POPULAR

SCIENTIFIC

HELMHOLTZ

POPULAR LECTURES

ON

SCIENTIFIC SUBJECTS.

Just published, in 1 vol. uniform.

HELMHOLTZ'S POPULAR LECTURES on SCIENTIFIC
SUBJECTS, SECOND SERIES, translated by E. ATKINSON, Ph.D. F.C.S.
With numerous Woodcuts. Crown 8vo. price 7*. Gd.

LIST of the LECTURES :—

I. Gnstav Magnus ; In Memoriam.— II. On the Origin and Significance
of Geometrical Axioms.-lII. Optics in its Relation to Painting. 1,
Form ; «, Shade ; 8, Colour ; 4, Harmony of Colour -IV. On the Forma-
tion of the Planetary System. -V. On the Freedom of Academical
Teaching.— VI. On Thought in Medicine.

HELMHOLTZ on the SENSATIONS of TONE as a Physio-
logical Basis for the Theory of Music. Translated, with the Author's
sanction, from the Third German Edition, with Additional Notes and
an Additional Appendix, by ALEXANDER J. ELLIS, F.R.S. &c. 8vo.
price 36*.

•ft is hardly too much to say that this
volume far exceeds in value any and
every rimilar work.' ORCHESTRA.
' The most important contribution

tmpor,

to the science of music which has at
any period been received from a sin/tie
source.' MUSICAL STANDARD.

• The present book supersedes all
other treatises on the physics of
musical sound and the necessary

relations of this to systems of melody
""'"PALL MALL GAZETTE.

' It is unnecessary for us to say
that this famous book will be wel-
comed alike by the physicist, the
acoustician, and the musician. It is
one of the most original works of the
second half of this century.'

QUARTERLY JOURNAL OF SCIENCE.

London, LONGMANS & CO.

BxLibria
C. K. OGDEtf

POPULAR LECTURES

ON

SCIENTIFIC SUBJECTS.

BY

H. HELMHOLTZ,

PROFESSOR OF PHYSICS EST THE UMVEliSITT OF BERLIN.
TRANSLATED BY

E. ATKINSON, PH.D. F.C.S.

PROFESSOR OF EX PE RIMKNT A I, SCIENCE, STAFF COLLEGE.

FIRST SERIES.
WITH AN INTRODUCTION by PROFESSOR TTNDALL

(fcbitian.

LONDON :
LONGMANS, GREEN, AND CO.

1881.

All rights reserved.

Q

T-r •>•>-•> A -0V

— - ^ - •

SANTA E

H1-7

TEANSLATOE'S PEEFACE.

IN bringing this Translation of Helmholtz's Popular
Scientific Lectures before the public, I have to thank Mr.
A. J. Ellis for having placed at the disposal of the
Publishers the translation of the third Lecture ; and also
Dr. Francis, the Editor of the * Philosophical Magazine,'
for giving me permission to use the translation of the fifth
Lecture, which originally appeared in that Journal.

In addition to the Editorial charge of the book, my
own task has been limited to the translation of two of the
Lectures. I should have hesitated to undertake the work,
had I not from the outset been able to rely upon the aid
of several gentlemen whose names are appended to the
Contents. One advantage gained from this division of
labour is, that the publication of the work has been
accelerated; but a far more important benefit has been
secured to it, in the co-operation of translators who have
brought to the execution of their task special knowledge
of their respective subjects.

E. ATKINSON.

AUTHOE'S PBEFACE.

IN COMPLIANCE with many requests, I beg to offer to the
public a series of popular Lectures which I have delivered
on various occasions. They are designed for readers who,
without being professionally occupied with the study of
Natural Science, are yet interested in the scientific results
of such studies. The difficulty, felt so strongly in printed
scientific lectures, namely, that the reader cannot see the
experiments, has in the present case been materially
lessened by the numerous illustrations which the publishers
have liberally furnished.

The first and second Lectures have already appeared in
print ; the first in a university programme, which, how-
ever, was not published. The second appeared in the
'Kieler Monatsschrift' for May, 1853, but, owing to the
restricted circulation of that journal, became but little
known ; both have, accordingly, been reprinted. The
third and fourth Lectures have not previously appeared.

These Lectures, called forth as they have been by
incidental occasions, have not, of course, been composed
in accordance with a rigidly uniform plan. Each of them
has been kept perfectly independent of the others. Hence

viii AUTHOR'S PREFACE.

some amount of repetition has been unavoidable, and the
first four may perhaps seem somewhat confusedly thrown
together. If I may claim that they have any leading
thought, it would be that I have endeavoured to illustrate
the essence and the import of Natural laws, and their
relation to the mental activity of man. This seems to me
the chief interest and the chief need in Lectures before a
public whose education has been mainly literary.

I have but little to remark with reference to individual
Lectures. The set of Lectures which treat of the
Theory of Vision have been already published in the
* Preussische Jahrbiicher,' and have acquired, therefore,
more of the character of Eeview articles. As it was
possible in this second reprint to render many points
clearer by illustrations, I have introduced a number of
woodcuts, and inserted in the text the necessary explan-
ations. A few other small alterations have originated in
my having availed myself of the results of new series of
experiments.

The fifth Lecture, on the Interaction of Natural
Forces, originally published sixteen years ago, could not
be left entirely unaltered in this reprint. Yet the alter-
ations have been as slight as possible, and have merely
been such as have become necessary by new experimental
facts, which partly confirm the statements originally made
and partly modify them.

The seventh Lecture, on the Conservation of Force,
developes still further a portion of the fifth. Its main
object is to elucidate the cardinal physical ideas of work,
and of its unalterability. The applications and conse-

AUTHOR'S PREFACE. ix

quences of the law of the Conservation of Force are com-
paratively more easy to grasp. They have in recent times
been treated by several persons in a vivid and interesting
manner, so that it seemed unnecessary to publish the cor-
responding part of the cycle of lectures which I delivered
on this subject; the more so as some of the more
important subjects to be discussed will, perhaps in the
immediate future, be capable of more definite treatment
than is at present possible.

On the other hand, I have invariably found that the
fundamental ideas of this subject always appear difficult
of comprehension not only to those who have not passed
through the school of mathematical mechanics ; but even
to those who attack the subject with diligence and in-
telligence, and who possess a tolerable acquaintance with
natural science. It is not to be denied that these ideas
are abstractions of a quite peculiar kind. Even such a
mind as that of Kant found difficulty in comprehending
them; as is shown by his controversy with Leibnitz.
Hence I thought it worth while to furnish in a popular
form an explanation of these ideas, by referring them to
many of the better known mechanical and physical ex-
amples ; and therefore I have only for the present given
the first Lecture of that series which is devoted to this
object.

The last Lecture was the opening address for the
' Naturforscher-Versammlung,' in Innsbruck. It was not
delivered from a complete manuscript, but from brief
notes, and was not written out until a year after. The
present form has, therefore, no claim to be considered an

x AUTHOR'S PREFACE.

accurate reproduction of that address. I have added it to
the present collection, for in it I have treated briefly what
is more fully discussed in the other articles. Its title to
the place which it occupies lies in the fact that it attempts
to bring the views enunciated in the preceding Lectures
into a more complete and more comprehensive whole.

In conclusion, I hope that these Lectures may meet
with that forbearance which lectures always require when
they are not heard, but are read in print.

THE AUTHOE.

CONTENTS.

LECTURE PAGE

I. ON THE RELATION OP NATURAL SCIENCE TO SCIENCE IN
GENERAL. Translated by H. W. EVE, Esq., M.A., F.C.S.,
Wellington College 1

II. ON GOETHE'S SCIENTIFIC RESEARCHES. Translated by H. W.

EVE, Esq 29

III. ON THE PHYSIOLOGICAL CAUSES OF HARMONY IN Music.

Translated by A. J. ELLIS, Esq., M.A., F.R.S. . . .53

IV. ICE AND GLACIERS. Translated by Dr. ATKINSON, F.C.S.,

Professor of Experimental Science, Staff College ... 95

V. ON THE INTERACTION OF THE NATURAL FORCES. Translated

by Professor TYNDALL, LL.D., F.R.S 137

VI. THE RECENT PROGRESS OF THE THEORY OF VISION. Translated

by Dr. PYE-SMITH, B.A., F.R.C.P., Guy's Hospital .

i. The Eye as an Optical Instrument . . . .175

ii. The Sensation of Sight 202

in. The Perception of Sight 237

VII. ON THE CONSERVATION OF FOKCE. Translated by Dr. AT-
KINSON 277

VIII. ON THE AIM AND PROGRESS OF PHYSICAL SCIENCE. Translated

by Dr. W. FLIGHT, F.C.S., British Museum . . .319

INTBODUCTION.

IN the year 1850, -when I -was a student in the University of
Marburg, it was my privilege to translate for the 'Philosophical
Magazine' the celebrated memoirs of Clausius, then just pub-
lished, on the Moving Force of Heat.

In 1851, through the liberal courtesy of the late Professor
Magnus, I was enabled to pursue my scientific labours in his
laboratory in Berlin. One evening during my residence there
my friend Dr. Du Bois-Eaymond put a pamphlet into my hands,
remarking that it was 'the production of the first head in Europe
since the death of Jacobi,' and that it ought to be translated
into English. Soon after my return to England I translated
the essay and published it in the 'Scientific Memoirs,' then
brought out under the joint-editorship of Huxley, Henfrey,
Francis, and myself.

This essay, which was communicated in 1847 to the Physical
Society of Berlin, has become sufficiently famous since. It was
entitled 'Die Erhaltung der Kraft,' and its author was Helmholtz,
originally Military Physician in the Prussian service, afterwards
Professor of Physiology in the Universities of Konigsberg and
Heidelberg, and now Professor of Physics in the University of
Berlin.

Brought thus face to face with the great generalisation of
the Conservation of Energy, I sought, to the best of my ability,
to master it by independent thought in all its physical details.
I could not forget my indebtedness to Helmholtz and Clausius,

XIV INTRODUCTION.

or fail to see the probable influence of their writings on the
science of the coming time. For many years, therefore, it was
my habit to place every physical paper published by these
eminent men within the reach of purely English readers.

The translation of the lecture on the ' Wechselwirkung der
Naturkrafte/ printed in the following series, had this origin.
It appears here with the latest emendations of the author
introduced by Dr. Atkinson.

The evident aim of these Lectures is to give to those 'whose
education has been mainly literary,' an intelligent interest
in the researches of science. Even among such persons the
reputation of Helmholtz is so great as to render it almost super-
fluous for me to say that the intellectual nutriment here offered
is of the very first quality.

Soon after the publication of the 'Tonempfindungen' by
Helmholtz, I endeavoured to interest the Messrs. Longman in the
work, urging that the publication of a translation of it would
be an honour to their house. They went carefully into the
question of expense, took sage counsel regarding the probable
sale, and came reluctantly to the conclusion that it would not
be remunerative.1 I then recommended the translation of these
' Populare Vortrage,' and to this the eminent publishers imme-
diately agreed.

Hence the present volume, brought out under the editorship
of Dr. Atkinson, of the Staff4 College, Sandhurst. The names
of the translators are, I think, a guarantee that their work will
be worthy of their original.

JOHN TYNDALL.

ROTAL INSTITUTION:
March 1873.

1 Since the date of the foregoing letter from Professor Tyndall, Messrs.
Longman & Co. have made arrangements for the translation of Helmholtz's
Tonempjindungen, by Mr. Alexander J. Ellis, F.R.S. &c.

OX THE

EELATION OF NATUEAL SCIENCE1
TO GENERAL SCIENCE.

Academical Discourse delivered at Heidelberg, November 22, 1862,
BY DK. H. HELMHOLTZ, SOMETIME TROKECTOK.

TO-DAY we are met, according to annual custom, in grateful
commemoration of an enlightened sovereign of this kingdom,
Charles Frederick, who, in an age when the ancient fabric of
European society seemed tottering to its fall, strove, with lofty
purpose and untiring zeal, to promote the welfare of his sub-
jects, and, above all, their moral and intellectual development-
Kightly did he judge that by no means could he more effectually
realise this beneficent intention than by the revival and the
encouragement of this University. Speaking, as I do, on such
an occasion, at once in the name and in the presence of the
whole University, I have thought it well to try and take, as far

1 The Gorman word Naturwissunschaft has no exact equivalent in modern
English, including, as it does, both the Physical and the Natural Sciences.
Curiously enough, in the original charter of the Royal Society, the phrase
Natural Knowledge covers the same ground, but is there used in opposition
to supernatural knowledge. (Note in Buckle's Civilisation, vol. ii. p. 341.) —
TR.

2 ON THE RELATION OF

a* is permitted by the narrow standpoint of a single student
a general view of the connection of the several sciences, and c
their study.

It may, indeed, be thought that, at the present day, those
relations between the different sciences which have led us to
combine them under the name Universitas Litterarum, have
become looser than ever. We see scholars and scientific men
absorbed in specialities of such vast extent, that the most
universal genius cannot hope to master more than a small
section of our present range of knowledge. For instance, the
philologists of the last three centuries found ample occupation
in the study of Greek and Latin ; at best they added to it the
knowledge of two or three European languages, acquired for
practical purposes. But now comparative philology aims at
nothing less than an acquaintance with all the languages of all
branches of the human family, in order to deduce from them
the laws by which language itself has been formed, and to this
gigantic task it has already applied itself with superhuman
industry. Even classical philology is no longer restricted to
the study of those works which, by their artistic perfection
and precision of thought, or because of the importance of their
contents, have become models of prose and poetry to all ages.
On the contrary, we have learnt that every lost fragment of
an ancient author, every gloss of a pedantic grammarian, every
allusion of a Byzantine court-poet, every broken tombstone
found in the wilds of Hungary or Spain or Africa, may con-
tribute a fresh fact, or fresh evidence, and thus serve to increase
our knowledge of the past. And so another group of scholars are
busy with the vast scheme of collecting and cataloguing, for the
•use of their successors, every available relic of classical antiquity.
Add to this, in history, the study of original documents, the
critical examination of parchments and papers accumulated in
the archives of states and of towns ; the combination of details
scattered up and down in memoirs, in correspondence, and in
biographies ; the deciphering of hieroglyphics and cuneiform in-
scriptions; in natural history the more and more comprehensive
classification of minerals, plants, and animals, as well living as

NATURAL SCIENCE TO GENERAL SCIENCE. 3

extinct; and there opens out before us an expanse of knowledge the
contemplation of which may well bewilder us. In all these sciences
the range of investigation widens as fast as the means of obser-
vation improve. The zoologists of past times were content to
have described the teeth, the hair, the feet, and other external
characteristics of an animal. The anatomist, on the other hand,
confined himself to human anatomy, so far as he could make
it out by the help of the knife, the saw, and the scalpel, with
the occasional aid of injections of the vessels. Human anatomy
then passed for an unusually extensive and difficult study. Now
we are no longer satisfied with the comparatively rough science
which bore the name of human anatomy, and which, though
without reason, was thought to be almost exhausted. We
have added to it comparative anatomy — that is, the anatomy
of all animals — and microscopic anatomy, both of them sciences
of infinitely wider range, which now absorb the interest of
students.

The four elements of the ancients and of mediaeval alchemy
have been increased to sixty-four, the last four of which are
due to a method invented in our own University, which pro-
mises still further discoveries. l But not merely is the number
of the elements far greater, the methods of producing compli-
cated combinations of them have been so vastly improved, that
what is called organic chemistry, which embraces only com-
pounds of carbon with oxygen, hydrogen, nitrogen, and a few
other elements, has already taken rank as an independent
science.

' As the stars of heaven for multitude ' was in ancient times
the natural expression for a number beyond our comprehension,
Pliny even thinks it almost presumption (' rem etiam Deo im-
probam') on the part of Hipparchus to have undertaken to
count the stars and to determine their relative positions. And
yet none of the catalogues up to the seventeenth centuiy, con-
structed without the aid of telescopes, give more than from

1 That is the method of spectrum analysis, due to Bunscn and Kirchoft', both
of Heidelberg. The elements alluded to are caesium, rubidium, thallium, and
iridium.

B2

4 ON THK RELATION OF

1,000 to 1,500 stars of magnitudes from the first to the fifth.
At present several observatories are engaged in continuing these
catalogues down to stars of the tenth magnitude ; so that up-
wards of 200,000 fixed stars are to be catalogued and their places
accurately determined. The immediate result of these obser-
vations has been the discovery of a great number of new
planets; so that, instead of the six known in 1781, there are
now seventy-five.1

The contemplation of this astounding activity in all branches
of science may well make us stand aghast at the audacity of
man, and exclaim with the Chorus in the ' Antigone ' : ' Who
can survey the whole field of knowledge 1 Who can grasp the
clues, and then thread the labyrinth 1 ' One obvious consequence
of this vast extension of the limits of science is, that every
student is forced to choose a narrower and narrower field for
his own studies, and can only keep up an imperfect acquaintance
even with allied fields of research. It almost raises a smile to
hear that in the seventeenth century Kepler was invited to
Gratz as professor of mathematics and moral philosophy : and
that at Leyden, in the beginning of the eighteenth, Boerhave
occupied at the same time the chairs of botany, chemistry, and
clinical medicine, and therefore practically that of pharmacy as
well. At present we require at least four professors, or, in an
university with its full complement of teachers, seven or eight,
to represent all these branches of science. And the same is
true of other faculties.

One of my strongest motives for discussing to-day the con-
nection of the different sciences is that I am myself a student
of natural philosophy; and that it has been made of late a
reproach against natural philosophy that it has struck out a
path of its own, and has separated itself more and more widely
from the other sciences which are united by common philological
and historical studies. This opposition has, in fact, been long
apparent, and seems to me to have grown up mainly under the
influence of the Hegelian philosophy, or, at any rate, to have

1 At the end of November 1864, the 82nd of the small planets, Alcmene, was
discovered. There are now 109.

NATURAL SCIENCE TO GENERAL SCIENCE. 5

been brought out into more distinct relief by that philosophy.
Certainly, at the end of the last century, when the Kantian
philosophy reigned supreme, such a schism had never been pro-
claimed; on the contrary, Kant's philosophy rested on exactly
the same ground as the physical sciences, as is evident from his
own scientific works, especially from his 'Cosmogony,' based
upon Newton's Law of Gravitation, which afterwards, under
the name of Laplace's Nebular Hypothesis, came to be uni-
versally recognised. The sole object of Kant's 'Critical Phi-
losophy ' was to test the sources and the authority of our
knowledge, and to fix a definite scope and standard for the
researches of philosophy, as compared with other sciences.
According to his teaching, a principle discovered a priori by
pure thought was a rule applicable to the method of pure
thought, and nothing further ; it could contain no real, positive
knowledge. The ' Philosophy of Identity ' l was bolder. It
started with the hypothesis that not only spiritual phenomena,
but even the actual world — nature, that is, and man — were the
result of an act of thought on the part of a creative mind,
similar, it was supposed, in kind to the human mind. On this
hypothesis it seemed competent for the human mind, even with-
out the guidance of external experience, to think over again the
thoughts of the Creator, and to rediscover them by its own
inner activity. Such was the view with which the ' Philosophy
of Identity' set to work to construct a priori the results of
other sciences. The process might be more or less successful in
matters of theology, law, politics, language, art, history, in short,
in all sciences the subject-matter of which really grows out of
our moral nature, and which are therefore properly classed
together under the • name of moral sciences. The state, the
church, art and language, exist in order to satisfy certain moral
needs of man. Accordingly, whatever obstacles nature, or
chance, or the rivalry of other men may interpose, the eiforts of
the human mind to satisfy its needs, being systematically directed
to one end, must eventually triumph over all such fortuitous

1 So called because it proclaimed the identity not only of subject and object,
but of contradictories, such as existence and non-existence. — Til.

6 ON THE RELATION OF

hindrances. Under these circumstances, it would not be a
downright impossibility for a philosopher, starting from an exact
knowledge of the mind, to predict the general course of human
development under the above-named conditions, especially if
he has before his eyes a basis of observed facts, on which to
build his abstractions. Moreover, Hegel was materially assisted,
in his attempt to solve this problem, by the profound and philo-
sophical views on historical and scientific subjects with which
the writings of his immediate predecessors, both poets and phi-
losophers, abound. He had, for the most part, only to collect
and combine them, in order to produce a system calculated to
impress people by a number of acute and original observations.
He thus succeeded in gaining the enthusiastic approval of most
of the educated men of his time, and in raising extravagantly
sanguine hopes of solving the deepest enigma of human life ; all
the more sanguine doubtless, as the connection of his system
was disguised under a strangely abstract phraseology, and was
perhaps really understood by but few of his worshippers.

But even granting that Hegel was more or less successful in
constructing, a priori, the leading results of the moral sciences,
still it was no proof of the correctness of the hypothesis of
Identity, with which he started. The facts of nature would
have been the crucial test. That in the moral sciences traces of
the activity of the human intellect and of the several stages of
its development should present themselves, was a matter of
course ; but surely, if nature really reflected the result of the
thought of a creative mind, the system ought, without difficulty,
to find a place for her comparatively simple phenomena and
processes. It was at this point that Hegel's philosophy, we
venture to say, utterly broke down. His system of nature
seemed, at least to natural philosophers, absolutely crazy. Of
all the distinguished scientific men who were his contem-
poraries, not one was found to stand up for his ideas. Accord-
ingly, Hegel himself, convinced of the importance of winning
for his philosophy in the field of physical science that recog-
nition which had been so freely accorded to it elsewhere,
launched out, with unusual vehemence and acrimony, against

NATURAL SCIENCE TO GENERAL SCIENCE. 7

the natural philosophers, and especially against Sir Isaac Newton,
as the first and greatest representative of physical investigation.
The philosophers accused the scientific men of narrowness; the
scientific men retorted that the philosophers were crazy. And
so it came about that men of science began to lay some stress on
the banishment of all philosophic influences from their work ;
while some of them, including men of the greatest acuteness,
went so far as to condemn philosophy altogether, not merely as
useless, but as mischievous dreaming. Thus, it must be con-
fessed, not only were the illegitimate pretensions of the Hegelian
system to subordinate to itself all other studies rejected, but no-
regard was paid to the rightful claims of philosophy, that is,
the criticism of the sources of cognition, and the definition of
the functions of the intellect.

In the moral sciences the course of things was different,
though it ultimately led to almost the same result. In all
branches of those studies, in theology, politics, jurisprudence,
aesthetics, philology, there started up enthusiastic Hegelians,
who tried to reform their several departments in accordance
with the doctrines of their master, and, by the royal road of
speculation, to reach at once the promised land and gather in
the harvest, which had hitherto only been approached by long
and laborious study. And so, for some time, a hard and fast
line was drawn between the moral and the physical sciences ;
in fact, the very name of science was often denied to the
latter.

The feud did not long subsist in its original intensity. The
physical sciences proved conspicuously, by a brilliant series of
discoveries and practical applications, that they contained a
healthy germ of extraordinary fertility ; it was impossible any
longer to withhold from them recognition and respect. And
even in other departments of science, conscientious investigators-
of facts soon protested against the over-bold flights of specu-
lation. Still, it cannot be overlooked that the philosophy of
Hegel and Schelling did exercise a beneficial influence ; since their
time the attention of investigators in the moral sciences had
been constantly and more keenly directed to the scope of those

8 ON THE RELATION OF

sciences, and to their intellectual contents, and therefore the
great amount of labour bestowed on those systems has not
been entirely thrown away.

We see, then, that in proportion as the experimental inves-
tigation of facts has recovered its importance in the moral
sciences, the opposition between them and the physical sciences
has become less and less marked. Yet we must not forget
that, though this opposition was brought out in an unnecessarily
exaggerated form by the Hegelian philosophy, it has its founda-
tion in the nature of things, and must, sooner or later, make
itself felt. It depends partly on the nature of the intellectual
processes the two groups of sciences involve, partly, as their
very names imply, on the subjects of which they treat. It is
not easy for a scientific man to convey to a scholar or a jurist a
clear idea of a complicated process of nature ; he must demand
of them a certain power of abstraction from the phenomena, as
well as a certain skill in the use of geometrical and mechanical
conceptions, in which it is difficult for them to follow him. On
the other hand an artist or a theologian will perhaps find the
natural philosopher too much inclined to mechanical and
material explanations, which seem to them commonplace, and
chilling to their feeling and enthusiasm. Nor will the scholar
or the historian, who have some common ground with the
theologian and the jurist, fare better with the natural philo-
sopher. They will find him shockingly indifferent to literary
treasures, perhaps even more indifferent than he ought to be to
the history of his own science. In short, there is no denying
that, while the moral sciences deal directly with the nearest
and dearest interests of the human mind, and with the insti-
txitions it has brought into being, the natural sciences are con-
cerned with dead, indifferent matter, obviously indispensable
for the sake of its practical utility, but apparently without any
immediate bearing on the cultivation of the intellect.

It has been shown, then, that the sciences have branched
out into countless ramifications, that there has grown up
between different groups of them a real and deeply felt opposi-
tion, that finally no single intellect can embrace the whole range

NATURAL SCIENCE TO GENERAL SCIENCE.

or even a considerable portion of it. Is it still reasonable to
keep them together in one place of education ? Is the union
of the four faculties to form one University a mere relic of the
Middle Ages 1 Many valid arguments have been adduced for
separating them. Why not dismiss the medical faculty to the
hospitals of our great towns, the scientific men to the Poly-
technic Schools, and form special seminaries for the theologians
and jurists? Long may the German universities be preserved
from such a fate ! Then, indeed, would the connection between
the different sciences be finally broken. How essential that
connection is, not only from an university point of view, as
tending to keep alive the intellectual energy of the country, but
also on material grounds, to secure the successful application of
that energy, will be evident from a few considerations.

First, then, I would say that union of the different faculties
is necessary to maintain a healthy equilibrium among the in-
tellectual energies of students. Each study tries certain of our
intellectual faculties more than the rest, and strengthens them
accordingly by constant exercise. But any sort of one-sided
development is attended with danger ; it disqualifies us for
using those faculties that are less exercised, and so renders us
less capable of a general view ; above all it leads us to overvalue
ourselves. Any one who has found himself much more suc-
cessful than others in some one department of intellectual labour,
is apt to forget that there are many other things which they can
do better than he can : a mistake — I would have every student
remember — which is the worst enemy of all intellectual
activity.

How many men of ability have forgotten to practise that
criticism of themselves which is so essential to the student, and
so hard to exercise, or have been completely crippled in their
progress, because they have thought dry, laborious drudgery
beneath them, and have devoted all their energies to the quest
of brilliant theories and wonder-working discoveries ! How
many such men have become bitter misanthropes, and put an end
to a melancholy existence, because they have failed to obtain
among their fellows that recognition which must be won by

10 ON THE RELATION OF

labour and results, but which is ever withheld from mere self-con-
scious genius ! And the more isolated a man is, the more liable
is he to this danger ; while, on the other hand, nothing is more
inspiriting than to feel yourself forced to strain every nerve to
win the admiration of men whom you, in your turn, must admire.

In comparing the intellectual processes involved in the
pursuit of the several branches of science, we are struck by
certain generic differences, dividing one group of sciences from
another. At the same time it must not be forgotten that every
man of conspicuous ability has his own special mental constitution
which fits him for one line of thought rather than another.
Compare the work of two contemporary investigators even
in closely allied branches of science, and you will generally be
able to convince yourself that the more distinguished tlfe men are
the more clearly does their individuality come out, and the less
qualified would either of them be to canyon the other's researches.
To-day I can, of course, do nothing more than characterise
some of the most general of these differences.

I have already noticed the enormous mass of the materials
accumulated by science. It is obvious that the organisation-
and arrangement of them must be proportionately perfect, if
we are not to be hopelessly lost in the maze of erudition.
One of the reasons why we can so far surpass our predecessors
in each individual study is that they have shown us how to
organise our knowledge.

This organisation consists, in the first place, of a mechanical
arrangement of materials, such as is to be found in our cata-
logues, lexicons, registers, indexes, digests, scientific and literary
annuals, systems of natural history, and the like. By these
appliances thus much at least is gained, that such know-
ledge as cannot be carried about in the memory is immedi-
ately accessible to anyone who wants it. With a good lexicon a
school-boy of the present day can achieve results in the inter-
pretation of the classics which an Erasmus, with the erudition
of a lifetime, could hardly attain. Works of this kind form, so
to speak, our intellectual principal with the interest of which
we trade : it is, so to speak, like capital invested in land. The

NATURAL SCIENCE TO GENERAL SCIENCE. 11

learning buried in catalogues, lexicons, and indexes looks as
bare and uninviting as the soil of a farm ; the uninitiated cannot
see or appreciate the labour and capital already invested there ;
to them the work of the ploughman seems infinitely dull, weary,
and monotonous. But though the compiler of a lexicon or of
a system of natural history must be prepared to encounter
labour as weary and as obstinate as the ploughman's, yet it
need not be supposed that his work is of a low type, or that it is
by any means as dry and mechanical as it looks when we have
it before us in black and white. In this, as in any other sort of
scientific work, it is necessary to discover every fact by careful
observation, then to verify and collate them, and to separate
what is important from what is not. All this requires a
man with a thorough grasp both of the object of the
compilation and of the matter and methods of the science;
and for such a man every detail has its bearing on the
whole, and its special interest. Otherwise dictionary-making
would be the vilest drudgery imaginable.1 That the influence
of the progressive development of scientific ideas extends to
these works is obvious from the constant demand for new
lexicons, new natural histories, new digests, new catalogues of
stars, all denoting advancement in the art of methodising and
organising science.

But our knowledge is not to lie dormant in the shape of
catalogues. The very fact that we must carry it about in black
and white shows that our intellectual mastery of it is incomplete.
It is not enough to be acquainted with the facts; scientific
knowledge begins only when their laws and their causes are un-
veiled. Our materials must be worked up by a logical process ;
and the first step is to connect like with like, and to elaborate a
general conception embracing them all. Such a conception, as
the name implies, takes a number of single facts together, and
stands as their representative in our mind. We call it a general
conception, or the conception of a genus, when it embraces a
number of existing objects; we call it a law when it embraces a
series of incidents or occurrences. When, for example, I have
1 Condcndnque lexica mnndat damnatis. — Tit.

12 ON THE RELATION OK

made out that all mammals— that is, all warm-blooded, vivi-
parous animals— breathe through lungs, have two chambers in
the heart, and at least three tympanal bones, I need no longer
remember these anatomical peculiarities in the individual cases
of the monkey, the dog, the horse, and the whale; the general
rule includes a vast number of single instances, and represents
them in my memory. When I enunciate the law of refraction,
not only does this law embrace all cases of rays falling at all
possible angles on a plane surface of water, and inform me of
the result, but it includes all cases of rays of any colour incident
on transparent surfaces of any form and any constitution what-
soever. This law, therefore, includes an infinite number of
cases, which it would have been absolutely impossible to carry
in one's memoiy. Moreover, it should be noticed that not only
does this law include the cases which we ourselves or other men
have already observed, but that we shall not hesitate to apply it
to new cases, not yet observed, with absolute confidence in the
reliability of our results. In the same way, if we were to find
a new species of mammal, not yet dissected, we are entitled to
assume, with a confidence bordering on a certainty, that it has
lungs, two chambers in the heart, and three or more tympanal
bones.

Thus, when we combine the results of experience by a pro-
cess of thought, and form conceptions, whether general concep-
tions or laws, we not only bring our knowledge into a form in
which it can be easily used and easily retained, but we actually
enlarge it, inasmuch as we feel ourselves entitled to extend the
rules and the laws we have discovered to all similar cases that
may be hereafter presented to us.

The above-mentioned examples are of a class in which the
mental process of combining a number of single cases so as to
form conceptions is unattended by farther difficulties, and can be
distinctly followed in all its stages. But in complicated cases it
is not so easy completely to separate like facts from unlike, and
to combine them into a clear well-defined conception. Assume
that we know a man to be ambitious ; we shall perhaps be able
to predict with tolerable certainty that if he has to act under

NATURAL SCIENCE TO GENERAL SCIENCE. 13

certain conditions, he will follow the dictates of his ambition,
and decide on a certain line of action. But, in the first place,,
we cannot define with absolute precision what constitutes an
ambitious man, or by what standard the intensity of his ambition
is to be measured: nor, again, can we say precisely what degree
of ambition must operate in order to impress the given direction
on the actions of the man under those particular circumstances.
Accordingly, we institute comparisons between the actions of
the man in question, as far as we have hitherto observed them,
and those of other men who in similar cases have acted as he
has done, and we draw our inference respecting his future actions
without being able to express either the major or the minor pre-
miss in a clear, sharply defined form — perhaps even without hav-
ing convinced ourselves that our anticipation rests on such an
analogy as I have described. In such cases our decision proceeds
only from a certain psychological instinct, not from conscious
reasoning, though in reality we have gone through an intellectual
process identical with that which leads ns to assume that a
newly discovered mammal has lungs.

This latter kind of induction, which can never be perfectly
assimilated to forms of logical reasoning, nor pressed so far as to
establish universal laws, plays a most important part in human
life. The whole of the process by which we translate our sen-
sations into perceptions depends upon it, as appears especially
from the investigation of what are called illusions. For in-
stance, when the retina of the eye is irritated by a blow, we
imagine we see a light in our field of vision, because we have,
throughout our lives, felt irritation in the optic nerves only
when there was light in the field of vision, and have become
accustomed to identify the sensations of those nerves with the
presence of light in the field of vision. Moreover, such is the
complexity of the influences affecting the formation both of
character in general and of the mental condition at any given
moment, that this same kind of induction necessarily plays a
leading part in the investigation of psychological processes. In
fact, in ascribing to ourselves free-will, that is, full power to act
as we please without being subject to a stern inevitable law of

14 ON THE RELATION OF

causality, we deny in toto the possiblity of referring at least one
of the ways in which our mental activity expresses itself to a
rigorous law.

We might possibly, in opposition to logical induction which
reduces a question to clearly denned universal propositions, call
this kind of reasoning cesthetie induction, because it is most con-
spicuous in the higher class of works of art. It is an essential
part of an artist's talent to reproduce by words, by form, by
colour, or by music, the external indications of a character or a
state of mind, and by a kind of instinctive intuition, uncon-
trolled by any definable rule, to seize the necessary steps by
which we pass from one mood to another. If we do find that
the artist has consciously worked after general rules and abstrac-
tions, we think his work poor and commonplace, and cease to
admire. On the contrary, the works of great artists bring be-
fore us characters and moods with such a lifelikeness, with such
a wealth of individual traits and such an overwhelming con-
viction of truth, that they almost seem to be more real than the
reality itself, because all disturbing influences are eliminated.

Now if, after these reflections, we proceed to review the
different sciences, and to classify them according to the method
by which they must arrive at their results, we are brought face
to face with a generic difference between the natural and the
moral sciences. The natural sciences are for the most part in
a position to reduce their inductions to sharply defined general
rules and principles; the moral sciences, on the other hand, have,
in by far the most numerous cases, to do with conclusions
arrived at by psychological instinct. Philology, in so far as it
is concerned with the interpretation and emendation of the
texts handed down to us, must seek to feel out, as it were, the
meaning which the author intended to express, and the accessory
notions which he wished his words to suggest : and for that pur-
pose it is necessary to start with a correct insight, both into the
personality of the author, and into the genius of the language
in which he wrote. All this affords scope for {esthetic, but
not for strictly logical, induction. It is only possible to pass
judgment, if you have ready in your memory a great number of

NATURAL SCIENCE TO GENERAL SCIENCE. 15

similar facts, to be instantaneously confronted with the question
you are trying to solve. Accordingly, one of the first requisites
for studies of this class is an accurate and ready memory.
Many celebrated historians and philologists have, in fact,
astounded their contemporaries by their extraordinary strength of
memory. Of course memory alone is insufficient without a
knack of everywhere discovering real resemblance, and without
a delicately and fully trained insight into the springs of human
action; while this again is unattainable without a certain
warmth of sympathy and an interest in observing the working
of other men's minds. Intercourse with our fellow-men in
daily life must lay the foundation of this insight, but the study
of history and art serves to make it richer and completer, for
there we see men acting under comparatively unusual conditions,
and thus come to appreciate the full scope of the energies which
lie hidden in our breasts.

None of this group of sciences, except grammar, lead us, as a
rule, to frame and enunciate general laws, valid under all circum-
stances. The laws of grammar are a product of the human
will, though they can hardly be said to have been framed de-
liberately, but rather to have grown up gradually, as they were
wanted. Accordingly, they present themselves to a learner
rather in the form of commands, that is, of laws imposed by
external authority.

With these sciences theology and jurisprudence are naturally
connected. In fact, certain branches of history and philology
serve both as stepping-stones and as handmaids to them. The
general laws of theology and jurisprudence are likewise com-
mands, laws imposed by external authority to regulate, from a
moral or juridical point of view, the actions of mankind ; not
laws which, like those of nature, contain generalisations from a
vast multitude of facts. At the same time the application of a
grammatical, legal, moral, or theological rule is couched, like the
application of a law of nature to a particular case, in the forms of
logical inference. The rule forms the major premiss of the
syllogism, while the minor must settle whether the case in ques-
tion satisfies the conditions to which the rule is intended to

16 OX THK RELATION OF

apply. The solution of this latter problem, whether in gram-
matical analysis, where the meaning of a sentence is to be
evolved, or in the legal criticism of the credibility of the facts
alleged, of the intentions of the parties, or of the meaning of
the documents they have put into court, will, in most cases, be
again a matter of psychological insight. On the other hand, it
should not be forgotten that both the syntax of fully developed
languages and a system of jurisprudence gradually elaborated, as
ours has been, by the practice of more than 2,000 years,1 have
reached a high pitch of logical completeness and consistency; so
that, speaking generally, the cases which do not obviously fall
under some one or other of the laws actually laid down are quite
exceptional. Such exceptions there will always be, for the legis-
lation of man can never have the absolute consistency and
perfection of the laws of nature. In such cases there is no-
course open but to try and guess the intention of the legislator;
or, if needs be, to supplement it after the analogy of his decisions
in similar cases.

Grammar and juiisprudence have a certain advantage as
means of training the intellect, inasmuch as they tax pretty
equally all the intellectual powers. On this account secondary
education among modern European nations is based mainly
upon the grammatical study of foreign languages. The mother-
tongue and modern foreign languages, when acquired solely by
practice, do not call for any conscious logical exercise of thought,
though we may cultivate by means of them an appreciation for
artistic beauty of expi-ession. The two classical languages,
Latin and Greek, have, besides their exquisite logical subtlety
and aesthetic beauty, an additional advantage, which they seem
to possess in common with most ancient and original languages
—they indicate accurately the relations of words and sentences
to each other by numerous and distinct inflexions. Languages
are, as it were, abraded by long use ; grammatical distinctions
are cut down to a minimum for the sake of brevity and rapidity

» It should be remembered that the Roman law, which has only partially
nnd indirectly influenced English practice, is the recognised basis of German
jurisprudence. — Ti:.

NATURAL SCIENCE TO GENERAL SCIENCE. 17

of expression, and are thus made less and less definite, as is
obvious from the comparison of any modern European language
with Latin ; in English the process has gone further than in
any other. This seems to me to be really the reason why the
modern languages are far less fitted than the ancient for instru-
ments of education.1

As grammar is the staple of school education, legal studies
are used, and rightly, as a means of training persons of maturer
age, even when not specially required for professional purposes.

We now come to those sciences which, in respect of the kind
of intellectual labour they require, stand at the opposite end
of the series to philology and history ; namely, the natural and
physical sciences. I do not mean to say that in many branches
even of these sciences an instinctive appreciation of analogies
and a certain artistic sense have no part to play. On the
contrary, in natural history the decision which characteristics
are to be looked upon as important for classification, and which
as unimportant, what divisions of the animal and vegetable
kingdoms are more natural than others, is really left to an
instinct of this kind, acting without any strictly definable rule.
And it is a very suggestive fact that it was an artist, Goethe,
who gave the first impulse to the researches of comparative
anatomy into the analogy of corresponding organs in different
animals, and to the parallel theory of the metamorphosis of
leaves in the vegetable kingdom; and thus, in fact, really
pointed out the direction which the science has followed ever
since. But even in those departments of science where we
have to do with the least understood vital processes, it is,
speaking generally, far easier to make out general and compre-
hensive ideas and principles, and to express them in definite
language, than in cases where we must base our judgment on
the analysis of the human mind. It is only when we come to
the experimental sciences to which mathematics are applied,
and especially when we come to pure mathematics, that we

' Those to whom German is not a foreign tongue may, perhaps, be per-
mitted to hold different views on the efficacy of modern languages in educa-
tion.— TR.

18 ON THE RELATION OF

see the peculiar characteristics of the natural and physical
sciences fully brought out.

The essential differentia of these sciences seems to me to
consist in the comparative ease with which the individual
results of observation and experiment are combined under
general laws of unexceptionable validity and of an extra-
ordinarily comprehensive character. In the moral sciences, on
the other hand, this is just the point where insuperable diffi-
culties are encountered. In mathematics the general propo-
sitions which, under the name of axioms, stand at the head of
the reasoning, are so few in number, so comprehensive, and so
immediately obvious, that no proof whatever is needed for
them. Let me remind you that the whole of algebra and
aiithmetic is developed out of the three axioms : —

' Things which are equal to the same things are equal to-
one another.'

' If equals be added to equals, the wholes are equal.'

' If unequals be added to equals, the wholes are unequal.'
And the axioms of geometry and mechanics are not more
numerous. The sciences we have named are developed out of
these few axioms by a continual process of deduction from
them in more and more complicated cases. Algebra, however,,
does not confine itself to finding the sum of the most hetero-
geneous combinations of a finite number of magnitudes, but in-
the higher analysis it teaches us to sum even infinite series,
he terms of which increase or diminish according to the most
various laws ; to solve, in fact, problems which could never be
completed by direct addition. An instance of this kind shows
us the conscious logical activity of the mind in its purest and
most perfect form. On the one hand we see the laborious nature
of the process, the extreme caution with which it is necessary
to advance, the accuracy required to determine exactly the
scope of such universal principles as have been attained, the
difficulty of forming and understanding abstract conceptions.
On the other hand, we gain confidence in the certainty, the
range, and the fertility of this kind of intellectual work.

The fertility of the method comes out more strikingly in

NATURAL SCIENCE TO GENERAL SCIENCE. 19

applied mathematics, especially in mathematical physics, in-
cluding, of course, physical astronomy. From the time when
Newton discovered, by analysing the motions of the planets on
mechanical principles, that every particle of ponderable matter
in the universe attracts every other particle with a force vary-
ing inversely as the square of the distance, astronomers have
been able, in virtue of that one law of gravitation, to calculate
with the greatest accuracy the movements of the planets to the
remotest past and the most distant future, given only the posi-
tion, velocity, and mass of each body of our system at any one
time. More than that, we recognise the operation of this law
in the movements of double stars, whose distances from us are
so great that their light takes years to reach us; in some
cases, indeed, so great that all attempts to measure them have
failed.

This discovery of the law of gravitation and its consequences
is the most imposing achievement that the logical power of the
human mind has hitherto performed. I do not mean to say
that there have not been men who in power of abstraction have
equalled or even surpassed Newton and the other astronomers,
who either paved the way for his discovery, or have carried it
out to its legitimate consequences; but there has never been
presented to the human mind such an admirable subject as
those involved and complex movements of the planets, which
hitherto had served merely as food for the astrological super-
stitions of ignorant star-gazers, and were now reduced to a single
law, capable of rendering the most exact account of the minutest
detail of their motions.

The principles of this magnificent discovery have been suc-
cessfully applied to several other physical sciences, among which
physical optics and the theory of electricity and magnetism are
especially worthy of notice. The experimental sciences have
one great advantage over the natural sciences in the investiga-
tion of general laws of nature : they can change at pleasure the
conditions under which a given result takes place, and can thus
confine themselves to a small number of characteristic instances,
in order to discover the law. Of course its validity must then
c2

20 ON THE RELATION OF

stand the test of application to more complex cases. Accord-
ingly the physical sciences, when once the right methods have
been discovered, have made proportionately rapid progress.
Not only have they allowed us to look back into primaeval
chaos, where nebulous masses were forming themselves into
suns and planets, and becoming heated by the energy of their
contraction ; not only have they permitted us to investigate
the chemical constituents of the solar atmosphere and of the
remotest fixed stare, but they have enabled us to turn the
forces of surrounding nature to our own uses and to make them
the ministers of our will.

Enough has been said to show how widely the intellectual
processes involved in this group of sciences differ, for the most
part, from those required by the moi'al sciences. The mathe-
matician need have no memory whatever for detached facts, the
physicist' hardly any. Hypotheses based on the recollection of
similar cases may, indeed, be useful to guide one into the right
track, but they have no real value till they have led to a precise
and strictly defined law. Nature does not allow us for a moment
"to doubt that we have to do with a rigid chain of cause and
effect, admitting of no exceptions. Therefore to us, as her
students, goes forth the mandate to labour on till we have dis-
covered unvarying laws ; till then we dare not rest satisfied, for
then only can our knowledge grapple victoriously with time
and space and the forces of the universe.

The iron labour of conscious logical reasoning demands great
perseverance and great caution ; it moves on but slowly, and is
rarely illuminated by brilliant flashes of genius. It knows
little of that facility with which the most varied instances come
thronging into the memory of the philologist or the historian.
Rather is it an essential condition of the methodical progress of
mathematical reasoning that the mind should remain concen-
trated on a single point, undisturbed alike by collateral ideas on
the one hand, and by wishes and hopes on the other, and moving
on steadily in the direction it has deliberately chosen. A cele-
brated logician, Mr. John Stuart Mill, expresses his conviction
that the inrluctive sciences have of late done more for the advance

NATU1UL SCIENCE TO GENERAL SCIENCE. 21

of logical methods than the labours of philosophers properly so
called. One essential ground for such an assertion must un-
doubtedly be that in no department of knowledge can a fault
in the chain of reasoning be so easily detected by the incorrect-
ness of the results as in those sciences in which the results of
reasoning can be most directly compared with the facts of
nature.

Though I have maintained that it is in the physical sciences,
and especially in such branches of them as are treated mathe-
matically, that the solution of scientific problems has been most
successfully achieved, you will not, I trust, imagine that I wish
to depreciate other studies in comparison with them. If the
natural and physical sciences have the advantage of great per-
fection in form, it is the privilege of the moral sciences to deal
with a richer material, with questions that touch more nearly
the interests and the feelings of men, with the human mind
itself, in fact, in its motives and the different branches of its
activity. They have, indeed, the loftier and the more difficult
task, but yet they cannot afford to lose sight of the example of
their rivals, which, in form at least, have, owing to the more
ductile nature of their materials, made greater progress. Not
only have they something to learn from them in point of method,
but they may also draw encouragement from the greatness of
their results. And I do think that our age has learnt many
lessons from the physical sciences. The absolute, unconditional
reverence for facts, and the fidelity with which they are col^
lected, a certain distrustfulness of appearances, the effort to
detect in all cases relations of cause and effect, and the tendency
to assume their existence, which distinguish our century from
preceding ones, seem to me to point to such an influence.

I do not intend to go deeply into the question how far
mathematical studies, as the representatives of conscious logical
reasoning, should take a more important place in school educa-
tion. But it is, in reality, one of the questions of the day. In
proportion as the range of science extends, its system and or-
ganisation must be improved, and it must inevitably come about
that individual students will find themselves compelled to go

22 ON THE RELATION OF

through a stricter course of training than grammar is in a
position to supply. What strikes me in my own experience
of students who pass from our classical schools to scientific and
medical studies, is, first, a certain laxity in the application of
strictly universal laws. The grammatical rules in which they
have been exercised are for the most part followed by long
lists of exceptions; accordingly they are not in the habit of
relying implicitly on the certainty of a legitimate deduction
from a strictly universal law. Secondly, I find them for the
most part too much inclined to trust to authority, even in cases
where they might form an independent judgment. In fact, in
philological studies, inasmuch as it is seldom possible to take in
the whole of the premisses at a glance, and inasmuch as the de-
cision of disputed questions often depends on an aesthetic feeling
for beauty of expression, and for the genius of the language,
attainable only by long training, it must often happen that the
student is referred to authorities even by the best teachers.
Both faults are traceable to a certain indolence and vagueness
of thought, the sad effects of which are not confined to sub-
sequent scientific studies. But certainly the best remedy for
both is to be found in mathematics, where there is absolute
certainty in the reasoning, and no authority is recognised but •
that of one's own intelligence.

So much for the several branches of science considered as
exercises for the intellect, and as supplementing each other in
that respect. But knowledge is not the sole object of man upon
«arth. Though the sciences arouse and educate the subtlest
powers of the mind, yet a man who should study simply for the
sake of knowing, would assuredly not fulfil the purpose of his
existence. We often see men of considerable endowments, to
whom their good or bad fortune has secured a comfortable
livelihood or good social position, without giving them, at the
«ame time, ambition or energy enough to make them work,
<lragging out a weary, unsatisfied existence, while all the time
they fancy they are following the noblest aim of life by constantly
devoting themselves to the increase of their knowledge, and the
cultivation of their minds. Action alone gives a man a life

NATURAL SCIENCE TO GENERAL SCIENCE. 23

•worth living ; and therefore he must aim either at the practical
application of his knowledge, or at the extension of the limits
of science itself. For to extend the limits of science is really to
•work for the progress of humanity. Thus we pass to the second
link, uniting the different sciences, the connection, namely,
between the subjects of which they treat.

Knowledge is power. Our age, more than any other, is in a
position to demonstrate the truth of this maxim. We have
taught the forces of inanimate nature to minister to the wants
of human life and the designs of the human intellect. The
application of steam has multiplied our physical strength a
million-fold ; weaving and spinning machines have relieved us
of labours the only merit of which consisted in a deadening
monotony. The intercourse between men, with its far-reaching
influence on material and intellectual progress, has increased to
an extent of which no one could have even dreamed within the
lifetime of the older among us. But it is not merely on the
machines by which our powers are multiplied ; not merely on
rifled cannon and armour-plated ships ; not merely on accumu-
lated stores of money and the necessaries of life, that the power of
a nation rests : though these things have exercised so unmistak-
able an influence that even the proudest and most obstinate des-
potisms of our times have been forced to think of removing restric-
tions on industry, and of conceding to the industrious middle classes
a due voice in their councils. But political organisation, the
administration of justice, and the moral discipline of individual
citizens are no less important conditions of the preponderance
of civilised nations; and so surely as a nation remains in-
accessible to the influences of civilisation in these respects, so
surely is it on the high road to destruction. The several con-
ditions of national prosperity act and react on each other;
where the administi-ation of justice is uncertain, where the
interests of the majority cannot be asserted by legitimate means,
the development of the national resources, and of the power
depending upon them, is impossible; nor, again, is it possible
to make good soldiers except out of men who have learnt under
just laws to educate the sense of honour that characterises an

24 ON THE RELATION OF

independent man, certainly not out of those who have lived the
submissive slaves of a capricious tyrant.

Accordingly every nation is interested in the progress of know-
ledge on the simple ground of self-preservation, even were there no
higher wants of an ideal character to be satisfied; and not merely
in the development of the physical sciences, and their technical
application, but also in the progress of legal, political, and moral
sciences, and of the accessory historical and philological studies.
No nation which would be independent and influential can afford
to be left behind in the race. Nor has this escaped the notice of the
cultivated peoples of Europe. Never before was so large a part
of the public resources devoted to universities, schools, and
scientific institutions. "We in Heidelberg have this year occasion
to congratulate ourselves on another rich endowment granted by
our government and our parliament.

I was speaking, at the beginning of my address, of the in-
creasing division of labour and the improved organisation among
scientific workers. In fact, men of science form, as it were, an
organised army labouring on behalf of the whole nation, and
generally under its direction and at its expense, to augment the
stock of such knowledge as may serve to promote industrial
enterprise, to increase wealth, to adorn life, to improve political and
social relations, and to further the moral development of indivi-
dual citizens. After the immediate practical results of their work
we forbear to inquire; that we leave to the uninstructed. We
are convinced that whatever contributes to the knowledge of
the forces of nature or the powers of the human mind is worth
cherishing, and may, in its own due time, bear practical fruit,
very often where we should least have expected it. Who, when
Galvani touched the muscles of a frog with different metals,
and noticed their contraction, could have dreamt that eighty
years afterwards, in virtue of the self-same process, whose
earliest manifestations attracted his attention in his anatomical
researches, all Europe would be traversed with wires, flashing
intelligence from Madrid to St. Petersburg with the speed of
lightning? In the hands of Galvani, and at first even in
Volta's, electrical currents were phenomena capable of exerting

NATURAL SCIENCE TO GENERAL SCIENCE. 25-

only the feeblest forces, and could not be detected except by the
most delicate apparatus. Had they been neglected, on the
ground that the investigation of them promised no immediate
practical result, we should now be ignorant of the most import-
ant and most interesting of the links between the various forces
of nature. When young Galileo, then a student at Pisa, noticed
one day during divine service a chandelier swinging backwards
and forwards, and convinced himself, by counting his pulse, that
the duration of the oscillations was independent of the arc
through which it moved, who could know that this discovery
would eventually put it in our power, by means of the pendulum,
to attain an accuracy in the measurement of time till then
deemed impossible, and would enable the storm-tossed seaman
in the most distant oceans to determine in what degree of longi-
tude he was sailing 1

Whoever, in the pursuit of science, seeks after immediate
practical utility, may generally rest assured that he will seek in
vain. All that science can achieve is a perfect knowledge and a
perfect understanding of the action of natural and moral forces.
Each individual student must be content to find his reward in-
rejoicing over new discoveries, as over new victories of mind
over reluctant matter, or in enjoying the aasthetic beauty of a
well-ordered field of knowledge, where the connection and the
filiation of every detail is clear to the mind, and where all
denotes the presence of a ruling intellect ; he must rest satisfied
with the consciousness that he too has contributed something to
the increasing fund of knowledge on which the dominion of man
over all the forces hostile to intelligence reposes. He will,
indeed, not always be permitted to expect from his fellow -men
appreciation and reward adequate to the value of his work. It
is only too true that many a man to whom a monument ha*
been erected after his death would have been delighted to receive
during his lifetime a tenth part of the money .spent in doing
honour to his memory. At the same time, we must acknowledge-
that the value of scientific discoveries is now far more fully recog-
nised than formerly by public opinion, and that instances of the
authors of great advances in science starving in obscurity have

•26 ON THE RELATION OF

Taecome rarer and rarer. On the contrary, the governments and
peoples of Europe have, as a rule, admitted it to be their duty
-to recompense distinguished achievements in science by appro-
priate appointments or special rewards.

The sciences have then, in this respect, all one common aim,
to establish the supremacy of intelligence over the world:
while the moral sciences aim directly at making the resources of
intellectual life more abundant and more interesting, and seek
to separate the pure gold of truth from alloy, the physical
sciences are striving indirectly towards the same goal, inasmuch
as they labour to make mankind more and more independent of
the material restraints that fetter their activity. Each student
works in his own department, he chooses for himself those tasks
for which he is best fitted by his abilities and his training.
But each one must be convinced that it is only in connection
with others that he can further the great work, and that therefore
he is bound, not only to investigate, but to do his utmost to
make the results of his investigation completely and easily
accessible. If he does this, he will derive assistance from others,
and will in his turn be able to render them his aid. The annals
.of science abound in evidence how such mutual services have
been exchanged, even between departments of science apparently
most remote. Historical chronology is essentially based on
astronomical calculations of eclipses, accounts of which are pre-
served in ancient histories. Conversely, many of the important
data of astronomy — for instance, the invariability of the length
of the day, and the periods of several comets — I'est upon ancient
histories 1 notices. Of late years, physiologists, especially Briicke,
have actually undertaken to draw up a complete system of all
the vocables that can be produced by the organs of speech, and to
base upon it propositions for an universal alphabet, adapted to
all human languages. Thus physiology has entered the service
-of comparative philology, and has already succeeded in account-
ing for many apparently anomalous substitutions, on the ground
that they are governed, not as hitherto supposed, by the laws of
euphony, but by similarity between the movements of the mouth
that produce them. Again, comparative philology gives us

NATURAL SCIENCE TO GENERAL SCIENCE. 27

information about the relationships, the separations, and the
migrations of tribes in prehistoric times, and of the degree of
civilisation which they had reached at the time when they
parted. For the names of objects to which they had already
learnt to give distinctive appellations reappear as words common
to their later languages. So that the study of languages actually
gives us historical data for periods respecting which no other
historical evidence exists.1 Yet again I may notice the help
which not only the sculptor, but the archaeologist, concerned
with the investigation of ancient statues, derives from anatomy.
And if I may be permitted to refer to my own most recent studies,
I would mention that it is possible, by reference to physical
acoustics and to the physiological theory of the sensation of
hearing, to account for the elementary principles on which our
musical system is constructed, a problem essentially within the
sphere of aesthetics. In fact, it is a general principle that the
physiology of the organs of sense is most intimately connected
with psychology, inasmuch as physiology traces in our sensations
the results of mental processes which do not fall within the
sphere of consciousness, and must therefore have remained inac-
cessible to us.

I have been able to quote only some of the most striking
instances of this interdependence of different sciences, and such
as could be explained in a few words. Natui-ally, too, I have
tried to choose them from the most widely separated sciences.
But far wider is of course the influence which allied sciences
exert upon each other. Of that I need not speak, for each of
you knows it from his own experience.

In conclusion, I would say, let each of us think of himself,
not as a man seeking to gratify his own thirst for knowledge,
or to promote his own private advantage, or to shine by his
own abilities, but rather as a fellow-labourer in one great com-
mon work bearing upon the highest interests of humanity.
Then assuredly we shall not fail of our reward in the approval
•of our own conscience and the esteem of our fellow-citizens.

1 See, for example, Mommsen's Rome, Book I. ch. ii. — Tis.

28 ON THE RELATION OF NATURAL SCIENCE.

To keep up these relations between all searchers after truth and
all branches of knowledge, to animate them all to vigorous co-
operation towards their common end, is the great office of the
Universities. Therefore is it necessary that the four faculties
should ever go hand in hand, and in this conviction will we
strive, so far as in us lies, to press onward to the fulfilment of
our great mission.

29

ON

GOETHE'S SCIENTIFIC RESEARCHES.

A Lecture delivered before the German Society of Konigsberg, in the
Spring of 1853.

IT could not but be that Goethe, whose comprehensive genius
•was most strikingly apparent in that sober clearness with which
he grasped and reproduced with lifelike freshness the realities
of nature and human life in their minutest details, should, by
those very qualities of his mind, be drawn towards the study of
physical science. And in that department, he was not content
with acquiring what others could teach him, but he soon at-
tempted, as so original a mind was sure to do, to strike out an in-
dependent and a very characteristic line of thought. He directed
his energies not only to the descriptive but also to the experi-
mental sciences ; the chief results being his botanical and
osteological treatises on the one hand, and his theory of colour-
on the other. The first germs of these researches belong for
the most part to the last decade of the eighteenth century,
though some of them were not completed nor published till
later. Since that time science has not only made great progress,
but has widely extended its range. It has assumed in some
respects an entirely new aspect, it has opened out new fields of
research and undergone many changes in its theoretical views.
I shall attempt in the following Lecture to sketch the rela-
tion of Goethe's researches to the present standpoint of science,
and to bring out the guiding idea that is common to them all.

30 ON GOETHE'S SCIENTIFIC RESEARCHES.

The peculiar character of the descriptive sciences— botany r
zoology, anatomy, and the like — is a necessary result of the
work" imposed upon them. They undertake to collect and sift
an enormous mass of facts, and, above all, to bring them into a
logical order or system. Up to this point their work is only
the dry task of a lexicographer ; their system is nothing more
than a muniment-room in which the accumulation of papers is
so arranged that any one can find what he wants at any moment.
The more intellectual part of their work and their real interest
only begins when they attempt to feel after the scattered traces
of law and order in the disjointed, heterogeneous mass, and out
of it to construct for themselves an orderly system, accessible at
a glance, in which every detail has its due place, and gains
additional interest from its connection with the whole.

In such studies, both the organising capacity and the insight
of our poet found a congenial sphere — the epoch was moreover
propitious to him. He found ready to his hand a sufficient
store of logically arranged materials in botany and comparative
anatomy, copious and systematic enough to admit of a compre-
hensive view, and to indicate the way to some happy glimpse
of an all-pervading la\v ; while his contemporaries, if they made
any efforts in this direction, wandered without a compass, or
else they were so absorbed in the dry registration of facts, that
they scarcely ventured to think of anything beyond. It was
reserved for Goethe to introduce two ideas of infinite fruit-
fulness.

The first was the conception that the differences in the
anatomy of different animals are to be looked upon as variations
from a common phase or type, induced by differences of habit,
locality, or food. The observation which led him to this fertile
conception was by no means a striking one ; it is to be found in
a monograph on the intermaxillary bone, written as early as
1786. It was known that in most vertebrate animals (that is,
mammalia, birds, amphibia, and fishes) the upper jaw consists
of two bones, the upper jaw-bone and the intermaxillary bone.
The former always contains in the mammalia the molar and
the canine teeth, the latter the incisors. Man, who is dis-

ON GOETHE'S SCIENTIFIC RESEARCHES. 31

tinguished from all other animals by the absence of the
projecting snout, has, on the contrary, on each side only one
bone, the upper jaw-bone, containing all the teeth. This being
so, Goethe discovered in the human skull faint traces of the
sutures which in animals unite the upper and middle jaw-bones,,
and concluded from it that man had originally possessed an
intermaxillary bone, which had subsequently coalesced with the
upper jaw-bone. This obscure fact opened up to him a source
of the most intense interest in the field of osteology, generally
so much decried as the driest of studies. That details of
structure should be the same in man and in animals when the
parts continue to perform similar functions had involved
nothing extraordinary. In fact, Camper had already attempted,
on this principle, to trace similai'ities of structure even between
man and fishes. But the persistence of this similarity, at least
in a rudimentary form, even in a case when it evidently does
not correspond to any of the requirements of the complete
human structure, and consequently needs to be adapted to
them by the coalescence of two parts originally separate, was
what struck Goethe's far-seeing eye, and suggested to him a
far more comprehensive view than had hitherto been taken.
Further studies soon convinced him of the universality of his
newly discovered principle, so that in 1795 and 1796 he was
able to define more clearly the idea that had struck him in 1786r
and to commit it to writing in his ' Sketch of a General Intro-
duction to Comparative Anatomy.' He there lays down with
the utmost confidence and precision that all differences in the-
structure of animals must be looked upon as variations of a
single primitive type, induced by the coalescence, the alteration,
the increase, the diminution, or even the complete removal of
single parts of the structm-e ; the very principle, in fact, which
has become the leading idea of comparative anatomy in its-
present stage. Nowhere has it been better or more clearly ex-
pressed than in Goethe's writings. Subsequent authorities have
made but few essential alterations in his theory. The most
important of these is, that we no longer undertake to construct
a common tyye for the whole animal kingdom, but are content

32 ON GOETHE'S SCIENTIFIC RESEARCHES.

with one for each of Cuvier's great divisions. The industry of
Goethe's successors has accumulated a well-sifted stock of facts,
infinitely more copious than what he could command, and has
followed up successfully into the minutest details what he could
only indicate in a general way.

The second leading conception which science owes to Goethe
enunciated the existence of an analogy between the different
parts of one and the same organic being, similar to that which
we have just pointed out as subsisting between corresponding
parts of different species. In most organisms we see a great
repetition of single parts. This is most striking in the veget-
able kingdom ; each plant has a great number of similar stem
leaves, similar petals, similar stamens, and so on. According
to Goethe's own account, the idea first occurred to him while look-
ing at a fan-palm at Padua. He was struck by the immense
variety of changes of form which the successively developed
stem-leaves exhibit, by the way in which the first simple root
leaflets are replaced by a series of more and more divided leaves,
till we come to the most complicated.

He afterwards succeeded in discovering the transformation
of stem-leaves into sepals and petals, and of sepals and petals
into stamens, nectaries, and ovaries, and thus he was led to the
doctrine of the metamorphosis of plants, which he published in
1790. Just as the anterior extremity of vertebrate animals
takes different forms, becoming in man and in apes an arm, in
other animals a paw with claws, or a forefoot with a hoof, or a
fin, or a wing, but always retains the same divisions, the same
position, and the same connection with the trunk, so the leaf
appears as a cotyledon, stem-leaf, sepal, petal, stamen, nectary,
ovary, etc., all resembling each other to a certain extent in origin
and composition, and even capable, under certain unusual con-
ditions, of passing from one form into the other, as, for example,
may be seen by any one who looks carefully at a full-blown rose,
where some of the stamens are completely, some of them partially,
changed into petals. This view of Goethe's, like the other, is
now completely adopted into science, and enjoys the universal
assent of botanists, though of course some details are still

ON GOETHE'S SCIENTIFIC RESEARCHES. 33

matters of controversy, as, for instance, whether the bud is a
single leaf or a branch.

In the animal kingdom, the composition of an individual
out of several similar parts is very striking in the great sub-
kingdom of the articulata — for example, in in sects and worms. The
larva of an insect, or the caterpillar of a butterfly, consists of a
number of perfectly similar segments ; only the first and last of
them differ, and that but slightly, from the others. After their
transformation into perfect insects, they furnish clear and simple
exemplifications of the view which Goethe had grasped in his
doctrine of the metamorphosis of plants, the development,
namely, of apparently very dissimilar forms from parts origin-
ally alike. The posterior segments retain their original simple
form ; those of the breastplate are drawn closely together, and
develop feet and wings, while those of the head develop jaws
and feelers ; so that in the perfect insect, the original segments
are recognised only in the posterior part of the body. In the
vertebrata, again, a repetition of similar parts is suggested by
the vex-tebral column, but has ceased to be observable in the ex-
ternal form. A fortunate glance at a broken sheep's skull,
which Goethe found by accident on the sand of the Lido at
Venice, suggested to him that the skull itself consisted of a series
of very much altered vertebne. At first sight, no two things
can be more unlike than the broad uniform cranial cavity of the
mammalia, inclosed by smooth plates, and the narrow cylindrical
tube of the spinal marrow, composed of short, massy, jagged
bones. It was a bright idea to detect the transformation in
the skull of a mammal ; the similarity is more striking in the
amphibia and fishes. It should be added that Goethe left this
idea unpublished for a long time, apparently because he was not
quite sure how it would be received. Meantime, in 1806, the
same idea occurred to Oken, who introduced it to the scientific
world, and afterwards disputed with Goethe the priority of
discovery. In fact, Goethe had waited till 1817, when the
opinion had begun to find adherents, and then declared that he
had had it in his mind for thirty years. Up to the present day
the number and composition of the vertebrae of the skull are a

34 ON GOETHE'S SCIENTIFIC RESEARCHES.

subject of controversy, but the principle has maintained it»
ground.

Goethe's views, however, on the existence of a common type
in the animal kingdom do not seem to have exercised any direct
influence on the progress of science. The doctrine of the meta-
morphosis of plants was introduced into botany as his distinct
and recognised property; but his views on osteology were at-
first disputed by anatomists, and only subsequently attracted
attention when the science had. apparently on independent
grounds, found its way to the same discovery. He himself com-
plains that his first ideas of a common type had encountered
nothing but contradiction and scepticism at the time when
he was working them out in his own mind, and that even
men of the freshest and most original intellect, like the two-
Von Humboldts, had listened to them with something like
impatience. But it is almost a matter of course that in any
natural or physical science, theoretical ideas attract the attention
of its cultivators only when they are advanced in connection
with the whole of the evidence on which they rest, and thus
justify their title to recognition. Be that as it may, Goethe is-
entitled to the credit of having caught the first glimpse of the
guiding ideas to which the sciences of botany and anatomy were
tending, and by which their present form is determined.

But great as is the respect which Goethe has secured by his
achievements in the descriptive natural sciences, the denuncia-
tion heaped by all physicists on his researches in their depart-
ment, and especially on his ' theory of colour,' is at least as uncom-
promising. This is not the place to plunge into the controversy
that raged on the subject, and so I shall only attempt to state
clearly the points at issue, and to explain what principle was
involved, and what is the latent significance of the dispute.

To this end it is of some importance to go back to the history
of the origin of the theory, and to its simplest form, because at
that stage of the controversy the points at issue are obvious, and
admit of easy and distinct statement, unincumbered by disputes
about the correctness of detached facts and complicated theories.

Goethe himself describes very gracefully, in the confession at

ox GOETHE'S SCIENTIFIC RESEARCHES. 35

the end of his ' Theory of Colour,' how he came to take up the
subject. Finding himself unable to grasp the aesthetic principles
involved in effects of colour, he resolved to resume the study of
the physical theory, which he had been taught at the university,
and to repeat for himself the experiments connected with it.
With that view he borrowed a prism of Hofrath Blitter, of Jena,
but was prevented by other occupations from carrying out his
plan, and kept it by him for a long time unused. The owner of
the prism, a very orderly man, after several times asking in vain,
sent a messenger with instructions to bring it back directly.
Goethe took it out of the case, and thought he would take one
more peep through it. To make certain of seeing something, he
turned it towards a long white wall, under the impression that
as there was plenty of light there he could not fail to see a
brilliant example of the resolution of light into different colours ;
a supposition, by the way, which shows how little Newton's
theory of the phenomena was then present to his mind. Of
course he was disappointed. On the white wall he saw no
colours ; they only appeai-ed where it was bounded by darker
objects. Accordingly he made the observation — which, it should
be added, is fully accounted for by Newton's theory — that
colour can only be seen through a prism where a dark object
and a bright one have the same boundary. Struck by this
observation, which was quite new to him, and convinced that it
was irreconcilable with Newton's theory, he induced the owner
of the prism to relent, and devoted himself to the question with
the utmost zeal and interest. He prepared sheets of paper with
black and white spaces, and studied the phenomenon under
every variety of condition, until he thought he had sufficiently
proved his rules. He next attempted to explain his supposed
discovery to a neighbour, who was a physicist, and was dis-
agreeably surprised to be assured by him that the experiments
were well known, and fully accounted for in Newton's theory.
Every other natural philosopher whom he consulted told him
exactly the same, including even the brilliant Lichtenberg,
whom he tried for a long time to convert, but in vain. He
studied NeAvton's writings, and fancied he had found some

D2

36 ON GOETHE'S SCIENTIFIC RESEARCHES.

fallacies in them which accounted for the error. Unable to con-
vince any of his acquaintances, he at last resolved to appear
before the bar of public opinion, and in 1791 and 1792 published
the first and second parts of his ' Contributions to Physical
Optics.'

In that work he describes the appearances presented by white
discs on a black ground, black discs on a white ground, and
coloured discs on a black or white ground, when examined
through a prism. As to the results of the experiments, there is
no dispute whatever between him and the physicists. He de-
scribes the phenomena' he saw with great truth to nature ; the
style is lively, and the arrangement such as to make a conspectus
of them easy and inviting ; in short, in this as in all other cases
where facts are to be described, he proves himself a master. At
the same time he expresses his conviction that the facts he has
adduced are calculated to refute Newton's theory. There are
two points especially which he considers fatal to it : first, that
the centre of a broad white surface remains white when seen
through a prism; and secondly, that even a black streak on a
white ground can be entirely decomposed into colours.

Newton's theory is based on the hypothesis that there exists
light of different kinds, distinguished from one another by the
tsensation of colour which they produce in the eye. Thus there
is red, orange, yellow, green, blue, and violet light, and light of
all intermediate colours. Different kinds of light, or differently
coloured lights, produce, when mixed, derived colours, which to
a certain extent resemble the original colours from which they
are derived ; to a certain extent form new tints. White is a
mixture of all the before-named colours in certain definite pro-
portions. But the primitive colours can always be repi'oduced
by analysis from derived colours, or from white, while themselves
incapable of analysis or change. The cause of the colours of
transparent and opaque bodies is, that when white light falls
upon them they destroy some of its constituents and send to
the eye other constituents, but no longer mixed in. the right
proportions to produce white light. Thus a piece of red glass
looks red because it transmits only red rays. Consequently all

ON GOETHE'S SCIENTIFIC RESEARCHES. 37

colour is derived solely from a change in the proportions in
which light is mixed, and is, therefore, a property of light, not
of the coloured bodies, which only furnish an occasion for its
m anifestation.

A prism refracts transmitted light; that is to say, deflects it
so that it makes a certain angle with its original direction; the
rays of simple light of different colours have, according to
Newton, different refrangibilities, and therefore, after refraction
in the prism, pursue different courses and separate from each
other. Accordingly a luminous point of infinitely small dimen-
sions appears, when seen through the prism, to be first displaced,
and, secondly, extended into a coloured line, the so-called pris-
matic spectrum, which shows what are called the primary
colours in the order above-named. If, however, you look at a
broader luminous surface, the spectra of the points near the
middle are superposed, as may be seen from a simple geometrical
investigation, in such proportions as to give white light, except
at the edges, where certain of the colours are free. This white
surface appears displaced, as the luminous point did; but in-
stead of being coloured throughout, it has on one side a margin
of blue and violet, on the other a margin of red and yellow. A
black patch between two bright surfaces may be entirely covered
by their coloured edges; and when these spectra meet in the
middle, the red of the one and the violet of the other combine
to form purple. Thus the colours into which, at first sight, it
seems as if the black were analysed are in reality due, not to
the black strip, but to the white on each side of it.

It is evident that at the first moment Goethe did not recol-
lect Newton's theory well enough to be able to find out the
physical explanation of the facts I have just glanced at. It was
afterwards laid before him again and again, and that in a
thoroughly intelligible form, for he speaks about it several times
in terms that show he understood it quite correctly. But he is
still so dissatisfied with it that he persists in his assertion that
the facts just cited are of a nature to convince any one who
observes them of the absolute incorrectness of Newton's theory.
Neither here nor in his later controversial writings does he ever

38 ON GOETHE'S SCIENTIFIC RESEARCHES.

clearly state in what he conceives the insufficiency of the ex-
planation to consist. He merely repeats again and again that
it is quite absurd. And yet I cannot see how any one, whatever
his views about colour, can deny that the theory is perfectly
insistent with itself; and that if the hypothesis from which it
starts be granted, it explains the observed facts completely and
even simply. Newton himself mentions these spurious spectra
in several passages of his optical works, without going into
any special elucidation of the point, considering, of course, that
the explanation follows at once from, his hypothesis. And he
seems to have had good reason to think so; for Goethe no sooner
began to call the attention of his scientific friends to the pheno-
mena than all with one accord, as he himself tells us, met his
difficulties with this explanation from Newton's principles, which,
though not actually in his writings, instantly suggested itself to
every one who knew them.

A reader who tries to realise attentively and thoroughly
every step in this part of the controversy is apt to experience at
this point an uncomfortable, almost a painful, feeling to see a man
of extraordinary abilities persistently declaring that there is an
obvious absurdity lurking in a few inferences appai-ently quite
clear and simple. He searches and searches, and at last unable,
with all his efforts, to find any such absurdity, or even the ap-
pearance of it, he gets into a state of mind in which his own
ideas are, so to speak, crystallised. But it is just this obvious,
flat contradiction that makes Goethe's point of view in 1792 so
interesting and so important. At this point he has not as yet
developed any theory of his own ; thei-e is nothing under dis-
cussion but a few easily grasped facts, as to the correctness of
•which both pai'ties are agreed, and yet both hold distinctly
opposite views; neither of them even understands what his
opponent is driving at. On the one side are a number of phy-
sicists, who, by a long series of the ablest investigations, the
most elaborate calculations, and the most ingenious inventions,
have brought optics to such perfection that it, and it alone,
among the physical sciences, was beginning almost to rival
Astronomy in accuracy. Some of them have made the pheno-

ON GOETHE'S SCIENTIFIC; RESEARCHES. 39

mena the subject of direct investigation ; all of them, thanks
to the accuracy with which it is possible to calculate beforehand
the result of every variety in the construction and combination
of instruments, have had the opportunity of putting the infer-
ences deduced from Newton's views to the test of experiment,
and all, without exception, agree in accepting them. On the other
side is a man whose remarkable mental endowments, and
whose singular talent for seeing through whatever obscures
reality, we have had occasion to recognise, not only in poetry, but
also in the descriptive parts of the natural sciences ; and this
man assures us with the utmost zeal that the physicists are
wrong : he is so convinced of the correctness of his own view,
that he cannot explain the contradiction except by assuming
naiTOwness or malice on their part, and finally declares that he
cannot help looking upon his own achievement in the theory of
colour as far more valuable than anything he has accomplished
in poetry.1

So flat a contradiction leads us to suspect that there must
be behind some deeper antagonism of principle, some difference
of organisation between his mind and theirs, to prevent them
from understanding each other. I will try to indicate in the
following pages what I conceive to be the grounds of this anta-
gonism.

Goethe, though he exercised his powers in many spheres
of intellectual activity, is nevertheless, par excellence, a poet.
Now in poetry, as in every other art, the essential thing is to
make the material of the art, be it words, or music, or colour,
the direct vehicle of an idea. In a perfect work of art, the idea
must be present and dominate the whole, almost unknown to
the poet himself, not as the result of a long intellectual process,
but as inspired by a direct intuition of the inner eye, or by an
outburst of excited feeling.

An idea thus embodied in a work of ait, and dressed in the
garb of reality, does indeed make a vivid impression by appeal-
ing directly to the senses, but loses, of course, that universality
and that intelligibility which it would have had if presented in
1 See Eckermann's Conversations.

40 ox GOETHE'S SCIENTIFIC RESEARCHES.

the form of an abstract notion. The poet, feeling how the
charm of his works is involved in an intellectual process of this
type, seeks to apply it to other materials. Instead of trying to
arrange the phenomena of nature under definite conceptions,
independent of intuition, he sits down to contemplate them as
he would a work of art, complete in itself, and ceitain to yield
up its central idea, sooner or later, to a sufficiently susceptible
student. Accordingly, when he sees the skull on the Lido,
which suggests to him the vertebral theory of the cranium, he
remarks that it serves to revive his old belief, already confirmed
by experience, that Nature has no secrets from the attentive
observer. So again in his first conversation with Schiller on
the 'Metamorphosis of Plants.' To Schiller, as a follower of
Kant, the idea is the goal, ever to be sought, but ever unattain-
able, and therefore never to be exhibited as realised in a phe-
nomenon. Goethe, on the other hand, as a genuine poet,
conceives that he finds in the phenomenon the direct expression
of the idea. He himself tells us that nothing brought out
more sharply the separation between himself and Schiller.
This, too, is the secret of his affinity with the natural philosophy
of Schelling and Hegel, which likewise proceeds from the
assumption that Nature shows us by direct intuition the several
steps by which a conception is developed. Hence too the ardour
with which Hegel and his school defended Goethe's scientific
views. Moreover, this view of Nature accounts for the war
which Goethe continued to wage against complicated experi-
mental researches. Just as a genuine work of art cannot bear
retouching by a strange hand, so he would have us believe
Nature resists the interference of the experimenter who tortures
her and disturbs her ; and, in revenge, misleads the impertinent
kill-joy by a distorted image of herself.

Accordingly, in his attack upon Newton he often sneei\s at
spectra, tortured through a number of narrow slits and glasses,,
and commends the experiments that can be made in the open air
under a bright sun, not merely as particularly easy and parti-
cularly enchanting, but also as particularly convincing ! The
poetic turn of mind is very marked even in his morphological

ON GOETHE'S SCIENTIFIC RESEARCHES. 41

researches. If we only examine what has really been accom-
plished by the help of the ideas which he contributed to science,
we shall be struck by the very singular relation which they bear
to it. No one will refuse to be convinced if you lay before him
the series of transformations by which a leaf passes into a
stamen, an arm into a fin or a wing, a vertebra into the occipital
bone. The idea that all the parts of a flower are modified leaves
reveals a connecting law which surprises us into acquiescence.
But now try and define the leaf-like organ, determine its essential
characteristics, so as to include all the forms that we have named.
You will find yourself in a difficult}', for all distinctive marks
vanish, and you have nothing left, except that a leaf in the
wider sense of the term is a lateral appendage of the axis of
a plant. Try then to express the proposition 'the parts of the
flower are modified leaves ' in the language of scientific defi-
nition, and it reads, ' the parts of the flower are lateral appen-
dages of the axis.' To see this does not require a Goethe. So
again it has been objected, and not unjustly, to the vertebral
theory, that it must extend the notion of a vertebra so much
that nothing is left but the bai^e fact — a vertebra is a bone. We
are equally perplexed if we try to express in clear scientific-
language what we mean by saying that such and such a part of
one animal corresponds to such and such a part of another. We
do not mean that their physiological use is the same, for the
same piece which in bird serves as the lower jaw, becomes
in mammals a tiny tympanal bone. Nor would the shape, the
position, or the connection of the part in question with other
parts serve to identify it in all cases. But yet it has been found
possible in most cases, by following the intermediate steps, to
determine with tolerable certainty which parts correspond to
each other. Goethe himself said this very clearly : he says, in
speaking of the vertebi-al thory of the skull, ' Such an aper^u,
such an intuition, conception, representation, notion, idea, or
whatever you choose to call it, always retains something
esoteric and indefinable, struggle as you will against it ; as a
general principle, it may be enunciated, but cannot be proved y
in detail it may l>e exhibited, but can never be put in a cut and

42 ON GOETHE'S SCIENTIFIC RESEARCHES.

dry form.' And so, or nearly so, the problem stands to this
day. The difference may be brought out still more clearly if we
•consider how physiology, which investigates the relations of vital
processes as cause and effect, would have to treat this idea of a
common type of animal structure. The science might ask, Is
it, on the one hand, a correct view, that during the geological
periods that have passed over the earth, one species has been
developed from another, so that, for example, the breast-fin of
the fish has gradually changed into an arm or a wing ? Or
again, shall we say that the different species of animals were
created equally perfect — that the points of resemblance between
them are to be ascribed to the fact that in all vertebrate animals
the first steps in development from the egg can only be effected
by Nature in one .way, almost identical in all cases, and that
the later analogies of structure are determined by these features,
common to all embryos ? Probably the majority of observers
incline to the latter view,1 for the agreement between the
embryos of different vertebrate animals, in the earlier stages, is
very striking. Thus even young mammals have occasionally
rudimentary gills on the side of the neck, like fishes. It seems,
in fact, that what are in the mature animals corresponding parts
originate in the same way during the process of development, so
that scientific men have lately begun to make use of embryology
as a sort of check on the theoretical views of comparative ana-
tomy. It is evident that by the application of the physiological
views just suggested, the idea of a common type would acquire
definiteness and meaning as a distinct scientific conception.
Goethe did much : he saw by a happy intuition that there was a
law, and he followed up the indications of it with great shrewdness.
But what law it was he did not see ; nor did he even try to
find it out. That was not in his line. Moreover, even in the
present condition of science, a definite view on the question is
impossible ; the very form in which it should be proposed is
scarcely yet settled. And therefore we readily admit that in this
department Goethe did all that was possible at the time when he
lived. I said just now that he treated nature like a work of
1 This was written before the appearance of Darwin's Oriyin of Species.

ON GOETHE'S SCIENTIFIC RESEARCHES. 43

art. In his studies on morphology, he reminds one of a spectator
at a play, with strong artistic sympathies. His delicate instinct
makes him feel how all the details fall into their places, and
work harmoniously together, and how some common purpose
governs the whole ; and yet while this exquisite order and sym-
metry give him intense pleasure he cannot formulate the dominant
idea. That is reserved for the scientific critic of the drama,
while the artistic spectator feels perhaps, as Goethe did in the
presence of natural phenomena, an antipathy to such dissection,
fearing, though without reason, that his pleasure may be spoilt
by it.

Goethe's point of view in the Theory of Colour is much the
same. We have seen that he rebels against the physical theory
just at the point where it gives complete and consistent expla-
nations from principles once accepted. Evidently it is not the
insufficiency of the theory to explain individual cases that is a
stumbling-block to him. He takes offence at the assumption
made for the sake of explaining the phenomena, which seem to
him so absurd, that he looks upon the interpretation as no inter-
pretation at all Above all, the idea that white light could be
composed of coloured light seems to have been quite inconceiv-
able to him • at the very beginning of the controversy, he rails
at the disgusting Newtonian white of the natural philosophers,
an expression which seems to show that this was the assumption
that most annoyed him.

Again, in his later attacks on Newton, which were not
published till after his Theory of Colour was completed, he
rather strives to show that Newton's facts might be explained
on his own hypothesis, and that therefore Newton's hypothesis
was not fully proved, than attempts to prove that hypothesis
inconsistent with itself or with the facts. Nay, he seems to
consider the obviousness of his own hypothesis so overwhelming,
that it need only be brought forward to upset Newton's entirely.
There are only a few passages where he disputes the experiments
described by Newton. Some of them, apparently, he could not
succeed in refuting, because the result is not equally easy to
observe in all positions of the lenses used, and because he was

44 ox GOETHE'S SCIENTIFIC RESEARCHES.

unacquainted with the geometrical relations by which the most
favourable positions of them are determined. In other experi-
ments on the separation of simple coloured light by means of
prisms alone, Goethe's objections are not quite groundless, inas-
much as the isolation of single colours cannot by this means be
so effectually carried out, that after refraction through another
prism there are no traces of other tints at the edges. A com-
plete isolation of light of one colour can only be effected by
very carefully arranged apparatus, consisting of combined
prisms and lenses, a set of experiments which Goethe postponed
to a supplement, and finally left unnoticed. When he complains-
of the complication of these contrivances, we need only think
of the laborious and roundabout methods which chemists must
often adopt to obtain certain elementary bodies in a pure form ;
and we need not Ije surprised to find that it is impossible to
solve a similar problem in the case of light in the open air in a
garden, and with a single prism in one's hand.1 Goethe must,
consistently with his theory, deny in toto the possibility of
isolating pure light of one colour. Whether he ever experi-
mented with the proper apparatus to solve the problem remains
doubtful, as the supplement in which he promised to detail
these experiments was never published.

To give some idea of the passionate way in which Goethe,
usually so temperate and even courtier-like, attacks Newton, I
quote from a few pages of the controversial part of his work
the following expressions, which he applies to the propositions
of this consummate thinker in physical and astronomical
science- -' incredibly impudent' ; ' mere twaddle' ; ' ludicrous ex-
planation' ; ' admirable for school-children in a go-cart' ; ' but I
see nothing will do but lying, and plenty of it.'2

1 I venture to add that 1 am acquainted with the impossibility of decom-
posing or changing simple coloured light, the two principles which form the
basis of Newton's theory, not merely by hearsay, but from actual observation,
having been under the necessity in one of my own researches of obtaining light
of one colour in a state of the greatest possible purity. (See I'oggendorfTs-
Annulet,, vol. Ixxxvi. p. f>01, on Sir D. Brewster's Xtw 'Analysis of Sunlight.)

8 Something parallel to this extraordinary proceeding of Goethe's may be
found in Hobbes's attack on Wallis. — TK.

ON GOETHE'S SCIENTIFIC RESEARCHES. 45

Thus, in the theory of colour, Goethe remains faithful to
his principle, that Nature must reveal her secrets of her own
free will ; that she is but the transparent repi*esentation of the
ideal world. Accordingly, he demands, as a preliminary to the
investigation of physical phenomena, that the observed facts
shall be so arranged that one explains the other, and that thus
we may attain an insight into their connection without ever
having to trust to anything but our senses. This demand of
Tiis looks most attractive, but is essentially wrong in principle.
For a natui*al phenomenon is not considei'ed in physical science
to be fully explained until you have traced it back to the
ultimate forces which are concerned in its production and its
maintenance. Now, as we can never become cognisant of forces
qua forces, but only of their effects, we are compelled in every
explanation of natural phenomena to leave the sphere of sense,
and to pass to things which are not objects of sense, and are
denned only by abstract conceptions. When we find a stove
warm, and then observe that a fire is burning in it, we say,
though somewhat inaccurately, that the former sensation is
explained by the latter. But in reality this is equivalent to say-
ing, we are always accustomed to find heat where fire is burn-
ing ; now, a fire is burning in the stove, therefore we shall find
heat there. Accordingly we bring our single fact under a more
general, better-known fact, rest satisfied with it, and call it
falsely an explanation. Evidently, however, the generality of the
observation does not necessarily imply an insight into causes; such
an insight is only obtained when we can make out what forces
are at work in the fire, and how the effects depend upon them.
But this step into the region of abstract conceptions, which
must necessarily be taken if we wish to penetrate to the causes
of phenomena, scares the poet away. In writing a poem he
has been accustomed to look, as it were, right into the subject,
and to reproduce his intuition without formulating any of the
steps that led him to it. And his success is proportionate to
the vividness of the intuition. Such is the fashion in which he
would have Nature attacked. But the natural philosopher in-
sists on transporting him into a world of invisible atoms and

46 ON GOETHE'S SCIENTIFIC RESEARCHES.

movements, of attractive and repulsive forces, whose intricate
actions and reactions, though governed by strict laws, can
scarcely be taken in at a glance. To him the impressions ^of
sense are not an irrefragable authority ; he examines what claim
they have to be trusted ; he asks whether things which they
pronounce alike are really alike, and whether things which they
pronounce different are really different ; and often finds that he
must answer, no ! The result of such examination, as at present
understood, is that the organs of sense do indeed give us informa-
tion about external effects produced on them, but convey those
effects to our consciousness in a totally different form, so that
the character of a sensuous perception depends not so much on
the properties of the object perceived as on those of the organ
by which we receive the information. All that the optic nerve
conveys to us, it conveys under the form of a sensation of light,
whether it be the rays of the sun, or a blow in the eye, or an
electric current passing through it. Again, the auditory nerve
translates everything into phenomena of sound, the nerves of the
skin into sensations of temperature or touch. The same electric
current whose existence is indicated by the optic nerve as a flash
of light, or by the organ of taste as an acid flavour, excites in
the nerves of the skin the sensation of burning. The same ray
of sunshine, which is called light when it falls on the eye, we
call heat when it falls on the skin. But on the other hand, in
spite of their different effects upon our organisation, the daylight
which enters through our windows, and the heat radiated by an
iron stove, do not in reality differ more or less from each other
than the red and blue constituents of light. In fact, just as in
the Undulatory Theory the red rays are distinguished from the
blue rays only by their longer period of vibration, and their
smaller refrangibility, so the dark heat rays of the stove have a
still longer period and still smaller refrangibility than the red
rays of light, but are in every other respect exactly similar to
them. All these rays, whether luminous or non-luminous, have
heating properties, but only a certain number of them, to which
for that reason we give the name of light, can penetrate through
the transparent part of the eye to the optic nerve, and excite a

ox GOETHE'S SCIENTIFIC RESEARCHES. 47

sensation of light. Perhaps the relation between our senses and
the external world may be best enunciated as follows : our sen-
sations are for us only symbols of the objects of the external
world, and correspond to them only in some such way as written
characters or articulate words to the things they denote. They
give us, it is true, information respecting the properties of things
without us, but no better infonnation than we give a blind man
about colour by verbal descriptions.

We see that science has arrived at an estimate of the senses
very different from that which was present to the poet's mind.
And Newton's assertion that white was composed of all the
colours of the spectrum was the first germ of the scientific view
which has subsequently been developed. For at that time there
were none of those galvanic observations which paved the way
to a knowledge of the functions of the nerves in the production
of sensations. Natural philosophers asserted that white, to the
eye the simplest and purest of all our sensations of colour, was
compounded of less pure and complex materials. It seems to
have flashed upon the poet's mind that all his principles were
unsettled by the results of this assertion, and that is why the
hypothesis seems to him so unthinkable, so ineffably absurd.
We must look upon his theoiy of colour as a forlorn hope, as
a desperate attempt to rescue from the attacks of science the
belief in the direct truth of our sensations. And this will ac-
count for the enthusiasm with which he strives to elaborate and to
defend his theory, for the passionate irritability with which he
attacks his opponent, for the overweening importance which he
attaches to these researches in comparison with his other achieve-
ments, and for his inaccessibility to conviction or compromise.

If we now turn to Goethe's own theories on the subject,
we must, on the grounds above stated, expect to find that he
cannot, without being untrue to his own principle, give us-
anything deserving to be called a scientific explanation of the
phenomena, and that is exactly what happens. He starts with
the proposition that all colours are darker than white, that they
have something of shade in them (on the physical theory, white
compounded of all colours must necessarily be brighter than

48 ox GOETHE'S SCIENTIFIC RESEARCHES.

any of its constituents). The direct mixture of dark and light,
of black and white, gives grey ; the colours must therefore owe
their existence to some form of the co-operation of light and
shade. Goethe imagines he has discovered it in the phenomena
presented by slightly opaque or hazy media. Such media usually
look blue when the light falls on them and they are seen in
front of a dark object, but yellow when a bright object is looked
at through them. Thus in the daytime the air looks blue
against the dark background of the sky, and the sun, when
viewed, as is the case at sunset, through a thick and hazy
stratum of air, appears yellow. The physical explanation of
this phenomenon, which, however, is not exhibited by all such
media, as, for instance, by plates of unpolished glass, would lead
us too far from the subject. According to Goethe, the semi-opaque
medium imparts to the light something corporeal, something of
the nature of shade, such as is requisite, he would say, for the
formation of colour. This conception alone is enough to perplex
any one who looks upon it as a physical explanation. Does he
mean to say that material particles mingle with the light and
fly away with it ? But this is Goethe's fundamental experiment,
this is the typical phenomenon under which he tries to reduce
all the phenomena of colour, especially those connected with
the prismatic spectrum. He looks upon all transparent bodies
as slightly hazy, and assumes that the prism imparts to the
image which it shows to an observer something of its own
opacity. Here, again, it is hard to get a definite conception of
what is meant. Goethe seems to have thought that a prism
never gives perfectly defined images, but only indistinct, half-
obliterated ones, for he puts them all in the same class with the
double images which are exhibited by parallel plates of glass
and by Iceland spar. The images formed by a prism are, it
is true, indistinct in compound light, but they are perfectly
defined when simple light is used. If you examine, he says, a
bright siirface on a dark ground through a prism, the image is
displaced and blurred by the prism. The anterior edge is
pushed forward over the dark background, and consequently a
hazy light on a dark ground appears blue, while the other edge

ON GOETHE'S SCIENTIFIC RESEARCHES. 49

is covered by the image of the black surface which comes after it,
and, consequently, being a light image behind a hazy dark colour,
appears yellowish-red. But why the anterior edge appears in
front of the ground, the posterior edge behind it, and not vice
versd, he does not explain. Let us analyse this explanation,
and try to grasp clearly the conception of an optical image.
When I see a bright object reflected in a mirror, the reason is
that the light which proceeds from it is thrown back exactly as
if it came from an object of the same kind behind the mirror.
The eye of the observer receives the impression accordingly,
and therefore he imagines he really sees the object. Every one
knows there is nothing real behind the mirror to correspond to
the image — that no light can penetrate thither, but that what
is called the image is simply a geometrical point, in which the
reflected rays, if produced backwards, would intersect. And,
accordingly, no one expects the image to produce any real effect
behind the mirror. In the same way the prism shows us images
of objects which occupy a different position from the objects
themselves ; that is to say, the light which an object sends to
the prism is refracted by it, so that it appears to come from an
object lying to one side, called the image. This image, again>
is not real ; it is, as in the case of reflection, the geometrical
point in which the refracted rays intersect when produced back-
wards. And yet, according to Goethe, this image is to produce
real effects by its displacement; the displaced patch of light
makes, he says, the dark space behind it appear blue, just as an
imperfectly transparent body would, and so again the displaced
dark patch makes the bright space behind appear reddish-yellow.
That Goethe really treats the image as an actual object in the
place it appears to occupy is obvious enough, especially as he is
compelled to assume, in the course of his explanation, that the
blue and red edges of the bright space are respectively before
and behind the dark image which, like it, is displaced by the
prism. He does, in fact, remain loyal to the appearance pre-
sented to the senses, and treats a geometrical locus as if it were
a material object. Again, he does not scruple at one time to
make red and blue destroy each other, as, for example, in the

I. E

50 ON GOETHE'S SCIENTIFIC RESEARCHES.

blue edge of a red surface seen through the prism, and at
•another to construct out of them a beautiful purple, as when
the blue and red edges of two neighbouring white surfaces
meet in a black ground. And when he comes to Newton's
more complicated experiments, he is driven to still more mar-
vellous expedients. As long as you treat his explanations as a
pictorial way of representing the physical processes, you may
acquiesce in them, and even frequently find them vivid and
characteristic, but as physical elucidations of the phenomena
they are absolutely irrational.

In conclusion, it must be obvious to every one that the
theoretical part of the Theory of Colour is not natural philo-
sophy at all ; at the same time we can, to a certain extent, see
that the poet wanted to introduce a totally different method
into the study of Nature, and more or less understand how he
came to do so. Poetry is concerned solely with the ' beautiful
show ' which makes it possible to contemplate the ideal ; how
that show is produced is a matter of indifference. Even nature
is, in the poet's eyes, but the sensible expression of the spiritual.
The natural philosopher, on the other hand, tries to discover the
levers, the cords, and the pulleys which work behind the scenes,
and shift them. Of course the sight of the machinery spoils
the beautiful show, and therefore the poet would gladly talk it
out of existence, and ignoring cords and pulleys as the chimeras
of a pedant's brain, he would have us believe that the scenes
shift themselves, or are governed by the idea of the drama.
And it is just characteristic of Goethe that he, and he alone
among poets, must needs bi-eak a lance with natural philosophers.
Other poets are either so entirely carried away by the fire of
their enthusiasm that they do not trouble themselves about the
disturbing influences of the outer world, or else they rejoice
in the triumphs of mind over matter, even on that unpropitious
battlefield. But Goethe, whom no intensity of subjective feeling
could blind to the realities around him, cannot rest satisfied
until he has stamped reality itself with the image and super-
scription of poetry. This constitutes the peculiar beauty of his
poetry, and at the same time fully accounts for his resolute

ON GOETHE'S SCIENTIFIC RESEARCHES. 51

hostility to the machinery that every moment threatens to
disturb his poetic repose, and for his determination to attack
the enemy in his own camp.

But we cannot triumph over the machinery of matter
by ignoring it ; we can triumph over it only by subordinating
it to the aims of our moral intelligence. We must familiarise
ourselves with its levers and pulleys, fatal though it be to poetic
contemplation, in order to be able to govern them after our own
will, and therein lies the complete justification of physical
investigation, and its vast importance for the advance of human
civilisation.

From what I have said it will be apparent that Goethe did
follow the same line of thought in all his contributions to science,
but that the problems he encountered were of diametrically
opposite characters. And, perhaps, when it is understood how
the self-same characteristic of his intellect, which in one branch
of science won for him immortal renown, entailed upon him
egregious failure in the other, it will tend to dissipate, in the
minds of many worshippers of the great poet, a lingering pre-
judice against natural philosophers, whom they suspect of being
blinded by narrow professional pride to the loftiest inspirations
of genius.

53

ON THE

PHYSIOLOGICAL CAUSES OF HAEMONY
IN MUSIC.

A Lecture delivered in Bonn during the Winter of 1857.

LADIES AND GENTLEMEN, — In the native town of Beethoven, the
mightiest among the heroes of harmony, no subject seemed
to me better adapted for a popular audience than music itself.
Following, therefore, the direction of my researches during the
last few years, I will endeavour to explain to you what physics
and physiology have to say regarding the most cherished art of
the Rhenish land — music and musical relations. Music has
hitherto withdrawn itself from scientific treatment more than
any other art. Poetry, painting, and sculpture borrow at least
the material for their delineations from the world of experience.
They portray nature and man. Not only can their material be
critically investigated in respect to its correctness and truth
to nature, but scientific art-criticism, however much enthusiasts
may have disputed its right to do so, has actually succeeded in
making some progress in investigating the causes of that aesthetic
pleasure which it is the intention of these arts to excite. In
music, on the other hand, it seems at first sight as if those were
still in the right who reject all ' anatomisation of pleasurable
sensations.' This art, borrowing no part of its material from
the experience of our senses, not attempting to describe, and

54 ON THE PHYSIOLOGICAL CAUSES OF

only exceptionally to imitate the outer world, necessarily with-
draws from scientific consideration the chief points of attack
which other arts present, and hence seems to be as incompre-
hensible and wonderful as it is certainly powerful in its effects.
We are, therefore, obliged, and we purpose, to confine ourselves,
in the first place, to a consideration of the material of the art,
musical sounds or sensations. It always struck me as a wonder-
ful and peculiarly interesting mystery, that in the theory of
musical sounds, in the physical and technical foundations of
music, which above all other arts seems in its action on the
mind as the most immaterial, evanescent, and tender creator of
incalculable and indescribable states of consciousness, that here
in especial the science of purest and strictest thought — mathe-
matics— should prove pre-eminently fertile. Thorough bass is a,
kind of applied mathematics. In considering musical intervals,,
divisions of time, and so forth, numerical fractions, and some-
times even logarithms, play a prominent part. Mathematics
and music ! the most glaring possible opposites of human
thought! and yet connected, mutually sustained! It is as-
if they would demonstrate the hidden consensus of all the
actions of our mind, which in the revelations of genius makes
us forefeel unconscious utterances of a mysteriously active
intelligence.

When I considered physical acoustics from a physiological
point of view, and thus more closely followed up the part which
the ear plays in the perception of musical sounds, much became
clear of which the connection had not been previously evident.
I will attempt to inspire you with some of the interest which
these questions have awakened in my own mind, by endeavour-
ing to exhibit a few of the results of physical and physiological
acoustics.

The short space of time at my disposal obliges me to confine
my attention to one particular point; but I shall select the
most important of all, which will best show you the significance
and results of scientific investigation in this field ; I mean the
foundation of concord. It is an acknowledged fact that the
numbers of the vibrations of concordant tones bear to each

HARMONY IN MUSIC. 55

other ratios expressible by small whole numbers. But why I
What have the ratios of .small whole numbers to do with con-
cord 1 This is an old riddle, propounded by Pythagoras, and
hitherto unsolved. Let us see whether the means at the com-
mand of modern science will furnish the answer.

First of all, what is a musical tone? Common experience
teaches us that all sounding bodies are in a state of vibration.
This vibration can be seen and felt ; and in the case of loud
sounds we feel the trembling of the air even without touching
the sounding bodies. Physical science has ascertained that any
series of impulses which produce a vibration of the air will, if
repeated with sufficient rapidity, generate sound.

This sound becomes a musical tone, when such rapid im-
pulses recur with perfect regularity and in precisely equal times.
Irregular agitation of the air generates only noise. The pitch
of a musical tone depends on the number of impulses which
take place in a given time ; the more there are in the same time
the higher or sharper is the tone. And, as before remarked,,
there is found to be a close relationship between the well-known
harmonious musical intervals and the number of the vibrations
of the air. If twice as many vibrations are performed in the
same time for one tone as for another, the first is the octave
above the second. If the numbers of vibrations in the same
time are as 2 to 3, the two tones form a fifth ; if they are as 4
to 5, the two tones form a major third.

If you observe that the numbers of the vibrations which
generate the tones of the major chord C E G c are in the ratio
of the numbers 4:5:6:8, you can deduce from these all
other relations of musical tones, by imagining a new major
chord, having the same relations of the numbers of vibrations,.
to be formed upon each of the above-named tones. The num-
bers of vibrations within the limits of audible tones which
would be obtained by executing the calculation thus indicated
are extraordinarily different. Since the octave above any tone
has twice as many vibrations as the tone itself, the second octave
above will have four times, the third has eight times as many.
Our modern pianofortes have seven octaves. Their highest

56 ON THE PHYSIOLOGICAL CAUSES OF

tones, therefore, perform 128 vibrations in the time that their
lowest tone makes one single vibration.

The deepest C, which our pianos usually possess answers to
the sixteen-foot open pipe of the organ — musicians call it the
* contra-C ' — and makes thirty-three vibrations in one second of
time. This is very nearly the limit of audibility. You will
have observed that these tones have a dull, bad quality of sound
on the piano, and that it is difficult to determine their pitch and
the accuracy of their tuning. On the organ the contra-C is
somewhat more powerful than on the piano, but even here some
uncertainty is felt in judging of its pitch. On larger organs
there is a whole octave of tones below the contra-C, reaching to
the next low,er C, with 16^ vibrations in a second. But the ear
can scarcely separate these tones from an obscure drone ; and
the deeper they are the more plainly can it distinguish the sepa-
rate impulses of the air to which they are due. Hence they
are used solely in conjunction with the next higher octaves, to
strengthen their notes, and produce an impression of greater
depth.

With the exception of the organ, all "musical instruments,
however diverse the methods in which their sounds are pro-
duced, have their limit of depth at about the same point in the
scale as the piano ; not because it would be impossible to produce
slower impulses of the air of sufficient power, but because the
ear refuses its office, and hears slower impulses separately, without
gathering them up into single tones.

The often-repeated assertion of the French physicist Savart,
that he heard tones of eight vibrations in a second, upon a
peculiarly constructed instrument, seems due to an error.

Ascending the scale from the contra-C, pianofortes usually
have a compass of seven octaves, up to the so-called five-accented
c, which has 4,224 vibrations in a second. Among orchestral
instruments it is only the piccolo flute which can reach as high,
and this will give even one tone higher. The violin usually
mounts no higher than the e below, which has 2,640 vibrations
— of course we except the gymnastics of heaven-scaling virtuosi,
who are ever striving to excruciate their audience by some new

HARMONY IN MUSIC. 57

impossibility. Such performers may aspire to three whole
octaves lying above the five-accented c, and very painful to the
ear, for their existence has been established by Despretz, who,
by exciting small tuning-forks with a violin bow, obtained and
heard the eight-accented c, having 32,770 vibrations in a second.
Here the sensation of tone seemed to have reached its upper
limit, and the intervals were really undistinguishable in the
later octaves.

The musical pitch of a tone depends entirely on the number
of vibrations of the air in a second, and not at all upon the
mode in which they are produced. It is quite indifferent whether
they are generated by the vibrating strings of a piano or violin,
the vocal chords of the human larynx, the metal tongues of the
harmonium, the reeds of the clarionet, oboe, and bassoon, the
"trembling lips of the trumpeter, or the air cut by a sharp edge
in organ pipes and flutes.

A tone of the same number of vibrations has always the
same pitch, by whichever one of these instruments it is pro-
duced. That which distinguishes the note A of a piano, for
example, from the equally high A of the violin, flute, clarionet,
or trumpet, is called the quality of the tone, and to this we shall
have to recur presently.

As an interesting example of these assertions, T beg to show you a
peculiar physical instrument for producing musical tones, called the
siren, Fig. 1, which is especially adapted to establish the properties
resulting from the ratios of the numbers of vibrations.

In order to produce tones upon this instrument, the portvents g0
and g, are connected by means of flexible tubes with a bellows. The
air enters into round brass boxes, a0 and aj, and escapes by the per-
forated covers of these boxes at c0 and cr But the holes for the
escape of air are not perfectly free. Immediately before the covers
of both boxes there are two other perforated discs, fastened to a per-
pendicular axis k, which turns with great readiness. In the figure,
only the perforated disc can be seen at c0, and immediately below it
is the similarly perforated cover of the box. In the upper box, cp
only the edge of the disc is visible. If then the holes of the disc are
precisely opposite to those of the cover, the air can escape freely
But if the disc is made to revolve, so that some of its unperforated

HARMONY IN MUSIC. 59*

portions stand before the holes of the box, the air cannot escape at
all. On turning the disc rapidly, the vent-holes of the box are alter"
nately opened and closed. During the opening, air escapes ; during
the closure, no air can pass. Hence the continuous stream of air from
the bellows is converted into a series of discontinuous puffs, which,
when they follow one another with sufficient rapidity, gather them-
selves together into a tone.

Each of the revolving discs of this instrument (which is more
complicated in its construction than any one of the kind hitherto
made, and hence admits of a much greater number of combinations
of tone) has four concentric circles of holes, the lower set having
8, 10, 12, 18, and the upper set 9, 12, 15, and 16 holes respectively.
The series of holes in the covers of the boxes are precisely the same
as those in the discs, but under each of them lies a perforated ring,,
which can be so arranged, by means of the stops i i i i, that the
corresponding holes of the cover can either communicate freely with
the inside of the box, or are entirely cut off from it. We are thus
enabled to use any one of the eight series of holes singly, or com-
bined two and two, or three and three together, in any arbitrary
manner.

The round boxes, h0 h0 and h, hu of which halves only are drawn
in the figure, serve by their resonance to soften the harshness of the
tone.

The holes in the boxes and discs are cut obliquely, so that when
the air enters the boxes through one or more of , the series of holes,
the wind itself drives the discs round with a perpetually increasing
velocity.

On beginning to blow the instrument, we first hear separate im-
pulses of the air, escaping as puffs, as often as the holes of the disc
pass in front of those of the box. These puffs of air follow one an-
other more and more quickly, as the velocity of the revolving discs
increases, just like the puff's of steam of a locomotive on beginning to
move with the train. They next produce a whirring and whizzing,
which constantly becomes more rapid. At last we hear a dull drone,-
which, as the velocity further increases, gradually gains in pitch and
strength.

Suppose that the discs have been brought to a velocity of 3.3 re-
volutions in a second, and that the series with 8 holes has been
opened. At each revolution of the disc all these 8 holes will pass
before each separate hole of the cover. Hence there will be 8 puffs
for each revolution of the disc, or 8 times 33, that is, 264 puffs in a

•60 ON THE PHYSIOLOGICAL CAUSES OF

.second. This gives us the once-accented c' of our musical scale [that
is, ' middle c,' written on the leger line between the bass and treble
.staves]. But on opening the series of 16 holes instead, we have twice
as many, or 16 times 33, that is, 528 vibrations in a second. We
hear exactly the octave above the first c', that is, the twice-accented
c'' [or c on the third space of the treble staff]. By opening both the
.series of 8 and 16 holes at once, we have both c' and c" at once, and
can convince ourselves that we have the absolutely pure concord of
the octave. By taking 8 and 12 holes, which give numbers of vibra-
tions in the ratio of 2 to 3, we have the concord of a perfect fifth.
Similarly 12 and 16 or 9 and 12 give fourths, 12 and 15 give a major
third, and so on.

The upper box is furnished with a contrivance for slightly sharpen-
ing or flattening the tgnes which it produces. This box is movable
upon an axis, and connected with a toothed wheel, which is worked
by the driver attached to the handle d. By turning the handle
slowly while one of the series of holes in the upper box is in use, the
tone will be sharper or flatter, according as the box moves in the
opposite direction to the disc, or in the same direction as the disc.
When the motion is in the opposite direction, the holes meet those of
the disc a little sooner than they otherwise would, the time of vibra-
tion of the tone is shortened, and the tone becomes sharper. The
•contrary ensues in the other case.

Now, on blowing through 8 holes below and 16 above, we have a
perfect octave, as long as the upper box is still ; but when it is in
motion, the pitch of the upper tone is slightly altered, and the octave
becomes false.

On blowing through 12 holes above and 18 below, the result is a
perfect fifth as long as the upper box is at rest, but if it moves the
concord is perceptibly injured.

These experiments with the siren show us, therefore :—

1. That a series of puffs following one another with sufficient
rapidity produce a musical tone.

2. That the more rapidly they follow one another, the sharper is
the tone.

3. That when the ratio of the number of vibrations is exactly 1 to
2, the result is a perfect octave ; when it is 2 to 3, a perfect 'fifth ;
when it is 3 to 4, a pure fourth, and so on. The slightest alteration
in these ratios destroys the purity of the concord.

You will perceive, from what has been hitherto adduced,

HARMONY IN MUSIC. 61

that the human ear is affected by vibrations of the air, within
certain degrees of rapidity — viz. from about 20 to about 32,000
in a second — and that the sensation of musical tone arises from
this affection.

That the sensation thus excited is a sensation of musical
tone does not depend in any way upon the peculiar manner in
which the air is agitated, but solely on the peculiar powers of
sensation possessed by our ears and auditory nerves. I re-
marked, a little while ago, that when the tones are loud the
agitation of the air is perceptible to the skin. In this way
deaf nrntes can perceive the motion of the air which we call
sound. But they do not hear, that is, they have no sensation of
tone in the ear. They feel the motion by the nerves of the skin,
producing that peculiar description of sensation called whirring.
The limits of the rapidity of vibration within which the ear
feels an agitation of the air to be sound, depend also wholly
upon the peculiar constitution of the ear.

When the siren is turned slowly, and hence the puffs of
air succeed each other slowly, you hear no musical sound. By
the continually increasing rapidity of its revolution, no essential
change is produced in the kind of vibration of the air. Nothing
new happens externally to the ear. The only new result is the
sensation experienced by the ear, which then for the first time
begins to be affected by the agitation of the air. Hence the
more rapid vibrations receive a new name, and are called Sound.
If you admire paradoxes, you may say that aerial vibrations do
not become sound until they fall upon a hearing ear.

I must now describe the propagation of sound through the
atmosphere. The motion of a mass of air through which a
tone passes belongs to the so-called wave-motions — a class of
motions of great importance in physics. Light, as well as
sound, is one of these motions.

The name is derived from the analogy of waves on the sur-
face of water, and these will best illustrate the peculiarity of
this description of motion.

When a point in a surface of still water is agitated — as by
throwing in a stone — the motion thus caused is propagated in

•62 ON THE PHYSIOLOGICAL CAUSES OF

the form of waves, which spread in rings over the surface of
the water. The circles of waves continue to increase even after
rest has been restored at the point first affected. At the same
time the waves become continually lower, the further they are
removed from the centre of motion, and gradually disappear. On
each wave-ring we distinguish ridges or crests, and hollows or
troughs.

Crest and trough together form a wave, and we measure its
length from one crest to the next.

While the wave passes over the surface of the fluid, the
particles of the water which form it do not move on with it.
This is easily seen, by floating a chip of straw on the water.
When the waves reach the chip, they raise or depress it, but
when they have passed over it the position of the chip is not
perceptibly changed.

Now a light floating chip has no motion different from that
of the adjacent particles of water. Hence we conclude that
these particles do not follow the wave, but, after some pitching
up and down, remain in their original position. That which
really advances as a wave is, consequently, not the particles of
water themselves, but only a superficial form, which continues
to be built up by fresh particles of water. The paths of the
separate particles of water are more nearly vertical circlas, in
which they revolve with a tolerably uniform velocity, as long
as the waves pass over them.

In Fig. 2 the dark wave-line A B 0 represents a section of the
surface of the water over which waves are running in the direction
of the arrows above a and c. The three circles a, b, and c represent
the paths of particular particles of water at the surface of the wave.
The particle which revolves in the circle b is supposed, at the time
that the surface of the water presents the form A B C, to be at its
highest point B, and the particles revolving in the circles a and
c to he simultaneously in their lowest positions.

The respective particles of water revolve in these circl< s in the
•direction marked by the arrows. The dotted curves represent other
positions of the passing waves, at equal intervals of time, partly
"before the assumption of the A B C position (as for the crests be*-
tween a and b), and partly after the same (for the crests between b

HARMONY IN MUSIC.

and c). The positions of the crests are marked with figures. The
same figures in the three circles show where the respective revolving
particle would be, at the moment the wave assumed the corresponding
form. It will be noticed that the particles advance by equal arcs of
the circles, as the crest of the wave advances by equal distances
parallel to the water level.

In the circle b it will be further seen that the particle of water in
its positions 1, 2, 3 hastens to meet the approaching wave-crests',
] , 2, 3, rises on its left-hand side, is then carried on by the crest from
4 to 7 in the direction of its advance, afterwards halts behind it,
sinks down again on the right side, and finally reaches its original
position at 13. (In the Lecture itself, Fig. 2 was replaced by a
working model, in which the movable particles, connected by threads,
really revolved in circles, while connecting elastic threads represented
the surface of the water.)

FIG. 2.
e „

78 9 10 11 1!4 13

-^* X'X'^xTX?^^'

;<,x;<>

><sr« ' ^><^<u
^S£»? ^--'-'---^^

All particles at the surface of the water, as you see by this draw-
ing, describe equal circles. The particles of water at different depths
move in the same way, but as the depths increase, the diameters of
their circles of revolution rapidly diminish.

In this way, then, arises the appearance of a progressive motion
along the surface of the water, while in reality the moving particles
of water do not advance with the wave, but perpetually revolve in
their small circular orbits.

To return from waves of water to waves of sound. Ima-
gine an elastic fluid like air to replace the water, and the
w ives of this replaced water to be compressed by an inflexible
plate laid on their surface, the fluid being prevented from escap-
ing laterally from the pressure. Then on the waves being thus
flattened out, the ridges where the fluid had been heaped up

64 ON THE PHYSIOLOGICAL CAUSES OF

will produce much greater density than the hollows, from which
the nuid had been removed to form the ridges. Hence the
ridges are replaced by condensed strata of air, and the hollows
by rarefied strata. Now further imagine that these compressed
waves are propagated by the same law as before, and that also
the vertical circular orbits of the several particles of water
are compressed into horizontal straight lines. Then the waves
of sound will retain the peculiarity of having the particles of
air only oscillating backwards and forwards in a straight line,
while the wave itself remains merely a progressive form of
motion, continually composed of fresh particles of air. The
immediate result then would be waves of sound spreading out
horizontally from their origin.

But the expansion of waves of sound is not limited, like
those of water, to a horizontal surface. They can spread out in
any direction whatsoever. Suppose the circles generated by
a stone thrown into the water to extend in all directions of space,
and you will have the spherical waves of air by which sound is
propagated.

Hence we can continue to illustrate the peculiarities of the
motion of sound by the well-known visible motions of waves
of water.

The length of a wave of water, measured from crest to
crest, is extremely diflerent. A falling drop, or a breath of air,
gently curls the surface of the water. The waves in the wake
of a steamboat toss the swimmer or skiff severely. But the
waves of a stormy ocean can find room in their hollows for the
keel of a ship of the line, and their ridges can scarcely be
overlooked from the mast-head. The waves of sound present
similar differences. The little curls of water with short lengths
of wave correspond to high tones, the giant ocean billows to
deep tones. Thus the contrabass C has a wave thirty-five feet
long, its higher octave a wave of half the length, while the
highest tones of a piano have waves of only three inches in
length.

i The exact lengths of waves corresponding to certain notes, or symbols of
tone, depend upon the standard pitch assigned to one particular note, and

HARMONY IN MUSIC. 65

You perceive that the pitch of the tone corresponds to the
length of the wave. To this we should add that the height of
the ridges, or, transferred to air, the degree of alternate con-
densation and rarefaction, corresponds to the loudness and
intensity of the tone. But waves of the same height may
have different forms. The crest of the ridge, for example, may
be rounded off or pointed. Corresponding varieties also occur
in waves of sound of the same pitch and loudness. The so-
called timbre or quality of tone is what corresponds to the form
of the waves of water. The conception of form is transferred
from waves of water to waves of sound. Supposing waves of
water of different forms to be pressed flat as before, the surface,
having been levelled, will of course display no differences of
form, but, in the interior of the mass of water, we shall have
different distributions of pressure, and hence of density, which
exactly correspond to the differences of form in the still uncom-
pressed surface. In this sense then we can continue to speak of

FIG. 3.

the form of waves of sound, and can represent it geometrically.
We make the curve rise where the pressure, and hence density,
increases, and fall where it diminishes — just as if we had a
compressed fluid beneath the curve, which would expand to
the height of the curve in order to regain its natural density.

Unfortunately, the form of waves of sound, on which de-
pends the quality of the tones produced by various sounding
bodies, can at present be assigned in only a very few cases.

Among the forms of waves of sound which we are able to
determine with more exactness is one of great importance, here
termed the simple or pure wave-form, and represented in Fig. 3.

this differs in different countries. Hence the figures of the author have
been left unreduced. They are sufficiently near to those usually adopted in
England, to occasion no difficulty to the reader in these general remarks. — TK
I. P

66

ON THE PHYSIOLOGICAL CAUSES OF

It can be seen in waves of water only when their height is
small in comparison with their length, and they rim over a
smooth surface without external disturbance, or without any
action of wind. Ridge and hollow are gently rounded off,
equally broad and symmetrical, so that, if we inverted the curve,
the ridges would exactly fit into the hollows, and conversely.
This form of wave would be more precisely defined by saying

FIG. 4

that the particles of water describe exactly circular orbits of
small diameters, with exactly uniform velocities. To this simple
wave-form corresponds a peculiar species of tone, which, from
reasons to be hereafter assigned, depending upon its relation to
quality, we will term a simple tone. Such tones are produced
by striking a tuning-fork and holding it before the opening of a
properly tuned resonance tube. The tone of tuneful human

HARMONY IN MUSIC. 67

voices, singing the vowel oo in too, in the middle positions of their
register, appears not to differ materially from this form of wave.
We also know the laws of the motion of strings with suffi-
cient accuracy to assign in some cases the form of motion which
they impart to the air. Thus Fig. 4 represents the forms suc-
cessively assumed by a string struck, as in the German Zither,
by a pointed style [the plectrum of the ancient lyra, or the quill
of the old harpsichord, which may be easily imitated on a
guitar]. A a represents the form assumed by the string at the
moment of percussion. Then, at equal intervals of time, follow
the forms B, C, D, E, F, G ; and then, in inverse order, F, E, D,
C, B, A, and so on in perpetual repetition. The form of motion
which such a string, by means of an attached sounding-board,
imparts to the surrounding air, probably corresponds to the
broken line in Fig. 5, where h h indicates the position of equili-
brium, and the letters a b c d e f g show the line of the wave
which is produced by the action of several forms of string
marked by the corresponding capital letters in Fig. 4. It is
easily seen how greatly this form of wave (which of course

FIG. 5.

could not occur in water) differs from that of Fig. 3 (inde-
pendently of magnitude), as the string only imparts to the air a
series of short impulses, alternately directed to opposite sides.1
The waves of air produced by the tone of a violin would, on

FIG. 6.

the same principle, be represented by Fig. 6. During each

1 It is here assumed that the sounding-board and air in contact with it
immediately ohey the impulse given by the end of the string without exercising
a perceptible reaction on the motion of the string.

F2

68 ON THE PHYSIOLOGICAL CAUSES OF

period of vibration the pressure increases uniformly, and at the
end falls back suddenly to its minimum.

It is to such differences in the forms of the waves of sound
that the variety of quality in musical tones is due. We may
even carry the analogy further. The more uniformly rounded the
form of wave, the softer and milder is the quality of tone. The
more jerking and angular the wave-form, the more piercing the
quality. Tuning-forks, with their rounded forms of wave (Fig.
3), have an extraordinarily soft quality; and the qualities of
tone generated by the zither and violin resemble in harshness
the angularity of their wave-forms. (Figs. 5 and 6.)

Filially, I would direct your attention to an instructive
spectacle, which I have never been able to view without a cer-
tain degree of .physico-scientific delight, because it displays to
the bodily eye, on the surface of water, what otherwise could
only be recognised by the mind's eye of the mathematical thinker
in a mass of air traversed in all directions by waves of sound.
I allude to the composition of many different systems of waves,
as they pass over one another, each undisturbedly pursuing its
own path. We can watch it from the parapet of any bridge
spanning a river, but it is most complete and sublime when
viewed from a cliff beside the sea. It is then rare not to see
innumerable systems of waves, of various length, propagated in
various directions. The longest come from the deep sea and dash
against the shore. Where the boiling breakers burst shorter
waves arise, and run back again towards the sea. Perhaps
a bird of prey darting after a fish gives rise to a system of
circular waves, which, rocking over the undulating surface, are
propagated with the same regularity as on the mirror of an in-
land lake. And thus, from the distant horizon, where white
lines of foam on the steel blue surface betray the coming trains
of wave, down to the sand beneath our feet, where the impres-
sion of their arcs remains, there is unfolded before our eyes a
sublime image of immeasurable power and unceasing variety,
which, as the eye at once recognises its pervading order and law,
enchains and exalts without confusing the mind.

Now, just in the same way you must conceive the air of a

HARMONY IN MUSIC. 69

concert-hall or ball-room traversed in every direction, and not
merely on the surface, by a variegated orowd of intersecting
wave-systems. From the mouths of the male singers proceed
waves of six to twelve feet in length ; from the lips of the song-
stresses dart shorter waves, from eighteen to thirty-six inches
long. The rustling of silken skirts excites little curls in the
air, each instrument in the orchestra emits its peculiar waves,
and all these systems expand spherically from their respective
centres, dart through each other, are reflected from the walls of
the room, and thus rush backwards and forwards, until they
succumb to the greater force of newly generated tones.

Although this spectacle is veiled from the material eye, we
have another bodily organ, the ear, specially adapted to reveal
it to us. This analyses the interdigitation of the waves, which
in such cases would be far more confused than the intersection
of the water undulations, separates the several tones which
compose it, and distinguishes the voices of men and women —
nay, even of individuals — the peculiar qualities of tone given
out by each instrument, the rustling of the dresses, the footfalls
of the walkers, and so on.

It is necessary to examine the circumstances with greater
minuteness. When a bird of prey dips into the sea, rings of
waves arise, which are propagated as slowly and regularly upon
the moving surface as upon a surface at rest. These rings are
cut into the curved surface of the waves in precisely the same
way as they would have been into the still surface of a lake.
The form of the external surface of the water is determined in
this, as in other more complicated cases, by taking the height
of each point to be the height of all the ridges of the waves
which coincide at this point at one time, after deducting the sum
of all similarly simultaneously coincident hollows. Such a sum of
positive magnitudes (the ridges) and negative magnitudes (the
hollows), where the latter have to be subtracted instead of being
added, is called an algebraical sum. Using this term, then, we
may say that the height of every point of the surface of the
water is equal to the algebraical sum of all the portions of tJie
waves ivhich at that moment there concur.

70 ON THE PHYSIOLOGICAL CAUSES OF

It is the same with the waves of sound. They, too, are
added together at every point of the mass of air, as well as
in contact with the listener's ear. For them also the degree of
condensation and the velocity of the particles of air in the
passages of the organ of hearing are equal to the algebraical
sums of the separate degrees of condensation and of the velo-
cities of the waves of sound, considered apart. This single motion
of the air produced by the simultaneous action of various sound-
ing bodies, has now to be analysed by the air into the separate
parts which correspond to their separate effects. For doing this
the ear is much more unfavourably situated than the eye. The
latter surveys the whole undulating surface at a glance. But the
ear can, of course, only perceive the motion of the particles of air
which impinge upon it. And yet the ear solves its problem with
the greatest exactness, certainty, and determinacy. This power
of the ear is of supreme importance for hearing. Were it not
present it would be impossible to distinguish different tones.

Some recent anatomical discoveries appear to give a clue to
the explanation of this important power of the ear.

You will all have observed the phenomena of the sympathetic
production of tones in musical instruments, especially stringed
instruments. The string of a pianoforte when the damper is
raised begins to vibrate as soon as its proper tone is produced
in its neighbourhood with sufficient force by some other means.
When this foreign tone ceases the tone of the string will be
heard to continue some little time longer. If we put little paper
riders on the string they will be jerked off when its tone is thus
produced in the neighbourhood. This sympathetic action of
the string depends on the impact of the vibrating particles of
air against the string and its sounding-board.

Each separate wave-crest (or condensation) of air which
passes by the string is, of course, too weak to produce a sensible
motion in it. But when a long series of wave-crests (or con-
densations) strike the string in such a manner that each succeed-
ing one increases the slight tremor which resulted from the
action of its predecessors, the effect finally becomes sensible.
It is a process of exactly the same nature as the swinging of a.

HARMONY IN MUSIC. 71

heavy bell. A powerful man can scarcely move it sensibly by
a single impulse. A boy, by pulling the rope at regular intervals
corresponding to the time of its oscillations, can gradually bring
it into violent motion.

This peculiar reinforcement of vibration depends entirely
on the rhythmical application of the impulse. When the bell
has been once made to vibrate as a pendulum in a very small
arc, and the boy always pulls the rope as it falls, and at a time
that his pull augments the existing velocity of the bell, this
velocity, increasing slightly at each pull, will gradually become
considerable. But if the boy apply his power at irregular in-
tervals, sometimes increasing and sometimes diminishing the
motion of the bell, he will produce no sensible effect.

In the same way that a mere boy is thus enabled to swing
a heavy bell, the tremors of light and mobile air suffice to set
in motion the heavy and solid mass of steel contained in a
tuning-fork, provided that the tone which is excited in the air
is exactly in unison with that of the fork, because in this case
also every impact of a wave of air against the fork increases
the motions excited by the like previous blows.

This experiment is most conveniently performed on a fork,
Fig. 7, which is fastened to a sounding-board, the air being
excited by a similar fork of precisely the same pitch. If one is
struck, the other will be found after a few seconds to be sound-
ing also. Then damp the first fork, by touching it for a moment
with a finger, and the second will continue the tone. The
second will then bring the first into vibration, and so on.

But if a veiy small piece of wax be attached to the ends of
one of the forks, whereby its pitch will be rendered scarcely
perceptibly lower than the other, the sympathetic vibration of
the second fork ceases, because the times of oscillation are no
longer the same in each. The blows which the waves of air
excited by the first inflict upon the sounding-board of the second
fork, are indeed for a time in the same direction as the motions
of the second fork, and consequently increase the latter, but
after a very short time they cease to be so, and consequently
destroy the slight motion which they had previously excited.

72 ON THE PHYSIOLOGICAL CAUSES OF

Lighter and more mobile elastic bodies, as for example
strings, can be set in motion by a much smaller number of
aerial impulses. Hence they can be set in sympathetic motion
much more easily than tuning-forks, and by means of a musical
tone which is far less accurately in unison with themselves.

Now, then, if several tones are sounded in the neighbour-
hood of a pianoforte, no string can be set in sympathetic
vibration unless it is in unison with one of those tones. For
example, depress the forte pedal (thus raising the dampers), and
put paper riders on all the strings. They will of course leap

off when their strings are put in vibration. Then let several
voices or instruments sound tones in the neighbourhood. All
those riders, and only those, will leap off which are placed upon
strings that correspond to tones of the same pitch as those
sounded. You perceive that a pianoforte is also capable of
analysing the wave confusion of the air into its elementary con-
stituents.

The process which actually goes on in our ear is probably
very like that just described. Deep in the petrous bone out of
which the internal ear is hollowed lies a peculiar organ, the
cochlea or snail shell — a cavity filled with water, and so called

HARMONY IN MUSIC.

73

from its resemblance to the shell of a common garden snail.
This spiral passage is divided throughout its length into three
sections, upper, middle, and lower, by two membranes stretched
in the middle of its height. The Marchese Corti discovered
some very remarkable formations in the middle section. They
FIG. 8.

consist of innumerable plates, microscopically small, and
arranged orderly side by side, like the keys of a piano. They are
connected at one end with the fibres of the auditory nerve, and
at the other with the stretched membrane.

Fig. 8 shows this extraordinarily complicated arrangement

74 ON THE PHYSIOLOGICAL CAUSES OF

for a small part of the partition of the cochlea. The arches
•which leave the membrane at d and are reinserted at e, reach-
ing their greatest height between m and o, are probably the
parts which are suited for vibration. They are spun round
with innumerable fibrils, among which some nerve fibres can be
recognised, coming to them through the holes near c. The
transverse fibres g, h, i, k, and the cells o, also appear to belong
to the nervous system. There are about three thousand arches
similar to cl e, lying orderly beside each other, like the keys of'
a piano in the whole length of the partition of the cochlea.

In the so-called vestibulum, also, where the nerves expand
upon little membranous bags swimming in water, elastic appen-
dages, similar to stiff hairs, have been lately discovered at the
ends of the nerves. The anatomical arrangement of these
appendages leaves scarcely any room to doubt that they are set
into sympathetic vibration by the waves of sound which are
conducted through the ear. Now if we venture to conjecture
— it is at present only a conjecture, but after careful considera-
tion I am led to think it very probable — that every such
appendage is tuned to' a certain tone like the strings of a piano,
then the recent experiment with a piano shows you that when
(and only when) that tone is sounded the corresponding hair-
like appendage may vibrate, and the corresponding nerve-fibre
experience a sensation, so that the presence of each single such
tone in the midst of a whole confusion of tones must be in-
dicated by the corresponding sensation.

Experience then shows us that the ear really possesses the
power of analysing waves of air into their elementary forms.

By compound motions of the air, we have hitherto meant
such as have been caused by the simultaneous vibration of
several elastic bodies. Now, since the forms of the waves of
sound of different musical instruments are different, there is
room to suppose that the kind of vibration excited in the pas-
sages of the ear by one such tone will be exactly the same as
the kind of vibration which in another case is there excited by
two or more instruments sounded together. If the ear analyses.
the motion into its elements in the latter case, it cannot well

HARMONY IN MUSIC. 75

avoid doing so in the former, where the tone is due to a single
source. And this is found to be really the case.

I have previously mentioned the form of wave with gently
rounded crests and hollows, and termed it simple or pure (p. 65).
In reference to this form the French mathematician Fourier has
established a celebrated and important theorem which may be
translated from mathematical into ordinary language thus : Any
form of wave whatever can be compounded of a number of
simple waves of different lengths. The longest of these simple
waves has the same length as that of the given form of wave,
the others have lengths one half, one third, one fourth, &c., as
great.

By the different modes of uniting the crests and hollows of
these simple waves, an endless multiplicity of wave-forms may
be produced.

FIG. 9.

For example, the wave-curves A and B, Fig. 9, represent waves
of simple tones, B making twice as many vibrations as A in a second

76

ON THE PHYSIOLOGICAL CAUSES OF

of time, and being consequently an octave higher in pitch. 0 and D,
on the other hand, represent the waves which result from the super-
position of B on A. The dotted curves in the first halves of 0 and D
are repetitions of so much of the figure A. In 0, the initial point e
of the curve B coincides with the initial point d0 of A. But in D,
the deepest point b.2 of the first hollow in B is placed under the
initial point of A. The result is two different compound-curves, the
first C having steeply ascending and more gently descending crests,
but so related that by reversing the figure the elevations would
exactly fit into the depressions. But in D we have pointed crests and
flattened hollows, which are, however, symmetrical with respect to
right and left.

FIG. 10.

Other forms are shown in Fig. 10, which are also compounded of
two simple waves, A and B, of which B makes three times as many
vibrations in a second as A, and consequently is the twelfth higher
in pitch. The dotted curves in C and D are, as before, repetitions of

HARMONY IN MUSIC. 77

A. 0 lias flat crests and flat hollows, D has pointed crests and
pointed hollows.

These extremely simple examples will suffice to give a conception
of the great multiplicity of forms resulting from this method of com-
position. Supposing that instead of two, several simple waves were
selected, with heights and initial points arbitrarily chosen, an endless
variety of changes could be effected, and, in point of fact, any given
form of wave could be reproduced.1

When various simple waves concur on the surface of water,
the compound wave-form has only a momentary existence,
because the longer waves move faster than the shorter, and
consequently the two kinds of wave immediately separate,
giving the eye an opportunity of recognising the presence of
several systems of waves. But when waves of sound are
similarly compounded, they never separate again, because long
and short waves traverse air with the same velocity. Hence
the compound wave is permanent, and continues its course
unchanged, so that when it strikes the ear there is nothing-
to indicate whether it originally left a musical instrument in
this form, or whether it had been compounded on the way
out of two or more undulations.

Now what does the ear do ? Does it analyse this compound
wave? Or does it grasp it as a whole? The answer to these
questions depends upon the sense in which we take them. We
must distinguish two different points — the audible sensation^ as
it is developed without any intellectual interference, and the
conception, which we form in consequence of that sensation.
We have, as it were, to distinguish between the material ear of
the body and the spiritual ear of the mind. The material ear
does precisely what the mathematician effects by means of
Fourier's theorem, and what the pianoforte accomplishes when
a confused mass of tones is presented to it. It analyses those
wave-forms which were not originally due to simple undulations,,
such as those furnished by tuning-forks, into a sum of simple

1 Of course the waves could not overhang, but waves of such a form would
have no possible analogue in waves of sound [which the reader will recollect
are not actually in the forms here drawn, but have only condensations and1
rarefactions, conveniently replaced by these forms, p. G4].

78 ON THE PHYSIOLOGICAL CAUSES OF

tones, and feels the tone due to each separate simple wave sepa-
rately, whether the compound wave originally proceeded from a
source capable of generating it, or became compounded on the
way.

For example, on striking a string, it will give a tone correspond-
ing, as we have seen, to a wave-form widely different from that of a
simple tone. When the ear analyses this wave-form into a sum of
simple waves, it hears at the same time a series of simple tones cor-
responding to these waves.

Strings are peculiarly favourable for such an investigation, be-
cause they are themselves capable of assuming extremely different
forms in the course of their vibration, and these forms may also be
considered, like those of aerial undulations, as compounded of simple
waves. Fig. 4, p. 66, shows the consecutive forms of a string struck by
a simple rod. Fig. 11, p. 79, gives a number of other forms of vibration
of a string, corresponding to simple tones. The continuous line shows
the extreme displacement of the string in one direction, and the
dotted line in the other. At a the string produces its fundamental
tone, the deepest simple tone it can produce, vibrating in its whole
length, first on one side and then on the other. At b it falls into
two vibrating sections, separated by a single stationary point |3, called
a node (knot). The tone is an octave higher, the same as each of the
two sections would separately produce, and it performs twice as many
vibrations in a second as the fundamental tone. At c we have two
nodes, y3 and yv and three vibrating sections, each vibrating three
times as fast as the fundamental tone, and hence giving its^twelfth.
At dj there are three nodes, 8lf S2, 83, and four vibrating sections,
each vibrating four times as quickly as the fundamental tone, and
giving the second octave above it.

In the same way forms of vibration may occur with 5, 6, 7, &c.,
vibrating sections, each performing respectively 5, 6, 7, &c., times as
many vibrations in a second as the fundamental tone, and all other
vibrational forms of the string may be conceived as compounded of a
sum of such simple vibrational forms.

The vibrational forms with stationary points or nodes may be
produced by gently touching the string at one of these points either
with the finger or a rod, and rubbing the string with a violin bow,
plucking it with the finger, or striking it with a pianoforte hammer.
The bell-like harmonics or flageolet-tones of strings, so much used in
violin playing, are thus produced.

HARMONY IN MUSIC.

79

Now suppose that a string has been excited, and, after its tone has
been allowed to continue for a moment, it is touched gently at its middle
point /3, Fig. 11 b, or d.2t Fig. 11 d. The vibrational forms a and c,
for which this point is in motion, will be immediately checked and
destroyed ; but the vibratio nal forms b and d, for which this point is
at rest, will not be disturbed, and the tones due to them will continue
to be heard. In this way we can readily discover whether certain
members of the series of simple tones are contained in the compound
tone of a string when excited in any given way, and the ear can be
rendered sensible of their existence.

Fie. 11.

When once these simple tones in the sound of a string have been
thus rendered audible, the ear will readily be able to observe them in
the untouched string after a little accurate attention.

The series of tones which are thus made to combine with a given
fundamental tone is perfectly determinate. They are tones which
perform twice, thrice, four times, &c., as many vibrations in a second
as the fundamental tone. They are called the upper partials, or
harmonic overtones, of the fundamental tone. If this last be c, the

80 ON THE PHYSIOLOGICAL CAUSES OF

series may be written as follows in musical notation [it being-
understood that, on account of the temperament of a piano, these are
not precisely the fundamental tones of the 'corresponding strings on
that instrument, and that in particular the upper partial, V b , is
necessarily much flatter than the fundamental tone of the correspond-
ing note on the piano].

. ba.«3£- & :£"

Not only strings, but almost all kinds of musical instruments,
produce waves of sound which are more or less different from
those of simple tones, and are therefore capable of being com-
pounded out of a greater or less number of simple waves. The
ear analyses them all by means of Fourier's theorem better than
the best mathematician, and on paying sufficient attention can
distinguish the separate simple tones due to the corresponding
simple waves. This corresponds precisely to our theory of the
sympathetic vibration of the organs described by Corti. Ex-
periments with the piano, as well as the mathematical theory of
sympathetic vibrations, show that any upper partials which may
be present will also produce sympathetic vibrations. It follows,
therefore, that in the cochlea of the ear every external tone
will set in sympathetic vibration, not merely the little plates
with their accompanying nerve-fibres, corresponding to its
fundamental tone, but also those corresponding to all the upper
partials. and that consequently the latter must be heard as
well as the former.

Hence a simple tone is one excited by a succession of simple
wave-forms. All other wave-forms, such as those produced by
the greater number of musical instruments, excite sensations of
a variety of simple tones.

Consequently, all the tones of musical instruments must in
strict language, so far as the sensation of musical tone is
concerned, be regarded as chords with a predominant funda-
mental tone.

HARMONY IN MUSIC. 81

The whole of this theory of upper partials or harmonic
overtones will perhaps seem new and singular. Probably few
or none of those present, however frequently they may have
heard or performed music, and however fine may be their
musical ear, have hitherto perceived the existence of any such
• tones, although, according to my representations, they must be
always and continuously present. In fact, a peculiar act of
attention is requisite in order to hear them, and unless we know
how to perform this act the tones remain concealed. As you
are aware, no perceptions obtained by the senses are merely
sensations impressed on our nervous systems. A peculiar
intellectual activity is required to pass from a nervous sensation
to the conception of an external object, which the sensation has
aroused. The sensations of our nerves of sense are mere
symbols indicating certain external objects, and it is usually
only after considerable practice that we acquire the power of
drawing correct conclusions from our sensations respecting the
corresponding objects. Now it is a universal law of the per-
ceptions obtained through the senses that we pay only so much
attention to the sensations actually experienced as is sufficient
for us to recognise external objects. In this respect we are very
one-sided and inconsiderate partisans of practical utility; far
more so indeed than we suspect. All sensations which have no
direct reference to external objects, we are accustomed, as a
matter of coiirse, entirely to ignore, and we do not become
aware of them till we make a scientific investigation of the
action of the senses, or have our attention directed by illness to
the phenomena of our own bodies. Thus we often find patients,
when suffering under a slight inflammation of the eyes, become
for the first time aware of those beads and fibres known as
inouches volantes swimming about within the vitreous humour
of the eye, and then they often hypochondriacally imagine all
sorts of coming evils, because they fancy that these appearances
are new, whereas they have generally existed all their lives.

Who can easily discover that there is an absolutely blind
point, the so-called punctum caecum, within the retina of every
healthy eye ? How many people know that the only objects they

82 ON THE PHYSIOLOGICAL CAUSES OF

see single are those at which they are looking, and that all other
objects behind or before these appear double ? I could adduce
a long list of similar examples, which have not been brought to
light till the actions of the senses were scientifically investigated,
and which remain obstinately concealed till attention has been
drawn to them by appropriate means — often an extremely diffi-
cult task to accomplish.

To this class of phenomena belong the upper partial tones.
It is not enough for the auditory nerve to have a sensation. The
intellect must reflect upon it. Hence my former distinction of
a material and a spiritual ear.

"We always hear the tone of a string accompanied by a certain
combination of upper partial tones. A different combination of
such tones belongs to the tone of a flute, or of the human
voice, or of a dog's howl. Whether a violin or a flute, a man
or a dog, is close by us is a matter of interest for us to know, and
our ear takes care to distinguish the peculiarities of their tones
with accuracy. The means by which we can distinguish them,
however, is a matter of perfect indifference.

"Whether the cry of the dog contains the higher octave or the
twelfth of the fundamental tone has no practical interest for us,
and never occupies our attention. The upper partials are con-
«eque.ntly thrown into that unanalysed mass of peculiarities of a
tone which we call its quality. Now as the existence of upper
partial tones depends on the wave-form, we see, as I was able to
state previously (p. 65), that the quality of tone corresponds to
iheform of wave.

Tha upper partial tones are most easily heard when they are
not in harmony with the fundamental tone, as in the case of
bells. The art of the bell-founder consists precisely in giving
bells such a form that the deeper and stronger partial tones shall
be in harmony with the fundamental tone, as otherwise the bell
would be unmusical, tinkling like a kettle. But the higher
partials are always out of harmony, and hence bells are unfitted
for artistic music.

On the other hand, it follows, from what has been said, that
the upper partial tones are all the more difficult to hear,

HARMONY IN MUSIC. 83

the more accustomed we are to the compound tones of which
they form a part. This is especially the case with the human
voice, and many skilful observers have consequently failed to
discover them there.

The preceding theory was wonderfully corroborated by leading
to a method by which not only I myself, but other persons,
were enabled to hear the upper partial tones of the human voice.

No particularly fine musical ear is required for this purpose,
as was formerly supposed, but only proper means for directing
the attention of the observer.

Let a powerful male voice sing the note e k to the

vowel o in ore, close to a good piano. Then lightly touch on the
piano the note b' fe 1§r^f'=:~ in. the next octave above, and listen

attentively to the sound of the piano as it dies away. If this
b' fe is a real upper partial in the compound tone uttered by
the singer, the sound of the piano will apparently not die away
at all, but the corresponding upper partial of the voice will be
heard as if the note of the piano continued.1 By properly
varying the experiment, it will be found possible to distinguish
the vowels from one another by their upper partial tones.

The investigation is rendered much easier by Urming the ear
with small globes of glass or metal, as in Fig 12. The larger
opening a is directed to the source of sound, and the smaller
funnel-shaped end is applied to the drum of the ear. The in-
closed mass of air, which is almost entirely separated from
that without, has its own proper tone or key-note, which will be
heard, for example on blowing across the edge of the opening a.
If then this proper tone of the globe is excited in the external
air, either as a fundamental or upper partial tone, the included
mass of air is brought into violent sympathetic vibration, and

1 In repeating this experiment the observer must remember that the e ft of
the piano is not a true twelfth below the b'h. Hence the singer should first be
given b'h from the piano, which he will naturally sing as b h, an octave lower,
and then take a true fifth below it. A skilful singer will thus hit the true
twelfth and produce the required upper partial b'b. On the other hand, if he
sings efe from the piano, his upper partial b'V. will probably beat with that of
the piano.— TK.

a 2

84 ON THE PHYSIOLOGICAL CAUSES OF

the ear thus connected with it hears the corresponding tone
with much increased intensity. By this means it is extremely
easy to determine whether the proper tone of the globe is or is.
not contained in a compound tone or mass of tones.

FIG. 12.

On examining the vowels of the human voice, it is easy ix>
recognise, with the help of such resonators as have just been de-
scribed, that the upper partial tones of each vowel are peculiarly
strong in certain parts of the scale : thus O in ore has its upper
partials in the neighbourhood of b' fe. A in father in the neigh
bourhood of b" £ (an octave higher). The following gives a
general view of those portions of the scale where the upper
partials of the vowels, as pronounced in the north of Germany,
are particularly strong.

Names of Notes. :£ ,,

/ 6* .p.6''b ltd"

35-6"* £<*'"

TJOAAEI O U

1 on o a a u ee eu u

in in in in in iu in ' in

cool ore Scotch f«t fate feel French French

nearly nearly nearly nearly nearly nearly

Donders/' d b'ti. 1 c"'j /'" g? o"

1 The corresponding English vowel sounds are probably none of them pre-
cisely the same as those pronounced by the author. It is necessaiy to note this,

HARMONY IN MUSIC. 85

The following easy experiment clearly shows that it is in-
ilifferent whether the several simple tones contained in a com-
pound tone like a vowel uttered by the human voice come from
one source or several. If the dampers of a pianoforte are raised,
not only do the sympathetic vibrations of the strings furnish
tones of the same pitch as those uttered beside it; but if we sing
A (a in father) to any note of the piano, we hear an A quite
clearly returned from the strings; and if E (a in fare or fate),
O (o in hole or ore), and U (po in cool), be similarly sung to the
note, E, 0, and U will also be echoed back. It is only necessary
to hit the note of the piano with great exactness.1 Now the

for a very slight variation in pronunciation would produce a change in the
fundamental tone, and consequently a more considerable change in the position
of the upper partials. The tones given by Bonders, which are written below
the English equivalents, are cited on the authority of Helmholtz's Tonem-
pfindungen, 3rd edition, 1870, p. 171, where Helmholtz says: ' Bonders'* results
differ somewhat from mine, partly because his refer to a Butch, and mine to a
North German, pronunciation, and partly because Bonders, not having had the
assistance of tuning forks, could not always correctly determine the octave to
which the sounds belong.' Also (ib. p. 167) the author remarks that b"V- answers
only to the deep German a (which is the broad Scotch a', or aw without
labialisation), and that if the brighter Italian a (English a in father) be used,
the resonance rises a third, to d'". Br. C. L. Merkel, of Leipzig, in his Phy-
siologic der menschlichen Sprache, 18G6, p. 109, after citing Helmholtz's experi-
ments as detailed in his Tonempfindungen, gives the following as ' the pitches
of the vowels according to his most recent examination of his own habits of
speech, as accurately as he is able to note them.'

cool hole ore Scotch father French French fat fare fate feel

nearly

' Here the note a applies to the timbre obscur of A with low larynx, and b to
the timbre clair of A with high larynx, and similarly the vowel E may pass
from d" to e" by nan-owing the channel in the mouth. The intermediate
vowels O, A, have also two different timbres, and hence their pitch is not fixed ;
the most frequent are consequently written over one another ; the lower note is
for the obscure, and the higher for the bright timbre. But the vowel U seems
to be tolerably fixed as a', just as its parents U and I are upon d and a", and it
has consequently the pitch of the ordinary a' tuning fork.' — TK.

1 My own experience shows that if any vowel at any pitch be loudly and

86 ON THE PHYSIOLOGICAL CAUSES OF

sound of the vowel is produced solely by the sympathetic vibra-
tion of the higher strings, which correspond with the upper
partial tones of the tone sung.

In this experiment the tones of numerous strings are excited
by a tone proceeding from a single source, the human voice,
which produces a motion of the air, equivalent in form, and;
therefore in quality, to that of this single tone itself.

We have hitherto spoken only of compositions of waves of
different lengths. We will now compound waves of the same
length which are moving in the same direction. The result will
be entirely different, according as the elevations of one coincide
with those of the other (in which case elevations of double the
height and depressions of double the depth are produced), or the
elevations of one fall on the depi-essions of the other. If both
waves have the same height, so that the elevations of one exactly
fit into the depressions of the other, both elevations and depres-
sions will vanish in the second case, and the two waves will
mutually destroy each other. Similarly two waves of sound, as
well as two waves of water, may mutually destroy each other,
when the condensations of one coincide with the rarefactions of
the other. This remarkable phenomenon, wherein sound is
silenced by a precisely similar sound, is called the interference of
sounds.

This is easily proved by means of the siren already described.
On placing the upper box so that the puffs of air may proceed
simultaneously from the rows of twelve holes in each wind chest,
their effect is reinforced, and we obtain the fundamental tone of

sharply sung, or called out, beside a piano of which the dampers have been
raised, that vowel will be echoed back. There is generally a sensible pause
before the echo is heard. Before repeating the experiment with a new vowel,
whether at the same or a different pitch, damp all the strings and then again
raise the dampers. The result can easily be made audible to a hundred persons
at once, and it is extremely interesting and instructive. It is peculiarly so if
different vowels be sung to the same pitch, so that they have all the same
fundamental tone, and the upper partials only differ in intensity. For female

voices the pitches jgja J ^- a' to c" are favourable for all vowels. This is a

fundamental experiment for the theory of vowel sounds, and should be re-
peated by all who are interested in speech.— TR.

HARMONY IN MUSIC. 87

the corresponding tone of the siren very full and strong. But
on arranging the boxes so that the upper puffs escape when the
lower series of holes is covered, and conversely the fundamental
tone vanishes, and we only hear a faint sound of the first upper
partial, which is an octave higher, and which is not destroyed
by interference under these circumstances.

Interference leads us to the so-called musical beats. If two
tones of exactly the same pitch are produced simultaneously, and
their elevations coincide at first, they will never cease to coincide,
and if they did not coincide at first they never will coincide.

The two tones will either perpetually reinforce, or perpetually
destroy each other. Biit if the two tones have only approxi
matively equal pitches, and their elevations at first coincide, so
that they mutually reinforce each other, the elevations of one
will gradually outstrip the elevations of the other. Times will
come when the elevations of the one fall upon the depressions of
the other, and then other times when the more rapidly advanc-
ing elevations of the one will have again reached the elevations
of the other. These alternations become sensible by that alter-
nate increase and decrease of loudness, which we call a beat.
These beats may pften be heard when two instruments which
are not exactly in unison play a note of the same name.
When the two or three strings which are struck by the same
hammer on a piano are out of tune, the beats may be distinctly
heard. Very slow and regular beats often produce a fine effect
in sostenuto passages, as in sacred part-songs by pealing through
the lofty aisles like majestic waves, or by a gentle tremor giving
the tone a character of enthusiasm and emotion. The greater
the difference of the pitches, the quicker the beats. As long as
no more than four to six beats occur in a second, the ear readily
distinguishes the alternate reinforcements of the tone. If the
beats are more rapid the tone grates on the ear, or, if it is high,
becomes cutting. A grating tone is one interrupted by rapid
breaks, like that of the letter R, which is produced by inter-
rupting the tone of the voice by a tremor of the tongue or
uvula.1

1 The trill of the uvula is called the Northumbrian burr, and is not

88 ON THE PHYSIOLOGICAL CAUSES OF

When the beats become more rapid, the ear finds a con-
tinually increasing difficulty when attempting to hear them sepa-
rately, even though there is a sensible roughness of the tone.
At last they become entirely undistinguishable, and, like the
separate puffs which compose a tone, dissolve as it were into a
continuous sensation of tone.1

Hence, while every separate musical tone excites in the
auditory nerve a uniform sustained sensation, two tones of dif-
ferent pitches mutually disturb one another, and split up into
separable beats, which excite a feeling of discontinuity as dis-
agreeable to the ear as similar intermittent but rapidly repeated
sources of excitement are unpleasant to the other organs of
sense; for example, nickering and glittering light to the eye,
scratching with a brush to the skin. This roughness of tone is
the essential character of dissonance. It is most unpleasant to
•the ear when the two tones differ by about a semitone, in which
case, In the middle portions of the scale, from twenty to forty
beats ensue in a second. When the difference is a whole tone,
the roughness is less; and when it reaches a third it usually
disappears, at least in the higher parts of the scale. The (minor
or major) third may in consequence pass as a consonance. Even
when the fundamental tones have such widely different pitches
that they cannot produce audible beats, the upper partial tones
may beat and make the tone rough. Thus, if two tones form a
fifth (that is, one makes two vibrations in the same time as the
other makes three), there is one upper partial in both tones
which makes six vibrations in the same time. Now, if the ratio
of the pitches of the fundamental tones is exactly as 2 to 3, the
two upper partial tones of six vibrations are precisely alike, and
do not destroy the harmony of the fundamental tones. But if
this ratio is only approximatively as 2 to 3, then these two upper

known out of Northumberland, in England. In France it is called the r
grasseye or provenyai, and is the commonest Parisian sound of r. The
uvula trill is also very common in Germany, but it is quite unknown in
Italy.— TK.

1 The transition of beats into a harsh dissonance was displayed by means of
two organ pipes, of which one was gradually put more and more out of tune
with the other.

HARMONY IN MUSIC, 89

partials are not exactly alike, and hence will beat and roughen
the tone.

It is very easy to hear the beats of such imperfect fifths,
because, as our pianos and organs are now tuned, all the fifths
are impure, although the beats are very slow. By properly
directed attention, or still better with the help of a properly
tuned resonator, it is easy to hear that it is the particular upper
partials here spoken of that are beating together. The beats are
necessarily weaker than those of the fundamental tones, because
the beating upper partials are themselves weaker. Although we
are not usually clearly conscious of these beating upper partials,
the ear feels their effect as a want of uniformity or a roughness in
the mass of tone, whereas a perfectly pure fifth, the pitches being
precisely in the ratio of 2 to 3, continues to sound with perfect
smoothness, without any alterations, reinforcements, diminutions,
or roughnesses of tone. As has already been mentioned, the siren
proves in the simplest manner that the most perfect consonance
of the fifth precisely corresponds to this ratio between the pitches.
We have now learned the reason of the roughness experienced
when any deviations from that ratio has been produced.

In the same way two tones which have their pitches ex-
actly in the ratios of 3 to 4, or 4 to 5, and consequently form
a perfect fourth or a perfect major third, sound much better
when sounded together, than two others of which the pitches
slightly deviate from this exact ratio. In this manner, then,
any given tone being assumed as fundamental, there is a pre-
cisely determinate number of other degrees of tone which can
be sounded at the same time with it, without producing any
want of uniformity or any roughness of tone, or which will
at least produce less roughness than any slightly greater or
smaller intervals of tone under the same circumstances.

This is the reason why modern music, which is essentially
based on the harmonious consonance of tones, has been compelled
to limit its scale to certain determinate degrees. But even in
ancient music, which allowed only one part to be sung at a time,
and hence had no harmony in the modern sense of the word,
it can be shown that the upper partial tones contained in all

90 ON THE PHYSIOLOGICAL CAUSES OF

musical tones sufficed to determine a preference in favour of
progressions though certain determinate intervals. When an
upper partial tone is common to two successive tones in a
melody, the ear recognises a certain relationship between them,
serving as an artistic bond of union. Time is, however, too
short for me to enlarge on this topic, as we should be obliged
to go far back into the history of music.

I will but mention that there exists another kind of secondary
tones, which are only heard when two or more loudish tones
of different pitch are sounded together, and are hence termed
combinational.1 These secondary tones are likewise capable of
beating, and hence producing roughness in the chords. Suppose
a perfectly just major third c' e' wr~f~ (ratio of pitches, 4 to 5)
is sounded on the siren, or with properly tuned organ pipes, or

/vs.

on a violin ;2 then a faint C Sg==p two octaves deeper than the

-ic
c' will be heard as a combinational tone. The same C is also

heard when the tones e' g' ^b -L (ratio of pitches 5 to 6) are

sounded together.3

If the three tones c', e', g', having their pitches precisely in
the ratios 4, 5, and 6, are struck together, the combinational
tone C is produced twice4 in perfect tinison, and without beats.
But if the three notes are not exactly thus tuned,5 the two C

1 These are of two kinds, differential and summational, according as their
pitch is the difference or sum of the pitches of the two generating tones.
The former are the only combinational tones here spoken of. The discovery
of the latter was entirely due to the theoretical investigations of the author. —
TK.

2 In the ordinary tuning of the English concertina this major third is just,
and generally this instrument shows the differential tones very -well. The
major third is very false on the harmonium and piano. — TR.

3 This minor third is very false on the English concertina, harmonium, or
piano, and the combinational tone heard is consequently very different from the
true C.— TK.

* The combinational tone c, an octave higher, is also produced once from
the fifth c' g'. — TR.

5 As on the English concertina or harmonium, on both of which the con-
sequent effect may be well heard.— TR.

HARMONY IN MUSIC. 91

combinational tones will have different pitches, and produce
faint beats.

The combinational tones are usually much weaker than
the upper partial tones, and hence their beats are much less
rough and sensible than those of the latter. They are conse-
quently but little observable, except in tones which have scarcely
any upper partials, as those produced by flutes or the closed
pipes of organs. But it is indisputable that on such instruments-
part-music scarcely presents any line of demarcation between
harmony and dysharmony, and is consequently deficient both in
strength and character. On the contrary, all good musical
qualities of tones are comparatively rich in upper partials,
possessing the five first, which form the octaves, fifths, and
major thirds of the fundamental tone. Hence, in the mixture
stops of the organ, additional pipes are used, giving the series
of upper partial tones corresponding to the pipe producing the
fundamental tone, in order to generate a penetrating, powerful
quality of tone to accompany congregational singing. The im-
portant part played by the upper partial tones in all artistic
musical effects is here also indisputable.

We have now reached the heart of the theory of harmony.
Harmony and dysharmony are distinguished by the undisturbed
current of the tones in the former, which are as flowing as when
produced separately, and by the disturbances created in the latter,
in which the tones split up into separate beats. All that we
have considered tends to this end. In the first place the phe-
nomenon of beats depends on the interference of waves. Hence
they could only occur if sound were due to undulations. Next,
the determination of consonant intervals necessitated a capability
in the ear of feeling the upper partial tones, and analysing the
compound systems of waves into simple undulations, according
to Fourier's theorem. It is entirely due to this theorem that
the pitches of the upper partial tones of all serviceable musical
tones must stand to the pitch of their fundamental tones in the
ratios of the whole numbers to 1, and that consequently the
ratios of the pitches of concordant intervals must correspond
with the smallest possible whole numbers. How essential is.

•92 ON THE PHYSIOLOGICAL CAUSES OF

the physiological constitution of the ear which we have just
•considered, becomes clear by comparing it with that of the eye.
Light is also an undulation of a peculiar medium, the lumi-
nous ether, diffused through the universe, and light, as well
as sound, exhibits phenomena of interference. Light, too, has
waves of various periodic times of vibration, which produce
in the eye the sensation of colour, red having the greatest
periodic time, then orange, yellow, green, blue, violet; the
periodic time of violet being about half that of the outermost
red. But the eye is unable to decompose compound systems of
luminous waves, that is, to distinguish compound colours from
one another. It experiences from them a single, unanalysable,
simple sensation, that of a mixed colour. It is indifferent to
the eye whether this mixed colour results from a union of
fundamental colours with simple or with non-simple ratios of
periodic times. The eye has no sense of harmony in the same
meaning as the ear. There is no' music to the eye.

^Esthetics endeavour to find the principle of artistic beauty
in its unconscious conformity to law. To-day I have endea-
voured to lay bare the hidden law, on which depends the
-agreeableness of consonant combinations. It is in the truest
;sense of the word unconsciously obeyed, so far as it depends on
the upper partial tones, which, though felt by the nerves, are
not usually consciously present to the mind. Their com-
patibility or incompatibility, however, is felt without the hearer
knowing the cause of the feeling he experiences.

These phenomena of agreeableness of tone, as determined
solely by the senses, are of course merely the first step towards
the beautiful in music. For the attainment of that higher
beauty which appeals to the intellect, harmony and dysharmony
-are only means, although essential and powerful means. In
dysharmony the auditory nerve feels hurt by the beats of incom-
patible tones. It longs for the pure efflux of the tones into
harmony. It hastens towards that harmony for satisfaction and
rest. Thus both harmony and dysharmony alternately urge
-and moderate the flow of tones, while the mind sees in their
immaterial motion an image of its own perpetually streaming

HARMONY IN MUSIC. 93

thotights and moods. Just as in the rolling ocean, this move-
ment, rhythmically repeated, and yet ever varying, rivets our
attention and hurries us along. But whereas in the sea, blind
physical forces alone are at work, and hence the final impression
on the spectator's mind is nothing but solitude — in a musical
work of art the movement follows the outflow of the artist's
own emotions. Now gently gliding, now gracefully leaping,.
now violently stirred, penetrated or laboriously contending
with the natural expression of passion, the stream of sound, in
primitive vivacity, bears over into the hearer's soul unimagined
moods which the artist has overheard from his own, and
finally raises him up to that repose of everlasting beauty, of
which God has allowed but few of his elect favourites to be the
heralds.

But I have reached the confines of physical science, and
must close.

95

ICE AND GLACIERS.

A Lecture delivered at Frank fort-on-t he-Main, and at Heidelberg,
in February 1865.

THE world of ice and of eternal snow, as unfolded to us on the
summits of the neighbouring Alpine chain, so stern, so solitary,
so dangerous, it may be, has yet its own peculiar charm. Not
only does it enchain the attention of the natural philosopher,
who finds in it the most wonderful disclosures as to the present
and past history of the globe, but every summer it entices
thousands of travellers of all conditions, who find there mental
and bodily recreation. While some content themselves with
admiring from afar the dazzling adornment which the pure,
luminous masses of snowy peaks, interposed between the deeper
blue of the sky and the succulent green of the meadows, lend
to the landscape, others more boldly penetrate into the strange
world, willingly subjecting themselves to the most extreme
degrees of exertion and danger, if only they may fill themselves
with the aspect of its sublimity.

I will not attempt what has so often been attempted in vain
— to depict in words the beauty and magnificence of nature,
whose aspect delights the Alpine traveller. I may well presume
that it is known to most of you from your own observation ; or,
it is to be hoped, will be so. But I imagine that the delight
and interest in the magnificence of those scenes will make you
the more inclined to lend a willing ear to the remarkable results
of modern investigations on the more prominent phenomena of

96 ICE AND GLACIERS.

the glacial world. There we see that minute peculiarities of
ice, the mere mention of which might at other times be regarded
as a scientific subtlety, are the causes of the most important
changes in glaciers ; shapeless masses of rock begin to relate-
their histories to the attentive observer, histories which often
stretch far beyond the past of the human race into the
obscurity of the primeval world; a peaceful, uniform, and
beneficent sway of enormous natural forces, where at first
sight only desert wastes are seen, either extended indefi-
nitely in cheerless, desolate solitudes, or full of wild, threat-
ening confusion — an arena of destructive forces. And thus
I think I may promise that the study of the connection or
those phenomena of which I can now only give you a very short
outline will not only afford you some prosaic instruction, but
will make your pleasure in the magnificent scenes of the high
mountains more vivid, your interest deeper, and your admiration,
more exalted.

Let me first of all recall to your remembrance the chief
features of the external appearance of the snow-fields and of
the glaciers ; and let me mention the accurate measurements
which have contributed to supplement observation, before I pass
to discuss the casual connection of those processes.

The higher we ascend the mountains the colder it becomes.
Our atmosphere is like a warm covering spread over the earth •
it is well-nigh entirely transparent for the luminous darting
rays of the sun, and allows them to pass almost without appre-
ciable change. But it is not equally penetrable by obscure
heat-rays, which, proceeding from heated terrestrial bodies,,
struggle to diffuse themselves into space. These are absorbed
by atmospheric air, especially when it is moist ; the mass of air
is itself heated thereby, and only radiates slowly into space the
heat which has been gained. The expenditure of heat is thus
retarded as compared with the supply, and a certain store of
heat is retained along the whole surface of the earth. But on
high mountains the protective coating of the atmosphere is far
thinner — the radiated heat of the ground can escape thence
more freely into space; there, accordingly, the accumulated

ICE AND GLACIERS. 97

store of heat and the temperature are far smaller than at lower
levels.

To this must be added another property of air which acts
in the same direction. In a mass of air which expands, part of
its store of heat disappears; it becomes cooler, if it cannot
acquire fresh heat from without. Conversely, by renewed com-
pression of the air, the same quantity of heat is reproduced
which had disappeared during expansion. Thus if, for instance,
south winds drive the warm air of the Mediterranean towards
the north, and compel it to ascend along the great mountain-
wall of the Alps, where the air, in consequence of the diminished
pressure, expands by about half its volume, it thereby becomes
very greatly cooled — for a mean height of 11,000 feet, by from
18° to 30° C., according as it is moist or dry — and it thereby
deposits the greater part of its moisture as rain or snow. If
the same wind, passing over to the north side of the mountains
as Eohn-wind, reaches the valleys and plains, it again becomes
condensed, and is again heated. Thus the same current of air
which is warm in the plains, both on this side of the chain and
on the other, is bitterly cold on the heights, and can there
deposit snow, while in the plain we find it insupportably
hot.

The lower temperature at greater heights, which is due to
both these causes, is, as we know, very marked on the lower
mountain chains of our neighbourhood. In central Europe it
amounts to about 1° C. for an ascent of 480 feet; in winter it
is less— 1° for about 720 feet of ascent. In the Alps the differ-
ences of temperature at great heights are accordingly far more
considerable, so that upon the higher parts of their peaks and
slopes the snow which has fallen in winter no longer melts in
summer. This line, above which snow covers the ground!
throughout the entire year, is well known as the snow-line ; on
the northern side of the Alps it is about 8,000 feet high, on tho-
southern side about 8,800 feet. Above the snow-line it may
on sunny days be very warm ; the unrestrained radiation of
the sun, increased by the light reflected from the snow, often
becomes utterly unbearable; so that the tourist of sedentary

98 ICE AND GLACIERS.

habits, apart from the dazzling of his eyes, which he must pro-
tect by dark spectacles or by a veil, usually gets severely sun-
burnt in the face and hands, the result of which is an inflam-
matory swelling of the skin and great blisters on the surface.
More pleasant testimonies to the power of the sunshine are the
vivid colours and the powerful odour of the small Alpine flowers
which bloom in the sheltered rocky clefts among the snow-fields.
Notwithstanding the powerful radiation of the sun the tempera-
ture of the air above the snow-fields only rises to 5°, or at most
8° ; this, however, is sufficient to melt a tolerable amount of the
superficial layers of snow. But the warm hours and days are
too short to overpower the great masses of snow which have
fallen during colder times. Hence the height of the snow-line
does not depend merely on the temperature of the mountain
slope, but also essentially on the amount of the yearly snow-
fall. It is lower, for instance, on the moist and warm south
slope of the Himalayas than on the far colder but also far drier
north slope of the same mountain. Corresponding to the moist
climate of western Europe, the snow-fall upon the Alps is very
great, and hence the number and extent of their glaciers are
comparatively considerable, so that few mountains of the earth
can be compared with them in this respect. Such a develop-
ment of the glacial world is, as far as we know, met with only
on the Himalayas, favoured by the greater height; in Greenland
and in Northern Norway, owing to the colder climate ; in a few
islands in Iceland ; and in New Zealand, from the more abun-
dant moisture.

Places above the snow-line are thus characterised by the
fact that the snow which in the course of the year falls on its
surface does not quite melt away in summer, but remains to
some extent. This snow, which one summer has left, is pro-
tected from the further action of the sun's heat by the fresh
quantities that fall upon it during the next autumn, winter, and
spring. Of this new snow also next summer leaves some
remains, and thus year by year fresh layers of snow are accu-
mulated one above the other. In those places where such an
accumulation of snow ends in a steep precipice, and its inner

ICE AND GLACIERS. 99

structure is thereby exposed, the regularly stratified yearly
layers are easily recognised.

But it is clear that this accumulation of layer upon layer
cannot go on indefinitely, for otherwise the height of the snow
peak would continually increase year by year. But the more
the snow is accumulated the steeper are the slopes, and the
greater the weight which presses upon the lower and older
layers and tries to displace them. Ultimately a state must be
reached in which the snow-slopes are too steep to allow fresh
snow to rest upon them, and in which the burden which presses
the lower layers downwards is so great that these can no longer
retain their position on the sides of the mountain. Thus, part
of the snow which had originally fallen on the higher regions of
the mountain above the snow-line, and had there been pro-
tected from melting, is compelled to leave its original position and
seek a new one, which it of course finds only below the snow-
line on the lower slopes of the mountain, and especially in the
valleys, where however, being exposed to the influence of a
warmer air, it ultimately melts and flows away as water. The
descent of masses of snow from their original positions some-
times happens suddenly in avalanches, but it is usually very
gradual in the form of glaciers.

Thus we must discriminate between two distinct parts of
the ice-fields; that is, first, the snow which originally fell —
called firn in Switzerland — above the snow-line, covering the
slopes of the peaks as far as it can hang on to them, and filling
up the upper wide kettle-shaped ends of the valleys forming
widely extended fields of snow or firnmeere. Secondly, the
glaciers, called in the Tyrol firner, which as prolongations of
the snow-fields often extend to a distance of from 4,000 to 5,000
feet below the snow-line, and in which the loose snow of the
snow-fields is again found changed into transparent solid ice.
Hence the name glacier, which is derived from the Latin,
glades ; French, glace, glacier.

The outward appearance of glaciers is very characteristically
described by comparing them, with Goethe, to -currents of ice.
They generally stretch from the snow-fields along the depth of
H 2

100

ICE AND GLACIERS.

the valleys, filling them throughout their entire breadth, and
often to a considerable height. They thus follow all the cur-
vatures, windings, contractions, and enlargements of the valley.
Two glaciers frequently meet the valleys of which unite. The
two glacial currents then join in one common principal current,,
filling up the valley common to them both. In some places,
these ice-currents present a tolerably level and coherent surface,.
FIG. 13.

but they are usually traversed by crevasses, and both over the
surface and through the crevasses countless small and large
water-rills ripple, which carry off the water formed by the
melting of the ice. United, and forming a stream, they burst,
through a vaulted and clear blue gateway of ice, out at the
lower end of the larger glacier.

On the surface of the ice there is a large quantity of blocks
of stone, and of rocky debris, which at the lower end of the

ICE AND GLACIERS. 101

glacier are heaped up and form immense walls ; these are called
the lateral and terminal moraine of the glacier. Other heaps
of rock, the central moraine, stretch along the surface of the
glacier in the direction of its length, forming long regular dark
lines. These always start from the places where two glacier
streams coincide and unite. The central moraines are in such
places to be regarded as the continuations of the united lateral
moraines of the two glaciers.

The formation ©f the central moraine is well represented in
the view above given of the Unteraar Glacier (Fig. 13). In
the background are seen the two glacier currents emerging from
•different valleys ; on the right from the Schreckhorn, and on
the left from the Finsteraarhorn. From the place where they
unite the rocky wall occupying the middle of the picture de-
scends, constituting the central moraine. On the left are- seen
individual large masses of rock resting on pillars of ice, which
are known as glacier tables.

To exemplify these circumstances still further, I lay before
you in Fig. 14 a map of the Mer de Glace of Chamouni, copied
from that of Forbes.

The Mer de Glace in size is well known as the largest glacier
in Switzerland, although in length it is exceeded by the Aletsch
Glacier. It is formed from the snow-fields that cover the
heights directly north of Mont Blanc, several of which, as the
Grande Jorasse, the Aiguille Yerte (a, Figs. 14 and 15), the
Aiguille du Geant (b), Aiguille du Midi (c), and the Aiguille
du Dru (d), are only 2,000 to 3,000 feet below that king of the
European mountains. The snow-fields which lie on the slopes
and in the basins between these mountains collect in three prin-
cipal currents, the Glacier du Geant, Glacier de Lechaud, and
Glacier du Talefre, which, ultimately united as represented
in the map, form the Mer de Glace; this stretches as an ice-
current 2,600 to 3,000 feet in breadth down into the valley
of Chamouni, where a powerful stream, the Arveyron, bursts
from its lower end at k, and plunges into the Arve. The low-
est precipice of the Mer de Glace, which is visible from the
valley of Chamouni, and forms a large cascade of ice, is com-

SANTA BARBARA

102

ICE AND GLACIERS.

monly called Glacier des Bois, from a small village which lies
below.

Most of the visitors at Chamouni only set foot on the lowest-

FIG. 14.

O—

part of the Mer de Glace from the inn at the Montanvert, and
when they are free from giddiness cross the glacier at this place
to the little house on the opposite side, the Chapeau (n).

ICE AND GLACIERS.

Although, as the map shows, only
a comparatively very small portion
of the glacier is thus seen and
crossed, this way shows sufficiently
the magnificent scenes, and also
the difficulties of a glacier excur-
sion. Bolder wanderers march
upwards along the glacier to the
Jardin, a rocky cliff clothed with
some vegetation, which divides the
glacial current of the Glacier du
Talefre into two branches; and
bolder still they ascend yet higher,
to the Col du Geant (11,000 feet
above the sea), and down the
Italian side to the valley of
Aosta.

The surface of the Mer de Glace
shows four of the rocky walls which
we have designated as medial mo-
raines. The first, nearest the east
side of the glacier, is formed where
the two arms of the Glacier du Ta-
lefre unite at the lower end of the
Jardin ; the second proceeds from
the union of the glacier in ques-
tion with the Glacier de Lechaud ;
the third, from the union of the last
with the Glacier du Geant ; and the
fourth, finally, from the top of the
rock-ledge which stretches from the
Aiguille du Geant towards the cas-
cade (g) of the Glacier du Geant.

To give you an idea of the
slope and the fall of the glacier,
I have given in Fig. 15 a longi-
tudinal section of it according to

104 ICE AND GLACIERS.

the levels and measurements taken by Forbes, with the view of
the right bank of the glacier. The letters stand for the same
objects as in Fig. 14 ; p is the Aiguille de Lechaud, q the Aiguille
Noire, r the Mont Tacul, f is the Col du Geant, the lowest point
in the high wall of rock that surrounds the upper end of the snow-
fields which feed the Mer de Glace. The base line corresponds to
a length of a little more than nine miles : on the right the heights
above the sea are given in feet. The drawing shows very distinctly
how small in most places is the fall of the glaeier. Only an approxi-
mate estimate could be made of the depth, for hitherto nothing
certain has been made out in reference to it. But that it is every
deep is obvious from the following individual and accidental
observations.

At the end of a vertical rock wall of the Tacul, the edge of the
Glacier du Geant is pushed forth, forming an ice wall 140 feet in
height. This would give the depth of one of the upper arms of the
glacier at the edge. In the middle and after the union of the three
glaciers the depth must be far greater. Somewhat below the j unc-
tion Tyndall and Hirst sounded a moulin, that is, a cavity through
which the surface glacier waters escape, to a depth of 160 feet ; the
guides alleged that they had sounded a similar aperture to a depth
of 350 feet, and had found no bottom. From the usually deep
trough-shaped or gorge-like form of the bottom of the valleys,
which is constructed solely of rock walls, it seems improbable
that for a breadth of 3,000 feet the mean depth should only be 350
feet; moreover, from the manner in which ice moves, there must
necessarily be a very thick coherent mass beneath thecrevassed part.
To render these magnitudes more intelligible by refer-
ence to more familiar objects, imagine the valley of Heidel-
berg filled with ice up to the Molkencur, or higher, so that
the whole town, with all its steeples and the castle, is
buried deeply beneath it; if, further, you imagine this mass
of ice, gradually extending in height, continued from the
mouth of the valley up to Neckargemiind, that would about
correspond to the lower united ice-current of the Mer de Glace.
Or, instead of the Khine and the Nahe at Bingen, suppose two
ice-currents uniting which fill the Rhine valley to its upper

ICE AND GLACIERS. 105

border as far as we can see from the river, and then the united
currents stretching downwards to beyond Asmannshausen and
Burg Rheinstein ; such a current would also about correspond
to the size of the Mer de Glace.

Fig. 16, which is a view of the magnificent Gorner Glacier
seen from below, also gives an idea of the size of the masses of
ice of the larger glaciers.

FIG. 16.

The surface of most glaciers is dirty, from the numerous
pebbles and sand which lie upon it, and which are heaped together
the more the ice under them and among them melts away. The ice
of the surface has been partially destroyed and rendered crumbly.
In the depths of the crevasses ice is seen of a purity and clear-
ness with which nothing that we are acquainted with on the
plains can be compared. From its purity it shows a splendid
blue, like that of the sky, only with a greenish hue. Crevasses

106 ICE AND GLACIERS.

in which pure ice is visible in the interior occur of all sizes ; in
the beginning they form slight cracks in which a knife can scarcely
be inserted ; becoming gradually enlarged to chasms, hundreds or
even thousands, of feet in length, and twenty, fifty, and as much
as a hundred feet in breadth, while some of them are immeasurably
deep. Their vertical dark blue walls of crystal ice, glistening
with moisture from the trickling water, form one of the most
splendid spectacles which nature can present to us ; but, at the
same time, a spectacle strongly impregnated with the excitement
of danger, and only enjoyable by the traveller who feels perfectly
free from the slightest tendency to giddiness. The tourist must
know how, with the aid of well-nailed shoes and a pointed
Alpenstock, to stand even on slippery ice, and at the edge of a
vertical precipice the foot of which is lost in the darkness of
night, and at an unknown depth. Such crevasses cannot always
be evaded in crossing the glacier ; at the lower part of the Mer
de Glace, for instance, where it is usually crossed by travellers,
we are compelled to travel along some extent of precipitous
banks of ice which are occasionally only four to six feet in breadthr
and on each side of which is such a blue abyss. Many a traveller,
who has crept along the steep rocky slopes without fear, there
feels his heart sink, and cannot turn his eyes from the yawning
chasm, for he must first carefully select every step for his feet.
And yet these blue chasms, which lie open and exposed in the
daylight, are by no means the worst dangers of the glacier ;
though, indeed we are so organised that a clanger which we
perceive, and which therefore we can safely avoid, frightens us
far more than one which we know to exist, but which is veiled
from our eyes. So also it is with glacier chasms. In the lower
part of the glacier they yawn before us, threatening death and
destruction, and lead us, timidly collecting all our presence of
mind, to shrink from them ; thus accidents seldom occur. On the
upper part of the glacier, on the contrary, the surface is covered
with snow j this, when it falls thickly, soon arches over the-
naiTower crevasses of a breadth of from four to eight feet, and
forms bi-idges which quite conceal the crevasse, so that the-
traveller only sees a beautiful plane snow surface before him.

ICE AND GLACIERS. 107

If the snow bridges are thick enough, they will support a man ;.
but they are not always so, and these are the places where men,
and even chamois, are so often lost. These dangers may readily
be guarded against if two or three men are roped together at
intervals of ten or twelve feet. If then one of them falls into a
crevasse, the two others can hold him, and draw him out again.

In some places the crevasses may be entered, especially
at the lower end of a glacier. In the well-known glaciers of
Grindelwakl, Kosenlaui, and other places, this is facilitated
by cutting steps and arranging wooden planks. Then any one
who does not fear the perpetually trickling water may explore
these crevasses, and admire the wonderfully transparent and
pure crystal walls of these caverns. The beautiful blue colour
which they exhibit is the natural colour of perfectly pure water ;
liquid water as well as ice is blue, though to an extremely small
extent, so that the colour is only visible in layers of from ten to
twelve feet in thickness. The water of the Lake of Geneva and
of the Lago di Garda exhibits the same splendid colour as ice.

The glaciers are not everywhere crevassed ; in places where
the ice meets with an obstacle, and in the middle of great glacier
currents the motion of which is uniform, the surface is perfectly
coherent.

Fig. 17 represents one of the more level parts of the Mer de
Glace at the Montanvert, the little hoiise of which is seen in the
background. The Gries Glacier, where it forms the height of
the pass from the Upper Rhone valley to the Tosa valley, may
even be crossed on horseback. We find the greatest disturbance
of the surface of the glacier in those places where it passes
from a slightly inclined part of its bed to one where the slope is
steeper. The ice is there torn in all directions into a quantity
of detached blocks, which by melting are usually changed into
wonderfully shaped sharp ridges and pyramids, and from time to
time fall into the interjacent crevasses with a loud rumbling
noise. Seen from a distance such a place appears like a wild
frozen waterfall, and is therefore called a cascade ; such a cascade-
is seen in the Glacier du Talefre at 1, another is seen in the
Glacier du Geant at g, Fig. 19, while a third forms the lower

108

ICE AND GLACIERS.

end of the Mer de Glace. The latter, already mentioned as the
Olacier des Bois, which rises directly from the trough of the
valley at Chamouni to a height of 1,700 feet, the height of the
Konigstuhl at Heidelberg, affords at all times a chief object of

FIG. 17.

admiration to the Chamouni toui'ist. Fig. 18 represents a view
of its fantastically rent blocks of ice.

We have hitherto compared the glacier with a current
as regards its outer form and appearance. This similarity, how-
ever, is not merely an external one : the ice of the glacier does,
indeed, move forwards like the water of a stream, only more

ICE AND GLACIEKS.

109-

slowly. That this must be the case follows from the con-
siderations by which I have endeavoured to explain the origin
of a glacier. For as the ice is being constantly diminished at

FIG. 18.

the lower end by melting, it would entirely disappear if fresh ice
did not continually press forward from above, which, again, is
made up by the snowfalls on the mountain tops.

But by careful ocular observation we may convince ourselves
that the glacier does actually move. For the inhabitants of the

110 ICE AND GLACIEKS.

valleys, who have the glaciers constantly before their eyes, often
-cross them, and in so doing make use of the larger blocks
of stone as sign posts — detect this motion by the fact that their
guide posts gradually descend in the course of each year. And
as the yearly displacement of the lower half of the Mer de
Glace at Chamouni amounts to no less than from 400 to 600
feet, you can readily conceive that such displacements must
ultimately be observed, notwithstanding the slow rate at which
they take place, and in spite of the chaotic confusion of crevasses
and rocks which the glacier exhibits.

Besides rocks and stones, other objects which have acci-
dentally alighted upon the glacier are dragged along. In 1788
the celebrated Genevese Saussure, together with his son and a
company of guides and porters, spent sixeen days on the Col du
Geant. On descending the rocks at the side of the cascade of the
Glacier du Geant, they left behind them a wooden ladder. This
was at the foot of the Aiguille Noire, where the fourth band of
the Mer de Glace begins ; this line thus marks at the same time
the direction in which ice travels from this point. In the year
1832, that is, forty-four years after, fragments of this ladder were
found by Forbes and other travellers not far below the junction
of the three glaciers of the Mer de Glace, in the same line (at
s, Fig. 19), from which it results that these parts of the glacier
must on the average have each year descended 375 feet.

In the year 1827 Hugi had built a hut on the central
moraine of the Unteraar Glacier for the purpose of making
observations ; the exact position of this hut was determined by
himself and afterwards by Agassiz, and they found that each
year it had moved downwards. Fourteen years later, in the
year 1841, it was 4,884 feet lower, so that every year it had on
the average moved through 349 feet. Agassiz afterwards found
that his own hut, which he had erected on the same glacier, had
moved to a somewhat smaller extent. For these observations a
long time was necessary. But if the motion of the glacier be
observed by means of accurate measuring instruments, such as
theodolites, it is not necessary to wait for years to observe that ice
moves — a single day is sufficient.

ICE AND GLACIERS.

Ill

Such observations have in recent times been made by
several observers, especially by Forbes and by Tyndall. They
show that in summer the middle of the Mer de Glace moves
through twenty inches a day, while towards the lower terminal
cascade the motion amounts to as much as thirty-five inches in
a day. In winter the velocity is only about half as great. At

FIG. 19.

the edges and in the lower layers of the glacier, as in a flow of
water, it is considerably smaller than in the centre of the sur-
face.

The upper sources of the Mer de Glace also have a slower
motion, the Glacier du Geant thirteen inches a day, and the
Glacier du Lechaud nine inches and a half. In different
glaciers the velocity is in general very various, according to the

112 ICE AND GLACIERS.

size, the inclination, the amount of snow-fall, and other circum-
stances.

Such an enormous mass of ice thus gradually and gently
moves on, imperceptibly to the casual observer, about an inch
an hour — the ice of the Col du Geant will take 120 years before
it reaches the lower end of the Mer de Glace — but it moves
forward with uncontrollable force, before which any obstacles
that man could oppose to it yield like straws, and the traces
of which are distinctly seen even on the granite walls of the
valley. If, after a series of wet seasons, and an abundant fall
of snow on the heights, the base of a glacier advances, not
merely does it crush dwelling houses, and break the trunks of
powerful trees, but the glacier pushes before it the boulder walls
which form its terminal moraine without seeming to experience
any resistance. A truly magnificent spectacle is this motion,
so gentle and so continuous, and yet so powerful and so irre-
sistible.

I will mention here that from the way in which the glacier
moves we can easily infer in what places and in what directions
crevasses will be formed. For as all layers of the glacier do
not advance with equal velocity, some points remain behind
others ; for instance, the edges as compared with the middle.
Thus if we observe the distance from a given point at the edge to
a given point of the middle, both of which were originally in the
same line, but the latter of which afterwards descended more
rapidly, we shall find that this distance continually increases;
and since the ice cannot expand to an extent corresponding to
the increasing distance, it breaks up and forms crevasses, as seen
along the edge of the glacier in Fig. 20, which represents the
Gorner Glacier at Zermatt. It would lead me too far if I were
here to attempt to give a detailed explanation of the formation
of the more regular system of crevasses, as they occur in certain
parts of all glaciers ; it may be sufficient to mention that the
conclusions deducible from the considerations above stated are
fully borne out by observation.

I will only draw attention to one point— what extremely
small displacements are sufficient to cause ice to form hundreds.

ICE AND GLACIERS.

113

of crevasses. The section of the Mer de Glace (Fig. 21, at g,
c, h) shows places where a scarcely perceptible change in the
inclination of the surface of the ice occurs of from two to four
degrees. This is sufficient to produce a system of cross crevasses
on the surface. Tyndall more especially has urged and con-
firmed by observation and measurements, that the mass of ice

FIG. 20.

of the glacier does not give way in the smallest degree to ex-
tension, but when subjected to a pull is invariably torn asunder.
The distribution of the boulders, too, on the surface of the
glacier is readily explained when we take their motion into
account. These boulders are fragments of the mountains between,
which the glacier flows. Detached partly by the weathering of

ICE AND GLACIERS.

the stone, and partly by the freez-
ing of water in its crevices, they
fall, and for the most part on the
edge of the mass of ice. There
they either remain lying on the
surface, or if they have originally
burrowed in the snow, they ulti-
mately reappear in consequence of
the melting of the superficial layers
of ice and snow, and they accumu-
late especially at the lower end of
the glacier, where more of the ice
between them has been melted.
The blocks which are gradually
borne down to the lower end of
the glacier are sometimes quite
colossal in size. Solid rocky masses
of this kind are met with in the
lateral and terminal moraines,
which are as large as a two-storied
house.

The masses of stone move in
lines which are always nearly pa-
rallel to each other and to the lon-
gitudinal direction of the glacier.
Those, therefore, that are already
in the middle remain in the middle,
and those that He on the edge
remain at the edge. These latter
are the more numerous, for during
the entire course of the glacier fresh
boulders are constantly falling on
the edge, but cannot fall on the
middle. Thus are formed on the
edge of the mass of ice the lateral
moraines, the boulders of which
partly move along with the ice,

ICE AND GLACIERS. 115

partly glide over its surface, and partly rest on the solid rocky
base near the ice. But when two glacier streams unite, their
coinciding lateral moraines come to lie upon the centre of the
united ice-stream, and then move forward as central moraines
parallel to each other and to the banks of the stream, and they
show, as far as the lower end, the boundary -line of the ice which
originally belonged to one or the other of the arms of the glacier.
They are very remarkable as displaying in what regular parallel
bands the adjacent parts of the ice-stream glide downwards. A
glance at the map of the Mer de Glace, and its four central
moraines, exhibits this very distinctly.

On the Glacier du Geant and its continuation in the Mer de
Glace, the stones on the surface of the ice delineate, in alternately
greyer and whiter bands, a kind of yearly rings which were
first observed by Forbes. For since in the cascade at g, Fig. 21,
more ice slides down in summer than in winter, the surface of
the ice below the cascade forms a series of terraces as seen in.
the drawing, and as those slopes of the terraces which have a
northern aspect melt less than their upper plane surfaces, the
former exhibit purer ice than the latter. This, according to
Tyndall, is the probable origin of these dirt bands. At first
they run pretty much across the glacier, but as afterwards their
centre moves somewhat more rapidly than the ends, they
acquire farther down a curved shape, as represented in the
map, Fig. 19. By their curvature they thus show to the
observer with what varying velocity ice advances in the dif-
ferent parts of its course.

A very peculiar part is played by certain stones which are
imbedded in the lower surface of the mass of ice, and which
have partly fallen there through crevasses, and may partly have
been detached from the bottom of the valley. For these stones
are gradually pushed with the ice along the base of the valley,
and at the same time are pressed against this base by the
enormous weight of the superincumbent ice. Both the stones
imbedded in the ice as well as the rocky base are equally
hard, but by their friction against each other they are ground
to powder with a power compared to which any human exertion,
i 2

116 ICE AND GLACIERS.

of force is infinitely small. The product of this friction is an
extremely fine powder, which, swept away by water, appears
lower down in the glacier brook, imparting to it a whitish or
yellowish muddy appearance.

The rocks of the trough of the valley, on the contrary, on
which the glacier exerts year by year its grinding power, are
polished as if in an enormous polishing machine. They remain
as rounded, smoothly polished masses, in which are occasional
scratches produced by individual harder stones. Thus we see
them appear at the edge of existing glaciers, when after a series
of dry and hot seasons the glaciers have somewhat receded.
But we find such polished rocks as remains of gigantic ancient
glaciers to a far greater extent in the lower parts of many
Alpine valleys. In the valley of the Aar more especially, as
far down as Meyringen, the rock-walls polished to a con-
siderable height are very characteristic. There also we find
the celebrated polished plates, over which the way passes, and-
which are so smooth that furrows have had to be hewn into
them and rails erected to enable men and animals to traverse
them in safety.

The former enormous extent of glaciers is recognised by
ancient moraine-dykes and by transported blocks of stone, as
well as by these polished rocks. The blocks of stone which
have been carried away by the glacier are distinguished from
those which water has rolled down, by their enormous magni-
tude, by the perfect retention of all their edges which are not
at all rounded off, and finally by their being deposited on the
glacier in exactly the same order in which the rocks of which
they formed part stand in the mountain ridge; while the
stones which currents of water carry along are completely
mixed together.

From these indications, geologists have been able to prove
that the glaciers of Chamouni, of Monte Rosa, of the St. Gott-
hard, and the Bernese Alps, formerly penetrated through the
valley of the Arve, the Rhone, the Aar, and the Rhine to the
more level part of Switzerland and the Jura, where they have
deposited their boulders at a height of more than a thousand

ICE AND GLACIERS. 117

feet above the present level of the lake of Neufchatel. Similar
traces of ancient glaciers are found upon the mountains of the
British Islands, and upon the Scandinavian Peninsula.

The drift-ice too of the Arctic Sea is glacier ice; it is
pushed down into the sea by the glaciers of Greenland, becomes
detached from the rest of the glacier, and floats away. In
Switzerland we find a similar formation of drift-ice, though on
a far smaller scale, in the little Marjelen See, into which part
of the ice of the great Aletsch Glacier pushes down. Blocks
of stone which lie in drift-ice may make long voyages over the
.sea. The vast number of blocks of granite which are scattered
on the North German plains, and whose granite belongs to the
Scandinavian mountains, has been transported by drift-ice at
the time when the European glaciers had such an enormous
extent.

I must unfortunately content myself with these few refer-
ences to the ancient history of glaciers, and revert now to the
processes at present at work in them.

From the facts which I have brought before you it results
that the ice of a glacier flows slowly like the current of a very
viscous substance, such for instance as honey, tar, or thick
magma of clay. The mass of ice does not merely flow along
the ground like a solid which glidas over a precipice, but it
bends and twists in itself; and although even while doing this
it moves along the base of the valley, yet the parts which are
in contact with the bottom and the sides of the valley are per-
ceptibly retarded by the powerful friction ; the middle of the
surface of the glacier, which is most distant both from the
bottom and the sides, moving most rapidly. Rendu, a Savoyard
priest, and the celebrated natural philosopher Forbes, were the
first to suggest the similarity of a glacier with a current of a
viscous substance.

Now you will perhaps inquire with astonishment how it is
possible that ice, which is the most brittle and fragile of sub-
stances, can flow in the glacier like a viscous mass ; and you
may perhaps be disposed to regard this as one of the wildest
and most improbable statements that have ever been made by

118 ICE AND GLACIERS.

philosophers. I will at once admit that philosophers themselves
were not a little perplexed by these results of their investiga-
tions. But the facts were there, and could not be got rid of.
How this mode of motion originated was for a long time quite
enigmatical, the more so since the numerous crevasses in glaciers
were a sufficient indication of the well-known brittleness of ice;
and as Tyndall correctly remarked, this constituted an essential
difference between a stream of ice and the flow of lava, of tar,
of honey, or of a current of mud.

The solution of this strange problem was found, as is so
often the case in the natural sciences, in apparently recondite
investigations into the nature of heat, which form one of the
most important conquests of modern physics, and which constitute
what is known as the mechanical theory of heat. Among a
great number of deductions as to the relations of the diverse
natural forces to each other, the principles of the mechanical
theory of heat lead to certain conclusions as to the dependence
of the freezing-point of water on the pressure to which ice and
water are exposed.

Every one knows that we determine that one fixed point of
our thermometer scale which we call the freezing-point or zero
by placing the thermometer in a mixture of pure water and ice.
Water, at any rate when in contact with ice, cannot be cooled
below zero without itself being converted into ice ; ice cannot
be heated above the freezing-point without melting. Ice and
water can exist in each other's presence at only one temperature,
the temperature of zero.

Now, if we attempt to heat such a mixture by a flame
beneath it, the ice melts, but the temperature of the mixture is
never raised above that of 0° so long as some of the ice remains
unmelted. The heat imparted changes ice at zero into water
at zero, but the thermometer indicates no increase of temperature.
Hence physicists say that heat has become latent, and that water
contains a certain quantity of latent heat beyond that of ice at
the same temperature.

On the other hand, when we withdraw more heat from
the mixture of ice and water, the water gradually freezes : but

ICE AND GLACIERS. 119

as long as there is still liquid water, the temperature remains
at zero. Water at 0° has given up its latent heat, and has
become changed into ice at 0°.

Now a glacier is a mass of ice which is everywhere inter-
penetrated by water, and its internal temperature is therefore
everywhere that of the freezing-point. The deeper layers, even
of the fields of neve, appear on the heights which occur in our
Alpine chain to have everywhere the same temperature. For,
though the freshly fallen snow of these heights is, for the most
part, at a lower temperature than that of 0°, the first hours of
warm sunshine melt its surface and form water, which
trickles into the deeper colder layers, and there freezes, until it
has throughout been brought to the temperature of the freezing-
point. This temperature then remains unchanged. For, though
by the sun's rays the surface of the ice may be melted, it cannot
be raised above zero, and the cold of winter penetrates as little
into the badly conducting masses of snow and ice as it does
into our cellars. Thus the interior of the masses of neve, as
well as of the glacier, remains permanently at the melting-
point.

But the temperature at which water freezes may be altered
by strong pressure. This was first deduced from the mechanical
theory of heat by James Thomson of Belfast, and almost simul-
taneously by Clausius of Zurich ; and, indeed, the amount of
this change may be correctly predicted from the same reasoning.
For each increase of a pressure of one atmosphere the freezing-
point is lowered by the T-r5^h part of a degree Centigrade.
The brother of the former, Sir W. Thomson, the celebrated
Glasgow physicist, made an experimental confirmation of this
theoretical deduction by compressing in a suitable vessel a mix-
ture of ice and snow. This mixture became colder and colder
as the pressure was increased, and to the extent required by the
mechanical theory.

Now, if a mixture of ice and water becomes colder when it
is subjected to increased pressure without the withdrawal of
heat, this can only be effected by some free heat becoming latent;
that is, some ice in the mixture must melt and be converted

120 ICE AND GLACIERS.

into water. In this is found the reason why mechanical pressure
can influence the freezing-point. You know that ice occupies
more space than the water from which it is formed. When
water freezes in closed vessels, it can burst not only glass vessels,
but even iron shells. Inasmuch, therefore, as in the compressed
mixture of ice and water some of the ice melts and is converted
into water, the volume of the mass diminishes, and the mass
can yield more to the pressure upon it than it could have
done without such an alteration of the freezing-point. Pres-
sure furthers in this case, as is usual in the interaction of
various natural forces, the occurrence of a change, that is
fusion, which is favourable to the development of its own
activity.

In Sir W. Thomson's experiments water and ice were con-
fined in a closed vessel from which nothing could escape. The
case is somewhat different when, as with glaciers, the water dis-
seminated in the compressed ice can escape through fissures.
The ice is then compressed, but not the water which escapes.
The compressed ice becomes colder in conformity with the lower-
ing of its freezing-point by pressure; but the freezing-point of
water which is not compressed is not lowered. Thus under
these circumstances we have ice colder than 0° in contact with
water at 0°. The consequence is that around the compressed
ice water continually freezes and forms new ice, while on the
other hand part of the compressed ice melts.

This occurs, for instance, when only two pieces of ice are
pressed against each other. By the water which freezes at their
surfaces of contact they are firmly joined into one coherent
piece of ice. With powerful pressure, and the chilling therefore
great, this is quickly effected; but even with a feeble pressure it
takes place, if sufficient time be given. Faraday, who discovered
this property, called it the regelation of ice; the explanation of
this phenomenon has been much controverted ; I have detailed
to you that which I consider most satisfactory.

This freezing together of two pieces of ice is very readily
effected by pieces of any shape, which must not, however, be at
a lower temperature than 0°, and the experiment succeeds best

ICE AND GLACIERS. 121

-when the pieces are already in the act of melting.1 They need
•only be strongly pressed together for a few minutes to make them
-adhere. The more plane are the surfaces in contact, the more
complete is their union. But a very slight pressure is sufficient
if the two pieces are left in contact for some time.2

This property of melting ice is also utilised by boys in
making snow-balls and snow-men. It is well known that this
only succeeds either when the snow is already melting, or at
any rate is only so much lower than 0° that the warmth of the
hand is sufficient to raise it to this temperature. Yery cold
snow is a dry loose powder which does not stick together.

The process which children carry out on a small scale in
making snow-balls takes place in glaciers on the very largest
.scale. The deeper layers of what was originally fine loose neve
are compressed by the hugh masses resting on them, often
amounting to several hundred feet, and under this pressure they
cohere with an ever firmer and closer structure. The freshly
fallen snow originally consisted of delicate microscopically fine
ice-spicules, united and forming delicate six-rayed, feathery stars
of extreme beauty. As often as the upper layers of the snow-
fields are exposed to the sun's rays, some of the snow melts;
water permeates the mass, and on reaching the lower layers of
still colder snow, it again freezes ; thus it is that the firn first
becomes granular and acquires the temperature of the freezing-
point. But as the weight of the superincumbent masses of snow
continually increases by the firmer adherence of its individual
granules, it ultimately changes into a dense and perfectly hard
mass.

This transformation of snow into ice may be artificially
fleeted by using a corresponding pressure.

We have here (Fig. 22) a cylindrical cast-iron vessel, A A ;
the base, B B, is held by three screws, and can be detached, so as
to remove the cylinder of ice which is formed. After the vessel

1 In the Lecture a series of small cylinders of ice, which had been prepared
<by a method to be afterwards described, were pressed with their plane ends
-against each other, and thus a cylindrical bar of ice produced.

2 Vide the additions at the end of this Lecture.

122

ICE AND GLACIERS.

FIG. 22.

has lain for a while in ice- water, so as to reduce it to the tempera-
ture of 0°, it is packed full of snow, and then the cylindrical
plug, C C, which fits the inner aperture, but moves in it with
gentle friction, is forced in with the aid of an hydraulic press.
The press used was such that the pressure to which the snow
was exposed could be increased to fifty atmospheres. Of course
the looser snow contracts to a very small volume under such a
powerful pressure. The pressure is removed, the cylindrical
plug taken out, the hollow
again filled up with snow,
and the process repeated un-
til the entire form is filled
with the mass of ice, which
no longer gives way to pres-
sure. The compressed snow
which I now take out, you
will see, has been transformed
into a hard, angular, and
translucent cylinder of ice;
and how hard it is appears
from the crash which ensues
when I throw it to the
ground. Just as the loose
snow in the glaciers is pressed
together to solid ice, so also
in many places ready-formed
irregular pieces of ice are
joined and form clear and
compact ice. This is most re-
markable at the base of the

glacier cascades. These are glacier falls where the upper part of
the glacier ends at a steep rocky wall, and blocks of ice shoot
down as avalanches over the edge of this wall. The heap of
shattered blocks of ice which accumulate become joined at the
foot of the rock- wall to a compact, dense mass, which then con-
tinues its way downwards as glacier. More frequent than such
cascades, where the glacier-stream is quite dissevered, are places.

ICE AXD GLACIERS. 123

where the base of the valley has a steeper slope, as, for instance,
the places in the Mer de Glace (Fig. 14), at g, of the Cascade of
the Glacier du Geant, and at i and h of the great terminal
cascade of the Glacier des Bois. The ice splits there into
thousands of banks and clifis, which then recombine towards the
bottom of the steeper slope and form a coherent mass.

This also we may imitate in our ice-mould. Instead of the
snow I take irregular pieces of ice, press them together; add new
pieces of ice, press them again, and so on, until the mould is full.
When the mass is taken out it forms a compact coherent cylinder
of tolerably clear ice, which has a perfectly sharp edge, and is an
accurate copy of the mould.

This experiment, which was first made by Tyndall, shows
that a block of ice may be pressed into any mould just like a
piece of wax. It might, perhaps, be thought that such a block
had, by the pressure in the interior, been first reduced to powder
so fine that it readily penetrated every crevice of the mould, and
then that this powdered ice, like snow, was again combined by
freezing. This suggests itself the more readily, since while the
press is being worked a continual creaking and cracking is heard
in the interior of the mould. Yet the mere aspect of the cylinders
pressed from blocks of ice shows us that it has not been formed
in this manner; for they are generally clearer than the ice
which is produced from snow, and the individual larger pieces
of ice which have been used to produce them are recognised,
though they are somewhat changed and flattened. This is
most beautiful when clear pieces of ice are laid in the form
and the rest of the space stuffed full of snow. The cylinder is
then seen to consist of alternate layers of clear and opaque
ice, the former arising from the pieces of ice, and the latter from
the snow ; but here also the pieces of ice seem pressed into flat
discs.

These observations teach, then, that ice need not be com-
pletely smashed to fit into the prescribed mould, but that it may
give way without losing its coherence. This can be still more
completely proved, and we can acquire a still better insight into
the cause of the pliability of ice, if, we press the ice between

124 ICE AND GLACIERS.

two plane wooden boards, instead of in the mould, into which
we cannot see.

I place first an irregular cylindrical piece of natural ice,
taken from the frozen surface of the river, with its two plane
terminal surfaces between the plates of the press. If I begin to
work, the block is broken by pressure ; every crack which forms
extends through the entire mass of the block ; this splits into a
heap of larger fragments, which again crack and are broken the
more the press is worked. If the pressure is relaxed, all these
fragments are, indeed, reunited by freezing, but the aspect of the

FIG. 23. FIG. 24.

whole indicates that the shape of the block has 'resulted less
from pliability than from fracture, and that the individual frag-
ments have completely altered their mutual positions.

The case is quite different when one of the cylinders which
we have formed from snow or ice is placed between the plates of
the press. As the press is worked the creaking and cracking is
heard, but it does not break; it gradually changes its shape,
becomes lower and at the same time thicker ; and only when it
has been changed into a tolerably flat circular disc does it begin
to give way at the edges and form cracks, like crevasses on
a small scale. Fig. 23 shows the height and diameter of such a

ICE AND GLACIERS.

125

cylinder in its original condition; Fig. 24 represents its ap-
pearance after the action of the press.

A still stronger proof of the pliability of ice is afforded
when one of our cylinders is forced through a narrow aperture..
With this view I place a base on the previously described mould,
which has a conical perforation, FlG> 25

the external aperture of which
is only two thirds the diameter
of the cylindrical aperture of
the form. Fig. 25 gives a sec-
tion of the whole. If now I
insert into this one of the com-
pressed cylinders of ice, and force
down the plug a, the ice is forced
through the narrow aperture in
the base. It at first emerges as
a solid cylinder of the same dia-
meter as the aperture; but as
the ice follows more rapidly in
the centre than at the edges, the free terminal surface of the
cylinder becomes curved, the end thickens, so that it could not
be brought back through the aperture, and it ultimately splits
off. Fig. 26 exhibits a series of shapes which have resulted in
this manner.1

FIG. 26.

Here also the cracks in the emerging cylinder of ice exhibit
a surprising similarity with the longitudinal rifts which divide

1 In this experiment the lower temperature of the compressed ice sometimes
extended so far through the iron form, that the water in the slit between the
base plate and the cylinder froze and formed a thin sheet of ice, although the
pieces of ice as well as the iron mould had previously laid in ice-water, and could,
not be colder than 0°.

126 ICE AND GLACIERS.

a glacier current where it presses through a narrow rocky pass
into a wider valley.

In the cases which we have described we see the change
in shape of the ice taking place before our eyes, whereby
the block of ice retains its coherence without breaking into
individual pieces. The brittle mass of ice seems rather to yield
like a piece of wax.

A closer inspection of a clear cylinder of ice compressed
from clear pieces of ice, while the pressure is being applied,
shows us what takes place in the interior ; for we then see an
innumerable quantity of extremely fine radiating cracks shoot
through it like a turbid cloud, which mostly disappear, though
not completely, the moment the pressure is suspended. Such a
compressed block is distinctly more opaque immediately after
the experiment than it was before; and the turbidity arises,
as may easily be observed by means of a lens, from a great
number of whitish capillary lines crossing the interior of the
mass of what is otherwise clear. These lines are the optical
expression of extremely fine cracks l which interpenetrate the
mass of the ice. Hence we may conclude that the compressed
block is travelled by a great number of fine cracks and fissures
which render it pliable ; that its particles become a little dis-
persed, and are therefore withdrawn from pressure, and that
immediately afterwards the greater part of the fissures disappear,
owing to their sides freezing. Only in those places in which the
surfaces of the small displaced particles do not accurately fit to
each other some fissured spaces remain open, and are discovered
as white lines and surfaces by the reflection of the light.

These cracks and laminae also become more perceptible when

1 These cracks arc probably quite empty and free from air, for they are also
formed when perfectly clear and air-free pieces of ice are pressed in the form
which has been previously filled •with water, and where, therefore, no air
could gain access to the pieces of ice. That such air-free crevices occur in
glacier ice has been already demonstrated by Tyndall. When the compressed
ice afterwards melts, these crevices fill up with water, no air being left.
They are then, however, far less visible, and the whole block is therefore
clearer. And just for this reason they could not originally have been filled
with water.

ICE AND GLACIERS. 127

the ice — which, as I before mentioned, is below zero immediately
after pressure has been applied — is again raised to this tempera-
ture and begins to melt. The crevices then fill with water,
and such ice then consists of a quantity of minute granules
from the size of a pin's head to that of a pea, which are closely
pushed into one another at the edges and projections, and in
part have coalesced, while the narrow fissures between them
are full of water. A block of ice thus formed of ice-granules
adheres firmly together ; but if particles be detached from its
corners they are seen to consist of these angular granules. Gla-
cier ice, when it begins to melt, is seen to possess the same
structure, except that the pieces of which it consists are mostly
larger than in artificial ice, attaining the size of a pigeon's egg.

Glacier ice and compressed ice are thus seen to be substances
of a granular structure, in opposition to regularly crystallised
ice, such as is formed on the surface of still water. We here
meet with the same differences as between calcareous spar and
marble, both of which consist of carbonate of lime ; but while
the former is in large, regular crystals, the latter is made up of
irregularly agglomerated crystalline grains. In calcareous spar,
as well as in crystallised ice, the cracks produced by inserting the
point of a knife extend through the mass, while in granular ice a
crack which arises in one of the bodies where it must yield does
not necessarily spread beyond the limits of the granule.

Ice which has been compressed from snow, and has thus from
the outset consisted of innumerable very fine crystalline needles,
is seen to be particularly plastic. Yet in appearance it materially
differs from glacier ice, for it is very opaque, owing to the great
quantity of air which was originally inclosed in the flaky mass
of snow, and which remains there as extremely minute bubbles.
It can be made clearer by pressing a cylinder of such ice between
wooden boards ; the air-bubbles appear then on the top of the
cylinder as a light foam. If the discs are again broken, placed
in the mould, and pressed into a cylinder, the air may gradually
be more and more eliminated, and the ice be made clearer. No
doubt in glaciers the originally whitish -mass of ne>e is thus
gradually transformed into the clear, transparent ice of the glacier

128 ICE AND GLACIERS.

Lastly, when streaked cylinders of ice formed from pieces of
snow and ice are pressed into discs, they become finely streaked,
for both their clear and their opaque layers are uniformly ex-
tended.

Ice thus striated occurs in numerous glaciers, and is no doubt
caused, as Tyndall maintains, by snow falling between the blocks of
ice ; this mixture of snow and clear ice is again compressed in the
subsequent path of the glacier, and gradually stretched by the
motion of the mass : a process quite analogous to the artificial
one which we have demonstrated.

Thus to the eye of the natural philosopher the glacier, with
its wildly heaped ice-blocks, its desolate, stony, and muddy sur-
face, and its threatening crevasses, has become a majestic stream
whose peaceful and regular flow has no parallel ; which, accord-
ing to fixed and definite laws, narrows, expands, is heaped up,
or, broken and shattered, falls down precipitous heights. If we
trace it beyond its termination we see its waters, uniting to a
copious brook, burst through its icy gate and flow away. Such
a brook, on emerging from the glacier, seems dirty and turbid
enough, for it carries away as powder the stone which the
glacier has ground. We are disenchanted at seeing the won-
drously beautiful and transparent ice converted into such muddy
water. But the water of the glacier streams is as pure and
beautiful as the ice, though its beauty is for the moment concealed
and invisible. We must search for these waters after they have
passed through a lake in which they have deposited this pow-
dered stone. The Lakes of Geneva, of Thun, of Lucerne, of
Constance, the Lago Maggiore, the Lake of Como, and the Lago
di Garda are chiefly fed with glacier waters ; their clearness and
their wonderfully beautiful blue or blue-green colour are the
delight of all travellers.

Yet, leaving aside the beauty of these waters, and considering
only their utility, we shall have still more reason for admiration.
The unsightly mud which the glacier streams wash away
forms a highly fertile soil in the places where it is deposited ;
for its state of mechanical division is extremely fine, and it i&
moreover an utterly unexhausted virgin soil, rich in the mineral

ICE AND GLACIERS. 129

food of plants. The fruitful layers of fine loam which extend
along the whole Rhine plain as far as Belgium, and are
known as Loess, are nothing more than the dust of ancient
glaciers.

Then, again, the irrigation of a district, which is effected by
the snow-fields and glaciers of the mountains, is distinguished
from that of other places by its comparatively greater abundancy,
for the moist air which is driven over the cold mountain peaks
deposits there most of the water it contains in the form of snow.
In the second place, the snow melts most rapidly in summer,
and thus the springs which flow from the snow-fields are
most abundant in that season of the year in which they are
most needed.

Thus we ultimately get to know the wild, dead ice- wastes
from another point of view. From them trickles in thousands
of rills, springs, and brooks the fructifying moisture which
enables the industrious dwellers of the Alps to procure succulent
vegetation and abundance of nourishment from the wild moun-
tain slopes. On the comparatively small surface of the Alpine
chain they produce the mighty streams the Rhine, the Rhone,
the Po, the Adige, the Inn, which for hundreds of miles form
broad, rich river-valleys, extending through Europe to the
German Ocean, the Mediterranean, the Adriatic, and the Black
Sea. Let us call to mind how magnificently Goethe, in ' Maho-
met's Song,' has depicted the course of the rocky spring, from its
origin beyond the clouds to its union with Father Ocean. It
would be presumptuous after him to give such a picture in other
than his own words : —

And along, in triumph rolling,
Names he gives to regions ; cities
Grow amain beneath his feet.

On and ever on he rushes ;
Spire and turret fiery crested
Marble palaces, the creatures
Of his wealth, he leaves behind.

130 ICE AND GLACIERS.

Pine-built houses bears the Atlas
On his giant shoulders. O'er his
Head a thousand pennons rustle,
Floating far upon the breezes,
Tokens of his majesty.

And so beareth he his brothers,
And his treasures, and his children,
To their primal sire expectant,
All his bosom throbbing, heaving
With a wild tumultuous joy.

THEODORE MAKTIN'S Translation.

ICE AND GLACIEKS. 131

ADDITIONS.

THE theory of the revelation of ice has led to scientific discussions
between Faraday and Tyndall on the one hand, and James and Sir W.
Thomson on the other. In the text I have adopted the theory of the
latter, and must now accordingly defend it.

Faraday's experiments show that a very slight pressure, not more
than that produced by the capillarity of the layer of water between
two pieces of ice, is sufficient to freeze them together. James Thom-
son observed that in Faraday's experiments pressure which could
freeze them together was not utterly wanting. I have satisfied my-
self by my own experiments that only veiy slight pressure is necessary.
It must, however, be remembered that the smaller the pressure the
longerwill be the time required to freeze the two pieces, and that then the
junction will be very narrow and very fragile. Both these points are
readily explicable on Thomson's theory. For under a feeble pressure
the difference in temperature between ice and water will be very
small, and the latent heat will only be slowly abstracted from the
layers of water in contact with the pressed parts of the ice, so that a
long time is necessary before they freeze. We must further take into
account that we cannot in general consider that the two surfaces are
quite in contact ; under a feeble pressure which does not appreciably
alter their shape, they will only touch in what are practically three
points. A feeble total pressure on the pieces of ice concentrated on
such narrow surfaces will always produce a tolerably great local
pressure under the influence of which some ice will melt, and the
water thus formed will freeze. But the bridge which joins them will
never be otherwise than narrow.

Under stronger pressure, which' may more completely alter the
shape of the pieces of ice, and fit them against each other, and which
will melt more of the surfaces that are first in contact, there will
be a greater difference between the temperature of the ice and water,
and the bridges will be more rapidly formed, and be of greater
extent.

132 ICE AND GLACIERS.

In order to show the slow action of the small differences of tempera-
ture which here come into play, I made the following experiments.

A glass flask with a drawn-out neck was half filled with water,
which was boiled until all the air in the flask was driven out. The
neck of the flask was then hermetically sealed. When cooled, the
flask was void of air, and the water within it freed from the pressure
of the atmosphere. As the water thus prepared can be cooled con-
siderably below 0° C. before the first ice is formed, while when ice is
in the flask it freezes at 0° C., the flask was in the first* instance
placed in a freezing mixure until the water was changed into ice. It
was afterwards permitted to melt slowly in a place the temperature
of which was + 2° C., until the half of it was liquefied.

The flask thus half filled with water, having a disc of ice
swimming upon it, was placed in a mixture of ice and water, being
quite surrounded by the mixture. After an hour, the disc within
the flask was frozen to the glass. By shaking the flask the disc was
liberated, but it froze again. This occurred as often as the shaking
was repeated.

The flask was permitted to remain for eight days in the mixture^
which was kept throughout at a temperature of 0° C. During this
time a number of very regular and sharply defined ice-crystals were
formed, and augmented very slowly in size. This is perhaps the best
method of obtaining beautifully formed crystals of ice.

While, therefore, the outer ice which had to support the pressure
of the atmosphere slowly melted, the water within the flask, whose
freezing-point, on account of a defect of pressure, was 0'0075° C.
higher, deposited crystals of ice. The heat abstracted from the
water in this operation had, moreover, to pass through the glass of
the flask, which, together with the small difference of temperature,
explains the slowness of the freezing process.

Now as the pressure of one atmosphere on a square millimetre
amounts to about ten grammes, a piece of ice weighing ten grammes,
which lies upon another and touches it in three places, the total
surface of which is a square millimetre, will produce on these surfaces
a pressure of an atmosphere. Ice will therefore be formed more
rapidly in the surrounding water than it was in the flask, where the
side of the glass was interposed between the ice and the water.
Even with a much smaller weight the same result will follow in the
course of an hour. The broader the bridges become, owing to the
freshly formed ice, the greater will be the surfaces over which the
pressure exerted by the upper piece of ice is distributed, and the

ICE AND GLACIERS. 133

feebler it will become; so that with such feebla pressure the bridges
can only slowly increase, and therefore they will be readily broken
when we try to separate the pieces.

It cannot, moreover, be doubted that in Faraday's experiments, in
which two perforated discs of ice were placed in contact on a hori-
zontal glass rod, so that gravity exerted no pressure, capillary attrac-
tion is sufficient to produce a pressure of some grammes between the
plates, and the preceding discussions show that such a pressure, if
adequate time be given, can form bridges between the plates.

If, on the other hand, two of the above-described cylinders of ice
are powerfully pressed together by the hands, they adhere in a few
minutes so firmly, that they can only be detached by the exertion of a
considerable force, for which indeed that of the hands is sometimes
inadequate.

In my experiments I found that the force and rapidity with which
the pieces of ice united were so entirely proportional to the pressure
that I cannot but assign this as the actual and sufficient cause of their
union.

In Faraday's explanation, according to which regelation is due to
a contact action of ice and water, I find a theoretical difficulty. By
the water freezing, a considerable quantity of latent heat must be set
free, and it is not clear what becomes of this.

Finally, if ice in its change into water passes through an inter-
mediate viscous condition, a mixture of ice and water which was kept
for days at a temperature of 0° must ultimately assume this condition
in its entire mass, provided its temperature was uniform throughout ;
this however is 'never the case.

As regards what is called the plasticity of ice, James Thomson
has given an explanation of it in which the formation of cracks in the
interior is not presupposed. No doubt when a mass of ice in different
parts of the interior is exposed to different pressures, a portion of the
more powerfully compressed ice will melt ; and the latent heat neces-
sary for this will be supplied by the ice which is less strongly com-
pressed, and by the water in contact with it. Thus ice would melt
at the compressed places, and water would freeze in those which
are not pressed : ice would thus be gradually transformed and yield
to pressure. It is also clear that, owing to the very small conduc-
tivity for heat which ice possesses, a process of this kind must be ex-
tremely slow, if the compressed and colder layers of ice, as in glaciers,
are at considerable distances from the less compressed ones, and from
the water which furnishes the heat for melting.

134 ICE AND GLACIERS.

To test this hypothesis, I placed in a cylindrical vessel, between-
two discs of ice of three inches in diameter, a smaller cylindrical piece
of an inch in diameter. On the uppermost disc I placed a wooden
disc, and this I loaded with a weight of twenty pounds. The section
of the narrow piece was thus exposed to a pressure of more than an
atmosphere. The whole vessel was packed between pieces of ice, and
left for five days in a room the temperature of which was a few
degrees above the freezing-point. Under these circumstances the ice
in the vessel, which was exposed to the pressure of the weight, should
melt, and it might be expected that the narrow cylinder on which
the pressure was most powerful should have been most melted.
Some water was indeed formed in the vessel, but mostly at the ex-
pense of the larger discs at the top and bottom, which being nearest
the outside mixture of ice and water could acquire heat through
the sides of the vessel. A small welt, too, of ice, was formed round
the surface of contact of the narrower with the lower broad piece,
which showed that the water, which had been formed in conse-
quence of the pressure, had again frozen in places in which the
pressure ceased. Yet under these circumstances there was no ap-
preciable alteration in the shape of the middle piece which was most
compressed.

This experiment shows that although changes in the shape of the
pieces of ice must take place in the course of time in accordance with
J. Thomson's explanation, by which the more strongly compressed
parts melt, and new ice is formed at the places which are freed from
pressure, these changes must be extremely slow when the thickness
of the pieces of ice through which the heat is conducted is at all con-
siderable. Any marked change in shape by melting in a medium the
temperature of which is everywhere 0°, could not occur without
access of external heat, or from the uncompressed ice and water ;
and with the small differences in temperature which here come into
play, and from the badly conducting power of ice, it must be ex-
tremely slow.

That on the other hand, especially in granular ice, the formation
of cracks, and the displacement of the surfaces of those cracks, render
such a change of form possible, is shown by the above-described ex-
periments on pressure; and that in glacier ice changes of form thus
occur, follows from the banded structure, and the granular aggrega-
tion which is manifest on melting, and also from the manner in which
the layers change their position when moved, and so forth. Hence, I
doubt not that Tyndall has discovered the essential and principal

ICE AND GLACIERS. 135

cause of the motion of glaciers, in referring it to the formation of
cracks and to regelation.

I would at the same time observe that a quantity of heat, which
is far from inconsiderable, must be produced by friction in the larger
glaciers. It may be easily shown by calculation that when a mass
of firn moves from the Col du Ge"ant to the source of the Arveyron,
the heat due to the mechanical work would be sufficient to melt a
fourteenth part of the mass. And as the friction must be greatest
in those places that are most compressed, it will at any rate be suf-
ficient to remove just those parts of the ice which offer most resistance
to motion.

I will add, in conclusion, that the above-described granular
structure of ice is beautifully shown in polarised light. If a small
clear piece is pressed in the iron mould, so as to form a disc of about
five inches in thickness, this is sufficiently transparent for investiga-
tion. Viewed in the polarising apparatus, a great number of variously
coloured small bands and rings are seen in the interior ; and by
the arrangement of their colours it is easy to recognise the limits
of the ice-granules, which, heaped on one another in irregular order
of their optical axes, constitute the plate. The appearance is es-
sentially the same when the plate has just been taken out of the
press, and the cracks appear in it as whitish lines, as afterwards when
these crevices have been filled up in consequence of the ice beginning
to melt.

In order to explain the continued coherence of the piece of ice
during its change of form, it is to be observed that in general the
cracks in the granular ice are only superficial, and do not extend
throughout its entire mass. This is directly seen during the pressing
of the ice. The crevices form and extend in different directions, like
cracks produced by a heated wire in a glass tube. Ice possesses a
certain degree of elasticity, as may be seen in a thin flexible plate. A
fissured block of ice of this kind will be able to undergo a displacement
at the two sides which form the crack, even when these continue to
adhere in the unfissured part of the block. If then part of the fissure
at first formed is closed by regelation, the fissure can extend in the
opposite direction without the continuity of the block being at any
time disturbed. It seems to me doubtful, too, whether in compressed
ice and in glacier ice, which apparently consists of interlaced poly-
hedral granules, these granules, before any attempt is made to separate
them, are completely detached from each other, and are not rather
connected by ice-bridges which readily give way ; and whether these

136 ICE AND GLACIERS.

latter do not produce the comparatively firm coherence of the apparent
heap of granules.

The properties of ice here described are interesting from a physical
point of view, for they enable us to follow so closely the transition
from a crystalline body to a granular one ; and they give the causes
of the alteration of its properties better than in any other well-known
example. Most natural substances show no regular crystalline struc-
ture; our theoretical ideas refer almost exclusively to crystallised
and perfectly elastic bodies. It is precisely in this relationship that
the transition from fragile and elastic crystalline ice into plastic
granular ice is so very instructive.

is:

ON THE

INTEKACTION OF NATUEAL FOECES.

A Lecture delivered February 7, 1854, at Konigsberg, in Prussia.

A NEW conquest of very general interest has been recently made
by natural philosophy. In the following pages I will endeavour
to give an idea of the nature of this conquest. It has reference
to a new and universal natural law, which rules the action
of natural forces in their mutual relations towards each other,
and is as influential on our theoretic views of natural processes
as it is important in their technical applications.

Among the practical arts which owe their progress to the
development of the natural sciences, from the conclusion of the
middle ages downwards, practical mechanics, aided by the mathe-
matical science which bears the same name, was one of the most
prominent. The character of the art was, at the time referred
to, naturally very different from its present one. Surprised and
stimulated by its own success, it thought no problem beyond its
power, and immediately attacked some of the most difficult and
complicated. Thus it was attempted to build automaton figures
which should perform the functions of men and animals. The
marvel of the last century was Vaucanson's duck, which fed
and digested its food ; the flute-player of the same artist, which
moved all its fingers correctly ; the writing-boy of the elder, and
the pianoforte-player of the younger, Droz ; which latter, when
performing, followed its hands with its eyes, and at the con-

138 ON THE INTERACTION OF NATURAL FORCES.

elusion of the piece bowed courteously to the audience. That
men like those mentioned, whose talent might bear comparison
with the most inventive heads of the present age, should spend
so much time in the construction of these figures, which we
at present regard as the merest trifles, would be incompre-
hensible if they had not hoped in solemn earnest to solve a
great problem. The writing-boy of the elder Droz was publicly
exhibited in Germany some years ago. Its wheelwork is so
complicated that no ordinary head would be sufficient to de-
cipher its manner of action. When, however, we are informed
that this boy and its constructor, being suspected of the black
art, lay for a time in the Spanish Inquisition, and with diffi-
culty obtained their freedom, we may infer that in those days
even such a toy appeared great enough to excite doubts as to its
natural origin. And though these artists may not have hoped
to breathe into the creature of their ingenuity a soul gifted with
moral completeness, still there were many who would be willing
to dispense with the moral qualities of their servants, if at the
same time their immoral qualities could also be got rid of; and
to accept, instead of the mutability of flesh and bones, services
which should combine the regularity of a machine with the
durability of brass and steel.

The object, therefore, which the inventive genius of the
past century placed before it with the fullest earnestness, and
not as a piece of amusement merely, was boldly chosen, and
was followed up with an expenditure of sagacity which has
contributed not a little to enrich the mechanical experience
which a later time knew how to take advantage of. We no
longer seek to build machines which shall fulfil the thousand
services required of one man, but desire, on the contrary, that
a machine shall perform one service, and shall occupy in doing
it the place of a thousand men.

From these efforts to imitate living creatures, another idea,
also by a misunderstanding, seems to have developed itself, and
which, as it were, formed the new philosopher's stone of the
seventeenth and eighteenth centuries. It was now the en-
deavour to construct a perpetual motion. Under this term was

ON THE INTERACTION OF NATURAL FORCES. 139

understood a machine which, without being wound up, without
consuming in the working of it falling water, wind, or any
other natural force, should still continue in motion, the motive
power being perpetually supplied by the machine itself. Beasts
and human beings seemed to correspond to the idea of such an
apparatus, for they moved themselves energetically and in-
cessantly as long as they lived, and were never wound up ;
nobody set them in motion. A connexion between tho supply
of nourishment and the development of force did not make
itself apparent. The nourishment seemed only necessary to
grease, as it were, the wheelwork of the animal machine, to
replace what was used up, and to renew the old. The develop-
ment of force out of itself seemed to be the essential peculiarity,
the real quintessence of organic life. If, therefore, men were to
be constructed, a perpetual motion must first be found.

Another hope also seemed to take up incidentally the second
place, which in our wiser age would certainly have claimed the
first rank in the thoughts of men. The perpetual motion was
to produce work inexhaustibly without corresponding consump-
tion, that is to say, out of nothing. Work, however, is money.
Here, therefore, the great practical problem which the cunning
heads of all centuries have followed in the most diverse ways,
namely, to fabricate money out of nothing, invited solution.
The similarity with the philosopher's stone sought by the
ancient chemists was complete. That also was thought to
contain the quintessence of organic life, and to be capable of
producing gold.

The spur* which drove men to inquiry was sharp, and the
talent of some of the seekers must not be estimated as small.
The nature of the problem was quite calculated to entice
poring brains, to lead them round a circle for years, deceiving
ever with new expectations which vanished upon nearer approach,
and finally reducing these dupes of hope to open insanity. The
phantom could not be grasped. It would be impossible to give
a history of these efforts, as the clearer heads, among whom the
elder Droz must be ranked, convinced themselves of the futility
of their experiments, and were naturally not inclined to speak

140 ON THE INTERACTION OF NATURAL FORCES.

much about them. Bewildered intellects, however, proclaimed
often enough that they had discovered the grand secret; and as
the incorrectness of their proceedings was always speedily mani-
fest, the matter fell into bad repute, and the opinion strength-
ened itself more and more that the problem was not capable of
solution; one difficulty after another was brought under the
dominion of mathematical mechanics, and finally a point was
reached where it could be proved that at least by the use of
pure mechanical forces no perpetual motion could be generated.

We have here arrived at the idea of the driving force or
power of a machine, and shall have much to do with it in future.
I must therefore give an explanation of it. The idea of work
is evidently transferred to machines by comparing their per-
formances with those of men and animals, to replace which
they were applied. We still reckon the work of steam-engines
according to horse-power. The value of manual labour is de-
termined partly by the force which is expended in it (a strong
labourer is valued more highly than a weak one), partly,
however, by the skill which is brought into action. Skilled
workmen are not to be had in any quantity at a moment's
notice ; they must have both talent and instruction, their edu-
•cation requires both time and trouble. A machine, on the
contrary, which executes work skilfully, can always be multi-
plied to any extent ; hence its skill has not the high value of
human skill in domains where the latter cannot be supplied by
machines. Thus the idea of the quantity of work in the case
of machines has been limited to the consideration of the expen-
diture of force ; this was the more important, as indeed most
machines are constructed for the express purpose of exceeding,
by the magnitude of their effects, the powers of men and animals.
Hence, in a mechanical sense, the idea of work has become
identical with that of the expenditure of force, and in this way
I will apply it in the following pages.

How, then, can we measure this expenditure, and compare
it in the case of different machines 1

I must here conduct you a portion of the way — as short a
portion as possible — over the uninviting field of mathematico-

ON THE INTERACTION OF NATURAL FORCES. 141

mechanical ideas, in order to bring you to a point of view from
which a more rewarding prospect will open. And though the
example which I will here choose, namely, that of a water-mill
with iron hammer, appears to be tolerably romantic, still, alas!
I must leave the dark forest valley, the foaming brook, the
spark-emitting anvil, and the black Cyclops wholly out of sight,
and beg a moment's attention for the less poetic side of the
question, namely, the- machinery. This is driven by a water-
wheel, which in its turn is set in motion by the falling water.
The axle of the water-wheel has at certain places small projec-
tions, thumbs, which, during the rotation, lift the heavy hammer
and permit it to fall again. The falling hammer belabours the
mass of metal which is introduced beneath it. The work
therefore done by the machine consists, in this case, in the lift-
ing of the hammer, to do which the gravity of the latter must
be overcome. The expenditure of force will, in the first place,
other circumstances being equal, be proportional to the weight
of the hammer; it will, for example, be double when the weight
of the hammer is doubled. But the action of the hammer
depends not upon its weight alone, but also upon the height
from which it faHs. If it falls through two feet, it will produce
a greater effect than if it falls through only one foot. It is,
however, clear that if the machine, with a certain expenditure
of force, lifts the hammer a foot in height, the same amount of
force must be expended to raise it a second foot in height. The
work is therefore not only doubled when the weight of the
hammer is increased twofold, but also when the space through,
which it falls is doubled. From this it is easy to see that the
work must be measured by the product of the weight into the
space through which it ascends. And in this way, indeed, we
measure in mechanics. The unit of work is a foot-pound, that
is, a pound weight raised to the height of one foot.

While the work in this case consists in the raising of the
heavy hammer-head, the driving force which sets the latter in
motion is generated by failing water. It is not necessary that
the water should fall vertically, it can also flow in a moderately
inclined bed ; but it must always, where it has water-mills to-

142 ON THE INTERACTION OF NATURAL FORCES.

set in motion, move from a higher to a lower position. Ex-
periment and theory concur in teaching that when a hammer
of a hundredweight is to be raised one foot, to accomplish this
at least a hundredweight of water must fall through the space
•of one foot ; or, what is equivalent to this, two hundredweight
must fall half a foot, or four hundredweight a quarter of a foot,
•&c. In short, if we multiply the weight of the falling water
by the height through which it falls, and regard, as before, the
product as the measure of the work, then the work performed
by the machine in raising the hammer can, in the most favour-
able case, be only equal to the number of foot-pounds of water
which have fallen in the same time. In practice, indeed, this
ratio is by no means attained : a great portion of the work of
the falling water escapes unused, inasmuch as part of the force
is willingly sacrificed for the sake of obtaining greater speed.

I will further remark that this relation remains unchanged
whether the hammer is driven immediately by the axle of the
wheel, or whether — by the intervention of wheel work, endless
screws, pulleys, ropes — the motion is transferred to the hammer.
We may, indeed, by such arrangements succeed in raising a
hammer of ten hundredweight, when by the first simple arrange-
ment the elevation of a hammer of one hundredweight might
alone be possible ; but either this heavier hammer is raised to
only one tenth of the height, or tenfold the time is required to
raise it to the same height ; so that, however we may alter, by
the interposition of machinery, the intensity of the acting force,
:still in a certain time, during which the mill-stream furnishes
us with a definite quantity of water, a certain definite quantity
of work, and no more, can be performed.

Our machinery, therefore, has in the first place done nothing
more than make use of the gravity of the falling water in order
to overpower the gravity of the hammer, and to raise the latter.
When it has lifted the hammer to the necessary height, it again
liberates it, and the hammer falls upon the metal mass which is
pushed beneath it. But why does the falling hammer here exer-
cise a greater force than when it is permitted simply to press with
its own weight on the mass of metal ? Why is its power greater

ON THE INTERACTION OF NATURAL FORCES. 143

as the height from which it falls is increased, and the greater
therefore the velocity of its fall? We find, in fact, that the
work pel-formed by the hammer is determined by its velocity.
In other cases, also, the velocity of moving masses is a means
of producing great effects. I only remind you of the destruc-
tive effects of musket-bullets, which in a state of rest are the
most harmless things in the world. I remind you of the wind-
mill, which derives its force from the moving air. It may
appear surprising that motion, which we are accustomed to
regard as a non-essential and transitory endowment of bodies,
can produce such great effects. But the fact is, that motion
appears to us, under ordinary circumstances, transitory, because
the movement of all terrestrial bodies is resisted perpetually
by other forces, friction, resistance of the air, <fec., so that the
motion is incessantly weakened and finally arrested. A body,
however, which is opposed by no resisting force, when once set
in motion moves onward eternally with undiminished velocity.
Thus we know that the planetary bodies have moved without
change through space for thousands of years. Only by resist-
ing forces can motion be diminished or destroyed. A moving
body, such as the hammer or the musket-ball, when it strikes
against another, presses the latter together, or penetrates it,
until the sum of the resisting forces presented by the body
struck to pressure, or to the separation of its particles, is suffi-
ciently great to destroy the motion of the hammer or of the
bullet. The motion of a mass regarded as taking the place of
working force is called the living force (vis viva) of the mass.
The word ' living ' has of course here no reference whatever to
living beings, but is intended to represent solely the force of the
motion as distinguished from the state of unchanged rest — from
the gravity of a motionless body, for example, which produces
an incessant pressure against the surface which supports it, but
does not produce any motion.

In the case before us, therefore, we had first power in the
form of a falling mass of water, then in the form of a lifted
hammer, and thirdly in the form of the living force of the
falling hammer. We should transform the third form into the

144 ON THE INTERACTION OF NATURAL FORCES.

second, if we, for example, permitted the hammer to fall upon
a highly elastic steel beam strong enough to resist the shock.
The hammer would rebound, and in the most favourable case-
would reach a height equal to that from which it fell, but would
never rise higher. In this way its mass would ascend; and at
the moment when its highest point has been attained it would
represent the same number of raised foot-pounds as before it
fell, never a greater number ; that is to say, living force can
generate the same amount of work as that expended in its pro-
duction. It is therefore equivalent to this quantity of work.

Our clocks are driven by means of sinking weights, and our
watches by means of the tension of springs. A weight which
lies on the ground, an elastic spring which is without tension,
can produce no effects : to obtain such we must first raise the
weight or impart tension to the spring, which is accomplished
when we wind up our clocks and watches. The man who winds
the clock or watch communicates to the weight or to the spring
a certain amount of power, and exactly so much as is thus com-
municated is gradually given out again during the following
twenty-four hours, the original force being thus slowly consumed
to overcome the friction of the wheels and the resistance which
the pendulum encounters from the air. The wheel work of the
clock therefore develops no working force which was not pre-
viously communicated to it, but simply distributes the force
given to it uniformly over a longer time.

Into the chamber of an air-gun we squeeze, by means of a
condensing air-pump, a great quantity of air. When we after-
wards open the cock of the gun and admit the compressed air
into the barrel, the ball is driven out of the latter with a force
similar to that exerted by ignited powder. Now we may de-
termine the work consumed in the pumping-in of the air, and
the living force which, upon firing, is communicated to the ball,
but we shall never find the latter greater than the former.
The compressed air has generated no working force, but simply
gives to the bullet that which has been previously communicated
to it. And while we have pumped for perhaps a quarter of an
hour to charge the gun, the force is expended in a few seconds

ON THE INTERACTION OF NATURAL FORCES. 145

when the bullet is discharged ; but because the action is com-
pressed into so short a time, a much greater velocity is imparted
to the ball than would be possible to communicate to it by the
unaided effort of the arm in throwing it.

From these examples you observe, and the mathematical
theory has corroborated this for all purely mechanical, that is
to say, for moving forces, that all our machinery and apparatus
generate no force, but simply yield up the power communicated
to them by natural forces, — falling water, moving wind, or by
the muscles of men and animals. After this law had been
established by the great mathematicians of the last century, a
perpetual motion, which should make use solely of pure me-
chanical forces, such as gravity, elasticity, pressure of liquids
and gases, could only be sought after by bewildered and ill-in-
structed people. But there are still other natural forces which
are not reckoned among the purely moving forces, — heat,
electricity, magnetism, light, chemical forces, all of which never-
theless stand in manifold relation to mechanical processes.
There is hardly a natural process to be found which is not
accompanied by mechanical Actions, or from which mechanical
work may not be derived. Here the question of a perpetual
motion remained open ; the decision of this question marks the
progress of modern physics, regarding which I promised to
address you.

In the case of the air-gun, the work to be accomplished in
the propulsion of the ball was given by the arm of the man
who pumped in the air. In ordinary firearms, the condensed
mass of air which propels the bullet is obtained in a totally
• different manner, namely, by the combustion of the powder.
Gunpowder is transformed by combustion for the most part
into gaseous products, which endeavour to occupy a much
greater space than that previously taken up by the volume of
the powder. Thus you see that, by the use of gunpowder, the
work which the human arm must accomplish in the case of the
air-gun is spared.

In the mightiest of our machines, the steam-engine, it is a
strongly compressed aeriform body, water vapour, which, by its

146 ON THE INTERACTION OF NATURAL FORCES.

effort to expand, sets the machine in motion. Here also we do
not condense the steam by means of an external mechanical
force, but by communicating heat to a mass of water in a closed
boiler, we change this water into steam, which, in consequence
of the limits of the space, is developed under strong pressure.
In this case, therefore, it is the heat communicated which gene-
rates the mechanical force. The heat thus necessary for the
machine we might obtain in many ways : the ordinary method
is to procure it from the combustion of coal.

Combustion is a chemical process. A particular constituent
of our atmosphere, oxygen, possesses a strong force of attraction,
or, as is said in chemistry, a strong affinity for the constituents
of the combustible body, which affinity, however, in most cases
can only exert itself at high temperatures. As soon as a portion
of the combustible body, for example the coal, is sufficiently
heated, the carbon unites itself with great violence to the
oxygen of the atmosphere and forms a peculiar gas, carbonic
acid, the same that we see foaming from beer and champagne.
By this combination light and heat are generated; heat is
generally developed by any combination of two bodies of strong
affinity for each other ; and when the heat is intense enough,
light appears. Hence in the steam-engine it is chemical pro-
cesses and chemical forces which produce the astonishing work
of these machines. In like manner the combustion of gun-
powder is a chemical process, which in the barrel of the gun
communicates living force to the bullet.

While now the steam-engine developes for us mechanical
work out of heat, we can conversely generate heat by mechanical
forces. Each impact, each act of friction does it. A skilful
blacksmith can render an iron wedge red-hot by hammering.
The axles of our carriages must be protected by careful greasing
from ignition through friction. Even lately this property has
been applied on a large scale. In some factories, where a sur-
plus of water power is at hand, this surplus is applied to cause
a strong iron plate to rotate rapidly upon another, so that they
become strongly heated by the friction. The heat so obtained
warms the room, and thus a stove without fuel is provided.

ON THE INTERACTION OF NATURAL FORCES. 147

Now could not the heat generated by the plates be applied to a
small steam-engine, which in its turn should be able to keep
the rubbing plates in motion 1 The perpetual motion would
thus be at length found. This question might be asked, and
could not be decided by the older mathematico-mechanical
investigations. I will remark beforehand, that the general
law which I will lay before you answers the question in the
negative.

By a similar plan, however, a speculative American set
some time ago the industrial world of Europe in excitement.
The magneto-electric machines often made use of in the case of
rheumatic disorders are well known to the public. By impart-
ing a swift rotation to the magnet of such a machine we obtain
powerful currents of electricity. If those be conducted through
water, the latter will be resolved into its two components,
oxygen and hydrogen. By the combustion of hydrogen, water
is again generated. If this combustion takes place, not in
atmospheric air, of which oxygen only constitutes a fifth part,
but in pure oxygen, and if a bit of chalk be placed in the flame,
the chalk will be raised to its white heat, and give us the sun-
like Drummond's light. At the same time the flame developes a
considerable quantity of heat. Our American proposed to utilise
in this way the gases obtained from electrolytic decomposition,
and asserted, that by the combustion a sufficient amount of
heat was generated to keep a small steam-engine in action,
which again drove his magneto-electric machine, decomposed the
water, and thus continually prepared its own fuel. This would
certainly have been the most splendid of all discoveries; a
perpetual motion which, besides the force that kept it going,
generated light like the sun, and warmed all around it. The
matter was by no means badly thought out. Each practical
step in the affair was known to be possible ; but those who at
that time were acquainted with the physical investigations
which bear upon this subject, could have affirmed, on first
hearing the report, that the matter was to be numbered among
the numerous stories of the fable-rich America ; and indeed a
fable it remained.

148 ON THE INTERACTION OF NATURAL FORCES.

It is not necessary to multiply examples further. You will
infer from those given in what immediate connection heat,
electricity, magnetism, light, and chemical affinity, stand with
mechanical forces.

Starting from each of these different manifestations of
natural forces, we can set every other in motion, for the most
part not in one way merely, but in many ways. It is here as
with the weaver's web —

Where a step stirs a thousand threads,

The shuttles shoot from side to side,

The fibres flow unseen,

And one shock strikes a thousand combinations.

Now it is clear that if by any means we could succeed, as
the above American professed to have done, by mechanical
forces, in exciting chemical, electrical, or other natural pro-
cesses, which, by any circuit whatever, and without altering
permanently the active masses in the machine, could produce
mechanical force in greater quantity than that at first applied,
a portion of the work thus gained might be made use of to
keep the machine in motion, while the rest of the work might
be applied to any other purpose whatever. The problem was
to find, in the complicated net of reciprocal actions, a track
through chemical, electrical, magnetical, and thermic processes,
back to mechanical actions, which might be followed with a
final gain of mechanical work : thus would the perpetual motion
be found.

But, warned by the futility of former experiments, the public
had become wiser. On the whole, people did not seek much
after combinations which promised to furnish a perpetual
motion, but the question was inverted. It was no more asked,
How can I make use of the known and unknown relations of
natural forces so as to construct a perpetual motion ? but it was
asked, If a perpetual motion be impossible, what are the rela-
tions which must subsist between natural forces ? Everything
was gained by this inversion of the question. The relations of
natural forces, rendered necessary by the above assumption,

ON THE INTERACTION OF NATURAL FORCES. 149

might be easily and completely stated. It was found that all
known relations of forces harmonise with the consequences of
that assumption, and a series of unknown relations were dis-
covered at the same time, the correctness of which remained to
be proved. If a single one of them could be proved false, then
a perpetual motion would be possible.

The first who endeavoured to travel this way was a French-
man named Carnot, in the year 1824. In spite of a too limited
conception of his subject, and an incorrect view as to the nature
of heat which led him to some erroneous conclusions, his ex-
periment was not quite unsuccessful. He discovered a law which
now bears his name, and to which I will return further on.

His labours remained for a long time without notice, and it
was not till eighteen years afterwards, that is in 1842, that
different investigators in different countries, and independent of
Carnot, laid hold of the same thought. The first who saw
truly the general law here referred to, and expressed it correctly,
was a German physician, J. R. Mayer of Heilbronn, in the year
1842. A little later, in 1843, a Dane named Colding pre-
sented a memoir to the Academy of Copenhagen, in which the
same law found utterance, and some experiments were described
for its further corroboration. In England, Joule began about
the same time to make experiments having reference to the same
subject. We often find, in the case of questions to the solution
of which the development of science points, that several heads,
quite independent of each other, generate exactly the same series
of reflections.

I myself, without being acquainted with either Mayer or
Colding, and having first made the acquaintance of Joule's
experiments at the end of my investigation, followed the same
path. I endeavoured to ascertain all the relations between the
different natural processes, which followed from our regarding
them from the above point of view. My inquiry was made
public in 1847, in a small pamphlet bearing the title, ' On the
Conservation of Force.'1

1 There is a translation of this important Essay in the Scientific Memoirs,
New Series, p. 114.— J. T.

150 ON THE INTERACTION OF NATURAL FORCES.

Since that time the interest of the scientific public for this
subject has gradually augmented, particularly in England, of
which I had an opportunity of convincing myself during a visit
last summer. A great number of the essential consequences of
the above manner of viewing the subject, the proof of which
was wanting when the first theoretic notions were published,
have since been confirmed by experiment, particularly by those
of Joule ; and during the last year the most eminent physicist,
of France, Regnault, has adopted the new mode of regarding the
question, and by fresh investigations on the specific heat of gases
has contributed much to its support. For some important con-
sequences the experimental proof is still wanting, but the number
of confirmations is so predominant, that I have not deemed it
premature to bring the subject before even a non-scientific
audience.

How the question has been decided you may already infer
from what has been stated. In the series of natural processes
there is no circuit to be found, by which mechanical force can
be gained without a corresponding consumption. The per-
petual motion remains impossible. Our reflections, however,
gain thereby a higher interest.

We have thus far regarded the development of force by natural
processes, only in its relation to its usefulness to man, as me-
chanical force. You now see that we have arrived at a general
law, which holds good wholly independent of the application
which man makes of natural forces ; we must therefore make the
expression of our law correspond to this more general signifi-
cance. It is in the first place clear, that the work which, by
any natural process whatever, is performed under favourable con-
ditions by a machine, and which may be measured in the way
already indicated, may be used as a measure of force common to
all. Further, the important question arises, If the quantity of
force cannot be augmented except by corresponding consump-
tion, can it be diminished or lost ? For the purposes of our
machines it certainly can, if we neglect the opportunity to
convert natural processes to use, but as investigation haa
proved, not for nature as a whole.

ON THE INTERACTION OF NATURAL FORCES. 151

In the collision and friction of bodies against each other,
the mechanics of former years assumed simply that living force
was lost. But I have already stated that each collision and each
act of friction generates heat ; and, moreover, Joule has estab-
lished by experiment the important law, that for every foot-
pound of force which is lost a definite quantity of heat is always
generated, and that when work is performed by the consump-
tion of heat, for each foot-pound thus gained a definite quantity
of heat disappears. The quantity of heat necessary to raise the
temperature of a pound of water a degree of the Centigrade
thermometer, corresponds to a mechanical force by which a
pound weight would be raised to the height of 1,350 feet : we
name this quantity the mechanical equivalent of heat. I may
mention here that these facts conduct of necessity to the conclu-
sion, that heat is not, as was formerly imagined, a fine impon-
derable substance, but that, like light, it is a peculiar shivering
motion of the ultimate particles of bodies. In collision and
friction, according to this manner of viewing the subject, the
motion of the mass of a body which is apparently lost is converted
into a motion of the ultimate particles of the body ; and con-
versely, when mechanical force is generated by heat, the motion
of the ultimate particles is converted into a motion of the mass.

Chemical combinations generate heat, and the quantity of
this heat is totally independent of the time and steps through
which the combination has been effected, provided that other
actions are not at the same time brought into play. If, however,
mechanical work is at the same time accomplished, as in the
case of the steam-engine, we obtain as much less heat as is
equivalent to this work. The quantity of work produced by
chemical force is in general very great. A pound of the purest
coal gives, when burnt, sufficient heat to raise the temperature
of 8,086 pounds of water one degree of the Centigrade ther-
mometer ; from this we can calculate that the magnitude of the
chemical force of attraction between the particles of a pound
of coal and the quantity of oxygen that corresponds to it, is
capable of lifting a weight of 100 pounds to a height of twenty
miles. Unfortunately , in our steam-engines we have hitherto

152 ON THE mTERACTION OF NATUBAL FORCES.

been able to gain only the smallest portion of this work, the
greater part is lost in the shape of heat. The best expansive
engines give back as mechanical work only 18 per cent, of the
heat generated by the fuel.

From a similar investigation of all the other known physical
and chemical processes, we arrive at the conclusion that Nature
as a whole possesses a store of force which cannot in any way be
either increased or diminished, and that therefore the quantity
of force in Nature is just as eternal and unalterable as the
quantity of matter. Expressed in this form, I have named the
general law ' The Principle of the Conservation of Force.'

"We cannot create mechanical force, but we may help our-
selves from the general storehouse of Nature. The brook and
the wind, which drive our mills, the forest and the coal-bed,
which supply our steam-engines and warm our rooms, are to us
the bearers of a small portion of the great natural supply which
we draw upon for our purposes, and the actions of which we
can apply as we think fit. The possessor of a mill claims the
gravity of the descending rivulet, or the living force of the
moving wind, as his possession. These portions of the store of
Nature are what give his property its chief value.

Further, from the fact that no portion of force can be abso-
lutely lost, it does not follow that a portion may not be in-
applicable to human purposes. In this respect the inferences
drawn by William Thomson from the law of Carnot are of im-
portance. This law, which was discovered by Carnot during his
endeavours to ascertain the relations between heat and me-
chanical force, which, however, by no means belongs to the
necessary consequences of the conservation of force, and which
Clausius was the first to modify in such a manner that it no
longer contradicted the above general law, expresses a certain
relation between the compressibility, the capacity for heat, and
the expansion by heat of all bodies. It is not yet completely
proved in all directions, but some remarkable deductions having
been drawn from it, and afterwards proved to be facts by ex-
periment, it has attained thereby the highest degree of pro-
bability. Besides the mathematical form in which the law was

ON THE INTERACTION OF NATURAL FORCES. 153

first expressed by Carnot, we can give it the following move
general expression : — ' Only when heat passes from a warmer to
a colder body, and even then only partially, can it be converted
into mechanical work.'

The heat of a body which we cannot cool further, cannot be
changed into another form of force— into electric or chemical
force for example. Thus in our steam-engines we convert a
portion of the heat of the glowing coal into work, by permitting it
to pass to the less warm water of the boiler. If, however, all the
bodies in Nature had the same temperature, it would be impos-
sible to convert any portion of their heat into mechanical work.
According to this we can divide the total force store of the
universe into two parts, one of which is heat, and must continue
to be such ; the other, to which a portion of the heat of the
warmer bodies, and the total supply of chemical, mechanical,
electrical, and magnetical forces belong, is capable of the most
varied changes of form, and constitutes the whole wealth of
change which takes place in Nature.

But the heat of the warmer bodies strives perpetually to pass
to bodies less warm by radiation and conduction, and thus to
establish an equilibrium of temperature. At each motion of a
terrestrial body a portion of mechanical force passes by friction
or collision into heat, of which only a part can be converted
back again into mechanical force. This is also generally the case
in every electrical and chemical process. From this it follows
that the first portion of the store of force, the unchangeable heat,
is augmented by every natural process, while the second portion,
mechanical, electrical, and chemical force, must be diminished ;
so that if the universe be delivered over to the undisturbed
action of its physical processes, all force will finally pass into
the form of heat, and all heat come into a state of equilibrium.
Then all possibility of a further change would be at an end, and
the complete cessation of all natural processes must set in. The
life of men, animals, and plants could not of course continue if
the sun had lost his high temperature, and with it his light, — if
all the components of the earth's surface had closed those com-
binations which their affinities demand. In short, the universe

154 ON THE INTERACTION OF NATURAL FORCES.

from that time forward would be condemned to a state of
eternal rest.

These consequences of the law of Carnot are, of course, only
valid provided that the law, when sufficiently tested, proves to
be universally correct. In the meantime there is little prospect
of the law being proved incorrect. At all events, we must
admire the sagacity of Thomson, who, in the letters of a long-
known little mathematical formula which only speaks of the
heat, volume, and pressure of bodies, was able to discern con-
sequences which threatened the universe, though certainly after
an infinite period of time, with eternal death.

I have already given you notice that our path lay through
a thorny and unrefreshing field of mathematico-mechanical
developments. We have now left this portion of our road
behind us. The general principle which I have sought to lay
before you has conducted us to a point from which our view is a
wide one; and aided by this principle, we can now at pleasure
regard this or the other side of the surrounding world according
as our interest in the matter leads us. A glance into the narrow
laboratory of the physicist, with its small appliances and com-
plicated abstractions, will not be so attractive as a glance at the
wide heaven above us, the clouds, the rivers, the woods, and the
living beings around us. While regarding the laws which have
been deduced from the physical processes of terrestrial bodies as
applicable also to the heavenly bodies, let me remind you that
the same force which, acting at the earth's surface, we call
gravity (Schwere), acts as gravitation in the celestial spaces, and
also manifests its power in the motion of the immeasurably
distant double stars, which are governed by exactly the same
laws as those subsisting between the earth and moon; that
therefore the light and heat of terrestrial bodies do not in any
way differ essentially from those of the sun or of the most dis-
tant fixed star ; that the meteoric stones which sometimes fall
from external space upon the earth are composed of exactly the
same simple chemical substances as those with which we are
acquainted. We need, therefore, feel no scruple in granting that
general laws to which all terrestrial natural processes are subject

ON THE INTERACTION OF NATURAL FORCES. 155

are also valid for other bodies than the earth. We will, there-
fore, make use of our law to glance over the household of the
universe with respect to the store of force, capable of action,
which it possesses.

A number of singular peculiarities in the structure of our
planetary system indicate that it was once a connected mass,
with a uniform motion of rotation. Without such an assump-
tion it is impossible to explain why all the planets move in the
same direction round the sun, why they all rotate in the same
direction round their axes, why the planes of their orbits and
those of their satellites and rings all nearly coincide, why all
their orbits differ but little from circles, and much besides.
From these remaining indications of a former state astronomers
have shaped an hypothesis regarding the formation of our
planetary system, which, although from the nature of the case
it must ever remain an hypothesis, still in its special traits is so
well supported by analogy, that it certainly deserves our atten-
tion ; and the more so, as this notion in our own home, and
within the walls of this town,1 first found utterance. It was
Kant who, feeling great interest in the physical description of
the earth and the planetary system, undertook the labour of
studying the works of Newton ; and, as an evidence of the depth
to which he had penetrated into the fundamental ideas of
Newton, seized the notion that the same attractive force of all
ponderable matter which now supports the motion of the planets
must also aforetime have been able to form from matter loosely
scattered in space the planetary system. Afterwards, and inde-
pendent of Kant, Laplace, the great author of the ' Mecanique
celeste,' laid hold of the same thought, and introduced it among
astronomers.

The commencement of our planetary system, including the
sun, must, according to this, be regarded as an immense nebulous
mass which filled the portion of space now occupied by our
system far beyond the limits of Neptune, our most distant
planet. Even now we discern in distant regions of the firma-
ment nebulous patches the light of which, as spectrum analysis
1 Koriigsberg.

156 ON THE INTERACTION OF NATURAL FORCES.

teaches, is the light of ignited gases ; and in their spectra we see
more especially those bright lines which are produced by ignited
hydrogen and by ignited nitrogen. "Within our system, also,
comets, the crowds of shooting stars, and the zodiacal light ex-
hibit distinct traces of matter dispersed like powder, which
moves, however, according to the law of gravitation, and is, at
all events, partially retarded by the larger bodies and incor-
porated in them. The latter undoubtedly happens with the
shooting stars and meteoric stones which come within the range
of our atmosphere.

If we calculate the density of the mass of our planetary
system, according to the above assumption, for the time when
it was a nebulous sphere, which reached to the path of the
outermost planet, we should find that it would require several
millions of cubic miles of such matter to weigh a single grain.

The general attractive force of all matter must, however,
impel these masses to approach each other, and to condense, so
that the nebulous sphere became incessantly smaller, by which,
according to mechanical laws, a motion of rotation originally
slow, and the existence of which must be assumed, would
gradually become quicker and quicker. By the centrifugal
force, which must act most energetically in the neighbourhood
of the equator of the nebulous sphere, masses could from time
to time be torn away, which afterwards would continue their
courses separate from the main mass, forming themselves into
single planets, or, similar to the great original sphere, into
planets with satellites and rings, until finally the principal mass
condensed itself into the sun. With regard to the origin of
heat and light this theory originally gave no information.

When the nebulous chaos first separated itself from other
fixed star masses it must not only have contained all kinds of
matter which was to constitute the future planetary system,
but also, in accordance with our new law, the whole store of
force which at a future time ought to unfold therein its wealth
of actions. Indeed, in this respect an immense dower was
bestowed in the shape of the general attraction of all the particles
for each other. This force, which on the earth exerts itself as

ON THE INTERACTION OF NATURAL FORCES. 157

gravity, acts in the heavenly spaces as gravitation. As terrestrial
gravity when it draws a weight downwards performs work and
generates vis viva, so also the heavenly bodies do the same when
they draw two portions of matter from distant regions of- space
towards each other.

The chemical forces must have been also present, ready to
act ; but as these forces can only come into operation by the
most intimate contact of the different masses, condensation
must have taken place before the play of chemical forces began.

Whether a still further supply of force in the shape of heat
was present at the commencement we do not know. At all
events, by aid of the law of the equivalence of heat and work,
we find in the mechanical forces existing at the time to which
we refer such a rich source of heat and light, that there is no
necessity whatever to take refuge in the idea of a store of these
forces originally existing. When, through condensation of the
masses, their particles came into collision and clung to each
other, the vis viva of their motion would be thereby annihilated,
and must reappear as heat. Already in old theories it has been
calculated that cosmical masses must generate heat by their col-
lision, but it was far from anybody's thought to make even a
guess at the amount of heat to be generated in this way. At
present we can give definite numerical values with certainty.

Let us make this addition to our assumption — that, at the
commencement, the density of the nebulous matter was a van-
ishing quantity as compared with the present density of the sun
and planets : we can then calculate how much work has been
performed by the condensation ; we can further calculate how
much of this work still exists in the form of mechanical force,
as attraction of the planets towards the sun, and as vis viva of
their motion, and find by this how much of the force has been
converted into heat.

The result of this calculation1 is, that only about the 454th

part of the original mechanical force remains as such, and that

the remainder, converted into heat, would be sufficient to raise

a mass of water equal to the sun and planets taken together,

1 See note on page 172.

158 ON THE INTERACTION OF NATURAL FORCES.

not less than twenty-eight millions of degrees of the Centigrade
scale. For the sake of comparison, I will mention that the
highest temperature which we can produce by the oxyhydrogen
blowpipe, which is sufficient to fuse and vaporise even platinum,
and which but few bodies can endure without melting, is esti-
mated at about 2,000 degrees. Of the action of a temperature
of twenty-eight millions of such degrees we can form no notion.
If the mass of our entire system were pure coal, by the com-
bustion of the whole of it only the 3,500th part of the above
quantity would be generated. This is also clear, that such a
great development of heat must have presented the greatest
obstacle to the speedy union of the masses ; that the greater
part of the heat must have been diffused by radiation into
space, before the masses could form bodies possessing the present
density of the sun and planets, and that these bodies must once
have been in a state of fiery fluidity. This notion is corroborated
by the geological phenomena of our planet ; and with regard
to the other planetary bodies, the flattened form of the sphere,
which is the form of equilibrium of a fluid mass, is indicative
of a former state of fluidity. If I thus permit an immense
quantity of heat to disappear without compensation from our
system, the principle of the conservation of force is not thereby
invaded. Certainly for our planet it is lost, but not for the
universe. It has proceeded outwards, and daily proceeds out-
wards into infinite space ; and we know not whether the medium
which transmits the undulations of light and heat possesses an
end where the rays must return, or whether they eternally
pursue their way through infinitude.

The store of force at present possessed by our system is also
equivalent to immense quantities of heat. If our earth were
by a sudden shock brought to rest in her orbit — which is not to
be feared in the existing arrangement of our system — by such
a shock a quantity of heat would be generated equal to that
produced by the combustion of fourteen such earths of solid
coal. Making the most unfavourable assumption as to its capa-
city for heat — that is, placing it equal to that of water — the
mass of the earth would thereby be heated 11,200 degrees; it

ON THE INTERACTION OF NATURAL FORCES. 159

wcmld, therefore, be quite fused, and for the most part converted
into vapour. If, then, the earth, after having heen thus brought
to rest, should fall into the sun — which, of course, would be the
case — the quantity of heat developed by the shock would be 400
times greater.

Even now from time to time such a process is repeated on a
small scale. There can hardly be a doubt that meteors, fireballs,
and meteoric stones are masses which belong to the universe,
and before coming into the domain of our earth, moved like the
planets round the sun. Only when they enter our atmosphere
do they become visible and fall sometimes to the earth. In
order to explain the emission of light by these bodies, and the
fact that for some time after their descent they are very hot,
the friction was long ago thought of which they experience in
passing through the air. We can now calculate that a velocity
of 3,000 feet a second, supposing the whole of the friction to be
expended in heating the solid mass, would raise a piece of
meteoric iron 1,000° C. in temperature, or, in other words,
to a vivid red heat. Now the average velocity of the
meteors seems to be thirty to fifty times the above amount. To
compensate this, however, the greater portion of the heat is
doubtless carried away by the condensed mass of air which
the meteor drives before it. It is known that bright
meteors generally leave a luminous trail behind them, which
probably consists of severed portions of the red-hot surfaces.
Meteoric masses which fall to the earth often burst with a
violent explosion, which may be regarded as a result of the
quick heating. The newly-fallen pieces have been for the most
part found hot, but not red-hot, which is easily explainable by
the circumstance, that during the short time occupied by the
meteor in passing through the atmosphere, only a thin superficial
layer is heated to redness, while but a small quantity of heat
has been able to penetrate to the interior of the mass. For
this reason the red heat can speedily disappear.

Thus has the falling of the meteoric stone, the minute rem-
nant of processes which seem to have played an important part
in the formation of the heavenly bodies, conducted us to the

160 ON THE INTERACTION OF NATURAL FORCES.

present time, where we pass from the darkness of hypothetical
views to the brightness of knowledge. In what we have said,
however, all that is hypothetical is the assumption of Kant and
Laplace, that the masses of our system were once distributed as
nebulae in space.

On account of the rarity of the case, we will still further
remark in what close coincidence the results of science here
stand with the earlier legends of the human family, and the
forebodings of poetic fancy. The cosmogony of ancient nations
generally commences with chaos and darkness. Thus, for ex-
ample, Mephistopheles says : —

Part of the Part am I, once All, in primal night,
Part of the Darkness which brought forth the Light|
The haughty Light, which now disputes the space,
And claims of Mother Night her ancient place.

Neither is the Mosaic tradition very divergent, particularly
when we remember that that which Moses names heaven, is
different from the blue dome above us, and is synonymous with
space, and that the unformed earth and the waters of the great
deep, which were afterwards divided into waters above the fir-
mament and waters below the firmament, resembled the chaotic
components of the world : —

' In the beginning God created the heaven and the earth.

'And the earth was without form, and void; and darkness
was upon the face of the deep. And the spirit of God moved
upon the face of the waters.'

And just as in nebulous sphere, just become luminous, ani
in the new red-hot liquid earth of our modern cosmogony light
was not yet divided into sun and stars, nor time into day and
night, as it was after the earth had cooled.

'And God divided the light from the darkness.

' And God called the light day, and the darkness He called
night. And the evening and the morning were the first day.'

And now, first, after the waters had been gathered together
into the sea, and the earth had been laid dry, could plants and
animals be formed.

ON THE INTERACTION OF NATURAL FORCES. 161

Our earth bears still the unmistakable traces of its old fiery
fluid condition. The granite formations of her mountains exhibit
a structure, which can only be produced by the crystallisation of
fused masses. Investigation still shows that the temperature in
mines and borings increases as we descend ; and if this increase
is uniform, at the depth of fifty miles a heat exists sufficient to
fuse all our minerals. Even now our volcanoes project from
time to time mighty masses of fused rocks from their interior,
as a testimony of the heat which exists there. But the cooled
crust of the earth has already become so thick, that, as may be
shown by calculations of its conductive power, the heat coming
to the surface from within, in comparison with that reaching the
earth from the sun, is exceedingly small, and increases the tem-
perature of the surface only about ^th of a degree Centigrade ;
so that the remnant of the old store of force which is enclosed
as heat within the bowels of the earth has a sensible influence
upon the processes at the earth's surface only through the instru-
mentality of volcanic phenomena. Those processes owe their
power almost wholly to the action of other heavenly bodies,
particularly to the light and heat of the sun, and partly also, in
the case of the tides, to the attraction of the sun and moon.

Most varied and numerous are the changes which we owe to
the light and heat of the sun. The sun heats our atmosphere
irregularly, the warm rarefied air ascends, while fresh cool air
flows from the sides to supply its place : in this way winds are
generated. This action is most powerful at the equator, the
' warm air of which incessantly flows in the upper regions of the
atmosphere towards the poles ; while just as persistently at the
earth's surface, the trade-wind carries new and cool air to the
equator. Without the heat of the sun, all winds must of neces-
sity cease. Similar currents are produced by the same cause in
the waters of the sea. Their power may be inferred from the
influence which in some cases they exert upon climate. By
them the warm water of the Antilles is carried to the British
Isles, and confers upon them a mild uniform warmth, and rich
moisture ; while, through similar causes, the floating ice of the
North Pole is carried to the coast of Newfoundland and produces

162 ON THE INTERACTION OF NATURAL FORCES.

raw cold. Further, by the heat of the sun a portion of the
water is converted into vapour, which rises in the atmosphere,
is condensed to clouds, or falls in rain and snow upon the earth,
collects in the form of springs, brooks, and rivers, and finally
reaches the sea again, after having gnawed the rocks, carried
away light earth, and thus performed its part in the geologic
changes of the earth ; perhaps besides all this it has driven our
water-mill upon its way. If the heat of the sun were with-
drawn, there would remain only a single motion of water,
namely, the tides, which are produced by the attraction of the
sun and moon.

How is it, now, with the motions and the work of organic
beings ? To the builders of the automata of the last century,
men and animals appeared as clockwork which was never wound
up, and created the force which they exerted out of nothing.
They did not know how to establish a connexion between the
nutriment consumed and the work generated. Since, however,
we have learned to discern in the steam-engine this origin of
mechanical force, we must inquire whether something similar
does not hold good with regard to men. Indeed, the con-
tinuation of life is dependent on the consumption of nutritive
materials : these are combustible substances, which, after diges-
tion and being passed into the blood, actually undergo a slow
combustion, and finally enter into almost the same combinations
with the oxygen of the atmosphere that are produced in an open
fire. As the quantity of heat generated by combustion is inde-
pendent of the duration of the combustion and the steps in
which it occurs, we can calculate from the mass of the con-
sumed material how much heat, or its equivalent work, is
thereby generated in an animal body. Unfortunately, the diffi-
culty of the experiments is still very great ; but within those
limits of accuracy which have been as yet attainable, the ex-
periments show that the heat generated in the animal body
corresponds to the amount which would be generated by the
chemical processes. The animal body therefore does not differ
from the steam-engine as regards the manner in which it obtains
heat and force, but does differ from it in the manner in which

ON THE INTERACTION OF NATURAL FORCES. 163

the force gained is to be made use of. The body is, besides,
more limited than the machine in the choice of its fuel ; the
latter could be heated with sugar, with starch-flour, and butter,
just as well as with coal or wood ; the animal body must dissolve
its materials artificially, and distribute them through its system;
it must, further, perpetually renew the used-up materials of its
organs, and as it cannot itself create the matter necessary for this,
the matter must come from without. Liebig was the first to
point out these various uses of the consumed nutriment. As
material for the perpetual renewal of the body, it seems that
certain definite albuminous substances whieh appear in plants,
and form the chief mass of the animal body, can alone be used.
They form only a portion of the mass of nutriment taken daily ;
the remainder, sugar, starch, fat. are really only materials for
warming, and are perhaps not to be superseded by coal, simply
because the latter does not permit itself to be dissolved.

If, then, the processes in the animal body are not in this
respect to be distinguished from inorganic processes, the question
arises, Whence comes the nutriment which constitutes the source
of the body's force 1 The answer is, from the vegetable king-
dom • for only the material of plants, or the flesh of herbivorous
animals, can be made use of for food. The animals which live
on plants occupy a mean position between carnivorous animals,
in which we reckon man, and vegetables, which the former
could not make use of immediately as nutriment. In hay and
grass the same nutritive substances are present as in meal and
flour, but in less quantity. As, however, the digestive organs
of man are not in a condition to extract the small quantity
of the useful from the great excess of the insoluble, we submit,
in the first place, these substances to the powerful digestion of
the ox, permit the nourishment to store itself in the animal's
body, in order in the end to gain it for ourselves in a more
agreeable and useful form. In answer to our question, there-
fore, we are referred to the vegetable world. Now when what
plants take in and what they give out are made the subjects of
investigation, we find that the principal part of the former
consists in the products of combustion which are generated by

164 ON THE INTERACTION OF NATURAL FORCES.

the animal. They take the consumed carbon given off in respi-
ration, as carbonic acid, from the air, the consumed hydrogen as
water, the nitrogen in its simplest and closest combination as
ammonia ; and from these materials, with the assistance of small
ingredients which they take from the soil, they generate anew
the compound combustible substances, albumen, sugar, oil, on
which the animal subsists. Here, therefore, is a circuit which
appears to be a perpetual store of force. Plants prepare fuel
and nutriment, animals consume these, burn them slowly in
their lungs, and from the products of combustion the plants
again derive their nutriment. The latter is an eternal source of
chemical, the former of mechanical forces. Would not the
combination of both organic kingdoms produce the perpetual
motion 1 We must not conclude hastily : further inquiry shows,
that plants are capable of producing combustible substances
only when they are under the influence of the sun. A portion
of the sun's rays exhibits a remarkable relation to chemical
forces, — it can produce and destroy chemical combinations ; and
these rays, which for the most part are blue or violet, are called
therefore chemical rays. We make use of their action in the
production of photographs. Here compounds of silver are
decomposed at the place where the sun's rays strike them. The
same rays overpower in the green leaves of plants the strong
chemical affinity of the carbon of the carbonic acid for oxygen,
give back the latter free to the atmosphere, and accumulate the
other, in combination with other bodies, as woody fibre, starch,
oil, or resin. These chemically active rays of the sun disappear
completely as soon as they encounter the green portions of the
plants, and hence it is that in Daguerreotype images the green
leaves of plants appear uniformly black. Inasmuch as the
light coming from them does not contain the chemical rays, it is
unable to act upon the silver compounds. But besides the
blue and violet, the yellow rays play an important part in the
growth of plants. They also are comparatively strongly ab-
sorbed by the leaves.

Hence a certain portion of force disappears from the sun-
light, while combustible substances are generated and accumu-

ON THE INTERACTION OF NATURAL FORCES. 165

lated in plants ; and -we can assume it as very probable, that the
former is the cause of the latter. I must indeed remark, that
we are in possession of no experiments from which we might
determine whether the vis viva of the sun's rays which have
disappeared corresponds to the chemical forces accumulated
during the same time ; and as long as these experiments are
wanting, we cannot regard the stated relation as a certainty.
If this view should prove correct, we derive from it the natter-
ing result, that all force, by means of which our bodies live and
move, finds its source in the purest sunlight; and hence we
are all, in point of nobility, not behind the race of the great
monarch of China, who heretofore alone called himself Son of
the Sun. But it must also be conceded that our lower fellow-
beings, the frog and leech, share the same ethereal origin, as
also the whole vegetable world, and even the fuel which comes
to us from the ages past, as well as the youngest offspring of
the forest with which we heat our stoves and set our machines
in motion.

You see, then, that the immense wealth of ever-changing
meteorological, climatic, geological, and organic processes of our
earth are almost wholly preserved in action by the light- and
heat-giving rays of the sun ; and you see in this a remarkable
example, how Proteus-like the effects of a single cause, under
altered external conditions, may exhibit itself in nature. Besides
these, the earth experiences an action of another kind from its
central luminary, as well as from its satellite the moon, which
exhibits itself in the remarkable phenomenon of the ebb and
flow of the tide.

Each of these bodies excites, by its attraction upon the
waters of the sea, two gigantic waves, which flow in the same
direction round the world, as the attracting bodies themselves
apparently do. The two waves of the moon, on account of her
greater nearness, are about 31 times as large as those excited
by the sun. One of these waves has its crest on the quarter of
the earth's surface which is turned towards the moon, the other
is at the opposite side. Both these quarters possess the flow
of the tide, while the regions which lie between have the ebb.

166 ON THE INTERACTION OF NATUEAL FORCES.

Although in the open sea the height of the tide amounts to
only about three feet, and only in certain narrow channels,
where the moving water is squeezed together, rises to thirty
feet, the might of the phenomenon is nevertheless manifest
from the calculation of Bessel, according to which a quarter of
the earth covered by the sea possesses, during the flow of the
tide, about-22,000 cubic miles of water more than during the
ebb, and that therefore such a mass of water must, in 6£ hours,
flow from one quarter of the earth to the other.

The phenomenon of the ebb and flow, as already recognised
by Mayer, -combined with the law of the conservation of force,
stands in remarkable connexion with the question of the stability
of our planetary system. The mechanical theory of the plane-
tary motions discovered by Newton teaches, that if a solid body
in absolute vacua, attracted by the sun, move around him in
the same manner as the planets, this motion will endure un-
changed through all eternity.

Now we have actually not only one, but several such planets,
which move around the sun, and by their mutual attraction
create little changes and disturbances in each .other's paths.
Nevertheless Laplace, in his great work, the ' Mecanique celeste,'
has proved that in our planetary system all these disturbances
increase and diminish periodically, and can never exceed certain
limits, so that by this cause the eternal existence of the plane-
tary system is unendangered.

But 1 have already named two assumptions which must be
made : first, that the celestial spaces must be absolutely empty ;
and secondly, that the sun and planets must be solid bodies.
The £rst is at least the case as far as astronomical observations
reach, for they have never been able to detect any retardation
of the planets, such as would occur if they moved in a resisting
medium. But on a body of less mass, the comet of Encke,
changes are observed of such a nature : this comet describes
ellipses round the sun which are becoming gradually smaller.
If this kind of motion, which certainly corresponds to that
through a resisting medium, be actually due to the existence of
such a medium, .a time will come when the comet will strike

ON THE INTERACTION OF NATURAL FORCES. 167

the sun ; and a similar end threatens all the planets, although
after a time, the length of which baffles our imagination to con-
ceive of it. But even should the existence of a resisting medium
appear doubtful to us, there is no doubt that the planets are
not wholly composed of solid materials which are inseparably
bound together. Signs of the existence of an atmosphere are
observed on the Sun, on Venus, Mars, Jupiter, and Saturn.
Signs of water and ice upon Mars ; and our earth has undoubt-
edly a fluid portion on its surface, and perhaps a still greater
portion of fluid within it. The motions of the tides, however,
produce friction, all friction destroys vis viva, and the loss in
this case can only affect the vis viva of the planetary system.
We come thereby to the unavoidable conclusion, that every
tide, although with infinite slowness, still with certainty dimi-
nishes the store of mechanical force of the system ; and as a
consequence of this, the rotation of the planets in question
round their axes must become more slow. The recent careful
investigations of the moon's motion made by Hansen, Adams,
and Delaunay, have proved that the earth does experience such
a retardation. According to the former, the length of each
sidereal day has increased since the time of Hipparchus by the
•J-f part of a second, and the duration of a century by half a
quarter of an hour ; according to Adams and Sir W. Thomson,
the increase has been almost twice as great. A clock which
went right at the beginning of a century, would be twenty-two
seconds in advance of the earth at the end of the century.
Laplace had denied the existence of such a retardation in the
case of the earth ; to ascertain the amount, the theory of lunar
motion required a greater development than was possible in his
time. The final consequence would be, but after millions of
years, if in the meantime the ocean did not become frozen,
that one side of the earth would be constantly turned towards
the sun, and enjoy a perpetual day, whereas the opposite side
would be involved in eternal night. Such a position we observe
in our moon with regard to the earth, and also in the case
of the satellites as regards their planets ; it is, perhaps,
due to the action of the mighty ebb and flow to which these

168 OX THE INTERACTION OF NATURAL FORCES.

bodies, in the time of their fiery fluid condition, were sub-
jected.

I would not have brought forward these conclusions, which
again plunge us in the most distant future, if they were not
unavoidable. Physico-mechanical laws are, as it were, the
telescopes of our spiritual eye, which can penetrate into the
deepest night of time, past and to come.

Another essential question as regards the future of our
planetary system has reference to its future temperature and
illumination. As the internal heat of the earth has but little
influence on the temperature of the surface, the heat of the sun
is the only thing which essentially affects the question. The
quantity of heat falling from the sun during a given time upon
a given portion of the earth's surface may be measured, and
from this it can be calculated how much heat in a given time is
sent out from the entire sun. Such measurements have been
made by the French physicist Pouillet, and it has been found
that the sun gives out a quantity of heat per hour equal to that
which a layer of the densest coal 10 feet thick would give out
by its combustion ; and hence in a year a quantity equal to the
combustion of a layer of 17 miles. If this heat were drawn
uniformly from the entire mass of the sun, its temperature
would only be diminished thereby 1^ of a degree Centigrade
per year, assuming its capacity for heat to be equal to that of
water. These results can give us an idea of the magnitude of
the emission, in relation to the surface and mass of the sun ;
but they cannot inform us whether the sun radiates heat as a
glowing body, which since its formation has its heat accumulated
within it, or whether a new generation of heat by chemical
processes is continually taking place at the sun's surface. At
all events, the law of the conservation of force teaches us that
no process analogous to those known at the surface of the earth
can supply for eternity an inexhaustible amount of light and
heat to the sun. But the same law also teaches that the store
of force at present existing as heat, or as what may become
heat, is sufficient for an immeasurable time. With regard to
the store of chemical force in the sun, we can form no conjee-

ON THE INTERACTION OF NATURAL FORCES. 169

ture, and the store of heat there existing can only be determined
by very uncertain estimations. If, however, we adopt the very
probable view, that the remarkably small density of so large a
body is caused by its high temperature, and may become greater
in time, it may be calculated that if the diameter of the sun
were diminished only the ten-thousandth part of its present
length, by this act a sufficient quantity of heat would be gene-
rated to cover the total emission for 2,100 years. So small a
change it would be difficult to detect even by the finest astro-
nomical observations.

Indeed, from the commencement of the period during which
we possess historic accounts, that is, for a period of about 4,000
years, the temperature of the earth has not sensibly diminished.
From these old ages we have certainly 110 thermornetric observa-
tions, but we have information regarding the distribution of
certain cultivated plants, the vine, the olive tree, which are
very sensitive to changes of the mean annual temperature, and
we find that these plants at the present moment have the same
limits of distribution that they had in the times of Abraham
and Homer ; from which we may infer backwards the constancy
of the climate.

In opposition to this it has been urged, that here in Prussia
the German knights in former times cultivated the vine, cellared
their own wine and drank it, which is no longer possible. From
this the conclusion has been drawn, that the heat of our climate
has diminished since the time referred to. Against this, how-
ever, Dove has cited the reports of ancient chroniclers, accord-
ing to which, in some peculiarly hot years, the Prussian grape"
possessed somewhat less than its usual quantity of acid. The
fact also speaks not so much for the climate of the country as
for the throats of the German drinkers.

But even though the force store of our planetary system is
so immensely great, that by the incessant emission which has
occurred during the period of human history it has not been
sensibly diminished, even though the length of the time which
must flow by before a sensible change in the state of our plane-
tary system occurs ia totally incapable of measurement, still the

170 ON THE INTERACTION OF NATURAL FORCES.

inexorable laws of mechanics indicate that this store of force,
which can only suffer loss and not gain, must be finally exhausted.
Shall we terrify ourselves by this thought 1 Men are in the
habit of measuring the greatness and the wisdom of the universe
by the duration and the profit which it promises to their own
race ; but the past history of the earth already shows what an
insignificant moment the duration of the existence of our race
upon it constitutes. A Nineveh vessel, a Roman sword, awake
in us the conception of grey antiquity. What the museums of
Europe show us of the remains of Egypt and Assyria we gaze
upon with silent astonishment, and despair of being able to carry
our thoughts back to a period so remote. Still must the human
race have existed for ages, and multiplied itself before the
Pyramids or Nineveh could have been erected. We estimate
the duration of human history at 6,000 years ; but immeasur-
able as this time may appear to us, what is it in comparison with
the time during which the earth carried successive series of rank
plants and mighty animals, and no men ; during which in our
neighbourhood the amber-tree bloomed, and dropped its costly
gum on the earth and in the sea; when in Siberia, Europe, and
North America groves of tropical palms flourished; where
gigantic lizards, and after them elephants, whose mighty remains
we still find buried in the earth, found a home 1 Different
geologists, proceeding from different premises, have sought to
estimate the duration of the above-named creative period, and
vary from a million to nine million years. The time during
•which the earth generated organic beings is again small when
compared with the ages during which the world was a ball of
fused rocks. For the duration of its cooling from 2,000° to 200°
Centigrade the experiments of Bishop upon basalt show that
about 350 millions of years would be necessary. And with
regard to the time during which the first nebulous mass con-
densed into our planetary system, our most daring conjectures
must cease. The history of man, therefore, is but a short ripple
in the ocean of time. For a much longer series of years than
that during which he has already occupied this world, the exist-
ence of the present state of inorganic nature favourable to the

ON THE INTERACTION OF NATURAL FORCES. 171

duration of man seems to be secured, so that for ourselves and
for long generations after us we have nothing to fear. But the
same forces of air and water, and of the volcanic interior, which
produced former geological revolutions, and buried one series of
living forms after another, act still upon the earth's crust. They
more probably will bring about the last day of the human race
than those distant cosmical alterations of which we have spoken,
forcing us perhaps to make way for new and more complete
living forms, as the lizards and the mammoth have given place
to us and our fellow-creatures which now exist.

Thus the thread which was spun in darkness by those who
sought a perpetual motion has conducted us to a universal law
of nature, which radiates light into the distant nights of the
beginning and of the end of the history of the universe. To
our own race it permits a long but not an endless existence ; it
threatens it with a day of judgment, the dawn of which is still
happily obscured. As each of us singly must endure the
thought of his death, the race must endure the same. But
above the forms of life gone by, the human race has higher
moral problems before it, the bearer of which it is, and in the
completion of which it fulfils its destiny.

172 ON THE INTERACTION OF NATURAL FORCES.

NOTE TO PAGE 157.

I must here explain the calculation of the heat which must
be produced by the assumed condensation of the bodies of our
system from scattered nebulous matter. The other calculations,
the results of which I have mentioned, are to be found partly
in J. K. Mayer's papers, partly in Joule's communications, and
partly by aid of the known facts and method of science : they
are easily performed.

The measure of the work performed by the condensation of
the mass from a state of infinitely small density is the potential
of the condensed mass upon itself. For a sphere of uniform
density of the mass M, and the radius R, the potential upon
itself V — if we call the mass of the earth m, its radius r, and
the intensity of gravity at its surface g — has the value

V-3

Let us regard the bodies of our system as such spheres, then
the total work of condensation is equal to the sum of all their
potentials on themselves. As, however, these potentials for

different spheres are to each other as the quantity — -' they all

Jfcl

vanish in comparison with the sun ; even that of the greatest
planet, Jupiter, is only about the one hundred- thousandth part
of that of the sun; in the calculation, therefore, it is only
necessary to introduce the latter.

To elevate the temperature of a mass M of the specific heat
IT, t degrees, we need a quantity of heat equal to Mer£ ; this
corresponds, when A.g represents the mechanical equivalent of
the unit of heat, to the work A^Mo-i. To find the elevation of

ON THE INTERACTION OF NATURAL FORCES. 173

temperature produced by the condensation of the mass of the
sun, let us set

we have then

/=

5. A. R. m. <

For a mass of water equal to the sun we have a = 1 ; then
the calculation with the known values of A, M, R, m, and r,
gives

t = 28611000° Cent.

The mass of the sun is 738 times greater than that of all
th3 planets taken together; if, therefore, we desire to make the
water mass equal to that of the entire system, we must multiply

738

the value of t by the fraction - - - , which makes hardly a sensible
739

alteration in the result.

When a spherical mass of the radius R condenses more and
more to the radius Ru the elevation of temperature thereby
produced is

6' A . ma-

R,)

_
6'AKjmo- I R0 !

Supposing, then, the mass of the planetary system to be at
the commencement, not a sphere of infinite radius, but limited,
say of the radius of the path of Neptune, which is six thousand
times greater than the radius of the sun, the magnitude

T? 1

-i will then be equal to .-77777., and the above value of t would
K0 6000

have to be diminished by this inconsiderable amount.

From the same formula we can deduce that a diminution of

174 ON THE INTERACTION OF NATURAL FORCES.

- of the radius of the sun would generate work in a water
10000

mass equal to the sun, equivalent to 2,861 degrees Centigrade.
And as, according to Pouillet, a quantity of heat corresponding to
1£ degree is lost annually in such a mass, the condensation
referred to would cover the loss for 2,289 years.

If the sun, as seems probable, be not everywhere of the
same density, but is denser at the centre than near the surface,
the potential of its mass and the corresponding quantity of heat
will be still greater.

Of the now remaining mechanical forces, the vis viva of the
rotation of the heavenly bodies round their own axes is, in
comparison with the other quantities, very small, and may be
neglected. The vis viva of the motion of revolution round the
sun, if fj. be the mass of a planet, and p its distance from the
sun, is

K

Omitting the quantity x~ as very small compared with ^-, and
dividing by the above value of Y, we obtain

L = 5 p
V 3 M'

The mass of all the planets together is - of the mass of

738

the sun ; hence the value of L for the entire system is

175

THE RECENT PROGRESS OF THE
THEORY OF VISION,

A Course of Lectures delivered in Frankfort and Heidelberg, and Republished
in the Prevssische Jahrbiicher, 1868.

I. THE EYE AS AN OPTICAL INSTRUMENT.

THE physiology of the senses is a border land in which the two
great divisions of human knowledge, natural and mental science,
encroach on one another's domain; in which problems arise
which are important for both, and which only the combined
labour of both can solve.

No doubt the first concern of physiology is only with
material changes in material organs, and that of the special
physiology of the senses is with the nerves and their sensations, so
far as these are excitations of the nerves. But, in the course
of investigation into the functions of the organs of the senses,
science cannot avoid also considering the apprehension of external
objects, which is the result of these excitations of the nerves, and
for the simple reason that the fact of a particular state of mental
apprehension often reveals to TIS a nervous excitation which
would otherwise have escaped our notice. On the other hand,
apprehension of external objects must always be an act of our
power of realization, and must therefore be accompanied by con-
sciousness, for it is a mental function. Indeed the further exact
investigation of this process has been pushed, the more it has
revealed to us an ever-widening field of such mental functions,

176 RECENT PROGRESS OF THE THEORY OF VISION.

the results of which are involved in those acts of apprehension
by the senses which at first sight appear to be most simple
and immediate. These concealed functions have been but little
discussed, because we are so accustomed to regard the appre
hension of any external object as a complete and direct whole,
which does not admit of analysis.

It is scarcely necessary for me to remind my present readers
of the fundamental importance of this field of inquiry to almost
every other department of science. For apprehension by the
senses supplies after all, directly or indirectly, the material of all
human knowledge, or at least the stimulus necessary to develope
every inborn faculty of the mind. It supplies the basis for the
whole action of man upon the outer world ; and if this stage of
mental processes is admitted to be the simplest and lowest of its
kind, it is none the less important and interesting. For there
is little hope that he who does not begin at the beginning of
knowledge will ever arrive at its end.

It is by this path that the art of experiment, which has
become so important in natural science, found entrance into the
hitherto inaccessible field of mental processes. At first this will
be only so far as we are able by experiment to determine the
particular sensible impressions which call up one or another
conception in our consciousness. But from this first step will
follow numerous deductions as to the nature of the mental pro-
cesses which contribute to the result. I will therefore endeavour
to give some account of the results of physiological inquiries so
far as they bear on the questions above mentioned.

I am the more desirous of doing so because I have lately
completed1 a complete survey of the field of physiological optics,
and am happy to have an opportunity of putting together in a
compendious form the views and deductions on the present sub-
ject which might escape notice among the numerous details of a
book devoted to the special objects of natm-al science. I may
state that in that work I took great pains to convince myself of
the truth of every fact of the slightest importance by personal

1 Prof. Helmholtz's Handbook of Physiological Optics was published at
Leipzig in 1867.

THE EYE AS AN OPTICAL INSTRUMENT. 177

observation and experiment. There is no longer much contro-
versy on the more important facts of observation, the chief
difference of opinion being as to the extent of certain individual
differences of apprehension by the senses. During the last few
years a great number of distinguished investigators have, under
the influence of the rapid progress of ophthalmic medicine,
worked at the physiology of vision; and in proportion as the num-
ber of observed facts has increased, they have also become more
capable of scientific arrangement and explanation. I need not
remind those of my readers who are conversant with the sub-
ject how much labour must be expended to establish many facts
which appear comparatively simple and almost self-evident.

To render what follows understood in all its bearings, I shall
first describe the physical characters of the eye as an optical
instrument; next the physiological processes of excitation and
conduction in the parts of the nervous system which belong to
it ; and lastly, I shall take up the psychological question, how
mental apprehensions are produced by the changes which take
place in the optic nerve.

The first part of our inquiry, which cannot be passed over
because it is the foundation of what follows, will be in great
part a repetition of what is already generally known, in order to
bring in what is new in its proper place. But it is just this
part of the subject which excites so much interest, as the real
starting point of that remarkable progress which ophthalmic
medicine has made during the last twenty years — a progress
which for its rapidity and scientific character is perhaps without
parallel in the history of the healing art.

Every lover of his kind must rejoice in these achievements
which ward off or remove so much misery that formerly we
were powerless to help, but a man of science has peculiar reason
to look on them with pride. For this wonderful advance has
not been achieved by groping and hicky finding, but by deduction
rigidly followed out, and thus carries with it the pledge of still
future successes. As once astronomy was the pattern from
which the other sciences learned how the right method will lead

I. N

178 RECENT PROGRESS OF THE THEORY OF VISION.

to success, so does ophthalmic medicine now display how much
may be accomplished in the treatment of disease by extended
application of well-understood methods of investigation and
accurate insight into the causal connection of phenomena. It is
no wonder that the right sort of men were drawn to an arena
which offered a prospect of new and noble victories over the
opposing powers of nature to the true scientific spirit — the
spirit of patient and cheerful work. It was because there were
so many of them that the success was so brilliant. Let me be
permitted to name out of the whole number a representative of
each of the three nations of common origin which have con-
tributed most to the result : Von Graefe in Germany, Donders
in Holland, and Bowman in England.

There is another point of view from which this advance in
ophthalmology may be regarded, and that with equal satisfac-
tion. Schiller says of science : —

Wer um die Gottin freit, suche in ihr nicht das Weib.1
Who woos the goddess must not hope the wife,

And history teaches us, what wa shall have opportunity of
seeing in the present inquiry, that the most important practical
results have sprung unexpectedly out of investigations which
might seem to the ignorant mere busy trifling, and which even
those better able to judge could only regard with the intellec-
tual interest which pure theoretical inquiry excites.

Of all our members the eye has always been held the choicest
gift of Nature — the most marvellous product of her plastic
force. Poets and orators have celebrated its praises ; philoso-
phers have extolled it as a crowning instance of perfection in
an organism ; and opticians have tried to imitate it as an un-
surpassed model. And indeed the most enthusiastic admiration
of this wonderful organ is only natural, when we consider what
functions it performs ; when we dwell on its penetrating power,
on the swiftness of succession of its brilliant pictures, and on the

1 From Schiller's Spruche. Literally, ' Let not him who seeks the love of
a goddess expect to find in her the woman.'

THE EYE AS AN OPTICAL INSTRUMENT. 179

riches which it spreads before our sense. It is by the eye alone
that we know the countless shining worlds that fill immeasur-
able space, the distant landscapes of our own earth, with all the
varieties of sunlight that reveal them, the wealth of form and
colour among flowers, the strong and happy life that moves in
animals. Next to the loss of life itself that of eyesight is the
heaviest.

But even more important than the delight in beauty and ad-
miration of majesty in the creation which we owe to the eye, is the
security and exactness with which we can judge by sight of the
position, distance, and size of the objects which surround us. For
this knowledge is the necessary foundation for all our actions, from
threading a needle through a tangled skein of silk to leaping from
cliff to cliff when life itself depends on the right measurement
of the distance. In fact, the success of the movements and ac-
tions dependent on the accuracy of the pictures that the eye gives
us forms a continual test and confirmation of that accuracy. If
sight were to deceive us as to the position and distance of external
objects, we should at once become aware of the delusion on
attempting to grasp or to approach them. This daily verification
by our other senses of the impressions \ve receive by sight
produces so firm a conviction of its absolute and complete truth
that the exceptions taken by philosophy or physiology, however
well grounded they may seem, have no power to shake it.

No wonder then that, according to a wide-spread conviction,
the eye is looked on as an optical instrument so perfect that
none formed by human hands can ever be compared with it,
and that its exact and complicated construction should be
regarded as the full explanation of the accuracy and variety
of its functions.

Actual examination of the performances of the eye as an
optical instrument carried on chiefly during the last ten years
has brought about a remarkable change in these views, just as in
so many other cases the test of facts has disabused our minds
of similar fancies. But as again in similar cases reasonable
admiration rather increases than diminishes when really impor-
tant functions are more clearly understood and their object
N 2

180 RECENT PKOGRESS OF THE THEORY OF VISION.

better estimated, so it may well be with our more exact know-
ledge of the eye. For the great performances of this little
organ can never be denied ; and while we might consider our-
solves compelled to withdraw our admiration from one point of
view, we must again experience it from another.

Regarded as an optical instrument, the eye is a camera
obscura. This apparatus is well known in the form used by
photographers (Fig. 27). A box constructed of two parts, of
.which one slides in the other, and blackened, has in front a
combination of lenses fixed in the tube h i on the inside, which
refract the incident rays of light, and unite them at the back
FIG. 27.

of the instrument into an optical image of the objects which lie in
front of the camera. When the photographer first arranges his
instrument, he receives the image upon a plate of ground glass, g.
It is there seen as a small and elaborate picture in its natural
colours, more clear and beautiful than the most skilful painter
could imitate, though indeed it is upside down. The next
step is to substitute for this glass a prepared plate upon which the
light exerts a permanent chemical effect, stronger on the more
brightly illuminated parts, weaker on those which are darker.
These chemical changes having once taken place are permanent :
by their means the image is fixed upon the plate.

THE EYE AS AN OPTICAL INSTRUMENT. 181

The natural camera obscura of the eye (seen in a diagram-
matic section in Fig. 28) has its blackened chamber globular in-
stead of cubical, and made not of wood, but of a thick, strong,
white substance known as the sclerotic coat. It is this which
is partly seen between the eyelids as ' the white of the eye.'
This globular chamber is lined with a delicate coat of winding
blood-vessels covered inside by black pigment. But the apple
of the eye is not empty like the camera : it is filled with a
transparent jelly as clear as water. The lens of the camera

obscura is represented, first, by a convex transparent window
like a pane of horn (the cornea), which is fixed in front of the
sclerotic like a watch glass in front of its metal case. This
union and its own firm texture make its position and its curva-
ture constant. But the glass lenses of the photographer are
not fixed ; they are moveable by means of a sliding tube which
can be adjusted by a screw (Fig. 27, r), so as to bring the objects
in front of the camera into focus. The nearer they are, the
farther the lens is pushed forward ; the farther off, the more it

182 RECENT PROGRESS OF THE THEORY OF VISION.

is screwed in. The eye has the same task of bringing at one
time near, at another distant, objects to a focus at the back of
its dark chamber. So that some power of adjustment or ' ac-
commodation ' is necessary. This is accomplished by the move-
ments of the crystalline lens (Fig. 28, L), which is placed a
short distance behind the cornea. It is covered by a curtain of
varying colour, the iris (J), which is perforated in the centre by
a round hole, the pupil, the edges of which are in contact with
the front of the lens. Through this opening we see through
the transparent and, of course, invisible lens the black chamber
within. The crystalline lens is circular, bi-convex, and elastic.
It is attached at its edge to the inside of the eye by means of a
circular band of folded membrane which surrounds it like a
plaited ruff, and is called the ciliary body or Zonule of Zinn
(Fig. 28, * *). The tension of this ring (and so of the lens
itself) is regulated by a series of muscular fibres known as the
ciliary muscle (Cc). When this muscle contracts, the tension of
the lens is diminished, and its surfaces — but chiefly the front
one — become by its physical property of elasticity more convex
than when the eye is at rest ; its refractive power is thus in-
creased, and the images of near objects are brought to a focus
on the back of the dark chamber of the eye.

Accordingly the healthy eye when at rest sees distant objects
distinctly : by the contraction of the ciliary muscle it is ' ac-
commodated ' for those which are near. The mechanism by
which this is accomplished, as above shortly explained, was
one of the greatest riddles of the physiology of the eye since the
time of Kepler ; and the knowledge of its mode of action is of
the greatest practical importance from the frequency of defects
in the power of accommodation. No problem in optics has given
rise to so many contradictory theories as this. The key to its
solution was found when the French surgeon Sanson first observed
very faint reflections of light through the pupil from the two
surfaces of the crystalline lens, and thus acquired the character
of an unusually careful observer. For this phenomenon was
anything but obvious ; it can only be seen by strong side illumi-
nation, in darkness otherwise complete, only when the observer

THE EYE AS AN OPTICAL INSTRUMENT. 183

takes a certain position, and then all he sees is a faint misty re-
flection. But this faint reflection was destined to become a
shining light in a dark corner of science. It was in fact the
first appearance observed in the living eye which came directly
from the lens. Sanson immediately applied his discovery to
ascertain whether the lens was in its place in cases of impaired
vision. Max Langenbeck made the next step by observing that
the reflections from the lens alter during accommodation. These
alterations were employed by Cramer of Utrecht, and also inde-
pendently by the present writer, to arrive at an exact knowledge
of all the changes which the lens undergoes during the process
of accommodation. I succeeded in applying to the moveable eye
in a modified form the principle of the heliometer, an instrument
by which astronomers are able so accurately to measure small
distances between stars in spite of their constant apparent
motion in the heavens, that they can thus sound the depths of
the region of the fixed stars. An instrument constructed for
the purpose, the ophtltalmometer, enables us to measure in the
living eye the curvature of the cornea, and of the two surfaces
of the lens, the distance of these from each other, <kc., with
greater precision than could before be done even after death.
By this means we can ascertain the entire range of the changes
of the optical apparatus of the eye so far as it affects accom-
modation.

The physiological problem was therefore solved. Oculists,
and especially Bonders, next investigated the individual defects
of accommodation which give rise to the conditions known as
long sight and short sight. It was necessary to devise trust-
worthy methods in order to ascertain the precise limits of the
power of accommodation even with inexperienced and unin-
structed patients. It became apparent that very different con-
ditions had been confounded as short sight and long sight, and
this confusion had made the choice of suitable glasses uncertain.
It was also discovered that some of the most obstinate and
obscure affections of the sight, formerly reputed to be ' nervous,'
simply depended on certain defects of accommodation, and
could be readily removed by using suitable glasses. Moreover,

184 EECENT PROGKESS OF THE THEORY OF VISION.

Bonders l proved that the same defects of accommodation are
the most frequent cause of squinting, and Von Graefe2 had
already shown that neglected and progressive shortsightedness
tends to produce the most dangerous expansion and deformity of
the back of the globe of the eye.

Thus connections were discovered, where least expected,
between the optical discovery and important diseases, and the
result was no less beneficial to the patient than interesting to
the physiologist.

We must now speak of the curtain which receives the
optical image Avhen brought to a focus in the eye. This is the
retina, a thin membranous expansion of the optic nerve which
forms the innermost of the coats of the eye. The optic nerve
(Fig. 2, 0) is a cylindrical cord which contains a multitude of
minute fibres protected by a strong tendinous sheath. The
nerve enters the apple of the eye from behind, rather to the
inner (nasal) side of the middle of its posterior hemisphere.
Its fibres then spread out in all directions over the front of
the retina. They end by becoming connected, first, with
ganglion cells and nuclei, like those found in the brain ; and,
secondly, with structures not elsewhere found, called rods and
cones. The rods are slender cylinders; the cones, or bulbs,
somewhat thicker, flask-shaped structures. All are ranged per-
pendicular to the surface of the retina, closely packed together,
so as to form a regular mosaic layer behind it. Each rod is
connected with one of the minutest nerve fibres, each cone with
one somewhat thicker. This layer of rods and bulbs (also
known as membrana Jacobi) has been proved by direct experi-
ments to be the really sensitive layer of the retina, the structure
in which alone the action of light is capable of producing a
nervous excitation.

There is in the retina a remarkable spot which is placed
near its centre, a little to the outer (temporal) side, and which

1 Professor of Physiology in the University of Utrecht.

2 This great ophthalmic surgeon died in Berlin at the early age of forty-
two.

THE EYE AS AN OPTICAL INSTRUMENT. 185

from its colour is called the yellow spot. The retina is here

somewhat thickened, but in the middle of the yellow spot is
found a depression, the fovea centralis, where the retina is

186 RECENT PROGRESS OF THE THEORY OF VISION.

reduced to those elements alone which are absolutely necessary
for exact vision. Fig. 29, from Henle, shows a thin transverse
section of this central depression made on a retina which had
been hardened in alcohol. Lh (Lamina kyalina, membrana
limitang) is an elastic membrane which divides the retina from
the vitreous. The bulbs (seen at b) are here smaller than else-
where, measuring only the 400th part of a millimetre in dia-
meter, and form a close and regular mosaic. The other, more
or less opaque, elements of the retina are seen to be wanting,
except the corpuscles (<?), which belong to the cones. At f are
seen the fibres which unite these with the rest of the retina.
This consists of a layer of fibres of the optic nerve (n) in front,
and two layers of nerve cells (gli and gle), known as the internal
and external ganglion layers, with a stratum of fine granules
(gri) between them. All these parts of the retina are absent at
the bottom of the fovea centralis, and their gradual thinning
away at its borders is seen in the diagram. Nor do the blood
vessels of the retina enter the fovea, but end in a circle of
delicate capillaries around it.

This fovea, or pit of the retina, is of great importance for
vision, since it is the spot where the most exact discrimination
of distances is made. The cones are here packed most closely
together, and receive light which has not been impeded by other
semi-transparent parts of the retina. We may assume that a
single nervous fibril runs from each of these cones through the
trunk of the optic nerve to the brain, without touching its
neighbours, and there produces its special impression, so that
the excitation of each individual cone will produce a distinct
and separate effect upon the sense.

The production of optical images in a camera obscura depends
on the well-known fact that the rays of light which come off
from an illuminated object are so broken or refracted in passing
through the lenses of the instrument, that they follow new
directions which bring them all to a single point, the focus, at
the back of the camera. A common burning glass has the
same property ; if we allow the rays of the sun to pass through

THE EYE AS AN OPTICAL INSTRUMENT. 187

it, and hold a sheet of white paper at the proper distance behind
it, we may notice two effects. In the first place (and this is
often disregarded) the burning lens, although made of trans-
parent glass, throws a shadow like any opaque body ; and next
we see in the middle of this shadow a spot of dazzling brilliance,
the image of the sun. The rays which, if the lens had not
been there, would have illuminated the whole space occupied by
the shadow, are concentrated by the refracting power of the
burning glass upon the bright spot in the middle, and so both
light and heat are more intense there than where the unrefracted
solar rays fall. If, instead of the disc of the sun, we choose a
star or any other point as the source of light, its light will be
united into a point at the focus of the lens, and the image of
the star will appear as such upon the white paper. If there is
another fixed star near the one first chosen, its light will be
collected at a second illuminated point on the paper ; and if the
star happen to send out red rays, its image on the paper will
also appear red. The same will be true of any number of
neighbouring stars, the image of each corresponding to it in
brilliance, colour, and relative position. And if, instead of a
multitude of separate luminous points, we have a continuous
series of them in a bright line or surface, a similar line or sur-
face will be produced upon the paper. But here also, if the
piece of paper be put to the proper distance, all the light that
proceeds from any one point will be brought to a focus at a
point which corresponds to it in strength and colour of illumi-
nation, and (as a corollary) no point of the paper receives light
from more than a single point of the object.

If now we replace our sheet of white paper by a prepared
photographic plate, each point of its surface will be altered by
the light which is concentrated on it. This light is all derived
from the corresponding point in the object, and answers to it in
intensity. Hence the changes which take place on the plate
will correspond in amount to the chemical intensity of the rays
which fall upon it.

This is exactly what takes place in the eye. Instead of the
burning glass we have the cornea and crystalline lens; and

188 RECENT PROGRESS OF THE THEORY OF VISION.

instead of the piece of paper, the retina. Accordingly, if an
optically accurate image is thrown upon the retina, each of its
cones will be reached by exactly so much light as proceeds from
the corresponding point in the field of vision; and also the
nerve fibre which arises from each cone will be excited only by
the light proceeding from the corresponding point in the field,
while other nerve fibres will be excited by the light proceeding
from other points of the field. Fig. 30 illustrates this effect.
The rays which come from the point A in the object of vision
are so broken that they all unite at a on the retina, while those
from B unite at b. Thus it results that the light of each separate
bright point of the field of vision excites a separate impression;
that the difference of the several points of the field of vision in
degree of brightness can be appreciated by the sense; and lastly,

FIG. 30.

that separate impressions may each arrive separately at the seat
of consciousness.

If now we compare the eye with other optical instruments,
we observe the advantage it has over them in its very large
field of vision. This for each eye separately is 160° (nearly two
right angles) laterally, and 120° vertically, and for both together
somewhat more than two right angles from right to left. The
field of view of instruments made by art is usually very small,
and becomes smaller with the increased size of the image.

But \ve must also admit, that we are accustomed to expect
in these instruments complete precision of the image in its
entire extent, while it is only necessary for the image on the
retina to be exact over a very small surface, namely, that of the
yellow spot. The diameter of the central pit corresponds in

THE EYE AS AN OPTICAL INSTRUMENT. 189

the field of vision to an angular magnitude which can be covered
by the nail of one's forefinger when the hand is stretched out as
far as possible. In this small part of the field our power of vision
is so accurate that it can distinguish the distance between two
points, of only one minute angular magnitude, i.e. a distance
equal to the sixtieth part of the diameter of the finger-nail.
This distance corresponds to the width of one of the cones of
the retina. All the other parts of the retinal image are seen
imperfectly, and the more so the nearer to the limit of the
retina they fall. So that the image which we receive by the
eye is like a picture, minutely and elaborately finished in the
centre, but only roughly sketched in at the borders. But
although at each instant we only see a very small part of the
field of vision accurately, we see this in combination with what
surrounds it, and enough of this outer and larger part of the
field, to notice any striking object, and particularly any change
that takes place in it. All of this is unattainable in a telescope.
.But if the objects are too small, we cannot discern them at
all with the greater part of the retina.

When, lost in boundless blue on high,
The lark pours forth his thrilling song,1

the ' ethereal minstrel ' is lost until we can bring her image to a
focus upon the central pit of our retina. Then only are we able
to see her.

To look at anything means to place the eye in such a position
that the image of the object falls on the small region of per-
fectly clear vision. This we may call direct vision, applying
the term indirect to that exercised with the lateral parts of the
retina — indeed with all except the yellow spot.

The defects which result from the inexactness of vision and

the smaller number of cones in the greater part of the retina

are compensated by the rapidity with which we can turn the

eye to one point after another of the field of vision, and it is

1 The lines in the well-known passage of Faust : —

Wenn ttber uns im blauen Raum verloren

Ihr schmetternd Lied die Lerche singt.

190 RECENT PROGRESS OF THE THEORY OF VISION.

this rapidity of movement which really constitutes the chief
advantage of the eye over other optical instruments.

Indeed the peculiar way in which we are accustomed to give
our attention to external objects, by turning it only to one
thing at a time, and as soon as this has been taken in hastening
to another, enables the sense of vision to accomplish as much
as is necessary ; and so we have practically the same advantage
as if we enjoyed an accurate view of the whole field of vision
at once. It is not in fact until we begin to examine our sen-
sations closely that we become aware of the imperfections of
indirect vision. Whatever we want to see we look at, and see
it accurately ; what we do not look at, we do not as a rule care
for at the moment, and so do not notice how imperfectly we
see it.

Indeed, it is only after long practice that we are able to turn
our attention to an object in the field of indirect vision (as is
necessary for some physiological observations) without looking
at it, and so bringing it into direct view. And it is just as
difficult to fix the eye on an object for the number of seconds
required to produce the phenomenon of an after-image.1 To
get this well defined requires a good deal of practice.

A great part of the importance of the eye as an organ of
expression depends on the same fact ; for the movements of the
eyeball — its glances — are among the most direct signs of the
movement of the attention, of the movements of the mind, of
the person who is looking at us.

Just as quickly as the eye turns upwards, downwards, and
from side to side, does the accommodation change, so as to bring
the object to which our attention is at the moment directed into
focus; and thus near and distant objects pass in rapid suc-
cession into accurate view.

All these changes of direction and of accommodation take
place far more slowly in artificial instruments. A photographic
camera can never show near and distant objects clearly at once,
nor can the eye ; but the eye shows them so rapidly one after

i Vide infra, p. 224.

THE EYE AS AN OPTICAL INSTRUMENT. 191

another that most people, who have not thought how they see,
do not know that there is any change at all.

Let us now examine the optical properties of the eye further.
We will pass over the individual defects of accommodation
which have been already mentioned as the cause of short and
long sight. These defects appear to be partly the result of our
artificial way of life, partly of the changes of old age. Elderly
persons lose their power of accommodation, and their range of
clear vision becomes confined within more or less narrow limits.
To exceed these they must resort to the aid of glasses.

But there is another quality which we expect of optical
instruments, namely, that they shall be free from dispersion —
that they be achromatic. Dispersion of light depends on the
fact that the coloured rays which united make up the white
light of the sun are not refracted in exactly the same degree by
any transparent substance known. Hence the size and position
of the optical images thrown by these differently coloured rays
are not quite the same : they do not perfectly overlap each other
in the field of vision, and thus the white surface of the image
appears fringed with a violet or orange, according as the red or
blue rays are broader. This of course takes off so far from the
sharpness of the outline.

Many of my readers know what a curious part the inquiry
into the chromatic dispersion of the eye has played in the
invention of achromatic telescopes. It is a celebrated instance
of how a right conclusion may sometimes be drawn from two
false premises. Newton thought he had discovered a relation
between the refractive and dispersive powers of various trans-
parent materials, from wtiich it followed that no achromatic
refraction was possible. Euler,1 on the other hand, concluded
that, since the eye is achromatic, the relation discovered by
Newton could not be correct. Reasoning from this assumption,
he constructed theoretical rules for making achromatic instru-
ments, and Dollancl 2 carrisd them out. But Dolland himself

1 Leonard Euler born at Basel, 1707 ; died at St. Petersburg, 1783.

2 John Dolland, F.R.S., born 1706; died in London, 17G1.

192 RECENT PROGRESS OF THE THEORY OF VISION.

observed that the eye could not be achromatic, because its
construction did not answer to Euler's rules; and at last
Fraunhofer l actually measured the degree of chromatic aberra-
tion of the eye. An eye constructed to bring red light from,
infinite distance to a focus on the retina can only do the same
with violet rays from a distance of two feet. With ordinary
light this is not noticed because these extreme colours are the
least luminous of all, and so the images they produce are
scarcely observed beside the more intense images of the inter-
mediate yellow, green, and blue rays. But the effect is very
striking when we isolate the extreme rays of the spectrum by
means of violet glass. Glasses coloured with cobalt oxide allow
the red and blue rays to pass, but stop the green and yellow
ones, that is, the brightest rays of the spectrum. If those of
my readers who have eyes of ordinary focal distance will look
at lighted street lamps from a distance with this violet glass,
they will see a red flame surrounded by a broad bluish violet halo.
This is the dispersive image of the flame thrown by its blue
and violet light. The phenomenon is a simple and complete
proof of the fact of chromatic aberration in the eye.

Now the reason why this defect is so little noticed under
ordinary circumstances, and why it is in fact somewhat less
than a glass instrument of the same construction would have,
is that the chief refractive medium of the eye is water, which
possesses a less dispersive power than glass.2 Hence it is that
the chromatic aberration of the eye, though present, does not
materially affect vision with ordinary white illumination.

A second defect which is of great importance in optical
instruments of high magnifying power is 'what is known as
spherical aberration. Spherical refracting surfaces approximately
unite the rays which proceed from a luminous point into a
single focus, only when each ray falls nearly perpendicularly
upon the corresponding part of the refracting surface. If all
those rays which form the centre of the image are to be exactly

1 Joseph Fraunhofer born in Bavaria, 1787; died at Munich, 182G.

2 But still the diffraction in the eye is rather greater than an instrument
made with water would produce under the same conditions.

THE EYE AS AN OPTICAL INSTRUMENT. 193

united, a lens with other than spherical surfaces must be used,
and this cannot be made with sufficient mechanical perfection.
Now the eye has its refracting surfaces partly elliptical ; and
so here again the natural prejudice, in its favour led to the
erroneous belief that spherical aberration was thus prevented.
But this was a still greater blunder. More accurate investi-
gation showed that much greater defects than that of spherical
aberration are present in the eye, defects which are easily
avoided with a little care in making optical instruments, and
compared with which the amount of spherical aberration becomes
very unimportant. The careful measurements of the curvature of
the cornea, first made by Senff of Dorpat, next, with a better adap-
ted instrument, the writer's ophthalmometer already referred to ,.
and afterwards carried out in numerous cases by Donders, Knapp,
and others, have proved that the cornea of most human eyes is
not a perfectly symmetrical curve, but is variously bent in different
directions. I have also devised a method of testing the ' center-
ing ' of an eye during life, i.e. ascertaining whether the cornea
and the crystalline lens are symmetrically placed with regard
to their common axis. By this means I discovered in the eyes
I examined slight but distinct deviations from accurate centering.
The result of these two defects of construction is the condition
called astigmatism, which is found more or less in most human
eyes, and prevents our seeing vertical and horizontal lines at the
same distance perfectly clearly at once. If the degree of astig-
matism is excessive, it can be obviated by the use of glasses with
cylindrical surfaces, a circumstance which .has lately much
attracted the attention of oculists.

Nor is this all. A refracting surface which is imperfectly
elliptical, an ill-centered telescope, does not give a single illu-
minated point as the image of a star, but, according to the sur-
face and arrangement of the refracting media, elliptic, circular
or linear images. Now the images of an illuminated point, as the
human eye brings them to focus, are even more inaccurate : they
are irregularly radiated. The reason of this lies in the con-
struction of the crystalline lens, the fibres of which are arran-
ged around six diverging axes (shown in Fig. 31). So that the

i. o

194 RECENT PROGRESS OF THE THEORY OF VISION.

rays which we see around stars and other distant lights are
images of the radiated structure of our lens ; and the univer-
sality of this optical defect is proved by any figure with diverg-
ing rays being called ' star-shaped.' It is from the same cause
that the moon, while her crescent is still narrow, appears to
many persons double or threefold.

Now, it is not too much to say that if an optician wanted to
sell me an instrument which had all these defects, I should think
myself quite justified in blaming his carelessness in the strongest
terms, and giving him back his instrument. Of course, I shall not
do this with my eyes, and shall be only too glad to keep them as
F -- long as I can — defects and all. Still,

the fact that, however bad they may
be, I can get no others, does not at
all diminish their defects, so long
as I maintain the narrow but in-
disputable position of a critic on
purely optical grounds.

We have, however, not yet done
with the list of the defects of the eye.
We expect that the optician
will use good, clear, perfectly
transparent glass for his lenses.
If it is not so, a bright halo
will appear around each illuminated surface in the image : what
should be black looks grey, what should be white is dull. But
this is just what occurs in the image our eyes give us of the
outer world. The obscurity of dark objects when seen near
very bright ones depends essentially on this defect ; and if we
throw a strong light l through the cornea and crystalline lens,
they appear of a dingy white, less transparent than the ' aqueous
humour ' which lies between them. This defect is most apparent
in the blue and violet rays of the solar spectrum : for there
comes in the phenomenon of fluorescence 2 to increase it.

1 E.g. from a lamp, concentrated by a bull's-eye condenser.

2 This term is given to the property which certain substam

of

THE EYE AS AN OPTICAL INSTRUMENT. 195

In fact, although the crystalline lens looks so beautifully
clear when taken out of the eye of an animal just killed, it is
far from optically uniform in structure. It is possible to see
the shadows and dark spots within the eye (the so-called ' en-
toptic objects ') by looking at an extensive bright surface — the
clear sky, for instance — through a very narrow opening. And
these shadows are chiefly due to the fibres and spots in the lens.

There are also a number of minute fibres, corpuscles and
folds of membrane, which float in the vitreous humour, and are
seen when they come close in front of the retina, even under
the ordinary conditions of vision. They are then called muscce
volitantes, because when the observer tries to look1 at them,
they naturally move with the movement of the eye. They seem
continually to flit away from the point of vision, and thus look
like flying insects. These objects are present in every one's eyes,
and usually float in the highest part of the globe of the eye, out
of the field of vision, whence on any sudden movement of the
eye they are dislodged and swim freely in the vitreous humour.
They may occasionally pass in front of the central pit, and so
impair sight. It is a remarkable proof of the way in which we
observe, or fail to observe, the impressions made on our senses,
that these musace volitantes often appear something quite new
and disquieting to persons whose sight is beginning to suffer
from any cause ; although, of course, there must have been the
same conditions long before.

A knowledge of the way in which the eye is developed in man
and other vertebrates explains these irregularities in the struc-
ture of the lens and the vitreous body. Both are produced by

becoming for a time faintly luminous as long as they receive violet and blue
light. The bluish tint of a solution of quinine, and the green colour of
uranium glass, depend on this property. The fluorescence of 'the cornea and
crystalline lens appears to depend upon the presence in their tissue of a very
small quantity of a substance like quinine. For the physiologist this property
is most valuable, for by its aid he can see the lens in a living eye by thruw-
ing on it a concentrated beam of blue light, and thus ascertain that it is placed
close behind the iris, not separated by a large ' posterior chamber,' as was long
supposed. But for seeing, the fluorescence of the cornea and lens is siuiply
disadvantageous.

i Vide supra, p. 189.

02

196 RECENT PROGRESS OF THE THEORY OF VISION.

an invagination of the integument of the embryo. A dimple
is first formed, this deepens to a round pit, and then expands
until its orifice becomes relatively minute, when it is finally
closed and the pit becomes completely shut off. The cells of
the scarf-skin which line this hollow form the crystalline lens,
the true skin beneath them becomes its capsule, and the loose
tissue which underlies the skin is developed into the vitreous
humour. The mark where the neck of the fossa was sealed is
still to be recognised as one of the ' entoptic images ' of many
adult eyes.

The last defect of the human eye which must be noticed is
•pIG 32 the existence of certain in-

equalities of the surface
which receives the optical
image. Not far from the
centre of the field of vision
there is a break in the
retina, where the optic-
nerve enters. Here there
is nothing but nerve fibres
and blood-vessels ; and, as
the cones are absent, any
rays of light which fall on
the optic nerve itself are
unperceived. This ' blind
spot' will therefore pro-
duce a corresponding gap
in the field of vision, where nothing will be visible. Fig. 32
shows the posterior half of the globe of a right eye which has
been cut across. R is the retina with its branching blood-vessels.
The point from which these diverge is that at which the optic
nerve enters. To the reader's left is seen the ' yellow spot.'

Now the gap caused by the presence of the optic nerve is no
slight one. It is about 6° in horizontal and 8° in vertical
dimension. Its inner border is about 12° horizontally distant
from the ' temporal ' or external side of the centre of distinct

THE EYE AS AN OPTICAL INSTRUMENT. 197

vision. The way to recognise this blind spot most readily is
doubtless known to many of my readers. Take a sheet of white
paper and mark on it a little cross ; then to the right of this, on
the same level, and about three inches off, draw a round black
spot half an inch in diameter. Now, holding the paper at arm's
length, shut the left eye, fix the right upon the cross, and bring
the paper gradually nearer. When it is about eleven inches
from the eye, the black spot will suddenly disappear, and will
again come into sight as the paper is moved nearer.

This blind spot is so large that it might prevent our seeing
eleven full moons if placed side by side, or a man's face at a
distance of only six or seven feet. Mariotte,1 who discovered
the phenomenon, amused Charles II. and his courtiers by
showing them how they might see each other with their heads
cut off.

There are, in addition, a number of smaller gaps in the field
of vision, in which a small bright point, a fixed star for example,
may be lost. These are caused by the blood-vessels of the retina.
The vessels run in the front layers, and so cast their shadow on
the part of the sensitive mosaic which lies behind them. The
larger ones shut off the light from reaching the rods and cones
altogether, the more slender at least limit its amount.

These splits in the picture presented by the eye may be re-
cognised by making a hole in a card with a fine needle, and
looking through it at the sky, moving the card a little from side
to side all the time. A still better experiment is to throw sun-
light through a small lens upon the white of the eye at the
outer angle (temporal canthus), while the globe is turned as
much as possible inwards. The shadow of the blood-vessels is
then thrown across on to the inner wall of the retina, and we
see them as gigantic branching lines, like fig. 32 magnified.
These vessels lie in the front layer of the retina itself, and, of
course, their shadow can only be seen when it falls on the
proper sensitive layer. So that this phenomenon furnishes a
proof that the hindmost layer is that which is sensitive to light.
And by its help it has become possible actually to measure the
1 Edme. Mariotte, born in Burgundy, died at Paris, 1684.

J198 RECENT PROGRESS OF THE THEORY OF VISION.

distance between the sensitive and the vascular layers of the
retina. It is done as follows : —

If the focus of the light thrown on to the white of the eye
(the sclerotic) is moved slightly backwards and forwards, the
shadow of the blood-vessels and its image in the field of vision
will, of course, move also. The extent of these movements can
be easily measured, and from these data Heinrich Miiller, of
Wiirzburg — whose too early loss to science we still deplore — de-
termined the distance between the two foci, and found it exactly
to equal the thickness which actually separates the layer of rods
and cones from the vascular layer of the retina.

The condition of the point of clearest vision (the yellow
spot) is disadvantageous in another way. It is less sensitive to
weak light than the other parts of the retina. It has been long
known that many stars of inferior magnitude — for example, the
Coma Berenicce and the Pleiades— are seen more brightly if
looked at somewhat obliquely than when their rays fall fall
upon the eye. This can be proved to depend partly on the
yellow colour of the macula, which weakens blue more than
other rays. It may also be partly the result of the absence of
vessels at this yellow spot which has baeii noticed above, which
interferes with its free communication with the life-giving
blood.

All these imperfections would be exceedingly troublesome in
an artificial camera obscura and in the photographic picture it
produced. But they are not so in the eye — so little, indeed, that
it was very difficult to discover some of them. The reason of
their not interfering with our perception of external objects is
not simply that we have two eyes, and so one makes up for the
defects of the other. FOF even when we da not use both, and in
the case of persons blind of one eye, the impression we receive
from the field of vision is free from the defects which the irre-
gularity of the retina would otherwise occasion. The chief
reason is that we are continually moving the eye, and also that
the imperfections almost always, affect those parts of the field to
which we are not at the moment directing our attention.

THE EYE AS AN OPTICAL INSTRUMENT. 199

But, after all it remains a wonderful parodox, that we are
so slow to observe these and other peculiarities of vision (such
as the after-images of bright objects), so long as they are not
strong enough to prevent our seeing external objects. It is a
fact which we constantly meet, not only in optics, but in study-
ing the perceptions produced by other senses on the conscious-
ness. The difficulty with which we perceive the defect of the
blind spot is well shown by the history of its discovery. Its
existence was first demonstrated by theoretical arguments.
While the long controversy whether the perception of light re-
sided in the retina or the choroid was still undecided, Mariotte
asked himself what perception there was where the choroid is
deficient. He made experiments to ascertain this point, and in
the course of them discovered the blind spot. Millions of men
had used their eyes for ages, thousands had thoiight over the
nature and cause of their functions, and, after all, it was only
by a remarkable combination of circumstances that a simple
phenomenon was noticed which would apparently have revealed
itself to the slightest observation. Even now, anyone who tries
for the first time to repeat the experiment which demonstrates
the existence of the blind spot, finds it difficult to divert his
attention from the fixed point of clear vision, without losing
sight of it in .the attempt. Indeed, it is only by long practice in
optical experiments that even an experienced observer is able, as
soon as he shuts one eye, to recognise the blank space in the field
of vision which corresponds to the blind spot.

Other phenomena of this kind have only been discovered by
accident, and usually by persons whose senses were peculiarly
acute, and whose power of observation was unusually stimu-
lated. Among these may be mentioned Goethe, Purkinje,1 and
Johannes Miiller.2 When a subsequent observer tries to repeat
on his own eyes these experiments as he finds them described,
it is of course easier for him than for the discoverer ; but even

1 A distinguished embryologist, for many years professor at Breslau : he died
at Prague, 1869, set. 82.

2 A great biologist, in the full sense of the term. He was professor of
physiology at Berlin, and died 18J8, net. 57. His Manual of Physiology was
translated into English by the late Dr. Baly.— TR.

200 RECENT PROGRESS OF THE THEORY OF VISION.

now there are many of the phenomena described by Purkinje
which have never been seen by anyone else, although it cannot
be certainly held that they depended on individual peculiarities
of this acute observer's eyes.

The phenomena of which we have spoken, and a number
of others also, may be explained by the general rule that
it is much easier to recognise any change in the condition of
a nerve than a constant and equable impression on it. In
accordance with this rule, all peculiarities in the excitation of
separate nerve fibres, which are equally present during the
whole of life (such as the shadow of the blood-vessels of the eye.
the yellow colour of the central pit of the retina, and most ot
the fixed entoptic images), are never noticed at all ; and if we
want to observe them we must employ unusual modes of illu-
mination and, particularly, constant change of its direction.

According to our present knowledge of the conditions of
nervous excitation, it seems to me to be very unlikely that we
have here to do with a simple property of sensation ; it must, I
think, be rather explained as a phenomenon belonging to our
power of attention, and I now only refer to the question in
passing, since its full discussion will come afterwards in its
proper connection.

So much for the physical properties of the eye. If I am
asked why I have spent so much time in explaining its imper-
fection to my readers, I answer, as I said at first, that I have
not done so in order to depreciate the performances of this
wonderful organ or to diminish our admiration of its construc-
tion. It was my object to make the reader understand, at the
first step of our inquiry, that it is not any mechanical perfection
of the organs of our senses which secures for us such wonderfully
true and exact impressions of the outer world. The next section
of this inquiry will introduce much bolder and more paradoxical
conclusions than any I have yet stated. We have now seen
that the eye in itself is not by any means so complete an optical
instrument as it at first appears : its extraordinary value depends
upon the way in which we use it : its perfection is practical, not

THE EYE AS AN OPTICAL INSTRUMENT. 201

absolute, consisting not in the avoidance of every error, but in
the fact that all its defects do not prevent its rendering us the
most important and varied services.

From this point of view, the study of the eye gives us a deep
insight into the true character of organic adaptation generally.
And this consideration becomes still more interesting when
brought into relation with the great and daring conceptions
which Darwin has introduced into science, as to the means by
which the progressive perfection of the races of animals and
plants has been carried on. Wherever we scrutinise the con-
struction of physiological organs, we find the same character of
practical adaptation to the wants of the organism ; although,
perhaps, there is no instance which we can follow out so minutely
as that of the eye.

For the eye has every possible defect that can be found in an
optical instrument, and even some which are peculiar to itself;
but they are all so counteracted, that the inexactness of the
image which results from their presence very little exceeds,
under ordinary conditions of illumination, the limits which are
set to the delicacy of sensation by the dimensions of the retinal
cones. But as soon as we make our observations under some-
what changed conditions, we become aware of the chromatic
aberration, the astigmatism, the blind spots, the venous shadows,
the imperfect transparency of the media, and all the other de-
fects of which I have spoken.

The adaptation of the eye to its function is, therefore, most
complete, and is seen in the very limits which are set to its
defects. Here the result which may be reached by innumerable
generations working under the Darwinian law of inheritance,
coincides with what the wisest Wisdom may have devised
beforehand. A sensible man will not cut firewood with a razor,
and so we may assume that each step in the elaboration of the
eye must have made the organ more vulnerable and more slow
in its development. We must also bear in mind that soft,
watery animal textures must always be unfavourable and diffi-
cult material for an instrument of the mind.

One result of this mode of construction of the eye, of which

202 RECENT PROGRESS OF THE THEORY OF VISION.

we shall see the importance bye and bye, is that clear and com-
plete apprehension of external objects by the sense of sight is
only possible when we direct our attention to one part after
another of the field of vision in the manner partly described
above. Other conditions, which tend to produce the same limit-
ation, will afterwards come under our notice.

But, apparently, we are not yet come much nearer to under-
standing sight. We have only made one step : we have learnt
how the optical arrangement of the eye renders it possible to
separate the rays of light which come in from all parts of the
field of vision, and to bring together again all those that have
proceeded from a single point, so that they may produce their
effect upon a single fibre of the optic nerve.

Let us see, therefore, how much we know of the sensations
of the eye, and how far this will bring us towards the solution
of the problem.

II. THE SEXSATION OF SIGHT.

IN the first section of our subject we have followed the course
of the rays of light as far as the retina, and seen what is the
result produced by the peculiar arrangement of the optical
apparatus. The light which is reflected from the separate
illuminated points of external objects is again united in the
sensitive terminal structures of separate nerve fibres, and thus
throws them into action without affecting their neighbours.
At this point the older physiologists thought they had solved
the problem , so far as it appeared to them to be capable of solu-
tion. External light fell directly upon a sensitive nervous
structure in the retina, and was, as it seemed, directly felt there.
But during the last century, and still more during the 6rst
quarter of this, our knowledge of the processes which take
place in the nervous system was so far developed, that Johannes
Miiller, as early as the year 1826,1 when writing that great
work on the ' Comparative Physiology of Vision,' which marks

1 The year in which he was appointed Extraordinary Professor of Phy-
siology in the University of Bonn.

THE SENSATION OF SIGHT. 203

an epoch in science, was able to lay down the most important
principles of the theory of the impressions derived from the
senses. These principles have not only been confirmed in all
important points by subsequent investigation, but have proved
of even more extensive application than this eminent physio-
logist could have suspected.

The conclusions which he arriysd at are generally compre-
hended under the name of the theory of the Specific Action of
the Senses. They are no longer so novel that they can be
reckoned among the latest advances of the theory of vision,
which form the subject of the present essay. Moreover, they
have been frequently expounded in a popular form by others as
well as by myself.1 But that part of the theory of vision with
which we are now occupied is little more than a further develop-
ment of the theory of the specific action of the senses. I must,
therefore, beg my reader to forgive me if, in order to give him
a comprehensive view of the whole subject in its proper connec-
tion, I bring before him much which he .already knows, while I
also introduce the more recent additions to our knowledge in
their appropriate places.

All that we apprehend of the external world is brought to
our consciousness by means of certain changes which are pro-
duced in our organs of sense by external impressions, and
transmitted to the brain by the nerves. It is in the brain that
these impressions first become conscious sensations, and are
combined so as to produce our conceptions of surrounding ob-
jects. If the nerves which convey these impressions to the
brain are cut through, thje sensation, and the perception of the
impression, immediately cease. In the case of the eye, the
proof that visual perception is not produced directly in each
retina, but only in the brain itself by means of the impressions
transmitted to it from both eyes, lies in the fact (which I shall
afterwards more fully explain) that the visual impression of any
solid object of three dimensions is only produced by the combi-
nation of the impressions derived from both eyes.

1 ' On the Nature of Special Sensations in Man,' KSnigsberger naturu>iss",n-
schaftliche Unterhaltungen, vol. iii. 1852. ' Human Vision,' a popular Scien-
tific Lecture by H. Helmholtz, Leipzig, 1855.

204 RECENT PROGRESS OF THE THEORY OF VISION.

What, therefore, we directly apprehend is not the immediate
action of the external exciting cause upon the ends of our
nerves, but only the changed condition of the nervous fibres
which we call the state of excitation or functional activity.

Now all the nerves of the body, so far as we at present
know, have the same structure, and the change which we call
excitation is in each of them a process of precisely the same
kind, whatever be the function it subserves. For while the
task of some nerves is that already mentioned, of carrying sen-
sitive impressions from the external organs to the brain, others
convey voluntary impulses in the opposite direction, from the
brain to the muscles, causing them to contract, and so moving
the limbs. Other nerves, again, carry an impression from the
brain to certain glands, and call forth their secretion, or to the
heart and to the blood-vessels, and regulate the circulation.
But the fibres of all these nerves are the same clear cylindrical
threads of microscopic minuteness, containing the same oily and
albuminous material. It is true that there is a difference in the
diameter of the fibres, but this, so far as we know, depends only
upon minor causes, such as the necessity of a certain strength
and of getting room for a certain number of independent con-
ducting fibres. It appears to have no relation to their pe-
culiarities of function.

Moreover, all nerves have the same electro-motor actions, as
the researches of Du Bois Reymond l prove. In all of them the
condition of excitation is called forth by the same mechanical,
electrical, chemical, or thermometric changes. It is propagated
with the same rapidity, of about one hundred feet in the
second, to each end of the fibres, and produces the same changes
in their electro-motor properties. Lastly, all nerves die when
submitted to like conditions, and, with a slight apparent differ-
ence according to their thickness, undergo the same coagulation
of their contents. In short, all that we can ascertain of ner-
vous structure and function, apart from the action of the other
organs with which they are united and in which during life we
see the proofs of their activity, is precisely the same for all the
1 Professor of Physiology in the University of Berlin.

THE SENSATION OF SIGHT. 205

different kinds of nerves. Very lately tbe French physiologists
Philippeau and Vulpian, after dividing the motor and sensitive
nerves of the tongue, succeeded in getting the upper half of the
sensitive nerve to unite with the lower half of the motor.
After the wound had healed, they found that irritation of the
upper half, which in normal conditions would have been felt as
a sensation, now excited the motor branches below, and thus
caused the muscles of the tongue to move. We conclude from
these facts that all the difference which is seen in the excitation
of different nerves depends only upon the difference of the
organs to which the nerve is united, and to which it transmits
the state of excitation.

The nerve fibres have been often compared with telegraphic
wires traversing a country, and the comparison is well fitted to
illustrate this striking and important peculiarity of their mode
of action. In the network of telegraphs we find everywhere
the same copper or iron wires carrying the same kind of move-
ment, a stream of electricity, but producing the most different
results in the various stations according to the auxiliary apparatus
with which they are connected. At one station the effect is the
ringing of a bell, at another a signal is moved, and at a third a
recording instrument is set to work. Chemical decompositions
may be produced which will serve to spell out the messages, and
even the human arm may be moved by electricity so as to
convey telegraphic signals. When the Atlantic cable was being
laid, Sir William Thomson found that the slightest signals
could be recognised by the sense of taste, if the wire was laid
upon the tongue. Or, again, a strong electric current may be
transmitted by telegraphic wires in order to ignite gunpowder
for blasting rocks. In short, every one of the hundred different
actions which electricity is capable of producing may be called
forth by a telegraphic wire laid to whatever spot we please, and
it is always the same process in the wire itself which leads to
these diverse consequences. Nerve fibres and telegraphic wires
are equally striking examples to illustrate the doctrine that the
same causes may, under different conditions, produce different
results. However commonplace this may now sound, mankind

206 RECENT PROGRESS OF THE THEORY OF VISION.

had to work long and hard before it was understood, and before
this doctrine replaced the belief previously held in the constant
and exact correspondence between cause and effect. And we
can scarcely say that the truth is even yet universally recog-
nised, since in our present subject its consequences have been
till lately disputed.

Therefore, as motor nerves, when irritated, produce move-
ment, because they are connected with muscles, and glandular
nerves secretion, because they lead to glands, so do sensitive
nerves, when they are irritated, produce sensation, because they
are connected with sensitive organs. But we have very different
kinds of sensation. In the first place, the impressions derived
from external objects fall into five groups, entirely distinct from
each other. These correspond to the five senses, and their
difference is so great that it is not possible to compare in quality
a sensation of light with one of sound or of smell. We will
name this difference, so much deeper than that between com-
parable qualities, a difference of the mode, or kind, of sensation,
and will describe the differences between impressions belonging
to the same sense (for example, the difference between the
various sensations of colour) as a difference of quality.

Whether by the irritation of a nerve we produce a muscular
movement, a secretion or a sensation, depends upon whether we
are handling a motor, a glandular, or a sensitive nerve, and not
at all upon what means of irritation we may use. It may be
an electrical shock, or tearing the nerve, or cutting it through,
or moistening it with a solution of salt, or touching it with a
hot wire. In the same way (and this great step in advance was
due to Johannes M tiller) the kind of sensation which will ensue
when we irritate a sensitive nerve, whether an impression of
light, or of sound, or of feeling, or of smell, or of taste, will be
produced, depends entirely upon which sense the excited nerve
subserves, and not at all upon the method of excitation we
adopt.

Let us now apply this to the optic nerve, which is the object
of our present inquiry. In the first place, we know that no
kind of action upon any part of the body, except the eye and

THE SENSATION OF SIGHT. 207

the nerve which belongs to it, can ever produce the sensation of
light. The stories of somnambiilists, which are the only argu-
ments that can be adduced against this belief, we may be
allowed to disbelieve. But, on the other hand, it is not light
alone which can produce the sensation of light upon the eye,
but also any other power which can excite the optic nerve. If
the weakest electrical currents are passed through the eye they
produce flashes of light. A blow, or even a slight pressure
made upon the side of the eyeball with the finger, makes an
impression of light in the darkest room, and, under favourable
circumstances, this may become intense. In these cases it is
important to remember that there is no objective light produced
in the retina, as some of the older physiologists assumed, for
the sensation of light may be so strong that a second observer
could not fail to see through the pupil the illumination of the
retina which would follow, if the sensation were really produced
by an actual development of light within the eye. But nothing
of the sort has ever been seen. Pressure or the electric current
excites the optic nerve, and therefore, according to Miiller's law,
a sensation of light results, but under these circumstances,
at least, there is not the smallest spark of actual light.

In the same way, increased pressure of blood, its abnormal
constitution in fevers, or its contamination with intoxicating or
narcotic drugs, can produce sensations of light to which no
actual light corresponds. Even in cases in which an eye is
entirely lost by accident or by an operation, the irritation of the
stump of the optic nerve while it is healing is capable of pro-
ducing similar subjective effects. It follows from these facts
that the peculiarity in kind which distinguishes the sensation of
light from all others does not depend upon any peculiar qualities
of light itself. Every action which is capable of exciting the
optic nerve is capable of producing the impression of light ; and
the purely subjective sensation thus produced is so precisely
similar to that, caused by external light, that persons unacquain-
ted with these phenomena readily suppose that the rays they
pee are real objective beams.

Thus we see that external light produces no other effects in

208 RECENT PROGRESS OF THE THEORY OF VISION.

the optic nerve than other agents of an entirely different nature.
In one respect only does light differ from the other causes which
are capable of exciting this nerve : namely, that the retina,
being placed at the back of the firm globe of the eye, and further
protected by the bony orbit, is almost entirely withdrawn from
other exciting agents, and is thus only exceptionally affected by
them, while it is continually receiving the rays of light which
stream in upon it through the transparent media of the eye.

On the other hand, the optic nerve, by reason of the peculiar
structures in connection with the ends of its fibres, the rods and
cones of the retina, is incomparably more sensitive to rays of
light than any other nervous apparatus of the body, since the
rest can only be affected by rays which are concentrated enough
to produce noticeable elevation of temperature.

This explains why the sensations of the optic nerve are for
us the ordinary sensible sign of the presence of light in the field
of vision, and why we always connect the sensation of light
with light itself, even where they are really unconnected. But
we must never forget that a survey of all the facts in their natu-
ral conneection puts it beyond doubt that external light is only
one of the exciting causes capable of bringing the optic nerve
into functional activity, and therefore that there is no exclusive
relation between the sensation of light and light itself.

Now that we have considered the action of excitants upon
the optic nerve in general, we will proceed to the qualitative
differences of the sensation of light, that is to say, to the various
sensations of colour. We will try to ascertain how far these
differences of sensation correspond to actual differences in exter-
nal objects.

Light is known in Physics as a movement which is propa-
gated by successive waves in the elastic ether distributed
through the universe, a movement of the same kind as the circles
which spread upon the smooth surface of a pond when a stone
falls on it, or the vibration which is transmitted through our
atmosphere as sound. The chief difference is, that the rate with
which light spreads, and the rapidity of movement of the minute

THE SENSATION OF SIGHT. 209

particles which form the waves of ether, are both enormously
greater than that of the waves of water or of air. The waves
of light sent forth from the sun differ exceedingly in size, just as
the little ripples whose summits are a few inches distant from
each other differ from the waves of the ocean, between whose
foaming crests lie valleys of sixty or a hundred feet. But, just
as high and low, short and long waves, on the surface of water,
do not differ in kind, but only in size, so the various waves
of light which stream from the sun differ in their height and
length, but move all in the same manner, and show (with certain
differences depending upon the length of the waves) the same
remarkable properties of reflection, refraction, interference,
diffraction, and polarisation. Hence we conclude that the
undulating movement of the ether is in all of them the same-
We must particularly note that the phenomena of interference,
under which light is now strengthened, and now obscured by
light of the same kind, according to the distance it has traversed,
prove that all the rays of light depend upon oscillations of waves ;
and further, that the phenomena of polarisation, which differ
according to different lateral directions of the rays, show that
the particles of ether vibrate at right angles to the direction in
which the ray is propagated.

All the different sorts of rays which T have mentioned
produce one effect in common. They raise the temperature of
the objects on which they fall, and accordingly are all felt by our
skin as rays of heat.

On the other hand, the eye only perceives one part of these
vibrations of ether as light. It is not at all cognisant of the
waves of great length, which I have compared with those of the
ocean ; these, therefore, are named the dark heat-rays. Such
are those which proceed from a warm but not red-hot stove, and
which we recognise as heat, but not as light.

Again, the waves of shortest length, which correspond with
the very smallest ripples pi'oduced by a gentle breeze, are so
slightly appreciated by the eye, that such rays are also generally
regarded as invisible, and are known as the dark cheimcK'vays.

Between the very long and the very short waves of ether
I. p

210 RECENT PROGRESS OF THE THEORY OF VISION.

there are waves of intermediate length, which strongly affect
the eye, but do not essentially differ in any other physical
property from the dark rays of heat and the dark chemical rays.
The distinction between the visible and invisible rays depends
only on the different length of their waves and the different
physical relations which result therefrom. We call these middle
rays Light, because they alone illuminate our eyes.

When we consider the heating property of these rays we also
call them luminous heat ; and because they produce such a very
different impression on our skin and on our eyes, heat was
universally considered as an entirely different kind of radiation
from light, until about thirty years ago. But both kinds of ra-
diation are inseparable from one another in the illuminating rays
of the sun ; indeed, the most careful recent investigations prove
that they are precisely identical. To whatever optical processes
they may be subjected, it is impossible to weaken their illumi-
nating power without at the same time, and in the same degree,
diminishing their heating and their chemical action. Whatever
produces an undulatory movement of ether, of course produces
thereby all the effects of the undulation, whether light, or heat,
or fluorescence, or chemical change.

Those undulations which strongly affect our eyes, and which
we call light, excite the impression of different colours, accord-
ing to the length of the waves. The undulations with the
longest waves appear to us red ; and as the length of the waves
gradually diminishes they seem to be golden-yellow, yellow,
green, blue, violet, the last colour being that of the illuminating
rays which have the smallest wave-length. This series of
colours is universally known in the rainbow. We also see it if we
look towards the light through a glass prism, and a diamond
sparkles with hues which follow in the same order. In passing
through transparent prisms, the primitive beam of white light,
which consists of a multitude of rays of various colour and
various wave-length, is decomposed by the different degree of re-
fraction of its several parts, referred to in the last essay ; and
thus each of its component hues appears separately. These

THE SENSATION OF SIGHT. 211

colours of the several primary forms of light are best seen in
the spectrum produced by a narrow streak of light passing
through a glass prism ; they are at once the fullest and the most
brilliant which the external world can show.

When several of these colours are mixed together, they give
the impression of a new colour, which generally seems more or
less white. If they were all mingled in precisely the same pro-
portions in which thoy are combined in the sun-light, they
would give the impression of perfect white. According as the
rays of greatest, middle, or least wave-length predominate in
such a mixture, it appears as reddish-white, greenish-white,
bluish-white, and so on.

Everyone who has watched a painter at work knows that
two colours mixed together give a
new one. Xow, although the results
of the mixture of coloured light
differ in many particulars from those
of the mixture of pigments, yet on
the whole the appearance to the eye
is similar in both cases. If we
allow two different coloured lights to
fall at the same time upon a white
screen, or upon the same part of

our retina, we see only a single compound colour, more or less
different from the two original ones.

The most striking difference between the mixture of pig-
ments and that of coloured light is, that while painters make
green by mixing blue and yellow pigments, the union of blue
and yellow rays of light produces white. The simplest way of
mixing coloured light is shown in Fig. 33. p is a small flat
piece of glass ; b and g are two coloured wafers. The observer
looks at b through the glass plate, while g is seen reflected in
the same ; and if g is put in a proper position, its image exactly
coincides with that of b. It then appears as if there was a
single wafer at b, with a colour produced by the mixture of the
two real ones. In this experiment the light from b, which
traverses the glass pane, actually unites with that from g, which
p2

212 RECENT PROGRESS OF THE THEORY OF VISION.

is reflected from it, and the two combined pass on to the retina
at o. In general, then, light, which consists of undulations of
different wave-lengths, produces different impressions upon our
eye, namely, those of different colours. But the number of
hues which we can recognise is much smaller than that of the
various possible combinations of rays with different wave-lengths
which external objects can convey to our eyes. The retina
cannot distinguish between the white which is produced by the
union of scarlet and bluish-green light, and that which is com-
posed of yellowish-green and violet, or of yellow and ultramarine
blue, or of red, green, and violet, or of all the colours of the
spectrum united. All these combinations appear identically as
white ; and yet, from a physical point of view, they are very
different. In fact, the only resemblance between the several
combinations just mentioned is, that they are indistinguishable
to the human eye. For instance, a surface illuminated with
red and bluish-green light would come out black in a photograph ;
while another lighted with yellowish green and violet would
appear very bright, although both surfaces alike seem to the
eye to be simply white. Again, if we successively illuminate
coloured objects with white beams of light of various composi-
tion, they will appear differently coloured. And whenever we
decompose two such beams by a prism, or look at them through
a, coloured glass, the difference batween them at once becomes
evident.

Other colours, also, especially when they are not strongly
pronounced, may, like pure white light, be composed of very
different mixtures, and yet appear indistinguishable to the eye,
while in every other property, physical or chemical, they are
entirely distinct.

Newton first showed how to represent the system of colours
distinguishable to the eye in a simple diagrammatic form ; and
by the same means it is comparatively easy to demonstrate the
law of the combination of colours. The primary colours of the
spectrum are arranged in a series around the circumference of a
circle, beginning with red, and by imperceptible degrees passing

THE SENSATION OF SIGHT. 213

through the various hues of the rainbow to violet. The red
and violet are united by shades of purple, which on the one side
pass off to the indigo and blue tints, and on the other through
crimson and scarlet to orange. The middle of the circle is left
white, and on lines which run from the centre to the circumfer-
ence are represented the various tints which can be produced by
diluting the full colours of the circumference until they pass
into white. A colour-disc of this kind shows all the varieties
of hue which can be produced with the same amount of light.
It will now be found possible so to arrange the places of the
several colours in this diagram, and the quantity of light which
each reflects, that when we have ascertained the resultants of
FIG. 84.

Green

Blue

Violet Purple

two colours of different known strength of light (in the same
way as we might determine the centre of gravity of two bodies
of different known weights), we shall then find their combina-
tion-colour at the ' centre of gravity ' of the two amounts of
light. That is to say, that in a properly constructed colour-disc,
the combination-colour of any two colours will be found upon
a straight line drawn from between them ; and compound colours
which contain more of one than of the other component hue,
will be found in that proportion nearer to the former, and further
from the latter.

We find, however, when we have drawn our diagram, that
those colours of the spectrum which are most saturated in nature

214 RECENT PROGRESS OF THE THEORY OF VISION.

and which must therefore be placed at the greatest distance from
the central white, will not arrange themselves in the form of a
circle. The circumference of the diagram presents three pro-
jections corresponding to the red, the green, and the violet, so
that the colour circle is more properly a triangle, with the
corners rounded off, as seen in Fig. 34. The continuous line
represents the curve of the colours of the spectrum, and the
small circle in the middle the white. At the corners are the
three colours I have mentioned,1 and the sides of the triangle
show the transitions from red through yellow into green, from
green through bluish-green and ultramarine to violet, and from
violet through purple to scarlet.

Newton used the diagram of the colours of the spectrum (in
a somewhat different form from that just given) only as a con-
venient way of representing the facts to the eye.; but recently
Maxwell has succeeded in demonstrating the strict and even
quantitative accuracy of the principles involved in the construc-
tion of this diagram. His method is to produce combinations of
colours on swiftly rotating discs, painted of various tints in
sectors. When such a disc is turned rapidly roiand, so that the
eye can no longer follow the separate hues, they melt into a uni-
form combination-colour, and the quantity of light which belongs
to each can be directly measured by the breadth of the sector of
the circle it occupies. Now the combination-colours which are
produced in this manner are exactly those which would result if
the same qualities of coloured light ilhiminated the same surface
continuously, as can be experimentally proved. Thus have the
relations of size and number been introduced into the apparently
inaccessible region of colours, and their differences in quality
have been reduced to relations of quantity.

All differences between colours may be reduced to three, which
may be described as difference of tone, difference of fulness, or, as
it is technically called, ' saturation,' and difference of brightness.
The differences of tone are those which exist between the several

1 The author has restored violet as a primitive colour in accordance with
the experiments of J. J. Miiller, having in the first edition adopted the opinion
of Maxwell that it is blue.

THE SENSATION OF SIGHT. 215

colours of the spectrum, and to which we give the names red,
yellow, blue, violet, purple. Thus, with regard to tone, colours
form a series which returns upon itself ; a series which we com-
plete when we allow the terminal colours of the rainbow to pass
into one another through purple and crimson. It is in fact the
same which we describe as arranged around the circumference of
the colour disc.

The fulness or saturation of colours is greatest in the pure
tints of the spectrum, and becomes less in proportion as they are
mixed with white light. This, at least, is true for colours pro-
duced by external light, but for our sensations it is possible to
increase still further the apparent saturation of colour, as we
shall presently see. Pink is a whitish-crimson, flesh-colour a
whitish-scarlet, and so pale green, straw-colour, light blue, Ac.,
are all produced by diluting the corresponding colours with
white. All compound colours are, as a rule, less saturated than
the simple tints of the spectrum.

Lastly, we have the difference of brightness, or strength of
light, which is not represented in the colour-disc. As long as we
observe coloured rays of light, difference in brightness appeal's
to be only one of quantity, not of quality. Black is only dark
ness — that is, simple absence of light. But when we examine
the colours of external objects, black corresponds just as much to
a peculiarity of surface in reflection, as does white, and therefore
has as good a right to be called a colour. And as a matter of
fact, we find in common language a series of terms to express
colours with a small amount of light. We call them dark (or
rather in English, deep) when they have little light but are 'full '
in tint, and grey when they are 'pale.' Thus dark blue conveys
the idea of depth in tint, of a full blue with a small amount of
light ; while grey- blue is a pale blue with a small amount of
light. In the same way, the colours known as maroon, brown,
and olive are dark, more or less saturated tints of red, yellow
and green respectively.

In this way we may reduce all possible actual (objective)
differences in colour, so far as they are appreciated by the eye, to
three kinds ; difference of hue (tone), difference of fulness (satura-

216 RECENT PROGRESS OF THE THEORY OF VISION.

tion), and difference of amount of illumination (brightness). It
is in this way that we describe the system of colours in ordinary
language. But we are able to express this threefold difference
in another way.

I said above that a properly constructed colour-disc ap-
proaches a triangle in its outline. Let us suppose for a moment
that it is an exact rectilinear triangle, as made by the dotted line
in Fig. 34 ; how far this differs from the actual condition we
shall have afterwards to point out. Let the colours red, green,
and violet be placed at the corners, then we see the law which
was mentioned above : namely that all the colours in the in-
terior and on the sides of the triangle are compounds of the
three at its corners. It follows that all differences of hue depend
upon combinations in different proportions of the three primary
colours. It is best to consider the three just named as primary ;
the old ones red, yellow, and blue are inconvenient, and were
only chosen from experience of painters' colours. It is impossible
to make a green out of blue and yellow light.

We shall better understand the remarkable fact that we are
able to refer all the varieties in the composition of external light
to mixtures of three primitive colours, if in this respect we
compare the eye with the ear.

Sound, as I mentioned before, is, like light, an undulating
movement, spreading by waves. In the case of sound also, we
have to distinguish waves of various length which produce upon
our ear impressions of different quality. We recognise the long
waves as low notes, the short as high-pitched, and the ear may
receive at once many waves of sound — that is to say, many
notes. But here these do not melt into compound notes in the
same way that colours, when perceived at the same time and
place, melt into compound colours. The eye cannot tell the
difference, if we substitute orange for red and yellow ; but if we
hear the notes C and E sounded at the same time, we cannot
put D instead of them, without entirely changing the impres-
sion upon the ear. The most complicated harmony of a full
orchestra becomes changed to our perception if we alter any one
of its notes. No accord (or consonance of several tones) is, at

THE SENSATION OF SIGHT. 217

least for the practised ear, completely like another, composed of
different tones ; whereas, if the ear perceived musical tones as
the eye colours, every accord might be completely represented by
combining only three constant notes, one very low, one very
high, and one intermediate, simply changing the relative strength
of these three primary notes to produce all possible musical
effects.

In reality we find that an accord only remains unchanged to
the ear, when the strength of each separate tone which it con-
tains remains unchanged. Accordingly, if we wish to describe
it exactly and completely, the strength of each of its component
tones must be exactly stated.

In the same way, the physical nature of a particular kind of
light can only be fully ascertained by measuring and noting the
amount of light of each of the simple colours which it contains.
But in sunlight, in the light of most of the stars, and in flames,
we find a continuous transition of colours into one another
through numberless intermediate gradations. Accordingly,
we must ascertain the amount of light of an infinite number of
compound rays if we would arrive at an exact physical know-
ledge of sun or star light. In the sensations of the eye we need
distinguish for this purpose only the varying intensities of three
components.

The practised musician is able to catch the separate notes of
the various instruments among the complicated harmonies of an
entire orchestra, but the optician cannot directly ascertain the
composition of light by means of the eye ; he must make use of
the prism to decompose the light for him. As soon, however,
as this is done, the composite character of light becomes ap-
parent, and he can then distinguish the light of separate fixed
stars from one another by the dark and bright lines which the
spectrum shows him, and can recognise what chemical elements
are contained in flames which are met with on the earth, ov
even in the intense heat of the sun's atmosphere, in the fixed stars
or in the nebulae. The fact that light derived from each separate
source carries with it certain permanent physical peculiarities
is the foundation of spectrum analysis — that most brilliant dis-

218 RECENT PROGRESS OF THE THEORY OF VISION.

covery of recent years, which has opened the extreme limits of
celestial space to chemical analysis.

- There is an extremely interesting and not very uncommon
defect of sight •which is known as colour-blindness. In this
condition the differences of colour are reduced to a still more
simple system than that described above ; namely, to combina-
tions of only two primary colours. Persons so affected are called
colour blind, because they confound certain hues which appear
very different to ordinary eyes. At the same time they distin-
guish other colours, and that quite as accurately, or even (as it
seems) rather more accurately, than ordinary people. They are
usually ' red-blind '; that is to say, there is no red in their
system of colours, and accordingly they see no difference which
is produced by the addition of red. All tints are for them
varieties of blue and green, or, as they call it, yellow. Accord-
ingly scarlet, flesh-colour, white, and bluish- green appear to
them to be identical, or at the utmost to differ in brightness.
The same applies to crimson, violet, and blue, and to red,
orange, yellow, and green. The scarlet flowers of the geranium
have for them exactly the same colours as its leaves. They
cannot distinguish between the red and the green signals of
trains. They cannot see the red end of the spectriTm at all.
Very full scarlet appears to them almost black, so that a red-
blind Scotch clergyman went to biay scarlet cloth for his gown,
thinking it was black.1

In this particular of discrimination of colours, we find
remarkable inequalities in different parts of the retina. In the
first place, all of us are red-blind in the outermost part of our
field of vision. A geranium-blossom when moved backwards
and forwards just within the field of sight, is only recognised as
a moving object. Its colour is not seen, so that if it is waved
in front of a mass of leaves of the same plant it cannot be dis-
tinguished from them in hue. In fact, all red colours appear
much darker when viewed indirectly. This red-blind part of

1 A similar story is told of Dalton, the author of the « Atomic Theory.'
He was a Quaker, and went to the Friends' Meeting, at Manchester, in a pair
of scarlet stockings, which some wag had put in place of his ordinary dark grey
ones. — TB.

THE SENSATION OF SIGHT. 219

the retina is most extensive on the inner or nasal side of the
field of vision ; and according to recent researches of Woinow,
there is at the furthest limit of the visible field a narrow zone
in which all distinction of colours ceases and there only remain
differences of brightness. In this outermost circle everything
appears white, grey, or black. Probably those nervous fibres
which convey impressions of green light are alone present in
this part of the retina.

In the second place, as I have already mentioned, the middle
of the retina, just around the central pit, is coloured yellow.
This makes all blue light appear somewhat darker in the centre
of the field of sight. The effect is particularly striking with
mixtures of red and greenish-blue, which appear white when
looked at directly, but acquire a blue tint when viewed at a
slight distance from the middle of the field ; and, on the other
hand, when they appear white here, are red to direct vision.
These inequalities of the retina, like the others mentioned in
the former essay, are rectified by the constant movements of
the eye. We know from the pale and indistinct colours of the
external world as usually seen, what impressions of indirect
vision correspond to those of direct ; and we thus learn to judge
of the colours of objects according to the impression which they
would make on us if seen directly. The result is, that only
unusual combinations and unusual or .special direction of atten-
tion enable us to recognise the difference of which I have been
speaking.

The theory of colours, with all these marvellous and com-
plicated relations, was a riddle which Goethe in vain attempted
to solve; nor were we physicists and physiologists more suc-
cessful. I include myself in (the number ; for I long toiled at
the task, without getting any nearer my object, until I at last
discovered that a wonderfully simple solution had been dis-
covered at the beginning of this century, and had been in print
ever since for anyone to read who chose. This solution was
found and published by the same Thomas Young1 who first
showed the right method of arriving at the interpretation of
i Born at Milverton, in Somersetshire, 1773, died 18*2.

220 RECENT PROGRESS OF THE THEORY OF VISION.

Egyptian hieroglyphics. He was one of the most acute men
who ever lived, but had the misfortune to be too far in advance
of his contemporaries. They looked on him with astonishment,
but could not follow his bold speculations, and thus a mass of
his most important thoughts remained buried and forgotten in
the ' Transactions of the Royal Society,' until a later generation
by slow degrees arrived at the rediscovery of his discoveries,
and came to appreciate the force of his arguments and the
accuracy of his conclusions.

In proceeding to explain the theory of colours proposed by
him, I beg the reader to notice that the conclusions afterwards
to be drawn upon the nature of the sensations of sight are quite
independent of what is hypothetical in this theory.

Dr. Young supposes that there are in the eye three kinds
of nerve-fibres, the first of which, when irritated in any way,
produces the sensation of red, the second the sensation of green,
and the third that of violet. He further assumes that the first
are excited most strongly by the waves of ether of greatest
length ; the second, which are sensitive to green light, by the
waves of middle length ; while those which convey impressions
of violet are acted upon only by the shortest vibrations of ether.
Accordingly, at the red end of the spectrum the excitation of
those fibres which are sensitive to that colour predominates;
hence the appearance of this part as red. Further on there is
added an impression upon the fibres sensitive to green light,
and thus results the mixed sensation of yellow. In the middle
of the spectrum, the nerves sensitive to green become much
more excited than the other two kinds, and accordingly green
is the predominant impression. As soon as this becomes mixed
with violet the result is the colour known as blue ; while at the
most highly refracted end of the spectrum the impression pro-
duced on the fibres which are sensitive to violet light overcomes
every other,1

1 The precise tint of the three primary colours cannot yet be precisely
ascertained by experiment. The red alone, it is certain from the experience
of the colour-blind, belongs to the extreme red of the spectrum. At the other
end Young took violet for the primitive colour, while Maxwell considers
that it is more properly blue. The question is still an open one : according

THE SENSATION OF SIGHT, 221

It will be seen that this hypothesis is nothing more than a
further extension of Johannes Miiller's law of special sensation.
Just as the difference of sensation of light and warmth depends
dernonstrably upon whether the rays of the sun fall upon nerves
of sight or nerves of feeling, so it is supposed in Young's hypo-
thesis that the difference of sensation of colours depends simply
upon whether one or the other kind of nervous fibres are more
strongly affected. When all three kinds are equally excited,
the result is the sensation of white light.

The phenomena that occur in red-blindness must be referred
to a condition in which the one kind of nerves, which are sensi-
tive to red rays, are incapable of excitation. It is possible
that this class of fibres are wanting, or at least very sparingly
distributed, along the edge of the retina, even in the normal
human eye.

It must be confessed that both in men and in quadrupeds
we have at present no anatomical basis for this theory of colours ;
but Max Schultze has discovered a structure in birds and reptiles
which manifestly corresponds with what we should expect to
find. In the eyes of many of this group of animals there are
found among the rods of the retina a number which contain a
red drop of oil in their anterior end, that namely which is turned
towards the light ; while other rods contain a yellow drop, and
others none at all. Now there can be no doubt that red light
will reach the rods with a red drop much better than light of
any other colour, while yellow and green light, on the contrary,
will find easiest entrance to the rods with the yellow drop.
Blue light would be shut off almost completely from both, but
would affect the colourless rods all the more effectually. We
may therefore with great probability regard these rods as the
terminal organs of those nervous fibres which respectively
convey impressions of red, of yellow, and of blue light.

I have myself subsequently found a similar hypothesis very
convenient and well fitted to explain in a most simple manner

to J. J. Mttller's experiments (Archiv fur OphtJialmologie, XV. 2. p. 208^)
violet is more probable. The fluorescence of the retina is herd a source of
difficulty.

222 RECENT PROGRESS OF THE THEORY OF VISION.

certain peculiarities which have been observed in the perception
of musical notes, peculiarities as enigmatical as those we have
been considering in the eye. In the cochlea of the internal ear
the ends of the nerve fibres lie regularly spread out side by side,
and provided with minute elastic appendages (the rods of Corti)
arranged like the keys and hammers of a piano. My hypothesis
is, that here each separate nerve fibre is constructed so as to
take cognizance of a definite note, to which its elastic fibre
vibrates in perfect consonance. This is not the place to describe
the special characters of our sensations of musical tones which
led me to frame this hypothesis. Its analogy with Young's
theory of colours is obvious, and it refers the origin of overtones,
the perception of the quality of sounds, the difference between
consonance and dissonance, the formation of the musical scale,
and other acoustic phenomena, to as simple a principle as that
of Young. But in the case of the ear, I could point to a much
more distinct anatomical foundation for such a hypothesis, and
since that time, I have been able actually to demonstrate the
relation supposed; not, it is true, in man or any vertebrate
animals, whose labyrinth lies too deep for experiment, but in
some of the marine Crustacea. These animals have external
appendages to their organs of hearing which may be observed
in the living animal, jointed filaments to which the fibres of the
auditory nerve are distributed ; and Hensen, of Kiel, has satis-
fied himself that some of these filaments are set in motion by
certain notes, and others by different ones.

It remains to reply to an objection against Young's theory
of colour. I mentioned above that the outline of the colour-
disc, which marks the position of the most saturated colours
(those of the spectrum), approaches to a triangle in form ; but
our conclusions upon the theory of the three primary colours
depend upon a perfect rectilinear triangle inclosing the complete
colour-system, for only in that case is it possible to produce all
possible tints by various combinations of the three primary
colours at the angles. It must, however, be remembered that
the colour-disc only includes the entire series of colours which
actually occur in nature, while our theory has to do with the

THE SENSATION OF SIGHT. 223

analysis of our subjective sensations of colour. We need then
only assume that actual coloured light does not produce sensa-
tions of absolutely pure colour; that red, for instance, even
when completely freed from all admixture of white light, still
does not excite those nervous fibres alone which are sensitive
to impressions of red, but also, to a very slight degree, those
which are sensitive to green, and perhaps to a still smaller-
extent those which are sensitive to violet rays. If this be so,
then the sensation which the purest red light produces in the
eye is still not the purest sensation of red which we can conceive
of as possible. This sensation could only be called forth by a
fuller, purer, more saturated red than has ever been seen in
this world.

It is possible to verify this conclusion. We are able to
produce artificially a sensation of the kind I have described.
This fact is not only important as a complete answer to a
possible objection to Young's theory, but is also, as will readily
be seen, of the greatest importance for understanding the real
value of our sensations of colour. In order to describe the
experiment I must first give an account of a new series of
phenomena.

The result of nervous action is fatigue, and this will be
proportioned to the activity of the function performed, and the
time of its continuance. The blood, on the other hand, which
flows in through the arteries, is constantly performing its func-
tion, replacing used material by fresh, and thus carrying away
the chemical results of functional activity; that is to say,
removing the source of fatigue.

The process of fatigue as the result of nervous action, takes
place in the eye as well as other organs. When the entire
retina becomes tired, as when we spend some time in the open
air in brilliant sunshine, it becomes insensible to weaker light,
so that if we pass immediately into a dimly lighted room we see
nothing at first ; we are blinded, as we call it, by the , previous
brightness. After a time the eye recovers itself, and at last we
are able to see, and even to read, by the same dim light which
at first appeared complete darkness.

224 RECENT PROGRESS OF THE THEORY OF VISION.

It is thus that fatigue of the entire retina shows itself.
But it is possible for separate parts of that membrane to become
exhausted, if they alone have received a strong light. If we
look steadily for some time at any bright object, surrounded by
a dark background — it is necessary to look steadily in order that
the image may remain quiet upon the retina, and thus fatigue
a sharply defined portion of its surface — and afterwards turn
our eyes upon a uniform dark-grey surface, we see projected
upon it an after-image of the bright object we were looking at
just before, with the same outline but with reversed illumin-
ation. What was dark appears bright, and what was bright
dark, like the first negative of a photographer. By care-
fully fixing the attention, it is possible to produce very elaborate
after-images, so much so that occasionally even printing can
be distinguished in them. This phenomenon is the result of
a local fatigue of the retina. Those parts of the membrane
upon which the bright light fell before, are now less sensitive to
the light of the dark-grey background than the neighbouring
regions, and there now appears a dark spot upon the really uni-
form surface, corresponding in extent to the surface of the retina
which before received the bright light.

( I may here remark that illuminated sheets of white paper
are sufficiently bright to produce this after-image. If we look at
much brighter objects— at flames, or at the sun itself — the effect
becomes complicated. The strong excitement of the retina does
not pass away immediately, but produces a direct or positive
after-image, which at first unites with the negative or indirect
one produced by the fatigue of the retina. Besides this the
effects of the different colours of white light differ both in
duration and intensity, so that the after-images become coloured,
and the whole phenomenon much more complicated.)

By means of these after-images it is easy to convince oneself
that the impression produced by a bright surface begins to di-
minish after the first second, and that by the end of a single
minute it has lost from a quarter to half of its intensity. The
simplest form of experiment for this object is as follows. Cover
half of a white sheet of paper with a black one, fix the eye upon

THE SENSATION OF SIGHT. 225

some point of the white sheet near the margin of the black, and
after 30 to 60 seconds draw the black sheet quickly away, with-
out losing sight of the point. The half of the white sheet
which is then exposed appears suddenly of the most brilliant
brightness ; and thus it becomes apparent how very much the
first impression produced by the upper half of the sheet had
become blunted and weakened, even in the short time taken by
the experiment. And yet, what is also important to remark,
the observer does not at all notice this fact, until the contrast
brings it before him.

Lastly, it is possible to produce a partial fatigue of the
retina in another way. We may tire it for certain colours only,
by exposing either the entire retina, or a portion of it, for a
certain time (from half a minute to five minutes) to one and the
same colour. According to Young's theory, only one or two
kinds of the optic nerve fibres will then be fatigued, those
namely which are sensitive to impressions of the colour in ques-
tion. All the rest will remain unaffected. The result is, that
when the after-image appears, red, we will suppose, upon a grey
background, the uniformly mixed light of the latter can only
produce sensations of green and violet in the part of the retina
which has become fatigued by red light. This part is made red-
blind for the time. The after-image accordingly appears of a
bluish green, the complementary colour to red.

It is by this means that we are able to produce in the retina
the pure and primitive sensations of saturated colours. If, for
instance, we wish to see pure red, we fatigue a part of our retina
by the bluish green of the spectrum, which is the complementary
colour of red. We thus make this part at once green-blind and
violet-blind. We then throw the after-image upon the red of as
perfect a prismatic spectrum as possible ; the image immediately
appears in full and burning red, while the red light of the
spectrum which surrounds it, although the purest that the world
can offer, now seems to the unfatigued part of the retina less
saturated than the after-image, and looks as if it were covered
by a whitish mist.

These facts are perhaps enough. I will not accumulate fur-

I. Q

226 RECENT PROGRESS OF THE THEORY OF VISION.

ther details, to understand which it would be necessary to enter
upon lengthy descriptions of many separate experiments.

"We have already seen enough to answer the question
whether it is possible to maintain the natural and innate convic-
tion that the quality of our sensations, and especially our sensa-
tions of sight, give us a true impression of corresponding
qualities in the outer world. It is clear that they do not.
The question was really decided by Johannes Miiller's deduction
from well-ascertained facts of the law cf specific nervous energy.
Whether the rays of the sun appear to us as colour, or as
warmth, does not at all depend upon their own properties, but
simply upon whether they excite the fibres of the optic nerve,
or those of the skin. Pressure upon the eyeball, a feeble current
of electricity passed through it, a narcotic drug carried to the
retina by the blood, are capable of exciting the sensation of
light just as well as the sunbeams. The most complete differ-
ence offered by our several sensations, that namely between those
of sight, of hearing, of taste, of smell, and of touch — this
deepest of all distinctions, so deep that it is impossible to draw
any comparison of likeness, or unlikeness, between the sensations
of colour and of musical tones — does not, as we now see, at all
depend upon the nature of the external object, but solely upon
the central connections of the nerves which are affected.

We now see that the question whether within the special
range of each particular sense it is possible to discover a coin-
cidence between its objects and the sensations they produce, is
of only subordinate interest. What colour the waves of ether
shall appear to us when they are perceived by the optic nerve
depends upon their length. The system of naturally visible
colours offers us a series of varieties in the composition of light,
but the number of those varieties is wonderfully reduced from
an unlimited number to only three. Inasmuch as the most im-
portant property of the eye is its minute appreciation of locality,
and as it is so much more perfectly organised for this purpose
than the ear, we may be well content that it is capable of re-
cognising comparatively few differences in quality of light; the
ear, which in the latter respect is so enormously better provided,

THE SENSATION OF SIGHT. 227

has scarcely any power of appreciating differences of locality.
But it is certainly matter for astonishment to anyone who
trusts to the direct information of his natural senses, that
neither the limits within which the spectrum affects our eyes
nor the differences of colour which alone remain as the simpli-
fied effect of all the actual differences of light in kind, should
have any other demonstrable import than for the sense of sight.
Light which is precisely the same to our eyes, may in all other
physical and chemical effects be completely different. - Lastly,
we find that the unmixed primitive elements of all our sensa-
tions of colour (the perception of the simple primary tints)
cannot be produced by any kind of external light in the natural
unfatigued condition of the eye. These elementary sensations
of colour can only be called forth by artificial preparation of the
organ, so that, in fact, they only exist as subjective phenomena.
We see, therefore, that as to any correspondence in kind of ex-
ternal light with the sensations it produces, there is only one
bond of connection between them, a bond which at first sight
may seem slender enough, but is in fact quite sufficient to lead
to an infinite number of most useful applications. This law of
correspondence between what is subjective and objective in
vision is as follows : —

Similar light produces under like conditions a like sensation
of colour. Light which under like conditions excites unlike
sensations of colour is dissimilar.

When two relations correspond to one another in this manner,
the one is a sign for the other. Hitherto the notions of a ' sign '
and of an 'image' or representation have not been carefully
enough distinguished in the theory of perception; and this
seems to me to have been the source of numberless mistakes
and false hypotheses. In an ' image ' the representation must
be of the same kind as that which is represented. Indeed, it is
only so far an image as it is like in kind. A statue is an image
of a man, so far as its form reproduces his : even if it is exe-
cuted on a smaller scale, every dimension will be represented in
proportion. A picture is an image or representation of the
original, first because it represents the colours of the latter by
Q2

228 RECENT PROGRESS OF THE THEORY OF VISION.

similar colours, secondly because it represents a part of its re-
lations in space — those, namely, -which belong to perspective—*
by corresponding relations in space.

Functional cerebral activity and the mental conceptions
which go with it may be ' images ' of actual occurrences in the
outer world, so far as the former represent the sequence in time
of the latter, so far as they represent likeness of objects by
likeness of signs — that is, a regular arrangement by a regular
arrangement.

This is obviously sufficient to enable the understanding to
deduce what is constant from the varied changes of the external
world and to formulate it as a notion or a law. That it is also
sufficient for all practical purposes we shall see in the next chap-
ter. But not only uneducated persons who are accustomed to
trust blindly to their senses, even the educated, who know that
their senses may be deceived, are inclined to demur to so com-
plete a want of any closer correspondence in kind between actual
objects and the sensations they produce than the law I have just
expounded. For instance, natural philosophers long hesitated
to admit the identity of the rays of light and of heat, and ex-
hausted all possible means of escaping a conclusion which seemed
to contradict the evidence of their senses.

Another example is that of Goethe, as I have endeavoured
to show elsewhere. He was led to contradict Newton's theory of
colours, because he could not persuade himself that white, which
appears to our sensation as the purest manifestation of the
brightest light, could be composed of darker colours. It was
Newton's discovery of the composition of light that was the first
germ of the modern doctrine of the true functions of the senses ;
and in the writings of his contemporary, Locke, were correctly
laid down the most important principles on which the right in-
terpretation of sensible qualities depends. But, however clearly
we may feel that here lies the difficulty for a large number of
people, I have never found the opposite conviction of certainty
derived from the senses so distinctly expressed that it is possible
to lay hold of the point of error ; and the reason seems to me to
lie in the fact that beneath the popular notions on the subject lie
other and more fundamentally erroneous conceptions.

THE SENSATION OF SIGHT. 229

We must not be led astray by confounding the notions of a
phenomenon and an appearance,. The colours of objects are
phenomena caused by certain real differences in their consti-
tution. They are, according to the scientific as well as to the
uninstructed view, no mere appearance, even though the way
in which they appear depends chiefly upon the constitution of
our nervous system. A ' deceptive appearance ' is the result of
the normal phenomena of one object being confounded with those
of another. But the sensation of colour is by no means a decep-
tive appearance. There is no other way in which colour can
appear ; so that there is nothing which we could describe as
the normal phenomenon, in distinction from the impressions of
colour received through the eye.

Here the principal difficulty seems to me to lie in the notion
of quality. All difficulty vanishes as soon as we clearly under-
stand that each quality or property of a thing is, in reality,
nothing else but its capability of exercising certain effects upon
other things. These actions either go on between similar parts
of the same body, and so produce the differences of its aggregate
condition ; or they proceed from one body upon another, as in
the case of chemical reactions ; or they produce their effect on
our organs of special sense, and are there recognised as sensations,
as those of sight, with which we have now to do. Any of these ac-
tions is called a ' property, 'when its object is understood without
being expressly mentioned. Thus, when we speak of the ' solu-
bility ' of a substance, we mean its behaviour towards water ;
when we speak of its ' weight,' we mean its attraction to the
earth ; and in the same way we may correctly call a substance
' blue,' understanding, as a tacit assumption, that we are only
speaking of its action upon a normal eye.

But if what we call a property always implies an action of
one thing on another, then a property or quality can never de-
pend upon the nature of one agent alone, but exists only in re-
lation to, and dependent on, the nature of some second object,
which is acted upon. Hence, there is really no meaning in
talking of properties of light which belong to it absolutely, in-
dependent of all other objects, and which we may expect to find

230 RECENT PROGRESS OF THE THEORY OF VISION.

represented in the sensations of the human eye. The notion of
such properties is a contradiction in itself. They cannot possibly
exist, and therefore we cannot expect to find any coincidence of
our sensations of colour with qualities of light.

These considerations have natui-ally long ago suggested
themselves to thoughtful minds ; they may he found clearly ex-
pressed in the writings of Locke and Herbart,1 and they are
completely in accordance with Kant's philosophy. But in former
times, they demanded a more than usual power of abstraction
in order that their truth should be understood ; whereas now
the facts which we have laid before the reader illustrate them
in the clearest manner.

After this excursion into the world of abstract ideas, we
return once more to the subject of colour, and will now ex-
amine it as a sensible ' sign ' of certain external qualities, either
of light itself or of the objects which reflect it.

It is essential for a good sign to be constant — that is, the
same sign must always denote the same object. Now we have
already seen that in this particular our sensations of colour are
imperfect; they are not quite uniform over the entire field of
the retina. But the constant movement of the eye supplies
this imperfection, in the same way as it makes up for the un-
equal sensitiveness of the different parts of the retina to form.

We have also seen that when the retina becomes tired, the
intensity of the impression produced on it rapidly diminishes,
but here again the usual effect of the constant movements of the
eye is to equalise the fatigue of the various parts, and hence we
rarely see after-images. If they appear at all, it is in the case
of brilliant objects like very bright flames, or the sun itself.
And, so long as the fatigue of the entire retina is uniform, the re-
lative brightness and colour of the different objects in sight re-
mains almost unchanged, so that the effect of fatigue is gradually
to weaken the apparent illumination of the entire field of vision.

1 Johann Friedrich Herbart, born .1776, died 1841, professor of philosophy
at Konigsberp an<l Gottingen, author of Psychologic ah Wissenschaft, neu-
yeyruitdet auf Erfahrung, Metaphysik und Mathematik. — TR.

THE SENSATION OF SIGHT. 231

This brings us to consider the differences in the pictures
presented by the eye, which depend on different degrees of illu-
mination. Here again we meet with instructive 'facts. We
look at external objects under light of very different intensity,
varying from the most dazzling sunshine to the pale beams of
the moon ; and the light of the full moon is 150,000 times less
than that of the sun.

Moreover, the colour of the illumination may vary greatly.
Thus, we sometimes employ artificial light, and this is always
more or less orange in colour ; or the natural daylight is altered,
as we see it in the green shade of an arbour, or in a room with
coloured carpets and curtains. As the brightness and the colour
of the illumination changes, so of course will the brightness and
colour of the light which the illuminated objects reflect to our
eyes, since all differences in local colour depend upon different
bodies reflecting and absorbing various proportions of the
several rays of the sun. Cinnabar reflects the rays of great
length without any obvious loss, while it absorbs almost the
whole of the other rays. Accordingly, this substance appears
of the same red colour as the beams which it throws back into
the eye. If it is illuminated with light of some other colour,
without any mixture of red, it appears almost black.

These observations teach what we find confirmed by daily
experience in a hundred ways, that the apparent colour and
brightness of illuminated objects varies with the colour and
brightness of the illumination. This is a fact of the first im-
portance for the painter, for many of his finest effects depend
on it.

But what is most important practically is for us to be able
to recognise surrounding objects when we see them : it is only
seldom that, for some artistic or scientific purpose, we turn our
attention to the way in which they are illuminated. Now what
is constant in the colour of an object is not the brightness and
colour of the light which it reflects, but the relation between
the intensity of the different coloured constituents of this light,
on the one hand, and that of the corresponding constituents of
the light which illuminates it on the other. This proportion

232 RECENT PROGRESS OF THE THEORY OF VISION.

alone is the expression of a constant property of the object in
question.

Considered theoretically, the task of judging of the colour
of a body under changing illumination would seem to be im-
possible ; but in practice we soon find t'lat we are able to j udge
of local colour without the least uncertainty or hesitation, and
under the most different conditions. For instance, white paper
in full moonlight is darker than black satin in daylight, but we
never find any difficulty in recognising the paper as white and
the satin as black. Indeed, it is much more difficult to satisfy
ourselves that a dark object with the sun shining on it reflects
light of exactly the same colour, and perhaps the same bright-
ness, as a white object in shadow, than that the proper colour
of a white paper in shadow is the same as that of a sheet of the
same kind lying close to it in the sunlight. Grey seems to us
something altogether different from white, and so it is, regarded
as a proper colour ; ' for anything which only reflects half the
light it receives must have a different surface from one which
reflects it all. And yet the impression upon the retina of a grey
surface under illumination may be absolutely identical with that
of a white surface in the shade. Every painter represents a
white object in shadow by means of grey pigment, and if he has
correctly imitated nature, it appears pure white. In order to
convince one's self of the identity in this respect— i.e. as illumi-
nation colours — of grey and white, the following experiment
may be tried. Cut out a circle in grey paper, and concentrate
a strong beam of light upon it with a lens, so that the limits of
the illumination exactly correspond with those of the grey circle.
It will then be impossible to tell that there is any artificial il-
lumination at all. The grey looks white.2

1 The local or proper colour of an object (Korperfarbe} is that which it
shows in common white light, while the 'illumination-colour,' as I have
translated Lichtfarbe, is that which is produced by coloured light. Thus the
red of some sandstone rocks seen by common white light is their proper colour,
that of a snow mountain in the rays of the setting sun is an illumination-
colour.— TR.

2 The demonstration is more striking if the grey disk is placed on a sheet
of white paper in diffused light. — TR.

THE SENSATION OF SIGHT. 233

We may assume, and the assumption is justified by certain
phenomena of contrast, that illumination of the brightest white
we can produce, gives a true criterion for judging of the darker
objects in the neighbourhood, since, under ordinary circum-
suances, the brightness of any proper colour diminishes in pro-
portion as the illumination is diminished, or the fatigue of the
retina increased.

This relation holds even for extreme degrees of illumination,
so far as the objective intensity of the light is concerned, but
not for our sensation. Under illumination so brilliant as to ap-
proach what would be blinding, degrees of brightness of light-
coloured objects become less and less distinguishable ; and, in
the same way, when the illumination is very feeble, we are un-
able to appreciate slight differences in the amount of light re-
flected by dark objects. The result is that in sunshine local
colours of moderate brightness approach the brightest, whereas
in moonlight they approach the darkest. The painter utilises
this difference in order to represent noonday or midnight scenes,
although pictures, which are usually seen in uniform daylight, do
not really admit of any difference of brightness approaching that
between sunshine and moonlight. To represent the former, he
paints the objects of moderate brightness almost as bright as the
brightest ; for the latter, he makes them almost as dark as the
darkest.

The effect is assisted by another difference in the sensation
produced by the same actual conditions of light and colour. If
the brightness of various colours is equally increased, that of
red and yellow becomes apparently stronger than that of blue.
Thus, if we select a red and a blue paper which appear of the
same brightness in ordinary daylight, the red seems much
brighter in full sunlight, the blue in moonlight or starlight.
This peculiarity in our pei'ception is also made use of by
painters ; they make yellow tints predominate when represent-
ing landscapes in full sunshine, while every object of a moon-
light scene is given a shade of blue. But it is not only local
colour which is thus affected ; the same is true of the colours of
the spectrum.

234 RECENT PROGRESS OF THE THEORY OF VISION.

These examples show very plainly how independent our
judgment of colours is of their actual amount of illumination.
In the same way, it is scarcely affected by the colour of the
illumination. We know, of course, in a general way that
candle-light is yellowish compared with daylight, but we only
learn to appreciate how much the two kinds of illumination
differ in colour when we bring them together of the same in-
tensity— as, for example, in the experiment of coloured shadows.
If we admit light from a cloudy sky through a narrow opening
into a dark room, so that it falls sideways on a horizontal sheet
of white paper, while candle-light falls on it from the other side,
and if we then hold a pencil vertically upon the paper, it will
of course throw two shadows : the one made by the daylight
will be orange, and looks so ; the other made by the candle-light
is really white, but appears blue by contrast. The blue and the
orange of the two shadows are both colours which we call white,
when we see them by daylight and candle-light respectively.
Seen together, they appear as two very different and tolerably
saturated colours, yet we do not hesitate a moment in recognising
white paper by candle-light as white, and very different from
orange. *

The most remarkable of this series of facts is that we can
separate the colour of any transparent medium from that of
objects seen through it. This is proved by a number of experi-
ments contrived to illustrate the effects of contrast. If we look
through a green veil at a field of snow, although the light re-
flected from it must really have a greenish tint when it reaches
our eyes, yet it appears, on the contrary, of a reddish tint, from
the effect of the indirect after-image of green. So completely
are we able to separate the light which belongs to the trans-
parent medium from that of the objects seen through it.2

The changes of colour in the last two experiments are known
as phenomena of contrast. They consist in mistakes as to local

1 This experiment with diffused white day-light may also be made with
moonlight.

2 A number of similar experiments will be found described in the author's
Handluch der physiologischen Optlk, pp. 398-411.

THE SENSATION OF SIGHT. 236

colour, which for the most part depend upon imperfectly defined
after-images. l This effect is known as successive contrast, and is
experienced when the eye passes over a series of coloured objects.
But a similar mistake may result from our custom of judging
of local colour according to the brightness and colour of the
various objects seen at the same time. If these relations happen
to be different from what is usual, contrast phenomena ensue.
When, for example, objects are seen under two different coloured
illuminations, or through two different coloured media (whether
real or apparent), these conditions produce what is called simul-
taneous contrast. Thus in the experiment described above of
coloured shadows thrown by daylight and candle-light, the
doubly illuminated surface of the paper being the brightest object
seen, gives a false criterion for white. Compared with it, the
really white but less bright light of the shadow thrown by the
candle looks blue. Moreover, in these curious effects of contrast,
we must take into account that differences in sensation which
are easily apprehended appear to us greater than those less
obvious. Differences of colour which are actually before our
eyes are more easily apprehended than those which we only keep
in memory, and contrasts between objects which are close to one
another in the field of vision are more easily recognised than
when they are at a distance. All this contributes to the effect.
Indeed, there are a number of subordinate circumstances affect-
ing the result which it would be very interesting to follow out
in detail, for they throw great light upon the way in which we
judge of local colour: but we must not pursue the inquiry fur-
ther here. I will only remark that all these effects of contrast
are not less interesting for the scientific painter than for the
physiologist, since he must often exaggerate the natural pheno-
mena of contrast, in order to produce the impression of greater
varieties of light and greater fulness of colour than can be
actually produced by artificial pigments.

Here we must leave the theory of the Sensations of Sight.

1 These after-images have been described as ' accidental images,' positive
when of the same colour as the original colour, negative when of the com-
plementary colour. — TK.

236 RECENT PROGRESS OF THE THEORY OF VISION.

This part of our inquiry has shown us that the qualities of
these sensations can only be regarded assigns of certain different
qualities, which belong sometimes to light itself, sometimes to
the bodies it illuminates, but that there is not a single actual
quality of the objects seen which precisely corresponds to our
sensations of sight. Nay, we have seen that, even regarded as
signs of real phenomena in the outer world, they do not possess
the one essential requisite of a complete system of signs — namely,
constancy — with anything like completeness; so that all that
we can say of our sensation of sight is, that ' under similar
conditions, the qualities of this sensation appear in the same
way for the same objects.'

And yet, in spite of all this imperfection, we have also found
that by means of so inconstant a system of signs, we are able
to accomplish the most important part of our task — to recognise
the same proper colours wherever they occur ; and, considering
the difficulties in the way, it is surprising how well we succeed.
Out of this inconstant system of brightness and of colours,
varying according to the illumination, varying according to the
fatigue of the retina, varying according to the part of it affected,
we are able to determine the proper colour of any object, the
one constant phenomenon which corresponds to a constant
quality of its surface; and this we can do, not after long
consideration, but by an instantaneous and involuntary de-
cision.

The inaccuracies and imperfections of the eye as an optical
instrument, and those which belong to the image on the retina,
now appear insignificant in comparison with the incongruities
which we have met with in the field of sensation. One might
almost believe that Nature had here contradicted herself on
purpose, in order to destroy any dream of a pre-existing har-
mony between the outer and the inner world.

And what progress have we made in our task of explaining
Sight 1 It might seem that we are further off than ever ; the
riddle only more complicated, and less hope than ever of finding
out the answer. The reader may perhaps feel inclined to
reproach Science with only knowing how to break up with

THE SENSATION OF SIGHT. 2'.\7

fruitless criticism the fair world presented to us by our sense?,
in order to annihilate the fragments.

Woe! woe!

Thou hast destroyed

The beautiful world

With powerful fist ;

In ruin 'tis hurled,

By the blow of a demigod shattered.

The scattered

Fragments into the void we carry,

Deploring

The beauty perished beyond restoring.1

and may feel determined to stick fast to the ' sound common
sense ' of mankind, and believe his own senses more than phy-
siology.

But there is still a part of our investigation which we have
not touched — that into our conceptions of space. Let us see
whether, after all, our natural reliance upon the accuracy of
what our senses teach us, will not be justified even before the
tribunal of Science.

III. THE PERCEPTION OF SIGHT.

THE colours which have been the subject of the last chapter
are not only an ornament we should be sorry to lose, but are
also a means of assisting us in the distinction and recognition
of external objects. But the importance of colour for this
purpose is far less than the means which the rapid and far-
reaching power of the eye gives us of distinguishing the various

1 Bayard Taylor's translation of the passage in Faust : —
Du hast sie zerstbrt
Die schbne Welt
Mit miichtiger Faust ;
Sie stUrzt, sie zerfallt,
Bin Halbgott liat sie zersohlagen.
Wir tragen

Die Trttmmern ins Nichts hinUber,
TTnd klagen
Ueber die verlorne SchSne.

238 RECENT PROGRESS OF THE THEORY OF VISION.

relations of locality. No other sense can be compared with the
eye in this respect. The sense of touch, it is true, can distin-
guish relations of space, and has the special power of judging
of all matter within reach, at once as to resistance, volume, and
weight ; but the range of touch is limited, and the distinction
it can make between small distances is not nearly so accurate
as that of sight. Yet the sense of touch is sufficient, as experi-
ments upon persons born blind have proved, to develop complete
notions of space. This proves that the possession of sight is
not necessary for the formation of these conceptions, and we
shall soon see that we are continually controlling and correcting
the notions of locality derived from the eye by the help of the
sense of touch, and always accept the impressions on the latter
sense as decisive. The two senses, which really have the same
task, though with very different means of accomplishing it,
happily supply each other's deficiencies. Touch is a trustworthy
and experienced servant, but enjoys only a limited range, while
sight rivals the boldest flights of fancy in penetrating to illimit-
able distances.

This combination of the two senses is of great importance
for our present task ; for, since we have here only to do with
vision, and since touch is sufficient to produce complete concep-
tions of locality, we may assume these conceptions to be already
complete, at least in their general outline, and may, accordingly,
confine our investigation to ascertaining the common point of
agreement between the visual and tactile perceptions of space.
The question how it is possible for any conception of locality to
arise from either or both of these sensations, we will leave till
last.

It is obvious, from a consideration of well-known facts, that
the distribution of our sensations among nervous structures
separated from one another does not at all necessarily bring
with it the conception that the causes of these sensations are
locally separate. For example,, we may have sensations of light,
of warmth, of various notes of music, and also perhaps of an
odour, in the same room, and may recognise that all these agents
are diffused through the air of the room at the same time, and

THE PERCEPTION OF SIGHT. 239

without any difference of locality. When a compound colour
falls upon the retina, we are conscious of three separate elemen-
tary impressions, probably conveyed by separate nerves, without
any power of distinguishing them. We hear in a note struck
on a stringed instrument or in the human voice, different tones
at the same time, one fundamental, and a series of harmonic
overtones, which also are probably received by different nerves,
and yet we are unable to separate them in space. Many
articles of food produce a different impression of taste upon
different parts of the tongue, and also produce sensations of
odour by their volatile particles ascending into the nostrils from
behind. But these different sensations, recognised by different
parts of the nervous system, are usually completely and in-
separably united in the compound sensation which we call
taste.

No doubt, with a little attention it is possible to ascertain
the parts of the body which receive these sensations, but, even
when these are known to be locally separate, it does not follow
that we must conceive of the som-ces of these sensations as
separated in the same way.

We find a corresponding fact in the physiology of sight —
namely, that we see only a single object with our two eyes,
although the impression is conveyed by two distinct nerves. In
fact, both phenomena are examples of a more universal law.

Hence, when we find that a plane optical image of the
objects in the field of vision is produced on the retina, and that
the different parts of this image excite different fibres of the
optic nerve, this is not a sufficient ground for our referring
the sensations thus produced to locally distinct regions of our
field of vision. Something else must clearly be added to pro-
duce the notion of separation in space.

The sense of touch offers precisely the same problem. When
two different parts of the skin are touched at the same time,
two different sensitive nerves, are excited, but the local separ-
ation between these two nerves is not a suflicient ground for our
recognition of the two parts which have been touched as dis-
tinct, and for the conception of two different external objects

240 RECENT PROGRESS OF THE THEORY OF VISION.

which follows. Indeed this conception will vary according to
circumstances. If we touch the table with two fingers, and
feel under each a grain of sand, we suppose that there are
two separate grains of sand ; but if we place the two fingers
one against the other, and a grain of sand between them,
we may have the same sensations of touch in the same two
nerves as before, and yet, under these circumstances, we suppose
that there is only a single grain. In this case, our consciousness
of the position of the fingers has obviously an influence upon
the result at which the mind arrives. This is further proved by
the experiment of crossing two fingers one over the other and
putting a marble between them, when the single object will pro-
duce in the mind the conception of two.

What, then, is it which comes to help the anatomical dis-
tinction in locality between the different sensitive nerves, and
in cases like those I have mentioned, produces the notion of
separation in space ? In attempting to answer this question,
we cannot avoid a controversy which has not yet been decided.

Some physiologists, following the lead of Johannes Miiller,
would answer that the retina or skin, being itself an organ
which is extended in space, receives impressions which carry
with them this quality of extension in space ; that this concep-
tion of locality is innate ; and that impressions derived from
external objects are transmitted of themselves to corresponding
local positions in the image produced in the sensitive organ.
We may describe this as the Innate or Intuitive Theory of con-
ceptions of Space. It obviously cuts short all further inquiry
into the origin of these conceptions, since it regards them as
something original, inborn, and incapable of further explana-
tion.

The opposing view was put forth in a more general form by
the early English philosophers of the sensational school — by
Molyneux,1 Locke, and Jurin.2 Its application to special

1 William Molyneux, author of Dioptrica Nova, was born in Dublin, 1656,
and died in the same city. 1698.

2 James Jurin, M.D., Sec. R. S., physician to Guy's Hospital, and President

THE PERCEPTION OF SIGHT. 241

physiological problems has only become possible in very modern
times, particularly since we have gained more accurate know-
ledge of the movements of the eye. The invention of the stereo-
scope by Wheatstone (p. 249) made the difficulties and imper-
fections of the Innate Theory of sight much more obvious than
before, and led to another solution which approached much
nearer to the older view, and which we will call the Empirical
Theory of Vision. This assumes that none of our sensations
give us anything more than ' signs ' for external objects and
movements, and that we can only learn how to interpret these
signs by means of experience and practice. For example, the con-
ception of differences in locality can only be attained by means
of movement, and, in the field of vision, depends upon our expe-
rience of the movements of the eye. Of course this Empirical
Theory must assume a difference between the sensations of
•various parts of the retina, depending upon their local diffe-
rence. If it were not so, it would be impossible to distinguish
any local difference in the field of vision. The sensation of red,
when it falls upon the right side of the retina, must in some
way be different from the sensation of the same red when it
affects the left side ; and, moreover, this difference between the
two sensations must be of another kind from that which we
recognise when the same spot in the retina is successively affected
by two different shades of red. Lotze1 has named this diffe-
rence between the sensations which the same colour excites when
it affects different parts of the retina, the local sign of the sen-
sation. We are for the present ignorant of the nature of this
difference, but I adopt the name given by Lotze as a convenient
expression. While it would be premature to form any
further hypothesis as to the nature of these ' local signs,' there
can be no doubt of their existence, for it follows from the fact

of the Royal College of Physicians, was born in 1384, and died in 1760. Besides
works on the Contraction of the Heart, on Vis Viva, &c., h*e published, in 1738,
a treatise on Distinct and Indistinct Vision. — TR.

1 Rudolf Hermann Lotze, Professor in the University of Gottingen, origin-
ally a disciple of Herbart (v. supra), author of Allgemeine Physiologic des
menschlichen Korpers, 1851.— TR.

I. B

242 RECENT PROGRESS OF THE THEORY OF VISION.

that we are able to distinguish local differences in the field of
vision.

The difference, therefore, between the two opposing views is
as follows. The Empirical Theory regards the local signs
(whatever they really may be) assigns the signification of which
must be learnt, and is actually learnt, in order to arrive at a
knowledge of the external world. It is not at all necessary to
suppose any kind of correspondence between these local signs
and the actual differences of locality which they signify. The
Innate Theory, on the other hand, supposes that the local signs
are nothing else than direct conceptions of differences in space as
such, both in their nature and their magnitude.

The reader will see how the subject of our present inquiry
involves the consideration of that far-reaching opposition
between the system of philosophy which assumes a pre-existing
harmony of the laws of mental operations with those of the
outer world, and the system which attempts to derive all
correspondence between mind and matter from the results of
experience.

So long as we confine ourselves to the observation of a
field of two dimensions, the individual parts of which offer no, or,
at any rate, no recognisable, difference in their distances from the
eye — so long, for instance, as we only look at the sky and distant
parts of the landscape, both the above theories practically offer
an equally good explanation of the way in which we form con-
ceptions of local relations in the field of vision. The extension
of the retinal image corresponds to the extension of the actual
image presented by the objects before us; or, at all events, there
are no incongruities which may not be reconciled with the Innate
Theory of sight without any very difficult assumptions or
explanations.

The first of these incongruities is that in the retinal picture
the top and bottom and the right and left of the actual image
are inverted. This is seen in Fig. 30 to result from the rays of
light crossing as they enter; the pupil the point a is the retinal
image o(A,bo££. This has always been a difficulty in the theory

THE PERCEPTION OF SIGHT. 243

of vision, and many hypotheses have been invented to explain it.
Two of these have survived. We may, with Johannes M tiller,
regard the conception of upper and lower as only a relative
distinction, so far as sight is concerned — that is, as only affecting
the relation of the one to the other ; and we must further sup-
pose that the feeling of correspondence between what is upper
in the sense of sight and in the sense of touch is only acquired
by experience, when we see the hands, which feel, moving in
the field of vis-ion. Or, secondly, we may assume with Fick '
that, since all impressions upon the retina must be conveyed to
the brain in order to be there perceived, the nerves of sight and
those of feeling are so arranged in the brain as to produce a
correspondence between the notion they suggest of upper and
under, right and left. This supposition has, however, no pre-
tence of any anatomical facts to support it.

The second difficulty for the Intuitive Theory is that, while
we have two retinal pictures, we do not see double. This diffi-
culty was met by the assumption that both retinae when they
are excited produce only a single sensation in the brain, and
that the several points of each retina correspond with each
other, so that each pair of corresponding or 'identical' points
produces the sensation of a single one. Now there is an actual
anatomical arrangement which might perhaps support this
hypothesis. The two optic nerves cross before entering the
brain, and thus become united. Pathological observations make
it probable that the nerve fibres from the right-hand halves of
both retinse pass to the right cerebral hemisphere, those from
the left halves to the left hemisphere.2 But although corre-
sponding nerve fibres would thus be brought close together, it
has not yet been shown that they actually unite in the
brain.

1 Ludwig Fick, late Professor of Medicine in the University of Marburg,
the brother of Prof. Adolf Fick, of Zurich.

2 We may compare the arrangement to that of the reins of a pair of horses :
the inner fibres only of each optic nerve cross, so that thoi-e which run to the
right half of the brain are the outer fibres of the right and the inner of the left
retina, while those which run to the left cerebral hemisphere are the outer

244 RECENT PROGRESS OF THE THEORY OF VISION.

These two difficulties do not apply to the Empirical Theory,
since it only supposes that the actual sensible 'sign/ whether it
be simple or complex, is recognised as the sign of that which it
signifies. An uninstructed person is as sure as possible of the
notions he derives from his eyesight, without ever knowing that
he has two retime, that there is an inverted picture on each, or
that there is such a thing as an optic nerve to be excited, or a
brain to receive the impression. He is not troubled by his
retinal images bring inverted and double. He knows what im-
pression such and such an object in such and such a position
makes on him thrcmgh his eyesight, and governs himself
accordingly. But the possibility of learning the signification of
the local signs which belong to our sensations of sight, so as to
be able to recognise the actual relations which they denote, de-
pends, first, on our having movable parts of our own body with-
in sight ; so that, when we once know by means of touch what
relation in space and what movement is, we can further learn
what changes in the impressions on the eye correspond to the
voluntary movements of a hand which we can see. In the
second place, when we move our eyes while looking at a field of
vision filled with objects at rest, the retina, as it moves, changes
its relation to the almost unchanged position of the retinal
picture. We thus learn what impression the same object makes
upon different parts of the retina. An unchanged retinal
picture, passing over the retina as the eye turns, is like a pair
of compasses which we move over a drawing in order to measure
its parts. Even if the 'local signs' of sensation were qxiite
arbitrary, thrown together without any systematic arrangement
(a supposition which 1 regard as improbable), it would still be
possible by means of the movements of the hand and of the eye,
as just described, to ascertain which signs go together, and which
correspond in different regions of the retina to points at similar
distances in the two dimensions of the field of vision. This is

fibres of the left and the inner of the right retina ; just as the inner reins of
both horses cross, so that the outer rein of the off horse and the inner of the
near one run together to the driver's right hand, while the inner rein of the off
and the outer of the near horse pass to his left hand. — Tn.

THE PERCEPTION OF SIGHT. 245

in accordance with experiments by Fechner,1 Yolkmann,2 and
myself, which prove that even the fully developed eye of an
adult can only accurately compare the size of those lines or
angles in the field of vision, the images of which can be thrown
one after another upon precisely the same spot of the retina by
means of the ordinary movements of the eye.

Moreover, we may convince ourselves by a simple experi-
ment that the harmonious results of the perceptions of feeling
and of sight depend, even in the adult, upon a constant com-
parison of the two, by means of the retinal pictures of our hands
as they move. If we put on a pair of spectacles with prismatic
glasses, the two flat surfaces of which converge towards the
right, all objects appear to be moved over to the right. If we
now try to touch anything we see, taking care to shut the eyes
before the hand appears in sight, it passes to the right of the
object ; but if we follow the movement of the hand with the
eye, we are able to touch what we intend, by bringing the retinal
image of the hand up to that of the object. Again, if we handle
the object for one or two minutes, watching it all the time, a
fresh correspondence is formed between the eye and the hand, in
spite of the deceptive glass, so that we are now able to touch
the object with perfect certainty, even when the eyes are shut.
And we can even do the same with the other hand without see-
ing it, which proves that it is not the perception of touch which
has been rectified by comparison with the false retinal images,
but, on the contrary, the perception of sight, which has been
corrected by that of touch. But, again, if, after trying this ex-
periment several times, we take off the spectacles and then look
at any object, taking care not to bring our hands into the field of
vision, and now try to touch it with our eyes shut, the hand
will pass beyond it on the opposite side — that is. to the left.
The new harmony which wag established between the percep-

1 Gustav Theodor Fechner, author of Elemente tier Psyclwphytik, I860 ; also
known as a satirist. — Tn.

2 Alfred Wilhelm Volkmann, successively Professor of Physiology at Leipzig,
Dorpat, and Halle ; author of Phys'wlogische Untr.rsucliungen im Gebiete dtr
Optik, 1864, &c.— TK.

246 RECENT PROGRESS OF THE THEORY OF VISION.

tions of sight and of touch continues its effects, and thus leads
to fresh mistakes when the normal conditions are restored.

In preparing objects with needles under a compound micro-
scope, we must learn to harmonise the inverted microscopical
image with our muscular sense; and we have to get over a
similar difficulty in shaving before a looking-glass, which changes
light to left.

-. These instances, in which the image presented in the two
dimensions of the field of vision is essentially of the same kind
as the retinal images, and resembles them, can be equally well
explained (or nearly so) by the two opposite theories of vision
to which I have referred. But it is quite another matter when
we pass to the observation of near objects of three dimensions.
In this case there is a thorough and complete incongruity be-
tween our retinal images on the one hand, and, on the other,
the actual condition of the objects as well as the correct impres-
sion of them which we receive. Here we are compelled to choose
between the two opposite theories, and accordingly this depart-
ment of our subject — the explanation of our Perception of
Solidity or Depth, in the field o" vision, and that of binocular
vision on which the former chiefly depends — has for many years
become the field of much investigation and no little controversy.
And 110 wonder, for we have already learned enough to see
that the questions which have here to be decided are of funda-
mental importance, not only for the physiology of sight, but for a
correct understanding of the true nature and limits of human
knowledge generally.

Each of our eyes projects a plane image upon its own retina.
However we may suppose the conducting nerves to be arranged,
the two retinal images when united in the brain can only
reappear as a plane image. But instead of the two plane
retinal images, we find that the actual impression on our mind
is a solid image of three dimensions. Here, again, as in the
system of colours, the outer world is richer than our sensation
by one dimension ; but in this case the conception formed by
the mind completely represents the reality of the outer world.

THE PERCEPTION OF SIGHT. 247

It is important to remember that this perception of depth is
fully as vivid, direct, and exact as that of the plane dimensions
of the field of vision. If a man takes a leap from one rock to
another, his life depends just as much upon his rightly estimat-
ing the distance of the rock on which he is to alight, as upon
his not misjudging its position, right or left; and, as a matter
of experience, we find that we can do the one just as quickly
and as surely as the other.

In what way can this appreciation of what we call depth,
solidity, and direct distance come about ? Let us first ascertain
what are the facts.

At the outset of the inquiry we must bear in mind that the
perception of the solid form of objects and of their relative
distance from us is not quite absent, even when we look at
them with only one eye and without changing our position.
Now the means which we possess in this case are just the same
as those which the painter can employ in order to give the
figures on his canvas the appearance of being solid objects, and
of standing at different distances from the spectator. It is part
of a painter's merit for his figures to stand out boldly. Now
how does he produce the illusion 1 We shall find, in the first
place, that in painting a landscape he likes to have the sun
near the horizon, which gives him strong shadows; for these
throw objects in the foreground into bold relief. Next he
prefers an atmosphere which is not quite clear, because slight
obscurity makes the distance appear far off. Then he is fond
of bringing in figures of men and cattle, because, by help of
these objects of known size, we can easily measure the size and
distance of other parts of the scene. Lastly, houses and other
regular productions of art are also useful for giving a clue to
the meaning of the picture, since they enable us easily to recog-
nise the position of horizontal surfaces. The representation of
solid forms by drawings in correct perspective is most successful
in the case of objects of regular and symmetrical shape, such as
buildings, machines, and implements of various kinds. For we
know that all of these are chiefly bounded either by planes
which meet at a right angle or by spherical and cylindrical

248 RECENT PROGRESS OF THE THEORY OF VISION.

surfaces ; and this is sufficient to supply what the drawing does
not directly show. Moreover, in the case of figures of men
or animals, our knowledge that the two sides are symmetrical
further assists the impression conveyed.

But objects of unknown and irregular shape, as rocks or
masses of ice, baffle the skill of the most consummate artist ;
and even their representation in the most complete and perfect
manner possible, by means of photography, often shows nothing
but a confused mass of biack and white. Yet, when we have
these objects in reality before our eyes, a single glance is enough
for us to recognise their form.

The first who clearly showed in what points it is impossible
for any picture to represent actual objects was the great master
of painting, Leonardo da Vinci,1 who was almost as distinguished
in natural philosophy as in art. He pointed out in his Trattato
Jetta Pittura, that the views of the outer world presented by
each of our eyes are not precisely the same. Each eye sees in
its retinal image a perspective view of the objects which lie be-
fore it; but, inasmuch as it occupies a somewhat different position
in space from the other, its point of view, and so its whole per-
spective image, is different. If I hold up my finger and look at
it first with the right and then with the left eye, it covers, in the
picture seen by the latter, a part of the opposite wall of the
room which is more to the right than in the picture seen by the
right eye. If I hold up my right hand with the thumb towards
me, I. see with the right eye more of the back of the hand, with
the left more of the palm ; and the same effect is produced when-
ever we look at bodies of which the several parts are at different
distances from our eyes. But when I look at a hand repre-
sented in the same position in a painting, the right eye will see
exactly the same figure as the left, and just as much of either
the palm or the back of it. Thus we see that actual solid objects

i Born at Vinci, near Florence, 1452 ; died at Cloux, near Amboise, 1519.
Mr. Hallam says of his scientific writings, that they are ' more like revelations
of physical truths vouchsafed to a single mind, than the superstructure of its
reasoning upon any established basis. . . . He first laid down the grand
principle of Bacon, that experiment and observation must be the guides to just
theory in the investigation of nature.' — TB.

THE PERCEPTION OF SIGHT. 249

present different pictures to the two eyes, while a painting
shows only the same. Hence follows a difference in the impres-
sion made upon the sight which, the utmost perfection in a re-
presentation on a flat surface cannot supply.

The clearest proof that seeing with two eyes, and the diffe-
rence of the pictures presented by each, constitute the most im-
portant cause of our perception of a third dimension in the
field of vision, has been furnished by Wheatsone's invention of
the stereoscope.1 I may assume that this instrument and the
peculiar illusion which it produces are well known. By its
help we see the solid shape of the objects represented on the
stereoscopic slide, with the same complete evidence of the senses
with which we should look at the real objects themselves.
This illusion is produced by presenting somewhat different
pictures to the two eyes — to the right, one which represents the
object in perspective as it would appear to that eye, and to the
left one as it would appear to the left. If the pictures are
otherwise exact and drawn from two different points of view
corresponding to the position of the two eyes, as can be easily
done by photography, we receive on looking into the stereoscope
precisely the same impression in black and white as the object
itself would give.

Anyone who has sufficient control over the movements of
his eyes does not need the help of an instrument in order to
combine the two pictui-es on a stereoscopic slide into a single
solid image. It is only necessary so to direct the eyes, that
each of them shall at the same time see corresponding points in
the two pictures : but it is easier to do so by help of an instru-
ment which will apparently bring the two pictures to the same
place.

In Wheatstone's original stereoscope, represented in Fig. 35,
the observer looked with the right eye into the mirror b, and
with the left into the mirror a. Both mirrors were placed at
an angle to the observer's line of sight, and the two pictures
were so placed at k and g that their reflected images appeared
at the same place behind the two mirrors; but the right eye
1 Described in the FhilosojMcal Transactions for 1838.— TR.

250 RECENT PROGRESS OF THE THEORY OF VISION.

saw the picture g in the mirror b, while the left saw the picture
k in the mirror a.

A. more convenient instrument, though it does not give such
FIG. 35.

sharply denned effects, is the ordinary stereoscope of Bre \vster,1

shown in Fig. 36. Here the two pictures are placed on the

same slide and laid in the lower part of the stereoscope, which

FIG..

is divided by a partition s. Two slightly prismatic glasses with

1 Sir David Brewstcr, Professor of Mathematics at Edinburgh, born 1781,
died 1868.— TK.

THE PERCEPTION OF SIGHT. 251

convex surfaces are fixed at the top of the instrument which
show the pictures somewhat further off, somewhat magnified,
and at the same time overlapping each other, so that both appear
to be in the middle of the instrument. The section of the
double eye-piece shown in Fig. 37 exhibits the position and
shape of the right and left prisms. Thus both pictures are
apparently brought to the same spot, and each eye sees only
the one which belongs to it.

The illusion produced by the stereoscope is most obvious
and striking when other means of recognising the form of an
object fail. This is the case with geometrical outlines of solid
figures, such as diagrams of crystals, and also with representa-
tions of irregular objects, especially when they are transparent,

so that the shadows do not fall as we are accustomed to see
them in opaque objects. Thus glaciers in stereoscopic photo-
graphs often appear to the unassisted eye an incomprehensible
chaos of black and white, but when seen through a stereoscope
the clear transparent ice, with its fissures and polished surfaces,
comes out as if it were real. It has often happened that when
I have seen for the first time buildings, cities or landscapes,
with which I was familiar from stereoscopic pictures, they
seemed familiar to me ; but I never experienced this impression
after seeing any number of ordinary pictures, because these
so imperfectly represent the real effect upon the senses.

The accuracy of the stereoscope is no less wonderful. Dove1
has contrived an ingenious illustration of this. Take two pieces
of paper printed with the same type, or from the same copper-
plate, and hence exactly alike, and put them in the stereoscope

1 Heinrich VVilheltn Dove, Professor in the University of Berlin, author of
Optiache Studien (1859) ; also eminent for his researches in meteorology and
electricity.

His paper, Anwenditng des Stereoskops urn falsches von echtem Papiergcld zn
untemcheiden, was published in 1859. — TB.

252 RECENT PKOGRESS OF THE THEORY OF VISION.

in place of the two ordinary photographs. They will then unite
into a single completely flat image, because, as we have seen
above, the two retinal images of a flat picture are identical.
But no human skill is able to copy the letters of one copperplate
on to another so perfectly that there shall not be some difference
between them. If, therefore, we print off the same sentence
from the original plate and a copy of it, or the same letters with
different specimens of the same type, and put the two pieces of
paper into the stereoscope, some lines will appear nearer and
some further off than the rest. This is the easiest way of de-
tecting spurious bank notes. A suspected one is put in a
stereoscope along with a genuine specimen of the same kind, and
it is then at once seen whether all the marks in the combined
image appear on the same plane. This experiment is also im-
portant for the theory of vision, since it teaches us in a most
striking manner how vivid, sure, and minute is our judgment
as to depth derived from the combination of the two retinal
images.

We now come to the question how is it possible for two
different flat perspective images upon the retina, each of them
representing only two dimensions, to combine so as to present a
solid image of three dimensions.

We must first make sure that we are really able to distinguish
between the two flat images offered us by our eyes. If I hold
my finger up and look towards the opposite wall, it covers a
different part of the wall to each eye, as I mentioned above.
1 Accordingly I see the finger twice, in front of two different places
on the wall ; and if I see a single image of the wall, I must see
a double image of the finger.

Now in ordinary vision we try to recognise the solid form
of surrounding objects, and either do not notice this double
image at all, or only when it is unusually striking. In order
to see it we must look at the field of vision in another way — in
the way that an artist does who intends to draw it. He tries
to forget the actual shape, size, and distance of the objects that
he represents. One would think that this is the more simple

THE PERCEPTION OF SIGHT. 253

and original way of seeing things ; and hitherto most physio-
logists have regarded it as the kind of vision which results
most directly from sensation, while they have looked on ordinary
solid vision as a secondary way of seeing things, which has to be
learned as the result of experience. But every draughtsman
knows how much harder it is to appreciate the apparent form
in which objects appear in the field of vision, and to measure
the angular distance between them, than to recognise what is
their actual form and comparative gize. In fact, the knowledge
of the true relations of surrounding objects of which the artist
cannot divest himself, is his greatest difficulty in drawing from
nature.

Accordingly, if we look at the field of vision with both
eyes, in the way an artist does, fixing our attention upon the
outlines, as they would appear if projected on a pane of glass
between us and them, we then become at once aware of the
difference between the two retinal images. We see those objects
double which lie further off or nearer than the point at which
we are looking, and are not too far removed from it laterally to
admit of their position being sufficiently seen. At first we can
only recognise double images of objects at very different dis-
tances from the eye, but by practice they will be seen with
objects at nearly the same distance.

All these phenomena, and others like them, of double images
of objects seen with both eyes, may be reduced to a simple rule
which was laid down by Johannes Miiller : — ' For each point of
one retina there is on the other a corresponding point.' In the
ordinary flat field of vision presented by the two eyes, the images
received by corresponding points as a rule coincide, while images
received by those which do not correspond do not coincide. The
corresponding points in each retina (without noticing slight de-
viations) are those which are situated at the same lateral and
vertical distance from the point of the retina at which rays of
light come to a focus when we fix the eye for exact vision, namely
the yellow spot.

The reader will remember that the intuitive theory of vision
of necessity assumes a complete combination of those sensations

254 RECENT PROGRESS OF THE THEORY OF VISION.

which are excited by impressions upon corresponding, or, as
Miiller calls them, 'identical' points. This supposition was
most fully expressed in the anatomical hypothesis that two nerve
fibres which arise from corresponding points of the two retina?
actually unite so as to form a single fibre, either at the com-
missure of the optic nerves or in the brain itself. I may, how-
ever, remark that Johannes Miiller did not definitely commit
himself to this mechanical explanation, although he suggested
its possibility. He wished his law of identical points to be re-
garded simply as an expression of facts, and only insisted that
the position in the field of vision of the images they receive is
always the same.

But a difficulty arose. The distinction between the double
images is comparatively imperfect, whenever it is possible to
combine them into a single view ; a striking contrast to the ex-
traordinary precision with which, as Dove has shown, we can
judge of stereoscopic relief. Yet the Litter power depends upon
the same differences, between the two retinal pictures which
cause the phenomenon of double images. The slight difference
of distance between the objects represented in the right and left
half of a stereoscopic photograph, which suffices to produce the
most striking effect of solidity, must be increased twenty or
thirty-fold before it can be recognised in the production of a
double image, even if we suppose the most careful observation
by one who is well practised in the experiment.

Again, there are a number of other circumstances which
make the recognition of double images either easy or difficult.
The most striking instance of the latter is the effect of relief.
The more vivid the impression of solidity, the more difficult are
double images to see, so that it is easier to see them in stereo-
scopic pictures than in the actual objects they represent. On
the other hand, the observation of double images is facilitated
by varying the colour and brightness of the lines in the two
stereoscopic pictures, or by putting lines in both which exactly
correspond, and so will make more evident by contrast the im-
perfect coalescence of the other lines. All these circumstances
ought to have no influence, if the combination of the two images

THE PERCEPTION OF SIGHT. 255

in our sensation depended upon any anatomical arrangement of
the conducting nerves.

Again, after the invention of the stereoscope, a fresh difficulty
arose in explaining our perceptions of solidity by the differences
between the two retinal images. First, Briicke1 called attention
to a series of facts which apparently made it possible to reconcile
the new phenomena discovered with the theory of the innate
identity of the sensations conveyed by the two retinse. If we
carefully follow the way in which we look at stereoscopic pic-
tures or at real objects, we notice that the eye follows the dif-
ferent outlines one after another, so that we see the ' fixed point '
at each moment single, while the other points appear double.
But, usually, our attention is concentrated upon the fixed point,
and we observe the double images so little that to many people
they are a new and surprising phenomenon when first pointed out.
Now since in following the outlines of these pictures, or of an
actual image, we move the eyes unequally this way and that,
sometimes they converge, and sometimes diverge, according as
we look at points of the outline which are apparently nearer or
further off ; and these differences in movement may give rise to
the impression of different degrees of distance of the several
lines.

Now it is quite true, that by this movement of the eye
while looking at stereoscopic outlines, we gain a much more
clear and exact image of the raised surface they represent, than
if we fix our attention upon a single point. Perhaps the simple
reason is that when we move the eyes we look at every point of
the figure in succession directly, and therefore see it much more
sharply defined than when we see only one point directly and
the others indirectly. But Briicke's hypothesis, that the per-
ception of solidity is only produced by this movement of the
eyes, was disproved by experiments made by Dove, which showed
that the peculiar illusion of stereoscopic pictures is also produced
when they are illuminated with an electric spark. The light
then lasts for less than the four thousandth part of a second.
In this time heavy bodies move so little, even at great velocities,
1 Professor of Physiology in the University of Vienna.

256 RECENT PROGRESS OF THE THEORY OF VISION.

that they seem to be at rest. Hence there cannot be the
slightest movement of the eye, while the spark lasts, which
can possibly be recognised ; and yet we receive the complete
impression of stereoscopic relief.

Secondly, such a combination of the sensations of the two
eyes as the anatomical hypothesis assumes, is proved not to
exist by the phenomenon of stereoscopic lustre, which was also
discovered by Dove. If the same surface is made white in one
stereoscopic picture and black in another, the combined image
appears to shine, though the paper itself is quite dull. Stereo-
scopic drawings of crystals are made so that one shows white
lines on a black ground, and the other black lines on a white
ground. When looked at through a stereoscope they give the
impression of a solid crystal of shining graphite. By the same
means it is possible to produce in stereoscopic photographs the
still more beautiful effect of the sheen of water or of leaves.

The explanation of this curious phenomenon is as follows : —
A dull surface, like unglazed white paper, reflects the light
which falls on it equally in all directions, and, therefore, always
looks equally bright, from whatever point it is seen ; hence, of
course, it appears equally bright to both eyes. On the other
hand, a polished surface, beside the reflected light which it
scatters equally in all directions, throws back other beams by
regular reflection, which only pass in definite directions. Now
one eye may receive this regularly reflected light and the other
not; the surface will then appear much brighter to the one than
to the other, and, as this can only happen with shining bodies,
the effect of the black and white stereoscopic pictures appears
like that of a polished surface.

Now if there were a complete combination of the impressions
produced upon both retinae, the union of white and black would
give grey. The fact, therefore, that when they are actually
combined in the stereoscope they produce the effect of lustre —
that is to say, an effect which cannot be produced by any kind
of uniform grey surface — proves that the impressions on the two
retina? are not combined into one sensation.

That, again, this effect of stereoscopic lustre does not depend

THE PERCEPTION OF SIGHT. 257

upon an alternation between the perceptions of the two eyes,
on what is called the ' rivalry of the retinae,' is proved by illu-
minating stereoscopic pictures for an instant with the electric
spark. The same effect is perfectly produced.

In the third place, it can be proved, not only that the
images received by,. the two eyes do not coalesce in our sensa-
tion, but that the two sensations which we receive from the
two eyes are not exactly similar ; that they can, on the contrary,
be readily distinguished. For if the sensation given by the
light eye were indistinguishably the same as that given by the
^left, it would follow that, at least in the case of the electric
spark (when no movements of the eye can help ns in distin-
guishing the two images;, it would make no difference whether
we saw the right-hand stereoscopic picture with the right eye,
and the left with the left, or put the two pictures into the
stereoscope reversed, so as to see that intended for the right eye
with the left, and that intended for the left eye with the right.
But practically we find that it makes all the difference, for if
we make the two pictures change places, the relief appears to
be inverted : what should be further off seems nearer, what
should stand out seems to fall back. Now since, when we look
at objects by the momentary light of the electric spark, they
always appear in their true relief and never reversed, it follows
that the impression produced on the right eye is not indistin-
guishable from that on the left.

Lastly, there are some very curious and interesting pheno-
mena seen when two pictures are ptit before the two eyes at
the same time which cannot be combined so as to present the
appearance of a single object. If, for example, we look with
one eye at a page of print, and with the other at an engraving,1
there follows what is called the ' rivalry ' of the two fields of
vision. The two images are not then seen at the same time,
one covering the other; but at some points one prevails, and at
others the other. If they are equally distinct, the places where

1 The practised obferver is able to do this without any apparatus, but most
persons will find it necessary to put the two objects in a stereoscope or, at least,
to hold a book, or a sheet of paper, or the hand in front of the face, to serve for
the partition in the stereoscope. — TK.

I. S l

258 RECENT PROGRESS OF THE THEORY OF VISION.

one or the other appears usually change after a few seconds.
But if the engraving presents anywhere in the field of vision a
uniform white or black surface, then the printed letters which
occupy the same position in the image presented to the other
eye, will usually prevail exclusively over the uniform surface of
the engraving. In spite, however, of what former observers
have said to the contrary, I maintain that it is possible for the
observer at any moment to control this rivalry by voluntary
direction of his attention. If he tries to read the printed sheet,
the letters remain visible, at least at the spot where for the mo-
ment he is reading. If, on the contrary, he tries to follow the
outline and shadows of the engraving, then these prevail. I
find, moreover, that it is possible to fix the attention upon a
very feebly illuminated object, and make it prevail over a much
brighter one, which coincides with it in the retinal image of the
other eye. Thus, I can follow the watermarks of a white piece
of paper and cease to see strongly-marked black figures in the
other field. Hence the retinal rivalry is not a trial of strength
between two sensations, but depends upon our fixing or failing
to fix the attention. Indeed there is scarcely any phenomenon
so well fitted for the study of the causes which are capable of
determining the attention. It is not enough to form the
conscious intention of seeing first with one eye and then with
the other ; we must form as clear a notion as possible of what
we expect to see. Then it will actually appear. If, on the
other hand, we leave the mind at liberty without a fixed inten-
tion to observe a definite object, that alternation between the
two pictures ensues which is called retinal rivalry. In this
case, we find that, as a rule, bright and strongly marked objects
in one field of vision prevail over those which are darker and
less distinct in the other, either completely or at least for a time.
We may vary this experiment by using a pair of spectacles
with different coloured glasses. We shall then find, on looking
at the same objects with both eyes at once, that there ensues a
similar rivalry between the two colours. Everything appears
spotted over first with one and then with .the other. After a
time, however, the vividness of both colours becomes weakened,

THE PERCEPTION OF SIGHT. 259

partly by the elements of the retina which are affected by each
of them being tired, and partly by the complementary after-
images which result. The alternation then ceases, and there
ensues a kind of mixture of the two original colours.

It is much more difficult to fix the attention upon a colour
than upon such an object as an engraving. For the attention
upon which, as we have seen, the whole phenomenon of ' rivalry '
depends, fixes itself with constancy only upon such a picture as
continually offers something new for the eye to follow. But we
may assist this by reflecting on the side of the glasses next the
eye letters or other lines upon which the attention can fix.
These reflected images themselves are not coloured, but as soon
as the attention is fixed upon one of them we become conscious
of the colour of the corresponding glass.

These experiments on the rivalry of colours have given rise
to a singular controversy among the best observers; and the
possibility of such difference of opinion is an instructive hint
as to the nature of the phenomenon itself. One party, includ-
ing the names of Dove, Regnault,1 Briicke, Ludwig,2 Panum,3
and Hering,4 maintains that the result of a binocular view of
two colours is the true combination-colour. Other observers, as
Heinrich Meyer of Zurich, Volkmann, Meissner,5 and Funke,6
declare quite as positively that, under these conditions, they
have never seen the combination- colour. I myself entirely agree
with the latter, and a careful examination of the cases in which
I might have imagined that I saw the combination-colour has
always proved to me that it was the result of phenomena of
contrast. Each time that I brought the true combination-colour
side by side with the binocular mixture of colours, the diffe-
rence between the two was very apparent. On the other hand,

1 The distinguished French chemist, father of the well-known painter who
was killed in the second siege of Paris.

Professor of Physiology in the University of Leipzig.
Professor of Physiology in the University of Kiel.

Ewald Hering, Professor of Physiology in the University of Prague,
late y in the Josephsakademie of Vienna.

Professor of Physiology in the University of Gottingen.
Professor of Physiology in the University of Freiburg.— TR.
s 2

260 KECENT PROGRESS OF THE THEORY OF VISION.

there can of course be no doubt that the observers I first named
really saw what they profess, so that there must here be great
individual difference. Indeed with certain experiments which
Dove recommends as particularly well fitted to prove the correct-
ness of his conclusion, such as the binocular combination of
complementary polarisation-colours into white, I could not
myself seethe slightest trace of a combination-colour.

This striking difference in a comparatively simple observa-
tion seems to me to be of great interest. It is a remarkable
confirmation of the supposition above made, in accordance with
the Empirical Theory of Vision, that in general only those sen-
sations are perceived as separated in space, which can be
separated one from another by voluntary movements. Even
when we look at a compound colour with one eye, only three
separate sensations are, according to Young's theory, produced
together ; but it is impossible to separate these by any move-
ment of the eye, so that they always remain locally united.
Yet we have seen that even in this case we may become conscious
of a separation under certain circumstances; namely, when it
is seen that part of the colour belongs to a transparent covering.
When two corresponding points of the retinae are illuminated
with different colours, it will be rare for any separation between
them to appear in ordinary vision ; if it does, it will usually
take place in the part of the field of sight outside the region of
exact vision. But there is always a possibility of separating
the compound impression thus produced into its two parts,
which will appear to some extent independent of each other, and
will move with the movements of the eye ; and it will depend
upon the degree of attention which the observer is accustomed
to give to the region of indirect vision and to double images,
whether he is able to separate the colours which fall on both
retinae at the same time. Mixed hues, whether looked at with
one eye or with both, excite many simple sensations of colour
at the same time, each having exactly the same position in the
field of vision. The difference in the way in which such a
compound-colour is regarded by different people depends upon
whether this compound sensation is at once accepted as a coherent

THE PERCEPTION OF SIGHT. 261

whole without any attempt at analysis, or whether the observer
is able by praciice to recognise the parts of which it is composed,
and to separate them from one another. The former is our
usual (though not constant) habit when looking with one eye,
while we are more inclined to the latter when using both. But
inasmuch as this inclination must chiefly depend upon practice
in observing distinctions, gained by preceding observation, it is
easy to understand how great individual peculiarities may arise.
If we carefully observe the rivalry which ensues when we
try to combine two stereoscopic drawings, one of which is in
black lines on a white ground and the other in white lines on
black, we sha.ll see that the white and black lines which affect
nearly corresponding points of each retina al\v ays remain visible
side by side — an effect which of course implies that the white
and black grounds are also visible. By this means the brilliant
surface, which seems to shine like black lead, makes a much
more stable impression than that produced under the operation
of retinal rivalry by entirely different drawings. If we cover
the lower half of the white figure on a black ground with a
sheet of printed paper, the upper half of the combined stereo-
scopic image shows the phenomenon of Lustre, while in the
lower we see Retinal Rivalry between the black lines of the
figure and the black marks of the type. As long as the observer
attends to the solid form of the object represented, the black
and white outlines of the two stereoscopic drawings cany on in
common the point of exact vision as it moves along them, and
the effect can only be kept up by continuing to follow both.
He must steadily keep his attention upon both drawings, and
then the impression of each will be equally combined. There
is no better way of preserving the combined effect of two stereo-
scopic pictures than this. Indeed it is possible to combine (at
least partially and for a short time) two entirely different draw-
ings when put into the stereoscope, by fixing the attention upon
the way in which they cover each other, watching, for instance,
the angles at which their lines cross. But as soon as the
attention turns from the angle to follow one of the lines which
makes it, the picture to which the other line belongs vanishes-

262 RECENT PROGRESS OF THE THEORY OF VISION.

Let us now put together the results to which our enquiry
into binocular vision has led us.

I. The excitement of corresponding points of the two
retinae is not indistinguishably combined into a single impres-
sion ; for, if it were, it would be impossible to see Stereoscopic
Lusti'e. And we have found reason to believe that this effect
is not a consequence of Retinal Rivalry, even if we admit the
latter phenomenon to belong to sensation at all, and not rather
to the degree of attention. On the contrary, the appearance of
lustre is associated with the restriction of this rivalry.

II. The sensations which are produced by tne excitation of
corresponding points of each retina are not indistinguishably
the same ; for otherwise we should not be able to distinguish
the true from the inverted or ' pseudoscopic ' relief, when two
stereoscopic pictures are illuminated by the electric spark.

III. The combination of the two different sensations received
from corresponding retinal points is not produced by one of
them being suppressed for a time ; for, in the first place, the
perception of solidity given by the two eyes depends upon our
being at the same time conscious of the two different images,
and, in the second, this perception of solidity is independent of
any movement of the retinal images, since it is possible under
momentary illumination.

We therefore learn that two distinct sensations are trans-
mitted from the two eyes, and reach the consciousness at the
same time and without coalescing; that accordingly the com-
bination of these two sensations into the single picture of the
external world of which we are conscious in ordinary vision is
not produced by any anatomical mechanism of sensation, but by
a mental act.

IV. Further, we find that there is, on the whole, complete,
or at least nearly complete, coincidence as to localisation in the
field of vision of impressions of sight received from correspond-
ing points of the retinae ; but that when wo refer both impres-
sions to the same object, their coincidence of localisation is much
disturbed.

If this coincidence were the result of a direct function of

THE PERCEPTION OF SIGHT. 263

sensation, it could not be disturbed by the mental operation
which refers the two impressions to the same object. But we
avoid the difficulty, if we suppose that the coincidence in localisa-
tion of the corresponding pictures received from the two eyes
depends upon the power of measuring distances at sight which
we gain by experience — that is, on an acquired knowledge of the
meaning of the ' signs of localisation.' In this case it is simply
one kind of experience opposing another ; and we can then
understand how the conclusion that two images belong to the
same object should influence our estimation of their relative
position by the measuring power of the eye, and how in conse-
quence the distance of the two images from the fixed point in
the field of vision should be regarded as the same, although it
is not exactly so in reality.

But if the practical coincidence of corresponding points as
to localisation in the two fields of vision does not depend upon
sensation, it follows that the original power of comparing
different distances in each separate field of vision cannot depend
upon direct sensation. For, if it were so, it would follow that
the coincidence of the two fields would be completely established
by direct sensation, as soon as the observer had got his two
fixed points to coincide and a single meridian of one eye to
coincide with the corresponding one of the other.

The reader sees how this series of facts has driven us by
force to the Empirical Theory of Vision. It is right to mention
that lately fresh attempts have been made to explain the origin
of our perception of solidity and the phenomena of single and
double binocular vision by the assumption of some ready-made
anatorrr'cil mechanism. We cannot criticise these attempts
here : it would lead us too far into details. Although many of
these hypotheses are veiy ingenious (and at the same time very
indefinite and elastic), they have hitherto always proved insuffi-
cient ; because the actual world offers us far more numerous
relations than the authors of these attempts could provide for.
Hence, as soon as they have airanged one of their systems to
explain any particular phenomenon of vision, it is found not to

264 RECENT PROGRESS OF THE THEORY OF VISION.

answer for any other. Then, in order to help out the hypothesis,
the very doubtful assumption has to be made that, in these
other cases, sensation is overcome and extinguished by opposing
experience. But what confidence could we put in any of our
perceptions if we were able to extinguish our sensations as we
please, whenever they concern an object of our attention, for
the sake of previous conceptions to which they are opposed 1
At any rate, it is clear that in every case where experience must
finally decide, we shall succeed much better in forming a correct
notion of what we see, if we have no opposing sensations to
overcome, than if a correct judgment must be formed in spite
of them.

It follows that the hypotheses which have been successively
framed by the various supporters of intuitive theories of vision,
in order to suit one phenomenon after another, are really quite
unnecessary. No fact has yet been discovered inconsistent with
the Empirical Theory : which does not assume any peculiar
modes of physiological action in the nervous system, nor any
hypothetical anatomical structures ; which supposes nothing
more than the well-known association between the impressions
we receive and the conclusions we draw from them, according
to the fundamental laws of daily experience. It is true that
we cannot at present offer any complete scientific explanation
of the mental operations involved, and there is no immediate
prospect of our doing so. But since these operations actually
exist, and since hitherto every form of the intuitive theory has
been obliged to fall back on their reality when all other explana-
tion failed, these mysteries of the laws of thought cannot be
regarded from a scientific point of view as constituting any
deficiency in the Empirical Theory of Vision.

It is impossible to draw any line in the study of our percep-
tions of space which shall sharply separate those which belong
to direct Sensation from those which are the result of Expe-
rience. If we attempt to draw such a boundary, we find that
experience proves more minute, more direct and more exact
than supposed sensation, and in fact proves its own superiority
by overcoming the latter. The only supposition which does

THE PERCEPTION OF SIGHT. 265

not lead to any contradiction is that of the Empirical Theory,
which regards all our perceptions of space as depending upon
experience, and not only the qualities, but even the local signs
of the sense of sight as nothing more than signs, the meaning
of which we have to learn by experience.

We become acquainted with their meaning by comparing
them with the result of our own movements, with the changes
which we thus produce in the outer world. The infant first begins
to play with its hands. There is a time when it does not know
how to turn its eyes or its hands to an object which attracts its
attention by its brightness or colour. When a little older, a
child seizes whatever is presented to it, turns it over and over
again, looks at it, touches it, and puts it in his mouth. The
simplest objects are what a child likes best, and he always
prefers the most primitive toy to the elaborate inventions of
modern ingenuity. After he has looked at such a toy every
day for weeks together, he learns at last all the perspective
images which it presents ; then he throws it away and wants a
fresh toy to handle like the first. By this means the child
learns to recognise the different views which the same object
can afford in connection with the movements which he is con-
stantly giving it. The conception of the shape of any object,
gained in this manner, is the result of associating all these
visual images. When we have obtained an accurate conception
of the form of any object, we are then able to imagine what
appearance it would present if we looked at it from some other
point of view. All these different views are combined in the
judgment we form as to the dimensions and shape of an object.
And, consequently, when we are once acquainted with this, we
can deduce from it the various images it would present to the
sight when seen from different points of view, and the various
movements which we should have to impress upon it in order
to obtain these successive images.

I have often noticed a striking instance of what I have been
saying in looking at stereoscopic pictures. If, for example, we
look at elaborate outlines of complicated crystalline forms, it is
often at first difficult to see what they mean. When this is the

266 RECENT PROGRESS OF THE THEORY OF VISION.

case, I look out two points in the diagram which correspond,
and make them overlap by a voluntary movement of the eyes.
But as long as I have not made out what kind of form the drawings
are intended to represent, I find that my eyes begin to diverge
again, and the two points no longer coincide. Then I try to
follow the different lines of the figure, and suddenly I see what
the form represented is. From that moment my two eyes pass
over the outlines of the apparently solid body with the utmost
ease, and without ever separating. As soon as we have gained
a correct notion of the shape of an object, we have the rule for
the movements of the eyes which are necessary for seeing it.
In carrying out these movements, and thus receiving the visual
impressions we expect, we retranslate the notion we have formed
into reality, and by finding this retranslation agrees with the
original, we become convinced of the accuracy of our con-
ception.

This last point is, I believe, of great importance. The mean-
ing we assign to our sensations depends upon experiment, and
not upon mere observation of what takes place around us. We
learn by experiment that the correspondence between two pro-
cesses takes place at any moment that we choose, and under con-
ditions which we can alter as we choose. Mere observation
would not give us the same certainty, even though often repeated
under different conditions. For we should thus only learn that
the processes in question appear together frequently (or even
always, as far as our experience goes); but mere observation
would not teach us that they appear together at any moment we
select.

Even in considering examples of scientific observation,
methodically carried out, as in astronomy, meteorology, or
geology, we never feel fully convinced of the causes of the
phenomena observed until we can demonstrate the working of
these same forces by actual experiment in the laboratory. So
long as science is not experimental it does not teach us the know-
ledge of any new force.1

1 An interesting paper, applying this view of the ' experimental ' character

THE PERCEPTION OF SIGHT. 267

It is plain that, by the experience which we collect in the
way I have been describing, we are able to learn as much cf the
meaning of sensible 'signs' as can afterwards be verified by
further experience ; that is to say, all that is real and positive in
our conceptions.

It has been hitherto supposed that the sense of touch confers
the notion of space and movement. At first, of course, the only
direct knowledge we acquire is that we can produce by an act
of volition, changes of which we are cognisant by means of touch
and sight. Most of these voluntary changes are movements, or
changes in the relations of space; but we can also produce
changes in an object itself. Now, can we recognise the move-
ments of our hands and eyes as changes in the relations of space
without knowing it beforehand 1 and can we distinguish them
from other changes which affect the properties of external
objects ? I believe we can. It is an essentially distinct cha-
racter of the relations of Space that they are changeable rela-
tions between objects which do not depend on their quality
or quantity, while all other material relations between objects
depend upon their properties. The perceptions of sight prove
this directly and easily. A movement of the eye which
causes the retinal image to shift its place upon the retina always
produces the same series of changes as often as it is repeated,
whatever objects the field of vision may contain. The effect is
that the impressions which had before the local signs «0, a1? «2»
«3, receive the new local signs b0, 6,, b2,b3, and this may always
occur in the same way, whatever be the quality of the impres-
sions. By this means we learn to recognise such changes as
belonging to the special phenomena which we call changes in
space. This is enough for the object of Empirical Philosophy,
and we need not further enter upon a discussion of the
question, how much of universal conceptions of space is de-
rived a priori, and how much a posteriori.1

of progressive science to Zoology, has been published by M. Lacaze Duthkrs,
in the first number of his Archives de Zoologie. — TK.

1 The question of the origin of our conceptions of space is discussed by Mr.
Bain on empirical principles in his treatise on The Senses and the Intellect, pp.
114-118, 189-194, 245, 363-392, <tc.— TR.

268 RECENT PROGRESS OF THE THEORY OF VISION.

An objection to the Empirical Theory of Vision might be
found in the fact that illusions of the senses are possible ; for if
we have learnt the meaning of our sensations from experience,
they ought always to agree with experience. The explanation
of the possibility of illusions lies in the fact that we trans-
fer the notions of external objects, which would be correct
under normal crnditioiis, to cases in which unusual circum-
stances have altered the retinal pictures. What I call ' obser-
vation under normal conditions' implies not only that the
rays of light must pass in straight lines from each visible point
to the cornea, but also that we must use our eyes in the way
they should be used in order to receive the clearest and most
easily distinguishable images. This implies that we should
successively bring the images of the separate points of the out-
line of the objects we are looking at upon the centres of both retinse
(the yellow spot), ar.d also move the eyes so as to obtain the
surest comparison between their various positions. Whenever
we deviate from these conditions of normal vision, illusions are
the result. Such are the long recognised effects of the refrac-
tion or reflection of rays of light before they enter the eye. But
there are many other causes of mistake as to the position of the
objects we see — defective accommodation when looking through
one or two small openings, improper convergence when looking
with one eye only, irregular position of the eyeball from ex-
ternal pressure or from paralysis of its muscles. Moreover,
illusions may come in from certain elements of sensation not
being accurately distinguished ; as, for instance, the degree of
convergence of the two eyes, of which it is difficult to form an
accurate judgment when the muscles which produce it become
fatigued.

The simple rule for all illusions of sight is this : we always
believe that we see such objects as would, under conditions of
normal vision, produce the retinal image of which we are actually
conscious. If these images are such as could not be produced
by any normal kind of observation, we judge of them according
to their nearest resemblance; and in forming this judgment, we
more easily neglect the parts of sensation which are imperfectly

THE PERCEPTION OF SIGHT. 269

than those which are perfectly apprehended. When more than
one interpretation is possible, we usually waver involuntarily
between them; but it is possible to end this uncertainty by
bringing the idea of any of the possible interpretations we
choose as vividly as possible before the mind by a conscious
effort of the will.

These illusions obviously depend upon mental processes
which may be described as false inductions. But there are, no
doubt, judgments which do not depend upon our consciously
thinking over former observations of the same kind, and ex-
amining whether they justify the conclusion which we form.
I have, therefore, named these ' unconscious judgments ; ' and
this term, thoiigh accepted by other supporters of the Empirical
Theory, has excited much opposition, because, according to
generally-accepted psychological doctrines, a. judgment, or logical
conclusion, is the culminating point of the conscious operations
of the mind. But the judgments which play so great a part in
the perceptions we derive from our senses cannot be expressed
in the ordinary form of logically analysed conclusions, and it is
necessary to deviate somewhat from the beaten paths of psycho-
logical analysis in order to convince ourselves that we really
have here the same kind of mental operation as that involved
in conclusions usually recognised as such. There appears to
me to be in reality only a superficial difference between the
' conclusions ' of logicians and those inductive conclusions of
which we recognise the result in the conceptions we gain of the
outer world through our sensations. The difference chiefly
depends upon the former conclusions being capable of expression
in words, while the latter are not ; because, instead of words,
they only deal with sensations and the memory of sensations.
Indeed, it is just the impossibility of describing sensations,
whether actual or remembered, in words, which makes it so
difficult to discuss this department of psychology at all.

Besides the knowledge which has to do with Notions, and
is, therefore, capable of expression in words, there is another
department of our mental operations, which may be described
as knowledge of the relations of those impressions on the senses

270 RECENT PROGRESS OF THE THEORY OF VISION.

which are not capable of direct verbal expression. For instance
when we say that we ' know ' l a man, a road, a fruit, a perfume,
we mean that we have seen, or tasted, or smelt, these objects.
We keep the sensible impression fast in our memory, and we
shall recognise it again when it is repeated, but we cannot
describe the impression in words, even to ourselves. And yet
it is certain that this kind of knowledge (Kennen) may attain
the highest possible degree of precision and certainty, and is so
far not inferior to any knowledge (Wissen) which can be ex-
pressed in words; but it is not directly communicable, unless
the object in question can be brought actually forward, or the
impression it produces can be otherwise represented — as by
drawing the portrait of a man instead of producing the man
himself.

It is an important part of the former kind of knowledge to
be acquainted with the particular innervation of muscles, which
is necessary in order to produce any effect we intend by moving
our limbs. As children, we must learn to walk; we must
afterwards learn how to skate or go on stilts, how to ride, or
swim, or sing, or pronounce a foreign language. Moreover,
observation of infants shows that they have to learn a number
of things which afterwards they will know so well as entirely
to forget that there was ever a time when they were ignorant
of them. For example, every one of us had to learn, when an
infant, how to turn his eyes toward the light in order to see.
This kind of ' knowledge ' (Kennen) we also call ' being able ' to
do a thing (konnen), or ' understanding ' how to do it (verstehen),
as, ' I know how to ride,' ' I am able to ride,' or ' I understand
how to ride.' 2

It is important to notice that this ' knowledge ' of the effort
of the will to be exerted must attain the highest possible degree

1 In German this kind of knowledge is expressed by the verb kennen (cog-
noscere, connaitre), to be acquainted with, while wissen (scire, savoir), means
to be aware of. The former kind of knowledge is only applicable to objects
directly cognisable by the senses, whereas the latter applies to notions or con-
ceptions which can be formally stated as propositions. — TR.

2 The German word konnen is said to be of the same etymology as kennen,
and so their likeness in form would be explained by their likeness in meaning.

THE PERCEPTION OF SIGHT. 271

of certainty, accuracy, and precision, for us to be able to main-
tain so artificial a balance as is necessary for walking on stilts
or for skating, for the singer to know how to strike a note with
his voice, or the violin-player with his finger, so exactly that its
vibration shall not be out by a hundredth part.

Moreover, it is clearly possible, by using these sensible
images of memory instead of words, to produce the same kind
of combination which, when expressed in words, would be
called a proposition or a conclusion. For example, I may know
that a certain person with whose face I am familiar has a pecu-
liar voice, of which I have an equally lively recollection. I
should be able with the utmost certainty to recognise his face
and his voice among a thousand, and each would recall the other.
But I cannot express this fact in words, unless I am able to add
some other characters of the person in question which can be
better defined. Then I should be able to resort to a syllogism
and say, 'This voice which I now hear belongs to the man
whom I saw then and there.' But universal, as well as
particular conclusions, may be expressed in terms of sensible
impressions, instead of words. To prove this I need only refer
to the effect of works of art. The statue of a god would not
be capable of conveying a notion of a definite character and
disposition, if I did not know that the form of face and the ex-
pression it wears have usually or constantly a certain definite
signification. And, to keep in the domain of the perceptions
of the senses, if I know that a particular way of looking, for
which I have learnt how to employ exactly the right kind of
innervation, is necessary in order to bring into direct vision a
point two feet off and so many feet to the right, this also is a
universal proposition which applies to every case in which I
have fixed a given point at that distance before, or may do so
hereafter. It is a piece of knowledge which cannot be expressed
in words, but is the result which sums up my previous success-
ful expeiience. It may at any moment become the major
premiss of a syllogism, whenever, in fact, I fix a point in the
supposed position and feel that I do so by looking as that major
proposition states. This perception of what I am doing is my

272 RECENT PROGRESS OF THE THEORY OF VISION.

minor proposition, and the ' conclusion ' is that the object I am
looking for will be found at the spot in question.

Suppose that I employ the same way of looking, but look
into a stereoscope. I am now aware that there is no real object
before me at the spot lam looking at ; but I have the same
sensible impression as if one were there ; and yet I am unable
to describe this impression to myself or others, or to characterise
it otherwise than as 'the same impression which would arise
in the normal method of observation, if an object were really
there.' It is important to notice this. No doubt the physiologist
can describe the impression in other ways, by the direction of
the eyes, the position of the retinal images, and so on; but
there is no other way of directly defining and characterising the
sensation which we experience. Thus we may recognise it as
an illusion, but yet we cannot get rid of the sensation of this
illusion; for we cannot extinguish our remembrance of its
normal signification, even when we know that in the case
before us this does not apply — just as little as we are able to
drive out of the mind the meaning of a word in our mother
tongue, when it is employed as a sign for an entirely different
purpose.

These conclusions in the domain of our sensible perceptions
appear as inevitable as one of the forces of nature, and hence
their results seem to be directly apprehended, without any effort
on our part ; but this does not distinguish them from logical
and conscious conclusions, or at least from those which really
deserve the name. All that we can do by voluntary and con-
scious effort, in order to come to a conclusion, is, after all, only
to supply complete materials for constructing the necessary
premisses. As soon as this is done, the conclusion forces itself
upon us. Those conclusions which (it is supposed) may be
accepted or avoided as we please, are not worth much.

The reader will see that these investigations have led us to
a field of mental operations which has been seldom entered by
scientific explorers. The reason is that it is difficult to express
these operations in words. They have been hitherto most dis-

THE PERCEPTION OF SIGHT. 273

cussed in writings on sesthetics, where they play an important
part as Intuition, Unconscious Ratiocination, Sensible Intel-
ligibility, and such obscure designations. There lies under all
these phrases the false assumption that the mental operations
we are discussing take place in an undefined, obscure, half-con-
scious fashion ; that they are, so to speak, mechanical operations,
and thus subordinate to conscious thought, which can be ex-
pressed in language. I do not believe that any difference in
kind between the two functions can be proved. The enormous
superiority of knowledge which has become ripe for expression
in language, is sufficiently explained by the fact that, in the
first place, speech makes it possible to collect together the ex-
perience of millions of individuals and thousands of generations,
to preserve them safely, and by continual verification to make
them gradually more and more certain and universal ; while, in
the second place, all deliberately combined actions of mankind,
and so the greatest part of human power, depend on language.
In neither of these respects can mere familiarity with phenomena
(das Kennen} compete with the knowledge of them which can
be communicated by speech ( das Wissen] ; and yet it does not
follow of necessity that the one kind of knowledge should be of
a different nature from the other, or less clear in its operation.

The supporters of Intuitive Theories of Sensation often
appeal to the capabilities of new-born animals, many of which
show themselves much more skilful than a human infant. It
is quite clear that an infant, in spite of the greater size of its
brain, and its power of mental development, learns with extreme
slowness to perform the simplest tasks; as, for example, to
direct its eyes to an object or to touch what it sees with its
hands. Must we not conclude that a child has much more to
learn than an animal which is safely guided, but also restricted,
by its instincts? It is said that the calf sees the udder and
goes after it, but it admits of question whether it does not simply
smell it, and make those movements which bring it nearer to
the scent.1 At any rate, the child knows nothing of the mean-
ing of the visual image presented by its mother's breast. It
1 See Darwin on the Expression of the Emotions, p. 47. — TK.

1. T

274 RECENT PROGRESS OF THE THEORY OF VISION.

often turns obstinately away from it to the wrong side and tries
to find it there. The young chicken very soon pecks at grains
of corn, but it pecked while it was still in the shell, and when
it hears the hen peck, it pecks again, at first seemingly at
random. Then, when it has by chance hit upon a grain, it
may, no doubt, learn to notice the field of vision which is at the
moment presented to it. The process is all the quicker because
the whole of the mental furniture which it requires for its life
is but small.

We need, however, further investigations on the subject in
order to throw light upon this question. As far as the observa-
tions with which I am acquainted go, they do not seem to me to
prove that anything more than certain tendencies is born with
animals. At all events one distinction between them and man
lies precisely in this, that these innate or congenital tendencies,
impulses or instincts are in him reduced to the smallest possible
number and strength.1

There is a most striking analogy between the entire range
of processes which we have been discussing, and another System
of Signs, which is not given by nature, but arbitrarily chosen,
and which must undoubtedly be learned before it is understood.
I mean the words of our mother tongue.

Learning how to speak is obviously a much more difficult
task than acquiring a foreign language in after life. First, the
child has to guess that the sounds it hears are intended to be
signs at all ; next, the meaning of each separate sound must be
foxind out, by the same kind of induction as the meaning of
the sensations of sight or touch ; and yet we see children by the
end of their first year already understanding certain words and
phrases, even if they are not yet able to repeat them. We may
sometimes observe the same in dogs.

Now this connection between Names and Objects, which
demonstrably must be learnt, becomes just as firm and inde-
structible as that between Sensations and the Objects which
produce them. We cannot help thinking of the usual sigriifica-

1 See on this subject Bain on the Sen»es and the Intellect, p. 293 ; also a
paper on ' Instinct ' in Nature, Oct. 10, 1872.

THE PERCEPTION OF SIGHT. 275

tion of a word, even when it is used exceptionally in some other
sense; we cannot help feeling the mental emotions which a
fictitious narrative calls forth, even when we know that it is not
true ; just in the same way as we cannot get rid of the normal
signification of the sensations produced by any illusion of the
senses, even when we know that they are not real.

There is one other point of comparison which is worth notice.
The elementary signs of language are only twenty-six letters,
and yet what wonderfully varied meanings can we express and
communicate by their combination ! Consider, in comparison
with this, the enormous number of elementary signs with which
the machinery of sight is provided. We may take the number
of fibres in the optic nerves as two hundred and fifty thousand.
Each of these is capable of innumerable different degrees of
sensation of one, two, or three primary colours. It follows that
it is possible to construct an immeasurably greater number of
combinations here than with the few letters which build up our
words. Nor must we forget the extremely rapid changes of
which the images of sight are capable. No wonder, then, if our
senses speak to us in language which can express far more delicate
distinctions and richer varieties than can be conveyed by words.

This is the solution of the riddle of how it is possible to see;
and, as far as I can judge, it is the only one of which the facts
at present known admit. Those striking and broad incongruities
between Sensations and Objects, both as to quality and to
localisation, on which we dwelt, are just the phenomena which
are most instructive ; because they compel us to take the right
road. And even those physiologists, who try to save frag-
ments of a pre-established harmony between sensations and
their objects, cannot but confess that the completion and refine-
ment of sensory perceptions depend so largely upon experience,
that it must be the latter which finally decides whenever they
contradict the supposed congenital arrangements of the organ.
Hence the utmost significance which may still be conceded to
any such anatomical arrangements is that they are possibly
capable of helping the first practice of our senses.

T2

276 RECENT PROGRESS OF THE THEORY OF VISION.

The correspondence, therefore, between the external world
and the Perceptions of Sight rests, either in whole or in part,
upon the same foundation as all our knowledge of the actual
world — on experience, and on constant verification of its accuracy
by experiments which we perform with every movement of our
body. It follows, of course, that we are only warranted in ac-
cepting the reality of this correspondence so far as these means
of verification extend, which is really as far as for practical pur-
poses we need.

Beyond these limits, as, for example, in the region of
Qualities, we are in some instances able to prove conclusively
that there is no correspondence at all between Sensations and
their Objects.

Only the relations of time, of space, of equality, and those
which are derived from them, of number, size, regularity of
coexistence and of sequence — ' mathematical relations,' in short
— are common to the outer and the inner world, and here we
may indeed look for a complete correspondence between our con-
ceptions and the objects which excite them.

But it seems to me that we should not quarrel with the
bounty of Nature because the greatness, and also the emptiness,
of these abstract relations have been concealed from us by the
manifold brilliance of a system of signs; since thus they can be
the more easily surveyed and used for practical ends, while yet
traces enough remain visible to guide the philosophical spirit
aright, in its search after the meaning of sensible Images and
Signs.

277

ON THE CONSERVATION OF FORCE.

Introduction to a Series of Lectures delivered at Carhruhe in the
Winter 0/1862-1863.

As I have undertaken to deliver here a series of lectures, I
think the best way in which I can discharge that duty will be
to bring before you, by means of a suitable example, some view
of the special character of those sciences to the study of which
I have devoted myself. The natural sciences, partly in con-
sequence of their practical applications, and partly from their
intellectual influence on the last four centuries, have so pro-
foundly, and with such increasing rapidity, transformed all the
relations of the life of civilised nations ; they have given these
nations such increase of riches, of enjoyment of life, of the
preservation of health, of means of industrial and of social
intercourse, and even such increase of political power, that every
educated man who tries to understand the forces at work in the
world in which he is living, even if he does not wish to enter
upon the study of a special science, must have some interest in
that peculiar kind of mental labour which works and acts in
the sciences in question.

On a former occasion I have already discussed the character-
istic differences which exist between the natural and the mental
sciences as regards the kind of scientific work. I then en-
deavoured to show that it is more especially in the thorough
conformity with law which natural phenomena and natural
products exhibit, and in the comparative ease with which laws
can be stated, that this difference exists. Not that I wish by
any means to deny, that the mental life of individuals and

278 ON THE CONSERVATION OF FORCE.

peoples is also in conformity with law, as is the object of philo-
sophical, philological, historical, moral, and social sciences to
establish. But in mental life, the influences are so interwoven,
that any definite sequence can but seldom be demonstrated. In
Nature the converse is the case. It has been possible to discover
the law of the origin and progress of many enormously extended
series of natural phenomena with such accuracy and complete-
ness that we can predict their future occurrence with the greatest
certainty ; or in cases in which we have power over the con-
ditions under which they occur, we can direct them just accord-
ing to our will. The greatest of all instances of what the
human mind can effect by means of a well-recognised law of
natural phenomena is that afforded by modern astronomy. The
one simple law of gravitation regulates the motions of the
heavenly bodies not only of our own planetary system, but also of
the far more distant double stars; from which, even the ray
of light, the quickest of all messengers, needs years to reach our
eye; and, just on account of this simple conformity with law,
the motions of the bodies in question can be accurately pre-
dicted and determined both for the past and for future years and
centuries to a fraction of a minute.

On this exact conformity with law depends also the certainty
with which we know how to tame the impetuovis force of steam,
and to make it the obedient servant of our wants. On this
conformity depends, moreover, the intellectual fascination which
chains the physicist to his subjects. It is an interest of quite a
different kind to that which mental and moral sciences afford.
In the latter it is man in the various phases of his intellectual
activity who chains us. Every great deed of which history tells
us, every mighty passion which art can represent, every picture
of manners, of civic arrangements, of the culture of peoples of
distant lands or of remote times, seizes and interests vis, even if
there is no exact scientific connection among them. We con-
tinually find points of contact and comparison in our own con-
ceptions and feelings ; we get to know the hidden capacities and
desires of the mind, which in the ordinary peaceful course of
civilised life remain unawakened.

ON THE CONSERVATION OF FORCE. 279

It is not to be denied that, in the natural sciences, this kind
of interest is wanting. Each individual fact, taken by itself,
can indeed arouse our curiosity or our astonishment, or be useful
to us in its practical applications. But intellectual satisfaction
we obtain only from a connection of the whole, just from its
conformity with law. Reason we call that faculty innate in us
of discovering laws and applying them with thought. For the
unfolding of the peculiar forces of pure reason in their entire
certainty and in their entire bearing, there is no more suitable
arena than inquiry into Nature in the wider sense, the mathe-
matics included. And it is not only the pleasure at the successful
activity of one of our most essential mental powers , and the vie-
torious subjections to the power of our thought and will of an
external world, partly unfamiliar, and partly hostile, which is the
reward of this labour ; but there is a kind, I might almost say,
of artistic satisfaction, when we are able to survey the enormous
wealth of Nature as a regularly-ordered whole — a kosmos, an
image of the logical thought of our own mind.

The last decades of scientific development have led us to the
recognition of a new universal law of all natural phenomena,
which, from its extraordinarily extended range, and from the
connection which it constitutes between natural phenomena of
all kinds, even of the remotest times and the most distant
places, is especially fitted to give us an idea of what I have de-
scribed as the character of the natural sciences, which I have
chosen as the subject of this lecture.

This law is the Law of the Conservation oj Force, a term
the meaning of which I must first explain. It is not absolutely
new; for individual domains of natural phenomena it was
enunciated by Newton and Daniel Bernoulli ; and Rumford and
Humphry Davy have recognised distinct features of its presence
in the laws of heat.

The possibility that it was of universal application was
first stated by Dr. Julius Robert Mayer, a Schwabian physician
(now living in Heilbronn), in the year 1842, while almost
simultaneously with, and independently of him, James Prescot
Joule, an English manufacturer, made a series of important and

280 ON THE CONSERVATION OF FORCE.

difficult experiments on the relation of heat to mechanical
force, which supplied the chief points in which the comparison
of the new theory with experience was still wanting.

The law in question asserts, that the quantity of force which
can be brought into action in the whole of Nature is unchange-
able, and can npither be increased nor diminished. My first
object will be to explain to you what is understood by quantity
of force ; or, as the same idea is more popularly expressed with
reference to its technical application, what we call amount of
work in the mechanical sense of the word.

The idea of work for machines, or natural processes, is taken
from comparison with the working power of man ; and we can
therefore best illustrate from human labour the most important
features of the question with which we are concerned. In
speaking of the work of machines and of natural forces we
must, of course, in this comparison eliminate anything in which
activity of intelligence comes into play. The latter is also
capable of the hard and intense work of thinking, which tries a
man just as muscular exertion does. But whatever of the
actions of intelligence is met with in the work of machines, of
corn-be is due to the mind of the constructor and cannot be
assigned to the instrument at work.

Now, the external work of man is of the most varied kind
as regards the force or ease, the form and rapidity, of the
motions used on it, and the kind of work produced. But both
the arm of the blacksmith who delivers his powerful blows with
the heavy hammer, and that of the violinist who produces the
most delicate variations in sound, and the hand of the lace-
maker who works with threads so fine that they are on the verge
of the invisible, all these acquire the force which moves them
in the same manner and by the same organs, namely, the muscles
of the arm. An arm the muscles of which are lamed is in-
capable of doing any work ; the moving force of the muscle
must be at work in it, and these must obey the nerves, which
bring to them orders from the brain. That member is then
capable of the greatest variety of motions ; it can compel the
most varied instruments to execute the most diverse tasks.

ON THE CONSERVATION OF FORCE. 281

Just so is it with machines : they are used for the most
diversified arrangements. We produce by their agency an infinite
variety of movements, with the most various degrees of force
and rapidity, from powerful steam-hammers and rolling-mills,
where gigantic masses of iron are cut and shaped like butter, to
spinning and weaving-frames, the work of which rivals that
of the spider. Modern mechanism has the richest choice of
means of transferring the motion of one set of rolling wheels to
another with greater or less velocity ; of changing the rotating
motion of wheels into the up-and-down motion of the piston-rod,
of the shuttle, of falling hammers and stamps ; or, conversely,
of changing the latter into the former; or it can, on the other
hand, change movements of uniform into those of varying
velocity, and so forth. Hence this extraordinarily rich utility
of machines for so extremely varied branches of industry. But
one thing is common to all these differences ; they all need a
'moving force, which sets and keeps them in motion, just as the
works of the human hand all need the moving force of the
muscles.

Now, the work of the smith requires a far greater and more
intense exertion of the muscles than that of the violin-player ;
and there are in machines corresponding differences in the power
and duration of the moving force required. These differences,
which correspond to the different degree of exertion of the
muscles in human labour, are alone what we have to think of
when we speak of the amount of work of a machine. We
have nothing to do here with the manifold character of the
actions and arrangements which the machines produce ; we are
only concerned with an expenditure of force.

This very expression which we use so fluently, 'expenditure
of force,' which indicates that the force applied has been ex-
pended and lost, leads us to a further characteristic analogy be-
tween the effects of the human arm and those of machines. The
greater the exertion, and the longer it lasts, the more is the arm
tired, and the more is the store of its moving force for the time
exhausted. We shall see that this peculiarity of becoming
exhausted by work is also met with in the moving forces of

282 ON THE CONSERVATION OF FORCE.

inorganic nature ; indeed, that this capacity of the human arm
of being tired is only one of the consequences of the law with
which we are now concerned. When fatigue sets in, recovery
is needed, and this can only be effected by rest and nourishment.
We shall find that also in the inorganic moving forces, when
their capacity for work is spent, there is a possibility of repro-
duction, although in general other means must be used to this
end than in the case of the human arm.

From the feeling of exertion and fatigue in our muscles,
we can form a general idea of what we understand by amount
of work; but we must endeavour, instead of the indefinite
estimate afforded by this comparison, to form a clear and precise
idea of the standard by which we have to measure the amount
of work. This we can do better by the simplest inorganic
moving forces than by the actions of our muscles, which are a
very complicated apparatus, acting in an extremely intricate
manner.

Let us now consider that moving force which we know best,
and which is simplest — gravity. It acts, for example, as such
in those clocks which are driven by a weight. This weight,
fastened to a string, which is wound round a pulley connected
with the first toothed wheel of the clock, cannot obey the pull
of gravity without setting the whole clockwork in motion.
Now I must beg you to pay special attention to the following
points : the weight cannot put the clock in motion without itself
sinking; did the weight not move, it could not move the clock,
and its motion can only be such a one as obeys the action of
gravity. Hence, if the clock is to go, the weight must con-
tinually sink lower and lower, and must at length sink so far
that the string which supports it is run out. The clock then
stops. The useful effect of its weight is for the present exhausted.
Its gravity is not lost or diminished ; it is attracted by the earth
as before, but the capacity of this gravity to produce the motion
of the clockwork is lost. It can only keep the weight at rest in
the lowest point of its path, it cannot farther put it in motion.

But we can wind up the clock by the power of the arm, by
which the weight is again raised. When this has been done, it

ON THE CONSERVATION OF FORCE. 283

has regained its former capacity, and can again set the clock in
motion.

We learn from this that a raised weight possesses a moving
fores, but that it must necessarily sink if this force is to act ;
that by sinking, this moving force is exhausted, but by using
another extraneous moving force — that of the arm — its activity
can be restored.

The work which the weight has to perform in driving the
clock is not indeed great. It has continually to overcome the
small resistances which the friction of the axles and teeth, as
well as the resistance of the air, oppose to the motion of the
wheels, and it has to furnish the force for the small impulses
and sounds which the pendulum produces at each oscillation.
If the weight is detached from the clock, the pendulum swings
for a while before coming to rest, but its motion becomes each
moment feebler, and ultimately ceases entirely, being gradually
used up by the small hindrances I have mentioned. Hence, to
keep the clock going, there must be a moving force, which,
though small, must be continually at work. Such a one is the
weight.

We get, moreover, from this example, a measure for the
amount of work. Let us assume that a clock is driven by a
weight of a pound, which falls five feet in twenty-four hours.
If we fix ten such clocks, each with a weight of one pound,
then ten clocks will be driven twenty- four hours ; hence, as
each has to overcome the same resistances in the same time as
the others, ten times as much work is performed for ten pounds
fall through five feet. Hence, we conclude that the height of the
fall being the same, the work increases directly as the weight.

Now, if we increase the length of the string so that the
weight runs down ten feet, the clock will go two days instead
of one; and, with double the height of fall, the weight will
overcome on ihe second day the same resistances as on the first,
and will therefore do twice as much work as when it can only
run down five feet. The weight being the same, the work in-
creases as the height of fall. Hence, we may take the product
of the weight into the height of fall as a measure of work, at

284 ON THE CONSERVATION OF FORCE.

any rate, in the present case. The application of this measure
is, in fact, not limited to the individual case, but the universal
standard adopted in manufactures for measuring magnitude of
work is a foot pound — that is, the amount of work which a
pound raised through a foot can produce '

We may apply this measure of work to all kinds of
machines, for we should be able to set them all in motion by
means of a weight sufficient to turn a pulley. We could thus
always express the magnitude of any driving force, for any
given machine, by the magnitude and height of fall of such a
weight as would be necessary to keep the machine going with
its arrangements until it had performed a certain work. Hence
it is that the measurement of work by foot pounds is universally
applicable. The use of such a weight as a driving force would
not indeed be practically advantageous in those cases in which
we were compelled to raise it by the power of our own arm ; it
would in that case be simpler to work the machine by the direct
action of the arm. In the clock we use a weight so that we
need not stand the whole day at the clockwork, as we should
have to do to move it directly. By winding up the clock we
accumulate a store of working capacity in it, which is sufficient
for the expenditure of the next twenty-four hours.

The case is somewhat different when Nature herself raises
the weight, which then works for us. She does not do this
with solid bodies, at least not with such regularity as to be
utilised ; but she does it abundantly with water, which, being
raised to the tops of mountains by meteorological processes,
returns in streams from them. The gravity of water we use as
moving force, the most direct application being in what are
called overshot wheels, one of which is represented in Fig. 38.
Along the circumference of such a wheel are a series of buckets,
which act as receptacles for the water, and, on the side turned
to the observer, have the tops uppermost ; on the opposite side
the tops of the buckets are upside-down. The water flows at
M into the buckets of the front of the wheel, and at F, where

1 This is the technical measure of work ; to convert it into scientific measure
it must be multiplied by the intensity of gravity.

OX THE CONSERVATION OF FORCE.

285

the mouth begins to incline downwards, it flows out. The
buckets on the circumference are filled on the side turned to
the observer, and empty on the other side. Thus the former
are weighted by the water contained in them, the latter not ; the
weight of the water acts continuously on only one side of the
wheel, draws this down, and thereby turns the wheel ; the other

side of the wheel offers no resistance, for it contains no water.
It is thus the weight of the falling water which turns the wheel,
and furnishes the motive power. But you will at once see that
the mass of water which turns the wheel must necessarily fall
in order to do so, and that though, when it has reached the
bottom, it has lost none of its gravity, it is no longer in a

286 ON THE CONSERVATION OF FORCE. .

position to drive the wheel, if it is not restored to its original
position, either by the power of the human arm or by means of
some other natural force. If it can flow from the mill-stream
to still lower levels, it may be used to work other wheels. But
when it has reached its lowest level, the sea, the last remainder
of the moving force is used up, which is due to gravity — that
is, to the attraction of the earth, and it cannot act by its weight
until it has been again raised to a high level. As this is
actually effected by meteorological processes, you will at once
observe that these are to be considered as sources of moving
force.

"Water-power was the first inorganic force which man learnt
to use instead of his own labour or of that of domestic animals.
According to Strabo, it was known to King Mithridates of Pontus,
who was also otherwise celebrated for his knowledge of Nature ;
near his palace there was a water-wheel. Its use was first in-
troduced among the Romans in the time of the first Emperors.
Even now we find water-mills in all mountains, valleys, or
wherever there are rapidly-flowing regularly-filled brooks and
streams. We find water-power used for all purposes which
can possibly be effected by machines. It drives mills which grind
corn, saw-mills, hammers and oil-presses, spinning- frames and
looms, and so forth. It is the cheapest of all motive powers, it
flows spontaneously from the inexhaustible stores of Nature ; but
it is restricted to a particular place, and only in mountainous
countries is it present in any quantity ; in level countries exten-
sive reservoirs are necessary for damming the rivers to produce
any amount of water-power.

Before passing to the discussion of other motive forces I
must answer an objection which may readily suggest itself.
"We all know that there are numerous machines, systems of
pulleys, levers and cranes, by the aid of which heavy burdens
may be lifted by a comparatively small expenditure of force.
We have all of us often seen one or two workmen hoist heavy
masses of stones to great heights, which they would be quite
unable to do directly ; in like manner, one or two men, by means
of a crane, can transfer the largest and heaviest chests from

ON THE CONSERVATION OF FORCE.

287

a ship to the quay. Now, it may be asked, If a large, heavy
weight had been used for driving a machine, would it not be
very easy, by means of a crane or a system of pulleys, to raise it
anew, so that it could again be used FIG. 39.

as a motor, and thus acquire motive
power, without being compelled to
use a corresponding exertion in rais-
ing the weight ?

The answer to this is, that all
these machines, in that degree in
which for the moment they facili-
tate the exertion, also prolong it, so
that by their help no motive power
is ultimately gained. Let us assume
that four labourers have to raise
a load of four hundredweight by
means of a rope passing over a
single pulley. Every time the rope
is pulled down through four feet,
the load is also raised through four
feet. But now, for the sake of com-
parison, let us suppose the same
load hung to a block of four pul-
leys, as represented in Fig. 39. A
single labourer would now be able
to raise the load by the same exer-
tion of force as each one of the
four put forth. But when he pulls
the rope through four feet, the load
only rises one foot, for the length
through which he pulls the rope,
at a, is uniformly distributed
in the block over four ropes, so
that each of these is only shortened
by a foot. To raise the load, therefore, to the same height,
the one man must necessarily work four times as long as the
four together did. But the total expenditure of work is the

288

OX THE CONSERVATION OF FORCE.

same, whether four labourers work for a quarter of an hour or
one works for an hour.

If; instead of human labour, we introduce the work of a
weight, and hang to the block a load of 400, and at a, where
otherwise the labourer works, a weight of 100 pounds, the block
is then in equilibrium, and, without any appreciable exertion of
the arm, may be set in motion. The weight of 100 pounds
sinks, that of 400 rises. Without any measurable expenditure
of force, the heavy weight has been raised by the sinking of the
smaller one. But observe that the smaller weight will have
sunk through four times the distance that the greater one has

FIG. 40.

risen. But a fall, of 100 pounds through four feet is just as
much 400 foot-pounds as a fall of 400 pounds through one foot.
The action of levers in all their various modifications is pre-
cisely similar. Let a b, Fig. 40, be a simple lever, supported
at c, the arm c b being four times as long as the other arm a c.
Let a weight of one pound be hung at b, and a weight of four
pounds at a, the lever is then in equilibrium, and the least pres-
sure of the finger is sufiicient, without any appreciable exertion
of force, to place it in the position a' b!, in which the heavy
weight of four pounds has been raised, while the one-pound
weight has sunk. But here, also, you will observe no work has
been gained, for while the heavy weight has been raised through
one inch, the lighter one has fallen through four inches ; and

ON THE CONSERVATION OF FORCE.

289

four pounds through one inch is, as work, equivalent to the
product of one pound through four inches.

Most other fixed parts of machines may be regarded as
modified and compound levers ; a toothed- wheel, for instance as
a series of levers, the ends of which are represented by the in-
dividual teeth, and one after the other of which is put inactivity
in the degree in which the tooth in question seizes or is seized

FIG. 41.

by the adjacent pinion. Take, for instance, the crabwinch, re-
presented in Fig. 41. Suppose the pinion on the axis of the barrel
of the winch has twelve teeth, and the toothed-wheel, HH,
seventy-two teeth, that is six times as many as the former. The
winch must now be turned round six times before the toothed-
wheel, H, and the barrel, D, have made one turn, and before the
rope which raises the load has been lifted by a length equal to
the circumference of the barrel. The workman thus requires
six times the time, though to be sure only one-sixth of the exer-
i. u

290

ON THE CONSERVATION OF FORCE.

tion, which he would have to use if the handle were directly
applied to the barrel, D. In all these machines, and parts of
machines, we find it confirmed that in proportion as the velocity
of the motion increases its power diminishes, and that when the
power increases the velocity diminishes, but that the amount of
work is never thereby increased.

In the overshot mill-wheel, described above, water acts by
its weight. But there is another form of mill-wheels, what is

FIG. 42.

called the undershot wheel, in which it only acts by its impact,
as represented in Fig. 42. These are used where the height
from which the water comes is not great enough to flow on the
upper part of the wheel. The lower part of undershot wheels
dips in the flowing water which strikes against their float-boards
and carries them along. Such wheels are used in swift-flowing
streams which have a scarcely perceptible fall, as, for instance,
on the Rhine. In the immediate neighbourhood of such a wheel,
the water need not necessarily have a great fall if it only strikes

ON THE CONSERVATION OF FORCE. 291

with considerable velocity. It is the velocity of the water,
exerting an impact against the float-boards, which acts in this
case, and which produces the motive power.

Windmills, which are used in the great plains of Holland
and North Germany to supply the want of falling water, afford
another instance of the action of velocity. The sails are driven
by air in motion — by wind. Air at rest could just as little
drive a windmill as water at rest a water-wheel. The driving
force depends here on the velocity of moving masses.

A bullet resting in the hand is the most harmless thing in
the world ; by its gravity it can exert no great effect ; but when
fired and endowed with great velocity it drives through all ob-
stacles with the most tremendous force.

If I lay the head of a hammer gently on a nail, neither its
small weight nor the pressure of my arm is quite sufficient to
drive the nail into the wood ; but if I swing the hammer and
allow it to fall with great velocity, it acquires a new force,
which can overcome far greater hindrances.

These examples teach us that the velocity of a moving mass
can act as motive force. In mechanics, velocity in so far as it
is motive force, and can produce work, is called vis viva. The
name is not well chosen ; it is too apt to suggest to us the force
of living beings. Also in this case you will see, from the in-
stances of the hammer and of the bullet, that velocity is lost, as
such, when it produces working power. In the case of the
water-mill, or of the windmill, a more careful investigation of
the moving masses of water and air is necessary to prove that
part of their velocity has been lost by the work which they
have performed.

The relation of velocity to working power is most simply
and clearly seen in a simple pendulum, such as can be con-
structed by any weight which we suspend to a cord. Let M, Fig.
43, be such a weight, of a spherical form ; A B, a horizontal
line drawn through the centre of the sphere ; P the point at
which the cord is fastened. If now I draw the weight M on
one side towards A, it moves in the arc M a, the end of which,
a, is somewhat higher than the point A in the horizontal line,
u 2

292

ON THE CONSERVATION OF FORCE.

The weight is thereby raised to the height A a. Hence my
arm must exert a certain force to bring the weight to a. Gravity
resists this motion, and endeavours to bring back the weight to
M, the lowest point which it can reach.

Now, if after I have brought the weight to a I let it go, it
obeys this force of gravity and returns to M, arrives there with
a certain velocity, and no longer remains quietly hanging at M as
it did before, but swings beyond M towards b, where its motion

stops as soon as it has traversed on the side of B an arc equal
in length to that on the side of A, and after it has risen to a
distance B b above the horizontal line, which is equal to the
height A a, to which my arm had previously raised it. In b the
pendulum returns, swings the same way back through M towards
a, and so on, until its oscillations are gradually diminished,
and ultimately annulled by the resistance of the air and by
friction.

You see here that the reason why the weight, when it comes

ON THE CONSERVATION OF FORCE. 293

from a to M, and does not stop there, but ascends to b, in oppo-
sition to the action of gravity, is only to be sought in its velocity.
The velocity which it has acquired in moving from the height
A a is capable of again raising it to an equal height, B b. The
velocity of the moving mass, M, is thus capable of raising this
mass; that is to say, in the language of mechanics, of perform-
ing work. This would also be the case if we had imparted such
a velocity to the suspended weight by a blow.

Prom this we learn further how to measure the working
power of velocity — or, what is the same thing, the vis viva of
the moving mass. It is equal to the work, expressed in foot
pounds, which the same mass can exert after its velocity has
been used to raise it, under the most favourable circumstances,
to as great a height as possible.1 This does not depend on the
direction of the velocity ; for if we swing a weight attached to
a thread in a circle, we can even change a downward motion
into an upward one.

The motion of the pendulum shows us very distinctly how
the forms of working power hitherto considered — that of a
raised weight and that of a moving mass — may merge into one
another. In the points a and b, Fig. 43, the mass has no
velocity ; at the point M it has fallen as far as possible, but
possesses velocity. As the weight goes from a to m the work of
the raised weight is changed into vis viva; as the weight goes
further from m to b the vis viva is changed into the work of a
raised weight. Thus the work which the arm originally im-
parted to the pendulum is not lost in these oscillations, provided
we may leave out of consideration the influence of the resistance
of the air and of friction. Neither does it increase, but it con-
tinually changes the form of its manifestation.

Let us now pass to other mechanical forces, those of elastic
bodies. Instead of the weights which drive our clocks, we find
in time-pieces and in watches, steel springs which are coiled in

1 The measure of vis viva in theoretical mechanics is half the product of the
weight into the square of the velocity. To reduce it to the technical measure of
the work we must divide it by the intensity of gravity ; that is, by the velocity
at the end of the first second of a freely fdling body.

294 ON THE CONSERVATION OF FORCE.

winding up the clock, and are uncoiled by the working of the
clock. To coil up the spring we consume the force of the arm;
this has to overcome the resisting elastic force of the spring as
we wind it up, just as in the clock we have to overcome the force
of gravity which the weight exerts. The coiled spring can,
however, perform work; it gradually expends this acquired
capability in driving the clockwork.

If I stretch a crossbow and afterwards let it go, the stretched
string moves the arrow ; it imparts to it force in the form of
velocity. To stretch the cord my arm must work for a few
seconds ; -this work is imparted to the arrow at the moment it
is shot off. Thus the crossbow concentrates into an extremely
short time the entire work which the arm had communicated in
the operation of stretching ; the clock, on the contrary, spreads
it over one or several days. In both cases no work is produced
which my arm did not originally impart to the instrument, it is
only expended more conveniently.

The case is somewhat different if by any other natural pro-
cess I can place an elastic body in a state of tension without
having to exert my arm. This is possible and is most easily
observed in the case of gases.

If, for instance, I discharge a firearm loaded with gunpowder
the greater part of the mass of the powder is converted into
gases at a very high temperature, which have a powerful ten-
dency to expand, and can only be retained in the narrow space
in which they are formed, by the exercise of the most powerful
pressure. In expanding with enormous force they propel the
bullet, and impart to it a great velocity, which we have already
seen is a form of work.

In this case, then, I have gained work which my arm has
not pel-formed. Something, however, has been lost — the gun-
powder, that is to say, whose constituents have changed into
other chemical compounds, from which they cannot, without
further ado, be restored to their original condition. Here, then,
a chemical change has taken place, under the influence of which
work has been gained.

ON THE CONSERVATION OF FORCE.

295

Elastic forces are produced in gases by the aid of heat, on a
far greater scale.

Let us take, as the most simple instance, atmospheric air.
In Fig. 44 an apparatus is represented such as Regnault used
for measuring the expansive force of heated gases. If no great
accuracy is required in the measurement, the apparatus may be
arranged more simply. At C is a glass globe filled with dry

FIG. 44.

air, which is placed in a metal vessel, in which it can be heated
by steam. It is connected with the U-shaped tube, S s, which
contains a liquid, and the limbs of which communicate with
each other when the stop-cock B, is closed. If the liquid is in
equilibrium in the tube S s when the globe is cold, it rises in the
leg s, and ultimately overflows when the globe is heated. If,
on the contrary, when the globe is heated, equilibrium be re-
stored by allowing some of the liquid to flow out at K, as the

296 ON THE CONSERVATION OF FORCE.

globe cools it will be drawn up towards n. In both cases
liquid is raised, and work thereby produced.

The same experiment is continuously repeated on the largest
scale in steam-engines, though, in order to keep iip a continual
disengagement of compressed gases from the boiler, the air in
the globe in Fig. 44, which would soon reach the maximum of
its expansion, is replaced by water, which is gradually changed
into steam by the application of heat. But steam, so long as it
remains as such, is an elastic gas which endeavours to expand
exactly like atmospheric air. And instead of the column of
liquid which was raised in our last experiment, the machine is
caused to drive a solid piston which imparts its motion to other
parts of the machine. Fig. 45 represents a front view of the
working parts of a high-pressure engine, and Fig. 46 a section.
The boiler in which steam is generated is not represented ; the
steam passes through the tube z z, Fig. 46, to the cylinder A A,
in which moves a tightly fitting piston C. The parts between
the tube z z and the cylinder A A, that is the slide valve in the
valve-chest K K, and the two tubes d and e allow the steam to
pass first below and then above the piston, while at the same
time the steam has free exit from the other half of the cylinder.
When the steam passes under the piston, it forces it upward ;
when the piston has reached the top of its course the position
of the valve in K K changes, and the steam passes above the
piston and forces it down again. The piston-rod acts by means
of the connecting-rod P, on the crank Q of the fly-wheel X and
sets this in motion. By means of the rod s, the motion of the
tod regulates the opening and closing of the valve. But we
need not here enter into those mechanical arrangements, how-
ever ingeniously they have been devised. We are only interested
in the manner in which heat produces elastic vapour, and how
this vapour, in its endeavour to expand, is compelled to move
the solid parts of the machine, and furnish work.

You all know how powerful and varied are the effects of
which steam-engines are capable ; with them has really begun
the great development of industry which has characterised our
century before all others. Its most essential superiority over

FIG. 45.

FIG. 46.

ON THE CONSERVATION OF FORCE. 299

motive powers formerly known is that it is not restricted to a
particular place. The store of coal and the small quantity of
water which are the sources of its power can be brought every-
where, and steam-engines can even be made movable, as is the
case with steam-ships and locomotives. By means of these
machines we can develop motive power to almost an indefinite
extent at any place on the earth's surface, in deep mines and
even on the middle of the ocean ; while water and wind mills
are bound to special parts of the surface of the land. The loco-
motive transports travellers and goods over the land in numbers
and with a speed which must have seemed an incredible fable to
our forefathers, who looked upon the mail-coach with its six
passengers in the inside, and its ten miles an hour, as an enor-
mous progress. Steam-engines traverse the ocean independently
of the direction of the wind, and, successfully resisting storms
which would drive sailing-vessels far away, reach their goal at
the appointed time. The advantages which the concourse of
numerous and variously skilled workmen in all branches offers
in large towns where wind and water power are wanting, can
be utilised, for steam-engines find place everywhere, and supply
the necessary crude force; thus the more intelligent human
force may be spared for better purposes ; and, indeed, wherever
the nature of the ground or the neighbourhood of suitable lines
of communication present a favourable opportunity for the
development of industry, the motive power is also present in the
form of steam-engines.

We see, then, that heat can produce mechanical power; but
in the cases which we have discussed we have seen that the
quantity of force which can be produced by a given measure of
a physical process is always accurately defined, and that the
further capacity for work of the natural forces is either
diminished or exhausted by the work which has been performed.
How is it now with Heat in this respect?

This question was of decisive importance in the endeavour
to extend the law of the Conservation of Force to all natural
processes. In the answer lay the chief difference between the
older and newer views in these respects. Hence it is that many

300 ON THE CONSERVATION OF FORCE.

physicists designate that view of Nature corresponding to the
law of the conservation of force with the name of Mechanical
Theory of Heat.

The older view of the nature of heat was that it is a sub-
stance, very fine and imponderable indeed, but indestructible,
and unchangeable in quantity, which is an essential fundamental
property of all matter. And, in fact, in a large number of
natural processes, the quantity of heat which can be demon-
strated by the thermometer is unchangeable.

By conduction and radiation, it can indeed pass from hotter
to colder bodies ; but the quantity of heat which the former
lose can be shown by the thermometer to have reappeared in
the latter. Many processes, too, were known, especially in the
passage of bodies from the solid to the liquid and gaseous states,
in which heat disappeared — at any rate, as regards the ther-
mometer. But when the gaseous body was restored to the
liquid, and the liquid to the solid state, exactly the same quantity
of heat reappeared which formerly seemed to have been lost.
Heat was said to have become latent. On this view, liquid water
differed from solid ice in containing a certain quantity of heat
bound, which, just because it was bound, could not pass to the
thermometer, and therefore was not indicated by it. Aqueous
vapour contains a far greater quantity of heat thus bound.
But if the vapour be precipitated, and the liquid water restored
to the state of ice, exactly the same amount of heat is liberated
as had become latent in the melting of the ice and in the va-
porisation of the water.

Finally, heat is sometimes produced and sometimes disappears
in chemical processes. But even here it might be assumed that
the various chemical elements and chemical compounds contain
certain constant quantities of latent heat, which, when they
change their composition, are sometimes liberated and sometimes
must be supplied from external sources. Accurate experiments
have shown that the quantity of heat which is developed by a
chemical process — for instance, in burning a pound of pure car-
bon into carbonic acid — is perfectly constant, whether the com-
bustion is slow or rapid, whether it takes place all at once or

ON THE CONSERVATION OF FORCE. 301

by intermediate stages. This also agreed very well with the
assumption, which was the basis of the theory of heat, that
heat is a substance entirely unchangeable in quantity. The
natural processes which have here been briefly mentioned, were
the subject of extensive experimental and mathematical investi-
gations, especially of the great French physicists in the last
decade of the former, and the first decade of the present,
century ; and a rich and accurately- worked chapter of physics
had been developed, in which everything agreed excellently
with the hypothesis — that heat is a substance. On the other
hand, the invariability in the quantity of heat in all these pro-
cesses could at that time be explained in no other manner
than that heat is a substance.

But one relation of heat — namely, that to mechanical work
— had not been accurately investigated. A French engineer,
Sadi Carnot, son of the celebrated War Minister of the Revolu-
tion, had indeed endeavoured to deduce the work which heat
performs, by assuming that the hypothetical caloric endeavoured
to expand like a gas ; and from this assumption he deduced in
fact a remarkable law as to the capacity of heat for work, which
even now, though with an essential alteration introduced by
Clausius, is among the bases of the modern mechanical theory
of heat, and the practical conclusions from which, so far as
they could at that time be compared with experiments, have
held good.

But it was already known that whenever two bodies in
motion rubbed against each other, heat was developed anew,
and it could not be said whence it came.

The fact is universally recognised ; the axle of a carriage
which is badly greased and where the friction is great, becomes
hot — so hot, indeed, that it may take fire ; machine- wheels with
iron axles going at a great rate may become so hot that they
weld to their sockets. A powerful degree of friction is not,
indeed, necessary to disengage an appreciable degree of heat;
thus, a lucifer-match, which by rubbing is so heated that the
phosphoric mass ignites, teaches this fact. Nay, it is enough to
rub the dry hands together to feel the heat produced by friction,

302

ON THE CONSERVATION OF FORCE.

and which is far greater than the heating which takes place
when the hands lie gently on each other. Uncivilised people
use the friction of two pieces of wood to kindle a fire. With "
this view, a sharp spindle of hard wood is made to revolve
rapidly on a base of soft wood in the manner represented in
Fig. 47.

So long as it was only a question of the friction of solids, in
which particles from the surface become detached and com-
pressed, it might be supposed that some changes in structure of

FIG. 47.

the bodies rubbed might here liberate latent heat, which would
thus appear as heat of friction.

But heat can also be produced by the friction of liquids, in
which there could be no question of changes in structure, or of
the liberation of latent heat. The first decisive experiment of
this kind was made by Sir Humphry Davy in the commence-
ment of the present century. In a cooled space he made two
pieces of ice rub against each other, and thereby caused them
to melt. The latent heat which the newly formed water must

ON THE CONSERVATION OF FORCE. 303

have here assimilated could not have been conducted to it by
the cold ice, or have been produced by a change of structure ; it
could have come from no other cause than from friction, and
must have been created by friction.

Heat can also be produced by the impact of imperfectly
elastic bodies as well as by friction. This is the case, for
instance, when we produce fire by striking flint against steel, or
when an iron bar is worked for some time by powerful blows
of the hammer.

If we inquire into the mechanical effects of friction and of
inelastic impact, we find at once that these are the processes
by which all terrestrial movements are brought to rest. A
moving body whose motion was not retarded by any resisting
force would continue to move to all eternity. The motions of
the planets are an instance of this. This is apparently never
the case with the motion of the terrestrial bodies, for they are
always in contact with other bodies which are at rest, and
rub against them. We can, indeed, very much diminish their
friction, but never completely annul it. A wheel which turns
about a well-worked axle, once set in motion continues it for a
long time ; and the longer, the more truly and smoother the
axle is made to turn, the better it is greased, and the less the
pressure it has to support. Yet the vis viva of the motion
which we have imparted to such a wheel when we started it,
is gradually lost in consequence of friction. It disappears, and
if we do not carefully consider the matter, it sterns as if the vis
viva which the wheel had possessed had been simply destroyed
without any substitute.

A bullet which is rolled on a smooth horizontal surface
continues to roll until its velocity is destroyed by friction on
the path, caused by the very minute impacts on its little
roughnesses.

A pendulum which has been put in vibration can continue
to oscillate for hours if the suspension is good, without being
driven by a weight ; but by the friction against the surrounding
air, and by that at its place of suspension, it ultimately comes
to rest.

304 ON THE CONSERVATION OF FORCE.

A stone which has fallen from a height has acquired a certain
velocity on reaching the earth ; this we know is the equivalent
of a mechanical work; so long as this velocity continues as such,
we can direct it upwards by means of suitable arrangements,
and thus utilise it to raise the stone again. Ultimately the
stone strikes against the earth and comes to rest; the impact has
destroyed its velocity, and therewith apparently also the me-
chanical work which this velocity could have effected.

If we review the results of all these instances, which each of
you could easily add to from your own daily experience, we shall
see that friction and inelastic impact are processes in which me-
chanical work is destroyed, and heat produced in its place.

The experiments of Joule, which have been already men-
tioned, lead us a step further. He has measured in foot pounds
the amount of work which is destroyed by the friction of solids
and by the friction of liquids ; and, on the other hand, he has
determined the quantity of heat which is thereby produced, and
has established a definite relation between the two. His experi-
ments show that when heat is produced by the consumption of
work, a definite quantity of work is required to produce that
amount of heat which is known to physicists as the unit of heat;
the heat, that is to say, which is necessary to raise one gramme
of water through one degree centigrade. The quantity of work
necessary for this is, according to Joule's best experiments,
equal to the work which a gramme would perform in falling
through a height of 425 metres.

In order to show how closely concordant are his numbers,
I will adduce the results of a few series of experiments which
he obtained after introducing the latest improvements in his
methods.

1. A series of experiments in which water was heated by
friction in a brass vessel. In the interior of this vessel a ver-
tical axle provided with sixteen paddles was rotated, the eddies
thus produced being broken by a series of projecting barriers,
in which parts were cut out large enough for the paddles to pass
through. The value of the equivalent was 424'9 metres.

2. Two similar experiments, in which mercury in an iron

OX THE CONSERVATION OF FORCE. 305

vessel was substituted for water in a brass one, gave 425 and
426-3 metres.

3. Two series of experiments, in which a conical ring rubbed
against another, both surrounded by mercury, gave 426'7 and
425-6 metres.

Exactly the same relations between heat and work were also
found in the reverse process — that is, when work was produced
by heat. In order to execute this process under physical con-
ditions that could be controlled as perfectly as possible, per-
manent gases and not vapours were used, although the latter
are, in practice, more convenient for producing large quantities
of work, as in the case of the steam-engine. A gas which is
allowed to expand with moderate velocity becomes cooled.
Joule was the first to show the reason of this cooling. For the
gas has, in expanding, to overcome the resistance which the
pressure of the atmosphere and the slowly yielding side of the
vessel oppose to it : or, if it cannot of itself overcome this
resistance, it supports the arm of the observer which does it.
Gas thus performs work, and this work is produced at the cost
of its heat. Hence the cooling. If, on the contrary, the gas is
suddenly allowed to issue into a perfectly exhausted space where
it finds no resistance, it does not become cool, as Joule has
shown ; or if individual parts of it become cool, others become
warm; and, after the temperature has become equalised, this
is exactly as much as before the sudden expansion of the
gaseous mass.

How much heat the various gases disengage when they are
compressed, and how much work is necessary for their compres-
sion; or, conversely, how much heat disappears when they ex-
pand under a pressure equal to their own counterpressure, and
how much work they thereby effect in overcoming this counter-
pressure, was partly known from the older physical experiments,
and has partly been determined by the recent experiments of
Regnault by extremely perfect methods. Calculations with the
best data of this kind give us the value of the thermal equiva-
lent from experiments : —

306 ON THE CONSERVATION OF FORCE.

With atmospheric air . -. » . 426-0 metres

„ oxygen , , . . . 425-7 „

„ nitrogen .. ... . ' . . . 431-3 „

„ hydrogen . ... . . 425*3 „

Comparing these numbers with those which determine the
equivalence of heat and mechanical work in friction, as close an
agreement is seen as can at all be expected from numbers which
have been obtained by such varied investigations of different
observers.

Thus then : a certain quantity of heat may be changed into
a definite quantity of work ; this quantity of work can also be
retransformed into heat, and, indeed, into exactly the same
quantity of heat as that from which it originated; in a me-
chanical point of view, they are exactly equivalent. Heat is a
new form in which a quantity of work may appear.

These facts no longer permit us to regard heat as a substance,
for its quantity is not unchangeable. It can be produced anew
from the vis viva of motion destroyed; it can be destroyed, and
then produces motion. We must rather conclude from this that
heat itself is a motion, an internal invisible motion of the
smallest elementary particles of bodies. If, therefore, motion
seems lost in friction and impact, it is not actually lost, but only
passes from the great visible masses to their smallest particles;
while in steam-engines the internal motion of the heated gaseous
particles is transferred to the piston of the machine, accumulated
in it, and combined in a resultant whole.

But what is the nature of this internal motion can only be
asserted with any degree of probability in the case of gases.
Their particles probably cross one another in rectilinear paths in
all directions, until, striking another particle, or against the side
of the vessel, they are reflected in another direction. A gas
would thus be analogous to a swarm of gnats, consisting, how-
ever, of particles infinitely small and infinitely more closely
packed. This hypothesis, which has been developed by Krb'nig,
Clausius, and Maxwell, very well accounts for all the phenomena

What appeared to the earlier physicists to be the constant

ON THE CONSERVATION OF FORCE. 307

quantity of heat is nothing more than the whole motive power
of the motion of heat, which remains constant so long as it is not
transformed into other forms of work, or results afresh from them.

We turn now to another kind of natural forces which can
produce work — I mean the chemical. We have to-day already
come across them. They are the ultimate cause of the work
which gunpowder and the steam-engine produce; for the heat
which is consumed in the latter, for example, originates in the
combustion of carbon — that is to say, in a chemical process. The
burning of coal is the chemical union of carbon with the oxygen
of the air, taking place under the influence of the chemical
affinity of the two substances.

We may regard this force as an attractive force between the
two, which, however, only acts through them with extraordinary
power, if the smallest particles of the two substances are in
closest proximity to each other. In combustion this force acts ;
the carbon and oxygen atoms strike against each other and
adhere firmly, inasmuch as they form a new compound — carbonic
acid — a gas known to all of you as that which ascends from all
fermenting and fermented liquids — from beer and champagne.
Now this attraction between the atoms of carbon and of oxygen
performs work just as much as that which the earth in the
form of gravity exerts upon a raised weight. When the weight
falls to the ground, it produces an agitation, which is partly
transmitted to the vicinity as sound waves, and partly remains
as the motion of heat. The same result we must expect
from chemical action. When carbon and oxygen atoms have
rushed against each other, the newly-formed particles of carbonic
acid must be in the most violent molecular motion — that is, in
the motion of heat. And this is so. A pound of carbon burned
with oxygen to form carbonic acid, gives as much heat as is
necessary to raise 80 -9 pounds of water from the freezing to
the boiling point ; and just as the same amount of work is pro-
duced when a weight falls, whether it falls slowly or fast, so also
the same quantity of heat is produced by the combustion of
carbon, whether this is slow or rapid, whether it takes place all
at once, or by successive stages.

308 ON THE CONSERVATION OF FORCE.

When the carbon is burned, we obtain in its stead, and in
that of the oxygen, the gaseous product of combustion — carbonic
acid. Immediately after combustion it is incandescent. When
it has afterwards imparted heat to the vicinity, we have in the
carbonic acid the entire quantity of carbon and the entire
quantity of oxygen, and also the force of affinity quite as strong
as before. But the action of the latter is now limited to hold-
ing the atoms of carbon and oxygen firmly united ; they can no
longer produce either heat or work any more than a fallen weight
can do work if it has not been again raised by some extraneous
force. When the carbon has been burnt we take no further
trouble to retain the carbonic acid ; it can do no more service,
we endeavour to get it out of the chimneys of our houses as
fast as we can.

Is it possible, then, to tear asunder the particles of carbonic
acid, and give to them once more the capacity of work which
they had before they were combined, j ast as we can restore the
potentiality of a weight by raising it from the ground 1 It is
indeed possible. We shall afterwards see how it occurs in the
life of plants; it can also be effected by inorganic processes,
though in roundabout ways, the explanation of which would
lead us too far from our present course.

This can, however, be easily and directly shown for another
element, hydrogen, which can be burnt just like carbon. Hy-
drogen with carbon is a constituent of all combustible vegetable
substances, among others, it is also an essential constituent of
the gas which is used for lighting our streets and rooms ; in the
free state it is also a gas, the lightest of all, and burns when
ignited with a feebly luminous blue flame. In this combustion
— that is, in the chemical combination of hydrogen with oxygen,
a very considerable quantity of heat is produced ; for a given
weight of hydrogen, four times as much heat as in the combus-
tion of the same weight of carbon. The product of combustion
is water, which, therefore, is not of itself further combustible,
for the hydrogen in it is completely saturated with oxygen.
The force of affinity, therefore, of hydrogen for oxygen, like
that of carbon for oxygen, performs work in combustion,

ON THE CONSERVATION OF FORCE.

309

which appears in the form of heat. In the water which
has been formed during combustion, the force of affinity
is exerted between the elements as before, but its capacity
for work is lost. Hence the two elements must be again sepa-
rated, their atoms torn apart, if new effects are to be produced
from them.

This we can do by the aid of currents of electricity. In the
apparatus depicted in Fig. 48, we have two glass vessels filled
with acidulated water, a and a „ which are separated in the
middle by a porous plate moistened with water. In both sides
are fitted platinum wires, k, which are attached to platinum

plates, i and i ,. As soon as a galvanic current is transmitted
through the water by the platinum wires, k, you see bubbles of
gas ascend from the plates i and i j. These bubbles are the two
elements of water, hydrogen on the one hand, and oxygen on
the other. The gases emerge through the tubes g and g ,. If
we wait until the upper part of the vessels and the tubes have
been filled with it, we can inflame hydrogen at one side; it
burns with a blue flame. If I bring a glimmering spill near
the mouth of the other tube, it bursts into flame, just as happens
with oxygen gas, in which the processes of combustion are far
more intense than in atmospheric air, where the oxygen mixed
with nitrogen is only one-fifth of the whole volume.

310

ON THE CONSERVATION OF FORCE.

If I hold a glass flask filled with water over the hydrogen
flame, the water, newly formed in combustion, condenses upon it.

If a platinum wire be held in the almost non-luminous
flame, you see how intensely it is ignited ; in a plentiful current
of a mixture of the gases, hydrogen and oxygen, which have
been liberated in the above experiment, the almost infusible
platinum might even be melted. The hydrogen which has here
been liberated from the water by the electrical current has re-
gained the capacity of producing large quantities of heat by a

FIG. 49.

lit-

fresh combination with oxygen ; its affinity for oxygen has re-
gained for it its capacity for work.

We here become acquainted with a new source of work, the
electric current which decomposes water. This current is itself
produced by a galvanic battery, Fig. 49. Each of the four
vessels contains nitric acid, in which there is a hollow cylinder
of very compact carbon. In the middle of the carbon cylinder
is a cylindrical porous vessel of white clay, which contains
dilute sulphuric acid ; in this dips a zinc cylinder. Each zinc
cylinder is connected by a metal ring with the carbon cylinder
of the next vessel, the last zinc cylinder, n, is connected with

ON THE CONSERVATION OF FORCE. 311

one platinum plate, and the first carbon cylinder, p, with the
other platinum plate of the apparatus for the decomposition of
water.

If now the conducting circuit of this galvanic apparatus is
completed, and the decomposition of water begins, a chemical
process takes place simultaneously in the cells of the voltaic
battery. Zinc takes oxygen from the surrounding water and
undergoes a slow combustion. The product of combustion
thereby produced, oxide of zinc, unites further with sulphuric
acid, for which it has a powerful affinity, and sulphate of zinc,
a saline kind of substance, dissolves in the liquid. The oxygen,
moreover, which is withdrawn from it is taken by the water
from the nitric acid surrounding the cylinder of carbon, which is
very rich in it, and readily gives it up. Thus, 'in the galvanic
battery zinc burns to sulphate of zinc at the cost of the oxygen
of nitric acid.

Thus, while one product of combustion, water, is again
separated, a new combustion is taking place — that of zinc.
While we there reproduce chemical affinity which is capable of
work, it is here lost. The electrical current is, as it were, only
the carrier which transfers the chemical force of the zinc
uniting with oxygen and acid to water in the decomposing cell,
and uses it for overcoming the chemical force of hydrogen and
oxygen.

In this case, we can restore work which has been lost, but
only by using another force, that of oxidising zinc.

Here we have overcome chemical forces by chemical forces,
through the instrumentality of the electrical current. But we
can attain the same object by mechanical forces, if we produce
the electrical current by a magneto-electrical machine, Fig. 50.
If we turn the handle, the anker R R1, on which is coiled
copper- wire, rotates in front of the poles of the horse -shoe
magnet, and in these coils electrical currents are produced, which
can be led from the points a and 6. If the ends of these wires
are connected with the apparatus for decomposing water, we
obtain hydrogen and oxygen, though in far smaller quantity than
by the aid of the battery which we used before. But this pro-

312 ON THE CONSEEVATION OF FORCE.

cess is interesting, for the mechanical force of the arm which
Fm. 50.

turns the wheel produces the work which is required for separ-
ating the combined chemical elements. Just as the steam-

ON THE CONSERVATION OF FORCE. 313

engine changes chemical into mechanical force the magneto-elec-
trical machine transforms mechanical force into chemical.

The application of electrical currents opens out a large
number of relations between the various natural forces. We
have decomposed water into its elements by such currents, and
should be able to decompose a large number of other chemical
compounds. On the other hand, in ordinary galvanic batteries
electrical currents'are produced by chemical forces.

In all conductors through which electrical currents pass they
produce heat ; I stretch a thin platinum wire between the ends
n and p of the galvanic battery, Fig. 49 ; it becomes ignited
and melts. On the other hand, electrical currents are pro-
duced by heat in what are called thermo-electric elements.

Iron which is brought near a spiral of copper wire, traversed
by an electrical current, becomes magnetic, and then attracts
other pieces of iron, or a suitably placed steel magnet. We thus
obtain mechanical actions which meet with extended applications
in the electrical telegraph, for instance. Fig. 51, represents a
Morse's telegraph in one-third of the natural size. The essen-
tial part is a horse-shoe shaped iron core, which stands in the
copper spirals b b. Just over the top of this is a small steel
magnet c c, which is attracted the moment an electrical current,
arriving by the telegraph wire, traverses the spirals b b. The
magnet c c is rigidly fixed in the lever d d, at the other end of
which is a style ; this makes a mark on a paper band, drawn
by a clock-work, as often and as long as c c is attracted by the
magnetic action of the electrical current. Conversely, by revers-
ing the magnetism in the iron core of the spirals bb, we should
obtain in them an electrical current just as we have obtained such
currents in the magneto-electrical machine, Fig. 50 ; in the spirals
of that machine there is an iron core which, by being approached
to the poles of the large horse-shoe magnet, is sometimes magnet-
ised in one and sometimes in the other direction.

I will not accumulate examples of such relations; in subse-
quent lectures we shall come across them. Let us review
these examples once more, and recognise in them the law which
is common to all.

314

ON THE CONSERVATION OF FORCE.

A raised weight can produce work, but in doing so it must
necessarily sink from its height, and, when it has fallen as deep
as it can fall, its gravity remains as before, but it can no longer
do work.

A stretched spring can do work, but in so doing it becomes
loose. The velocity of a moving mass can do work, but in doing
so it comes to rest. Heat can perform work ; it is destroyed in

FIG. 51.

the operation. Chemical forces can perform work, but they ex-
haust themselves in the effort.

Electrical currents can perform work, but to keep them up
we must consume either chemical or mechanical forces, or heat.

We may express this generally. It is a universal character of
all known natural forces that their capacity for work is ex-
hausted in the degree in which they actually perform work.

We have seen, further, that when a weight fell without per-
forming any work, it either acquired velocity or produced heat.

ON THE CONSEEVATION OF FORCE. 315

We might also drive a magneto-electrical machine by a falling
weight; it would then furnish electrical currents.

We have seen that chemical forces, when they come into
play, produce either heat or electrical currents or mechanical
work.

We have seen that heat may be changed into work ; there
are apparatus (thermo-electric batteries) in which electrical cur-
rents are produced by it. Heat can directly separate chemical
compounds ; thus, when we burn limestone, it separates carbonic
acid from lime.

Thus, whenever the capacity for work of one natural force
is destroyed, it is transformed into another kind of activity.
Even within the circuit of inorganic natural forces, we can
transform each of them into an active condition by the aid of
any other natural force which is capable of work. The connec-
tions between the various natural forces which modern physics
has revealed, are so extraordinarily numerous that several
entirely different methods may be discovered for each of these
problems.

I have stated how we are accustomed to measure mechanical
work, and how the equivalent in work of heat may be found.
The equivalent in work of chemical processes is again measured
by the heat which they produce. By similar relations, the
equivalent in work of the other natural forces may be expressed
in terms of mechanical work.

If, now, a certain quantity of mechanical work is lost, there
is obtained, as experiments made with the object of determining
this point show, an equivalent quantity of heat, or, instead of
this, of chemical force ; and, conversely, when heat is lost, we
gain an equivalent quantity of chemical or mechanical force ;
and, again, when chemical force disappears, an equivalent of
heat or work ; so that in all these interchanges between various
inorganic natural forces working force may indeed disappear
in one form, but then it reappears in exactly equivalent
quantity in some other form ; it is thus neither increased nor di-
minished, but always remains in exactly the same quantity.
We shall subsequently see that the same law holds good also

316 ON THE CONSERVATION OF FORCE.

for processes in organic nature, so far as the facts have been
tested.

It follows thence that the total quantity of all the forces ca-
pable of work in the whole, universe remains eternal and un-
changed throughout all their changes. All change in nature
amounts to this, that force can change its form and locality
without its quantity being changed. The universe possesses,
once for all, a store of force which is not altered by any change
of phenomena, can neither be increased nor diminished, and
which maintains any change which takes place on it.

You see how, starting from considerations based on the
immediate practical interests of technical work, we have been
led up to a universal natural law, which, as far as all previous
experience extends, rules and embraces all natural processes;
which is no longer restricted to the practical objects of human
utility, but expresses a perfectly general and particularly cha-
racteristic property of all natural forces, and which, as regards
generality, is to be placed by the side of the laws of the unalter-
ability of mass, and the unalterability of the chemical elements.

At the same time, it also decides a great practical question
which has been much discussed in the last two centuries, to the
decision of which an infinity of experiments has been made
and an infinity of apparatus constructed — that is, the question
of the possibility of a perpetual motion. By this was under-
stood a machine which was to work continuously without the
aid of any external driving force. The solution of this problem
promised enormous gains. Such a machine would have had all
the advantages of steam without requiring the expenditure of
fuel. Work is wealth. A machine which could produce work
from nothing was as good as one which made gold. This
problem had thus for a long time occupied the place of gold
making, and had confused many a pondering brain. That a
perpetual motion could not be produced by the aid of the then
known mechanical forces could be demonstrated in the last
century by the aid of the mathematical mechanics which had at
that time been developed. But to show also that it is not
possible even if heat, chemical forces, electricity, and magnetism

ON THE CONSERVATION OF FORCE. 317

were made to co-operate, could not be done without a know-
ledge of our law in all its generality. The possibility of a per-
petual motion was first finally negatived by the law of the con-
servation of force, and this law might also be expressed in the
practical form that no perpetual motion is possible, that force
cannot be produced from nothing; something must be con-
sumed.

You will only be ultimately able to estimate the importance
and the scope of our law when you have before your eyes a
series of its applications to individual processes in nature.

What I have to-day mentioned as to the origin of the
moving forces which are at our disposal, directs us to something
beyond the narrow confines of our laboratories and our manu-
factories, to the great operations at work in the life of the earth
and of the universe. The force of falling water can only flow
down from the hills when rain and snow bring it to them. To
furnish these, we must have aqueous vapour in the atmosphere,
which can only be effected by the aid of heat, and this heat
comes from the sun. The steam-engine needs the fuel which
the vegetable life yields, whether it be the still active life of the
surrounding vegetation, or the extinct life which has produced
the immense coal deposits in the depths of the earth. The
forces of man and animals must be restored by nourishment ;
all nourishment comes ultimately from the vegetable kingdom,
and leads us back to the same source.

You see then that when we inquire into the origin of the
moving forces which we take into our service, we are thrown
back upon the meteorological processes in the earth's atmosphere,
on the life of plants in general, and on the sun.

THE AIM AND PROGRESS OF
PHYSICAL SCIENCE.

An Opening Address delivered at the Naturforscher Versammh
Inmbruck, 1869.

IN accepting the honour you have done me in requesting me to
deliver the first lecture at the opening meeting of this year's
Association, it appears to me to be more in keeping with the im-
port of the moment and the dignity of this assembly that, in
place of dealing with any particular line of research of my own,
I should invite you to cast a glance at the development of all the
branches of physical science represented on these occasions.
These branches include a vast area of special investigation,
material of almost too varied a character for comprehension, the
range and intrinsic value of which become greater with each
year, while no bounds can be assigned to its increase. During
the first half of the present century we had an Alexander von
Humboldt, who was able to scan the scientific knowledge of his
time in its details, and to bring it within one vast generalisation.
At the present juncture, it is obviously very doubtful whether
this task could be accomplished in a similar way, even by a
mind with gifts so peculiarly suited for the purpose as Humboldt's
was, and if all his time and work were devoted to the purpose.
We, however, working as we do to advance a single depart-
ment of science, can devote but little of our time to the
simultaneous study of the other branches. As soon as we enter
upon any investigation, all our powers have to be concentrated
on a field of narrowed limit. We have not only, like the philo-

320 AIM AND PROGRESS OF PHYSICAL SCIENCE.

logian or historian, to seek out and search through books and
gather from them what others have already determined about
the subject under inquiry ; that is but a secondary portion of
our work. We have to attack the things themselves, and in
doing so each offers new and peculiar difficulties of a kind quite
different from those the scholar encounters ; while in the ma-
jority of instances, most of our time and labour is consumed by
secondary matters that are but remotely connected with the
purpose of the investigation.

At one time, we have to study the errors of our instru-
ments, with a view to their diminution, or, where they cannot
be removed, to compass their detrimental influence ; while at
other times we have to watch for the moment when an organism
presents itself under circumstances most favourable for research.
Again, in the course of our investigation we learn for the first
time of possible errors which vitiate the result, or perhaps
merely raise a suspicion that it may be vitiated, and we find
ourselves compelled to begin the work anew, till every shadow
of doubt is removed. And it is only when the observer takes
such a grip of the subject, so fixes all his thoughts and all his
interest upon it that he cannot separate himself from it for
weeks, for months, even for years, cannot force himself away
from it, in short, till he has mastered every detail, and feels
assured of all those results which must come in time, that a
perfect and valuable piece of work is done. You are all aware
that in every good research, the preparation, the secondary
operations, the control of possible errors, and especially in the
separation of the results attainable in the time from those that
cannot be attained, consume far more time than is really required to
make actual observations or experiments. How much more
ingenuity and thought are expended in bringing a refractory
piece of brass or glass into subjection, than in sketching out the
plan of the whole investigation ! Each of you will have ex-
perienced such impatience and over-excitement during work
where all the thoughts are directed on a narrow range of
questions, the import of which to an outsider appears trifling
and contemptible because he does not see the end to which the

AIM AND PROGRESS OF PHYSICAL SCIENCE. 321

preparatory work tends. I believe I am correct in thus de-
scribing the work and mental condition that precedes all those
great results which hastened so much the development of science
after its long inaction, and gave it so powerful an influence over
every phase of human life.

The period of work, then, is no time for broad comprehensive
survey. When, however, the victory over difficulties has
happily been gained, and results are secured, a period of repose
follows, and our interest is next directed to examining the bear-
ing of the newly established facts, and once more venturing on
a wider survey of the adjoining territory. This is essential, and
those only who are capable of viewing it in this light can hope
to find useful starting-points for further investigation.

The preliminary work is followed by other work, treating
of other subjects. In the course of its different stages, the ob-
server will not deviate far from a direction of more or less nar-
rowed range. For it is not alone of importance to him that he
may have collected information from books regarding the region
to he explored. The human memory is, on the whole, proportion-
ately patient, and can store up an almost incredibly large amount
of learning. In addition, however, to the knowledge which the
student of science acquires from lectures and books, he requires
intelligence, which only an ample and diligent perception can
give him ; he needs skill, which comes only by repeated experi-
ment and long practice. His senses must be sharpened for cer-
tain kinds of observation, to detect minute differences of form,
colour, solidity, smell , &c. , in the obj ect under examination; his hand
must be equally trained to the work of the blacksmith, the lock-
smith, and the carpenter, or the draughtsman and the violin-
player, and, when operating with the microscope, must surpass
the lace-maker in delicacy of handling the needle. Moreover,
when he encounters superior destructive forces, or performs
bloody operations upon man or beast, he must possess the courage
and coolness of the soldier. Such qualities and capabilities,
partly the result of natural aptitude, partly cultivated by long
practice, are not so readily and so easily acquired as the mere
massing of facts in the memory ; and hence it happens that an

I. T

322 AIM AND PROGRESS OF PHYSICAL SCIENCE.

investigator is compelled, during the entire labours of his life,
to strictly limit his field, and to confine himself to those branches
which suit him best.

We must not, however, forget that the more the individual
worker is compelled to narrow the sphere of his activity, so
much the more will his intellectual desires induce him not to
sever Ids connection with the subject in its entirety. How shall
he go stout and cheerful to his toilsome work, how feel confident
that what has given him so much labour will not moulder use-
lessly away, but remain a thing of lasting value, unless he
keeps alive within himself the conviction that he also has added
a fragment to the stupendous whole of Science which is to
make the reasonless forces of nature subservient to the moral
purposes of humanity ?

An immediate practical use cannot generally be counted on
a priori for each particular investigation. Physical science, it
is true, has by the practical realisation of its results transformed
the entire life of modern humanity. But, as a rule, these appli-
cations appear under circumstances when they are least expected ;
to search in that direction generally leads to nothing unless cer-
tain points have already been definitely fixed, so that all that has
to be done is to remove certain obstacles in the way of practical
application. If we search the records of the most important
discoveries, they are either, especially in earlier times, made by
workmen who their whole lives through did but one kind of
work, and, either by a happy accident, or by a searching, re-
peated, tentative experiment, hit upon some new method ad-
vantageous to their particular handicraft; others there are,
and this is especially the case in most of the recent discoveries,
which are the fruit of a matured scientific acquaintance with
the subject in question, an acquaintance that in each instance
had originally been acquired without any direct view to

Our Association represents the whole of natural science. To-
day are assembled mathematicians, physicists, chemists and
zoologists, botanists and geologists, the teacher of science and
the physician, the technologist and the amateur who finds

AIM AND PROGRESS OF PHYSICAL SCIENCE. 323

scientific pursuits relaxation from other occupation. Here
each of us hopes to meet with fresh impulse and encourage-
ment for his peculiar work; the man who lives in a small
country place hopes to meet with the recognition, otherwise
unattainable, of having aided in the advance of science; he
hopes by intercourse with men pursuing more or less the
same object to mark the aim of new researches. We re-
joice to find among us a goodly proportion of members re-
presenting the cultivated classes of the nation; we see influ-
ential statesmen among us. They all have an interest in
our labours ; they look to us for further progress in civili-
sation, further victories over the powers of nature. They it
is who place at our disposal the actual means for carrying
on our labours and are therefore entitled to inquire into
the results of those labours. It appears to me, therefore,
appropriate on this occasion to take account of the progress of
science as a whole, of the objects it aspires to, and the magni-
tude of the efforts made to attain them.

Such a survey is desirable ; that it lies beyond the powers
of any one man to accomplish with even an approximate com-
pleteness such a task as this is clear from what I have already
said. If I stand here to-day with such a problem entrusted to
me, my excuse must be that no other would attempt
it, and I hold that an attempt to accomplish it, even if
with small success, is better than none whatever. Besides,
a physiologist has perhaps more than all others immediate oc-
casion to maintain a clear and constant view of the entire field,
for in the present state of things it is peculiarly the lot of the
physiologist to receive help from all other branches of science
and to stand in alliance with them. In physiology, in fact, the
importance of the vast strides to which I shall allude has been
chiefly felt, while to physiology, and the leading controversies
arising in it, some of the most valuable discoveries are directly
due.

If I leave considerable gaps in my survey, my excuse must
be the magnitude of the task, and the fact that the pressing
summons of my friend the secretary of this Association reached
Y 2

324 AIM AND PEOGRESS OF PHYSICAL SCIENCE.

me but recently, and that too in the course of my summer
holiday in the mountains. The gaps which I may leave will
at all events be abundantly tilled up by the proceedings of the
Sections.

Let us then proceed to our task. In discussing the progress
of physical science as a whole, the first question which presents
itself is, By what standard are we to estimate this progress ?

To the uninitiated, this science of ours is an accumulation
of a vast number of facts, some of which are conspicuous for
their practical utility, while others are merely curiosities, or
objects of wonder. And, if it were possible to classify this
unconnected mass of facts, as was done in the Linnean system,
or in encyclopaedias, so that each may be readily found when
required, such knowledge as this would not deserve the name
of science, nor satisfy either the scientific wants of the hviman
mind, or the desire for progressive mastery over the powers of
nature. For the former requires an intellectual grasp of the
connection of ideas, the latter demands our anticipation of a
result in cases yet untried, and under conditions that we
propose to introduce in the course of our experiment. Both
are obviously arrived at by a knowledge of the law of the
phenomena.

Isolated facts and experiments have in themselves no value,
however great their number may be. They only become
valuable in a theoretical or practical point of view when they
make us acquainted with the law of a series of uniformly
recurring phenomena, or, it may be, only give a negative result
showing an incompleteness in our knowledge of such a law, till
then held to be perfect. From the exact and universal con-
formity to law of natural phenomena, a single observation of a
condition that we may presume to be rigorously conformable to
law, suffices, it is true, at times to establish a rule with the
highest degree of probability ; just as, for example, we assume
our knowledge of the skeleton of a prehistoric animal to be
complete if we find only one complete skeleton of a single
individual. But we must not lose sight of the fact that the isolated
observation is not of value in that it is isolated, but because it

AIM AND PROGRESS OF PHYSICAL SCIENCE. 325

is an aid to the knowledge of the conformable regularity in
bodily structure of an entire species of organisms. In like
manner, the knowledge of the specific heat of one small frag-
ment of a new metal is important because we have no grounds
for doubting that any other pieces of the same metal subjected
to the same treatment will yield the same result.

To find the law by which they are regulated is to under-
stand phenomena. For law is nothing more than the general
conception in which a series of similarly recurring natural
processes may be embraced, Just as we include in the concep-
tion ' mammal ' all that is common to the man, the ape, the
dog, the lion, the hare, the horse, the whale, &c., so we com-
prehend in the law of refraction that which we observe to
regularly recur when a ray of light of any colour passes in any
direction through the common boundary of any two transparent
media.

A law of nature, however, is not a mere logical conception
that we have adopted as a kind of memoria technica to enable
us to more readily remember facts. We of the present day
have already sufficient insight to know that the laws of nature
are not things which we can evolve by any speculative method.
On the contrary, we have to discover them in the facts; we
have to test them by repeated observation or experiment, in
constantly new cases, under ever- varying circumstances ; and in
proportion only as they hold good under a constantly increasing
change of conditions, in a constantly increasing number of cases,
and with greater delicacy in the means of observation, does
our confidence in their trustworthiness rise.

Thus the laws of nature occupy the position of a power
with which we are not familiar, not to be arbitrarily selected
and determined in our minds, as one might devise various
systems of animals and plants one after another, so long as the
object is only one of classification. Before we can say that our
knowledge of any one law of nature is complete, we must see
that it holds good without exception, and make this the test of
its correctness. If we can be assured that the conditions under
which the law operates have presented themselves, the result

326 AIM AND PROGRESS OF PHYSICAL SCIENCE.

must ensue without arbitrariness, without choice, without our
co-operation, and from the very necessity which regulates the
things of the external world as well as our perception. The
law then takes the form of an objective power, and for that
reason we call it force.

For instance, we regard the law of refraction objectively as
a refractive force in transparent substances; the law of chemical
affinity, as the elective force exhibited by different bodies towards
one another. In the same way, we speak of electrical force of
contact of metals, of a force of adhesion, capillary force, and so
on. Under these names are stated objectively laws which for
the most part comprise small series of natural processes, the
conditions of which are somewhat involved. In science our con-
ceptions begin in this way, proceeding to generalisations from a
number of well-established special laws. We must endeavour
to eliminate the incidents of form and distribution in space which
masses under investigation may present by trying to find from
the phenomena attending large visible masses laws for the opera-
tion of infinitely small particles ; or, expressed objectively, by
resolving the forces of composite masses into the forces of their
smallest elementary particles. But precisely in this, the simplest
form of expression of force — namely, of mechanical force acting
on a poiii t of the mass — is it especially clear that force is only
the law of action objectively expressed. The force arising from
the presence of such and such bodies is equivalent to the ac-
celeration of the mass on which it operates multiplied by this
mass. The actual meaning of such an equation is that it ex-
presses the following law : if such and such masses are present
and no other, such and such acceleration of their individual
points occurs. Its actual signification may be compared with
the facts and tested by them. The abstract conception of force
we thus introduce implies, moreover, that we did not discover
this law at random, that it is an essential law of phenomena.

Our desire to comprehend natural phenomena, in other words
to ascertain their laws, thus takes another form of expression —
that is, we have to seek out the forces which are the causes of
the phenomena. The conformity to Jaw in nature must be con-

AIM AND PROGRESS OF PHYSICAL SCIENCE. 327

ceived as a causal connection the moment we recognise that it is
independent of our thought and will.

If then we direct our inquiry to the progress of physical
science as a whole, we shall have to judge of it by the measure
in which the recognition and knowledge of a causative connec-
tion embracing all natural phenomena has advanced.

On looking back over the history of our sciences, the first
great example we find of the subjugation of a wide mass of facts
to a comprehensive law occurred in the case of theoretical me-
chanics, the fundamental conception of which was first clearly
propounded by Galileo. The question then was to find the
general propositions that to us now appear so self-evident, that
all substance is inert, and that the magnitude of force is to be
measured not by its velocity, but by changes in it. At first the
operation of a continually acting force could only be represented
as a series of small impacts. It was not till Leibnitz and Newton,
by the discovery of the differential calculus, had dispelled the
ancient darkness which enveloped the conception of the infinite,
and had clearly established the conception of the Continuous and
of continuous change, that a full and productive application of
the newly-found mechanical conceptions made any progress. The
most singular and most splendid instance of such an application
was in regard to the motion of the planets, and I need scarcely
remind you here how brilliant an example astronomy has been for
the development of the other branches of science. In its case,
by the theory of gravitation, a vast and complex mass of facts
were first embraced in a single principle of great simplicity, and
such a reconciliation of theory and fact established as has never
been accomplished in any other department of science, either
before or since. In supplying the wants of astronomy, have
originated almost all the exact methods of measurement as well
as the principal advances made in modern mathematics; the
science itself was peculiarly fitted to attract the attention of the
general public, partly by the grandeur of the objects under in-
vestigation, partly by its practical utility in navigation and
geodesy, and the many industrial and social interests arising
from them.

328 AIM AND PROGRESS OF PHYSICAL SCIENCE.

Galileo began with the study of terrestrial gravity. Newton
extended the application, at first cautiously and hesitatingly, to
the moon, then boldly to all the planets. And, in more recent
times, we learn that these laws of the common inertia and
gravitation of all ponderable masses hold good of the movements
of the most distant double stars of which the light has yet
reached us.

During the latter half of the last and the first half of the
present century came the great progress of chemistry, which
conclusively solved the ancient problem of discovering the ele-
mentary substances, a task to which so much metaphysical
speculation had been devoted. Reality has always far exceeded
even the boldest and wildest speculation, and, in the place of
the four primitive metaphysical elements — fire, water, air, and
earth — we have now the sixty-five simple bodies of modern
chemistry. Science has shown that these elements are really
indestructible, unalterable in their mass, unalterable also in their
properties ; in short, that from every condition into which they
may have been converted, they can invariably be isolated, and
recover those qualities which they previously possessed in the
free state. Through all the varied phases of the phenomena of
animated and inanimate nature, so far as we are acquainted
with them, in all the astonishing results of chemical decompo-
sition and combination, the number and diversity of which the
chemist with unwearied diligence augments from year to year,
the one law of the immutability of matter prevails as a necessity
that knows no exception. And chemistry has already pressed
on into the depths of immeasurable space, and detected in the
most distant suns or nebulae indications of well-known terrestrial
elements, so that doubts respecting the prevailing homogeneity
of the matter of the universe no longer exist, though certain
elements may perhaps be restricted to certain groups of the
heavenly bodies.

From this invariability of the elements follows another and
wider consequence. Chemistry shows by actual experiment that
all matter is made up of the elements which have been already
isolated. These elements may exhibit great differences as regards

AIM AND PKOGRESS OF PHYSICAL SCIENCE. 329

combination or mixture, the mode of aggregation or molecular
structure — that is to say, they may vary the mode of their
distribution in space. In their properties, on the other hand,
they are altogether unchangeable; in other words, when referred
to the same compound, as regards isolation, and to the same
state of aggregation, they invariably exhibit the same properties
as before. If, then, all elementary substances are unchangeable
in respect to their properties, and only changeable as regards
their combination and their states of aggregation — that is, in
respect to their distribution in space — it follows that all changes
in the world are changes in the local distribution of elementary
matter, and are eventually brought about through Motion.

If, however, motion be the primordial change which lies at
the root of all the other changes occurring in the world, eveiy
elementary force is a force of motion, and the ultimate aim of
physical science must be to determine the movements which are
the real causes of all other phenomena, and discover the motive
powers on which they depend; in other words, to merge itself
into mechanics.

Though this is clearly the final consequence of the qualitative
and quantitative immutability of matter, it is after all an ideal
proposition, the realisation of which is still very remote. The
field is a prescribed one, in which we have succeeded in tracing
back actually observed changes to motions and forces of motion
of a definite kind. Besides astronomy, may be mentioned the
purely mechanical part of physics, then acoustics, optics, and
electricity ; in the science of heat and in chemistry, strenuous
endeavours are being made towards perfecting definite views
respecting the nature of the motion and position of mole-
cules, while physiology has scarcely made a definite step in this
direction.

This renders all the more important, therefore, a noteworthy
advancement of the most general importance made during the
last quarter of a century in the direction we are considering.
If all elementary forces are forces of motion, and all, consequently,
of similar nature, they should all be measurable by the same
standard, that is, the standard of the mechanical forces. And

330 AIM AND PROGRESS OF PHYSICAL SCIENCE.

that this is actually the fact is now regarded as proved. The
law expressing this is known under the name of the law of the
Conservation of Force.

For a small group of natural phenomena it had already been
pronounced by Newton, then more definitely and in more general
terms by D. Bernouilli, and so continued of recognised appli-
cation in the greater part of the then known purely mechanical
processes. Certain amplifications at times attracted attention,
like those of Ruinford, Davy, and Montgolfier. The first,
however, to compass the clear and distinct idea of this law, and
to venture to pronounce its absolute universality, was one whom
we shall have soon the pleasure of hearing from this platform,
Dr. Robert Mayer, of Heilbronn. While Dr. Mayer was led
by physiological questions to the discovery of the most general
form of this law, technical questions in mechanical engineering
led Mr. Joule, of Manchester, simultaneously, and independently
of him, to the same considerations ; and it is to Mr. Joule that
we are indebted for those important and laborious experimental
researches in that department where the applicability of the law
of the conservation of force appeared most doubtful, and where
the greatest gaps in actual knowledge occurred, namely, in the
production of work from heat, and of heat from work.

To state the law clearly it was necessary, in contradistinction
to Galileo's conception of the intensity of force, that a new
mechanical idea should be elaborated, which we may term the
conception of the quantity of force, and which has also been
called quantity of work or of energy.

A way to this conception of the quantity of force had been
prepared partly, in theoretical mechanics, through the conception
of the amount of vis viva of a moving body, and partly by
practical mechanics through the conception of the motive power
necessary to keep a machine at work. Practical machinists had
already found a standard by which any motive power could be
measured, in the determination of the number of pounds that
it could lift one foot in a second ; and, as is known, a horse-power
was defined to be equivalent to the motive power required to
lift seventy kilogrammes one metre in each second.

AIM AND PROGRESS OF PHYSICAL SCIENCE. 331

Machines, and the motive powers required for their move-
ment, furnish, in fact, the most familiar illustrations of the
uniformity of all natural forces expressed by the law of the
conservation of force. Any machine which is to be set in motion
requires a mechanical motive power. Whence this power is
derived or what its form is of no consequence, provided only
it be sufficiently great and act continuously. At one time we
employ a steam-engine, at another a water-wheel or turbine,
here horses or oxen at a whim, there a windmill, or, if but little
power is required, the human arm, a raised weight, or an electro-
magnetic engine. The choice of the machine is merely depen-
dent on the amount of power we would use, or the force of
circumstance. In the watermill the weight of the water flowing
down the hills is the agent; it is lifted to the hills by a
meteorological process, and becomes the source of motive power
for the mill. In the windmill it is the vis viva of the moving
air which drives round the sails ; this motion also is due to a
meteorological operation of the atmosphere. In the steam-engine
we have the tension of the heated vapour which drives the pis-
ton to and fro ; this is engendered by the heat arising from the
combustion of the coal in the fire-box, in other words, by a
chemical process ; and in this case the latter action is the source
of the motive power. If it be a horse or the human arm which
is at work, we have the muscles stimulated throvigh the nerves,
directly producing the mechanical force. In order, however,
that the living body may generate muscular power, it must be
nourished and breathe. The food it takes separates again from
it, after having combined with the oxygen inhaled from the air,
to form carbonic acid and water. Here again, then, a chemical
process is an essential element to maintain muscular power.
A similar state of things is observed in the electro-magnetic
machines of our telegraphs.

Thus, then, we obtain mechanical motive force from the
most varied processes of nature in the most different ways ; but
it will also be remarked in only a limited quantity. In doing
so we always consume something that nature supplies to us. In
the watermill we use a quantity of water collected at an eleva-

332 AIM AND PROGRESS OF PHYSICAL SCIENCE.

tion, coal in the steam-engine, zinc and sulphuric acid in the
electro-magnetic machine, food for the horse ; in the windmill
we use up the motion of the wind, which is arrested by the sails.

Conversely, if we have a motive force at our disposal, we can
develop with it forms of action of the most varied kind. It
will not be necessary in this place to enumerate the countless
diversity of industrial machines, and the varieties of work which
they perform.

Let us rather consider the physical differences of the possible
performance of a motive power. With its help we can raise
loads, pump water to an elevation, compress gases, set a railway
train in motion, and through friction generate heat. By its aid
we can turn magneto -electric machines, and produce electric
currents, and with them decompose water and other chemical
compounds having the most powerful affinities, render wires in-
candescent, magnetise iron, &c.

Moreover, had we at our disposal a sufficient mechanical
motive force, we could restore all those states and conditions
from which, as was seen above, we are enabled at the outset to
derive mechanical motive power.

As, however, the motive power derived from any given
natural process is limited, so likewise is there a limitation to the
total amount of modifications which we may produce by the use
of any given motive power.

These deductions, arrived at first in isolated instances from
machines and physical apparatus, have now been welded into a
law of nature of the widest validity. Every change in nature
is equivalent to a certain development, or a certain consumption
of motive force. If motive power be developed, it may either
appear as such, or be directly used up again to form other changes
equivalent in magnitude. The leading determinations of this
equivalency are founded on Joule's measurements of the me-
chanical equivalent of heat. When, by the application of heat,
we set a steam-engine in motion, heat proportional to the work
done disappears within it ; in short, the heat which can warm a
given weight of water one degree of the Centigrade scale is able,
if converted into work, to lift the same weight of water to a

ATM AND PROGRESS OF PHYSICAL SCIENCE. 333

height of 425 metres. If we convert work into heat by friction
we again use, in heating a given weight of water one degree
Centigrade, the motive force which the same quantity of water
would have generated in flowing down from a height of 425
metres. Chemical processes generate heat in definite proportion,
and in like manner we estimate the motive power equivalent to
such chemical forces ; and thus the energy of the chemical force
of affinity is also measurable by the mechanical standard. The
same holds true for all the other forms of natural forces, but it
will not be necessary to pursue the subject further here.

It has actually been established, then, as a result of these
investigations, that all the forces of nature are measurable by
the same mechanical standard, and that all pure motive forces
are, as regards performance of work, equivalent. And thus
one great step towards the solution of the comprehensive
theoretical task of referring all natural phenomena to motion
has been accomplished.

Whilst the foregoing considerations chiefly seek to elucidate
the logical value of the law of the conservation of force, its
actual signification in the general conception of the processes of
nature is expressed in the grand connection which it establishes
between the entire processes of the universe, through all dis-
tances of place or time. The universe appears, according to
this law, to be endowed with a store of energy which, through
all the varied changes in natural processes, can neither be
increased nor diminished, which is maintained therein in ever-
varying phases, but, like matter itself, is from eternity to
eternity of unchanging magnitude: acting in space, but not
divisible, as matter is, with it. Every change in the world
simply consists in a variation in the mode of appearance of this
store of energy. Here we find one portion of it as the vis viva of
moving bodies, there as regular oscillation in light and sound ;
or, again, as heat, that is to say, the irregular motion of in-
visible particles; at another point the energy appears in the
form of the weight of two masses gravitating towards each
other, then as internal tension and pressure of elastic bodies, or
as chemical attraction, electrical tension, or magnetic distri-

334 AIM AND PROGRESS OF PHYSICAL SCIENCE.

bution. If it disappear in one form, it reappears as surely in
another ; and whenever it presents itself in a new phase we are
certain that it does so at the expense of one of its other forms.

Carnot's law of the mechanical theory of heat, as modified
by Clausius, has, in fact, made it clear that this change moves
in the main continuously onward in a definite direction, so that
a constantly increasing amount of the great store of energy in
the universe is being transformed into heat.

We can, therefore, see with the mind's eye the original
condition of things in which the matter composing the celestial
bodies was still cold, and probably distributed as chaotic vapour
or dust through space ; we see that it must have developed heat
when it collected together under the influence of gravity. Even
at the present time Spectrum analysis (a method the theoretical
principles of which owe their origin to the mechanical theory
of heat) enables us to detect remains of this loosely distributed
matter in the nebulse; we recognise it in the meteor-showers
and comets ; the act of agglomeration and the development of
heat still continue, though in our portion of the stellar system
they have ceased to a great extent. The chief part of the
primordial energy of the matter belonging to our system is now
in the form of solar heat. This energy, however, will not
remain locked up in our system for ever : portions of it are
continually radiating from it, in the form of light and heat,
into infinite space. Of this radiation our earth receives a share.
It is these solar heat-rays which produce on the earth's surface
the winds and the currents of the ocean, and lift the watery
vapour from the tropical seas, which, distilling over hill and
plain, returns as springs and rivers to the sea. The solar rays
impart to the plant the power to separate from carbonic acid
and water those combustible substances which serve as food for
animals, and thus, in even the varied changes of organic life,
the moving power is derived from the infinitely vast store of
the universe.

This exalted picture of the connection existing between all the
processes of nature has been often presented to us in recent
times ; it will suffice here that I direct attention to its leading

AIM AND PROGRESS OF PHYSICAL SCIENCE. 335

features. If the task of physical science be to determine laws, a
step of the most comprehensive significance towards that object
has here been taken.

The application of the law of the conservation of force to
the vital processes of animals and plants, which has just been
discussed, leads us in another direction in which our knowledge
of nature's conformity to law has made an advance. The law
to which we referred is of the most essential importance in lead-
ing questions of physiology, and it was for this reason that Dr.
Mayer and I were led on physiological grounds to investigations
having especial reference to the conservation of force.

As regards the phenomena of inorganic nature all doubts
have long since been laid to rest respecting the principles of the
method. It was apparent that these phenomena had fixed laws,
and examples enough were already known to make the finding
of such laws probable.

In consequence, however, of the greater complexity of the
vital processes, their connection with mental action, and the
unmistakable evidence of adaptability to a purpose which
organic structures exhibit, the existence of a settled conformity
to law might well appear doubtful, and, in fact, physiology has
always had to encounter this fundamental question : Are all vital
processes absolutely conformable to law ? Or is there, perhaps,
a range of greater or less magnitude within which an excep-
tion prevails ? More or less obscured by words, the view of
Paracelsus, Helmont, and Stahl, has been, and is at present,
held, particularly outside Germany, that there exists a soul of
life (' Lebensseele ') directing the organic processes which is en-
dowed more or less with consciousness like the soul of man.
The influence of the inorganic forces of nature on the organism
was still recognised on the assumption that the soul of life only
exercises power over matter by means of the physical and chemi-
cal forces of matter itself; so that without this aid it could ac-
complish nothing, but that it possessed the faculty of suspending
or permitting the operation of the forces at pleasure.

After death, when no longer subject to the control of the
soul of life or vital force, it was these very chemical forces of

"S36 AIM AND PROGRESS OF PHYSICAL SCIENCE.

organic matter which brought about decomposition. In short,
through all the different modes of expressing it, whether it was
termed the Arch'aus, the anima inscia, or the vital force and
the restorative power of nature, the faculty to build up the
body according to system, and to suitably accommodate it to
external circumstances, remained the most essential attribute
of this hypothetically controlling principle of the vitalistic
theory with which, therefore, by reason of its attributes, only
the name of soul fully harmonised.

It is apparent, however, that this notion runs directly counter
to the law of the conservation of force. If vital force were
for a time to annul the gravity of a weight, it could be raised
without labour to any desired height, and subsequently, if the
action of gravity were again restored, could perform work of any
desired magnitude. And thus work could be obtained out of
nothing without expense. If vital force could for a time suspend
the chemical affinity of carbon for oxygen, carbonic acid could
be decomposed without work being employed for that purpose,
and the liberated carbon and oxygen could perform new
work.

In reality, however, no trace of such an action is to be met
with as that of the living organism being able to generate an
amount of work without an equivalent expenditure. When we
consider the work done by animals, we find the operation com-
parable in every respect with that of the steam-engine. Animals,
like machines, can only move and accomplish work by being
continuously supplied with fuel (that is to say, food) and air
containing oxygen ; both give off again this material in a burnt
state, and at the same time produce heat and work. All investi-
gation, thus far, respecting the amount of heat which an animal
produces when at rest is in no way at variance with the assump-
tion that this heat exactly corresponds to the equivalent, ex-
pressed as work, of the forces of chemical affinity then in
action.

As regards the work done by plants, a source of power, in
every way sufficient, exists in the solar rays which they require
for the increase of the organic matter of their structures.

AIM AND PROGRESS OF PHYSICAL SCIENCE. 337

Meanwhile it is true that exact quantitative determinations of
the equivalents of force, consumed and produced in the vegetable
as well as the animal kingdom, have still to be made in order
to fully establish the exact accordance of these two values.

If, then, the law of the conservation of force hold good also
for the living body, it follows that the physical and chemical
forces of the material employed in building up the body are
in continuous action without intermission and without choice,
and that their exact conformity to law never suffers a moment's
interruption.

Physiologists, then, must expect to meet with an uncon-
ditional conformity to law of the forces of nature in their in-
quiries respecting the vital processes ; they will have to apply
themselves to the investigation of the physical and chemical
processes going on within the organism. It is a task of vast
complexity and extent ; but the workers, in Germany especially,
are both numerous and enthusiastic, and we may already affirm
that their labours have not been unrewarded, inasmuch as our
knowledge of the vital phenomena has made greater progress
during the last forty years than in the two preceding cen-
turies.

Assistance, that cannot be too highly valued, towards the
elucidation of the fundamental principles of the doctrine of
life, has been rendered on the part of descriptive natural history,
through Darwin's theory of the evolution of organic forms, by
which the possibility of an entirely new interpretation of organic
adaptability is furnished.

The adaptability in the construction of the functions of the
living body, most wonderful at any time, and with the progress
of science becoming still more so, was doubtless the chief reason
that provoked a comparison of the vital processes with the
actions of a principle acting like a soul. In the whole external
world we know of but one series of phenomena possessing simi-
lar characteristics, we mean the actions and deeds of an intelli-
gent human being, and we must allow that in innumerable in-
stances the organic adaptability appears to be so extraordinarily
superior to the capacities of the human intelligence that we

338 AIM AND PROGRESS OF PHYSICAL SCIENCE.

might feel disposed to ascribe to it a higher rather than a lower
character.

Before the time of Darwin only two theories respecting
organic adaptability were in vogue, both of which pointed to
the interference of free intelligence in the course of natural pro-
cesses. On the one hand it was held, in accordance with the
vitalistic theory, that the vital processes were continuously di-
rected by a living soul ; and, on the other, recourse was had to an
act of supernatural intelligence to account for the origin of every
living species. The latter view indeed supposes that the causal
connection of natural phenomena had been broken less often,
and allows of a strict scientific examination of the processes
observable in the species of human beings now existing ; but
even it is not able to entirely explain away those exceptions to
the law of causality, and consequently it enjoyed no considerable
favour as opposed to the vitalistic view, which was powerfully
supported, by apparent evidence, that is, by the natural desire
to find similar causes behind similar phenomena.

Darwin's theory contains an essentially new creative thought.
It shows how adaptability of structure in organisms can re-
sult from a blind rule of a law of nature without any interven-
tion of intelligence. I allude to the law of transmission of
individual peculiarities from parent to offspring, a law long
known and recognised, and only needing a more precise defi-
nition. If both parents have individual peculiarities in com-
mon, the majority of their offspring also possess them : and if
among the offspring there are some which present these peculiar-
ities in a less marked degree, there will, on the other hand,
always be found among a great number, others in which the
same peculiarities have become intensified. If, now, these be
selected to propagate offspring, a greater and greater intensifica-
tion of these peculiarities may be attained and transmitted.
This is, in fact, the method employed in cattle-breeding and
gardening, in order with greater certainty to obtain new breeds
and varieties, with well-marked different characters. The ex-
perience of artificial breeding is to be regarded, from a scientific
point of view, as an experimental confirmation of the law under

AIM AND PROGRESS OF PHYSICAL SCIENCE. 339

discussion ; and, in fact, this experiment has proved successful,
and is still doing so, with species of every class of the animal
kingdom, and, with respect to the most different organs of the
body, in a vast number of instances.

After the general application of the law of transmission had
been established in this way, it only remained for Darwin to
discuss the bearings of the question as regards animals and
plants in the wild state. The result which has been arrived at
is that those individuals which are distinguished in the struggle
for existence by some advantageous quality, are the most likely
to produce offspring, and thus transmit to them their advan-
tageous qualities. And in this way from generation to genera-
tion a gradual adjustment is arrived at in the adaptation of each
species of living creation to the conditions under which it has to
live until the type has reached such a degree of perfection that
any substantial variation from it is a disadvantage. It will
then remain unchanged so long as the external conditions of its
existence remain materially unaltered. Such an almost abso-
lutely fixed condition appears to be attained by the plants and
animals now living, and thus the continuity of the species, at
least during historic times, is found to prevail.

An animated controversy, however, still continues, concern-
ing the truth or probability of the Darwinian theory, for the
most part respecting the limits that should be assigned to the
variation of species. The opponents of this view would hardly
deny that, as assumed by Darwin, hereditary differences of race
could have arisen in one and the same species; or, in other words,
that many of the forms hitherto regarded as distinct species of
the same genus have been derived from the same primitive form.
Whether we must restrict our view to this, or whether, perhaps,
we venture to derive all mammals from one original marsupial,
or, again, all vertebrates from a primitive lancelet, or all plants
and animals together from the slimy protoplasm of a protis-
ton, depends at the present moment rather on the leanings of
individual observers than on facts. Fresh links, connecting
classes of apparently irreconcilable type, are always presenting
themselves; the actual transition of forms, into others widely
z 2

340 AIM AND PROGRESS OF PHYSICAL SCIENCE.

different, has already been traced in regularly deposited geo-
logical strata, and has come to be beyond question; and since
this line of research has been taken up, how numerous are the
facts which fully accord with Darwin's theory, and give special
effect to it in detail !

At the same time, we should not forget the clear interpreta-
tion Darwin's grand conception has supplied of the till then
mysterious notions respecting natural affinity, natural systems,
and homology of organs in various animals; how by its aid the
remarkable recurrence of the structural peculiarities of lower
animals in the embryos of others higher in the scale, the special
kind of development appearing in the series of palseontological
forms, and the peculiar conditions of affinity of the faunas and
floras of limited areas have, one and all, received elucidation.
Formerly natural affinity appeared to be a mere enigmatical, and
altogether groundless, similarity of forms ; now it has become a
matter for actual consanguinity. The natural system certainly
forced itself as such upon the mind, although theory strictly
disavowed any real significance to it ; at present it denotes an
actual genealogy of organisms. The facts of palseontological
and embryological evolution and of geographical distribution
were enigmatical wonders so long as each species was regarded
as the result of an independent act of creation, and cast a
scarcely favourable light on the strange tentative method which
was ascribed to the Creator. Darwin has raised all these isolated
questions from the condition of a heap of enigmatical wonders
to a great consistent system of development, and established de-
finite ideas in the place of such a fanciful hypothesis as, among
the first, had occui-red to Goethe, respecting the facts of the
comparative anatomy and the morphology of plants.

This renders possible a definite statement of problems for
further inquiry, a great gain in any case, even should it happen
that Darwin's theory does not embrace the whole truth, and
that, in addition to the influences which he has indicated, there
should be found to be others which operate in the modification
of organic forms.

While the Darwinian theory treats exclusively of the gra-

AIM AND PROGRESS OF PHYSICAL SCIENCE. 341

dual modification of species after a succession of generations, we
know that a single individual may adapt itself, or become
accustomed, in a certain degree, to the circumstances under which
it has to live ; and that even during the single life of au indi-
vidual a distinct progress towards a higher development of
organic adaptability may be attained. And it is more especially
in those forms of organic life where the adaptability in structure
has reached the highest grade and excited the greatest admiration,
namely, in the region of mental perception, that, as the latest
results of physiology teach us, this individual adaptation plays
a most prominent part.

Who has not marvelled at the fidelity and accuracy of the
information which our senses convey to us from the surround-
ing world, more especially those of the far-reaching eye ? The
information so gained furnishes the premisses for the conclusions
which we come to, the acts that we perform ; and unless our
senses convey to us correct impressions, we cannot expect to act
accurately, so that results shall correspond with our expectations.
By the success or failure of our acts we again and again test
the truth of the information with which our senses supply us,
and experience, after millions of repetitions, shows ns that this
fidelity is exceedingly great, in fact, almost free from exceptions.
At all events, these exceptions, the so-called illusions of the
senses, are rare, and are only brought about by very special and
unusual circumstances.

Whenever we stretch forth the hand to lay hold of some-
thing, or advance the foot to step upon some object, we must
first form an accurate optical image of the position of the
object to be touched, its form, distance, <fec., or we shall fail.
The certainty and accuracy of our perception by the senses
must at least equal the certainty and accuracy which our actions
have attained after long practice j and the belief, therefore, in
the trustworthiness of our senses is no blind belief, but one, the
accuracy of which has been tested and verified again and again
by numberless experiments.

Were this harmony between the perceptions through the
senses and the objects causing them, in other words, this basia

342 AIM AND PROGRESS OF PHYSICAL SCIENCE.

of all our knowledge, a direct product of the vital principle, its
formative power would, in fact, then have attained the highest
degree of perfection. But an examination of the actual facts
at once destroys in the most merciless manner all belief in a
preordained harmony of the inner and external world.

I need not call to mind the startling and unexpected results of
ophthalmometrical and optical research which have proved the
eye to be a by no means more perfect optical instrument than
those constructed by human hands; but, on the contrary, to
exhibit, in addition to the faults inseparable from any dioptric
instrument, others that in an artificial instrument we should
severely condemn ; nor need I remind you that the ear conveys
to us sounds from without in no wise in the ratio of their
actual intensity, but strangely resolves them and modifies them,
intensifying or weakening them in very different degrees, ac-
cording to their varieties of pitch.

These anomalies, however, are as nothing compared with
those to be met with in examining the nature of the sensations
by which we become acquainted with the various properties of
the objects surrounding us. Here it can at once be proved
that no kind and no degree of similarity exists between the
quality of a sensation and the quality of the agent inducing it,
and portrayed by it.

In its leading features this was demonstrated by Johannes
Miiller in his law of the Specific Action of the Senses. Accord-
ing to him, each nerve of sense possesses a peculiar kind of
sensation. A nerve, we know, can be rendered active by a vast
number of exciting agents, and the same agent may likewise
affect different organs of sense ; but, however it be brought
about, we never have in nerves of sight any other sensation
than that of light ; in the nerves of the ear any other than a
sensation of sound ; in short, in each individual nerve of sense
only that sensation which corresponds to its peculiar specific
action. The most marked differences in the qualities of sensation,
in other words, those between the sensations of different senses,
are, then, in no way dependent on the nature of the exciting
agent, but only on that of the nerve apparatus under operation.

AIM AND PROGRESS OF PHYSICAL SCIENCE. 343

The bearing of M tiller's law has been extended by later re-
search. It appears highly probable that even the sensations of
different colours and different pitch, as well as qualitative pecu-
liarities of luminous sensations inter se, and of sonorous sensa-
tions inter se, also depend on the excitation of systems of fibres,
with distinct character and endowed with different specific
energy, of nerves of sight and hearing respectively. The infi-
nitely more varied diversity of composite light is in this way
referable to sensations of only threefold heterogeneous character,
in other words, to mixtures of the three primary colours. From
this reduction in the number of possible differences it follows
that very different composite light may appear the same. In
this case it has been shown that no kind of physical similarity
whatever corresponds to the subjective similarity of different
composite light of the same colour. By these and similar facts
we are led to the very important conclusion that our sensations
are, as regards their quality, only signs of external objects, and
in no sense images of any degree of resemblance. An image
must, in certain respects, be analogous to the original object ; a
statue, for instance, has the same corporeal form as the human
being after which it is made ; a picture the same colour and per-
spective projection. For a sign it is sufficient that it become
apparent as often as the occurrence to be depicted makes its ap-
peai-ance, the conformity between them being restricted to their
presenting themselves simultaneously ; and the correspondence
existing between our sensations and the objects producing them
is precisely of this kind. They are signs which we have learned
to decipher, and a language given us with our organisation by
which external objects discourse to us — a language, however,
like our mother tongue, that we can only learn by practice and
experience.

Moreover, what has been said holds good not only for the
qualitative differences of sensations, but also, in any case, for
the greatest and most important part, if not the whole, of our
various perceptions of extension in space. In their bearings on
this question the new doctrine of binocular vision and the in-
vention of the stereoscope have been of importance. All that

344 AIM AND PROGRESS OF PHYSICAL SCIENCE.

the sensation of the two eyes could convey to us directly, and
without psychical aid, was, at the most, two somewhat different
flat pictures of two dimensions as they lay on the two retinae ;
instead of this we perceive a representation with three dimen-
sions of the things around us. We are sensible as well of
the distance of objects not too far removed from us as of their
perspective juxtaposition, and compare the actual magnitude of
two objects of apparently unequal size at different distances
from us with greater certainty than the apparent equal magni-
tudes of a finger, say, and the moon.

One explanation only of our perception of extension in
space, which stands the test of each separate fact, can in my
judgment be brought forward by our assuming with Lotze that
to the sensations of nerve-fibres, differently situated in space,
certain differences, local signs, attach themselves, the significa-
tions of which, as regards space, we have to learn. That a
knowledge of their signification may be attained by these hypo-
theses, and with the help of the movements of our body, and
that we can at the same time learn which are the right move-
ments to bring about a desired result, and become conscious
of having arrived at it, has in many ways been established.

That experience exercised an enormous influence over the
signification of visual pictures, and, in cases of doubt, is generally
the final arbiter, is allowed even by those physiologists who
wish to save as much as possible of the innate harmony of the
senses with the external world. The controversy is at present
almost entirely confined to the question of the proportion at
birth of the innate impulses that can facilitate training in the
understanding of sensations. The assumption of the existence
of impulses of this kind is unnecessary, and renders difficult in-
stead of elucidating an interpretation of well-observed phenomena
in adults.1

It follows, then, that this subtile and most admirable harmony
existing between our sensations and the objects causing them is
substantially, and with but few doubtful exceptions, a conformity

1 A further exposition of these conditions will be found in the lectures on
the Recent Progress of the Theory of Vision, pp. 175 et seq.

AIM AND PROGRESS OF PHYSICAL SCIENCE. 345

individually acquired, a result of experience, of training, the
recollection of former acts of a similar kind.

This completes the circle of our observations, and lands us
at the spot whence we set out. We found at the beginning
that what physical science strives after is the knowledge of laws,
in other words, the knowledge how at different times under the
same conditions the same results are brought about ; and we
found in the last instance how all laws can be reduced to laws of
motion. We now find, in conclusion, that our sensations are
merely signs of changes taking place in the external world, and
can only be regarded as pictures in that they represent succes-
sion in time. For this very reason they are in a position to
show directly the conformity to law, in regard to succession
in time, of natural phenomena. If, under the same natural
circumstances, the same action take place, a person observing it
under the same conditions will find the same series of impressions
regularly recur. That which our organs of sense perform is
clearly sufficient to meet the demands of science as well as the
practical ends of the man of business who must rely for support
on the knowledge of natural laws, acquired, partly in voluntarily
by daily experience, and partly purposely by the study of
science.

Having now completed our survey, we may, perhaps, strike
a not unsatisfactory balance. Physical science has made active
progress, not only in this or that direction, but as a vast whole,
and what has been accomplished may warrant the attainment of
further progress. Doubts respecting the entire conformity to
law of nature are more and more dispelled ; laws more general
and more comprehensive have revealed themselves. That the
direction which scientific study has taken is a healthy one its
great practical issues have clearly demonstrated ; and I may here
be permitted to direct particular attention to the branch of science
more especially my own. In physiology particularly scientific
work had been crippled by doubts respecting the necassary con-
formity to law, which means, as we have shown, the intelligi-
bility of vital phenomena, and this naturally extended itself to
the practical science directly dependent on physiology, namely,

346 AIM AND PROGRESS OF PHYSICAL SCIENCE.

medicine. Both have received an impetus, such as had not
been felt for thousands of years, from the time that they seri-
ously adopted the method of physical science, the exact observa-
tion of phenomena and experiment. As a practising physician,
in my earlier days, I can personally bear testimony to this. I
was educated at a period when medicine was in a transitional
stage, when the minds of the most thoughtful and exact were
filled with despair. It was not difficult to recognise that the old
predominant theorising methods of practising medicine were al-
together untenable ; with these theories, however, the facts on
which they had actually been founded had become so inextric-
ably entangled that they also were mostly thrown overboard.
How a science should be built up anew had already been seen in
the case of the other sciences ; but the new task assumed colossal
proportions; few steps had been taken towards accomplishing
it, and these first efforts were in some measure but crude and
clumsy. We need feel no astonishment that many sincere and
earnest men should at that time have abandoned medicine as
unsatisfactory, or on principle given themselves over to an ex-
aggerated empiricism.

But well-directed efforts produced the right result more
quickly even than many had hoped for. The application of the
mechanical ideas to the doctrine of circulation and respiration,
the better interpretation of thermal phenomena, the more re-
fined physiological study of the nerves, soon led to practical re-
sults of the greatest importance ; microscopic examination of
parasitic structures, the stupendous development of pathological
anatomy, irresistibly led from nebulous theories to reality. We
found that we now possessed a much clearer means of distinguish-
ing, and a clearer insight into the mechanism of the process of
disease than the beats of the pulse, the urinary deposit, or the
fever type of older medical science had ever given us. If I
might name one department of medicine in which the influence of
the scientific method has been, perhaps, most brilliantly displayed,
it would be in ophthalmic medicine. The peculiar constitution of
the eye enables us to apply physical modes of investigation as
well in functional as in anatomical derangements of the living

AIM AND PROGRESS OF PHYSICAL SCIENCE. 347

organ. Simple physical expedients, spectacles, sometimes spheri-
cal, sometimes cylindrical or prismatic, suffice, in many cases, to
cure disorders which in earlier times left the organ in a condition
of chronic incapacity ; a great number of changes, on the other
hand, which formerly did not attract notice till they induced
incurable blindness, can now be detected and remedied at the
outset. From the very reason of its presenting the most favour-
able ground for the application of the scientific method, ophthal-
mology has proved attractive to a peculiarly large number of ex-
cellent investigators, and rapidly attained its present position, in
which it sets an example to the other departments of medicine,
of the actual capabilities of the true method, as brilliant as that
which astronomy for long had offered to the other branches of
physical science.

Though in the investigation of inorganic nature the several
European nations showed a nearly uniform advancement, the
recent progress of physiology and medicine is pre-eminently due
to Germany. I have already spoken of the obstacles which
formerly delayed progress in this direction. Questions respect-
ing the nature of life are closely bound up with psychological
and ethical inquiries. It demands, moreover, that we bestow
on it unwearied diligence for purely ideal purposes, without any
approaching prospect of the pure science becoming of practical
value. And we may make it our boast that this exalted and
self-denying assiduity, this labour for inward satisfaction, not
for external success, has at all times peculiarly distinguished the
scientific men of Germany.

What has, after all, determined the state of things in the
present instance is in my opinion another circumstance,
namely, that we are more fearless than others of the consequences
of the entire and perfect truth. Both in England and France
we find excellent investigators who are capable of working with
thorough energy in the proper sense of the scientific methods ;
hitherto, however, they have almost always had to bend to
social or ecclesiastical prejudices, and could only openly express
their convictions at the expense of their social influence and
their usefulness.

348 AIM AND PROGEESS OF PHYSICAL SCIENCE.

Germany has advanced with bolder step : she has had the
full confidence, which has never been shaken, that truth fully
known brings with it its own remedy for the danger and dis-
advantage that may here and there attend a limited recognition
of what is true. A labour-loving, frugal, and moral people
may exercise such boldness, may stand face to face with truth ;
it has nothing to fear though hasty or partial theoi-ies be advo-
cated, even if they should appear to trench upon the foundations
of morality and society.

We have met here on the southern frontier of our country.
In science, however, we recognise no political boxmdaries, for
our country reaches as far as the German tongue is heard,
wherever German industry and German intrepidity in striving
after truth find favour. And that it finds favour here is shown
by our hospitable reception, and the inspiriting words with
which we have been greeted. A new medical faculty has been
established here. We will wish it in its career rapid progress
in the cardinal virtues of German science, for then it will not
only find remedies for bodily suffering, but become an active
centre to strengthen intellectual independence, steadfastness to
conviction and love of truth, and at the same time be the means
of deepening the sense of unity throughout our country.

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Text -Books of Science.

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TEXT-BOOKS PREPARING FOE PUBLICATION.

SOUND. By W. G. ADAMS. M.A. Professor of Natural Philosophy
and Astronomy, King's College, London.

PHYSICAL GEOGRAPHY. By the Key. GEORGE BUTLKK,

M.A. Principal of Liverpool College ; Editor of ' The Public Schools Atlas of
Modern Geography.'

SUBMARINE TELEGRAPHY. By W. H. PREECE, C.E.

Divisional Engineer, Post Office Telegraphs ; and J. SFVEWRIGHT. M.A. Super-
intendent (Engineering Department), Post Office Telegraphs. With numerous
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ECONOMICAL APPLICATIONS of HEAT ; including

Combustion, Evaporation, Furnaces, Flues, and Boilers. By C. P. B. SHET.LKY,
Civil Engineer, and Professor of Manufacturing Art and Machinery at King's
College, London. With a Chapter on the Probable Future Development of
the Science of Heat, by C. WILLIAM SIEMENS, F.R.S.

PHYSICAL OPTICS. By G. G. STOKRS, M.A. D.C.L. Fellow of
Pembroke College, Cambridge ; Lucasian Professor of Mathematics in the
"University of Cambridge ; and Secretary to the Royal Society.

A TEXT-BOOK of MINERALOGY. By H. BAUERMAN,

F.G.S. Associate of the Royal School of Mines. In Two Parts, which may
be had separately. PART I. Systematic Mineralogy, now in the press. PART II.
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The STEAM ENGINE, a Text-Book for the Use of Engineering
Students and Candidate* for the Science and Art Department Examinations.
By GEORGE C. V. HOLMES, C.E. late Whitworth Scholar, Secretary of the
Institute of Naval Architects. Small 8vo. Woodcuts.

ZOOLOGY and COMPARATIVE A "NT ATOMY, including
the Principles of Zoological Science. By ANDREW WILSON, Pli.D. &c. Lecturer
on Zoology and Comparative Anatomy in the Edinburgh Medical School.
~ ~ 3vo. Woodcuts.

TWENTY-THREE TEXT-BOOKS NOW PUBLISHED.
A TREATISE on PHOTOGRAPHY. By W. DE WITELFSLIE

ABNEr, F.R.S. Captain in the Corps of Royal Engineers, and late Instructor
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Text-Books of Science.

On the STRENGTH of MATERIALS and STRUC-
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By Sir JOHN ANDERSON, C.E. LL.D. F.K.S.E. Superintendent of Machinery to
the War Department. Price 3*. 6d.

INTRODUCTION to the STUDY of ORGANIC

CHEMISTRY ; the CHEMISTRY of CARBON and its COMPOUNDS. By
HENRY E. ARMSTRONG, Ph.D. F.C.S. Professor of Chemistry in the London
Institution. "With 8 Figures on Wood. Price 3s. 6d.

ELEMENTS of ASTRONOMY. By ROBERT STAWELL BALL,
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RAILWAY APPLIANCES. A Description of Details of
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METALS, their PROPERTIES and TREATMENT.

By CHARLES LOUDON BLOXAM, Professor of Chemistry in King's College,
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PRINCIPLES of MECHANICS. By T. M. GOODEVE, M.A.

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The ELEMENTS of MECHANISM, designed for Students
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The ART of ELECTRO -METALLURGY, including all
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ALGEBRA and TRIGONOMETRY. By the Rev. WILLIAM
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NOTES on the ELEMENTS of ALGEBRA and

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^ELECTRICITY and MAGNETISM. By FLEEMING Jrancnc,
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THEORY of HEAT. By J. CLERK MAXWELL, M.A. LL.D. Edin.
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TECHNICAL ARITHMETIC and MENSURATION.

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Text- Books of Science.

KEY to MERRIFIELD'S TEXT-BOOK of TECHNI-
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INTRODUCTION to the STUDY of INORGANIC

CHEMISTRY. By WILLIAM ALLEV MILLER, M.D. LL.D. F.R.S. late Pro-
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TELEGRAPHY. By W. H. PREECE, C.E. Divisional Engineer
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The STUDY of ROCKS. An Elementary Text-Book of Petrology,
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WORKSHOP APPLIANCES, including Descriptions of the
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STRUCTURAL and PHYSIOLOGICAL BOTANY. By

OTTO WILHELM THOME, Ordinary Professor of Botany at the School of
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MANUAL of QUALITATIVE ANALYSIS and

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INTRODUCTION to the STUDY of CHEMICAL

PHILOSOPHY ; the PRINCIPLES of THEORETICAL and SYSTEMATIC
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ELEMENTS of MACHINE DESIGN ; an Introduction to

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PLANE and SOLID GEOMETRY. By the Rev. H. W
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OCTOIBIEIR, 188O.

GENERAL LISTS OF NEW WORKS

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HISTORY, POLITICS, HISTORICAL MEMOIRS &c.

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Cox's Athenian Empire, 'is. Gd.

— Greeks and Persians, 2*. Gd.

Curteis's Rise of the Macedonian Empire, 2t. M.

lime's Rome to it8 Capture hy the Gauls, 2s. 6d.

Merivale's Roman Triumvirates, 2*. 6<t.

Sankey's Spartan and Tbebau Supremacies, 2*. 6d.
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Creighton's Shilling History of England (Introductory Volume).
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Creighton's (Rev. M.) Tudors and the Reformation, 1485-1603, 9d.

Rowley's Rise of the People, 1215-1485, 9d.

Rowley's Settlemeu, of the Constitution, 1683-1778, 9d.

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Short's History of the Church of England. Crown 8vo. 7*. 6d.
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Taylor's Manual of the History of India. Crown 8vo. 7*. 6d.
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Mill's (John Stuart) Autobiography. 8vo. 7*. 6d.
Missionary Secretariat of Henry Venn, B.D. Sve-. Portrait. 18*.
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Kohl's Life of Mozart. Translated by Lady Wallace. 2 vols. crown 8vo. 21*.
Spedding's Letters and Life of Francis Bacon. 7 vols. 8vo. £4. 4*.
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Ainos's View of the Science of Jurisprudence. 8vo. 18*.

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Kalisch's Path and Goal. Svo. 12*. Gd.
Lewis on Authority in Matters of Opinion. Svo. 14*.
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Cetshwayo's Dutchman. By C. Vijn. Translated by Bishop Colenso. Or. Svo. 5*.

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Th« Public Schools Atlas of Ancient Geography. Imperial 8vo. 7*. M.
_ _ _ Atlas of Modern Geography. Imperial 8vo. 5*.

London, LONGMANS & CO.

General Lists of New Works.

NATURAL HISTORY & POPULAR SCIENCE.
Arnott's Elements of Physics or Natural Philosophy. Crown 8vo. 12*. Gd. .
Brande's Dictionary of Science, Literature, and Art. 3 vols. medium 8vo. GSs
Buckton's T«wn and Window Gardening. Crown 8vo. 2*.
Decaisn* and Le Maout.'s General System of Botany. Imperial 8vo. 81*. Gd.
Dixon's Rural Bird Life. Crown 8vo. Illustrations, Is. Gd.
Ganot's Elementary Treatise on Physics, by Atkinson. Large crown 8vo. 15*.

— Natural Philosophy, by Atkinson. Crown 8vo. It. Gd.
G-ore'g Art, of Scientific Discovery. Crown 8vo. 15*.
Grove's Correlation of Physical Forces. 8vo. 15*.
Hartwig's Aerial World. 8ro. 10*. Cd. Polar World. 8vo. 10*. Gd.

— Sea and its Living Wonders. 8vo. 10*. Gd.

— Subterranean World. 8vo. 10*. Gd. Tropical World. 8vo. 10*. Gd.
Haughton's Principles of Animal Mechanics. 8vo. 21*.

— Six Lectures on Physical Geography. 8vo. 15*.
Heer's Primaeval World of Switzerland. 2 vols. 8vo. 16*.
Helmholtz's Lectures on Scientific Subjects. 2 vols. cr. 8vo. 7.». 6d. each.
Helmholte on the Sensations of Tone, by Ellis. 8vo. 36*.
Hullah's Lectures on the History of Modern Music. 8vo. 8*. (id.

— Transition Period of Musical History. 8vo. 10*. Gd.
Keller's Lake Dwellings of Switzerland, by Lee. 2 vols. royal 8vo. 42*.
Kirby and Spence's Introduction to Entomology. Crown 8vo. 5*.
Lloyd's Treatise on Magnetism. 8vo. 10*. 6d.

— — on the Wave-Theory of Light. 8vo. 10*. 6d.
Loudon's Encyclopaedia of Plants. 8vo. 42*.

Lubbock on the Origin of Civilisation & Primitive Condition of Man. 8vo. 18*.
Macalister'B Zoology and Morphology of Vertebrate Auimals. 8vo. 10*. Gd.
Nicols' Puzzle of Life. Crown 8vo. 3*. Gd.
Owen's Comparative Anatomy and Physiology of the Vertebrate Animals. 3 vols.

8vo. 73*. Gd.

Proctor's Light Science for Leisure Hours. 2 vols. crown 8vo. 7*. Gd. each.
Rivers's Orchard House. Sixteenth Edition. Crown 8vo. 5*

— Rose Amateur's Guide. Fcp. 8vo. 4*. 6<J.
Stanley's Familiar History of British Birds. Crown 8vo. 6*.
Text-Books of Science, Mechanical aud Physical.

Abney's Photography, 3i. Gd.

Anderson's (Sir John) Strength of Materials, 3*. Gd.

Armstrong's Organic Chemistry, 3*. Gd.

Ball's Astronomy, 6*.

Barry's Railway Appliances. 3*. fid. Bloxam's Metals, 3*. Gd.

Goodeve's Elements of Mechanism, St. 6d.
— Principles of Mechanics, 3*. 6d.

Gore's Electro-Metallurgy. 6*.

Griffin's Algebra and Trigonometry. 3*. Gd.

Jenkin's Electricity and Magnetism, 3*. Gd.

Maxwell's Theory of Heat, 3*. Gd.

Mcrrifield's Technical Arithmetic and Mensuration, 3*. Gd.

Miller's Inorganic Chemistry, 'As. 6d.

Preocc & Sivewright's Telegraphy, 8*. Gd.

Rutley's Study of Rocks, 4*. Gd.

Shelley's Workshop Appliances, 3*. Gd.

London, LONGMANS & CO.

General Lists of New Works.

Text-Books of Science -continued.

Thome's Structural and Physiological Botany, 6*.

Thorpe's Quantitative Chemical Analysis, 4*. 6<J.

Thorpe & Muir's Qualitative Analysis, 3*. 6d.

Tilden's Chemical Philosophy, 3*. 6rf.

Unwln's Machine Design, St. 6d.

Watson's Plane and Solid Geometry, 3*. 6d.
Tyudall on Sound. Crown 8vo. 10*. 6d.

— Contributions to Molecular Physics. 8vo. 16*.

— Fragments of Science. 2 vols. post 8 vo. 16*.

— Heat a Mode of Motion, 6th Edition, 13th Thousand. Crown 8vo. 12*.

— Notes on Electrical Phenomena. Crown 8vo. 1*. sewed, 1*. 6d. cloth.

— Notes of Lectures on Light. Crown 8vo. 1*. sewed, 1*. 6d. cloth.

— Lectures on Light delivered in America. Crown 8vo. It. 6d.

— Lessons in Electricity. Crown 8vo. 2*. 6d.
Von Gotta on Rocks, by Lawrence. Post 8vo. 14*.
Woodward's Geology of England and Wales. Crown 8vo. 14*.
Wood's Bible Animals. With 112 Vignettes. 8vo. 14*.

— Homes Without Hands. 8vo. 14*. Insects Abroad. 8vo. 14*.

— Insects at Home. With 700 Illustrations. 8vo. 14*.

— Out of Doors. Crown 8vo. 7*. 6d. Strange Dwellings. Crown 8vo. 7*. 6d.

CHEMISTRY &. PHYSIOLOGY.

Auerbach's Anthracen, translated by W. Crookes, F.R.S. 8vo. 12*.

Buckton's Health in the House, Lectures on Elementary Physiology. Cr. 8vo. 2*.

Crookes's Handbook of Dyeing and Calico Printing. 8vo. 42*.

— Select Methods in Chemical Analysis. Crown 8vo. 12*. 6d.
Kingzett's Animal Chemistry. 8vo. 18*.

— History, Products and Processes of the Alkali Trade. 8vo. 12*.
Miller's Elements of Chemistry, Theoretical and Practical. 3 vols. 8vo. Part I .

Chemical Physics, 16*. Part II. Inorganic Chemistry, 24*. Part III. Organic

Chemistry, Section I. price 31*. 6d.

Thudichnm's Annals of Chemical Medicine. Vol. I. 8vo. 14*.
Tilden's Practical Chemistry. Pep. 8vo. 1*. Sd.
Watts's Dictionary of Chemistry. 7 vols. medium 8vo. £10. 16*. Gd.
— Third Supplementary Volume, in Two Parts. PAKT I. 36*.

THE FINE ARTS &, ILLUSTRATED EDITIONS.

Bewick's Select Fable? of JEsop and others. Crown 8vo. 7*. 6d. demy 8vo. 18*.
Doyle's Fairyland ; Pictures from the Elf-World. Folio, 15*.
Dresser's Arts and Art Industries of Japan. [fn preparation.

Ingelow"s Poems. Illustrated Edition. Fcp. 4to. Woodcuts, 21*.
Jameson's Sacred and Legendary Art. 6 vols. square crown STO.
Legends of the Madonna. 1 vol. 21*.

— — — Monastic Orders. 1 vol. 21*.

_ _ _ Sainte and Martyrs. 2 vols. 31*. 6d.

— — — Saviour. Completed by Lady Eastlake. 2 vols. 42*.
Longman's Three Cathedrals Dedicated to St. Pan) . Square crown 8vo. 21*.
Macaulay's Lays of Ancient Rome. With 90 Illustrations. Fcp. 4to. 21*.
Macfarren's Lectures on Harmony. 8vo. 12*.

Miniature Edition of Macaulay's Lays of Ancient Rome. Imp. 16mo. 10*. 6d.
Moore's Irish Melodies. With 161 Plates by D. Maclise, RJL Super-royal 8vo. 21*.

London, LONGMANS & CO.

General Lists of New Works.

Moore's Lalla Rookh, illustrated by Tenniel. Square crown 8vo. 10*. 6d.
Perry on Greek and Roman Sculpture. 8vo [./» preparation.

THE USEFUL ARTS, MANUFACTURES &c.

Bourne's Catechism of the Steam Engine. Fcp. 8vo. 6*.

— Examples of Steam, Air, and Gas Engines. 4to. 70*.

— Handbook of the Steam Engine. Fcp. 8vo. 9*.

— Recent Improvements in the Steam Engine. Fcp. 8vo. 6*.

— Treatise on the Steam Engine. 4to. 42*.
068/3 Encyclopaedia of Civil Engineering. 8vo. 25*.
Culley's Handbook of Practical Telegraphy. 8vo. 16*.

Eastiake's Household Taste in Furniture, &c. Square crown 8vo. 14*.
Fairbairn's Useful Information for Engineers. 3 vols. crown 8vo. 31*. 6ct.

— Applications of Oast and Wrought Iron. 8vo. 16*.

— Mills and MUlwork. 1 vol. 8vo. 25*.
Gwflt's Encyclopaedia of Architecture. 8vo. 52*. 6d.

Hobson's Amateur Mechanic's Practical Handbook. Crown 8vo. 2*. 6d.
Hoskold's Engineer's Valuing Assistant. 8vo. 31*. 6d.
Kerl's Metallurgy, adapted by Crookes and Rb'hrig. 3 vols. 8vo. £4. 19*.
London's Encyclopaedia of Agriculture. 8vo. 21*.

— — Gardening. 8vo. 21*.

MItcheU's Manual of Practical Assaying. 8vo. 31*. 6d.
Korthcott's Lathes and Turning. 8vo. 18*.

Payen's Industrial Chemistry Edited by B. H. Paul, Ph.D. 8vo. 42*.
Piesse's Art of Perfumery. Fourth Edition. Square crown 8vo. 21*.
Stoney's Theory of Strains in Girders. Royal 8vo. 36*.
Thomas on Coal, Mine-Gases and Ventilation. Crown 8vo. 10*. 6d.
Tire's Dictionary of Arts, Manufactures, & Mines. 4 vols. medium 8vo. £7. 7*.
Ville on Artificial Manures. By Crookes. 8vo. 21*.

RELIGIOUS & MORAL WORKS.

Abbey & Overton's English Church in the Eighteenth Century. 2 vols. 8vo. 36*.

Arnold's (Rev. Dr. Thomas) Sermons. 6 vols. crown 8vo. 5*. each.

Bishop Jeremy Taylor's Entire "Works. With Life by Bishop Heber. Edited by

the Rev. C. P. Eden. 10 vols. 8vo. £5. fi*.
Bonltbee's Commentary on the 39 Articles. Crown 8vo. 6*.

— History of the Church of England, Pre-Reformation Period. 8vo. 15*.
Browne's (Bishop) Exposition of the 39 Articles. 8vo. 16*.

Bunsen's Angel-Messiah of Buddhists, &c. 8vo. 10* 6d.

Colenso's Lectures on the Pentateuch and the Moabite Stone. 8vo. 12*.

Colenso on the Pentateuch and Book of Joshua. Crown 8vo. 6*.

— — PART VII. completion of the larger Work. 8vo. 24*.
Gender's Handbook of the Bible. Post 8vo. 7*. 6d.
Conybeare & Howson'sLife and Letters of St. Paul :—

library Edition, with all the Original Illustrations, Maps, Landscapes on
Steel, Woodcuts, &c. 2 volg. 4to. 42*.

Intermediate Edition, with a Selection of Maps, Plates, and Woodcuts.
2 vols. square crown 8vo. 21*.

Student's Edition, revised and condensed, with 46 Illustrations and Maps.
1 vol. crown 8vo. 7*. 6d. ^

London, LONGMANS & CO.

General Lists of New Works. 9

Drammond's Jewish Messiah. «TO. 16*.

EUicott's (Bishop) Commentary on St. Paul's Epistles. STO. GalatUng, It. «d.

Ephesians, 8*. 6d. Pastoral Epistles, 10*. 6d. Philippians, ColoaslanB, and

Philemon, 10*. 6<i. Thessalonians, It. 6d.
Ellicott's Lectures on the Life of our Lord. 8vo. 12*.
Ewald's History of Israel, translated by Carpenter. 5 Tola. STO. 63*.

— Antiquities of Israel, translated by Solly. $vo. 12*. 6d.
Gospel (The) for the Nineteenth Century. 4th Edition. 8vo. 10*. 6d.
Hopkins's Christ the Consoler. Pop. 8vo. 2*. 6d.

Jukes's Types of Genesis. Crown 8vo. 7*. 6d.

— Second Death and the Restitution of all Things. Crown STO. 3*. 6d.
Kalisch's Bible Studies. PART I. the Prophecies of Balaam. STO. 10*. 6d.

— _ _ PART H. the Book of Jonah. 8vo. 10*. 6d.

— Historical and Critical Commentary on the Old Testament; with a
New Translation. Vol. I. Genesis, STO. 18*. or adapted for the General
Reader, 12*. Vol. H. Exodus, 15*. or adapted for the General Reader, 12*.
Vol. m. Leviticus, Part I. 15*. or adapted for the General Reader, 8*.
Vol. IV. Leviticus, Part H. 15*. or adapted for the General Reader, 8*.

Lyra G«rmanica : Hymns translated by Miss Winkworth. Fcp. STO. 5*.
Manning's Temporal Mission of the Holy Ghost. STO. 8*. 6d.
Martineau's EndeaTours after the Christian Life. Crown STO. 7*. 6d.

— Hymns of Praise and Prayer. Crown STO. 4*. 6d. 32mo. 1*. 6d.

— Sermons, Hours of Thought on Sacred Things. 2 TO!S. 7*. 6d. each.
MeriTale's (Dean) Lectures on Early Church History. Crown STO. 5*.

Mill's Three Essays on Religion. STO. 10*. 6d.

Missionary Secretariat of Henry Venn, B.D. STO. Portrait. 18*.

MonseU's Spiritual Songs for Sundays and Holidays. Fcp. STO. 5*. 18mo. 2*.

MUller's (Max) Lectures on the Science of Religion. Crown STO. 10*. M.

Newman's Apologia pro Vita Sua. Crown STO. 6*.

Passing Thoughts on Religion. By Miss Sewell. Fcp. STO. 3*. 6d.

Sewell's (Miss) Preparation for the Holy Communion. 82mo. 3*.

Smith's Voyage and Shipwreck of St. Paul. Crown STO. 7*. 6d.

Supernatural Religion. Complete Edition. 3 TO!S. STO. 36*.

Thoughts for the Age. By Miss Sewell. Fcp. STO. 3*. 6d.

Vaughan's Trident, Crescent, and Cross ; the Religions History of India. 8TO.9*.6d.

Whately's Lessons on the Christian ETidences. ISmo. 6d.

White's Four Gospels in Greek, with Greek-English Lexicon. 32mo. 5*.

TRAVELS, VOYAGES Sec.

Baker's Rifle and Hound in Ceylon. Crown STO. 7*. M.

— Eight Years in Ceylon. Crown STO. 7*. 6<i.

Ball's Alpine Guide. 3 vols.post STO. with Maps and Illustration* :— L Western
Alps, 6*. 6d. II. Central Alps, 7*. 6d. III. Eastern Alps, 10*. 6d.

Ball on Alpine TraTelling, and on the Geology of the Alps, 1*.

Bent's Freak of Freedom, or the Republic of San Marino. Crown STO. 7*. 6d.

Brassey's Sunshine and Storm in the East. STO. 21*.

— Voyage in the Yacht 'Sunbeam.' Cr. 8m 7*. M. School Edition, 2*.

London, LONGMANS & CO.

10

General Lists of New Work,.

Edwards's (A. B.) Thousand Miles up the Nile. Imperial 8vo. 42*.
Hassall's San Remo and the Western Riviera. Crown 8vo. 10*. 6d.
Macnamara's Medical Geography of India. 8vo. 21*.
Miller's Wintering in the Riviera. Post 8vo. Illustrations, 1 2*. 6d.
Packe's Guide to the Pyrenees, for Mountaineers. Crown 8vo. 7*. 6<t
Rigby's Letters from Prance, &c. in 1789. Crown 8vo. 10*. 6d.
Shore's Flight of the ' Lapwing ', Sketches in China and Japan. 8vo.
The Alpine Club Map of Switzerland. In Pour Sheets. 42*.

WORKS OF FICTION.

Blues and Buffs. By Arthur Mills. Crown 8vo. 6*.

Hawthorne's (J.) Yellow-Cap and other Pairy Stories. Crown 8vo. 6.1.

The Crookit Meg. By Shirley. Crown 8vo. 6*.

Cabinet Edition of Stories and Tales by Miss SeweU :—

Ivors, 2*. 6d.

Amy Herbert, 2*. 6d.
Cleve Hall, 2*. 6d.
The Earl's Daughter, 2s. 6d.
Experience of Life, 2*. 6d.
Gertrude, 2*. 6d.

Katharine Ashton, 2*. 6rf.
Laneton Parsonage, ?*. 6d.
Margaret Percival, 3t. 6d.
Ursula, 3*. 6d.

Novels and Tales by the Right Hon. the Earl of Beaconsfield, K.G. Cabinet
Edition, complete in Ten Volumes, crown 8vo. price £3.

Lothair, 6*. Henrietta Temple, 6*.

Coningsby, 6*. Contarini Fleming, 6*.

Sybil, 6*. Alroy, Ixion, &c. 6*.

Tancred, 6*. The Young Duke, &c. 6*.

Venetia, 6*. | Vivian Grey, 6*.

Klein's Pastor's Narrative. Translated by Marshall. Crown 8vo. Map, 6*.
The Modern Novelist's Library. Each Work in crown 8vo. A Single Volume,
complete in itself, price 2.!. boards, or 2*. 6d. cloth :—

By the Earl of Beaconsfield, K.G.
Lothair.
Coningsby.
Sybil. '
Tancred.
Venetia.

' Henrietta Temple.
Contarini Fleming.
Alroy, Ixion, &c.
The Young Duke, &c.
Vivian Grey.
By Anthony Trollope.
Barchester Towers.
The Warden.

By the Author of ' the Rose Garden.'
Unawares.

By Major Whyte-Melville.

Digby Grand.

General Bounce.

Kate Coventry.

The Gladiators.

Good for Nothing.

Holmby House.

The Interpreter.

The Queen's Maries.
By the Author of ' the Atelier du Lys.'

Mademoiselle Mori.

The Atelier du Lys.
By Various Writers.

Atherstone Priory.

The Burgomaster's Family.

Elsa and her Vulture.

The Six Sisters of the Valleys.
Lord Beaconsfield's Novels and Tales. 10 vols. cloth extra, gilt edges, 30*.
Whispers from Fairy Land. By the Right Hon. Lord Brabourne. With Nine
Illustrations. Crown 8vo. 3*. Sd.

Higgledy-Piggledy ; or, Stories for Everybody and Everybody's Children. By
the Right Hon. Lord Brabourne. With Nine Illustrations from Designs by
R. Doyle. Crown 8vo. 3*. 6d.

London, LONGMANS & CO.

General Lists of New Works. 11

POETRY SL THE DRAMA.

Bailey's Festus, a Poem. Crown 8vo. 12*. 6d.

Bowdler's Family Shakspeare. Medium 8vo. 14*. 6 vols. fcp. 8vo. 21*.

Cayley's Iliad of Homer, Homometrically translated. 8vo. 12*. 6d.

Conington's .ffineid of Virgil, translated into English Verse. Crown 8vo. 9*.

Cooper's Tales from Euripides. Fcp. 8vo. 3*. 6d.

Horace's Epistles, Book II. and ars Poetica, annotated by Cox. 12mo.

Ingelow's Poems. New Edition. 2 vols. fcp. 8vo. 12*.

Macaulay's Lays of Ancient Rome, with Ivry and the Armada. 16mo. 3*. 6d.

Ormsby's Poem of the Cid. Translated. Post 8vo. 5*.

Bouthey's Poetical Works. . Medium 8vo. 14*.

Yonge's Horatii Opera, Library Edition. 8vo. 21*.

RURAL SPORTS, HORSE & CATTLE MANAGEMENT &c.

Elaine's Encyclopaedia of Rural Sports. 8vo. 21*.
Francis's Treatise on Fishing in all its Branches. Post 8vo. 1C*.
Horses and Roads . By Free-Lance. Crown 8vo. 6*.
Miles's Horse's Foot, and How to Keep it Sound. Imperial 8vo. 12*. 6d.
Plain Treatise on Horse-Shoeing. Post 8vo. 2*. 6d.

— Stables and Stable-Fittings. Imperial 8vo. 15*.

— Remarks on Horses' Teeth. Post 8vo. 1*. 6d.
Nevile's Horses and Riding. Crown 8vo. 6*.
Ronalds's Fly-Fisher's Entomology. 8vo. 14*.
Steel's Bovine Pathology, or Diseases of the Ox. 8vo.
Btonehenge's Dog in Health and Disease. Square crown 8vo. 7*. 6d.

Greyhound. Square crown 8vo. 15*.

Yonatt's Work on the Dog. 8vo. 6*.

— — — Horse. 8vo. 7*. 6d.

Wilcocks's Sea-Fisherman. Post 8vo. 12*. 6d.

WORKS OF UTILITY &, GENERAL INFORMATION.

Acton's Modern Cookery for Private Families. Fcp. 8vo. 6s.

Black's Practical Treatise on Brewing. 8vo. 10*. 6d.

Buckton's Food and Home Cookery. Crown 8vo. 2*.

Bull on the Maternal Management of Children. Fcp. 8vo. 2*. Bd.

Bull's Hints to Mothers on the Management of their Health during the Period of

Pregnancy and in the Lying-in Room. Fcp. 8vo. 2*. 6d.
Campbell-Walker's Correct Card, or How to Play at Whist. Fcp. 8ro. 2*. 6d.
Crump's English Manual of Banking. 8vo. 15*.

Johnson's (W. Si J. H.) Patentee's Manual. Fourth Edition. 8vo. 10*. 6d.
Longman's Chess Openings. Fcp. 8vo. 2*. 6<t
Macleod'i Economics for Beginners. Small crown 8vo. 2*. M.

— Elements of Economics. Small crown 8vo. [In the frett.

London, LONGMANS & CO.

12 General Lists of New Works.

Macleod's Theory and Practice of Banking. 2 vols. 8vo. 26*.

— Elements of Banking. Fourth Edition. Crown 8vo. 5s.
M'Culloch's Dictionary of Commerce and Commercial Navigation. 8vo. 63*.
Maunder's Biographical Treasury. !'cp. 8vo. 6*.

— Historical Treasury. Frp. 8vo. 6*.

— Scientific and Literary Treasury. Fcp. 8vo. 6*.

— Treasury of Bible Knowledge, edited by Ayre. Fcp. 8vo. 6*.

— Treasury of Botany, edited by Liiidley & Moore. Two Parts, 12*.

— Treasury of Geography. Fcp. 8vo. 6*.

Treasury of Knowledge and Library of Reference. Fcp. 8vo. 6*.

— Treasury of Natural History. Fcp. 8vo. 6*.
Pereira's Materia Medica, by Bentley and Redwood. 8vo. 25*.

Pewtner"s Comprehensive Specifier ; Building-Artificers' Work. Crown 8vo. 6*.
Pierce's Three Hundred Chess Problems and Studies. Fcp. 8vo. 7*. 6</.
Pole's Theory of the Modern Scientific Game of Whist. Fcp. 8vo. 2*. 6d.
Scott's Farm Valuer. Crown 870. 5*.

— Rents and Purchases. Crown 8vo. 6*.
Smith's Handbook for Midwives. Crown 8vo. 5*.

The Cabinet Lawyer, a Popular Digest of the Laws of England. Fcp. 8vo. 9*.
West on the Diseases of Infancy and Childhood. 8vo. 18*.
Wilson on Banking Reform. 8vo. Is. 6d.

— on the Resources of Modern Countries 2 vols. 8vo. 24*.

MUSICAL WORKS BY JOHN HULLAH, LL.D.

Chromatic Scale, with the Inflected Syllables, on Large Sheet. 1*. 6d.

Card of Chromatic Scale. Id.

Exercises for the Cultivation of the Voice. For Soprano or Tenor, 2*. 6d.

Grammar of Musical Harmony. Royal 8vo. 2 Parts, each 1*. Gd.

Exercises to Grammar of Musical Harmony. 1*.

Grammar of Counterpoint. Part I. super-royal 8vo. 2*. 6d.

Hullah's Manual of Singing. Parts I. & II. 2*. 6d. ; or together, 5*.

Exercises and Figures contained in Parts I. and II. of the Manual. Books

I. & II. each 8d.
Large Sheets, containing the Figures in Part I. of the Manual. Nos. 1 to 8 in

a Parcel. 6*.
Large Sheets, containing the Exercises in Part I. of the Manual. Noa. 9 to 40,

in Four Parcels of Eight Nos. each, per Parcel. 6*.
Large Sheets, the Figures in Part II. Nos. 41 to 53 iu a Parcel, »*.
Hymrns for the Young, set to Music. Royal 8vo. 8d.
Infant School Songs. 6d.

Notation, the Musical Alphabet. Crown 8vo. 6<i.
Old English Songs for Schools, Harmonised. 6<i.
Rudiments of Musical Grammar. Royal 8vo. 3*.
School Songs for 2 and 3 Voices. 2 Books, 8vo. each 6d.
Time and Tune in the Kleiceutary School. Crowu 8vo. 2*. fid.
Exercises and Figures in the same. Crown 8vo. 1*. or 2 Parts, 6d. each.

London, LONGMANS & CO.

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