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Thb Science of Mechanics. A Historical and Crit- 
ical Exposition of its Principles. Translated from 
the Second German Edition by T. J. McCormack. 
250 Cuts. 534 Pages. Half Morocco, Gilt Top. 
Price, $2.50. 

Popular Scientific Lectures. Translated by T. 
}. McCormack. 313 Pages. 44 Cuts. Cloth, 
$1.00 ; Paper, 35 cents. 

Contributions to the Analysis of the Sensations. 
With new additions by the author. Translated 
by C. M. Williams. Pages, 208. 37 Cuts. Price, 
f 1.25, net. 





















Translation and original matter copyrighted, 1890, 1893, and 1897 by 

The Open Coart Publishing Co. 

FOR the preparation of the present excellenE transladoa of 
my BdtrSge zur Analyst der Empfindungen I am under 
profound obligations to The Open Court Publishing Companf 
Not a little of the progress of psychology is owing to the strenuous 
efiorts which the promoters of (he science have made to find the 
main explaaaiion of its problems in the principle of association 
and these investigations have received a fresh impulse from the 
results of neural anatomy and neural physiology. 1 am of opinion 
however, that the idea advanced in the present work, agreeably to 
which as many physico-chemical neural processes are to be aS' 
snmed as there are distinguishable qualities of sensation, is also 
paasessed of heuristic value, and that there is reasonable hope that 
SI some future lime it, too, will receive elucidation from the si()a' 
of physiological chemistry. Admittedly, this idea, which is but a 
coiwistent, monistic conception of Multer's principle of the specific 
energies, is not in accord with prevailing notions. By the example 
and influence of a great authority it has become the custijm to rel- 
egate the explanation of differtnt qualities of sensation to unknown 
domains, and to regard all neural processes as absolutely alike 
qualitatively and only quantitatively different. I had occasion as 
early as 1863 (Varlfsungtn iiber PsychofJiysik, Vienna, Sommer, 
p. 33) to point out how little such a conception is calculated to lead 
to a profonnder knowledge of our sensations, and how little justifi- 
able it is, even from a physical point of view, to regard all electric 





neural currents as physical processes qualitatively the same in 
kind. One has only to think of a current through copper, through 
sulphate of copper, or through acidulated water. A few inquirers 
only, like Hering, still uphold Muller's doctrine in its original sig- 
nification, and under these circumstances the opportunity of pre- 
senting my thoughts to a new public is doubly valuable. 

£. Mach. 
Vienna, September, 1896. 


THE frequent excursioDS which 1 have made into Ibis province 
have all sprung from the profound conviction that the foun- 
dations of science as a whole, and of physics in particular, await 
their next greatest elucidations from the side of biology, and eapa- 
cially from the analysis of the sensations. 

I am aware, of course, ihat I can contribute but liltle to the 
attainment of this end. The very fact that my invest iga (ions have 
been carried on, not in the way of a profession, but only at odd 
moments, and frequently only after long interruptions, must de- 
tract considerably from the value of my scattered publications, or 
perhaps even lay me open to the secret charge of desultoriness 
So much the more, therefore, am I under especial obligations to 
those investigators, such as E, Hering, V. Hensen, W. Preycr 
and others, who have directed attention either to the mailer of my 
■writings or lo their methodological o 
The present compendious 
i, perhaps, will place 
favorable light, for it will be s 
raiud the lamr probUm, no ma 
the single facts investigated. 
:o the title of physiologist, a 

I supplementary presentation of 

attitude in a somewhat more 

thai in all cases I have bad in 

r how varied or numerous were 

Although I can lay no claim what- 

].nd still less lo that of philosopher, 

yet I venture to hope that the work thus undertaken, purely from 

a strong; desire for self enlightenment, by a physicist unconstrained 

by the conventional barriers of the specialist, may not be entirely 


without valne for others also, even thongh I may not be every^ 
where in the right. 

My natural bent for the study of these questions received its 
strongest stimulus from Fechner's Elemente der Psychophysik 
(Leipsic, i860), but my greatest assistance was derived from 
Hering's solution of the two problems referred to in the footnote 
of page 35 and in the text of page 81. 

To readers who, for any reason, desire to avoid more general 
discussions, t recommend the omission of the first and last chap- 
ters. For me, however, the conception of the whole and the con- 
ception of the parts are so intimately related that I should scarcely 
be able to separate them. 

The Author. 

Prague, November, 1885. 


THE MATTER conlained in 
tioned to its siza. If this 

book is by do means propor- 
vere so, the foHowing treatise, 
rich as it is in saggeslioQS bearitig on some of the fundamental 
problems of scientific and philosophical theory, must be a bulk}' 
one. The author has not, however, entered into any detailed ap- 
plication of the conclusions drawn from his observations and expe- 
riments, but has contented himself with a succinct exposition o( 
those conclusions, leaving to the reader the very pleasurable task 
of following out (he many trains of thought opened np by tbem 
The German edition of the book has been the subject of great in- 
terest and discussion. To the English text the author has added 
considerable new matter in the notes on pages 4, 20, zi, 26, 39, 
40. 56, 78, 82-83, 115. and in the two Appendices. 

The manuscript and proofs of this edition have had the advan- 
tage of revisal by Mr, T. J. McCormack, of La Salle, Illinois 
translator of the author's Science of Mtchanics. who also 1 
pendently rendered the "Introductory Remarks" and Appendii I. 
— matter which originally appeared in The Afonisl, 


Boston, December, 1896. 



Introductory Remarks. Antimetaphysical i 

The Chief Points of View for the Investigation of the Senses. 27 

The Space-Sensations of the Eye 41 

Investigation of Space-Sensation Continued 57 

The Sight-Sensations. — ^Their Relations to One Another and 

to Other Psychical Elements 82 

Time-Sensation 109 

Sensations of Tone 119 

PhysicsT — Influence of the Preceding Investigations on the 

Mode of its Conception 151 

Appendix I. — Facts and Mental Symbols 185 

Appendix II. — "A New Acoustic Experiment by E. Mach " . 197 

Addenda 200 




T^HE splendid success achieved by physical scicDce 

1-*- in modern times, a success which is not restricted 
to its own sphere but embraces that of other sciences 
which employ its help, has brought it about that phys- 
ical ways of thinking and physical modes of procedure 
enjoy on all hands unwonted prominence, and that the 
greatest expectations are associated with their employ- 
ment. In keeping with this drift of modern inquiry, 
the physiology of the senses, gradually leaving the 
paths which were opened by men like Goethe, Scho- 
penhauer, and others, but with particular success by 
Johannes MuUer, has also assumed an almost exclu- 
sively physical character. This tendency must appear 
to us as not exactly the proper one, when we reflect that 
physics despite its considerable development never- 
theless constitutes but a portion of a larger collective 
body of knowledge, and that it is unable, with its lim- 
ited intellectual implements, created for limited and 
special purposes, to exhaust all the subject-matter 


of science. Without renouncing the support of phys- 
ics, it is possible for the physiology of the senses, not 
only to pursue its own course of development, but also 
to afford to physical science itself powerful assistance ; 
a point which the following simple considerations will 
serve to illustrate. 

Colors, sounds, temperatures, pressures, spaces, 
times, and so forth, are connected with one another in 
manifold ways ; and with them are associated moods of 
mind, feelings, and volitions. Out of this fabric, that 
which is relatively more fixed and permanent stands 
prominently forth, engraves itself in the memory, and 
expresses itself in language. Relatively greater per- 
manency exhibit, first, certain complexes of colors, 
sounds, pressures, and so forth, connected in time and 
space, which therefore receive special names, and are 
designated bodies. Absolutely permanent such com- 
plexes are not. 

My table is now brightly, now dimly lighted. Its 
temperature varies. It may receive an ink stain. One 
of its legs may be broken. It may be repaired, polished, 
and replaced part for part. But for me, amid all its 
changes, it remains the table at which I daily write. 

My friend may put on a different coat. His counte- 
nance may assume a serious or a cheerful expression. 
His complexion, under the effects of light or emotion, 
may change. His shape may be altered by motion, 


or be definitely changed. Yet the number of the per- 
manent features presented, compared with the number 
of the gradual alterations, is always so great, that the 
latter may be overlooked. It is the same friend with 
whom I take my daily walk. 

My coat may receive a stain, a tear. My very man- 
ner of expression shows that we are concerned here 
with a sum-total of permanency, to which the new ele- 
ment is added and from which that which is lacking is 
subsequently taken away. 

Our greater intimacy with this sum-total of per- 
manency, and its preponderance as contrasted with 
the changeable, impel us to the partly instinctive, 
partly voluntary and conscious economy of mental rep- 
resentation and designation, as expressed in ordinary 
thought and speech. That which is perceptually repre- 
sented in a single image receives a single designation, 
a single name. 

As relatively permanent, is exhibited, further, that 
complex of memories, moods, and feelings, joined to 
a particular body (the human body), which is denom- 
inated the"I" or "Ego." I may be engaged upon 
this or that subject, I may be quiet or animated, ex- 
cited or ill-humored. Yet, pathological cases apart, 
enough durable features remain to identify the ego. 
Of course, the ego also is only of relative permanency.^ 


After a first survey has been obtained, by the form- I 
ation of the substance-concepts "body " and "ego" 
(matter and soul), the will is impelled to a more exact 
examination of the changes that take place in these 
relatively permanent existences. The changeable fea- 
tures of bodies and of the ego, in fact, are exactly what 1 
moves the will to this examination. Here the com- 
ponent parts of the complex are first exhibited as its J 

disllnct, doDbled, or eslirely wanting), and the little habits that are 

roGle of a face (bat 


served o 


n the 

est hn 

man b 

inl. howBve 

, there ate ihd 



.her h 

( nor other 

need regret. 



death, vi 

Iit7. may even 


t tboughl 




lines. Ribof 






, Pari., 1888 

chicBBo. teas. 

priacipal rOle in piesecving the cD 

of the eg 

aeral s 

t. Ge 

nerally, I am 

in perlecl ai:co 









properties. A fruit is sweetj but it can also be bitter. 
Also, other fruits may be sweet. The red color we are 
seeking is found in many bodies. The neighborhood 
of some bodies is pleasant ; that of others, unpleasant. 
Thus, gradually, different complexes are found to be 
made up of common elements. The visible, the aud- 
ible, the tangible, are separated from bodies. The 
visible is analysed into colors and into form. In the 
manifoldness of the colors, again, though here fewer 
in number, other component parts are discerned — 
such as the primary colors, and so forth. The com- 
plexes are disintegrated into elements. 

The useful habit of designating such relatively per- 
manent compounds by j/«^/rf names, and of apprehend- 
ing them by single thoughts, without going to the 
trouble each time of an analysis of their component 
parts, is apt to come into strange conflict with the 
tendency to isolate the component parts. The vague 
image which we have of a given permanent complex, 
being an image which does not perceptibly change 
when one or another of the component parts is taken 
away, gradually establishes itself as something which 
exists by itself. Inasmuch as it is possible to take 
away singly every constituent part without destroying 
the capacity of the image to stand for the totality and 
of being recognised again, it is imagined that it is pos- 

sible to subtract all the parts and to have something 
still remaining. Thus arises the monstrous notion of 
a thing in itself, unknowable and different from its • 
"phenomenal" existence. 

Thing, body, matter, are nothing apart from their 
complexes of colors, sounds, and so forth — nothing 
apart from their so-called attributes. That Protean, 
supposititious problem, which springs up so much in 
philosophy, of a single thing with many attributes, 
arises wholly from a mistaking of the fact, that sum- 
mary comprehension and precise analysis, although 
both are provisionally justifiable and for many pur- 
poses profitable, cannot and must not be carried on 
simultaneously. A body is one and unchangeable only 
so long as it is unnecessary to consider its details. 
Thus both the earth and a billiard-ball are spheres, if 
the purpose in hand permits our neglecting deviations 
from the spherical form, and great precision is not 
necessary. But when we are obliged to carry on in- 
vestigations in orography or microscopy, both bodies 
cease to be spheres. 

Man possesses, in its highest form, the power of 
consciously and arbitrarily determining his point of 
view. He can at one time disregard the most salient 
features of an object, and immediately thereafter give 
attention to its smallest detailsj now consider a sta* 
tionary current, without a thought of its contents, and 


: the width of a Fraunhofer line in the 
spectrum ; he can rise at will to the most general ab- 
stractions or bury himself ia the minutest particulars. 
The animal possesses this capacity in a far less degree. 
It does not assume a point of view, but is usually 
forced to it. The babe who does not know its father 
with his hat on, the dog that is perplexed at the new 
coat of its master, have both succumbed in this conflict 
of points of view. Who has not been worsted in similar 
plights? Even the man of philosophy at times suc- 
cumbs, as the grotesque problem, above referred to, 

In this last case, the circumstances appear to fur- 
nish a real ground of justification. Colors, sounds, 
and the odors of bodies are evanescent. But the tan- 
gible part, as a sort of constant, durable nucleus, not 
readily susceptible of annihilation, remains behind ; 
appearing as the vehicle of the more fugitive proper- 
ties annexed to it. Habit, thus, keeps our thought 
firmly attached to this central nucleus, even where the 
knowledge exists that seeing, hearing, smelling, and 
touching are intimately akin in character. A further 
consideration is, that owing to the singularly extensive 
development of mechanical physics a kind of higher 
reality is ascribed to space and time than to colors, 
sounds, and odors; agreeably to which, the temporal 
and spatial links of colors, sounds, and odors appear 
to be more real than the colors, sounds, and odors 
themselves. The physiology of the senses, however. 


demonstrates, that spaces aad times may just as ap- 
propriately be called sensations as colors and sounds. 

The ego, and the relation of bodies to the ego, give 
rise to similar pseu do -problems, the character of which 
may be briefly indicated as follows : 

Let those complexes of colors, sounds, and 
forth, commonly called bodies, be designated, for the 
sake of simplicity, hy ABC. . . ; the complex, known 
asourownbody, which constitutes a part of the former, 
may be called K LM . . - ; the complex composed o£ , 
volitions, memory-images, and the rest, we shall repre- 
sent hy a fiy. . . Usually, now, the complex a0y. . . 
KLM. ... as malting up the ego, is opposed to the 
complex ABC. . ., as making up the world of sub- 
stance; sometimes, also, apy. . . is viewed as ego, 
and KLM. . ABC. . . as world of substance. Now, 
at first blush, AB C . . . appears independent of the \ 
ego, and opposed to it as a separate existence. But 
this independence is only relative, and gives way upon 
closer inspection. Much, it is true, may change in the 
complex afiy . . . without a perceptible change being 
induced inABC. . . ; and viW versa. But many changes 
in afly... do pass, by way of changes in KLM. . ., 
to A BC. . .; and vue versa. (As, for example, when 
powerful ideas burst forth into acts, or our environ- 
ment induces noticeable changes in our body.) At the 
same time the group KLM. . . appears to be more 


intimately connected with a 0y . . . and vi'ith AS C. . ., 
than the latter do with one another; relations which 
find their expression in common thought and speech. 

Precisely viewed, however, it appears that the group 
ABC... is always codetermined by K L M. A cube 
of wood when seen close at hand, looks large ; when 
seen at a distance, small; it looks different with the 
right eye from what it does with the left ; sometimes 
it appears double ; with closed eyes it is invisible. 
The properties of the same body, therefore, appear 
modified by our own body; they appear conditioned 
by it. But where, now, is that same body, which to 
the appearance is so different ? All that can be said 
is, that with different KLM different ABC... are 

We see an object having a point S. If we touch 
S, that is, bring it into connexion with our body, we 
receive a prick. We can see S, without feeling the 
prick. But as soon as we feel the prick we find S. 
The visible point, therefore, is a permanent fact or »«- 


\rifl/^r Fs^hia, 

ii. Leipsic and 



ckus, to which the prick is annexed, according to cir- 
cumstances, as something accidental. From the fre- 
quency of such occurrences we ultimately accustom 
ourselves to regard all properties of bodies as "effects" 
proceeding from permanent nuclei and conveyed to 
the ego through the medium of the body ; which effects 
we call sensations. By this operation, however, our 
imagined nuclei are deprived of their entire sensory 
contents, and converted into mere mental symbols. 
The assertion, then, is correct that the world consists 
only of our sensations. In which case we have knowl- 
edge only of sensations, and the assumption of the nu- 
clei referred to, or of a reciprocal action between them, 
from which sensations proceed, turns out to be quite 
idle and superfluous. Such a view can only suit with 
a half-hearted realism or a half-hearted philosophical 

Ordinarily the complex a^y . . . KLM . . . is con- I 
trastedasegowith theconnplex^^C Those elements ' 
only oiABC... that more strongly alter a^y.. ., as 
a prick, a pain, are wont to be comprised in the ego. 
Afterwards, however, through observations of the kind 
just referred to, it appears that the right to annex 
ABC... to the ego nowhere ceases. In conformity 
with this view the ego can be so extended as ultimately 
to embrace the entire world. ^ The ego is not sharply 

iWhen I say Ihat Ihe table. Ihe Ir*e, and sa tarlh, are my sensations, 


marked oH, its limits are very indefinite and arbitrarily 
displaceabte. Only by failing to observe this fact, and 
by unconsciously narrowing those limits, while at the 
same time we enlarge them, arise, in the conflict of 
points of view, the metaphysical difficulties met with in 
this connexion. 

As soon as we have perceived that the supposed 
unities "body " and "ego" are only makeshifts, de- 
signed for provisional survey and for certain practical 
ends (so that we may take hold of bodies, protect our- 
selves against pain, and so forth), we find ourselves 
obliged, in many profound scientific investigations, to 
abandon them as insufficient and inappropriate. The 
antithesis of ego and world, sensation (phenomenon) 
and thing, then vanishes, and we have simply to deal 
with the connexion of the elements afiy... ABC . 
K LM . - ., of which this antithesis was only a partially 
appropriate and imperfect expression. This connex- 
ion is nothing more nor less than the combination of 
the above-mentioned elements with other similar ele- 
ments (time and space). Science has simply to accept 
this connexion, and to set itself aright (get its bear- 
ings) in the intellectual environment which is thereby 
furnished, without attempting to explain its existence. 

InTolTBS B res! ulenston at my ega. On Ibe etnalloDsl Bids iJso snch eilen- 


ian who is Attliy ^^^ 

intheothecband ^^^M 
A wall ^^H 


On a superficial examination the complex apy.. . 
appears to be made up of much more evanescent ele- 
ments than ARC... and K LM . . . in which last the 
flcnicnts seem to be connected with greater stability 
and in a more permanent manner (being joined to solid 
nucloi as it were). Although on closer inspection the 
elements of all complexes prove to be homogeneous, yet 
in spite of the knowledge of this fact, the early notion 
of an antithesis of body and spirit easily regains the 
ascendancy in the mind. The philosophical spiritualist 
is often sensible of the difficulty of imparting the needed 
solidity to his mind-created world of bodies ; the ma- 
terialist is at a loss when required to endow the world 
of matter with sensation. The monistic point of view, 
which artificial reflexion has evolved, is easily clouded 
by our older and more powerful instinctive notions. 

The difficulty referred to is particularly felt in the ' 
following case. In the complex ABC. . ., which i 
hiiT« called the world of matter, we find as parts, not 
only our own body JTZ J/". . ., hut also the bodies of 
other persons (oc animals-) K'L'.V. . ., K~L~M~. . 
to whkh, by analogy. w« imagine otb^' a'0'y' . . 
«r'*/t''f "■ - ■• annexed, stmtiartoa/f }'. . . So tongas I 
we deal with ITL 'M'. • .. we find oanelves in a di 
oc^faly familiar province at every point aenso oa l^ " 
•ceessible to ns. When, bovever. we inqoiie aftei 
tke seasktioos or feeUngs appurtenant to the body 


K' L' M' . . ., we no longer find the elements we seek 
in the province of sense : we adii them in thought. Not 
only is the domain which we now enter far less familiar 
to us, but the transition into it is also relatively un- 
safe. We have the feeling as if we were plunging into 
an abyss. ^ Persons who adopt this method only, will 
never thoroughly rid themselves of this sense of inse- 
curity, which is a frequent source of illusive problems. 
But we are not restricted to this course. Let us 
consider, first, the reciprocal relations of the elements 
of the complex ^j9C. . ., without regarding .^Z J/. . . 
(our body). All pliysjcai investigations are of this 
sort. A white bullet falls upon a bell ; a sound is 
heard. The bullet turns yellow before a sodium lamp, 
red before a lithium lamp. Here the elements (v4.5C . .) 
appear to be connected only with one another and to be 
independent of our body {KI.M. . .). But if we take 
santonine, the bullet again turns yellow. If we press 
one eye to the side, we see two bullets. If we close 
our eyes entirely, we see none at all. If we sever the 

tboughf o[ anolher way of dEacenl never t 

iCdutied to me. 

1 remarked the 

hoy of my own, wbile walking on Iha walls 

eeall this feeling 

every time I occupy myselE wllb the reflexli 

nd I frankly con- 

feu that tbis BccidentBl ei^erienee or mi 

ne helped It. co 

nfiroi my opinion 

npon Ihia point, which I havo now long held 

. Thehahiiofp 

.Distiiiig the same 

methodB in DiBlerial and psychical queslLons 

ctmrvBy. A child, on the piercing oE the 

wall of a hou! 

ifl in which ilhaa 

long dwelt, may eipticience a ferltable enl 

world-view, and 

In the SUDS >nanDeiasUglil scienlific hint 

may ollen atton 

Igieal enlighten- 


auditory nerve, no sound is heard. The elements 
ABC. . ., therefore, are not only connected among 
one another, but also with KLM. To this extent, 
and to this extent only, do we call ABC . . . sensations, 
and regard A B C as belonging to the ego. In this way, 
accordingly, we do not find the gap between bodies 
and sensations above described, between what is with- 
out and what is within, between the material world 
and the spiritual world. ^ All elements ABC..., 
KLM. . . constitute a single coherent mass only, in 
which, when any one elennent is disturbed, all is put 
in motion ; except that a disturbance in KLM. . . has 
a more extensive and profound action than in ABC. 
A magnet in our neighborhood disturbs the particles 
of iron near it; a falling boulder shakes the earth; 
but the severing of a nerve sets in motion the luhoh 
system of elements.' 

That traditional gulf between physical and psycho- 
logical research, accordingly, exists only for the habit- 
ual stereotyped method of observation. A color is a 
physical object so long as we consider its dependence 
upon its luminous source, upon other colors, upon 
heat, upon space, and so forth. Regarding, however, its 
dependence upon the retina (the elements KLM. . ,), 


mraoDUCTOJiY xsstAS^s. 

it becomes a psychological object, a sensation. Not 
the subject, but the direction of our investigation, is 
different in the two domains. 

Both in reasoning from the observation of the 
bodies of other men or animals, to the sensations which 
they possess, as well as in investigating the influence 
of our own body upon our own sensations, we must 
complete observed facts by analogy. This is accom- 
plished with much greater readiness and certainty, 
when it relates, say, only to nervous processes, which 
cannot be fully observed in our own bodies — that is, 
when it is carried out in the more familiar physical 
domain — than when it is made in connexion with psy- 
chical processes. Otherwise there is no essential dif- 

The considerations advanced will gain in strength 
and vividness by a concrete example. Thus, I lie 
upon my sofa. If I close my right eye, the picture 
represented in the accompanying cut is presented to 
my left eye. In a frame formed by the ridge of my 
eyebrow, by my nose, and by my moustache, appears 
a part of my body, so far as visible, with its environ- 
ment.^ My body differs from other human bodies — 
beyond the fact that every intense motor idea is imme- 
diately expressed by a movement of it, and that its 


vided B, to use the apposite expression of a friend' of 
mine made upon seeing this drawing, passes through 
my skin. Reflexions hke that for the field of vision 
maybe made with regard to the province of touch and 
the perceptual domains of the other senses. 

Reference has already been made to the different 
chaiacter of the groups of elements designated by 
ABC. . . and a (iy. As a matter of fact, when we 
see a green tree before us, or remember a green tree, 
that is, represent a green tree to ourselves, we are per- 
fectly aware of the difference of the two cases. The 
represented tree has a much less determinate, a much 
more changeable form ; its green is much paler and 
more evanescent ; and, what is of especial note, it is 
plainly situate in a differeni domain. A movement 
that vie propose to execute is never more than a repre- 
sented movement, and appears in a different sphere 
from that of the executed movement, which always 
takes place when the image is vivid enough, The state- 
ment that the elements A and « appear in different 
spheres, means, if we go to the bottom of it, simply 
this, that these elements are united with different other 
elements. Thus far, therefore, the fundamental consti- 
tuents of ABC..., a0y... would seem to be the 
same (colors, sounds, spaces, times, motor sensations 


er o£ Vie; 


. . .), and only the character of their connexion differ- 
ent. I 
Ordinarily pleasure and pain are regarded as dif- I 
ferent from sensations. Yet not only tactile sensa- 
tions, but all other kinds of sensations, may pass 
gradually into pleasure and pain. Pleasure and pai 
also may be justly termed sensations. Only tliey are 
not so well analysed and so familiar as the common 
sensations. In fact, sensations of pleasure and pain, 
however faint they may be, really make up the con- 
tents of all so-called emotions. Thus, perceptions, 
ideas, volition, and emotion, in short the whole inner 
and outer world, are composed of a sinall number of 
homogeneous elements connected in relations of vary- 
ing evanescence or permanence. Usually, these ele- 
ments are called sensations. But as vestiges of a one- 
sided theory inhere in that term, we prefer to speak 
simply of elements, as we have already done. The aim 
of all research is to ascertain the mode of connexion 
of these elements.^ 

That in this complex of elements, which funda- 
mentally is one, the boundaries of bodies and of the 
ego do not admit of being established in a manner 
definite and sufficient for all cases, has already been 
remarked. The comprehending of the elements that 


are most intimately connected with pleasure and pain, 
under one ideal mental -economical unity, the ego, is 
a work of the highest significance for the intellect in 
the functions which it performs for the pain-avoiding, 
pleasure- seeking will. The delimitation of the ego, 
therefore, is instinctively effected, is rendered familiar, 
and possibly becomes fixed through heredity. Owing 
to their high practical value, not only for the individ- 
ual, but for the entire species, the composites " ego " 
and "body" assert instinctively their claims, and 
operate with all the power of natural elements. In 
special cases, however, in which practical ends are not 
concerned, but where knowledge is an object in itself, 
the delimitation in question may prove to be insuffi- 
cient, obstructive, and untenable.' 

The primary fact is not the /, the ego, but the ele- 
ments (sensations). The elements constitute the/. / 
have the sensation green, signifies that the element 
green occurs in a given complex of other elements (sen- 
sations, memories). When / cease to have the sensa- 
tion green, when / die, then the elements no longer 

association, ^^^| 

nical iinitv. ' 


occur in their ordinary, familiar way of 

That is all. Only an ideal mental-economical unity, 

not a real unity, has ceased to exist. ^ 

If a knowledge of the connexion of the elements 
(sensations) does not sufBce us, and we ask. Who pos- 
sesses this connexion of sensations, Who experiences 
the sensations? then we have succumbed to the habit of 
subsuming every element (every sensation) under some 
vnanalysed complex, and we are falling back impercept- 
ibly upon an older, lower, and more limited point of 

IThBenoisooiadefinlie, nnalterable, sharply-bomded unity. None of 

ditiduai Life; in facl their alieration is even Bought after by IhB individual. 
Coatinmly alone is imponanl. This vien accords admirably nith the posilion 
which Weismaoa bas Tacenll; reached by biological invcsliga lions. ("Zuc 
Frags der Unslerbllchkeit der Einxelligen," Binlog. Cmlralil., Vol. IV., Nos. 
II. 33 ; compare especially pages 654 and 655, where Ihe Bcisaion o[ Ihe Indi- 

of predisposiDgiQdoFcoDBeivlngnhat is contaiaed la the ego. This coaleni 
•nd not the ego is the principal thing. This comeal, however, is not confined 
■a Che individual. With the eicepUou of some insignificaiit and valueless 

Individual. The tga Is unsavable. It is partly (he knowledge of this fact, 

lies. In the long run wc shall net be able 10 close our eyes to this simple 
trutb, wblch is the immediate outcome of psyi:boIi>gica1 analysis. We shall 

dividual lite gmaUy changes, and which, In sleep or during absorption in 
SDtpe idea, just in onr very happiesi moments, may bo pa.lially or wholly ab- 
UDl. Weshallthenbewillineto renounce /■'frci./iKi/ immortality, and not 

will preclude the disrcgar. 
[It iriU be seen from the. 

at a freer and more enlightened view of hfe,»hii:h 
d of other eBOS and the over-eslitnation of our own. 
ibovB remarks that I consider that form of immoc- 

Carus upholda, and whic 
T&c Opni CMrl. Fi<«damc 

h maybe found in his discussions in Tk, M„ni.l. 
iitat ProbtiiUi, etc.— Mach, iBg;.] 

tThe habit of Irealini 

in science reourkable [arms. First, th« oervotu 



The so-called unity of consciousness is not an argu- 
ment in point. Since the apparent antithesis of real 
world and perceived world is due entirely to our mode 
of view, and no actual gulf exists between them, a rich 
and variously interconnected content of consciousness 
is in no respect more difficult to understand than a 
rich and diversified interconnexion of the world. 

If we regard the ego as a real unity, we become in- 
volved in the following dilemma: either we must set 
over against the ego a world of unknowable entities 
(which would be quite idle and purposeless), or we 
must regard the whole world, the egos of other people 
included, as comprised in our own ego (a proposition to 
which it is difficult to yield serious assent). 

But if we take the ego simply as a practical unity, 
put together for purposes of provisional survey, or 

s^aleiD Is aepETBIed frcm the body as Ihc seat of the aensalions. tn the ner- 

ne^ ol what tnluro teaearch will da for tha I:Dn- 
'. psfcbical. The (act that tha diSerem argana 
^•a^i\csMf anntcltd wElh, and ccd be leadily 
bsbly the foundation of tha " psychical uaitT." 
a serioualv discosecd, "Hon Iha peicept of a 
e headotunianf- Now, although Ihia 


simply as a more strongly coherent group of elements, 

less strongly connected with other groups of this kind, 
questions like those above discussed will not arise and 
research will have an unobstructed future. 

In his philosophical notes Lichtenberg says ; " We 
become conscious of certain percepts that are not de- 
pendent upon us ; of .others that we at least think are 
dependent upon us. "Where is the border-line? We 
know only the existence of our sensations, percepts, 
and thoughts. We should say, Jt thinks, just as we 
say, // lightens. It is going too far to say cogilo, if we 
translate cogilo by / think. The assumption, or pos- 
tulation, of the ego is a mere practical necessity." 
Though the method by which Lichtenberg arrived at 
this result is somewhat different from ours, we must 
nevertheless give our full assent to his conclusion. 

Bodies do not produce sensations, but complexes 
of sensations (complexes of elements) make up bodies. 
If, to the physicist, bodies appear the real, abiding 
existences, whilst sensations are regarded merely as 
their evanescent, transitory show, the physicist for- 
gets, in the assumption of such a view, that all bodies 
are but thought-symbols for complexes of sensations 
[complexes of elements). Here, too, the elements form 
the real, immediate, and ultimate foundation, which it 
is the task of physiological research to investigate. By 
the recognition of this fact, many points of psychology 


and physics assume moie distinct and more economical 
forms, qpd many spurious problems are disposed of. 
For us, therefore, the world does not consist of 
mysterious entities, which by their interaction with 
another, equally mysterious entity, the ego, produce 
sensations, which alone are accessible. For us, colors, 
sounds, spaces, times, . . . are the ultimate elements, 
whose given connexion it is our business to investi- 
gate. ^ In this investigation we must not allow our- 

H have aloars fell it ai a slroke of special goad fonune, ibal earl; In 


atterwari! eipe 

ibe El 

■ peril 


■ philc 


ibniptlT dawDed upn 

■.t day D 


.rid with my eE' 







3l Ihii 

J thOQKbt did D 


lil a liler 


,d, yet 


manls in my way. Only by altera. 

ate sludii 

a in pby 

sics and in lh< 

of Ibe senses, snd by blatoilco-pliyBical id' 


,ns [since abo 

atlar having eadcavored in vain 

iflid by a physico-psycho- 

iDEical monadDloer< have I altaini 

id to any 


la of philosopher 

. I ODiyseel 

physics a paial cf view tbai need . 

:ioI be ct 

langed 1 

carried over into Ibe domain ol 

' another 


; for, nltimal. 

Biy, all muhl 

physics . 

thifi requireipeol. What I Bay I 

have pro 



also do nnt wish 10 offer Ibis e>. 

position i 

If mine 1 

.s a special a 


Il ii rather my helieC that every di 

, vrbo makes 

■ cararnl mrvay of eny eilcnsive 1 


point of view 

1876), Also 

alt DtHkin drr tS'cU nach dim Pr 



1870, p. as8: 

Enelish traaslalioii, 0. C. Pub, Co 

., Cblcag. 

o,iB9j), . 

ind J. Popper 


liful book, DaiRcchI n Itim vn. 

iJil P/ln 

'ben (Lcipsic. 

i8?B, p. 6l>. 

bava adYBDcad allied thonghli. 


3 alBD m 

,y paper, V^trdit Wfw 


selves to be impeded by such intellectual abridgments 
and delimitations as body, ego, matter, mind, etc., 
which have been formed for special, practical purposes 
and with wholly provisional and limited ends in view. 
On the contrary, the fittest forms of thought must be 
created in and by that research itself, just as is done 
in every special science. In place of the traditional, 
instinctive ways of thought, a freer, fresher view, con- 
forming to developed experience, must be substituted. 

c, ^^ 

Science always takes its origin in the adaptation of 
thought to some definite field of experience. The re- | 
suits of the adaptation are thought-elements, which j 
are able to represent the field. The outcome, of | 
course, is different, according to the character and ex- 
tent of the province surveyed. If the province of ex- 
perience in question is enlarged, or if several provinces 1 
heretofore disconnected are united, the traditional, 
familiar thought-elements no longer sufHce for the ex- 
tended province. In the struggle of acquired habit 
with the effort after adaptation, problems arise, which 
disappear when the adaptation is perfected, to make 
room for others which have arisen in the interim. 

To the physicist, qud physicist, the idea of ' ' body " 

ScifKlific Uctt 

■i h-rcib-'Tec^ AM'iii. 

, Chi' J 

bonld ^^H 


is productive o£ a real facilitation of view, and is not 
the cause of disturbance. So. also, the person with 
purely practical aims, is materially assisted by the idea 
of the / or ego. For, unquestionably, every form of 
thought that has been designedly or undesignedly con- 
structed for a given purpose, possesses for that pur- 
pose a /i?rwanf«/ value. When, however, research in 
physics and in psychology nneets, the ideas held in the 
one domain prove to be untenable in the other. From 
the attempt at mutual adaptation arise the various 
atomic and monadic theories — which, however, never 
attain their end. If we regard snisaiions, in the sense ' 
above defined, as the elements of the world, the prob- i 
lems referred to are practically disposed of, and the ' 
first and most important adaptation effected. This 
fundamental view (without any pretension to being a 
philosophy for all eternity) can at present be adhered 
to in all provinces of experience; it is consequently 
the one that accommodates itself with the least expen- 
diture of energy, that is, more economically than any 
other, to the present temporary colleelive state of knowl- 
edge. Furthermore, in the consciousness of its purely 
economical office, this fundamental view is eminently 
tolerant. It does not obtrude itself into provinces in 
which the current conceptions are still adequate. It 
is ever ready, upon subsequent extensions of the do* 
main of experience, to yield the field to a better con- 

The philosophical point of view of the average 


man — if that term may be applied to the naive realism 

of the ordinary individual — has a claim to the highest 
consideration. It has arisen in the process of im- 
measurable time without the conscious assistance of 
man. It is a product of nature, and is preserved and 
sustained by nature. Everything that philosophy has 
accomplished— the biological value of every advance, 
nay, of every error, admitted — is, as compared with 
it, but an insignificant and ephemeral product of art. 
The fact is, every thinker, every philosopher, the mo- 
ment he is forced to abandon his narrow intellectual 
province by practical necessity, immediately returns 
to the universal point of view held by all men in com- 

To discredit this point of view is not then the pur- 
pose of the foregoing "introductory remarks. " The 
task which we have set ourselves is simply to show why 
and to what purpose for the greatest portion of life we 
hold it, and why and for yih'aX. purpose we are provisorily 
obliged to abandon it. No point of view has absoIutSj 
permanent validity. Each has importance only for 
some given end.* 

lIMDli!:re'B scourged ^"aWoiO^h^sj l^v Li Mariagt /arc 


St ^ 



IS (AV,Y,-* d. 

- Erfah- 

chUchiWMbtsriff). Ave 

nirins has s 

ISD undertaken tba 

it eipUining ihe desclopi 

nenl ot phil 

DSophy OQ the basis 

Ed by Ihe history d( civili 

which waa evoked by a 


ence wilh Dr. Paul 




"\T fE WILL now take, from the point of view at- 
* ' tained, a broad and general survey of the special 
problems that will engage our attention. 

When once the inquiring intellect has gained, 
through adaptation, the habit of connecting two 
things, A and £, in thought, it always thereafter seeks 
to retain this habit, even where the circumstances are 
slightly altered. Wherever A makes its appearance, 
S is added in thought. The principle here formulated, 
which has its root in an effort for economy, and is par- 
ticularly noticeable in the work of great investigators, 
may be termed the principle of continuity. 

Every observed variation in the connexion of A 
and B which is sufficiently Jarge to be noticed makes 
itseU felt as a disturbance of the above-mentioned 
habit, and continues to do so until the latter is sufK- 
ciently modified to eliminate the disturbance. We 
have become accustomed to seeing light deflected in 

passing from air to glass, and vice versa. But the de- i 
flexion differs noticeably in different cases, and the 
habit gained in some cases cannot be carried over un- 
disturbed to new cases, until we are prepared to asso- 
ciate with every particular angle of incidence a par- 
ticular angle of refraction — a condition satisfied by 
the discovery of the so-called law of refraction, or by 
acquirement of familiarity with the rule contained in 
the same. Thus another and modifying principle con- 
fronts that of continuity; we will call it ihe principie 
of sufficient delerminateness , or svfficienl differenliation. 

The joint action of the two principles may be very 
well illustrated by a further analysis of the example 
cited. In order to deal with the phenomena exhibited 
in the change of color of light, the idea of the law of 
refraction must still be retained, but with every par- 
ticular color a particular index of refraction must be 
associated. We soon perceive that with every par- 
ticular temperature also, a particular index of refrac- 
tion must be associated ; and so on. 

In the end, this process leads to temporary con- 
tentment and satisfaction, the two things A and B 
being conceived as so connected that to every observ- 
able change of the one there corresponds a dependent 
change of the other. It may happen that A as well 
as B is conceived as a complex of components, and 
that to every particular component of A a particular 
component of B corresponds. This occurs, for ex- 
ample, when ^ is a spectrum, and A the correspond- 



ing sample of a compound to be tested, m which case 
to every component part of the spectrum one of the 
components of the matter volatilised before the spec- 
troscope is referred, independently of the others. Only 
through complete familiarity with this relation can the 
principle of sufEcient determinateness be satisfied. 

Suppose, now, that we are considering a color- 
sensation 5, not in its dependence on A, the heated 
matter tested, but in its dependence on the elements 
of the retinal process, JV^. In such case, not the <f;'«rf 
but only the direction of the investigation is changed. 
None of the preceding observations lose their force, 
and the principles to be followed remain the same. 
And this holds good, of course, of all sensations. 

Now, sensation may be analysed in itself, imme- . 
diately, that is, psychologically (which was the course 
adopted by Johannes MiJller), or the co-ordinate physi- 
cal (physiological) processes may be investigated ac- 
cording to the methods of physics (the course usually 
preferred by the modern school of physiologists), or, 
finally, the connexion of psychologically observable 
data with the corresponding physical (physiological) 
processes may be followed up^a mode of procedure 
which will carry us farthest, since in this method ob- 
servation is directed to all sides, and one investigation 
serves to support the other. We shall endeavor to attain 
this last-named end wherever it appears practicable. 


This being our object, then, it is evident that the 
principle of continuity and that of sufficient determi- 
nateness can be satisfied only on the condition that 
with the same B (this or that sensation) is always as- 
sociated the same N {the same nerve -pro cess), and for 
every observable change of ^ a corresponding change 
of N is discoverable. If B is psychologically analysa- 
ble into a number of independent components, then 
we shall rest satisfied only on the discovery, in N, of 
such components as correspond to the former. In a 
word, for all psychically observable details of .5 we 
have to seek the corresponding physical details of N. 

We may thus establish a guiding principle for ouf ' 
' investigations, which may be termed the principle of 
the complete parallelism of the psychical and physical. 
According to our fundamental conception, which rec- 
ognises no gulf between the two provinces (the psychi- 
cal and the physical), this principle is almost a matter | 
of course ; but we may also enunciate it, as I did years 
ago, without the help of this fundamental conception, 
as a heuristic principle of research,^ 

the ^H 
mi- ^^^ 


As the prim 
a few concrete ■ 

iple is stated in rather abstract form, 
examples may now be given. Wherever j 

iB6j); tan^tt Rcichirfs and DhMs 
Ltkrr von Jen Bevrtgvngiemfjfindunt 
principle is Also implfcitlf contaii 
KAr^(/«rm.aiD/A«, Vol. XLVl., 

Wrkung drr T/I,tmtickt« FmieiiuKe . 
sAericife der H'iener Aktuitmie, Vol, LI 
Archhi. iBej, p. 6^4, and GnaidtiaiiH e 
■<• (Laipiic : Engelmaim, 1875, p,6j). T 
d in an ulicle or mine in Ficli[a-B.£k 


I have a sensatian of space, whether through the sen- 
sation of sight or through that of touch, or in any other 
way, I am obliged to assume the presence of a nerve- 
process in all cases the same in kind. For all time- 
sensations, also, I must suppose like nerve- processes. 
If I see figures which are the same in size and shape 
but differently colored, I seek, in connexion with the 
difierenl color- sensations, certain identical space-sen- 
sations with their appurtenant identical nerve-pro- 
cesses. If two figures are similar (that is, if they yield 
partly identical space-sensations) then the appurtenant 
nerve- processes contain partly identical components. 
If two different melodies have the same rhythm, then, 
side by side with the different tone-sensations exists in 
both cases an identical time-sensation with identical 
appurtenant nerve- processes. If two melodies of dif- 
ferent pitch are identical, then the tone-sensations as 
well as their physical conditions, have, in spite ol the 
different pitch, identical constituents. If the seem- 
ingly limitless multiplicity of color-sensations is sus- 
ceptible of being reduced, by psychological analysis 
(self- observation), to six elements (fundamental sen- 
sations), a like simplification may be expected for the 
system of nerve-processes. II our system of space-sen- 
sations appears in the character of a threefold mani- 
foldness, its system of co-ordinated nerve -processes 
will likewise present itself as such. 



This principle has, moreover, always been more or 
less consciously, more or less consistently, followed. 

For example, when Helmhollz assumes for every 
tone-sensation a special nerve-fifare in the ear (with its 
appurtenant nerve -process), when he resolves clangs, 
or compound sounds, into tone-sensations, when he 
refers the affinity of compound tones to the presence 
of like tone-sensations (and nerve-processes),' we have 
in this method of procedure a practical illustration of 
our principle. Merely its application is not complete, 
as will be later shown. Brewster,' guided by a psycho- 
logical but defective analysis of color-sensations, and 
by imperfect physical experiments,' was led to the view 
that, corresponding to the three sensations, red, yelli 
and blue, there existed likewise physically only three 
kinds of light, and that, therefore, Newton's assump- 
tion of an unlimited number of kinds of light, with a 
continuous series of refractive indices, was erroneous. 

. LoDdon: LooKmaas.Cre 

1 TrcatiK DB Oflki 

Imbolti [PkjiMa^cal Oftici 




Brewster might easily fall into the error of regarding 
green as a compound sensation. But had he reflected 
that color-sensation may make its appearance entirely 
without physical light, he would have confined his con- 
clusions to the nerve-process and left untouched New- 
ton's assumptions in the province of physics, which are 
as well founded as his own. Thomas Young corrected 
this error. He perceived that an unlimited number of 
kinds of physical light with an uninterrupted series of 
refractive indices (and wave-lengths) were compatible 
with a small number of color-sensations and nerve- 
processes, that a discrete number of col or- sensations 
did answer to the continuum of deflexions in the prism 
(to the continuum of the space-sensations). But even 
Young did not apply the principle with full conscious- 
ness or strict consistency, wholly apart from the fact 
that he allowed himself to be misled, in his psycho- 
logical analysis, by physical prejudices. Young, too, 
first assumed, as fundamental sensations, red, yellow, 
and blue, for which he later substituted red, green, 
and violet — misled, as Alfred Mayer, of Hoboken, has 
admirably shown, ^ by a physical error of Wollaston's. 


bsl[tDted tor bEE fend an 


The direction in which the theory of color-sensation, 

which has reached a high degree of perfection through 
Hering, has still to be modified, was pointed out by 
me many years ago in another place,* 

caDdlliDDS or sensalEon almoBl alwajB Riva rise to composile sensiliana, 
and Ihal tbs compoDents of sensatioii seldom make Ibeir ^ 





. Careful physical stud;, therefor 

mine the perceptloa of fellow and blue in g 
is actoally coalained in ii. Certainly no oi 
allhoBgb. as a tact, spectmtd-jellow and sj 

It al the 

ryof CI 


with the : 

■ lack. 

red, grcea. yellow, blue, which Heriag adopted, were £i^t | 
nacdo da Vinci, and later by Mach and Aubeil. That the assertion wilb ra- 
gard tg Leonardo da Vinci was loanded upon an error appeared lo me, from 
Ihe very first, in view of the coaceptions prevalent at bis time, highly prob- 
able. Let us bear what he himself says in hia «»* ifPiilKliKg (Noa. DJ4 
and J55 in the translation of Heinrich Lodwig. Q^rUinKkri/tn, ,ur K*Hit- 
gachKhU, Vieiins, BranmalleT, iSSl, Vol. XVni], "134. Of simple colon 
there are six. The first of these is while, although philosophers admit oai- 

lolors, the other of their absence. But. inasiBUch as Ihr pailttrr camnalOl 

witlunU Iktw, we shall include Ibe^e two also aiuong Iho other 

that white in Ibis clasaificalion is the first amoug the simple 

the second, green the third, blue the fourth, red the fifth, bl 

And the while we will let represent the light, without which c 

color, the yellow Ihe eanh, the gieea the water, blue the si. 

id say 


1 tbeir ton 

sntfi, partly with con 
fundamental color- 
iiervation^ of all s. 

Dd blue." This will suffice 10 show thai 
arlljwilh ohserralions toneeraing pig- 
ural philosophy, but no( with the aubjeet 

:d Leonardo da Vinci's book 


The examples adduced will sufSce to explain the 
significance of the above-enunciated principle of in- 
quiry, and at the same time to show that this principle 
is not entirely new. In formulating the principle, 
years ago, I had no other object than that of setting 
clearly before my own mind a truth which I had long 
instinctively felt. 

As we recognise no real gulf between the physical 
and the psychical, it is a matter of course that, in the 
study of the sense-organs, general physical as well as 
special biological observations may be employed. 

Isad 10 the canviclion IbRl the artists, and amoni; Ihem EspBCia]t;hB bimsell, 

l^iloufk. Berlin, 1S74,; 
ing the Ihcoir of coloc-i 
mentnl BcDsaliona wblle, bl: 
coiroaponding (chemical) pr. 


Much that appears to us difficult of comprehension 
when we draw a parallel between a sense-organ and a ' 
physical apparatus, is rendered quite obvious in the 
light of the theory of evolution, simply by assuming 
that we are concerned with a living organism with par- 
ticular memories, particular habits and manners, which 
owe their origin to a long and eventful race-history. 
I shall condense what I have to say on this subject 
into a footnote of some length.^ Even teleological 




h« theory of 

volnlion t 


10 logy ii 




nlar, was 

win, by SpeDcer 

IBS5). It r 





tion if tlu: Emolions, Late 






ted ideal" in 

the Dam 



yself i 

f Ibe idea 

the the- 



UKglilTfcktl lilt 




and moB. 

nstraetl-VB dis 

ussinns, in the way of a 





1 applicati 



ersary Addt 

ess o[ Hering 

On Mimoi 



fcr, 1870. (English translation, Open 

Puhlbhing Com- 



eago, I 

395)- A3 a 

□d bereditTorr 




1 il wo refletl that o/-fa™™i, which 

werapartof the patent- 

body, imigraU and becoma 

the basis oE 







pe^k Engli 
The prob 


oughl as, 


mplB. . 

the fact 

h, etc 

em involved 
5 apparently 1 

n the (ac 


mic ma 


ved by th 

insight, bat 


cently \ 




d^aik as 


of hered- 


es greatly 

r enlighlenmenl. 




ich might b 
Ihe parent 

e found in the 
organ! Bin only 




an make 

ended sh 




n (he E 


that the 


body ta n 


can increa 

m shows. 




length of 


ned propa 


ally condit 

on each othe 




staled tha 

plants [rem 

re blooxi 


spring ia Iheir 

early the 




hl=h this c 

orj, Th* so-c 

l«d reHt 

, If 




conceptioDS, as aids to investigatioD, are not to be 
shunned. It is true, our comprehension of the facts 
of reality is not enhanced by referring them to an un- 

kind-ill 1B65, I think—. 

Hlh Roll 

ett, wht 

1 was oiperimenting wi 

i.h pigeon, 


were placed in s cold liq 

uid, whe 

ther th* 

1 latter was water, mere 

iiry, or sul- 

phoricBcid. Nowsincai 

qnench its thirst, the cor 

have 10 do 

here with H habit adapted 

1 to an ei 



node of life 

and flHdhT inheritance. 



ork on the application c 

nliis flppropriatfl to its exi 


Golli, i 

in later writingH. 

has described many phr 

the sort—I will relate, al 

1 recall with a great det 

il ot pic 

ot .873, my 

little bo; bToughl me a 

en from Its 

neal, and desired to raise 

it, Bnt 

the matter was not ao easy. Th 

e tiiile ani- 

ma] could not be induced 

to Bwall 

would certainly soon hf 

.ve fallen a 

victim to the indignities 

oding i( by 

[orce. I then (ell into th. 

B tollowi 

ing trail 

1 of thpuEbt: "Whethe 

tor not the 

Darwinian Iheoiy is con 

nev-bc™ child would corlBlnly 

perish if il 


impulse to suck, which 1 

itilo actiiily qnite autom 

atieally 1 

.nd mechanically by the appro] 

iriate e»ci- 


m) must eiist likewisB 

In the case 

of lbs bird." I eiened 

myself ( 

smalliniect was stuck np 

and swnog rapidly aho 

at the head 

of the bird. Immedialelj the bin 

1 its bill, beat its wings. 1 

md eagerly 

>Dd. 1 ho 


I for setting 

thaimpolseand theaiiloi 

eeplibly BtroBger ind gre, 

snatch at the food, and, 


nially Fa 

; from that 


of itself 

.tellect de- 

YBleped, the required ar 

Munl of 

ching inde- 

pendenca, Iha animal to. 

3k on, little by- little, all the eharacteris 

tlc ways of 


ring f=U in- 

leileclUBl Bctivitr) it wai 

uslful ai 

od friendly. In the evE 

ning, other 

sought out 

the highest places in th 

and wc, 

lid become quiet only when it was 

pravEnled by Iha ceiling 1 

Irom Roii 


r. Here again we have an inherited 

habit adapted 10 an end. 

On the 

Df darkness, the demeai 

anim*l changEd totally. 



led, It milled itsfeathei 

s, began to 


known World-Purpose, itself problematic. Neverthe- 
less, the question as to the value that a given function ^ 
has for the existence of an organism, or as to what are 

would regard wilh aniieiy an arm-chair, which slood in Iha sbaiJow; ano 



g. a coal-hod 

by the Slove, esp 

cially when 1 

wiih raited doTer, rese 


W5. The fear of 

pints is the 


ernfrellgions. Neith 

r scientiGc an 

alysis nor the cs 



sm of a David Straoas 

a» applied t 

mylbs, which. ( 

r the strong 

ted, Kill all at 



ed. and in ■ 

s (tearota wor 

e, hope of a 


U long coniinuB .0 e.i 

and tiniujoliolla 

ble insUncU 

of lb 

in. J«« as Ibe birds 

slands (accord in 

It to Darwin] 

I be 

ear of man only after 



many generations, Ibat 

i«g or flesh. 

leach ns thee 

palhy with the conceptions of the a 

e of witchcraft. 

-I will here 

other cniioua fact, for 




Iter part of his 

fe land-pro- , 

Caraiolfl). My father 

occupied himself much with 



nlberry silk- J 


been raised 

h«:ome «- 1 


□Kly helpless and depend en 

. When the 

me for passing ii 

""^"^ ^d 



TmyH^ ^1 



pare the nsaal bundles 

of straw tor 

colony of ailk-v 

orms. n» ^H 

e worms peris 

ed. end onlj a s 

nallpordon. ^ 


aplation) spun their cocootts. ' 


as mj sister believes sb 


degree, in the 





lioinsl probably be left 


='l these r^ 



oism of the Uno 

nscloos. A ^H 


eachJDR beyond the i 

eri Ihom inleltiR 

hle.-^psy. ^H 


n sense, toiioil 

ed upon Ibe the. 



panic ulars. woul 

yield Hohei ^^| 

a a]I previous specula 

on has done. 

-These ohservatl 




c, 18B0. »bich 

n when Schneider's valnable ■ 
contains many that a» aimi- 

thUrUcki wm.. Leips 



Balms of mil. 



ee with regard to Ibo r 

l!on and physic. 

process, the 


pecies, etc., 

re easontially d 

ffereni from 


and perception-impnls 

es to be quit 

n important 

dily may per 

aps be eipected 

trnm Weis- 

t. Jena. 18S3 (English ■iraoslalio 

n. JEJM^ o» 


and Kindnd BUhgica 

P^DhUmt, Ol 

ndoD Press, 


its acquired by 


its actual contributions to the existence, of the same, 
may be of great assistance in the comprehension of 
this function.' Of course we must not suppose, on 
this account, as many Darwinians have done, that we 

mathemslics] precision aod depth o[ tiia prescnUlinn ol the probLeid. Bui 
Id be clearly shown b; Ibe lormalion or new racES, which msinuin ihemsalvea 

ceitalol; be eiened on the 
certainly DOI 

1 lo Ibe ( 

; ol Ihe I 

[o Wei! 

(I have lo 

ISuch leleological conceptions have often be 
IB. The rBBiarfc, tnr eiainple, Ihat a risible obji 

le eye. We nnderstand Ihraugb it, ilsa, bsw tha . 
r its sarvlval, was obliged lo adjnst itself lo Ibe leq 
I adapl itself 10 (eel Iha ratios of lig hi -intensity. T 
ir. or the fundamenlBl psycba-phjsical formula ol 
il as Bometbiog fundamental, but as Ibe ixpl^a 

on tbe works of C. Lloyd Mat- 

ilensi<lE3 of object 

{Sitmxgiherickli dcr Wiener AkaiUn 
jar Piyekiatrie, NBuwied and Leipsio, 
dfmit. Vol. LVII., laes). m ihe last-i 


rally, h 


Lll., 1B65; VitHilMhnichri/t 
I : ^itzun^berickte der Wienrr Aka- 
■d paper, praceeding frotu tbe pos- 
lulale of tbe parallelism between the psychical aud the physical, or, as I (hen 

1 abandoned tbe milrical fiyrmula of Fccbner (the 
brought forward another concepIioQ of Ihe tundamenl 
of which tor light-sensalionlnever disputed. This . 
doubt from the malhematlcal development there foand. Thus one cannot 

my tonndation, If by this is understood Ibe t/iilricBl/nrmnla. How could I 
maintain tbe prnforiionalil]/ between eicilatinn and sensation st the aamo 
time with the tagarillimit dependence? It was sufficient for me to render ttif 


have "mechanically explained " a function, when we 
discover that it is necessary for the survival of the 
species. Darwin himself is doubtless quite free from 
this short-sighted conception. The physical means by 
which a function is developed still remains a physical 
problem ; while the mode and reason of an organism's 
voluntary adaptation continues to be a psychological 
problem. The preservation of the species is only 
one, though ail actual and very valuable, point of de- 
parture for inquiry, but it is by no means the last and 
the highest. Species have certainly been destroyed, 
and new ones have as certainly arisen. The pleasure- 
seeking and pain-avoiding wiil, therefore, is directed 
perforce beyond the preservation of the species. It 
preserves the species when it is advantageous to do so ; 
transforms it when it is advantageous ; and destroys 
it when its continuance would not be advantageous. 
Were it directed merely to the preservation of the spe- 
cies, it would move aimlessly about in a vicious circle, 
deceiving both itself and all individuals. This would 
be the biological counterpart of the notorious "per- 
petual motion " of physics.' 






T^HE tree with its hard, rough, grey trunk, its num- 
-'- berless branches swayed by the wind, its smooth 
soft, shining leaves, appears to us at first a single, in- 
divisible whole. In like manner, we regard the sweet, 
round, yellow fruit, the warm, bright fire, with its 
manifold moving tongues, as a single thing. One name 
designates the whole, one word draws forth from the 
depths of oblivion all associated memories, as if they 
were strung upon a single thread. 

The reflexion of the tree, the fruit, or the fire in a 
mirror is visible, but not tangible. When we turn our 
glance away or close our eyes, we can touch the tree, 
taste the fruit, feel the fire, but we cannot see them. 
Thus the apparently indivisible thing is separated into 
parts, which are not only connected with one another 
but are also joined to other conditions. The visible 
is separable from the tangible, from that which may 
be tasted, etc. 

The visible also appears at first sight to be a single 


thiDg. But we may see a round, yellow fruit together 
with a yellow, star-shaped blossam. A second fruit is 
just as round as the 6rst, but is green or red. Two 
things may be alike in color but unlike in form ; they 
may be different in color but like in form. Thus sen- 
sations of sight are separable into color-sensations and 
space-sensa lions. 

Color- sen sat ion, into the details of which we shall 
not enter here, is essentially a sensation of favorable 
or unfavorable chemical conditions of life. In the pro- 
cess of adaptation to these conditions, color-sensation 
may have been developed and modified.^ Light in- 

ICompBTB Grant Allen, Tim Csler-Siiic -(U,r.Aaa: Trllbnet 1 Co., i8?9). 

wiOi a philoldgisl. Prof. F. PDlla of Dresden 

un this BubJBCl, and both of as 

soon came lo [he conclusion [haL the views 

ol Magnus could not bold their 

natatfll »;iBQCB or of pbilology 

s ot our dlecussion » tbo other 

these were oever made public, Msanlime. boncvei. Ihe matter was disj;>DsedoI 

by E-Kranse. and notably by A, Matty. I sh 

11 take the liberty of BddiBK only 

r. Magnus. V^cd we 

sr Virgil's deatli, n 

^X!o i 

ition is J 



troduces organic life. The green chlorophyll and the 

(complementary) red hfemoglobin play a prominent 
part in the chemical processes of the plant-body and 
in the contrary processes of the animal body. The two 
substances present themselves to us in the most varied 
modifications of tint. The discovery of the visual 
purple, observations in photography and photochem- 
istry render the conception of processes of sight as 
chemical processes permissible. The role which color 
plays in analytical chemistry, in spectrum -analysis, in 
crystallography, is well known. It suggests a new con- 
ception for the so-called vibrations of light, according 
to which they are regarded, not as mechanical, but as 
chemical vibrations, as successive union and separa- 
tion, as an oscillatory process of the same sort that takes 
place, though only in one direction, in photo-chemical 
phenomena. This conception, which is substantially 
supported by recent investigations in abnormal dis- 
persion, accords with the electro-magnetic theory of 
light. In the case of electrolysis, in fact, chemistry 
yields the most intelligible conception of the electric 

)I lis Darwinian theory i 

made wilh caution in another dire 

tlion. We like to picture 

condillon in wbicb tli« coIoi-seoES i 

s Isckicg, or in which lit 

eiiUs, aa/h-^trfiWf another in wtich 

the iiiinnir it is natural to proce. 

3d from the simple to thai 

Nature. The color-senae 

is beinn enriched or impo' 

can tell? Isit not possible that, wit 

h IhB awakcnini! of intelli 

nwot artificial CDDtrivanqe. Ihewhc 

inlellecl,— whii:h certainly Is chiefly 

called in play from this i 



current, regarding the two components of the electro- 
lyte as passing through each other in opposite direc- 
tions. It is likely, therefore, that in a future theory 
of colors, many biologico-psychological and chemico- 
physical threads will be united. 

Adaptation to the chemical conditions of life which i 
manifest themselves in color, renders locomotion neces- 
sary to a far greater extent than adaptation to those ' 
which manifest themselves through taste and smelL 
At least this is so in the case of man, concerning whom 
alone we are able to judge with immediacy and cer- 
tainty. The close association of space-sensation ^a 
mechanical factor) with color-sensation (a chemical i 
factor) is herewith rendered intelligible. We shall now j 
proceed to the analysis of space -sensations. 

In examining two figures which are alike but dil- 
ferently colored (for example, two letters of the same 
size and shape, bat of difierent colors), 
we recc^nise their sameness of form at 
the first glance, in spite of the differ- 
ence of color-sensation. The sight-per- 
ceptions, therefore, must contain some 
like sensatioa-com portents. These are the space-scu- 
sadons — which are the same in the two cases. 



We will now investigate the character of the space- 
sensations that physiologically condition the recogni- 
tion of a figure. First, it is clear that this recognition 
is not the result of geometrical considerations — which 
are a matter, not of sensation, but of intellect. On the 
contrary, the space-sensations Tn question serve as the 
starting-point and foundation of all geometry. Two 
figures may be geometrically congruent, but physio- 
logically quite different, as is shown by the two ad- 

joined squares (Fig. 3), which could never be recog- 
nised as the same without mechanical and intellectual 
operations.* A few simple experiments will 
render us familiar with the relations here in- ^r 

volved. Look at the spot in Fig. 4. Place ^^^ 
the same spot twice or several times in ex- ^'8*- 
actly the same position in a row (Fig. 5) ; the result 
is a peculiar, agreeable impression, and we recognise 

SitBHngs&ericktr dir t* 





F'E- S. 

at once and without difficulty the identity of all the 
figures. Turning, however, one spot half way around 
with respect to the other (Fig. 6), their 
identity of form is not recognisable 
without intellectual assistance. On 
FiK- 6- the other hand, if we place two of the 

u^ spots in positions symmetrical to the 

^^r ^^ median plane of the observer (Fig. 7), 
^^W^P^ the relationship of form is strikingly 
apparent. But if the plane of symme- 
try diverges considerably from the median plane of 
the observer, as in Fig. 8, the affinity of form is rec- 
ognisable only by turning the figure around 
^r or by an intelUclual act. On the other hand, 
4^k the affinity of form is again apparent on con- 
^tf^F trasting with such a spot the same spot ro- 
^^ tated through an angle of iSo° in the same 
Fig. 8. plane (Fig. 9). In this case we have the so- 

jtt called centric symmetry, 
^^r If we reduce all the dimensions of the spot 

r^^^ proportionately, we obtain a geometrically 
similar spot. But as the geometrically con- 
gruent is not necessarily physiologically (op- 
** ticajjy) congruent, nor the geometrically 
symmetrical necessarily optically symmetrical, analo- 
gously the geometrically similar is not necessarily op- 

«... « 

tically similar. If the geometrically similar spots be 
placed beside each other in the same relative positions 
(Fig. lo), the two will also appear optically similar. 
Turning one of the spots around destroy; 
blance (Fig. 1 1). If we sub- 
stitute for one of the spots 
a spot symmetrical to the 
other in respect to the me- 
dian plane of the observer 
(Fig. 12), a symmetrical 
similarity will be produced 
which has also an optical 
value. The turning of one of the figures through i8o° 
in its own plane, producing thereby ceatrically sym- 
metrical similarity, has also a physiologico- optical 
value (Fig. 13). 

In what, now, does the essential nature of optical 
similarity, as contrasted with geometrical similarity, 
consist? In geometrically similar figures, all homolo- 
gous distances are proportional. But this is an affair 
of the intellect, not of sensation. If we place beside a 
triangle with the sides a, 6, c, a triangle with the sides 
2a, 2^, 2c, we do not recognise the simple relation of 
the two immediately, but intellectually, by measure- 
ment. If the similarity is to become optically percep- 
tible, the proper position must be added. That a 
simple intellectual relationship of two objects does not 


necessarily condition a similarity of sensation, may be 
perceived by comparing two triangles having respec- 
tively the sides a, b, c, and a + jw, ^ + wi, cA-m. The 
two triangles do not look at all alike. Similarly all 
conic sections do not look alike, although all stand in 
a simple geometric relation to each other ; still less do 
curves of the third order exhibit optical similarity; etc 


We may obtain an idea of the physiological sig- 
nificance of the direction of a given straight line or 
curve-element, by the following reflexion. Let j'=^/(.r) 
be the equation of a plane curve. We can read at a 
glance the course of the values of dyjdx on the curve, 
for they are determined by its slope ; and the eye givea 
us, likewise, qualitative information concerning the 
values of d^y/dx^, for they are characterised by the 
curvature. The question naturally presents itself why 
can we not arrive at as immediate conclusions con- 
cerning the values i/^^y/i/a;*, d*^y/dx*, etc. The an- 
swer is easy. What we see are not the differential 
coefficients, which are an intellectual affair, but only 
the direction of the curve-elements, and the declination 
of the direction of one curve-element from that of an- 

In fine, since we are immediately cognisant of the 
similarity of figures lying in similar positions, and are 
also able to distinguish without ado the special case of 
congruity, therefore our space-sensations yield us in- 
formation concerning likeness or unlikeness of directions , 
and equality or inequality of spatial dimensions. 

It is extremely probable that sensations of space 
are produced by the motor apparatus of the eye. With- 
out entering into particulars, we may observe, first, 
that the whole apparatus of the eye, and especially 
the motor apparatus, is symmetrical with respect to 


the median plane of the head. Hence, symmetncal 

movements of looking wiU determine like or approxi 
mately like space-sensations. Children constantly con- 
found the letters b and d, as also p and q. Adults, 
too, do not readily notice a change from left to right 
unless some special points of apprehension for sense 
or intellect render it perceptible. The symmetry of 
the motor apparatus of the eye is very perfect. The 
like excitation of its symmetrical organs would, by it- 
self, scarcely account for the distinction of right and 
left. But the whole human body, especially the brain, 
is affected with a slight asymmetry, — which leads, for 
example, to the preference of one (generally the right) 
hand, in motor functions. And this leads, again, to a 
further and better development of the motor functions 
of the right side, and to a modification of the attend- 
ant sensations. After the space-sensations of the eye 
have become associated, through writing, with the mo- 
tor functions of the right hand, a confusion of those 
vertically symmetrical figures with which the art and 
habit of writing are concerned no longer ensues. This 
association may, indeed, become so strong that re- 
membrance follows only the accustomed tracks, and 
we read, for example, the reflexion of written or printed 
words in a mirror only with the greatest difficulty. 
The confusion of right and left still occurs, however, 
with regard to figures which have no motor, but only 
a purely optical (for example, ornamental) interest. 
A noticeable difference between right and left must be 


felt, moreover, by animals, as in many predicaments 
they have no other means of finding their way. The 
similarity of sensations connected with symmetrical 
motor functions is easily remarked by the attentive 
observer. If, for example, supposing my right hand 
to be employed, I grasp a micrometer-screw or a key 
with m-j left hand, I am certain {unless 1 reflect be- 
forehand) to turn it in the wrong direction, — that is, I 
always perform the movement which is symmetrical 
to the usual movement, confusing the two because of 
the similarity of the sensation. The observations of 
Heidenhain regarding the reflected writing of persons 
hypnotised on one side should also be cited in this 

With looking upwards and looking downwards, 
fundamentally different space-sensations are asso- 
ciated, as ordinary observation will show. This is, 
moreover, comprehensible, since the motor apparatus 
of the eye is asymmetrical with respect to a horizontal 
plane. The direction of gravity is so very decisive 
and important for the motor apparatus of the rest of 
the body that the same factor has assuredly also found 
its expression in the apparatus of the eye, which serves 
the rest. It is well known that the symmetry of a 
landscape and of its reflexion in water is not felt. 
The portrait of a familiar personage, when turned up- 
side down, is strange and puzzling to a person who 
does not recognise it intellectually. If we place our- 
selves behind the head of a person lying upon a couch 


and unreflectingly give ourselves up to the impression 
which the face makes upon us, we shall find that it is 
altogether strange, especially when the person speaks. 
The letters b and /, and li and q, are not confused by 

Our previous remarks concerning symmetry, simi- 
larity, and the rest, naturally apply not only to plane 
figures, but also to those in space. Hence, we have 
yet a remark to add concerning the sensation of space- 
depth. Looking at objects afar off and looking at 
objects near at hand determine different sensations. 
These sensations viust not be confused, because of the 
supreme importance of the difference between nea* ' 
and far, both for animals and human beings. They ' 
cannot be confused because the motor apparatus is 
asymmetrical with respect to a plane perpendicular to 
the direction from front to rear. The observation that 
the bust of a familiar personage cannot be replaced by 
the mould in which the bust is cast is quite analogous 
to the observations consequent upon the inversion of 

If equal distances and like directions excite like 
space-sensations, and directions symmetrical with re- 
spect to the median plane of the head excite similar 
space-sensalions, the explanation of the above-cited 
facts is not far to seek. The straight line has, in all j 
its elements, the same direction, and everywhere ex- 



cites the same space-sensations. Hen 
aesthetic value. Moreover, straight lines which lie in 
the median plane or are perpendicular to it are brought 
into special relief by the circumstance that, through 
this position of symmetry, they occupy a like position 
to the two halves of the visual apparatus. Every other 
position of the straight line is felt as awryness, or as 
a deviation from the position of symmetry. 

The repetition of the same space-figure in the same 
position conditions a repetition of the same space-sen- 
sation. Ail lines connecting prominent (noticeable) 
homologous points have the same direction and excite 
the same sensation. Likewise when merely geometri- 
cally similar figures are placed side by side in the same 
positions, this relation holds. The sameness of the 
dimensions alone is absent. But when the positions 
are disturbed, this relation, and with it, the impression 
of unity — the iesthetic impression — are also disturbed. 

In a figure symmetrical with respect to the median 
plane, similar space-sensations corresponding to the 
symmetrical directions take the place of the tdctiiical 
space-sensations. The right half of the figure stands 
in the same relation to the right half of the visual ap- 
paratus as the left half of the figure does to the left 
half of the visual apparatus. If we alter the sameness 
of the dimensions, the sensation of symmetrical simi- 
larity is still felt. An oblique position of the plane of 
symmetry disturbs the whole effect. 

If we turn a figure through i8o°, contrasting it 


with ilself in its original position, centric symmetry is 
produced. That is, if two pairs of homologous points 
be connected, the connecting lines will cut each other 
at a point O, through which, as their point of bisec- 
tion, all lines connecting homologous points will pass. 
Moreover, in the case of centric symmetry, all lines of 
connexion between homologous points have the same 
direction, ^ — a fact which produces an agreeable sensa- 
tion. If the sameness of the dimensions is eliminated, 
there still remains, for sensation, centrically symmetri- 
cal simiiarity. 

Regularity appears to have no special physiological 
value, in distinction from symmetry. The value of 
regularity probably lies rather in its manifold symmetry, 
which is perceptible in more than one single position. 


The correctness of these observations will be ap- 
parent on glancing over the work of Owen Jones — A 
Grammar of Ornament (London, 1865). In almost 
every plate one finds new and different kinds of sym- 
metry as fresh testimony in favor of the conceptions 
above advanced. The art of decoration, which, like') 
pure instrumental music, aims at no ulterior end, but 
ministers only to pleasure in form (and color), is the 
best source of material for our present studies. Writ- 
ing is governed by other considerations than that of 
beauty. Nevertheless, we find among the twenty-four 
large Latin letters ten which are vertically symmetri- 



cal (A, H, I, M, O, T, V, W, X, Y), five which are 
horizontally symmetrical (B, C, D, E, K), three which 
are centrically symmetrical (N, S, Z), and only six 
which are unsymmetrical (F, G, L, P, Q, R). 

It is to be remarked again that the geometrical 
and the physiological properties of a figure in space 
are to be sharply distinguished. The physiological 
properties are determined by the geometrical proper- 
ties coincidently with these, but are not determined 
by these solely. On the other hand, physiological 
properties very probably gave the first impulse to 
geometrical investigations. The straight line doubt- 
less attracted attention not because of its being the 
shortest line between two points, but because of 
its physiological simplicity. The plane likewise pos- 
sesses, in addition to its geometrical properties, a spe- 
cial physiologico- optical (eesthetic) value, which claims 
notice for it, as will be shown later on. The division 
of the plane and of space by right angles has not only 
the advantage of producing equal parts, but also an 
additional and special symmetry-value. The circum- 
stance that congruent and similar geometrical figures 
can be brought into positions where their relationship 
is physiologically felt, led, no doubt, to an earlier 
investigation of these kinds of geometrical relation- 
ship than of those that are less noticeable, such as af- 
finity, collineation, and others. Without the co-ope- 

ration of sense- perception and understanding, a scien- 
tific geometry is inconceivabJe, But H. Hankel has 
admirably shown in his History of Mathematics (Leip- 
sic, 1874) that in the Greek geometry the factor of 
pure understanding, iu the Indian, on the other hand, 
that of sense, very considerably predominated. The 
Hindus make use of the principles of symmetry and 
similarity (see, for example, p. 206 of Hankel's book) 
with a generality which is totally foreign to the Greeks. 
Hankel's proposition to unite the rigor of the Greek 
method with the perspicuity of the Indian in a new 
mode of presentation is ■well worthy consideration. 
Furthermore, in so doing, we should only be following 
in the footsteps of Newton and John Bernoulli, who 
have made a still more genera! application of the prin- 
ciple of similitude in mechanics. The advantages that 
the principle of symmetry afiords in the last-named 
province, I have shown elsewhere,* 

I [ bave given Iess complele discDssloDS of (he leadini; tboughts at Ibie 
chipler iatbe paper already mentiDnSid.^eJC'-iAiiAiUKrviiZa^fi nnd Win- 
trbt (1861), tunber inFicbWsZfilKiri/t/arPiilftafi/r. Vol. XL VI., iSGj. p.j 
and in TTttJ^armn^Lisnidi.aadS^'Hnir/rftiiyi) DOW also pnbtiBbed tn my 
PapHtaT Scimtijic Lictiatj, Iranslated by Tbomas J. McCcrmack, Open Cod it 
Publlsbing Co., Cbicago, iSg4. With ragstd to tbe use of tbe principle ot 

d by Thomas J. McComack, 1893, Open Conj - - - - ■ 




sdela pcTccftiun da beaa 

larad, bj J. L. 
, iSsi. Id this 

cbsnoingly w 

[ten book Sore! make 



of nfilillm 

, Appliq 

liona o( this kind I hadlrealod 

only briefly, a 

a beak on uslhelica. On the 

Mher band. 1 

believe I bava penclr 

ted dee 


aspect of the principle 

— Mach 



That space-sensatioQ is connected with motor pro- 
cesses has long since ceased to be disputed. Opinions 
difier only as to how this connexion is to be repre- 

If two congruent images of different colors fall in 
sticcession on the same parts of the retina, they are 
at once recognised as identical figures. We may, 
therefore, regard different space-sensations as con- 
nected with different parts of the retina. But that 
these space-sensations are not unalterably restricted to 
particular parts of the retina, we perceive on moving 






our eyes freely and voluntarily, whereby the objects 
observed do not change their position or forni, although 
their images are displaced on the retina. 

If I look straight before me, fixing my eyes upon 
an object O, an object A, which is reflected on the 
retina in a, at a certain distance below the point of 
most distinct vision, appears to me to be situated at a 
certain height. If I now raise my eyes, fixing them 
upon B, A retains its former height. It would neces- 
sarily appear lower down if the 
position of the image on the 
retina, or the arc oa, alone de- 
termined the space- sensation. I 
•'iB- 's- can raise my glance as far as A 

and farther without a change in this relation. Thus, 
the physiological process which conditions the volun- 
tary raising of the eye, can entirely or partly take the 
place of the height-sensation, is homogeneous with it, 
or, in brief, algebraically su mm alienable with it. If 
I turn my eyeball upward by a slight pressure of the 
finger, the object A actuaJly appears to sink, propor- 
tionately to the shortening of the arc oa. The same 
thing happens when, by any other unconscious or in- 
voluntary process — for example, through a cramp of 
the muscles of the eye^the eyeball is turned upward. 
According to an experience now familiar to opticians 
for some decades patients with paralysis of the rectus 
extemus reach too far to the right in attempting to 
grasp objects at the right. Since they need to exert a I 


Stronger impulse of the will than persons of sound 
eyes, in order to fix their glance upon an object to the 
right, the thought naturally suggests itself that the 
will to look to the right determines the optical space- 
sensation "right." Some years ago,i I put this ob- 
servation into the form of an experiment, which every 
one can try for himself. Let the eyes be turned as far 
as possible towards the left and two large lumps of 
moderately hard putty firnnly pressed against the right 
side of each eye-ball. If, now, we attempt to glance 
quickly to the right, we shall succeed only very im- 
perfectly, owing to the incompletely spherical form 
of the eyes, and the objects will suffer a strong dis- 
placement to the right. Thus the mere wUl to look to 
the right imparts to the images at certain points of the 
retina a larger "rightward value," as we may term it 
for brevity. The experiment is, at first, surprising. 
It will soon be perceived, however, that both facts — 
viz., that by voluntarily turning the eyes to the right, 
objects are not displaced, and that by the forced, in- 
voluntary turning of the eyes to the right, objects are 
displaced to the left — together amount to the same 
thing. My eye, which I wish to, and cannot, turn to 
the right, may be regarded as voluntarily turned to the 
right and compulsorily turned back by an outer force. 

Shortly SI 

ly GrandUnun dtr Lthri i 



The will to perform movements of the eyes, or the 
innervation to the act, is itself the space-sensation. 
This follows naturally from the preceding considera- 
tion.* If we have a sensation of itching or pricking in a 
certain spot, by which our attention is sufficiently se- 
cured, we immediately grasp at the spot with the cor- | 
rect amount of movement. In the same manner we 
turn our eyes with the correct amount of exertion to- 
wards an object reflected on the retina, as soon as this 
exerts a sufficient stimulus to -draw our attention. By 
virtue of organic apparatus and long exercise we hit 
immediately upon the exact degree of innervation 
necessary to enable us to fix our eyes upon an object 
reflected on a certain point of the retina. If the eyes 
are already turned towards the right, and we begin to 
give our attention to an object further to the right or 
the left, a new innervation of the same sort is algebra- 
ically added to that already present. A disturbance 
of the process arises only when extraneous, involun- 
tary innervations or outward moving forces are added 
to the innervations determined by the will. 

Years ago, while occupied with the questions now 
under discussion, I noticed a peculiar phenomenon, 

n the aipression which waa first immediaialr mggMled lo 

>e full 

! inquiry. 


which has not yet, to my knowledge, been described. 
In 3 very dark room we fix our eyes upon a light A, 
and then suddenly look at a light lower down, B. At 
this, the light A appears to make a rapid sweep A A' 
(quickly ended) upwards. The light B, of course, 
does the same — but to avoid complications, this is not 
indicated in the diagram. The sweep is, of course, an 
after-image, which enters consciousness only on com- 
pletion, or shortly before completion, of the glance- 
movement, but^and 
this is the remark- 
able point — with po- 
sitional values that 
correspond, not to the 
later, but to the ear- 
lier innervations and 
position of the eye. 
Similar phenomena 

are often noticed in experiments with Holtz's elec- 
trical machine. If the experimenter is surprised by 
a spark during a glance downwards, the spark often 
appears high above the electrodes. If it yields a per- 
manent after-image, the latter appears, of course, be- 
low the electrodes. The preceding phenomena an- 
swer to the so-called personal equation of astronomers, 
except that they are confined to the province of sight. 
By what organic apparatus this relation is determined 
cannot be decided now, biat it is probably of some 


value in preventing confusion of position in i 
ments o( the eyes. 

For the sake of simplicity we have hitherto re- 
garded only the eyes as in motion, and have considered 
the heati (and the body generally) as at rest. I(, now, 
we move the head about without intentionally fixing 
the eyes upon any object, the objects 
motionless. But at the same time another observer 
may notice that the eyes, like frictionless, inert masses, 
take no part in the turning movements. Still more 
noticeable is the phenomenon if 
we turn for a considerable tinie 
and with continuous motion about 
a ^~e^ticat axis, tn tbe direction 
of the hands of a clock viewed 
tiom above. In this case, as Breucx has observed, tbe 
open or closed e\'es torn, about ten times to a full revo- 
latwik qI tbe body, in tbe opposite direction to that ol 
die dock-luiids, witb a onifona ox>tioci, and as frc- 
qottBdy back again in tbe opposite diiectkm by jezks. 
TIm process is r^teseoted in dte diagimm ol Fig. 17. 
Ott O T., die times are laid ofi as absossa^ tbe an^es 
fc a cribe J in tbe <Ui«ctioa of the dodk-baads a>e laid 
«C «s otufioates vp««nl% and Ae aa^es descxflied ■ 


f, now, ^^J 

1' fixing ^H 

b server '^^^1 
11 more ^^H 

canv 0Jt GOivsfKNMzs tn dw iwlaffwi <■ ne bo^s 
0#.f to Ae <ela£v«^ a»d OCCio dK a 



tion of the eyes. No one, on repeating the experi- 
ment, can avoid the conclusion that we are concerned 
here with an automatic (unconscious) movement of 
the eyes, reflexively excited by the rotation of the 
body. How this motion is brought about remains, 
naturally, to be investigated. A simple conception 
would be that the excitation, uniformly reaching two 
antagonistic organs of innervation on the turning of 
the body, is answered by one with a uniform stream of 
innervation, while the other gives its impulse of inner- 
vation only after the lapse of a certain time, like a 
filled rain-gauge suddenly overturning. For us it suf- 
fices, provisorily, to know that this automatic, uncon- 
scious compensational movement of the eye is actually 

The slower unconscious compensational movement 
of the eye (the jerking motion leaving behind it no op- 
tical impression) is thus the cause of the retention of 
position by objects seen during the turning of the body 
— a thing which is very important for orientation. If, 
now, in turning our head, we also voluntarily turn the 
eyes in the same direction, fixing them upon one ob- 
ject after another, we must overcompensate the auto- 
matic, involuntary innervation by the voluntary inner- 
vation. We need the same innervation as if the whole 
angle turned through were described by the eye alone. 
In this way is explained why, when we turn about, the 
whole optical space appears to us a continuity and not 
an aggregation of fields of vision ; and why, at the 



same time, the optical objects remain stationary. That 
which we see of our own body, in turning, we see, for 

obvious reasons, optically in motion. 

Thus we arrive at the practically valuable concep- 
tion of our body as in nnotion. in a fixed space. We 
understand why it is that, in our numerous turnings 
and ramblings in the streets and in buildings, and in 
our passive turnings in a wagon or in the cabin of a 
ship — yea, even in the dark — we do not lose our sense 
of direction, though it is true that the primary co- 
ordinates from which we started gradually sink un- 
noticed into unconsciousness, and we soon begin to 
reckon from new objects around us. That peculiar 
state of confusion as to locality in which we some- 
times find ourselves on suddenly awaking at night, 
where we look about helplessly for the window or the 
table, is probably due to dreams of movement imme- 
diately preceding our awaking. 

Similar phenomena to those which manifest them- 
selves on the rotation of the body make their appear- 
ance in connexion with the movements of the body 
generally. If I move my head or my whole body side- 
wise, I do not lose sight of an object on which my 
eyes rest. The latter seems to continue motionless, 
while the more distant objects undergo a movement in 
the same direction as that of the body, the nearer an 
opposite, parallactic displacement. The parallactic 
displacements to which we are accustomed are per- 
ceived, but do not cause us any disturbance and are 



^^P correctly 
^^ of a Plat 




correctly interpreted. But in the monocular 
of a Plateau wire-net, the parallactic displacements, 
which in the present case are unusual as regards 
amount and direction, immediately attract the eye, 
and apparently present to us a revolving object' 

When I turn my head, I not only see that part of 
it turning which I am able to see (as will be imme- 
diately understood from the foregoing) but I also fed 
it turning. This is due to the fact that conditions exist 
in the province of touch which are quite analogous to 
those in the province of sight.* When I reach out my 
hand to grasp an object, a sensation of touch is com- 
bined with a sensation of innervation. If I look to- 
wards the object, a luminous sensation is substituted 
for the sensation of touch. Even where objects are not 
touched, skin-sensations may always be perceived when 
the attention is turned to them, and these, combined 


hachtungen Ober roonocnlaie Stare 

•oacofie" {SilcHHgi- 

btricUc dcr Hytnir Aka 

dfrni. Vol. LVHL. 1S6B). 

»Tha VIEW that thi 

'. sense oE Bight and the Bense of 

touch involve, so to 

ipeik, the S3 IDG space-! 

ansa as B cammon elamaal, was 1 

le;. Viderol alia [Ltilraiur lis. 

ttmglis) is of opin- 

ion that the space-sanse 

, of the hiind i< flltOBOlherdifferen 


s of Dr. Th. Loewj 

iliiniKi nack Lxti 


U.MB man blind from I 

lirth dnas no., after heing apera.a. 

Inpon, piiwiardia- 

ipheiea nith nhich he is familiar 1 


with changing innervations, also yield a conception of^ 
our body as in motion, which quite accords with that 1 
acquired by optical means. 

Thus, in active movements, the skin- sensations are ] 
delocalised, as we may briefly express it. In passive 
movements of the body, reflex, unconscious innerva- 
tions and movements of compensation make their ap- 
pearance. In turning round to the right, for example, 
my skin-sensations are connected with the same inner- 
vations as would be combined with the touching of 
objects in turning to the right, I feel "myself turning 
to the right. If I am passively turned toward the 
right, the reflex endeavor arises to compensate the 
turning. I either actually remain standing and feel 
myself at rest, or I repress the motion toward the left. 
But for this I need to exert the same voluntary inner- 
vation as for an active turning to the right, which has , 
also the same sensation as its result. 

At the time when my work on the Sensaf ions qf^ I 
M&vemenl^ was written, I had not yet attained to a J 
thoroughly comprehensive view of the simple relation J 
here described. I encountered, consequently, difficul-' 
ties in the explanation of certain phenomena, observed'J 
by Breuer and myself, which are now easy of explana-J 
tion, and which I will briefly notice. If an observ 




be shut up In a closed receptacle, aad the receptacle 
be set in rotation toward the right, the same will ap- 
pear to the observer in rotation, although every ground 
of inference for relative rotation is wanting, if his 
eyes perform involuntary, compensatory movements 
to the left, the images on the retina will be displaced, 
with the result that he has the sensation of movement 
toward the right. If, however, he fixes his eyes upon 
the receptacle, he must voluntarily compensate the in- 
voluntary movements, and thus again he is conscious 
of movement tbwards the right. It is plain, there- 
fore, that Breuer's explanation of the apparent motion 
of optical vertigo is correct, and also that this move- 
ment cannot be made to disappear by the voluntary 
fixation of the eyes. The remaining cases of optical 
vertigo noticed in my work may be disposed of in like 

In voluntary forward motion or rotation, we have 
not only a sensation of every single successive position 
of the parts of our body, but also the much more sim- 
ple sensation of movement forward or of turning round. 
As a fact, we do not form the notion of forward move- 
ment from the percepts of the various individual move- 
ments of the legs, or at least are not constrained to do 
so. There are cases, indeed, in which the sensation 
of forward movement is un.doubtedly present while 
that of the movements of the legs is altogether lack- 

■B Br-j-rguHgstinf^nJxiigiTi. 


iog. This is true, for instance, of a railway- journey, 
or even of the thought of such a journey, and may oc- 
cur also in recalling a distant place, etc. The only 
possible explanation of this can be that the wiil to 
move farwan/ or to ium about, which furnishes to the 
extremities their motor impulses, — impulses which 
may be further modified by particular innervations, — 
is of a comparatively simple nature. The conditions 
existing here are probably similar to, although more 
complicated than, those connected with the movements 
of the eyes, which Hering has so felicitously inter- 
preted, and to which we shall presently return. 

The following experinients and reflexions, which 
form a sequel to an earlier publication of mine, will 
perhaps assist us in obtaining a correct view of these 

If we take our stand upon a bridge, and look fix- 
edly at the water flowing beneath, we shall generally 
have the sensation of being ourselves at rest, whilst 
the water will seem in motion. Prolonged gazing, 
however, almost invariably results in the sensation 
that suddenly the bridge, with the observer and his 
whole environment, begins to move in the direction 
opposite to that of the water, while the water assumes 
the appearance of being at rest.' The re/a/ive motioa. 

lAs vie all kooiT, ibe mo» vaiied (orms of Ibe same impress 


"Pace-sensations continued. 

of the objects is in both cases the same, and there 
must therefore be some adequate physiological reason 
why at one time one, and at another, another part of 
them is felt to move. In order to investigate the mat- 
ter at my leisure, I had the simple apparatus con- 
structed which is represented in Fig. 18. An oil-cloth 
of simple pattern is drawn horizontally over two rol- 
lers, two metres long and fixed three metres apart in 
bearings, and is kept in uniform motion by means of a 
crank. Across the oil-cloth 
and about thirty centime- 
tres above it, is stretched 
a string ff, with a knot A', 
which serves as a fixation- 
point for the eye of the 
observer stationed at A. 
Now, if the oil-cloth be set 

In motion in the direction of the arrow, and the ob- 
server follow the pattern with his eyes, he will see it in 
motion, himself and his surroundings at rest. On the 
other hand, if he gazes at the knot, he and the whole 
room will presently appear in motion in the contrary 
direction to the arrow, while the oil-cloth will stand 
still. This change in the aspect of the motion takes 
more or less time according to the mental condition 
of the observer, but usually requires only a few sec- 
onds. If we once get the knack of it, the two impres- 


sions may be made to alternate with some rapidity ' 
and at will. Every following of the oil-cloth brings 
the observer to rest, every fixation of K, or non-atten- 
tion to the oil-cloth, by which its pattern becomes 
blurred, sets the observer in motion. This phenom- 
enon, of course, must not be confounded with the fa- 1 
miliar Plateau-Oppel phenomenon, which is a local u 
tinal effect. In the preceding experiment, the entire 
environment, so far as it is distinctly visible, is in mo- 
tion, whilst in the latter a moving veil is drawn along 
in front of the object, which is at rest. The attendant 
stereoscopic phenomena,- — for example, the appear- 
ance of the thread and knot underneath the transparent 
oil-cloth, — are quite immaterial in this connexion.' 

Before we proceed to the explanation of the expe- 
riment, it will be well to introduce a few variations. 
An observer stationed at £ seems, under the 5 
conditions, to be speeding, with all his surroundi 
towards the left. We now place above the oil-cloth 
TT, Fig. 19, a mirror SS, inclined at an angle of 45° 
to the horizon. We observe the reflexion TT in SS, 
after having placed on our nose a shade ««, which in- 

Oppel p) 

Vierordt, who BubaequenUy tupre! 


r Hid I 



tercepts the direct view of TT from the eye, O. If 
yy moves in the direction of the arrow, while we are 
looking at K' , the reflexion of K, we shall presently 
fancy ourselves sinking downward with the whole 
room, whereas if the motion be 
reversed we shall seem to ascend 
as if in a balloon,^ Finally, the 
experiments with the paper drum, 
which I have elsewhere described, 
and to which the following ex- ^ ^ 

planation also applies, should be 
cited here. None of these phenomena are purely op- 
tical, but all are accompanied by unmistakable motor 
sensations of the whole body. 


What form, now, must our thoughts take on, in or- 
der to acquire the simplest explanatory setting for the 
preceding phenomena? Objects in motion exert, as is 
well known, a peculiar motor stimulus upon the eye, 
and draw our attention and look after them. If the eye 
really follows them, we must assume, from what has 
gone before, that the objects move. But if the eye is 
kept at rest, and is forcibly restrained from following 
the moving objects, the constant stimulus to motion 
proceeding from the latter must be counterbalanced 

lewas ii»Dg upward 


by an equally constant stream of innervation flowing 
to the motor apparatus of the eye, exactly as if the 
motionless point on which the eyes rest were moving 
uniformly in the opposite direction, and we were fol- 
lowing that with our eyes. But when this process be- 
gins, all motionless objects on which the eyes are fast- 
ened must appear in motion. It is obviously unneces- 
sary that this stream of innervation should always be 
consciously and deliberately called into action. All 
that is requisite is that it should proceed from the 
same centre and by the same paths as intentional fixa- 

No special apparatus is necessary for observing 
the foregoing phenomena. They are to be met with 
on all hands. I walk forward by a simple act of the 
will. My legs perform their functions without special 
intervention on my part. My eyes are fixed stead- 
fastly upon their goal without suffering themselves to 
be drawn aside by the niotion of the retinal images 
consequent upon progression. All this is brought 
about by a single act of the will, and this act of the 
I will itself is the sensation of forward movement. The 
same process, or at least a part of it, must also be set 
up, if the eyes are made to resist permanently the ex- 
citation of a mass of moving objects. Hence the motor i 
sensations experienced in the foregoing experiments. 

The eyes of a child on a railway-train will be ob- 
served to follow almost uninterruptedly and with a ] 
jerking motion the objects outside, which appear to it \ 


to be running. The adult has the same sensation if 
he will passively yield himself to the natural impres- 
sions. If I am riding forwards, the whole space to my 
left, for obvious reasons, rota.tes, in the direction of the 
hands of a watch, about a very distant vertical axis, 
and the space to my right does the same, but in the 
opposite direction. Only when I resist following the 
objects with my eyes, does the sensation of forward 
motion arise. 

Without doing violence to the facts described in 
my book on The Sensations 0/ Movement, the preceding 
observations suggest the possibility of modifying the 


theoretical i 

)ie-w there taken of the facts, as we shall 

point out ii 

1 the following. 1 It is extremely probable 

IMy views . 

reKatding the Eensatlocs ot movemenl have been repeatedly 

■ttBclwd. >E is « 

ainiEd solelj al 

Uie *^/«*i«i, to whicU I atlBchad comparallvely lilile \m- 

l am leady and willing 10 modify my views in accordance 

Dvered Facts, tbe present work will tcstity. lbs deciiion as 

in .be riibt 1 will cbeerfolly leave to the tulore. On the other 

hand, obsercsiio 

ns have been made that strongly favnt the theory propounded 


sr, and Brown. To these belong, first, the facts collected by 

•/■at^gitdu c«' 

igrii ptriediquc interna lin«al dt icicnai midicalli h A>nttcr- 

</-«, .879). Cus 

e observed, indlseases of the middle ear, that leBei turnings 

ot the head WEr, 

! induced when air was blown inlo ibe cavity of tbe tympa- 

nam, and round 


umiags which he had felt during the injection of liquids. 


own ("On a Case of Dyepoptio Vertigo," iVKK^yBfi^/Ai 

Jltyai S^-rly >f 

pBthological TEt 


increased intensity and lengthened duration of the sensation 


'cry tnrniDg of the body— Bm most remarkable of all are the 

Wiiliam JamesC'The Sense of Diziinessin Doat-MalBS,' 

.C««-™» J«.rn 

atqfOl^g,. Vol. IV„ .&8al. JameB discovered in deaf-mutes 

■ ■tHkini; and r 



that an organ exists in the head— it may be called the 
terminal organ {TO) — which reacts upon acceUratiotts, 

Ll nncenaiutf in Ibeir walk n 

The viev Is unleniibia Ibst we Bnive at knonledKa oF eqqilibrinm and < 
movement loUty by means ol Ihe semicircular canals. On the coDlrBt7, it i 
eitremelr probable that lower animelB, in whom this orEau is eatirelf nan 

lerimenta in Ihis din 
«i In his work, ^""i 

Id. But the eiperimBnts which Lubbock has 
I, aid Wasfs. become much more compre- 
don dI SEDsaliDDS of movement. Ab eiperi- 

s which I bav« bciefiy described before (/Ins 

idered observable. T 

lis. in the same diiecti 
gives a view of the i 







r the r 



ve, wilh 



ling ma- 





halt Ih 


velocity and in the e 

■.^. The tollowing figure Rli'es the gear- 
a-piece », and the receiver gg. revolve 
g-wheels. rigidly connected togellier. re- 
Ibe cog-wheel 0:1 be r^ thai of M also r. 

screws, is laid upon the boliom ot Ihe receiver and so adjusted that, on roU- 
tion, Ihe redeiions in it remain al test. It is then perpendicular lo the uii 

hole L,\i so adjusted to the open tubs of the eye-piece, wilh its teSecting anr- 
face downward, that, on rotation, the images seen throngh the hole, in the 
mirrored teaeiioo ot 5' in S, remain not loulesa. Then S- stands perpendicu- 
Isi to Ihe axis ol the eye-piece With the aid ot a brush we may now mark 
upon the mirror i' a point P. whose pOEition is not altered on rotation (■ re- 


.nd by means of which we are made aware of move- 
ments. But instead of imagining that special motor 

1 whicli is easily sccomplished atler h few lr\s\i), and so plac. 


sensations exist, which proceed from this apparatus 

from a sense-organ, we may assume that this organ 
mply disengages innervations after the manner of re- 
Innervation may be voluntary and conscious 
or involuntary and unconscious. The two different 
organs from which these proceed may be designated 
by the letters WI and UI. Both sorts of innervation 


hypolhenuse and 


rotation ONPQ. 




loMbA'Cand w 

ha axis 


points o( the alia 

can sol 


is centred. Tta 

rky in 


accordingly tall 


l>o shows the Held 

t vlsira 

lly upon AC. is re 

diieclion AC and p 

The ray OR, oa U 

coiBd at £ and emct 

Dltie direction or 7 

cienUormyanperiments, 11 

a turned ao rapidly 

(hat ttie 

ago by refleiion co 


i; prism above the 

appeared to mo unn 

nenta, I ha.a bilbei 

all vertebrates (bird 

, Gshesl, 

alitor SiisatisHi f 

lly COD- 



may pass to the oculo-motor apparatus (OM) and to 
the locomotor apparatus (ZAf). 

Let us now consider the accompanying diagram. 
We induce by the will, that is by a stimulus from IVI, 
an active movement, which passes in the direction of 
the unfeathered arrows, to OM anA LM. The appur- 
tenant innervation is directly felt. In this case, there- 
fore, a special sensation ol movement, differing from 
the innervation, is unnecessary. If the motion in the 
direction of the unfeathered arrows is a passive one 

(taking us by sur- , * 

prise), then, as ex- 
perience shows, re- 
flexes proceed from 
TO over UI, which 
produce compensa- 
tory movements, indi- 
cated by the feathered 
arrows. If WI takes no part in the process, and the 
compensation is effected, both the motion and the ne- 
cessity for motor sensation cease. But if the compen- 
satory movement is intentionally suppressed, that is, 
by intervention from IVI, then the same innervation is 
necessary for achieving this result as for active move- 
ment, and it consequently produces the same motor 

The terminal organ TO is accordingly so adjusted 
to WI and l/I that upon a given motor stimulus in 
the first, contrary innervations are set up in the last 


two. But further, we have to notice the following dif- ] 
ference iu the relation of TO to WI and UI. For 
TO, the motor excitation i s naturally the same whether 
the movement induced is passive or active. In active 
movements, too, the innervations proceeding from WI 
would eventually be neutralised by TO and UJ, did not 
inhibitory innervations proceed simultaneously with : 
the willed innervations from WIto TO and UI. The 1 
influence of TO upon (fVmust be conceived as much 
weaker than that of TO upon UI. If we should picture 
to ourselves three animals, WI, UI, and TO, between 
whom there was a division of labor, such that the first 
executed only movements of attack, the second only , 
those of defence or flight, while the third filled the i 
post of sentinel, all of whom were united into a single ' 
new organism in which IfVheld the dominant position, 
we should have a conception approximately corre- 
sponding to the relation represented. There is much 
in favor of such a conception of the higher animals.' 
I do not offer the preceding view as a complete and 
perfectly apposite picture of the facts, On the con- 
trary, I am fully aware of the defects in my treatment. 

lit I grasp a little bird in my band, the bird vill behave loiiards my hand 

wuficii bss been rumtBhed by the subEequEHI noiks of Bieueraiid Kreldt. 
The latter has succeeded in caosiiiK cenain specimens of the CroiUcea b 
substituta lerrum Hmatuni (or iheir natutal otoliths, and they h»Ta theD ra 


But the attempt to reduce to a quality of sensation, in 
accordance with the cardiual principle evolved in our 
investigation (p. 28), all sensations of space and move- 
ment arising in the province of sight and touch during 
change o£ place, or even as a shadow in remembrance 
of locomotion, or at the thought of a distant spot, etc., 
will be found justifiable. The assumption that this 
quahty of sensation is the will, so far as the latter is 
occupied with position in space and spatial relation, 
or the sensation of innervation, does not forestall fu- 
ture investigation and only represents the facts as they 
are known at the present time.^ 

I I. 
From the discussions of the previous chapter rela- 
tive to symmetry and similarity, we may immediately 
draw the conclusion that to like directions of lines 
which are seen, the same kind of inuervation-sensa- 
tions, and to lines symmetrical with respect to the 
median plane very similar sensations of innervation 
correspond, but that with looking upwards and look- 
ing downwards, or with looking at objects afar off and 
at ihe objects near at hand, very different sensations 
of innervation are associated, — as we should naturally 
be led to expect from the symmetrical arrangement of 
the motor apparatus of the eye. With this single per- 
ception we dispose of a long chain of peculiar physi- 
ologico-optical phenomena, which have as yet received 

1 Comparo HeripB's opinion given in Hermann's Handiuch drr Fhysiatosl.; 


scarcely any attention. I now come to the point whichj 
physically regarded at least, is the most important. 

The space of the geometrician is a mental construct 
of threefold manifoldness, that has grown up on the 
basis of manual and intellectual operations. Optical 
space (Hering's " sight space ") bears a somewhat 
complicated geometrical relationship to the former. 
The matter may be best expressed in familiar terms by 
saying that optical space represents geometrical space 
(Euclid's space) in a sort of reUeve-perspective^s. rela- 
tion of things which may be teleologically explained. 
In any event, optical space also is a threefold mani- 
foldness. The space of the geometrician exhibits at 
every point and in all directions the same properties — 
a quality which is by no means characteristic of phys- 
iological space. But the influence of physiological 
space may nevertheless be abundantly observed in ge- 
ometry. Such is the case, for example, when we dis- 
tinguish between convex and concave curvatures. The 
geometrician should really know only the amount of ■ 
deviation from the mean of the ordinates. 

As long as we conceive the (12) muscles of the eye 
to be separately innervated, we are not in a position 1 
to explain this fundamental fact. I felt this difficulty 
for yearsj and also recognised the direction in which, I 
on the principle of the parallelism of the physical and 
the psychical, the explanation was to be sought ; but 


owing to my defective experience in this province, the 
solution itself remained hidden from me. All the bet- 
ter, therefore, am I able to appreciate the service ren- 
dered by Hering, who discovered it. To the three 
optical space co-ordinates, viz., to the sensations of 
height, breadth, and depth, corresponds according to 
the showing of this investigator (Hering, Beitrage zur 
Physiolftgie, Leipsic, Engelmann, 1861-1865) simply a 
threefold innervation, which turns the eyes to the right 
or to the left, raises or lowers them, and causes them 
to converge, according to the respective needs of the 
case. This is the point which I regard as the most 
important and essential.^ Whether we regard the in- 
nervation itself as the space -sensation, or whether we 
conceive the space-sensation as ulterior to the inner- 
vation, — a question neither easy nor necessary to de- 
cide, — nevertheless Hering's statement throws a flood 
of light on the psychical obscurity of the visual pro- 
cess. The phenomena cited by myself with regard to 
symmetry and similarity, moreover, accord excellently 
with this conception. But it is unnecessary, I think, 
to substantiate further their agreement.' 





"This conception also removes a difficulty which I atill felt in 1871. 


1 which 1 gave ulleradce in my lecture on •■SymTneliy" (Prague: Ci 


!7i).-^o» translatcti into English in my Popular Sciiotific Li^nrii. Cbic 

• go, 

f by 

.r aymmetry, allhongh originally acqniied by the eyes, conld col havo 1 

infinsd B.cln3ively to the visnal organs. By thousands of years ot prat 





IN normal psychical life, sight -sensations do not 
make their appearance alone, but are accompa- 
nist hy other sensations. We do not see cflitmJ im- 
agas in an optical space, but we perceive the /wAer 
round sbotit us in their many and varied sensaoas 
qualities. Deliberate analysis is needed to single out 
the 8i|;ht-sensBlions from these complexes. Eves tbe 
total perceptions themselves are almost invariably ac- 
companied by thoughts, wishes, and impulses. By 
BMUlions are excited, in animals, the movements xA 
adaptation demanded by tbeir conditions o! Hie- B 
these conditions are sample, alteting but litde and 
slowly, immediate seasoay exdtatioB is : 

rrwriIlHa.n»iH-tmiymTm«eo, i^»imatt.tmr 


Higher intellectual development is unnecessary. But 
the case is different where the conditions of life are 
intricate and variable. Here so simple a mechanism 
of adaptation can neither develop, nor would it lead 
to the accomplishment of the required ends. 

Lower species devour everything that comes in 
their way and that excites the proper stimulus. A 
more highly developed anirnal must seek its food at 
risks to itself ; when found, must seize it at the right 
spot, or capture it by cunning, and cautiously test its 
character. Long trains of varied memories must pass 
before its mind before one is sufficiently strong to out- 
weigh the antagonistic considerations and to excite the 
appropriate movement. Here, therefore, a sum of 
associated remembrances (or experiences) coincidently 
determining the adaptive movements, accompany and 
confront the sensations, la this consists the intellect. 

In the young o£ higher animals, presenting com- 
plex conditions of life, the complexes of sensations nec- 
essary to excite adaptive movements are frequently 
of a very complicated nature.^ With the development 
of intelligence, the parts of these complexes necessary 

Hen lowards the light ; \a short, (hat certain animils oUea sded under certain 

C. Lta;d Mori-an.- 



to produce the excitation constantly diminish, and thftfl 
sensations are more and more supplemented and re- 1 
placed by the intellect, as may be daily observed in 1 

children and adolescent animals. 

Representation by images and ideas, therefore, has , 
to supply the place of sensations, where the latter are 
imperfect, and to carry to their issue processes ini- 
tially determined by sensations alone. But in normal 
life, representation cannot supplant sensation, where 
this is at all present, except with the greatest danger 
to the organism. As a fact, there is, in normal psy- i 
chical life, a marked difference between the two spe- i 
cies of psychical factors. I see a blackboard before 
me. I can, with the greatest vividness, represent to 
myself on this blackboard, either a hexagon drawn in 
clear, white lines, or a colored figure. But, pathologi- 
cal cases apart, I always distinguish what I see and 
what I rtprfseni to myself. In the transition to repre- 
sentation, I am aware that my attention is turned from 
my eyes, and directed elsewhere. In consequence o£ 
this attention, the spot seen upon the blackboard and 
the one represented to myself as situated in the same 
place differ as by a fourth co-ordinate. It would not 
be a complete description of the facts to say that the \ 
representation overlays the object as the images r 
fleeted in a transparent plate of glass overlay the bod- I 
ies seen through it. We are confronted here, (or ti 


time being, with a fundamental psychological fact, 
the physiological explanatioE of which will sometime 
undoubtedly be discovered. 

Where the development of intelligence has reached 
a high point, such as is presented now in the com- 
plex conditions of human life, representation may fre- 
quently absorb the whole of attention, so that events 
in the neighborhood of the reflecting person are not 
noticed, and questions addressed to him are not heard ; 
— a state which persons unused to it are wont to call 
absent-mindedness, although it might with more ap- 
propriateness be called present-mindedness. If the 
person in question is disturbed in such a state, he has 
a very distinct sensation of the labor involved in the 
transference of his attention. 

It is well to note this sharp division between rep- 
resentations and sensations, as it is an excellent safe- 
guard against carelessness in psychological explana- 
tions of sense-phenomena. The well-known theory 
of " unconscious reasoning " would never have reached 
its present extended development if more heed had 
been paid to this circumstance. 

The organ of representation can for the nonce be 
conceived as one which, in a diminished degree, is 
susceptible of all the specific energies of the sense 
and motor organs, so that, according to the special 
attention evoked, now this, now that specific energy 


is excited in it. Such an organ is eminently qualified 
for physiological mediation between the different en- 
ergies. As is shown by experiments with animals 
whose cerebrum has been removed, there are prob- 
ably, in addition to the organ of representation, a 
number of other, analogous organs of mediation, whose 
processes are unconscious. 

That wealth of representative life with which we are 
personally acquainted from self -observation, doubtless 
made its first appearance with man. But the begin- 
nings of this expression of life, in which nothing but 
the relations of the various parts of the organism to 
one another is manifested, go back with no less cer- 
tainty to quite primitive stages in the animal scale. 
On the other hand, the parts of single organs must also, 
by mutual adaptation, sustain a reciprocal relation to 
one another analogous to that of the parts of the or- 
ganism as a whole. The two retinas, with their motor 
mechanism of accommodation and of luminous adjust- 
ment, controlled by light sensations, afford a very 
clear and familiar example of such a relation. Physio- 
logical experiment and simple self- observation teach 
us that such an organ has its own adaptive habits, its 
own peculiar memory, one might almost say its own 

The most instructive observations in this connex- 
ion are probably those of Johannes Muller, collected 
in his excellent work on "The Phantasms of Sight" 
(C/eier die phantasiiscken Gesichtserscheinungen. Cob- 


lenz, i8a6j. The sight-phantasms observed by Miiller 
and others in the waking state are entirely without the 
control of either the will or the reason. They are in- 
dependent phenomena, connected not with the organ 
of representation, but with the sense-organs, and have 
thoroughly the character of processes objectively seen. 
They are veritable imagination and memory phenom- 
ena of sense. 

Those processes which (according to Miiller) are 
normally induced in the visual substance by excita- 
tions of the retina, and which condition the act of 
seeing, may also, under certain conditions, be spon- 
taneously produced in the visual substance without 
excitation of the retina, becoming there the source 
of phantasms or hallucinations. We speak of sense- 
memory when the phantasms are closely allied in char- 
acter to objects seen before, of hallucinatiaiu when the 
phantoms arise more freely and independently. But 
no sharp distinction betv/een the two cases can be 

II am acquaiatsd irith iiU miDDBror sighl-phaDtsims fnm By own si- 
perlcQci!. The mingling d{ phanlasm i vitb DbJecK Indistinctly saen. thelsllgr 

BDgTObBed with the sLudy of pulse-tracings and sphyemegrepfay, tha £Da white 

with lorma ol thli a 


When we withdraw the retina from the influence 
of outward excitations, and turn the attention to the 
field of vision alone, traces of phantasms are almost 
always present. Indeed, they make their appearance 
when the outer excitations are merely weak and indis- 
tinct, in a poor and dull light, or when we look, for 
example, at a surface covered with dim, blurred spots, 
or at a cloud, or at a grey wall. The figures which 
we then seem to see, provided they are not produced 
by a direct act of attention in selecting and combining 
distinctly visible spots, are certainly not products of 
representation, but constitute, at least in part, sponta- 
neous phantasms, which, for the time being and at 
E points, take forcible precedence over the retinal 


All marked and independent appearance of phan- 
tasms without excitation of the retina — dreams and 
the half-waking state excepted — must, by reason of 
their biological purposelessness, be accounted patho- 
logical. In like manner, we are constrained to regard 
every abnormal dependence of phantasms upon the 
will as pathological. Such, very likely, are the states 
that occur in insane persons who regard themselves as 
very powerful, as God, etc. 


After these introductory considerations we may 
now turn to the consideration of a few physiologico- 
optical phenomena, the full explaoatiou of which, it is 
true, is still distant, but which are best understood as 
the expressions of an ind-ependeni life on the part of 
the sense-organs. 


We usually see with both eyes, and agreeably to 
definite needs of life, not colors and forms, but bodies 
in space. Not the elements of the complex, but the 
physiologico-optical complex entire, is of importance. 
This complex the eye seeks to fill out and supplement, 
according to the habits acquired (or inherited) under 
its environment, whenever, as a result of special cir- 
cumstances, the appearance of the complex is incom- 
plete. This occurs oftenest in monocular vision, but 
is also possible in the binocular observation of very 
distant objects where the stereoscopic differences con- 
sequent upon the distance of the eyes from each other 

We generally perceive, not light and shadow, but 
objects in space. The shading of bodies is scarcely 
noticed. Differences of illumination produce differ- 
ences in the sensation of depth, and help to define the 
form of bodies where the stereoscopic differences are 
insufficient, — a condition which is very noticeable in 
the observation of distant mountains. 

Very instructive, in this relation, is the image on 
the dull plate of the photographic camera. We are 
oftea astounded at the brightness of the lights and the 
depth of the shadows, which were not noticed in the 
bodies themselves but are striking when brought into 
a single plane. I remember quite well that, in my 
childhood, all shading appeared to me an unjustifiable 
disfigurement of drawing, and that an outline-sketch 
was much more satisfactory to me. It is likewise 


well-known that whale peoples, for instance the Chi- 
nese, despite a well-developed artistic technique, do 
not shade at all, or shade only in a defective manner. 
The following experiment, which I made many 
years ago, illustrates very clearly the above-noticed 
relation between light -sensation and the sensation of 
depth. We place a visiting-card, bent cross- 
wise, before us on the desk, so that its bent 
edge is towards us. Let the light fall from 
the left. The half abdeis then much lighter, 
the half beef much darker — a fact which 
is, however, scarcely perceived in unprej- '^*'*' 

udiced observation. We now close one eye. Here- 
upon, part of the space-sensations disappear. Still 
we see the bent card in space and nothing noticeable 
in the illumination. But as 
soon as we succeed in see- 
ing the bent edge depressed 
instead of raised, the light 
and the shade stand out as 
if painted thereon. Such 
an inversion is possible, be- 
cause depth is not deter- 
mined in monocular vision. 

If in Fig. 25, 1 O represents the eye, abc a. section of 
a bent card, and the arrow the direction of the light, 
ab will appear lighter than dc. Also in 2, ab will ap- 
pear lighter than be. Plainly, the eye must acquire 
the habit of interchanging the illumination of the sur- 

face- elements and the fall of the depth-sensation. The ' 

fall and the depth diminish, with diminishing illumina- 
tion, towards the right, when the light falls from the 
left (1) ; contrariwise, when it falls from the right. 
Since the wrappings of the ball in which the retina is 
embedded are translucent, it is not a matter of indiffer- 
ence for the distribution of light upon the retina 
whether the light falls from the right or the left. Ac- 
cordingly, things are so arranged that, without any 
aid of judgment, a fixed habit of the eye is developed, 
by means of which illumination and depth are def- 
initely connected. If, by virtue of another habit then, 
it is possible to bring a part of the retina into conflict 
with the first habit, as in the above experiment, the 
effect is made manifest by remarkable sensations. 

The purpose of the preceding remarks is merely to 
point out the character of the phenomenon under con- 
sideration and to indicate the direction in which a 
physiological explanation (exclusive of psychological 
speculation) is to be sought. We will further remark 
that, with respect to interchangeable quaUties of sen- 
sation, a principle similar to that of the conservation 
of energy seems to hold. Differences of illumination 
are partly transformed into differences of perspective 
depth, and in this transformation are weakened in their 
first capacity. At the expense of differences of depth, 
on the other hand, differences of illumination may be 
augmented. An analogous observation will be made 
later on in another connexion. 


The habit of observing bodies as such, that is, of 
giving attention to a large and spatially cohering mass 
of light-sensations, carries within it a source of pe- 
culiar and ever astonishing phenomena. A two-colored 
painting or drawing, for instance, appears in general 

: take the one or the 
rhe puzzle pictures, in 

quite different according as 
other color as the backgroiini 
which, for example, an ap- 
parition makes its appear- 
ance between tree-trunks as 
soon as the dark trees are 
taken as the background, 
and the bright sky as the 
object, are well known. In 
exceptional instances only 
do background and object 
possess the same form — 
a configuration frequently 
employed in ornamental de- 
signs, as maj' be seen in '''*■ "*■ 
Fig. 25, taken from page 15 of the afore- mentioned 
Grammar of Ornament, also in Figs. 20 and 32 of Plate 
35, and in Fig, 13 of Plate 43 of that work. 


The phenomena of spai 
[he monocular observatioE 

e vision which accompany 
of a perspective drawing. 


or, what amounts to the same thing, the monocular 
observation of a spatial object, are generally very 
lightly passed over, as being self-evident in nature. 
But I am of the opinion that there is yet much to be 
investigated in these phenomena. One and the same 
perspective drawing may represent an unlimited num- 
ber of different objects, and consequently the space- 
sensation can be only in part determined by such a 
drawing. If, therefore, despite the many bodies con- 
ceivable as belonging to the figure, only a few are 
really seen with the full character of objectivity, there 
must exist some good reason for the coincidence. It 
cannot arise from the adducing of auxiliary consider- 
ations in thought, nor from the awakening of conscious 
remembrances in any form, but must depend on cer- 
tain organic habitudes of the visual sense. 

If the visual sense acts in conformity with the hab- 
its which it has acquired through adaptation to the 
life- conditions of the species and the individual, we 
may, in the first place, assume that it proceeds ac- 
cording to the principle of Probability; that is, those 
functions which have been most frequently excited to- 
gether before, will afterwards tend to make their ap- 
pearance together when only one is excited. For ex- 
ample, those particular sensations of depth which in 
the past have been most frequently associated with a i 
given perspective figure, ■will be extremely likely to 
reproduce themselves again when that figure makes 
its appearance, although not necessarily co-determined \ 


thereby. Furthermore, a principle of economy ap- 
pears to manifest itself in the observation of perspec- 
tive drawings; that is to say, the visual sense never 
of itself puts forth greater efforts than are demanded 
by the excitation. The two principles coincide in their 
results, as we shall presently see. 

The following may serve as a detailed illustration 
of the above. When we look at a straight line in a 
perspective drawing, we always see it as a straight 
line in space, although the straight line as a perspec- 
tive drawing may correspond to an unlimited number 
of different plane spatial curves. But only in the spe- 
cial case where the plane of a curve passes through 
the centre of one eye, will it be delineated on the retina 
in question as a straight line (or as a great circle), and 
only in the yet more special case where the plane of 
the curve passes through the centres of both eyes, will 
it be delineated on both as a straight line. It is thus 
extremely improbable that a plane curve should ever 
appear a straight line, 'while on the other hand a 
straight line in space is always reflected upon both 
retinas as a straight line. The most probable object, 
therefore, answering to a perspective straight line, is 
a spatial straight line. 

The straight line has various geometrical proper- 
ties. But these geometrical properties, for example the 



familiar characteristic of being the shortest distance be- 
tween two points, are not physiologically of importance. 
It is of far more consequence that straight lines lying 
in the median plane or perpendicular thereto are phy- 
siologically symmetrical to themselves. A vertical 
lying in the median plane is aiso physiologically dis- 
tinguished by its perfect uniformity of depth-sensa- 
tion, and by its coincidence with the direction of grav- 
ity. All vertical straight lines may be readily and 
quickly made to coincide with the median plane, and 
consequently partake of this physiological advantage. 
But the spatial straight line generally, must be physio- 
logically distinguished by some different mark. Its 
sameness of direction in all its elements has already 
been pointed out. In addition to this, however, it is 
to be noted that every point of a straight line in space 
marks the mean of the depth-sensations of the neigh- 
boring points. Thus the straight line in space repre- 
sents a viinimuvi of departure from the mean of the depth- 
sensations ; and the assumption forthwith presents 
itself that the straight line is seen with the least effort. 
The visual sense acts therefore in conformity with the 
principle of economy, and, at the same time, in con- 
formity with the principle of probability, when it ex- 
hibits a preference for straight lines.' 


«! "SiDB* ilraighl lii 









umin bcllK 


|b> line 





bly be prod 


The deviation of a sensation from the mean of the 
adjacent sensations is always noticeable, and exacts 
a special eSort on the part of the sense-organ. Every 
new turn of a curve, every projection or depression of 
a surface, involves a deviation of some space-sensa- 
tion from the mean of the surrounding field on which 
the attention is directed. The plane is distinguished 
physiologically by the fact that this deviation from 
the mean is a minimum, or for each point in particu- 
lar = 0. In looking through a stereoscope at a spotted 
surface, the separate images of which have not yet 
been combined into a binocular view, we experience 
a peculiarly agreeable impression when the whole is 
suddenly flattened out into a plane. The aesthetic im- 
pressions produced by the circle and the sphere seem 
to have their source mainly in the fact that the above- 
mentioned deviation from the mean is the same for all 

That the deviation from the mean of adjacent parts 
plays a r81e in light- sensation I pointed out many 
years ago.* If a row of black and white sectors, such 

^H bu 

des LrcblreiEss auf 
[iS6sl. Vol. 52. Con- 
rViftw. (,868), Vol. i7i 
Its, {"Ueber dlt Ab- 


as are shown in Fig. 27, be painted on a strip of 
paper A A BB, and this be then wrapped about a cyl- 
inder the axis of which is parallel to AB, there will be 
produced, on the rapid rotation of the latter, a grey 
field with increasing illumination from B to A, in 
which, however, a bright line aa, and a dark line 
/3y3, make their appearance. The points which corre- 
spond to the indentations « arc not physically brighter 
than the neighboring parts, but their light-intensity 


exceeds the mean intensity of the immediately adja- 
cent parts, while, on the other hand, the light- intensity 
at p falls short of the mean intensity of the adjacent 
parts.' This deviation from the mean is distinctly 
felt, and accordingly imposes a special burden upon 
the organ of sight. Of what significance this circum- 
stance is for saliency and the sharp spatial definitioD 
of objects, I pointed out long ago. 



With regard to the depth- sensation excited by a 
drawing viewed monocularly, the following experi- 
ments are instructive. Fig. 28 is a plane quadrilateral 
with its two diagonals. If we regard it monocularly, 
it is most easily seen, according to the law of prob- 
ability, as a plane. In the great majority of cases, 
objects which are not plane, /urf^ the eye to the vision 
of depth. Where this compulsion is 
lacking, the plane object is the most 
probable and at the same time the easi- 
est for the organ of sight. 

The same drawing may be also 
viewed monocularly as a tetrahedron, 
the edge bd ol which lies in front of Kg* 

ac, or as a tetrahedron, the edge bd of which lies 
back of ac. The influence of the imagination and the 
will upon the visual process is extremely limited ; it 
is restricted to the directing of the attention and to 
the selection of the appropriate disposition of the organ 
of sight for one of a number of cases given by habit, 
of which, however, each one, when chosen, runs its 
course with mechanical certainty and precision. Look- 
ing at the point e, we can, as a fact, produce either 
of the two optically possible tetrahedrons at will, ac- 
cording as we represent to ourselves bd nearer or far- 
ther away than a e. The organ of sight is practised in 


the representation of these two cases, since it often 
happens that one body is partly concealed by another. 

The same figure may, finally, be seen as a four- 
sided pyramid, if we imagine the conspicuously situ- 
ated point of intersection e before or behind the plane 
abed. This is difficult to do, if ifrfand aec are two 
perfectly straight lines, because it conflicts with the 
habit of the organ of sight to see, without constraint, 
a straight line bent ; the effort is successful only be- 
cause the point c has a conspicuous position. But if 
there is a slight indentation at e, the attempt involves 
no difficulty. 

The effect of a linear perspective drawing is felt as 
unerringly by one who is ignorant of perspective as by 
one who is thoroughly conversant with the theorj, 
provided the former is able to disregard the plane of 
the drawing, ^a condition readily fulfilled in monoc- 
ular observation- Reflexion, and even the remem- 
brance of seen objects, have, according to my belief, 
little or nothing to do with the effect in question. 
Why the straight lines of a drawing are seen as spa- 
tial straight lines, has already been pointed out. 
Where straight lines appear to converge to a point in 
the plane of the drawing, the converging or approach- 
ing ends are referred, according to the principle of 
probability and economy, to like or to nearly lika 
depth. Herewith we have the effect of the vanishing 
points. Such lines may be seen parallel, but there is 
no necessity for such an impression. If we hold the 


drawing, Fig. 29, on a level with the eye, it may rep- 
resent to us a glance down a passage-way. The ends 
^hcf are referred to like distances. If the distance 
is great, the lines ae, bf, eg, dh appear horizontal. If 
we raise the drawing, the ends efgh rise, and the floor 
abef seems to have an upward slope. 
Upon lowering the drawing, the op- 
posite phenomenon is presented ; and 
analogous changes may be observed 
by moving the drawing towards the 
right or the left. In these facts, the '''*■ "■ 

elements of perspective effect find simple and clear ex- 

Plane drawings, provided they consist entirely of 
straight lines, everywhere intersecting each other at 
right angles, almost always appear plane. If oblique 
intersections and curved lines occur, the lines easily 
pass out of the plane ; as is shown, for 
example, by Fig. 30, which may, without 
difBcuity, be conceived ^s a curved sheet 
of paper. When outlines, such as are 
represented in Fig. 30, have assumed defi- 
nite spatial form, and are seen as the ^^-v- 
boundary of a surface, the latter, to describe it briefly, 
appears as fiat as possible, that is to say, is presented 
with a minimum of deviation from the mean of the 


The peculiar action of lines intersecting obliquely 
in the plane of the drawing (or on the retina), whereby 
the same are mutually and jointly forced out of the 
plane of the drawing (or out of the plane perpendicu- 
lar to the line of sight) was first observed 
by me on the occasion of the above-men- 
tioned (p. 91) experiment with the monoc- 
ular inversion of a card. The card in Fig. 
31, whose edge be when turned outwards is 
* in a vertical position, assumes, on my seeing 

be depressed, a recumbent position, like that of a book 
lying open upon my table, with the result that b a.'^- 
■^R^t^ farther away than e. When one is perfectly ac- 
quainted with the phenomenon, the inversion may 
be performed with almost 
every object, and one can 
always observe along with 
the change of form (along 
with the flapping) a remark- 
able simultaneous change 
of position. The effect is 
especially astonishing in the case of transparent ob- 
jects. Let abed he a section of a glass cube lying on 
a table ii, and let O be the eye. (Fig. 33.) On 
monocular inversion, the angle a is projected to a'. 

ihen dipped la 


b to the nearer point b', c to ^, and d to d'. The ' 
cube will seem to stand obliquely on its edge ^ upon 
the table t' f. In order that the drawing might afford 
a better survey of the phenomenon, the two views 
have been represented behind, not within one another. 
If a drinking-glass partly filled with a colored liquid 
be substituted for the cube, it will be seen, together 
with the surface of the liquid, in a similar oblique po- 

With sufQcient attention, the same phenomena 
may be provoked in any linear drawing. If we place 
the page containing Fig. 31 vertically before us, and 
observe it monocularly, w^e shall see b project if ^^ be 
raised, but if be be depressed b will retreat and e 
will project and come nearer to the observer. It 
may be said, briefly, that the legs of acute angles are 
thrust out on different sides of the plane of the draw- 
ing, or of the plane perpendicular to the line of sight, 
but that the legs of obtuse angles are thrust out on 
the same side. We may also say that all angles ex- 
hibit the tendency to become right angles. 

I was not long in discovering that the phenomenon 
referred to differed in no essential respect from that 
presented by Zollner's pseudoscopy. Although these 
phenomena have been much studied, no satisfactory 
explanation of them has as yet been offered. Natur- 
ally such superficial explanations as, for instance, the 
assumption that we are chiefly accustomed to see right 
angles, are inadmissible, if the investigation is not ut- 



terly to miscarry or to be prematurely broken off. We 
see oblique-angled objects often enough, but never, 
without artificial preparation, the motionless, oblique 
surface of a liquid, as we did in the experiment given 
above. Yet, the eye, it would seem, prefers the oblique 
liquid surface to an oblique-angled body. 

The elemental power displayed in these processes 
has, I believe, its root in far simpler habits of the or- 
gan of sight, — habits whose origin doubtless antedates 
the civilised life of man. 1 have essayed to explain 
the phenomena in question by a contrast of directions 
analogous to the contrast of colors, but without arriv- 
ing at a satisfactory result. The principle of economy 
likewise affords me no enlightenment. 

A somewhat greater prospect of success seems to 
be offered by the principle of probability. Let us con- 
ceive the retina as a perfect sphere and imagine the 
eye fixed upon the vertex of an angle a in space. The 
planes passing through the centre of the eye and the 
lines containing the angle, project the latter upon the 
retina, describing thereon a spherical segment having 
the angle A, which represents the angle of the monoc- 
ular image. An infinite number of values for a, now, 
varying from o° to 180°, may correspond to a constant 
value of A, as will be seen, if we reflect that the lines 
including the objective angle may assume every pos- 
sible position in the planes yielding their projections. 


Consequently, to a, seen ftngle A we may have corre- 
sponding, all the possible values of the objective angle 
a that can be obtained by causing each of the sides, 
6 and c, of the triangle to vary between o" and 180°. 
The result is, supposing the calculation to 
be performed in a definite manner, that larger 
angles are the most probable objects cor- 
responding to observed acute angles, and 
smaller angles the most likely counterparts of 
observed obtuse angles. I was not, however, 
in a position to determine whether the phe- 
nomena in question, which we might be in- '*' "' 
clined to regard as geometrically alike, could also be 
regarded ^s physiologually t\ie same — a question which 
is both essential and important. Moreover, the whole 
conception has still a slightly too artificial cast for me. 

A plane linear di 
quently appears pla 
vary and motion be 
sort will 
a solid body 
a former 
of Lissajou! 
phase, appe; 
excellent exs 

wing, monocularly observed, fre- 

. But if the angles be made to 

troduced, every drawing of this 

d form. We generally see, then, 

I, such as I have described on 

The well-known acoustic figures 

which on varying their difference of 

to lie on a revolving cylinder, afford an 

pie of the process in question. 

trMadimii ifWa). Vol. jS. 


Here, again, reference mif;ht be made to our habit 
of constantly dealing witti solid bodies. In fact, solid 
bodies engaged in revolutions and turnings continually 
surround us. Indeed, the whole material world in 
which we move is, to a certain extent, a continuous 
solid body ; and without the help of solid bodies we 
could never attain to the conception of geometrical 
space. We do not generally notice the position of 
the single points of a body in space, but apprehend 
directly its dimensions. Herein lies, for the unprac- 
tised, the main difficulty of drawing a perspective pic- 
ture. Children, who are accustomed to seeing bodies 
in their real dimensions, do not understand perspec- 
tive foreshortenings, and are far better satisfied with 
simple contours, with outline-drawings. I can well 
remember this condition of mind, and through this 
remembrance am able to comprehend the drawings of 
the ancient Egyptians, who represent all parts of the 
body as far as possible in their true dimensions, thus 
pressing them, as it were, into the plane of the draw- 
ing, as plants are pressed in a herbarium. In the fres- 
coes of the Pompeians, too, we still meet with a per- 
ceptible disinclination to foreshortening, although 
here the sense of perspective is already manifest. The 
ancient Italians, on the other hand, in the conscious- 
ness of their perfect mastery of the subject, often 
amuse themselves with excessive and sometimes even 
unbeautiful foreshortenings, which occasionally de- 
mand of the eye considerable exertion. 


There can be no question, therefore, but the see- 
ing of solid bodies with the distances between their 
salient points unchanged ls much easier to us through 
habit than is the elimination of the marks of solidity, 
which is always the result, in the first place, of de- 
liberate analysis. Accordingly, we may expect that 
wherever a coherent mass, which from its common 
coloring is apprehended as a unil, exhibits spatial al- 
teration, the altering process will be seen preferably 
as the motion of a solid body. I must confess, how- 
ever, that this conception is little satisfactory to me. 
I believe, rather, that here, too, an elemental habit of 
the organ of sight is at the root of the matter, — a habit 
which was not originally acquired by the conscious 
experience of the individual, but, on the contrary, 
antecedently facilitated our apprehension of the move- 
ments of solid bodies. If we should assume, for ex- 
ample, that every diminution of the transverse dimen- 
sion of an optical sensation-mass to which the atten- 
tion was directed had the tendency to induce a cor- 
responding augmentation of the dimension of depth, 
and vice versa, we should have a process quite anal- 
ogous to that which we ha-ve already considered above 
and which was compared to the conservation of en- 
ergy. This view is certainly much simpler and sup- 
plies an adequate explanation. Furthermore, it en- 
ables us to comprehend more easily how so elemental 


a habit could be acquired, how it could find expiessioc 
in the organism, and how the tendency for the same 
could be inherited. 

As a sort of counterpart to the rotation of solid 
bodies exhibited to us by the organ of sight, I will 
cite here an additional observation. If an egg, or 
ellipsoid with dull, uniform surface be rolled over the 
top of a table, but in such manner that it does not 
turn about its axis of generation, but performs jolting 
movements, we shall fancy we see, on viewing it bi- 
nocularly, a liquid body, or large oscillating drop. The 
phenomenon is still more noticeable if the egg, with 
its longitudinal axis in a horizontal position, be set 
in moderately rapid rotation about a vertical axis. 
This effect is immediately destroyed when marks, 
whose movements we may follow, are made upon the 
surface of the egg. A rotating solid body is then seen. 

The explanations offered in this chapter are cer- 
tainly far from complete, yet I believe that the con- 
siderations adduced will have some effect in stimulat- 
ing and preparing the way for a more exact and thor- 
ough study of these phenomena. 


TVifUCH more difficult than the investigation of 
^^■*~ space-sensation is that of time-sensation. Many 
sensations make their appearance with, others with- 
out, space -sensation. But time-sensation accompani es 
every other sensation, and can be wholly separat ed 
from """" We are referred, therefore, in our in- 
vestigations here, to the variations of time-sensation. 
With this psychological difficulty is associated an- 
other, consisting of the fact that the physiological 
processes underlying the time-sensation are less known, 
more radical, and more thoroughly concealed than the 
processes underlying the other sensations. Our analy- 
sis, therefore, must confine itself chiefly to the psycho- 
logical side, without approaching the question from 
its physical aspect, as is possible, in part at least, in 
the provinces of the other senses. 


That a defiDite, specific titne-sensation exists, ap- 
pears to me beyond all doubt. The rhythmical iden- 
tity of the two adjoined measures, which vary utterly 

in the order of their tones, is immediately recognised. 
We have not to do here with a matter of the under- 
standing or of reflexion, but with one of sensation. 
In the same manner that bodies of diSerent colors 
may possess the same spatial form, so here we have 
two tonal entities which, acoustically, are differently 
colored, but possess the same temporal form. As in 
the one case we pick out by an immediate act of 
feeling the identical spatial components, so here we 
immediately detect the identical temporal components, 
or the sameness of the rhythm. 


On hearing a number of strokes of a bell, which 
are exactly alike acoustically, I discriminate between 
the first, second, third, and so on. Do the accompany- 
ing thoughts, perhaps, or other accidental sensations, 
with which the strokes of the bell happen to be asso- 
ciated, afford these distinguishing marks ? 1 do not 
believe that any one will seriously uphold this view. 
How uncertain and unreliable would our estimate of { 
time prove in such an event ! What would become of I 

TIME-SEtfSA TION. 1 1 1 

it if that accidental background of thought and sensa- 
tion should suddenly vanish from memory ? 

While I am reflecting upon something, the clock 
strikes, but I give no heed to it. After it has finished 
striking, it may be of importance to me to count the 
strokes. And as a fact, there arise in my memory dis- 
tinctly one, two, three, four strokes. I give here my 
whole attention to this recollection, and by this means 
the subject on which I was reflecting during the striking 
of the clock, for the moment completely vanishes from 
me. The supposed background against which I could 
note the strokes of the bell, is now wanting to me. 
By what mark, then, do I distinguish the second stroke 
from the first? Why do I not regard all the strokes, 
which in other respects are identical, as one} Because 
each is connected for me with a special time-sensation 
which starts up into consciousness along with it. In 
like manner, I distinguish an image present in my 
memory from a creation of fancy by a specific time- 
sensation different from that of the present moment. 

^ Since, so long as we are conscious, time-sensation 
is always present, it is probable that it is connected 
with the organic consumption necessarily associated 
with consciousness, ^that we feel the work ofatUnlion 
as time. During severe effort of attention time is long 
to us, during easy employment short. In phlegmatic 
conditions, when we scarcely notice our surroundings, 



the hours pass rapidly away. When our attentioo ia 
completely exhausted, we sleep. In dreamless sleep, 
. the sensation of time is lacking.^ When profound steep 
intervenes, yesterday is connected with to-day only by 
an iotellectual bond. . 

The fatiguing of the organ of consciousness goes 
on continually in waking hours, and the labor of at- 
tention increases just as continually. The sensations 
connected with greater expenditure of attention ap- 
pear to us to happen later. 

Normal as well as abnormal psychical acts appear 
to accord with this conception. Since the attention 
cannot be fixed upon two different sense-organs at 
once, the sensations of two organs can never occur to- 
gether and yet be accompanied by an absolutely equiva- 
lent effort of attention. Seemingly, therefore, the one 
occurs later than the other. A parallel of this so- 
called personal equation of astronomers, having ita 
ground in analogous facta, is also frequently observed 
in the same sense-province. It is a welt-known fact 
that an optical impression which arises physically 
later may yet, under certain circumstances, appear to 
occur earlier. It sometimes happens, for example, 
that a surgeon, in bleeding, first sees the blood burst 
forth and afterwards his lancet enter.' Dvorak has 
shown,* in a series of experiments which he carried 

iCompBre Fechner, I^ksfkjuik. Lelpilc, 1B60. Vql. n., p. 13). 
iDvorik, "Ueber ADslQga dei persenlichan Dlffereai zwischen beidon 

GtuOickuft dtr Wiiantcha/lni. (Matk.-mUnm. CUtta). voa 1. Ulii, 1871- 


out at my desire, years ago, that this relation may be 
produced at will, the object on which the attention is 
centred appearing (even in the case of an actual tar- 
diness of 1/8-1/6 of a second) earlier than that indi- 
rectly seen. It is quite possible that the familiar ex- 
perience of the surgeon may find its explanation in 
this fact. The time which the attention requires to 
turn from one place at which it is occupied, to an- 
other, is shown in the following experiment instituted 
by me.' Two bright red squares measuring two centi- 
metres across and situated on 
a black background eight cen- 
timetres apart, are illuminated 
in a perfectly dark room by an 
electric spark concealed from 
the eye. The square directly '"^^"- *^'° *"'- """ 

seen appears red, but that *^' 

indirectly seen appears ^««,— -and often quite in- 
tensely so. The tardy attention finds the indirectly 
seen square when it is already in the stage of Purkinje's 
positive after-image. A Geissler's tube with two bright 
red spots at a short distance from one another, exhib- 
its, on the passage of a single discharge, the same 



The following interesting experience should be 
cited here. Frequently 1 have been sitting in my room, 

1 CommuBicBUd by Dvorak, ;«. cit. 


absorbed in work, while in an adjacent room experi- 
ments in explosions were being carried on. It regu- 
larly occurred that I shrank back startled, before I 
heard the report. 

Since the attention is especially inert in dreams, 
naturally the most peculiar anachronisms occur in this 
state, as every one has doubtless observed. For in- 
stance, we dream of a man who rushes at us with a 
revolver and shoots, awake suddenly, and perceive 
the object which, by its fall, has produced the entire 
dream. Now there is nothing absurd in assuming 
that the acoustic excitation enters simultaneously dif- 
ferent nerve-tracks and is met there by the attention 
in some inverted order, just as, in the case above 
mentioned, I perceived first the general disturbance 
of the organism and afterwards the report of the ex- 
plosion. But in many cases it is undoubtedly sufficient 
to assume the introduction of sensations into the frame- 
work of a dream already present. 

If time-sensation is conditioned by progressive or- 

mption' or by the corresponding steady 

sgmplion, or, for Ihal mailer, Ihc accumulation of a " taliftue- 
. Tbe eccealricitiea of dreams may all be accounted tor by 

tad (hat tome sensalioDi a 


ions da not 

1. whiJe others enter wilh 


ully and to 

lata. Theintellecl 

B Deeps only in pan. W 

y sensibly, 

D drssms, wlih per- 

lona deceased, but with n 


of th6.r d 

sBch by their ecc'ea- 
amed very vividly ol 

liei, tal are immediaieli p 

adfied .g 


1 DQce die 

11. Thawaiec flowed dow 


oping cka 

nel, .way Irom ifaa 


increase of the effort following upon attention, then it 
is intelligible why physiological time is not reversible 
but moves only in one direction. As long as we are 
in the waking state consumption and the labor of at- 
tention can only increase, not diminish. The two ac- 
companying bars of music, _^ .^ . ^~-^ 

which present a symmetry o a f f f \f f f f ? 
to the eye and to the under- ' ' LU | LU 1 I 
standing, show nothing of the sort as regards the sen- 
sation of time. In the province of rhythm, and of 
time in general, there is no symmetry. 


It is a perfectly natural, though somewhat imper- 
fect conception, to regard the organ of consciousness 
as capable, in a weakened degree, of all the specific 
energies, of which each sense-organ is capable only of 
A few. Hence the shadowy and evanescent character 
of representation as compared with sensation, through 
which it must be constantly nourished and revivified. 

wilh Ihi .ubjecl P( .pace-KDsalioa 


donlT I noticed ihe detMlivo p=r 

■ Iwiikar Bllid will. ™«. in wbic 

da« il J(=l Us o.ygen from ? " 1 Iho 

ugbl. "1 

5 produc 

Th. bobbles from <be Bame. moun 

Ed npwar 

ID Seippel. ill6>.— U<c 



The rhythm represented in the following diagram 
appears physiologically similar to the preceding, but 
only when similarly-marked bars are taken in the two 


— that is, when the attention is introduced at homol- 
ogous points of time. Two physical time-figures may 
be termed similar when all the parts of the one stand 
in the same relation to one another as do the homol- 
ogous parts of the other. But physiological similarity 
makes its appearance only when the above condition 
is likewise fulfilled. Furthermore, so far as I am able 
to judge, we recognise the identity of the time-ratios 
of two rhythms only when the same are capable ol 
being represented by very small whole numbers. Thus 
we really notice immediately, only the identity or non- 
identity of two times, and, in the latter case, recog- 
nise the ratio of the two only by the fact that one part 
is exactly contained in the other. Herewith we have 
an explanation of the fact that, in marking time, the 
time is always divided into absolutely equal parts,* 

IThe simiUrity o( ipicE-fignreB wonld bo tell, according to Ihia theory. 


TN tone-sensations, also, we are restricted mainly to 
^ psychological analysis. As before, the initial ele- 
ments of the investigation are all we can offer. 

Among the sensations of tone possessing greatest 
importance for us are those produced by the human 
voice, in the form of utterances of pleasure and pain, 
of expressions of the will, and of the communication 
of thoughts by speech, etc. The voice and the organ 
of hearing doubtless bear a close relation to each other. 
The simplest and distinctest form in which sensations 
of tone reveal their remarkable characteristics is music. 
Will, feeling, vocal expression and vocal sense-recep- 
tivity have certainly a strong physiological connexion. 
There is a good deal of truth in the remark of Schopen- 


bauer' that music represents the will, and in fact gen- 
erally in the designation of music as a language of 
emotion ; although this is scarcely the whole truth. 

Following the precedent of Darwin, H. Berg has 
attempted to derive music from the amatory cries of 
monkeys.' We should be blind not to recognise the 
service rendered and enlightenment conveyed by the 
work of Darwin and Berg. Even at the present day, 
music has power to touch sexual chords, and is, as a 
fact, widely made use of in courtship. But as to the 
question wherein consists the agreeable quality of 
music, Berg makes no satisfactory answer. And see- 
ing that in the matter of harmony he adopts Helm- 
holtz's position of the avoidance of beats and assumes 
that the males who howled least disagreeably received 
the preference, we may be justified in wondering why 
the most intelligent of these animals were not prompted 
to maintain silence altogether. 

The importance of tracing the connexion of a given 
biological phenomenon with the preservation of the 
species, and of indicating its phylogenetic origin, can- 
not be underrated. But we must not imagine that in 
having accomplished this we have solved all the prob- 
lems connected wilh the phenomenon. Surely no one 
will think of explaining the specific sensation of sexual 

I. -Riini, DU UM mn dtr Mutik, Bstlio, iSjg. 


pleasure byshoTvingits connexion with the preservation 
oi the species. We should be more likely to acknowl- 
edge that the species is preserved because the sensa- 
tion accompanying sexual indulgence is pleasurable. 
Although music may actually remind us of the court- 
ship of distant progenitors, it must, if it was ever used 
for wooing, have contained at the start some positive 
agreeable quality, which does not, of course, preclude 
its being re-cnforced at the present time by that mem- 
ory. To take an analogous case from individual life, 
the smell of an oil-lamp which has just been extin- 
guished almost always agreeably reminds me of the 
magic lantern which I admired as a child. Yet in it- 
self the smell of the lamp is none the less disgusting 
for this reason. Nor does the man who is reminded, 
by the scent of roses, of a pleasant experience, believe, 
on this account, that the perfume was not previously 
agreeable. It has only gained by the association.' 
And if the view referred to cannot sufficiently explain 
the agreeable quality of music per se, it assuredly can 
contribute still less to th« solution of special ques- 
tions, as, for instance, why, in a given case, a fourth 
is preferred to a fifth. 

A rather partial view of the sensations of tone 
would be obtained if we were to consider only the 


province of speech and music. Seasations of tone are 
not only a means of communicating ideas, of express- 
ing pleasure and pain, of discriminating between the 
voices of men, women, and children ; they are not 
alone signals of the exertion or passion experienced 
by the person speaking or calling ; they also consti- 
tute the means by which we distinguish between large 
and small bodies when sounding, between the tread ol 
large and small animals. The highest tones, the very 
ones which the vocal organs of man cannot produce, 
presumably are of extreme importance for the deter- 
mination of the direction from which sounds proceed,' 
In fact, it is more than likely that these latter func- 
tions of sensations of tone antedated, in the animal 
world, by a long period, those which merely perform a 
part in the social life of animals. J 

There is no on« but will cheerfully acknowledge 
the decided advance wrought by Helmholtz in the 
analysis of sensations of audition.' Following his 
principles, we recognise in noises combinations of mu- 
sical sounds, oTwhlch the number, pitch, and intensity 
vary with the time. In compound musical sounds, or 
clangs, we generally hear, along with the fundamental 

iMacb, "Bemerkuntcea dber die FcncHDa der Ohrtdnschel" (TVMHt'i 

iMelmhotu. Dii Ltkri 



n, the partial tones or harmonics in, 3«, 4«, etc. 
of which corresponds to simple pendular vibrations. 
If two such musical sounds, the fundamentals of which 
correspond to the rates of vibration « and m, be mel- 
odicaJly or harmonically combined, there may result, 
if certain relations of n and m are satisfied,' a partial 
coincidence of the harmonics, whereby in the first case 
the relationship of the two sounds is rendered per- 
ceptible, and in the second a diminution of beats is 
effected. All this cannot be disputed, although it may 
not be deemed exhaustive. 

We may also give our assent to Helmholtz's phys- 
iological theory of the auditive organ. The facts ob- 
served on the simultaneous sounding of simple notes 
make it highly probable that there exist, correspond- 
ing to the series of vibration-rates, a series of terminal 
nervous organs, so that for all the different rates of 
vibration there are different sympathetic end-organs, 
each of which responds to only a few, closely adjacent 
rates of vibration. It is a question of lesser importance 
whether this functioa is exercised by the organ of 

If we assume with Helmholtz that all noises admit 
of being resolved into sensations of tone varying in 
duration, it is evidently superfluous to seek for a special 
auditive organ for noises. A long time ago (in the 

iThe /lb hurnoDic otn coincitlH mith the rtholai irbaa/KT", Ibal 


, each ^^H 

D rations. , ^^\ 


winter of 1872-1873) I took up the question of the re- 
lation of noises (especially that of sharp reports) to 
musical tones, and found that all transitions between 
the two may be observed. A tone of one hundred and 
twenty-eight full vibrations, heard through a small ra- 
dial slit in a slowly revolving disc, contracts, when its 
duration is reduced to from two to three vibrations, to 
a short, sharp concussion (or weak report) of very in- 
distinct pitch, while with from four to five vibrations, 
the pitch is still perfectly distinct. * On the other hand, 
with sufficient attention, a pitch, though not a very 
definite one, may be detected in a report even when the 
latter is produced by an aperiodic motion of the air 
(the wave of an electric spark, exploding soap-bubbles 
filled with zH-^O). We may easily convince our- 
selves, furthermore, that in a piano from which the 
damper has been lifted, large exploding bubbles mainly 
excite to sympathetic vibration the lower strings, while 
small ones principally affect the higher strings. This 
fact, it seems clear to me, demonstrates that the same 
organ may be the mediator of both tone and noise sen- 
sation. We must imagine that weak aperiodic vibra- 
tions of the air having short durations excite all, though 
preferably the small and more mobile end-organs, whilst 
the powerful and more lasting disturbances of this sort 
affect also the larger and heavier end-organs, which 
from being less damped perform vibrations of greater 
amplitude and are thus noticed ; and furthermore that 

1 Pot faU eipluulion saa Appeadii II. — TVwM. 



even in the case of comparatively weak periodic vibra- 
tions of the air, the excitation, by an accumulation of 
effects, is manifested in some definite member of the 
series of end-organs.^ The sensation excited by a re- 
port of low or high pitch is qualitatively the same as 
that produced by striking at once a large numbSr of 
adjacent piano-keys, only more intense and of shorter 
duration. Moreover, in the single excitation produced 
by a report, the beats connected with periodic inter- 
mittent excitations are eliminated. 
Yet despite the recognition with which the theory 
of Helmholtz has met, there have not been wanting 
voices which have called attention to its incomplete- 
ness. The lack of a positive factor in the explanation 
of harmony has been very generally felt, the mere ab- 
sence of beats not being regarded as a sufficient and 
satisfactory characterisation of harmony. Thus A. v. 
Oettingen' feels the want of some expressed pesiiwe 
element characteristic of each interval, and refuses to 
regard the value of an interval as dependent upon the 
physical accident of the overtones contained in the 
sounds. He believes that the positive element in ques- 
tion is to be found in the accompanying remembrance 

II Kive an icconnt of pari of ray experiments, iihicb were a ccDtinuatiDB 

ibGequenlly Irested IbsB 
ilt>ne (Dorpit, 1866), p. 9 


of the 

monies of 
interval hi 


Q fundamental tone (or tonic), as the h«r- 
which the composite notes or clangs of the 
.ve often occurred, or in the accompanying 
remembrance of the common overtone (or plionicli be- 
longing to the two (pp. 40, 47). On the negative side 
of his criticisms I am in complete agreement with Voa 
Oettingen. But "remembrance" does not quite fill 
the need of the theory, for consonance and dissonance 
are not matters of representative activity, hut of sen- 
sation. My opinion, therefore, is that A. von Oettin- 
gen's conception is physiologically inadequate. His 
enunciation of the principle of duality, however, (or of 
the principle of the tonic and phonic relationship of 
composite notes), as also his conception of disson- 
ances as indeterminate composite raiisical sounds ad- 
mitting of more than one interpretation (p. 224) ap- 
pear to me to be valuable and positive £ 

y Fofidar Sciintific Licit 


I myself, as early as 1863*, and also later,* had 
made some critical remarks on the theory of Hehn- 
holtz, and in 1866, in a small work* which appeared 
shortly before that of Von Oettingen, very definitely 
pointed out some demands which a more perfect the- 
ory of the subject would have to satisfy. Since, how- 
ever, up to the present time my remarks have, to my 
knowledge, nowhere met with serious consideration, I 
shall revert to them here at length. 

We shall start with the idea that a series of deh' 
nitely graduated sonant end-organs exists, the mem- 
bers of which, as the rate of vibration increases, suc- 
cessively yield their maximum response, and we shall 
ascribe to each end-organ its particular (specific) en- 
ergy. Then there are as many specific energies as 
there are end-organs, and a like number of rates of 
vibration auditively distinguishable by us. 

Further, we not only eiislmgvisk between tones, 
but we assign to them also their ordinal places in a se- 
ries. Of three tones of different pitch, we recognise 
the middle one immediately as such. We feel imme- 
diately which rates of vibration lie near together and 

iMacb, "Zur Theorie des GehOrorgana" {SilnHngsbtrlckii drr Wttmr 

iFhhU'x ZlittchTift fltr Pkilosafkii, iBSj). 
tt» Mid pp. 1] el Mq., 46 and ifi. 

. S« the Pref- 



which lie far apart. This is readily enough explained 
for neighboring tones. For, if we represent the vibra- 
tion-amplitudes of a certain tone symbolically by the 
curve a be, Fig. 35, and imagine this curve gradually 
moved in the direction of the arrow, then, since ne- 
cessarily several organs always yield simultaneous re- 
sponses, neighboring tones will always have faint, 
common excitations. But distant tones also possess a 
certain similarity; and even between the highest and 
lowest tones we can detect a resemblance. Conse- 
quently, in accordance with the principle of investiga- 

tion by which w 

we are obliged to assume 
in all tone -sensations 
common factors. Conse- 
quently, again, there can- 
not be as many specific 
energies as there are dis- 
tinguishable tones. For 
the understanding of the 
facts with which we are 
here concerned, it suffices to assume only two energies, 
which are excited in different proportions by different 
rates of vibration. Further complexity of the sensa- 
tions of tone is not excluded by these facts, but on the 
contrary is rendered probable by phenomena to be dis- 
cussed later. 

Careful psyehologieal analysis of the tonal series 
leads immediately to this view. But even supposing 
we assume a special energy for every rod of Corti, and 

reflect that these energies are similar to one another, 
that is, contain common elements, virtually we arrive 
at the same conception. For let us assume, merely 
in order to have a definite picture before us, that, in 
the transition from the lowest to the highest rates of 
vibration, the tonal sensation varies similarly to the 
color-sensation in passing from pure red to pure yel- 
low, say by the gradual admixture of yellow. We can 
fully retain, on this view, the idea that there is for 
every distinguishable rate of vibration a special ap- 
propriate end-organ ; but in that case not absolutely 
different energies, but always the same two energies, 
only in different proportions, are disengaged by the 
different organs.^ 

How does it happen, now, that a number of notes 
simultaneously sounded are distinguished, seeing that 
we should naturally expect them to blend into a single 
sensation ; or that two tones of different pitch do not 
blend to a mixed tone of intermediate pitch P The 
fact that this docs not happen, lends a still more 
definite shape to the conception which we have to 
form. The case is probably similar to that of a grad- 
uated series of mixed reds and yellows situated at dif- 
ferent points of space, which are likewise distinguished 


and do not blend. As a fact, the sensarioD which ensues 
when the attention passes from one tone to another is 
similar to that which accompanies the wandering of 
the fixation-point in the field of vision. The tonal 
series is an analogue of space, but of a space of one 
dimension limited in both directions and exhibiting 
no symmetry like that, for instance, of a straight line 
tunning from right to left in a direction perpendicular 
to the median plane. It more resembles a vertical 
right line, or one running from the front to the rear 
in the median plane. But while colors are not con- 
fined to certain points in space, but may move about, 
which is the reason we so easily separate space-sensa- 
tions from color-sensations, the case is different with 
tone -sensations. A particular tone -sensation can oc- 
cur only at a particular point of the said one-dimen- 
sional space, on which the attention must in each case 
be fixed if the tone-sensation in question is to be dis- 
tinctly perceived. We may now imagine that differ- 
ent tone -sensations have their origin in different parts 
of the auditive substance, or that, in addition to the 
two energies whose ratio determines the timbre of 
high and deep tones, a third exists, which is similar 
to the sensation of innervation, and which comes into 
play in the fixation of tones. Or both conditions might 
occur together. At present it may be regarded as 
neither possible nor necessary to come to a conclusion 
in the matter. 

That the province of tone-sensation ofiers an an- 


alogy to space, and to a space having no symmetry, 
unconsciously expresses itself in language. We speak 
of high tones and deep tones, not of right tones and 
left tones, although our musical instruments suggest 
the latter designation as a very natural one. 

In one of my earliest publications' I supported the 
view that the fixation of tones was connected with a 
varying tension of the tensor lympani. I am now un- 
able to maintain this view in the light of subsequent 
observations and experiments which I have made. 
Nevertheless, the space-analogy does not fall to the 
ground for this reason ; but merely the appropriate 
physiological element remains to be discovered.' 

I The > 


n thai the 


in th 




hsd som«<h 


1 likewise noti 


of 1B63, 

find it to 

Singinn is 

d accide 

bear 00 

snob an hypo 

sis. leaoh 

DM tar be 



lIsUDlog B 

th all Ihe parti, 

in bavini! an 


to think tba 



DKOf .h 

s broad a 




icb is, m 

vary p 

ractisod . 

nger. Icons 


the HHsailo 

ns whicb 

in listen 

ng 10 .in 

King, ar 

e doubtle 

s occasionally 

- Heed In the 



B the picluie 

cb, when 



. pertor, 

■> the plan 

or organ. When 

I imagine n. 


tba nol 

inlo belnE merely th 


fotraaDces than . de 

n hear by 


": 1 


gree with 


oini. (C 

mp, Strieker: 

Dn \ 

gui. Pwi 

, iSSj). 

opinion wKb regar 

Bws on langu 

(Comp. Slri 


a, 1880.) 


my own cis 

.it wbiQb 

tbink r 


to loudly 

n my ear. M 

over, I b»Ye 

no doub 

thai Ibo 


be diie 


by (he ringin 


by Ihe * 

mall children 

d words w 

epcal. N 


been coDvi 

ced by 

iricker tb 

nary an 

miliar, though 

Ibe only po 

sibU w» 

by wbicb 

>P«cb 1 

really «.««-, 



one note sound later than the other. This then 
draws the attention alter it. With a little practice it 
is possible to decompose a. chord (as, for instance, 5) 
into its elements and to hear the constituent tones by 
themselves (as in 6). These and the following experi- 
ments are better and more convincingly carried out 
upon a physhamionica than on a piano, owing to the 
greater duration of the tones. 

Especially astonishing is the phenomenon pro- 
duced when we cause one note of a cord, on which 
the attention is fixed, to be damped. The attention 
then passes over to the note nearest to it, which comes 
out with the distinctness of a note that has just been 
struck. The impression made by the experiment is 
quite similar to that which we receive when, absorbed 
in work, we suddenly hear the regular striking of the 
clock emerge into distinctness after having entirely 
vanished from consciousness. In the latter case the 
entire tonal effect passes the threshold of conscious- 
ness, whilst in the former a part is augmented. If in 
:ample, we fix the attention upon the upper 

note, letting go, successively from above, the Iteya 
damping the other notes, the effect obtained is ap- 
proximately that of 8. If, in 9, we fix the attention 
on the lowest note, and proceed in the reverse order, 



we obtain the impression represented in lo. The | 
same chordal combination sounds quite different ac- 
cording to the part on which the attention is fixed. 
If, in II or 12, I fix ray attention on the upper note. 

the timbre alone appears to be altered. But if in ii, 
the attention be fixed upon the bass, the entire acous- 
tic mass will seem to sink in depth ; while in la it 
will appear to rise if we regard closely the succession i 
e-f. It is quite evident, in fine, that chords act the 
part of clangs (or compound notes embracing both 
fundamentals and harmonics). The facts here ad- 
vanced remind us strongly of the changing impression 
received when, in observing an ornamental design, the 
attention is alternately fixed on different points. 

We may also recall to mind here the involuntary 
wandering of the attention which takes place during 
the continuous and uniform sounding of a note on the 
harmonium, where if the note lasts several minutes, 
all the overtones will of themselves successively emerge 
into full distinctness.' The process appears to point 
to a sort of fatigue for the note on which the attention 
has long been fixed. This fatigue, moreover, is rejj- 

ICompire aij Elnltilung in dit HiSmMtiscki Mmlklktarii, p. 19 


dered quite probable by an experiment which I have 
described at length in another place.* 

The relations we have here been describing, touch- 
ing sensations of tone, might be illustrated perhaps 
more palpably by some such parallel as the following. 
Suppose that our two eyes were capable of only a single 
movement, that they could only follow, by changing 
motions of symmetrical convergence, the 
points of a horizontal straight line lying 
in the median plane ; and suppose that 
the nearest points on this line fixed by 
the eyes were pure red, and those farthest 
away, corresponding to the position of 
parallelism, were pure yellow, while be- 
tween them lay all intermediate shades ; 
then the system of sight-sensations so 
constructed would quite palpably resemble the facts 
presented by sensations of tone. 

FiR. 36. 

On the view hitherto developed, an important fact, 
which we shall now state, remains unintelligible, 
though its explanation is absolutely necessary if the 
theory is to lay any claim to completeness. If two 
series of tones be begun at two different points on the 
scale, but be made to maintain throughout the same 
ratios of vibration, we shall recognise in both the same 



melody, by a mere act of sensation, just as readily and^ 
immediately as we recognise in two geometrically sim 
ilar figures, similarly situated, the same form. Like 
melodies, differently situated on the scale, might be 
deflominated tonal constructs of like tonal form, or theyJ 
might be denominated similar tonal constructs, from* 
their space- analogues. 

Even in a series of only two tones, the samenesal 
of the vibrational ratios is at once recognised. Thus! 
the series c-f, d— g, e-a, etc., which have all the same 
vibrational ratios (3:4), are immediately recognised as 
like intervals, as fourths. Such is the fact, in its sim- 
plest form. The ability to pick out and recognise in- 
tervals is the first thing required of the student of 
music who is desirous of becoming thoroughly familiar j 
with his province. 

In a little work," well worth reading, by Mr. E. I 
Kulke, mention is made, bearing on this point, of ana 
original method of instruction by P. Cornelius — a de-fl 
scription of which I will here complete from Kulke's 
own lips. According to Cornelius, it is a wonderful I 
help in the recognition of intervals to make note of I 
particular pieces of music, folk-songs, etc., which be- I 
gin with these intervals. The Overture to Tannhauser, I 
for example, begins with a fourth. If I hear a fourth 1 
I at once remark that the series of tones is the same I 
as that beginning the Overture to Tannhauser and \ 

i«ng drr Mtiadii. E<n Btil 


by this means recognise the intep^al. In like manner, 
the Overture to Fidelio may be used as the represen- 
tative of the third ; and so oa. This excellent device, 
which I have put to the test in my lectures on acous- 
tics and have found very effective, apparently compli- 
cates matters. One would naturally suppose that it 
would be easier to make note of an interval than of a 
melody. Nevertheless, a melody offers a greater hold 
to memory than does an interval, just as an individual 
countenance is more easily remarked and associated 
with a name than is a certain facial angle or a nose. 
Every one makes note of faces and associates with 
them names ; but Leonardo da Vinci arranged noses 

And as every interval in a series of tones is made 
perceptible in characteristic manner, so it is with the 
harmonic combinations of tones. Every third, every 
fourth, every major or minor triad has its character- 
istic color, by which it is recognised independently of 
the pitch of the fundamental, and independently of 
the number of beats, which rapidly increase with in- 
creasing pitch, 

A tuning-fork held before one ear is very feebly 
heard by the other ear. If two slightly discordant, beat- 
ing tuning-forks are held in front of the same ear, the 
beats ate very distinct. But if one of the forks be 
placed before one ear, and the other before the other, 
the beats will be greatly weakened. Two forks of har- 
monic interval always sound slightly rougher before 


one ear. But the character of the harmony is pre- 
served when one is placed before each ear.^ Discord 
also remains quite perceptible in this experiment. 
Harmony and discord are certainly not determined by 
beats alone. 

In melodic as well as in harmonic combinations, 
notes whose rates of vibrations bear to one another 
some simple ratio, are distinguished (i) by their agree- 
ableness, and (2), by a sensation characlerisiie of this 
ratio. As for the agreeable quality, there is no deny- 
ing but this \s partly explained by the coincidence o£ 
the overtones, and, in the case of harmonic combi- 
nation, by the consequent effacement of the beatf, re- 
sulting always where the ratios of the numbers repre- 
senting the vibrations satisfy certain simple conditions. 
But the experienced and unprejudiced student of mu- 
sic is not entirely satisfied with this explanation. He 
is disturbed by the preponderant rSle accorded to the 
accident of acoustic color, and notices that tones fur- 
ther stand to each other in a positive relation of con- 
trast, like colors, except that, in the case of colors, no 
such definite agreeable relations can be specified. 

The fact that a sort of contrast really does exist 
among tones is almost forced upon our notice. A 
smooth, unchanging tone is something very unpleas- 
ing and characterless, like a single uniform color en- 
veloping our entire surroundings. A lively effect is 

Leipsle, 186a. p. ;]C. 

■ SllLtMt, 


produced only on the addition of a second tone, a sec- 
ond color. In like manner, if we cause a tone gradu- 
ally to mount in pitch, as in experiments with the 
siren, all contrast is lost. Contrast exists, however, 
between tones farther apart, and not merely between 
those immediately following one another, as the ac- 
companying example will show. Passage 2 sounds 

quite diSerent after i from what it does alone, 3 sounds 
difierent from 2, and even 5 different from 4 imme- 
diately following 3. 

Let us turn now to the second point, the charac- 
ieriilic sensation corresponding to each interval, and 
ask if this can be explained on the current theory. If 
a fundamental « be melodically or harmonically com- 
bined with its third w(, the fifth harmonic of ^^ first 
note (5«) will coincide with the fourth of the second 
note (4W). This, according to the theory of Helm- 
holtz, is the tommon feature characterising all third- 
combinations. If I combine the notes C and E, or F 
and A, representing their harmonics in the cut on the 
next page, then, as a fact, in the one case the harmonics 
marked | and in the other those marked J coincide ; 
and in both cases the coincidence is between the fifth 
harmonic of the lower and the fourth harmonic of the 

higher note. Be it noted, however, that this co: 
mon feature exists solely for the understanding, being 
the result of a purely physical and intellectual anal- 
ysis, and has nothing to do with sensation. For sensa~ 
tion the real coincidence in the first case is between 
the e's, and in the second between the a's, which are 
entirely different notes. On the assumption that there 


f a c 

4fi JO C» 




t = = 

a c-sharp e 



exists for every distinguishable rate of vibration an 
appurtenant specific energy, we are obliged, more 
than on any other theory, to ask where is the common 
component of sensation hidden that characterises every 
, third combination? 

I must insist on this distinction of mine not being 
regarded as a piece of pedantic hair-splitting. I pro- 
pounded the question involving it about twenty years 
ago, at the same time with my question as to wherein 

physiological similarity of form, as distinguished from 
geometrical, consisted ; and it is not a whit more un- 
necessary than was that, whose superfluity, too, in the 
issue, was disproved. If we are to suffer a physical 
or mathematical characteristic of the third interval to 
stand as a mark of the tVitA-scnsation, then we should 
content ourselves, as Euler did,^ with the coincidence 
of every fourth and fifth vibration — a conception which 
was, after all, not so bad, provided it could be supposed 
that sound continued its course in the nerve-tracts, 
also, &s periodic motion, a view which even A. Seebeck 
(fogg. Ann., Vol. 68) regarded as possible. With re- 
gard to this particular point, Helmholtz's coincidence 
of 5» and 4w is in no respect less symbolical and does 
not offer greater enlightenment. 


So far 1 have presented my arguments with the 
conviction that I should not find it necessary to make 
a single retrograde step of importance. This feeling 
does not accompany me in the same measure in the 
development of the following hypothesis, which, in 
all its essential features, was suggested to me a long 
time ago. Yet the hypothesis may at least serve to 
clear up and illustrate, from the positive side also, the 
requirement which I believe a more complete theory 
of tone- sensations is bound to meet. 

We will begin by supposing that it is an extremely 

I &uLflt. Ttntfmm navat ttuwriat fHumicat, PfitrOpaU, \Ji^ p. jSi 


important vital condition for an animal of simple or- 
ganisation to perceive slight periodic motions of the 
medium in which it lives. If (owing to the relatively 
excessive size of its organs, and its consequent lack 
of receptivity for such rapid changes) its attention is 
too sluggishly transferred, the period of the impinging 
vibrations is too short, or their amplitude too small, 
to permit the single phases of the excitation to enter 
consciousness, it may nevertheless be possible under 
certain conditions for the animal to perceive the ac- 
ciimulaUd sensation- effects of the oscillatory excita- 
tion. The organ of hearing will outstrip the organ of 
touch.' Now an end-organ capable of vibration (say 
an auditory cilium) responds, by virtue of its physical 
qualities, not to every rate of vibration, nor to one only, 
but ordinarily to several, at a considerable distance 
apart.' Therefore, as soon as the whole continuum 
of vibrational rates between certain limits becomes of 
importance for the animal, a small number of end- 
organs no longer suffice, but the need of a whole series 
of such organs of graduated sonancy arises. The or- 
gan of Corti is regarded as such a system. 

It can hardly be expected, however, that a mem- 
ber of Corti's organ will respond to only one rate o£ 

ablB thenrore whetbar snima: 
11 their voJontikry movamEDte pi 
ise. Di whether wllh lb«tn Ihel 

ane." Arrk./ilT' Miirstksp. Anal., XX., p. iti6). 
*A> V. Hensen, tw eiampte, bus oblorved 

en Or- 



vibration. On the contrary, we must suppose that it 
responds with enfeebled but graduated intensity (per- 
haps from being divided by nodes) to the rates of 
vibration in, zn, ^», etc., as also to the rates of vi- 
bration w/a, «/3, n/4, etc. Inasmuch as the assump- 
tion of a special energy for each rate of vibration has 
proved untenable, we may imagine, agreeably to re- 
marks made above, that in the first place, only two 
sensation -energies, Dull (_£>) and Clear (C), are ex- 
cited. The resultant sensation we will represent sym- 
holically (somewhat as we do in mixed colors) by 
pD-\-qC; or, making /-f? = l ^^^ regarding y as a 
function /(n) of the rate of vibration,* by [1 — /(«)] 
/)+/(«) C The sensation arising will now correspond 
to the number of the vibrations producing the oscillatory 
excitation, on whatever member of Corti's series the 
excitation may light. And consequently the current 
conception will not be materially disturbed by the new 
hypothesis. For, since the member R^ responds most 
powerfully to «, and only in a much more enfeebled 
degree to in, ^n, or to n/i, n/^, Ji„ vibrating with n 
even in case of an aperiodic impulse, therefore the 
sensation [!—/(«)] iP-f/(«) C will still be predom- 
inantly associated with R„. 

Welt-attested cases of double hearing (compare 
Stumpf, loc. cit., p. 206, et seq.) point forcibly to the 
conclusion that the ratios in ■which the energies D and 
C are disengaged are dependent upon the end-organ, 

IThua, lo ukam vert aimpla eiusple, wa might ni>ke/(ii) — k.loi-ii. 


and not upon the rate of vibration — a conclusion which 
would also not affect our conception. 

A member R„ accordingly, responds powerfully to 
«, and also, though more weakly, to an, 3/1, .... , 
h/2, »/3 .... with the sensations belonging to these 
rates of vibration. It is, however, extremely improb- 
able that exactly the same sensation is excited whether 
R^ responds to n, or whether R^ responds to n. On 
the contrary, it is probable that every time the mem- 
bers of Corti's series respond to ^partial tone, the sen- 
sation receives a weak supplementary coloring, which we 
will represent symbolically, for the fundamental tone 
by Z^, for the overtones by Z^, Z^, . . . ., and for the 
undertones by Z,, Z,,. . . . On this supposition, sen- 
sations of tone would be somewhat richer in composi- 
tion than would follow from the formula [1 — /C")] -^ 
-\-/{fi) C. The sensations which Corti's series, as ex- 
cited by the fundamentals, yields, constitute a province 
with the supplementary coloring Z^, the excitation of 
the same series by the first overtone yields a special 
province of sensation with, the supplementary coloring 
Zj, etc. The Z's may be either unchanging elements, 
or may themselves, again, consist of two components, 
i/and V, and form series represeotable by [1 — y(«)] 
^-\- /if) ^- But at present the decision on this last 
point is immaterial. 

It is true that tYie physiological eieraeats Z,, Z,, .... 
have yet to be found. Yet the very perception that 
they have to be sought seems to me of importance. 


Let us see what form the piovince of tone- sensations 
would take on if we regarded Z^, Z,, .... as given. 
Our example is a melodic or harmonic major- 
third combination, whose rates of vibration are n-^^p 
and TO := 5/; the lowest of the overtones common to 
the two is 5n^4W^20/, the highest of the under- 
tones common to the two is /. Then we obtain the 
following table ;• 

t!i=Co.<i series: 






respond to the talet 




4> = ^ 
5/ = 4 

«i<h the mppre- 
liona : 






to the rates ol v[- 

a>/ = j(4» 



«[th the supple- 



Thus in the third combioation, the supplementary 
sensations Z^, Z,, and Z,, Zi, which are characteristic 
of the third, make their appearance even when the 

lit will be observed that the aDaLysis of the loDe-seasations hi 
rollons Ibe same path as the currem analysis of color-BeasaliDtu 

ev Ihat to the endless physical differsncei 


parallelism, the number of the sonulidu- 





notes contain no overtones, while the former (Z,, Z,) 
are strengthened when, either in the open air or at 
least in the ear, overtones do occur. The diagram 
may be easily generalised to include any interval. 

These supplementary colorings, though scarcely J 
noticeable in single tones, or in running continuously ] 
through the scale, become conspicuous in combina- , 
tions of tones having certain rates of vibrations, just I 
as the contrasts of faintly colored, almost white lights 1 
become vivid when these are brought together. And, 
furthermore, the same contrast-colorings always corre- 
spond to the same ratios of vibrations, no matter what , 
the pitch. 

In this manner it is intelligible how tones may i 
receive, by melodic and harmonic combination with 1 
others, the most varied colorings, which are wanting J 
to them when singly sounded. 

The elements Z^, Z^ . . . must not be conceived as.l 
unvarying and fixed in number. On the contrary, it j 
is to be supposed that the number of perceptible Z's | 
depends on the organisation, on the training of the i 
ear, and on the attention. According to this concep- J 
tion, the ear does not directly cognise ratios of vibra- J 
tions but only the supplennentary colorings conditioned ■ 
by these. The tonal series symbolically represented 1 
by [I— /C«)]-0-t-/{«)C" is not infinite but limited. | 
Since /(«) may vary between the values and 1, jE7 J 
and C are the extremes, the terminal sensations cor- ' 
responding to the lowest and highest tones. If the] 



number oi vibrations sinks considerably below or rises 
considerably above that of the fundamental of the 
longest and the shortest Corti fibre, a weak response 
only will take place, but no alteration of the quality 
of the semsatioo. Likewise, the sensation due to the 
interval must disappear in the neighborhood of the 
limits of hearing ; first, because in general differances 
between sensations of tone cease at this point, and, 
further, because at the upper boundary the members 
of the Corti series susceptible of being excited by the 
undertones, are lacking, as are also at the lower boun- 
dary those which react on the overtones. 


Passing in review again the conception gained, we 
see that with few exceptions the conclusions reached 
by Helmholtz may be all retained. Noises and com- 
posite sounds may be decomposed into musical tones. 
For every perceptible rate of vibration there corres- 
ponds a particular nervous end-organ. In place of 
the numerous specific energies raquired by this theory, 
however, we substitute but two, which render the re- 
lationship of all tonal sensations intslligible, and by 
the rfile which we assign to the attention, likewise 
enable us to keep perceptually dislimt, several tones 
when sounded together. By the hypothesis «f the 
multiple reaponae of the members of the Corti series, 
and that of supplementary acoustic colorings, the sig- 



nificance of accidental acoustic tints is diminii 

and we get a glimpse of the direction in which, not- 
ably on the ground of musical facts, the pasiiive char- 
acteristics of intervals are to be sought. Finally, by 
the latter conception, Von Oettingen's principle of 
duality acquires a basis, which might perhaps com- 
mend itself to this investigator himself better than his 
assumption of "memory " ; while at the same time it 
becomes manifest why the duality cannot be a perfect 


To a person accustomed to looking at things frot 
the point of view of the theory of evolution, the higbi 
development of modern music as well as the spon4 
taneous and sudden appearance of great musical talei 
seem, at first glance, a most singular and problematii 
phenomenon. What could this remarkable develop- 
ment of the power of hearing have had to do with t 
preservation of the species? Does it not far i 
the measure of the necessary or the useful ? What c 
possibly be the significance of a fine discriminativi 
sense of pitch? Of what use to us is a perceptivi 
sense of intervals, or of the acoustic colorings of < 
chestral music? 

As a matter of fact, the same question may be pre 
posed with reference to every art, no matter from whi 
province of sense its material is derived. The qui 
tion is pertinent, also, with regard to the intelligei 


of a Newton, an Euler, or their like, which apparently 
far transcends the necessary measure. But the ques- 
tion is most obvious with reference to music, which 
satisfies no practical need and for the most part de- 
picts nothing. Music, however, is closely allied to 
the decorative arts. In order to be able to see, a per- 
son must have the power of distinguishing the direc- 
tions of lines. Having 3. fine power of distinction, such 
a person may acquire, as a sort of collateral product 
of his education, a feeling for agreeable combinations 
of lines. The case is the same with the sense of color- 
harmony following upon the development of the power 
of distinguishing colors, and so, too, it undoubtedly 
is with respect to music. 

We must bear in mind that talent and genius, 
however gigantic their achievements may appear to us, 
constitute but a slight departure from normal endow- 
ment. Talent may be resolved into the possession of 
psychical power slightly above the average in a certain 
province. And as for genius, it is talent supplemented 
by a capacity of adaptation extending beyond the 
youthful period, and by the retention of freedom to 
overstep routine barriers. The naivety of the child 
delights us, and produces almost always the impres- 
sion of genius. But this impression as a rule quickly 
disappears, and we perceive that the very same utter- 
ances which, as adults, we are wont to ascribe to free- 
dom, have their source, in the child, in a lack of fixed 


Talent and genius, as Weismann has aptly shown, ^ 
do not make their appearance slowly and by degrees 
in the course of generations ; nor can they be the re- 
sult of accumulated effort and practice on the part 
of ancestors ; but they manifest themselves spontan- 
eously and suddenly. Taken in connexion with the 
preceding, this, too, is intelligible, if we will but re- 
flect that descendants are not exact reproductions of 
their ancestors, but exhibit the qualities of the latter 
with some variations, now slightly diminished, now 
slightly augmented in amount. 

1 Weismann, Ueher die Vererbung, Jena, 1883, (English translation, Claren- 
don Press, Oxford, 1889,) p. 43. 



WHAT gain does physics derive from the preced- 
ing investigations? In the first place, a very 
wide-spread prejudice is removed, and with it, a bar- 
rier. There is no rift between the psychical and the 
physical, no within and ■without, no sensation to which 
an outward, different thing corresponds. There is but 
one kind of elements, out of which this supposititious 
within and without is fornaed — elements which are 
themselves within and without according to the light 
in which, for the time being, they are viewed. 

The world of sense belongs to the physical and 
the psychical domain alike. As, in studying the be- 

(See my ErkM-^ng dir ArbiU. Pn 
'-Tbe Economical Nature of Physic 
noiF in my Psfular Scitntific Lccturi 

coDsidersd in this cbapler, bsforo. 
IlvD, 1871, and iliia (be suay on 
iiiry." first publiahsd in iBSi, and 


havior of gases, by disregarding variations of tempera- 
ture we reach Mariotte's law, but by expressly con- 
sidering them, Gay Lussac's, while throughout our 
object of investigation remains the same, so, too, we 
study physics in its broadest signification when in 1 
searching into the connexions of the world of sense | 
we leave the body enlirely out of aecouni, whereas we 
pursue the psychology of the senses when we direct our 
main attention to the body and above all to our ner- 
vous system. Our body, like every other, is part of 
the world of sense ; the boundary-line between the | 
physical and the psychical is solely practical and con- 
ventional. If, for the higher purposes of science, we 
erase this dividing-line, and consider all connexions 
as equivalent, new paths of investigation cannot fail to 
be opened up. 

We must regard it as an additional gain that the 
physicist is now no longer overawed by the traditional 
intellectual implements of physics. If ordinary "mat- 
ter" must be regarded merely as a highly natural, 
unconsciously constructed mental symbol for a com- 
plex of sensuous elements, much more must this be 
the case with the artificial hypothetical atoms and 
molecules of physics and chemistry. The value of 
these implements for their special, limited purposes 
is not one whit destroyed. As before, they remain 
still economical symbolisations of the world of experi- 
ence. But we have as little right to expect from them. 


as from the symbols of algebra (to use an apposite 
analogue), more than we have put into them, and cer- 
tainly not more enlightenment and revelation than 
from experience itself. We are on our guard now, 
even in the province of physics, against overestimat- 
ing the value of our symbols. Still less, therefore, 
should the monstrous idea ever enter our heads of em- 
ploying atoms to explain psychical processes ; seeing 
that atoms are but the symbols of certain peculiar 
complexes of sensuous elements which we meet with 
in the narrow domain of physics. 

The sciences may be distinguished according to 
the matter of which they treat, as also by their man- 
ner of treating it. Further, all science has for its aim 
the representation of facts in ihought, either iox practical 
ends, or for removing int^U^ct ual discomioit. Resum- 
ing the terminology of the "Introductory Remarks," 
science, it may be said, arises where in any manner 
the elements ABC ... or the elements KLM . . . are 
reproduced or representatively mimicked by the ele- 
ments a^y. . . . , or the latter by one another. For 
example, physics (in its broadest signification) arises 
through representatively reproducing by a^y . . . the 
elements ABC in their relations to one another ; the 
physiology or psychology of the senses, through repro- 
ducing in like manner the relations of ABC . . . to 
KLM. . . ; physiology, through reproducing the rela- 


rions of KLM. . . to one another and to ABC . . . ; 
while the reproducing of the a^y • ■ - themsehres by 
other a/Sy leads to the psychological sciences proper. 
Now one might be of the opinion, say, with respect 
to physics, that the portrayal of the senae-given /acft 
is of less importance than the atoms, forces, and laws 
by which they are portrayed, and which form, so to 
speak, the nucleus of the sense-given facts. But un- I 
biassed reflexion discloses that every practical and in- \ 
ttlUctual need is satis&ed the moment our thoughts 
have acquired the power to represent the facts of the 
senses completely. Such representation, consequently, 
is the end and aim of physics ; while atoms, forces, i 
and laws are merely means facilitating the representa- , 
tion. Their value extends as far, and as far only, as 
the help they afford. 


Our knowledge of a natural phenomenon, say of I 
an earthquake, is as complete as possible when our 1 
thoughts BO marshal before the eye of the mind all the 
relevant sense-given facts of the case that they may 
be regarded almost as a substitute for the latter, and 
the facts appear to us as old familiar figures, having 
no power to occasion surprise. When, in imagina- 
tion, we hear the subterranean thunders, feel the oscil- 
lation of the earth, figure to ourselves the sensation 
produced by the rising and sinking of the ground, the 
cracking of the walls, the falling of the plaster, the I 


movement of the furniture and the pictures, the stop- 
ping of the clocks, the rattling and smashing of win- 
dows, the wrenching of the door-posts, the jamming 
of the doors ; when we see in mind the oncoming un- 
dulation passing over a forest as lightly as a gust of 
wind over a field of grain, breaking the branches of 
the trees ; when we see the town enveloped in a cloud 
of dust, hear the bells begin to ring in the towers ; 
further, when the subterranean processes, which are 
at present unknown to us, shall stand out in full sen- 
suous reality before our eyes, so that we shall see the 
earthquake advancing as we see a waggon approaching 
in the distance till finally we feel the earth shaking be- 
neath our feet, — then more insight than this we cannot 
have, and more we do not require. If we cannot com^ 
bine the partial facts in their right and required pro- 
portions without the aid of certain auxiliary concep- 
tions drawn from mathematics, it yet remains true thai 
the latter merely enable our thoughts to grasp gradu- 
ally and piecemeal what they are unable to grasp all 
at once. These auxiliary conceptions would be de- 
void of value, could we not reach, by their help, the 
graphic representation of the sense-given facts. 

When I see in thought a white beam of light which 
falls upon a prism issue forth in a fan-shaped band of 
colors having certain angles which I can specify be- 
forehand ; when I see its real spectrum- image, ob- 
tained upon a screen by interposing a lens, and in that 
image, at points determinable in advance, Fraunhofer's 



lines; when I see, in my mind, how these self-same 
lines alter their position on the prism being tumed, 
on its substance being changed, or on the thermom- 
eter in contact with it altering its register, then I know 
all that I can require. All auxiliary conceptions, laws, 
and formula, are but quantitative norms, regulating 
my sensory representation of the facts. The latter is 
the end, the former are the mtam. 

The adaptation of thoughts to facts, accordingly, 
is the aim of all scientific research. In this, science 
only deliberately and consciously pursues what in daily 
life goes on unnoticed and of its own accord. As soon, 
as we become capable of self-observation, we find our 
thoughts, in large measure, already adjusted to the 
facts. Our thoughts marshal the elements before us 
in groups copying the order of the sense-given facts. 
But the limited supply of the mental elements cannot | 
keep pace with the constantly augmenting sweep of 
experience. Almost every new fact necessitates a new 
adaptation, which finds its expression in the operation 
known Adjudgment. 

This process of judgment is easily followed in chil- 
dren. A child, on its first visit from the town to the 
country, strays, for instance, into a large meadow, 
looks about, and says wonderingly : "We are in a ! 
ball. The world is a blue ball.'" Here we have two \ 

I This case 1b not flctitioua, bql wab obiomd ia mj thre&^eu old child. 


judgments. What is the process accompanying their 
formation? In the first instance, the existing percept 
1 image of the company "we" is broad- 
■epresentative image by union with 
the similarly existing percept of a ball. Likewise, in 
the second judgment, the image of the "world" (i.e., 
ail the objects of the environment) is supplemented 
by combination with the image of an enveloping blue 
ball (the percept of which must also have been pres- 
ent, since otherwise the name for it would have been 
wanting). A judgment is thus always a supplementing 
or amendment of the deficiencies of a sensuous per- 
cept to represent completely a sensuous fact. If the 
judgment can be expressed in words, then the new 
percept is never more than a combination of formerly 
established memory-images, which can also be elicited 
in other persons by words. 

The process of judgment, therefore, in the present 
case consists in the enrichnnent, extension, and sup- 
plementation of existing sensuous percepts by other 
existing sensuous percepts, agreeably to the require- 
ments of definite sense-given facts. If the process is 
over with, and the image has assumed a familiar shape, 
making its appearance in consciousness as a distinct 
and intact product, then we have no longer to do with 
a judgment but merely with a phenomenon of memory. 
To the forming of such "intuitive knowledge," as 
Locke calls it, natural science and mathematics mainly 
owe their growth. Consider, for example, the follow- 


iag Statements : (i) the tree has a root ; (3) the frog ' 
has no claws ; (3) the caterpillar is transformed into a 
butterfly; (4) weak sulphuric acid dissolves zinc ; (5) 
friction electrifies glass; (6) an electric current de- 
flects a magnetic needle ; (7) a cube has six surfaces, 
eight corners, twelve edges. The first statement em- 
bodies a spatial extension of the percept tree, the 
second a correction of a percept too hastily generalised 
from habit, the third, fourth, fifth, and sixth embody 
temporal extensions of tfieir respective representa- 
tions. The seventh proposition is an example of geo- 
metrical "intuition," 


Intuitive knowledge of the sort just described, im- 
presses itself upon the memory and makes its appear- 
ance there in the form of recollections which spon- 
taneously supplement every fact presented by the 
senses. But the facts not being all alike, only their 
common elements are emphasised, and so we reach a 
principle which holds a paramount place in memory — 
the principle of broadest possible generalisation or con- 
tinuity. On the other hand, if memory is to satisfy 
the requirements made by the dissimilarities of facts, 
and be of real practical use, it must conform to the 
principle of su0cienl differentiation. Even the animal 
is reminded, by soft, bright red and yellow fruits (seen 
without exertion on the tree), of their sweet taste, and 
by green hard fruits (which are seen with difficulty), of 

their sour taste. The insect- hunting monkey snatches 
at everything th&t buzzes and dies, but avoids the 
yellow and black fly, the wasp. Here we have ex- 
pressed, distinctly enough, the combined efiort for 
greatest possible gentralisation and continuity and for 
praeiically sufficient differentiation of memory. And both 
ends are attained by the same means, the selection and 
emphasis of those particular elements of the sensuous per- 
ception which are determinative of the direction which 
the thought must pursue to suit the experience. The 
physicist proceeds in quite an analogous manner, when 
e says (generalising) : All transparent solids refract 
incident light towards the perpendicular, and when he 
adds (diHerentiating) : amorphous bodies and isomeric 
crystals simply, the rest doubly. 

A considerable portion of mental adaptation takes 

|)lace unconsciously and involuntarily, under the nat- 
ural guidance of the facts presented to the senses. If 
this adaptation has become sufficiently comprehensive 
to embrace the vast majority of the occurring facts, 
and subsequently we come upon a fact which runs vio- 
lently counter to the customary course of our thought 
without our being able to discover at once the deter- 
minative factor likely to lead to a ve-m differentiation, 
then ^problem arises. The new, unusual, and marvel- 
lous acts as a stimulus, which irresistibly attracts the 
attention. Practical considerations, or even bare in- 


I y tellectual discomfort, may engender a volitional fra 
of mind requiring the removal of the contradiction, 
a consequent new mental adaptation. Thus arises 
purposive thought-adaptation, investigation. 

For example, we have all, at some time or another, 
quite contrary to the common run of our experience, 
observed a lever or pulley lifting by means of a small 
weight a large weight. We seek the differentiating 
factor, which in the sensuous phenomenon itself is not 
immediately given. We compare a number of different 
instances falling under the same category, note the 
varying influences exerted by the weights and the arms 
ef the lever, and then, only after having mastered by 
strenuous independent efforts of our reasoning powers 
the abstract conceptions of "moment" and "work," 
do we reach the satisfactory solution of the problem. 
"Moment" or "work" is the differentiating element. 
The noting of the factors ' ' moment "or " work " hav- 
ing become a mental habitude, the problem no longer 

What do we do when we abstract? What is an I 
abstraction ? What is a concept ? Is there a sensu- 
ous image corresponding to every concept ? I cannot I 
represent to myself a general man. I can at most rep- | 
resent to myself a particular man, or perhaps one com- 
ning such accidental peculiarities of different men as ] 
z not exclusive of each other. A general triangle, I 


which is at once right-angled and equilateral, cannot 
be imagined. Further, the image thus rising into con- 
sciousness at the name of the concept, and accompany- 
ing the conceptual process, is not the concept. In 
fact, generally, words, being designations which from 
necessity must be used to describe many different per- 
cepts, are far from being identical with concepts. A 
child who has seen for the first time a black dog and 
heard it named, soon afterward calls a large and 
swiftly-running black beetle, "dog"; or a pig or a 
sheep, "dog."' Any similarity whatever reminding 
him of the first-named percept naturally leads to the 
use of its name. The point of similarity need not 
be at all the same in the successive cases. It may 
reside, for instance, in one case in the color, again in 
the motion, then in the form, then in the external cov- 
ering ; and so on. Of a concept there is no question. 
Thus, a child calls the feathers of a bird "hairs"; 
the horns of a cow "feelers "; a brush, the beard of 
its father, and the down of a dandelion, without dis- 
tinction, a "brush"; and so on.' Most adults treat 
words in the same manner, only less noticeably so, 
because they have a larger vocabulary at their dis- 
posal. The illiterate man calls a rectangle a square, 
and occasionally, too, a cube, a square, because of its 
rectangular boundaries. The science of language, and 

IThni [he Mireomanni called Ihs Ijana sscl aeroBB Ihs Danubs by (he 
Romuit "dogs," ud Ihs loniaiu csUeel the x^/"!""- "t the Nils ttam the 
liurds ol Iheli oalive undetbraah, - crocodiles.- (Herodotni, II„ 69.I 



a numbei of autfaeoticated historical examples, show 
that even nations do not act differently.^ 

A concept is never a finished percept. In using a 
word denoting a concept, there is nothing involved id 
the word but a simple impulse to perform some famil- 
iar sensory operation, as the restill of viihich a defi- 
nite sensuous element (the mark of the concept) is 
obtained. For example, when I think of the concept 
"heptagon," I enumerate the angles of a figure visi- 
bly before me or of its image in my consciousness ; 
and when in so doing 1 reach seven, in which case the 
sound, the numeral, or my finger announces the sensu- 
ous mark, then by this very act the given percept falls 
under the given concept. In speaking of a "square 
number," I seek to resolve the number given into - 
components typified by the operation 5X 5i 6 X ^i *^to., I 
the sensuous characteristic of which, being the equal- 
ity of the two factors multiplied, is patent. The same 
holds good of every concept. The sensuous activity 
excited by the word may be made up of a number 
of operations, one of which may involve the other. 
But the result is always a sensuous element not bejor 

In looking at or in imagining a heptagon, the fact \ 
of its having seven angles need not be present to my 
mind. This fact is distinctly cognised only on count- 
ing. Frequently, the new sensuous element may be 
so obvious (as it is, for instance, in the case of thei 

J Sai WhElnajf, Lifi and Grrmlk ^Langtatt. 




rsYsics. iti 

triangle) that the operation of counting seems un- 
necessary. Such cases, however, are exceptional, and 
constitute the main source of misunderstandings con- 
cerning the nature of concepts. I do not directly see, 
by an act of sight, in the case of conic sections (the 
ellipse, parabola, hyperbola) that these curves may 
be all subsumed under the same concept ; but I can 
discover the fact by cutting a cone, and by construct- 
ing the equation for conies. 

When, therefore, we apply abstract concepts to a 
fact, the fact merely acts upon us as an impulse to per- 
form a definite operation of the senses, which opera- 
tion introduces new sensuous elements, determining 
the subsequent course of our thought with reference 
to the fact. By this activity we enrich and extend the 
fact, which before was too meagre for us. We do 
what the chemist does with his colorless solution of 
salts, when by a given operation he obtains from it a 
yellow or brown precipitate, having the power to dif- 
ferentiate the career of his thought. The concept of 
the physicist is a precise and definite reaction-activity, 
which enriches a fact with new sensuous elements. 


To revert to an earlier example, when we behold 
a lever, we are impelled to measure the length of 
its arms, to weigh its weigfits, and to multiply the 
numbers representing the lengths of its arms by the 
numbers representing the values of its weights. If 



the same sensuous numerical symbol corresponds 1 
both products, we expect equilibrium. We have here 
gained a new sensuous element which was not an- 
tecedently given in the bare fact itself, but which_ 
now differentiates the career of our thought, 
will keep well in mind that thought by concepts is 
reaction -activity which must be thoroughly practised, 
we shall understand the well-known fact that no on 
can familiarise himself with mathematics or physic 
or with any natural science by mere reading withou^ 
practical exercise. Comprehension here depends en^ 
tirely on action. In fact, it is impossible in any p 
ince to grasp the higher abstractions without a prat 
tical working knowledge of its details. 

Facts then ate extended and enriched, and ulti- 
mately again simplified by the action of concepts. 
For, when the new determinative sensuous element 
is found (say, the number representing the virtual 
moments of the lever), then this alone is investigated, 
and the most diverse groups of facts are found ) 
resemble and not to resemble each other solely 1 
virtue of this element. Thus here also, as in the cast 
of intuitive knowledge above mentioned, everythin 
is reducible to the discovery, selection, and emphasid 
of the determinative sensuous elements. Investigatioi 
here only reaches by a ronndabout way what is imme^ 
diately presented to intuitive cognition. 

The chemist with his reactions, the physicist witi 
bis measuring rod, scales, and galvanometer, and tl 


mathematician, all treat facts in quite the same way; 
the only difference being that the latter needs to go 
least outside of the elements a^y . . . KLM in his 
extension of facts. The aids of the mathematician are 
always conveniently at hand. The investigator and 
all his thought are a fragment only of nature, like 
everything else. A real chasm between him and other 
parts does not exist. All elements are equivalent. 

On the preceding theory, the essence of abstrac- 
tion is not exhausted by terming it (with Kant) nega- 
tive attention. It is true that, in abstracting, the at- 
tention is turned away from many sensuous elements, 
but on the other hand, it is turned toward other and 
ff^W sensuous elements; and precisely this latter fact 
is the essential feature. Every abstraction is founded 
on the prominence given to certain sensuous elements. 

The facts given by the senses, therefore, are alike 
the starting-point and the goal of all the mental adap- 
tations of the physicist. The thoughts which follow 
the sense-given fact immediately are the most famil- 
iar, the strongest, and the most intuitive. Where we 
cannot at once follow a new fact, the strongest and 
most familiar thoughts press forward to lend to it 
their richer and preciser moulds. This process is the 
source of every hypothesis and speculation in science. 

I which latter all find their warrant in the mental adap- ^^^ 

tation that has developed and ultimately given them ^^H 


birth. Thus we think oE the planets as projectiles, 
figure to ourselves an electric body as covered with 
a fluid that acts at a distance, think of heat as a sub- 
stance that passes from one body to another, until 
finally the new facts become as familiar and as intui- 
tive as the older ones, which we had used as mental 
helps. Even where immediate intuition is out of the 
question, the thoughts of the physicist, by carefully 
observing the principle of continuity and of sufficient 
differentiation, become ordered in an economically as- 
sorted system of conceptual reactions, which lead, at 
least by the shortest path, to intuitive knowledge. 


Let us now consider the results of mental adapta- 1 
tion. Thoughts can adapt themselves only to what is 
constant in the facts ; the mental reconstruction of c. 
stani elements alone can yield advantage in point of j 
economy. Herein is contained the ultimate ground 
of our effort for continuity in thought, that is, for the ! 
preservation of the greatest possible constancy, and 
by it, too, the results of the adaptation are rendered j 


The unconditionally constant we term substance, j 
I see a body upon turning my eyes in its direction. I ] 
can see it without touching it, I can touch it without ] 

ICtoB^ne mi Aftchamicr. Bng trantv., Chicaeo, t^n. V- Vf. 


seeing it. Although thus the actual appearance of the 
component elements of the complex is joined to con- 
ditions, I yet have these conditions too absolutely in 
my hands to appreciate or notice them markedly. I 
regard the body, or the complex of elements, or the 
nucleus of this complex, as always present, whether, 
for the moment, it is the object of my senses or not. 
Having always ready the thought of this complex, or, 
symbolically, the thought of its nucleus, I gain the 
advantage of being able to predict, and avoid the dis- 
advantage of ever being surprised. My behavior is 
the same vith regard to the chemical elements, which 
also appear to me unconditionally constant. Although 
here my mere willing it is not sufficient to make of the 
complexes in question sensuous facts, and although in 
the present case outward aids also are necessary, I 
yet leave these aids out of account as soon as they 
have become familiar to me, and look upon the chem- 
ical elements throughout as constant. The man who 
believes in atoms does the same with these auxiliary 

In the same manner as with the complex of ele- 
ments corresponding to a body, we may also proceed, 
on a higher plane of thought-adaptation, with entire 
provinces of facts. In speaking of electricity, mag- 
netism, light, and heat, even when not associating 
substances with these names, we yet ascribe constancy 
to these provinces of facts, leaving entirely out of ac- 
count the familiar eondiiions under which they ap- 


pear; and we hold the ideas which reproduce them 
always in readiness, thereby gaining an advantage 
similar to that explained above. When 1 say a body 
is "electric," far more nnemories arise in my mind, 
and my expectations are associated with far m 
definite groups of facts, than if I had emphasised, forfl 
instance, the attractions displayed in the single cases. 
Yet this hypostasising may have its disadvantages, also. 
In the first place, in proceeding thus, we always follow 
the same historical paths. It may be important, how- ^ 
ever, to recognise that there is no such thing as a spe- 
cific electrical fact, that every such fact can just as 
well be regarded, for example, as a chemical one, or 
as a thermal one, or rather that all physical facts are 
made up, in an ultimate analysis, of the same sensu- 
ous elements (colors, pressures, spaces, times), and 
that we are merely reminded by the term "electric" 
of that particular form in which we first became ac- 
quainted with the fact. 

If we have once accustomed ourselves to regard 
the body, to and from which we can, at pleasure, turn 
our glance and touching hand, as constant, then it is 
easy for us to do the same in cases in which the C' 
ditions of sensuous manifestation lie entirely without I 
our reach — for example, in the case of the sun and 
moon, which we cannot touch, or of parts of the world 
which we have seen but once and shall perhaps never 
see again, or that we know only by description. Such 
a method of procedure nnay have a high importance 


in an undisturbed and economical conception of the 
world, but it is certainly not the only legitimate 
method. It would be merely a consistent additional 
step, if we were to regard the whole past, which is, 
indeed, still present in its vestiges (since, for instance, 
we see the stars where they were thousands of years 
ago) and the whole future, which is present in germ 
(since, for example, our solar system will be seen 
where it now is, thousands of years hence) as con- 
stant. The ^•aXxTe passage of iime, in fact, is dependent 
solely on conditions of sensuous activity. Were a 
special purpose given, even this step might be haz- 

Really unconditioned constancy does not exist, as 
will be evident from the preceding considerations. 
We attain to the idea of absolute constancy only as 
we overlook or underrate conditions, or as we regard 
them as always given, or as we deliberately disregard 
them. There is but one sort of constancy, which em- 
braces all forms, namely, constancy of connexion (or 
of relatietC). 

The majority of the propositions of natural science 
express such constancies of connexion : " The tadpole 
is metamorphosed into a frog; chlorate of sodium 
makes its appearance in the form of cubes. Rays of 
light are rectilinear. Bodies fall with an acceleration 
of 9-81 (»r/«f *)." When these constancies are ex- 




pressed in concepts, we call them laws. Force (in ^ 
the mechanical signification") is likewise merely a con- 
stancy of connexion. When I say that a body A ex- 
erts a force on a body B, I mean that B, on coming 
into contraposition with A, is immediately affected 
by a certain acceleration with respect to A. 

The singular illusion, that the substance A is the 
absolutely constant vehicle of a force which takes effect 
immediately on .^'s being contraposed to A, is easily 
shattered. If we, or more exactly speaking, our sense- i 
organs, be put in the place of B, here a condition in- I 
tervenes, which, seeing that it is possible at any time 
to fulfil it, is invariably disregarded, and thus A ap- 
pears to us absolutely constant. Similarly, a magnet, 
which we see as often as we care to look in its direc- 
tion, appears to us the constant vehicle of a mag- 
netic force, which becomes operative only upon being 
brought near to a particle of iron, which we cannot 
disregard as easily as ourselves without noticing the 
fact.^ The phrases, "No matter without force, no 
force without matter," which are but abortive attempts 
to remove a self-incurred contradiction, become su- 
perfluous on our recognising only constancies of con^ 

To tlia child BTerjlhini 

Given a sufficient constancy of environment, there 
is developed a corresponding constancy of thought. ■., 
By virtue of this constancy our thoughts are spon- 
taneously impelled to complete all incompletely ob- 
served facts. The impulse in question is not prompted , 
by the individual facts as observed at the time; nor 
is it intentionally evoked ; but we find it operative in 
ourselves entirely without oiir personal intervention. 
It confronts us like a power from without, yet as a 
power which continually accompanies and assists us, 
as a thing of which we stand in need, in order to sup- 
ply the deficiencies of the fact. Although it is devel- 
oped by experience, it contains more than is contained 
in the single experience. The impulse in a certain 
measure enriches the single fact Through it the latter 
is more to us. By this impulse we have always a larger 
portion of nature in our field of vision than the inex- 
perienced man has, with the single fact alone. For 
the human being, with his thoughts and his impulses, 
is himself merely a piece of nature, which is added to 
the single fact. This impulse, however, can lay no 
claim to infallibility, and there exists no necessity 
compelling the facts to correspond to it. Our con 
fidence in it rests entirely upon the supposition, which 
has been substantiated by numerous trials, of the suf- 
ficiency of the mental adaptation, — a supposition. 

however, which must be prepared to be c 
at any moment. 

Not all our ideas representing facts have the same 
constancy. Whenever we have a special interest in 
the representation of facts, we endeavor to support 
and corroborate ideas of lesser constancy by ideas of 
greater constancy, or to replace them by the latter. 
Thus Newton conceived the planets as projectiles, 
although Kepler's laws were already well known, the 
tides as attracted by the moon, although the facts of 
their movement had long been ascertained. We be- 
lieve we understand the suction of a pump, the Bowing 
of a siphon, only as we add in thought the pressure | 
of the air. Similarly we seek to conceive electrical, J 
optical, and thermal processes as mtchanical proces- 
ses. This need of the support of weaker thoughts by 
stronger thoughts is also called the need of causality, 
and is the moving spring of all explanation in science. 
We naturally prefer, as the foundation of this process, 
the strongest and most thoroughly tested thoughts, 
and these are given us by our much exercised mechan- 
ical functions, which we may test anew at any moment 
without many or cumbersome appliances. Hence the 
authority of mechanical explanations, especially those 
by pressure and impact. A corresponding and still , 
higher authority attaches to mathematical thoughts, 
for in their development we stand in need of no ex- ] 
traneous means whatever, but on the contrary, 
variably carry most of the material for experimenting I 




about with us. But if we are once apprised of this, 
the need of mechanical explaaatioas is appreciably 

It was said above that man himself is a fragment 
of nature. Let me illustrate this by an example. For 
the chemist a substance may be sufficiently character- 
ised merely by his sensations. In this case the chem- 
ist himself supplies, by inner means, the whole wealth 
of fact necessary to the determination of his course of 
thought. But in other cases, resources to reaction by 
the help of outward means may be necessary. When 
an electric current flows round a magnetic needle situ- 
ated in its plane, the north pole of the needle is de- 
flected to my left if I imagine myself as Ampfere's 
swimmer in the current. I enrich the fact (current 
and needle) which is insufficient in itself to define 
the direction of my thought, by introducing myself 
into the experiment by an inner reaction. I may like- 
wise lay my watch in the plane of the circuit, so that 
the hand moves in the direction of the current. Then 
the south pole falls in front of, the north pole behind 
the dial. Or I may make of the circuit traversed by 
the current a sun-dial (on the plan of which the watch 



i., pp. 84, 304.4S5.I 
iiiion ibowi, tint 
r«n/ (Ida. 


in fact was modelled), so arranging it that the shadow \ 
follows the current. In this case the north pole will 
move towards the shadowed side of the plane of the 
current. The two last- mentioned reactions are out- 
ward reactions. The two species of reactions coulci 
not be made use of indiscriminately if a chasm existec 
between myself and the world. Nature is a singlel 
whole. The fact that the two species of reaction are | 
not known in ail cases, and that frequently the ob- 
server appears to be entirely without influence, proves 1 
nothing against the view advanced. 

Whenever it happens, in a complexus of elements, ' 
that some of the elements get replaced by others, 
necessarily the constancy of the connexion is changed. 
In such cases it is desirable to discover a constancy 
which survives this change. J. R. Mayer first felt I 
this need, and satisfied it by enunciating his concept I 
of "force," which corresponds to the technical me- 
chanical concept of "work" (Poncelet) or more ex- 
actly to the more general concept of "energy." Mayer ] 
conceives this force (or energy) as something abst 
lutely constant (as a store of something, as a sub- I 
stance), and so goes back to the strongest and most I 
intuitive thoughts. We perceive, from Mayer's strug- 
gle with expressions, with general philosophical | 
phrases, etc. (noticeable in the first and second of his 1 
treatises), that he at first felt instinctively and intuitivety\ 

■V i 

PHYSICS, 175 ^^1 

the urgent need 

of such a concept. But the great ^^H 

achievement was accomplished only upon his adapting ^^^H 

the existing phys 

cal concepts to the requirements of ^^H 

the facts and his needs.* ^^^H 


ailing body, we note the i:Diislanc;c=V?7:i, which ^^H 

ipcess inlhe tormf-^tizcl/i. Making the entire ^^H 

possibis dlsunce ot dssc 

Dck at sometbini, Ifi^nratively a sub- ^^H 

sumce) which, when Ihe 

event occurs, is converted [com the /■ 1. ^^^H 


l.atltj>*'+«-f>/sbeo,adecoQiIanl, \ ^^H 

Irom the form >«' inls Ih 

erorni>-t'>/i,bnl which always pre- //^ ^^H 

serves ila lol.l yslue iio 

banged. Such > congeplicn is well ( ^^H 

qualified lo meel eur .«d 

> and to turn our thoughts into famil- t. 1*' ^^H 

regard f,^ and vt/1 as eq 

parespIiblB Irace of suel 

Bifl/a diMppeais/i' ma 

reappear (far instance. In the rebound ot an elastic ^^^H 

bali), then thii coDceplio 

serves a highly practical purpose. IComp. Ntach. ^^^H 

]»9. Ibe admirable work 

of J. Popper, Da pkyMMichm Crund^Uu dtr ^^H 

™jr.) ^" 


all freel7, but in gradually sinking heals another 

body or renders ilelectri 

than an entirely new constancy lakes the place o( 

tbeEiel. NdlhiDg compe 

a us 10 regard ttie quantity of heal generated or the 

eleclric poleolial produce 

(enniaing thai the hea! lA 

\aSt itawd/sr txaltly at nxc* 01 the corresponding 

fk- i> arhilr^rj. nolwilh 

Marer'i »ud that led bim 

to write down hi. equation, which ai rogsrda the 

facU was not as yet san 

sfied and which is generally incorrect it Ihe right 

UDlta are doi selected. 

■tancy of coaneiion only. In revtriibU processei 

(proeesaos Ihal are indepe 

ndenl o( lime) we find ftriodic cbangea of elements 


inlhisotoquiYaience. H 

eat may lake th. place of >*', and in place o( this 

again the same/*' may r 

which are not reversible (changes dependent on 

uivalence is idle. Whether or not beat which can 

no longer reappear as »«, 

mighi be slnick by Ihe pnf^lisHalUy between fh 

think that this certainly could not depend upon uii 

arbitrary conception but 
■■T, to regard fk and ; k 

<,nlilf Dt Bleclriclty as equivalent, this conception 

rviceable, and (be idea would aecessarilj hate re- 

qnirad modlBcation un.i 

liicity. Thai fi^.(rt>' of 

heat was so readily offered in the inquiry, was a 

fortonals historical citcu 


ona.— Mayer's unusually powerful intellectual in- 


Upon sufficient adaptation, the facts are spontane- 1 
ously reproduced by the thoughts, and incompletely \ 
given facts are completed. Physics can act only a 
quantitative norm regulating and giving a moi^ precise 
conformation to the spontaneously flowing thoughts, 
suitably to definite practical or scientific needs. When 
I see a body thrown horizontally, the vivid picture of 
a projectile in motion rises before my mind. But the 
artilleryman or the physicist requires more. He must 
know, for example, that if on applying the measuring- 
rod M to the horizontal abscissas of the projectile's , 
path, he can count to i, 2, 3, 4 ... . he must, on ap- 
plying the measure M' to the vertical ordinates, also 
count to I, 4, 9, 16 ... . in order to reach a point of 
the path. The function of physics consists, therefore, 
in teaching that a fact which, on a definite reaction X 
yields a sensory mark E, also yields, on the giving of 1 
a different reaction R', a second sensory mark £". By 
this means it is possible to supply more exactly the 
deficiencies of incompletely given facts. 

cepmal ihounht, h 

□ed the mscliui- 


The space of the geometrician is by no means made 
up wholly of the system of sp^ce-sensaiians (of the 
senses of sight and touch), but consists rather of a 
large body oi physical observations, having the space- 
sensations as their point of departure. In the very 
fact of the geometrician's regarding his space as con- 
stituted at all points and in all directions alike, he 
goes far beyond the space given by sight and touch, 
which by no means possesses this simple property 
(p. So). Without experience in physia the geometri- 
cian would never have reached this conception. The 
fundamental propositions of geometry have, as a fact, 
been acquired wholly by means of physical observa- 
tions, by the superposition of measures of length and 
of angles, by the application of rigid bodies to one an- 
other. Without propositions of congruence, no geom- 
etry. Apart from the fact that spatial images would 
never have been produced ia us without physical ex- 
perience, we should, even granting their existence, 
never have been able to apply them to one another 
and to test their congruence, without this knowledge. 
When we feel compelled to imagine an isosceles triangle 
as having equal angles at its base, our compulsion is 
due to the remembrance of powerful past experiences. 
If the proposition had its source in "pure intuition," 
there would be no necessity for learning it.^ That 

ITbe melhod of Euclid Is nndoufalcdlT eicbIImii for tliB iaitructiOD oE 



discoveries may be made by sheer power of geometrical 
imagination, and are made so daily, merely proves 
that the memory of a given experience can reveal to 
the mind features which in the original observation 
escaped unnoticed; just as in the after-image of a 
brightly-lighted lamp, new and previously unseen de- 
tails may be discovered. Even the theory of numbers 
must be looked at in some such manner ; its funda- 
mental propositions can hardly be viewed as entirely 
independent of physical experience. 

The cogency of geometry (and of all mathematics) 
is due, not to the fact that its theories are arrived at 
by some select and special kind of cognition, but only 
to the fact that the empirical material which is at its 
base is particularly convenient and handy, has been put 
to the test an untold number of times, and can be sub- 
jected again at any moment to the same tests. More- 
over, the province of space -experience is far more 
limited than that of the whole of experience. The 
conviction of having essentially exhausted this limited 
province soon arises and produces the necessary self- 

A self-confidence similar to that of the geometri- 
cian is doubtless also possessed by the composer and 

: decorative painter, who have both gained, the 
former in the domain of sensations of tone, the latter 

a Ibe pDXibEe i 

in that of sensations of color, a broad and rich ex- 
perience. To the one no space-figure will occur the 
elements of which are not weil known to him, and the 
two others will meet with no new combinations of tone 
or of color that are unfamiliar to them. But the in- 
experienced beginner in geometry will be no less sur- 
prised and disappointed than the young musician or 

The mathematician, the composer, the decorator, 
and the student of natural science, when indulging in 
speculative ?i\^t%, pursue quite anaf'fg-cKJ modes of pro- 
cedure, despite the differences of their matter and aim. 
The former, it is true, owing to his more limited ma- 
terial, has the advantage of the others as regards the 
certainty of his procedure; while the latter for the 
opposite reason is at a disadvantage as compared 
with the others. 


In like manner, the time of the physicist does not 
coincide with the system of X\xa^-sensaiions. When the 
physicist wishes to determine a period of time, he ap- 
phes, as his instruments of measurement, identical 
processes or processes assumed to be identical, such as 
vibrations of a pendulum, the rotations of the earth, 
etc. The fact connected with the time-sensation is in 
this manner made the subject of a reaction, and the 
result of the latter, the number which is obtained, 
serves, in place of the ^\\a&-sensaiioH, to determine 

more exactly the subsequent movement of the thought. 
In like manner, we regulate our thoughts concerning 
thermal processes not according to the sensation of 
warmth which bodies yield us, but according to the 
much more definite sensation which is obtained from 
ihermomeirical reactions by simply noting the height of 
the mercury. Usually a space-sensation (the dial of 
a clock) is substituted for the sensation of time, and 
for this, again, a number is put. For example, if we 
represent the excess of the temperature of a cooling 
body over that of its surroundings by 5 ^ ©r"**, then 
t is this number. 

The relation which the quantities of an equation 
actually represent, is usually (analytically) a more 
general one than that which is meant to be repre- 
sented by the equation. Thus in the equation {x/d)* 
-\- {y/fiy — 1 all possible values of x have an analytical 
meaning, and yield corresponding values of y. But if 
the equation be used to represent an ellipse, then only 
the values ol x <C^a and y <ib have a geometrical (or 
real) significance. 

Similarly, it would have to be expressly added, if. 
this were not obvious, that the equation S=^6t~*' re- 
presents the real process only for increasing values 

If we imagine the natural course of diSerent 
events, say the cooling of one body and the free des- 
cent of a second, represented by equations involving 
time, the time may be eliminated from these equa> 


tions, and we may express, for example, the space 
traversed by the falling body in terms of the excess of 
temperature. Thus viewed, the elements appear sim- 
ply as dependent on one another. But the meaning of 
such an equation must be more exactly defined by 
premising that only increasing distances of descent or 
decreasing temperatures are to be inserted successively 

Time is not reversible. A warm body set in cool 
surroundings simply cools off but does not grow warm 
again. With increasing time-sensations only decreas- 
ing excesses of temperature are connected., A house 
in flames burns down but never builds itself up 
again. A plant does not decrease in size and creep 
into the earth, hut grows out of it, increasing in size. 
The irreversibility of time reduces itself to the fact 
that the value-changes of physical quantities always 
take place in definite directions. Of the two analytical 
possibilities one only is actual. We do not need to 
see in this fact a metaphysical problem. 


T PURSUED in my youth physical sa^ philosoph' 
■*- ical studies, particularly psychology, with equal 
ardor. At that time there was hardly a question of aa 
experimental psychology, of a relation of psychologi- 
cal to physiological research. Neither did the physii 
of that day think of a psychological analysis of the no- 
tions it was constantly employing. How the notions 
of "body," "matter," "atom," etc., originated, was 
not investigated. Objects were given the inviolability 
of which physicists never questioned and with which 
they unconcernedly pursued their labors. 

The fields of physical and psychological research^ 
thus stood side by side unreconciled, each having iti 
own particular concepts, methods, and theories. Ni 
one doubted that the two departments were in som< 

iWritUn in 1B91, ""d published in The M^iit ol Januaiy, 1891 (Vol. IlJ 
No. 1), In contiauacloD at Ihe dlscuEGloa wllb Dr. Paul Cnnis i - - - - 
or Tkt Meniii on ■■ Some guestions ot Paycho-phT>ics.' ' The 
Bial rersrenpei sro omltied. Proleasor Macta li eip;ainiD|t (he 
led him 10 >bandan his earlf position, that Nalure haa two >i 
and a psvrholaeical, which view he likeni to thnl held bj the iditer oI 7 

10- ^n 




way connected. But the nature of the connexion ap- 
peared an insoluble riddle, as it still appears to Dubois- 
Reymond. • 

Now although this condition of things was not 
such as to satisfy my mind, it was nevertheless nat- 
ural that as a student I should seek to acquire tenta- 
tively the dominant views of the two provinces and to 
put them into consistent connexion with one another. 

I thus formed provisorily the view that Nature has 
two sides — a physical and a psychological side. If 
psychical life is to be harmonised at all with the the- 
ories of physics, we are obliged, I reasoned, to con- 
ceive of atoms as feeling (ensouled). The various 
dynamic phenomena of the atoms would then repre- 
sent the physical processes, whilst the internal states 
connected therewilh would be the phenomena of psychic 
life. If we accept in faith and seriousness the atom- 
istic speculations of the physicists and of the early 
psychologists (on the unity of the soul), I still see 
no other way of arriving at a tenable monistic con- 

It is unnecessary to emphasise at length here the 
prominent part which the artificial scaffolding em- 
ployed in the construction of knowledge plays in 
I these monadic theories as contradistinguished from 
the facts which really deserve to be known, and the 
scant satisfaction which such theories afford in the 
long run. As a fact, employnnent with this cumbrous 
artifice was in my case the vexy means that gave rise 


to ray better conviction, which was already latent^ 

In the further progress of my physical work I sol 
discovered that it was very necessary shar ply Jo ^ 
tinguish between what we set and what we mentally 
supph^. When, for example, I imagine heat as a sub- 
stance (a fluid) that passes from one body to another, 
I follow with ease the phenomena of conduction and 

bI proceasas wilb wbich he oia in- 

ind impact were probably the only o^ 
iimalelj acquainted. Ibotighl Dili the 
:a-day, (bougb in a modified [oiin. I, 

eall, do 

COD I eat ion lb 

I io phy 



an be 





Bit particlBB i 

at bes 





diis kind affor 



of bun 


but only eoato 


tbe Dtief 

te pb,s 





ch, for ..- 

ample, reprod 



of (be 

world by a div 

(0= + 





oes iad 

ed app 

first elaoceth 




tlompta at 

./*,.,«( moE 

Bdio the 


iho lights o( 

a .mgU 

golher: (he lb 


ed? In 

er lo make 


rylhing hat reqo 

to be P.J.- 

ch[dallj corme 

ted. as 




by om 

e. Th 


eical m 

reals on a mou 






lai ic lb 



ti .he phy.- 

"" "Txa » 




nl the 


Hion in 

tho leil 


.. thai the 











Md via viria 





roaciiona upon 

ed by cu 

Tbe idea 


up by the 

elimmali™ e 



ioES d 






^P exchan 


exchange. This idea led Black, who established it, 
to the discovery of specific heat, of the latent heat of 
fusion and vaporisation, and so forth. This same idea 
of a constant quantity of heat-substance, on the other 
hand, prevented Black's successors from using their 
eyes. They no longer observe the fact which every 
savage knows, that heat is produced by friction. 
the help of his undulatory theory Huygens follows 
with ease the phenomena of luminous reflexion and 
refraction. The same theory prevents him (for he 
thinks solely of the longitudinal waves with which he 
is familiar), from rightly grasping the fact of polai 
tion which he himself discovered, but which Newton, 
on the other hand, untrammelled by theories, perceives 
at once. The conception of fluids acting at a distance 
on conductors charged with electricity facilitates our 
view of the behavior of the objects charged, but it 
stood in the way of HiM discovery of the specific induc- 
tive capacity, which was reserved for the eye of Fara- 
day undimmed by traditional conceptions. 

Valuable, therefore, as are the conceptions which 
we mentally (theoretically) supply in investigating 
facts, bringing to bear, as they do, older, richt 
general, and more familiar experiences on facts that 
stand alone, thus affording us a broader field of view, 
nevertheless, the same conceptions may lead us astray 
as classical examples and our own experience demon- 
strate. For a theory, indeed, always puts in the place 
of a fact something different^ something more simple. 




V As 

which is qualified to represent the fact in some certaSk 
' aspect, but for the very reason that it ts different does 
not represent it in other aspects. When in the place 
of light Huygens mentally put the familiar phenom- 
enon of sound, light itself appeared to him as a thing 
that he knew, but with respect to polarisation, which 
sound-waves lack, as a thing with which he was doubly 
unacquainted. Our theories are abstractions, which, 
while placing in relief what is important in certain 
deitrniinate cases, neglect almost necessarily, or even 
disguise, what is important in other cases. The law 
of refraction looks upon rays of light as homogeneous 
straight lines, and that is sufJicient for the comprehen- | 
sion of the geometrical aspect of the matter. But the ' 
propositions relating to refraction will never lead us 
to the fact that the rays of light are periodical, that 
they interfere. On the contrary, the favorite and 
familiar conception of a ray as an undifferentiated 
straight line is more likely to render this discovery 

The instances in which the resemblance between a 
fact and its theoretical conception extends /iirtinr than 
we ourselves postulate, are rare. But when this hap- 
pens, the theoretical conception may lead to the dis- 
covery of new facts, a case of which conical refraclioa(._ 
circular polarisation, and Hertz's electric waves furnisl 
examples that militate against those above advanced^ 
As a general rule, however, there is every reason ftJ 
distinguishing sharply between our theoretical com 



ceptions of phenomena and that which we observe. 
The former must be regarded merely as auxiliary in- 
struments which have been created for a definite pur- J' 
pose and which possess permanent value only with 
respect to that purpose. No serious person will im- 
agine for a moment that real circles with angles and 
sines perform functions in the refraction of light. 
Every one, on the contrary, regards the formula 
sin«/sin>?^n as a kind of geometrical model which 
simply imilates inform the refraction of light and iakes 
its place in our mind. Now, in this sense, I take it, 
all theoretical conceptions of physics — caloric, elec- 
tricity, light*waves, molecul-es, atoms, and energy^ — 
must be regarded as mere helps or expedients to facil- 
itate our consideration of things. Even within the 
domain of physics itself the greatest care must be ex- 
ercised in transferring theories from one department 
to another, and above all more information is not to 
be expected from a theory than from the facts them- 

On the other hand, there is no lack of instances 
showing the far greater confusion which was produced 
by the direct transference of theories, methods, and 
inquiries that were legitimate in physics, into the field 
of psychology. 

Allow me to illustrate this by a few examples. 

A physicist observes an image on the retina of an 
excised eye, notices that it is turned upside down with 
respect to the objects imaged, and puts to himself 


very naturally the question. How does a luminous^ 
point situated at the top come to be reflected on the 
retina at the bottom f He answers this question by the 
aid of studies in dioptrics. If, now, this question, 
which is perfectly legitimate in the province of phys- 
ics, be transferred to the domain of psychology, only 
obscurity will be produced. The question why we see 
the inverted retinal image upright, has no meaning as 
a psychological problem. The light- sensations of the 
separate spots of the retina are connected with sensa- 
tions of locality from the very outset, and we name the 
places that correspond to the parts down, up. To the 
perceiving subject such a question cannot present it- 
^^L It is the same with the well-known theory of pro- 

^H jcction. The problem of the physicist is, to seek the 

^H luminous object-point of a point imaged on the retina 

^H of the eye, in the backward prolonged ray passing 

^H through the centre of the eye. For the perceiving 

^B subject this problem does not exist, as the light-sensa- 

^H tions of the retinal spots are connected from the be- 

^H ginning with determinate space-sensations. The en- 

^H tire theory of the psychological origin of the "external " 

^H world by the projection of sensations outwards is 

^B founded in my opinion on a mistaken transference of 

^H a physically formulated inquiry into the province of 

^H psychology. Our sensations of sight and touch are 

^1 bound up with, are connected with, various dtffereiU ■ 

^B sensations of space, that is to say, the sensations tn < 



question have an existence by the side of one another 
or outside of one another, exist, in other words, in a 
spatial field, in which our body fills but a part. That 
table is thus selt-evidently outside of my body. A pro- 
jection-problem does not present itself, is neither con- 
sciously nor unconsciously solved. 

A physicist (Mariotte) discovers that a certain spot 
on the retina is blind. He is accustomed to associat- 
ing with every spatial point an imaged point, and with 
every imaged point a sensation. Hence the question 
arises, What do we see at the points corresponding to 
the blind spots, and how is the gap in the image filled 
out ? If the unfounded influence of the physicist's 
methods on the discussion of psychological questions 
be excluded, it will be found that no problem exists at 
all here. We see twining at the blind spots, the gap in 
the image is not filled out. The gap, furthermore, is 
not felt, for the reason that a defect of light-sensation 
at a spot blind from the beginning can no more be per- 
ceived as a gap in the image than the blindness say of 
the skin of the back can be so perceived. 

I have intentionally chosen simple and obvious ex- 
amples, as they can best render clear what unneces- 
sary confusion is caused by the careless transference 
of a conception or mode of thought which is valid and 
serviceable in one domain, into another. 

In the work of a celebrated German ethnographer 
I recently read the following sentence: "This tribe 
of people deeply degraded itself by the practice of 



cannibalism." By its side lay the book of an Eng- 
lish inquirer who deals with the same subject. The 
latter simply puts the question why certain South-Sea 
Islanders eat human beings, finds out in the course of 
his inquiries that our own ancestors were once canni- 
bals, and comes to understand the position the Hindus 
take in the matter -a point of view that occurred once 
to my five year-old boy who while eating a piece of 
meat stopped, suddenly shocked, and cried out, '^We 
are cannibals to the animals ! " " Thou shalt not eat 
human beings" is a very beautiful maxim ; but in the 
mouth of the ethnographer it sullies the calm and 
noble lustre ot unprepossession by which we so gladly 
discover the true inquirer. But a step further and we 
shail say, "Man must not be descended from mon- 
keys," "The earth shalt not rotate," " Matter ca^A/ 
not everywhere to fill space," "E.netgy must be con- 
stant," and so on. I believe that our procedure differs 
from that just characterised only in degree and not in 
kind, when we transfer views reached in the province 
of physics, with the dictunn of sovereign validity, into 
the domain of psychology, where they should be tested 
anew with respect to their serviceability. In such 
cases we are subject to dogma, if not to dogma which 
is forced upon us by a power from without like our 
scholastic forefathers, yet to that which we have cre- 
ated ourselves. And what result of research is there 
that could not become a dogma by long habit and use, 
since the very skill which we have acquired in familiar 



intellectual situations deprives us of the freshness and 
unprepos session which are so requisite in the new ! 

Now that I have set forth in general outlines the 
position I take, I may perhaps be able to explain my 
opposition to the dualism 0/ feeling and melton. This 
dualism is to my mind artificial and unnecessary. Its 
origin is analogous to that of certain pseudo-mathe- 
matical problems, -^having come from an improper 
formulation of the questions involved. 

In the investigation of purely physical processes 
we generally employ concepts of so abstract a char- 
acter that as a rule we think only cursorily, or not at 
all, of the sensations that lie at their base. For ex- 
ample, when 1 ascertain the fact that an electric cur- 
rent having the strength of i Ampfere develops loj- 
cubic centimetres of oxyhydrogcn gas at o' C. and 760 
mm mercury -pressure in a minute, I am readily dis- 
posed to attribute to the objects defined a reality 
wholly independent of my sensations. But I am 
obliged, in order to arrive at what I have determined, 
to conduct the current through a circular wire having 
a definite measured radius, so that the current, the 
intensity of terrestrial magnetism being given, shall 
turn the magnetic needle at its centre a certain angu- 
lar distance out of the meridian. The intensity of 
terrestrial magnetism must have been disclosed by a 
definite observed period of vibration of a magnetic 
needle of measured dimensions, known weight, and 
so forth. The determination of the oxyhydrogcn gas 



is no less intricate. The whole statement, so simple 
in its appearance, is based upon an almost unending 
ll series of simple sensory observations (sensations), par- 
' ticularly if we take into consideration the observations 
that assure the adjustment of the apparatus, which 
may have been performed in part long before the ac- ' 
tual experiment. Now it can easily happen to the 
physicist who does not study the psychology of his 
operations, that he does not (to reverse a well-known 
saying) see the trees for the woods, that he slurs over 
the sensory elements at the foundation of his work. 
Now I maintain that every physical concept is nothing 
but a certain definite connexion of the sensory elements 
which 1 denote hy A £ C . . ., and that every physical 
fact rests therefore on such a connexion. These eJe- 
tnents — elements in the sense that no further resolu- 
tion has as yet been made of them— are the simplest 
building-stones of the physical world that we have yet 
been able to reach. 

Physiological research also may be of a purely 
physical character. I can follow the course of a phys- 
ical process as it propagates itself through a sensitive 
nerve to the spinal cord and brain of an animal and re- 
turns by various paths to the muscles, whose contrac- 
tion produces further effects in the environment of 
the animal. I need not think, in so doing, of any feel- 
ing on the part of the aninnal; what I investigate is a 
purely physical object. Very much is lacking, it is 
true, to our complete comprehension of the details of 


this process, and the assurance that it is all motion 
can neither console rae nor deceive me with respect 
lo my ignorance. 

Long prior to scientific psychology people had 
perceived that the behavior of an animal confronted 
by physical influences is much better grasped, that is 
understood, by attributing to the animal sensations like 
our own. To that which I see, to my sensations, I 
have to supply mentally the sensations of the animal, 
which are not to be found in the province of my own 
sensation. This opposition appears even more abrupt 
to the scientific inquirer who is investigating a nervous 
process by the aid of colorless abstract concepts, and 
is required for example to add mentally to that process 
the sensation green. This last may actually appear 
as something entirely nove], and we may ask ourselves 
how it is that this miraculous thing is produced from 
chemical processes, electrical currents, and the like.' 

Psychological analysis has taught us that this sur- 
prise is unjustifiable, since the physicist deals with 

IThe totLonring n v. legitimale question : To irhai hind of nervons pr<i- 
ces»l Is tlie sensation green lo he menially added? Si 

sensations in all his work. The same analysis may 
also show us that the mental addition by analogy of 
sensations and complexes of sensations which at the 
time being are not present in the field of sense or 
' cannot even come into it, is daily practised by the 
physicist, as, for example, when he imagines the moon 
an inert heavy mass, although he cannot touch the 
moon but can only see it. The totally strange charac- 
ter of the intellectual situation above described is 
therefore an illusion. 

The illusion disappears when I make observations 
(psychologically) on my own person, which are lim- 
ited to the sensory sphere. Before me lies the leaf of 
a plant. The green (.^) of the leaf is united with a 
certain optical sensation of space {B) and sensation of 
touch (C), and with the visibility of the sun or the 
lamp {D). If the yellow {E) of a sodium flame takes 
the place of the sun, the green (A) will pass into 
brown (F). If the chlorophyl granules be removed,— 
an operation representable, like the preceding one, by 
elements, — the green {A') will pass into white (£?). 
All these observations are physical observations. But 
the green {A") is also united with a certain process on 
my retina. There is nothing to prevent me in prin- 
ciple from physically investigating this process in my 
own eye in exactly the same manner as in the cases . 
previously set forth, and from reducing it to its ele- 
ments X y Z. ... If this were not possible in the case 
of my own eye, it might be accomplished with that 


', exactly ^^H 

>enrience ^^^ 

of another, and the gap filled out by analogy, 
as in physical investigations. Now in its dependence 
upon S C D. . . ., A is a physical eUment, in its de- 
pendence on X y^ ... it is a sensation. The green 
{^A ), however, is not altered at all in itself, whether 
we direct our attention to the one or to the other form 
of dependence. J see, therefore, no opposition of physi-') 
cal and psychical, no duality, but simply identity. In the 
sensory sphere of my consciousness everything is at 
once physical and psychical. 

The obscurity of this intellectual situation has, I 
take it, arisen solely from the transference of a phys- 
ical prepossession to the domain of psychology. The 
physicist says : I find everywhere bodies and the mo- 
tions of bodies only, no sensations ; sensations, there- 
fore, must be something entirely different from the 
physical objects I deal with. The psychologist accepts 
the second portion of this declaration. To him, it is 
true, sensation is given, but there corresponds to it a 
mysterious physical something which conformably to 
physical prepossession must be different from sensa- 
tion. But what is it that is the really mysterious 
thing ? Is it the Physis or the Psyche ? Or is it per- 
haps both I It would almost appear so, as it is now 
the one and now the other that is intangible. Or does 
the whole argument rest on a vicious circle ? 

I believe that the latter is the case. For me the) 
elements designated by .^^ ^ C . . are immediatelyt 
and indubitably given, and (or me they can never/ 


afterwards be volatilised away by considerations which 
ultimately are always based on their existence.' 

For that department of special research having for 
its subject the sensory, physical, and psychical prov- 
ince which is not made superfluous by this general 
orientation and which cannot be forestalled, only the 
relations oi A B C . . . remain to be ascertained. This 
may be expressed symbolically by saying that it is the 
purpose and end of special research to find equations 
of the form/ {A, B, C . . .) = o. 

This whole train of reasoning has for me simply 
the significance of negative orientation for the avoid- 
ance of pseud o -problems. Moreover, I intentionally 
restrict myself here to the question of sense-percep- 
tions, for the reason that at the start exact special re- 
search will hud here alone a safe basis of operations. 





TN A box having double walls, the intervening space 
■^ of which is packed with sawdust, is placed an 
electric tuning-fork, reed-pipe, or other musical in- 
strument which can be easily excited from without. 
(See next page, Fig. 37, which is drawn from memory.) 
From this box runs a tube which divides into two 
branches. One of these branches leads to a KOnig's 
manometric capsule ; the other is carried close to a 
pasteboard disc where it breaks but on the other side 
is continued again to the ear of the observer. The 
pasteboard disc, which can be turned like the disc of 
an electrical machine, has a radial slit of variable 
angular width, and carries at the proper inclination to 
its axis a mirror into which the observer can look 
through the slit. 

Exciting the apparatus in the box, and putting the 
eye close to the disc, which is now set in rotation, the 
ear receives the impression of a uniform tone, the 

lEiliBEt (rom io/Bi. PiQBno, August, 1873. Roprioled lo olucidale tha 



duration of which is curtailed by the slit. In the ro- 
tating mirror is seen the image of the manometric 
gas-jet, which is resolved into distinct and single 
flames, the resultant action of the slit being that the 

Fig. 37. 

(Diagram Explaining "A New Acoustic Experiment bt E. Mach." 

Drawn from memory.) 

7*, electric tuning-fork. BB^ box with double walls. R^ resonator. ///, 
tube. M^ Manometric capsule. 22, rotating disc with variable slit WW. 
oOf mirror attached to the disc behind the slit. £» the ear. O, the eye. 

observer sees as many vibrations as he Aears. We can 
count thus, by enumerating the images of the flames, 
the number of vibrations reaching the ear, and so con- 
vince ourselves that for the production of the sensa- 


tion of tone a certain number of vibrations are required. 
If the ear receives too few vibrations no tone is no- 
ticed, but only a short, sharp concussion, in which no 
pitch is distinguishable. A low tone of one hundred 
and twenty-eight full vibrations is recognisable as a 
tone of definite pitch only upon four to five vibrations 
striking the ear ; with two or three vibrations it pro- 
duces only a sharp concussion. In the case of low 
tones the harmonics are distinctly heard when the fun- 
damental, from its brief duration, is undistinguish- 


Paob 97, LAST FO«TN0TB. — ^Add th« wofdi : "Tha same phe- 
Bomwia may also he obssrved in connazkm witk tka shadow of 
ths meen and of the plansts (Seeliger, AMmndiungtn dsr JfUn- 
ch^ntr AhadeuM, II. CI., XIX. Bd., II. JLtbtkefl., x896).«' 

Paob 105. — ^Add as a footnote to the last liao ol paragraph xx: 
"Compare 00 this point Jaoqnos Looh, CMcr den Nackvmt von 
ContrasterschHnungen ini Gebiete der RaumimpJImdungin d4t Augei^ 
Archly f, Fhyiiologit, Bd. 60, 1895. " 


v(flC....th8eiHBplBlM. Sm«&- 

Auiillsr; ccDceptioDB. iss-'S^' ^^^^| 

Abslraclion. i6o at soq., i6j. 

Beats, in bumonr, ao, iq, tjBL ^^^H 

Aecele rati DOS, organ resetlDI upon, 
74 SI seq. 

Beetlei, 81 tootnole. ^^^H 
Benndorf, 41 lootnota. ^^^H 

BfrR, H.. iv>. ^^ 

Acute angles, vision of, 103-103. 

Berkeley. 6j tootnole. 

iti. 'ifi, IS!). 

Black, >Bs. 

£slbelics. repstitlonlD, 55-j6; aita- 

clatioo in, .... 

Blind apDl of the eye, 1B9. 

Aller-imnne!, 61. ..3. .78. 

Amp*re'a iwlmmet, 173. 


Anachronlima In dieama. 114. 

Bod,, the hnnian. iU rel.Uon 10 the 

An^lysi., J. 


BrBuer, 61, 66, 67. 73. 78. 

AuimalB, their psychical powata, 81- 


of. 68. 

raUtion, ?4 tooaotB «t seq. 

Bush, 31. 

Aieocietion, in UEthelics. lai. 

Atomic tHeories, is, .84 tooDHila. 

Caloric. .83. 

Atteatioo. work of. tell as time, iii 

Caraa, Dr. Paul, m foolnole, iS Icot- 

etwq; time roqairod lor ill iraos- 

Camalllr. need ot, i;i( and will, 173 


Attribolea. G. 

AiibBrl, M (ootnolB. 

seq., .41«seq.,i47. 





erebiml, iiO. 

Color- SBi 

ol Ibe aDcienU 

of eaviroDDisDI and Iboufihl, 

mplion, organic, o[ conscioua- 
, gives ri» lo lenjB of lime. 

.iiilj, principiB of. 17. ijS bI 

istimonei, i38Bt>Bq. 
lius. P.. i}6. 

of, m aighl-sensalion, 96, 

f, 41 fODtOOll, 106. 


omLslcfi objects, ;g laoUiDte; Ait- foimuiiDn ot tbe lanal mtIm, ii 

llldsiDDs ot BeniB, g foolnolB. Law, dEfiniilon of, ijS. 

Indlu gBdmelry, jfi- 

Liaht-sensaliona, deviatl 

lndi.ida»l. Sut. and, 40 (ootnote- 

gSitheir relation withs 

IndividDalitr. 4 laotaate. 

lanorv,liqp, 6j, 71. 76 el seq.; sensa- 


Lisssjous. loj. 

Irlellenl and sensation, 4S, 8»-S4. 

Locomolion, 44- 

Intervals, musical, characleristic 

LoBWS'. Dr. Th., 6i footno 

Intnitive knowledge, 157 et seq. 

looiani, .61 

ent. 10*. 



Jetkine P.D1 

0° of of»> in 

KIM. . ., the totnpleiea. Ses £ 
Knowledge ot natate, what com 

Lubbock, Sir John. 74 loolnote, 
Ludnig, Heinrlch, 34 footnote. 

agnua. H.. 4a footnclo. 
■irchfeld, pea^anu of, 41 fool 

Mayer, Alfred, 33- 
Mayer, J- R., m-m- 

Melody, 136. 

Memory, organic, 3fi foolnoler in 

Mathod. in pbrsica ind ] 

I si ■»!., ij fooBiole. 
Mill, 173 rooInoM. 
Mirror-Kiilioi!, ijilootnc 
Molecular phTBJU, 13 few 

Morgan, C. Llo^d, : 

Molha, 81 (so 

",6j-79, i3"fooUiDi< 

Mjlbi, jB [ootDole. 

bodlsa, melaptiTiici 

Organ for motor lanudaD, J^ at i 
arlentatiim. unia ol, IS4. 
Olber iDindalbBiiDnr*, |] •! laq., igj. 
Oulalde and Inside, 14. iji, iSg. 
Overtones, 113. 115. "«. i»,I««I»*l.. 

Per&pEtlive, monacal It, ti-HtS; Im- 
car, iDo; elemenli ol, loi ; Inrer- 
BioQ ol, ID3; foreBboitenlDiii doe 

Pliundlar, 11] (aolnot*. 

Phaolasmt, 8j-Eg. 

Pbilosopher, tbs •coariod. iG fooi- 

Phonlc. 116. 

Pli>loKeoy. ■■ siplHiwiJon. iio-iit. 

Physhanoonica. 133- 
Fbrsicil and piycbical. no doalily 
botwoan, iM- 

Inflaenca on (be olber aclences, 
I9S : ill gain (rom Iba analyiia ol 


rah SENSATIONS. ^^^^^^B 

^H PigeoDS, briiuleiE, 37 (oolnoie. 

Ksaction-activlty, concepts a, 163. ^^^^H 

H Plgme-ls, 3, fooinol.. 

H PUne, the geDmelrical, jj. 97. 

174. ^^^H 

^H PlUH-memDrr. JG lanUlQle. 

^H Pliteau-Oppel pheDomenoa, 70, 

Recognition of space-figures, 4j el ^^^^| 

Reflected writing, 30-31. ^^^H 

■ PLeisors .ad p>in, iB. 

RGfracClon, 18. 33, 159, >S7. ^^H 

^H PdlrchTomr, 41 loomote. 


Relative mallon. eiperimBaU In, 69. ^^^^H 

^1 Popper, J,, 17 (ootnole, 13 foomolo, 

Keller, gg el seq. ^^^H 

^H Poiiiive, r>ctor in the eiplanBIion of 

KepelitioD, of space-figures. 33-3; ; ■ ^^^^H 

principle in iesthetics. 33-36. ^^^H 

^1 Potanlial function, and light-EgnsEi- 

^H (ion. 38 footnotfl ; lot toolnole. 

aon, 84-EI3 : organ of, 83 et hk|.; of ^^H 

H Prejudice, ig lootnole. 

tacts in thoughi. >J3. ^^^H 

1 Reproduction, mental, 13G; of facte ^^^^H 

1 by thoughts, rye. ^^^1 

^1 Probubilllf, principle o[, m. <16. i«^ 

Research, aim ot special, igG. ^^^^H 

^1 '04- 

H Problems, oriRia at. 14 ; nXiirc of, 

^H Projectile, eiample ot, v/t. 

^B PioJBClian, theory of. 188. 

Uhythms, identical, recognised, 117; ^^^H 

^1 Piopecties. 7. 9. 

hace no symmetiy, iij. ^^^H 

^. ^^^H 

^H Psychical procssses, not eiplained 

H by atoms, 153. 

Ri^hl and left, confounded, 30-31. ^^H 

Right angles, vision ol, 103. ^^^H 

^H PiycIiGloB)' of the Beaaes, i5i-iS3< 

Rabxn. W., 113 ^^H 

^H Psycho-physical law of Fschner.jg 

^1 Pulley, example of, 160. 

^H Piirklnje's atter-imaEe, 113. 

^H Putiy, eiperimeol wJIh lumps of, SB. 

^H PiuEle-picInrea, g3. 

optical, 98. ^^^H 

■ Qnaliti«ofaen8atioa,79. 

seq. ^^^H 

^H Quantity, of heat and electricity, 175 

SauliTeTson'^es footnote. ^^^1 


■ Ray. of light. 1S6. 

..„,....„,.. J 

rND£X. io^^^^l 

Scientist. hl> BlnigglB tot eiislenoe. 

Space, and time,? el seq.; ooncepiion ^H 

white. 97-98. 

Seebeek. A.. ,41. 

Seelieer. 100. 

Semi-clrcnlaT Maala. ihclr rDnclion 

,ield, 49; defined as wiU, 59-60, ^H 

Species, preservation of, 40, lao, ^^^| 

analysinii. 99 hi seq.; intarcbanEe- 

Specific energies, 85; ii;-ii6: in ^^H 

«b!Bqu=Utia>of.*|i; of titne.a nevr 

aBdition.ri7et seq.,140; two onir ^^H 

■pecific energy. 1.6; and UDder- 

required for the perception ot ^^H 

Senaalions. «, ;. 10. j» el seq.. 14, iB : 

sleioenta o( the world. 15: of move- 

Specific inductive capacity, iSj. ^^^H 

Spectrum, aS-n), 3., i;;. ^^H 

inlellect. relalioaa between. 81-S4 ; 

Spencer, 36 footnote, %i footnote. ^^^H 

lie at the basis o( all thapliyaicist's 

Sphere. 97. ^^1 

worn, igi el seq.; atiributinE o(, to 

Spiritualism, philosophical, 11, ^^H 

HDimels and olhei people, 11 Foot- 

nola, 191. 

Seuae, illniiions of, 9 footnote ; Tway- 

oryotB?; world of. IJI. 

a«,,. .60. t64. 

properties 95, ^^H 

Sense-organa, their origin, evolution, 

and functions. 36-40; have their 

Stampf, 119 footnoie, 143. ^^^H 

Shading of bodies, 9° e> >eq. 

Sighl. Sea KinW. 

of COmplelHB, Si. 

SiRhl-apace, Bo. 

Silk-worm, adaptive power of. jB 

Supplemealiag. See Compltting. ^^^H 

Surfaces, fiat, loi footnote. j^^^H 

Similar tonal codBlructi, .36. 

\ Srmbols. economical, iji et seq. - ^^H 

46 el seq. 

Similiiude, principle of, in roeehan- 

Symmetry. 46; verlicai. 51; laeldng ^^H 

ics, 56. 

in rhythm, iij; in music, 116 foot- ^^1 

Snowfall, produces rising motion oE 

TaDDhluser. overture lo, ij6. ^^1 

Teleology, in research. 36-40, So- ^^1 

Solid bodies, vision of, loj-ioS. 

Temperature, eicess of, substituted ^^^H 

Sorel, J. L„ Jfi footnote. 





Vaoiebieepomle. ]«. ^^H 


Venice] lines, gS. ^^H 

Vertigo, optica], 671 ill deer.miilea, ^^M 

Tbl.,,,„, S„B.JI„. 

Vibrallonal Tatea. 149 et leq. ^^^H 

Il...,b, b, ...c.p«. . ,...,».- 

Vibrations, nnmber ot, necsBiarji to ^^^| 


Appendix It. 

Vieroidt, 70. 

Itab,,, „, ,„, 

lootnote. 88 toatnote. 137- 

.1. .»-.,.. .n, ta..,.ibm„ bf. 

Viilnoso, mnaieal. egd of, 11 foolnole. 

Visiting card, eiperimenl ot. gr, 102. 

„., b. .ii™..i.d ■,.« ™u. 

Visual, parple. 43; apparaWs. 4!t-So; 

proeass, Bi ; sense, organic and ^^ 


.„,,S„.,il..l...l.>.. .r,„;^ 

WeiEmann,9> f Dotocle. 3fi footnote, 


Wbiiliog macbine for ob>e[vin|! Ihe 

coQducl ot animals in rotation, 74 

bet o( TibratioQS De«..ary lor 

S9« 5e<i.,6Sii» the sensation ol 

TDbic. llG. 

Toucb, compared witb beorieg. .4* 

Witcbcra'tt. ,8 ^M 

Witbin and «^^--;m4,^"-. *■ ^1 

i Word's, naiure of, ^^| 



yeung, ThomM, 5J. ^^^| 


m WORKS or xxnst macb. 



Tratislated from the Second Gerinaii E 

ijoCuls, 534 PsEes. Half Morocco, Gill Top, Margmal Aual^Bes, 
Exhaustive Index. Price fa. 30. 


ThB Inclined PImb. 


TheirAppliqalIco Id Fluid. 


Their Applicaiicn 10 Gases. 



Views ot Time. Space, and 


AchieYBOienU of Newton. 


of the Newtonian Ennocia. 

Principle of Ro»ction. 

Criticism ol the Principle of Reae- 

HOD ud ot tho Concept of Mbu. 




OF Mechahic*. 


of y.-- p-/™. 


of Least Conslraint 


of Least Action. 

Y.iiDB of the Centre 0! Gr.vity. 

and Consetvatioa ot Areai, 


L«wi of Impact. 


D'AI«oborf. Principle. 

FOllKAL DmiLo 



The Iioperlmecrlcal PcoblHrns. 


1 MechaniiK. 

The Ecc 

omy of Sdeno* 



kibla book 

:i. and Btaauldcall up ihe thouehij wtaicta pniilsD* whan 

I (hit i> Dot sufficieally oflen Profeiisoi Uach li > 

le comblnatlan «f gitu milhenia Ileal ksowledge with 
eimnpIiEcd not onl^ by tbt elegant illnBtritioni ot me- 

sbouDdiD this I 
tapbr of bulleti 

lit also Irom bis brUl>> 
reCul smij o[ Piofesi 

Dent."— ProE. A. G. Grsanbl 

n how Ehfl prindplBi o( moi 
ij lakfl tbfllr oriEiu. and ho« 
eat value, oill find Dr, Uacl 

d London. EaRlan 

"Miich'9 Mechanics 


■ion from all inlereiledinlhepcDiresi o 


'- TluPk^iicalRniira, Mew 

York and London. 

■' Mr. T. J. McCormaek. by hia efle 

li»B Ira 

was no light task, or this masterly treat 

se upon 

he nrlieil and moat tnoda- 

mental o( the sciences, has rendered n 

sliiht < 

errlcc to IbaEBEliih apeak- 

a laak ol the (raaiasl diCcnttr, and 


tion. Dr. Much bas created for his own ivotka the severest pcssiblo stundard ^^H 

of judemeal. Tc e.pect no more (rom tbe bookg ot such a ii.aster than from ^H 

the elemsQIarr piodnctlooa of an ordinary tt^achec in the science oould be ^H 

Daduo moderation. Our aothor haa lifted what, to oiuiy of ns, was i, one ^^M 

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pleasure from the nairow methods of the teit-book to wherelbs ■dencels ^^H 

conneiioD between all the phyaica] so innces, taken toeetber."— r*< Jft'ni-r ^^H 

Journal, London, Eniilaad. ^^^| 

"As a history of mechanic, the work Is admirable."-?-*/ N^io-. New ^^| 


England. ^^| 

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force unknown in the mathematical tait-hooks .... is admirably fitted to ^^1 

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chanioal science."— Ca-iBiiaii Mining and Mickanical Rrvicw. Ottawa, Can. ^^H 

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mneh as hs ought te abont physics, we can commend it most heartily us ■ ^^^H 

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"The book as a whole is nnique, and is a»Iuable addidoti 10 *DJ llbruy ^^| 

or science or phJiosophy. . . . Reproductions of quaint old portraili and ^^^H 

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HeiinK, in Stiina. ^H 

and that is the perfection of the translation. It is a common faall Itaat books ^^H 

of the greatest interest and value in the original are ohenesl butchered or ^^| 

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t\oa.--Sailw<t^ Afi. ^^1 




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