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L161 O-1096

ON

HUMAN AND ANIMAL
PSYCHOLOGY

BY

WILHELM WUNDT

PROFESSOR OF PHILOSOPHY AT THE UNIVERSITY OF LEIPZIG

Translated from the Second German Edition

BY

J. E. CREIGHTON & E. B. TITCHENER

LONDON

SWAN SONNENSCHEIN & CO., LIM.

NEW YO^K: THE MACMILLAN CO.

1907

15 o

FIRST EDITION, October, 1894.
SECOND EDITION, June, 1896.
THIRD EDITION, November igoi,
FOURTH EDITION, August, 1907.

4?
ILL
A/

TRANSLATORS' PREFACE

6 i

THE present volume is the first of Professor Wundt's
writings to be made generally accessible to the English-
speaking public. Its comparatively popular and intro-
ductory character will, it is hoped, render it especially accept-
able both to those beginning the study of psychology, to whom
the technicalities of the author's Grundzuge would present very
considerable difficulties, and to workers in other departments of
science who may desire some knowledge of the methods and
results of the new psychological movement.

The translators have endeavoured throughout to retain the
oral form of the original Lectures. They have aimed, at the
same time, to furnish a literal, as distinguished from a verbal,
rendering of the German text. In view of the confusion which
still obtains in English psychological terminology, they have
attempted a precise use of words even at the occasional cost of
literary effect. No word or phrase, however, has been em-
ployed which has not already received the sanction of well-known
psychological writers.

J. E. CREIGHTON.
E. B. TITCHENER.

CORNELL UNIVERSITY, ITHACA, N.Y.

211262.

TRANSLATORS' PREFACE TO SECOND
EDITION.

ri"1 HE Translators have made but few changes, and those of

minor importance, in the text of this edition. The

system of nomenclature adopted in the first issue of the

work has met with general approval, and therefore remains

unchanged. A few words and phrases have been altered, here

and there, in the interests of greater clearness and precision ;

and an index of names and subjects has been added.

CORNELL UNIVERSITY, ITHACA, N.Y.
I5th April, 1896.

AUTHOR'S PREFACE TO SECOND
EDITION

WHEN I was asked some years since by the publisher of
this work to undertake its revision, I felt some hesita-
tion in complying with his request. The first edition
of the Lectures appeared thirty years ago ; and during that
time there had not only been a great advance in experimental
psychology, but my own scientific knowledge and convictions
had been considerably increased and modified. Thirty years
ago the science was no more than a programme for the future.
Except in psychophysics, where Fechner had just broken
ground, everything remained still to do ; and distrust and sus-
picion met the investigator at every turn. As for myself, I had
had but little experience in the difficult work of psychological
analysis, which the gradual development of the experimental
methods has done so much to further ; and set about my task
with more zeal than discretion. So that for years before the
appearance of the first edition of my Physiological Psychology,
in which I took up the same problem with more modesty and
caution, I had learned to look upon the Lectures as wild oats
of my youthful days, which I would gladly have forgotten.
But, unfortunately, hypotheses and views represented in them
would every now and again be confused with or counted among
my more mature convictions.

That I have resolved to undertake a- second edition despite
these somewhat discouraging facts, and in preference to the
more grateful task of writing a new work of similar character,,
is due in the main to two circumstances. In the first place, I

vi Author s Preface to Second Edition

thought that, though the original volumes were defective both in
general execution and in many points of detail, still a certain
number of their chapters might stand unchanged, while I
should perhaps be unable to attain again the freshness and
force which characterised the first expression of my views.
Secondly, every statement in the former edition about which I
had modified or abandoned my original opinion seemed to lay
upon me an obligation which I would fain discharge to the
limit of my ability. Nevertheless, I will not omit in this place
the express declaration that I no longer recognise as mine any
view formulated in the earlier edition which is not admitted into
the present. The elimination of everything that more recent
inquiry had superseded has considerably diminished the size ol
the work. It has also suffered curtailment by the total exclu-
sion of the discussions of social psychology which occupied a
large portion of the second volume of the original book. It has
been a matter of principle with me to restrict the contents of
the Lectures to the individual psychology of man and the
animals. As a matter of fact, the amount of material which
social psychology has at its disposal is now so great, and the
position of the science with regard to the points discussed has
undergone so radical a change, that revision of the old chapters
would necessarily mean rewriting. But within the prescribed
limits, I have adhered to my former plan of not attempting any
completeness of exposition, but rather of taking full advantage
of the lecture form and confining myself to the treatment of
topics which I thought especially characteristic of the spirit
and trend of modern psychology. At the same time, it seemed
permissible to make the work in some sense supplementary to
my other writings by devoting few words to subjects which I
have elsewhere discussed in detail, and giving more attention to
topics which are less prominent, particularly in my Physiologi-
cal Psychology. Thus I have based the discussion of Weber's
law entirely upon the method of just noticeable differences,
although this is the most imperfect of the measurement-methods
-and would hardly now be employed in investigations which

Author 's Preface to Second Edition vii

made any claim to scientific accuracy. Again, in developing
the theory of spatial localisation I have retained my previous
plan of elucidating its much-misunderstood fundamental con-
ceptions, and of the sensations attaching to movement have
only dealt with muscle-sensations, although the rdle of certain
complexes of pressure-sensations in the surrounding parts is
really not less important. The reader who desires a deeper
insight into psychology will, I hope, not omit to refer in such
cases to my more systematic work, which is more especially
devoted to the investigation of the physiological correlates of
psychical processes.

The first edition of these Lectures was principally based upon
Fechner's Psychophysik and my own Beitrdge zur Theorie der
Sinneswahrnehmungen, which appeared between 18*58 and 1862.
The lectures dealing with these subjects have undergone the
least alteration in the second edition. I may perhaps be also
allowed to state that the treatment of the problem of the
causality of will in Lecture XXIX. stands for the most part
precisely as it did in my previous exposition. The following
lectures of the second edition present portions of the older work
in revised form: I. (I., II., of the former edition), II. (VII.), III.
(VIII.), IV. (IX.), VIII. (XIV.), IX. (XV.), X., XI. (XVI.,
XVII.), XII. (XXL), XIII. (XXII.), XXIX. (LV., LVI.) ;
entirely rewritten are V. (XL), VI. (X.), VII. (XIII.), XIV.
(XXX.), XXV. (XXXI.), XXVI. (LI., LIL), XXVIII. (XLII.) ;
new are : XV., XVL, XVIL, XVIIL, XIX., XX., XXL,
XXIL, XXIIL, XXIV., XXVIL, XXX. Very little of the
lectures of the first edition not quoted here has been included in
the present volume.

W. WUNDT.
LEIPZIG, Aptil, 1892.

CONTENTS.

PAGE

LECTURE FIRST i-ii

Philosophical Anticipations of Psychology, 1-5. Spiritualism
and Materialism, 5-7. Methods and Aids of Psychological
Investigation, 7-11.

LECTURE SECOND 12-32

Analysis of Mental Processes, 12-15. Idea and Sensation, 15-17.
Intensity and Quality of Sensation, 17, 18. Measurement of
the Intensity of Sensation, 18-32.

LECTURE THIRD 33-49

Estimation of the Intensity of Sensation, 33-39. Mathematical
Expression of the Law of Sensation-intensities, 39-42. Signi-
ficance of Negative Sensation-values, 42-47. Unit of Stimulus
and Unit of Sensation, 47-49.

LECTURE FOURTH 50-63

A Just Noticeable Sensation, 50-56. Upper and Lower Limit of
Weber's Law, 56-59. Psychological Interpretation of the
Law, 59-63.

LECTURE FIFTH 64-86

Quality of Sensation, 64-66. Tone-sensations ; Beats, 67-73.
Clang-colour, 73-75. Simultaneous Clangs, 75-77. Noises,
77, 78. Measurement of Differences of Tone-sensations, 78-81.
The Tonal Scale, 81-84. Relation to Weber's Law, 84-86.

LECTURE SIXTH 87-107

Light-sensations ; Sensations of Colour and Brightness, 87, 88.
Analysis and Mixture of Colours, 88-95. The Three Primary
Colours, 96-98. Leonardo's Four Principal Colours, 99-103.
Theory of Light-sensations, 103-107.

LECTURE SEVENTH 108-119

Relation of the Senses of Sight and Hearing, 108. Positive and
Negative After-images, 108-110. Mechanical and Chemical
Senses, no, in. Phenomena of Contrast, in-ii8. General
Law of Relativity, 118, 119.

LECTURE EIGHTH 120-133

Reflex Movements, 120-126. Purposiveness of the Reflex,
126-128. Development of the Reflexes of Touch and Sight,
128-133.

LECTURE NINTH 134-148

Muscle-sensations : their Influence upon Localisation, 134-138.
Connexion of Sensations of Movement with other Sensations,
138-142. Influence of Practice upon Reflex Movements,

Contents

143-145. Arrangement in Space a Process of Association,
145-148.

LECTURE TENTH 149-169

Influence of Ocular Movement on Spatial Vision, 149-156. Geo-
metrical Optical Illusions, 156, 157. Spatial Perceptions of the
Sense of Touch, 157-160. Accidental and Congenital Blind-
ness, 161-163. Why are not Visual Objects Inverted? 163-167.
Concluding Remarks upon the Theory of Space-construction,
167-169.

LECTURE ELEVENTH 170-181

The Separation of Visual Ideas; Influence of Boundary Lines,
170-172. Ideas of Depth, 172-176. Relations between
Apparent Magnitude and Distance of Objects, 176-181.

LECTURE TWELFTH 182-194

Binocular Vision ; Difference of the Two Retinal Images, 182-186.
The Stereoscope ; Simplest Stereoscopic Experiments, 186-190.
Theory of Stereoscopic Vision, 190-194.

LECTURE THIRTEENTH 195-209

Combination of Similar Stereoscopic Images, 195-197. Idea-
tional Change in Stereoscopic Combination, 197-199. Reflec-
tion and Lustre ; Theory of Lustre, 199-205. Phenomena of
Suppression in Binocular Vision, 205-209.

LECTURE FOURTEENTH 210-222

The Feelings, 210-213. Sense-feelings, 213-217. Common
Feeling and the other Total Feelings, 217-221. Relation of
Feeling to Idea, 221, 222.

LECTURE FIFTEENTH 223-234

Relation of Feeling to Will ; Impulse and Desire, 223, 224.
Development of Will, 224-228. Simple and Complex Volun-
tary Acts, 228-233. Psychological Elements in Voluntary
Action, 233, 234.

LECTURE SIXTEENTH 235-251

The Concept of Consciousness, 235-239. Condition of Ideas in
Consciousness, 239-243. Perception and Apperception ; Clear-
ness and Distinctness of Ideas, 244-247. Phenomena accom-
panying Apperception, 247,248. Attention, 249,250. Self-
consciousness, 250, 251.

LECTURE SEVENTEENTH 252-265

Development of Attention ; Passive and Active Apperception,
252-255. Attention and Will ; Fluctuations of Attention,
256-258. Range of Consciousness : Formation and Division
of Rhythmical Series, 258-265.

LECTURE EIGHTEENTH 266-281

Temporal Course of Ideas, 266, 267. Personal Difference of
Astronomers : Eye and Ear Method, 267-271. Method of
Registration, 272-276. Reaction-time, 276-278. Temporal
Determination of Mental Processes, 278-281.

LECTURE NINETEENTH . . 282-294

Qualitative Change of Ideas, 282-283. Association of Ideas ;
Simultaneous Association ; Complication, 283-286. Assimi-
lation, 286-290. Theory of Simultaneous Association, 290-294.

Contents

PAGE

LECTURE TWENTIETH 295-307

Successive Associations, 295-297. Association by Similarity
and Contiguity, 297. Cognition and Recognition as Simple
Forms of Association, 298-303. Theory of Successive Associa-
tions, 304-306. Indirect Association, 306, 307.

LECTURE TWENTY- FIRST 308-322

Concepts and Judgments, 308-311. Distinguishing Marks of
Intellectual Processes, 312-314. Development of the Intellec-
tual Functions, 314-316. Mental Derangement, 316-322.

LECTURE TWENTY-SECOND 323-339

Dreams, 323-327. Sleep-walking, 327, 328. Hypnotism and
Suggestion, 328-335. Auto-suggestion and Post-hypnotic In-
fluence, 335-337. Errors of the ' Hypnotism-psychology,'
337-339-

LECTURE TWENTY-THIRD 340-352-"

Problems of Animal Psychology ; Deficiencies of the Science,
340-345. Methodological Rules, 345, 346. Acts of Cognition
and Recognition among Animals, 347-350. Association among
the Lower Animals, 350-352.

LECTURE TWENTY-FOURTH 353-366

Mentality of the Higher Animals, 353-357. Animal Play, 357,
358. Alleged Formation of Judgments and Concepts, 358-36*.
General Significance of Association, 362-364. Man and the
.Animals, 364-366.

LECTURE TWENTY-FIFTH 367-380-

Connexion of Affective States in Consciousness, 367-369. Sen-
sory Accompaniments of Compound Feelings, 370,371.
Emotion, 371-377. Intellectual Feelings, 378-380.

LECTURE TWENTY-SIXTH 381-394

Expression of the Emotions, 381-385. Impulsive and Volitional
Action, 385-388. Instinctive Action, 388, 389. Theories of
Instinct, 389-394.

LECTURE TWENTY-SEVENTH 395-410

Instinctive Action in Man, 395-397. Acquired Instincts, 397-399.
Connate Instincts, 399-401. Practice, Imitation, and Inherit-
ance, 402-406. Relation of Animal to Human Instinct,
406-410.

LECTURE TWENTY-EIGHTH 411-422

Social Instincts ; Temporary Associations and Friendships of
Animals, 411. Animal Marriage, 412,413. Animal Societies
and States, 414-422.

LECTURE TWENTY-NINTH 423-436

Voluntary Action, 423, 424. The Causality of Will, 424-428.
Relation of the Individual to the General Will, 428-432.
Character as the Ultimate Cause of Will, 432-436.

LECTURE THIRTIETH 437-454

Concluding Remarks ; The Question of Immortality, 437-440.
The Principle of Psychophysical Parallelism, 440-445. Old
and New Phrenology, 445-448. The Empirical Significance
of the Principle of Parallelism, 448-451. The Nature of Mind,
451-454.

LECTURE I

I. PHILOSOPHICAL ANTICIPATIONS OF PSYCHOLOGY. II. SPIRITUAL-
ISM AND MATERIALISM. III. METHODS AND AIDS OF PSYCHO-
LOGICAL INVESTIGATION.

PSYCHOLOGY, even in our own day, shows more clearly
than any other experiential science traces of the con-
flict of philosophical systems. We may regret this influence
in the interest of psychological investigation, because it has
been the chief obstacle in the way of an impartial examination
of mental life. But in the light of history we see that it was
inevitable. Natural science has gradually taken shape from a
natural philosophy which paved the way for it, and the effects
of which may still be recognised in current scientific theory.
That these effects are more fundamental and more permanent
in the case of psychology is intelligible when we consider the
problem which is set before it. Psychology has to investigate
that which we call internal experience, i.e., our own sensation
and feeling, our thought and volition, in contradistinction to the
objects of external experience, which form the subject matter
of natural science. Man himself, not as he appears from with-
out, but as he is in his own immediate experience, is the real
problem of psychology. Whatever else is included in the circle
of psychological discussion, the mental life of animals, the
common ideas and actions of mankind which spring from simi-
larity of mental nature, and the mental achievements of the
individual or of society, all this has reference to the one
original problem, however much our understanding of mental
life be widened and deepened by the consideration of it. But
the questions with which psychology thus comes into contact
are at the same time problems for philosophy. And philosophy

B

2 Lectures on Human and Animal Psychology

had made various attempts to solve them long before psycho-
logy as an experiential science had come into being.

The psychology of to-day, then, neither wishes to deny to
philosophy its right to occupy itself with these matters, nor is
able to dispute the close connection of philosophical and psy-
chological problems. But in one respect it has undergone a
radical change of standpoint It refuses to regard psychological
investigation as in any sense dependent upon foregone meta-
physical conclusions. It would rather reverse the relation of
psychology to philosophy, just as empirical natural science long
ago reversed its relation to natural philosophy, in so far, that
is, as it rejected all philosophic speculations which were not
based upon experience. Instead of a psychology founded upon
philosophical presuppositions, we require a philosophy to whose
speculations value is ascribed only so long as they pay regard
at every step to the facts of psychological, as well as to those
of scientific, experience.

It will, therefore, be a matter of principle for us in these lec-
tures to stand apart from the strife of philosophic systems. But
since the thought of to-day is subjected on all sides to the in-
fluence of a philosophic past which counts its years by thou-
sands, and since the concepts and general notions under which
an undifferentiated philosophy arranged the facts of mental life
have become part of the general educated consciousness, and
have never ceased to hinder the unprejudiced consideration of
things as they are, it is our bounden duty to characterise and
justify the standpoint which we propose to adopt. We will,
therefore, first of all glance for a moment at the history of
philosophy before the appearance of psychology.

In the beginnings of reflective thought, the perception of the
external world preponderates over the internal experience of
idea and thought, of feeling and will. The earliest psychology
is therefore Materialism : the mind is air, or fire, or ether,
always some form of matter, however attenuated this matter
may become in the effort to dematerialise it. Plato was the
first among the Greeks to separate mind from body. Mind he
regarded as the ruling principle of the body. And this separa-
tion paved the way for the future one-sided dualism which con-
sidered sensible existence as the obscuring and debasing of an

Philosophical Anticipations of Psychology 3

ideal, purely mental being. Aristotle, who combined with the
gift of speculation a marvellous keenness of observation, at-
tempted to harmonise these opposites by regarding mind as the
principle which vitalises and informs matter. He saw the
direct operation of mental powers in the forms of animals, in
the expression of the human figure at rest and in movement,
even in the processes of growth and nutrition. And he gene-
ralised all this in his conclusion that mind is the creator of all
organic form, working upon matter as the sculptor works on
marble. Life and mentality were for him identical terms ;
even the vegetable world was on his theory endowed with
mind. But, apart from this, Aristotle penetrated more deeply
than any of his predecessors into the facts of mental experience.
In his work upon the mind, the first in which psychology was
ever treated as an independent science, he sharply separates
from one another the fundamental mental activities ; and, so
far as the knowledge of his time allowed, sets forth their causal
connections.

The Middle Ages were wholly dominated by the Aristotelian
psychology, and more especially by its basal proposition that
mind is the principle of life. But with the dawn of the modern
period begins in psychology, as elsewhere, the return to
Platonism. Another influence combined with this to displace
Aristotelianism ; namely, the development of modern natural
science and the mechanical metaphysics which this develop-
ment brought with it. The result of these influences was the
origin of two psychological schools, which have disputed with
one another down to the present day, Spiritualism and
Materialism. It is a curious fact that the thought of a single
man has been of primary importance in the development of
both these standpoints. Descartes, the mathematician and
philosopher, had defined mind, in opposition to Aristotle, as
exclusively thinking substance ; and following Plato, he ascribed
to it an original existence apart from the body, whence it has
received in permanent possession all those ideas which transcend
the bounds of sensible experience. This mind, in itself unspatial,
he connected with the body at one point in the brain, where it
was affected by processes in the external world, and in its turn
exercised influence upon the body.

4 Lectitres on Human and Animal Psychology

Later Spiritualism has not extended its views far beyond
these limits. It is true that Leibniz, whose doctrine of monads
regarded all existence as an ascending series of mental forces,
attempted to substitute for the Cartesian mind-substance a more
general principle, approximating once more to the Aristotelian
concept of mind. But his successor Christian Wolff returned to
the Cartesian dualism. Wolff is the originator of the so-called
theory of mental faculties, which has influenced psychology
down to the present day. This theory, based upon a superficial
classification of mental processes, was couched in terms of a
number of general notions, memory, imagination, sensibility,
understanding, etc., which it regarded as simple and funda-
mental forces of mind. It was left for Herbart, one of the
acutest thinkers of our century, to give a convincing proof of the
utter emptiness of this ' theory.' Herbart is at the same time
the last great representative of that modern Spiritualism which
began with Descartes. For the works of Kant and of the other
philosophers who came after him, Fichte, Schelling, and Hegel,
belong to a different sphere. In Herbart we still find the
concept of a simple mind-substance, which Descartes introduced
into modern philosophy, but pushed to its extreme logical
conclusion, and at the same time modified by the first principles
of Leibniz' monadology. And the consistency of this final
representative of speculative psychology makes it all the more
plain that any attempt to derive the facts of mental life from
the notion of a simple mind and its relation to other existences
different from or similar to itself must be vain and fruitless.
Think what lasting service Herbart might have done psychology,
endowed as he was in exceptional measure with the power of
analysing subjective perception, had he not expended the best
part of his ingenuity in the elaboration of that wholly imaginary
mechanics of ideation, to which his metaphysical presuppositions
led him. Still, just because he carried the concept of a simple
mind-substance to its logical conclusion, we may perhaps ascribe
to his psychology, besides its positive merits, this negative value,
that it showed as clearly as could be the barrenness of
Spiritualism. All that is permanent in Herbart's psychological
works we owe to his capacity of accurate observation of mental
fact ; all that is untenable and mistaken proceeds from his

Spiritualism and Materialism 5

metaphysical concept of mind and the secondary hypotheses
which it compelled him to set up. So that the achievements
of this great Spiritualist show most plainly that the path which
he travelled, apart from all the contradictions into which it led
him, cannot ever be the right road for psychology. This notion
of a simple mental substance was not reached by analysis of
mental phenomena, but was superimposed upon them from
without. To assure the pre-existence and immortality of the
soul, and (secondarily) to conform in the most direct way with
the logical principle that the complex presupposes the simple,
it seemed necessary to posit an indestructible and therefore
absolutely simple and unalterable mind-atom. It was then the
business of psychological experience to reconcile itself with this
idea as best it might.

When Descartes denied mind to animals, on the ground that
the essence of mind consists in thought, and man is the only
thinking being, he cou'd have little imagined that this proposi-
tion would do as much as the strictly mechanical views which
he represented in natural philosophy to further the doctrines
which are the direct opposite of the Spiritualism which he
taught, the doctrines of modern Materialism. If animals are
natural automata, and if all the phenomena which general
belief refers to sensation, feeling, and will are the result of purely
mechanical conditions, why should not the same explanation
hold of man ? This was the obvious inference which the
Materialism of the seventeenth and eighteenth centuries drew
from Descartes' principles.

The nai've Materialism with which philosophy began had
simply ascribed some kind of corporeality to mental existence.
But this modern Materialism took as its first principles
physiological hypotheses ; thought, sense, and idea are
physiological functions of certain organs within the nervous
system. Observation of the facts of consciousness is of no avail
until these are derived from chemical and physical processes.
Thought is simply a result of brain activity. Since this activity
ceases when circulation is arrested and life departs, thought is

6 Lectures on Human and Animal Psychology

nothing more than a function of the substances of which the
brain, is composed.

More particularly were the scientific investigators and
physicians of the time inclined, by the character of their pursuits,
to accept this explanation of mental life in terms of what seemed
to them intelligible scientific facts. The Materialism of to-day
has made no great advance in this or in any other direction upon
the views promulgated in the last century, e.g. by de la Mettrie,
and developed by Helvetius, Holbach, and others. But this
equating of mental process and brain function, which makes
psychology a department of cerebral physiology, and therefore
a part of a general atomic mechanics, sins against the very
first rule of scientific logic, that only those connections of facts
may be regarded as causal which obtain between generically
similar phenomena. Our feelings, thoughts, and volitions cannot
be made objects of sensible perception. We can hear the word
which expresses the thought, we can see the man who has
thought it, we can dissect the brain in which it arose ; but the
word, the man, and the brain are not the thought. And the
blood which circulates in the brain, the chemical changes which
take place there, are wholly different from the act of thought
itself.

Materialism, it is true, does not assert that these are the
thought, but that they form it. As the liver secretes bile, as the
muscle exerts motor force, so do blood and brain, heat and
electrolysis, produce idea and thought. But surely there is no
small difference between the two cases. We can prove that bile
arises in the liver by chemical processes which we are able, in
part at least, to follow out in detail. We can show, too, that
movement is produced in muscles by definite processes, which
are again the immediate result of chemical transformation. But
cerebral processes give us no shadow of indication as to how our
mental life comes into being. For the two series of phenomena
are not comparable. We can conceive how one motion may be
transformed into another, perhaps also how one sensation or
feeling is transformed into a second. But no system of cosmic
mechanics can make plain to us how a motion can pass over into
a sensation or feeling.

At the same time modern Materialism pointed out a more

Methods and Aids of Psychological Investigation 7

legitimate method of research. There are numerous experiences
which put beyond all doubt the connection of physiological
cerebral function on the one hand and of mental activity on the
other. And to investigate this connection by means of experi-
ment and observation is assuredly a task worth undertaking.
But we do not find that Materialism, even in this connection, has
made a single noteworthy contribution to our positive knowledge.
It has been content to set up baseless hypotheses regarding the
dependence of mental function upon physical process ; or it has
been concerned to refer the nature of mental forces to some
known physical agency. No analogy has been too halting, no
hypothesis too visionary, for its purpose. It was for some time
a matter of dispute whether the mental force had more resem-
blance to light or to electricity. Only on one point was there
general agreement, that it was not ponderable.

In our day the conflict between Materialism and Spiritualism,
which was raging in the middle of the century, has almost worn
itself out. It has left behind it nothing of value for science ; and
that will not surprise any one who is acquainted with its details.
For the clash of opinion was centred once more round the old
point : in the questions concerning mind, the seat of mind, and
its connection with body. Materialism had made the very same
mistake which we have charged to the spiritualistic philosophy.
Instead of plunging boldly into the phenomena which are pre-
sented to our observation and investigating the uniformities of
their relation, it busied itself with metaphysical questions, an
answer to which, if we may expect it at all, can only be based
upon an absolutely impartial consideration of experience, which
refuses to be bound at the outset by any metaphysical
hypothesis.

HI

We find, then, that Materialism and Spiritualism, which set
out from such different postulates, converge in their final result.
The most obvious reason of this is their common methodological
error. The belief that it was possible to establish a science of
mental experience in terms of speculation, and the thought that
a chemical and physical investigation of the brain must be the

8 Lectures on Human ana Animal Psychology

first step towards a scientific psychology led alike to mistakes
in method. The doctrine of mind must be primarily regarded
as an experiential science. Were this otherwise, we should not
be able so much as to state a psychological problem. The
standpoint of exclusive speculation is, therefore, as unjustifiable
in psychology as it is in any science. But more than this, so
soon as we take our stand upon the ground of experience, we
have to begin our science, not with the investigation of those
experiences which refer primarily only to objects more or less
closely connected with mind, but with the direct examination ot
mind itself, that is, of the phenomena from which its existence
was long ago inferred, and which formed the original incentive
to psychological study. The history of the science shows us
that mind and the principal mental functions were distinguished
before there was any idea that these functions were connectec
with the brain. It was not any doubt as to the purpose of this
organ which led to the abstraction which lies at the foundation
of the doctrine of mind, but simply observation of mental
phenomena. Sense, feeling, idea, and will seemed to be related
activities ; and they appeared, further, to be bound together by
the unity of self-consciousness. The mental processes began,
therefore, to be looked upon as the actions of a single being.
But since these actions were found again to be intimately
connected with bodily functions, there necessarily arose the
question of assigning to mind a seat within the body, whether
in the heart, or the brain, or any other organ. It was reserved
for later investigation to show that the brain is the sole organ
which really stands in close connection with the mental life.

But if it be sensation, feeling, idea, and will which led in
the first instance to the assumption of mind, the only natural
method of psychological investigation will be that which begins
with just these facts. First of all we must understand their
empirical nature, and then go on to reflect upon them. For it
is experience and reflection which constitute each and every
science. Experience comes first ; it gives us our bricks : reflec-
tion is the mortar, which holds the bricks together. We cannot
build without both. Reflection apart from experience and ex-
perience without reflection are alike powerless. It is therefore
essential for scientific progress that the sphere of experience be

Methods and Aids of Psychological Investigation 9

enlarged, and new instruments of reflection from time to time
invented.

But how is it possible to extend our experience of sensations,
feelings, and thoughts ? Did not mankind feel and think
thousands of years ago, as it feels and thinks to-day ? It does,
indeed, seem as though our observation of what goes on in the
mind could never extend beyond the circle to which our own
consciousness confines it. But appearances are deceptive. Long
ago the step was taken which raised the science of psychology
above the level of this its first beginning, and extended its
horizon almost indefinitely. History, dealing with the expe-
rience of all times, has furnished us with a picture in the large
of the character, the impulses, and the passions of mankind.
More especially is it the study of language and linguistic de-
velopment, of mythology and the history of religion and custom,
which has approached more and more closely, as historical
knowledge has increased, to the standpoint of psychological
inquiry.

The belief that our observation is confined to the brief span
of our individual life, with its scanty experience, was one of the
greatest obstacles to psychological progress in the days of the
earlier empiricism. And the opening up of the rich mines of
experience to which social psychology gives us access, for the
extension of our own subjective perceptions, is an event of
importance and of promise for the whole circle of the mental
sciences. Nor is that all. A second fact, of still greater import
for the solution of the simplest and therefore, most general
psychological problems, is the attempt that has been made to
discover new methods of observation. One new method has
been found ; it is that of experiment, which, though it revolu-
tionized the natural sciences, had not up to quite recent times
found application in psychology. When the scientific inves-
tigator is inquiring into the causes of a phenomenon, he does
not confine himself to the investigation of things as they are
given in ordinary perception. That would never take him to
his goal, though he had at his command the experiences of all
time. Thunderstorms have been recorded, indeed carefully
described, since the first beginnings of history : but what a
storm was could not be explained until the phenomena of

io Lectures on Human and Animal Psychology

electricity had become familiar, until electrical machines had
been constructed and experiments made with them. Then the
matter was easy. For when once the effects of a storm had
been observed and compared with the effect of an electric
spark, the inference was plain that the discharge of the machine
was simply a storm in miniature. What the observation of a
thousand years had left unexplained was understood in the
light of a single experiment. Even astronomy, a science which
we might think must of its very nature be confined to observa-
tion, is in its more recent development founded in a certain
sense upon experiment. So long as mere observations were
taken, the general opinion that the earth was fixed, and that
the sun and stars moved round it, could not be overthrown. It
is true that there were many phenomena which made against
this belief ; but simple observation could not furnish means for
the attainment of a better explanation. Then came Copernicus,
with the thought : ' Suppose I stand upon the sun ! ' and
henceforth it was the earth that moved, and not the sun ; the
contradictions of the old theory disappeared, and the new
system of the universe had come into being. But it was an
experiment that had led to this, though an experiment of
thought. Observation still tells us that the earth is fixed, and
the sun moving ; and if the opposite view is to become clear,
we must just repeat the Copernican experiment, and take our
stand upon the sun.

It is experiment, then, that has been the source of the
decided advance in natural science, and brought about such
revolutions in our scientific views. Let us now apply experi-
ment to the science of mind. We must remember that in every
department of investigation the experimental method takes on
an especial form, according to the nature of the facts investi-
gated. In psychology we find that only those mental pheno-
mena which are directly accessible to physical influences can
be made the subject matter of experiment. We cannot experi-
ment upon mind itself, but only upon its outworks, the organs
of sense and movement which are functionally related to mental
processes. 3o~^li--?y-? r Z--P.?ychQ]o^cal^jSLXperiment is at th
same time physiological, just as there are physical processes
corresponding to the mental processes of sensation, idea, and

Methods and Aids of Psychological Investigation 1 1

_wiiL . This is, of course, no reason for denying to experiment
the character of a psychological method. It is simply due to
the general conditions of our mental life, one aspect of which is
its constant connection with the body.

The following lectures are intended as an introduction to
psychology. They do not attempt any exhaustive exposition
of the methods and results of experimental psychological inves-
tigation. That would have to assume previous knowledge
which cannot here be presupposed. Neither shall we include
in the range of our discussion the facts of social psychology,,
whose contents is extensive enough to demand an independent
treatise. We shall confine ourselves to the mental life of the
individual ; and within those limits it will be the human mind
to which we shall for the most part devote ourselves. At the
same time it appears desirable, for the right understanding of
individual mental development, that we should now and again
institute a brief comparison with the mental life of animals.

LECTURE II

: I. ANALYSIS OF MENTAL PROCESSES. II. IDEA AND SENSATION.
III. INTENSITY AND QUALITY OF SENSATION. IV. MEASURE-
MENT OF THE INTENSITY OF SENSATION.

I

SO soon as ever the dawn of knowledge had broken upon
us through the portals of the senses, we began to compare
objects, to reflect upon them. The first work of thought was to
-set things in their places, to transform the chaos of sense-
impressions into an intelligible cosmos. But after everything
else has been arranged, there still remains something which has
as yet no place, ourselves : our feeling, willing, and thinking ;
^o that the question arises : how can our own mental life be
made the subject of investigation like the objects of this external
world of things about us ? And yet can such a question be
asked ? Is it not really self-contradictory ? It is as though we
required that the tone should hear itself, or the ray of light hi
sensed by itself.

It is, indeed, true that here, as we enter upon the study o\
.psychology, a peculiar difficulty presents itself. If we try to
observe our mental activities, the observer and the observed
object are one and the same. But the most important condition
of a trustworthy observation is always thought to consist in the:
mutual independence of object and observer. Nevertheless, we
should be overhasty if we disputed the possibility of psy-
chological observation in general because of this unavoidable
limitation of the science. Only so much is true : that the
peculiarities of the object, in this case as in others, imply special
conditions of its observation. These can be stated in two rules.
First : so long as we confine ourselves to introspection, without
calling in any assistance from outside, mental processes may not
>be observed directly while they are taking place. We must

Analysis of Mental Processes- 13;

T

Ijmit- ourselves to analysing thenyso-Jar jisj3Q.ssihlft T from the
effects_jw.hich they leave hphind in our memory Secondly :
wherever in is possible, we must endeavour so to control our
mental processes by means of objective stimulation of the
external organs (particularly of the sense-organs, with the
physiological functioning of which definite psychoses are
regularly connected) that the disturbing influence which the
condition of observation tends to exercise upon them is
counteracted. This control is given by experiment. Not only
does experiment, here as elsewhere, enable us- to produce a
phenomenon, and to regulate its conditions,. at our pleasure: it
possesses in psychology an especial importance, in that it alone
renders self-observation possible during the course of a mental
process.

Let us now seek, in accordance with the first rule which we
established, to recall the general impression which any particular
mental experience has left upon us. This impression will always
be that of a composite process. Some parts- of it, images of
external objects, we designate Ideas ; others,, the pleasurable or
painful reactions of our own mind upon these ideas, Feelings ;
others, again, we term Efforts, or Impulses, or Volitions. It is
certainly true that these elements of mental life never occur
separately, but always in connection with, always in dependence
upon, one another. Nevertheless, it seems absolutely necessary,
at the beginning of a psychological investigation, to follow the
example of discrimination already set by language, and to
separate out the most important factors of this complex inner
life and subject each of them in turn. to. a special analysis.

Now, if these elements are all interconnected and inter-
dependent, it is clear that, other things equal, we might begin
the analysis which we contemplate with, any one of them.
Nevertheless, external reasons render it hardly possible to choose
any other method of procedure than that of commencing with
an investigation of ideas. We conceive of an. idea as the image
of some external object. We can, therefore, transfer to these
images of external objects the abstraction which we always
make in the case of the logical notions of the objects ; we
can consider them just as though the feelings, impulses, and
volitions, which in fact invariably accompany them, did not

14 Lectiires on Human and Animal Psychology
exist. On the other hand, in the case of these feeling's and

* o

impulses themselves, it is impossible to carry out an abstraction
of the kind, because we are not in a position even to describe
them without constant reference to the ideas with which they
are associated. Granted that this results merely from the fact
that all our designations took their origin from distinctions made
between objects of the external world, and were only applied
to our inner experiences at a comparatively late date, still
it remains true that this general trend of the development of
our knowledge necessarily determines the manner in which
psychology sets to work to analyse those inner experiences.

By an idea, then, we shall understand that mental state or
mental process which we refer to something outside of our-
selves, whether this attribute of externality be thought of as
directly applicable in the present, or as applied to an object
which has been directly given us in the past, or even as applied
to an object which is only possible, and not actual. Under
ideas, therefore, we include (i) sense-perceptions, which
depend upon direct excitation of the organs of sense ; (2)
memories of such sense-perceptions; and (3) images of fancy, be
these what they may. The terminology adopted in many
Psychologies, according to which the images of memory and
fancy are alone designated ' ideas,' while the direct effects of
sense-impression are termed exclusively ' perceptions,' we must
judge to be unjustifiable and misleading. It lends colour to
the view that there is some essential psychological difference
between these two kinds of mental process, whereas such a
difference is nowhere discoverable. Even the reflection upon
which the distinction is based, the thought that images of
memory and fancy do not correspond to objects actually pre-
sented to us, is not universally valid. And, in the same way,
sense-perceptions may very well be themselves taken for
illusions of sense. So that the characteristics, by means of
which two kinds of ideas are distinguished, can never be more
than secondary, while the distinction itself cannot always be
satisfactorily carried through.

An idea, in the general sense in which we are here using the
word, is always something composite. A visual image is made
up of spatially distinguishable parts ; a sound is constituted of

Idea and Sensation 15

clangs, while it is also conceived of as coming to us in a certain
direction, z.., is associated with spatial ideas. Our first problem

e t consists in the determination of

their simplest constituent elements, and in the investigation of
the psychological properties . jdfjjiese. We call the psycholo.-
gical elements of ideas Sensations. Thus we speak of the idea
of a house, of a table, of the sun or moon, but of the sensations
of blue, yellow, warm, cold, or of a tone of definite pitch. This
use of the word 'sensation/ we must notice, like the use of ' idea '
in the general sense mentioned above, has only become current
in recent psychology. In the earlier treatises, and still to some
extent in popular writings and belles lettres, we find the word
'sensation' employed with the same meaning as 'feeling.'
Here, and in what follows, we shall consistently adhere to the
definition just given, according to which sensations are merely
the simplest and most elemental psychological constituents of
the idea.

II

But the analysis of ideas into sensations does not conclude
the task which we have set ourselves, the analysis of those
mental processes which are referable to external objects. For
in every sensation, again, we distinguish two properties, one
which we name its strength or intensity, and another which we
call its quality. Neither can exist in the absence of the other.
Every sensation, be it of sound, heat, cold, taste, or what not,
is possessed at once of a certain intensity and a certain
quality. But, as a general rule, the two attributes can be
varied independently of each other. We can sound a musical
note, e.g., at first quite softly, and then, by gradually increasing
its strength, pass it through all possible degrees of intensity,
while its quality remains unaltered. Or we can strike different
notes one after the other, and so obtain different qualities,
while we still keep, if we will, one and the same intensity of
tone throughout. Here quality has changed ; intensity re-
mains constant. This possibility of varying the two consti-
tuents of sensation independently of each other depends upon
the fact that the motions in external nature, by the operation
of which upon our sense-organs sensation in general was origi-

1 6 Lectiires on Human and Animal Psychology

nally occasioned, present two aspects, either of which may also
vary without affection of the other.

The processes of motion which, by their operation upon our
senses, give rise to sensations, we commonly denominate
stimuli, or more particularly sense-stimuli. Accordingly, we
generally understand by stimulus the external motion-process,
which, after it has acted upon the sense-organ and been con-
ducted by sensory nerves to the brain, is accompanied by the
mental process of sensation. Thus we regard the sound-waves
of the air or the light-waves set up in surrounding space as
stimuli, corresponding to our sensations of sound and light. In/
the same way, those motion-processes which are aroused, by
the agency of such external stimuli, in our sense-organs and m
the brain, may also be regarded as processes of stimulation or
as constituents of the entire stimulation-process. For the sake
of clearness, we will call these last internal stimuli. If we seem
always to have the external stimuli primarily in mind when we
are speaking of the relation of ' stimulus ' to sensation, this is
only because they are the more easily accessible to objective
investigation. But wherever we can show good reason for the
belief that the peculiar form taken on by a stimulus-process in
the sense-organs, the sensory nerves, and the sense-centres of
the brain exercises a determining influence upon a particular
sensation, we shall, of course, be constrained to take into con-
sideration the character of the internal stimuli and the transfor-
mations which occur in the conversion of an external into an
internal stimulus.

Now, in whichever of these two senses we employ the notion
of ' stimulus,' we are able to vary both the intensity and the
form of any stimulation-process. But the intensity of stimulus
corresponds to the intensity of sensation, the form of stimulus
to its quality. (Thus, in the case of sound and light, the inten-
sity of the sensations corresponds to the extent or amplitude of
vibration, their quality to its rapidity. The quality of tone we
call pitch ; the quality of light, colour.) Although, therefore,
intensity and quality of sensation do not exist independently of
each other, yet psychological analysis is able to distinguish them
for its own purposes. In doing this, it is only completing an
abstraction which was begun when ideas were separated out

Intensity and Quality of Sensation 17

from the totality of mental life, and continued a step farther in
the subdivision of ideas into elementary sensations.

HI

We begin, then, with an investigation of the intensity of sen-
sations. And we leave for the present out of account everything
which has reference to their qualitative aspect.

If we compare with each other two different sensations of the
same modality, we are undoubtedly able to pass judgment re-
garding their intensities. Our judgment runs either : The sen-
sations are of equal intensity, or: They are not of equal in-
tensity. The midday sun we assert to be brighter than the
moon, the roar of a cannon louder than the crack of a pistol,
a hundredweight heavier than a pound. These comparative
judgments are taken directly from sensation. We really state
in them merely this : that the sensations which the sunshine,
the cannon, and the hundredweight arouse in us are more in-
tensive than the sensations which we have from the moon, a
pistol-shot, or a pound-weight. There is therefore possible a
quantitative comparison of sensations. We can say of two sen-
sations that they are of equal intensity, or that this one is of a
greater or less intensity than the other. There our measure-
ment of sensation ordinarily rests. We are not able to say how
much stronger or how much weaker one is than another. We
cannot estimate in the least whether the sun is a hundred or "a
thousand times brighter than the moon, the cannon a hundred
or a thousand times louder than the pistol. Our ordinary
measurement of sensation tells us only of ' equality,' of a ' more,'
or of a ' less,' never of a 'so much more ' or ' less.' And
this natural measurement is, therefore, as good as none at all
when an exact determination of intensity is required. Although,
perhaps, we may be able to observe that, as a general rule, in-
tensity of sensation increases and diminishes with intensity of
stimulus, yet we have not the remotest idea whether the two
vary in the same ratio, or whether one increases more slowly or
more quickly than the other. In a word, we know nothing of
the law of the dependence of sensation upon stimulus. If we
are to discover this, we must necessarily begin by finding a
more exact measurement for sensation. We must be able to

C

1 8 Lectures on Human and Animal Psychology

say : a stimulus of the intensity I occasions a sensation of the
intensity I, a stimulus of the intensity 2 a sensation of the
intensity 2 or 3 or 4, and so on. But, to do this, we must know
what it means to say that ' this sensation is twice,' or ' three
times,' or ' four times as great as that.'

Now, we have said above that it is possible to strike a note
first of all very gently, at an intensity at which it can only just
be heard, and then gradually to increase this intensity, until we
reach a point at which the note is as loud as it can be made.
Between these upper and lower limits the tone-sensation has
passed, not by leaps and bounds, but smoothly and uniformly,
through all its possible intensities. And the same is true of
other sense-impressions. From every sensation-quality we can
construct a one-dimensional series of sensation-intensities, which
pass over into one another without break or gap. In such a
series we may, first of all, quantitatively distinguish every mem-
ber from every other member ; we say that the one of two com-
pared sensations is the stronger, the other the weaker. But
more than that. We find no difficulty in stating, after succes-
sive comparisons, that the difference of intensity in one case
was greater than it was in another.

Now, as the result of these very obvious considerations, there
arise for psychological investigation two separate questions.
The first is : what is the basis of this natural measurement of
sensation-intensities, which enables us directly, without knowing
anything about the external affection of our senses, quantita-
tively to compare different sensations ? And the second,
which, as soon as stated, becomes a problem in experimental
psychology, runs : may not this crude and inaccurate natural
measurement be transformed into an exact one ; so that, e.g.,
we might be able to state how much stronger or weaker a given
sensation was than another with which we compared it ? We
will try to answer this second question first.

IV

At first sight the attempt to measure the intensity of sensa-
tions may appear overbold. How can we hope to reach any
result when no definite measure is contained in the sensation
itself? But if we take a little time to consider how it is that

Measurement of the Intensity of Sensation 19

the measurement of magnitude in general is carried out, matters
will begin to look more hopeful.

For all measurement there is required a standard. And this
standard can never be the measured object itself. Thus we
may measure the time of an occurrence by a clock ; and what
the clock shows us is a uniform motion. Or we measure longer
periods of time by days, months, and years ; and these corre-
spond to uniformly repeated changes in external nature. That
is, we measure time by space. But to measure space, on the
other hand, we employ time. The length of the road over
which we have travelled we estimate by the time that the
journey has taken. And when we mark the successive divi-
sions upon a scale, we must do it in a time order. So that the
original measurement-units of space and time always coincide :
an hour is just as much an hour of space-experience as an hour
of time-experience. Space gives us our only means of measur-
ing time, and time our best means of measuring space. Never-
theless, there is a noteworthy difference in the way in which
each of these two measures depends upon the other. For
space-measurement it is only necessary that time should be al-
ready existent ; it is not requisite that we should possess an
exact measure of time. When we are constructing a scale, we
must mark in one unit after another ; but, that once done, we
do not need in every particular measurement to compute the
number of units which the scale embraces. We measure directly
with the whole scale ; that is, we take all at once, simultane-
ously, what was constructed gradually. To carry out the most
exact spatial measurement we need have no more than the
general notions ' earlier,' ' later/ ' simultaneous.' Then, when
space has been measured, we come back to time, in order to
divide it up by the help of our spatial measurements.

All exact measurement is, therefore, spatial measurement.
Times, forces, everything that can be considered as magnitude,
we measure by a spatial standard. Now, when we talk of com-
paring the intensities of sensations, we imply that sensations are
magnitudes. And although a direct comparison of sensation-
intensities does not enable us to do more than pronounce them
' less ' or ' greater ' or ' equal/ that is in itself no obstacle in
the way of obtaining an exact measurement. For at first we

2O Lectures on Human and Animal Psychology

possessed only the vague ideas of ' earlier,' ' later,' and ' simul-
taneous ' in the case of time ; and yet we are now able to
measure with very great accuracy temporal differences, the mere
cognition of which would have far transcended our original
powers. Indeed, it is just the same with sensation as with time,
and with all the other magnitudes which, like these two, are
primarily mental magnitudes. Temporal and spatial magnitudes
are alike distinguished in the first place only as ' equal,' ' greater,'
or ' less.' We quickly arrive at an exact determination of the
latter, since we are able to measure each new space-magnitude
by magnitudes already known. But the measurement of mental
magnitudes is apparently attended with greater difficulties. In
this sphere it was until recently only the movement of thought,
time, which had been subjected to an exact measurement, by
the substitution, for movement of ideas in us, of movements of
objects without us, and especially those movements with which
the impression of uniform regularity was invariably connected.

An exact means of measuring time cannot, then, be obtained
from time alone ; we must call in the aid of movement in space.
In the same way, we shall never be able to discover a means of
measuring sensation in sensation itself, but must take into con-
sideration the relation of its magnitude to other measurable
magnitudes. And there is no magnitude which presents itself \\
more obviously for this purpose than that of the stimulus, from
which the sensation arises. Indeed, the stimulus furnishes us
not merely with the most obvious, but with our only possible,
means of measuring sensation. There is no other magnitude
which stands in any such direct relation to the magnitude of
sensation.

The only assistance which sensation itself renders us in this
measurement is that of the ordinary distinction of sensation as
of ' greater,' Mess,' and 'equal' intensity. Everything else must
be derived from the measurement of stimulus. If two sensations
are of equal intensity, our first thought is that the external
stimuli are also of the same intensity in the two cases. But
measurement of them shows not seldom that this surmise is
wrong ; that stimuli of different intensity may occasion sensa-
tions of equal intensity. A weak eye finds ordinary daylight so
intense that it involuntarily closes ; but the normal eye displays

Measurement of the Intensity of Sensation 2 1

no such tendency, except when looking directly at the sun. If
we fall into a swoon, or into deep sleep, we do not sense the
prick of a needle which, in the waking state, would cause us
acute pain. Indeed, facts of that kind have been observed from
the beginning of time. This greater or less receptivity of the
organism, in face of external stimuli, we call sensibility or excita-
bility. We say that a weak eye is more excitable than a strong
one ; that we are more sensitive awake than asleep. But we do
not ordinarily think of measuring this excitability. And yet the
measure is given at once, if we only ascertain the intensities of
the stimuli which, on different occasions, give rise to a sensation
of equal intensity. If the stimuli are of equal intensity in both
cases, the excitability is the same ; if the stimulus in the first
case were twice or three times as strong as it is in the second, the
excitability in the former experiment was half or a third as great
as it is in the latter. In short, excitability is inversely propor-
tional to the intensity of the stimuli employed for the production
of equally intensive sensations.

Already, then, we have gained one result, which is not un-
important for our proposed measurement. We have discovered
a method of eliminating the differences of excitability which
may be found to exist in different individuals or in the same
individual at different times. And we are thereby in a condition
to propose and define a unit of excitability, such as has been
universally accepted for time, supposing, of course, that its
proposition shall prove to possess any real significance.

A further basis of measurement is given with the increase and
decrease of sensation-intensity. What we all know with regard
to this is only that the intensity of sensation increases and de-
creases with the intensity of stimulus. If the ' sound in our
ear ' increases, we know that the external sound has become
louder, always provided that we have no reason to assume a
change of sensibility in our sense-organs. Originally this con-
clusion regarding increase of the external stimulus was merely
an inference from increased intensity of sensation. Not until
we have made those physical processes which constitute the
stimulus the object of separate investigation can we attain to
the definite conviction that this conclusion was correct. But in
pursuing such an investigation we come to make stimulus inde-

22 Lectiires on Human and Animal Psychology

pendent of sensation, and so are on the road towards the dis-
covery of a valid measurement of stimulus.

Now, if our entire knowledge were confined to this fact, that
sensation increases and decreases with stimulus, we should not
have gained very much. But there are facts of direct and un-
assisted observation which tell us something, even if in the most
general terms, of the law which governs the intensive relations
of stimulus and sensation.

Every one knows that in the stillness of night we hear things
which are unperceived in the noise of day. The gentle ticking
of the clock, the distant bustle of the streets, the creaking of the
chairs in the room, impress themselves upon our ear. And
every one knows that amid the confused hubbub of the market-
place, or the roar of a railway-train, we may lose what our
neighbour is saying to us, or even fail to hear our own voice.
The stars which shine so brightly at night are invisible by day ;
and although we can see the moon in the day-time, she is far
paler than at night. Every one who has had to do with weights
knows that if to a gramme in the hand we add a second gramme,
the difference is clearly noticed ; but if we add it to a kilo-
gramme, there is no knowledge of the increase.

All these experiences are so common that we think them
self-evident. Really, that is by no means the case. There
cannot be the least doubt that the clock ticks just as loudly by
day as by night. In the clamour of the street or amid the
noise of the railway we speak, if anything, more loudly than is
usual. Moon and stars do not vary in the intensity of their
light. And no one will deny that a gramme weighs the same
whether it is added to one gramme or to a thousand.

The sound of the clock, the light of the stars, the pressure of
the gramme weight, all these are sensation-stimuli, and stimuli
whose intensity always remains the same. What, then, do
these experiences teach us ? Evidently nothing else than this :
that one and the same stimulus will be sensed as stronger or
weaker, or not sensed at all, according to the circumstances
under which it operates. But what kinds of change in the cir-
cumstances are there, which can produce this alteration in sen-
sation ? On considering the matter closely, we discover that
the change is everywhere of one kind. The tick of the clock is

Measurement of the Intensity of Sensation 23

a weak stimulus for our auditory nerves, which we hear plainly
when it is given by itself, but not when it is added to a strong
stimulus of rattling wheels and all the other turmoil. The
light of the stars is a stimulus for the eye ; but if its stimulation
is added to the strong stimulus of daylight, we do not notice it,
although we sense it clearly when it is joined to the weak
stimulus of twilight. The gramme weight is a stimulus for our
skin which we sense when it is united to a present stimulus of
equal strength, but which vanishes when it is combined with a
stimulus of a thousand times its own intensity.

We can, therefore, lay it down as a general rule that a stimu-
lus, in order to be noticed, may be so much the smaller if the
stimulus already present is weak, but must be so much the
larger the stronger this pre-existing stimulation is. From this
alone we can see, in a general way, how our apprehension of a
stimulus depends upon the intensity of it. It is plain that this
dependence is not quite so simple as might have been expected
beforehand. The simplest relation would evidently be that we
should estimate increase of sensation in direct proportion to
increase of stimulus-intensity. So that if the sensation I should
correspond to a stimulus of the intensity I, sensation 2 would
correspond to intensity 2, and sensation 3 to intensity 3, and
so on. But if this simplest of all relations prevailed, a stimu-
lus added to a present strong stimulus would occasion as great
an increase in sensation as if it were added to a present weak
stimulus ; the light of the stars would make as large an addition
to the daylight as to the night. This we know not to be the
case ; the stars are invisible by day. The increase which they
occasion in our sensation is not noticeable, whereas this increase
is very considerable indeed in the twilight. . So that this much
is made out as regards our comparative measurement of sensa-
tion-intensities, that they do not increase proportionally to the
increase of stimulus, but more slowly. But when we attempt
to decide what the relation which obtains actually is, everyday
experiences do not suffice. We have need of exact and special
measurements.

However, before we apply ourselves to the task of making
these measurements, it is necessary that we should be quite
clear as to the meaning of the questions which are before us

24 Lectures on Human and Animal Psychology

and the importance of the answers which we may expect to find
to them. If we increase two stimuli of different intensities,
e.g., a gramme and a kilogramme,- by the same unit, e.g., by
the pressure of a gramme, we come upon the fact that the ad-
dition to the smaller weight is quite plainly perceived, whereas
the addition to the larger one is almost or altogether imper-
ceptible. This fact may be interpreted a priori in two ways,
(i) It may be that the addition made to the stronger stimulus
produces absolutely a smaller increase in sensation than the
same addition made to the weaker. (2) Or it may be that the
sensation-increase is the same in both cases, but that the
stronger stimulus requires a greater increase in sensation than
the weaker, if the differences are to be equally clear in conscious-
ness. If the first hypothesis is correct, the measurements which
we are to make will have direct reference to the relation be-
tween stimulus-increase and the corresponding sensation-in-
crease ; if the second, then the law of which we are in search
will refer only to our apprehension and comparative estimation
of sensations, and not to these themselves. Now, without these
activities of apprehension and comparison, it is impossible for
us to formulate any judgment whatsoever concerning sensation-
intensities, from which it follows that the results of our measure-
ment of sensation must, in the first instance, be interpreted on
the alternative hypothesis : that all that we can get at directly
is the relation between alteration of stimulus and our appre-
hension of this alteration. It was with this in mind that I was
careful to say above, not that a given stimulus-increase produces
a smaller sensation-increase when added to a strong, than when
added to a weak, stimulus, but that in our estimation this in-
crease is smaller. If the absolute sensation-increase is smaller,
that can only be due to the working of another law, that of
the parallelism of our estimation of a sensation-increase and its
actual magnitude. Now, obviously, an answer to the question
of the validity of such a hypothesis as that can only be looked
for at the conclusion of a detailed investigation of the relation
existing between the intensities of stimulus and sensation. This
is the investigation upon which we are now to embark. You
will, perhaps, allow me, for the sake of brevity, to speak in what
follows simply of ' sensation,' when I should more correctly say

Measurement of the Intensity of Sensation 25

" apprehension ' or ' estimation of sensation.' But I shall do
so with the repeated caution that this mode of expression is
only provisional, and with the assurance that I shall not fail in
a later lecture to enter fully upon the question whether the im-
plicit assumption that our apprehension of alterations in sensa-
tion-intensity runs parallel with the alterations themselves is
correct, or whether it must ultimately give place to some other.

This being understood, then, the problem immediately before
us takes the following shape. We are to determine what in-
crease of sensation corresponds to equal increases of stimulus,
or, in other words, to discover what stimulus-increase corre-
sponds to equal increases in sensation.

How to execute these measurements is something which our
everyday experiences suggest. A direct measurement of sensa-
tion-intensities we saw to be impossible. It is only sensation-
differences which we can take account of. Experience showed
us what very unequal sensation-differences might correspond to
equal differences of stimulus. In most cases we find that the
same stimulus-difference would be sensed or not sensed accord-
ing to circumstances ; that, e.g., a gramme is sensed when added
to another gramme, but not when added to a kilogramme. We
should think very much less of the statement that a gramme
added to a gramme produced a considerable difference, added
to a kilogramme a slight difference, in sensation. And the
reason is not far to seek. It is difficult to say whether one
sensation-difference is just smaller or just larger than another ;
but we have generally no hesitation in calling two sensations
equal. We are quite sure that the stars are invisible by day ;
but we might be in doubt as to whether the full moon is brighter
by night than in the day-time. Our inquiry will, therefore, lead
to results most quickly, if we start out with some arbitrary
stimulus-intensity, observe what sensation it arouses, and then
see how long we can increase the stimulus without having the
sensation seem to change. If we carry out such observations
with stimuli of varying magnitude, we shall certainly be obliged
to vary the stimulus-increase which is just capable of producing
a difference in sensation. A light, to be just visible in the twi-
light, need not be nearly so bright as starlight ; it must be far
brighter to be just perceptible by day. If now we institute

26 Lectures on H^lman and Animal Psychology

these observations for all possible stimulus-intensities, and note
for each intensity the magnitude of the stimulus-increase neces-
sary to produce a just perceptible increase of sensation, we shall
get a series of numerical values, in which is definitely and im-
mediately expressed the law according to which sensation alters
as stimulus is increased.

Experiments by this method are especially easy to carry out
upon the sensations of light, sound, and pressure. We will con-
sider the last of these first, since they are the most simple. The
experimenter lays his hand comfortably upon a table. The
chosen weight is placed upon it. Then a very small weight is
added to this, and the question put whether the observer, who,
of course, must not look at his hand during the experiment,
notices any difference. If the answer is negative, a somewhat
larger weight is taken, and the same procedure is continued
until the increment of weight is found, which is just large
enough to be sensed clearly. When an experiment has been
concluded with one standard weight, a second and third are
taken, and so on, until the magnitude of the just necessary in-
crement of weight has been determined for a sufficient number
of standards.

We find a surprisingly simple result. The addition to the
original weight, which is just enough to produce a noticeable
difference in sensation, always stands in the same proportion to
it. Suppose, e.g., that we had found that the necessary addition
to a gramme was a quarter of a gramme. Then if, instead of
grammes, we took pennyweights or ounces or pounds, we should
have to add a quarter of a pennyweight to the pennyweight, a
quarter of an ounce to the ounce, a quarter of a pound to the
pound, in order to obtain a just noticeable difference. Or, if
we confine ourselves to grammes, we must add two and a half
to ten, twenty-five to a hundred, two hundred and fifty to a
kilogramme.

These figures explain the familiar fact that the difference be-
tween heavy weights, to be cognisable, must be larger than the
difference between light ones. But they also give us the exact
formulation of the law which governs the relation of sensation
of pressure to force of pressure exerted. You can hold this law
in mind by remembering a single number, the number ex-

Measurement of the Intensity of Sensation 27

pressing the proportion of the added weight to the standard.
Experimental results show that this proportion is, on the
average and approximately, that of 1:3. Whatever magnitude
of pressure may be exerted upon the skin, we sense its increase
or decrease so soon as the amount added to or subtracted from
it is one-third of the original.

Experiments of the same kind, but in greater number and
with greater accuracy, have been made with lifted weights.
Here, of course, the conditions are not so simple. When we
lift a weight, we have not only a pressure-sensation in the hand
which holds it, but also a sensation in the muscles of the arm
which raise hand and weight together. This second sensibility
is much finer than that of pressure proper. Indeed, it has been
experimentally shown that if lifting is allowed, an addition of
merely y-^ to the original weight produces a difference in sensa-
tion. Our sensibility to weight with lifting is, therefore, some
five times as great as our sensibility to weight which simply
exerts pressure. And the law of the dependence of sensation
upon stimulus may be similarly expressed in terms of the sensa-
tion of lifting, the fraction ^ being replaced by y^- or -j^. This
proportion holds whether the weight is large or small, whether
we are speaking of ounces, pounds, or grammes. It tells us
that there must be added to a hundred grammes six, to a thou-
sand grammes sixty, to every standard weight j^j- of its own.
amount, if a difference in sensation is to be apprehended.

To determine the objective magnitude of weights , we employ
the balance ; to measure accurately the objective intensity of
light, we use a photometer, or light-measurer. This is in principle
an instrument by means of which the brightness of a given light
is measured by reference to, and
expressed in units of another light
of constant brightness. A very
simple form of the photometer is
that schematically outlined in
Fig. I. A vertical rod, s, is fixed
in front of a white screen, w. Be-
hind the rod is placed the light n,
the intensity of which is regarded
as the unit of measurement. Beside n is set the light /, whose

28 Lectures on Human and Animal Psychology

intensity is to be measured. Both lights throw a shadow on the
white screen. Neither shadow is as dark as it would be if there
were present simply the one light which produces it ; each is
illuminated by the other light, and the greater the intensity of
this other light, the brighter will the shadow appear. Suppose
that both shadows are equally bright ; that would mean that the
intensities of the two lights are equal. But suppose, again, that
the shadow cast by the normal light, the brightness unit, is
darker than the other ; this means that the intensity of the light
which is to be measured is less than unity. We can readily
determine how much less by moving the normal light somewhat
farther back, for it is a law of optics that the intensity of a light
is inversely proportional to the square of the distance of the
luminous body. If the light, which was standing at the distance
of one metre from the white screen, is moved in a straight line
to a distance of ten metres, the intensity of the light falling upon
the screen is reduced from 100 to I ; at the distance of ten
metres it is a hundred times less than it was at the distance of
one metre. We can easily institute in this way a quantitative
comparison of a light of unknown intensity with a given normal
light. We have only to shift the two lights to such distances
that the darkness of the shadows cast upon the screen appears to
:be precisely the same ; then we measure the distance of each
light from the screen, and the inverse ratio of the squares of
the two distances gives us the relation of the intensities of
the lights.

We can turn this same method to good account for the
measurement of the dependence of light-sensations upon inten-
sity of light-stimulus. The strong illumination of the shadowless
part of the screen and the weak illumination of the shadows both
give rise to light-sensations, which are of course the more
different the darker the shadows. If we set out with two lights
of equal intensities, situated at the same distance behind the rod
(say, two exactly similar stearine candles), the two shadows will
'be of the same intensity ; i.e., they are equally different from the
bright background upon which they are thrown. If now we
move one candle farther and farther away, the shadow cast by it
becomes weaker, and its difference from the illuminated back-
ground less, till finally a point is reached at which this difference

Measurement of the Intensity of Sensation 29

vanishes altogether. By measuring first the distance of the
stationary candle from the screen, and secondly the distance of
the candle which has been moved so far back that its shadow
has just disappeared, we obtain the data necessary for the formu-
lation of the law of the increase of light-sensation with increasing
intensity of light-stimulus. So long as only the stationary
candle was there, the total illumination of the screen was due to
it. When the other candle is moved up from a distance its light
adds something to the whole amount of illumination present
But this increase is at first unnoticeable ; the point where it be-
comes noticeable is fixed by the appearance of a second shadow
of the rod. The place which this shadow comes to occupy is, of
course, illuminated by the nearer candle, and not by the more
distant one ; and as soon as the latter has approached near
enough to produce a noticeable increase in the total illumination
the shadow must appear ; it is an index, so to speak, pointing
to an increase of illumination. And we now possess, in the
inverse ratio of the squares of the distances of the two candles-
from the screen, the relation of those light-intensities which con-
dition a just noticeable difference of light-sensation. Suppose,.
e.g., that the first candle was placed at a distance of one metre,
and the second (which casts a just noticeable shadow) at a
distance of ten metres, then the light-intensities stand to one
another as 100 : I ; or, in other words, the intensity of the first
candle must be increased by one-hundredth, if its increase is to
effect an increase of sensation. We have here pursued exactly
the same method as in our experiments with weights. There we
added to a heavy weight a lighter one, which just noticeably
increased the sensation of pressure ; here we add to a strong
illumination a weaker one, which just noticeably increases the
light-sensation. It only remains to extend these observations to
different stimulus-intensities, as was done in the experiments
with weights. Just as we varied our normal weights, so must we
vary the luminosity of the standard candle by known amounts.
That is very easily done. It is only necessary to move the
candle backwards or forwards, and to calculate its luminosity
from the distance at which it stands from the illuminated screen.
Experiments made in this way soon convince us that the dis-
tances of the two candles always bear the same relation to one

30 Lectures on Human and Animal Psychology

another. If the second candle had to be placed at a distance of
ten metres when the first stood at one metre, it must be placed
at a distance of ten feet when the latter stands at one foot, at
twenty metres or twenty feet when the distance in the other
case is two metres or two feet, from which it follows that light-
intensities which condition a just noticeable difference of sensa-
tion always preserve the same relation to one another. They
stand to each other as I : 100, as 2 : 200, etc. But this is the law
which we discovered in our experiments with weights, and the
law can just as well here be expressed by the number defining
the relation of the just noticeable increase of illumination to the
original illumination. This number is approximately y^- ; that
is, every light-stimulus must be increased by Y^-, if its increase
is to be sensed.

It is not hard to institute similar experiments in the sphere
of sound. The intensity of the sound produced by the fall of a
body upon some underlying surface increases with the magni-
tude of its weight and the height of its fall. If we always em-
ploy the same body, we can vary the intensity of the sound at
will by varying the height of fall. Intensity and height of fall
are directly proportional to one another. A fall from twice or
three times the standard height produces a sound twice or three
times as loud as the normal sound. A good way of turning
this principle to account for the investigation of sound-intensi-
ties which do not differ very greatly from one another is indi-
cated in the schematic representation of the sound-pendulum

given in Fig. 2. We take
two ivory balls, / and q, of
exactly the same size, and
suspended by cords of equal
length. Between the balls is
placed a block of hard wood,
c. If one of the two balls is
let fall from any chosen height
against the block, the result-
ing sound is directly propor-
tional to the height of its fall,

which can be measured by the angle through which the ball
was raised from the position of rest. The angle is read off from

' IG ' 2 '

Measurement of the Intensity of Sensation 3 1

a graduated circular scale placed behind the block. The height
of fall of the ball p, e.g., is the distance ac ; for the ball q } the
distance be. That is, the balls strike the block with the velocity
which they would have possessed had they fallen vertically from
the points a and b. If ac and be are made equal by moving both
balls through the same angle, the two sounds are naturally of
equal intensity ; but if they are different, the sounds are also of
different loudnesses. As we pass by slow degrees from equality
to larger and larger differences of height of fall, dropping the
balls in quick succession, so that the sounds may be accurately
compared, we find that for some time there is no noticeable
difference of sound, despite the difference in height of fall. Not
until this difference has reached a certain magnitude does the
difference of sound begin to be noticeable. At that point the
height of fall is measured for both balls. The difference, of
course, gives us the amount by which a standard sound-intensity,
measured by the total height of fall, must be increased if we are
to obtain a just noticeable difference of sensation. Suppose, e.g.,
that the first ball had fallen through ten centimetres and the
second through eleven. That would mean that the standard
sound-intensity must be increased by -^ before a difference
could be sensed. By making similar measurements over a very
large number of heights of fall, we shall learn whether this
relation is constant when the sound-intensity is increased or
diminished. Just the same is found to hold here as in the case
of weights and light-intensities : the relation of stimulus-incre-
ment to stimulus-intensity always remains the same. Every
sound must be increased by about one-third for the production
of a clear increase of sensation.

We have found, then, that all the senses, whose stimuli we
can subject to exact measurement, obey a uniform law. How-
ever unequal may be the delicacy of their apprehension of sen-
sation-differences, this law is valid for all : that the increase of
stimulus necessary to produce an equally noticeable difference
of sensation bears a constant ratio to the total stimulus-inten-
sity. The figures which express this ratio in the several sense
departments may be shown in tabular form as follows :

32 Lectures on Human and Animal Psychology

Light-sensation . . . y^-

Muscle . . . tV

Pressure (

Sound )

These figures are far from giving as exact a measure as might
be desired. But they are at least adapted to convey a general
notion of the relative sensibility of the different senses. First
of all stands the eye. Next comes muscle ; the muscular sen-
sation affords an accurate measure of the differences of lifted
weights. Last, and on an approximate equality, stand the ear
and the skin.

This important law, which gives in so simple a form the rela-
tion of our apprehension of sensation to the stimulus which
occasions it, was discovered by the physiologist Ernst Heinricb
Weber, and has been called after him Weber's law. He, how-
ever, examined its validity only in special cases. That the law
holds for all departments of sense was proved by Gustav Theodor
Fechner. Psychology owes to him the first comprehensive in-
vestigation of sense, the foundation of an exact theory of sen-
sation.

LECTURE III

I. ESTIMATION OF THE INTENSITY OF SENSATION. 11. MATHEMATICAL
EXPRESSION OF THE LAW OF SENSATION-INTENSITIES. III. SIGNI-
FICANCE OF NEGATIVE SENSATION-VALUES ; UNIT OF STIMULUS AND
UNIT OF SENSATION.

1

THE question might, with some show of reason, be raised
as to whether the law which we have discovered is valid
for our quantitative estimation of sensation-magnitudes in general,
or whether it possesses only a more limited importance. For
all that we have directly ascertained is this : in what proportion
the just noticeable sensation-difference stands to the stimulus-
increment which conditions it. But, as a matter of fact, it will
be easily seen that the determination of this proportion is simply
a special case in the determination of a more general relation
of dependency.

No one will doubt that it is possible to pass gradually by
very small sensation-differences to very large ones. Suppose
that we take a sensation which has increased by a just notice-
able magnitude, and that we allow this second sensation to
increase again by a just noticeable difference ; the difference
between the first and third will be clearer than that between
the first and the second. And if we proceed in this way, always
increasing by a just noticeable increment, we shall finally arrive
at a sensation-intensity which is very much greater indeed than
that of the sensation from which we set out. And we shall
have correspondingly reached a very considerable difference of
stimulus-intensity. Had we passed directly from the weak
stimulus to the strong, and therefore from the weak to the
strong sensation, we should never have been able to gain any
exact information as to the dependency of sensation upon
stimulus. Taking steps of such length from sensation to sensa-
tion, we should not have been able to decide whether the

33 D

34 Lectures on Human and Animal Psychology

sensation had increased in the same proportion as the stimulus.
A result which we could only have attained to with difficulty,
if we had tried to alternate between large sensation-differences,
comes out of itself if we gradually increase the stimuli in such
a way as to pass invariably from one just noticeable sensation-
difference to another. By how much any one sensation exceeds
any other is just as difficult to determine from their immediate
comparison as it would be to say how many more grains of
wheat there are in one heap than in a second. If we want to
know that, we must just set to work and count every single
grain. And, similarly, if we wish to learn how much more
intense a second sensation is than a first, our best method will
be to analyse the sensations into those elements which are the
equivalents of just noticeable differences.

It is true that in following this method we can never compare
more than one sensation with another. But if we have once
established a sensation-unit, we can easily determine by com-
parison with it the magnitude of any other sensation whatever.
Let us assume that we have adopted, as the unit of cutaneous
pressure-sensibility, the sensation occasioned by the pressure of
I gramme. We have found that the relation in which sensa-
tion increases with increase of stimulus is expressed in the case
of pressure-sensations by the fraction ^ ; i.e., the external
pressure must increase by ^ of its intensity, if it is to produce
a just noticeable increase of the pressure-sensation. We can,
therefore, just distinguish i-^- grammes from I gramme ; while
we can only distinguish 2\ from 2, or 3|, i.e., 4 grammes
from 3, etc. Now if we regard all equally noticeable sensation-
increments as equal magnitudes, then obviously the magnitude
of the just noticeable sensation-increase occasioned by the
pressure of I gramme is equal to the just noticeable increase
of the sensation occasioned, e.g., by a pressure of 10 grammes.
So that we may think of any increase of a sensation of whatever
intensity as being entirely made up of a number more or less
of just noticeable sensation-increments. We may assume that
these begin at the point where the external stimulus just suffices
to excite a sensation. Now, then, we are in a position to give
quantitative expression to sensation-intensity, however great or
small this may be. One sensation is twice, three times, or four

Estimation of the Intensity of Sensation 35

times as intensive as another, when it is made up of twice, three
times or four times as great a number of equal sensation-in-
crements. This system of measurement presupposes that we
follow up sensation in its gradual increase. But that is the
case, strictly speaking, in all measurement. All the measures
which we possess consist of a series of measurement-units.
The unit which we have chosen for sensation is the just notice-
able increment. If a sensation is made up of four times as
many units as another, then it is four times as great as that
other ; just as a scale on which four inches are marked is four
times as long as one which measures only one inch. If we
merely estimated the relation of the two scales as regards length,
our comparison would perhaps not be very accurate. An exact
judgment is only possible by the application to each of the
same measurement-unit. And it is precisely similar with sensa-
tion.

The method of measuring sensations of various intensities by
the addition of just noticeable differences would, however, be
very cumbrous. We can plainly reach our end very much
more quickly so soon as we have learned the law according to
which sensation-increase is correlated with increase of stimulus.
Having formulated such a law, we could predict that exactly
so great an increase of stimulus would condition so great an
increase of sensation.

As a matter of fact, we possess a law of this kind. Weber's
law tells us that a stimulus must always increase in a like ratio,
if the corresponding increase of sensation is to be equally
noticeable. So that, for practical purposes, any question of
sensation-measurement may now be put in the form : by how
many units, or by how many equally noticeable magnitudes
will, on Weber's law, a given sensation be increased, if we
increase the stimulus by a definite number of its units ? Or
conversely : how great must a given stimulus be made, in order
that the sensation may increase by a definite number of sensa-
tion units ? Let us take pressure-sensations once more, for
purposes of illustration. You will remember that the sensation
occasioned by I gramme must be intensified by - gramme for
it to increase by I unit. Suppose now that we wished to learn
how much the pressure must be intensified for the sensation to

36 Lectures on Human and Animal Psychology

FIG. 3.

increase by 6 such units. We imagine
the sensation-units arranged upon a scale.
At the zero-point of this scale, which we
will place for the moment arbitrarily at a
stimulus of I gramme, we draw a perpendi-
cular of any length to represent the gramme.
In order now to represent the magnitude of
pressure for a sensation increased by I unit,
we must lengthen the perpendicular at I
by of the perpendicular at o.

Similarly at 2, we must lengthen the perpendicular I by ;
at 3, the perpendicular 2 by ^, etc. Since the perpendiculars
constantly increase, these incremental parts will also of course
become larger ; we have to draw upon our scale lines of con-
tinually increasing length. And it is plain that the magnitude
of each of these lines stands to that of the perpendicular drawn
at zero in the same relation in which the weight, occasioning
the sensation-increase marked upon the scale, stands to the
initial weight of one gramme. The question being, what weight
has to be applied to produce a sensation-difference equal to 6
sensation-units, we have only now to measure how much longer
the perpendicular at 6 is than the perpendicular at o.

If we connect the upper ends of the perpendiculars drawn
upon our sensation-scale to represent stimulus-magnitudes, we
obtain a curved line ascending more steeply as we approach the
higher values of the scale. This curve obviously shows the de-
pendence of our measurement of sensation-intensities upon the
corresponding stimuli, not only for the points I, 2, 3, etc., but
also for all points situated between these, e.g., for 15, i \. If we
wish to discover what intensity of stimulus corresponds to some
particular point lying between two unit values, we need only
connect the point in question by a perpendicular with the curve
representing the alteration of stimulus. The magnitude of the
required stimulus is represented by the length of this perpen-
dicular. The sensation-difference which corresponds to a point
on the scale lying in this way between two unit values is, of
course, not perceptible by us ; but it would be quite wrong to
infer from this that it has no existence whatsoever. For we can
only reach perceptible differences by heaping up, as it were, a

Estimation of the Intensity of Sensation 37

great number of imperceptible differences. It is mere chance
that the just noticeable sensation-differences in our illustration
fall exactly at the points I, 2, 3. If we were to take as our
initial weight or f gramme instead of I gramme, the whole
scale would be shifted to the left, and the points where the
numerals now stand would then fall between two numerals of
this second scale. But the law of the variation of sensation-
with stimulus-intensity would remain precisely as before. Our
measurement on any scale is discrete, but the scale itself is con-
tinuous. We cannot, you see, proceed from one weight to
another so as to pass through all possible intermediate weights ;
but we interpolate between 2 grammes ^ T ^, 10 * 00> or perhaps
even a 6 ^ - of a gramme, if we wish to be exceedingly accurate
in weighing. But no one would maintain that a weight of less
than 10 ooo of a gramme is no weight at all. And just as there
are differences of weight, which no balances can detect, so there
are differences of sensation, which we are unable to cognise.

Now there can be no doubt that the scale which we have been
using to measure sensations, is not one particularly suited to its
purpose. We started out from the simplest possible stimulus-
magnitude, from the pressure of I gramme, our unit of weight.
We made the zero-point of our scale correspond to this point,
and proceeded to fill in our sensation-units to the right of it.
But when we have done this, we have not put ourselves in a
position to determine anything more than by how much we must
increase the weight of a gramme in order to obtain a definite
increase of sensation-units ; or how many sensation-units have
been added to the pressure sensation of one gramme, when we
are being stimulated by a weight of definitely greater magni-
tude. We do not know in the least how great the sensation is
which is occasioned by I gramme ; i.e., how many sensation-
units are to be reckoned to the left of the zero point on one
scale. The way to determine this is obviously to set out, not
from a definite stimulus-unit, but from the unit of sensation ;
and to measure onwards in terms of this, from the point where
sensation begins. If, then, we wish our scale to be a natural one,
we shall take the point at which sensation begins for our zero-
point. But this is not at the same time the zero-point of
stimulus. Some stimuli are so weak that they are not sensed at

38 Lectitres on Human and Animal Psychology

all. In order to occasion a sensation, the stimulus must have
attained a definite magnitude, which in each case is determined
by the character of the sense organ. The case here is similar
to that of sensation-differences. These are only perceived if
the stimulus-differences are of a certain intensity. In the same
way sensations in general are only perceived when the stimulus
has attained a certain magnitude. It might, perhaps, be sup-
posed that the two cases are not only similar, but identical
that the intensity of the stimulus necessary to produce a sensa-
tion at all is equal to the intensity of stimulus-difference which
gives rise to a just noticeable difference of sensation. But it
may be easily seen that this is impossible. The intensity of a
stimulus-difference is always directly dependent on the total
stimulus-intensity, and decreases with decrease of the latter. So
that if the stimulus becomes infinitely small, we should be forced
to assume that the stimulus-difference must also become infinite-
ly small. That however is contradicted by experience, which
shows us that every stimulus must have attained a definite
measurable magnitude, if it is to produce a sensation.

If, therefore, we follow our former method, and erect per-
pendiculars to express the stimuli which correspond to the
series of sensations, we must draw at the zero-point a line whose
length represents the magnitude of the stimulus which occasions
a just noticeable sensation. If we keep to our sensations of
pressure, and find that -^ of a gramme is the magnitude of
weight sufficient to excite a just noticeable pressure-sensation,,
we shall represent this weight by a perpendicular at the zero
point. At i, which is removed from o by a just noticeable differ-
ence, the vertical representing the stimulus will, in accordance
with the dependency of sensation upon stimulus, be -^ longer ;
i.e., the stimulus whose original magnitude was -$ or yf^ will
here be yj^-, etc. In short, we obtain the same relative increase
of stimulus and sensation that we had upon our former scale
(Fig. 3), the only difference being, that the new vertical at O
now stands for -^ of a gramme, and not for I gramme.

To answer all the questions that come up in any sense-depart-
ment, then, two measurements are in general sufficient ; first, the
measurement of the constant relation in which sensation-intensity
varies with variations in the intensity of the stimulus ; and

The Law of Sensation-intensities 39

secondly, the measurement of the just noticeable sensation.
The first measurement enables us to divide up the sensation-
scale ; by calling in the aid of stimuli we can mark it off into
equal parts. The second measurement gives us its zero-point,
and thus renders the scale ready for practical use. If we have
found in the sphere of pressure-sensations that the constant ratio
is ^, and that the just noticeable sensation is produced by -^
gramme, we can dispense with all further measurement, and
solve any problem presented to us. Suppose that we wish to
know the intensity of a sensation excited by the pressure of I
gramme. We take our scale, and begin with the zero-point.
The pressure at o is -^ gramme ; the pressure at I is ^ greater ;
the pressure at 2 is greater than it was at I, etc. We proceed
in this way till we come to a pressure of I gramme, and then
count up how many units of our sensation scale have been em-
ployed up to that point. We shall find that we have used nearly
14 units ; so that if we press upon the skin first with $, and
then with I gramme, we have passed over 14 just noticeable
differences. And the nearer we come to I gramme, the greater
are the pressure-differences to which the just noticeable differ-
ences correspond. The first unit corresponds to of the original
stimulus, or -j^- gramme. If the sensation increased directly as
the stimulus, our 14 units would correspond to an increase of 4-|
or not quite gramme ; while, as a matter of fact, they require
an increase of pressure of $, or almost a whole gramme.

II

This method of determining the intensity of sensation by pro-
ceeding gradually from weak to strong stimuli through just
noticeable differences would, however, be exceedingly tedious
in practice. Direct observation would possess over it the advan-
tage of greater brevity. The question, therefore, suggests itself,
whether we cannot discover some shorter method, which would
permit us to pass at one step from -^ to I gramme, instead of
using, as we did above, no less than 14 intermediate stages.
This question may be answered in the affirmative, as a some-
what closer consideration of the dependency existing between
sensation and stimulus will convince us.

Sensations and stimuli are interdependent magnitudes. Both

4O Lectures on Human and Animal Psychology

are capable of numerical expression. The numerical values
which stand for sensations increase with the increase of the
numerical values of stimulus. The simplest relation in such a
case would plainly be this : that corresponding to the stimuli
expressible by the numbers I, 2, 3, etc., there existed sensations
which were also expressible by those numbers. We should then
say that sensation-intensity is directly proportional to intensity
of stimulus. This simple relation, however, does not hold ;
stimuli increase far more rapidly than sensations. Now there
are, of course, countless forms of the relations of dependency
existing between numerical values, where one numerical series
increases faster than the other. If, for instance, we multiply
every number by itself, we obtain from the series, I, 2, 3, 4
. . . another series, I, 4, 9, 16. . . . The first numbers
are known as the square roots of the second ; the latter are
called the squares, or second powers, of the first. So that if these
two series expressed the relation of stimulus and sensation, we
should say the sensation is equal to the square root of the
stimulus. A similar numerical series, differing from this only
by its more rapid increase, can be obtained by multiplying each
number by itself twice or three times, and so obtaining its third
or fourth power. If either of these series expressed the rate of
stimulus increase, we should say that the sensation is equal to
the third or fourth root of the stimulus. But sensation-intensity
increases neither as the square root, nor the cube root, nor as
any other root of the stimulus-intensity. This is plain from the
fact that the stimulus-increments which condition definite in-
creases of sensation-intensity stand in a constant ratio to the
total stimulus-magnitude. Since, therefore, the relative stimulus-
increments always remain equal, the relative numerical incre-
ments in the series of numbers representing the stimuli must
also be constant. This is not the case in the series cited. In
the series, I, 4, 9, 16 . . . e. g., the numerical increments
are successively 3, 5, 7, and the numbers to which these incre-
ments are referable, I, 4, 9 ; but the ratios -f-, -|, f-, are not equal.
If this case actually corresponded to the sensation-law, we must
have obtained the fractions, -f-, |-, ^, etc., or others which gave a
constant result when the division was made. But neither the
second nor the third nor any other powers give such a series.

The Law of Sensation-intensities 41

On the other hand, there is another numerical relation of very
general application which exactly corresponds to the relation
between stimulus and sensation.

If we cast a glance at an ordinary table of logarithms, we
notice that the numbers in it are entered in two columns ; one
contains the ordinary numbers, the other the logarithmic
numbers. We see at once that these latter increase more slowly
than do the ordinary numbers ; just as magnitudes of sensation
increase more slowly than magnitudes of stimulus. If the
number i, e.g., stands on the one side, we find o on the other, as
its logarithm. The logarithm of 10 is I, of 100 is 2, etc. Here
also, then, in the case of numbers and their logarithms, we have
two series which increase in very different ways. And if we
look more closely, we find that this similarity is more than
merely external. The logarithms of I, 10, 100, 1,000, are o, I,

2, 3. What is the relation of the increase of those numbers to
their magnitude ? When i is increased to 10, 9 is added ; when
10 is increased to 100, 90 ; when 100 to 1,000, 900. The ratios
of this increase are, therefore, -f-, -f-^, -f^-. But these ratios are
all equal, i.e., all equal to 9. Now this is an expression of the
law which regulates the increase of sensation. Sensations in-
crease by equal magnitudes, when the increase of stimuli is such
that each increment stands in a constant relation to the particular
total stimulus-magnitude ; and the logarithms increase by equal
magnitudes, when the increase of their numbers is such that
each increment stands always in the same ratio to the corre-
sponding numerical magnitude. So that we can say that sensa-
tions increase as logarithms when stimuli increase as their
numbers ; or, still more shortly since we may express any
stimulus-magnitude by some definite number sensation increases
as the logarithm of stimulus.

Logarithmic tables were naturally in use long before psycho-
logy felt the necessity of them. Indeed, the expression of the
dependency of sensation upon stimulus is merely that of a very
simple relation, of frequent occurrence in the expression of the
dependency of magnitudes in general. The logarithms o, 1,2,

3, e.g., differ each from its neighbour by the same amount, I ;
while the corresponding numbers I, 10, IOO, I,OOO, differ from
one another by the same multiple : i.e., by ten times their value

42 Lectures on Hitman and Animal Psychology

in each instance. But if this were the only rule we possessed
for finding logarithms, the process would be exceedingly tedious.
The matter is happily very much simpler. If we raise a number
to all its possible powers, we get from it, of course, other
numbers. Thus io l =io; io 2 =ioo; io 3 =i,ooo. It is clear
that by thus raising the powers of a single number we can
obtain any number whatsoever. For if we take the ij, i|-, i^
powers of 10, they give us numbers lying between 10 and 100 ;
the powers 2j, 2^-, 2\, give numbers between loo and 1,000.
And if we take all the possible fractional powers, we shall obtain
all the possible numbers between 10 and 100, between 100 and
1,000, etc. In order to obtain also the numbers which are
smaller than 10, we must not multiply the number 10, but
divide it so many times by itself. We must raise it, as the
mathematicians say, to negative powers. Thus io- 1 -j^; io- 2
= -j-^j-, etc. But between io 1 and io- 1 stands 10 or io 1 - 1 : i.e., I.
If we take as well the intermediate fractions of these negative
powers, there result all the possible fractional numbers ; while
between the powers o and I come all the numbers between I
and io. We have, therefore, obtained every possible number
simply by raising the single number io to all its powers. Now,
if we compare the powers o, I, 2, 3, with the corresponding
numbers I, io, IOO, 1,000, we see that the latter stand to one
another in the same ratio as the logarithms to their numbers.
The former increase by equal increments, when the numbers
resulting from the involution increase by equal multiples. The
indices of the powers are therefore nothing but the logarithms
of the numbers which we obtain by the process of involution.
And we can now formulate the sensation-law as follows : sensa-
tions stand to their stimuli as the indices to the numbers arising
from involution.

HI

But now a certain doubt may arise with regard to this
paralleling of indices and logarithms with sensations. There
are negative indices, as we have seen ; and, consequently>
negative logarithms. If we divide the number IO by itself once,
twice, three times, and four times, we obtain the powers
O, -i, -2, -3, or the logarithms o, -I, -2, -3. The number of these

Significance of Negative Sensation-values 43,

negative logarithms is just as unlimited as the number of the
positive. This will be perfectly intelligible when we remember
that the negative powers and logarithms signify fractions. If we
continue the series io-\ io- 2 , io- 3 , or ^ y^-, y^-V^ we reach
successively smaller and smaller fractions. Just as the series of
whole numbers only terminates at infinity, so with the series of
fractional numbers. If, then, we wish to reach zero by the
method which we have described, it will be necessary to divide
io by itself an infinite number of times. Thus the logarithm
corresponding to zero is negative, and infinitely large. But is
all this applicable to sensations ? Are sensations ever negative ?
And can there be sensations which, besides being negative, are
also infinite ?

When we speak of negative sensations, we ordinarily under-
stand by the term sensations which are opposite in direction to-
other sensations which we call positive. Cold, e.g.> is a negative
sensation as opposed to hot. But it would be equally correct
to call cold positive, and thus to make hot a negative sensation.
The terms v positive ' and ' negative ' are, here as elsewhere, the
expression of an opposition. The negative is by no means
nothing : it is just as much a real magnitude as the positive ;
and the terms we apply are in themselves arbitrary. A shop-
keeper reckoning up his effects, counts everything which he has in
the till, or that others owe him, as positive ; his own debts he
regards as negative. If, on the other hand, he is estimating his
debts, he considers them as positive, and the contents of the till,
and his loans as negative. The result is the same in both cases.
Or if a geometrician wishes to distinguish directions in space, he-
names that direction negative which he does not name positive ;
which becomes which is quite immaterial. Just in the same way
we characterise the logarithms of fractions as negative because
we have already used the positive denomination for the
logarithms of whole numbers. We must guard ourselves against
supposing that we have here anything more than a mere con-
vention, even though this convention is the most natural and
obvious.

The question arises then whether we may not speak of
negative sensations, using the word in the above sense of simple
opposition. No one will hesitate to answer this question in the

-44 Lectures on Human and Animal Psychology

affirmative, if it can be once shown that such an opposition
exists among sensations. It is of course unnecessary to say that
oppositions like that of hot and cold do not concern us in the
present instance. Hot and cold are differences of sensation-
quality, about the nature of which we have here as little
to inquire as about the differences between agreeable and
disagreeable, pleasant and unpleasant. It is true that these
attributes are predicated of sensations of opposite character.
And if we were subjecting these to a special investigation, we
might not only justifiably, but very naturally, express the
antitheses of hot and cold, pleasurable and painful, by positive
and negative magnitudes. But our business in this first instance
ns only with the intensity of sensation ; and all other sensation-
iproperties are, therefore, excluded* from our consideration.

We found the natural zero-point of our scale to be the point
where sensation begins, where we first sense at all. Can there
be sensations which are not sensed ; or does the putting of that
-question involve a contradiction of terms ?

There certainly is a contradiction. But it is only an apparent
-one, due to an equivocal use of the word ' sense.' We have
-already seen that there exist sensation-differences which are
not sensed (p. 22). It is obvious that two different meanings
have been given to the word. In its first signification the sensa-
tion is simply something which depends upon an alteration of
stimulus, no matter whether we detect this alteration or not.
But, secondly, it is our discovery of such alteration, which is
denoted by sensation. And this is equally true for sensations
'taken absolutely. In speaking of sensations which are
too weak to be sensed we are regarding them as something
independent of our apprehension of them ; we are considering
them merely as conditioned by external stimuli. We can put
the matter in this way. A sensation-difference is not at all
identical with a sensed difference ; the latter implies a definite
intensity of the former. And a sensation may exist long before
it can be sensed. We only sense it when it reaches a definite
intensity. But though in this statement we recognise the
equivocation, we have not done away with it. The equivocation
is explained by the fact that when the word first appeared in
language the nai've consciousness which produced it knew only

Significance of Negative Sensation-values 45,

those sensations and sensation-differences which it was itself able
to recognise as such. Not till scientific reflection had arisen
was the human mind forced to the conclusion that there must
be sensations and sensation-differences- which it was inadequate
to recognise for the reason that sensations neither arise nor
alter abruptly, but only through continuous gradations.

So that there is nothing left for us but to use the word ' sensa-
tion ' here and in what follows to express all those sensations and
sensation-differences which we do- not perceive, but whose
existence we must assume to explain those which we do perceive,
as well as sensations in the narrower sense of processes which we
are able clearly to apprehend. Where it becomes necessary to
make a distinction we will call sensations and sensation-differ-
ences of the latter class ' noticeable/ and of the former ' unnotice-
able.' Now, since we observe that a sensation must have attained
a certain magnitude if it is to become noticeable, and that, other
things being equal, it gains in intensity the greater its magnitude
becomes, we are surely justified in- taking as the zero-point of
our sensation-scale the point where sensation becomes just
noticeable. That settled, we shall naturally call the noticeable
sensations, to the right of that point, positive; the unnoticeable
sensations, to the left of it, negative. For noticeable and
unnoticeable denote a direct antithesis, as valid as that of cold
and hot, or of opposing directions in space.

We conclude, therefore, that our comparison of the relation
in which sensation stands to stimulus with the relation of
logarithms to their numbers holds with regard to this further
point of the opposition between positive and negative. And
we can now produce our scale beyond the zero-point in a nega-
tive direction until the stimulus vanishes, as has been done in
Fig. 4. And now at length we have our sensation-law in its

most general form. How many
units must we enter on the
negative side to the left of o-
before we reach the zero-point
of the stimulus? The stimu-
lus zero-point in this connec-
tion is not, of course, the ex-
ternal process of movement

46 Lectitres on Human and Animal Psychology

affecting our sense-organs, and which has just attained the
lower limit of efficiency, but the internal stimulus in the brain
resulting from the former, and paralleled as physical process with
the mental process of sensation. For it may be assumed that
there are external stimuli too weak to reach the brain, whether
because of their inability to affect the organ of sense, or because
they cannot be conducted from it to the brain. This assumed,
where will the line which expresses the increase of stimulus
with increase of sensation cut the sensation-scale? We can
obviously extend our negative sensation-units to infinity with-
out arriving at that point ; for if we suppose, e.g., that the
stimulus decreases by ^ of its magnitude at each division of the
scale, it yet decreases more and more slowly ; and though at
last it becomes exceedingly small, it does not disappear so long
as the negative sensation-units which we are positing are ex-
pressible in numbers. Only when these numbers become
infinite may we assume that the corresponding stimulus-magni-
tudes are also infinitely small, i.e., so small that we may without
hesitation regard them as zero. Once more, then, we have the
same relation as that of logarithms to their numbers. If we
extend further and further the fractional series -fa, ^ s , 10 1 00 , we
do not come upon any fraction, however small, which is not
greater than O. We should only reach o at infinity; and, there-
fore, the negative logarithm corresponding to it is infinitely
large. In the same way, we may conceive of a stimulus as
divided and subdivided as long as we please, and nevertheless
the smallest particle of it would still be a stimulus. The
stimulus only becomes equal to zero at infinity, and the nega-
tive sensation corresponding to a stimulus equal to zero must,
therefore, be infinitely great ; and since a negative sensation
means the same thing as an unnoticeable sensation, an in-
finitely great negative sensation will simply be that sensation
which is less noticeable than any other, just as it may be
asserted of o and oo that the first is smaller and the latter
larger than any other number.

Our analogy between the logarithmic law and the law of
sensation is now incomplete in one point only. We saw that
all possible numbers can be obtained by raising a single num-
ber to all its possible powers The positive powers give us the

Units of Stimulus and Sensation 47

whole numbers ; the negative, the fractions ; and the zero
power gives us unity. All these facts we have found to possess
a definite significance in the case of sensation. But we have
left one point still undetermined ; that is the number whose
involution gives us all the other numbers that are possible. In
the instance which we took, we raised the number 10 to the
powers o, I, 2, 3, and obtained the series I, 10, 100, 1,000. Had
we taken some other number than 10 and raised it to those
powers, we should have obtained a different series. It is im-
portant, therefore, to know what number it is which has been
chosen as the base by whose involution the other numbers are
expressed.

It is obvious that this must also be an important question for
the sensation-law, since sensations stand to stimuli as their in-
dices to the numbers obtained by involution ; and it is evident
that we can only say what stimulus-magnitudes correspond to
the sensations j, 2, 3, if we know what definite number was
taken as the base in this case of involution. Our choice of that
number is entirely arbitrary. For our sensation-scale it is im-
material ; it conditions only the divisions of the scale. We
shall plainly have the most convenient division if it is so carried
out that magnitudes of sensation may be calculated directly
from magnitudes of stimulus, and vice versd. But this is possible
only when sensation is the simple logarithm of stimulus, and
not some multiple or fraction of this logarithm ; and this
depends entirely on the absolute magnitude of our unit of
stimulus and our unit of sensation. Both of these magnitudes
may be arbitrarily chosen when we have once made it clear to our-
selves what they mean. We have already seen that the stimulus
must be taken as equal to I where the sensation is equal to o
i.e., is just noticeable, for i, 10, 100, are all equal to I ; or, in
other words, the logarithm of I is always o. That determines
once for all the magnitude of the stimulus-unit. Now, if the
sensation I is also to come at the point where its stimulus is the
number corresponding to the logarithm I, we must mark it (lO
being, e.g., the base employed) at the point where the stimulus
has attained the magnitude 10. Had 100 been the basal number,
we must have placed I where the stimulus had the magnitude
100, and so on. For io l =iO, IOO 1 IOO, and every number

48 Lectures on Hitman and Animal Psychology

raised to the first power is equal to itself. Further, if we mark-
in more of our sensation-units, the divisions 2, 3, 4, take their
necessary places where the stimulus-magnitudes are 100, i,ooo r
10,000, etc. For io 2 =ioo; io 3 = 1,000; io*= 10,000. This is
all required by our law, as we have seen, if the stimulus 10
corresponds to the sensation i ; so that now we have also de-
termined our sensation-unit. It is equal to the number which
we have chosen as base. Under these conditions, when the
stimulus is represented by the number obtained by involution,
the sensation corresponds to the index ; or the sensation is
equal to the logarithm of the stimulus.

In our ordinary logarithmic tables 10 is the base by whose
involution all the numbers are obtained. So that, if we wish to
calculate sensations from stimuli, we have only to call that
sensation I which is occasioned by a stimulus-magnitude ten
times as great as that which lies at the limit of noticeability.
Having done this, it is only necessary, when a particular
stimulus-intensity is given, to look up in the logarithmic tables
the number which expresses that intensity ; the logarithm in
the next column gives at once the magnitude of sensation. To
return to our previous example, if a weight of -^ gramme pro-
duces a just noticeable sensation, we call -^ gramme stimulus
I. Pressure by ten times this stimulus, i.e., by gramme, we
call sensation I. Now it is easy to determine at what weight
the sensation is any whole or fractional number of times
greater, or by how much the weight must be increased in order
to condition a particular increase of sensation. If we wish to
get a sensation 2.\ times as intense as sensation I, we refer to
our table, and find for the logarithm 2'5 the number 316. That
means 316 stimulus-units, or V?r 6 =6'3 grammes. Or if the
problem is to determine how great the sensation is which is
occasioned by a stimulus of 5,000 units (100 grammes), we look
up the number 5,000, and find its logarithm, 3*698. That is, a
pressure of 100 grammes produces a sensation which is 3-698
times as great in intensity as the sensation arising from the
pressure of ^ of a gramme.

We have now completely answered the question which was
before us. Not only have we discovered the law of the de-
pendency of sensation upon stimulus, but we have indicated

Significance of Negative Sensation-values 49

the method by which the intensity either of sensation or of
stimulus can be calculated when the intensity of its correlate is
given. This method is simplicity itself, for it presupposes no
more knowledge than that of the multiplication-table and no
more apparatus than a book of logarithms.

LECTURE IV

I. THE JUST NOTICEABLE SENSATION. 11. UPPER AND LOWER LIMIT
OF WEBER'S LAW. III. PSYCHOLOGICAL INTERPRETATION OF THE
LAW.

1

FOR the solution of all the problems which may arise in
any definite sense-department, there are required, as we
have seen, two kinds of measurement. First, we must
know the constant relation in which alteration of sensation-
intensity stands to alteration of the intensity of stimulus ; and,
secondly, the magnitude of the just noticeable sensation must
be determined. The first of these measurements we have
carried out ; the second now remains to be performed.

Pressure-sensations afford us the simplest conditions for our
investigations. We lay upon that portion of the skin whose
sensibility is to be tested small weights, preferably of cork or
pith, and seek to ascertain what magnitude of weight is
necessary for the production of a just noticeable sensation.
Observations made in this way have shown that the sensibility
of the skin at different parts of its surface is very far from being
uniform. The most sensitive portions are the forehead, temples,
eyelids, the outer surface of the fore-arm, and the back of the
hand. We can usually sense on these parts weights of only
.g-i-3- gramme. Less sensitive are the inside of the fore-arm, the
cheeks, and the nose, and very much less sensitive than these
the palm of the hand, the abdomen, and the thigh. Here the
sensibility sinks to about -fa gramme. On some specially
protected parts, e.g., the nails and the heel, the just noticeable
weight rises as high as a whole gramme.

Far more adequate for the apprehension of weak stimuli is
our organ of hearing. A mere touch of the external auditory

The Just Noticeable Sensation 51

meatus or any contact with the tympanic membrane excites, as
we all know, a fairly strong sound-sensation. And even a distant
sound must be very weak indeed to be imperceptible. In
making observations for the determination of the limit of
auditory sensibility, we must, of course, never forget to take
into account all the conditions upon which the intensity is
dependent. If, e.g., we measure the sensibility of an ear by the
sound produced by a falling weight, we must know, not only
the magnitude and material of the weight, but also the material
of the body upon which it falls. And we must, further, de-
termine the rapidity of its fall and the distance of our ear from
the place where the sound is produced. It has been discovered
that a normally sensitive ear can just sense the sound made by
a cork pellet, weighing I milligramme, in falling through a
height of i millimetre, at a distance of 91 millimetres. That
we may expect to find considerable difference in different
individuals is a matter of course, justified by our everyday
experience. Diseases of the sense-organ affect our hearing ;
and, in addition to this, as old age draws on, the acuteness of
this sense usually declines, passing through the most various
stages from hardness of hearing to complete deafness one
of the commonest defects of sense.

If we are to use the sound-magnitude which we have just
determined as a unit of stimulus, we must be able to compare
with it the intensity of all other sounds which are employed as
stimuli. The comparison is not difficult. Given the sound
whose intensity is to be measured, we need only to remove it
to the distance at which it just disappears. It is then precisely
as great as the sound made by a cork weighing I milligramme,
falling through a height of I millimetre upon a sheet of glass,
at a dista