps " (Wurtz, ' La Theorie
atomique,' 7""^ ed., 1893, p. 9, &c.)
" L'opposition meme, qu'il profes-
sait pour les doctrines du reforma-
teur [Lavoisier] semble avoir con-
tribuc II discrediter les travaux de
Richter : son lieure n'etait pas
venue ; Tinterot etait ailleurs, et
en Allemagne, comme en France et
en Angleterre, les esprits dtaient
entraines par le courant des id^es
nouvelles" (ibid., p. 13).

THE ATOMIC VIEW OF NATURE. 395

many chemists previous to Dalton had to be interpreted
as referring not only to such quantities as the balance
could determine, but to the very smallest immeasurable
particles of which chemical substances consist. For
this purpose Dalton adopted what was known as the
atomic view of matter. The conception of matter as
made up of independent particles, which for our means
and methods prove not only indestructible but likewise
indivisible, was revived as the ancient theory of attraction
had been. Combined with the Newtonian view that
weight is a universal property of all matter, it made the
two fundamental rules of chemical action intellig-ible :
the two facts — first, that the total weight of substances
remains always the same, be they combined in ever so
many different ways ; and secondly, that all substances,
be they in large or in small quantities, combine with each
other, or separate from each other, in definite and fixed
proportions. This view could not be consistently main-
tained, except it was referred to the smallest particles
into which matter is practically divisible : the figures
expressing the combining numbers were viewed by Dalton
as representing the relative weights of the actual atoms
or elements of matter. That the ultimate particles of
matter have definite weights is the reason why substances
combine in fixed proportions, and why the combining
weight of the compound is the sum of the combining
weights of the constituents.

As the gravitation formula had given rise to a sur-
prising activity in physical astronomy, to a long series
of exact measurements, and to theoretical deductions of a
purely mathematical kind, so the atomic theory of Dalton

396 SCIENTIFIC THOUGHT.

in the early years of the century fixed the tasl^ of chemists
for a long time ahead.

To begin with, an enormous amount of work had to

be done in determining the actual proportions in which

9. elementary substances combine. A very large share of

Berzelius. _ "^ ./ o

this work belongs to Berzelius, who by a great number
of very accurate determinations confirmed inductively
the correctness of Dalton's theory. And even more im-
portant than the confirmation of the theory was the great
harvest of actual knowledge of the things and processes
of nature which was collaterally gathered, whilst chemists
were trying to prove or to refute existing opinions.

Indeed, whilst the atomic theory of Dalton was the
first step towards a systematic and comprehensive study
of chemical phenomena — i.e., of the qualitative varieties
under which matter presents itself to us on the surface
of this globe — the extension which was gained in the
domain of actual facts was much greater than the simpli-
fication which the theory had attempted to give. The
number of elements or simple bodies, which in Lavoisier's
time hardly exceeded thirty, increased before the year
1830 to more than double : the number of new compounds,
unknown before, has probably never been counted. Com-
pared with this growth of actual knowledge of facts, the
development of the theory was slow and uncertain. The
view of nature from the atomic point of view marks
indeed a great contrast to that from the astronomical
^g point of view. We now live about as long after the
tti*eoi'y''and refomi of cheuiistry through Lavoisier and Dalton as
iompared." Laplacc livcd after the reform of physical astronomy

WoUaston's

THE ATOMIC VIEW OF NATURE. 397

through Newton. But who could compare the state of
chemistry at the present day with that of astronomy in
the age of Laplace ? There, every step had tended to
show that the one Newtonian formula sufficed to coin-
prehend all cosmic phenomena ; here, the simplification
introduced by Dalton has had to give way to a series
of modifications which have rendered the atomic theor}'
one of the most complicated machineries ever introduced
into science. Let us review in brief the fate of Dalton's
hypothesis during the century which followed. Quite in
the early years of the atomic theory, Wollaston propheti- ii.

WoUastL..

cally foretold that if once an accurate knowledge were prophecy,
gained of the relative weights of elementary atoms, philo-
sophers would not rest satisfied with the determination
of mere numbers, but v/ould have to gain a geometrical
conception of how the elementary particles were placed
in space. Van't Hoff' s ' La Chimie dans I'Espace ' — pub-
lished at Eotterdam in 1875 — was the first practical reali-
sation of this prophecy. Many stages had to be gone
through before this latest phase of the atomic view was
attained. Had it been the case that every elementary sub-
stance combines with any other substance only in one
fixed numerical proportion, no necessity would have ex-
isted to look upon the atomic numbers as anything else
than equivalents. But it was found that though the
combining numbers were fixed they were not always the
same ; it was found that if a substance combined in two
or more proportions with any other, the larger proportions
were always exact multiples of the smallest proportion.
And this — the rule or law of multiple pi'oportioTis — was

398

SCIENTIFIC THOUGHT.

1^. exactly what gave to Dalton's view its great plausibility/

propo?uons. ^^^^ ^^ ^^^® elementary atom of each substance had a definite

weight, it might be that not one atom only combined with

one other, but that one combined with two, or two with

three, and so on. Indeed it was soon found that this was

^ The different factors of thought
which combined to give the atomic
theory that definiteness and useful-
ness which it attained through and
since Dalton lay ready-made before
him ; but no one had seen so clearly
as he did how to combine them.
Proust had taught how to distin-
guish between chemical compounds
and mixtures. W^hen he prepared
carbonate of copper artiiicialij', he
found that it had the same com-
position as the mineral which he
found in nature. Richter had
shown that definite proportions de-
scribe the quantities in which acids
and bases exist in neutral salts.
Fischer had attached to his transla-
tion of Berthollet's work the first
table of equivalent quantities of
bases and acids which combine to
neutralise each other. Richter, and
after him Gay - Lussac, had also
found that the quantities of dif-
ferent metals which dissolve in the
same quantity of acid to form
saturated solutions combine also
with the same weights of oxygen
to form oxides. Richter, and after
him Proust, had found that certain
metals, like iron and mercury, form
more than one fixed compound with
oxygen, but without perceiving that
the different quantities of oxygen
in these fixed compounds stand in
simple proportions to each other.
So far as the theoretical side is
concerned, the idea that bodies
are formed of distinct particles —
the notion of the ultimate hetero-
geneousness or discontinuity of mat-
ter— was not only familiar to the
ancients, but was adopted by many
physicists before Dalton; though the

chemical specialists who prepared
the way for Dalton do not seem to
have made use of this idea. Boer-
haave, and before him Boyle, had
spoken of atoms and of the massulce
or particles. Theories were not
wanting that these ultimate par-
ticles differed in size and form, nor
the opposite view, that the par-
ticles which combined had the same
weight. The latter was the view
of Higgins, in the exposition of
which (1790) he entangled himself
in contradictions, losing his chance
of being one of the founders of the
atomic theory. As Wurtz and Kopp
and others who have carefully in-
vestigated the rival claims have
said : This honour of founding the
atomic theory belongs undividedly
to Dalton. It seems important to
notice that his experiments with
mixtures of gases, which must have
begun about 1790, impressed upon
him the idea that different gases
could exist independently of each
other in the same sjjace, suggesting
the conception that neither of them
filled the whole space, but that
they consisted of discontinuous par-
ticles. He himself refers to these
first investigations as containing
the germ of his later opinions. It
must, however, be borne in mind
that Dalton was only imperfectly
acquainted with the writings of
contemporary — especially Conti-
nental— writers, and that he had
a wholesome distrust for state-
ments of facts which he had not
verified or observed himself. All
this is very clearly stated in Kopp's
' Entwickelung der Chemie,' p. 285,
&c.

THE ATOMIC VIEW OF NATURE.

399

actually the case. The lowest number according to which
any substance entered into combination with any other
was called the atomic weight or equivalent. '

There was, so far, no necessity to look upon atomic
weights as anything else than numbers fixing a propor-
tion. The unit could be selected arbitrarily. It was not
long before that element, hydrogen, which entered into
compounds in the relatively smallest weight was taken as
an arbitrary unit, and all other elements and compounds
were tabulated according to the relative amount of their
weights required to form compounds with hydrogen or
with any other element — e.g., oxygen — the equivalent of
which with hydrogen was known.-^

13.
Equivalents.

•' For many years after the enun-
ciation of the atomic theory great
uncertainty and much difference
of opinion existed on this and
other points. The man who did
most to elaborate the edifice of
which Dalton had laid the founda-
tions, who filled in the outlines and
invented the language of chemistry,
was Berzelius. He jDroceeded in-
ductively and galhei'ed materials
from all sides ; to him are also
owing the greatest number of ac-
curate analyses, especially of inor-
ganic substances. When he began
his labours he was favourably dis-
posed towards Dalton's hypothesis ;
he clearly saw its capabilities, but also
that it was based only upon a happy
suggestion, that it was introduced
more by deductive than by induc-
tive reasoning, and that it needed
to be exhaustively tested and veri-
fied. After ten years, during which
he published in Gilbert's ' Annalen '
and in Thomson's ' Annals of Philo-
sophy ' many series of investigations,
he was able in 1818 to publish, in
his ' Essay on Chemical Proportions
and on the Chemical Effects of

Electricity ' (French translation,
1819 ; German translation, 1820),
the first systematic and complete
exposition of the atomic theory.
The beginning of a really exact
treatment of chemistry has been
dated by H. Rose, the greatest an-
alytical chemist of the century, from
this year 1818 — the year in which
Dalton's hyi^othesis was proved
and generally accepted. Others
have dated the beginning from
1808, when Dalton published his
theory; others again from 1776,
when Lavoisier destroyed the older
phlogiston theory and appealed to
the balance ; others again from
Black's discovery of latent heat in
1760. In an international history
of thought it is not of much in-
terest to decide whose claims to be
the founder of modern chemistry
as a science are best established.
Every one of these dates marks an
epoch in the advance of an im-
portant and independent branch of
research. Black took an important
step in the foundation of physical
chemistry through his introduction
of the conception of the quantity

400 SCIENTIFIC THOUGHT.

A great door was now opened, not only for actual
observation and research, but also for speculation — i.e.,
for abstract thought. Some substances, if they entered
into combination with hydrogen, required more than one
unit of hydrogen, and it might therefore be that the pro-
portion of the combining weight of hydrogen with any
substance did not correctly give the atomic weight of the
latter, but merely a multiple or sub-multiple of it. Thus,
assuming oxygen combined with hydrogen in the propor-
tion of 8 parts of the former to 1 part of the latter, a
possibility was that the proportion might more correctly
be written 16 to 2 than 8 to 1. Then, again, were the
equivalent or atomic weights necessarily whole numbers ?
Were combinations all binary, such as acids and alkalies
forming salts ? and were more complex compounds resolv-
able into binary compounds of simpler binary compounds ?
Further, assuming the proportions fixing the combining
weights to be known, how did the volumes of bodies com-
bine?— was there a rule of volumes as there was of weights?
and lastly, what was the reason or cause which made sub-
stances change their combinations, forming new ones, what
did chemical affinity consist in, what did it depend on,
how could it be defined and measured ?

Considering that we have to do with a large number of
independent, apparently unchangeable, elements, entering
into many thousands of differing compounds, the task of

of heat. Lavoisier led the way in I purely arithmetical relations, and

the development of the purely arith-
metical department of chemistry,
in the exclusive study of which
physical chemistry was greatly
neglected. Dalton suggested a
formula which lent itself admir-
ably to the representation of these

Berzelius elaborated this and in-
vented a practical nomenclature.
Black and Dalton threw out novel
ideas ; Lavoisier and Berzelius ela-
borated great systems and created
great schools which numbered many
converts and industrious workers.

THE ATOMIC VIEW OF NATURE.

401

the chemist was enormous, offering a large, ahnost limit-
less, field of research and speculation. Let us see under
what leading ideas this knowledge has been arranged.

In the gradual development and clearer definition of
these conceptions a general rule of thought seems to
have unconsciously guided philosophers probably more
than in any other department of knowledge. It is the
rule of simplicity.-^ How the human mind should have
arrived at the old formula of " simplex sigillum veri " is
difficult to understand on any other ground than that of
convenience and expediency. The prevailing impression,
indeed, which the world of phenomena makes on the mind
of an unbiassed observer must be the very reverse of sim-
plicity or unity of law and purpose. That, nevertheless,
the knowledge of some simple relations in time, number,
and space would enable the human intellect to acquire a
considerable insight into the course of events and the
order of Nature's processes must have come to philosophers

14.

" Simplex

sigillum

veri."

1 The progress of chemical theory
is the history of the attempt to
find simple relations of number and
form, representing the countless
combinations of elementary sub-
stances ; and of the growing con-
viction that nearly every simpli-
fication must, in course of time,
be abandoned. No formula remains
unchallenged except the doctrine of
fixed and fixed multiple proportions,
and that only if we confine our-
selves to solid compounds ; but the
proportions themselves are not ac-
curately known, though no pheno-
menon exists which disproves the
assumption that thej' are invariable.
The original conception of the atom
as a round hard Vjody had to be
abandoned for the more complicated

VOL. I.

notion of a molecule, an assemblage
of atoms ; the conception of elemen-
tary bodies had to be amplified by
that of compound elements or
radicles ; the idea that the atomic
weights were multiples of a lowest
number had to be abandoned ; the
binary theory of the combination
of bodies was replaced by the theory
of radicles, of nuclei, of types ; the
simple nature of the elementary
particles had to give way to a
complicated atomicity, from which
there had to be again distinguished
the valency or capacity of satura-
tion of the elementary constitu-
ents. It is a progress from simpler
to more and more complex methods
of representation.

2 c

402

SCIENTIFIC THOUGHT.

as a kind of revelation, and it is not surprising that it
came late in the course of civilisation.^

Nothing can have tended more in this direction than
the success of the Newtonian gravitation formula, and of
the simple laws of motion, which, at the time of the birth
of modern chemistry, stood firmly established as the key
to all problems of physical astronomy. No wonder that
men were on the look-out for correspondingly simple —
perhaps analogous — relations in the world of molecular
phenomena. One of the earliest suggestions, which came
forward soon after Dalton's atomic view had helped to
establish the prevailing rule of fixed and of multiple pro-
portions in the chemical combinations and reactions of
matter, was the idea that, as to each element belonged a
definite combining number, all these numbers must be the
multiple of the lowest among them, the equivalent or
atomic weight of hydrogen. This is Prout's celebrated
hypothesis, hypothcsis, which had some ardent admirers, and which
has been repeatedly abandoned and revived in the course
of this century.^ It is hardly possible to maintain it any
longer, since the accurate and elaborate measurements of

Prout's

^ Except indeed the Pythagorean
notions are regarded as an anticipa-
tion of it.

" The hypothesis of Prout, pub-
lished anonymously in 1815, and
warmly defended by Thomson, has
been again and again revived. From
the beginning it was put forward
together with the suggestion that
the diiferent elementary substances
might after all turn out to be all
derived from one and the same
primary form of matter, and that
the atoms of this might in the
atoms of our present elements
merely be aggregated in different
numbers and figures, held together
by forces, which bj^ the means and

processes at our command could
not be broken up. This primary
substance might then be either
hydrogen, the lightest in weiglit of
known substances, or some other
substance of which hydrogen itself
was an atomic multiple. Abroad,
Pi'out's Iwpothesis was disproved
by Berzelius's accurate determina-
tions, in England by Turner's, and
about 1830 it fell into oblivion. It
was again revived in 1840 by Dumas,
who, as well as his followers, Lau-
rent and Gerhai-dt, favoured the
idea that the explanation of the
different properties of chemical com-
pounds, notably organic compounds,
was to be found in the arrangement

THE ATOMIC VIEW OF NATURE.

403

Stas, who began with a belief in the hypothesis, led to the
result " that the simplicity supposed by Front's hypothesis
to exist in the ratios of weights which come into play in
chemical processes has experimentally not been found ; it
does not exist in reality." ^

I of the elementary atoms, in the
' structure rather than in the material
drflfefeiice of the elements them-
selves. The development of this
view in the modern chemistry of
" ty23es " and "structures" will
always go hand in hand with an
avowed or tacit belief in the exist-
ence of an ultimate uniformity of
substance, out of which by a diver-
sity of configuration of atoms the
infinite variety of compounds is
produced. The accurate measure-
ments of Stas had again about the
year I860 disproved the hypothesis
of Prout. It has. however, again
turned up in recent scientific litera-
ture. The theories of evolution,
physical and philosophical, the dis-
coveries of the spectroscope regard-
ing the small number of elements
contained in the photosphere of the
sun, the periodic laws of Lothar
Meyer and Mendeleeff and the
stereometric theory of the carbon-
compounds, of which I shall speak
later on, all point to the con-
clusion that our so-called elements
are composite bodies, and favour a
view, similar to that of Prout, that
possibly a single kind of matter
may form the only substance of
which atoms, molecules, elements,
and compounds are made up. Pro-
fessor Crookes in his address to the
chemical section of the British
Association in 1886 revived inter-
est in the subject. After quot-
ing a variety of authorities, he
sums up : " From these passages,
which might easily be multiplied,
it plainly appears that the notion —
not necessarily of the decomposi-
bility, but at any rate of the com-
plexibility of our supposed elements
— is, so to speak, in the air of

science, waiting to take a further
and more definite development. It
is important to keep before men's
minds the idea of the genesis of the
elements ; this gives some form to
our conceptions, and accustoms the
mind to look for some physical pro-
duction of atoms." Further on he
coins the word " protyle " (from
■nrpdorrjAud uArj)to denote the original
kind of matter, and thus reminds us
that, though speculations of this
nature are not infrequent in English
philosophy since Roger Bacon, the
English language has no word to
denote what the Germans call
"Urstoff," the Romans "prima
materia," the Greeks to crrotxewv or
simplj' i/'Atj. The line of thought
which again and again leads philo-
sophers to speculate on this "prima
materia" and upon a hypothesis
similar to that of Prout is interest-
ing and noteworthy, though it must
be acknowledged that, so far, no
real scientific benefit has been de-
rived from it, and that it rather
tends to upset the only firm founda-
tion of modern chemistry, the fixity
of the equivalent proportions as we
now use and know them, ilende-
leeli himself, in his excellent Fara-
day lecture on the periodic law
('Journal of the Chemical Societv,'
1889, p. 634, &c.) distinctly refuses
to recognise any connection between
the periodic law and the idea of an
unique matter.

1 Stas, quoted by Ostwald,
'Lehrbueh derAllgemeinen Chemie,'
vol. i. 2nd ed., Leipzig, 1891, p. 129.
The revival of the hypothesis of
Prout about the middle of the cen-
tury was owing to the discovery by
Dumas and Stas of the fact that
Berzelius's figure, 12 •'20, for the

404 SCIENTIFIC THOUGHT.

Prout's simple but incorrect assumption belongs to the
age which witnessed the decomposition of many com-
pounds into their two constituents by Davy's successful
use of the galvanic battery, at the poles of which the
two elements of substances made their separate appear-
ance. Substances which had always been considered
as elemental and permanent, such as many oxides and
earths, came to be ranged among the list of binary com-
pounds. This lent plausibility to the idea that even the
supposed elements themselves might ultimately prove to
be aggregates — differing in number and figure — of the
elementary particles of one and the same primary sub-
stance. Though with Prout's hypothesis this view has
been repeatedly held and refuted, another theory — recom-
mended likewise by its simplicity — had its origin in the
discoveries of Davy, and the further development of them
by Berzelius. This is the so-called electro-chemical or
binary theory of chemical compounds. The dual combina-
tion of one elementary substance with another, and again
of two dual compounds with each other, and so on,
even to the most complicated compounds, was to be the
simple type of chemical combination. This view, so

atomic weight of carbon, taking called laws of phenomena. This

oxygen as 16, was incorrect. An | consideration, so familiar to astron-

account of the long series of deter- omers, was, I believe, quite over-

minations of this important con- j looked in many of the best hand-

stant will be found in the same i books during the earlier half of our

work, p. 82, &c. I believe that in | century, and it is even yet hardly

the first edition of this work will ' touched upon in the ordinary text-

also be found the first consistent books. The result is an entirely

attempt to introduce into chemical erroneous impression produced on

data an estimate of the degree of ' the popular mind as to the degree

accuracy or the amount of error of certainty which belongs to

which attaches to our knowledge of scientific statements,
the constants of nature and the so-

THE ATOMIC VIEW OF NATURE.

405

simple and plausible, governed research for a long period,
but has finally been abandoned as insufficient/

Another blow was dealt at the simple theory by which Discovery of

isomerism.

^ The electro-chemical theory of
Davy and Berzelius was, after about
fifteen years of development, during
which period the use of the signifi-
cant terms electro - positive and
electro-negative was not consistent,
finally enunciated bj^ Berzelius in
1818 in his ' Essay on the theory of
Chemical Proportions and on the
Chemical Action of Electricity.'
From that time it reigned almost
supreme for twenty years, when
both physical and chemical dis-
coveries began to show its insuffici-
ency. A very concise account of it
is given in Kopp's ' Entwickelung
der Chemie,' and in E. von Meyer's
' History of Chemistry,' translated
bj' M'Gowan (Macmillan & Co.,
1891). Berzelius clung to it to the
last, and at the present moment
there exists a widespread opinion
that the future will see a revival
and modified acceptance of the
Davy -Berzelius theory. In rela-
tion to this Helmholtz's celebrated
Faraday lecture of the year 1881
should be read (see the reprint in
Helmholtz's ' VortrJige und Reden,'
vol. ii.) The jDeculiarity of the elec-
tro-chemical theory was that it was
an atomic theory as well as a theory
of chemical affinity. When it was
abandoned, the two distinct in-
terests, that of developing the
atomic view, so as to give a correct
description of the constitution of
chemical compounds and reactions,
and that of giving an explanation
of chemical affinity, fell for a time
asunder. The former interest pre-
ponderated, owing mainly to two
reasons, the one theoretical, the
other practical. The theoretical
reason was the need of a difierent
method of systematicallj^ arranging
the chaos of new organic compounds

with which chemistry became
crowded about the year 1840.
Berzelius had created the nomen-
clature and notation of chemistry ;
but this proved insufficient to de-
scribe and grasp the processes and
products of the many carbon com-
pounds. The practical reason which
cast into the background the study
of chemical affinity and its nature
was the growing demands of manu-
facturing chemistry. This was
during a long period occupied
mainly with the analysis and syn-
thesis of new products, or with new
and simpler methods for producing
well-known compounds. The study
of reactions and of the products of
bodies was practically of more in-
terest than that of the forces which
governed them. The question of
the cost of producing chemical pro-
ducts was for a long time a second-
ary one. Towards the end of our
century both theoretical and prac-
tical considerations forced upon
chemists the necessity of making
themselves acquainted with the
different forms of energy which are
at our command in chemical as well
as in mechanical operations, and
this has led to a renewal of the
study of chemical and mechanical
energy, and of the nature and laws
of chemical affinity. Economy in
practical chemistry can be divided
into two branches : the economy of
materials and the economy of
energy. The great developments
in the course of this century have
consisted largely in utilising by-
products and in avoiding waste of
substance. We are now only ap-
proaching the second problem :
how to put the energy which is at
our command to the best use.

406

SCIENTIFIC THOUGHT.

Berzelius united Dalton's and Davy's researches into a
comprehensive system of chemistry. The identity or
difference of chemical substances seemed in the early part
of the century to be fixed by the constituent elements and
their quantitative proportions determined by a qualitative
and quantitative analysis. This simple view had to be
abandoned when Wohler in 1823, Liebig in 1824, and
Taraday in 1825 found that entirely different qualities,
indicating a different constitution, could belong to bodies
having the same elements in the same numerical propor-
tions.-^ The composition of a compound had to be dis-
tinguished from its constitution, the elementary from the
constituent analysis and formula. It took forty years
before the great variety of views which were brought
forward with the purpose of explaining how composition
and constitution of the same aggregate of elements might

^ This phenomenon is termed
" Isomerism," from the Greek word
l(roiJ,eprjs, which signifies " having
equal parts." The term was intro-
duced by Berzelius in 1830, after
he had satisfied himself that com-
pounds existed, differing widely
in their properties, which contain
the same constituent elements in
the same proportions, and which
combine with other bodies in the
same proportions to form neutral
salts. This he found to be the case
with "racemic" and " tartaric" acid.
Up to that time he had hesitated
in accepting the growing evidence
that equal constituents in equal
proportions did not constitute
identity of compounds. Wohler in
1823 and Liebig in 1824 had found
the same numerical composition for
" cyanate " and "fulminate" of
silver. In 1825 Faraday found two
hydrocarbons which contained the
same proportions of carbon and

hydrogen, but showed totally differ-
ent properties, such as unequal
density in the gaseous state. Two
oxides of tin, having the same com-
position, were also known, and two
modifications of " phosphoric acid."
The explanation of these anomalies
caused Berzelius much difficulty.
He resorts to the notion of a
difference of grouping of the con-
stituent atoms. " The isomerism
of compounds," he says, "in itself
presupposes that the positions of
the atoms in them must be difiler-
ent" (see E. von Meyer, 'History
of Chemistry,' p. 238). A. Rau in
his ' Theorien der modernenChemie'
(3 parts, Braunschweig, 1877-84)
gives in the appendix to the third
part a detailed history of isomerism.
He denies that Berzelius refers to
the different position of atoms in
order to explain isomerism ; he at-
tributes this suggestion to Dumas
in 1833.

THE ATOMIC VIEW OF NATURE.

407

differ, could be approximately brought into line and order.
This period was filled by the development of the chem-
istry of organic compounds. The chemical substances n.

■^ ^ -^ _ Organic-

which make up the framework and numerous tissues chemistry.
of all living beings, the juices and products of vegetable,
the food and the excreta of animal organisms, consist
mostly of a few elementary bodies, combined according
to numbers which are highly complex and unintelligible.
Most of these compounds, if removed from the organism
which contained them, proved to be subject to rapid de-
composition. An increasing number of stable compounds,
however, were in course of time prepared from these
residues, and these formed especially the subject of organic
analysis. Already Lavoisier had indicated how some
system might be brought into the apparent complexity
of these organic bodies ; and this view was adopted by
Berzelius and incorporated in his dual or binary system.-^

^ Kopp's account of the develop-
ment of Berzelius's views on organic
compounds is most interesting and
instructive. As late as 1814 he
could not reconcile the composition
of organic acids, such as oxalic acid,
with the atomic theory ; but re-
newed efEorts and improved methods
of analysis taught him in the fol-
lowing years how to apply the
atomic formulae to the description
of such compounds. " He was
the first to show the only right
road to inform ourselves regarding
the constitution of these bodies,
the method, namely, of analysing
their combinations with inorganic
substances of known atomic weight.
. . . He had also a great share in
establishing the view that the ratios
of combination in organic com-
pounds are analogous to those
of inorganic substances, and that

theories of the former must begin
by comparing them with the lat-
ter" (' Geschichte der Chemie,' vol.
i. p. 398 ; cf. also ' Die Entwickel-
ung der Chemie,' p. 532, &c.) To
Berzelius is thus due more than to
any other man the breaking down
of the barrier which had before his
time divided the chemistry of or-
ganic from that of inorganic sub-
stances. For a considerable time
Berzelius did not look upon organic
compounds as Vjinary — in fact, in
1814 he assumed that the difference
between organic and inorganic com-
pounds lay in this, that the latter
were all binary, whereas the former
were ternary or quaternary. The
French chemists, under the influ-
ence of Lavoisier's oxygen theory,
favoured the binary view, and this
was much strengthened by Ga.y-
Lussac's researches on cyanogen (in

408 SCIENTIFIC THOUGHT.

It was supposed that the simple and well-known elements
of these bodies might have the property of forming
primarily combinations which were more firmly knit
together than others, that these primary combinations
might then as it were take the place of elements and
act like them, forming with others of similar constitution,
or with the simple elements themselves, more complex
compounds. In these higher compounds they might
behave like elementary bodies, entering into and being
expelled from them in their own proper combinations
without being broken up into the ultimate elementary
constituents. One of the functions of the living organism
was by the action of the vital forces to produce these
primary compounds or complex atoms. It was thus
thought that as inorganic bodies were made up of con-
stitvients which were elements, so organic bodies were
made up of constituents which were themselves partly
compounds. A new term had to be coined for those
constituents which might comprise both elementary
bodies and these primary compounds which behaved
like elements in organic substances. This was the term
" Eadicle." A radicle might be an element or a com-
pound.-^ Tor a long time it was thought that these

1815), a compound of carbon and pound elements or radicles (Kopp,

nitrogen, which was shown to behave ' Geschichte der Chemie,' vol. iv. p.

like an element. Ampere in the 269).

followingyear showed how the salts ^ The term "radicle," to desig-
of ammonia could be brought into nate the j^rincipal constituent of a
line with the salts of other al- compound, was used as far back as
kalies by considering them to con- 1787 in the discussions through
tain a compound element (consist- which the French chemists reform-
ing of nitrogen and hydrogen) in ed the nomenclature of chemistry
place of a simple element. Jn his (Kopp, 'Geschichte,' &c., vol. iv.
celebrated es.say of 1818 Berzelius p. 266). It acquired a more defi-
defines organic acids as binary nite meaning about the year 1835,
compounds of oxygen with com- when Liebig, in common with Ber-

THE ATOMIC VIEW OF NATURE.

409

complex radicles, as distinguished from the elements,
were produced mainly — if not exclusively — in the organ-
ism of the plant or of the animal. Liebig himself, who is.

Liebig's de-

favoured this view, and who first brought organic chem- finitionof

" ^ organic

istry in its application to agriculture and physiology chemistry.
under the notice of a large circle of readers, introduced
this branch of the subject with the designation of the
chemistry of compound radicles, inorganic or mineral
chemistry being termed the chemistry of simple radicles.
The radicles were, according to Liebig, the true elements
of organic chemistry. The binary system of Berzelius
received another attack led by the celebrated French
chemists Laurent and Gerhardt, with whom Dumas tem-
porarily allied himself. It was about the year 1840 that
the idea of " substitution " entered the list of formulae
by which chemical philosophers attempted to systematise tio"
and simplify the ever-growing number of definite com-
pounds, supplied mainly by organic analysis.'^ It was

19.

Substitu-

zelius and with Dumas, established
what is now called the older radicle-
theory of organic compounds. As
Kopp has shown (' Entwiekelung
der Chemie, p. 576, &c. ), it remained
undecided at that time whether
these organic radicles had actual
existence, or whether they were
merely a convenient symbolism, —
whether they could be isolated, like
cyanogen, or whether they existed
only in combinations, — whether
they were fixed and unchangeable,
or whether they could themselves
be converted one into another, —
whether the same compound could
be referred — for convenience sake
— to more than one constituent rad-
icle. " By most chemists the defini-
tion of organic chemistry given by
Liebig ('Organic Chemistry,' 1843)

was adopted, that it was the chem-
istry of compound radicles ; . . .
that these radicles really existed
in the compounds as definite con-
stituents ; and if it was then said
that these radicles were mostly
hypothetical, this was understood
as meaning that some of them were
known in the free state, others not "
(p. 581).

^ Even before that time the views
of many eminent chemists had been
greatly influenced by the discoveries
and experiments of two great na-
tural philosophers of this country
who kept themselves free from the
theoretical considerations which had
led Berzelius in the elaboration of
his electro-chemical and binary sys-
tem. These were the researches of
Davy regarding the so-called hydro-

410

SCIENTIFIC THOUGHT.

found that one or more atoms in an organic compound,
notably of hydrogen, might be replaced by an equal
number of atoms of other elements, and that such pro-
ducts of substitution retained similar qualities, and could
be mutually converted into each other, the type of the
compound remaining the same. The process of substitu-
tion led to the conception of " Types," which remained
the same whilst the individual compounds varied ac-
cording to the different elements which were introduced.

geu acids of cliloiue, bromine, and
iodine, and the investigations of
Graham into the salts of phosphoric
acid and its different modifications.
Davy, though together with Ber-
zeHus the founder of the electro-
chemical theory, had found it neces-
sary to modify the oxygen theory
of Lavoisier — viz. , that oxygen was
necessarily the acid - forming ele-
ment : he, and after him Dulong
in France, had explained the so-
called oxygen acids like sulphuric
acid as hydrogen compounds of
certain compound radicles (SO4)
exactly as hydrochloric acid is a
hydrogen acid of the simple radicle
chlorine. Graham's discovery of
three modifications of phosphoric
acid, and of the diiierent power of
saturation of these three modifica-
tions, led to long discussions as to
what is really meant by a neutral
salt. Liebig in the year 1838, in
an important memoir gathering to-
gether the conclusions which these
facts, not easily reconciled with
Berzelius's system, had led him to,
emphasised there the twofold pos-
sibilitj' of regarding metallic salts
either with Berzelius as binary
combinations of oxides with an-
hydrous acids, or else as products
of substitution of hydrogen com-
pounds, hydrogen being replaced
by metals. The choice might then

depend on considerations of con-
venience : the one view might be
more suitable for inorganic — notably
metallic — compounds, the other for
organic compounds. The hydrogen
theory was thus introduced along-
side of the oxj'gen theory ; substi-
tution was introduced alongside of
simple combination. Though iu
this stage the radicle theory was
already threatened, it was still pos-
sible to uphold the binary theory,
though it was not necessary. Chlo-
rine could act in the same way as
oxygen, ' being an electro - negative
element. But when, in pursuing
the line of investigation opened out,
it was found that chlorine, the
electro-negative element, could take
the place of hydrogen in organic
compounds without changing their
chemical character, the binary
theory, based upon polar (electri-
cal) contrasts, became insufficient
as a means of explanation or even
of classification. Dumas was the
first to indicate this (1834), though
he attempted to save the electro-
chemical or polar theory by stating
that the two electrically opposite
constituents of an organic com-
pound might contain the same
elements in the opposite electrical
positions (Kopp, ' Entwickelung der
Chemie,' pp. 564, 595, &c. )

THE ATOMIC VIEW OF NATURE.

411

Whilst the " Eadicle " theory of Berzelius and Liebig
sought to simplify the study of chemical compounds by
reducing them to a definite number of complex atoms, the
" Type " theory of Laurent and Gerhardt sought to attain 20.

Type

the same object by establishing a small number of simple tiieoiy.
formulae, corresponding to well-known simple substances,
under which the vast number of organic compounds could
be grouped.-^ The conception of a " type " exhibiting

^ Tlie type theory was slowly and
hesitatinglj' developed. Dumas,
whose researches about 1835 pre-
pared the way, did not himself
draw the immediate consequences ;
this was done by Laurent, "who
maintained that the structure and
chemical character of organic com-
pounds are not materially altered
by the entrance of chlorine and the
separation of hydrogen " (E. v.
Meyer, ' History of Chemistry, ' p.
261). Laurent then elaborated his
theory of " Nuclei. " They remind
one of Berzelius's and Liebig's radi-
cles. The nuclei were the ground-
work of organic compounds ; they
were not unalterable as the radicles
had been considered to be. Dumas,
who at first rejjudiated Laurent's
ideas, was later on, through his
own experimental discoveries, led to
adopt similar views. The " radicle,"
as the permanent constituent in or-
ganic compounds — corresponding to
the elements in inorganic chemistry
— had given way to the changeable
nucleus, which onlj' preserved its
form ; the unchangeable principle
was found in the form, the structure
or type, instead of in the substance
of the sim[)le or composite consti-
tuents. This led to an extensive
study of the forms of chemical
compounds — as expressed by their
formulae, and apart from the study
of the properties of the original
constituents. Types were invented.

frequently in a somewhat arbitrary
manner. " The ultimate result was
that an empty scheme of formula-
tion carried the day over what was
really good in this doctrine" (ibid.,
p. 264). " The unitary conception
was to step into the place of the
dualistic. . . . Every chemical com-
pound forms a complete whole, and
cannot therefore consist of two
parts. The chemical character is
dependent primarily upon the ar-
rangement and number of the
atoms, and in a lesser degree upon
their chemical nature '' (p. 265).
This is the beginning of the second
great step which was taken in the
elaboration of the atomic view of
matter and nature. The atomic view
first became a scientific instrument,
when arithmetical relations of a
definite and unalterable kind were
suggested and proved to exist ; it
became a yet more useful instru-
ment, when to the arithmetical
there were added geometrical con-
ceptions. Position, ari-angement,
and structure are conceptions
which involve ideas of distance and
space. It is true that for a long
time these terms were used merely
symbolically ; the ultimate conse-
quences of such conceptions can
however not be avoided. The his-
tory of chemical theory in the
second half of the nineteenth cen-
tury is a proof of this.

412

SCIENTIFIC THOUGHT.

certain stable qualities with a multitude of changing
varieties was a notion familiar to other branches of natural
history. The idea of substituting one element for another
gave the death-blow to the theory of Berzelius, which
assumed that elements paired with each other, according
to some polar contrast. It was found, for instance, that
the element chlorine, which stood on one side of the
scale — the electro-negative — could take the place of the
opposite electro-positive element hydrogen.

In the course of time the conception of types was much
changed, and became more and more complicated ; it had
however the effect of finally destroying the binary view of
chemical composition, and restoring in its place the older
unitary conception.

All these attempts to simplify the study of chemical
compounds, by reducing them to simple or complex ele-
ments, or to pairs of simpler combinations, or by ranging
them according to types, were useful in many ways in
extending the knowledge of bodies, in indicating new
methods of inquiry, and in suggesting instructive experi-
ments : ^ none of them were universally accepted in the

^ About that time — so far as
chemistry proper, i.e., the study of
compounds and of reactions was
concerned — there existed two main
currents of thought, the most illus-
trious and influential representa-
tives of which were Kekule (1829-
96, first professor at Ghent, then
since 1865 at Bonn), and Kolbe
(1818-1884, first professor at Mar-
burg, then since 1865 at Leipsic).
As teachers and centres of aca-
demic influence, though in differ-
ent, frequently opposite directions,
these two eminent men continued
the work started in Germany by

Liebig, Wohler, and Bunsen. To
them as a third can be added the
name of A. W. von Hofmann (1818-
1892), who, through his twenty
years' residence in London, did much
to introduce a knowledge of German
chemistry and German teaching
methods in England, and who from
1865 established the modern Berlin
school of chemistry. It would be
impossible to enter here into details
as to how — mainly through the influ-
ence of these three men — the work
begun by Liebig and Wohler was
extended, and how especially also
the great development of chemical

THE ATOMIC VIEW OF NATURE.

413

middle of the century.^ It thus happened that a variety 21.

Uncertainty

of circumstances combined to bring into prominence, and m chemical

^ ■*■ theory about

subsequently into general acceptance, the modern view of of'^ti^'cei!

tury.

industry in Germany was brought
about ; a creation almost as charac-
teristic of German intellect, and
probably more lastingly beneficial,
than the political changes which
mark the same period in history.
More important for a history of
Thought is it to note how Kolbe
attached himself to the school of
Wohler and Berzelius, and tried to
preserve the continuity of thought
in developing the fruitful ideas con-
tained in the writings of the latter.
" He united the conclusions from
his own researches with the declin-
ing theory of Berzelius ; he endued
the latter with new life by throw-
ing aside whatever of it was dead,
and replacing this by vigorous
principles. From his own and other
investigations he came to the con-
clusion that the unalterability of
radicles, as taught by Berzelius,
could no longer be maintained, since
the facts of substitution had to be
taken into account." He especially
developed Berzelius's idea of paired
compounds. (See E. v. Meyer's
'History of Chemistry,' p. 295.)
Kolbe's joint work with Frankland
was of the greatest importance to
science. The influence of Kolbe
was also largely of a polemical
nature, inasmuch as he and some
others, notably F. Mohr (whose
name will have to be mentioned in
a later chapter), protested energeti-
cally against the formal character
of much of the writings and work
produced by the French school
which opposed the views of Ber-
zelius. This school, of which
Dumas, Laurent, and Gerhardt
were the founders, and which
exerted a very marked and beneficial
influence through the teaching and
the finished literary productions of

Wurtz (1817-84), was closely allied
with the school of Kekule in Ger-
many, who indeed began by logi-
cally developing Gerhardt's ideas,
being afterwards led to special views
and methods of his own, through
which he became the real founder
of the so-called structural formulae, \
and of the doctrine of the linking
of atoms. I must here especially
record my indebtedness to the ad-
mirable historical essays of Wurtz
('Theorie atomique,' T""* ed., 1893,
and ' History of Chemical Theory,'
transl. by Watts). For clearness
and elegance of style, they are
quite as marked as are Kopp's
historical works for breadth, im-
partiality, and philosophical in-
sight.

^ The adherents of the theory of
substitution and types, sometimes
called the "modern," also the
" French," school, urged against
the followers of Berzelius, which
adhered to the "electro-chemical"
or "radicle" view, that since an
electro - positive element could be
replaced by a contrary one, there
was no sense in upholding the
polar difference. They pointed out
that organic substances M'ere not
electrolytic ; and they criticised the
artificial invention and multiplica-
tion of new radicles which had no
real existence, as arbitrary. On
the other side, the followers of
Berzelius objected to the entire
ignoring by the new school of
the really existing electro-chemi-
cal differences, and reproved them
for having destroyed the connec-
tion between organic and inorganic
chemistry, and for having intro-
duced a purely formal systematisa-
tion according to merely external
differences. They rightly upheld

414

SCIENTIFIC THOUGHT.

the " atomicity " or " valency " of chemical substances —
be they elements or compounds. This most recent de-
velopment of chemical systematisation originated in Eng-
land/ whereas the " radicle " theory belonged more to the

the view that an understanding of
chemical reactions must ultimately
depend upon a study of the nature
and degree of chemical affinity, and
maintained that so far the connec-
tion of chemical with electrolj'tic
phenomena afforded the only clue
to the compreliension of the nature
of chemical affinity. The atomic
theory had now absorbed all in-
terest, to the detriment of a physi-
cal theory of chemical affinity such
as Berthollet had attempted. it
was held that by ignoring the
electro - chemical differences, the
" modern " school lost the only re-
maining chance of explaining, and
not merely classifying, chemical phe-
nomena. A good exposition of the
latter argument will be found in
A. Rau, ' Die Theorien der moder-
uen Chemie.'

^ The number is small of the Eng-
lish names whicli about the middle
of this century figured prominently
in the discussions by which, in the
German and French annals of
science, correcter views on the con-
stitution of chemical compounds
were gradually elaborated. Kane's
work was overlooked, but William-
son, Odling, and Frankland have
had a vei'y marked influence ; and,
as in so many other sciences, pioneer
work in modern chemistry was done
in this country, notablj^ by Frank-
land. Liebig, after his visit to
England in 1837, wrote to Wohler :
" I have traversed England, Ireland,
and Scotland in all directions, have
seen much that is astonishing, but
have learnt little : whence is scien-
tific knowledge to come in England,
as the teachers are so inferior ?
Among older men, Thomson is still
the best ; among younger men,

Graham : modest and
he makes the most beautiful dis-
coveries. Nevertheless, a splendid
nation," &c., &c. ('Liebig's und
Wohler's Briefwechsel,' vol. i. p.
113.) From what I stated above
(chapter iii. p. 296, &c.),weare, how-
ever, quite prepared to find that
the idea which more than any
other has brought some order and
system into modern chemical theory,
and which has united the diverg-
ing currents of the foreign schools,
has come from England. Frank-
land more than any other ralist
be^l'ooked upon as the origina-
tor of the modern theory of the
atomicity or valency of chemical
elements and compounds. The
history of this conception can be
well studied in the collection of
scientific papers which he published
with valuable introductions in 1877
(' Experimental Reseai'ches in Pure,
AjDplied, and Physical Cliemistry,'
London, van Voorst). His re-
searches commenced in those years
when great confusion existed in or-
ganic chemistry, "when the wildest
theories of the constitution of or-
ganic compounds created but little
surprise ; the assertion, for instance,
that an atom of carbon was united
with four atoms of hj'drogen and
two of chlorine would scarcely have
been considered intrinsically impro-
bable, and certainly not impossible"
{loc. cit., p. 26). Tlie idea existed
that bodies could enterinto combina-
tion with other bodies, notably or-
ganic radicles, and could still retain
in such combination tlieir oi-iginal
affinities unimpaired ; a new term,
that of "conjugate," "copulated,"
or "paired" compounds, had been
invented and adopted by Berzelius.

THE ATOMIC VIEW OF NATURE.

415

German, and the " type " theory to the French, school of
chemists. But the idea of the " atomicity" and " valency"
or saturating capacity of the element of any substance was
not possible without the clear notion of the " molecule "
as distinct from the " atom." This idea had lain dormant
in the now celebrated but long forgotten law of Avogadro,
which was established in the year 1811, almost immedi-
ately after the appearance of Dalton's atomic theory.

The atomic theory may be regarded in two distinct 22.

Two aspects

ways, and it is instructive from the point of view of the oft'i?

'' ■*- atomic

history of thought to see how these two different aspects t'^^ory.
of the theory have gradually presented themselves. The
older and vague atomic theory professed to be a theory of
the constitution of bodies, and to afford the basis for an
explanation of physical phenomena ; in order to do this,
forces of attraction and repulsion between the particles of

It appears that this theory was
largely based upon a compound
prepared by Buusen, and called
" cacodyl." This compound was one
of the few organic radicles which
contained a metal — arsenic. Frank-
land, partly alone, partly in union
with Kolbe, entered upon a series
of researches which had two distinct
objects. Both these objects were
foreign to that school which had
given up the radicle theory, and
which, by looking upon organic
compounds as essentially different
from inorganic compounds, had lost
that important clue — the connec-
tion of the two branches of chemis-
try. These objects were the isola-
tion of the so-called radicles or
compound elements and the pre-
paration of other " organo- metal-
lic " bodies. The latter research
led to new insight into the nature
jf chemical combinations. " I had

not proceeded far," says Frankland,
" in the investigation of the organo-
metallic compounds before the facts
brought to light began to impress
upon me the existence of a fixity in
the maximum combining value or
capacity of saturation in the metal-
lic elements which had not before
been suspected. ... It was evi-
dent that the atoms of zinc, tin,
arsenic, antimony, &c., had only
room, so to speak, for the attach-
ment of a fixed and definite number
of the atoms of other elements, or,
as I should now express it, of the
bonds of other elements. This
hypothesis, which was communi-
cated to the Royal Society on May
10, 1852, constitutes the basis of
what has since been called the doc-
trine of atomicity or equivalence of
elements ; and it was, so far as I
am aware, the first announcement
of that doctrine" (ibid., p. 145).

416

SCIENTIFIC THOUGHT.

matter had to be assumed, and elaborate calculations as to
the integral or resultant effect of these elementary forces
had to be instituted, or at least formulated. An interest-
ing and typical case of these attempts was the theory of
Boscovich, referred to in the last chapter.^ In looking
back on the history of science, it can now be safely stated
that, ingenious as those theories were, they led to no re-
sults in the direction of the calculation of the molar and
molecular properties of bodies, or if they did, they yielded
none which could not be gained by the opposite view which
regarded matter as continuous. The atomic theory, how-
ever, did good service from another point of view, when
through Eichter, Dalton, Proust, and Berzelius the fact
that bodies combine only in definite proportions of weight,
or their simple multiples, became firmly established. The
authors of this discovery were driven to the atomic view

^ See also Berthollet, ' Statique
chimique,' 1803, vol. i. : " Les
puissances qui produisent les phen-
omenes cliimiques sont toutes deri-
vees de I'attraction mutuelle des
molecules des corps, k laquelle on a
donne le nom d'affinite, pour la
distiuguer de I'attraction astrono-
mique. II est probable que I'une
et I'autre ne sont qu'une meine
propriete " (p. 1). " II y a des
sciences qui peuvent parvenir h, un
certain degre de perfection sans le
secours d'aucune tlieorie, et seule-
ment par le moyen d'un ordre ar-
bitraire qu'on etablit entre les obser-
vations des faits uaturels, dout elles
s'occupent principalement ; mais
il n'en est pas le meme en chimie,
oil les observations doivent naitre
presque tou jours de I'experience
meme et oil les faits resultent de la
reunion factice des circonstances qui
doivent les produire. Pour tenter
les experiences, il faut avoir un but,

etre guide par une hypothese . . .
ainsi les suppositions plus ou moins
illusoires et meme des chimeres qui
sont aujourd'hui ridicules, mais qui
ont engage aux tentatives les plus
laborieuses, ont dte necessaires, au
berceau de la chimie. Par leur
moyen les faits se sont multiplife,
un grand nombre de proprietds
a et6 constate, et plusieurs arts
se sont perfectiounds " (p. 4).
" Si les proprietes chimiques des
differentes substances sont dues a
leur affinite et h leurs dispositions
particulieres, celles des combin-
aisons qu'elles forment dependent
de la saturation respective, des
changements de constitution qui
sont dus a Taction reciproque, du
degrd de la force qui maintient la
combinaison ; ainsi les proprietes
des substances simples sont non
seulement la cause des combinaisons,
mais encore celle de leurs propres
affections" (vol. ii. p. 552).

THE ATOMIC VIEW OF NATUKE.

417

of matter as the most convenient method of expressing the
formnlre of chemical compounds. Ever since that time 23.

A conveni-

the atomic view has served as a kind of symbolism by fit sym-

J J bolism.

which different chemical elements could be characterised,
their compounds described, and the actual weights prac-
tically calculated. And here we must note the reserve
with which some of the greatest representatives of
chemical science expressed themselves up to the middle
of the century regarding the actual physical existence of
those elementary particles with which they operated so
freely in their formulae, and which they even represented
by balls and coloured discs in their demonstrations.
Wollaston, one of the first who accepted Dalton's ^ views

^ Dalton does not seem to have
been troubled by any philosophical
doubts or by the anticiimtion of
the mathematical difficulties which
would stand in the way of a con-
sistent development of the atomic
view. He was led to formulate and
employ his atomic theory bj' ponder-
ing over the most convenient man-
ner in which certain chemical facts
— the facts of definite and multiple
jiroportions — and certain phj-sical
discoveries — the separate existence
of aqueous vapour from the other
constituents of the air — could be
represented, and he adopted the
view suggested by Newton in his
' Queries,' " that matter was formed
in solid, massy, hard, impenetrable,
movable particles " (see Sir H.
Roscoe, ' John Dalton,' Century
Series, p. 128, &c.) Wollaston and
Davy were much more cautious :
the former foresaw the complicated
and far-reaching mathematical pro-
blems which were involved in the
atomic view, the latter thought
the generalisation premature. His
labours had been largely in the
direction of showing that bodies

VOL. I.

which had been looked upon as
elementary were compound, and
he "doubts whether we have yet
obtained elements" (ibid., p. 155).
Even as late as 1826, in his award
to Dalton of the Royal Medal, he
speaks of his " Development of the
Chemical Theory of Definite Pro-
portions, u&ually called the Atomic
Theory," he emphasises its practical
usefulness, " making the statics of
chemistry depend upon simple
questions in subtraction or multi-
plication, and enabling the student
to deduce an immense number of
facts from a few well authenticated,
accurate, experimental results." He
refers to "Wollaston's table of equi-
valents, which " separates the prac-
tical part of the doctrine from the
atomical or hypothetical part." It
has, in fact, been maintained that
the hesitancy which Wollaston dis-
played on this subject deprived him
of his well-deserved share of the
glory which the introduction of the
atomic view of matter has shed
upon Dalton and Berzelius. (See
Peacock, ' Life of Dr Young,' p.
469.)

2 D

418

SCIP]NTIFIC THOUGHT.

as to fixed and multiple proportions, expressed himself
with great reserve as to the value of the atomic hypothesis,
and when drawing up a table of atomic weights, he pre-
ferred to call them equivalents — a term used already by
Cavendish — as implying no other meaning than that they
fix the proportions in which bodies combine into, or sep-
arate out of, compounds. Davy was hesitating and re-
luctant to admit any hypothesis as to the ultimate con-
stitution of matter. Liebig ^ and Faraday,^ at a somewhat

^ " In endeavouring to develop
the theory ^\■hich at present pre-
vails respecting the cause of the
unchangeableuess of chemical pro-
portions, let it not be forgotten
that its truth or falsehood has
nothing whatever to do with the
natural law itself. The latter is
the expression of universal experi-
ence ; it remains true, invariably
and immutably, however our no-
tions respecting its cause may from
time to time vary and change."
Thus wrote Liebig (' Familiar Let-
ters on Chemistry,' 1844) at a time
when great confusion existed as to
the real atomic or smallest com-
bining weights which should be
assigned to the chemical elements ;
when in consequence many chemists
preferred to discard the word
"atomic weight" altogether, and to
revert to the term equivalent (see
Kopp, ' Entwickelung der Chemie,'
p. 718, &c.) Dumas in 1840 de-
clared that the teini atomic weight
did not deserve the confidence with
which chemists made use of it : if
he could he would banish the word
atom from chemistry, convinced as
he was that science should not
transgress the limit of that which
could be known by experience.
Liebig, in 1839, about the time
when his important memoirs on the
constitution of organic bases and
acids appeared in his ' Annals,' em-

phasised likewise the fact that
equivalents never change ; but he
doubted whether chemists would
ever agree as to the relative atomic
weights, and he hoped the time was
not far distant when they would
all return again to equivalents
(ibid., p. 438). In France an in-
fluential school, headed bj' the
eminent M. Berthelot, up to the
present day limits itself to the use
of equivalents. See Berthelot, ' La
Synthese chimique,' 7'"" ed., p.
164 n.

^ The objections which Faraday
urged against the notion of atom
and atomic weight seem to come
from a different quarter. In 1834,
when explaining his researches on
electro - chemical action, he saj's
('Exper. Res.,' No. 869): "If we
adopt the atomic theory or jahrase-
ology, then the atoms of bodies
which are equivalents to each other
in their ordinary chemical action
have equal quantities of electricity
naturally associated with them.
But I must confess I am jealous of
the term atom; for though it is
very easy to talk of atoms, it is
very difficult to form a clear idea
of their nature, especial!}- when
compound bodies are under consid-
eration." Ten years later, in his
' Speculation touching Conduction
and the Nature of Matter ' (see
'Exper. Res.,' voh ii. p. 285),

THE ATOMIC VIEW OF NATURE.

419

later date, appeared similarly averse to admit the physical
existence of atoms in the older sense, and warned chemists
against the introduction of unnecessary and unproven
hypotheses. Even Gerhard t, as late as 1856, opposed
the idea that chemical formulae could express the actual
constitution of substances : they were merely a convenient
symbolism, a kind of alphabet, by which reactions between
different elements or compounds could be conveniently
described, and the proportional weights of the constituents
or the products could be ascertained.^ Accordingly, it was
also maintained that formulae could be written in very
different ways, expressive of the different processes and
reactions which had in special cases to be considered.^

Although, therefore, chemical research was governed all
through the century by the atomic view of matter, it does

he says: "The word atom, which
can never be used without involving
much that is purely hypothetical,
IS often intended to be used to
express a simple fact. . . . There
can be no doubt that the words
definite proportions, equivalents,
primes, &c., which did and do ex-
press fully all the facts of what is
usually called the atomic theory in
chemistry, were dismissed because
they were not expressive enough,
and did not say all that was in the
mind of him who used the word
atom in their stead ; they did not
express the hypothesis as well as
the fact." He then enlarges on the
necessity of the atomic view, and
expresses his preference for the form
wliich Boscovich had given to it over
" the more usual notion," as accord-
ing to the latter " matter consists
of atoms and intervening space,"
whilst with the former " matter is
everywhere present, and there is no
intervening space unoccupied by it "

(ibid., pp. 290, 291). It is evidently
the objection to action at a dis-
tance, uncommunicated action,
which is implied in the ordinary
atomic view of matter, that makes
Faraday jealous of the term atom.
This objection was quite foreign
to the chemists abroad who in the
middle of the centurj' elaborated
the atomic view of matter and na-
ture ; it belongs to a different direc-
tion of thought, which will occupj-
us in a later chapter.

^ In his ' Traite de Chimie or-
ganique,' which he brought out as
a continuation of the French edi-
tion of Berzelius's ' Treatise of In-
organic Chemistry ' in the years
185-3 to 1856. See Kopp, ' Ent-
wickelung der Chemie,' pp. 747,
796, 800,'" 809, 819, 834.

" Even the combining weight
or equivalent of an element, that
datum upon which — since Kichter
and Dalton — the whole sj'stem of
chemistry has been built up, was

420

SCIENTIFIC THOUGHT.

24.

Neglect of
the study
of affinity.

not appear that philosophers considered the existence and
nsefuhiess of chemical formulas as a proof of the physical
existence of atoms, or of smallest indivisible particles of
matter, in the older sense of the theory. Hand in hand
with this purely formal and experimental treatment of
chemical phenomena went the almost absolute neglect
with which questions referring to chemical affinity were
treated. The word was little more than a name for an
unknown something.

How it came to pass that substances had more or less
affinity for each other, what was meant by a chemical
compound, symbolically expressed by writing two or more
letters, near or above each other, in a square or in a circle,
united by parentheses or brackets, did not seem to trouble
chemical philosophers at all. To compare the problem of
chemistry with that of astronomy, the former for a great
part of our century resembled that phase of astronomical
knowledge in which stellar maps and catalogues, plans of
orbits and orreries, were considered sufficient, giving a pic-
ture of a certain constellation of the heavenly bodies, but
no idea of how these configurations were maintained and
altered. In fact, chemistry was for a long time a science
purely of numbers, to which was attached a natural his-
tory of the substances to which these numbers belonged.
The geometrical arrangement of the formulas was usually
looked upon as only symbolical : of the dynamical changes
which take place in time, and imply the knowledge of

considered to be represented by
more than one number in in-
stances where the same metal had
several basic or acid oxides, as in
the case of nitrogen and phosphorus
(ibid., p. 805). Laurent in ' Comptes

Rendus,' 1844, vol. xix. p. 1099, says :
" Le meme corps simple se presente
tantot avec certaines proprietds,
tantot avec d'autres, il entre dans
les corps composes, tantot avec un
certain poids, tantot avec un autre."

THE ATOMIC VIEW OF NATURE.

421

25.
Kopp on

forces or movements, few took any notice whatever. In
spite of the enormous accumulation of well - arranged
knowledge, and the marvellous practical achievements of
chemistry, the foremost historian of that science could,
as late as 1873, write as follows : " No theory has as yet
been formed in chemistry which, starting from a definite tJjg"^y^^
principle, attempts to deduce the results of experience as ^^''^•
necessary consequences. The doctrines which have been
termed in chemistry theoretical are still only such as per-
mit us to bring connection into the results which practical
chemistry has gained in special directions ; or to form a
picture how we might think of them as mutually related."'^

^ Kopp, ' Eutwickelung der Clie-
mie,' 1873, p. 844. A generation
earlier Dumas had written (' Comp-
tes Rendus,' vol. x., 1840, pp.
171, 176, 178) : "Dans les vues de
relectrochimie la nature de leurs
particules elementaires doit deter-
miner les proprietes fondamentales
des corps, tandis que dans la theorie
des substitutions, c'est de la situa-
tion de ces particules, que les pro-
prietes derivent surtout. ... La
theorie des types . . . explique ce
que la loi des substitutions se con-
tente de preciser. Elle envisage
les corps organiques com me etant
formes des particules, qui peuvent
etre deplacees et remplacees, sans
que le corps soit detruit, pour ainsi
dire. . . . Voilh, done en presence
deux systemes : I'un qui attribue
le role principal h- la nature des ele-
ments, I'autre qui la reserve pour
le nombre et I'arrangement des
equivalents. Pousse a I'extreme
chacun d'eux . . . se trouverait
conduire k I'absurde." In 1861
Kekule, in his ' Lehrbuch der or-
ganischen Chemie ' (vol. i. p. 95),
declares that, " besides the laws of
fixed and multiple proportions of
weight (and in gaseous bodies also

of volume), chemistry had as yet
discovered no exact laws, . . . and
all so-called theoretical conceptions
were merely points of view which
possessed probability or conveni-
ence." And Wurtz ('La Theorie
atomique,' 1863) speaks of the
atomic hypothesis in terms which
might lead one to think we were on
the eve of an entirely different con-
ception of the phenomena of nature :
"Nous retiendrons I'hypothese aussi
longtemps qu'elle permettra d'inter-
preter fidelement les faits ; de les
grouper, de les relier entre eux et
d'en prevoir de nouveaux, aussi
longtemps, en un mot, qu'elle se
montrera feconde" (p. 2). "Les
considerations sur la valeur de com-
binaison des elements survivraient
a I'hypothese des atonies si celle-ci
venal t ti etre remplacee un jour
par une hj'pothese plus geut^rale.
Mais ce jour n'est pas arrive ; c'est
vainement qu'on chercherait h. dis-
crediter la premiere aussi longtemps
qu'elle se montrera feconde. Et sa
fecondite, sa puissance eclatent dans
les progr5s incessants de la science.
C'est elle qui vivifie les decouvertes
les plus recentes, comme elle a et^
depuis Dalton son immortel auteur,

422

SCIENTIFIC THOUGHT.

26.
The periodic
law.

This statement implies that even as late as the end of the
third quarter of the century, foremost thinkers hesitated to
attach a more than provisional importance to chemical sym-
bolism and the various elaborations of the atomic theory,
as chemical text- books then exhibited them. Similar
merely provisional theories have existed in other branches
of science. The theory of the two fluids in electricity
did good service for a long time in enabling philosophers
to define their ideas, to describe, calculate, and predict
phenomena. In optics, the so-called corpuscular theory
of light is still used with advantage as a convenient
means of summarising the laws of reflexion and re-
fraction ; similarly, in treatises on the conduction of heat,
the old caloric theory still holds a place alongside of the
more modern dynamical views. It may be questioned
whether the celebrated periodic law of Newlands, Lothar
Meyer, and Mendel^eff, which has brought some order
into the atomic and other numbers referring to the dif-
ferent elements, and has even made it possible to predict
the existence of unknown elements with definite pro-
perties, stands really in a firmer position than the once
well-known but now forgotten law of Bode,'^ according to

I'instrument le plus parfait pour
les conceptions elevees de la th^orie
et le guide le plus sur pour les
reclierchesexp(5rimentales" (p. 241).
And quite mournfully doesKopp re-
port at the close of his historical sur-
vey of the development of chemistry
( ' Entwickelutig,' &c.,p.829 ) ho w that
science about I860 again "turned
into the course which it had tried so
often, and had so often abandoned
as hopeless, endeavouring to gain
a knowledge liow the elementary
atoms are arranged in the smallest
particles of their compounds."

^ According to the relation, first
observed by Christian AVolfF and
Daniel Titiua, that the distances of
the planets from the sun obey ap-
proximately the formula 0 "4 4-0 "3
X 2", where n for Venus, Eai-tli,
Mars, &c., assumes the values 0, 1, 2,
&c., the planet corresponding to
n = 3 was missing. When, on the
discovery of Uranus in 1781, it was
found that this planet's distance
also agrees approximately with the
formula, Bode and von Zach drew
attention to this fact, and suggested
a systematic search for the missing

THE ATOMIC VIEW OF NATURE.

423

which the gap in the series which gives the distances
of the planets from the sun indicated the existence of a

planet, " a chercher uiie aiguille dans
une botte de foin." About the
same time that this search was
contemplated Piazzi found the first
of the small planets, which — like
the other subsequentlj' discovered
asteroids — corresponds very nearly
with the expected position in the
system. The periodic system of
the elements, according to which
the physical and chemical pro-
perties of all the elements show
a periodic dependence upon the
atomic weights, was first system-
atically stated by Newlands (in
1864) and by Lothar Meyer and
Mendeleefi on the Continent. The
latest edition of Meyer's treatise on
"Modern Theories of Chemistry," of
which only the first part, with the
title ' Die Atome und ihre Eigen-
schafteu ' has been published (post-
humously by the author's brother,
Breslau, 1896), gives a good idea of
how from small beginnings these
statistics of the atomic theory of
matter have grown into a great
accumulation of interestmg facts,
upon which a system of inorganic
chemistry can now be based which
compares with the system of or-
ganic chemistry founded upon the
types of Gerhardt in their orig-
inal or in some modified form,
and upon the "homologous" series
of hydrocarbon compounds. As
the typical arrangement of organic
compounds, or rather of carbon
compounds (for many real organic
compounds are not easily classed
by these methods), led to the sug-
gestion of the existence of many
compounds which were not known
at the time, and have since been
prepared, so the periodic arrange-
ment enabled Mendeleefi' to predict
the properties of missing numbers
of the periodic series. And al-
though this mapping out of the

elements according to their atomic
weights does not indicate how and
where the missing numbers are to
be found, as is the case with the
law of Titius and Bode, and still
more so with the homologous series
of carbon compounds, still it is
interesting to be able to state that
in several instances — notably on
the discovery of the new elements,
gallium (by Lecoq de Boisbaudran
in 1878), scandium (by Nilson in
1880), and germanium (by Winkler
in 1886) — the properties of these
substances confirmed to a very
great extent the predictions of
Mendeleeff. And when in 1894
Lord Rayleigh and Professor Ram-
say announced their discovery of a
new element in atmospheric air,
which, from its inertness, was
called argon, interesting sugges-
tions as to its properties were
drawn from speculations regarding
its probable position in the periodic
curve (see Lothar Meyer, loc. cit.,
p. 165). It is true that these
numerical regularities, which for
some minds possess a great fascina-
tion, are, so far, purely statistical.
It is possible to arrive by inter-
polation or extrapolation at valu-
able suggestions in statistics, in
meteorology, and in mining opera-
tions ; but so long as the actual
cause or intrinsic connection is not
known, which explains the neces-
sity of these regularities, they are
apt to be misleading, and have to
be used with great caution. Still,
the fact alone that they bring some
order into a bewildering mass of
figures and data makes them al-
most indispensable. For similar
reasons manj' chemists adopted
Gerhardt's types and homologous
series as affording a ready method
of classification, though not a ra-
tional explanation of phenomena.

424

SCIENTIFIC THOUGHT.

27.
Difference

between
chemical

reasoning.

planet between ]\Iars and Jupiter, anticipating the dis-
covery of the Asteroids, which have accordingly been
regarded as the fragments of the missing planet.

It tlius appears that purely " chemical reasoning," as it
has been called, has proved insufficient to establish the
vI"iJ?n'rJ°^' atomic view of nature on the same firm basis as has
supported the mechanical or astronomical view ever since
the age of Galileo and Newton.^ In the second half of
the century, the atomic view of matter has however
been put forward from a different side, and independent
researches have, in combination with the older chemical
theories, introduced so much definiteness into this line
of thought that " the Newtonian theory of gravitation is

^ "Many diagrams and models
of compound molecules have been
constructed. These are the re-
cords of the efforts of chemists to
imagine configui'ations of material
systems by the geometrical rela-
tions of which chemical phenomena
may be illustrated or explained.
No chemist, however, professes to
see in these diagrams anything
more than symbolic representations
of the various degrees of closeness
with which the different com-
ponents of the molecule are bound
together. In astronomy, on the
other hand, the configurations and
motions of the heavenly bodies are
on such a scale that we can ascer-
tain them by direct observation ;
. . . the doctrine of universal gravi-
tation not onlj- explains the ob-
served motions of our system, but
enables us to calculate the motions
of the system in which the astro-
nomical elements may have any ,
values whatever" (Clerk Maxwell, ;
" On the Dynamical Evidence I
of the Molecular Constitution of
Bodies," June 1875, 'Scientific
Papers,' vol. ii. p. 418). "The

chemists ascertain by experiment
the ratios of the masses of the
different substances in a compound.
From these they deduce the chemi-
cal equivalents of the different sub-
stances, that of a particular sub-
stance being taken as unity. The
only evidence made use of is that
furnished by chemical combination.
It is also assumed, in order to ac-
count for the facts of combination,
that the reason why substances
combine in definite ratios is, that
the molecules of the substances
are in the ratio of their chemical
equivalents, and that what we call
combination is an action which
takes place by a union of a mole-
cule of one substance to a molecule
of the other. This kind of reason-
ing, when presented in a proper
form, and sustained by proper evi-
dence, has a high degree of cogency.
But it is purely chemical reasoning ;
it is not dynamical reasoning. It
is founded on chemical experience,
not on the laws of motion " (Id.
article "Atom," 'Ency. Brit.,' 1875;
ibid., vol. ii. jj. 456).

THE ATOMIC VIEW OF NATURE.

425

not surer to us now than is the atomic or molecular
theory in chemistry and physics — so far, at all events, as
its assertion of heterogeneousness in the minute structure
of matter, apparently homogeneous to our senses, and to
our most delicate direct instrumental tests." ^

This side of the atomic view of matter has been de- 28.

Tlie kinetic

veloped by the study of the properties of bodies in the tiieory of
gaseous state, and, in its modern form, goes back to the
experiments of Gay-Lussac, which were almost simul-
taneous with those of Dalton.^ It is interesting to note
how little the latter recognised the importance of these
researches, when he rejected the so-called law of volumes,
according to which gases, under the same pressure, and
at equal temperatures, enter into, or separate out of,
chemical combination in definite and very simple pro-
portions of their volume. As, according to the law of
definite proportions, bodies (including gases) combine only

1 Lord Kelviu on " Capillar}' At-
traction," 1886. See 'Popular Lec-
tures and Addresses,' vol. i. p. 4.

■^ The first results referring to
the combining volumes of oxygen
and hydrogen gas in forming water
were given by Gay - Lussac and
Humboldt in a joint memoir. Their
experiments were carried on in
1805. Gay-Lussac continued the ex-
periments alone, extended tliem to
gaseous compounds, and published
his results in 1809 in the second
volume of the ' Memoires d'Arcueil.'
This was one year after the publi-
cation of Dalton's ' New System
of Chemical Philosophy,' and two
years after Thomas Thomson had
published a sketch of the atomic
theory in his text- book on Chem-
istry. The law of equal expansion
of all gases with temperature was
published by Dalton in 1801 ; the

law of pressures — that the volume
of a gas, at the same temperature,
is inversely as the pressure — was
jjublished by Boyle in 1662. It
goes on the Continent under the
name of Mariotte, who first made
it generally known about twelve
years later (see on this the fourth
appendix to the 2nd edition of
Tait's ' Properties of Matter,' 1890).
The law of temperatures was pub-
lished in 1802 by Gay-Lussac in
the ' Annales de Chimie et de Phys-
ique ' (vol. xliii. p. 137), where he
remarks that Charles, Professor of
Physics at the " Conservatoire," had
fifteen years earlier noted the prop-
erty indicated by this law. Both
these so-called laws of gases are
only accurate within certain not
very wide limits of temperature and
pressure.

426

.SCIENTIFIC THOUGHT.

according to definite proportions of their weight, it follows
that in the gaseous state these combining weights of bodies
have either equal volumes or such as stand in very simple
proportions. Now the amount of matter (measured by
weight) in the same volume is called the density of a gas.
It therefore follows, by putting Dalton's and Gay-Lussac's
discoveries together, that the combining weights of gases
are either directly proportional to their densities or to a
simple multiple thereof. Some years after this discovery
in 1809, Gay-Lussac extended his statement so as not
only to embrace elementary gases, such as hydrogen,
oxygen, and nitrogen, but also compounds, such as am-
monia, carbonic acid, hydrochloric acid, and showed how,
if they enter into chemical combination, they likewise do
so in the simple proportions of one volume of one, to one
or two volumes of the other.

Whilst chemists such as Gay-Lussac, Berzelius, and
others ^ recognised in the facts discovered by the first a

^ Dalton was the only person who
doubted the correctness of Gay-
Lussac's figures, although both
Thomson and Berzelius pointed out
to him tlie great support they
afforded to the atomic theory.
Berzelius also saw the usefulness
of the law of volumes in fixing the
smallest combining or atomic uum-
beis in cases where the reference to
weight alone left the matter unde-
cided. Thus he correctly inferred
that the formula of water should
be HoO, as we write it to-day, be-
cause two volumes of hj'drogen
combined with one of oxygen. But
it was unfortunate that, through
his want of appreciation of Avo-
gadro's further expositions, he was
unable to reconcile more completelj'
the appeal to volume with that to

weight, and that in consequence
great uncei'tainty reigned for a long
time in these matters. This in-
duced L. Gmelin to disregard the
volumetric relations in his system
of equivalents, to the great detri-
ment of those who in the middle of
the century were brought up with
very vague and unsatisfactorj' ex-
planations on this subject — differ-
ent numbers being used in books
on organic and inorganic chemistry.
A great confusion existed at that
time. Gerhardt showing good rea-
sons, based upon his observations of
the substitution of hydrogen in or-
ganic compounds and the system of
classification which he introduced,
why several of Gmelin's figures
should be doubled ; but the matter
was not cleared up till Cannizzaro

THE ATOMIC VIEW OF NATURE.

427

method for determining the combining weights of elements
or their simple multiples, they did not draw the natural
consequences as to the physical constitution of bodies in
the gaseous state which followed from these and other
facts which had been known before. It had been known
since the time of Boyle and Mariotte that equal volumes of
different gases under equal pressure change their volumes
equally if the pressure is varied equally, and it was also
known through Gay-Lussac himself that equal volumes of
different gases under equal pressure change their volumes
equally with equal rise of temperature. The like be- 29.

^ "^ Avogadro's

haviour of equal volumes of different gases towards pres- hypothesis,
sure, temperature, and chemical combination suggested
to Avogadro, and almost simultaneously to Ampere, the
very simple assumption that this is owing to the fact that
equal volumes of different gases contain an equal num-
ber of smallest independent particles of matter. This is
Avogadro's celebrated hypothesis. It was the first step in
the direct physical verification of the atomic view of mat-
ter, and if maintained by further experience, it was des-
tined to be one of the most important proofs of this view.
But this assumption or hypothesis had to be reconciled
with facts. It was, for instance, observed that a given
quantity of hydrochloric acid gas occupied the same

showed the real meaning and im-
portance of Avogadro's hj'pothesis.
A good exposition of the difference
of opinions which were held at that
time will be found in A. Wurtz,
' La Theorie atomique,' p. 55, &c.
See also Prof. Bedson's ' Memorial
Lecture' on Lothar Meyer (1896),
in tlie ' Journal of the Chemical
Society,' p. 519, &c. , and especi-

ally the graphic description by L.
Meyer himself of the meeting held
in September 1860 at Carlsruhe
for the purpose of ventilating these
important theoretical questions (L.
Meyer's translation of Canuizzaro's
' Sunto di un corso di filosofia
chimica,' in Ostwald's ' Classiker
der exacten Wissenschaften,' No.
30, Appendix, p. 58).

428

SCIENTIFIC THOUGHT.

volume as did each of the equivalent quantities, hydrogen
and chlorine, out of which it was compounded, and it
appeared that accordingly double the number of atoms
were condensed into the same volume. To explain this,
and yet maintain his original hypothesis, Avogadro was
forced into the conception of compound atoms or particles
— i.e., into the assumption that the smallest independent
particles need not be the elementary atoms of hydrogen
and chlorine themselves, but might be made up of two
or more of such atoms, chemically connected in such
a way that the expansion of the gas under increasing
temperature or decreasing pressure did not affect this
complex of elementary particles/ Such a compound

^ Avogadro published his memoir
ill the ' Journal de Physique ' in
1811, and Ampere expounded simi-
lar views three j'ears later in the
form of a letter to Berthollet in the
' Annales de Chimie.' Neithei- the
celebrity of Ampere nor the ex-
haustive explanations of Avogadro,
who was then an unknown author,
prevented this hypothesis, which
is now looked upon as a corner-
stone of the atomic view, from
falling into oblivion. Whewell
does not mention it. Even Kopp,
whose labours for many years
covered a field little cultivated by
most other chemists, that of physi-
cal chemistry, makes no mention
of Avogadro's and Ampere's hypo-
thesis in his gi-eat work on the
History of Chemistry, published
between the years 1843 and 18i7.
In his later work ('DieEntwickelung
der Chemie,' 1873) he enters ela-
borately into the causes which made
chemical philosophers overlook so
valuable a suggestion (p. 353, &c.)
Like Whewell's Historj', Poggen-
dorf's Dictionary (1863) was sil-
ent about Avogadro. The distinc-

tion between molecules and atoms
seemed to complicate matters ; be-
sides^ the new hypothesis was not
launched in conjunction with any
new experimental discoveries, as
had been the case with Dalton's,
Davy's, and Gay-Lussac's theories.
The first who again drew attention
to the subject was Dumas, who in
1826 began his investigations re-
garding the specific weight of
vapours — i.e., of bodies in a gaseous
state. He there drew attention to
the necessity of distinguishing be-
tween chemical and physical par-
ticles, but he does not yet con-
sistently use the terms atom and
molecule to denote the former and
the latter. In the meantime, how-
ever, a very important step had
been taken in the development of
the atomic view. lnlS19Dulongand
Petit published their experimental
researches concerning the specific
heat of a large number of element-
ary bodies — «.e., the measured quan-
tities of heat (compared with a
standard substance) which were
required to raise a number of
metals by one degree in tempera-

THE ATOMIC VIEW OF NATURE.

429

atom or complex was termed a molecule, and it was
assumed that molecules, or smallest individual particles
of chemical substances, might be made up of one or more
atoms of the same or of different substances. Avogadro
was able in this way to explain how a certain number of
molecules of hydrogen — each made up of two atoms —
combine with an equal number of molecules of chlorine ;
these being likewise composed of two atoms of chorine,
in order to form an equal number of molecules of hydro-
chloric acid, each of these consisting of two atoms — viz.,
one of chlorine and one of hydrogen. This view, which so.

, 11 1 1 T 1 Neglect of

Ampere likewise adopted, did not recommend itself to same.
chemists for many years ; not indeed till, about the year
1840, several eminent chemists — notably Laurent — were
independently led to consider chemical compounds as
formed by what is termed substitution instead of simple
combination.^ For, according to Avogadro's view, the for-

ture. They then found that these
quantities stood very nearly in in-
verse proportions to the atomic or
combining numbers. They at the
same time pointed out the un-
certainty which — in consequence
of the law of fixed multiple pro-
portions — existed regarding the
smallest figure which was to deter-
mine the combining weights ; they
chose those numbers which brought
out clearly the physical regularity
and coincidence which they had dis-
covered ; and they expressed their
result in the rule that the atoms of
all elementary bodies have the same
capacity for heat. Whereas Ber-
zelius ignored the theoretical dis-
cussions of Avogadro and Ampere,
he hailed the experimental data
of Dulong and Petit as most useful
in helping to fix correctly the real
equivalent numbers, a task to which,

as the fundamental requisite of all
chemistry, he devoted so much time
and labour. It must, however, be
noted that the law of Dulong and
Petit, now uuiversall}' accepted as
a fundamental fact in the atomic
theory, is, as little as the laws of
Boyle, Charles, and Gay - Lussac,
rigidly correct : it obtains within
certain limits. The experiments
of Dulong and Petit were extended
to compounds by F. Neumann in
1831. The connection of the specific
heat or thermal capacity of com-
pounds and that of their con-
stituents was fully investigated by
Regnault. A statement of the diffi-
culties and anomalies which still
exist will be found in L. Meyer's
'Die Atome und ihre Eigenschaften'
(p. 73, &c.) _

' A very important influence in
contributing to the gradual recog-

430

SCIENTIFIC THOUGHT.

mation of the molecule of hydrochloric acid depended upon
an exchange of places of the atomic constituents in the
molecules of the elementary substances, an atom of chlor-
ine being substituted for an atom of hydrogen in the
hydrogen molecule, and vice versd in the chlorine molecule.
About the middle of this century the conviction was thus
firmly established in the minds of chemical philosophers
that the simple symbolism by which Dalton and Berzelius
expressed chemical combinations and processes was in-
sufficient for the purpose of systematically arranging the

nition of the difierence between
atom and molecule belongs also to
Gerhardt, who emphasised a fact
known already to Berzelius — viz.,
tliat hydrogen according to his
notation appeared to combine with
other bodies always in paired atoms.
This fact remained unnoticed if the
atomic number of hydrogen was
put at 1, oxygen at 8, as was done by
English chemists and reintroduced
bj' Gmelin. Berzelius did not attach
a fundamental importance to this
fact. Blomstrand (' Die Chemie der
Jetztzeit,' 1869, p. 30) has shown
that this originated in his clinging
to Lavoisier's oxygen theory. Oxy-
gen was made the centre and meas-
ure of everything in chemistry, also
of the equivalence of substances :
Berzelius thus started from a
unit which was too large, and with
which the smaller value of hydrogen
could not be measured. Gerhardt
fully recognised the importance
of this fact ; showed in many
examples that the combining or
atomic weight of hj-drogen had
been fixed too high ; and proposed
to halve most of the organic fcr-
mulee. In this way he proposed
to bring harmony into the theory
of combining volumes and the
atomic theory. He partially suc-
ceeded in doing so, although in the

case of inorganic elements he went
too far. This important step,
which has been extolled by some,
and depreciated by other historians
of chemistry, is lucidly expounded
by Rau in his ' Theorien der mo-
deriien Cheujie ' (vol. ii. p. 107, &c.)
Wurtz (' Theorie atomique,' p. 64)
considers Gerliardt's influence as a
reform, and alludes to it as bringing
again into view the hypothesis of
Avogadro : " Voilk le theme d'Avo-
gadro et d'Ampfere, qui revient a
I'horizon, comme une etoile diri-
geante, apres une longue eclipse.
Et pourtant on ne pent pas dire
qu'elle ait ete pour Gerhardt, a
cette epoque du moins, un guide
exclusif. Les considerations mai-
tresses qu'il a invoquees sont plutot
d'ordre purement chimique. Elles
etaient justes, et il s'est trouve
qu'elles concordaient avec une idee
egalement juste et qui ^tait tombee
dans I'oubli. La distinction entie
deux espeees de petites particules,
molecules et atomes, qu'Avogadro
et Ampere avaient introduite in-
utilement dans la science, que M.
Dumas avait essay^ de faire revivre
dans sa Philosophie chimique, cette
distinction etait pent - etre faite
dans I'esprit de Gerhardt, mais elle
n'apparaissait pas encore dans son
Ian gage. "

I

THE ATOMIC VIEW OF NATURE.

431

growincr volume of chemical knowledge ; that the concep- si.

°. ^ ^ Develop-

tion of the atom must be extended and more closely de- mentofthe

"' atomic view.

fined ; that the proportions of weight were inadequate for
the purpose of distinguishing and identifying the many
organic compounds ; and especially that the relations of
volume and the arrangements of particles of matter in space
must be taken notice of, if the atomic view of matter was
to be made further serviceable for scientific purposes. That
purely geometrical relations, such as can be grasped only
by ovir space conceptions, are of importance in the chem-
ical composition of substances, was very evident, for
instance, in some of the optical properties of crystallised
organic substances. The discoveries of Pasteur, published 32.
in 1850, mark in this respect an epoch in science.^ He discovery of

•^ . -^ " chirality."

showed that there exist chemical substances which are
different, but only as a right-hand glove differs from a
left-hand one, a right-handed screw from a left-handed,

^ A special line of " physical " or
"mechanical" reasoning which bears
upon the atomic view of matter be-
gan with Biot's discovery in 1815
that certain fluids — notably organic
— have the property of rotating the
plane of polarisation of light which
passes through them. Later on he
extended this observation to the
vapours formed by such fluids.
Faraday found in 1846 that sub-
stances which are optically ' ' in-
active " become active in the
manner descriVjed under the influ-
ence of powerful electro-magnets.
An explanation of the phenomenon
by Fresnel, which was based upon
crystalline structure, would — for
liquids and vapours — have to be
applied to the structure of the mole-
cule itself. Pasteur found in 1850
that there exist two modifications

of tartaric acid, which differ in this
only, that one of them turns the
plane of polarisation to the right,
the other to the left, and that a
mixture of both in the proper pro-
portions is inactive. As far back
as 1860, in his 'Leions de Chimie,'
he put the question, "whether
the atoms in tartaric acid are ar-
ranged like the turns of a right-
handed screw, or situated in the
corners of an irregular tetrahedron,
or have they any other asymmetrical
grouping ? . . . There can be no doubt
that the atoms have an unsym-
metrical arrangement after the fash-
ion of mirrored images which cannot
be made to fall into each other"
(quoted by Van't Hofi", 'Die Lager-
ung der Atome im Raume,' Ger-
man translation, 2nd ed., p. 9).

432 SCIENTIFIC THOUGHT.

the image in a mirror from the original. Was it possible
any longer to suppress the conviction that the smallest
particles of matter, in forming chemical compounds, do
so not only in definite proportions of weight, but also in
definite geometrical distances and positions ?

About the middle of the century the atomic view of
matter had thus received considerable modifications. Or-
iginally suggested only to explain, describe, or symbolise
the fact that different substances combine in fixed, and
especially in fixed multiple proportions, it had to be
modified by a recognition of the fact that in gases at least
a distinction exists between particles which are closely
knit together — as it were, geometrically inseparable — and
such as can move away from each other. The latter
explain the increase of volume under increasing tempera-
ture or decreasing pressure. Geometrical distance came
in as the means of distinguishing the molecule from the
atom. And lastly, about 1850, the phenomena of right-
and left-handedness,^ discovered by Pasteur, suggested the
33. idea of geometrical position as well as of distance. The

Atom and

molecule, atoui had become a molecule, with a definite geometrical
arrangement.

It took, however, a full generation before, in the second
half of the century, these different suggestions for a modi-
fication of the atomic view became clear, before philo-
sophers took seriously the opinion that molecules and
atoms existed in reality, and were not merely a convenient
symbolism, as many great chemists during the first half
of the century were inclined to think. This change in
the habit of chemical thought has no doubt been greatly

1 Called by Lord Kelvin " chirality."

THE ATOMIC VIEW OF NATURE.

433

brought about by the development of the so-called kinetic
theory of gases in the second half of the century. This is
a physical, not a chemical, theory.

The kinetic theory of gases, invented for the purpose
of explaining the pressure which all bodies in the gaseous
state exert on the walls of the containing vessels, will
always be identified with the two names of Clausius in
Germany and Clerk Maxwell in England.^ But if we

•* Before the atomic view of matter
had, in the course of the last fifty
years, closely and definitely allied
itself with the kinetic view, it had
been allied with the astronomical
view of matter. In the last cen-
tury and the earlier decades of
the in-esent century we frequently
find the behaviour of a complex
of molecules or atoms compared
with that of a planetary system ;
but in addition to the forces of
attraction, those of repulsion had
to be resorted to in order to ex-
plain the expansiveness of gases.
Heat was then considered to be a
material substance, the particles of
which repelled each other. Daltou
favoured this view in the introduc-
tion to his 'New System of Chemical
Philosophy ' ; so did Berthollet and
most of the French physicists who
were brought up iu the school of
Newton and Laplace. Lasswitz, in
his ' Geschichte der Atomistik ' (2
vols., Hamburg, 1890), has traced
the ' Decline of Kinetic Atomism ' in
the seventeenth century under the
influence of the ' Corpuscular Philo-
sophy.' The kinetic view of matter
was allied with the Cartesian physi-
cal philosophy, which was dispelled
by Newtonianism in France and by
Kant's philosophy in Germany. In
consequence, when in Germany A.
Kronig published his ' Grundztige
einer Theorie der Gase ' in 1856,
philosophers who had been speculat-
ing iu the direction of a Newtonian

VOL. I.

atomism (see Fechner's 'Atomen-
lehre,' 1855; Redteubacher"s 'Dyua-
miden System,' 1857 ; and other
publications quoted by Rosenberger,
'Geschichte der Physik,' vol. iii. p.
536, &c. ) were much taken by sur-
prise. It had the immediate result
of inducing R. Clausius, who had
been occupied with similar re-
searches since 1850, to publish his
celebrated memoir, ' Ueber die Art
der Bewegung welehe wir Wiirme
nenuen' (Poggendorf's 'Annalen,'
vol. c, 1857). These two publica-
tions first called general attention
to the subject. Joule's paper,
which appeared in the ' Memoirs of
the Lit. and Phil. Soc. of Man-
chester,' had remained unnoticed,
but was reprinted by him, at the
request of Clausius, in the ' Philoso-
phical Magazine ' (4th ser. vol. xiv.)
iu 1857. Subsequently, the re-
searches of Paul du Bois-Reymond
and others unearthed a whole list
of authors who, in more or less
definite ways, had resorted to the
hypothesis of a rectilinear trans-
latory motion of the molecules in
order to explain the phenomena of
pressure and other properties of
gases. Among these, Daniel Ber-
noulli (in his ' Hydrodynamica,'
1738) seems to have expressed the
clearest views, and he is now usu-
ally named as the father of the
hypothesis. The fullest statement
of the historical data will be found
ill the posthumous second edition of

2 E

434

SCIENTIFIC THOUGHT.

34.
Joule's cal-
culations.

agree to date the real birth, not the incubation, of any
scientific idea from the moment when it was set forth
in definite figures, and with mathematical precision per-
mitting of a precise verification by actual test, the modern
theory of gases was born in Manchester in the school
of Dal ton, when Joule in 1857 actually calculated the
velocity with which a particle of hydrogen at ordinary
atmospheric pressure and temperature must be moving,
assuming that this atmospheric pressure is equilibrated by
the rectilinear motion and impact of the supposed particles
of the gas on each other and the walls of the containing
vessel. This meant taking the atomic view of matter in
real earnest, not merely symbolically, as chemists had done.
Joule gave up the older and vague ideas of a rotatory or a
vibratory motion of the particles of a gas which had been
floating about since the time of Hooke ^ in various theories,
and adopted the suggestion of Daniel Bernoulli, known to
him through Herapath, that all particles of gaseous matter
are in a natural state of rectilinear motion, which is
changed only by the encounter with other particles or by
the walls of the containing vessel on which they impinge,
and from which they rebound,'

Clausius, ' Die mechanische Wiirme-
theorie' (Brauu.schweig, 1889-91,
p. 2, &c.) See also 0. E. Maj-er,
' Die kiiietische Tlieorie der Case '
(2nd ed.,Breslau, 1895, part i. p. 11 ).

1 See Tait, ' Properties of Matter,'
2nd ed. , p. 289, also J. P. Joule's
Memoir on ' Heat and the Constitu-
tion of Elastic Fluids,' 1848, re-
printed in 'Scientific Papers,' vol.
i. p. 290, kc.

- The real [jroof that the kinetic,
in contradistinction to what we may
call the Newtonian, view of the
motion of the molecules of a gas is

the correct one, and that Newtonian
(attracting and repelling) forces
play only a subordinate, if any, part
in the observable phenomena of
gaseous bodies, is based ujjon Joule
and Thomson's experiments made
in 1853. It belongs to quite a
different line of reasoning, neither
chemical nor mechanical, but going
upon the principle introduced into
scientific thought aVjout the middle
of the century, that heat and work
are convertible terms and equivalent
quantities. Now, it was generally
a.ssumed, before Joule and Thomson

THE ATOMIC VIEW OF NATURE.

435

35.

Clausius's

This idea of the rectilinear motion of the particles of
matter in a free, i.e., a gaseous, state (the first attempt to
explain the physical properties of matter by giving a
numerical value to a molecular, not molar, quantity) was
not regarded by chemists, for it was indeed of little use in
explaining chemical combinations and reactions. It, how-
ever, very soon received an important addition under the first memoir
treatment of Clausius.^

The kinetic theory of gases had not been propounded
for the purpose of explaining chemical phenomena ; it
had grown out of repeated attempts to explain the nature
of heat, and the fact, established about ten years earlier
by Mayer and Joule, that heat can be transformed into
the mechanical energy of molar motion. The idea sug-
gested itself that if heat can disappear and be replaced
by the measurable motion of molar (measurably large)
masses, and vice versa, heat itself may be merely the
energy of the directly immeasurable movements of mole-
cular (immeasurably small) masses ; and as every body

made their careful experiments,
that if gaseous bodies were allowed
to expand, without doing work,
no change of temperature took
place — i.e., that heat neither ap-
peared nor disappeared. This would
mean that no work of either repel-
ling or attracting forces was done.
Joule and Thomson showed that
there was indeed a very slight cool-
ing, indicating that a small amount
of heat or energy was used up in
doing work against attracting forces
— the forces of cohesion. Had re-
pelling forces existed, their work
would have shown itself in a rise of
temperature. This line of reasoning
will occupy us in a subsequent
chapter (see 0. E. Meyer, ' Theorie
der Gase,' vol. i. p. 7, &c., also

Joule's ' Scientific Papers,' vol. ii.
p. 216, &c.)

^ How little chemical and physical
reasoning went hand in hand before
the middle of the century is seen
from the fact that only after Clau-
sius had published his first paper
(see note, p. 433), in which he came
to the conclusion that the molecules
or smallest physical particles of
simple (elementary) substances con-
sist of several atoms, was his atten-
tion drawn to the fact that some
French chemists, notably Dumas,
Laurent, and Gerhardt, had already,
by different arguments, arrived at
the conclusion that the molecules
of simple (elementary) gases consist
of several atoms (see Clausius, loc.
clt., p. 22, &c.)

436 SCIENTIFIC THOUGHT.

in the gaseous state shows the mechanical energy which
we call pressure or expansiveness, the attempt was made
to explain the phenomena of expansion, pressure, and
temperature of gases by a purely mechanical hypothesis.
This answered remarkably well. On the assumption that
the particles of a perfect gas possess a rectilinear motion,
the experimental formulae of Boyle and Mariotte, of Dal-
ton, and of Gay-Lussac, could be theoretically deduced.
It also became evident that under this conception the
forgotten statement of Avogadro must be correct, accord-
ing to which equal volumes of different gases, under equal
pressures and at equal temperatures, contain an equal
number of freely moving particles.
36. And when Clausius showed further that in perfect

Internal

energy of gascs Only a portion of the quantities of energy which
are measured as motion or as heat can be explained
by the assumed rectilinear motion of the particles of
gases, and that an internal motion of the particles them-
selves must be assumed, the new ideas became still more
exactly defined ; they included the conception familiar to
chemists of compound atoms or molecules. The smallest
individual particles of matter in the free state were them-
selves not simple bodies, but systems of still smaller
particles ; they were molecules composed of atoms ; the
symbols of chemists became descriptive of real physical
conditions ; the vague notions of radicles, types, or com-
pound atoms began to acquire geometrical and mechanical
definiteness.

Thus the atomic theory, known to the ancients, revived
by Dalton in the early years of the century, and em-
ployed by chemical philosophers for half a century as a

molecules.

THE ATOMIC VIEW OF NATURE.

437

37.
The atomic

physical
theory about
1800.

convenient symbolism, had, about the year 1860, been
accepted by physicists, and used not merely as a con- ^gptg^^g'^
venient symbolism, but as a physical reality.

Joule had actually calculated the velocity of a particle
of hydrogen gas. The atomic view of nature was now
taken in real earnest. To establish it still further, there
were required definite numerical data ^ as to the size of
the smallest particles (henceforth sometimes called atoms,
sometimes more correctly molecules) and their number,
and also clearer views as to the composition of the mole-
cules out of their elements, the chemical atoms.

The interest which attaches to this latest development
of the atomic theory is very great : it has brought about
a union of the researches of chemists and physicists, and
has made chemistry a province of natural philosophy.^ No
one has done more that the late Professor Clerk Max-

^ Numerical data regarding the
size and number of smallest physi-
cal particles contained in a given
volume of matter have been sup-
plied by various methods or various
"lines of reasoning." The best
summary will he found in Lord
Kelvin's lecture, " On the Size of
Atoms" (1883 : reprinted in 'Pop-
ular Lectures and Addresses,' vol.
i. p. 147 sqq.) The four lines of
reasoning are founded on the un-
dulatory theory of light, on the
phenomena of contact electricitj',
on capillary attraction, and on the
kinetic theory of gases. They
" agree in showing that the mole-
cules of ordinary matter must be
something like the one ten - mil-
lionth, or from the one ten -millionth
to the one hundred-millionth of a
centimetre in diameter."

■•^ " We can distinguish two kinds
of motion, atomic motion and mole-
cular motion. ... To this dis-

tinction corresponds the division
of natural philosophy into physics
and chemistry^, not rigidly, yet in
so far as chemistry is mainly oc-
cupied with the equilibrium of the
atoms, physics with the mechanics
of the molecules. Chemical equil-
ibrium, unchanged condition of the
molecules, exists if the affinity
which holds together the atoms
equilibrates the forces which tend
to loosen the composition of the
molecule : these forces consist in
the motion of the atoms. ... As
accordingly in a chemically stable
compound the atomic motions re-
main in lasting dynamical equil-
ibrium with the chemical forces, . . .
there remains for the examination
of the purely physical phenomena
in the first instance only the mole-
cular movements" (0. E. Meyer,
' Die kinetische Theorie der Gase,'
vol. i. p. 6).

438

SCIENTIFIC THOUGHT.

38.
Clerk Wax-
well. The
statisticiil
view of
nature.

well to develop the novel conceptions which here force
themselves upon us. Especially are we indebted to him
for the idea — marking an epoch in the history of scientific
thought — of the difference between historical knowledge
of natural phenomena and a merely statistical summary
of average results.^ If the atomic view of nature has to
be adopted seriously, as the development of the kinetic

1 See Clerk Maxwell's memoir,
' Illustrations of the Dynamical
Theory of Gases' (IS.'jQ : reprinted
in ' Scientific Papers,' vol. i. p. 377).
Clausius had in his second paper,
"On the average mean path of a
particle" (Poggendorf's 'Annalen,'
18.58), given an expression for this
quantity as depending on the aver-
age distance of two particles and on
the average diameter of the sphere
of action of a particle. As these
quantities are all only mean or aver-
age quantities, he had been obliged to
resort to a method which was then
novel in physical science, the method
of averages and the calculus of prob-
ability, which is its mathematical
expression. He had calculated the
probability of a certain motion of a
particle. Maxwell, who had in 1856
been engaged in writing his Adams
prize essay " On the stability of the
motion of Saturn's rings," had there
considered the possibility of these
rings being composed of a cloud of
scattered particles moving with all
possible velocities towards each
other and round some attracting
centre : he was thus familiar with
physical problems in which the
given data could be only average
quantities. He now undertook to
develop systematically the methods
necessary for treating such prob-
lems, of which we have only statis-
tical knowledge, and he there de-
veloped his famous law which gives
the distribution of different veloci-
ties in a crowd of particles moving

at random and in their collisions
obeying the condition of the con-
servation of energy. This investi-
gation marks an epoch in mathe-
matical physics and in the history
of the atomic view of nature. Like
all theorems connected with the
theory of probability, it has pro-
voked a large literatuie, the founda-
tions of the proof and the different
steps in the logic of the deductions
having been examined and criticised
in the most searching manner. The
expression given by Maxwell has
stood all these criticism.*, — "he has
demonstrated the possibility of
calculating in a strict manner the
averages which before him had only
been estimated, but which were
required for a further development
of the theory of gases." See 0. E.
Meyer, ' Die kinetische Theorie der
Gase,' 2nd ed.,vol. i. p. 45, &c., where
also a complete account is given of
the various steps by which the
doubts which attached to Maxwell's
theories and his proofs were at
length removed, and the "variety
of traps and pit -falls'" avoided
"which are met with even in the
elements of the subject" (see Tait,
" On the Foundations of the Kinetic
Theory of Gases," 'Trans, of the
Royal Soc. of Edinburgh,' 1886,
vol. xxxiii. part 1, p. 66). In a
later chapter of this history I in-
tend to trace the development of
the statistical view of nature, and
shall then have occasion to revert
to this subject.

THE ATOMIC VIEW OF NATURE. 439

theory of gases suggests, we begin to realise the enormous
numbers of individual elements of matter with which we
have to do in any physical or chemical operation or ex-
periment. The step which enabled mathematicians to
calculate molar and cosmical phenomena by looking upon
them as made up of an immeasurably, nay infinitely, large
number of elementary parts, be these of space or time,
was taken by Newton and Leibniz : its result was the
invention, development, and application of the infinitesi-
mal calculus. Our fundamental notions applied only to
integrals, to a summation of these differential properties.
It was the problem of the new calculus to deduce from
the simple differential properties, expressed in what is
called the differential equation, the results of finite ob-
servable quantities. This was done by a process of sum-
mation or integration. In this process the elements were,
however, all considered to be equal. This was an assump-
tion which, for the purposes of simplicity, might be safely
made in a first approximation. When, however, the kin-
etic theory of gases took seriously into account the motion,
velocity, number, and size of the constituent particles of
matter contained in any finite measurable volume, or por-
tion of matter, two distinct views presented themselves :
the one which looks only at the total or average result
and aspect of the phenomena, the other which looks at
the actual behaviour and properties of the component
parts, be these ever so numerous or ever so small. These
latter could no longer be regarded as differentials which
lose their independent existence in the process of summa-
tion : they had individual properties, which were not lost
in the aggregate. It is evident that chemists had been

440 SCIENTIFIC THOUGHT.

studying those properties of matter that are preserved
distinct in ever so large a number of individuals which
are characteristically and specifically alike : while physi-
cists had been mainly studying the properties of distance,
motion, velocity, and size, which, if added together, merge
themselves into a common sum, integral or average. It
does not follow that, even so far as these latter proper-
ties are concerned, the numberless individual particles of
matter behave alike ; their sizes, velocities, and move-
ments may be very different : indeed it is evident that,
in a large crowd of moving particles, they must be widely
different.
39. In assigning numbers to these data, it was therefore

Doctrine of

averages. clcar that Only average or mean values could be meant,
and that our actual physical knowledge of the individual
elements resembles that statistical information which we
possess, for instance, regarding the mortality, average
age, and general properties and ways of the members
of a great population. It is statistical knowledge, it is
not individual, historical, or biographical knowledge, that
we possess.

The individual behaviour of the single molecules, their
sizes, their velocities, the length of their paths, their vibra-
tions, rotations, and internal motions, remain unknown.
What can be known is only the average magnitudes of
these quantities, and possibly the extreme limits within
which these individual magnitudes vary. The great dif-
ferences exhibited by larger portions of different kinds
of matter — i.e., the chemical differences or qualities — were
reduced to the actual composition and qualities of the
molecules and atoms themselves. Chemists and physi-

THE ATOMIC VIEW OF NATURE. 441

cists were now alike compelled to venture on some more
definite hypothesis, descriptive of the great variety of
constitution which the molecules of chemically distinct
substances exhibit. These molecules show in their com-
bining numbers, and in their physical properties, great
fixity, excluding apparently all gradual transitions. The
manner in which they enter into, and again separate out
of, combinations and compounds, always regaining and
showing their original characteristics, forced more and
more upon natural philosophers the conviction that com-
pounds were merely geometrical arrangements of indi- 40.

. Geometrical

vidually independent atoms, and that these atoms must anangemeut

of atoms.

possess geometrically different forms and figures, enabling
them, without loss of their individuality, to enter into
varying configurations.

The conception of the molecule as a system of atoms,
geometrically arranged, had gradually grown from vague
suggestions in the minds of physicists as well as chemists
— i.e., of students of the quantitative as well as of those
of the qualitative properties of substances. To the former
it was especially the forms of crystals, to the latter the
different degrees of saturation of chemical substances,
that suggested a geometrical arrangement of atoms as
the constitution of the smallest particles or molecules
of different substances.

Ever since the study of the regular forms of minerals 41.
or of artificially prepared crystals was reduced to an graphy.
exact science by the labours of Haiiy, at the end of
the last century,^ the forms of these regular shapes
have been valued by investigators, for two distinct rea-

^ See above, chapter i. p. 116.

442 SCIENTIFIC THOUGHT.

sons. They seemed to afford a practical means of recog-
nising and obtaining in the laboratory substances in
their qualitative or chemical purity, if they were ele-
ments, or in identical chemical combinations, if they
were compounds. And secondly, these regular, recur-
ring forms, which, in many cases, exhibited characteristic
and geometrically fixed arrangements of plane surfaces,
appeared the only means by which we could gain an
insight into the grouping and the shape of the ultimate
particles, out of which, according to the atomic view,
molar substances were constituted. If the particles of
any substance, when set free to follow their most natural
movements by solution, by fusion, or by volatilisation,
meet again during the process of solidification in definite,
always recurring forms, the conclusion seems obvious
that the individual and ultimate particles possess
marked peculiarities in the different directions of space.
And it is almost inconceivable that these peculiarities
should consist in anything else than in distinct primitive
forms, arranged in varying, but geometrically definable,
meshes of a network. Accordingly, different systems
have been elaborated ever since the age of Haiiy, which
have the object of easily classifying, recognising, and
measuring crystalline structures, or, more ambitiously,
of discovering the number of simple forms and arrange-
ments of networks of which our spatial conceptions
admit. It is satisfactory to be able to state that
investigations of the latter kind, carried on from
seemingly different beginnings, have resulted in the
recognition of a certain limited number of forms of
symmetry. This symmetry is referred to points, called

THE ATOMIC VIEW OF NATURE.

443

centres, or to lines, called axes, or to planes of sym-
metry.^ French and German investigators have deduced
in different ways the different possible forms of sym-
metry, and have shown that in all thirty-two different
forms of symmetry or groups are geometrically possible.
These thirty-two fundamental groups of crystals can be
gathered up into six classes or types, according to the
different systems of crystallographic axes or the number
of planes of symmetry belonging to them,"

^ The question may be raised,
to what extent crystallography is
obliged to assume a molecular
structure of matter, or what sup-
port does the atomic view receive
from it ? On this point see Ost-
wald's ' Allgemeine Chemie,' vol. i.
p. 855, &c. The geometrical forms
of crystals can either be derived
from elementary poly hedra, as Haiiy
attempted to do bj' his " molecules
integrantes " and his theory of
decrescences, space being in this
system considered as continuously
filled ; or the elementary particles
may be considered to consist of
meshes of points geometrically ar-
ranged in the corners of a primitive
figure in three dimensions ; or ele-
mentary spheres or ellipsoids may
be supposed to be piled on each
other like cannon-balls. The two lat-
ter systems assume vacant spaces ;
the first view refers the crystalline
shape to some primitive crystal, and,
therefore, does not explain it. It
has accordingly been said that " the
structure of crystals is one of the
principal supports of the molecular
theory. In assuming continuous
matter without at least points
which are geometrically or kine-
matically distinct, the anisotropic
structure of crystals is quite un-
thinkable " (Lehmann, ' Molecular-
' physik,' vol. ii. p. 376). This view
does not agree with what Ostwald

says ('Allgemeine Chemie,' vol. i. p.
868) ; he considers that the struc-
ture of crystals affords no proof
for the molecular constitution of
matter, as the data of elasticity
by no means necessarily require
a molecular arrangement, but for-
mally can be ascribed as easily to
continuous matter. " Nevertheless
the molecular view has the advan-
tage of greater evidence, and leads
to the same results with much
greater simplicity, and hence more
convincingly." It seems, however,
that if chemical facts and physical
theory force upon us the atomic
view, crystallographic phenomena
force us to complete it by some
conception of geometrical arrange-
ments.

- This purely geometrical treat-
ment was ^introduced by Bravais
in his ' Etudes crystallograph-
iques' (1851), the much earlier
work of Hessel (' Krystallometrie,'
1831) having been forgotten. It
was further developed by L. Sohnke
( ' Entwickelung der Theorie der
Krystallstructur,' 1879), and com-
pleted by Curie (1884) and Min-
nigerode (1886). A concise sum-
mai-y will be found in Liebisch,
' Physikalische Krystallographie,'
Leipzig, 1891, pp. 3 to 50 ; also
Groth, ' Physikalische Krystallo-
graphie,' Leipzig, 1895, p. 324,
&c.

444 SCIENTIFIC THOUGHT.

42. An analogy has been pointed out ^ between the atomic
between theory in chemistry, by which Dalton explained the fixed
atoScfiaws simplc and multiple proportions of the combining weights

of various substances, and the molecular theory of crystal-
line structures, by which the fundamental forms of crystals
are defined and the accessory forms derived from them.
It has been found that if once a crystal has been defined
by a fundamental plane referred to three axes at fixed
angles, all other planes or faces can be defined by simple
multiples of the numbers which belong to the fundamental
plane, and which are called the parameters of the crystal.
This fundamental rule or law of crystallisation, termed by
Haiiy the law of derivation, stands thus in the same rela-
tion to the corpuscular theory of the structure of bodies
as the law of fixed multiple proportions stands to the
original atomic view of matter, and it is thought that it
may in the future lead to important results."

43. Another very remarkable discovery had been made by

Isomor- . .

phism. Mitscherlich in 1 8 2 3."^ This is the property which various
compounds possess of crystallising in the same forms,
although they contain different elements — such elements
being, however, joined together by similar formulae. The
elements are, as it were, interchangeable. This phe-

^ See Ostwald, ' Allgemeine
Chemie,' vol. i. p. 870.

- A question arises in this connec-
tion as to the accuracy of the crys-

a somewhat disturbed manner" {loc.
cit., vol. i. p. 890). This I under-
stand to mean that, if disturbing
circumstances could be removed,

tallographic law of the fixity of the the law of the fixity of angles and
angles. In respect of this Ostwald ! the simple multiples of the indices
says: "On examining the validity
of the fundamental laws of crystallo-
gi-aphy, it becomes evident that
they are only approximate, or per-
haps more correctly, that there exist
numerous circumstances which per-
mit them to show themselves only in

would obtain with the same accur-
acy as do the combining numbers
and their multiples in chemical
combinations.

^ See supra, chap. ii. p. 191 and
note.

THE ATOMIC VIEW OF NATURE.

445

nomenon has been called isomorphism. The discovery
has been of great practical value, as well as theoretical
interest. If the definite and invariable form of existence
which the crystal exhibits is considered as a proof of the
purity of a chemical substance, and if in the same crystal
one elementary substance can be replaced by one or several
other substances, then this substitution must take place in
definite proportions of weight, in the equivalent propor-
tions. Thus the production of such isomorphous crystals
affords a method of determining the relative atomic
weights or equivalents. As such it was hailed by Ber-
zelius ; the more so, as in no case did the equivalents
thus obtained contradict the numbers he had found by
other methods.-^ Theoretically, the property of isomor-
phism acquired a still greater interest when Mitscher-

' In the early days of the atomic
theory as developed by Berzelius,
great uncertainty existed as to the
numbers which wei'e to be chosen for
the atomic weights of the elements.
This was owing to the property of
fixed multiple ratios— it remaining
undecided which was the smallest
submultiple of a given combining
ratio in which any special element
could enter into combination.
Other methods were then used to
assist in deciding this point. The
law of volumes, and later the pro-
perties of isomorphism, were there-
fore hailed by Berzelius as welcome
aids in fixing the atomic numbers.
Both these methods are still used,
though the latter is not always de-
cisive. The most important method
according to the present state of our
knowledge is the determination of
the vapour density, where such can
be got, and that of the specific heat
in the solid state. It is mainly
owing to Caimizzaro (18.58) that

the apparent contradictions, which
were supposed to exist in the num-
bers arrived at by various methods,
were explained by reverting to
Avogadro's forgotten hypothesis.
The periodic law or arrangement of
the elements into classes showing
similar physical properties is like-
wise of use. A complete, lucid,
and exhaustive statement of the
most recent position of our know-
ledge of the true atomic weights
of the elements will be found in
Lothar Meyer's posthumous tract,
' Die Atome und ihre Eigenschaf-
ten,' Breslau, 1 896. In this valuable
book, as also in Ostwald's ' AUge-
meine Chemie,' vol. i., will also be
found an account of the degree of ac-
curacy which attaches to our present
knowledge of the atomic and com-
bining numbers, which form the
solid foundation of all quantitative
chemistry and all practical applica-
tions.

446 SCIENTIFIC THOUGHT.

lich discovered another crystalline property of certain
chemically pure substances. He found that some sub-
stances can crystallise in more than one distinct and
definite form. The alums and vitriols are typical of iso-
Poiymor- i^ioiT^^ism. As typical of the second property, which was
phism. termed by him dimorphism or polymorphism, we have
the well-known mineral calc-spar, which is dimorphous
with aragonite, both having the same chemical constitution
and properties. A typical example of dimorphism is the
mineral rutile, which is chemically the same substance as
the mineral anatase, both being chemically pure titanic
oxide. Among the elements, pure sulphur crystallises in
two different forms. The property of dimorphism seemed
at first to contradict the inference which Mitscherlich had
drawn from his first discovery — viz., that the crystalline
shape is expressive of the number and chemical connec-
tion of the smallest particles or atoms ; but the further
discovery, that if of two isomorphous bodies one is dimor-
phous, the other is likewise so, gave again a great support
to the geometrical conception of atomic complexes^ — i.e.,
" to the idea that chemical individuality is ultimately to be

explained not only by the number, but also by the mutual
fixed position and shape, of the atoms. And yet it seemed
a long way, and is a long way still, from the external,
visible, and well-marked shape of a crystal, with its
peculiar and well-defined geometrical, elastic, optical, and
thermal properties, to the primitive molecule, made up of
still more simple atoms, in the form, number, and arrange-
ment of which we are again and again tempted to see the
nature of chemical or qualitative individuality. To obtain
a clear view in this way would be to work our way from

THE ATOMIC VIEW OF NATUEE. 447

outside inward — a method which has rarely led to definite
results in scientific research.

A department of chemical science called structural 45.

. . I'll structural

chemistry — which has quite recently developed into a»d stereo-

■^ ^ chemistry.

stereo-chemistry — has during the last fifty years of the
century been working by the opposite method. Even
those organic chemists who ridiculed the notion that
a chemical formula, which on the surface of the paper
on which it is written cannot help making use of
geometrical position and proximities, is in any way a
picture of the arrangements of atoms in real space, were
nevertheless forced to avail themselves of this symbolism.
About the middle of the century, especially through the
researches of Frankland, followed by those of Couper and
Kekule, the phenomenon of multiple proportions was ex-
plained by introducing the notion of saturation. An
element which can combine with one or more atoms of
the same or of different elements or definite chemical
compounds was looked upon as having a chemical affinity
which might be wholly or only partially satisfied. The
different compounds arising out of such combinations
would then represent different degrees of saturation of
the first element; and it was evident that elements as
well as compounds could be arranged according to the
degrees of saturation of which they were capable. A
compound containing elements which possessed a greater
capacity for saturation than the combination afforded was
called unsaturated. The term valency was introduced to 46.
denote the degrees of saturation of elements and com- ^'•'^°''^-
pounds, which were therefore mono-, di-, or poly-valent,
according to the compounds existing in fixed simple or

448

SCIENTIFIC THOUGHT.

fixed multiple proportions. In a table of the valencies
or saturating capacities of elements and compounds, the
element hydrogen forms the unit and point of reference,
as it does in the scale of the atomic or combining weights,
and very remarkable relations and analogies have been
established between the periodic law of Mendeleeff and
the valency of the different elements. Nevertheless it
must be remarked that the valency of an element or
compound does not, according to our present knowledge,
show such absolute fixity as the equivalents or combining
weights do, or as the angles of crystallisation of chemically
pure substances do.^

The introduction of the conception of valency has had
an enormous influence on the development of the science
of chemistry, and this in a twofold direction. Its prac-
tical use was demonstrated by Kekule, when he placed
the idea of the tetravalency, or fourfold saturating capa-
city, of carbon in the front of his treatise of organic
chemistry,^ and by so doing gave a great impetus to
organic research. One of the first symbols used to denote

^ Not only are many of the ele-
ments, such as oxygen and phos-
phorus, classed ditiereutly by dif-
ferent chemists according as their
valency or saturating capacity is
put at a higher or lower multiple,
but compounds which are univer-
sally considered to be saturated
compounds, such as neutral salts
and water, form chemical combina-
tions according to their combining
numbers, which are quite defi-
nite and stable : such are the hy-
drated crystallised salts and the
double salts. These compounds
are called "molecular compounds."
Various explanations have been at-
tempted, but the fact remains that

" no characteristic distinction has
been found, either in physical or
chemical behaviour, between the
ordinary compounds and the mo-
lecular compounds ; and therefore,
strictly speaking, from the pheno-
mena exhibited, at pi-esent no other
conclusion can be drawn except
that chemical compounds do un-
doubtedly exist which cannot be
included in the structure scheme
which is based on the doctrine of
a constant valency " (see Nernst,
'Theoretical Chemistry,' transl. by
Palmer, London, 1895, p. 246).

^ A. Kekule (1829-1896), ' Lehr-
buch der organischen Chemie,' 1st
ed., Erlangen, 1859, and later.

THE ATOMIC VIEW OF NATCKE. 449

the valency of an element was to attach to it as many
lines as it possessed capacities of saturation. The capa-
cities of saturation or valencies thus appeared very early
as points of saturation, and the saturation itself as a
linkage. These geometrical artifices or expressions were,
for a long time, used merely as symbols, and to the
present day many eminent chemists refuse to attach to
them any real meaning : formulae of this kind were called
formula; of structure, not of constitution. One of the 47.

. PI c T ^ Atomic

most remarkable instances of the exact use of linkages linkage.
to explain the difference of a series of organic compounds,
all closely connected with each other, is the theory of the
so-called aromatic compounds, derived from benzene, which
we owe to Kekule. It has stood the criticism of more
than a quarter of a century, and has led to the most
wonderful practical knowledge of a large number of old
and new compounds.

It is not astonishing if, in the face of these remark-
able strides which geometrical symbols have led to,
an attempt has been made to form an actual con-
ception of the geometrical figure and grouping of the
atoms of which chemical molecules and compounds are
made up.

Space relations are the only ones in which the differ-
ence of symmetry and asymmetry can be at all conceived
by us ; and when chemical compounds were discovered
which show no other difference than that one of them
turns the plane of polarisation of a ray of light passing
through it to the right, the other to the left side, the
time seemed ripe to seek an explanation of this in a
purely stereometrical difference of form or grouping.

VOL. I. 2 F

450

SCIENTIFIC THOUGHT.

48
Tlie carbon

In 1874 two chemists, Le Bel and Van't Hoff", suggested
independently a picture of the tetravalent carbon atom,
which would explain how it could enter with its four
points or capacities of saturation into two compounds
having the same saturating substances, but arranged in
ways which were not geometrically superposable, but only
symmetrical, like a right- and left-hand glove, or the
images in a mirror. The suggestion amounts to this,
tetrahedron, that the carbou atom has the shape of a tetrahedron,
the four corners representing the four valencies or capa-
cities of saturation.^

The carbon tetrahedron is the last step which has been
taken in the development of the atomic view of matter
and of nature. No book on organic chemistry can now
well avoid introducing this and other similar ways of
representing chemical relations. On the further special-
isation of this conception will probably depend to a large
extent the future of our chemical theory- — i.e., of our at-
tempts to grasp the qualitative nature of different sub-
stances. It is clear that we are far on the way to realising
Wollaston's prophecy of the year 1808 — viz., "that the

^ This speculation was at first
looked upon with very great doubt.
Only few chemists of note took it
up ; others, such as Kolbe, who led
a consistent opposition to the ideas
and developments of structural
chemistry, treated it with ridicule.
Van't Hoff, ten years after the
publication of the first edition of
his pamphlet, ' La Chimie dans
I'Espace' (Rotterdam, 1875) re-
viewed the position in his ' Dix
Annies dans I'Histoire d'une Thd-
orie ' (translated by Marsh, Oxford,
1891), and, after reproducing the

two opposite reviews, with which
the original theorj' was met by
Wislicenus and Kolbe, was able to
state "that the theory in question
now forms part of elementary
chemical teaching, and is to be
found enunciated in the most
widely used text-books" (transla-
tion, p. 19). Further applica-
tions of the theory, especially to
the compounds of nitrogen, will be
found in the 2nd edition of the
German translation ' Die Lagerung
der Atome im Ilaume ' (Braunsch-
weig, 1894).

THE ATOMIC VIEW OF NATURE.

451

atomic theory could not rest contented with a knowledge
of the relative weights of elementary atoms, but would
have to be completed by a geometrical conception of the
arrangement of the elementary particles in all the three
dimensions of solid extension." ^

But though a further development of the atomic view,
not only " pondere " but also " mensura," may be expected
in the near future, the progress of chemistry, which has
benefited so much by this view of nature, will not de- 49.

Defects and

pend exclusively upon this line of thought, nor perhaps insufficiency
to so large an extent as it has done during the greater atomic view,
part of the century. We have seen how the atomic
theory of Dalton rose to the position of being more
than a convenient symbolism, and how it became a
physical theory of matter and of nature mainly by
the support which it received from a different line of
reasoning.

The development of this line of reasoning led to the
employment of the statistical method, a view quite
foreign to other branches of physical science.

The kinetic theory of gases itself had been elaborated
in connection with still another line of reasoning, with
the endeavour to get a clearer and more comprehensive
view of the nature of the different forces which the
astronomical as well as the atomic views had merely
accepted as given quantities without further examination.
We are thus necessarily led on to trace the history of

1 See WoUastoii's memoir, " On
Super -acid and Sub -acid Salts,"
read before the Rnyal Society, Jan.
8, 1808 (' Phil. Trans.,' 1808, p. 96,
kc), where he even suggests the

examination of the stability of ag-
gregates of particles in different con-
figurations, mentioning the tetra-
hedron, since become celebrated
through Pasteur and Van't Hoff.

452 SCIENTIFIC THOUGHT.

these other views of nature, which up to the middle of
the century had grown up independently.

The next chapter will accordingly deal with the
kinetic view of nature.

At the time when the atomic theory was firmly estab-
lished and defined, the great founders of chemical science
were well aware that the investigation and measurement
of chemical forces, of what was termed affinity, was just
as important a problem as the fixing of the combining
weights and the formula^ of chemical compounds.

Accordingly we find men like Bergmann, Berthollet,

Davy, Berzelius, and Faraday all propounding or suggest-

50. ing theories of chemical affinity, some of which, like the

Theories of ® _ . .

'^ftfnit'''^^ electro-chemical theory, remained long in use. The diffi-
culty, however, which was experienced in defining, and
still more in measuring, chemical affinity, and the absence
of a general system for the computation and calculation
of all physical quantities, retarded the progress of this
line of research compared with the study of the weights
or proportions of mass which existed in chemical processes,
and which were more easily ascertained by means of the
balance, and made intelligible by the atomic theory.

The tendency of chemical reasoning during the first
half of the century lay therefore in the direction of a
one-sided development of the knowledge of matter, its
definite constituents and infinite compounds, rather than
in a study of that equally important but more svibtle
quantity, now called energy, which appears or disappears,
but is never created or destroyed in physical or chemical
processes.

A clear recognition of this fundamental doctrine — nay,

THE ATOMIC VIEW OF NATURE. 453

even a name for the thing implied — did not exist Ijefore
the middle of the century. How both were gradually intro-
duced will be shown in another of the following chapters.

The atomic view or theory which gave such good help
in classifying and in studying the characteristic feature
of all chemical processes — the fact that they take place
according to definite proportions of weight — had also the
eftect of promoting a somewhat one-sided habit of thought
in the domain of chemical science itself.

The search for the elements, the fixing of their com-
bining weights and properties, absorbed a great deal of
time, labour, and ability.

The practical demands of the arts stimulated the pre- si.

Practical

paration of metals, of acids, and of alkalies, all of which influences,
possessed useful properties in their isolated, as distin-
guished from their natural, condition. This gave a stimu-
lus in practice to the invention of processes of disintegration,
and in reasoning to processes of analysis. The synthesis or
putting together was expected to take place easily, if once
the elements or constituent parts were got. In mineral
chemistry and metallurgy this is indeed very frequently
the case. It was soon found that it is not so in organic
chemistry, and that when in organic chemistry a synthesis
is effected, the product is frequently unlike that original
natural substance from the analysis or disintegration of
which the constituents or elements were procured.

It soon became evident that synthesis does not mean
merely addition. A certain order had to be observed in
the way of putting together, and this led to the introduc-
tion of structural, further of geometrical, formulae. Even
then, however, it was found that if a synthesis succeeded,

454

SCIENTIFIC THOUGHT.

it did not always produce a natural, l)ut frequently a
purely artificial, compound. The practical effect of this
discovery has been remarkable, not to say astonishing.
New industries have been founded, and a branch of
science has been created called " organic chemistry," but
more correctly the " chemistry of carbon compounds,"
which was undreamt of in the beginning of the century.
52. At that time "organic chemistry" meant that branch of

Change in o ./

orga'^nic*"' °^ ^^® scieucc which dealt with the compounds which were
chemistry. fQy^Y^^[ [y^ i\^q structurcs of the Vegetable and animal
kingdoms, and which were peculiar to them.^ This
meaning of tlie term " organic chemistry " has disap-
peared ; but the branch of science which deals specially
with the substances contained in living matter has not
disappeared. Only the development of chemistry on the
lines pre-eminently prescribed by the atomic view of
nature has diverted the attention of many investigators
and philosophers from the original problems of organic
chemistry — the study, the analysis, and the reproduction
or synthesis of such compounds as are immediately con-
nected with living matter.

To the extent that these problems which have not lain

1 The merit of having upheld the
twofold aspect of organic chem-
istry and of having urged the
necessity of two distinct ways of
analysing organic substances, be-
longs in this century pre-eminently
to Chevreul. Not only are his
' Recherches sur les Corps gras
d'Origine animale,' carried on from
1813 to 1823, a model work of
great theoretical and practical
value ; but he has in various writ-
ings, notably in his historical
memoirs ('Journal des Savants,'

1852-60), insisted on the necessity
of studying what he terms, after
Fourcroy, " les principes im-
mediats, qui constituent les
vegdtaux et les auimaux." This
study is based upon quite a different
method from that usuallj- called
" analyse el^mentaire. " Chevreul's
great work has been continued and
developed by M. Berthelot in his
celebrated book, ' Chimie organique
fondce sur la Synthese,' 1860, two
vols.

THE ATOMIC VIEW OF NATUEE. 455 !

specially on the lines marked out by the atomic view of '

nature have, in the course of time, reasserted themselves,

the atomic view itself has been regarded with less favour ]

by students who have made these problems their especial ;

study. In fact, one meets not infrequently with an in- i

clination to disparage the atomic theory, to point out

that it is merely a hypothesis, and that as such it ;

should only assist, but not govern, scientific research.^

In the domain of specially chemical reasoning we meet 53.

Criticisms ot >

with severe criticisms of the one-sided and formal develop- ^^^ atomic

'- view. '

ment to which the atomic view has led, of the playing with i

symbols and of their empty formalism ; notably structural I

chemistry and stereo-chemistry have not escaped severe ]

ridicule.2 Whilst it is not very evident how the school I

from which these criticisms proceed can in the long-run |

escape those logical consequences which are embodied ;

in stereo-chemistry, other criticisms claim our attention

I

^ See Berthelot, ' La Syutliese de I'esprit humain, uaturellement

chimique,' 7"'® ed., 1891, p. 167. porte h, substituer a la conception '•
" Le principal reproche, que Ton directe des choses . . . la vue plus

puisse adi-esser a la theorie ato- sin]2:)le . . . de leurs signes lepre- ]

mique, comuie a toutes les concep- sentatifs." '
tions analogues, c'est qu'elles con- ; ^ The late eminent Professor

duisent a operer sur ces rapports Hermann Kolbe of Leipsic, whose 1

uumeriques des elements et non labours both alone and jointlj' with '

sur les corps eux-memes, en rap- Fj-ankland have done so much to 1

portant toutes les reactions a une break down the formalism of the !

unite type, necessairement imag- older type theory, was especially |

inaire. Bref elles eulevent aux conspicuous by his virulent attacks I

phenomenes tout caractfere reel, | on the representatives of ' Modern }

et substituent h leur exposition Chemistry.' The controversy is I

veritable une suite de considerations elaborately and lucidly treated by i
symboliques, auxquelles I'esprir. se A. Rau in 'Die Theorien der

complait, parce qu'il s'y exerce modernen Chemie ' (Braunschweig, :

avec plus de facilite que sur les 1877-84, 3 jmrts), which contains |

realites proprement dites . . . les 1 very valuable historical references. I
symboles de la chimie presentant I am afraid it is greatly owing to
a cet egard d'ctranges seductions this party spirit that Kolbe's own
par la facilite algebrique de leurs ' greatness is hardly sufficiently
combinaisons et par les tendances known in this country.

456

SCIENTIFIC THOUGHT.

because they follow from distinctly defined and inde-
pendent lines of reasoning. The three criticisms can he
summed up in three distinct arguments, all three de-
manding our special and exhaustive study. These three
arguments may be summarised as follows : —

First. The atomic view is a hypothesis resting upon the
fact that substances combine in fixed and fixed multiple
proportions, and upon the further observation that bodies
both in the solid and liquid state show different properties
in different directions of space. But as to the nature
of the differences of the elements the atomic view gives no
information ; it simply asserts these differences, assumes
them as physical constants, and tries to describe them by
number and measurement.

The atomic view is therefore at best only a provisional
basis, a convenient resting-place,^ similar to that which
Newton found in physical astronomy, and on which has
been established the astronomical view of nature.

Second. The atomic view in its present development
gives us no insight into the nature of those forces on which
depend the formation or destruction of chemical com-
pounds. It neglects the study of chemical affinity. This
must be conducted on different lines of observation and

reasoning.

1 As these and other points re-
ferred to here will be taken up and
fully treated in future chapters of
this work, I abstain from giving
exhaustive references, limiting my-
self to such writings as will
give the reader a general idea of
the various attempts which have
been made to go beyond or behind
the Atomic View of Nature or to
supplement it by other views.

Very suggestive in the first instance
is Lord Kelvin's address to the
mathematical and physical section
of the British Association in 1884,
reprinted in the first volume of his
' Popular Lectures and Addresses,'
p. 218, &c., "Steps towards a Kin-
etic Theory of Matter."

- In respect of this the Introduc-
tion to the first edition of Lothar
Meyer's ' Modern Theories in Chem-

THE ATOMIC VIEW OF NATURE.

457

Third. The atomic view, as developed in chemical for-
mulae, has unduly favoured and promoted the analytical
tendency of research and thought, limiting synthesis
to such compounds as can be artificially prepared,
but neglecting that kind of synthesis by which com-
pounds are formed in nature, and especially in living
organisms/

As representative of these three lines of argument,
leading beyond or outside of the atomic view of nature,
I mention the three names of Lord Kelvin in England,
coupled with the kinetic — specially the vortex — theory of
matter; of Professor Ostwald in Germany, coupled with
the modern doctrines of chemical affinity ; and of M.
Berthelot in France, as especially identified with the de-
velopment of modern synthetical methods in chemistry.
In the next chapter I shall take up the line of thought
embodied in the first of these developments — the kinetic
view of nature. In order to understand the history of
this view, we shall have to go back to opinions held

istry,' written in 1862 and reprint-
ed in the subsequent editions and
also in the English translation by
Bedson and Williams (London, 1888),
gives a very lucid summary of the
historical developments. The pub-
lication of Meyer's book, by the
controversies it produced, did a
great deal to give " theoretical " or
" physical " chemistry a distinct and
independent position. Separate
chairs and laboratories for physical
chemistry have since been inaug-
urated, first at Leipsic and subse-
quently at other German univer-
sities. See Ostwald's article on
" Physikalische Chemie," in Lexis,
'Die deutschen Universitaten,' vol.

VOL. I.

ii. p. 50, &c. Professor Ostwald is
also the editor, since 1857, of the
first periodical devoted to physical
chemistry. To his great work,
entitled ' Allgemeine Chemie,'
which, since its first appearance
in 1884, has done so much for
"general" as distinguished from
" systematic " chemistry, and to his
numerous suggestive addresses, I
shall frequently have occasion to
refer.

^ See the works of M. Berthelot,
quoted above, pp. 454, 455 ; also
an address by Prof. Meldola before
the chemical section of the British
Association in 1895.

2 G

1

458 SCIENTIFIC THOUGHT. \

already in antiquity ; just as I showed that the astro- ;
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theories of older times, and that they owe their revival
and scientific usefulness to the fact that they have re-
ceived in recent days the precise treatment of exact |
measurement and mathematical reasoning. i

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