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OF THE

Theological Seminary,

PRINCETON, N. J.

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POPULAE LECTURES

ON

SCIENTIFIC SUBJECTS.

POPULAE LECTUEES

ON

SCIENTIFIC SUBJECTS.

/ "

H. 'hELMHOLTZ,

PROFESSOR OF PHYSIC:J IN THE UNIVEIISITX OF BERLIN.

TEANSLATED BY

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

PBOPESSOR OB- EXPERIMENTAL SCIENCE, STAFF COLLEGE.

WITH AN INTRODUCTION

BT

. PROFESSOR TYNDALL.

NEW YOEK:
D. APPLETON AND COMPANY,

549 & 551 BROADWAY.
1873.

AUTHOR'S PREFACE,

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 illustra-
tions which the publishers have liberally furnished.

The first and second Lectures have already appeared
in print; the first in a university programme which,
however, 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 pourse, been composed
in accordance y^iih. a rigidly u.?\iforin plan. Each of
theii^ has b^eiji kep^ perfiectly independent of the others.

viii AUTHORS PREFACE.

Hence 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 treats 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 explanations. 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 alterations
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 con-
sequences of the law of the Conservation of Force are
comparatively more easy to grasp. They have in recent

author's preface. ix

times been treated by several persons in a vivid and
interesting manner, so that it seemed unnecessary to
publish the corresponding 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 comprehend-
ing them ; as is shown by his controversy with Leibnitz.
Hence 1 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 examples ;
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 Innsbriick. 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 con-
sidered an 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

X author's preface.

preceding Lectures into a more complete and more com-
prehensive 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 AUTHOR.

TEANSLATOR'S PREFACE.

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 shoidd 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.

Staff College:
March 1873.

CONTENTS.

LECTTIRB PAGE

I. On the Eelation of 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 33

III. On the Physiological Causes of Harmony in Music.

Translated by A. J. Ellis, Esq., M.A., F.R.S. . . .61

IV. Ice and Glaciers. Translated by Dr. Atkinson, F.C.S.,

Professor of Experimental Science, Staff College . . .107

V. On the Interaction of the Natural Forces. Translated

by Professor Tyndall, LL.D., F.KS 153

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 . . . .197

II. The Sensation of Sight 229

m. The Perception of Sight 270

VII. On the Conservation of Force. Translated by Dr. At-

kinson .317

VIU, On the Aim and Progress of Physical Science. Translated

by Dr. W. Flight, F.C.S., British Museum , . . .363

INTRODUCTION.

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

In 1851, through the liberal courtesy of the late Pro-
fessor 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-Kaymond 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

Xvi INTRODUCTION.

Helmholtz and Clausius, or fail to see the probable in-
flueuce of their writiDgs 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 ' ^Yechselwirkung
der Naturkrafte,' printed in the following series, had this
ori<nn. 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 superfluous for me to say that the intel-
lectual nutriment here offered is of the very first quality.

Soon after the publication of the ' Tonempfindungen '
bv Helmholtz, I endeavoured to interest the Messrs. Long-
man in the work, urging that the publication of a trans-
lation 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.^
I then recommended the translation of these ' Populare
Vortrage,' and to this the eminent publishers immediately
agreed.

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

JOHN TYNDALL.

Royal Institution:

MarLh 1873.

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

ON THE

RELATION OF NATURAL SCIENCE*
TO GENERAL SCIENCE.

ACADEMICAL DISCOURSE DELIVERED AT HEIDELBERG,
NOVEMBER 22, 1862,

Br De. H. HELMHOLTZ, sometime peoeectob.

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 subjects, and, above all, their
moral and intellectual development. Eightly 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 pre-

' The German word Naturwissenschaft has no exact equivalent iu
modern English, including, as it does, both the Physical and the Natural
Sciences. Curioiisly enough, in the original charter of the Eoyal 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.)— Tb.

2 ON THE RELATION OF

sence of the whole University, I have thought it well to
try and take, as far as is permitted by the narrow stand-
point of a single student, a general view of the connection
of the several sciences, and of 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 Univeraitas Lit-
terarum, 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 know-
ledge of two or three European languages, acquired for
practical purposes. But now comparative philology aims
at nothing less than an acquaintance with all the lan-
guages 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 eveiy lost fragment of
an ancient author, every gloss of a pedantic grammarian,
eveiy allusion of a Byzantine court-poet, every broken
tombstone found in the wilds of Hungaiy or Spain or
Africa, may contribute 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.

NATURAL SCIENCE TO GENERAL SCIENCE. 6

Add to this, in history, the study of original documents,
the critical examination of parchments and papers accumu-
lated in the archives of states and of towns ; the combi-
nation of details scattered up and down in memoirs, in
correspondence, and in biographies ; the deciphering of
hieroglyphics and cuneiform inscriptions ; in natural
history the more and more comprehensive classification
of minerals, plants, and animals, as well living as 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 observation 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 diffi-
cult study. Now we are no longer satisfied with the
comparatively rpugh 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 promises still further discoveries.^ But

' That is the method of spectrum analysis, due to Bunsen and Kirchoff,
both of Heidelberg. The elements alluded to are caesium rubidium,
tha!liu7n, and iridium.

4 ON THE RELATION OF

not merely is the number of the elements far greater, the
methods of producing complicated combinations of them
have been so vastly improved, that what is called organic
chemistry, which embraces only compounds 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 improbam ') 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 century, constructed without the
aid of telescopes, give more than from 1,000 to 1,500
stars of magnitudes from the first to the fifth. At pre-
sent several observatories are eno^aged in continuino- these
catalogues down to stars of the tenth magnitude. So
that upwards of 200,000 fixed stars are to be catalogued
and their places accurately determined. The immediate
result of these observations 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.^

The contemplation of tins 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 know-
ledge ? Who can grasp the clues, and then thread the
labyrinth?' One obvious consequence of this vast exten-
sion 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

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

XATUEAL SCIEK-CE TO GET^RAL SCIENCE. 5

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 repre-
sent all these branches of science. And the same is true
of other faculties.

One of my strongest motives for discussing to-day the
connection 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 op-
position has, in fact, been long apparent, and seems to me
to have grown up mainly under the inSirence of the
Hegelian philosophy, or, at any rate, to Lave been brought
out into more distinct relief by that philosophy. Cer-
tainly, at the end of the last century, when the Kantian
philosophy reigned supreme, such a schism had never
been proclaimed ; on the contrary, Kant's philosophy
rested on exactly the same ground as the physical
sciences, as is evident from his own scientific works, es-
pecially from his ' Cosmogony,' based upon Newton's Law
of Grravitation, which afterwards, under the name of
Laplace's Nebular Hypothesis, came to be universally
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 disco-
vered a 'priori by pure thought was a rule applicable to
the method of pure thought, and nothing further ; it

6 ox THE RELATION OF

could contain no real, positive knowledge. The ' Phi-
losophy of Identity ' ^ 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 without the guidance of external ex-
perience, 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 Idertity ' 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, what-
ever obstacles nature, or chance, or the rivalry of other
men may interpose, the efforts of the human mind to
satisfy its needs, being systematically directed to one
end, must eventually triumph over all such fortuitous
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. More-
over, Hegel was materially assisted, in his attempt to
solve this problem, by the profound and philosophical
views on historical and scientific subjects, with which the
writings of his immediate predecessors, both poets and

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

NATUEAL SCIENCE TO GENERAL SCIENCE. t

philosophers, 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 suc-
cessful 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 develop-
ment 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 contemporaries, not one was
found to stand up for his ideas. Accordingly, 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 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

8 ON THE RELATION OF

that the philosophers were crazy. And so it came aboiif.
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 acute-
ness, went so far as to condemn philosophy altogether,
not merely as useless, but as mischievous dreaming.
Thus, it must be confessed, 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 dif-
ferent, 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 liealthy germ of extraordinary fertility ; it
was impossible any longer to withhold from them recog-
nition and respect. And even in other departments of
science, conscientious investigators of facts soon pro-
tested j^ gainst the over-bold flights of speculation. Still,
it cannot be overlooked that the philosophy of Hegel and
Schelling did exercise a beneficial influence ; since their

NATURAL SCIENCE TO GENERAL SCIENCE. 9

time the attention of investigators in the moral sciences
had been constantly and more keenly directed to the
scope of those sciences, and to their intellectual con-
tents, 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
investigation 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 foundation 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 liand an
artist or a theologian will perhaps find the natural philo-
sopher 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 philosopher. They will find him shockingly
indifferent to literary treasures, perhaps even more in-
different 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 institutions
it has brought into being, the natural sciences are con-

10 ox THE RELATION OF

cerned with dead, iDdifferent matter, obviously indispen-
sable 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
branclied out into countless ramifications, that there has
grown up between different groups of them a real and
deeply-felt opposition, tliat finally no single intellect can
embrace the whole range, or even a considerable por-
tion 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 ? 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 Polytechnic Schools, and form special semin-
aries for the theologians and jurists? Long may the
Grerman universities be preserved from such a fate !
Then, indeed, would the connection between the dif-
ferent 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
P'aculties is necessary to maintain a healthy equilibrium
among the intellectual energies of students. Each study
tries certain of our intellectual faculties more than the
rest, and strengthens them accordingly by constant exer-
cise. 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 our-
selves. Anyone who has found himself much more sue-

NATURAL SCIENCE TO GENERAL SCIENCE. 11

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 melan-
choly existence, because they have failed to obtain among
their fellows that recognition which must be won by
labour and results, but which is ever withheld from
mere self-conscious 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 the men
are, the more clearly does their individuality come out,
and the less qualified woujd either of them be to carry
on the other's researphes, To-day I can, of course, do
"2

12 ON THE RELATION OF

nothing more than characterise some of the most general
of these differences.

I have ah-eacly noticed the enormous mass of the
materials accumulated by science. It is obvious that
the organisation and arrangement of them must be pro-
portionately 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 know-
ledge.

This organisation consists, in the first place, of a
mechanical arrangement of materials, such as is to be
found in our catalogues, 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 knowledge as cannot be
carried about in the memory is immediately accessible to
anyone who wants it. With a good lexicon a school-boy
of the present day can achieve results in the interpreta-
tion 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 learning buried in cata-
logues, lexicons, and indexes looks as bare and uninviting
as the soil of a farm ; the uninitiated cannot see or ap-
preciate 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 scien-

NATURAL SCIENCE TO GENERAL SCIENCE. 13

tific 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 imagin-
able.^ 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 denot-
ing advancement in the art of methodising and organis-
ing 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 unveiled. 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 concep-
tion 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 made out that all mammals —
that is, all warm-blooded, viviparous animals — breathe
through lungs, have two chambers in the heart and at
least three tympanal bonef?, I need no longer remember
these anatomical peculiarities in the individual cases of
the monkey, the dog, the horse, and the whale ; the
* Condendaque lexica mandat damnatis. — Tb.

14 ON THE RELATION OF 1

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 sur-
face of water, and inform me of the residt, but it includes
all cases of rays of any colour incident on transparent
surfaces of any form and any constitution whatsoever.
This law, therefore, includes an infinite number of cases,
which it would have been absolutely impossible to carry
in one's memory. Moreover, it should be noticed that
not only does this law include the cases which we our-
selves or other men have already observed, but that we
shall not hesitate to apply it to new cases, not yet ob-
served, 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
process of thought, and form conceptions, whether general
conceptions or laws, we not only bring our knowledge
into a form in which it can be easily used and easily re-
tained, 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.

Tlie 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 diffi-
culties, 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

NATURAL SCIENCE TO GENERAL SCIENCE. 15

with tolerable certainty that if he has to act under 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 con-
stitutes an ambitious man, or by what standard the inten-
sity 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 premiss in a clear, sharply-defined form —
perhaps even without having 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 us to assume that
a newly-discovered mammal has lungs.

This latter kind of induction, which can never be per-
fectly 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 sensations into perceptions
depends upon it, as appears especially from the investiga-
tion of what are called illusions. For instance, 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.

16 ON THE RELATION OF

Moreover, such is the complexity of the influences affect-
ing 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 causality, we deny in toto the possibility of re-
ferring 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-defined universal
propositions, call this kind of reasoning cesthetic induc-
tion, because it is most conspicuous 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,
tlie external indications of a character or a state of mind,
and by a kind of instinctive intuition, uncontrolled 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
abstractions, we think his work poor and commonplace,
and cease to admire. On the contrary, the works of
great artists bring before us characters and moods with
such a lifelikeness, with such a wealth of individual traits
and such an overwhelming conviction 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 ;

NATURAL SCIENCE TO GENERAL SCIENCE. 17

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 con-
cerned 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 purpose 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 aesthetic, but not for strictly
logical induction. It is only possible to pass judgment,
if you have ready in your memory a great number of
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 coai*se
memory alone is insufficient without a knack of every-
where discovering real resemblance, and without a deli-
cately 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 circumstances. The laws of grammar are a
product of the human will, though they can hardly be

18 ON THE KELATION OF

said to have been framed deliberately, but rather to have
grown up gradually, as they were wanted. Accordingly,
they present themselves to a learner rather in the form
cf commands, that is, of laws imposed by external au-
thority.

With these sciences theology and jurisprudence are
naturally connected. In fact, certain branches of history
and philology serve both as stepping-stones and as hand-
maids to them. The general laws of theology and juris-
prudence are likewise commands, 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 natm*e, contain generalisations from a vast multitude
of facts. At the same time the application of a gramma-
tical, 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 question satisfies the conditions to
which the rule is intended to apply. The solution of this
latter problem, whether in grammatical 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 docu-
ments 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
full3^-developed languages and a system of jurisprudence
gradually elaborated, as ours has been, by the practice of
more than 2,000 years,^ have reached a high pitch of
logical completeness and consistency ; so that, speaking
generally, the cases which do not obviously fall under

' It should be remembered that the Eoman law, uhich has only parti-
ally and indirectly influenced English practice, is tliw recognised basis of
Geiinan jurisprudence. — Tb.

NATURAL SCIENCE TO GENERAL SCIENCE. 19

some one or other of the laws actually laid down are
quite exceptional. Such exceptions there will always be,
for the legislation 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 jurisprudence have a certain advantage
as means of training the intellect, inasmuch as they tax
pretty equall}^ all the intellectual powers. On this account
secondary education among modern European nations is
based mainly upon the grammatical study of foreign
languages. The motlier-tongue and modern foreign lan-
guages, 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 expression. The two classical languages, Latin
and Grreek, 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 mini-
mum for the sake of brevity and rapidity 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 instruments of education.'

* Those to whom German is not a foreign tongiie may, perhaps, be per-
mitted to hold different views on the efficacy of modern languages in
education. — Tb.

20 ON THE RELATION OF

As grammar is the staple of school education, legal
studies are used, and rightly, as a means of training per-
sons 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 oppo-
site 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, Groethe,
who gave the first impulse to the researches of compara-
tive anatomy into the analogy of corresponding organs in
different animals, and to the parallel theory of the meta-
morphosis 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 comprehensive ideas and prin-
ciples, 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 experi-
mental sciences to which mathematics are applied, and
especially when we come to pure mathematics, that we
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 indi-

NATURAL SCIENCE TO GENERAL SCIENCE. 21

vidual results of observation and experiment are com-
bined under general laws of unexceptionable validity and
of an extraordinarily comprehensive character. In the
moral sciences, on the other hand, chis is just the point
where insuperable difficulties are encountered. In mathe-
matics the general propositions 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 arithmetic 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 }je 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 heterogeneous combinations of a finite number of
magnitudes, but in the higher analysis it teaches us to
sum even infinite series, the 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 con-
ceptions. On the other hand, we gain confidence in the
certainty, the range, and the fertility of this kind of
intellectual work.

22 ON THE RELATION OF

The fertility of the method comes out more strikingly
in applied mathematics, especially in mathematical
physics, including, 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 varying in-
versely as the square of the distance, astronomers have
been able, in virtue of that one law of gTavitation, to
calculate with the greatest accuracy the movements of
the planets to the remotest past and the most distant
future, given only the position, velocity, and mass of each
body of our system at any one time. More than that, we
recog-nise 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 measm'e them have failed.

This discovery of the law of gravitation and its conse-
quences is the most imposing achievement that the
logical power of the human mind has hitherto per-
formed. 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 astrolo-
gical superstitions 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
successfully applied to several other physical sciences,
among which physical optics and the theory of electricity
and magnetism are especially worthy of notice. The ex-

NATURAL SCIENCE TO GENERAL SCIENCE. 23

perimental sciences have one great advantage over the
natural sciences in the investigation 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 stand the test of application to more complex cases.
Accordingly 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 becom-
ing heated by the energy of their contraction ; not only
have they permitted us to investigate the chemical con-
stituents of the solar atmosphere and of the remotest
fixed stars, but they have enabled us to turn the forces of
surrounding nature to our own uses and to make tliem the
ministers of our will.

Enough has been said to show how widely the intel-
lectual processes involved in this group of sciences differ,
for the most part, from those required by tne moral
sciences. The mathematician 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 discovered unvaiying laws ; till then we dare not rest
satisfied, for then only can our knowledge grapple victo-
riously 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

24 ON THE RELATION OF

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. Eather is it an essential
condition of the methodical progress of mathematical
reasoning that the mind should remain concentrated 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 celebrated logician, Mr. John Stuart Mill,
expresses his conviction that the inductive sciences have
of late done more for the advance of logical methods than
the labours of philosophers properly so called. One essen-
tial ground for such an assertion must undoubtedly be that
in no department of knowledge can a fault in the chain of
reasoning be so easily detected by the incorrectness of the
results as in those sciences in which the results of reason-
ing 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 mathematically, 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 perfection
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

N-ATURAL SCIENCE TO GENERAL SCIENCE. 25

method, but tliey 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 collected, a certain distrust-
fulness 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 pre-
ceding 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 con-
scious logical reasoning, should take a more important
place in school education. But it is, in reality, one of
the questions of the day. In proportion as the range of
science extends, its system and organisation must be
improved, and it must inevitably come about that in-
dividual students will find themselves compelled to go
through a stricter course of training than grammar is in
a position to supply. What strikes me in my own ex-
perience 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 gram-
matical 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 decision of disputed questions often
depends on an aesthetic feeling for beauty of expres-
sion, and for the genius of the language, attainable
only by long training, it must often happen that the

26 ON THE RELATION OF

student is referred to authorities even by the best
teachers. Both faults are traceable to a certain in-
dolence and vagueness of thought, the sad effects of
which are not confined to subsequent 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 earth. 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 same time, ambition or energy enough to make
them work, dragging 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 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

NATUEAL SCIENCE TO GENERAL SCIENCE. 27

the human intellect. The application of steam has
multiplied our physical strength a million-fold ; wea.ving
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 in-
fluence 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 multi-
plied; not merely on rifled cannon, and armour-plated
ships ; not merely on accumulated stores of money and
the necessaries of life, that the power of a nation rests ;
though these things have exercised so unmistakeable an
influence, that even the proudest and most obstinate
despotisms of our times have been forced to think of
removing restrictions on industry, and of conceding to
the industrious middle classes a due voice in their
counsels. 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 conditions of national prosperity act and react on
each other ; where the administration of justice is uncer-
tain, 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 inde-
pendent 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 knowledge on the simple ground of self-preservation,

28 ON THE RELATIO]!^ OF

even were there no higlier wants of an ideal character to
be satisfied ; and not merely in the development of the
physical sciences, and their teclmical 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 Eiu*ope.
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 congratu-
late ourselves on another rich endowment granted by our
government and our parliament.

I was speaking, at the beginning of my address, of the
increasing division of labour and the improved organisa-
tion 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 know-
ledge 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
individual citizens. After the immediate practical re-
sults 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 at-
tention in his anatomical researches, all Europe would
be traversed with wires, flashing intelligence from Madrid

NATUEAL SCIENCE TO GENEEAL SCIENCE. 29

to St. Petersburg witli the speed of lightning ? In the
hands of Gralvani, and at first even in Volta's, electrical
currents were phenomena capable of exerting 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 important and most interesting of the links
between the various forces of nature. When young
Gralileo, then a student at Pisa, noticed one day during
divine service a chandelier swinging backwards and for-
wards, 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 measure-
ment of time till then deemed impossible, and would
enable the storm-tossed seaman in the most distant oceans
to determine in what degree of longitude he was sailing ?
Whoever, in the pursuit of science, seeks after imme-
diate 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 dis-
coveries, as over new victories of mind over reluctant
matter, or in enjoying the aesthetic beauty of a well-
ordered field of knowledofe, 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 intelli-
gence reposes. He will, indeed, not always be permitted
to expect from his fellow-men appreciation and reward

30 ON THE EELATIOIS" OF

adequate to the value of his work. It is only too true,
that many a man to whom a monument has 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 recognised than formerly by public opinion,
and that instances of the authors of great advances in
science starving in obscurity have become 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 appropriate ap-
pointments 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 re-
straints 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 connec-
tion 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

NATUEAL SCIENCE TO GENEEAL SCIENCE. 31

are preserved in ancient histories. Conversely, many of
the important data of astronomy — for instance, the in-
variability of the length of the day, and the periods of
several comets — rest upon ancient historical 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 accounting for many apparently
anomalous substitutions, on the ground that they are
governed, not as hitlierto supposed, by the laws of eu-
phony, but by similarity between the movements of the
mouth that produce them. Again, comparative philo-
logy gives us 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 distinc-
tive 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.^ 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 hear-
ing, to account for the elementary principles on which
our musical system is constructed, a problem essentially
within the sphere of sesthetics. In fact^ it is a general
principle that the physiology of the organs of sense is

^ See, for example, Mommsen's Borne, Book I. ch. ii. — Tjr.

32 ON- THE RELATION OF NATURAL SCIENCE.

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 con-
ciousness, and must therefore have remained inaccessible
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.
Naturally, 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 him-
self, 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 common work bearing upon the
highest interests of humanity. Then assuredly we shall
not fail of our reward in the approval of our own con-
science and the esteem of our fellow-citizens. To keep
up these relations between all searchers after truth and
all branches of kno"wledge, to animate them all to vigo-
rous 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.

ON

GOETHE'S SCIENTIFIC RESEARCHES.

A LECTURE DELIVERED BEFORE THE GERMAIN SOCIETY OP
KONIGSBERG, IN THE SPRING OE 1853.

It could not but be that Groethe, whose comprehensive
genius was most strikingly apparent in that sober clear-
ness 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 ac-
quiring what others could teach him, but he soon at-
tempted, as so original a mind was sure to do, to strike
out an independent and a very characteristic line of
thought. He directed his energies, not only to the
descriptive, but also to the experimental 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

34 ON Goethe's scientific researches.

new fields of research and undergone many changes in its
theoretical views. I shall attempt in the following
Lecture to sketch the relation of Goethe's researches to
the present stand-point of science, and to bring out the
guiding idea that is common to them all.

Tlie peculiar character of the descrijDtive sciences —
botany, 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 lexico-
grapher ; 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, hetero-
geneous 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 mate-
rials in botany and comparative anatomy, copious and
systematic enough to admit of a comprehensive view,
and to indicate the way to some happy glimpse of an
all-pervading law ; while his contemporaries, if they made
any efforts in this direction, wandered without a com-
pass, or else they were so absorbed in the dry registra-
tion of facts, that they scarcely ventured to think of
anything beyond. It was reserved for Goethe to intro-
duce two ideas of infinite fruitfulness.

The first was the conception that the differences in the

ON goethe's scientific researches. 35

anatomy of different animals are to be looked upon as
variations from a common phase or type, induced by dif-
ferences 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, mam-
malia, 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 distinguished from all other animals by the ab-
sence 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, Groethe 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 inter-
maxillary 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 osteo-
logy, 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
similarities of structure even between man and fishes.
But the persistence of this similarity, at least in a rudi-
mentary 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 sepa-
rate, was what struck Groethe's far-seeing eye, and sug-
gested to him a far more comprehensive view than had
hitherto been taken. Fui-ther studies soon convinced
3

36 ON Goethe's scientific rese.4Eches.

liim 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 1786, and to
commit it to writing in his ' Sketch of a Greneral Intro-
duction to Comparative Anatomy.' He there lays down
with the utmost confidence and precision, that all differ-
ences in the structure of animals must be looked upon a^
variations of a single primitive type, induced by the
coalescence, the alteration, the increa-se, the diminution,
or even the complete removal of single parts of the
structure ; the very principle, in fact, which has become
the leading idea of comparative anatomy in its present
stage. Nowhere has it been belter or more clearly ex-
pressed than in Goethe's writings. Subsequent authorities
have made but few essential alterations in his theory.
Tije most important of these is, that we no longer under-
take to construct a common type for the whole animal
kingdom, but are content 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 sub-
sisting between corresponding parts of different species.
In most organisms we see a great repetition of single
parts. This is most striking in the vegetable 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
looking at a fan-palm at Padua. He was struck by the
immense variety of changes of form which the sue-

ox Goethe's scientific reseaeches. 37

cessively-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 discoveringf the transforma-
tion 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 extre-
mity 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, &c., all resembling each other to a certain extent
in origin and composition, and even capable, under
certain unusual conditions, 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 Groethe's, like the other, is now
completely adopted into science, and enjoys the universal
assent of botanists, though of course some details are still
matters of controversy, as, for instance, whether the bud
is a single leaf or a branch.

In the animal kingdom, the composition of an indi-
vidual out of several similar parts is very striking in the
great sub-kingdom of the articulata — for example, in
insects and worms. The larva of an insect, or the cater-
pillar 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 Groethe had

38 ON goethe's scientific reseaeches.

grasped in his doctrine of the metamorphosis of plants,
the development, namely, of apparently very dissimilar
forms from parts originally alike. The posterior seg-
ments retain their original simple form ; those of the
breast-plate 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 seg-
ments are recognised only in the posterior part of the
body. In the vertebrata, again, a repetition of similar
parts is suggested by the vertebral column, but has ceased
to be observable in the external form. A fortunate glance
at a broken sheep's skull, which Groethe found by acci-
dent on the sand of the Lido at Venice, suggested to him
that the skull itself consisted of a series of very much
altered vertebrfE. 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
cvlindrical 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 Groethe 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 G-oethe the priority
of discovery. In fact, Goethe had waited till 1817, when
the opinion had begun to find adherents, and then de-
clared 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 subject of controversy,
but the principle has maintained its 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

ON Goethe's scientific rese.\rches. 39

doctrine of the metamorphosis of plants was introduced
into botany as his distinct and recognised property ; but
his views on osteology were at first disputed by ana-
tomists, 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 en-
countered 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, Groethe 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 Groethe has secured
by his achievements in the descriptive natural sciences,
the denunciation heaped by all physicists on his re-
searches in their department, and especially on his
' theory of colour,' is at least as uncompromising. 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 prin-
ciple 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 dis-

40 ON Goethe's scientific rese.\kches.

tinct statement, unencumbered by disputes about the
correctness of detached facts and complicated theories.

Groethe himself describes veiy gracefully, in the con-
fession at 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 Biitter, 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 appeared 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

ON Goethe's scientific eeseaeches. 41

sufficiently proved his rules. He next attempted to ex-
plain his supposed discovery to a neighbour, who was a
physicist, and was disagreeably 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
Newton's writing's, and fancied he had found some falla-
cies in them which accounted for the error. Unable to
convince 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 paits of his 'Contri-
butions to Physical Optics,'

In that work he describes the appearances presented by
white discs on a black ground, black discs on a white
gTound, 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 describes 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 gTOund 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 sensation of colour which they produce in
the eye. Thus there is red, orange, yellow, gi-een, blue,

42 ON GOETHE S SCIENTIFIC EESEAKCHES.

and violet light, and light of all intermediate colours.
Different kinds of light, or differently colom-ed lights,
produce, when mixed, derived colours, which to a cer-
tain 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 proportions. But the pri-
mitive colours can always be reproduced by analysis
from derived colom*s, 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 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 manifestation.

A prism refracts transmitted light ; that is to say, de-
flects it so that it makes a certain angle with its original
direction ; the rays of simple light of diflferent colours
have, according to Newton, different refrangibilities, and
therefore, after refraction in the prism, pm'sue different
com'ses and separate from each other. Accordingly a
luminous point of infinitely small dimensions appearSj
when seen through the prism, to be first displaced, and
secondly, extended into a coloured line, the so-called
prismatic spectrum, which shows what are called the pri-
mary 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 pro-
portions 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 instead of being

ON Goethe's scientific reseakches. 43

coloui'ed 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 lirst moment Goethe did not
recollect 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 under-
stood 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
clearly state in what he conceives the insufficiency of the
explanation 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 consistent with itself; and that if the hypo-
thesis from which it starts be granted, it explains the
observed facts completely and even simply. Newton him-
self mentions these spurious spectra in several passages of
his optical works, without going into any special eluci-
dation 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 Groethe no
sooner began to call the attention of his scientific friends
to the phenomena, 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

44 0]^ Goethe's scientific researches.

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 expe-
rience at this point an uncomfortable, almost a painful
feeling to see a man of extraordinary abilities persist-
ently declaricg that there is an obvious absurdity lurking
in a few inferences apparently quite clear and simple.
He searches and searches, and at last unable, with
all his efforts, to find any such absm'dity, or even the
appearance 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 Groethe'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 ;
there is nothing under discussion but a few easily-grasped
facts, as to the correctness of which both parties are agreed,
and yet both hold distinctly opposite views ; neither
of them even understands what his opponent is di'iving
at. On the one side are a number of physicists, who,
by a long series of the ablest investigations, the most
elaborate calculations, and the most ingenious inven-
tions, have brought optics to such perfection, that it,
and it alone, among the physical sciences, was begin-
ning almost to rival astronomy in accui'acy. Some of
them have made the phenomena the subject of direct in-
vestigation ; 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
inferences deduced from Newton's views to the test of
experiment, and all, without exception, agree in ac-
cepting them. On the other side is a man whose
remarkable mental endowments, and whose singular
talent for seeing through whatever obscures reality, we

ON goethe's scientific reseahciie?. 45

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 narrowness or malice on their part, and finally
declares that he cannot help looking upon his own achieve-
ment in the theory of colour as far more valuable than
anything he has accomplished in poetry.^

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 con-
ceive to be the grounds of this antagonism.

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 essen-
tial 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 domi-
nate 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 outbui'st of
excited feeling.

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

46 ON Goethe's scientific kesearches.

dependent of intuition, he sits down to contemplate them
as he would a work of art, complete in itself, and certain to
yield up its central idea, sooner or later, to a sufficiently
susceptible student. Accordingly, wh^n 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 unattainable, and
therefore never to be exhibited as realised in a phenome-
non. 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 con-
ception 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, mis-
leads the impertinent kill-joy by a distorted image of
herself.

Accordingly, in his attack upon Newton he often
sneers 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 particularly enchanting, but also

ON Goethe's scientific reseakches. 47

as particularly convincing I The poetic turn of mind is
very marked even in his morphological researches. If
we only examine what has really been accomplished 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 con-
necting 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 difii-
culty, 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
appendages of the axis.' To see this does not require a
Groethe. 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 bare 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 a 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 toler-

48 ON GOETHE'S SCIENTIFIC RESEARCHES,

able certainty which parts correspond to each other.
Groethe himself said this very clearly : he says, in speaking
of the vertebral theory of the skull, ' Such an apergu,
such an intuition, conception, representation, notion, idea,
or whatever you choose to call it, always retains some-
thing esoteric and indefinable, struggle as you will
against it ; as a general principle, it may be enunciated,
but cannot be proved; in detail it may be exhibited,
but can never be put in a cut and 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,^ for the agreement between the embryos of dif-
ferent 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 the scientific men have
' This was written before the appearance of Darwin's OnV/tw of Specuie.

ON Goethe's scientific reseaeches. 49

lately begun to make use of embryology as a sort of
check on the theoretical views of comparative anatomy.
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. Groethe 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 Groethe did all that was possible
at the time when he lived. I said just now that he
treated nature like a work of 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 symmetry 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 Groethe 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 explanations 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

50 ox Goethe's scientific researches.

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 inconceivable 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 bin 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 unacquainted with the geometrical rela-
tions by which the most favourable positions of them are
determined. In other experiments on the separation of
simple coloured light by means of prisms alone, Groethe's
objections are not quite groundless, inasmuch as the isola-
tion of single colours cannot by this means be so effectu-
ally carried out, that after refraction through another
prism there are no traces of other tints at the edges. A
complete 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
Groethe postponed to a supplement, and finally left un-
noticed. When he complains of the complication of
these contrivances, we need only think of the laborious

ON Goethe's scientific researches. 51

and roundabout methods which chemists must often
adopt to obtain certain elementary bodies in a pure form ;
and we need not be 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.^ Goethe must, consistently with his theory, deny
in toto the possibility of isolating pure liglit of one colour.
Whether he ever experimented 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 ap-
plies to the propositions of this consummate thinker in
physical and astronomical science — 'incredibly impu-
dent;' ' mere twaddle ;' ' ludicrous explanation ;' 'admi-
rable for school-children in a go-cart ;' ' but I see nothing
will do but lying, and plenty of it.' ^

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 representa-
tion 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 ex-
plains the other, and that thus we may attain an insight

* I venture to add that I 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 obser-
vation, having been under the necessity in one of my own researches of
obtaining light of one colour in a state of the greatest possible piirity. (See
Poggendorft's Annalen, vol. Ixxxvi. p. 50], on Sir D. Brewster's Ntw Analysis
of Svnlight.)

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

52 ox Goethe's scientific eesearches.

into their connection without ever having to trust to any
thing but our senses. This demand of his looks most
attractive, but is essentially wrong in principle. For a
natural phenomenon is not considered 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 cognizant
of forces qua forces, but only of their effects, we are com-
pelled 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 defined only by abstract con-
ceptions. When we find a stove warm, and then observe
that a fire is burning in it, we say, though somewhat in-
accurately, that the former sensation is explained by the
latter. But in reality this is equivalent to saying, we
are always accustomed to find heat where fire is burning ;
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 intui-
tion 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 movements, of attractive and repulsive forces, whose

ON GOETHE'S SCIENTIFIC RESEAECHES. 58

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 information about external effects pro-
duced on them, but convey those effects to our conscious-
ness in a totally different form, so that the character of a
sensuous perception depends not so much on the proper-
ties 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 sensa-
tion 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 phe-
nomena 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 wliich 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 re-

54 ON GOETHE'S SCIENTIFIC EESEAECHES.

frangibility than the red rays of light, but are in eveiy
other respect exactly similar to them. All these rays,
whether luminous or non-luminous, have heating proper-
ties, 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 sensation of light. Perhaps the relation between
our senses and the external world may be best enunciated
as follows : our sensations 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 information 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 know-
ledge 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 mate-
rials. 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 theory of colour as a forlorn hope, as a desperate at-
tempt to rescue from the attacks of science the belief in
the direct truth of our sensations. And this will account
for the enthusiasm with which he strives to elaborate and
to defend his theory, for the passionate irritability with

ON GOETHE'S SCIENTIFIC RESEARCHES. 55

which he attacks his opponent, for the overweening im-
portance which he attaches to these researches in com-
parison with his other achievements, and for his inacces-
sibility to conviction or compromise.

If we now turn to Groethe'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 ex-
planation 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 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. Groethe 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 day time 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 sub-
ject. According to Goethe, the semi-opaque medium
imparls 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 anyone who looks upon it as a
physical explanation. Does he mean to say that ma-
terial particles mingle with the light and fly away with

56 ON Goethe's scientific eesearches.

it ? But this is Groethe's fundamental experiment, this
is the typical phenomenon under which he tries to reduce
all the phenomena of colour, especially tliose connected
with the prismatic spectrum. He looks upon all trans-
parent 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 per-
fectly 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 surface 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 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 an-
terior edge appears in front of the ground, the posterior
edge behind it, and not vice versa, 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. Everyone 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

ON goethe's scientific researches. 57

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 backwards.
And yet, according to G-oethe, 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 presented 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 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
marvellous expedients. As long as you treat his explana-
tions as a pictorial way of representing the physical
processes, you may acquiesce in them, and even frequently

58 ON Goethe's scientific researches.

find them vivid and characteristic, but as physical eluci-
dations of the phenomena they are absolutely irrational.

In conclusion, it must be obvious to everyone that the
theoretical part of the Theory of Colour is not natural
philosophy 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 con-
cerned 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 Groethe, that he,
and he alone among poets, must needs break 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 tha
triumphs of mind over matter, even on that unpropitious
battlefield. But G-oethe, 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 superscription of poetry. This constitutes
the peculiar beauty of his poetry, and at the same time
fully accounts for his resolute 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.

ON goethe's scientific reseaeches. 59

But we cannot triumpli over the machinery of matter
by ignoring it ; we can triumph over it only by subordi-
nating 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
Groethe did follow the same line of thought in all his
contributions to science, but that the problems he en-
countered were of diametrically opposite characters. And,
perhaps, when it is understood how the self-same cha-
racteristic of his intellect, which in one branch of science
won for him immortal renown, entailed upon him egre-
gious failure in the other, it will tend to dissipate, in the
minds of many worshippers of the great poet, a lingering
prejudice against natural philosophers, whom they sus-
pect of being blinded by narrow professional pride to the
loftiest inspirations of genius.
4

ON THE

PHYSIOLOGICAL CAUSES OF HARMONY
IN MUSIC.

A LECTURE DELIVERED IN BONN DURING THE WINTER OP 1857.

Ladies and GtENTLEMEN, — In the native town of Beet-
hoven, the mightiest among the heroes of harmony, no
subject seemed to me better adapted for a popular
audience thau music itself. Following, therefore, the
direction of my researches during the last few years, I
will endeavour to explain to you what physics and physio-
logy have to say regarding the most cherished art of the
Ehenish 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 scien-
tific 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

62 ON THE PHYSIOLOGICAL CAUSES OF

sight as if those were still in the right who reject all
' anatomisation of pleasurable sensations.' This art, bor-
rowing no part of its material from the experience of our
senses ; not attempting to describe, and only exceptionally
to imitate the outer world, necessarily withdi'aws 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 wonderful and peculiarly inte-
resting 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 — mathematics — should prove preeminently fer-
tile. Thorough bass is a kind of applied mathematics.
In considering musical intervals, divisions of time, and
so forth, numerical fractions, and sometimes even loga-
rithms, 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 physiolo-
gical 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

HARMONY IN MUSIC. 63

awakened in my own mind, by endeavouring to exhibit
a few of the results of physical and physiological
acoustics.

The short space of time at my disposal obliges me to con-
fine 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 acknow-
ledged fact that the numbers of the vibrations of concor-
dant tones bear to each other ratios expressible by small
whole numbers. But why ? What have the ratios of
small whole numbers to do with concord ? This is an old
riddle, propounded by Pythagoras, and hitherto unsolved.
Let us see whether the means at the command of modern
science will furnish the answer.

First of all, what is a musical tone ? Common expe-
rience 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 sufii-
cient rapidity, generate sound.

This sound becomes a musical tone, when such rapid
impulses 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

64 0]^ THE PHYSIOLOGICAL CAUSES OF

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 Gr 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 num-
bers of vibrations, to be formed upon each of the above-
named tones. The numbers of vibrations within the
limits of audible tones which would be obtained by
executing the calculation thus indicated, are extraordi-
narily 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 modem pianofortes have seven
octaves. Their highest 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 audi-
bility. 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 uncer-
tainty 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 lower 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 separate impulses of the air
to which they are due. Hence they are used solely in con-
junction with the next higher octaves, to strengthen their
notes, and produce an impression of greater depth.

HAEMONY IN MUSIC. 65

With the exception of the organ, all musical instru-
ments, however diverse the methods in which their sounds
are produced, 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 suffi-
cient 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 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 cf 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

6Q ON THE PHYSIOLOGICAL CAUSES 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 produced. 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, I 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 vibra-
tions.

In order to produce tones upon this instrument, the portventg
go and gi are connected by means of flexible tubes with a
bellows. The air enters into round brass boxes, ao and aj, and
escapes by the perforated covers of these boxes at Cq and Cj. 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 perpendicular axis k, which turns with great
readiness. In the figure, only the perforated disc can be seen at
Cq, and immediately below it is the similarly perforated cover of
the box. In the upper box, c,, 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 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 alternately
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 suflicient
rapidity, gather themselves 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 combina-

HAHMONY IN MUSIC.

67

Fia. I.

68 ox THE PHYSIOLOGICAL CAUSES OF

tions of tone) has fo^l^ 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 Avith 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 combined two and two, or three
and three together, in any arbitrary manner.

The round boxes, hg h^ and hj h,, of which halves only are
drawn in the figure, serve by their resonance to soften the harsh-
ness 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 per-
petually increasing velocity.

On beginning to blow the instrument, we first hear separate
impulses 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 another more and more quickly, as the velocity of
the revolving discs increases, just like the puffs of steam of a
locomotive on beginning to move with the train. They next
produce a whirring and whizzing, Avhich 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
33 revolutions in a second, and that the series Avith 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 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 con-
vince ourselves that we have the absolutely pure concord of the

HAEMOxYY IN MUSIC. 69

octave. By taking 8 and 12 holes, -which give numbers of
vibrations 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
sharpening or flattening the tones 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 vibration 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 ad-
duced, 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.

70 ON THE PHYSIOLOGICAL CAUSES OF

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 remarked, a little while ago, that
when the tones are loud the agitation of the air is per-
ceptible to the skin. In this way deaf mutes 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
winch 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 be-
come 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
surface of water, and these will best illustrate the pecu-
liarity of this description of motion.

AYhen a point in a surface of still water is agitated — as

HAEMONY IN MUSIC. 71

by throwing in a stone — the motion thus caused is pro-
pagated in 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 con-
tinually 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 con-
clude 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, con-
sequently, 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 circles, in which they re-
volve with a tolerably uniform velocity, as long as the
waves pass over them.

In Fig. 2 the dark wave-line, ABC, 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 re-

IZ ox THE PHYSIOLOGICAL CAUSES OF

volving in the circles a and c to be simultaneously in their lowest
positions.

The respective particles of water revolve in these circles in
the direction marked by the arrows. The dotted curves repre-
sent other positions of the passing waves, at equal intervals of
time, partly before the assumption of the ABC position (as for
the crests between a and b), and partly after the same (for tha
crests between b 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 ol
water in its positions 1, 2, 3, hastens to meet the approaching

Fig. 2.

■wave-crests. 1, 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, after-
wards 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 Avorking model, in which the movable
particles, connected by threads, really revolved in circles, while
connecting elastic threads represented the surface of the water.)

All particles at the surface of the water, as you see by this
drawing, describe equal circles. The particles of water at dif-
ferent depths move in the same way, but as the deptlis 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 par-
ticles of water do not advance with the wave, but perpetually
revolve in their small circular orbits.

HARMONY IN MUSIC. 73

To return from waves of water to waves of sound.
Imagine an elastic fluid like air to replace the water, and
the waves of this replaced water to be compressed b}^ an
inflexible plate laid on their surface, the fluid being pre-
vented from escaping laterally from the pressure. Then
on the waves being thus flattened out, the ridges where
the fluid had been heaped up will produce much greater
density than the hollows, from which the fluid had been
removed to form the ridges. Hence the ridges are re-
placed by condensed strata of air, and the hollows by
rarefied strata. Now further imagine that these com-
pressed 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 different. 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

74 ON THE PHYSIOLOGICAL CAUSES OF

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 corre-
spond 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.^
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 condensation 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 tinihre or
quality of tone is what corresponds to the fovin 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 uncompressed surface. In
this sense then we can continue to speak of 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

' The exact lengths of waves corresponding to certain iwtcs, or symbols
of tone, depend upon the standard pitch assigned to one particular note,
and 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. — Te.

HARMONY IN MUSIC. 75

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
depends the quality of the tones produced by various
sounding bodies, can at present be assigned in only a very
few cases.

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

Fig. 3.

It can be seen in waves of water only when their height
is small in comparison with their length, and they run
over a smooth surface without external disturbance, or
without any action of wind. Eidge and hollow are gently
rounded off, equally broad and symmetrical, so that, if ^7e
inverted the curve, the ridges would exactly fit into the
hollows, and conversely. This form of wave would be
more precisely defined by saying 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 rela-
tion 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 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

76

ox THE PHYSIOLOGICAL CAUSES OP

sufficient accuracy to assign in some cases the form of
motion which they impart to the air. Thus Fig. 4 repre-
sents the forms successively assumed by a string struck,
as in the German Zither^ by a pointed style, [the plectrum

Fig. 4.

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 percus-
sion. 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 sound-
ing board, imparts to the surrounding air, probably corre-
sponds to the broken line in Fig. 5, where h h indicates
the position of equilibrium, and the letters a b c d e f g
show the line of the wave which is produced by the action

HAEMOTsT IN MUSIC. 77

of several forms of string marked by the corresponding
capital letters in Fig. 4. It is easily seen how greatly
this form of Avave (which of course could not occur in

Tig. 5.

^-!L

o e g e c

r^— r^

water) differs from that of Fig. 3 (independently of mag-
nitude), as the string only imparts to the air a series of
short impulses, alternately directed to opposite sides.^

The waves of air produced by the tone of a violin
would, on the same principle, be represented by Fig. 6.

Fia. 6.

During each 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 uni-
formly 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 extra-
ordinarily soft quality; and the qualities of tone generated
by the zither and violin resemble in harshness the angu-
larity of their wave-forms. (Figs. 5 and 6.)

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

78 ox THE PHYSIOLOGICAL CAUSES OF

Finally, I would direct your attention to an instructive
spectacle, which I have never been able to view without a
certain degree of physico-scientific delight, because it dis-
plays 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, propa-
gated 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 inland 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 im-
pression 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 concert-hall or ballroom traversed in every direction,
and not merely on the surface, by a variegated crowd 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 songstresses dart shorter waves, from
eighteen to thirty-six inches long. The rustling of silken

HAEMONY IN MUSIC. 79

skirts excites little curls in the air, each instrument in
the orchestra emits its peculiar waves, and all these sys-
tems 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 regu-
larly 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 sur-
face 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 coin-
cide 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 alge-
braical 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 jportions of the
waves which at that moment there concur.

80 ox 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 velocities of the waves of sound, considered
apart. This single motion of the air produced by the
simultaneous action of various sounding bodies, has now
to be analysed by the ear 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 sym-
pathetic production of tones in musical instruments, espe-
cially 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 suffi-
cient 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.

HARMONY IN MUSIC. 81

Each separate wave-crest (or condensation) of air which
passes by the string is, of course, too weak to produce a sen-
sible motion in it. But when a long series of wave-crests
(or condensations) strike the string in such a manner that
each succeeding one increases the slight tremour 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 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 intervals, 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 tremours 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 sounding also. Then damp the first

82

ox THE PHYSIOLOGICAL CAUSES OF

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 very 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

Fio. 7.

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.

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.

HARMONY IN MUSIC. 83

Now, then, if several tones are sounded in the neigh-
bourhood of a pianoforte, no string can be set in sym-
pathetic 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 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 dis-
covered some very remarkable formations in the middle
section. They consist of innumerable plates, micro-
scopically 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 arrange-
ment for a small part of the partition of the cochlea. The
arches which leave the membrane at d and are re-inserted
at e, reaching 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
5

84

OK THE PHYSIOLOGICAL CiiUSES OF

them througli 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 d 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 appendages, similar to stiff hairs, have been lately
discovered at the ends of the nerves. The anatomical
arrangement of these appendages leaves scarcely any

HAEMONY IN MUSIC. 85

room to doubt that they are set into sympathetic vibra-
tion 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 consideration
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 sensa-
tion, so that the presence of each single such tone in the
midst of a whole confusion of tones must be indicated
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 dififerent musical instruments
are dififerent, there is room to suppose that the kind of
vibration excited in the passages 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
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. 75). In reference to this form the French mathe-
matician Fourier has established a celebrated and impor-
tant theorem which may be translated from mathematical
into ordinary language thus : Any form of wave what-
ever can he compounded of a number of simple waves of

86

ON THE PHYSIOLOGICAL CAUSES 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.

For example, the wave-curves A and B, Fig. 9, represent
Fig. 9.

.^4

waves of simple tones, B making twice as many vibrations as A in
a second of time, and being consequently an octave higher in pitch.
C and D, on the other hand, represent the waves which result
from the superposition of B on A. The dotted curves in the
first halves of C and D are repetitions of so much of the figure A.
In C, the initial point e of the curve B coincides with the initial
point do of A. But in D, the deepest point bg 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

HAEMONY m MUSIC.

87

and more gently descending crests, but so related that, by re-
versing 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.

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

FiQ. 10.

twelfth higher in pitch. The dotted curves in C and D are, as
before, repetitions of A. C has flat crests and flat hollows, D
has pointed crests and pointed hollows.

These extremely simple examples will suflice to give a con-
ception of the great multiplicity of forms resulting from this
method of composition. Supposing that instead of two, several
simple waves were selected, with heights and initial points
arbitrarily chosen, an endless variety of changes could be

88 ox THE PHYSIOLOGICAL CAUSES OF

effected, and, in point of fact, any given form of wave could be
reproduced.^

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 imme-
diately separate, giving the eye an opportunity of recog-
nising 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. \ye must distinguish two different
points— the audible sensation, as it is developed with-
out 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 tones, and

> 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 condensa-
tions and rarefactions, conveniently replaced by these forms, p. 73].

HARMOiinr m anisic. 89

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 com-
pounded on tlie way.

For example, on striking a string, it will give a tone corre-
sponding, 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 corresponding to these waves.

Strings are peculiarly favourable for such an investigation,
because they are themselves capable of assuming extremely dif-
ferent forms in the course of their vibration, and these forms
may also be considered, like those of aerial undulations, as com-
pounded of simple waves. Fig. 4, p. 76, shows the consecutive
forms of a string struck by a simple rod. Fig, 11, p. 90, gives a
number of other forms of vibration of a string, corresponding to
simple tones. The continuous line shows the extreme displace-
ment 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 tlie fundamental tone. At c we
have two nodes, yj and yg? ^^^ three vibrating sections, each
vibrating three times as fast as the fundamental tone and hence
giving its twelfth. At dj there are three nodes, ^j, ^21 ^3> ^^d
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

90

01^ THE PHYSIOLOGICAL CAUSES OF

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.

No'.v 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 ?2> Fig. 11 d. The vibra-
tional forms a and c, for which this point is in motion, will be
immediately checked and destroyed ; but the vibrational 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

Fig. 11.

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 ren-
dered sensible of their existence.

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

HAEMONY m MUSIC. 91

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
jmrtialSy or harmonic overtones, of the fundamental tone. If
this last be c, the series may be written as follows in musical
notation, [it being understood that, on account of the tempera-
ment of a piano, these are not precisely the fundamental tones of
the corresponding strings on that instrument, and that in par-
ticular the upper partial, h" b, is necessarily much flatter than the
fundamental tone of the corresponding note on the piano].

c c' d! c" d' g" h"\) c'" d'" e'"

12 3466789 10

Not only strings, but almost all kinds of musical in-
struments, produce waves of sound which are more or less
different from those of simple tones, and are therefore
capable of being compounded 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 mathe-
matician, and on paying sufficient attention can distin-
guish 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. Experiments 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 sympa-
thetic vibration, not merely the little plates with their
accompanying nerve-fibres, corresponding to its funda-
mental 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

92 ON THE PHYSIOLOGICAL CAUSES 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 pre-
dominant fundamental tone.

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 sensa-
tions 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 perceptions 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
onesided 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 accus-
tomed, as a matter of course, entirely to ignore, and we
do not become aware of them till we make a scientific

HARMONY IN MUSIC. 93

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 mouche^
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 jpunctum ccecuin, within the
retina of every healthy eye ? How many people know
that the only objects they 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 in-
vestigated, and which remain obstinately concealed, till
attention has been drawn to them by appropriate means
— often an extremely difficult 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 diff*erent
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 dis-
tinguish 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

94 ox THE PHYSIOLOGICAL CAUSES OF

or the twelfth of the fundamental tone, has no practical
interest for us, and never occupies our attention. The
upper partials are consequently thrown into that un-
analysed 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. 74), that the quality of tone corre-
sponds to the foTTn of wave.

The 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 un-
musical, 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, 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 b ^:-t?y- to

the vowel o in ore, close to a good piano. Then lightly

touch on the piano the note V b 'W^^ in the next octave

HAKMONY m MUSIC. 95

above, and listen attentively to the sound of the piano as
it dies away. If this 6' (7 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 corre-
sponding upper partial of the voice will be heard as if
the note of the piano continued.* 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 arming
the ear with small globes of glass or metal, as in Fig. 12.

Fig. 12.

.n;\

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 enclosed mass of air, which is almost
entirely separated from that without, has its own proper
tone or key-note, which w411 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 in-

' In repeating this experiment the observer must rememher that the e &
of the piano is not a true twelfth below the //fe. Hence the singer should
first be given 6' fe from the piano, which he will naturally sing as ia, 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'k. On
the other hand, if he sings e h. from the piano, his upper partial b' b -will
probably beat with that of the piano. — Tb.

96 ox THE PHYSIOLOGICAL CAUSES OF

eluded mass of air is brought into violent sympathetic
vibration, and 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.

On examining the vowels of the human voice, it is easy
to recognise, with the help of such resonators as have just
been described, that the upper partial tones of each vowel
are peculiarly strong in certain parts of the scale : thus
0 in ore has its upper partials in the neighbourhood of
h' [2, A in father in the neighbourhood of h" 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 par-
ticularly strong.

Names of Notes.
/ 6'l2

^b"h

:(?-6" h ;

^d"^

^d"t

r

tIS — —

— 1

— tr—

1

1 1

^' — 1—

f-

— i

la

t—

f"

— 1 —

u

' 00

in
cool

Dondere /'

0

0

in

ore

nearly

d

A
a

in

Scotch
nearly

b'h

A
a
in
fat
nearly

E
a

in ]
fflte f
nearly
C'Jf

ee
n

sel

fin

t/'

6

eu

in
French
nearly

1-

u

in
French
nearly

a"

* The corresponding English vowel sounds are probably none of them
precisely the same as those pronounced by the author. It is necessary to
note this, 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 Dunders,
which are written below the English equivalents, are cited on the authority
of Helmholtz's Tonempjindungen, 3rd edition, 1870, p. 171, where Helm-
holtz says : ' Donders's results differ somewhat from mine, partly because
his refer to a Dutch, and mine to a North German pronunciation, and partly
because Donders, not having had the assistance of tuning forks, could net
always correctly determine the octave to which the sounds belong,' Also
{ih. p. 167) the author remarks that h" fe 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'". Dr. C. L. Merkel, of Leipzig, in his Physiologic der menschlichtn

HAEMONY IN MUSIC. 97

The following easy experiment clearly shows that it is
indifferent whether the several simple tones contained in
a compound 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 vibra-
tions of the strings furnish tones bf the same jpitch as
those uttered beside it ; but if we sing A (« in father) to
any note of the piano, we hear an A quite clearly re-
turned from the strings ; and if E (a in fare or fate), 0
(o in hole or ore), and U {oo 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.^ Now the sound of the vowel is produced

Sprache, 1866, p. 109, after citing Helmholtz's experiments as detailed in
his Tonempfinduvgen, 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.'

v^.g I—

— -^=^*- -

A«

1

=-p f-

^•:Sjri=

-A

1 —

Z-&— ^^

B=-^=

— ^

=S^

— 1

1

U

0

0^

t
A A

0

a

1

A

E

E I

00

0

0

a a

eu

u

a

a

a ee

jn

in

in

in in

in

in

in

in

in in

cool

hole

ore

Scotch father
man

French

French

fat
V

fare

fate feel

nearly

' Here the note a applies to the timbre ohscur of A with low larynx, and
h to the timbre clair of A with high larynx, and similarly the vowel E may
pass from d" to e" by narrowing the channel in the muulh. The interme-
diate 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 tj 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.' — Tb.

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

98 OJf THE PHYSIOLOGICAL CAUSES OF

solely by the sympathetic vibration 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, equi-
valent 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 depres-
sions of double the depth are produced), or the elevations
of one fall on the depressions 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 eleva-
tions and depressions will vanish in the second case, and
the two waves will mutually destroy each other. Simi-
larly 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

have all the same fundamental tone, and the upper partials only differ in

intensity. For female voices the pitches T^-r^—^ a' to c" are favourable

for all vowels. This is a fundamental experiment for the theory of vowel
sounds, and should be repeated by all who are interested in speech. — Tb.

HAEMOFT m MUSIC. 99

we obtain the fundamental tone of 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 per-
petually destroy each other. But if the two tones have only
approximatively 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 advancing elevations of the
one will have again reached the elevations of the other.
These alternations become sensible by that alternate
increase and decrease of loudness, which we call a beat.
These beats may often 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 eflfect in sostenuto passages, as in
sacred part-songs, by pealing through the lofty aisles like
majestic waves, or by a gentle tremour giving the tone a
character of enthusiasm and emotion. The greater the
diflference 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

100 ON THE PHYSIOLOGICAL CAUSES OF

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 K, which is produced by interrupting the tone of
the voice by a tremour of the tongue or uvula.^

When the beats become more rapid, the ear finds a
continually-increasing difficulty when attempting to hear
them separately, even though there is a sensible rough-
ness of the tone. At last they become entirely undis-
tinguishable, and, like the separate puffs which compose
a tone, dissolve as it were into a continuous sensation
of tone.'^

Hence, while every separate musical tone excites in
the auditory nerve a uniform sustained sensation, two
tones of different pitches mutually disturb one another,
and split up into separable beats, which excite a feeling
of discontinuity as disagreeable to the ear as similar
intermittent but rapidly repeated sources of excitement
are unpleasant to the other organs of sense ; for example,
flickering and glittering light to the eye, scratching with
a brush to the skin. This roughness of tone is the es-
sential 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 conse-

' The trill of the uvula is called the Northumbrian burr, and is not
known out of Northumberland, in England. In France it is called the
r grass^nje, or j>rQve7i^al, and is the commonest Parisian sound of r. The
uvula trill is also very common in Germany, but it is quite unknown in
Italy.— Tb.

'^ 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.

HAEMONY m MUSIC. 101

quence pass as a consonance. Even when the fund imental
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
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 smooth-
ness, 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 devia-
tion from that ratio has been produced.

102 ON THE PHYSIOLOGICAL CAUSES OF

Tn the same way two tones, which have their pitches
exactly 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 precisely 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 inter-
vals of tone under the same circumstances.

This is the reason why modem music, which is essen-
tially 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 musical tones
sufficed to determine a preference in favour of pro-
gressions through 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.^ These secondary tones

• These are of two kinds, differential and summaiional, 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 dis-
covery of the latter was entirely due to the theoretical investigations of the
author. — Tn.

HAEMOFT IN MUSIC. 103

are likewise capable of beating, and hence producing
roughness in the chords. Suppose a perfectly just major

third c' e' S=^ (ratio of pitches, 4 to 5) is sounded on
the siren, or with properly-tuned organ pipes, or on a

violin;^ then a faint C ^^^^^ two octaves deeper than
the c' will be heard as a combinational tone. The same

C is also heard when the tones e' g' m=^ (ratio of
pitches 5 to 6) are sounded together.^

If the three tones c\ e\ g\ having their pitches precisely
in the ratios 4, 5, and 6, are struck together, the com-
binational tone C is produced twice ^ in perfect unison,
and without beats. But if the three notes are not
. exactly thus tuned,'* the two C 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 consequently 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 indisput-
able that on such instruments part-music scarcely presents
any line of demarcation between harmony and dyshar-
mony, and is consequently deficient both in strength and
character. On the contrary, all good musical qualities of
tone are comparatively rich in upper partials, possessing

* In the ordinary tuning of the English concertina this major third is
just, and generally this instrument shows the differential tones very \yell.
The major third is very false on the harmonium and piano. — Tr.

2 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— Ta,

3 The combinational tone c, an octave higher, is also produced once
from the fifth d ^'.— Tr.

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

104 ox THE PHYSIOLOGICAL CAUSES OF

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 con-
gregational singing. The important 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 har-
mony. 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
phenomenon 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 service-
able musical tones must stand to the pitch of their fun-
damental tones in the ratios of the whole numbers to 1,
and that consequently the ratios of the pitches of con-
cordant intervals must correspond with the smallest
possible whole numbers. How essential is the physio-
logical 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 luminous ether, diffused through the uni-
verse, and light, as well as sound, exhibits phenomena of
interference. Light, too, has waves of various periodic

HARMOifr IN MUSIC. 105

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 endeavoured to lay bare the hidden law, on which de-
pends 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 compatibility or incom-
patibility however is felt, without the hearer knowing
the cause of the feeling he experiences.

These phenomena of agreeableness of tone, as deter-
mined solely by the senses, are of course merely the first
step towards the beautiful in music. For the attainment
of that higher beauty which a^opeals to the intellect,
harmony and dysharmony are only means, although essen-
tial and powerful means. In dysharmony the auditory
nerve feels hurt by the beats of incompatible 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

106 THE PHYSIOLOGICAL CAUSES OF HAEMONT.

streaming thoughts and moods. Just as in the rolling
ocean, this movement, 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 contend-
ing 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 Grod has allowed but few of
his elect favourites to be the heralds.

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

ICE AND GLACIERS.

A LECTURE DELIVERED AT FRANKFORT-ON-THE-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
6

108 ICE AXD GLACIERS.

mag-nificence of tliose 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 the glacial world. There we see that minute pecu-
liarities 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 ob-
server, 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 indefinitely in cheerless, desolate
solitudes, or full of wild, threatening confusion — an arena
of destructive forces. And thus I think I may promise
that the study of the connection of 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 ob-
servation, before I pass to discuss the causal 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 lumi-
nous darting rays of the sun, and allows them to pass almost
without appreciable change. But it is not equally pene-
trable 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

ICE AND GLACIERS. . 109

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 com-
pared 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 store of heat and the temperatm'e 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 ex-
pands, part of its store of heat disappears ; it becomes
cooler, if it cannot acquire fresh heat from without.
Conversely, by renewed compression of the air, the same
quantity of heat is reproduced which had disappeared du-
ring 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 Fohn-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;

110 ICE AXD GLACIERS.

in winter it is less — 1° for about 720 feet of ascent.
In the Alps the differences 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 the
southern side about 8,800 feet. Above the snow-line it
may on sunny days be very warm ; the unrestrained radi-
ation of the sun, increased by the light reflected from the
snow, often becomes utterly unbearable ; so that the
tourist of sedentary habits, apart from the dazzling of his
eyes, which he must protect by dark spectacles or by a
veil, usually gets severely sunburnt in the face and hands,
the result of which is an inflammatory swelling of thei
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 amoug the snow-
fields. Notwithstanding the powerful radiation of the sun
the temperature 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 de-
pend 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

ICE AM) GLACIERS. Ill

that few mountains of the earth can be compared with
them in this respect. Such a development of the glacial
world is, as far as we know, met with only on the Hima-
layas, favoured by the greater height ; in Grreenland and
in I^orthern Norway, owing to the colder climate ; in a
few islands in Iceland ; and in New Zealand, from the
more abundant 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 protected 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 accumulated one
above the other. In those places where such an accu-
mulation of snow ends in a steep precipice, and its inner
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. Ulti-
mately 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 down-
wards 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
protected from melting, is compelled to leave its original
position and seek a new one, which it of course finds only

112 ICE A^T) GLACIERS.

below the snow-line on the lower slopes of the monntain,
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 sometimes happens suddenly in
avalanches^ but it is usually veiy 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
— QoXledifirn in Switzerland — above the snow-line, cover-
ing 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, glacies ; French, glace, glacier.

The outward appearance of glaciers is very character-
istically described by comparing them with Groethe to
currents of ice. They generally stretcli from the snow-
fields along the depth of the valleys, filling them through-
out their entire breadth, and often to a considerable
height. They thus follow all the curvatures, 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 cur-
rent, filling up the valley common to them both. In
some places these ice-currents present a tolerably level and
coherent surface, but they are usually traversed by cre-
vasses, 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

ICE AOT) GLACIERS.

113

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 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

Fm. 13.

length, forming loug 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 of the central moraine is well represented
in the view above given of the Unteraar Griacier. Fig. 1 3.

114 ICE AXD GLACIERS.

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 occupy-
ing the middle of the picture descends, 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
Chamovmi, copied from that of Forbes.

The 3Ier 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 Verte (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 principal cur-
rents, 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 Arvey-
ron, bursts from its lower end at k, and plunges into the
Arve. The lowest precipice of the Mer de Glace, wliich
is visible from the valley of Chamouni, and forms a large
cascade of ice, is commonly called Glacier des Bois, from
a small village which lies below.

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

ICE AND GLACIERS.

115

site side, the Clmpeau (n). Although, as the map shows,
only a comparatively very small portion of the glacier is
thus seen and crossed, this way shows sufficiently the

Fia 14.

%■

<^A

'^Mmm?^

^v

^4%
«?^,

»« •tf^'^ -»i«if^ *sn**~-c^ ^ '^ 4e wM ^^ " ^

.msvWf *, ■ 'SMS. \/ .'

magnificent scenes, and also the difficulties of a glacier
excursion. Bolder wanderers march upwards along the
glacier to the Jardin, a rocky cliff clothed with some

IIG ICE AND GLACIERS.

vegetation, which divides the glacial current of the Gla-
cier 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 moraines.
The first, nearest the east side of the glacier, is formed
where the two arms of the Glacier du Talefre unite at the
lower end of the Jardin ; the second proceeds from the
union of the glacier in question 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 cascade (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 longitudinal section of
it according to 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 glacier. 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 very deep is obvious from the following indivi-
dual and accidental observations.

At the end of a vertical rock wall of the Tacul, tlie
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

ICE AND GLACIERS.

117

the middle and after the union
of the three glaciers the depth
must be far greater. Somewhat
below the junction Tyndall and
Hirst sounded a moulin, that is
a cavity through which the sur-
face 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 the cre-
vassed part.

To render these magnitudes
more intelligible by reference to
more familiar objects, imagine
the valley of Heidelberg 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 ima-
gine 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

>^\^V^>

^i^- -

%■ \ . \ L-

118

ICE ASJ) GLACIERS.

united ice cun-ent of the Mer de Glace. Or, instead
of the Ehine and the Nahe at 13ingen, suppose two ice
currents uniting which fill the Rhine valley to its upper
border as far as we can see from the river, and then the
united currents stretching downwards to beyond Asmann-
shausen and Burg Eheinstein ; such a current would also
about correspond to the size of the Mer de Griace.

Fig. 16, which is a view of the magnificent Gorner

Fig. 16.

u lacier seen from below, also gives an idea of the size of
the masses of ice of the larger glaciers.

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 clearness with which

ICE AKT) GLACIERS, 119

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 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 ten-
dency 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 oc-
casionally only four to six feet in breadth, 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 care-
fully 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 tlie glacier ; though
indeed we are so organised that a danger which we per-
ceive, and which therefore we can safely avoid, frightens us
far more than one which we know to exist, but which

120 ICE AND GLACIERS.

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 ; this, when it falls thickly, soon arches over the
narrower crevasses of a breadth of from four to eight feet,
and forms bridges which quite conceal the crevasse, so that
the traveller only sees a beautiful plane snow surface
before him. 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 Grrindelwald, Eosenlaui, and other places, this is facili-
tated by cutting steps and arranging wooden planks.
Then anyone who does not fear the perpetually trickling
water may explore these crevasses, and admire the won-
derfully 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 theLago 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.

ICE AND GLACIERS.

121

Fig. 17 represents one of the more level parts of the
Mer de Glace at the Montanvert, the little house of
which is seen in the background. The Gries Glacier,
where it forms the height of the pass from the Upper
Ehone valley to the Tosa valley, may even be crossed on

Fig. 17.

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

122 ICE AND GLACIERS.

are usually changed into wonderfully shaped sharp ridges
and pyramids, and from time to time fall into the inter-
jacent 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. 14, while a third forms the lower end
of the Mer de Glace. The latter, already mentioned as
the Glacier 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 admiration to the Chamouni tourist.
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,
however, is not merely an external one : the ice of the
glacier does, indeed, move forwards like the water of a
stream, only more slowly. That this must be the case
follows from the considerations by which I have en-
deavoured to explain the origin of a glacier. For as the
ice is being constantly diminished at 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 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 tlie 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

ICE AND GLACIERS.

123

ultimately be observed, notwithstanding the slow rate at
which they take place, and in spite of the chaotic confu-
sion of crevasses and rocks which the glacier exhibits.

Besides rocks and stones, other objects which have
accidentally alighted upon the glacier are dragged along.

Fig. 18.

In 1788 the celebrated Genevese Saussure, together with
his son and a company of guides and porters, spent
sixteen days on the Col du Greant. On descending the rocks
at the side of the cascade of the Glacier du Geant, they

124

ICE AND GLACIERS.

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

Tig. 19.

^Miidik

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 Imt on the central
moraine of the Unteraar Glacier for the purpose of
making observations ; the exact position of this hut was

ICE AND GLACIERS. 125

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 observa-
tions 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.

Such observations have in recent times been made
by several observers, especially by Forbes and by Tyn-
dall. They show that in summer the middle of the
Mer de Glace moves through twenty inches a da,y, 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 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 Grlace 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 size, the inclination, the
amount of snow-fall, and other circumstances.

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 un-
controllable force, before which any obstacles that man
could oppose to it yield like straws, and the traces

126 ICE AXD GLACIERS.

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
irresistible.

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 ex'tent corresponding to the in-
creasing distance, it breaks up and forms crevasses,
as seen along the edge of the glacier in Fig, 20, which
represents the Grorner 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 con-
clusions 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
hiuidreds of crevasses. The section of the Mer de Glace
(P'ig. 21, at g, c, h) shows places where a scarcely

ICE AND GLACIERS.

127

perceptible cliange 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 of the glacier does not give way in the smallest

Fig. 20.

degree to extension, 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

128

ICE AND GLACIERS.

Fig. 21.

n

partly by the weathering of
the stone, and partly by the
^ ^ezing of water in its crevices,
1 1 ey fall, and for the most part
the edge of the mass of ice.
1 Iiere they either remain ly-
y on the surface, or if they
1 ve originally burrowed in
i 1 3 snow, they ultimately re-
j pear in consequence of the
1 siting of the superficial
1 ^ers of ice and snow, and
tl sy accumulate especially
t the lower end of the gla-
sr, where more of the ice
I tween them has been
I ilted. The blocks which are
idually borne down to the
I vei end of the glacier are
netimes quite colossal in
1 e. Solid rocky masses of
s kind are met with in the
1 iteral and terminal moraines,
^\]lich are as large as a two-
storied house.

The masses of stone move in
hues which are always nearly
]) "I rail el to each other and to
tli(j longitudinal direction of
lh(! glacier. Those, therefore,
th it are already in the middle
i( main in the middle, and
those that lie on the eda'e re-
main at the edge. These latter
are the more numerous, for
during the entire course of the
glacier, fresh boulders are con-

11

ICE AND GLACIERS. 129

stantly 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, 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 veiy 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
Grlace, 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 grayer 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 some-
what 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 different parts
of its course.

A very peculiar part is played by certain stones which

130 ICE AXD GLACIERS.

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 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 considerable height are very characteristic.
There also we find the celebrated polished plates, over
wliich 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

ICE AND GLACIERS. 131

distinguished from those which water has rolled down,
by their enormous magnitude, by the perfect retention
of all their edges which are not at all rounded off, and
finally by their being deposited on tlie 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 Eosa,
of the St. Grotthard, and the Bernese Alps, formerly
penetrated through the valley of the Arve, the Rhone,
the Aare, and the Ehine to the more level part of
Switzerland and the Jura, where they have deposited
their boulders at a height of more than a thousand 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 Scan-
dinavian Peninsula.

The drift-ice too of the Arctic Sea is glacier ice ; it
is pushed down into the sea by the glaciers of Grreenland,
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 G-erman 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
references to the ancient history of glaciers, and re-
vert now to the processes at present at work in them.

7

132 ICE A^^D GLACIERS.

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 glides 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.
Eendu, 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 enquire with astonishment how
it is possible that ice, which is the most brittle and
fragile of substances, 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 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 diff*erence
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

ICE AND GLACIERS. 133

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.

Everyone knows that we determine that one fixed
point of our thermometer scale which we call the freez-
ing-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 in-
dicates no increase of temperature. Hence physici^s
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 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
interpenetrated 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 every-

134 ICE AXD GLACIERS.

where 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. P'or, 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 simultaneously 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 -j-lj-th 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 suit-
able vessel a mixture 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 aiad be converted into water. In
this IS found the reason why mechanical pressure can
influence the freezing-point. You know that ice occu-

ICE AND GLACIEHS. 135

pies 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, there-
fore, 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. Pressure fur-
thers 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
confined in a closed vessel, from which nothing could
escape. The case is somewhat different when, as with
glaciers, the water disseminated 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 lowering 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 com-
pressed 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 suffi-
cient time be given. Faraday, who discovered this pro-
perty, called it the regelation of ice-, the explanation

136 ICE AXD GLACIERS.

of this phenomenon has been much controverted ; I
have detailed to you that which I consider most satis-
factory.

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 when the pieces are already in
the act of melting.^ 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 com-
plete is their union. But a very slight pressure is suffi-
cient if the two pieces are left in contact for some time.^

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 melt-
ing, or at any rate is only so much lower than O'' that
the warmth of the hand is sufficient to raise it to this
temperature. Very 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 huge masses rest-
ing 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

' In the Lectnrf^ a series of small cylinders of ice, which had been pre-
pared by a method to be afterwards described, were pressed with their plane
ends against each other, and thus a cylindrical bar of ice produced.

* Vide the additions at the end of this Lecture.

ICE AM) GLACIEKS.

137

the lower layers of still colder snow, it again freezes;
thus it is that the firn first becomes granular and ac-
quires 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
effected by using a corresponding pressure.

We have here (Fig. 22) a cylindrical cast-iron vessel,
A A ; the base, B B, is -p^^ .^2

held by three screws, and
can be detached, so as to
remove the cylinder of ice
which is formed. After
tlie vessel has lain for a
while in ice-water, so as
to reduce it to the tem-
perature 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 cylin-
drical plug taken out, the hollow again filled up with
snow, and the process repeated until the entire form is
filled with the mass of ice, which no longer gives way

138 ICE AXD GLACIERS.

to pressure. 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 remarkable 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 continues its
way downwards as glacier. More frequent than such cas-
cades, where the giacier-stream is quite dissevered, are
places 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 cliffs,
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 to-
gether ; 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 accm'ate
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

ICE AND GLACIERS. 139

every crevice of the mould, and then that this powdered
ice, like snow, was again combined by freezing. This sug-
gests 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 cylin-
ders 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 indi-
vidual larger pieces of ice which have been used to pro-
duce 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
completely 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 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 whole indicates that the shape of the
block has resulted less from pliability than from fracture,

140

ICE AXD GLACIERS.

and that the individual fragments 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 tole-
rably flat circular disc does it begin to give way at the
edofes and form cracks, like crevasses on a small scale.
Fig. 23 shows the height and diameter of such a cylinder
in its original condition ; Fig. 24 represents its appearance
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 aper-
ture. With this view I place a base on the previously
described mould, which has a conical perforation, the
external aperture of which is only two-thirds the dia-
meter of the cylindrical aperture of the form. Fig. 25
gives a section of the whole. If now I insert into this
one of the compressed cylinders of ice, and force down the
plug a, the ice is forced through the narrow aperture in

ICE AND GLACIERS.

141

Ihe base. It at first emerges as a solid cylinder of the

same diameter as the aper- _

1 . ^ ,f Fig. 25.

tore ; 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.^

Here also the cracks in the emerging cylinder of ice

exhibit a surprising similarity with the longitudinal rifts

Fig. 26.

which divide 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

' Id this experiment the lower temperature of the compressed ice some-
times 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°.

142 ICE AXD GLACIERS.

from clear pieces of ice, wliile 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 dis-
appear, 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 ' which inter-
penetrate the mass of the ice. Hence we may conclude
that the compressed block is traversed by a great num-
ber of fine cracks and fissures, which render it pliable ;
that its particles become a little dispersed, and are there-
fore withdrawn from pressure, and that immediately after-
wards 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 sm-faces by the reflection of
the light.

These cracks and laminae also become more perceptible
when the ice — which, as I before mentioned, is below zero
immediately after pressure has been applied — is again
raised to this temperature and begins to melt. The cre-

• These cracks are 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,
DO 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. 143

vices 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 sub-
stances of a granular structure, in opposition to regularly
crystallised ice, such as is formed on the surface of still
water. "VVe here meet with the same differences as be-
tween 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 enclosed 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

144 ICE AKD GLACIERS.

again broken, placed in the mould, and pressed into a
cylinder, the air may gradually be more and more elimi-
nated, and the ice be made clearer. No doubt in glaciers
the originally whitish mass of neve is thus gradually
transformed into the clear, transparent ice of the glacier.

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 extended.

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 hav^e demonstrated.

Thus to the eye of the natural philosopher the glacier,
with its wildly-heaped ice-blocks, its desolate, stony, and
muddy surface, and its threatening crevasses, has become
a majestic stream whose peaceful and regular flow has no
parallel ; which, according to fixed and definite laws, nar-
rows, 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 wondrously 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,

ICE AND GLACIERS. 145

of Constance, the Lago Maggiore, the Lake of Como, and
the Lago di Grarda 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 con-
sidering 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 is moreover an utterly
unexhausted virgin soil, rich in the mineral food of plants.
The fruitful layers of fine loam which extend along the
whole Ehine 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 distin-
guished 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 mountain slopes. On the
comparatively small surface of the Alpine chain they
produce the mighty streams, the Ehine, the Ehone, 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,

146 ICE AKD GLACIERS.

in ' Mahomet'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 rolHng,
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.

Pine-built houses bears the Atlaa
On his giant shoulders. O'er his
Head a thousand pennons rustle,
Floating far upon the breezes,
Tokens of hia 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 Martin's Translation,

ICE AND GLACIEKS. 147

ADDITIONS.

The theory of the regelation 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 Thomson observed that in Faraday's experiments, pres-
sure which could freeze them together was not utterly wanting.
I have satisfied myself by my own experiments that only very
slight pressure is necessary. It must, however, be remembered,
that the smaller the pressure the longer will 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 diflTerence
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 con-
tact, 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.

148 ICE AND GLACIERS.

In order to show the slow action of the small differences of
temperature 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 imril 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 pre-
pared can be cooled considerably 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 mixture 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
frerzing process.

Now as the pressure of one atmosphere on a square milli-
metre 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

ICE AKD GLACIEKS. 149

therefore be formed more rapidly in the surroundinp; water than
it was in the flask, wliere 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 feebler
it will become ; so that with such feeble 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 experi-
ments, in which two perforated discs of ice were placed in con-
tact on a horizontal glass rod, so that gravity exerted no pressure,
capillary attraction 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 diflTerent parts of the interior is exposed to diflferent pressures,

150 ICE AND GLACIERS.

a portion of the more powerfully compressed ice will melt ; and
the latent heat necessary for tliis will be supplied by the ice
which is less strongly compressed, 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
thitt, owing to the very small conductivity for heat which ice
possesses, a process of this kind must be extremely slow, if the
compressed and colder layers of ice, as in glaciers, are at con-
siderable distances from the less compressed ones, and from the
water which furnishes the heat for melting.

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 tem-
perature of which was a few degrees above the freezing-point.
Under these circumstances the ice in the vessel, which was ex-
posed 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 expense 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
consequence of the pressure, had again frozen in places in which
the pressure ceased. Yet under these circumstances there was
no appreciable alteration in the shape of the middle piece which
was most compressed.

This experiment shows, that although changes in the shape of
the piecf'S of ice must take place in the course of time in accord-
ance 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 w^hich the heat

ICE AND GLACIERS. 151

is conducted is at all considerable. 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 extremely slow.

That on the other hand, especially in granular ice, the forma-
tion of cracks, and the displacement of the surfaces of those
cracks, render such a change of form possible, is shown by the
above-described experiments on pressure ; and that in glacier
ice changes of form thus occur, follows from the banded struc-
ture, and the granular aggregation 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 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
Geant to the source of the x\rveyron, the heat due to the mecha-
nical 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 sufficient 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 trans-
parent for investigation. 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 essentially 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.

152 ICE AKD GLACIERS.

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 dif-
ferent 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 polyhedral granules, these granules, before any at-
tempt 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 latter do not produce the
comparatively firm coherence of the apparent heap of granules.

The properties of ice here described are interesting fiom a
physical point of view, for they enable us to follow so clostly
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 structure; 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.

ON THE

INTERACTION OF NATURAL FORCES.

A LECTURE DELIYEEED FEBRirARY 7, 1854, AT KONIGSBEEG,
IS 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 con-
quest. It has reference to a new and universal natural
law, which rules the actio q of natural forces in their
mutual relations towards each other, and is as influential
on our theoretic views of natural processes as it is im-
portant in their technical applications.

Among the practical arts which owe their progress to
the development of the natural sciences, from the con-
clusion of the middle ages downwards, practical mechanics,
aided by the mathematical 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 dif-
ferent 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

154 ON THE INTERACTIOX OF NATURAL FORCES.

animals. The marvel of the last century was Vaucanson's
duck, which fed and digested its food ; the flute-player of
tlie 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 conclusion 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, woidd be incom-
prehensible, 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 decipher 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 difficulty ob-
tained 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 in-
genuity 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, ser-
vices 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

ON THE INTERACTION OF NATURAL FORCES. 155

experience which a later time knew how to take advan-
tage 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 endeavour to construct a perpetual motion.
Under this term was 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 ener-
getically and incessantly as long as they lived, and
were never wound up ; nobody set them in motion. A
connexion between the 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 per-
petual motion was to produce work inexhaustibly without
corresponding consumption, that is to say, out of nothing.
Work, however, is money. Here, therefore, the great
8

156 ox THE INTERACTION OF NATURAL FORCES.

practical problem which the cunning heads of all cen-
turies 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 calcu-
lated 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 much about them. Bewildered intellects, however,
proclaimed often enough that they had discovered the
grand secret ; and as the incorrectness of their proceed-
ings was always speedily manifest, the matter fell into bad
repute, and the opinion strengthened 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 performances with those of men and
animals, to replace which they were applied. We still

ox THE INTERACTIOX OF XATITIAL FORCES, 157

reckon the work of steam-engines according to horse-
power. The value of manual labour is determined 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 work-
men are not to be had in any quantity at a moment's
notice ; they must have both talent and instruction, their
education requires both time and trouble. A machine,
on the contrary, which executes work skilfully, can always
be multiplied 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 expenditure of force ; this was
the more important, as indeed most machines are con-
structed for the express purposeof exceeding, by the mag-
nitude 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 expenditui'e, and com-
pare it in the case of different machines ?

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

158 ox THE IXTERACTION OF NATURAL FORCES.

places small projections, thumbs, wliich, during the rota-
tion, 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 lifting 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 falls. 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 falling 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 set in motion, move from a
higher to a lower position. Experiment and theory
concur in teaching, that when a hammer of a hundred-
weight is to be raised one foot, to accomplish this at
least a hundredweight of water must fall through the

ON THE INTERACTION OF NATURAL FORCES. 159

space of one foot ; or what is equivalent to this, two
hundredweight must fall half a foot, or four hundred-
weight 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 un-
changed whether the hammer is driven immediately by
the axle of the wheel, or whether — by the intervention
of wheelwork, endless screws, pulleys, ropes — the motion
is transferred to the hammer. We may, indeed, by such
arrangements succeed in raising a hammer of ten hun-
dredweight, when by the first simple arrangement 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

160 ON THE INTERACTIOX OF NATURAL FORCES.

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 r Why is
its power greater 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 performed by the
hammer is determined by its velocity. In other cases,
also, the velocity of moving masses is a means of pro-
ducing 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 windmill, 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, &c., so that the motion is
incessantly weakened and finally arrested. A body, how-
ever, 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 resisting forces can motion be diminished
or destroyed. A moving body, such as the hammer or the
musket-ball, when it strikes against another, preFses
the latter together, or penetrates it, until the sum of the
resisting forces presented by the body struck to pres-
sure, or to the separation of its particles, is sufficiently
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

ON THE INTERACTION OF NATURAL FOECES. 161

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 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 production. It is therefore equiva-
lent 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
communicated 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 wheelwork of the clock therefore developes

162 ON THE INTERACTION OF NATURAL FORCES.

no working force, which was not previously 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. \Mien
we afterwards 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 determine 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 com-
pressed air has generated no working force, but simply
gives to the bullet tliat which has been previously com-
municated to it. And while we have pumped for perhaps
a quarter of an hour to charge the gun, the force is ex-
pended in a few seconds when the bullet is discharged ;
but because the action is compressed 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 mathe-
matical 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 per-
petual motion, which should make use solely of pure
mechanical forces, such as gravity, elasticity, pressure of
liqidds and gases, coidd only be sought after by be-
wildered and ill-instructed people. But there are still
other natural forces which are not reckoned amonof the
purely moving forces, — heat, electricity, magnetism, light,

ON THE INTEUACTION" OF NATURAL FORCES, 163

cliemical forces, all of which nevertheless stand in mani-
fold relation to mechanical processes. There is hardly a
natm-al 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 ; tlie 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 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 generates
the mechanical force. The heat thus necessary for tiie
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 con-
stituent 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,

164 ON THE INTER ACTIOX OF NATURAL FORCES.

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 combina-
tion 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 processes and chemical
forces which produce the astonishing work of these
machines. In like manner the combustion of gunpowder
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 me-
chanical 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 surplus 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. Now could not
the heat generated by the plates be applied to a small
steam-engine, wliich in its turn should be able to keep
the rubbing plates in motion? 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.

ON THE INTERACTION OF NATURAL FORCES. 165

By a similar plan, however, a speculative American set
some time ago the industrial world of Europe in excite-
ment. The magneto-electric machines often made use of
in the case of rheumatic disorders are well known to the
public. By imparting 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 com-
bustion 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 cer-
tainly 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 phy-
sical 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.

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.

106 ON THE IXTERACTIOX OF NATURAL FORCES.

Starting from eacli of these different manifestations of
natm-al forces, we can set every other in motion, for tlie
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 me-
chanical forces, in exciting chemical, electrical, or other
natural processes, which, by any circuit whatever, and
without altering permanently the active masses in the
machine, could produce mechanical force in greater quan-
tity 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 relations 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, might

ox THE IXTEEACTION OF NATURAL FORCES. 1G7

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 i elations were
discovered at the same time, the correctness of which re-
mained 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
Frenchman 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 er-
roneous conclusions, his experiment was not quite unsuc-
cessful. 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 Grerman physician, J. R,
Mayer of Heilbronn, in the year 1842. A little later, in

1843, a Dane named Colding presented 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, fol-
lowed 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

1G8 ON THE IXTERACTION OF NATURAL FORCES.

view. My inquiry was made public in 1847, in a small
pamphlet bearing the title, ' On the Conservation of
Force.' ^

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 view-
ing 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 consequences the experimental proof is
still wanting, but the number of confirmations is so pre-
dominant, 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 me-
chanical force can be gained without a corresponding
consumption. The perpetual 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 mechanical force. You now see that we have
arrived at a general law, which holds good wholly inde-
pendent of the application which man makes of natural
forces ; we must therefore make the expression of our law
correspond to this more general significance. It is in the
first place clear, that the work which, by any natural pro-

' There is a translation of this important Essay in the Scientific Memoirs,
New Series, p. 114.— J. T.

ON THE INTERACTION OF NATURAL FORCES. 169

cess whatever, is performed under favourable conditions
by a machine, and which may be measured in the way
already indicated, may be used as a measure of force com-
mon to all. P'urther, the important question arises, If
the quantity of force cannot be augmented except by
corresponding consumption, 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 has proved, not for nature as a whole.

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 established by experiment the im-
portant 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 consumption 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 Cen-
tigrade 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 conclusion, that heat is not, as
was formerly imagined, a fine imponderable 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 mo-
tion of the mass of a body which is apparently lost is con-
verted into a motion of the ultimate particles of the
body ; and conversely, 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

170 ox THE IXTEUACTIOX OF NATURAL FOUCES.

of this heat is totally independent of the time and steps
through which the combination has been effected, pro-
vided 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 magnitftde
of the chemical force of attraction between the particles
of a pound of coal and the quantity of oxygen that cor-
responds to it, is capable of lifting a weight of 1 00 pounds
to a height of twenty miles. Unfortunately, in our steam-
engines we have hitherto 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 gene-
rated by the fuel.

From a similar investigation of all the other known
physical and chemical processes, we arrive at the conclu-
sion that Nature as a whole possesses a store of force
which cannot in any way be either increased or dimi-
nished, 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
ourselves 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 pur-
poses, and the actions of which we can apply as we think

ON THE INTEKACTION OF NATUEAL FOKCES. 171

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 he
absolutely lost, it does not follow that a portion may not
be inapplicable to human purposes. In this respect the
inferences drawn by William Thomson from the law of
Carnot are of importance. This law, which was discovered
by Carnot during his endeavours to ascertain the relations
between heat and mechanical 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 expan-
sion 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
experiment, it has attained thereby the highest degree of
probability. Besides the mathematical form in which
the law was first expressed by Carnot, we can give it the
following more 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 tlie 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.

172 ON THE INTEEACTION OF NATURAL FORCES.

and must continue to be such ; the other, to which a por-
tion of the heat of the warmer bodies, and the total sup-
ply 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 com23lete
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 combinations which their affinities demand.
In short, the universe 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 mean time 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 for-

ox THE INTERACTION OF NATURAL FORCES. 173

mula, which only speaks of the heat, volume, and pressure
of bodies, was able to discern consequences which threat-
ened 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-
meclianical 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 labora-
tory 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 immeasu-
rably 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 distant fixed star ; that the me-
teoric 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
are also valid for other bodies than the earth. We will,
therefore, make use of our law to glance over the house-

174 ox THE IXTEHACTIOX OF XATUEAL FORCES.

hold 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 assumption 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 re-
maininof 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 attention ; and the more so, as this notion
in our own home, and within the walls of this town,^ 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 dejDth 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 independent 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, in-
cluding 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
> Konigsberg.

ox THE INTERACTION OF NATURAL FORCES. 175

limits of Neptune, our most distant planet. Even now
we discern in distant regions of the firmament nebulous
patches the light of which, as spectrum analysis 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 exhibit 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 incorporated 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, how-
ever, 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 origi-
nally gave no information.

176 ox THE IXTERACTION OF NATURAL FORCES.

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 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, con-
densation 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 vivaoi 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.

ox THE INTERACTION OF NATURAL FORCES. 177

Let us make this addition to our assumption — that, at
the commencement, the density of the nebulous matter
was a vanishinf^ 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 motioiL,
and find by this how much of the force has been converted
into heat.

The result of this calculation^ 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, not less than twenty-eight millions
of degrees of the Centigrade scale. For the sake of compa-
rison, 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 estimated
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 combustion 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 cor-
roborated by the geological p?iaBnomena of our planet ;
and with regard to the other planetary bodies, the flat-
' See note on page 193.

178 ox THE IXTERACTIOX OF NATURAL FORCES.

tened form of the sphere, which is the form of equili-
brium 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 in-
vaded. Certainly for our planet it is lost, but not for the
universe. It has proceeded -outwards, and daily proceeds
outwards into infinite space ; and we know not whether
the medium which transmits the undulations of liglit
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 un-
favourable assumption as to its capacity for heat — that
is, placing it equal to that of water — the mass of the earth
would thereby be heated 11,200 degrees; it would, there-
fore, be quite fused, and for the most part converted into
vapom'. If, then, the earth, after having been thus
brought to rest, should fall into the sun — which, of
course, would be the case — the quantity of heat deve-
loped 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 fa-U 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

ON THE INTERACTION OF NATURAL FORCES. 179

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 lieating 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 tifty 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 sur-
faces. 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
remnant of processes which seem to have played an im-
portant part in the formation of the heavenly bodies,
conducted us to the 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
nebulse 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

180 ON THE INTERACTION OF NATURAL FORCES.

family, and the forebodings of poetic fancy. The cos-
mogony of ancient nations generally commences with
chaos and darkness. Thus for example 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, par-
ticularly 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 firmament and
waters below the firmament, resembled the chaotic com-
ponents of the world : —

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

' And the earth was without form, and void ; and dark-
ness 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,
and in the new red-hot liquid earth of our modern cosmo-
gony 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.

Our earth bears still the unmistakeable traces of its
old fiery fluid condition. The granite formations of her
mountains exhibit a structure, which can only be pro-

ON THE INTERACTION OF NATURAL FORCES. 181

duced by the crystallisation of fused masses. Investiga-
tion 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 pro-
ject 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
temperature of the surface only about g'^^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
surftice only through the instrumentality of volcanic
phaenomena. Those processes owe their power almost
wholly to the action of other heavenly bodies, particu-
larly 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
atiDOsphere 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
eartu's surface, the trade- wind carries new and cool air
to the equator. Without the heat of the sun, all winds
must of necessity 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

182 ON THE INTERACTION OF NATURAL FORCES.

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 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 withdrawn, 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 con-
sumed 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 continuation of life is dependent on the consumption
of nutritive materials : these are combustible substances,
which, after digestion 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
iu which it occurs, we can calculate from the mass of the

ON THE INTERACTION OF NATURAL FORCES. 183

consumed material how much heat, or its equivalent
work, is thereby generated in an animal body. Unfor-
tunately, the difficulty of the experiments is still very
great ; but within those limits of accuracy which have
been as yet attainable, the experiments show that the
heat generated in the animal body corresponds to the
amount which would be generated by the chemical pro-
cesses. 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 tlie
manner in which 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 mate-
rials 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 albu-
minous substances which 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 super-
seded 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 ? The answer
is, from the vegetable kingdom ; for only the material
of plants, or the flesh of herbivorous animals, can be

184 ox THE INTERACTION OF NATURAL FORCES.

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,
therefore, 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 the animal. They
take the consumed carbon given off in respiration, as
carbonic acid, from the air, the consumed hydrogen as
water, the nitrogen in its simplest and closest com-
bination as ammonia ; and from these materials, with the
assistance of small ingredients which they take from the
soil, they generate anew the compound combustible sub-
stances, albumen, sugar, oil, on which the animal subsists.
Here, therefore, is a circuit which appears to be a per-
petual store of force. Plants prepare fuel and nutri-
ment, 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 ? We must not conclude
hastily : fm'ther inquiry shows, that plants are capable of
producing combustible substances only when they are

ON THE INTERACTION OF NATURAL FORCES. 185

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 com-
pletely 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. In-
asmuch 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 absorbed by the
leaves.

Hence a certain portion of force disappears from the
sunlight, while combustible substances are generated and
accumulated 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 ex-
periments from which we might determine whether the
vis viva of the sun's rays which have disappeared corre-
sponds 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
flattering result, that all force, by means of which our
bodies live and move, finds its source in the piuest sun-

ISO ox THE IXTER ACTION OF NATURAL FORCES.

light ; and hence we are all, in point of nobility, not
behind the race of the great monarch of Cliina, 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 gethereal 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 con-
ditions, 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 phsenomenon 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. Tlie two waves of the moon,
on account of her greater nearness, are about 3J 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. Al-
though 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 phaenomenon is nevertheless
manifest from the calculation of Bessel, according to

ON THE INTERACTION OF NATURAL FORCES. 187

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 J hours, flow from one quarter
of the earth to the other.

The phsenomenon of the ebb and flow, as already recog-
nised by Mayer, combined with the law of the conserva-
tion of force, stands in remarkable connexion with the
question of the stability of our planetary system. The
mechanical theory of the planetary motions discovered
by Newton teaches, that if a solid body in absolute vacuo,
attracted by the sun, move around him in the same
manner as the planets, this motion will endure unchanged
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 peri-
odically, and can never exceed certain limits, so that by
this cause the eternal existence of the planetary system ia
unendangered.

But I have already named two assumptions which must
be made : first, that the celestial spaces must be abso-
lutely empty ; and secondly, that the sun and planets
must be solid bodies. The first 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 corre-
sponds to that through a resisting medium, be actually

188 0^1 THE IXTEUACTION OF NATtmAL FOHCES.

due to the existence of such a medium 5 a time will come
when the comet will strike the sun ; and a similar end
threatens all the planets, although after a time, the
length of which baffles our imagination to conceive 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 undoubtedly a fluid portion on its
sm'face, 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
diminishes 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 in-
creased since the time of Hipparchus by the gi^ 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

ox THE IXTERACTIOX OF XATUEAL FORCES. 189

the mean time tbe 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 bodies, in the time of their fiery fluid con-
dition, were subjected.

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

190 ox THE INTERACTION OF NATUEAL FORCES.

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 con-
servation 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 re-
gard to the store of chemical force in the sun, we can
form no conjecture, 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
generated to cover the total emission for 2,100 years.
So small a change it would be difficult to detect even by
the finest astronomical 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 cer-
tainly no thermometric observations, but we have infor-
mation 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 back-
wards the constancy of the climate.

ON THE INTERACTION OF NATURAL FORCES. 191

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, however. Dove has
cited the reports of ancient chroniclers, according to
which, in some peculiarly hot years, the Prussian grape
possessed somewhat less than its usual quantity of acid.
Tlie fact also speaks not so much for the climate of the
country as for the throats of the Grerman 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
histoiy it has not been sensibly diminished, even though
the length of the time which must flow by before a sen-
sible change in the state of our planetaiy system occurs
is totally incapable of measurement, still the 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 ? Men are in
the habit of measuring the greatness and the wisdom of
the universe by the duration and the profit which it pro-
mises to their own race ; but the past history of the earth
already shows what an insignificant moment th? duration
of the existence of our race upon it constitutes. A
Nineveh vessel, a Koman sword, awake in us the con-
ception 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 multi-
plied itself before the Pyramids or Nineveh could have
been erected. We estimate the duration of human his-
tory at 6,000 years ; but immeasurable as this time may

192 ON THE INTEEACTION OF NATURAL FORCES.

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 Sibe-
ria, Europe, and North America groves of tropical palms
flourished ; where gigantic lizards, and after them ele-
phants, whose mighty remains we still find buried in
the earth, found a home? Different geologists, pro-
ceeding from different premises, have sought to esti-
mate 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 re-
gard to the time during which the first nebulous mass
condensed 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 existence of the present
state of inorganic nature favourable to the duration of
man seems to be secured, so that for ourselves and for
long generations after us we have nothing to fear. But
tlie 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 com-
plete living forms, as the lizards and the mammoth

ON THE INTERACTION OF NATUHAL FORCES. 193

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 uni-
versal 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 judg-
ment, 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.

194 ON THE INTERACTION' OF NATURAL FORCES.

NOTE TO PAGE 177.

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 men-
tioned, are to be found partly in J. R. 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 K, the
potential upon itself V — if we call the mass of the earth
772, its radius r, and the intensity of gravity at its
surface g — has the value

,, 3 r^M^

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

M^

quantity -— , they all vanish in comparison with the sun ;

even that of the greatest planet, Jupiter, is only about the
one himdred-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 0-, t degrees, we need a quantity of heat equal to

ox THE INTEEACTION OF NATURAL FORCES. 195

Mat ; this corresponds, when A^ represents the mechanical
equivalent of the unit of heat, to the work kgM.aL To
find the elevation of temperature produced by the con-
densation of the mass of the sun, let us set

we have then

5 A.K

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

< = 28611000° Cent.

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

we must multiply the value of t by the fraction . which

739

makes hardly a sensible alteration in the result.

When a spherical mass of the radius R condenses more

and more to the radius E^, the elevation of temperature

thereby produced is

5*A . mcr 1 R, Rq J

or

3, rm r . R

5 ARim<

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 tlje path of Neptune, which
is six thousand times greater than the radius of the sun,

T>

the magnitude — ^ will then be equal to gQoo, and the above

value of t would have to be diminished by this inconsi-
derable amount.

196 ON THE INTERACTION OF NATURAL FORCES.

From the same formula we can deduce that a dimimition
of ^1^ of the radius of the sun would generate work in a
water mass equal to the sun, equivalent to 2,861 degrees
Centigrade. And as, according to Pouillet, a quantity of
heat corresponding to 1 J 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 vu 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 ins viva of the motion of
revolution round the sun, if /j, be the mass of a planet,
and p its distance from the sun, is

L =

grmfifl

\R 2p

h\-

Omitting the quantity -- as very small compared with -— ,
2p -tv

and dividing by the above value of V, we obtain

L 5 ^
V^ M*

The mass of all the planets together is ,— — of the mass

738

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

THE EECENT PEOGRESS OF THE
THEORY OF VISION.

A COURSE OF LECTURES DELIVERED IN FRANKFORT AND HEIDEL-
BERG, AND REPUBLISHED IN THE PREUSSISCHE JAHRBUCHER, 18C8.

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 doubfc 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 us 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 consciousness, 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 functionsj

108 KECEXT PEOGRESS OF THE THEORY OF VISION.

the results of which are involved in those acts of appre-
hension 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 ac-
customed to regard the apprehension 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 en-
trance 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 natm-e of the mental
processes which contribute to the result. I will therefore
endeavour to give some account of the results of physi-
ological inquiries so far as they bear on the questions
above mentioned.

I am the more desirous of doing so because I have
lately completed ' a complete survey of the field of physio-
logical optics, and am happy to have an opportunity of

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

THE EYE AS AN OPTICAL INSTRUMExYT. 199

putting together in a compendious form the views and
deductions on the present subject which might escape
notice among the numerous details of a book devoted to
the special objects of natural 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 observation and experiment. There is no longer
much controversy on the more important facts of obser-
vation, 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
number 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 subject 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 bearinofs,
I shall first describe the physical characters of the eye
as an optical instrument ; next the physiological pro-
cesses 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 appre-
hensions 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 whicli
excites so much interest, as the real starting point of

200 RECENT PROGRESS OF THE THEORY OF VISION.

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 achieve-
ments 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 lucky finding, but by deduction rigidly followed out,
and tlius carries with it the pledge of still future suc-
cesses. As once astronomy was the pattern from which
the other sciences learned how the right method will
lead to success, so does ophthalmic medicine now dis-
play 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 —
tlie 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 contributed most
to the result : Von Grraefe in Grermany, 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
satisfaction. Schiller says of science : —

AVer uni die Gottin freit, suche in ihr nicht das Weib.^
}Vho ivoos the goddess must not hope the wife.

• 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. 201

And history teaches us, what we shall have opportunity
of seeing in the present inquiry, that the most important
practical results have sprung unexpectedly out of investi-
gations which might seem to the ignorant mere busy
trifling, and which even those better able to judge could
only regard with the intellectual 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; philosophers have extolled it as a crowning
instance of perfection in an organism ; and opticians have
tried to imitate it as an unsurpassed model. And indeed
the most enthusiastic admiration of this wonderful organ
is only natural, when we consider what functions it per-
forms ; when we dwell on its penetrating power, on the
swiftness of succession of its brilliant pictures, and on
the riches which it spreads before our sense. It is by
the eye alone that we know the countless shining worlds
that fill immeasurable 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 admiration of majesty in the creation which we owe
to the eye, is the security and exactness with Avhich we
can judge by sight of the position, distance, and size of
tlie objects which surround us. For this knowledge is
the necessary foundation for all our actions, from thread-
ing a needle through a tangled skein of silk to leaping
from cliff to cliff when life itself depends on the right

202 RECENT PROGRESS OF THE . THEORY OF VISION.

measurement of the distance. In fact, the success of
the movements and actions dependent on the accuracy
of the pictures that the eye gives us forms a con-
tinual 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 im-
pressions we 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 con-
viction, 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 important functions are
more clearly understood and their object better esti-
mated, so it may well be with our more exact knowledge
of the eye. For the great performances of this little
organ can never be denied ; and while we might con-
sider ourselves 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

THE EYE AS AN OPTICAL INSTRUMENT.

203

parts, of which one slides in the otlier, 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 of the instrument into an
optical image of the objects which lie in front of the
camera. When the photographer first arranges his instru-
ment, 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 tlie
most skilful painter could imitate, tliough indeed it is
upside down. The next step is to substitute for this

Iw. 27.

glass a prepared plate upon which the light exerts a per-
manent chemical effect, stronger on the more brightly
illuminated parts, weaker on those which are darker.
These chemical changes having once taken place are per-
manent : by their means the image is fixed upon the plate.
The natural camera obscura of the eye (seen in a
diagrammatic section in Fig. 28) has its blackened
chamber globular instead 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
10

204 RECEXT PROGRESS OF THE THEORY OP VISION.

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 trans-
parent 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 curvature constant. But the
glass lenses of the photographer are not fixed ; they are
moveable by means of a sliding tube which can be ad-
justed 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 ; tlie farther off,
the more it 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

THE EYE AS AN OPTICAL INSTRUMENT. 205

power of adjustment or 'accommodation' is necessary.
This is accomplished by the movements 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 con-
tracts, the tension of the lens is diminished, and its sur-
faces— 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 increased, 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 'accommodated' 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 prac-
tical 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 reflexions of light through
the pupil from the two surfaces of the crystalline lens,

206 KECENT PEOGRESS OF TPIE THEORY OF VISION.

and thus acquired the character of an unusually careful
observer. For this phenomenon was anything but ob-
vious ; it can only be seen by strong side illumination,
in darkness otherwise complete, only when the observer
takes a certain position, and then all he sees is a faint
misty reflexion. But this faint reflexion was destined
to become a shining light in a dark corner of science. It
was in fact the first appearance observ^ed in the living
eye which came directly from the lens. Sanson imme-
diately 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
reflexions from the lens alter during accommodation.
These alterations were employed by Cramer of Utrecht,
and also independently by the present writer, to arrive
at an exact knowledge of all the changes which the lens
undergoes during the process of accommodation. I suc-
ceeded 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 con-
structed for the purpose, the ophthalmometer, 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, &c., 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
accommodation.

The physiological problem was therefore solved. Ocu-
lists, and especially Donders, next investigated the indi-
vidual defects of accommodation which give rise to the
conditions known as long sight and short sight. It was

THE EYE AS AN OPTICAL INSTRUMENT. 207

necessary to devise trustworthy raethods in order to
ascertain the precise limits of the power of accommoda-
tion even with inexperienced and uninstructed patients.
It became apparent that very different conditions had
been confounded as short sight and long sight, and this
confusion bad made the choice of suitable glasses un-
certain. It was also discovered that some of the most
obstinate and obscure aflfections 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 Donders * proved
that the same defects of accommodation are the most
frequent cause of squinting, and Von Grraefe* 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 when 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,

• Professor of Physiology in the University of Utrecht.

' This great ophthahnic surgeon died in Berlin at the early age of forty-two.

208 EECENT PROGRESS OF THE THEORY OF VISION.

with structures not elsewhere found, called rods and cones.
The rods are slender cylinders ; the cones, or bulbs, some-
wliat thicker, flask- shaped structures. All are ranged
perpendicular 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 experiments to be the really sensi-
tive 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 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 centrcdis,
where the retina is reduced to those elements alone which
are absolutely necessary for exact vision. Fig. 29, from
Henle, shows a thin transverse section of this central de-
pression made on a retina which had been hardened in
alcohol. Lh {Lamina hyalina, membrana limitans) is
an elastic membrane which divides the retina from the
vitreous. The bulbs (seen at 6) are here smaller than
elsewhere, measuring only the 400th part of a millimeter
in diameter, 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/ 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 exter-
nal 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

THE EYE AS AN OPTICAL INSTRUMENT.

209

thinning away at its borders is seen in the diagram. Nor
do the bli;od vessels of the retina enter the fovea^ but end
in a circle of delicate capillaries around it.

^ %Si

This fovea, or pit of the retina, is of great importance
for vision, since it is the spot where the most exact dis-

210 KECENT PROGRESS OF THE THEORY OF VISION".

crimination 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 excita-
tion 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 com-
mon burning glass has the same property ; if we allow the
rays of the sun to pass through it, and hold a sheet of white
paper at the proper distance behind it, we may notice two
eifects. In the first place (and this is often disregarded)
the burning lens, although made of transparent 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

THE EYE AS AN OPTICAL INSTRUMENT. 211

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 sur-
face, a similar line or surface 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 corre-
sponds to it in strength and colour of illumination, 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 pre-
pared 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 instead of the piece of paper, the retina. Accord-
ingly, 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. P'ig. 30 illustrates tliis effect.
Tlie 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 h. Thus it results that the
light of each separate bright point of the field of vision

212 EECEXT PROGRESS OF THE THEORY OP 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, that separate
impressions may each arrive separately at the seat of
consciousness.

If now we compare the eye with other optical instru-
ments, 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° verti-
cally, and for both together somewhat more than two
right angles from right to left. The field of view of in-

FiG. 30.

struments made by art is usually very small, and becomes
smaller with the increased size of the image.

But we 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 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 magni-
tude, i.e. a distance equal to the sixtieth part of the
diameter of the finger-nail. This distance corresponds to

THE EYE AS AN OPTICAL INSTRUMENT. 213

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 parti-
cularly 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,*

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 po-
sition that the image of the object falls on the small region
of perfectly 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 this rapidity of movement which

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

"Wenn iiber uns im blauen Eaum rerloren
Ihr schmetternd Lied die Lerche singt.

214 RECEXT PROGRESS OF THE THEORY OP VISION.

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 accu-
rate view of the whole field of vision at once. It is not in
tact until we begin to examine our sensations 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.* 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 move-
ments 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 dis-
tant objects pass in rapid succession into accurate view.

' Vide infra, p. 254.

THE EYE AS AN OPTICAL INSTRUMENT. 215

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 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 disper-
sion— that they be achromatic. Dispersion of light de-
pends 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
''^It^ the same ; they do not perfectly overlap each other
in the field of vision, and thus the white surface of the
image appears fringedwith 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 premisses. Newton

216 RECENT PHOGRESS OF THE THEORY OP VISIOJT.

thought he had discovered a relation between the re-
fractive and dispersive powers of various transparent
materials, from which it followed that no achromatic
refraction was possible. Euler,' on the other hand, con-
cluded that, since the eye is achromatic, the relation
discovered by Newton could not be correct. Keasoning
from this assumption, he constructed theoretical rules
for making achromatic instruments, and Dolland ^ carried
them out. But Dolland himself observed that the eye
could not be achromatic, because its construction did not
answer to Euler's rules ; and at last Fraunhofer^ actually
measured the degree of chromatic aberration of the eye.
An eye constructed to bring red light from infinite dis-
tance to a focus on the retina can only do the same with
violet rays from a distance of two feet. AYith 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 intermediate 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 phe-
nomenon 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

' Leonard Euler born at Basel, 1707 ; died at St. Petersburgh, 1783.

2 John Dolland, F.R.S. born 1706 ; died in London, 1761.

' Joseph Fraunhofer born in Bararia, 1787 ; died at Munich, 1826.

THE EYE AS AN OPTICAL INSTRUMENT. 217

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 dis-
persive power than glass. ^ Hence it is that the chro-
matic 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 surfiices
approximately unite the rays which proceed from a lumin-
ous 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 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 investigation 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 unim-
portant. The careful measurements of the curvature of the
cornea, first made by Senff of Dorpat, next, with a better
adapted instrument, the writer's ophthalmometer already
referred to, and afterwards carried out in numerous
cases by Bonders, Knapp, and others, have proved that
the cornea of most human eyes is not a perfectly sym-

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

218 RECEXT PROGRESS OF THE THEORY OF VISION.

metrical curve, but is variously bent in differfjnt direc-
tions. I have also devised a method of testing the
* centering ' 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 astig-
viatism, 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 astigmatism 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 im-
perfectly elliptical, an ill-centered telescope, does not
give a single illuminated point as the image of a star,

Fre. 31.

but, according to the surface and arrangement of the
refracting media, elliptic, circular, or linear images. Now
the images of an illuminated point, as the human eye
brings tliem to focus, are even more inaccurate : they are
irregularly radiated. The reason of this lies in the con-

THE EYE AS AN OPTICAL INSTRUMENT. 219

st ruction of the crystalline lens, the fibres of which are
arranged around six diverging axes (shown in Fig. 31). So
that the rays which we see around stars and other distant
liphts are imaees of the radiated structure of our lens ;
and the universality of this optical defect is proved by any
figure with diverging 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 three-
fold.

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 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 indisputable 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, per-
fectly 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 ^ through the cornea and crystalline lens,
they appear of a dingy white, less transparent than the
' aqueous humour ' which lies between them. This defect
* Eg. from a lamp, concentrated by a bull's-eye condenser.

220 RECENT PROGEESS OF THE THEORY OF YISIOIS-.

is most apparent in the blue and violet rays of the solar
spectrum ; for there comes in the phenomenon of fluo-
rescence ^ to increase it.

In fact, although the crystalline lens looks so beauti-
fully 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 ' entoptic 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 look^ 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 everyone'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

' This term is given to the property which certain substances possess of
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 throwing 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 simply disadvantageous.

* Vide su^rUy p. 213.

THE EYE AS AN OPTICAL INSTRUMENT. 221

remarkable proof of the way in which we observe, or fail
to observe, the impressions made on our senses, that these
viuscce volUantes often appear some-thing 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 structure of the lens and the vitreous body. Both
are produced by 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 the existence of certain inequalities 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 un-
perceived. This 'blind spot' will therefore produce a corre-
sponding 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. E 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.'

222 RECEXT PROGRESS OF THE THEORY OF VISION.

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° hori-
zontally distant from the ' temporal ' or external side of
the centre of distinct 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

Fig. 32.

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. Mariott^,^ who
liiscovered the phenomenon, amused Charles II. and his

» Edme. Mariotte born in Burgundy, died at Paris, 1684,

THE EYE AS AN OPTICAL INSTRUMENT. . 223

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, m 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 sensative
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
recoo-nised 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 sunlight 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 sensi-
tive 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 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,
tiie 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 Wurzburg — whose too early loss to
science we still deplore — determined the distance between
the two foci, and found it exactly to equal the thickness

224 RECENT PROGRESS OF THE THEORY OF VISION.

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 sensi-
tive to weak light than the other parts of the retina. It
has been long known that many stars of inferior magni-
tude— for example, the Coma Berenicce and the Pleiades
— are seen more brightly if looked at somewhat obliquely
than when their rays fall full 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 been noticed above, which interferes
with its free communication with the life-giving blood.

All these imperfections would be exceedingly trouble
some 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.
For even when we do 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
irregularity 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
directinof our attention.

o

But, after all it remains a wonderful paradox, 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

THE EYE AS AN OPTICAL INSTRUMENT. 225

external objects. It is a fact which we constantly meet,
not only in optics, but in studying the perceptions pro-
duced by other senses on the consciousness. The diffi-
culty 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 resided in the retina or the choroid was still unde-
cided, 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 thought over the nature and cause
of their functions, and, after all, it was only by a remark-
able combination of circumstances that a simple pheno-
menon 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 diffi-
cult 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 stimulated. Among these may be mentioned
Goethe, Purkinje,' and Johannes Miiller.^ When a sub-

' 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 1858, set. 57. His Manual of Physiology
was translated into English by the late Dr. Baly. — Tk.

226 RECENT PROGRESS OF THE THEORY OF VISION.

sequent observer tries to repeat on his own eyes these
experiments as he finds them described, it is of com-se
easier for him than for the discoverer ; but even 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 pecu-
liarities 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 condi-
tion 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 cen-
tral pit of the retina, and most of the fixed entoptic
images), are never noticed at all ; and if we want to
observe them we must employ unusual modes of illumina-
tion 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 sensa-
tion ; it must, I think, be rather explained as a pheno-
menon belonging to our power of attention, and I now
only refer to the question in passing, since its full discus-
sion 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 imperfection to my readers, I answer, as I said at first,
that I have not done so in order to depreciate the perfor-
mances of this wonderful organ or to diminish our admi-
ration of its construction. It was my object to make the
reader understand, at the first step of our inquiry, that it

THE EYE AS AN OPTICAL INSTRUMENT. 227

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 para-
doxical 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 first appears : its
extraordinary value depends upon the way in which we
use it : its perfection is practical, not 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 adapta-
tion 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 perfec-
tion of the races of animals and plants has been carried
on. Wherever we scrutinise the construction of physio-
logical organs, we find the same character of practical
adaptation to the wants of the organism ; although, per-
haps, 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 inexact-
ness 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 somewhat changed condi-
tions, we become aware of the chromatic aberration, t]\e
astigmatism, the blind spots^ the yenous shadows, the
11

228 RECENT PROGRESS OF THE THEORY OF VISION.

imperfect transparency of the media, and all the other
defects 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 w^e 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
difficult material for an instrument of the mind.

One result of this mode of construction of the eye, of
which we shall see the importance bye and bye, is tliat
clear and complete 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 limitation, will after-
wards come under our notice.

But, apparently, we are not yet come much nearer to un-
derstanding 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 sensa-
tions of the eye, and how far this will bring us towards the
solution of the problem.

II. The Sensation of Sight.

In tlie 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 solution.
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
first 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,^ when
writing that great work on the ' Comparative Physiology
of Vision,' which marks an epocli in science, was able to
lay down the most important principles of the theory of
the impressions derived from the senses. These prin-
ciples 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 arrived at are generally com-
prehended under the name of the theory of the Specific

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

230 RECENT PROGRESS OF THE THEORY OF VISION.

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.^ But
that part of the theory of vision with which we are now
occupied is little more than a further development of the
theory of the specific action of the senses. I must, there-
fore, beg my reader to forgive me if, in order to give him
a comprehensive view of the whole subject in its proper
connection, 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 produced in our organs of sense by external impres-
sions, 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 concep-
tions of surrounding objects. If the nerves which convey
these impressions to the brain are cut through, the sensa-
tion, and the perception of the impression, immediately
cease. In the case of the eye, the proof that visual per-
ception 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 after-
wards more fully explain) that the visual impression of
any solid object of three dimensions is only produced by
the combination of the impressions derived from both
eyes.

What, therefore, we directly apprehend is not the imme-
diate action of the external exciting cause upon the ends

• ' On the Nature of Special Sensations in Man,' Kbnigsberger naturwis-
senschaftliclie Untcrhaltungen, vol. iii. 1852. ' Human Vision,' a popular
Scientific Lecture by H. Helmholtz, Leipzig, 1855.

THE SENSATION OF SIGHT. 231

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 sensitive impressions from the external organs
to the brain, others convey voluntary impulses in the
opposite direction, from the brain to the muscles, caus-
ing 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 circula-
tion. But the fibres of all these nerves are the same
clear, cylindrical threads of microscopic minuteness, con-
taining 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
conducting fibres. It appears to have no relation to their
peculiarities of function.

Moreover, all nerves have the same electro-motor
actions, as the researches of Du Bois Reymond ^ prove.
In all of them the condition of excitation is called forth
by the same mechanical, electrical, chemical, or thermo-
metric 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 sub-
mitted to like conditions, and, with a slight apparent dif-

* Professor of Physiology in the University of Berlin.

232 RECENT PROGRESS OF THE THEORY OF VISION.

ference according to their thickness, undergo the same
coagulation of their contents. In short, all that we can
ascertain of nervous 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 different kinds of nerves.
Very lately the 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 differ-
ence 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 tele-
graphic wires traversing a country, and the comparison is
well fitted to illustrate this striking and important pecu-
liarity of their mode of action. In the net-work of tele-
graphs we find everywhere the same copper or iron wires
carrying the same kind of movement, a stream of elec-
tricity, 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

THE SENSATION OF SIGHT. 233

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, everyone 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 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
recognised, since in our present subject its consequences
have been till lately disputed.

Therefore, as motor nerves, when irritated, produce
movement, 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 sensi-
tive organs. But we have very different kinds of sensa-
tion. 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 com-
pare in quality a sensation of light with one of sound
or of smell. We will name this difference, so much
deeper than that between comparable qualities, a differ-
ence 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.

234 RECENT PROGRESS OF THE THEORY OF VISION.

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 irrita-
tion 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 Miiller) 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 enquiry. In the first place, we
know that no kind of action upon any part of the body
except the eye and the nerve which belongs to it, can
ever produce the sensation of light. The stories of som-
nambulists, which are the only arguments that can be
adduced against this belief, we may be allowed to dis-
believe. 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 eye-
ball 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 se-
cond observer could not fail to see through the pupil- the
illumination of the retina which would follow, if the

THE SENSATION OF SIGHT. 235

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 cir-
cumstances, at least, there is not the smallest spark of
actual light.

In the same way, increased pressure of blood, its ab-
normal 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 producing 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 ex-
ternal light, that persons unacquainted with these pheno-
mena readily suppose that the rays they see are real ob-
jective beams.

Thus we see that external light produces no other
effects in 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.

236 RECENT PROGHESS OF THE THEORY OF VISION.

On the other hand, the optic nerve, by reason of the
pecuHar 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 notice-
able 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 sen-
sation 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 natural connection puts it beyond
doubt that external light is only one of the exciting
causes capable of bringing the optic nerve into func-
tional 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 external objects.

Light is known in Physics as a movement which is
propagated by successive waves in the elastic ether distri-
buted 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 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 SEXSATION OF SIGHT. 237

the little ripples whose summits are a few inches distant
from each other differ from the waves of the ocean, be-
tween whose foaming crests lie valleys of sixty or a him-
dred 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 depend-
ing upon the length of the waves) the same remark-
able properties of reflection, refraction, interference, dif-
fraction, 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 par-
ticles of ether vibrate at right angles to the direction in
which the ray is propagated.

All the different sorts of rays which I have mentioned
produce one effect in common. They raise the tempera-
ture 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 cogni-
sant 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 produced by a gentle breeze,
are so slightly appreciated by the eye, that such rays are

238 RECENT TROGRESS OF THE THEORY OF VISION.

also generally regarded as invisible, and are known as the
dark chemical rays.

Between the very long and the very short waves of
ether 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 pro-
duce 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 radiation 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 pro-
cesses they may be subjected, it is impossible to weaken
their illuminating power without at the same time, and
in the same degree, diminishing their heating and their
chemical action. Whatever produces an undulatory move-
ment 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, according to the length of the waves. The un-
dulations 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

THE SENSATIOX OF SIGHT. 239

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 dia-
mond 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 de-
composed by the different degree of refraction of its
several parts, referred to in the last essay ; and thus
each of its component hues appears separately. These
colours of the several primary forms of light are best
seen in tlie 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.

Wlien 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 proportions in which they are com-
bined 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. Now,
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
pigments and that of coloured light is, that while

240 RECENT PROGHESS OF THE THEORY OP VISION.

painters make green by mixing blue and yellow pig-
ments, the union of blue and yellow rays of light pro-
duces 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 h through the
glass plate, while g is seen re-
flected in the same ; and if g is
put in a proper position, its image
exactly coincides with that of 6.
^ It then appears as if there was

FlO. 83. , n 1 ' ^ ^

a smgle wafer at 6, with a colour
produced by the mixture of the two real ones. In this
experiment the light from 6, which traverses the glass
pane, actually unites with that from g, which is reflected
from it, and the two combined pass on to the retina at
o. In general, then, light, which consists of undu-
lations of different wave-lengths, produces different im-
pressions 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 com-
binations of rays with different wave-lengths which ex-
ternal objects can convey to our eyes. The retina
cannot distinguish between the white which is pro-
duced by the union of scarlet and bluish-green light,
and that which is composed 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
indistinsruishable to the human eve. For instance, a sur-
face illuminated with red and bluish-green light would
come out black in a photograph ; while another lighted

THE SENSATION OF SIGHT. 241

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 ob-
jects with white beams of light of various composition,
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 between 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 in-
distinguishable 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 diagram-
matic 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 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 circumference are represented the various tints which
can be produced by diluting the full colours of the cir-
cumference 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 tliis diagram, and the quantity
of light which each reflects, that when we have ascer-
tained the resultants of two coloui-s of different known

242 RECENT PROGRESS OF THE THEORY OF VISIOIS".

strength of light (in the same way as we might determine
the centre of gravity of two bodies of different known
weights), we shaU then find their combination-colour
at the ' centre of gravity ' of the two amounts of light.

Fig. 34.

Green

Blue

WeUoyt

\ioUt

Furplo

Red

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 com-
pound 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 satu-
rated in nature, and Avhich must therefore be placed at
the greatest distance from the central white, will not
arrange themselves in the form of a circle. The circum-
ference of the diagram presents three projections cor-
responding 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 cor-

THE SENSATION OF SIGHT. 243

ners are the three colours I have mentioned,^ and the sides
of the triangle show the transitions from red through yellow
into green, from green through bluish-green and ultra-
marine to violet, and from violet through purple to scarlet.

Newton used the d iagram of the colours of the spectrum
(in a somewhat different form from that just given)
only as a convenient way of representing the facts to
the eye ; but recently Maxwell has succeeded in de-
monstrating the strict and even quantitative accuracy
of the principles involved in the construction 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 round,
so that the eye can no longer follow the separate hues,
they melt into a uniform 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 pro-
duced in this manner are exactly those which would result
if the same qualities of coloured light illuminated 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 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

' 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.

244 RECENT PROGRESS OF THE THEORY OF VISIOX.

which returns upon itself; a series which we complete
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 described 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 produced 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, &c., 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 appears to be only one of quantity, not of quality.
Black is only darkness — 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, bro^vn and olive are dark,
more or less saturated tints of red, yellow and green re-
spectively.

THE SENSATION OF SIGHT. 245

la this way we may reduce all possible actual (ob-
jective) differences in colour, so far as they are appre-
ciated by the eye, to three kinds ; difference of hue {tone),
difference of fulness {saturation), and difference of amount
of illumination {brightness). It is in this way that we de-
scribe 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
approaches 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 interior 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 undulat-
ing 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 notefs, 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

246 RECENT PROGRESS OF THE THEORY OF YlSIOIf,

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 J) instead of them, without entirely
changing the impression upon the ear. The most com-
plicated 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 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 un-
changed to the ear, when the strength of each separate
tone which it contains 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 knowledge of
sun or starlight. 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

THE SENSATION OF SIGHT. 247

harmonies of an entire orchestra, but the optician cannot
directly ascertain the composition of light by means of
the eye ; lie 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 apparent, 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, or even in the intense heat of the sun's at-
mosphere, 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 founda-
tion of spectral analysis — that most brilliant discovery of
recent years, which has opened the extreme limits of
celestial space to chemical analysis.

There is an extremely interesting and not very un-
common defect of sight which is known as colour-blind-
ness. In this condition the differences of colour are
reduced to a still more simple system than that described
above ; namely, to combinations 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 dis-
tinguish 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. Accordingly 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

248 RECENT PROGRESS OF THE THEORY OP VISION.

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 spectrum at all. Very full scarlet appears to them
almost black, so that a red-blind Scotch clergyman went
to buy scarlet cloth for his gown, thinking it was black.*

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 distinguished
from them in hue. In fact, all red colours appear much
darker when viewed indirectly. This red-blind part of 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 retma.

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 some-
what 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

' 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. 249

from the middle of the field ; and, on the other hand,
wlien they appear white here, are red to direct vision.
These inequalities of the retina, like the others men-
tioned in the former essay, are rectified by the con-
stant 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 luoiild
make on us if seen directly. The result is, that only
unusual combinations and unusual or special direction of
attention enable us to recognise the difference of which I
have been speaking.

The theory of colours, with all these marvellous and
complicated relations, was a riddle which Goethe in vain
attempted to solve ; nor were we physicists and physio-
logists more successful. 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 discovered at the
beginning of this century, and had been in print ever
since for any one to read who chose. This solution was
found and published by the same Thomas Young * who
first showed the right method of arriving at the in-
terpretation of 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 contempo-
raries. 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 Eoyal 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.

• Born at Milverton, in Somersetshire, 1773, died 1829.

250 RECEXT PROGRESS OF THE THEORY OF VISION.

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 tu 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 excita-
tion of those fibres which are sensitive to that colour pre-
dominates ; 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 sensa-
tion 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.^

It will be seen that this hypothesis is nothing more
than a further extension of Johannes Miiller's law of special

* 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 con-
siders that it is more properly blue. The question is still an open one:
acordinq; to J. J. Miiller's experiments {Archivfiir Ophthalmologic, XV.
2. p. 208) violet is more probable. The fluorescence of the retina is here
a source of difficulty.

THE SENSATION OF SIGHT. 251

sensation. Just as the difference of sensation of light and
warmth depends demonstrably upon whether the rays of
the sun fall upon nerves of sight or nerves of feeling, so
it is supposed in Young's hypothesis 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 sensitive to red rays, are incapable of excita-
tion. 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 e3^e.

It must be confessed that both in men and in quadru-
peds we have at present no anatomical basis for this
theory of colours ; but Max Schultze has discovered a struc-
ture 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 colour-
less 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 impres-
sions 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
12

252 RECENT PROGRESS OF THE THEORY OF VISION.

simple manner 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 sim-
ple 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 verte-
brate animals, whose labyrinth lies too deep for experi-
ment, 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 fila-
ments to which the fibres of the auditory nerve are dis-
tributed ; and Hensen, of Kiel, has satisfied 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 coloiu'-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 SENSATION OF SIGHT. 253

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 occiu: in nature, while our theory has to
do with the analysis of our subjective sensations of colour.
We need then only assume that actual coloured light does
not produce sensations of absolutely pure colour ; that
red, for instance, even when completely freed from all ad-
mixture 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 sen-
sation which the purest red light produces in the eye is
still not the purest sensation of red which we can con-
ceive of as possible. This sensation could only be called
forth by a fuller, pmer, 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 de-
scribed. 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 function, replacing used material by fresh,
and thus carrying away the chemical results of func-

254 RECENT PROGRESS OF THE THEORY OF VISIOX.

tional 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
diml}^ 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 ap-
peared complete darkness.

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 por-
tion 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 illumina-
tion. What was dark appears bright, and what was
bright dark, like the first negative of a photographer. By
carefully 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 phe-
nomenon 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 backgroimd than the neighbouring regions, and
there now appears a dark spot upon the really uniform
surface, corresponding in extent to the surface of the
retina which before received the bright light.

THE SENSATION" OF SIGHT. 255

(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 dii'ect or positive after-image, which at
first unites with the negative or indirect one pioduced 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 diminish 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 some point of
the white sheet near the margin of the black, and after
30 to 60 seconds draw the black sheet quickly away,
without 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 impres-

256 RECENT PROGRESS OF THE THEORY OF VISION.

sions of the colour in question. 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 accord-
ingly 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 satu-
rated 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 un-
fatigued 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 accumu-
late further 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
conviction that the quality of our sensations, and espe-
cially our sensations 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 la of specific nervous energy. Whether the rays

THE SENSATION OF SIGHT. 257

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 sen-
sation of light just as well as the sunbeams. The most
complete difference 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 like-
ness, or unlikeness, between the sensations of colour
and of musical tones — does not, as we now see, at all de-
pend 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 coincidence between its objects and the sen-
sations 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
important 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 recognising comparatively few
differences in quality of light ; the ear, which in the
latter respect is so enormously better provided, has scarcely
any power of appreciating differences of locality. But
it is certainly matter for astonishment to any one who

258 RECEXT PROGRESS OF THE THEORY OF YISIOX.

trusts to the direct information of his natural senses, that
neither the limits within which the spectrum affects our
eyes, nor the differences of coloiu: w^hich alone remain
as the simplified 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 piecisely 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 sensations of
colour (the perception of the simple primary tints) can-
not be produced by any kind of external light in the
natural unfatigued condition of the eye. These ele-
mentary 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, there-
fore, that as to any correspondence in kind of exter-
nal 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

THE SENSATION OF SIGHT. 259

executed on a smaller scalej 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 similar colours, secondly be-
cause it represents a part of its relations 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 chanoes 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 chapter. But not only un-
educated persons, who are accustomed to trust blindly to
their senses, even the educated, who know tliat 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 philo-
sophers long hesitated to admit the identity of the rays
of light and of heat, and exhausted all possible means of
escaping a conclusion which seemed to contradict the
evidence of their senses.

Another example is that of Groethe, as I have en-
deavoured 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 com-
posed of darker colours. It was Newton's discovery of

200 HECEXT PROGHESS OF THE THEORY OP YISIOJT.

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 interpretation 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 concep-
tions.

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 constitution. 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 ' decep-
tive 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 deceptive
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 understand 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

THE SENSATION OF SIGHT. 261

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 sensa-
tions, as those of sight, with which we have now to do.
Any of these actions is called a ' property,' when its
object is understood without being expressly mentioned.
Thus, when we speak of the ' solubility ' of a substance,
we mean its behaviour toward 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 depend upon the nature of one agent alone, but
exists only in relation 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, independent of all
other objects, and which we may expect to find repre-
sented 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 naturally long ago sug-
gested themselves to thoughtful minds ; they may be
found clearly expressed in the writings of Locke and
Herbart,' 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

' Johann Friedrich Herbart, born 1776, died 1841, professor of philo-
sophy at Konigsberg and Gottingen. author of Psychologie ah Wissew
schaft, neugegrundet auf Erfahrung, Metaphysik und Mathematik. — Te.

262 RECENT PROGRESS OF THE THEORY OF TISION.

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 examine 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 move-
ment of the eye supplies this imperfection, in the same
way as it makes up for the unequal 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 relative
brightness and colour of the different objects in sight
remains almost unchanged, so that the effect of fatigue
is gradually to weaken the apparent illumination of the
entire field of vision.

This brings us to consider the differences in the pictures
presented by the eye, which depend on different degrees
of illumination. Here again we meet with instructive
facts. We look at external objects under light of very
different intensity, varying from the most dazzling sun-
shine to the pale beams of the moon ; and the light of
the full moon is 1 50,000 times less than that of the sun.

THE SENSATION OF SIGHT. 263

Moreover, the colour of the ilhimination 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 illu-
mination 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 wave 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 importance for the painter, for many of
his finest efifects 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 pur-
pose, 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
alone is the expression of a constant property of the
object in question.

264 JRECEXT PEOGRESS OF THE THEORY OF VISION.

Considered theoretically, the task of judging of the
colour of a body under changing illumination would seem
to be impossible ; but in practice we soon find that we
are able to judge of local colour without the least un-
certainty 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 brightness, as a white object in sha-
dow, than that the proper colour of a white paper in
shadow is the same as that of a sl.eet 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 im-
pression upon the retina of a grey surface under illumi-
nation 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 illumination 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

' The local or proper colour of an object (Kbrperfarhe) 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 illu-
mination-colour.— Tb.

THE SENSATION OF SIGHT. 265

then be impossible to tell that there is any artificial il-
lumination at all. The grey looks white.'

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 circumstances, the brightness of any proper
colour diminishes in proportion as the illumination is
diminished, or the fatigue of the retina increased.

This relation holds even for extreme degrees of illu-
mination, so far as the objective intensity of the light is
concerned, but not for our sensation. Under illumination
so brilliant as to approach 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 unable to appreciate
slight differences in the amount of light reflected 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 uni-
form daylight, do not really admit of any difference of
brightness approaching that between sunshine and moon-
light. 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 sen-
sation produced by the same actual conditions of light and
colour. If the brightness of various colours is equally in-
creased, 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 demonstration is more striking if the grey disk is placed on a sheet
of white paper in diffused light. — Te.

2QQ RECENT PROGRESS OF THE THEORY OF VISION.

the red seems much brighter in full sunlight, the blue in
moonlight or starlight. This peculiarity in our perception
is also made use of by painters ; they make yellow tints
predominate when representing landscapes in full sun-
sliine, while every object of a moonlight 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.

These examples show very plainly how independent our
judgment of colours is of their actual amount of illu-
mination. 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 intensity — as, for example, in
the experiment of coloured shadotus. If we admit light
from a cloudy sky through a narrow opening into a dark
room, so that it falls sidesvays 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 to-
gether, 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

' This experiment with diffused white day-light may also be made with
moonlight.

THE SEI^SATIOI!^ OF SIGHT. 267

that of objects seen through it. This is proved by a
number of experiments contrived to illustrate the effects
of contrast. If we look through a green veil at a field of
snow, although the light reflected 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 aftei-image of green. So completely
are we able to separate the light which belongs to the
transparent medium from that of the objects seen
through it.'

The changes of colour in the two last experiments are
known as phenomena of contrast. They consist in mis-
takes as to local colour, which for the most part depend
upon imperfectly defined after-images.^ 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 phe-
nomena 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 shnultaneous
contrast. Thus in the experiment described above of
coloured shadows thrown by daylight and candle-light,
the doubly illuminated surface of the paper being tlie
brightest object seen, gives a false criterion for white. Com-
pared 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

* A number of similar experiments will be found described in the
author's Handbuch der fhysiologischen Optik, pp. 398-411.

2 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. — Tb.

268 BKCENT PROGRESS OF THE THEORY OF VISION.

that differences in sensation which are easily appre-
hended 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 affecting 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 further
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 phenomena 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. This part of our inqiiiry has shown us that tl>e
qualities of these sensations can only be regarded as signs
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 sensations of sight is,
that ' under similar conditions, the qualities of this sen-
sation appear in the same way for the same objects.'

And yet, in spite of all this imperfection, we have also

THE SENSATION OF SIGHT. 269

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
decision.

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 harmony between the outer
and the inner world.

And what progress have we made in our task of ex-
plaining Sight ? It might seem that we are farther 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 fruitless criticism the fair
world presented to us by our senses, in order to annihi-
late the fragments.

Woe ! woe !

Thou hast destroyed

The beautiful world

With powerful fist ;

In ruin 'tis hurled,

By the blow of a demigod shattered.

270 THE PEECEPTION OF SIGHT.

The scattered

Fragments into the void we carry,

DeyJoring

The beauty perished beyond restoring.*

and may feel determined to stick fast to the ' sound com-
mon sense ' of mankind, and believe his own senses more
than physiology.

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 tlie
accuracy of what our senses teach us, will not be justified
even before the tribunal of Science.

III. The Pehception of Sight.

The colours which have been the subject of the last
chapter are not only an ornament we sliould 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 relations of locality, No other
sense can be compared with the eye in this respect. The
sense of touch, it is true, can distinguish relations of
space, and has the special power of judging of all matter

* Bayard Taylor's translation of the passage in Faust : —

Du hast sie zerstort

Die schone Welt

Mit machtiger Faust ;

Sie stiirzt, sie zerfallt,

Ein Halbgott hat sie zerschlagen.

Wir tragen

Die Triimmern ins Nichts hiniiber,

Und klagen

Ueber die verlorne Schone.

THE PERCEPTION OF SIGHT. 271

within reach, at once as to resistance, volume, and weight;
but the range of touch is Hmited, and the distinction it
can make between small distances is not nearly so accu-
rate as that of sight. Yet the sense of touch is sufficient,
as experiments 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 con-
tinually 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 illimitable distances.

This combination of the two senses is of great im-
portance for our present task ; for, since we have heie
only to do with vision, and since touch is sufficient to
produce complete conceptions of locality, we may assume
these conceptions to be already complete, at least in their
general outline, and may, accordingly, confine our in-
vestigation to ascertaining the common point of agree-
ment 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,

272 RECENT PROGHESS OF THE THEORY OF VISION.

and may recognise that all these agents are diffused
throuo'h the air of the room at the same time, and without
any difference of locality. When a compound colour
falls upon the retina, we are conscious of three separate
elementary 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 fun-
damental, and a series of harmonic overtones, which also
are probably received by different nerves, and yet we are
unable to separate them in space. IMany 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 inseparably united in the compound sen-
sation which we call taste.

No doubt, with a little attention it is possible to
ascertain the parts of the body which receive these sen-
sations, but, even when these are known to be locally
separate, it does not follow that we must conceive of the
sources 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 convej^ed by two distinct
nerves. In fact, both phenomena are examj)les 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

THE PERCEPTION OF SIGHT. 27 3

must clearly be added to produce 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 separation between these two nerves is not a
sufficient ground for our recognition of the two parts
which have been touched as distinct, and for the concep-
tion of two different external objects which follows.
Indeed, this conception will vary according to circum-
stances. 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 circumstancf 5,
we suppose that there is only a single grain. In this case,
our consciousness of the position of the fingers has ob-
viously 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 produce
in the mind the conception of two.

What, then, is it which comes to help the anatomical
distinction 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, perceives impressions
which carry with them this quality of extension in space ;

274 hecext trogress of the theory of vision.

that this conception of locality is innate ; and that im-
pressions derived from external objects are transmitted of
themselves to corresponding local positions in the image
produced in tli^ sensitive organ. We may describe this as
the Innate or Intuitive Theory of conceptions of Space.
It obviously cuts short all further enquiry into the origin
of these conceptions, since it regards them as some-
thing 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,^ Locke, and Jurin.^ Its applica-
tion to special physiological problems has only become
possible in very modern times, particularly since we have
gained more accurate knowledge of the movements of the
eye. The invention of the stereoscope by Wheatstone
(p. 284) made the difficulties and imperfections 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 ex-
ternal objects and movements, and that we can only learn
how to interpret these signs by means of experience and
practice. For example, the conception of differences in
locality can only be attained by means of movement, and,
in the field of vision, depends upon our experience 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

» William Molyneux, author of Dioptrica Xova, 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 Presi-
dent of the Royal Collfge of Physicians, was born in 1684, and died in 1760.
Beside works on the Contraction of the Heart, on Vis viva, &c., he pub-
lished, in 17.38, a treatise on District and Indistinct Vision. — Ts.

THE PERCEPTION OF SIGHT. 275

difference. 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, more-
over, 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. Lotze ^ has named this difference
between the sensations which the same colour excites
when it affects different parts of the retina, the local sign
of the sensation. 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 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) as signs 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 magni-
tude.

' Eudolf Hermann Lotze, Professor in the University of Gottingen,
originally a disciple of Herbart (v. supra), author of Allgemeine Fhysiologie
des menschlichen Korpers, 1851. — Te.

13

276 RECENT PROGRESS OF THE THEORY OF VISION.

The reader will see how the subject of our present
enquiry involves the consideration of that far-reaching
opposition between the system of philosophy which as-
sumes 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 land-
scape, both the above theories practically offer an equally
good explanation of the way in which we form concep-
tions 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 of A, b of B.
This has always been a difficulty in the theory of vision,
and many hypotheses have been invented to explain it.
Two of these have survived. We may, with Johannes
Muller, 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 suppose that the feeling of corre-
spondence between what is upper in the sense of sight and
in the sense of touch is only acquired by experience.

THE PEECEPTION OF SIGHT. 277

when we see the hands, which feel, moving in the field of
vision. 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
siglit and those of feeling are so arranged in the brain as
to produce a correspondence between the notions they
suggest of upper and under, right and left. This sup-
position has, however, no pretence 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 difficulty was met by the assumption that both retinse
when they are excited produce only a single sensation in
the brain, and that the several points of each retina corre-
spond 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 retinae
pass to the right cerebral hemisphere, those from the left
halves to the left hemisphere.'* But although correspond-
ing nerve-fibres would thus be brought close together, it
has not yet been shown that they actually unite in the
brain.

' Liidwng Fick, late Professor of Medicine in the University of Marburg,
the brother of Prof. Adolf Fick, of Ziirich.

"^ 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 those 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 hemi-
sphere are the outer fibres of the left and the inner of the rifiht 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.— Te.

278 RECEXT 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
retinae, 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 being inverted and double. He knows
what impression such and such an object in such and
such a position makes on him through 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, depends, first, on
our having movable parts of our own body within sight ;
so that, when we once know by means of touch what rela-
tion in space and what movement is, we can further
learn what changes in the impressions on the eye cor-
respond 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 sensa-
tion were quite arbitrary, thrown together without any
systematic arrangement (a supposition which I regard as
improbable), it would still be possible by means of the
movements of the hand and of the eye, as just described,

THE PERCEPTION OF SIGHT. 279

to ascertain whicli 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 in accordance with experiments by Fechner,^
Volkmann,'^ 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 ex-
periment that the harmonious results of the perceptions
of feeling and of sight depend, even in the adult, upon a
constant comparison 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 any-
thing 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 per-
fect certainty, even when the eyes are shut. And we
can even do the same with the other hand without seeing
it, which proves that it is not the perception of touch

' Gustav Theodor Fechner, author of Elemente der Psychophysik, 1860 ;
also known as a satirist. — Tb.

"^ Alfred Wilhelm Volkmann, s\iccessive1y Professor of Physiology at .
Leipzig. Dorpat, and Halle; author oi Physiologische JJnters'uchungen im
Gehiete der Ojptik, 1864, &c.— Tb.

280 RECENT PROGRESS OF THE THEORY OF VISION.

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 experiment 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 was established between the percep-
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
microscope, we must learn to harmonise the inverted mi-
croscopical image with our muscular sense ; and we have
to get over a similar difficulty in shaving before a look-
ing-glass, which changes right 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 oppo-
site 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 between our retinal
images on the one hand, and, on the other, the actual
condition of the objects as well as the correct impression
of them which we receive. Here we are compelled to
choose between the two opposite theories, and accordingly
this department of our subject — the explanation of our
Perception of Solidity or Depth in the field of 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 no won-

THE PERCEPTION OF SIGHT. 281

der, 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. 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 estimating 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 enquiry 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

282 RECEXT PEOGRESS OF THE THEORY OF YISIOX.

standing at diiSferent 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? 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 atmo-
sphere 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 recognise 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 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 com-
plete and perfect manner possible, by means of photo-
graphy, often shows nothing but a confused mass of
black 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

THE PERCEPTIOJf OF SIGHT. 283

impossible for any picture to represent actual objects was
the great master of painting, Leonardo da Vinci,^ who
was almost as distinguished in natural philosophy as in
art. He pointed out in his Trattato della Plttura^ 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 before it ; but, inasmuch as it occupies a somewhat
different position in space from the other, its point
of view and so its whole perspective image is dif-
ferent. If T hold up my finger and look at it first
with the right and then with the left eye, it covers,
in the picture seen })y 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 whenever
we look at bodies of which the several parts are at
different distances from our eyes. But when I look at a
hand represented 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 present different pictures
to the two eyes, while a painting shows only tlie same.
Hence follows a difference in the impression made upon
the sight which the utmost perfection in a representation
on a flat surface cannot supply.

The clearest proof that seeing with two eyes, and the
difference of the pictures presented by each, constitute

' Born at Vinci, near Florence, 1452 ; died at Cloux, near Amboise, 1519.
Mr. Hallam says of his scientific writings, that they are 'more like revela-
tions of physical truths vouchsafed to a single mind, than the super-
structure 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.

284 RECENT PHOGRESS OP THE THEORY OP VISION.

the most important cause of our perception of a third
dimension in the field of vision, has been furnished by
Wheatstone's invention of the stereoscope.^ 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 dif-
ferent 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 pictiu: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 instrument 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 6, and wdth 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 saw the

* Described in the Philosophical Transactions for 1838. — Tb.

THE PERCEPTION OF SIGHT.

285

picture g in the mirror 6, while the left saw the picture
k in the mirror a.

A more convenient instrument, though it does not

Fig. 35.

give such sharply defined effects, is tlie ordinary stereo-
scope of Brewster,^ shown in Fig. 36. Here the two

Fig. 36.

pictures are placed on the same slide and laid in the

' Sir David Brewster, Professor of Mathematics at Edinburgh, born
1781, died 1868.— Tr.

286 RECENT PROGRESS OF THE THEORY OF VISION.

lower part of the stereoscope, which is divided by a
partition s. Two slightly prismatic glasses with convex
surfaces are fixed at the top of the instrument which
show the pictures somewhat further off, somewhat mag-
nified, and at the same time overlapping each other,
so that both appear to be in the middle of the instru-
ment. 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 geo-
metrical outlines of solid figures, such as diagrams of
crystals, and also with representations 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 photographs 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 build-
ings, cities or landscapes, with which I was familiar
from stereoscopic pictures, they seemed familiar to
me ; but I never experienced this impression after see-
ing any number of ordinary pictures, because these
but so imperfectly represent the real effect upon the
senses.

THE PERCEPTION" OF SIGHT. 287

The accuracy of the stereoscope is no less wonderful.
Dove ^ 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 in place of the two ordinary
photographs. They will then unite into a single com-
pletely 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 cop-
perplate 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 ste-
reoscope, some lines will appear nearer and some further
off than the rest. This is the easiest way of detecting
spurious bank notes. A suspected one is put in a stereo-
scope 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 ex-
periment is also important 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 com-
bine so as to present a solid image of three dimen-
sions.

' Heinrich "Wilhelm Dove, Professor in the University of Berlin, author
of Optische Studien (1859); also eminent for his researches in meteorology
and electricity.

His paper, Anwendung des StereosJcops umfalschea von echtcm Papiergcld
zu unterscheiden, was published in 1859. — Tb.

288 RECENT PROGRESS OF THE THEORY OF VISION.

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. 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 and original
way of seeing things ; and hitherto most physiologists
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 liow 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 size. 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

THE PERCEPTION OF SIGHT. 289

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
distances 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 e}es, the images received
by corresponding points as a rule coincide, while images
received by those which do not correspond do not co-
incide. The corresponding points in each retina (without
noticing slight deviations) 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 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 retinae actually
unite so as to form a single fibre, either at the commissure
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 iden-
tical points to be regarded 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

290 RECENT PROGRESS OF THE THEORY OF VISIOJ^.

double images is comparatively imperfect, whenever it is
possible to combine them into a single view ; a striking
contrast to the extraordinary precision with which, as
Dove has shown, we can judge of stereoscopic relief. Yet
the latter power depends upon ths 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 produc-
tion 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 stereoscopic 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 stereo-
scopic pictures, or by putting lines in both which exactly
correspond, and so will make more evident by contrast
the imperfect coalescence of the other lines. All these
circumstances ought to have no influence, if the com-
bination of the two images 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, Briicke ' called attention to a series

* Professor of Physiology in the University of Vienna.

THE PERCEPTION OF SIGHT. 291

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
retinae. If we carefully follow the way in which we
look at stereoscopic pictures or at real objects, we
notice that the eye follows the different 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 phe-
nomenon 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 suc-
cession 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
perception 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.

292 RECE]^ 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. Stereoscopic draw-
ings 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 direc-
tions, 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 eve may receive this regularly reflected light
and the other nut ; 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 poli^^hed
surface.

Now if there were a complete combination of the
impressions produced upon both retinae, the union of

THE PERCEPTION OF SIGHT. 293

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
retinae are not combined into one sensation.

That, again, this effect of stereoscopic lustre does not
depend upon an alternation between the perceptions
of the two eyes, on what is called the ' rivalry of the
retinae,' is proved by illuminating 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
sensation, 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 sen-
sation given by the right 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 us in distinguishing 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 stereo-
scope 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
indistinguishable from that on the left.

294 RECENT PROGRESS OF THE THEORY OF VISION.

Lastly, there are some very curious and interesting
phenomena seen when two pictures are put 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,^ 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
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
moment 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

' The practised observer 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. — Tu.

THE PERCEPTIOX OF SIGHT. 295

on 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 intention to ob-
serve 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 com-
pletely 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, 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 phe-
nomenon 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

296 RECENT PROGRESS OF THE THEORY OF VISION.

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, including the names of Dove, Reg-
nault,^ Briicke, Ludwig,^ Panum,^ and Hering,^ main-
tains that the result of a binocular view of two colours
is the true combination-colour. Other observers, as
Heinrich Meyer of Ziirich, Yolkm^ann, Meissner,^ and
Funke,^ 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 tlie 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
difference between the two was very apparent. On the
other hand, there can of course be no doubt that the ob-
servers I first naDied really saw what they profess, so that
there mast here be great individual difference. Indeed
with certain experiments which Dove recommends as par-
ticularly well fitted to prove the correctness of his con-
clusion, such as the binocular combination of comple-
mentary polarisation-colours into white, I could not
myself see the slightest trace of a combination-colour.

' 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,
lately in the Josephsakademie of Vienna.

* Professor of Physiology in the University of Gottingen.

* Professor of Physiology in the University of Freiburg. — Tk.

THE PERCEPTION OF SIGHT. 297

This striking difference in a comparatively simple
observation 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 sensations 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, ac-
cording to Young's theory, produced together ; but it is
impossible to separate these by any movement 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 whole without
any attempt at analysis, or whether the observer is able

298 RECENT PROGRESS OF THE THEORY OF VISION.

by practice to recognise the parts of which it is com-
posed, 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 incli-
nation 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 shall see that the white and
black lines which affect nearly corresponding points of each
retina always 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 com-
bined stereoscopic image shows the plienomenon of Lustre,
while in the lower we see Eetinal Eivalry 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 carry 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 stereoscopic pictures than this. Indeed it is
possible to combine (at least partially and for a short

THE PERCEPTION OP SIGHT. 299

time) two entirely different drawings 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

Let us now put together the results to which our
inquiry into binocular vision has led us.

I. The excitement of corresponding points of the two
retinae is not indistinguishably combined into a single
impression ; for, if it were, it would be impossible to see
Stereoscopic Lustre. And we have found reason to believe
that this effect is not a consequence of Eetinal Kivalry,
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 the excita-
tion of corresponding points of each retina are not in-
distinguishably 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 pro-
duced 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 move-
ment of the retinal images, since it is possible under
momentary illumination.

We therefore learn that two distinct sensations are trans-
U

300 RECENT PROGRESS OF THE THEORY OF VISION.

mitted from the two eyes, and reach the consciousness
at the same time and without coalescing ; that accordingly
the combination 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, com-
plete, or at least nearly complete, coincidence as to
localisation in the field of vision of impressions of sight
received from corresponding points of the retinae ; but
that when we refer both impressions to the same object,
their coincidence of localisation is much disturbed.

If this coincidence were the result of a direct function
of 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 localisation 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 consequence 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 origioal 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

THE PERCEPTION OF SIGHT. 301

fields would be completely established by direct sensation,
as soon as the observer had got his two fixed points to
coincide and a single raeridian 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 anatomical mechanism.
We cannot criticise these attempts here : it would lead
us too far into details. Although many of these hypo-
theses are very ingenious (and at the same time very
indefinite and elastic), they have hitherto always proved
insufiicient ; 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 arranged
one of their systems to explain any particular phe-
nomenon of vision, it is found not to 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 concep-
tions to which they are opposed ? 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 j udgment must be formed in
spite of them.

It follows that the hypotheses which have been suc-
cessively framed by the various supporters of intuitive

302 RECENT PROGRESS OF THE THEORY OF VISION.

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 no-
thing 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 ex-
perience. 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
explanation failed, these mysteries of the laws of thought
cannot be regarded from a scientific point of view as con-
stituting any deficiency in the empirical theory of vision.

It is impossible to draw any line in the study of our
perceptions of space which shall sharply separate those
which belong to direct Sensation from those which are
the result of Experience. 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 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 ex-
perience.

We become acquainted with their meaning by com-
paring them with the result of our own movements, with

THE PERCEPTION OF SIGHT. 303

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 olject can afford, in
connection with the movements which he is constantly
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 case, I look out two points

304 RECEXT PROGEESS OP THE THEORY OF VISION.

in the diagram which correspond, and make them overlap
by a volmitary movement of the eyes. But as long as I
have not made out what kind of form the drawings are in-
tended to represent, I find that ray 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 impres-
sions 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
conception.

This last point is, I believe, of great importance.
The meaning 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 cor-
respondence between two processes takes place at any
moment that we choose, and under conditions 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 PEECEPTION OF SIGHT. 305

the laboratory. So long as science is not experimental
it does not teach us the knowledge of any new force.*

It is plain that, by the experience which we collect in
the way I have been describing, we are able to learn
as much of 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 pro-
duce changes in an object itself. Now, can we recognise
the movements of our hands and eyes as changes in the
relations of space, without knowing it beforehand ? and
can we distinguish them from other changes which affect
the properties of external objects ? I believe we can. It
is an essentially distinct character of the Eolations of
Space that they are changeable relations bettueen 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
retiral 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 con-
tain. The effect is that the impressions which had
before the local signs a,,, a^, a^, a^, receive the new local
signs 60, 61, 62? ^3 5 ^^d this may always occur in the same

* An interesting paper, applying this view of the 'experimental' cha-
racter of progressive science to Zoology, has been published by M. Lacaze
Duthiers, in the first number of his Archives de Zoologie. — Tb.

306 RECENT PROGRESS OF THE THEORY OF VISION.

way, whatever be the quality of the impressions. By
this means we learn to recognise such changes as be-
longing 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 dis-
cussion of the question, how much of universal concep-
tions of space is derived a prioH, and how much a
posteriori ? ^

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 transfer the notions
of external objects, which would be correct under normal
conditions, to cases in which unusual circumstances have
altered the retinal pictures. What I call ' observation
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 outline of the objects we are
looking at upon the centres of both retinse (the yellow
spot), and also move the eyes so as to obtain the surest
comparison between their various positions. When-
ever we deviate from these conditions of normal vision,
illusions are the result. Such are the long recognised
effects of the refraction or reflection of rays of light
before they enter the eye. But there are many other

* The question of the origin of our conceptions of space is discussed by
Mr. Bain on empirical principles in his treatise on The Se7iscs and tlie In-
tellect, pp. lU-118, 189-194, 245, 363-392, &c.— Tb.

THE PEECEPTION OF SIGHT. 807

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
eye-ball from external 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 luould, 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
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 examining whether they justify the
conclusion which we form. I have, therefore, named
these ' unconscious judgments ; ' and this term, though
accepted by other supporters of the empirical theory,
has excited much opposition, because, according to
generally-accepted psychological doctrines, 2, judgment,

308 BECENT PROGRESS OP THE THEORY OP VISION".

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 neces-
sary to deviate somewhat from the beaten patlis of psy-
chological 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 super-
ficial 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 sensf^ttions. Indeed, it is just the impossibility of
describing sensations, whether actual or remembered, in
words, which makes it so diflBcult to discuss this depart-
ment of psychology at all.

Beside 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 which are not capable of direct
verbal expression. For instance, when we say that we
' know ' ^ 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

' In German this kind of knowledge is expressed by the verb hnnen
(cognoacere, co?inailre), to be acquriinted with, while tvissen (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 conceptions which can be formally stated as propositions. — Tb.

THE PERCEPTION OF SIGHT. 309

cannot describe the impression in words, even to our-
selves. And yet it is certain that this kind of know-
ledge {Kennen) may attain the highest possible degree
of precision and certainty, and is so far not inferior
to any knowledge {Wissen) which can be expressed 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 pro-
ducing the man himself.

It is an important part of the former kind of know-
ledge to be acquainted with the particular innervation of
muscles, which is necessary in order to produce any eifect
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 after-
wards they will know so well as entirely to forget that
there was ever a time when they were ignorant of them.
For example, everyone 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 (kdnnen), or ' understanding '
how to do it {verstehen\ as, ' I know how to ride,' ' I am
able to ride,' or ' I understand how to ride.' ^

It is important to notice that this ' knowledge ' of the
effort of the will to be exerted must attain the highest
possible degree of certainty, accuracy, and precision, for
us to be able to maintain so artificial a balance as is
necessary for Avalking on stilts or for skating, for the singer
to know how to strike a note with his voice, or the

^ The German word konnen is said to be of the same etymology as
kcnmn, and so their likeness in form would be explained by their likeness
in meaning.

310 KECEXT PEOGRESS OF THE THEORY OF YISIOX.

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 peculiar 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
1 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 imiversal, as well as particular conclusions, maybe
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 expression it wears have usually or constantly a cer-
tain definite signification. And, to keep in the domain
of the perceptions of the senses, if I know that a par-
ticular 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 successful experience. 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

THE PERCEPTION OF SIGHT. 311

do so by looking as that major proposition states. This
perception of what I am doing is my 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 I am 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 per-
ceptions appear as inevitable as one of the forces of
nature, and hence their results seem to be directly ap-
prehended, 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 conclu-
sion forces itself upon us. Those conclusions which (it is

312 RECEXT PROGRESS OF THE THEORY OF VISION.

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 discussed in writings on aesthetics,
where they play an important part as Intuition, Uncon-
scious Eatiocination, Sensible Intelligibility, 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-
conscious fashion ; that they are, so to speak, mechanical
operations, and thus subordinate to conscious thought,
which can be expressed in language. I do not l)elieve
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 phe-
nomena {das Kennen) compete with the knowledge of
them which can be communicated by speech (das Wis-
sen) ; 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

THE PERCEPTION OF SIGHT. 313

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 develop-
ment, 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. ^ At any rate, the
child knows nothing of the meaning of the visual image
presented by its mother's breast. It often turns obsti-
nately 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 sub-
ject in order to throw light upon this question. As far
as the observations 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, im-
pulses or instincts are in him reduced to the smallest
possible number and strength.^

' See Darwin on the Expression of the Emotiovs, p. 47- — Tr.
* See on this subject Bain on the Senses and the Intellect, p. 293 ; also a
paper on 'Instinct' in Nature, Oct. 10, 1872.

314 RECENT PROGRESS OF THE THEORY OP VISIOIT.

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 liow 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 found 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
indestructible as that between Sensations and the Objects
which produce them. We cannot help thinking of the
usual signification of a word, even when it is used
exceptionably 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

THE FERCEPTION OF SIGHT. 315

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 distinc-
tions 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 in-
structive ; because they compel us to take the right road.
And even those physiologists who try to save fragments
of a pre-established harmony between sensations and
their objects, cannot but confess that the completion and
refinement 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 signi-
ficance which may still be conceded to any such anatomi-
cal arrangements is that they are possibly capable of
helping the first practice of our senses.

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 know-
ledge of the actual world — on ex'perience^ 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 accepting the
reality of this correspondence so far as these means of

816 RECENT PROGRESS OF THE THEORY OF VISION.

verification extend, which is really as far as for practical
purposes we need.

Beyond these limits, as, for example, in the region of
Qualities, we are in some instances able to prove con-
clusively 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 conceptions 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 5^et traces enough remain visible
to guide the philosophical spirit aright, in its search after
the meaning of sensible Images and Signs.

ON THE CONSEEVATION OF FOECE.

INTKODTJCTION TO A SERIES OF LECTURES DELIVERED AT
CARLSRUHE LN THE WINTER OP 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 thoee
sciences to the study of which I have devoted myself.
The natural sciences, partly in consequence of their
practical applications, and partly from their intellectual
influence on the last four centuries, have so profoundly,
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 enjoy-
ment of life, of the preservation of health, of means of
industrial and of social intercourse, and even such in-
crease 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 be 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
characteristic differences which exist between the natural
and the mental sciences as regards the kind of scientific
work. I then endeavoured to show that it is more

318 ox THE COXSERVATIOX OF FORCE.

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 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 completeness
that we can predict their future occurrence with the
gTeatest certainty; or in cases in which we have power
over the conditions under which they occur, we can
direct them just according 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 ques-
tion, can be accurately predicted and determined both
for the past and for futm-e years and centuries to a frac-
tion of a minute.

On this exact conformity with law depends also the
certainty with which we know how to tame the impetuous
force of steam, and to make it the obedient servant of our
wants. On this conformity depends, moreover, the intel-
lectual fascination which chains the physicist to his sub-
jects. It is an interest of quite a different kind to that

ON THE CONSERVATION OF FORCE. 319

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 us, even if there is no exact scientific connec-
tion among them. We continually find points of contact
and comparison in our own conceptions 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.

It is not to be denied that, in the natural sciences, this
kind of interest is wanting. Each individual fact, taken
of itself, can indeed arouse our curiosity or our astonish-
ment, 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 tliat 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 mathematics
included. And it is not only the pleasure at the success-
ful activity of one of our most essential mental powers ;
and the victorious 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,

320 ON THE CONSEEVATION OF FORCE.

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 described as the character
of tlie natural sciences, which I have chosen as the sub-
ject of this lecture.

This law is the Laiu of the Conservation of Force, a
term the meaning of which I must first explain. It is not
absolutely new ; for individual domains of natural pheno-
mena it was enunciated by Newton and Daniel Ber-
noulli ; and Eumford 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 Eobert Mayer, a Schwabian
pliysician (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 difficult experiments on the rela-
tion 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
luliich can be brought into action in the whole of Nature
is unchangeable, and can neither be increased nor di-
minished. JSlj 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 me-
chanical 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 compari-

ON THE CONSERVATION OF FORCE. 321

son 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 exeution does. But whatever of the actions of
intelligence is met with in the work of machines, of course
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.

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

322 ON THE CONSERVATION OF FORCE.

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 move-
ments of uniform into those of varying velocity, and so
forth. Hence this extraordinarily rich utility of ma-
chines 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 ivork 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, ' expen-
diture of force,' which indicates that the force applied
has been expended and lost, leads us to a further charac-
teristic analogy between 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 inor-
jjanic 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

ox THE CONSERVATION OF FORCE. 323

inorganic moving forces, when their capacity for work is
spent, there is a possibility of reproduction, 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 ex-
ample 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
continually 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
15

324 ON THE CONSEEVATION OF FORCE.

done, it has regained its former capacity, and can again
set the clock in motion.

We learn from this that a raised weight possesses a
TYioving force^ 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 men-
tioned. 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 weiglit
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 weiglit.

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 the second day the same

ON THE CONSERVATION OF FORCE. 325

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 increases 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 any rate,
in the present case. The application of this measure is,
in fact, not limited to the individual case, but the uni-
versal 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 ap-
plicable. 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 ex-
penditure of the next twenty-foiu: 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 slie does it abundantly with water,

> This is the technical measure of -work; to convert it into scientific
measure it must be multiplied by the intensity of gravity.

326

ON THE COXSERVATION OF FORCE.

which, being raised to the tops of mountains by meteoro-
logical 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 circumfer-
ence of such a wheel are a series of buckets, which act as

Fig. 38.

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
P', %vhere the mouth begins to incline downwards, it flows
out. The buckets on the circumference are filled on the

ON THE CONSERVATION OF FORCE. 327

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 con-
tinuously 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 tm'ns the wheel,
and furnishes the motive power. But you will at once see
that the mass of water which turns the wheel must neces-
sarily 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 position to drive the Avheel, 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 domes-
tic 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 introduced among the
Eomans 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,

328 ox THE CONSERVATION OF FORCE.

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 re-
stricted to a particular place, and only in mountainous
countries is it present in any quantity ; in level countries
extensive 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 trans-
fer the largest and heaviest chests from 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 as a motor, and thus acquire
motive power, without being compelled to use a corre-
sponding exertion in raising the weight ?

The answer to this is, that all these machines, in that
degree in which for the moment they facilitate the exer-
tion, 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 comparison,
let us suppose the same load hung to a block of four
pulleys, as represented in Fig. 39. A single labourer
would now be able to raise the load by the same exertion
of force as each one of the four put forth. But when he

ON THE CONSERVATION OF FORCE.

329

Fio. 39.

pulls the rope throiigli 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 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 exer-
tion of the arm, may be set in
motion. The weight of 100
pounds sinks, that of 400 rises.
Without any measurable expen-
diture 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 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

330 ON THE CONSERVATION OF FORCE.

is precisely 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 6,
and a weight of four pounds at a, the lever is then in equi-
librium, and the least pressure of the finger is sufficient,
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

Fig. 40.

through one inch, the lighter one has fallen through
four inches ; and 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 in-
stance as a series of levers, the ends of which are repre-
sented by the individual teeth, and one after the other of
which is put in activity, in the degree in which the
tooth in question seizes, or is seized by the adjacent
pinion. Take, for instance, the crabwinch, represented in
Fig. 41. Suppose the pinion on the axis of the barrel of

ON THE CONSERVATION OP FORCE.

831

the winch has twelve teeth, and the toothed-wheel, H H,
seventy-two teeth, that is six times as many as the
former. The winch must now be tm-ned 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

Fig. 41.

time, though to be sure only one-sixth of the exertion,
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 wlien the power increases tlie 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,

332

ON THE CONSERVATION OP FORCE.

what is called the undershot wheels 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 instancej on

Fig. 42.

the Ehine. In the immediate neighbourhood of such a
wheel, the water need not necessarily have a great fall if
it only strikes with considerable velocity. It is the velo-
city of tlie 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 Grermaiiy to supply the want of falling water,
aft'ord another instance of the action of velocity. The

ON THE CONSERVATION OF FORCE. 333

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 obstacles 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 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, f*'om the instances 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 constructed 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. The weight is thereby

334

ON THE COXSERYATION OF FORCE.

raised to the height A a. Hence my arm must oxert 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 savings be-

FiG. 43.

yond M towards 6, 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.

ON THE CONSERVATION OF FORCE. 335

You see here that the reason why the weight, when it
comes from a to M, and does not stop there, but ascends
to 6, in opposition to the action of gravity, is only to be
sought in its velocity. The velocity which it has ac-
quired in moving from the height A a is capable of again
^raising it to an equal height, B h. The velocity of the
moving mass, M, is thus capable of raising this mass ;
that is to say, in the language of mechanics, of performing
work. This would also be the case if we had imparted
such a velocity to the suspended weight by a blow.

From this we learn further how to measure the workin g
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.^ 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 6, 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 6 the vis
viva is changed into the work of a raised weight. Thus the
work which the arm originally imparted to the pendulum
is not lost in these oscillations, provided we may leave out
of consideration the influence of the resistance of the air

' 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 falling body.

336 ON THE CONSERVATION OF FORCE.

and of friction. Neither does it increase, but it continually
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 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
process I can place an elastic body in a state of tension
witliout having to exert my arm. This is possible and
is most easily observed in the case of gases.

If, for instance, I discharge a fire-arm loaded ^^ith
gunpowder, the greater part of the mass of the powder is
converted into gases at a very high temperature, which
have a powerful tendency 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,

ON THE CONSERVATION OF FORCE.

337

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 performed. Something, however, has been lost ;
the gunpowder, 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.

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

Fig. 44.

Regnault used for measuring the expansive force of heated
gases. If no great accuracy is required in the measure-

338 ox THE CONSERVATION OF FORCE.

ment, the apparatus may be arranged more simply. At
C is a glass globe filled with dry 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 r is closed. If the liquid is in
equilibrium in the tube ss 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 restored by allowing some of the
liquid to flow out at R, as the 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
up 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, w^hich 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 re-
presents 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, F'ig. 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

ON THE CONSERVATION OF FORCE.

Ficr. 45.

339

340 ON THE CONSERVATION OF FORCE.

Fig. 46.

Oy THE CONSERVATION OF FORCE. 341

steam passes under the piston, it forces it upward ; when
the piston has rear'-hed 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 tliis in motion. By means of the
rod s, the motion of the rod regulates the opening and
closing of the valve. But we need not here enter into
those mechanical arrangements, however 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 motive powers formerly
known, is that it is not restricted to a particular place.
Tlie store of coal and the small quantity of water
which are the sources of its power can be brought
everywhere, and steam engines can even be made mov-
able, as is the case with steam-ships and locomotives.
By means of these machines we can develope motive
power to almost an indefinii)e 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 locomotive
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 enormous progress. Steam-engines
traverse the ocean independently of the direction of the
wind, and, successfully resisting storms which would drive

342 01^ THE CONSERVATION OF FORCE.

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 in-
telligent 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 farce 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 en-
deavour 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 physicists designate
that view of Nature corresponding to the law of the
conservation of force with the name of the Mechanical
Theoi^ of Heat.

The older view of the nature of heat was that it is a
substance, very fine and imponderable indeed, but in-
destructible, 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 demonstrated by the thermometer
is unchangeable.

ON THE CONSERVATION OF FORCE. 343

By conduction and radiation, it can indeed pass from
hotter to colder bodies ; but the quantity of heat which
tlie 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 dis-
appeared— at any rate, as regards the thermometer. 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 boimd. But if the vapour be pre-
cipitated, and the liquid water restored to the state of
ic3, exactly the same amount of heat is liberated as had
become latent in the melting of the ice and in the
vaporisation 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 composi-
tion, 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 carbon into carbonic acid, is perfectly con-
stant, whether the combustion is slow or rapid, whether
it takes 'place all at once or by intermediate stages. This
also a^;reed 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

314 ON THE CONSERVATION OF FOECE.

which have here been briefly mentioned, were the subject
of extensive experimental and mathematical investiga-
tions, 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 hjrpothesis — that heat is a substance.
On the other hand, the invariability in the quantity of
heat in all these processes 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 Revolution, had indeed endeavoured to deduce the
work which heat performs, by assuming that the hypo-
thetical 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 car-
riage which is badly greased and where the friction is
great, becomes hot — so hot, indeed, that it niay take fire ;
machine-wheels with iron axles going at a great rate may
become so hot that they weld to their sockets. A power-
ful degree of friction is not, indeed, necessary to disen-
gage 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

ON THE CONSEKVATION OF FORCE. 345

the dry hands together to feel the heat produced by fric-
tion, and which is far greater than the heating which
takes place when the hands lie gently on each other.
Uncivilized 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.

Fig. 47.

So long as it was only a question of the friction of
solids, in which particles from the surface become de-
tached and compressed, it might be supposed that some
changes in structure of 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 struc-
ture, or of the liberation of latent heat. The first de-
cisive experiment of this kind was made by Sir Humphry
Davy in the commencement of the present century. In

346 ON THE CONSERVATION OF FORCE.

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 have here assimilated
could not have been conducted to it by the cold ice, or
Lave 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 wliich 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 mo-
tion of the terrestrial bodies, for they are always in con-
tact with other bodies which are at rest, and rub against
them. We can, indeed, very much diminish their fric-
tion, 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 seems 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 fric-

ON THE CONSERVATION OP FOECE. 347

tion on the path, caused by the very minute impacts
on its little roughnesses.

A pendulum which has been put in vibration can con-
tinue 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.

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 mechanical
work which this velocity could have effected.

If we review the result of all these instances, which
each of you could easily add to from your own daily ex-
perience, we shall see that friction and inelastic impact
are processes in which mechanical work is destroyed, and
heat produced in its place.

The experiments of Joule, which have been already
mentioned, 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 experiments show tliat
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 wcrk necessary for this is, according to
Joule's best experiments, equal to the work which a
16

348 ON THE CONSERVATION OP FOECE.

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 vertical 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 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 conditions that could be controlled
as perfectly as possible, permanent gases and not vapours
were used, although the latter are, in practice, more con-
venient 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

ON THE CONSERVATION OF FORCE. 349

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 iudividual 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
compression ; or, conversely, how much heat disappears
when they expand under a pressure equal to their own
counterpressure, and how much work they thereby effect in
overcoming this counterpressure, was partly known from
the older physical experiments, and has partly been de-
termined by the recent experiments of Eegnault by
extremely perfect methods. Calculations with the best
data of this kind give us the value of the thermal equiva-
lent from experiments : —

With atmospheric air 4260 metres.

„ oxygen 4257 „

„ 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 origi-
nated ; in a mechanical 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

350 ON THE CONSERVATIOX OF FORCE.

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 par-
ticles 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 tliis 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 re-
flected in another direction. A gas would thus be
analogous to a swarm of gnats, consisting, however, of
particles infinitely small and infinitely more closely
packed. This hypothesis, which has been developed by
Kronig, Clausius, and Maxwell, very well accounts for all
the phenomena of gases.

What appeared to the earlier physicists to be the con-
stant quantity of heat is nothing more than the whole
motive power of the motion of heat, which remains con-
stant 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

ON THE CONSERVATION OF FORCE. 351

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 knowm
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
produced 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.

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 in-
candescent. When it has afterwards imparted heat to the
vicinity, we have in the carbonic acid the entire quantity

352 ON THE COl^SERVATION" OF FORCE.

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 holding the atoms of
carbon and oxygen firmly united ; they can no longer
proiuce 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 car-
bonic 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, just as
we can restore the potentiality of a weight by raising it
from the ground ? It is indeed possible. We shall after-
wards 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. Hydrogen 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 combustion of the same weight of carbon. The
product of combustion is water, which, therefore, is not of
itself further combustible, for the hjdrogen in it is com-
pletely saturated with oxygen. The force of affinity,

ON THE CONSERVATION OF FORCE. 353

therefore, of bydrogen for oxygen, like that of carbon for
oxygen, performs work in combustion, which appeals 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 separated, 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

Fig. 48.

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'. 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

354

ON THE COXSERYATIOIS' OF FORCE.

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.

If I hold a glass flask filled with water over the hydro-
gen flame, the water, newly formed in combustion, con-
denses 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

Fig. 49.

almost infusible platinum might even be melted. The
hydrogen which has here been liberated from the water
by the electrical current has regained the capacity of
producing large quantities of heat by a fresh combination
with oxygen ; its affinity for oxygen has regained 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.

ON THE COXSERVATION OF FOHCE. 355

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 while clay, which contains dilute sulphuric acid;
in this dips a zinc cylinder. Each zinc cylinder is con-
nected by a metal ring with the carbon cylinder of the
next vessel, the last zinc cylinder n is connected with one
platinum plate, and the first carbon cylinder, p, with the
other platinum plate of the apparatus for the decomposi-
tion of water.

If now the conducting circuit of this galvanic appa-
ratus 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 sur-
rounding 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 tlie
galvanic battery zinc burns to sulphate of zinc at ilie 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

356

0^ THE COXSERVATIOX OF FORCE.

forces, through the instrumentality of the electrical cur-
rent. But we can attain the same object by mechanical

Fig. 50.

forces, if we produce the electrical current by a magneto-
electrical machine, Fig. 50. If we turn the handle, the
anker E E^, on which is coiled copper-wire, rotates in froDt

ON THE CONSERVATION OF FORCE. 357

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 b. If the ends of these wires are con-
nected with the apparatus for decomposing water we
obtain hydrogen and oxygen, though in far smaller quan-
tity than by the aid of the battery which we used before.
But this process is interesting, for the mechanical force
of the arm which turns the wheel produces the work which
is required for separating the combined chemical ele-
ments. Just as the steam-engine changes chemical into
mechanical force, the magneto-electrical machine trans-
forms 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, elec-
trical currents are produced 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 essential
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

35S

Oy THE COXSERVATIOX OF FORCE.

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 cuiTent. Conversely, by reversing
the magnetism in the iron core of the spirals b b, we
should obtain in them an electrical current just as we

Fig. 61.

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 magnetised in
one and sometimes in the other direction.

I will not accumulate examples of such relations;
in subsequent lectures we shall come across them. Let
us review these examples once more, and recognise in
them the law which is common to all.

ON THE CONSERVATION OF FORCE. 359

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 the operation. Chemical forces
can perform wc-rk, but they exhaust 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 knoiun natural forces that their capacity
for work is exhausted in the degree in which they actu-
ally perform work.

We have seen, further, that when a weight fell without
performing any work, it either acquired velocity or pro-
duced heat. We might also drive a magneto-electrical
machine by a falling weight ; it would then furnish elec-
trical 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 currents are produced by it. Heat can directly
separate chemical compounds ; thus, when we burn lime-
stone, 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

S60 ON THE CONSEHTATION OF FORCE.

capable of work. The connections 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 pro-
duce. By similar relations, the equivalent in work of the
other natural forces may be expressed in terms of mechani-
cal 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 dimi-
nished, but always remains in exactly the same quantity.
We shall subsequently see that the same law holds good
also for processes in organic nature, so far as the facts
have been tested.

It follows thence that the total quantity of all the forces
capable of work m the whole universe remains eternal
and unchanged 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.

ON THE CONSEHVATION OF FORCE. 361

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 per-
fectly general and particularly characteristic 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 experi-
ments have been made and an infinity of apparatus con-
structed— that is, the question of the possibility of a per-
petual motion. By this was understood 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 mathe-
matical mechanics which had at that time been developed.
But to show also that it is not possible even if heat,
chemical forces, electricity, and mag-netism were made to
co-operate, could not be done without a knowledge of
our law in all its generality. The possibility of a per-
petual motion was first finally negatived by the law of
the conservation of force, and this law might also be ex-

302 ox THE COXSERTATIOJf OF FOKCE.

pressed in the practical form that no perpetual motion is
possible, that force cannot be produced from nothing ;
something must be consumed.

You will only be ultimately able to estimate the im-
portance and the scope of our law when you have before
your eyes a series of its applications to individual processes
on 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 manufactories, 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 AM) PEOGEISS OF
PHYSICAL SCIENCE.

AN OPENING ADDRESS DELIVERED AT THE NATURFOESCHER
YERSAMMLUNG, IN INNSBRTJCK, 1869.

In accepting the honour you have done me in request-
ing 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 import 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

364 AIM AKD PROGEESS OF PHYSICAL SCIENCE.

department 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 philologian 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
majority of instances, most of our time and labour is con-
sumed by secondary matters that are but remotely con-
nected 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 influ-
ence ; while at other times we have to watch for the
moment when an organism presents itself under circum-
stances 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

AIM AND PROGRESS OF PHYSICAL SCIENCE. 365

he attained, consume far more time than is really re-
quired to make actual observations or experiments. How
much more ingenuity and thought are expended in
bringing a refractory piece of brass or glass into sub-
jection, than in sketching out the plan of the whole
investigation ! Each of you will have experienced such
impatience and over-excitement during work where all
the thoughts are directed on a narrow range of ques-
tions, the import of which to an outsider appears trifling
and contemptible because he does not see the end to which
the preparatory work tends. I believe I am correct in
thus describing the work and mental condition that pre-
cedes 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 com-
prehensive 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 bearing of the newly esta-
blished 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 investi-
gation.

The preliminary work is followed by other work, treat-
ing of other subjects. In the course of its different
stages, the observer will not deviate far from a direction
of more or less narrowed range. F'or it is not alone of
importance to him that he may have collected information
from books regarding the region to be explored. The
human memory is, on the whole, proportionately patient,
and can store up an almost incredibly large amount of
learning. In addition, however, to the knowledge which

366 AIM AND PROGRESS OF PHYSICAL SCIENCE.

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 experiment and long practice. His
senses must be sharpened for certain kinds of observation,
to detect minute differences of form, colour, solidity,
smell, &c., in the object under examination ; his hand
must be equally trained to the work of the blacksmith,
the locksmith, and the carpenter, or the draughtsman and
the violin-player, and, when operating with the micro-
scope, must surpass the lace-maker in delicacy of handling
the needle. Moreover, when he encounters superior de-
structive 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 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 in-
dividual worker is compelled to narrow the sphere of his
activity, so much the more will his intellectual desires
induce him not to sever his 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 uselessly 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 prioH for each particular investigation. Physical

AIM AND PROGRESS OF PHYSICAL SCIENCE. 367

science, it is true, has by the practical realisation of its
results transformed the entire life of modern humanity.
But, as a rule, these applications appear under circum-
stances when they are least expected ; to search in that
direction generally leads to nothing unless certain points
have already been definitely fixed, so that all that has to
be done is to remove certain obstacles in the way of prac-
tical 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, repeated, tentative experiment, hit
upon some new method advantageous 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 sub-
ject in question, an acquaintance that m each instance
had originally been acquired without any direct view to
possible use.

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 ama-
teur who finds in scientific pursuits relaxation from other
occupation. Here each of us hopes to meet with fresh
impulse and encouragement for his peculiar work ; the
man who lives in a small country place hopes to meet
with the recognition, otherwise unattaioable, 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 rejoice to find among us
a goodly proportion of members representing the culti-
vated classes of the nation ; we see influential statesmen
among us. They all have an interest in our labours ;
they look to us for further progress in civilisation, fui'ther

368 AIM AND PROGEESS OF PHYSICAL SCIENCE.

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 enquire into the
results of those labours. It appears to me, therefore,
appropriate to this occasion to take account of the pro-
gress of science as a whole, of the objects it aspires to,
and the magnitude 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 ap-
proximate completeness 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 occasion 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 Asso-
ciation reached 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 filled
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 ?

AIM AI!^D PROGRESS OF PHYSICAL SCIENCE. 369

To the uninitiated, this science of ours is an accumula-
tion of a vast number of facts, some of which are con-
spicuous 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 human mind, or the
desire for progressive mastery over the powers of nature.
For the former requires an intellectual grasp of the con-
nection 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 be-
come 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, cnly
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 conformity 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 m that it is
isolated, but because it 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

370 AIM AND PROGRESS OF PHYSICAL SCIENCE.

the specific heat of one small fragment 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 laiu by which they are regulated is to
understand 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 conception ' mammal ' all that is common
to the man, the ape, the dog, the lion, the hare, the horse,
the whale, &c., so we comprehend 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 boimdary of any two transparent media.

A law of nature, however, is not a mere logical con-
ception 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 propor-
tion 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 ob-
servation, does oui* 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

AIM AND PROGRESS OF PHYSICAL SCIENCE. 371

without exception^ and make this the test of its correct-
ness. If we can be assured that the conditions under
which the law operates have presented themselves, the
result 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 dif-
ferent 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 generalizations
from a number of well-established special laws. We must
endeavour to eliminate the incidents of form and dis-
tribution in space which masses under investigation may
present by trying to find from the phenomena attending
large visible masses laws for the operation 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 point of the mass — is it
especially clear that force is only the law of action ob-
jectively expressed. The force arising from the presence
of such and such bodies is equivalent to the acceleration
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
17

372 AIM AND PROGRESS OF PHYSICAL SCIENCE.

individual points occurs. Its actual signification may be
compared with the facts and tested by them. The ab-
stract 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 coir^jprehend 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 law in nature must be conceived as a causal connection
the moment we recognise that it is independent of our
thouo'ht 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 connection 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 mechanics, the fundamental conception of
which was first clearly propounded by Oalileo. 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 con-
ception 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 applica-

AIM AND PEOGEESS OF PHYSICAL SCIENCE. 373

tion 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 gravi-
tation, 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 investigation, partly
by its practical utility in navigation and geodesy, and
the many industrial and social interests arising from
them.

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 dis-
covering the elementary 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 meta-
physical 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, un-
alterable in their mass, unalterable also in their properties j

374 AIM AIST) PROGRESS OF PHYSICAL SCIEx^CE.

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 decomposition and combination, the number
and diversity of which the chemist with unwearied dili-
gence augments from year to year, the one law of the
i 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 pre-
vailing 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 experi-
ment that all matter is made up of the elements which
have been already isolated. These elements may exhibit
great differences as regards combination or mixture, the
mode of ao^orecration 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 sub-
stances are unchangeable in respect to their properties,
and only changeable as regards their combination and
tlieir 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.

AIM AND PKOGRESS OF PHYSICAL SCIENCE. 375

If, however, motion be the primordial change which
lies at the root of all the other changes occurring in the
world, every 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 merg'^ 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 realization 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 molecules, wliile physiology has scarcely made
a definite step in this direction.

This renders all the more important, therefore, a note-
worthy 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 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 application in the greater part of the then
known purely mechanical processes. Certain amplifica-

376 AIM AND PROGRESS OF PHYSICAL SCIENCE.

tions at times attracted attention, like those of Rumford,
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 con-
tradistinction to Galileo's conception of the intensity
of force, that a new mechanical idea was 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. 377

Machines, and the motive powers required for their
movement, furnish, in fact, the most familiar illustra-
tions 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 dependent 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 piston to and fro ; this is engendered by the
heat arising from the combustion of the coal in the tire-
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 through 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 ob-
served in the electro-magnetic machines of our telegraphs.

378 AIM AND PEOGRESS OF PHYSICAL SCIENCE.

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 consuTne something that
nature supplies to us. In the watermill we use a quantity
of water collected at an elevation, 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 incandescent,
magnetise iron^ &c.

Moreover, had we at our disposal a sufficient me-
chanical motive force we could lestore 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.

AIM AND PROGRESS OP PHYSICAL SCIENCE. 379

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 equiva-
lency are founded on Joule's measurements of the me-
chanical equivalent of heat. When, by the application
of heat, we set a .«5team-engine in motion, heat propor-
tional 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 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 gene-
rate 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 con-
nection which it establishes between the entire processes

380 AIM AND PHOGRESS OF PHYSICAL SCIEXCE.

of the universe, through all distances of place or time.
The universe appears, according to this law, to be en-
dowed 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 invisible
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 ten-
sion, or magnetic distribution. 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 tlie 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 prin-
ciples of which owe their origin to the mechanical theory

AIM AND PROGHESS OP PHYSICAL SCIENCE. 381

of heat) enables us to detect remains of this loosely-
distributed naatter in the nebulae ; 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 features. If the task of physical
science be to determine laws, a step of the most com-
prehensive 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 leading questions
of physiology, and it was for this reason that Dr. Mayer

382 AIM AND PROGRESS OF PHYSICAL SCIEXCE

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 pur-
pose 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 exception
prevails r More or less obscured by words, the view of
Paracelsus, Helmont, and Stahl, has been, and is at
present, held, particulaily outside Germany, that there
exists a soul of life {'' Lebensseele") directing the organic
processes which is endowed more or less with conscious-
ness 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 chemical
forces of matter itself; so that without this aid it could
accomplish 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 organic matter which brought about decomposi-
tion. In short, through all the different modes of ex-
pressing it, whether it was termed the Archaus, the
anima inscia, or the vital force and the restorative

AIM AND PROGRESS OF PHYSICAL SCIENCE. 383

'power of nature^ the faculty to build up the body accord-
ing 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 comparable 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 investigation, thus far, respecting the amoimt
of heat which an animal produces when at rest is in
no way at variance with the assumption that this heat
exactly corresponds to the equivalent, expressed 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

384 AIM AKB PROGRESS OF PHYSICAL SCIENCE.

require for the increase of the organic naatter of their
structures. 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 inter-
mission and without choice, and that their exact con-
formity to law never suffers a momenfs interruption.

Physiologists, then, must expect to meet with an un-
conditional conformity to law of the forces of nature
in their inquiries 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 nu-
merous 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 centuries.

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 descrip-
tive 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

AIM AND PROGHESS OP PHYSICAL SCIENCE. 385

of the vital processes with the actions of a principle
actino: like a soul. In the whole external world we know
of but one series of phenomena possessing similar
characteristics, we mean the actions and deeds of an
intelligent human being ; and we must allow that in
innumerable instances the organic adaptability appears to
be so extraordinarily superior to the capacities of the
human intelligence that we might feel disposed to ascribe
to it a higher rather than a lower character.

Before the time of Darwin only two theories respect-
ing organic adaptability were in vogue, both of which
pointed to the interference of free intelligence in the
course of natural processes. On the one hand it was
held, in accordance with the vitalistic theory, that the
vital processes were continuously directed by a living
soul ; or, 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 examina-
tion 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 result from a blind rule of a law
of natiu'e without any intervention of intelligence. I
allude to the law of transmission of individual pecu-
liarities from parent to offspring, a law long known
and recognised, and only needing a «iore precise defi-
nition. If both parents have individual peculiarities

386 AIM AXD PROGRESS OF PHYSICAL SCIENCE.

in common, the majority of their offspring also possess
them ; and if among the offspring there are some which
present these peculiarities 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 propa-
gate offspring, a greater and greater intensification 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 experience of artificial breeding is to
be regarded, from a scientific point of view, as an ex-
perimental confirmation of the law imder 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 tlie most different organs
of the body, in a vast number of instances.

After the general application of the law of trans-
mission had been established in this way, it only re-
mained 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 inaividuals
whicli are distinguished in the struggle for existence
by some advantageous quality, are the most likely to
produce offspring, and thus transmit to them their ad-
vantageous qualities. And in this way from generation
to generation 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 sub-
stantial variation from it is a disadvantage. It will
then remain unchanged so long as the external con-
ditions of its existence remain materially unaltered.
Such an ala^ost absolutely fixed condition appears to

AIM AND PROGRESS OF PHYSICAL SCIENCE. 387

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, con-
cerning the truth or probability of tlie 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 origi-
nal marsupial, or, again, all vertebrates from a primitive
lancelet, or all plants and animals together from the slimy
protoplasm of a protiston, 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 different,
has already been traced in regularly deposited geological
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 in-
terpretation 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

388 AIM AND PROGRESS OF PHYSICAL SCIENCE.

and floras of limited areas have, one and all, received
elucidation. Formerly natural affinity appeared to be a
mere enigmatical, and altogether groimdless similarity
of forms ; now it has become a matter for actual consan-
guinity. 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 palaeonto-
logical 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 esta-
blished definite ideas in the place of such a fanciful
hypothesis as, among the first, had occurred to Groethe,
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
gradual 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 an individual 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

AIM AND PEOGRESS OF PHYSICAL SCIENCE. 389

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 surrounding 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 us 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
something, 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, &c., 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 ; 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 basis 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

390 AIM AND PROGRESS OF PHYSICAL SCIENCE.

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 re-
sults 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, intensify-
ing 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. Ac-
cording 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

AIM AND PROGKESS OF PHYSICAL SCIENCE. 391

senses, are, then, in no way dependent on the nature of
the exciting agent, but only on that of the nerve appa-
ratus under operation.

The bearing of Miiller's law has been extended by
later research. It appears highly probable that even the
sensations of different colours and different pitch, as well
as qualitative pf^culiarities of luminous sensations inter se,
and of sonorous sensations 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 infinitely more
varied diversity of composite light is in this way refer-
able 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 compo-
site light may appear the same. In this case it has been
shown tliat no kind of physical similarity whatever corre-
sponds 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 sigiis of external
objects, and in no sense images of any degree of re-
semblance. 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 de-
picted makes its appearance, the conformity between
them being restricted to their presenting themselves
simultaneously ; and the correspondence existing between
our sensations and the objects producing them is pre-
cisely of this kind. They are signs which we have
learned to decipher, and a language given us with our

392 AIM AND PROGRESS OF PHYSICAL SCIENCE.

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 invention of the stereoscope
liave been of importance. All that 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 dimensions of the thino's around us. We
are sensible as well of the distance of objects not
too far removed from us as of their perspective juxta-
position, and compare the actual magnitude of two
objects of apparently unequal size at different distances
from us with greater certainty than the apparent equal
magnitudes 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 tlie sensations of nerve-fibres, dif-
ferently situated in space, certain differences, local signs,
attach themselves, the significations of which, as regards
space, we have to learn. That a knowledge of their
signification may be attained by these hypotheses, and
^^ith 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

ATM AND PROGRESS OF PHYSICAL SCIENCE. 393

tlie 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 im-
pulses of this kind is unnecessary, and renders difficult
instead of elucidating an interpretation of well-observed
phenomena in adults.*

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 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
succession in time. P'or 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.

' A further exposition of these conditions will be found in the lectures on
the Recent Progress of the Theory of Vision, pp. 197 et seq.

394 ALM Am) PROGRESS OF PHYSICAL SCIEXCE.

That which our organs of sense perform is clearly suffi-
cient 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 involun-
tarily 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 di-
rection 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 necessary conformity to law,
which means, as we have shown, the intelligibility of
vital phenomena, and this naturally extended itself to
the practical science directly dependent on physiology,
namely, medicine. Both have received an impetus, such
as had not been felt for thousands of years, from the time
that they seriously adopted the method of physical science,
the exact ob-ervation of phenomena and experiment. As
a practising physician, in my earlier days, I can per-
sonally 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 altogether untenable ; with these theories, however,
the facts on which they had actually been founded had

AIM .'^D PROGRESS OF PHYSICAL SCIENCE. 395

become so inextricably entangled that they also were
mostly thrown overboard. How a science should be built
wp 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 exaggerated 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 refined physiological study
of the nerves, soon led to practical results of the greatest
importance ; microscopic examination of parasitic struc-
tures, the stupendous development of pathological anatomy,
irresistibly led from nebulous theories to reality. We
found that we now possessed a much clearer means of
distinguishing, 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 con-
stitution of the eye enables us to apply physical modes of
investigation as well in functional as in anatomical
derangements of the living organ. Simple physical ex-
pedients, spectacles, sometimes spherical, sometimes cylin-
drical or prismatic, suffice, in many cases, to cure dis-
orders 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
18

396 AIM AND PROGRESS OF PHYSICAL SCIENCE.

till they induced incurable blindness, can now be
detected and remedied at the outset. From the very
reason of its presenting the most favourable ground for
the application of the scientific method, ophthalmology
has proved attractive to a peculiarly large number of
excellent investigators, and rapidly attained its present
position, in which it sets an example to the other depart-
ments 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 ad-
vancement, the recent progress of physiology and medi-
cine is pre-eminently due to Grermany. I have already
spoken of the obstacles which formerly delayed progress in
this direction. Questions respecting 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 approach-
ing 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 satis-
faction, not for external success, has at all times peculiarly
distinguished the scientific men of Germany.

AA'hat has, after all, determined the state of things
in the present instance is in my opinion another cir-
cumstance, 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 inves-
tigators 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.

AIM AND PROGRESS OF PHYSICAL SCIENCE. 397

Grermany 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 disadvantage that may here and there
attend a limited recognition of what is true. A labour-
loving, frugal, and moral people may exercise such bold-
ness, may stand face to face with truth ; it has nothing
to fear though hasty or partial theories be advocated,
even if they should appear to trench upon the founda-
tions of morality and society.

We have met here on the southern frontier of our
country. In science, however, we recognise no political
boundaries, 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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Prof. JOHN TYNDALL, LLD., F.H.S.

I.
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ON SOUND.

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IIL

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The Expression of the Emotions
in Man and Animals.

By CHARLES DARWIN, F. R. S., Author of the " Origin of Species," etc., etc.

"Whatever one thinks of Mr. Darwin's theory, it must be admitted that his great
powers of observation are as conspicuous as ever in this inquiry. During a space ot
more than thirty years, he has, with exemplary patience, been accumulating informa-
tion from all available sources. The result of all this is undoubtedly the collection of a
mass of minute and trustworthy information which must possess the highest value,
whatever may be the conclusions ultimately deduced from it." — London Times.

" It is almost needless to say that Mr. Darwin has brought to this work vast stores
of erudition, accumulated treasures of careful observation, and all the devices of an
acute and fertile ingenuity; for these are qualities which are conspicuous in all he
writes. But it may be as well to add that the book is verj- attractive even to general
readers. It is comparatively light and easy reading, full of amusing anecdote ; and the
illustrations, whether due to the sun's rays or to the engraver's point, are excellent." —
Guardian.

" Those of our readers who know the charm of Darwin's former works, how he
leads his readers on to his conclusions in the clearest and most attractive English, will
experience more than their usual treat when they sit down to this book. Never was
more truly realized the saying about men laboring and others entering into the fruit of
their labors. The illustrations are excellent, and recourse has been had to photographs
in rendering the more telling of the physiognomical expressions. Even the most an-
tagonistic of anti-Darwinians will not hesitate to admit how much he has learned from
a careful study of the work before us." — Science Gossip.

RECENTLY PUBLISHED.

A NEW EDITION OF

Darwin's Origin of Species.

FROM THE SIXTH AND LAST ENGLISH EDITION,
Containing the Author'' s Latest Corrections and Additions,

From an entirely new set of stereotype plates. i2mo. Cloth. Price, $2.00.

D. APPLETON & CO., PubUshers.

An Important Work for Manufacturers, Chemists, and Students.

A HAND-BOOK

Chemical Technology.

By Rudolph Wagner, Ph. D.,

PROFESSOR OF CHEMICAL TECHNOLOGY AT THE UNIVERSITY OF WURTZBURG.

Translated and edited, from the eighth German edition, with extensive
Additions,

By Wm. Crookes, F. R. S.

With -^-^^ Illustrations. ivol.,2,vo. "jti pages. CZotA, $5.00.

The several editions of Professor Rudolph Wagner's *' Handbuch der

Chemise hen Technologies^ have succeeded each other so

rapidly, that no apology is needed in offering

a translation to the public.

Under the head of Metallurgic Chemistry, the latest methods of preparing Iron,
Cobalt, Nickel, Copper, Copper Salts, Lead and Tin and their Salts, Bismuth, Zinc,
Zinc Salts, Cadmium, Antimony, Arsenic, Mercury, Platinum, Silver, Gold, Man-
ganates, Aluminum, and Magnesium, are described. The various applicat'ons of the
Voltaic Current to Electro-Metallurgy follow under this division. The Preparation of
Potash and Soda Salts, the Manufacture of Sulphuric Acid, and the Recovery of Sul-
phur from Soda- Waste, of course occupy prominent places in the consideration of
chemical manufactures. It is difficult to over-estimate the mercantile value of Mond's
process, as well as the many new and important applications of Bisulphide of Carbon.
The manufacture of Soap will be found to include much detail. The Technology of
Glass, Stoneware, Limes and Mortars, will present much of interest to the Builder and
Engineer. The Technology of Vegetable Fibres has been considered to include the
preparation of Flax, Hemp, Cotton, as well as Paper-making; while the applications
of Vegetable Products will be found to include Sugar-boiling, Wine and Beer Brewing,
the Distillation of Spirits, the Baking of Bread, the Preparation of Vinegar, the Preser-
vation of Wood, etc.

Dr. Wagner gives much information in reference to the production of Potash from
Sugar-residues. The use of Baryta Salts is also fully described, as well as the prepa-
ration of Sugar from Beetroots. Tanning, the Preservation of Meat, Milk, etc., the
Preparation of Phosphorus and Animal Charcoal, are considered as belonging to the
Technology of Animal Products. The Preparation of the Materials for Dyeing has
necessarily required much space ; while the final sections of the book have been de-
voted to the Technology of Heating and Illumination.

D. APPLETON & CO., Publishers.

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