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Title: Harvard Psychological Studies, Volume 1 - Containing Sixteen Experimental Investigations from the Harvard Psychological Laboratory.
Author: Various
Language: English
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                          THE
                   Psychological Review


                    _EDITED BY_


  J. McKEEN CATTELL     and    J. MARK BALDWIN
  COLUMBIA UNIVERSITY          PRINCETON UNIVERSITY


              _WITH THE CO-OPERATION OF_

       ALFRED BINET, ÉCOLE DES HAUTES-ÉTUDES, PARIS;
       JOHN DEWEY, H.H. DONALDSON, UNIVERSITY OF CHICAGO;
       G.S. FULLERTON, UNIVERSITY OF PENNSYLVANIA;
       G.H. HOWISON, UNIVERSITY OF CALIFORNIA;
       JOSEPH JASTROW, UNIVERSITY OF WISCONSIN;
       G.T. LADD, YALE UNIVERSITY;
       HUGO MÜNSTERBERG, HARVARD UNIVERSITY;
       M. ALLEN STARR, COLLEGE OF PHYSICIANS AND SURGEONS, NEW YORK;
       CARL STUMPF, UNIVERSITY, BERLIN;
       JAMES SULLY, UNIVERSITY COLLEGE, LONDON.

H.C. WARREN, PRINCETON UNIVERSITY, _Associate Editor and Business Manager_.

         *       *       *       *       *



              Series of Monograph Supplements,
         Vol. IV., No. 1 (Whole No. 17), January, 1903.

              HARVARD PSYCHOLOGICAL STUDIES,

                       Volume I
                      CONTAINING

           Sixteen Experimental Investigations from the
               Harvard Psychological Laboratory.

                      EDITED BY
                 HUGO MÜNSTERBERG.


               PUBLISHED BI-MONTHLY BY
                THE MACMILLAN COMPANY,
             41 N. QUEEN ST., LANCASTER, PA.
               66 FIFTH AVENUE, NEW YORK.

  AGENT: G.E. STECHERT, LONDON (2 Star Yard, Cary St., W.C.)
  Leipzig (Hospital St., 10); PARIS (76 rue de Rennes).



                      PRESS OF
              THE NEW ERA PRINTING COMPANY
                    LANCASTER, PA.

       *       *       *       *       *



PREFACE.


The appearance of the HARVARD PSYCHOLOGICAL STUDIES does not indicate
an internal change in the work of the Harvard Psychological
Laboratory. But while up to this time the results of our
investigations have been scattered in various places, and have often
remained unpublished through lack of space, henceforth, we hope to
have in these STUDIES the opportunity to publish the researches of the
Harvard Laboratory more fully and in one place. Only contributions
from members of the Harvard Psychological Laboratory will be printed
in these volumes, which will appear at irregular intervals, and the
contributions will represent only our experimental work;
non-experimental papers will form an exception, as with the present
volume, wherein only the last one of the sixteen papers belongs to
theoretical psychology.

This first volume does not give account of all sides of our laboratory
work. An essential part of the investigations every year has been the
study of the active processes, such as attention, apperception, and
volition. During the last year several papers from these fields have
been completed, but we were unable to include them in this volume on
account of the space limits; they are kept back for the second volume,
in which accordingly the essays on the active functions will prevail,
as those on perception, memory, and feeling prevail in this volume. It
is thus clear that we aim to extend our experimental work over the
whole field of psychology and to avoid one-sideness. Nevertheless
there is no absence of unity in our work; it is not scattered work as
might appear at a first glance; for while the choice of subjects is
always made with relation to the special interests of the students,
there is after all one central interest which unifies the work and has
influenced the development of the whole laboratory during the years of
my direction.

I have always believed--a view I have fully discussed in my 'Grundzüge
der Psychologie'--that of the two great contending theories of modern
psychology, neither the association theory nor the apperception theory
is a satisfactory expression of facts, and that a synthesis of both
which combines the advantages without the defects of either can be
attained as soon as a psychophysical theory is developed which shall
consider the central process in its dependence, not only upon the
sensory, but also upon the motor excitement. This I call the _action
theory_. In the service of this theory it is essential to study more
fully the rôle of the centrifugal processes in mental life, and,
although perhaps no single paper of this first volume appears to offer
a direct discussion of this motor problem, it was my interest in this
most general question which controlled the selection of all the
particular problems.

This relation to the central problem of the rôle of centrifugal
processes involves hardly any limitation as to the subject matter;
plenty of problems offer themselves in almost every chapter of
psychology, since no mental function is without relation to the
centrifugal actions. Yet, it is unavoidable that certain groups of
questions should predominate for a while. This volume indicates, for
instance, that the æsthetic processes have attracted our attention in
an especially high degree. But even if we abstract from their
important relation to the motor functions, we have good reasons for
turning to them, as the æsthetic feelings are of all feeling processes
decidedly those which can be produced in the laboratory most purely;
their disinterested character makes them more satisfactory for
experimental study than any other feelings.

Another group of researches which predominates in our laboratory is
that on comparative psychology. Three rooms of the laboratory are
reserved for psychological experiments on animals, under the special
charge of Dr. Yerkes. The work is strictly psychological, not
vivisectional; and it is our special purpose to bring animal
psychology more in contact with those methods which have found their
development in the laboratories for human psychology. The use of the
reaction-time method for the study of the frog, as described in the
fifteenth paper, may stand as a typical illustration of our aim.

All the work of this volume has been done by well-trained
post-graduate students, and, above all, such advanced students were
not only the experimenters but also the only subjects. It is the rule
of the laboratory that everyone who carries on a special research has
to be a subject in several other investigations. The reporting
experimenters take the responsibility for the theoretical views which
they express. While I have proposed the subjects and methods for all
the investigations, and while I can take the responsibility for the
experiments which were carried on under my daily supervision, I have
left fullest freedom to the authors in the expression of their views.
My own views and my own conclusions from the experiments would not
seldom be in contradiction with theirs, as the authors are sometimes
also in contradiction with one another; but while I, of course, have
taken part in frequent discussions during the work, in the completed
papers my rôle has been merely that of editor, and I have nowhere
added further comments.

In this work of editing I am under great obligation to Dr. Holt, the
assistant of the laboratory, for his helpful coöperation.

       *       *       *       *       *



CONTENTS.


Preface: Hugo Münsterberg ......................................   i

STUDIES IN PERCEPTION.

  Eye-Movement and Central Anæsthesia: Edwin B. Holt ...........   3
  Tactual Illusions: Charles H. Rieber .........................  47
  Tactual Time Estimation: Knight Dunlap ....................... 101
  Perception of Number through Touch: J. Franklin Messenger .... 123
  The Subjective Horizon: Robert MacDougall .................... 145
  The Illusion of Resolution-Stripes on the Color-Wheel:
    Edwin B. Holt .............................................. 167

STUDIES IN MEMORY.

  Recall of Words, Objects and Movements: Harvey A. Peterson ... 207
  Mutual Inhibition of Memory Images: Frederick Meakin ......... 235
  Control of the Memory Image: Charles S. Moore ................ 277

STUDIES IN ÆSTHETIC PROCESSES.

  The Structure of Simple Rhythm Forms: Robert MacDougall ...... 309
  Rhythm and Rhyme: R.H. Stetson ............................... 413
  Studies in Symmetry: Ethel D. Puffer ......................... 467
  The Æsthetics of Unequal Division: Rosewell Parker Angier .... 541

STUDIES IN ANIMAL PSYCHOLOGY.

  Habit Formation in the Crawfish, Camburus affinis: Robert
    M. Yerkes and Gurry E. Huggins ............................. 565
  The Instincts, Habits and Reactions of the Frog: Robert
    Mearns Yerkes .............................................. 579

STUDIES IN PSYCHOLOGICAL THEORY.

  The Position of Psychology in the System of Knowledge:
    Hugo Münsterberg ........................................... 641



PLATES.

                                                       OPPOSITE PAGE
Plate  I .......................................................  20
  "   II .......................................................  24
  "  III .......................................................  28
  "   IV .......................................................  34
  "    V ....................................................... 190
  "   VI ....................................................... 198
  "  VII ....................................................... 200
  " VIII ....................................................... 314
  "   IX ....................................................... 417
  "    X ....................................................... 436

Charts of the Sciences, at end of volume.

       *       *       *       *       *



            STUDIES IN PERCEPTION.



       *       *       *       *       *



EYE-MOVEMENT AND CENTRAL ANÆSTHESIA.

BY EDWIN B. HOLT.


I. THE PROBLEM OF ANÆSTHESIA DURING EYE-MOVEMENT.


A first suggestion of the possible presence of anæsthesia during
eye-movement is given by a very simple observation. All near objects
seen from a fairly rapidly moving car appear fused. No further
suggestion of their various contour is distinguishable than blurred
streaks of color arranged parallel, in a hazy stream which flows
rapidly past toward the rear of the train. Whereas if the eye is kept
constantly moving from object to object scarcely a suggestion of this
blurred appearance can be detected. The phenomenon is striking, since,
if the eye moves in the same direction as the train, it is certain
that the images on the retina succeed one another even more rapidly
than when the eye is at rest. A supposition which occurs to one at
once as a possible explanation is that perchance during eye-movement
the retinal stimulations do not affect consciousness.

On the other hand, if one fixates a fly which happens to be crawling
across the window-pane and follows its movements continuously, the
objects outside swim past as confusedly as ever, and the image of the
fly remains always distinct. Here the eye is moving, and it may be
rapidly, yet both the fly and the blurred landscape testify to a
thorough awareness of the retinal stimulations. There seems to be no
anæsthesia here. It may be, however, that the eye-movement which
follows a moving object is different from that which strikes out
independently across the visual field; and while in the former case
there is no anæsthesia, perhaps in the latter case there is
anæsthesia.

Cattell,[1] in considering a similar experience, gives his opinion
that not the absence of fusion for the moving eye, but its presence
for the resting eye, needs explanation. "More than a thousand
interruptions per second," he believes, "give a series of sharply
defined retinal processes." But as for the fusion of moving objects
seen when the eyes are at rest, Cattell says, "It is not necessary and
would probably be disadvantageous for us to see the separate phases."
Even where distinct vision would be 'disadvantageous' he half doubts
if fusion comes to the rescue, or if even the color-wheel ever
produces complete fusion. "I have never been able," he writes, "to
make gray in a color-wheel from red and green (with the necessary
correction of blue), but when it is as nearly gray as it can be got I
see both red and green with an appearance of translucence."

   [1] Cattell, J. McK., PSYCHOLOGICAL REVIEW, 1900, VII., p. 325.

That the retina can hold apart more than one thousand stimulations per
second, that there is, in fact, no such thing as fusion, is a
supposition which is in such striking contrast to all previous
explanations of optical phenomena, that it should be accepted only if
no other theory can do justice to them. It is hoped that the following
pages will show that the facts do not demand such a theory.

Another simple observation is interesting in this connection. If at
any time, except when the eyes are quite fresh, one closes one's eyes
and attends to the after-images, some will be found which are so faint
as to be just barely distinguishable from the idioretinal light. If
the attention is then fixed on one such after-image, and the eyes are
moved, the image will suddenly disappear and slowly emerge again after
the eyes have come to rest. This disappearance during eye-movements
can be observed also on after-images of considerable intensity; these,
however, flash back instantly into view, so that the observation is
somewhat more difficult. Exner,[2] in speaking of this phenomenon,
adds that in general "subjective visual phenomena whose origin lies in
the retina, as for instance after-images, Purkinje's vessel-figure,
or the phenomena of circulation under discussion, are almost
exclusively to be seen when the eye is rigidly fixed on a certain
spot: as soon as a movement of the eye is made, the subjective
phenomena disappear."

   [2] Exner, Sigmund, _Zeitschrift f. Psychologie u. Physiologie
   der Sinnesorgane_, 1890, I., S. 46.

The facts here mentioned in no wise contradict a phenomenon recently
discussed by McDougall,[3] wherein eye-movements revive sensations
which had already faded. Thus an eye-movement will bring back an
after-image which was no longer visible. This return to vividness
takes place after the movement has been completed, and there is no
contention that the image is seen just during the movement.

   [3] McDougall, W., _Mind_, N.S., X., 1901, p. 52.

The disappearance of after-images during eye-movements is mentioned by
Fick and Gürber,[4] who seek to explain the phenomenon by ascribing it
to a momentary period of recovery which the retina perhaps undergoes,
and which would for the moment prevent further stimulations from being
transmitted to the optic nerve. Exner observes that this explanation
would not, however, apply to the disappearance of the vessel-figure,
the circulation phenomenon, the foveal figure, the polarization-sheaf
of Haidinger, Maxwell's spot, or the ring of Löwe; for these phenomena
disappear in a similar manner during movement. Exner offers another
and a highly suggestive explanation. He says of the phenomenon (_op.
citat._, S. 47), "This is obviously related to the following fact,
that objective and subjective impressions are not to be distinguished
as such, so long as the eye is at rest, but that they are immediately
distinguished if an eye-movement is executed; for then the subjective
phenomena move with the eye, whereas the objective phenomena are not
displaced.... This neglect of the subjective phenomena is effected,
however, not by means of an act of will, but rather by some central
mechanism which, perhaps in the manner of a reflex inhibition,
withholds the stimulation in question from consciousness, without our
assistance and indeed without our knowledge." The suggestion of a
central mechanism which brings about a reflex inhibition is the
significant point.

   [4] Fick, Eug., and Gürber, A., _Berichte d. ophthalmologischen
   Gesellschaft in Heidelberg_, 1889.

It is furthermore worth noting that movements of the eyelid and
changes in the accommodation also cause the after-images to disappear
(Fick and Gürber), whereas artificial displacement of the eye, as by
means of pressure from the finger, does not interfere with the images
(Exner).

Another motive for suspecting anæsthesia during eye-movement is found
by Dodge,[5] in the fact that, "One may watch one's eyes as closely as
possible, even with the aid of a concave reflector, whether one looks
from one eye to the other, or from some more distant object to one's
own eyes, the eyes may be seen now in one position and now in another,
but never in motion." This phenomenon was described by Graefe,[6] who
believed it was to be explained in the same way as the illusion which
one experiences in a railway coach when another train is moving
parallel with the coach in which one sits, in the same direction and
at the same speed. The second train, of course, appears motionless.

   [5] Dodge, Raymond, PSYCHOLOGICAL REVIEW, 1900, VII., p. 456.

   [6] Graefe, A., _Archiv f. Ophthalmologie_, 1895, XLI., 3, S.
   136.

This explanation of Graefe is not to be admitted, however, since in
the case of eye-movement there are muscular sensations of one's own
activity, which are not present when one merely sits in a coach. These
sensations of eye-movement are in all cases so intimately connected
with our perception of the movement of objects, that they may not be
in this case simply neglected. The case of the eye trying to watch its
own movement in a mirror is more nearly comparable with the case in
which the eye follows the movement of some independent object, as a
race-horse or a shooting-star. In both cases the image remains on
virtually the same point of the retina, and in both cases muscular
sensations afford the knowledge that the eye is moving. The
shooting-star, however, is perceived to move, and the question
remains, why is not the eye in the mirror also seen to move?

F. Ostwald[7] refutes the explanation of Graefe from quite different
considerations, and gives one of his own, which depends on the
geometrical relations subsisting between the axes of vision of the
real eye and its reflected image. His explanation is too long to be
here considered, an undertaking which indeed the following
circumstance renders unnecessary. While it is true that the eye cannot
observe the full sweep of its own movement, yet nothing is easier than
to observe its movement through the very last part of the arc. If one
eye is closed, and the other is brought to within about six inches of
an ordinary mirror, and made to describe little movements from some
adjacent part of the mirror to its own reflected image, this image can
almost without exception be observed as just coming to rest. That is,
the very last part of the movement _can_ be seen. The explanation of
Ostwald can therefore not be correct, for according to it not alone
some parts of the movement, but absolutely all parts alike must remain
invisible. It still remains, therefore, to ask why the greater part of
the movement eludes observation. The correct explanation will account
not only for the impossibility of seeing the first part of the
movement but also for the possibility of seeing the remainder.

   [7] Ostwald, F., _Revue Scientifique_, 1896, 4e Série, V., p.
   466.

Apart from the experience of the eye watching itself in a glass, Dodge
(_loc. citat._) found another fact which strongly suggested
anæsthesia. In the course of some experiments on reading, conducted by
Erdmann and Dodge, the question came up, how "to explain the meaning
of those strangely rhythmic pauses of the eye in reading every page of
printed matter." It was demonstrated (_ibid._, p. 457) "that the
rhythmic pauses in reading are the moments of significant
stimulation.... If a simple letter or figure is placed between two
fixation-points so as to be irrecognizable from both, no eye-movement
is found to make it clear, which does not show a full stop between
them."

With these facts in view Dodge made an experiment to test the
hypothesis of anæsthesia. He proceeded as follows (_ibid._, p. 458):
"A disc of black cardboard thirteen inches in diameter, in which a
circle of one-eighth inch round holes, one half inch apart, had been
punched close to the periphery all around, was made to revolve at such
a velocity that, while the light from the holes fused to a bright
circle when the eye was at rest, when the eye moved in the direction
of the disc's rotation from one fixation point, seen through the fused
circle of light, to another one inch distant, three clear-cut round
holes were seen much brighter than the band of light out of which they
seemed to emerge. This was only possible when the velocity of the
holes was sufficient to keep their images at exactly the same spot on
the retina during the movement of the eye. The significant thing is
that the individual round spots of light thus seen were much more
intense than the fused line of light seen while the eyes were at rest.
Neither my assistant nor I was able to detect any difference in
brightness between them and the background when altogether
unobstructed." Dodge finds that this experiment 'disproves' the
hypothesis of anæsthesia.

If by 'anæsthesia' is meant a condition of the retinal end-organs in
which they should be momentarily indifferent to excitation by
light-waves, the hypothesis is indeed disproved, for obviously the
'three clear-cut round holes' which appeared as bright as the
unobstructed background were due to a summation of the light which
reached the retina during the movement, through three holes of the
disc, and which fell on the same three spots of the retina as long as
the disc and the eyeball were moving at the same angular rate. But
such a momentary anæsthesia of the retina itself would in any case,
from our knowledge of its physiological and chemical structure, be
utterly inconceivable.

On the other hand, there seems to be nothing in the experiment which
shows that the images of the three holes were present to consciousness
just during the movement, rather than immediately thereafter. A
central mechanism of inhibition, such as Exner mentions, might
condition a central anæsthesia during movement, although the
functioning of the retina should remain unaltered. Such a central
anæsthesia would just as well account for the phenomena which have
been enumerated. The three luminous images could be supposed to remain
unmodified for a finite interval as positive after-images, and as such
first to appear in consciousness. Inasmuch as 'the arc of eye
movements was 4.7°' only, the time would be too brief to make possible
any reliable judgment as to whether the three holes were seen during
or just after the eye-movement. With this point in view, the writer
repeated the experiment of Dodge, and found indeed nothing which gave
a hint as to the exact time when the images emerged in consciousness.
The results of Dodge were otherwise entirely confirmed.


II. THE PHENOMENON OF 'FALSELY LOCALIZED AFTER-IMAGES.'


A further fact suggestive of anæsthesia during movement comes from an
unexpected source. While walking in the street of an evening, if one
fixates for a moment some bright light and then quickly turns the eye
away, one will observe that a luminous streak seems to dart out from
the light and to shoot away in either of two directions, either in the
same direction as that in which the eye moved, or in just the
opposite. If the eye makes only a slight movement, say of 5°, the
streak jumps with the eye; but if the eye sweeps through a rather
large arc, say of 40°, the luminous streak darts away in the opposite
direction. In the latter case, moreover, a faint streak of light
appears later, lying in the direction of the eye-movement.

This phenomenon was probably first described by Mach, in 1886.[8] His
view is essentially as follows: It is clear that in whatever direction
the eye moves, away from its luminous fixation point, the streak
described on the retina by the luminous image will lie on the same
part of the retina as it would have lain on had the eye remained at
rest but the object moved in the opposite direction. Thus, if the eye
moves to the right, we should expect the streak to appear to dart to
the left. If, however, the streak has not faded by the time the eye
has come to rest on a new fixation point (by supposition to the right
of the old), we should expect the streak to be localized to the left
of this, that is, to the right of the former fixation-point. In order
to be projected, a retinal image has to be localized with reference to
some point, generally the fixation-point of the eyes; and it is
therefore clear that when two such fixation-points are involved, the
localization will be ambiguous if for any reason the central apparatus
does not clearly determine which shall be the point of reference. With
regard to the oppositely moving streak Mach says:[9] "The streak is,
of course, an after-image, which comes to consciousness only on, or
shortly before, the completion of the eye-movement, nevertheless with
positional values which correspond, remarkably enough, not to the
later but to the earlier position and innervation of the eyes." Mach
does not further attempt to explain the phenomenon.

   [8] Mach, Ernst, 'Beiträge zur Analyze der Empfindungen,' Jena,
   1886.

   [9] Mach, _op. citat._, 2te Aufl., Jena, 1900, S. 96.

It is brought up again by Lipps,[10] who assumes that the streak ought
to dart with the eyes and calls therefore the oppositely moving streak
the 'falsely localized image.' For sake of brevity we may call this
the 'false image.' The explanation of Lipps can be pieced together as
follows (_ibid._, S. 64): "The explanation presupposes that sensations
of eye-movements have nothing to do with the projection of retinal
impressions into the visual field, that is, with the perception of the
mutual relations as to direction and distance, of objects which are
viewed simultaneously.... Undoubtedly, however, sensations of
eye-movements, and of head-and body-movements as well, afford us a
scale for measuring the displacements which our entire visual field
and every point in it undergo within the surrounding _totality of
space_, which we conceive of as fixed. We estimate according to the
length of such movements, or at least we deduce therefrom, the
distance through fixed space which our view by virtue of these
movements has traversed.... They themselves are nothing for our
consciousness but a series of purely intensive states. But in
experience they can come to _indicate_ distance traversed." Now in
turning the eye from a luminous object, _O_, to some other
fixation-point, _P_, the distance as simply contemplated is more or
less subdivided or filled in by the objects which are seen to lie
between _O_ and _P_, or if no such objects are visible the distance is
still felt to consist of an infinity of points; whereas the muscular
innervation which is to carry the eye over this very distance is an
undivided unit. But it is this which gives us our estimate of the arc
we move through, and being thus uninterrupted it will appear shorter
than the contemplated, much subdivided distance _OP_, just as a
continuous line appears shorter than a broken line. "After such
analogies, now, the movement of the eye from _O_ to _P_, that is, the
arc which I traverse, must be underestimated" (_ibid._, S. 67). There
is thus a discrepancy between our two estimates of the distance _OP_.
This discrepancy is felt during the movement, and can be harmonized
only if we seem to see the two fixation-points move apart, until the
arc between them, in terms of innervation-feeling, feels equal to the
distance _OP_ in terms of its visual subdivisions. Now either _O_ and
_P_ can both seem to move apart from each other, or else one can seem
fixed while the other moves. But the eye has for its goal _P_, which
ought therefore to have a definite position. "_P_ appears fixed
because, as goal, I hold it fast in my thought" (_loc. citat._). It
must be _O_, therefore, which appears to move; that is, _O_ must dart
backward as the eye moves forward toward _P_. Thus Lipps explains the
illusion.

   [10] Lipps, Th., _Zeitschrift f. Psychologie u. Physiologie der
   Sinnesorgane_, 1890, I., S. 60-74.

Such an explanation involves many doubtful presuppositions, but if we
were to grant to Lipps those, the following consideration would
invalidate his account. Whether the feeling of innervation which he
speaks of as being the underestimated factor is supposed to be a true
innervation-feeling in the narrower sense, or a muscular sensation
remembered from past movements, it would in the course of experience
certainly come to be so closely associated with the corresponding
objective distance as not to feel less than this. So far as an
innervation-feeling might allow us to estimate distance, it could have
no other meaning than to represent just that distance through which
the innervation will move the organ in question. If _OP_ is a distance
and _i_ is the feeling of such an innervation as will move the eye
through that distance, it is inconceivable that _i_, if it represent
any distance at all, should represent any other distance than just
_OP_.

Cornelius[11] brought up the matter a year later than Lipps. Cornelius
criticises the unwarranted presuppositions of Lipps, and himself
suggests that the falsely localized streak is due to a slight rebound
which the eye, having overshot its intended goal, may make in the
opposite direction to regain the mark. This would undoubtedly explain
the phenomenon if such movements of rebound actually took place.
Cornelius himself does not adduce any experiments to corroborate this
account.

   [11] Cornelius, C.S., _Zeitschrift f. Psychologie u.
   Physiologie der Sinnesorgane_, 1891, II., S. 164-179.

The writer, therefore, undertook to find out if such movements
actually are made. The observations were made by watching the eyes of
several subjects, who looked repeatedly from one fixation-point to
another. Although sometimes such backward movements seemed indeed to
be made, they were very rare and always very slight. Inasmuch as the
'false' streak is often one third as long as the distance moved
through, a movement of rebound, such as Cornelius means, would have to
be one third of the arc intended, and could therefore easily have been
noticed. Furthermore, the researches of Lamansky,[12] Guillery,[13]
Huey,[14] Dodge and Cline,[15] which are particularly concerned with
the movements of the eyes, make no mention of such rebounds.
Schwarz[16] above all has made careful investigations on this very
point, in which a screen was so placed between the observer and the
luminous spot that it intervened between the pupil and the light, just
before the end of the movement. Thus the retina was not stimulated
during the latter part of its movement, just when Cornelius assumed
the rebound to take place. This arrangement, however, did not in the
least modify the appearance of the false streak.

   [12] Lamansky, S., _Pflüger's Archiv f. d. gesammte
   Physiologie_, 1869, II., S. 418.

   [13] Guillery, _ibid._, 1898, LXXI., S. 607; and 1898, LXXIII.,
   S. 87.

   [14] Huey, Edmund B., _American Journal of Psychology_, 1900,
   XI., p. 283.

   [15] Dodge, Raymond, and Cline, T.S., PSYCHOLOGICAL REVIEW,
   1901, VIII., PP. 145-157.

   [16] Schwarz, Otto, _Zeitschrift J. Psychologie u. Physiologie
   der Sinnesorgane_, 1892, III., S. 398-404.

This work of Schwarz certainly proves that the explanation of
Cornelius is not correct. Schwarz found that the phenomenon takes
place as well when the head moves and the eyes are fixed relatively to
the head, as when the eyes alone move. He furthermore made this
observation. Meaning by _a_ the point of departure and by _b_ the goal
of either the eye-or the head-movement, movement, he says (_ibid._,
S. 400-2): "While oftentimes the streak of the after-image extended
uninterruptedly to the point _b_, or better seemed to proceed from
this point,--as Lipps also reported--yet generally, under the
experimental conditions which I have indicated, _two streaks_ could be
seen, _separated by a dark space between_; firstly the anomalous one"
(the false streak) "rather brilliant, and secondly a fainter one of
about equal or perhaps greater length, which began at the new
fixation-point _b_ and was manifestly an after-image correctly
localized with regard to the situation of this point. This last
after-image streak did not always appear; but it appeared regularly if
the light at _a_ was bright enough and the background dark.... It was
impossible for this second after-image streak to originate in the
point _b_, because it appeared equally when _b_ was only an imaginary
fixation-point.... This consideration makes it already conceivable
that the two parts of the total after-image _are two manifestations of
the one identical retinal stimulation, which are differently
localized_.... Therefore we must probably picture to ourselves that
the sensation from the strip of the retina stimulated during the quick
eye-movement is, _during the interval of movement or at least during
the greater part of it, localized as if the axis of vision were still
directed toward the original fixation-point. And when the new position
of rest is reached and the disturbance on the retinal strip has not
wholly died away, then the strip comes once more into consciousness,
but this time correctly localized with reference to the new position
of the axis of vision_. By attending closely to the behavior as
regards time of both after-image streaks, I can generally see the
normal after-image develop a moment later than the anomalous one"
(that is, the false streak). Schwarz finally suggests (S. 404) that
probably between the first and second appearances of the streak an
'innervation-feeling' intervenes which affords the basis for
localizing the second streak ('correctly') with reference to the new
position of the eye.

After this digression we return to consider how this phenomenon is
related to the hypothesis of anæsthesia during eye-movements. If we
accept the interpretation of Schwarz, there is one retinal process
which is perceived as two luminous streaks in space, localized
differently and referred to different moments of time. It is
surprising, then, that a continuous retinal process is subjectively
interpreted as two quite different objects, that is, as something
discontinuous. Where does the factor of discontinuity come in? If we
suppose the retinal disturbance to produce a continuous sensation in
consciousness, we should expect, according to every analogy, that this
sensation would be referred to one continuously existing object. And
if this object is to be localized in two places successively, we
should expect it to appear to move continuously through all
intervening positions. Such an interpretation is all the more to be
expected, since, as the strobic phenomena show, even discontinuous
retinal processes tend to be interpreted as continuously existing
objects.

On the other hand, if there were a central anæsthesia during
eye-movement, the continuous process in the retina could not produce a
continuous sensation, and if the interval were long enough the image
might well be referred to two objects; since also, in the strobic
appearances, the stimulations must succeed at a certain minimal rate
in order to produce the illusion of continuous existence and movement.

This consideration seemed to make it worth while to perform some
experiments with the falsely localized after-images. The phenomenon
had also by chance been noted in the case of the eye moving past a
luminous dot which was being regularly covered and uncovered. The
appearance is of a row of luminous spots side by side in space, which
under conditions may be either falsely or correctly localized. Since
these dots seemed likely to afford every phenomenon exhibited by the
streaks, with the bare chance of bringing out new facts, apparatus was
arranged as in Fig. 1, which is a horizontal section.

_DD_ is a disc which revolves in a vertical plane, 56 cm. in diameter
and bearing near its periphery one-centimeter holes punched 3 cm.
apart. _E_ is an eye-rest, and _L_ an electric lamp. _SS_ is a screen
pierced at _H_ by a one-centimeter hole. The distance _EH_ is 34 cm.
The disc _DD_ is so pivoted that the highest point of the circle of
holes lies in a straight line between the eye _E_ and the lamp _L_.
The hole _H_ lies also in this straight line. A piece of milk-glass
_M_ intervenes between _L_ and _H_, to temper the illumination. The
disc _DD_ is geared to a wheel _W_, which can be turned by the hand of
the observer at _E_, or by a second person. As the disc revolves, each
hole in turn crosses the line _EL_. Thus the luminous hole _H_ is
successively covered and uncovered to the eye _E_; and if the eye
moves, a succession of points on the retina is stimulated by the
successive uncovering of the luminous spot. No fixation-points are
provided for the eye, since such points, if bright enough to be of use
in the otherwise dark room, might themselves produce confusing
streaks, and also since an exact determination of the arc of
eye-movement would be superfluous.

[Illustration: Fig. 1.]

The eye was first fixated on the light-spot, and then moved
horizontally away toward either the right or the left. In the first
few trials (with eye-sweeps of medium length), the observations did
not agree, for some subjects saw both the false and the correct
streaks, while others saw only the latter. It was found later that
all the subjects saw both streaks if the arc of movement was large,
say 40°, and all saw only the correctly localized streak if the arc
was small, say 5°. Arcs of medium length revealed individual
differences between the persons, and these differences, though
modified, persisted throughout the experiments. After the subjects had
become somewhat trained in observation, the falsely localized streak
never appeared without the correctly localized one as well. For the
sake of brevity the word 'streak' is retained, although the appearance
now referred to is that of a series of separate spots of light
arranged in a nearly straight line.

The phenomena are as follows.--(1) If the arc of movement is small, a
short, correctly localized streak is seen extending from the final
fixation-point to the light-spot. It is brightest at the end nearer
the light. (2) If the eye-movement is 40° or more, a streak having a
length of about one third the distance moved through is seen on the
other side of the light from the final fixation-point; while another
streak is seen of the length of the distance moved through, and
extending from the final fixation-point to the light. The first is the
falsely, the second the correctly localized streak. The second, which
is paler than the first, feels as if it appeared a moment later than
this. The brighter end of each streak is the end which adjoins the
luminous spot. (3) Owing to this last fact, it sometimes happens, when
the eye-movement is 40° or a trifle less, that both streaks are seen,
but that the feeling of succession is absent, so that the two streaks
look like one streak which lies (unequally parted) on both sides of
the spot of light. It was observed, in agreement with Schwarz, that
the phenomenon was the same whether the head or the eyes moved. Only
one other point need be noted. It is that the false streak, which
appears in the beginning to dart from the luminous hole, does not
fade, but seems to suffer a sudden and total eclipse; whereas the
second streak flashes out suddenly _in situ_, but at a lesser
brilliancy than the other, and very slowly fades away.

These observations thoroughly confirmed those of Schwarz. And one
could not avoid the conviction that Schwarz's suggestion of the two
streaks being separate localizations of the same retinal stimulation
was an extremely shrewd conjecture. The facts speak strongly in its
favor; first, that when the arc of movement is rather long, there is a
distinct feeling of succession between the appearances of the falsely
and the correctly localized images; second, that when both streaks are
seen, the correct streak is always noticeably dimmer than the false
streak.

It is of course perfectly conceivable that the feeling of succession
is an illusion (which will itself then need to be explained), and that
the streak is seen continuously, its spacial reference only undergoing
an instantaneous substitution. If this is the case, it is singular
that the correctly seen streak seems to enter consciousness so much
reduced as to intensity below that of the false streak when it was
eclipsed. Whereas, if a momentary anæsthesia could be demonstrated,
both the feeling of succession and the discontinuity of the
intensities would be explained (since during the anæsthesia the
after-image on the retina would have faded). This last interpretation
would be entirely in accordance with the observations of
McDougall,[17] who reports some cases in which after-images are
intermittently present to consciousness, and fade during their
eclipse, so that they reappear always noticeably dimmer than when they
disappeared.

   [17] McDougall, _Mind_, N.S., X., 1901, p. 55, Observation II.

Now if the event of such an anæsthesia could be established, we should
know at once that it is not a retinal but a central phenomenon. We
should strongly suspect, moreover, that the anæsthesia is not present
during the very first part of the movement. This must be so if the
interpretation of Schwarz is correct, for certainly no part of the
streak could be made before the eye had begun to move; and yet
approximately the first third was seen at once in its original
intensity, before indeed the 'innervation-feelings' had reached
consciousness. Apparently the anæsthesia commences, it at all, after
the eye has accomplished about the first third of its sweep. And
finally, we shall expect to find that movements of the head no less
than movements of the eyes condition the anæsthesia, since neither by
Schwarz nor by the present writer was any difference observed in the
phenomena of falsely localized after-images, between the cases when
the head, and those when the eyes moved.


III. THE PERIMETER-TEST OF DODGE, AND THE LAW OF THE LOCALIZATION OF
AFTER-IMAGES.


We have seen (above, p. 8) how the evidence which Dodge adduces to
disprove the hypothesis of anæsthesia is not conclusive, since,
although an image imprinted on the retina during its movement was
seen, yet nothing showed that it was seen before the eye had come to
rest.

Having convinced himself that there is after all no anæsthesia, Dodge
devised a very ingenious attachment for a perimeter 'to determine just
what is seen during the eye-movement.'[18] The eye was made to move
through a known arc, and during its movement to pass by a very narrow
slit. Behind this slit was an illuminated field which stimulated the
retina. And since only during its movement was the pupil opposite the
slit, so only during the movement could the stimulation be given. In
the first experiments nothing at all of the illuminated field was
seen, and Dodge admits (_ibid._, p. 461) that this fact 'is certainly
suggestive of a central explanation for the absence of bands of fusion
under ordinary conditions.' But "these failures suggested an increase
of the illumination of the field of exposure.... Under these
conditions a long band of light was immediately evident at each
movement of the eye." This and similar observations were believed 'to
show experimentally that when a complex field of vision is perceived
during eye-movement it is seen fused' (p. 462).

   [18] Dodge, PSYCHOLOGICAL REVIEW, 1900, VII., p. 459.

Between the 'failures' and the cases when a band of light was seen, no
change in the conditions had been introduced except 'an increase of
the illumination.' Suppose now this change made just the difference
between a stimulation which left _no_ appreciable _after-image_, and
one which left _a distinct one_. And is it even possible, in view of
the extreme rapidity of eye-movements, that a retinal stimulation of
any considerable intensity should not endure after the movement, to be
_then_ perceived, whether or not it had been first 'perceived during
the movement'?

Both of Dodge's experiments are open to the same objection. They do
not admit of distinguishing between consciousness of a retinal process
during the moment of stimulation, and consciousness of the same
process just afterward. In both his cases the stimulation was given
during the eye-movement, but there was nothing to prove that it was
perceived at just the same moment. Whatever the difficulties of
demonstrating an anæsthesia during movement, an experiment which does
not observe the mentioned distinction can never disprove the
hypothesis.

[Illustration: Fig. 2.]

For the sake of a better understanding of these bands of light of
Dodge, a perimeter was equipped in as nearly the manner described by
him (_ibid._, p. 460) as possible. Experiments with the eye moving
past a very narrow illuminated slit confirmed his observations. If the
light behind the slit was feeble, no band was seen; if moderately
bright, a band was always seen. The most striking fact, however, was
that the band was not localized behind the slit, but was projected on
to that point where the eye came to rest. The band seemed to appear
at this point and there to hover until it faded away. This apparent
anomaly of localization, which Dodge does not mention, suggests the
localization which Schwarz describes of his streaks. Hereupon the
apparatus was further modified so that, whereas Dodge had let the
stimulation take place only during the movement of the eye across a
narrow slit between two walls, now either one of these walls could be
taken away, allowing the stimulation to last for one half of the time
of movement, and this could be either the first or the second half at
pleasure. A plan of the perimeter so arranged is given in Fig. 2.

_PBCDB'P_ is the horizontal section of a semicircular perimeter of 30
cm. radius. _E_ is an eye-rest fixed at the centre of the semicircle;
_CD_ is a square hole which is closed by the screen _S_ fitted into
the front pair of the grooves _GG_. In the center of _S_ and on a
level with the eye _E_ is a hole _A_, 2 cm. in diameter, which
contains a 'jewel' of red glass. The other two pairs of grooves are
made to hold pieces of milk-or ground-glass, as _M_, which may be
needed to temper the illumination down to the proper intensity. _L_ is
an electric lamp. _B_ and _B'_ are two white beads fixed to the
perimeter at the same level as _E_ and _A_, and used as
fixation-points. Although the room is darkened, these beads catch
enough light to be just visible against the black perimeter, and the
eye is able to move from one to the other, or from _A_ to either one,
with considerable accuracy. They leave a slight after-image streak,
which is, however, incomparably fainter than that left by _A_ (the
streak to be studied), and which is furthermore white while that of
_A_ is bright red. _B_ and _B'_ are adjustable along a scale of
degrees, which is not shown in the figure, so that the arc of
eye-movement is variable at will. _W_ is a thin, opaque, perpendicular
wall extending from _E_ to _C_, that is, standing on a radius of the
perimeter. At _E_ this wall comes to within about 4 mm. of the cornea,
and when the eye is directed toward _B_ the wall conceals the red spot
_A_ from the pupil. _W_ can at will be transferred to the position
_ED_. _A_ is then hidden if the eye looks toward _B'_.

The four conditions of eye-movement to be studied are indicated in
Fig. 3 (Plate 1.). The location of the retinal stimulation is also
shown for each case, as well as the corresponding appearance of the
streaks, their approximate length, and above all their localization.
For the sake of simplicity the refractive effect of the lens and
humors of the eye is not shown, the path of the light-rays being in
each case drawn straight. In all four cases the eye moved without
stopping, through an arc of 40°.

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT, 17. PLATE I.
               Fig. 3.
               HOLT ON EYE-MOVEMENT.]

To take the first case, Fig. 3:1. The eye fixates the light _L_, then
sweeps 40° toward the right to the point _B'_. The retina is
stimulated throughout the movement, _l-l'_. These conditions yield the
phenomenon of both streaks, appearing as shown on the black rectangle.

In the second case (Fig. 3:2) the wall _W_ is in position and the eye
so adjusted in the eye-rest that the light _L_ is not seen until the
eye has moved about 10° to the right, that is, until the axis of
vision is at _Ex_. Clearly, then, the image of _L_ falls at first a
little to the right of the fovea, and continues in indirect vision to
the end of the movement. The stimulated part of the retina is _l-l'_
(Fig. 3:2). Here, then, we have no stimulation of the eye during the
first part of its movement. The corresponding appearance of the streak
is also shown. Only the correctly localized streak is seen, extending
from the light _L_ toward the right but not quite reaching _B'_. Thus
by cutting out that portion of the stimulation which was given during
the first part of the movement, we have eliminated the whole of the
false image, and the right-hand (foveal) part of the correct image.

Fig. 3:3 shows the reverse case, in which the stimulation is given
only during the first part of the movement. The wall is fixed on the
right of _L_, and the eye so adjusted that _L_ remains in sight until
the axis of vision reaches position _Ex_, that is, until it has moved
about 10°. A short strip of the retina next the fovea is here
stimulated, just the part which in case 2 was not stimulated; and the
part which in case 2 was, is here not stimulated. Now here the false
streak is seen, together with just that portion of the correct streak
which in the previous case was not seen. The latter is relatively dim.

Thus it looks indeed as if the streak given during the first part of
an eye-movement is seen twice and differently localized. But one may
say: The twice-seen portion was in both cases on the fovea; this may
have been the conditioning circumstance, and not the fact of being
given in the early part of the movement.

We must then consider Fig. 3, case 4. Here the eye moves from _B_ to
_B'_, through the same arc of 40°. The wall _W_ is placed so that _L_
cannot be seen until the axis of vision has moved from _EB_ to _EL_,
but _then L_ is seen in direct vision. Its image falls full on the
fovea. But one streak, and that the correctly localized one, is seen.
This is like case 2, except that here the streak extending from _L_ to
the right quite reaches the final fixation-point _B'_. It is therefore
not the fact of a stimulation being foveal which conditions its being
seen in two places.

It should be added that this experiment involves no particular
difficulties of observation, except that in case 4 the eye tends to
stop midway in its movement when the spot of light _L_ comes in view.
Otherwise no particular training of the subject is necessary beyond
that needed for the observing of any after-image. Ten persons made the
foregoing observations and were unanimous in their reports.

This experiment leaves it impossible to doubt that the conjecture of
Schwarz, that the correct image is only the false one seen over again,
is perfectly true. It would be interesting to enquire what it is that
conditions the length of the false streak. It is never more than one
third that of the correct streak (Fig. 3:1; except of course under the
artificial conditions of Fig. 3:3) and may be less. The false streak
seems originally to _dart out_ from the light, as described by Lipps,
visibly growing in length for a certain distance, and then to be
suddenly eclipsed or blotted out _simultaneously_ in all its parts.
Whereas the fainter, correct streak flashes into consciousness _all
parts at once_, but disappears by fading gradually from one end, the
end which lies farther from the light.

Certain it is that when the false streak stops growing and is
eclipsed, some new central process has intervened. One has next to
ask, Is the image continuously conscious, suffering only an
instantaneous relocalization, or is there a moment of central
anæsthesia between the disappearance of the false streak and the
appearance of the other? The relative dimness of the second streak in
the _first moment_ of its appearance speaks for such a brief period of
anæsthesia, during which the retinal process may have partly subsided.

We have now to seek some experimental test which shall demonstrate
definitely either the presence or the absence of a central anæsthesia
during eye-movements. The question of head-movements will be deferred,
although, as we have seen above, these afford equally the phenomenon
of twice-localized after-images.


IV. THE PENDULUM-TEST FOR ANÆSTHESIA.


A. Apparatus must be devised to fulfil the following conditions. A
retinal stimulation must be given during an eye-movement. The moment
of excitation must be so brief and its intensity so low that the
process shall be finished before the eye comes to rest, that is, so
that no after-image shall be left to come into consciousness _after_
the movement is over. Yet, on the other hand, it must be positively
demonstrated that a stimulation of this _very same_ brief duration and
low intensity is amply strong enough to force its way into
consciousness if no eye-movement is taking place. If such a
stimulation, distinctly perceived when the eye is at rest, should not
be perceptible if given while the eye is moving, we should have a
valid proof that some central process has intervened during the
movement, to shut out the stimulation-image during that brief moment
when it might otherwise have been perceived.

Obviously enough, with the perimeter arrangement devised by Dodge,
where the eye moves past a narrow, illuminated slit, the light within
the slit can be reduced to any degree of faintness. But on the other
hand, it is clearly impossible to find out how long the moment of
excitation lasts, and therefore impossible to find out whether an
excitation of the same duration and intensity is yet sufficient to
affect consciousness if given when the eye is not moving. Unless the
stimulation is proved to be thus sufficient, a failure to see it when
given during an eye-movement would of course prove nothing at all.

Perhaps the most exact way to measure the duration of a light-stimulus
is to let it be controlled by the passing of a shutter which is
affixed to a pendulum. Furthermore, by means of a pendulum a
stimulation of exactly the same duration and intensity can be given to
the moving, as to the resting eye. Let us consider Fig. 4:1. If _P_ is
a pendulum bearing an opaque shield _SS_ pierced by the hole _tt_, and
_BB_ an opaque background pierced by the hole _i_ behind which is a
lamp, it is clear that if the eye is fixed on _i_, a swing of the
pendulum will allow _i_ to stimulate the retina during such a time as
it takes the opening _tt_ to move past _i_. The shape of _i_ will
determine the shape of the image on the retina, and the intensity of
the stimulation can be regulated by ground-or milk-glass interposed
between the hole _i_ and the lamp behind it. The duration of the
exposure can be regulated by the width of _tt_, by the length of the
pendulum, and by the arc through which it swings.

If now the conditions are altered, as in Fig. 4:2, so that the opening
_tt_ (indicated by the dotted line) lies not in _SS_, but in the fixed
background _BB_, while the small hole _i_ now moves with the shield
_SS_, it necessarily follows that if the eye can move at just the rate
of the pendulum, it will receive a stimulation of exactly the same
size, shape, duration, and intensity as in the previous case where the
eye was at rest. Furthermore, it will always be possible to tell
whether the eye does move at the same rate as the pendulum, since if
it moves either more rapidly or more slowly, the image of _i_ on the
retina will be horizontally elongated, and this fact will be given by
a judgment as to the proportions of the image seen.

It may be said that since the eye does not rotate like the pendulum,
from a fulcrum above, the image of _i_ in the case of the moving eye
will be distorted as is indicated in Fig. 4, _a_. This is true, but
the distortion will be so minute as to be negligible if the pendulum
is rather long (say a meter and a half) and the opening _tt_ rather
narrow (say not more than ten degrees wide). A merely horizontal
movement of the eye will then give a practically exact superposition
of the image of _i_ at all moments of the exposure.

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT, 17. PLATE PLATE II.
               Fig. 4.         Fig. 6.
               HOLT ON EYE-MOVEMENT.]

Thus much of preliminary discussion to show how, by means of a
pendulum, identical stimulations can be given to the moving and to the
resting eye. We return to the problem. It is to find out whether a
stimulation given during an eye-movement can be perceived if its
after-image is so brief as wholly to elapse before the end of the
movement. If a period of anæsthesia is to be demonstrated, two
observations must be made. First, that the stimulation is bright
enough to be _unmistakably visible_ when given to the eye at rest;
second, that it is not visible when given to the moving eye. Hence, we
shall have three cases.

    Case 1. A control, in which the stimulation is proved intense
    enough to be seen by the eye at rest.

    Case 2. In which the same stimulation is given to the eye
    during movement.

    Case 3. Another control, to make sure that no change in the
    adaptation or fatigue of the eye has intervened during the
    experiments to render the eye insensible to the stimulation.

Fig. 5 shows the exact arrangement of the experiment. The figure
represents a horizontal section at the eye-level of the pendulum of
Fig. 4, with accessories. _E_ is the eye which moves between the two
fixation-points _P_ and _P_'. _WONW_ is a wall which conceals the
mechanism of the pendulum from the subject. _ON_ is a rectangular hole
9 cm. wide and 7 cm. high, in this wall. _SS_ is the shield which
swings with the pendulum, and _BB_ is the background (cf. Fig. 4).
When the pendulum is not swinging, a hole in the shield lies behind
_ON_ and exactly corresponds with it. Another in the background does
the same. The eye can thus see straight through to the light _L_.

Each of these three holes has grooves to take an opaque card, _x_,
_y_, or _z_; there are two cards for the three grooves, and they are
pierced with holes to correspond to _i_ and _tt_ of Fig. 4. The
background _BB_ has a second groove to take a piece of milk-glass _M_.
These cards are shown in Fig. 6 (Plate II.) Card _I_ bears a hole 5
cm. high and shaped like a dumb-bell. The diameter of the end-circles
(_e_, _e_) is 1.3 cm., and the width of the handle _h_ is 0.2 cm. Card
_T_ is pierced by two slits _EE_, _EE_, each 9 cm. long and 1.3 cm.
high, which correspond to the two ends of the dumb-bell. These slits
are connected by a perforation _H_, 1.5 cm. wide, which corresponds to
the handle of the dumb-bell. This opening _EEHEE_ is covered by a
piece of ground-glass which serves as a radiating surface for the
light.

[Illustration: Fig. 5.]

The distance _EA_ (Fig. 5) is 56 cm., and _PP_' is 40 cm.; so that the
arc of eye-movement, that is, the angle _PEP_', is very nearly 40°,
of which the 9-cm. opening _ON_ 9° 11'. _SS_ is 2 cm. behind _ON_, and
_BB_ 2 cm. behind _SS_; these distances being left to allow the
pendulum to swing freely.

It is found under these conditions that the natural speed made by the
eye in passing the 9-cm. opening _ON_ is very well approximated by the
pendulum if the latter is allowed to fall through 23.5° of its arc,
the complete swing being therefore 47°. The middle point of the
pendulum is then found to move from _O_ to _N_ in 110[sigma][19]. If
the eye sweeps from _O_ to _N_ in the same time, it will be moving at
an angular velocity of 1° in 11.98[sigma] (since the 9 cm. are 9° 11'
of eye-movement). This rate is much less than that found by Dodge and
Cline (_op. cit._, p. 155), who give the time for an eye-movement of
40° as 99.9[sigma], which is an average of only 2.49[sigma] to the
degree. Voluntary eye-movements, like other voluntary movements, can
of course be slow or fast according to conditions. After the pendulum
has been swinging for some time, so that its amplitude of movement has
fallen below the initial 47° and therewith its speed past the middle
point has been diminished, the eye in its movements back and forth
between the fixation-points can still catch the after-image of _i_
perfectly distinct and not at all horizontally elongated, as it would
have to be if eye and pendulum had not moved just together. It appears
from this that certain motives are able to retard the rate of
voluntary movements of the eye, even when the distance traversed is
constant.

   [19] The speed of the pendulum is measured by attaching a
   tuning-fork of known vibration-rate to the pendulum, and
   letting it write on smoked paper as the pendulum swings past
   the 9-cm. opening.

The experiment is now as follows. The room is darkened. Card _T_ is
dropped into groove _z_, while _I_ is put in groove _y_ and swings
with the pendulum. One eye alone is used.

Case 1. The eye is fixed in the direction _EA_. The pendulum is
allowed to swing through its 47°. The resulting visual image is shown
in Fig. 7:1. Its shape is of course like _T_, Fig. 6, but the part _H_
is less bright than the rest because it is exposed a shorter time,
owing to the narrowness of the handle of the dumb-bell, which swings
by and mediates the exposure. Sheets of milk-glass are now dropped
into the back groove of _BB_, until the light is so tempered that
part _H_ (Fig. 7:1) is _barely but unmistakably_ visible as luminous.
The intensity actually used by the writer, relative to that of _EE_,
is fairly shown in the figure. (See Plate III.)

It is clear, if the eye were now to move with the pendulum, that the
same amount of light would reach the retina, but that it would be
concentrated on a horizontally narrower area. And if the eye moves
exactly with the pendulum, the visual image will be no longer like 1
but like 2 (Fig. 7). We do not as yet know how the intensities of _e_,
_e_ and _h_ will relatively appear. To ascertain this we must put card
_I_ into groove _x_, and let card _T_ swing with the pendulum in
groove _y_. If the eye is again fixed in the direction _EA_ (Fig. 5),
the retina receives exactly the same stimulation that it would have
received before the cards were shifted if it had moved exactly at the
rate of the pendulum. In the experiments described, the handle _h_ of
this image (Fig. 7:2) curiously enough appears of the same brightness
as the two ends _e_, _e_, although, as we know, it is stimulated for a
briefer interval. Nor can any difference between _e_, _e_ and _h_ be
detected in the time of disappearance of their after-images. These
conditions are therefore generous. The danger is that _h_ of the
figure, the only part of the stimulation which could possibly quite
elapse during the movement, is still too bright to do so.

Case 2. The cards are replaced in their first positions, _T_ in groove
_z_, _I_ in groove _y_ which swings. The subject is now asked to make
voluntary eye-sweeps from _P_ to _P'_ and back, timing his moment of
starting so as to bring his axis of vision on to the near side of
opening _ON_ at approximately the same time as the pendulum brings _I_
on the same point. This is a delicate matter and requires practice.
Even then it would be impossible, if the subject were not allowed to
get the rhythm of the pendulum before passing judgment on the
after-images. The pendulum used gives a slight click at each end of
its swing, and from the rhythm of this the subject is soon able to
time the innervation of his eye so that the exposure coincides with
the middle of the eye-movement.

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT, 17. PLATE III.
               Fig. 7.
               HOLT ON EYE-MOVEMENT.]

It is true that with every swing the pendulum moves more slowly past
_ON_, and the period of exposure is lengthened. This, however, only
tends to make the retinal image brighter, so that its disappearance
during an anæsthesia would be so much the less likely. The pendulum
may therefore be allowed to 'run down' until its swing is too slow for
the eye to move with it, that is, too slow for a distinct,
non-elongated image of _i_ to be caught in transit on the retina.

With these eye-movements, the possible appearances are of two classes,
according to the localization of the after-image. The image is
localized either at _A_ (Fig. 5), or at the final fixation-point (_P_
or _P'_, according to the direction of the movement). Localized at
_A_, the image may be seen in either of two shapes. First, it may be
identical with 1, Fig. 7. It is seen somewhat peripherally, judgment
of indirect vision, and is correctly localized at _A_. When the
subject's eye is watched, it is found that in this case it moved
either too soon or too late, so that when the exposure was made, the
eye was resting quietly on one of the fixation-points and so naturally
received the same image as in case 1, except that now it lies in
indirect vision, the eye being directed not toward _A_ (as in case 1)
but towards either _P_ or _P'_.

Second, the image correctly localized may be like 2 (Fig. 7), and then
it is seen to move past the opening _ON_. The handle _h_ looks as
bright as _e_, _e_. This appearance once obtained generally recurs
with each successive swing of the pendulum, and scrutiny of the
subject's eye shows it to be moving, not by separate voluntary
innervations from _P_ to _P'_ and then from _P'_ to _P_, but
continuously back and forth with the swing of the pendulum, much as
the eye of a child passively follows a moving candle. This movement is
purely reflex,[20] governed probably by cerebellar centers. It seems
to consist in a rapid succession of small reflex innervations, and is
very different from the type of movement in which one definite
innervation carries the eye through its 42°, and which yielded the
phenomena with the perimeter. A subject under the spell of this reflex
must be exercised in innervating his eye to move from _P_ to _P'_ and
back in single, rapid leaps. For this, the pendulum is to be
motionless and the eye is not to be stimulated during its movement.

   [20] Exner, Sigmund, _Zeitschrift f. Psychologie u. Physiologie
   der Sinnesorgane_, 1896, XII., S. 318. 'Entwurf zu einer
   physiologischen Erklärung der psychischen Erscheinungen,'
   Leipzig u. Wien, 1894, S. 128. Mach, Ernst, 'Beiträge zur
   Analyse der Empfindungen,' Jena, 1900, S. 98.

These two cases in which the image is localized midway between _P_ and
_P'_ interest us no further. Localized on the final fixation-point,
the image is always felt to flash out suddenly _in situ_, just as in
the case of the 'correctly localized' after-image streaks in the
experiments with the perimeter. The image appears in one of four
shapes, Fig. 7: 2 or 3, 4 or 5.

First, the plain or elongated outline of the dumb-bell appears with
its handle on the final fixation-point (2 or 3). The image is plain
and undistorted if the eye moves at just the rate of the pendulum,
elongated if the eye moves more rapidly or more slowly. The point that
concerns us is that the image appears _with its handle_. Two
precautions must here be observed.

The eye does not perhaps move through its whole 42°, but stops instead
just when the exposure is complete, that is, stops on either _O_ or
_N_ and considerably short of _P_ or _P'_. It then follows that the
exposure is given at the _very last_ part of the movement, so that the
after-image of even the handle _h_ has not had time to subside. The
experiment is planned so that the after-image of _h_ shall totally
elapse during that part of the movement which occurs after the
exposure, that is, while the eye is completing its sweep of 42°, from
_O_ to _P_, or else from _N_ to _P'_. If the arc is curtailed at point
_O_ or _N_, the handle of the dumb-bell will of course appear. The
fact can always be ascertained by asking the subject to notice very
carefully where the image is localized. If the eye does in fact stop
short at _O_ or _N_, the image will be there localized, although the
subject may have thoughtlessly said before that it was at _P_ or _P'_,
the points he had nominally had in mind.

But the image 2 or 3 may indeed be localized quite over the final
fixation-point. In this case the light is to be looked to. It is too
bright, as it probably was in the case of Dodge's experiments. It must
be further reduced; and with the eye at rest, the control (case I)
must be repeated. In the experiments here described it was always
found possible so to reduce the light that the distinct, entire image
of the dumb-bell (2, Fig. 7) never appeared localized on the final
fixation-point, although in the control, _H_, of Fig. 7:1, was always
distinctly visible.

With these two precautions taken, the image on the final
fixation-point is like either 3, 4, or 5. Shape 5 very rarely appears,
while the trained subject sees 4 and 3 each about one half the times;
and either may be seen for as many as fifteen times in succession.

Shape 4 is of course exactly the appearance which this experiment
takes to be crucial evidence of a moment of central anæsthesia, before
the image is perceived and during which the stimulation of the handle
_h_ completely elapses. Eight subjects saw this phenomenon distinctly
and, after some training in timing their eye-movements, habitually.
The first appearance of the handleless image was always a decided
surprise to the subject (as also to the writer), and with some
eagerness each hastened to verify the phenomenon by new trials.

The two ends (_e_, _e_) of the dumb-bell seem to be of the same
intensity as in shape 2 when seen in reflex movement. But there is no
vestige whatsoever of a handle. Two of the subjects stated that for
them the place where the handle should have been, appeared of a
velvety blackness more intense than the rest of the background. The
writer was not able to make this observation. It coincides
interestingly with that of von Kries,[21] who reports as to the phases
of fading after-images, that between the disappearance of the primary
image and the appearance of the 'ghost,' a moment of the most intense
blackness intervenes. The experiments with the pendulum, however,
brought out no ghost.

   [21] Von Kries, J., _Zeitschr. f. Psych, u. Physiol. d.
   Sinnesorgane_, 1896, XII., S. 88.

We must now enquire why in about half the cases shape 3 is still seen,
whereas shape 5 occurs very rarely. Some of the subjects, among whom
is the writer, never saw 5 at all. We should expect that with the
intensity of _H_ sufficiently reduced 4 and 5 would appear with equal
frequency, whereas 3 would be seen no oftener than 2; shape 5
appearing when the eye did not, and 4 when it did, move at just the
rate of the pendulum. It is certain that when 4 is seen, the eye has
caught just the rate of the pendulum, and that for 3 or 5 it has moved
at some other rate. We have seen above (p. 27) that to move with the
pendulum the eye must already move decidedly more slowly than Dodge
and Cline find the eye generally to move. Nothing so reliable in
regard to the rate of voluntary eye-movements as these measurements of
Dodge and Cline had been published at the time when the experiments on
anæsthesia were carried on, and it is perhaps regrettable that in the
'empirical' approximation of the natural rate of the eye through 40°
the pendulum was set to move so slowly.

In any case it is highly probable that whenever the eye did not move
at just the rate of the pendulum, it moved _more rapidly_ rather than
more slowly. The image is thus horizontally elongated, by an amount
which varies from the least possible up to 9 cm. (the width of the
opening in _T_), or _even more_. And while the last of the movement
(_O_ to _P_, or _N_ to _P'_), in which the stimulation of _H'_ is
supposed to subside, is indeed executed, it may yet be done so
_rapidly_ that after all _H'_ cannot subside, not even although it is
now less intense by being horizontally spread out (that is, less
concentrated than the vanished _h_ of shape 4). This explanation is
rendered more probable by the very rare appearance of shape 5, which
must certainly emerge if ever the eye were to move more slowly than
the pendulum.

The critical fact is, however, that shape 4 _does_ appear to a trained
subject in about one half the trials--a very satisfactory ratio when
one considers the difficulty of timing the beginning of the movement
and its rate exactly to the pendulum.

Lastly, in some cases no image appears at all. This was at first a
source of perplexity, until it was discovered that the image of the
dumb-bell, made specially small so as to be contained within the area
of distinct vision, could also be contained on the blind-spot. With
the pendulum at rest the eye could be so fixed as to see not even the
slight halo which diffuses in the eye and seems to lie about the
dumb-bell. It may well occur, then, that in a movement the image
happens to fall on the blind-spot and not on the fovea. That this
accounts for the cases where no image appears, is proved by the fact
that if both eyes are used, some image is always seen. A binocular
image under normal convergence can of course not fall on both
blind-spots. It may be further said that the shape 4 appears as well
when both eyes are used as with only one. The experiment may indeed as
well be carried on with both eyes.

Some objections must be answered. It may be said that the image of _h_
happens to fall on the blind-spot, _e_ and _e_ being above and below
the same. This is impossible, since the entire image and its halo as
well may lie within the blind-spot. If now _h_ is to be on the
blind-spot, at least one of the end-circles _e_, _e_ will be there
also, whereas shape 4 shows both end-circles of the dumb-bell with
perfect distinctness.

Again, it cannot properly be urged that during the movement the
attention was distracted so as not to 'notice' the handle. The shape
of a dumb-bell was specially chosen for the image so that the weaker
part of the stimulation should lie between two points which should be
clearly noticed. Indeed, if anything, one might expect this central,
connecting link in the image to be apperceptively filled in, even when
it did not come to consciousness as immediate sensation. And it
remains to ask what it is which should distract the attention.

In this connection the appearance under reflex eye-movement compares
interestingly with that under voluntary. If the wall _WONW_ (Fig. 5)
is taken from before the pendulum, and the eye allowed to move
reflexly with the swinging dumb-bell, the entire image is seen at each
exposure, the handle seeming no less bright than the end-circles.
Moreover, as the dumb-bell opening swings past the place of exposure
and the image fades, although the handle must fade more quickly than
the ends, yet this is not discernible, and the entire image disappears
without having at any time presented the handleless appearance.

B. Another test for this anæsthesia during movement is offered in the
following experiment. It is clear that, just as a light-stimulation is
not perceived if the whole retinal process begins and ends during a
movement, so also a particular phase of it should not be perceived if
that phase can be given complete within the time of the movement. The
same pendulum which was used in the previous experiment makes such a
thing possible. If in place of the perforated dumb-bell the pendulum
exposes two pieces of glass of nearly complementary colors, one after
the other coming opposite the place of exposure, the sensations will
fuse or will not fuse according as the pendulum swings rapidly or
slowly. But now a mean rate of succession can be found such as to let
the first color be seen pure before the second is exposed, and then to
show the second fused with the after-image of the first. Under some
conditions the second will persist after the first has faded, and will
then itself be seen pure. Thus there may be three phases in
consciousness. If the first color exposed is green and the second red,
the phases of sensation will be green, white, and perhaps red. These
phases are felt to be not simultaneous but successive. A modification
of this method is used in the following experiment. (See Fig. 8, Plate
IV.)

_T_ and _I_ here correspond to the cards _T_ and _I_ of Fig. 6.
_T_ consists of a rectangular opening, 9×5 cm., which contains three
pieces of glass, two pieces of green at the ends, each 2.8 cm. wide
and 7 cm. high, and a piece of red glass in the middle 3.4 cm. wide
and only 1.5 cm. high, the space above and below this width being
filled with opaque material. The shape of the image is determined as
before by the hole in _I_, which now, instead of being a dumb-bell, is
merely a rectangular hole 2 cm. wide and 5 cm. high. Exactly as
before, _T_ is fixed in the background and _I_ swings with the
pendulum, the eye moving with it.

The speed of the pendulum must be determined, such that if _I_ lies in
the front groove (Fig. 5, _x_) and the eye is at rest, the image will
clearly show two phases of color when _T_ swings past on the pendulum.
With _T_ and _I_ as described above, a very slow pendulum shows the
image green, red (narrow), and green, in succession. A very fast
pendulum shows only a horizontal straw-yellow band on a green field
(Fig. 8:5). There is but one phase and no feeling of succession.
Between these two rates is one which shows two phases--the first a
green field with a horizontal, reddish-orange band (Fig. 8:3), the
second quickly following, in which the band is straw-yellow (5). It
might be expected that this first phase would be preceded by an
entirely green phase, since green is at first exposed. Such is however
not the case. The straw-yellow of the last phase is of course the
fusion-color of the red and green glasses. It would be gray but that
the two colors are not perfectly complementary. Since the arrangement
of colors in _T_ is bilaterally symmetrical, the successive phases are
the same in whichever direction the pendulum swings.

[Illustration: MONOGRAPH SUPPLEMENT 17. PLATE IV.
               Fig. 8.
               HOLT ON EYE-MOVEMENT.]

It is desirable to employ the maximum rate of pendulum which will give
the two phases. For this the illumination should be very moderate,
since the brighter it is, the slower must be the pendulum. With the
degree of illumination used in the experiments described, it was found
that the pendulum must fall from a height of only 9.5° of its arc: a
total swing of 19°. The opening of _T_, which is 9 cm. wide, then
swings past the middle point of _I_ in 275[sigma].

Now when the eye moves it must move at this rate. If the eye is 56 cm.
distant from the opening, as in the previous case, the 9 cm. of
exposure are 9° 11' of eye-movement, and we saw above that 9° 11' in
110[sigma] is a very slow rate of movement, according to the best
measurements. Now it is impossible for the eye to move so slowly as 9°
11' in 275[sigma]. If, however, the eye is brought nearer to the
opening, it is clear that the 9 cm. of exposure become more than 9°
11' of eye-movement. Therefore the eye and the fixation-points are so
placed that _EA_ (Fig. 5) = 26 cm. and _PP'_ = 18 cm. The total
eye-movement is thus 38° 11', of which the nine-centimeter distance of
exposure is 19° 38'. Now the eye is found to move very well through
19° 38' in 275[sigma], although, again, this is much more than a
proportionate part of the total time (99.9[sigma]) given by Dodge and
Cline for a movement of the eye through 40°. The eye is in this case
also moving slowly. As before, it is permissible to let the pendulum
run down till it swings too slowly for the eye to move with it; since
any lessened speed of the pendulum only makes the reddish-orange phase
more prominent.

As in the experiment with the dumb-bell, we have also here three
cases: the control, the case of the eye moving, and again a control.

Case 1. _T_ swings with the pendulum. _I_ is placed in the front
groove, and the eye looks straight forward without moving. The
pendulum falls from 9.5° at one side, and the illumination is so
adjusted that the phase in which the band is reddish-orange, is
_unmistakably_ perceived before that in which it is straw-yellow. The
appearance must be 3 followed by 5 (Fig. 8).

Case 2. _T_ is fixed in the background, _I_ on the pendulum, and the
phenomena are observed with the eye moving.

Case 3. A repetition of case 1, to make sure that no different
adaptation or fatigue condition of the eye has come in to modify the
appearance of the two successive phases as at first seen.

The possible appearances to the moving eye are closely analogous to
those in the dumb-bell experiment. If the eye moves too soon or too
late, so that it is at rest during the exposure, the image is like _T_
itself (Fig. 8) but somewhat fainter and localized midway between the
points _P_ and _P'_. If the eye moves reflexly at the rate of the
pendulum, the image is of the shape _i_ and shows the two phases (3
followed by 5). It is localized in the middle and appears to move
across the nine-centimeter opening.

A difficulty is met here which was not found in the case of the
dumb-bell. The eye is very liable to come to a full stop on one of the
colored surfaces, and then to move quickly on again to the final
fixation-point. And this happens contrary to the intention of the
subject, and indeed usually without his knowledge. This stopping is
undoubtedly a reflex process, in which the cerebellar mechanism which
tends to hold the fixation on any bright object, asserts itself over
the voluntary movement and arrests the eye on the not moving red or
green surface as the exposure takes place. A comparable phenomenon was
found sometimes in the experiment with the dumb-bell, where an
eye-movement commenced as voluntary would end as a reflex following of
the pendulum. In the present experiment, until the subject is well
trained, the stopping of the eye must be watched by a second person
who looks directly at the eye-ball of the subject during each
movement. The appearances are very varied when the eye stops, but the
typical one is shown in Fig. 8:1. The red strip _AB_ is seldom longer
and often shorter than in the figure. That part of it which is
superposed on the green seldom shows the orange phase, being almost
always of a pure straw-yellow. The localization of these images is
variable. All observations made during movements in which the eye
stops, are of course to be excluded.

If now the eye does not stop midway, and the image is not localized in
the center, the appearance is like either 2, 4, or 5, and is localized
over the final fixation-point. 2 is in all probability the case of the
eye moving very much faster than the pendulum, so that if the movement
is from left to right, the right-hand side of the image is the part
first exposed (by the uncovering of the left-hand side of _T_), which
is carried ahead by the too swift eye-movement and projected in
perception on the right of the later portion. 3 is the case of the eye
moving at very nearly but not quite the rate of the pendulum. The
image which should appear 2 cm. wide (like the opening _i_) appears
about 3 cm. wide. The middle band is regularly straw-yellow, extremely
seldom reddish, and if we could be sure that the eye moves more slowly
than the pendulum, so that the succession of the stimuli is even
slower than in the control, and the red phase is surely given, this
appearance (3) would be good evidence of anæsthesia during which the
reddish-orange phase elapses. It is more likely, however, that the eye
is moving faster than the pendulum, but whether or not so
inconsiderably faster as still to let the disappearance of the reddish
phase be significant of anæsthesia, is not certain until one shall
have made some possible but tedious measurements of the apparent width
of the after-image. Both here and in the following case the _feeling
of succession_, noticeable between the two phases when the eye is at
rest, has _disappeared with the sensation of redness_.

The cases in which 5 is seen are, however, indisputably significant.
The image is apparently of just the height and width of _i_, and there
is not the slightest trace of the reddish-orange phase. The image
flashes out over the final fixation-point, green and straw-yellow,
just as the end-circles of the dumb-bell appeared without their
handle. The rate of succession of the stimuli, green--red--green, on
the retina, is identical with that rate which showed the two phases to
the resting eye: for the pendulum is here moving at the very same
rate, and the eye is moving exactly with the pendulum, as is shown by
the absence of any horizontal elongation of the image seen. The
trained subject seldom sees any other images than 4 and 5, and these
with about equal frequency, although either is often seen in ten or
fifteen consecutive trials. As in the cases of the falsely localized
images and of the handleless dumb-bell, movements of both eyes, as
well as of the head but not the eyes, yield the same phenomena. It is
interesting again to compare the appearance under reflex movement. If
at any time during the experiments the eye is allowed to follow the
pendulum reflexly, the image is at once and invariably seen to pass
through its two phases as it swings past the nine-centimeter opening.

The frequent and unmistakable appearance of this band of straw-yellow
on a non-elongated green field _without the previous phase in which
the band is reddish-orange_, although this latter was unmistakable
when the same stimulation was given to the eye at rest, is
authenticated by eight subjects. _This appearance, together with that
of the handleless dumb-bell, is submitted as a demonstration that
during voluntary movements of the eyes, and probably of the head as
well, there is a moment in which stimulations are not transmitted from
the retina to the cerebral cortex, that is, a moment of central
anæsthesia_. The reason for saying 'and _probably_ of the head as
well,' is that although the phenomena described are gotten equally
well from movements of the head, yet it is not perfectly certain that
when the head moves the eyes do not also move slightly within the
head, even when the attempt is made to keep them fixed.

Most of the criticisms which apply to this last experiment apply to
that with the dumb-bell and have already been answered. There is one
however which, while applying to that other, more particularly applies
here. It would be, that these after-images are too brief and
indistinct to be carefully observed, so that judgments as to their
shape, size, and color are not valid evidence. This is a perfectly
sensible criticism, and a person thoroughly convinced of its force
should repeat the experiments and decide for himself what reliance he
will place on the judgments he is able to make. The writer and those
of the subjects who are most trained in optical experiments find the
judgments so simple and easily made as not to be open to doubt.

In the first place, it should be remembered that only those cases are
counted in which the movement was so timed that the image was seen in
direct vision, that is, was given on or very near the fovea. In such
cases a nice discrimination of the shape and color of the images is
easily possible.

Secondly, the judgments are in no case quantitative, that is, they in
no case depend on an estimate of the absolute size of any part of the
image. At most the proportions are estimated. In the case of the
dumb-bell the question is, Has the figure a handle? The other
question, Are the end-circles horizontally elongated? has not to be
answered with mathematical accuracy. It is enough if the end-circles
are approximately round, or indeed are narrower than 9 cm.
horizontally, for at even that low degree of concentration the handle
was still visible to the resting eye. Again, in the experiment with
the color-phases, only two questions are essential to identify the
appearance 5: Does the horizontal yellow band extend quite to both
edges of the image? and, Is there certainly no trace of red or orange
to be seen? The first question does not require a quantitative
judgment, but merely one as to whether there is any green visible to
the right or left of the yellow strip. Both are therefore strictly
questions of quality. And the two are sufficient to identify
appearance 5, for if no red or orange is visible, images 1, 2, and 3
are excluded; and if no green lies to the right or left of the yellow
band, image 4 is excluded. Thus if one is to make the somewhat
superficial distinction between qualitative and quantitative
judgments, the judgments here required are qualitative. Moreover, the
subjects make these judgments unhesitatingly.

Finally, the method of making judgments on after-images is not new in
psychology. Lamansky's well-known determination of the rate of
eye-movements[22] depends on the possibility of counting accurately
the number of dots in a row of after-images. A very much bolder
assumption is made by Guillery[23] in another measurement of the rate
of eye-movements. A trapezoidal image was generated on the moving
retina, and the after-image of this was projected on to a plane
bearing a scale of lines inclining at various angles. On this the
degree of inclination of one side of the after-image was read off, and
thence the speed of the eye-movement was calculated. In spite of the
boldness of this method, a careful reading of Guillery's first article
cited above will leave no doubt as to its reliability, and the
accuracy of discrimination possible on these after-images.

   [22] Lamansky, S., (Pflüger's) Archiv f. d. gesammte
   Physiologie, 1869, II., S. 418.

   [23] Guillery, (Pflüger's) Archiv f. d. ges. Physiologie, 1898,
   LXXI., S. 607; and 1898, LXXIII., S. 87.

As to judgments on the color and color-phases of after-images, there
is ample precedent in the researches of von Helmholtz, Hering, Hess,
von Kries, Hamaker, and Munk. It is therefore justifiable to assume
the possibility of making accurately the four simple judgments of
shape and color described above, which are essential to the two proofs
of anæsthesia.


V. SUMMARY AND COROLLARIES OF THE EXPERIMENTS, AND A PARTIAL,
PHYSIOLOGICAL INTERPRETATION OF THE CENTRAL ANÆSTHESIA.


We have now to sum up the facts given by the experiments. The fact of
central anæsthesia during voluntary movement is supported by two
experimental proofs, aside from a number of random observations which
seem to require this anæsthesia for their explanation. The first proof
is that if an image of the shape of a dumb-bell is given to the retina
during an eye-movement, and in such a way that the handle of the
image, while positively above the threshold of perception, is yet of
brief enough duration to fade completely before the end of the
movement, it then happens that both ends of the dumb-bell are seen but
the handle not at all. The fact of its having been properly given to
the retina is made certain by the presence of the now disconnected
ends.

The second proof is that, similarly, if during an eye-movement two
stimulations of different colors are given to the retina, superposed
and at such intensity and rate of succession as would show to the
resting eye two successive phases of color (in the case taken,
reddish-orange and straw-yellow), it then happens that the first
phase, which runs its course and is supplanted by the second before
the movement is over, is not perceived at all. The first phase was
certainly given, because the conditions of the experiment require the
orange to be given if the straw-yellow is, since the straw-yellow
which is seen can be produced only by the addition of green to the
orange which is not seen.

These two phenomena seem inevitably to demonstrate a moment during
which a process on the retina, of sufficient duration and intensity
ordinarily to determine a corresponding conscious state, is
nevertheless prevented from doing so. One inclines to imagine a
retraction of dendrites, which breaks the connection between the
central end of the optic nerve and the occipital centers of vision.

The fact of anæsthesia demonstrated, other phenomena are now available
with further information. From the phenomena of the 'falsely
localized' images it follows that at least in voluntary eye-movements
of considerable arc (30° or more), the anæsthesia commences
appreciably later than the movement. The falsely localized streak is
not generated before the eye moves, but is yet seen before the
correctly localized streak, as is shown by the relative intensities of
the two. The anæsthesia must intervene between the two appearances.
The conjecture of Schwarz, that the fainter streak is but a second
appearance of the stronger, is undoubtedly right.

We know too that the anæsthesia depends on a mechanism central of the
retina, for stimulations are received during movement but not
transmitted to consciousness till afterward. This would be further
shown if it should be found that movements of the head, no less than
those of the eyes, condition the anæsthesia. As before said, it is not
certain that the eyes do not move slightly in the head while the head
moves. The movement of the eyes must then be very slight, and the
anæsthesia correspondingly either brief or discontinuous. Whereas, the
phenomena are the same when the head moves 90° as when the eyes move
that amount. It seems probable, then, that voluntary movements of the
head do equally condition the anæsthesia.

We have seen, too, that in reflex eye-or head-movements no anæsthesia
is so far to be demonstrated. The closeness with which the eye follows
the unexpected gyrations of a slowly waving rush-light, proves that
the reflex movement is produced by a succession of brief impulses
(probably from the cerebellum), each one of which carries the eye
through only a very short distance. It is an interesting question,
whether there is an instant of anæsthesia for each one of these
involuntary innervations--an instant too brief to be revealed by the
experimental conditions employed above. The seeming continuity of the
sensation during reflex movement would of course not argue against
such successive instants of anæsthesia, since no discontinuity of
vision during voluntary movement is noticeable, although a relatively
long moment of anæsthesia actually intervenes.

But decidedly the most interesting detail about the anæsthesia is that
shown by the extreme liability of the eye to stop reflexly on the red
or the green light, in the second experiment with the pendulum.
Suppose the eye to be moving from _P_ to _P'_ (Fig. 5); the
anæsthesia, although beginning later than the movement, is present
when the eye reaches _O_, while it is between _O_ and _N_, that is,
during the anæsthetic moment, that the eye is reflexly caught and held
by the light. This proves again that the anæsthesia is not retinal,
but it proves very much more; namely, that _the retinal stimulation is
transmitted to those lower centers which mediate reflex movements, at
the very instant during which it is cut off from the higher, conscious
centers_. The great frequency with which the eye would stop midway in
its movements, both in the second pendulum-experiment and in the
repetition of Dodge's perimeter-test, was very annoying at the time,
and the observation cannot be questioned. The fact of the habitual
reflex regulation of voluntary movements is otherwise undisputed.
Exner[24] mentions a variety of similar instances. Also, with the
moving dumb-bell, as has been mentioned, the eye having begun a
voluntary sweep would often be caught by the moving image and carried
on thereafter reflexly with the pendulum. These observations hang
together, and prove a connection between the retina and the reflex
centers even while that between the retina and the conscious centers
is cut off.

   [24] Exner, Sigmund, 'Entwurf zu einer physiologischen
   Erklärung der psychischen Erscheinungen,' Leipzig und Wien,
   1894, S. 124-129.

But shall we suppose that the 'connection' between the retina and the
conscious centers is cut off during the central anæsthesia? All that
the facts prove is that the centers are at that time not conscious. It
would be at present an unwarrantable assumption to make, that these
centers are therefore disconnected from the retina, at the optic
thalami, the superior quadrigeminal bodies, or wheresoever. On broad
psychological grounds the action-theory of Münsterberg[25] has
proposed the hypothesis that cerebral centers fail to mediate
consciousness not merely when no stimulations are transmitted to them,
but rather when the stimulations transmitted are not able to pass
through and out. The stimulation arouses consciousness when it finds a
ready discharge. And indeed, in this particular case, while we have no
other grounds for supposing stimulations _to_ the visual centers to be
cut off, we do have other grounds for supposing that egress _from_
these cells would be impeded.

   [25] Münsterberg, Hugo, 'Grundzüge der Psychologie,' Leipzig,
   1900, S. 525-561.

The occipital centers which mediate sensations of color are of course
most closely associated with those other centers (probably the
parietal) which receive sensations from the eye-muscles and which,
therefore, mediate sensations which furnish space and position to the
sensations of mere color. Now it is these occipital centers, mediators
of light-sensations merely, which the experiments have shown most
specially to be anæsthetic. The discharge of such centers means
particularly the passage of excitations on to the parietal
localization-centers. There are doubtless other outlets, but these are
the chief group. The movements, for instance, which activity of these
cells produces, are first of all eye-movements, which have to be
_directly_ produced (according to our present psychophysical
conceptions) by discharges from the centers of eye-muscle sensation.
The principal direction of discharge, then, from the color-centers is
toward the localization-centers.

Now the experiment with falsely and correctly localized after-images
proves that before the anæsthesia all localization is with reference
to the point of departure, while afterwards it is with reference to
the final fixation-point. The transition is abrupt. During the
anæsthesia, then, the mechanism of localization is suffering a
readjustment. It is proved that during this interval of readjustment
in the centers of eye-muscle sensation the way is closed to oncoming
discharges from the color-centers; but it is certain that any such
discharge, during this complicated process of readjustment, would take
the localization-centres by surprise, as it were, and might
conceivably result in untoward eye-movements highly prejudicial to the
safety of the individual as a whole. The much more probable event is
the following:

Although Schwarz suggests that the moment between seeing the false and
seeing the correct after-image is the moment that consciousness is
taken up with 'innervation-feelings' of the eye-movement, this is
impossible, since the innervation-feelings (using the word in the only
permissible sense of remembered muscle-sensations) must _precede_ the
movement, whereas even the first-seen, falsely localized streak is not
generated till the movement commences. But we do have to suppose that
during the visual anæsthesia, muscle-sensations of _present_ movement
are streaming to consciousness, to form the basis of the new
post-motum localization. And these would have to go to those very
centers mentioned above, the localization-centers or eye-muscle
sensation centers. One may well suppose that these incoming currents
so raise the tension of these centers that for the moment no discharge
can take place thither from other parts of the brain, among which are
the centers for color-sensations. The word 'tension' is of course a
figure, but it expresses the familiar idea that centers which are in
process of receiving peripheral stimulations, radiate that energy
_to_ other parts of the brain (according to the neural dispositions),
and probably do not for the time being receive communications
therefrom, since those other parts are now less strongly excited. It
is, therefore, most probable that during the incoming of the
eye-muscle sensations the centers for color are in fact not able to
discharge through their usual channels toward the localization-centers,
since the tension in that direction is too high. If, now, their other
channels of discharge are too few or too little used to come into
question, the action-theory would find in this a simple explanation of
the visual anæsthesia.

The fact that the anæsthesia commences appreciably later than the
movement so far favors this interpretation. For if the anæsthesia is
conditioned by high tension in the localization-centers, due to
incoming sensations from the eye-muscles, it could not possibly
commence synchronously with the movement. For, first the sensory
end-organs in the eye-muscles (or perhaps in the ligaments, surfaces
of the eye-sockets, etc.) have their latent period; then the
stimulation has to travel to the brain; and lastly it probably has to
initiate there a summation-process equivalent to another latent
period. These three processes would account very readily for what we
may call the latent period of the anæsthesia, as observed in the
experiments. It is true that this latent period was observed only in
long eye-and head-movements, but the experiments were not delicate
enough in this particular to bring out the finer points.

Finally, the conditioning of anæsthesia by movements of the head, if
really proved, would rather corroborate this interpretation. For of
course the position of the head on the shoulders is as important for
localization of the retinal picture as the position of the eyes in the
head, so that sensations of head-movements must be equally represented
in the localization centers; and head movements would equally raise
the tension on those centers against discharge-currents from the
color-centers.

The conclusion from the foregoing experiments is that voluntary
movements of the eyes condition a momentary, visual, central
anæsthesia.

       *       *       *       *       *



TACTUAL ILLUSIONS.

BY CHARLES H. RIEBER.


I.


Many profound researches have been published upon the subject of
optical illusions, but in the field of tactual illusions no equally
extensive and serious work has been accomplished. The reason for this
apparent neglect of the illusions of touch is obviously the fact that
the studies in the optical illusions are generally thought to yield
more important results for psychology than corresponding studies in
the field of touch. Then, too, the optical studies are more attractive
by reason of the comparative ease and certainty with which the
statistics are gathered there. An optical illusion is discovered in a
single instance of the phenomenon. We are aware of the illusion almost
immediately. But in the case of most of the illusions of touch, a
large number of experiments is often necessary in order to reveal any
approximately constant error in the judgments. Nevertheless, it seems
to me that the factors that influence our judgments of visual space,
though their effects are nearly always immediately apparent, are of no
more vital significance for the final explanation of the origin of our
notion of space than the disturbing factors in our estimations of
tactual space whose effects are not so open to direct observation.

The present investigation has for its main object a critical
examination of the tactual illusions that correspond to some of the
well-known optical illusions, in the hope of segregating some of the
various disturbing factors that enter into our very complex judgments
of tactual space. The investigation has unavoidably extended into a
number of near-lying problems in the psychology of touch, but the
final object of my paper will be to offer a more decisive answer than
has hitherto been given to the question, _Are the optical illusions
also tactual illusions, or are they reversed for touch?_

Those who have given their attention to illusions of sight and touch
are rather unequally divided in their views as to whether the
geometrical optical illusions undergo a reversal in the field of
touch, the majority inclining to the belief that they are reversed.
And yet there are not wanting warm adherents of the opposite view. A
comparison of the two classes of illusions, with this question in
view, appears therefore in the present state of divergent opinion to
be a needed contribution to experimental psychology. Such an
experimental study, if it succeeds in finding the solution to this
debate, ought to throw some further light upon the question of the
origin of our idea of space, as well as upon the subject of illusions
of sense in general. For, on the one hand, if touch and sight function
alike in our judgment of space, we should expect that like peripheral
disturbances in the two senses would cause like central errors in
judgment, and every tactual analogue of an optical illusion should be
found to correspond both in the direction of the error and, to a
certain extent, quantitatively with the optical illusion. But if, on
the other hand, they are in their origin and in their developed state
really disparate senses, each guided by a different psychological
principle, the illusion in the one sense might well be the reverse of
the corresponding illusion in the other sense. Therefore, if the
results of an empirical study should furnish evidence that the
illusions are reversed in passing from one field to the other, we
should be obliged to conclude that we are here in the presence of what
psychologists have been content to call the 'unanalyzable fact' that
the two senses function differently under the same objective
conditions. But if, on the contrary, it should turn out that the
illusions are not reversed for the two senses, then the theory of the
ultimate uniformity of the psychical laws will have received an
important defence.

These experiments were carried on in the Harvard Psychological
Laboratory during the greater part of the years 1898-1901. In all,
fifteen subjects coöperated in the work at different times.

The experimental work in the direction of a comparison of the optical
illusions with the tactual illusions, to the time of the present
investigation, has been carried on chiefly with the familiar optical
illusion of the overestimation of filled space. If the distance
between two points be divided into two equal parts by a point midway
between them, and the one of the halves be filled with intermediate
points, the filled half will, to the eye, appear longer than the open
half. James[1] says that one may easily prove that with the skin we
underestimate a filled space, 'by taking a visiting card, and cutting
one edge of it into a saw-toothed pattern, and from the opposite edge
cutting out all but two corners, and then comparing the feelings
aroused by the two edges when held against the skin.' He then remarks,
'the skin seems to obey a different law here from the eye.' This
experiment has often been repeated and verified. The most extensive
work on the problem, however, is that by Parrish.[2] It is doubtless
principally on the results of Parrish's experiments that several
authors of text-books in psychology have based their assertions that a
filled space is underestimated by the skin. The opposite conclusion,
namely, that the illusion is not reversed for the skin, has been
maintained by Thiéry,[3] and Dresslar.[4] Thiéry does not, so far as I
know, state the statistics on which he bases his view. Dresslar's
experiments, as Parrish has correctly observed, do not deal with the
proper analogue of the optical illusion for filled space. The work of
Dresslar will be criticised in detail when we come to the illusions
for active touch.

   [1] James, William: 'Principles of Psychology,' New York, 1893,
   Vol. II., p. 141.

   [2] Parrish, C.S.: _Amer. Journ. of Psy._, 1895, Vol. VI., p.
   514.

   [3] Thiéry, A.: _Philos. Studien_, 1896, Bd. XII., S. 121.

   [4] Dresslar, F.B.: _Amer. Journ. of Psy._, 1894, Vol. VI., p.
   332.

At the beginning of the present investigation, the preponderance of
testimony was found to be in favor of the view that filled space is
underestimated by the skin; and this view is invariably accompanied by
the conclusion, which seems quite properly to follow from it, that the
skin and the eye do not function alike in our perception of space. I
began my work, however, in the belief that there was lurking somewhere
in the earlier experiments a radical error or oversight. I may say
here, parenthetically, that I see no reason why experimental
psychologists should so often be reluctant to admit that they begin
certain investigations with preconceptions in favor of the theory
which they ultimately defend by the results of their experiments. The
conclusions of a critical research are in no wise vitiated because
those conclusions were the working hypotheses with which the
investigator entered upon his inquiry. I say frankly, therefore, that
although my experiments developed many surprises as they advanced, I
began them in the belief that the optical illusions are not reversed
for touch. The uniformity of the law of sense perception is prejudiced
if two senses, when affected by the same objective conditions, should
report to consciousness diametrically opposite interpretations of
these same objective facts. I may say at once, in advance of the
evidence upon which I base the assertion, that the belief with which I
began the experiments has been crystallized into a firm conviction,
namely, that neither the illusion for open or filled spaces, nor any
other optical illusion, is genuinely reversed for touch.


II.


I began my work on the problem in question by attempting to verify
with similar apparatus the results of some of the previous
investigations, in the hope of discovering just where the suspected
error lay. It is unnecessary for me to give in detail the results of
these preliminary series, which were quite in agreement with the
general results of Parrish's experiments. Distances of six centimeters
filled with points varying in number and position were, on the whole,
underestimated in comparison with equal distances without intermediate
point stimulations. So, too, the card with saw-toothed notches was
judged shorter than the card of equal length with all but the end
points cut out.

After this preliminary verification of the previous results, I was
convinced that to pass from these comparatively meager statistics,
gathered under limited conditions in a very special case, to the
general statement that the optical illusion is reversed in the field
of touch, is an altogether unwarranted procedure. When one reads the
summarized conclusions of these previous investigators, one finds it
there assumed or even openly asserted that the objective conditions of
the tactual illusion are precisely the same as those of the optical
illusion. But I contend that it is not the real analogue of the
optical illusion with which these experiments have been concerned.
The objective conditions are not the same in both. Although something
that is very much like the optical illusion is reversed, yet I shall
attempt to prove in this part of my paper, first, that the former
experiments have not been made with the real counterpart of the
optical illusion; second, that the optical illusion can be quite
exactly reproduced on the skin; third, that where the objective
conditions are the same, the filled cutaneous space is overestimated,
and the illusion thus exists in the same sense for both sight and
touch.

Let me first call attention to some obvious criticisms on Parrish's
experiments. They were all made with one distance, namely, 6.4
centimeters; and on only one region, the forearm. Furthermore, in
these experiments no attempt was made to control the factor of
pressure by any mechanical device. The experimenter relied entirely on
the facility acquired by practice to give a uniform pressure to the
stimuli. The number of judgments is also relatively small. Again, the
open and filled spaces were always given successively. This, of
course, involves the comparison of a present impression with the
memory of a somewhat remote past impression, which difficulty can not
be completely obviated by simply reversing the order of presentation.
In the optical illusion, the two spaces are presented simultaneously,
and they lie adjacent to each other. It is still a debated question
whether this illusion would exist at all if the two spaces were not
given simultaneously and adjacent. Münsterberg[5] says of the optical
illusion for the open and filled spaces, "I have the decided
impression that the illusion does not arise from the fact of our
comparing one half with the other, but from the fact that we grasp the
line as a whole. As soon as an interval is inserted, so that the
perception of the whole line as constituted of two halves vanishes,
the illusion also disappears." This is an important consideration, to
which I shall return again.

   [5] Münsterberg, H.: 'Beiträge zur Exper. Psy.,' Freiburg i.B.,
   1889, Heft II., S. 171.

Now, in my experiments, I endeavored to guard against all of these
objections. In the first place, I made a far greater number of tests.
Then my apparatus enabled me, firstly, to use a very wide range of
distances. Where the points are set in a solid block, the experiments
with long distances are practically impossible. Secondly, the
apparatus enabled me to control accurately the pressure of each point.
Thirdly, the contacts could be made simultaneously or successively
with much precision. This apparatus (Fig. 1) was planned and made in
the Harvard Laboratory, and was employed not only in our study of this
particular illusion, but also for the investigation of a number of
allied problems.

[Illustration: FIG. 1.]

Two æsthesiometers, A and B, were arranged in a framework, so that
uniform stimulations could be given on both arms. The æsthesiometers
were raised or lowered by means of the crank, C, and the cams, D and
E. The contacts were made either simultaneously or successively, with
any interval between them according to the position of the cams on the
crank. The height of the æsthesiometer could be conveniently adjusted
by the pins F and H. The shape of the cams was such that the descent
of the æsthesiometer was as uniform as the ascent, so that the
contacts were not made by a drop motion unless that was desired. The
sliding rules, of which there were several forms and lengths, could be
easily detached from the upright rods at _K_ and _L_. Each of the
points by which the contacts were made moved easily along the sliding
rule, and could be also raised or lowered for accommodation to the
unevenness of the surface of the skin. These latter were the most
valuable two features of the apparatus. There were two sets of points,
one of hard rubber, the other of metal. This enabled me to take into
account, to a certain extent, the factor of temperature. A wide range
of apparent differences in temperature was secured by employing these
two stimuli of such widely different conductivity. Then, as each point
was independent of the rest in its movements, its weight could also be
changed without affecting the rest.

In the first series of experiments I endeavored to reproduce for touch
the optical illusion in its exact form. There the open and the filled
spaces are adjacent to each other, and are presented simultaneously
for passive functioning of the eye, which is what concerns us here in
our search for the analogue of passive touch. This was by no means an
easy task, for obviously the open and the filled spaces in this
position on the skin could not be compared directly, owing to the lack
of uniformity in the sensibility of different portions of the skin. At
first, equivalents had to be established between two collinear open
spaces for the particular region of the skin tested. Three points were
taken in a line, and one of the end points was moved until the two
adjacent open spaces were pronounced equal. Then one of the spaces was
filled, and the process of finding another open space equivalent to
this filled space was repeated as before. This finding of two
equivalent open spaces was repeated at frequent intervals. It was
found unsafe to determine an equivalent at the beginning of each
sitting to be used throughout the hour.

Two sets of experiments were made with the illusion in this form. In
one the contacts were made simultaneously; the results of this series
are given in Table I. In the second set of experiments the central
point which divided the open from the filled space touched the skin
first, and then the others in various orders. The object of this was
to prevent fusion of the points, and, therefore, to enable the subject
to pronounce his judgments more rapidly and confidently. A record of
these judgments is given in Table II. In both of these series the
filled space was always taken near the wrist and the open space in a
straight line toward the elbow, on the volar side of the arm. At
present, I shall not undertake to give a complete interpretation of
the results of these two tables, but simply call attention to two
manifest tendencies in the figures. First, it will be seen that the
short filled distance of four centimeters is underestimated, but that
the long filled distance is overestimated. Second, in Table II., which
represents the judgments when the contacts were made successively, the
tendency to underestimate the short distance is less, and at the same
time we notice a more pronounced overestimation of the longer filled
distances. I shall give a further explanation of these results in
connection with later tables.


TABLE I.

           4 cm.               6 cm.               8 cm.
     Filled.  Open.       Filled.  Open.       Filled.  Open.

  F.   5.3     4.7         7.8     7.6          9.3     10.5
  F.   5.7     4.4         6.5     7.3          9.2     11.7
  F.   6.0     5.6         8.2     7.3          8.7     10.8
       ---     ---         ---     ---          ---     ----
  Av.  5.7     4.9         7.5     7.4          9.1     11.0

  R.   5.7     5.1         6.7     6.8          9.3     10.2
  R.   5.4     5.4         7.2     7.1          8.5     10.7
  R.   4.6     4.2         8.1     8.1          9.1     11.4
       ---     ---         ---     ---          ---     ----
  Av.  5.2     4.9         7.3     7.3          9.0     10.8

  K.   5.6     5.1         6.8     6.7          8.1      9.6
  K.   5.0     5.1         7.3     7.5          8.2     11.2
  K.   4.9     4.9         8.2     8.1         10.1     10.1
       ---     ---         ---     ---         ----     ----
  Av.  5.2     5.0         7.4     7.4          8.8     10.3


TABLE II.

           4 cm.               6 cm.               8 cm.
     Filled.  Open.       Filled.  Open.       Filled.  Open.

  F.   5.1     5.0         8.0     8.3          9.2     10.3
  F.   5.8     4.7         7.2     7.9          8.7     10.9
  F.   5.6     5.5         6.9     9.1          9.1     11.1
       ---     ---         ---     ---          ---     ----
  Av.  5.5     5.1         7.4     8.4          9.0     10.8

  R.   6.0     4.8         8.2     7.5          9.4     10.6
  R.   5.7     5.4         6.5     7.4         10.1      9.4
  R.   5.0     5.2         7.7     7.8          8.6     11.2
       ---     ---         ---     ---         ----     ----
  Av.  5.6     5.1         7.5     7.6          9.4     10.4

  K.   4.8     4.8         8.2     8.3          8.1      9.8
  K.   5.1     5.3         7.1     7.7         10.0     10.8
  K.   4.7     5.0         8.1     8.6          8.6      9.4
       ---     ---         ---     ---         ----     ----
  Av.  4.9     5.0         7.8     8.2          8.9     10.0

    The first two numbers in the first line signify that when an
    open distance of 4 cm. was taken, an adjacent open distance of
    4.7 cm. was judged equal; but when the adjacent space was
    filled, 5.3 cm. was judged equal. Each number in the column of
    filled distances represents an average of five judgments. All
    of the contacts in Table I. were made simultaneously; in Table
    II. they were made successively.


In the next series of experiments the illusion was approached from an
entirely different point of view. The two points representing the open
space were given on one arm, and the filled space on a symmetrical
part of the other arm. I was now able to use a much wider range of
distances, and made many variations in the weights of the points and
the number that were taken for the filled distance.

However, before I began this second series, in which one of the chief
variations was to be in the weights of the different points, I made a
brief preliminary series of experiments to determine in a general way
the influence of pressure on judgments of point distances. Only three
distances were employed, four, six and twelve centimeters, and three
weights, twelve, twenty and forty grams. Table III. shows that, for
three men who were to serve as subjects in the main experiments that
are to follow, an increase in the weight of the points was almost
always accompanied by an increase in the apparent distance.


TABLE III.

  Distances.    4 cm.             6 cm.            12 cm.

   Weights
   (Grams).  12   20   40     12   20   40     12    20    40

  R.        3.9  3.2  3.0    6.2  5.6  5.3    11.4  10.4   9.3
  F.        4.3  4.0  3.6    6.1  5.3  5.5    12.3  11.6  10.8
  B.        4.1  3.6  3.1    6.0  5.7  5.8    12.0  10.2   9.4
  P.        4.3  4.1  3.7    5.9  5.6  5.6    13.1  11.9  10.7

    In the standard distances the points were each weighted to 6
    grams. The first three figures signify that a two-point
    distance of 4 cm., each point weighing 6 grams, was judged
    equal to 3.9 cm. when each point weighed 12 grams. 3.2 cm.
    when each point weighed 20 grams, etc. Each figure is the
    average of five judgments.


Now the application of this principle in my criticism of Parrish's
experiments, and as anticipating the direction which the following
experiments will take, is this: if we take a block such as Parrish
used, with only two points in it, and weight it with forty grams in
applying it to the skin, it is plain that each point will receive one
half of the whole pressure, or twenty grams. But if we put a pressure
of forty grams upon a block of eight points, each point will receive
only one eighth of the forty, or five grams. Thus, in the case of the
filled space, the end points, which play the most important part in
the judgment of the distance, have each only five grams' pressure,
while the points in the open space have each twenty grams. We should,
therefore, naturally expect that the open space would be
overestimated, because of the decided increase of pressure at these
significant points. Parrish should have subjected the blocks, not to
the same pressure, but to a pressure proportional to the number of
points in each block. With my apparatus, I was easily able to prove
the correctness of my position here. It will be seen in Tables IV. to
VIII. that, when the sum of the weights of the two end points in the
open space was only just equal to the sum of the weights of all the
points in the filled space, the filled space was underestimated just
as Parrish has reported. But when the points were all of the same
weight, both in the filled and the open space, the filled space was
judged longer in all but the very short distances. For this latter
exception I shall offer an explanation presently.

Having now given an account of the results of this digression into
experiments to determine the influence of pressure upon point
distances, I shall pass to the second series of experiments on the
illusion in question. In this series, as has been already stated, the
filled space was taken on one arm and the open on the other, and then
the process was reversed in order to eliminate any error arising from
a lack of symmetry between the two regions. Without, for the present,
going into a detailed explanation of the statistics of this second
series of experiments, which are recorded in Tables IV., V., VI.,
VII. and VIII., I may summarize the salient results into these general
conclusions: First, the short filled distance is underestimated;
second, this underestimation of the filled space gradually decreases
until in the case of the filled distance of 18 cm. the judgments pass
over into pronounced overestimations; third, an increase in the number
of points of contact in the shorter distances increases the
underestimation, while an increase in the number of points in the
longer distance increases the overestimation; fourth, an increase of
pressure causes an invariable increase in the apparent length of
space. If a general average were made of the results given in Tables
IV., V., VI., VII. and VIII., there would be a preponderance of
evidence for the conclusion that the filled spaces are overestimated.
But we cannot ignore the marked tendencies in the opposite direction
for the long and the short distances. These anomalous results, which,
it will be remembered, were also found in our first series, call for
explanation. Several hypotheses were framed to explain these
fluctuations in the illusion, and then some shorter series of
experiments were made in different directions with as large a number
of variations in the conditions as possible, in the hope of
discovering the disturbing factors.


TABLE IV.¹

  4 Centimeters.

             A           B              D            E
        less = gr.  less = gr.     less = gr.   less = gr.
  R. (a)  7  2  1     8  1  1        6  2  2      5  1  4
     (b)  7  3  0     7  1  2        6  2  2      6  1  3
  F. (a)  6  3  1     7  1  2        7  0  3      6  0  4
     (b)  7  0  3     9  1  0        6  1  3      5  2  3
          -------    --------       --------     --------
         27  8  5    31  4  5       25  5 10     22  4 14

    ¹In columns _A_, _B_, and _C_ the filled spaces were made up
    of 4, 5 and 6 points, respectively. The total weight of the
    filled space in _A_, _B_ and _C_ was always just equal to the
    weight of the two points in the open space, 20 gr. In (_a_)
    the filled distance was given on the right arm first, in (_b_)
    on the left arm. It will be observed that this reversal made
    practically no difference in the judgments and therefore was
    sometimes omitted. In _D_ the filled space consisted of four
    points, but here the weight of each point was 10 gr., making a
    total weight of 40 gr. for the filled space, as against 20 gr.
    for the open space. In _E_ the weight of each was 20 gr.,
    making the total weight of the filled space 80 gr.


TABLE V.

  6 Centimeters.

              A          B          C          D          E
         less = gr. less = gr. less = gr. less = gr. less = gr.
  R. (a)  10  8  2   12  0  8   14  6  0   9   6  5   8  2  10
  F. (a)  12  4  4   12  6  2   12  4  4   8   3  9   6  3  11
  K. (a)  10  2  8   12  6  2   14  2  4   6   4 10   7  2  11
          --------   --------   --------   --------   --------
          32 14 14   36 12 12   40 12  8  23  13 24  21  7  32


TABLE VI.

  8 Centimeters.

              A          B          C          D          E
         less = gr. less = gr. less = gr. less = gr. less = gr.
  R. (a)   4  1  5    5  1  4    7  0  3    4  0  6    3  0  7
     (b)   4  0  6    5  1  4    6  1  3    4  1  5    2  1  7
  F. (a)   5  0  5    5  0  5    6  0  4    3  0  7    4  0  6
     (b)   5  1  4    6  1  3    8  0  2    4  1  5    2  3  5
  K. (a)   4  1  5    6  1  3    7  1  2    3  2  5    1  3  6
     (b)   4  0  6    7  0  3    6  1  3    4  0  6    3  0  7
           -------    -------    -------    -------    -------
          26  3 31   34  4 22   40  3 17   22  4 34   15  7 38


TABLE VII.

  12 Centimeters.

              A          B          C          D          E
         less = gr. less = gr. less = gr. less = gr. less =  gr.
  R. (a)  3  6  16   8  3  14  10  8  7    6  3  16   3  4   18
  F. (a)  5  7  13  10  5  10   9  6 10    6  4  15   5  1   19
  K. (a)  8  2  15   8  4  13  13  9  3    3  7  15   3  0   22
          --------   --------   -------    --------   ---------
         16 15  44  26 12  37  32 23 20   15 14  46  11  5   59


TABLE VIII.

  18 Centimeters.

              A          B          C          D          E
         less = gr. less = gr. less = gr. less = gr. less = gr.
  R. (a)   2  0  23   0  0  25   4  4  17   3  1  21   0  1  24
     (b)   3  1  21   1  0  24   5  3  17   1  6  18   0  2  23
  F. (a)   1  4  20   3  0  22   8  6  11   0  5  20   2  0  23
     (b)   2  3  20   2  1  22   6  7  12   1  4  20   0  3  22
  K. (a)   4  2  19   4  0  21   2  7  16   0  7  18   0  0  25
     (b)   1  0  24   2  6  17   8  0  17   2  6  17   1  0  24
           --------   --------   --------   --------   --------
          13 10 127  12  7 131  33 27  90   7 29 114   3  6 141

TABLES IV.-VIII.

The first line in column _A_ (Table IV.) signifies that out of 10
judgments, comparing an open space 4 cm., total weight 20 gr., with a
filled space of 4 points, total weight also 20 gr., the filled space
was judged less 7 times, equal 2 times, and greater once.


III.


The results of the investigation, thus far, point to the conclusion
that short filled spaces are underestimated, that long spaces are
overestimated, and that between the two there lies what might be
called an 'indifference zone.' This unexpected outcome explains, I
think, the divergent opinions of the earlier investigators of this
problem. Each theory is right in what it affirms, but wrong in what it
implicitly or openly denies.

I next set out to determine as precisely as possible how far the
factor of fusion, or what Parrish has called irradiation, enters into
the judgments. It was evident from the beginning of this whole
investigation that fusion or displacement of the points was very
common. The term 'irradiation' is, however, too specific a term to
describe a process that works in these two opposite directions. The
primary concern of these next experiments was, therefore, to devise
means for preventing fusion among the points before the subject
pronounced his judgment. With our apparatus we were able to make a
number of experiments that show, in an interesting way, the results
that follow when the sensations are not permitted to fuse. It is only
the shorter distances that concern us here. The longer distances have
already been shown to follow the law of optical illusion, that is,
that filled space is overestimated. The object of the present
experiments is to bring the shorter distances under the same law, by
showing, first, that the objective conditions as they have existed in
our experiments thus far are not parallel to those which we find in
the optical illusion. Second, that when the objective conditions are
the same, the illusion for the shorter distances follows the law just
stated.

In repeating some of the experiments reported in Tables IV.-VIII. with
varying conditions, I first tried the plan of using metallic points at
the ends of the spaces. Thus, by an apparent difference in the
temperature between the end points and the filling, the sensations
from the end points, which play the most important part in the
judgment of the length, were to a certain extent kept from fusing with
the rest. The figures in Table II. have already shown what may be
expected when the points are kept from fusing. Here, also, a marked
tendency in the direction of apparent lengthening of the distance was
at once observed. These short filled distances, which had before been
underestimated, were now overestimated. The same results follow when
metallic points are alternated with hard rubber points in the filling
itself.

This changing of the apparent temperature of the end points has, it
must be admitted, introduced another factor; and it might be objected
that it was not so much the prevention of fusion as the change in the
temperature that caused the judgments to drift towards overestimation.
I have statistics to show that this observation is in a way just.
Extremes in temperature, whether hot or cold, are interpreted as an
increase in the amount of space. This conclusion has also been
reported from a number of other laboratories. My contention at this
point is simply that there are certain conditions under which these
distances will be overestimated and that these are the very conditions
which bring the phenomenon into closer correspondence with the optical
illusion, both as to the stimuli and the subjective experience. Then,
aside from this, such an objection will be seen to be quite irrelevant
if we bear in mind that when the end points in the filled distance
were replaced by metallic points, metallic points were also employed
in the open distance. The temperature factor, therefore, entered into
both spaces alike. By approaching the problem from still another point
of view, I obtained even more conclusive evidence that it is the
fusion of the end points with the adjacent points in the short
distances that leads to the underestimation of these. I have several
series in which the end points were prevented from fusing into the
filling, by raising or lowering them in the apparatus, so that they
came in contact with the skin just after or before the intermediate
points. When the contacts were arranged in this way, the tendency to
underestimate the filled spaces was very much lessened, and with some
subjects the tendency passed over into a decided overestimation. This,
it will be seen, is a confirmation of the results in Table II.

I have already stated that the two series of experiments reported in
Section II. throughout point to the conclusion that an increase of
pressure is taken to mean an increase in the distance. I now carried
on some further experiments with short filled distances, making
variations in the place at which the pressure was increased. I found a
maximum tendency to underestimate when the central points in the
filled space were weighted more than the end points. A strong drift in
the opposite direction was noticed when the end points were heavier
than the intermediate ones. It is not so much the pressure as a whole,
as the place at which it is applied, that causes the variations in the
judgments of length. In these experiments the total weights of the
points were the same in both cases. An increase of the weight on the
end points with an equivalent diminution of the weights on the
intervening points gave the end points greater distinctness apparently
and rendered them less likely to disappear from the judgments.

At this stage in the inquiry as to the cause of the underestimation of
short distances, I began some auxiliary experiments on the problem of
the localization of cutaneous impressions, which I hoped would throw
light on the way in which the fusion or displacement that I have just
described takes place. These studies in the localization of touch
sensations were made partly with a modification of the Jastrow
æsthesiometer and partly with an attachment to the apparatus before
described (Fig. 1). In the first case, the arm upon which the
impressions were given was screened from the subject's view, and he
made a record of his judgments on a drawing of the arm. The criticism
made by Pillsbury[6] upon this method of recording the judgments in
the localization of touch sensations will not apply to my experiments,
for I was concerned only with the relative, not with the absolute
position of the points. In the case of the other experiments, a card
with a single line of numbered points was placed as nearly as possible
over the line along which the contacts had been made on the arm. The
subject then named those points on the card which seemed directly over
the points which had been touched.

   [6] Pillsbury, W.B.: Amer. Journ. of Psy., 1895, Vol. VII., p.
   42.

The results from these two methods were practically the same. But the
second method, although it obviously permitted the determination of
the displacements in one dimension only, was in the end regarded as
the more reliable method. With this apparatus I could be more certain
that the contacts were made simultaneously, which was soon seen to be
of the utmost importance for these particular experiments. Then, too,
by means of this æsthesiometer, all movement of the points after the
contact was made was prevented. This also was an advantage in the use
of this apparatus, here and elsewhere, which can hardly be
overestimated. With any æsthesiometer that is operated directly by the
hand, it is impossible to avoid imparting a slight motion to the
points and thus changing altogether the character of the impression.
The importance of this consideration for my work was brought forcibly
to my attention in this way. One of the results of these tests was
that when two simultaneous contacts are made differing in weight, if
only one is recognized it is invariably located in the region of the
contact with the heavier point. But now if, while the points were in
contact with the skin and before the judgment was pronounced, I gave
the lighter point a slight jar, its presence and location were thereby
revealed to the subject. Then, too, it was found to be an advantage
that the judgments were thus confined to the longitudinal displacement
only; for, as I have before insisted, it was the relative, not the
absolute position that I wished to determine, since my object in all
these experiments in localization was to determine what connection, if
any, exists between judgments upon cutaneous distances made indirectly
by means of localization, and judgments that are pronounced directly
upon the subjective experience of the distance.

In the first of these experiments, in which two points of different
weight were used, the points were always taken safely outside of the
threshold for the discrimination between two points in the particular
region of the skin operated on. An inspection of the results shown in
Figs. 2 and 3 will indicate the marked tendency of the heavier point
to attract the lighter. In Figs. 2 and 3 the heavy curves were plotted
from judgments where both heavy and light points were given together.
The dotted curve represents the localization of each point when given
alone. The height of the curves at any particular point is determined
by the number of times a contact was judged to be directly under that
point. The fact that the curves are higher over the heavy points shows
that, when two points were taken as one, this one was localized in the
vicinity of the heavier point. When points were near the threshold for
any region, it will be observed that the two points were attracted to
each other. But when the points were altogether outside the threshold,
they seemed strangely to have repelled each other. As this problem lay
somewhat away from my main interest here, I did not undertake to
investigate this peculiar fluctuation exhaustively. My chief purpose
was satisfied when I found that the lighter point is displaced toward
the heavier, in short distances. A further explanation of these
figures will be given in connection with similar figures in the next
section.

[Illustration: FIG. 2. Back of hand.]

[Illustration: FIG. 3. Forearm.]

This attraction of the heavier for the lighter points is, I think, a
sufficient explanation for the variations in judgments upon filled
distances where changes are made in the place at which the pressure is
applied. I furthermore believe that an extension of this principle
offers an explanation for the underestimation of cutaneous
line-distances, which has been frequently reported from various
laboratories. Such a straight line gives a subjective impression of
being heavier at the center. I found that if the line is slightly
concave at the center, so as to give the ends greater prominence and
thereby leave the subjective impression that the line is uniform
throughout its entire length, the line will be overestimated in
comparison with a point distance. Out of one hundred judgments on the
relative length of two hard-rubber lines of 5 cm. when pressed against
the skin, one of which was slightly concave, the concave line was
overestimated eighty-four times. For sight, a line in which the shaded
part is concentrated at the center appears longer than an objectively
equal line with the shading massed towards the ends.


IV.


In the last section, I gave an account of some experiments in the
localization of touch sensations which were designed to show how,
under varying pressure, the points in the filled distance are
displaced or fused and disappear entirely from the judgment. Our
earliest experiments, it will be remembered, yielded unmistakable
evidence that short, filled distances were underestimated; while all
of the secondary experiments reported in the last section have pointed
to the conclusion that even these shorter distances will follow the
law of the longer distances and be overestimated under certain
objective conditions, which conditions are also more nearly parallel
with those which we find in the optical illusion. I wish now to give
the results of another and longer set of experiments in the
localization of a manifold of touch sensations as we find them in this
same illusion for filled space, by which I hope to prove a direct
relation between the function of localization and the spatial
functioning proper.

These experiments were made with the same apparatus and method that
were used in the previous study in localization; but instead of two
points of different weights, four points of uniform weight were
employed. This series, therefore, will show from quite another point
of view that the fusion which takes place, even where there is no
difference in the weight, is a very significant factor in judgments of
distance on the skin.

[Illustration: Fig. 4.]

I need hardly say that here, and in all my other experiments, the
subjects were kept as far as possible in complete ignorance of the
object of the experiment. This and the other recognized laboratory
precautions were carefully observed throughout this work. Four
distances were used, 4, 8, 12 and 16 cm. At frequent intervals
throughout the tests the contact was made with only one of the points
instead of four. In this way there came to light again the interesting
fact which we have already seen in the last section, which is of great
significance for my theory--that the end points are located
differently when given alone than when they are presented
simultaneously with the other points. I give a graphic representation
of the results obtained from a large number of judgments in Figs. 4, 5
and 6. These experiments with filled spaces, like the earlier
experiments, were made on the volar side of the forearm beginning near
the wrist. In each distance four points were used, equally distributed
over the space. The shaded curve, as in the previous figures,
represents the results of the attempts to localize the points when all
four were given simultaneously. In the dotted curves, the end points
were given alone. The height of the curve at any place is determined
by the number of times a point was located immediately underneath that
particular part of the curve. In Fig. 4 the curve which was determined
by the localization of the four points when given simultaneously,
shows by its shape how the points appear massed towards the center. In
Fig. 5 the curve _AB_ shows, by its crests at _A_ and _B_, that the
end points tended to free themselves from the rest in the judgments.
But if the distance _AB_ be taken to represent the average of the
judgments upon the filled space 1, 2, 3, 4, it will be seen to be
shorter than what may be regarded as the average of the judgments upon
the corresponding open space, namely, the distance _A'B'_, determined
by the localizations of the end points alone. The comparative
regularity of the curve indicates that the subject was unable to
discriminate among the points of the filling with any degree of
certainty. The localizations were scattered quite uniformly along the
line. In these short distances the subject often judged four points as
two, or even one.

[Illustration: Fig. 5.]

[Illustration: Fig. 6.]

Turning to Fig. 6, we notice that the tendency is now to locate the
end points in the filled distance outside of the localization of these
same points when given without the intermediate points. It will also
be seen from the irregularities in these two longer curves that there
is now a clear-cut tendency to single out the individual points. The
fact that the curves here are again higher over point 4 simply
signifies that at this, the wrist end, the failure to discover the
presence of the points was less frequent than towards the elbow. But
this does not disturb the relation of the two series of judgments. As
I have before said, the first two sets of experiments described in
Section II. showed that the shorter filled distances are
underestimated, while the longer distances are overestimated, and that
between the two there is somewhat of an 'indifferent zone.' In those
experiments the judgments were made directly on the cutaneous
distances themselves. In the experiments the results of which are
plotted in these curves, the judgment of distances is indirectly
reached through the function of localization. But it will be observed
that the results are substantially the same. The longer distances are
overestimated and the shorter distances underestimated. The curves in
Figs. 4, 5 and 6 were plotted on the combined results for two
subjects. But before the combination was made the two main tendencies
which I have just mentioned were observed to be the same for both
subjects.

It will be remembered also that in these experiments, where the
judgment of distance was based directly on the cutaneous impression,
the underestimation of the short, filled distance was lessened and
even turned into an overestimation, by giving greater distinctness to
the end points, in allowing them to come in contact with the skin just
before or just after the filling. The results here are again the same
as before. The tendency to underestimate is lessened by this device.
Whenever, then, a filled space is made up of points which are
distinctly perceived as discrete--and this is shown in the longer
curves by the comparative accuracy with which the points are
located--these spaces are overestimated.

In all of these experiments on localization, the judgments were given
with open eyes, by naming the visual points under which the tactual
points seemed to lie. I have already spoken of the other method which
I also employed. This consisted in marking points on paper which
seemed to correspond in number and position to the points on the skin.
During this process the eyes were kept closed. This may appear to be a
very crude way of getting at the illusion, but from a large number of
judgments which show a surprising consistency I received the emphatic
confirmation of my previous conclusion, that filled spaces were
overestimated. These experiments were valuable also from the fact that
here the cutaneous space was estimated by the muscle sense, or active
touch, as it is called.

In the experiments so far described the filling in of the closed space
was always made by means of stationary points. I shall now give a
brief account of some experiments which I regard as very important for
the theory that I shall advance later. Here the filling was made by
means of a point drawn over the skin from one end of a two-point
distance to the other.

These experiments were made on four different parts of the skin--the
forehead, the back of the hand, the abdomen, and the leg between the
knee and the thigh. I here forsook the plan which I had followed
almost exclusively hitherto, that of comparing the cutaneous distances
with each other directly. The judgments now were secured indirectly
through the medium of visual distances. There was placed before the
subject a gray card, upon which were put a series of two-point
distances ranging from 2 to 20 cm. The two-point distances were given
on the skin, and the subject then selected from the optical distances
the one that appeared equal to the cutaneous distance. This process
furnished the judgments on open spaces. For the filled spaces,
immediately after the two-point distance was given a blunt stylus was
drawn from one point to the other, and the subject then again selected
the optical distance which seemed equal to this distance filled by the
moving point.

The results from these experiments point very plainly in one
direction. I have therefore thought it unnecessary to go into any
further detail with them than to state that for all subjects and for
all regions of the skin the filled spaces were overestimated. This
overestimation varied also with the rate of speed at which the stylus
was moved. The overestimation is greatest where the motion is slowest.

Vierordt[7] found the same result in his studies on the time sense,
that is, that the more rapid the movement, the shorter the distance
seems. But lines drawn on the skin are, according to him,
underestimated in comparison with open two-point distances. Fechner[8]
also reported that a line drawn on the skin is judged shorter than the
distance between two points which are merely touched. It will be
noticed, however, that my experiments differed from those of Vierordt
and Fechner in one essential respect. This difference, I think, is
sufficient to explain the different results. In my experiments the
two-point distance was held on the skin, while the stylus was moved
from one point to the other. In their experiments the line was drawn
without the points. This of course changes the objective conditions.
In simply drawing a line on the skin the subject rapidly loses sight
of the starting point of the movement. It follows, as it were, the
moving point, and hence the entire distance is underestimated. I made
a small number of tests of this kind, and found that the line seemed
shorter than the point distance as Fechner and Vierordt declared. But
when the point distance is kept on the skin while the stylus is being
drawn, the filling is allowed its full effect in the judgment,
inasmuch as the end points are perceived as stationary landmarks. The
subjects at first found some difficulty in withholding their judgments
until the movement was completed. Some subjects declared that they
frequently made a preliminary judgment before the filling was
inserted, but that when the moving point approached the end point,
they had distinctly the experience that the distance was widening. In
these experiments I used five sorts of motion, quick and heavy, quick
and light, slow and heavy, slow and light, and interrupted. I made no
attempt to determine either the exact amount of pressure or the exact
rate. I aimed simply at securing pronounced extremes. The slow rate
was approximately 3, and the fast approximately 15 cm. per second.

   [7] 'Zeitsinn,' Tübingen, 1858.

   [8] Fechner, G. Th., 'Elem. d. Psychophysik,' Leipzig, 1889; 2.
   Theil, S. 328.

I have already said that these filled spaces were invariably
overestimated and that the slower the movement, the greater, in
general, is the overestimation. In addition to the facts just stated I
found also, what Hall and Donaldson[9] discovered, that an increase in
the pressure of a moving point diminishes the apparent distance.

   [9] Hall, G. St., and Donaldson, H.H., 'Motor Sensations on the
   Skin,' _Mind_, 1885, X., p. 557.

Nichols,[10] however, says that heavy movements seem longer and light
ones shorter.

   [10] _Op. citat.,_ p. 98.


V.


There are several important matters which might properly have been
mentioned in an earlier part of this paper, in connection with the
experiments to which they relate, but which I have designedly omitted,
in order not to disturb the continuity in the development of the
central object of the research. The first of these is the question of
the influence of visualization on the judgments of cutaneous
distances. This is in many ways a most important question, and
confronts one who is making studies in tactual space everywhere. The
reader may have already noticed that I have said but little about the
factor of visualization in any of my experiments, and may have
regarded it as a serious omission. It might be offered as a criticism
of my work that the fact that I found the tactual illusions to exist
in the same sense as the optical illusions was perhaps due to the
failure to exclude visualization. All of the subjects declare that
they were unable to shut out the influence of visualizing entirely.
Some of the subjects who were very good visualizers found the habit
especially insistent. I think, however, that not even in these latter
cases does this factor at all vitiate my conclusions.

It will be remembered that the experiments up to this time fall into
two groups, first, those in which the judgments on the cutaneous
distances were reached by direct comparisons of the sensations
themselves; and secondly, those in which the sensations were first
localized and then the judgment of the distance read from these
localizations. Visualizing, therefore, entered very differently into
the two groups. In the first instance all of the judgments were made
with the eyes closed, while all of the localizations were made with
the eyes open. I was uncertain through the whole of the first group of
experiments as to just how much disturbance was being caused in the
estimation of the distance by visualizing. I therefore made a series
of experiments to determine what effect was produced upon the illusion
if in the one set of judgments one purposely visualized and in the
other excluded visualizing as far as possible. In my own case I found
that after some practice I could give very consistent judgments, in
which I felt that I had abstracted from the visualized image of the
arm almost entirely. I did not examine these results until the close
of the series, and then found that the illusion was greater for those
judgments in which visualization was excluded; that is, the filled
space seemed much larger when the judgment was made without the help
of visualization. It is evident, therefore, that the tactual illusion
is influenced rather in a negative direction by visualization.

In the second group of experiments, where the judgments were obtained
through the localization of the points, it would seem, at first sight,
that the judgments must have been very largely influenced by the
direct vision used in localizing the points. The subject, as will be
remembered, looked down at a card of numbered points and named those
which were directly over the contacts beneath. Here it should seem
that the optical illusion of the overestimation of filled spaces,
filled with points on the card, would be directly transmitted to the
sensation on the skin underneath. Such criticism on this method of
getting at the illusion has already been made orally to me. But this
is obviously a mistaken objection. The points on the card make a
filled space, which of course appears larger, but as the points
expand, the numbers which are attached to them expand likewise, and
the optical illusion has plainly no influence whatever upon the
tactual illusion.

A really serious objection to this indirect method of approaching the
illusion is, that the character of the cutaneous sensation is never so
distinctly perceived when the eyes are open as when they are closed.
Several subjects often found it necessary to close their eyes first,
in order to get a clear perception of the locality of the points;
they then opened their eyes, to name the visual points directly above.
Some subjects even complained that when they opened their eyes they
lost track of the exact location of the touch points, which they
seemed to have when their eyes were closed. The tactual impression
seems to be lost in the presence of active vision.

On the whole, then, I feel quite sure in concluding that the
overestimation of the filled cutaneous spaces is not traceable to the
influence of visualization. Parrish has explained all sporadic cases
of overestimation as due to the optical illusion carried over in
visualization. I have already shown that in my experiments
visualization has really the opposite effect. In Parrish's experiments
the overestimation occurred in the case of those collections of points
which were so arranged as to allow the greatest differentiation among
the points, and especially where the end-points were more or less
distinct from the rest. This, according to my theory, is precisely
what one would expect.

Those who have made quantitative studies in the optical illusion,
especially in this particular illusion for open and filled spaces,
have observed and commented on the instability of the illusion.
Auerbach[11] says, in his investigation of the quantitative variations
of the illusion, that concentration of attention diminishes the
illusion. In the Zöllner figure, for instance, I have been able to
notice the illusion fluctuate through a wide range, without
eye-movements and without definitely attending to any point, during
the fluctuation of the attention. My experiments with the tactual
illusion have led me to the conclusion that it fluctuates even more
than the optical illusion. Any deliberation in the judgment causes the
apparent size of the filled space to shrink. The judgments that are
given most rapidly and naïvely exhibit the strongest tendency to
overestimation; and yet these judgments are so consistent as to
exclude them from the category of guesses.

   [11] Auerbach, F., _Zeitsch. f. Psych. u. Phys. d.
   Sinnesorgane_, 1874, Bd. VII., S. 152.

In most of my experiments, however, I did not insist on rapid and
naïve judgments; but by a close observation of the subject as he was
about to make a judgment I could tell quite plainly which judgments
were spontaneous and which were deliberate. By keeping track of these
with a system of marks, I was able to collect them in the end into
groups representing fairly well the different degrees of attention.
The illusion is always greatest for the group of spontaneous
judgments, which points to the conclusion that all illusions, tactual
as well as visual, are very largely a function of attention.

In Section II. I told of my attempt to reproduce the optical illusion
upon the skin in the same form in which we find it for sight, namely,
by presenting the open and filled spaces simultaneously, so that they
might be held in a unitary grasp of consciousness and the judgment
pronounced on the relative length of these parts of a whole. However,
as I have already said, the filled space appears longer, not only when
given simultaneously, but also when given successively with the open
space. In the case of the optical illusion I am not so sure that the
illusion does not exist if the two spaces are not presented
simultaneously and adjacent, as Münsterberg asserts. Although, to be
sure, for me the illusion is not so strong when an interval is allowed
between the two spaces, I was interested to know whether this was true
also in the case of a touch illusion. My previous tables did not
enable me to compare the quantitative extent of the illusion for
successive and simultaneous presentation. But I found in two series
which had this point directly in view, one with the subject _F_ and
one in which _G_ served as subject, that the illusion was emphatically
stronger when the open and filled spaces were presented simultaneously
and adjacent. In this instance, the illusion was doubtless a
combination of two illusions--a shrinking of the open space, on the
one hand, and a lengthening of the filled space on the other hand.
Binet says, in his studies on the well-known Müller-Lyer illusion,
that he believes the illusion, in its highest effects at any rate, to
be due to a double contrast illusion.

This distortion of contrasted distances I have found in more than one
case in this investigation--not only in the case of distances in which
there is a qualitative difference, but also in the case of two open
distances. In one experiment, in which open distances on the skin were
compared with optical point distances, a distance of 10 cm. was given
fifty times in connection with a distance of 15 cm., and fifty times
in connection with a distance of 5 cm. In the former instance the
distance of 10 cm. was underestimated, and in the other it was
overestimated.

The general conclusion of the entire investigation thus far may be
summed up in the statement: _Wherever the objective conditions are the
same in the two senses, the illusion exists in the same direction for
both sight and touch._


VI.


Thus far all of my experiments were made with _passive_ touch. I
intend now to pursue this problem of the relation between the
illusions of sight and touch into the region of _active_ touch. I have
yielded somewhat to the current fashion in thus separating the passive
from the active touch in this discussion. I have already said that I
believe it would be better not to make this distinction so pronounced.
Here again I have concerned myself primarily with only one illusion,
the illusion which deals with open and filled spaces. This is the
illusion to which Dresslar[12] devoted a considerable portion of his
essay on the 'Psychology of Touch,' and which he erroneously thought
to be the counterpart of the optical illusion for open and filled
spaces. One of the earliest notices of this illusion is that given by
James,[13] who says, "Divide a line on paper into two equal halves,
puncture the extremities, and make punctures all along one of the
halves; then, with the finger-tip on the opposite side of the paper,
follow the line of punctures; the empty half will seem much longer
than the punctured half."

   [12] Dresslar, F.B., _Am. Journ. of Psy._, 1894, VI., p. 313.

   [13] James, W., 'Principles of Psychology,' New York, 1893,
   II., p. 250.

James has given no detailed account of his experiments. He does not
tell us how many tests were made, nor how long the lines were, nor
whether the illusion was the same when the open half was presented
first. Dresslar took these important questions into consideration, and
arrived at a conclusion directly opposite to that of James, namely,
that the filled half of the line appears larger than the open half.
Dresslar's conclusion is, therefore, that sight and touch function
alike. I have already said that I think that Parrish was entirely
right in saying that this is not the analogue of the familiar optical
illusion. Nevertheless, I felt sure that it would be quite worth the
while to make a more extensive study than that which Dresslar has
reported. Others besides James and Dresslar have experimented with
this illusion. As in the case of the illusion for passive touch, there
are not wanting champions of both opinions as to the direction in
which this illusion lies.

I may say in advance of the account of my experiments, that I have
here also found a ground of reconciliation for these two divergent
opinions. Just as in the case of the illusion for passive touch, there
are here also certain conditions under which the filled space seems
longer, and other conditions under which it appears shorter than the
open space. I feel warranted, therefore, in giving in some detail my
research on this illusion, which again has been an extended one. I
think that the results of this study are equally important with those
for passive touch, because of the further light which they throw on
the way in which our touch sense functions in the perception of the
geometrical illusions. Dresslar's experiments, like those of James,
were made with cards in which one half was filled with punctures. The
number of punctures in each centimeter varied with the different
cards. Dresslar's conclusion was not only that the filled space is
overestimated, but also that the overestimation varies, in a general
way, with the number of punctures in the filling. Up to a certain
point, the more holes there are in the card, the longer the space
appears.

I had at the onset of the present experiment the same feeling about
Dresslar's work that I had about Parrish's work, which I have already
criticised, namely, that a large number of experiments, in which many
variations were introduced, would bring to light facts that would
explain the variety of opinion that had hitherto been expressed. I was
confident, however, that what was most needed was a quantitative
determination of the illusion. Then, too, inasmuch as the illusion,
whatever direction it takes, is certainly due to some sort of
qualitative differences in the two kinds of touch sensations, those
from the punctured, and those from the smooth half, it seemed
especially desirable to introduce as many changes into the nature of
the filling as possible. The punctured cards I found very
unsatisfactory, because they rapidly wear off, and thus change the
quality of the sensations, even from judgment to judgment.

[Illustration: FIG. 7.]

The first piece of apparatus that I used in the investigation of the
illusion for open and filled space with active touch is shown in Fig.
7. A thimble _A_, in which the finger was carried, moved freely along
the rod _B_. The filled spaces were produced by rows of tacks on the
roller _C_. By turning the roller, different kinds of fillings were
brought into contact with the finger-tip. The paper _D_, on which the
judgments were recorded by the subject, could be slowly advanced under
the roller _E_. Underneath the thimble carrier there was a pin so
arranged that, by a slight depression of the finger, a mark was made
on the record paper beneath. A typical judgment was made as follows;
the subject inserted his finger in the thimble, slightly depressed the
carrier to record the starting points, then brought his finger-tip
into contact with the first point in the filled space. The subject
was, of course, all the while ignorant of the length or character of
the filling over which he was about to pass. The finger-tip was then
drawn along the points, and out over the smooth surface of the roller,
until the open space passed over was judged equal to the filled space.
Another slight depression of the finger registered the judgment on the
paper below. The paper was then moved forward by turning the roller
_E_, and, if desired, a different row of pins was put in place for
judgment by revolving the roller _C_. The dividing line between the
open and filled spaces was continuously recorded on the paper from
below by a pin not shown in the illustration.

The rollers, of which I had three, were easily removed or turned
about, so that the open space was presented first. In one of the
distances on each roller both spaces were unfilled. This was used at
frequent intervals in each series and served somewhat the same purpose
as reversing the order in which the open and filled spaces were
presented. With some subjects this was the only safe way of securing
accurate results. The absolute distances measured off were not always
a sure criterion as to whether the filled space was under-or
overestimated. For example, one rather erratic subject, who was,
however, very constant in his erratic judgments, as an average of
fifty judgments declared a filled space of 4 cm. to be equal to an
open space of 3.7 cm. This would seem, on the surface, to mean that
the filled space had been underestimated. But with these fifty
judgments there were alternated judgments on two open spaces, in which
the first open space was judged equal to the second open space of 3.2
cm. From this it is obvious that the effect of the filling was to
cause an overestimation--not underestimation as seemed at first sight
to be the case.

In another instance, this same subject judged a filled space of 12.0
cm. to be equal to an open space of 12.9 cm., which would seem to
indicate an overestimation of the filled space. But an average of the
judgments on two open spaces that were given in alternation shows that
an equivalence was set up between the two at 13.7 cm. for the second
open space. This would show that the filling of a space really
produced an underestimation.

The same results were obtained from other subjects. In my experiments
on the illusion for passive touch, I pointed out that it is unsafe to
draw any conclusion from a judgment of comparison between open and
filled cutaneous spaces, unless we had previously determined what
might be called a standard judgment of comparison between two open
spaces. The parts of our muscular space are quite as unsymmetrical as
the parts of our skin space. The difficulties arising from this lack
of symmetry can best be eliminated by introducing at frequent
intervals judgments on two open spaces. As I shall try to show later,
the psychological character of the judgment is entirely changed by
reversing the order in which the spaces are presented, and we cannot
in this way eliminate the errors due to fluctuations of the attention.

The apparatus which I used in these first experiments possesses
several manifest advantages. Chief among these was the rapidity with
which large numbers of judgments could be gathered and automatically
recorded. Then, in long distances, when the open space was presented
first, the subject found no difficulty in striking the first point of
the filled space. Dresslar mentioned this as one reason why in his
experiments he could not safely use long distances. His subjects
complained of an anxious straining of the attention in their efforts
to meet the first point of the filled space.

There are two defects manifest in this apparatus. In the first place,
the other tactual sensations that arise from contact with the thimble
and from the friction with the carrier moving along the sliding rod
cannot be disregarded as unimportant factors in the judgments.
Secondly, there is obviously a difference between a judgment that is
made by the subject's stopping when he reaches a point which seems to
him to measure off equal spaces, and a judgment that is made by
sweeping the finger over a card, as in Dresslar's experiments, with a
uniform motion, and then, after the movement has ceased, pronouncing
judgment upon the relative lengths of the two spaces. In the former
case the subject moves his finger uniformly until he approaches the
region of equality, and then slackens his speed and slowly comes to a
standstill. This of course changes the character of the judgments.
Both of these defects I remedied in another apparatus which will be
described later. For my present purpose I may disregard these
objections, as they affect alike all the judgments.

In making the tests for the first series, the subject removed his
finger after each judgment, so that the position of the apparatus
could be changed and the subject made to enter upon the new judgment
without knowing either the approximate length or the nature of the
filling of this new test. With this apparatus no attempt was made to
discover the effects of introducing changes in the rate of speed. The
only requirement was that the motion should be uniform. This does not
mean that I disregarded the factor of speed. On the contrary, this
_time_ element I consider as of the highest consequence in the whole
of the present investigation. But I soon discovered, in these
experiments, that the subjects themselves varied the rate of speed
from judgment to judgment over a wide range of rates. There was no
difficulty in keeping track of these variations, by recording the
judgments under three groups, fast, slow and medium. But I found that
I could do this more conveniently with another apparatus, and will
tell at a later place of the results of introducing a time element. In
these first experiments the subject was allowed to use any rate of
speed which was convenient to him.


TABLE IX.

       Subjects      P      R      F      Rr
             2=     3.8    3.6    2.9     2.8
             3=     4.1    4.1    4.2     3.9
             4=     4.7    5.1    4.3     4.3
  Filled     5=     5.2    5.6    5.8     6.0
  Spaces.    6=     6.0    6.3    6.4     5.2
             7=     6.8    6.5    6.6     7.0
             8=     7.5    7.6    7.2     7.4
             9=     8.3    8.1    8.2     8.6
            10=     8.9    9.1    8.7     8.5


TABLE X.

       Subjects      P      R      F      Rr
             2=     4.0    3.8    3.2     2.6
             3=     4.3    4.2    4.4     3.6
             4=     4.6    5.6    4.6     4.8
  Filled     5=     5.4    6.1    5.6     5.7
  Spaces.    6=     6.2    6.4    6.8     6.9
             7=     7.3    6.8    7.9     7.2
             8=     7.8    7.4    7.3     7.8
             9=     8.6    8.0    7.9     8.9
            10=     9.3    9.1    8.9     8.5

TABLES IX. AND X.

    First line reads: 'When the finger-tip was drawn over a filled
    distance of 2 cm., the subject _P_ measured off 3.8 on the
    open surface, the subject _R_ 3.6, etc.' Each number is the
    average of five judgments. In Table IX. the points were set at
    regular intervals. In Table X. the filling was made irregular
    by having some points rougher than the others and set at
    different intervals.


I can give here only a very brief summary of the results with this
apparatus. In Tables IX. and X. I give a few of the figures which will
show the tendency of the experiments. In these tests a different
length and a different filling were given for each judgment. The
result of the experiments of this group is, first, that the _shorter
filled spaces are judged longer and the longer spaces shorter_ than
they really were. Second, that an increase in the number of points in
the filled space causes no perceptible change in the apparent length.
Third, that when the filling is so arranged as to produce a tactual
rhythm by changing the position or size of every third point, the
apparent length of the space is increased. It will be noticed, also,
that this is just the reverse of the result that was obtained for
passive touch. These facts, which were completely borne out by several
other experiments with different apparatus which I shall describe
later, furnish again a reason why different investigators have
hitherto reported the illusion to exist, now in one direction, now in
the other. Dresslar drew the conclusion from his experiments that the
filled spaces are always overestimated, but at the same time his
figures show an increasing tendency towards an underestimation of the
filled spaces as the distances increased in length. I shall later, in
connection with similar results from other experiments on this
illusion, endeavor to explain these anomalous facts.

In section IV. I mentioned the fact that I found the illusion for
passive touch to be subject to large fluctuations. This is true also
of the illusion for active touch. When the finger-tip is drawn over
the filled, and then out over the open space, the limits between which
the stopping point varies is a much wider range than when the
finger-tip is drawn over two open spaces. In the latter case I found
the variation to follow Weber's Law in a general way. At first I
thought these erratic judgments were mere guesses on the part of the
subject; but I soon discovered a certain consistency in the midst of
these extreme fluctuations. To show what I mean, I have plotted some
diagrams based on a few of the results for three subjects. These
diagrams are found in Fig. 8. It will be observed that the curve which
represents the collection of stopping points is shorter and higher
where the judgments were on two open spaces. This shows plainly a
greater accuracy in the judgments than when the judgments were on a
filled and an open space, where the curves are seen to be longer and
flatter. This fluctuation in the illusion becomes important in the
theoretical part of my discussion, and, at the risk of apparently
emphasizing unduly an insignificant matter, I have given in Fig. 9 an
exact copy of a sheet of judgments as it came from the apparatus. This
shows plainly how the illusion wears away with practice, when one
distance is given several times in succession. The subject was allowed
to give his judgment on the same distance ten times before passing to
another. A glance at the diagram will show how pronounced the illusion
is at first, and how it then disappears, and the judgment settles down
to a uniform degree of accuracy. It will be seen that the short filled
space is at first overestimated, and then, with the succeeding
judgments, this overestimation is gradually reduced. In the case of
the longer filled distances (which could not be conveniently
reproduced here) the spaces were at first underestimated, and then
this underestimation slowly decreased.

[Illustration: FIG. 8.]

[Illustration: FIG. 9.]

None of the qualitative studies that have hitherto been made on this
illusion have brought to light this significant wearing away of the
illusion.


VII.


I have already spoken of the defects of the apparatus with which the
experiments of the previous chapter were made. I shall now give an
account of some experiments that were made with an apparatus designed
to overcome these difficulties. This is shown in Fig. 10. The block
_C_ was clamped to a table, while the block _A_ could be moved back
and forth by the lever _B_, in order to bring up different lengths of
filled space for judgment. For each judgment the subject brought his
finger back to the strip _D_, and by moving his finger up along the
edge of this strip he always came into contact with the first point of
the new distance. The lever was not used in the present experiment;
but in later experiments, where the points were moved under the finger
tip, which was held stationary, this lever was very useful in
producing different rates of speed. In one series of experiments with
this apparatus the filled spaces were presented first, and in another
series the open spaces were presented first. In the previous
experiments, so far as I have reported them, the filled spaces were
always presented first.

[Illustration: FIG. 10.]

In order to enable the subject to make proper connections with the
first point in the filled space, when the open space was presented
first, a slight depression was put in the smooth surface. This
depression amounted merely to the suggestion of a groove, but it
sufficed to guide the finger.

The general results of the first series of experiments with this
apparatus were similar to those already given, but were based on a
very much larger number of judgments. They show at once that the short
filled spaces are overestimated, while the longer spaces are
underestimated. The uniformity of this law has seemed to me one of the
most significant results of this entire investigation. In the results
already reported from the experiments with the former apparatus, I
have mentioned the fact that the judgments upon the distances
fluctuate more widely when one is filled and the other open, than when
both are open. This fluctuation appeared again in a pronounced way in
the present experiments. I now set about to discover the cause of this
variation, which was so evidently outside of the limits of Weber's
law.


TABLE XI.

                                I.                        II.
        Subjects.     R.      B.      A.        R.      B.       A.
             2=      3.1     3.2     3.7       2.7     2.5      3.1
             3=      4.5     4.4     4.1       4.1     4.0      3.6
             4=      5.3     5.0     4.3       4.2     4.6      4.6
             5=      6.0     5.1     5.8       5.9     5.2      4.3
             6=      6.8     5.6     6.2       6.9     5.3      6.0
             7=      7.4     7.2     6.9       7.6     7.3      6.8
             8=      8.1     8.4     7.3       8.3     9.7      7.8
             9=      9.3     9.0     8.5       9.5     8.9      8.7
  Filled    10=     10.1    10.0     8.1      10.3    10.0      9.2
  Spaces.   11=     10.5     9.3     9.7      10.6     8.7      9.6
            12=     11.7    10.6    10.6      11.8     9.7     10.2
            13=     12.3    10.9    10.9      11.1    10.2      9.6
            14=     12.2    11.5    12.2      10.4     9.6     11.3
            15=     13.6    12.3    11.9      13.1    10.1      9.6
            16=     14.1    13.5    14.1      12.3    13.2     13.3
            17=     14.9    12.9    14.6      14.1    12.6     13.7
            18=     15.0    15.3    14.9      15.0    15.3     13.8
            19=     15.2    14.6    15.2      14.1    13.9     14.2
            20=     17.1    16.5    15.7      16.1    16.4     14.7

    The first line of group I. reads: 'When the finger-tip was
    passed over a filled space of 2 cm., the subject _R_ measured
    off 3.1 cm. on the open space, the subject _B_ 3.2 cm., and
    the subject _A_ 3.7.' In group II., the numbers represent the
    distance measured off when both spaces were unfilled.


In my search for the cause of the variations reported previously I
first tried the plan of obliging the subject to attend more closely to
the filled space as his finger was drawn over it. In order to do this,
I held a piece of fine wire across the line of the filled space, and
after the subject had measured off the equal open space he was asked
to tell whether or not he had crossed the wire. The wire was so fine
that considerable attention was necessary to detect it. In some of the
experiments the wire was inserted early in the filled space, and in
some near the end. When it was put in near the beginning, it was
interesting to notice, as illustrating the amount of attention that
was being given to the effort of finding the wire, that the subject,
as soon as he had discovered it, would increase his speed, relax the
attention, and continue the rest of the journey more easily.

The general effect of this forcing of the attention was to increase
the apparent length of the filled space. This conclusion was reached
by comparing these results with those in which there was no compelled
attention. When the obstacle was inserted early, the space was judged
shorter than when it came at the end of the filled space. This shows
very plainly the effect of continued concentration of attention, when
that attention is directed intensely to the spot immediately under the
finger-tip. When the attention was focalized in this way, the subject
lost sight of the space as a whole. It rapidly faded out of memory
behind the moving finger-tip. But when this concentration of attention
was not required, the subject was able to hold together in
consciousness the entire collection of discrete points, and he
overestimated the space occupied by them. It must be remembered here
that I mean that the filled space with the focalized attention was
judged shorter than the filled space without such concentration of
attention, but both of these spaces were judged shorter than the
adjacent open space. This latter fact I shall attempt to explain
later. Many other simple devices were employed to oblige the subject
to fix his attention on the space as it was traversed by the finger.
The results were always the same: the greater the amount of attention,
the longer the distance seemed.

In another experiment, I tried the plan of tapping a bell as the
subject was passing over the filled space and asking him, after he had
measured off the equivalent open space, whether the sound had occurred
in the first half or in the second half of the filled space.

When the finger-tip was drawn over two adjacent open spaces, and
during the first a bell was tapped continuously, this kind of filled
space was underestimated if the distance was long and overestimated if
the distance was short. So, too, if a disagreeable odor was held to
the nostrils while the finger-tip was being drawn over one of the two
adjacent open spaces, the space thus filled by the sensations of smell
followed the law already stated. But if an agreeable perfume was used,
the distance always seemed shorter than when an unpleasant odor was
given.

In all of these experiments with spaces filled by means of other than
tactual sensations, I always compared the judgment on the filled and
open spaces with judgments on two open spaces, in order to guard
against any error due to unsymmetrical, subjective conditions for the
two spaces. It is difficult to have the subject so seat himself before
the apparatus as to avoid the errors arising from tension and flexion.
In one experiment, a piece of plush was used for the filled space and
the finger drawn over it against the nap. This filled space was judged
longer than a piece of silk of equal length. The sensations from the
plush were very unpleasant. One subject said, even, that they made him
shudder. This was of course precisely what was wanted for the
experiment. It showed that the affective tone of the sensation within
the filled space was a most important factor in producing an illusory
judgment of distance.

The overestimation of these filled spaces is evidently due in a large
measure to æsthetic motives. The space that is filled with agreeable
sensations is judged shorter than one which is filled with
disagreeable sensations. In other words, the illusions in judgments on
cutaneous space are not so much dependent on the quality of sensations
that we get from the outer world through these channels, as from the
amount of inner activity that we set over against these bare
sense-perceptions.

I have already spoken of the defects of this method of measuring off
equivalent distances as a means of getting at the quantitative amount
of the illusion. The results that have come to light thus far have,
however, amply justified the method. I had no difficulty, however, in
adapting my apparatus to the other way of getting the judgments. I had
a short curved piece of wire inserted in the handle, which could be
held across the line traversed, and thus the end of the open space
could be marked out. Different lengths were presented to the subject
as before, but now the subject passed his finger in a uniform motion
over the spaces, after which he pronounced the judgment 'greater,'
'equal,' or 'less.' The general result of these experiments was not
different from those already given. The short, filled spaces were
overestimated, while the longer ones were underestimated. The only
difference was found to be that now the transition from one direction
to the other was at a more distant point. It was, of course, more
difficult to convert these qualitative results into a quantitative
determination of the illusion.

Before passing to the experiments in which the open spaces were
presented first, I wish to offer an explanation for the divergent
tendencies that were exhibited through all the experiments of the last
two sections, namely, that the short filled spaces are overestimated
and the long spaces underestimated. Let us take two typical judgments,
one in which a filled space of 3 cm. is judged equal to an open space
of 4.2 cm., and then one in which the filled space is 9 cm., and is
judged equal to an open space of 7.4 cm. In the case of the shorter
distance, because of its shortness, after the finger leaves it, it is
held in a present state of consciousness for some moments, and does
not suffer the foreshortening that comes from pastness. This is,
however, only a part of the reason for its overestimation. After the
finger-tip has left the filled space, and while it is traversing the
first part of the open space, there is a dearth of sensations. The
tactual sensations are meager and faint, and muscular tensions have
not yet had time to arise. It is not until the finger has passed over
several centimeters of the distance, that the surprise of its
barrenness sets up the organic sensations of muscular strain. One
subject remarked naïvely at the end of some experiments of this kind,
that the process of judging was an easy and comfortable affair so long
as he was passing over the filled space, but when he set out upon the
open space he had to pay far more strict attention to the experiment.

By a careful introspection of the processes in my own case, I came to
the conclusion that it is certainly a combination of these two
illusions that causes the overestimation of the short filled
distances. In the case of the long distances, the underestimation of
the filled space is, I think, again due to a combination of two
illusions. When the finger-tip leaves the filled space, part of it,
because of its length, has already, as it were, left the specious
present, and has suffered the foreshortening effect of being relegated
to the past. And, on the other hand, after the short distance of the
open space has been traversed the sensations of muscular strain become
very pronounced, and cause a premature judgment of equality.

One subject, who was very accurate in his judgments, and for whom the
illusion hardly existed, said, when asked to explain his method of
judging, that after leaving the filled space he exerted a little more
pressure with his finger as he passed over the open space, so as to
get the same quantity of tactual sensations in both instances. The
muscular tension that was set up when the subject had passed out over
the open space a short way was very plainly noticeable in some
subjects, who were seen at this time to hold their breath.

I have thus far continually spoken of the space containing the tacks
as being the filled space, and the smooth surface as the open space.
But now we see that in reality the name should be reversed, especially
for the longer distances. The smooth surface is, after the first few
centimeters, very emphatically filled with sensations arising from the
organism which, as I have already intimated, are of the most vital
importance in our spatial judgments. Now, according to the most
generally accepted psychological theories, it is these organic
sensations which are the means whereby we measure time, and our
spatial judgments are, in the last analysis, I will not for the
present say dependent on, but at any rate fundamentally related to our
time judgments.


VIII.


In the last section I attempted to explain the overestimation of short
filled spaces, and the underestimation of long filled spaces by active
touch, as the result of a double illusion arising from the differences
in the manner and amount of attention given to the two kinds of
spaces when they are held in immediate contrast. This explanation was
of course purely theoretical. I have thus far offered no experiments
to show that this double illusion of lengthening, on the one hand, and
shortening, on the other, does actually exist. I next made some simple
experiments which seemed to prove conclusively that the phenomenon
does not exist, or at least not in so important a way, when the time
factor is not permitted to enter.

In these new experiments the filled and the open spaces were compared
separately with optical distances. After the finger-tip was drawn over
the filled path, judgment was given on it at once by comparing it
directly with an optical distance. In this way the foreshortening
effect of time was excluded. In all these experiments it was seen that
the filled space was judged longer when the judgment was pronounced on
it at once than when an interval of time was allowed, either by
drawing the finger-tip out over the open space, as in the previous
experiment, or by requiring the subject to withhold his judgment until
a certain signal was given. Any postponement of the judgment resulted
in the disappearance of a certain amount of the illusion. The
judgments that were made rapidly and without deliberation were subject
to the strongest illusion. I have already spoken of the unanimous
testimony which all who have made quantitative studies in the
corresponding optical illusions have given in this matter of the
diminution of the illusion with the lapse of time. The judgments that
were made without deliberation always exhibited the strongest tendency
to illusion.

I have already said that the illusion for passive touch was greatest
when the two spaces were presented simultaneously and adjacent.
Dresslar has mentioned in his studies on the 'Psychology of Touch,'
that the time factor cannot enter into an explanation of this
illusion; but the experiments of which I have just spoken seem to
point plainly to a very intimate relation between this illusion and
the illusions in our judgments of time. We have here presented on a
diminutive scale the illusions which we see in our daily experience in
comparing past with present stretches of time. It is a well-known
psychological experience that a filled time appears short in passing,
but long in retrospect, while an empty time appears long in passing,
but short in retrospect. Now this illusion of the open and filled
space, for the finger-tip, is at every point similar to the illusion
to which our time judgment is subject. If we pronounce judgment on a
filled space or filled time while we are still actually living in it,
it seems shorter than it really is, because, while we pay attention to
the discrete sensations of external origin, we lose sight of the
sensations of internal origin, which are the sole means whereby we
measure lapse of time, and we consequently underestimate such
stretches of time or space. But when the sensations from the outer
world which enter into such filled spaces or times exist only in
memory, the time-measuring sensations of internal origin are allowed
their full effect; and such spaces and times seem much longer than
when we are actually passing through them.

I dwell on this illusion at a length which may seem out of proportion
to its importance. My object has been to show how widely different are
the objective conditions here from what they are in the optical
illusion which has so often been called the analogue of this.
James[14] has said of this tactual illusion: 'This seems to bring
things back to the unanalyzable laws, by reason of which our feeling
of size is determined differently in the skin and in the retina even
when the objective conditions are the same.' I think that my
experiments have shown that the objective conditions are not the same;
that they differ in that most essential of all factors, namely, the
time element. Something very nearly the analogue of the optical
illusion is secured when we take very short open and filled tactual
spaces, and move over them very rapidly. Here the illusion exists in
the same direction as it does for sight, as has already been stated.
On the other hand, a phenomenon more nearly parallel to the tactual
illusion, as reported in the experiments of James and Dresslar, is
found if we take long optical distances, and traverse the open and
filled spaces continuously, without having both parts of the line
entirely in the field of view at any one moment. I made a few
experiments with the optical illusion in this form. The filled and
open spaces were viewed by the subject through a slot which was
passed over them. These experiments all pointed in the direction of an
underestimation of a filled space. Everywhere in this illusion, then,
where the objective conditions were at all similar for sight and
touch, the resulting illusion exists in the same direction for both
senses.

   [14] James, William, 'Principles of Psychology,' New York, II.,
   p. 250.

Throughout the previous experiments with the illusion for active touch
we saw the direct influence of the factor of time. I have yet one set
of experiments to report, which seems to me to prove beyond the
possibility of a doubt the correctness of my position. These
experiments were made with the apparatus shown in Fig. 10. The
subjects proceeded precisely as before. The finger-tip was passed over
the filled space, and then out over the open space, until an
equivalent distance was measured off. But while the subject was
drawing his fingers over the spaces, the block _A_ was moved in either
direction by means of the lever _B_. The subjects were all the while
kept ignorant of the fact that the block was being moved. They all
expressed great surprise on being told, after the experiments were
over, that the block had been moved under the finger-tip through such
long distances without their being able to detect it. The block always
remained stationary as the finger passed over one space, but was moved
either with or against the finger as it passed over the other space.


TABLE XII.

     A      B       C       D        E
     4     7.1     2.6     2.4      6.5
     5     8.3     3.1     3.3      8.7
     6     8.2     3.3     4.1      9.2
     7     9.7     3.6     3.7     10.1
     8    10.5     3.7     4.5     10.6
     9    12.4     4.8     5.1     11.5
    10    13.1     4.7     5.3     13.2
    11    13.3     5.3     6.1     14.6
    12    13.7     6.9     7.2     12.7
    13    14.6     7.5     8.1     13.2
    14    15.3     8.2     9.4     15.6
    15    15.7     8.7    10.3     14.9

    Column _A_ contains the filled spaces, columns _B_, _C_, _D_,
     _E_ the open spaces that were judged equal. In _B_ the block
    was moved with the finger, and in _C_ against the finger as it
    traversed the filled space, and in _D_ and _E_ the block was
    moved with and against the finger respectively as it passed
    over the open space. The block was always moved approximately
    one-half the distance of the filled space.


I have given some of the results for one subject in Table XII. These
results show at a glance how potent a factor the time element is. The
quantity of tactual sensations received by the finger-tip enters into
the judgment of space to no appreciable extent. With one subject,
after he had passed his finger over a filled space of 10 cm. the block
was moved so as almost to keep pace with the finger as it passed over
the open space. In this way the subject was forced to judge a filled
space of 10 cm. equal to only 2 cm. of the open space. And when the
block was moved in the opposite direction he was made to judge a
distance of 10 cm. equal to an open distance of 16 cm.

The criticism may be made on these experiments that the subject has
not in reality been obliged to rely entirely upon the time sense, but
that he has equated the two spaces as the basis of equivalent muscle
or joint sensation, which might be considered independent of the
sensations which yield the notion of time. I made some experiments,
however, to prove that this criticism would not be well founded. By
arranging the apparatus so that the finger-tip could be held
stationary, and the block with the open and filled spaces moved back
and forth under it, the measurement by joint and muscle sensations was
eliminated.

It will be observed that no uniform motion could be secured by simply
manipulating the lever with the hand. But uniformity of motion was not
necessary for the results at which I aimed here. Dresslar has laid
great stress on the desirability of having uniform motion in his
similar experiments. But this, it seems to me, is precisely what is
not wanted. With my apparatus, I was able to give widely different
rates of speed to the block as it passed under the finger-tip. By
giving a slow rate for the filled space and a much more rapid rate for
the open space, I found again that the subject relied hardly at all on
the touch sensations that came from the finger-tip, but almost
entirely on the consciousness of the amount of time consumed in
passing over the spaces. The judgments were made as in the previous
experiments with this apparatus. When the subject reached the point in
the open space which he judged equal to the filled space, he slightly
depressed his finger and stopped the moving block. In this way, the
subject was deprived of any assistance from arm-movements in his
judgments, and was obliged to rely on the tactual impressions received
at the finger-tip, or on his time sense. That these tactual sensations
played here also a very minor part in the judgment of the distance was
shown by the fact that these sensations could be doubled or trebled by
doubling or trebling the amount of space traversed, without
perceptibly changing the judgment, provided the rate of speed was
increased proportionately. Spaces that required the same amount of
time in traversing were judged equal.

In all these experiments the filled space was presented first. When
the open space was presented first, the results for four out of five
subjects were just reversed. For short distances the filled space was
underestimated, for long distances the filled space was overestimated.
A very plausible explanation for these anomalous results is again to
be found in the influence of the time factor. The open space seemed
longer while it was being traversed, but rapidly foreshortened after
it was left for the filled space. While on the other hand, if the
judgment was pronounced while the subject was still in the midst of
the filled space, it seemed shorter than it really was. The
combination of these two illusions is plainly again responsible for
the underestimation of the short filled spaces. The same double
illusion may be taken to explain the opposite tendency for the longer
distances.


IX.


The one generalization that I have thus far drawn from the
investigation--namely, that the optical illusions are not reversed in
passing from the field of touch, and that we therefore have a safe
warrant for the conclusion that sight and touch do function alike--has
contained no implicit or expressed assertion as to the origin of our
notion of space. I have now reached the point where I must venture an
explanation of the illusion itself.

The favorite hypothesis for the explanation of the geometrical optical
illusions is the movement theory. The most generally accepted
explanation of the illusion with whose tactual counterpart this paper
is concerned, is that given by Wundt.[15] Wundt's explanation rests on
variation in eye movements. When the eye passes over broken
distances, the movement is made more difficult by reason of the
frequent stoppages. The fact that the space which is filled with only
one point in the middle is underestimated, is explained by Wundt on
the theory that the eye has here the tendency to fix on the middle
point and to estimate the distance by taking in the whole space at
once without moving from this middle point. A different explanation
for this illusion is offered by Helmholtz.[16] He makes use of the
æsthetic factor of contrasts. Wundt insists that the fact that this
illusion is still present when there are no actual eye movements does
not demonstrate that the illusion is not to be referred to a motor
origin. He says, "If a phenomenon is perceived with the moving eye
only, the influence of movement on it is undoubtedly true. But an
inference cannot be drawn in the opposite direction, that movement is
without influence on the phenomenon that persists when there is no
movement."[17]

   [15] Wundt., W., 'Physiolog. Psych.,' 4te Aufl., Leipzig, 1893,
   Bd. II., S. 144.

   [16] v. Helmholtz, H., 'Handbuch d. Physiol. Optik,' 2te Aufl.,
   Hamburg u. Leipzig, 1896, S. 705.

   [17] Wundt, W., _op. citat._, S. 139.

Satisfactorily as the movement hypothesis explains this and other
optical illusions, it yet falls short of furnishing an entirely
adequate explanation. It seems to me certain that several causes exist
to produce this illusion, and also the illusion that is often
associated with it, the well-known Müller-Lyer illusion. But in what
degree each is present has not yet been determined by any of the
quantitative studies in this particular illusion. I made a number of
tests of the optical illusion, with these results: that the illusion
is strongest when the attention is fixed at about the middle of the
open space, that there is scarcely any illusion left when the
attention is fixed on the middle of the filled space. It is stronger
when the outer end-point of the open space is fixated than when the
outer end of the filled space is fixated. For the moving eye, I find
the illusion to be much stronger when the eye passes over the filled
space first, and then over the open space, than when the process is
reversed.

Now, the movement hypothesis does not, it seems to me, sufficiently
explain all the fluctuations in the illusion. My experiments with the
tactual illusion justify the belief that the movement theory is even
less adequate to explain all of the variations there, unless the
movement hypothesis is given a wider and richer interpretation than is
ordinarily given to it. In the explanation of the tactual illusion
which I have here been studying two other important factors must be
taken into consideration. These I shall call, for the sake of
convenience, the æsthetic factor and the time factor. These factors
should not, however, be regarded as independent of the factor of
movement. That term should be made wide enough to include these within
its meaning. The importance of the time factor in the illusion for
passive touch I have already briefly mentioned. I have also, in
several places in the course of my experiments, called attention to
the importance of the æsthetic element in our space judgments. I wish
now to consider these two factors more in detail.

The foregoing discussion has pointed to the view that the
space-perceiving and the localizing functions of the skin have a
deep-lying common origin in the motor sensations. My experiments show
that, even in the highly differentiated form in which we find them in
their ordinary functioning, they plainly reveal their common origin. A
formula, then, for expressing the judgments of distance by means of
the resting skin might be put in this way. Let _P_ and _P'_ represent
any two points on the skin, and let _L_ and _L'_ represent the local
signs of these points, and _M_ and _M'_ the muscle sensations which
give rise to these local signs. Then _M-M'_ will represent the
distance between _P_ and _P'_, whether that distance be judged
directly in terms of the localizing function of the skin or in terms
of its space-perceiving function. This would be the formula for a
normal judgment. In an illusory judgment, the temporal and æsthetic
factors enter as disturbing elements. Now, the point which I insist on
here is that the judgments of the extent of the voluntary movements,
represented in the formula by _M_ and _M'_, do not depend alone on the
sensations from the moving parts or other sensations of objective
origin, as Dresslar would say, nor alone on the intention or impulse
or innervation as Loeb and others claim, but on the sum of all the
sensory elements that enter, both those of external and those of
internal origin. And, furthermore, these sensations of external origin
are important in judgments of space, only in so far as they are
referred to sensations of internal origin. Delabarre says, "Movements
are judged equal when their sensory elements are judged equal. These
sensory elements need not all have their source in the moving parts.
All sensations which are added from other parts of the body and which
are not recognized as coming from these distant sources, are mingled
with the elements from the moving member, and influence the
judgment."[18] The importance of these sensations of inner origin was
shown in many of the experiments in sections VI. to VIII. In the
instance where the finger-tip was drawn over an open and a filled
space, in the filled half the sensations were largely of external
origin, while in the open half they were of internal origin. The
result was that the spaces filled with sensations of internal origin
were always overestimated.

The failure to recognize the importance of these inwardly initiated
sensations is the chief defect in Dresslar's reasoning. He has
endeavored to make our judgments in the illusion in question depend
entirely on the sensations of external origin. He insists also that
the illusion varies according to the variations in quantity of these
external sensations. Now my experiments have shown, I think, very
clearly that it is not the numerical or quantitative extent of the
objective sensations which disturbs the judgment of distance, but the
sensation of inner origin which we set over against these outer
sensations. The piece of plush, because of the disagreeable sensations
which it gives, is judged shorter than the space filled with closely
crowded tacks. Dresslar seems to have overlooked entirely the fact
that the feelings and emotions can be sources of illusions in the
amount of movement, and hence in our judgments of space. The
importance of this element has been pointed out by Münsterberg[19] in
his studies of movement.

   [18] Delabarre, E.B., 'Ueber Bewegungsempfindungen,' Inaug.
   Dissert., Freiburg, 1891.

   [19] Münsterberg, H., 'Beiträge zur Experimentellen Psychol.,'
   Freiburg i. B., 1892, Heft 4.

Dresslar says again, "The explanations heretofore given, wholly based
on the differences in the time the eye uses in passing over the two
spaces, must stop short of the real truth." My experiments, however,
as I have already indicated, go to prove quite the contrary. In short,
I do not think we have any means of distinguishing our tactual
judgments of time from our similar judgments of space. When the
subject is asked to measure off equal spaces, he certainly uses time
as means, because when he is asked to measure off equal times he
registers precisely the same illusion that he makes in his judgments
of spatial distances. The fact that objectively equal times were used
by Dresslar in his experiments is no reason for supposing that the
subject also regarded these times as equal. What I have here asserted
of active touch is true also of the resting skin. When a stylus is
drawn over the skin, the subject's answer to the question, How long is
the distance? is subject to precisely the same illusion as his answer
to the question, How long is the time?

I can by a simple illustration show more plainly what I mean by the
statement that the blending of the inner and outer sensations is
necessary for the perception of space. I shall use the sense of sight
for the illustration, although precisely the same reasoning would
apply to the sense of touch. Suppose that I sat in an entirely passive
position and gazed at a spot on an otherwise blank piece of paper
before me. I am perfectly passive so far as motion on my part is
concerned. I may be engaged in any manner of speculation or be in the
midst of the so-called active attention to the spot; but I must be and
for the present remain motionless. Now, while I am in this condition
of passivity, suppose the spot be made to move slowly to one side by
some force external to myself. I am immovable all the while, and yet
am conscious of this movement of the spot from the first position,
which I call _A_, to the new position, _A'_, where it stops. The
sensation which I now have is qualitatively different from the
sensation which I had from the spot in its original position. My world
of experience thus far has been a purely qualitative one. I might go
on to eternity having experiences of the same kind, and never dream of
space, or geometry, nor should I have the unique experience of a
geometrical illusion, either optical or tactual. Now suppose I set up
the bodily movements of the eyes or the head, or of the whole body,
which are necessary to follow the path of that point, until I overtake
it and once more restore the quality of the original sensation. This
circle, completed by the two processes of external activity and
restoration by internal activity, forms a group of sensations which
constitutes the ultimate atom in our spatial experience. I have my
first spatial experience when I have the thrill of satisfaction that
comes from overtaking again, by means of my own inner activity, a
sensation that has escaped me through an activity not my own. A being
incapable of motion, in a world of flux, would not have the spatial
experience that we have. A being incapable of motion could not make
the distinction between an outer change that can be corrected by an
internal change, and an outer change that cannot so be restored. Such
an external change incapable of restoration by internal activity we
should have if the spot on the paper changed by a chemical process
from black to red.

Now such a space theory is plainly not to be confused with the theory
that makes the reversibility of the spatial series its primary
property. It is evident that we can have a series of sensations which
may be reversed and yet not give the notion of space. But we should
always have space-perception if one half of the circular process above
described comes from an outer activity, and the other half from an
inner activity. This way of describing the reversibility of the
spatial series makes it less possible to urge against it the
objections that Stumpf[20] has formulated against Bain's genetic
space-theory. Stumpf's famous criticism applies not only to Bain, but
also to the other English empiricists and to Wundt. Bain says: "When
with the hand we grasp something moving and move with it, we have a
sensation of one unchanged contact and pressure, and the sensation is
imbedded in a movement. This is one experience. When we move the hand
over a fixed surface, we have with the feelings of movement a
succession of feelings of touch; if the surface is a variable one,
the sensations are constantly changing, so that we can be under no
mistake as to our passing through a series of tactual impressions.
This is another experience, and differs from the first not in the
sense of power, but in the tactile accompaniment. The difference,
however, is of vital importance. In the one case, we have an object
moving and measuring time and continuous, in the other case we have
coëxistence in space. The coëxistence is still further made apparent
by our reversing the movement, and thereby meeting the tactile series
in the inverse order. Moreover, the serial order is unchanged by the
rapidity of our movements."[21]

   [20] Stumpf, K., 'Ueber d. psycholog. Ursprung d.
   Raumvorstellung,' Leipzig, 1873, S. 54.

   [21] Bain, A., 'The Senses and the Intellect,' 3d ed., New
   York, 1886, p. 183.

Stumpf maintained in his exhaustive criticism of this theory, first,
that there are cases where all of the elements which Bain requires for
the perception of space are present, and yet we have no presentation
of space. Secondly, there are cases where not all of these elements
are present, and where we have nevertheless space presentation. It is
the first objection that concerns me here. Stumpf gives as an example,
under his first objection, the singing of a series of tones, C, G, E,
F. We have here the muscle sensations from the larynx, and the series
of the tone-sensations which are, Stumpf claims, reversed when the
muscle-sensations are reversed, etc. According to Stumpf, these are
all the elements that are required by Bain, and yet we have no
perception of space thereby. Henri[22] has pointed out two objections
to Stumpf's criticism of Bain's theory. He says that Bain assumes,
what Stumpf does not recognize, that the muscle sensations must
contain three elements--resistance, time, and velocity--before they
can lead to space perceptions. These three elements are not to be
found in the muscle sensations of the larynx as we find them in the
sensations that come from the eye or arm muscles. In addition to this,
Henri claims that Bain's theory demands a still further condition. If
we wish to touch two objects, _A_ and _B_, with the same member, we
can get a spatial experience from the process only if we insert
between the touching of _A_ and the touching of _B_ a continual
series of tactual sensations. In Stumpf's instance of the singing of
tones, this has been overlooked. We can go from the tone C to the tone
F without inserting between the two a continuous series of musical
sensations.

   [22] Henri, V., 'Ueber d. Raumwahrnehmungen d. Tastsinnes,'
   Berlin, 1898, S. 190.

I think that all such objections to the genetic space theories are
avoided by formulating a theory in the manner in which I have just
stated. When one says that there must be an outer activity producing a
displacement of sensation, and then an inner activity retaining that
sensation, it is plain that the singing of a series of tones ascending
and then descending would not be a case in point.

       *       *       *       *       *



TACTUAL TIME ESTIMATION.

BY KNIGHT DUNLAP.


I. GENERAL NATURE OF THE WORK.


The experiments comprised in this investigation were made during the
year 1900-1901 and the early part of the year 1901-1902. They were
planned as the beginning of an attempt at the analysis of the
estimation of time intervals defined by tactual stimulations. The only
published work in this quarter of the field so far is that of
Vierordt,[1] who investigated only the constant error of time
judgment, using both auditory and tactual stimulations, and that of
Meumann,[2] who in his last published contribution to the literature
of the time sense gives the results of his experiments with 'filled'
and 'empty' tactual intervals. The stimuli employed by Meumann were,
however, not purely tactual, but electrical.

   [1] Vierordt: 'Der Zeitsinn,' Tübingen, 1868.

   [2] Meumann, E.: 'Beiträge zur Psychologie des
   Zeitbewusstseins,' III., _Phil. Studien,_ XII., S. 195-204.

The limitation of time intervals by tactual stimulations offers,
however, a rich field of variations, which promise assistance in the
analytical problem of the psychology of time. The variations may be
those of locality, area, intensity, rigidity, form, consecutiveness,
and so on, in addition to the old comparisons of filled and empty
intervals, intervals of varying length, and intervals separated by a
pause and those not so separated.

To begin with, we have selected the conditions which are mechanically
the simplest, namely, the comparison of two empty time intervals, both
given objectively with no pause between them. We have employed the
most easily accessible dermal areas, namely, that of the fingers of
one or both hands, and introduced the mechanically simplest
variations, namely, in locality stimulated and intensity of
stimulation.

It was known from the results of nearly all who have studied the time
sense experimentally, that there is in general a constant error of
over- or underestimation of time intervals of moderate length, and
from the results of Meumann,[3] that variations in intensity of
limiting stimulation influenced the estimation decidedly, but
apparently according to no exact law. The problem first at hand was
then to see if variations introduced in tactual stimulations produce
any regularity of effect, and if they throw any new light on the
phenomena of the constant error.

   [3] Meumaun, E.: 'Beiträge zur Psychologie des Zeitsinns,' II.,
   _Phil. Studien_, IX., S. 264.

The stimulations employed were light blows from the cork tip of a
hammer actuated by an electric current. These instruments, of which
there were two, exactly alike in construction, were similar in
principle to the acoustical hammers employed by Estel and Mehner. Each
consisted essentially of a lever about ten inches in length, pivoted
near one extremity, and having fastened to it near the pivot an
armature so acted upon by an electromagnet as to depress the lever
during the passage of an electric current. The lever was returned to
its original position by a spring as soon as the current through the
electromagnet ceased. A clamp at the farther extremity held a small
wooden rod with a cork tip, at right angles to the pivot, and the
depression of the lever brought this tip into contact with the dermal
surface in proximity with which it had been placed. The rod was easily
removable, so that one bearing a different tip could be substituted
when desired. The whole instrument was mounted on a compact base
attached to a short rod, by which it could be fastened in any desired
position in an ordinary laboratory clamp.

During the course of most of the experiments the current was
controlled by a pendulum beating half seconds and making a mercury
contact at the lowest point of its arc. A condenser in parallel with
the contact obviated the spark and consequent noise of the current
interruption. A key, inserted in the circuit through the mercury cup
and tapping instrument, allowed it to be opened or closed as desired,
so that an interval of any number of half seconds could be interposed
between successive stimulations.

In the first work, a modification of the method of right and wrong
cases was followed, and found satisfactory. A series of intervals,
ranging from one which was on the whole distinctly perceptible as
longer than the standard to one on the whole distinctly shorter, was
represented by a series of cards. Two such series were shuffled
together, and the intervals given in the order so determined. Thus,
when the pile of cards had been gone through, two complete series had
been given, but in an order which the subject was confident was
perfectly irregular. As he also knew that in a given series there were
more than one occurrence of each compared interval (he was not
informed that there were exactly two of each), every possible
influence favored the formation each time of a perfectly fresh
judgment without reference to preceding judgments. The only fear was
lest certain sequences of compared intervals (_e.g._, a long compared
interval in one test followed by a short one in the next), might
produce unreliable results; but careful examination of the data, in
which the order of the interval was always noted, fails to show any
influence of such a factor.

To be more explicit with regard to the conditions of judgment; two
intervals were presented to the subject in immediate succession. That
is, the second stimulation marked the end of the first interval and
the beginning of the second. The first interval was always the
standard, while the second, or compared interval, varied in length, as
determined by the series of cards, and the subject was requested to
judge whether it was equal to, or longer or shorter than the standard
interval.

In all of the work under Group 1, and the first work under Group 2,
the standard interval employed was 5.0 seconds. This interval was
selected because the minimum variation possible with the pendulum
apparatus (½ sec.) was too great for the satisfactory operation of a
shorter standard, and it was not deemed advisable to keep the
subject's attention on the strain for a longer interval, since 5.0
sec. satisfied all the requirements of the experiment.

In all work here reported, the cork tip on the tapping instrument was
circular in form, and 1 mm. in diameter. In all, except one experiment
of the second group, the areas stimulated were on the backs of the
fingers, just above the nails. In the one exception a spot on the
forearm was used in conjunction with the middle finger.

In Groups 1 and 2 the intensity of stroke used was just sufficient to
give a sharp and distinct stimulation. The intensity of the
stimulation was not of a high degree of constancy from day to day, on
account of variations in the electric contacts, but within each test
of three stimulations the intensity was constant enough.

In experiments under Group 3 two intensities of strokes were employed,
one somewhat stronger than the stroke employed in the other
experiments, and one somewhat weaker--just strong enough to be
perceived easily. The introduction of the two into the same test was
effected by the use of an auxiliary loop in the circuit, containing a
rheostat, so that the depression of the first key completed the
circuit as usual, or the second key completed it through the rheostat.

At each test the subject was warned to prepare for the first
stimulation by a signal preceding it at an exact interval. In
experiments with the pendulum apparatus the signal was the spoken word
'now,' and the preparatory interval one second. Later, experiments
were undertaken with preparatory intervals of one second and 1-4/5
seconds, to find if the estimation differed perceptibly in one case
from that in the other. No difference was found, and in work
thereafter each subject was allowed the preparatory interval which
made the conditions subjectively most satisfactory to him.

Ample time for rest was allowed the subject after each test in a
series, two (sometimes three) series of twenty to twenty-four tests
being all that were usually taken in the course of the hour. Attention
to the interval was not especially fatiguing and was sustained without
difficulty after a few trials.

Further details will be treated as they come up in the consideration
of the work by groups, into which the experiment naturally falls.


II. EXPERIMENTAL RESULTS.


1. The first group of experiments was undertaken to find the direction
of the constant error for the 5.0 sec. standard, the extent to which
different subjects agree and the effects of practice. The tests were
therefore made with three taps of equal intensity on a single dermal
area. The subject sat in a comfortable position before a table upon
which his arm rested. His hand lay palm down on a felt cushion and the
tapping instrument was adjusted immediately over it, in position to
stimulate a spot on the back of the finger, just above the nail. A few
tests were given on the first finger and a few on the second
alternately throughout the experiments, in order to avoid the numbing
effect of continual tapping on one spot. The records for each of the
two fingers were however kept separately and showed no disagreement.

The detailed results for one subject (_Mr_,) are given in Table I. The
first column, under _CT_, gives the values of the different compared
intervals employed. The next three columns, under _S_, _E_ and _L_,
give the number of judgments of _shorter_, _equal_ and _longer_,
respectively. The fifth column, under _W_, gives the number of errors
for each compared interval, the judgments of _equal_ being divided
equally between the categories of _longer_ and _shorter_.

In all the succeeding discussion the standard interval will be
represented by _ST_, the compared interval by _CT_. _ET_ is that _CT_
which the subject judges equal to _ST_.


TABLE I.

      _ST_=5.0 SEC. SUBJECT _Mr._ 60 SERIES.

    _CT_       _S_       _E_       _L_       _W_
    4.         58         1         1         1.5
    4.5        45        11         4         9.5
    5.         32        13        15        21.5
    5.5        19        16        25        27
    6.          5         4        51         7
    6.5         1         2        57         2


We can calculate the value of the average _ET_ if we assume that the
distribution of wrong judgments is in general in accordance with the
law of error curve. We see by inspection of the first three columns
that this value lies between 5.0 and 5.5, and hence the 32 cases of
_S_ for _CT_ 5.0 must be considered correct, or the principle of the
error curve will not apply.

The method of computation may be derived in the following way: If we
take the origin so that the maximum of the error curve falls on the
_Y_ axis, the equation of the curve becomes

      y = ke^{-[gamma]²x²}

and, assuming two points (x_{1} y_{1}) and (x_{2} y_{2}) on the
curve, we deduce the formula

                        ____________
                   ±D \/ log k/y_{1}
  x_{1} = ---------------------------------
              ____________     ____________
            \/ log k/y_{1} ± \/ log k/y_{2}


where D = x_{1} ± x_{2}, and k = value of y when x = 0.

x_{1} and x_{2} must, however, not be great, since the condition
that the curve with which we are dealing shall approximate the form
denoted by the equation is more nearly fulfilled by those portions of
the curve lying nearest to the _Y_ axis.

Now since for any ordinates, y_{1} and y_{2} which we may select
from the table, we know the value of x_{1} ± x_{2}, we can compute
the value of x_{1}, which conversely gives us the amount to be added
to or subtracted from a given term in the series of _CT_'s to produce
the value of the average _ET_. This latter value, we find, by
computing by the formula given above, using the four terms whose
values lie nearest to the _Y_ axis, is 5.25 secs.

In Table II are given similar computations for each of the nine
subjects employed, and from this it will be seen that in every case
the standard is overestimated.


TABLE II. _ST_= 5.0 SECS.

    Subject.      Average ET.   No. of Series.
     _A_.            5.75           50
     _B_.            5.13           40
     _Hs_.           5.26          100
     _P_.            5.77           38
     _Mn_.           6.19           50
     _Mr_.           5.25           60
     _R_.            5.63           24
     _Sh_.           5.34          100
     _Sn_.           5.57           50


This overestimation of the 5.0 sec. standard agrees with the results
of some of the experimenters on auditory time and apparently conflicts
with the results of others. Mach[4] found no constant error. Höring[5]
found that intervals over 0.5 sec. were overestimated. Vierordt,[6]
Kollert,[7] Estel[8] and Glass,[9] found small intervals overestimated
and long ones underestimated, the indifference point being placed at
about 3.0 by Vierordt, 0.7 by Kollert and Estel and 0.8 by Glass.
Mehner[10] found underestimation from 0.7 to 5.0 and overestimation
above 5.0. Schumann[11] found in one set of experiments overestimation
from 0.64 to 2.75 and from 3.5 to 5.0, and underestimation from 2.75
to 3.5. Stevens[12] found underestimation of small intervals and
overestimation of longer ones, placing the indifference point between
0.53 and 0.87.

   [4] Mach, E.: 'Untersuchungen über den Zeitsinn des Ohres,'
   _Sitzungsber. d. Wiener Akad._, Math.-Nat. Kl., Bd. 51, Abth.
   2.

   [5] Höring: 'Versuche über das Unterscheidungsvermögen des
   Hörsinnes für Zeitgrössen,' Tübingen, 1864.

   [6] Vierordt: _op. cit._

   [7] Kollert, J.: 'Untersuchungen über den Zeitsinn,' _Phil.
   Studien_, I., S. 79.

   [8] Estel, V.: 'Neue Versuche über den Zeitsinn,' _Phil.
   Studien_, II., S. 39.

   [9] Glass R.: 'Kritisches und Experimentelles über den
   Zeitsinn,' _Phil. Studien_, IV., S. 423.

   [10] Mehner, Max: 'Zum Lehre vom Zeitsinn,' _Phil. Studien_,
   II., S. 546.

   [11] Schumann, F.: 'Ueber die Schätzung kleiner Zeitgrössen,'
   _Zeitsch. f. Psych._, IV., S. 48.

   [12] Stevens, L.T.: 'On the Time Sense,' _Mind_, XI., p. 393.

The overestimation, however, is of no great significance, for data
will be introduced a little later which show definitely that the
underestimation or overestimation of a given standard is determined,
among other factors, by the intensity of the stimulation employed. The
apparently anomalous results obtained in the early investigations are
in part probably explicable on this basis.

As regards the results of _practice_, the data obtained from the two
subjects on whom the greatest number of tests was made (_Hs_ and _Sh_)
is sufficiently explicit. The errors for each successive group of 25
series for these two subjects are given in Table III.


TABLE III.

       _ST_ = 5.0 SECONDS.

              SUBJECT _Hs_.             SUBJECT _Sh_.
    CT     (1)  (2)  (3)  (4)       (1)  (2)   (3)  (4)
    4.     2.5  2.5  1.5  2.5       0.     .5  0.    .5
    4.5    6.0  3.0  3.5  7.0       5.0   3.5  2.0   .5
    5.    14.0 11.0 11.0 11.0       8.5  11.5  4.0  7.0
    5.5   11.5 11.5  6.0 12.5      11.0  16.0 14.0 15.0
    6.    12.0  9.0  6.5  6.0       3.5   2.0  1.5  1.0
    6.5    4.0  3.5  4.0  3.5       4.0    .5  0.   0.


No influence arising from practice is discoverable from this table,
and we may safely conclude that this hypothetical factor may be
disregarded, although among the experimenters on auditory time
Mehner[13] thought results gotten without a maximum of practice are
worthless, while Meumann[14] thinks that unpracticed and hence
unsophisticated subjects are most apt to give unbiased results, as
with more experience they tend to fall into ruts and exaggerate their
mistakes. The only stipulation we feel it necessary to make in this
connection is that the subject be given enough preliminary tests to
make him thoroughly familiar with the conditions of the experiment.

   [13] _op. cit._, S. 558, S. 595.

   [14] _op. cit._ (II.), S. 284.


2. The second group of experiments introduced the factor of a
difference between the stimulation marking the end of an interval and
that marking the beginning, in the form of a change in locality
stimulated, from one finger to the other, either on the same hand or
on the other hand. Two classes of series were given, in one of which
the change was introduced in the standard interval, and in the other
class in the compared interval.

In the first of these experiments, which are typical of the whole
group, both of the subject's hands were employed, and a tapping
instrument was arranged above the middle finger of each, as above the
one hand in the preceding experiment, the distance between middle
fingers being fifteen inches. The taps were given either two on the
right hand and the third on the left, or one on the right and the
second and third on the left, the two orders being designated as _RRL_
and _RLL_ respectively. The subject was always informed of the order
in which the stimulations were to be given, so that any element of
surprise which might arise from it was eliminated. Occasionally,
however, through a lapse of memory, the subject expected the wrong
order, in which case the disturbance caused by surprise was usually so
great as to prevent any estimation.

The two types of series were taken under as similar conditions as
possible, four (or in some cases five) tests being taken from each
series alternately. Other conditions were the same as in the preceding
work. The results for the six subjects employed are given in Table IV.


TABLE IV.

         _ST_= 5.0 SECS. TWO HANDS. 15 INCHES.

    Subject.         Average RT.               No. of Series.
                   RRL.       RLL.*    (Table II.)
    _Hs._     4.92       6.55       (5.26)        50
    _Sh._     5.29       5.28       (5.34)        50
    _Mr._     5.02       6.23       (5.25)        60
    _Mn._     5.71       6.71       (6.19)        24
     _A._     5.34       5.89       (5.75)        28
    _Sn._     5.62       6.43       (5.47)        60

  *Transcriber's Note: Original "RRL"

From Table IV. it is apparent at a glance that the new condition
involved introduces a marked change in the time judgment. Comparison
with Table II. shows that in the cases of all except _Sh_ and _Sn_ the
variation _RRL_ shortens the standard subjectively, and that _RLL_
lengthens it; that is, a local change tends to lengthen the interval
in which it occurs. In the case of _Sh_ neither introduces any change
of consequence, while in the case of _Sn_ both values are higher than
we might expect, although the difference between them is in conformity
with the rest of the results shown in the table.

Another set of experiments was made on subject _Mr_, using taps on the
middle finger of the left hand and a spot on the forearm fifteen
inches from it; giving in one case two taps on the finger and the
third on the arm, and in the other one tap on the finger and the
second and third on the arm; designating the orders as _FFA_ and _FAA_
respectively. Sixty series were taken, and the values found for the
average _ET_ were 4.52 secs, for _FFA_ and 6.24 secs, for _FAA_, _ST_
being 5.0 secs. This shows 0.5 sec. more difference than the
experiment with two hands.

Next, experiments were made on two subjects, with conditions the same
as in the work corresponding to Table IV., except that the distance
between the fingers stimulated was only five inches. The results of
this work are given in Table V.


TABLE V.

       _ST_= 5.0 SECS. TWO HANDS. 5 INCHES.

    Subject  RRL.      RLL.    No. of Series.
    _Sh._    5.32      5.32         60
    _Hs._    4.40      6.80         60


It will be noticed that _Hs_ shows a slightly wider divergence than
before, while _Sh_ pursues the even tenor of his way as usual.

Series were next obtained by employing the first and second fingers on
one hand in exactly the same way as the middle fingers of the two
hands were previously employed, the orders of stimulation being 1, 1,
2, and 1, 2, 2. The results of sixty series on Subject _Hs_ give the
values of average _ET_ as 4.8 secs. for 1, 1, 2, and 6.23 sees, for 1,
2, 2, _ST_ being 5.0 secs., showing less divergence than in the
preceding work.

These experiments were all made during the first year's work. They
show that in most cases a change in the locality stimulated influences
the estimation of the time interval, but since the details of that
influence do not appear so definitely as might be desired, the ground
was gone over again in a little different way at the beginning of the
present year.

A somewhat more serviceable instrument for time measurements was
employed, consisting of a disc provided with four rows of sockets in
which pegs were inserted at appropriate angular intervals, so that
their contact with fixed levers during the revolution of the disc
closed an electric circuit at predetermined time intervals. The disc
was rotated at a uniform speed by an electric motor.

Experiments were made by stimulation of the following localities: (1)
First and third fingers of right hand; (2) first and second fingers of
right hand; (3) first fingers of both hands, close together, but just
escaping contact; (4) first fingers of both hands, fifteen inches
apart; (5) first fingers of both hands, thirty inches apart; (6) two
positions on middle finger of right hand, on same transverse line.

A standard of two seconds was adopted as being easier for the subject
and more expeditious, and since qualitative and not quantitative
results were desired, only one _CT_ was used in each case, thus
permitting the investigation to cover in a number of weeks ground
which would otherwise have required a much longer period. The subjects
were, however, only informed that the objective variations were very
small, and not that they were in most cases zero. Tests of the two
types complementary to each other (_e.g._, _RRL_ and _RRL_) were in
each case taken alternately in groups of five, as in previous work.


TABLE VI.

  _ST_= 2.0 SECS.

  _Subject W._

     (1) CT=2.0           (3) CT=2.2           (5) CT=2.0
      113  133           RRL     RLL          RRL       RLL
    S   3    3             9      20            5        21
    E  18   19            25      16           18        14
    L  24   28            16      14           17        15

  _Subject P._

     (1) CT=2.0          (3)CT={1.6            (5) CT={1.6
                               {2.4                   {2.4
      113  133         RRL(1.6)  RLL(2.4)    RRL(1.6)  RLL(2.4)
    S   2   16           12       16           15        10
    E  38   32           32       21           26        19
    L  10    2            6       15           14        21

  _Subject B._

     (1) CT=2.0          (2) CT=2.0           (6) CT=2.0
      113  133          112      122          aab        abb
    S   4   21            5       20            7         6
    E  23   19           22       24           40        38
    L  23   10           23        6            3         6

  _Subject Hy._

     (1) CT=2.0          (2) CT=2.4          (1a) CT=2.0
      113  133          112       122         113       133
    S  12   46           17        40          17        31
    E   9    2           14         8           9         7
    L  29    2           19         2          14         2

    In the series designated as (1a) the conditions were the same
    as in (1), except that the subject abstracted as much as
    possible from the tactual nature of the stimulations and the
    position of the fingers. This was undertaken upon the
    suggestion of the subject that it would be possible to perform
    the abstraction, and was not repeated on any other subject.


The results are given in Table VI., where the numerals in the
headings indicate the localities and changes of stimulation, in
accordance with the preceding scheme, and _'S'_, _'E'_ and _'L'_
designate the number of judgments of _shorter_, _equal_ and _longer_
respectively.

It will be observed that in several cases a _CT_ was introduced in one
class which was different from the _CT_ used in the other classes with
the same subject. This was not entirely arbitrary. It was found with
subject _W_, for example, that the use of _CT_ = 2.0 in (3) produced
judgments of shorter almost entirely in both types. Therefore a _CT_
was found, by trial, which produced a diversity of judgments. The
comparison of the different classes is not so obvious under these
conditions as it otherwise would be, but is still possible.

The comparison gives results which at first appear quite irregular.
These are shown in Table VII. below, where the headings (1)--(3),
etc., indicate the classes compared, and in the lines beneath them
'+' indicates that the interval under consideration is estimated as
relatively greater (more overestimated or less underestimated) in the
second of the two classes than in the first,--indicating the opposite
effect. Results for the first interval are given in the line denoted
'first,' and for the second interval in the line denoted 'second.'
Thus, the plus sign under (1)--(3) in the first line for subject _P_
indicates that the variation _RLL_ caused the first interval to be
overestimated to a greater extent than did the variation 133.


TABLE VII.

        SUBJECT _P._       SUBJECT _W._      SUBJECT _B._  SUBJECT _Hy._
     (1)--(3) (3)--(4)  (1)--(3) (3)--(5)  (2)--(1) (6)--(2)  (2)--(1)
First.   +        -         +        -         -        +         -
Sec.     +        +         -        +         +        +         +


The comparisons of (6) and (2), and (1) and (3) confirm the
provisional deduction from Table IV., that the introduction of a
_local change_ in an interval _lengthens_ it subjectively, but the
comparisons of (3) and (5), (3) and (4), and (2) and (1) show
apparently that while the _amount_ of the local change influences the
lengthening of the interval, it does not vary directly with this
latter in all cases, but inversely in the first interval and directly
in the second. This is in itself sufficient to demonstrate that the
chief factors of the influence of locality-change upon the time
interval are connected with the spatial localization of the areas
stimulated, but a further consideration strengthens the conclusion and
disposes of the apparent anomaly. It will be noticed that in general
the decrease in the comparative length of the first interval produced
by increasing the spatial change is less than the increase in the
comparative length of the second interval produced by a corresponding
change. In other words, the disparity between the results for the two
types of test is greater, the greater the spatial distance introduced.

The results seem to point to the existence of two distinct factors in
the so-called 'constant error' in these cases: first, what we may call
the _bare constant error_, or simply the constant error, which appears
when the conditions of stimulation are objectively the same as regards
both intervals, and which we must suppose to be present in all other
cases; and second, the particular lengthening effect which a change in
locality produces upon the interval in which it occurs. These two
factors may work in conjunction or in opposition, according to
conditions. The bare constant error does not remain exactly the same
at all times for any individual and is probably less regular in
tactual time than in auditory or in optical time, according to the
irregularity actually found and for reasons which will be assigned
later.


3. The third group of experiments introduced the factor of variation
in intensity of stimulation. By the introduction of a loop in the
circuit, containing a rheostat, two strengths of current and
consequently of stimulus intensity were obtained, either of which
could be employed as desired. One intensity, designated as _W_, was
just strong enough to be perceived distinctly. The other intensity,
designated as _S_, was somewhat stronger than the intensity used in
the preceding work.

In the first instance, sixty series were taken from Subject _B_, with
the conditions the same as in the experiments of Group 1, except that
two types of series were taken; the first two stimulations being
strong and the third one weak in the first type (_SSW_), and the order
being reversed in the second type (_WSS_). The results gave values of
_ET_ of 5.27 secs. for _SSW_ and 5.9 secs. for _WSS_.

In order to get comprehensive qualitative results as rapidly as
possible, a three-second standard was adopted in the succeeding work
and only one compared interval, also three seconds, was given,
although the subject was ignorant of that fact--the method being thus
similar to that adopted later for the final experiments of Group 2,
described above. Six types of tests were given, the order of
stimulation in the different types being _SSS, WWW, SSW, WWS, SWW_ and
_WSS_, the subject always knowing which order to expect. For each of
the six types one hundred tests were made on one subject and one
hundred and five on another, in sets of five tests of each type, the
sets being taken in varied order, so that possible contrast effect
should be avoided. The results were practically the same, however, in
whatever order the sets were taken, no contrast effect being
discernible.

The total number of judgments of _CT_, longer, equal, and shorter, is
given in Table VIII. The experiments on each subject consumed a number
of experiment hours, scattered through several weeks, but the relative
proportions of judgments on different days was in both cases similar
to the total proportions.


TABLE VIII.

    _ST=CT=_ 3.0 SECS.

          Subject _R_, 100.             Subject _P_, 105.
          L    E    S     d             L    E    S     d
    SSS   32   56   12   + 20     SSS   16   67   22   -  9
    WWW   11   53   36   - 25     WWW   19   72   14   +  5
    SSW    6   27   67   - 61     SSW   17   56   32   - 15
    WWS   57   36    7   + 50     WWS   37   61    7   + 30
    WSS   10   45   45   - 35     WSS    9   69   27   - 18
    SWW    3   31   66   - 63     SWW    3   64   33   - 25


By the above table the absolute intensity of the stimulus is clearly
shown to be an important factor in determining the constant error of
judgment, since in both cases the change from _SSS_ to _WWW_ changed
the sign of the constant error, although in opposite directions. But
the effect of the relative intensity is more obscure. To discover more
readily whether the introduction of a stronger or weaker stimulation
promises a definite effect upon the estimation of the interval which
precedes or follows it, the results are so arranged in Table IX. that
reading downward in any pair shows the effect of a decrease in the
intensity of (1) the first, (2) the second, (3) the third, and (4) all
three stimulations.


TABLE IX.

                  Subject _R._        Subject _P._

    (1) _SSS_     + 20                -  6
        _WSS_     - 35  - 55          - 18    - 12

        _SWW_     - 63                - 25
        _WWW_     - 25  - 38          +  5    + 30

    (2) _SSW_     - 61                - 15
        _SWW_     - 63  -  2          - 25    + 10

        _WSS_     - 35                - 18
        _WWS_     + 50  + 85          + 30    - 48

    (3) _SSS_     + 20                -  6
        _SSW_     - 61  - 81          - 15    -  7

        _WWS_     + 50                + 30
        _WWW_     - 25  - 75          +  5    - 25

    (4) _SSS_     + 20                -  6
        _WWW_     - 15  - 35          +  5    + 11


There seems at first sight to be no uniformity about these results.
Decreasing the first stimulation in the first case increases, in the
second case diminishes, the comparative length of the first interval.
We get a similar result in the decreasing of the second stimulation.
In the case of the third stimulation only does the decrease produce a
uniform result. If, however, we neglect the first pair of (3), we
observe that in the other cases the effect of a _difference_ between
the two stimulations is to lengthen the interval which they limit. The
fact that both subjects make the same exception is, however, striking
and suggestive of doubt. These results were obtained in the first
year's work, and to test their validity the experiment was repeated at
the beginning of the present year on three subjects, fifty series
being taken from each, with the results given in Table X.


TABLE X.

_ST_ = 3.0 secs. = _CT_.

         Subject _Mm._          Subject _A._          Subject _D._

         S   E   L     d        S   E   L     d       S   E   L     d
  SSS   24  13  13  - 11        7  30  13  +  6      10  31   9  -  1
  WSS   33   9   8  - 25       20  24   6  - 14      17  27   6  - 11
  SSW   19  15  16  -  3       23  16  11  - 12      10  31   9* -  1
  WWW   19  12  19     0       13  26  11  -  2       1  40   9  +  8
  SWW   18  30   2  - 16       23  21   6* - 17       7  38   5  -  2
  WWS   13  16  21  +  8       12  30   8  -  4      15  25  10  -  5

    *Transcriber's Note: Original "16" changed to "6", "19" to "9".


Analysis of this table shows that in every case a difference between
the intensities of the first and second taps lengthens the first
interval in comparative estimation. In the case of subject _Mm_ a
difference in the intensities of the second and third taps lengthens
the second interval subjectively. But in the cases of the other two
subjects the difference shortens the interval in varying degrees.

The intensity difference established for the purposes of these
experiments was not great, being less than that established for the
work on the first two subjects, and therefore the fact that these
results are less decided than those of the first work was not
unexpected. The results are, however, very clear, and show that the
lengthening effect of a difference in intensity of the stimulations
limiting an interval has its general application only to the first
interval, being sometimes reversed in the second. From the combined
results we find, further, that a uniform change in the intensity of
three stimulations is capable of reversing the direction of the
constant error, an intensity change in a given direction changing the
error from positive to negative for some subjects, and from negative
to positive for others.


III. INTERPRETATION OF RESULTS.


We may say provisionally that the _change_ from a tactual stimulation
of one kind to a tactual stimulation of another kind tends to lengthen
subjectively the interval which the two limit. If we apply the same
generalization to the other sensorial realms, we discover that it
agrees with the general results obtained by Meumann[15] in
investigating the effects of intensity changes upon auditory time, and
also with the results obtained by Schumann[16] in investigations with
stimulations addressed alternately to one ear and to the other.
Meumann reports also that the change from stimulation of one sense to
stimulation of another subjectively lengthens the corresponding
interval.

   [15] _op. cit._ (II.), S. 289-297.

   [16] _op. cit._, S. 67.

What, then, are the factors, introduced by the change, which produce
this lengthening effect? The results of introspection on the part of
some of the subjects of our experiments furnish the clue which may
enable us to construct a working hypothesis.

Many of the subjects visualize a time line in the form of a curve. In
each case of this kind the introduction of a change, either in
intensity or location, if large enough to produce an effect on the
time estimation, produced a distortion on the part of the curve
corresponding to the interval affected. All of the subjects employed
in the experiments of Group 2 were distinctly conscious of the change
in attention from one point to another, as the two were stimulated
successively, and three of them, _Hy_, _Hs_ and _P_, thought of
something passing from one point to the other, the representation
being described as partly muscular and partly visual. Subjects _Mr_
and _B_ visualized the two hands, and consciously transferred the
attention from one part of the visual image to the other. Subject _Mr_
had a constant tendency to make eye movements in the direction of the
change. Subject _P_ detected these eye movements a few times, but
subject _B_ was never conscious of anything of the kind.

All of the subjects except _R_ were conscious of more or less of a
_strain_, which varied during the intervals, and was by some felt to
be largely a tension of the chest and other muscles, while others felt
it rather indefinitely as a 'strain of attention.' The characteristics
of this tension feeling were almost always different in the second
interval from those in the first, the tension being usually felt to be
more _constant_ in the second interval. In experiments of the third
group a higher degree of tension was felt in awaiting a light tap than
in awaiting a heavy one.

Evidently, in all these cases, the effect of a _difference_ between
two stimulations was to introduce certain changes in sensation
_during_ the interval which they limited, owing to the fact that the
subject expected the difference to occur. Thus in the third group of
experiments there were, very likely, in all cases changes from
sensations of high tension to sensations of lower, or vice versa. It
is probable that, in the experiments of the second group, there were
also changes in muscular sensations, partly those of eye muscles,
partly of chest and arm muscles, introduced by the change of attention
from one point to another. At any rate, it is certain that there were
certain sensation changes produced during the intervals by changes of
locality.

If, then, we assume that the introduction of additional sensation
change into an interval lengthens it, we are led to the conclusion
that psychological time (as distinguished from metaphysical,
mathematical, or transcendental time) is perceived simply as the
quantum of change in the sensation content. That this is a true
conclusion is seemingly supported by the fact that when we wish to
make our estimate correspond as closely as possible with external
measurements, we exclude from the content, to the best of our ability,
the general complex of external sensations, which vary with extreme
irregularity; and confine the attention to the more uniformly varying
bodily sensations. We perhaps go even further, and inhibit certain
bodily sensations, corresponding to activity of the more peripherally
located muscles, that the attention may be confined to certain others.
But attention to a dermal stimulation is precisely the condition which
would tend to some extent to prevent this inhibition. For this reason
we might well expect to find the error in estimation more variable,
the 'constant error' in general greater, and the specific effects of
variations which would affect the peripheral muscles, more marked in
'tactual' time than in either 'auditory' or 'optical' time. Certainly
all these factors appear surprisingly large in these experiments.

It is not possible to ascertain to how great an extent subject _Sh_
inhibited the more external sensations, but certainly if he succeeded
to an unusual degree in so doing, that fact would explain the absence
of effect of stimulation difference in his case.

Explanation has still to be offered for the variable effect of
intensity difference upon the _second_ interval. According to all
subjects except _Sn_, there is a radical difference in attitude in the
two intervals. In the first interval the subject is merely observant,
but in the second he is more or less reproductive. That is, he
measures off a length which seems equal to the standard, and if the
stimulation does not come at that point he is prepared to judge the
interval as 'longer,' even before the third stimulation is given. In
cases, then, where the judgment with equal intensities would be
'longer,' we might expect that the actual strengthening or weakening
of the final tap would make no difference, and that it would make very
little difference in other cases. But even here the expectation of the
intensity is an important factor in determining tension changes,
although naturally much less so than in the first interval. So we
should still expect the lengthening of the second interval.

We must remember, however, that, as we noticed in discussing the
experiments of Group 2, there is complicated with the lengthening
effect of a change the _bare constant error_, which appears even when
the three stimulations are similar in all respects except temporal
location. Compare _WWW_ with _SSS_, and we find that with all five
subjects the constant error is decidedly changed, being even reversed
in direction with three of the subjects.

Now, what determines the direction of the constant error, where there
is no pause between the intervals? Three subjects reported that at
times there seemed to be a slight loss of time after the second
stimulation, owing to the readjustment called for by the change of
attitude referred to above, so that the second interval was begun, not
really at the second stimulation, but a certain period after it. This
fact, if we assume it to be such, and also assume that it is present
to a certain degree in all observations of this kind, explains the
apparent overestimation of the first interval. Opposed to the factor
of _loss of time_ there is the factor of _perspective_, by which an
interval, or part of an interval, seems less in quantity as it recedes
into the past. The joint effect of these two factors determines the
constant error in any case where no pause is introduced between _ST_
and _CT_. It is then perfectly obvious that, as the perspective factor
is decreased by diminishing the intervals compared, the constant error
must receive positive increments, _i.e._, become algebraically
greater; which corresponds exactly with the results obtained by
Vierordt, Kollert, Estel, and Glass, that under ordinary conditions
long standard intervals are comparatively underestimated, and short
ones overestimated.

On the other hand, if with a given interval we vary the loss of time,
we also vary the constant error. We have seen that a change in the
intensity of the stimulations, although the relative intensity of the
three remains constant, produces this variation of the constant error;
and the individual differences of subjects with regard to sensibility,
power of attention and inhibition, and preferences for certain
intensities, lead us to the conclusion that for certain subjects
certain intensities of stimulation make the transition from the
receptive attitude to the reproductive easiest, and, therefore, most
rapid.

Now finally, as regards the apparent failure of the change in _SSW_ to
lengthen the second interval, for which we are seeking to account; the
comparatively great loss of time occurring where the change of
attitude would naturally be most difficult (that is, where it is
complicated with a change of attention from a strong stimulation to
the higher key of a weak stimulation) is sufficient to explain why
with most subjects the lengthening effect upon the second interval is
more than neutralized. The individual differences mentioned in the
preceding paragraph as affecting the relation of the two factors
determining the constant error, enter here of course to modify the
judgments and cause disagreement among the results for different
subjects.

Briefly stated, the most important points upon which this discussion
hinges are thus the following: We have shown--

    1. That the introduction of either a local difference or a
    difference of intensity in the tactual stimulations limiting
    an interval has, in general, the effect of causing the
    interval to appear longer than it otherwise would appear.

    2. That the apparent exceptions to the above rule are, (_a_)
    that the _increase_ of the local difference in the first
    interval, the stimulated areas remaining unchanged, produces a
    slight _decrease_ in the subjective lengthening of the
    interval, and (_b_) that in certain cases a difference in
    intensity of the stimulations limiting the second interval
    apparently causes the interval to seem shorter than it
    otherwise would.

    3. That the 'constant error' of time judgment is dependent
    upon the intensity of the stimulations employed, although the
    three stimulations limiting the two intervals remain of equal
    intensity.

To harmonize these results we have found it necessary to assume:

    1. That the length of a time interval is perceived as the
    amount of change in the sensation-complex corresponding to
    that interval.

    2. That the so-called 'constant error' of time estimation is
    determined by two mutually opposing factors, of which the
    first is the _loss of time_ occasioned by the change of
    attitude at the division between the two intervals, and the
    second is the diminishing effect of _perspective_.

    It is evident, however, that this last assumption applies only
    to the conditions under which the results were obtained,
    namely, the comparison of two intervals marked off by three
    brief stimulations.

       *       *       *       *       *



PERCEPTION OF NUMBER THROUGH TOUCH.

BY J. FRANKLIN MESSENGER.


The investigation which I am now reporting began as a study of the
fusion of touch sensations when more than two contacts were possible.
As the work proceeded new questions came up and the inquiry broadened
so much that it seemed more appropriate to call it a study in the
perception of number.

The experiments are intended to have reference chiefly to three
questions: the space-threshold, fusion of touch sensations, and the
perception of number. I shall deny the validity of a threshold, and
deny that there is fusion, and then offer a theory which attempts to
explain the phenomena connected with the determination of a threshold
and the problem of fusion and diffusion of touch sensations.

The first apparatus used for the research was made as follows: Two
uprights were fastened to a table. These supported a cross-bar about
ten inches from the table. To this bar was fastened a row of steel
springs which could be pressed down in the manner of piano keys. To
each of these springs was fastened a thread which held a bullet. The
bullets, which were wrapped in silk to obviate temperature sensations,
were thus suspended just above the fingers, two over each finger. Each
thread passed through a small ring which was held just a little above
the fingers. These rings could be moved in any direction to
accommodate the bullet to the position of the finger. Any number of
the bullets could be let down at once. The main object at first was to
learn something about the fusion of sensations when more than two
contacts were given.

Special attention was given to the relation of the errors made when
the fingers were near together to those made when the fingers were
spread. For this purpose a series of experiments was made with the
fingers close together, and then the series was repeated with the
fingers spread as far as possible without the subject's feeling any
strain. Each subject was experimented on one hour a week for about
three months. The same kind of stimulation was given when the fingers
were near together as was given when they were spread. The figures
given below represent the average percentage of errors for four
subjects.

Of the total number of answers given by all subjects when the fingers
were close together, 70 per cent. were wrong. An answer was called
wrong whenever the subject failed to judge the number correctly. In
making out the figures I did not take into account the nature of the
errors. Whether involving too many or too few the answer was called
wrong. Counting up the number of wrong answers when the fingers were
spread, I found that 28 per cent. of the total number of answers were
wrong. This means simply that when the fingers were near together
there were more than twice as many errors as there were when they were
spread, in spite of the fact that each finger was stimulated in the
same way in each case.

A similar experiment was tried using the two middle fingers only. In
this case not more than four contacts could be made at once, and hence
we should expect a smaller number of errors, but we should expect
still to find more of them when the fingers are near together than
when they are spread. I found that 49 per cent. of the answers were
wrong when the fingers were near together and 20 per cent. were wrong
when they were spread. It happens that this ratio is approximately the
same as the former one, but I do not regard this fact as very
significant. I state only that it is easier to judge in one case than
in the other; how much easier may depend on various factors.

To carry the point still further I took only two bullets, one over the
second phalanx of each middle finger. When the fingers were spread the
two were never felt as one. When the fingers were together they were
often felt as one.

The next step was to investigate the effect of bringing together the
fingers of opposite hands. I asked the subject to clasp his hands in
such a way that the second phalanges would be about even. I could not
use the same apparatus conveniently with the hands in this position,
but in order to have the contacts as similar as possible to those I
had been using, I took four of the same kind of bullets and fastened
them to the ends of two æsthesiometers. This enabled me to give four
contacts at once. However, only two were necessary to show that
contacts on fingers of opposite hands could be made to 'fuse' by
putting the fingers together. If two contacts are given on contiguous
fingers, they are quite as likely to be perceived as one when the
fingers are fingers of opposite hands, as when they are contiguous
fingers of the same hand.

These results seem to show that one of the important elements of
fusion is the actual space relations of the points stimulated. The
reports of the subjects also showed that generally and perhaps always
they located the points in space and then remembered what finger
occupied that place. It was not uncommon for a subject to report a
contact on each of two adjacent fingers and one in between where he
had no finger. A moment's reflection would usually tell him it must be
an illusion, but the sensation of this illusory finger was as definite
as that of any of his real fingers. In such cases the subject seemed
to perceive the relation of the points to each other, but failed to
connect them with the right fingers. For instance, if contacts were
made on the first, second and third fingers, the first might be
located on the first finger, the third on the second finger, and then
the second would be located in between.

So far my attention had been given almost entirely to fusion, but the
tendency on the part of all subjects to report more contacts than were
actually given was so noticeable that I concluded that diffusion was
nearly as common as fusion and about as easy to produce. It also
seemed that the element of weight might play some part, but just what
effect it had I was uncertain. I felt, too, that knowledge of the
apparatus gained through sight was giving the subjects too much help.
The subjects saw the apparatus every day and knew partly what to
expect, even though the eyes were closed when the contacts were made.
A more efficient apparatus seemed necessary, and, therefore, before
taking up the work again in 1900, I made a new apparatus.

Not wishing the subjects to know anything about the nature of the
machine or what could be done with it, I enclosed it in a box with an
opening in one end large enough to allow the subject's hand to pass
through, and a door in the other end through which I could operate. On
the inside were movable wooden levers, adjustable to hands of
different width. These were fastened by pivotal connection at the
proximal end. At the outer end of each of these was an upright strip
with a slot, through which was passed another strip which extended
back over the hand. This latter strip could be raised or lowered by
means of adjusting screws in the upright strip. On the horizontal
strip were pieces of wood made so as to slide back and forth. Through
holes in these pieces plungers were passed. At the bottom of each
plunger was a small square piece of wood held and adjusted by screws.
From this piece was suspended a small thimble filled with shot and
paraffine. The thimbles were all equally weighted. Through a hole in
the plunger ran a thread holding a piece of lead of exactly the weight
of the thimble. By touching a pin at the top this weight could be
dropped into the thimble, thus doubling its weight. A screw at the top
of the piece through which the plunger passed regulated the stop of
the plunger. This apparatus had three important advantages. It was
entirely out of sight, it admitted of rapid and accurate adjustment,
and it allowed the weights to be doubled quickly and without
conspicuous effort.

For the purpose of studying the influence of weight on the judgments
of number I began a series of experiments to train the subjects to
judge one, two, three, or four contacts at once. For this the bare
metal thimbles were used, because it was found that when they were
covered with chamois skin the touch was so soft that the subjects
could not perceive more than one or two with any degree of accuracy,
and I thought it would take entirely too long to train them to
perceive four. The metal thimbles, of course, gave some temperature
sensation, but the subject needed the help and it seemed best to use
the more distinct metal contacts.

In this work I had seven subjects, all of whom had had some experience
in a laboratory, most of them several years. Each one took part one
hour a week. The work was intended merely for training, but a few
records were taken each day to see how the subjects progressed. The
object was to train them to perceive one, two, three, and four
correctly, and not only to distinguish four from three but to
distinguish four from more than four. Hence five, six, seven, and
eight at a time were often given. When the subject had learned to do
this fairly well the plan was to give him one, two, three, and four in
order, then to double the weight of the four and give them again to
see if he would interpret the additional weight as increase in number.
This was done and the results were entirely negative. The subjects
either noticed no difference at all or else merely noticed that the
second four were a little more distinct than the first.

The next step was to give a number of light contacts to be compared
with the same number of heavy ones--the subject, not trying to tell
the exact number but only which group contained the greater number. A
difference was sometimes noticed, and the subject, thinking that the
only variations possible were variations of number and position, often
interpreted the difference as difference in number; but the light
weights were as often called more as were the heavy ones.

So far as the primary object of this part of the experiment is
concerned the results are negative, but incidentally the process of
training brought out some facts of a more positive nature. It was
early noticed that some groups of four were much more readily
recognized than others, and that some of them were either judged
correctly or underestimated while others were either judged correctly
or overestimated. For convenience the fingers were indicated by the
letters _A B C D_, _A_ being the index finger. The thumb was not used.
Two weights were over each finger. The one near the base was called 1,
the one toward the end 2. Thus _A12 B1 C2_ means two contacts on the
index finger, one near the base of the second finger, and one near the
end of the third finger. The possible arrangements of four may be
divided into three types: (1) Two weights on each of two fingers, as
_A12 B12, C12 D12_, etc., (2) four in a line across the fingers, _A1
B1 C1 D1_ or _A2 B2 C2 D2_, (3) unsymmetrical arrangements, as _A1 B2
C1 D2_, etc. Arrangements of the first type were practically never
overestimated. _B12 C12_ was overestimated once and _B12 D12_ was
overestimated once, but these two isolated cases need hardly be taken
into account. Arrangements of the second type were but rarely
overestimated--_A2 B2 C2 D2_ practically never, _A1 B1 C1 D1_ a few
times. Once the latter was called eight. Apparently the subject
perceived the line across the hand and thought there were two weights
on each finger instead of one. Arrangements of the third type were
practically never underestimated, but were overestimated in 68 per
cent. of the cases.

These facts in themselves are suggestive, but equally so was the
behavior of the subject while making the answers. It would have hardly
done to ask the person if certain combinations were hard to judge, for
the question would serve as a suggestion to him; but it was easy to
tell when a combination was difficult without asking questions. When a
symmetrical arrangement was given, the subject was usually composed
and answered without much hesitation. When an unsymmetrical
arrangement was given he often hesitated and knit his brows or perhaps
used an exclamation of perplexity before answering, and after giving
his answer he often fidgeted in his chair, drew a long breath, or in
some way indicated that he had put forth more effort than usual. It
might be expected that the same attitude would be taken when six or
eight contacts were made at once, but in these cases the subject was
likely either to fail to recognize that a large number was given or,
if he did, he seemed to feel that it was too large for him to perceive
at all and would guess at it as well as he could. But when only four
were given, in a zigzag arrangement, he seemed to feel that he ought
to be able to judge the number but to find it hard to do so, and
knowing from experience that the larger the number the harder it is to
judge he seemed to reason conversely that the more effort it takes to
judge the more points there are, and hence he would overestimate the
number.

The comments of the subjects are of especial value. One subject (Mr.
Dunlap) reports that he easily loses the sense of location of his
fingers, and the spaces in between them seem to belong to him as much
as do his fingers themselves. When given one touch at a time and told
to raise the finger touched he can do so readily, but he says he does
not know which finger it is until he moves it. He feels as if he
willed to move the place touched without reference to the finger
occupying it. He sometimes hesitates in telling which finger it is,
and sometimes he finds out when he moves a finger that it is not the
one he thought it was.

Another subject (Dr. MacDougall) says that his fingers seem to him
like a continuous surface, the same as the back of his hand. He
usually named the outside points first. When asked about the order in
which he named them, he said he named the most distinct ones first.
Once he reported that he felt six things, but that two of them were in
the same places as two others, and hence he concluded there were but
four. This feeling in a less careful observer might lead to
overestimation of number and be called diffusion, but all cases of
overestimation cannot be explained that way, for it does not explain
why certain combinations are so much more likely to lead to it than
others.

In one subject (Mr. Swift) there was a marked tendency to locate
points on the same fingers. He made many mistakes about fingers _B_
and _C_ even when he reported the number correctly. When _B_ and _D_
were touched at the same time he would often call it _C_ and _D_, and
when _C_ and _D_ were given immediately afterward he seemed to notice
no difference. With various combinations he would report _C_ when _B_
was given, although _C_ had not been touched at the same time. If _B_
and _C_ were touched at the same time he could perceive them well
enough.

The next part of the research was an attempt to discover whether a
person can perceive any difference between one point and two points
which feel like one. A simple little experiment was tried with the
æsthesiometer. The subjects did not know what was being used, and were
asked to compare the relative size of two objects placed on the back
of the hand in succession. One of these objects was one knob of the
æsthesiometer and the other was two knobs near enough together to lie
within the threshold. The distance of the points was varied from 10 to
15 mm. Part of the time the one was given first and part of the time
both were given together. The one, whether given first or second, was
always given about midway between the points touched by the two. If
the subject is not told to look for some specific difference he will
not notice any difference between the two knobs and the one, and he
will say they are alike; but if he is told to give particular
attention to the size there seems to be a slight tendency to perceive
a difference. The subjects seem to feel very uncertain about their
answers, and it looks very much like guess-work, but something caused
the guesses to go more in one direction than in the other.

  Two were called less than one .... 16% of the times given.
   "    "     "      equal to   .... 48%    "         "
   "    "     "    greater than .... 36%    "         "

Approximately half of the time two were called equal to one, and if
there had been no difference in the sensations half of the remaining
judgments should have been that two was smaller than one, but two were
called larger than one more than twice as many times as one was called
larger than two. There was such uniformity in the reports of the
different subjects that no one varied much from this average ratio.

This experiment seems to indicate a very slight power of
discrimination of stimulations within the threshold. In striking
contrast to this is the power to perceive variations of distance
between two points outside the threshold. To test this the
æsthesiometer was spread enough to bring the points outside the
threshold. The back of the hand was then stimulated with the two
points and then the distance varied slightly, the hand touched and the
subject asked to tell which time the points were farther apart. A
difference of 2 mm. was usually noticed, and one of from 3 to 5 mm.
was noticed always very clearly.

I wondered then what would be the result if small cards set parallel
to each other were used in place of the knobs of the æsthesiometer. I
made an æsthesiometer with cards 4 mm. long in place of knobs. These
cards could be set at any angle to each other. I set them at first 10
mm. apart and parallel to each other and asked the subjects to compare
the contact made by them with a contact by one card of the same size.
The point touched by the one card was always between the points
touched by the two cards, and the one card was put down so that its
edge would run in the same direction as the edges of the other cards.
The result of this was that:

  Two were called less,  14 per cent.
   "    "     "   equal, 36   "   "
   "    "     " greater, 50   "   "

I then increased the distance of the two cards to 15 mm., the other
conditions remaining the same, and found that:

  Two were called less,  11 per cent.
   "    "     "   equal, 50   "   "
   "    "     " greater, 39   "   "

It will be noticed that the ratio in this last series is not
materially different from the ratio found when the two knobs of the
æsthesiometer were compared with one knob. The ratio found when the
distance was 10 mm., however, is somewhat different. At that distance
two were called greater half of the time, while at 15 mm. two were
called equal to one half of the time. The explanation of the
difference, I think, is found in the comments of one of my subjects. I
did not ask them to tell in what way one object was larger than the
other--whether longer or larger all around or what--but simply to
answer 'equal,' 'greater,' or 'less.' One subject, however, frequently
added more to his answers. He would often say 'larger crosswise' or
'larger lengthwise' of his hand. And a good deal of the time he
reported two larger than one, not in the direction in which it really
was larger, but the other way. It seems to me that when the two cards
were only 10 mm. apart the effect was somewhat as it would be if a
solid object 4 mm. wide and 10 mm. long had been placed on the hand.
Such an object would be recognized as having greater mass than a line
4 mm. long. But when the distance is 15 mm. the impression is less
like that of a solid body but still not ordinarily like two objects.

In connection with the subject of diffusion the _Vexirfehler_ is of
interest. An attempt was made to develop the _Vexirfehler_ with the
æsthesiometer. Various methods were tried, but the following was most
successful. I would tell the subject that I was going to use the
æsthesiometer and ask him to close his eyes and answer simply 'one' or
'two.' He would naturally expect that he would be given part of the
time one, and part of the time two. I carefully avoided any suggestion
other than that which could be given by the æsthesiometer itself. I
would begin on the back of the hand near the wrist with the points as
near the threshold as they could be and still be felt as two. At each
successive putting down of the instrument I would bring the points a
little nearer together and a little lower down on the hand. By the
time a dozen or more stimulations had been given I would be working
down near the knuckles, and the points would be right together. From
that on I would use only one point. It might be necessary to repeat
this a few times before the illusion would persist. A great deal seems
to depend on the skill of the operator. It would be noticed that the
first impression was of two points, and that each stimulation was so
nearly like the one immediately preceding that no difference could be
noticed. The subject has been led to call a thing two which ordinarily
he would call one, and apparently he loses the distinction between the
sensation of one and the sensation of two. After going through the
procedure just mentioned I put one knob of the æsthesiometer down one
hundred times in succession, and one subject (Mr. Meakin) called it
two seventy-seven times and called it one twenty-three times. Four of
the times that he called it one he expressed doubt about his answer
and said it might be two, but as he was not certain he called it one.
Another subject (Mr. George) called it two sixty-two times and one
thirty-eight times. A third subject (Dr. Hylan) called it two
seventy-seven times and one twenty-three times. At the end of the
series he was told what had been done and he said that most of his
sensations of two were perfectly distinct and he believed that he was
more likely to call what seemed somewhat like two one, than to call
what seemed somewhat like one two. With the fourth subject (Mr.
Dunlap) I was unable to do what I had done with the others. I could
get him to call one two for four or five times, but the idea of two
would not persist through a series of any length. He would call it two
when two points very close together were used. I could bring the knobs
within two or three millimeters of each other and he would report two,
but when only one point was used he would find out after a very few
stimulations were given that it was only one. After I had given up the
attempt I told him what I had been trying to do and he gave what seems
to me a very satisfactory explanation of his own case. He says the
early sensations keep coming up in his mind, and when he feels like
calling a sensation two he remembers how the first sensation felt and
sees that this one is not like that, and hence he calls it one. I pass
now to a brief discussion of what these experiments suggest.

It has long been known that two points near together on the skin are
often perceived as one. It has been held that in order to be felt as
two they must be far enough apart to have a spatial character, and
hence the distance necessary for two points to be perceived has been
called the 'space-threshold.' This threshold is usually determined
either by the method of minimal changes or by the method of right and
wrong cases.

If, in determining a threshold by the method of minimal changes--on
the back of the hand, for example, we assume that we can begin the
ascending series and find that two are perceived as one always until
the distance of twenty millimeters is reached, and that in the
descending series two are perceived as two until the distance of ten
millimeters is reached, we might then say that the threshold is
somewhere between ten and twenty millimeters. But if the results were
always the same and always as simple as this, still we could not say
that there is any probability in regard to the answer which would be
received if two contacts 12, 15, or 18 millimeters apart were given by
themselves. All we should know is that if they form part of an
ascending series the answer will be 'one,' if part of a descending
series 'two.'

The method of right and wrong cases is also subject to serious
objections. There is no lower limit, for no matter how close together
two points are they are often called two. If there is any upper limit
at all, it is so great that it is entirely useless. It might be argued
that by this method a distance could be found at which a given
percentage of answers would be correct. This is quite true, but of
what value is it? It enables one to obtain what one arbitrarily calls
a threshold, but it can go no further than that. When the experiment
changes the conditions change. The space may remain the same, but it
is only one of the elements which assist in forming the judgment, and
its importance is very much overestimated when it is made the basis
for determining the threshold.

Different observers have found that subjects sometimes describe a
sensation as 'more than one, but less than two.' I had a subject who
habitually described this feeling as 'one and a half.' This does not
mean that he has one and a half sensations. That is obviously
impossible. It must mean that the sensation seems just as much like
two as it does like one, and he therefore describes it as half way
between. If we could discover any law governing this feeling of
half-way-between-ness, that might well indicate the threshold. But
such feelings are not common. Sensations which seem between one and
two usually call forth the answer 'doubtful,' and have a negative
rather than a positive character. This negative character cannot be
due to the stimulus; it must be due to the fluctuating attitudes of
the subject. However, if the doubtful cases could be classed with the
'more than one but less than two' cases and a law be found governing
them, we might have a threshold mark. But such a law has not been
formulated, and if it had been an analysis of the 'doubtful' cases
would invalidate it. For, since we cannot have half of a sensation or
half of a place as we might have half of an area, the subject regards
each stimulation as produced by one or by two points as the case may
be. Occasionally he is stimulated in such a way that he can regard the
object as two or as one with equal ease. In order to describe this
feeling he is likely to use one or the other of the methods just
mentioned.

We might say that when the sum of conditions is such that the subject
perceives two points, the points are above the threshold, and when the
subject perceives one point when two are given they are below the
threshold. This might answer the purpose very well if it were not for
the _Vexirfehler_. According to this definition, when the
_Vexirfehler_ appears we should have to say that one point is above
the threshold for twoness, which is a queer contradiction, to say the
least. It follows that all of the elaborate and painstaking
experiments to determine a threshold are useless. That is, the
threshold determinations do not lead us beyond the determinations
themselves.

In order to explain the fact that a person sometimes fails to
distinguish between one point and two points near together, it has
been suggested that the sensations fuse. This, I suppose, means either
that the peripheral processes coalesce and go to the center as a
single neural process, or that the process produced by each stimulus
goes separately to the brain and there the two set up a single
activity. Somewhat definite 'sensory circles,' even, were once
believed in.

If the only fact we had to explain was that two points are often
thought to be one when they are near together, 'fusion' might be a
good hypothesis, but we have other facts to consider. If this one is
explained by fusion, then the mistaking of one point for two must be
due to diffusion of sensations. Even that might be admissible if the
_Vexirfehler_ were the only phenomenon of this class which we met. But
it is also true that several contacts are often judged to be more than
they actually are, and that hypothesis will not explain why certain
arrangements of the stimulating objects are more likely to bring about
that result than others. Still more conclusive evidence against
fusion, it seems to me, is found in the fact that two points, one on
each hand, may be perceived as one when the hands are brought
together. Another argument against fusion is the fact that two points
pressed lightly may be perceived as one, and when the pressure is
increased they are perceived as two. Strong pressures should fuse
better than weak ones, and therefore fusion would imply the opposite
results. Brückner[1] has found that two sensations, each too weak to
be perceived by itself, may be perceived when the two are given
simultaneously and sufficiently near together. This reënforcement of
sensations he attributes to fusion. But we have a similar phenomenon
in vision when a group of small dots is perceived, though each dot by
itself is imperceptible. No one, I think, would say this is due to
fusion. It does not seem to me that we need to regard reënforcement as
an indication of fusion.

   [1] Brückner, A.: 'Die Raumschwelle bei Simultanreizung,'
   _Zeitschrift für Psychologie_, 1901, Bd. 26, S. 33.

My contention is that the effects sometimes attributed to fusion and
diffusion of sensations are not two different kinds of phenomena, but
are identical in character and are to be explained in the same way.

Turning now to the explanation of the special experiments, we may
begin with the _Vexirfehler_.[2] It seems to me that the _Vexirfehler_
is a very simple phenomenon. When a person is stimulated with two
objects near together he attends first to one and then to the other
and calls it two; then when he is stimulated with one object he
attends to it, and expecting another one near by he hunts for it and
hits upon the same one he felt before but fails to remember that it is
the same one, and hence thinks it is another and says he has felt two
objects. Observers agree that the expectation of two tends to bring
out the _Vexirfehler_. This is quite natural. A person who expects two
and receives one immediately looks about for the other without waiting
to fixate the first, and therefore when he finds it again he is less
likely to recognize it and more likely to think it another point and
to call it two. Some observers[3] have found that the apparent
distance of the two points when the _Vexirfehler_ appears never much
exceeds the threshold distance. Furthermore, there being no distinct
line of demarcation between one and two, there must be many sensations
which are just about as much like one as they are like two, and hence
they must be lumped off with one or the other group. To the
mathematician one and two are far apart in the series because he has
fractions in between, but we perceive only in terms of whole numbers;
hence all sensations which might more accurately be represented by
fractions must be classed with the nearest whole number. A sensation
is due to a combination of factors. In case of the _Vexirfehler_ one
of these factors, viz., the stimulating object, is such as to suggest
one, but some of the other conditions--expectation, preceding
sensation, perhaps blood pressure, etc.--suggest two, so that the
sensation as a whole suggests _one-plus_, if we may describe it that
way, and hence the inference that the sensation was produced by two
objects.

   [2] Tawney, Guy A.: 'Ueber die Wahrnehmung zweier Punkte
   mittelst des Tastsinnes mit Rücksicht auf die Frage der Uebung
   und die Entstehung der Vexirfehler,' _Philos. Stud._, 1897, Bd.
   XIII., S. 163.

   [3] See Nichols: 'Number and Space,' p. 161. Henri, V., and
   Tawney, G.: _Philos. Stud._, Bd. XI., S. 400.

This, it seems to me, may account for the appearance of the
_Vexirfehler_, but why should not the subject discover his error by
studying the sensation more carefully? He cannot attend to two things
at once, nor can he attend to one thing continuously, even for a few
seconds. What we may call continuous attention is only a succession of
attentive impulses. If he could attend to the one object continuously
and at the same time hunt for the other, I see no reason why he should
not discover that there is only one. But if he can have only one
sensation at a time, then all he can do is to associate that
particular sensation with some idea. In the case before us he
associates it with the idea of the number two. He cannot conceive of
two objects unless he conceives them as located in two different
places. Sometimes a person does find that the two objects of his
perception are both in the same place, and when he does so he
concludes at once that there is but one object. At other times he
cannot locate them so accurately, and he has no way of finding out the
difference, and since he has associated the sensation with the idea of
two he still continues to call it two. If he is asked to locate the
points on paper he fills out the figure just as he fills out the
blind-spot, and he can draw them in just the same way that he can draw
lines which he thinks he _sees_ with the blind-spot, but which really
he only _infers_.

Any sensation, whether produced by one or by many objects, is one, but
there may be a difference in the quality of a sensation produced by
one object and that of a sensation produced by more than one object.
If this difference is clear and distinct, the person assigns to each
sensation the number he has associated with it. He gives it the name
two when it has the quality he has associated with that idea. But the
qualities of a sensation from which the number of objects producing it
is inferred are not always clear and distinct. The quality of the
sensation must not be confused with any quality of the object. If we
had to depend entirely on the sense of touch and always remained
passive and received sensations only when we were touched by
something, there is no reason why we should not associate the idea of
one with the sensation produced by two objects and the idea of two
with that produced by one object--assuming that we could have any idea
of number under such circumstances. The quality of a sensation from
which number is inferred depends on several factors. The number itself
is determined by the attitude of the subject, but the attitude is
determined largely by association. A number of facts show this. When a
person is being experimented on, it is very easy to confuse him and
make him forget how two feel and how one feels. I have often had a
subject tell me that he had forgotten and ask me to give him two
distinctly that he might see how it felt. In other words, he had
forgotten how to associate his ideas and sensations. In developing the
_Vexirfehler_ I found it much better, after sufficient training had
been given, not to give two at all, for it only helped the subject to
perceive the difference between two and one by contrast. But when one
was given continually he had no such means of contrast, and having
associated the idea of two with a sensation he continued to do so. The
one subject with whom I did not succeed in developing the
_Vexirfehler_ to any great extent perceived the difference by
comparing the sensation with one he had had some time before. I could
get him, for a few times, to answer two when only one was given, but
he would soon discover the difference, and he said he did it by
comparing it with a sensation which he had had some time before and
which he knew was two. By this means he was able to make correct
associations when otherwise he would not have done so. It has been
discovered that when a subject is being touched part of the time with
two and part of the time with one, and the time it takes him to make
his judgments is being recorded, he will recognize two more quickly
than he will one if there is a larger number of twos in the series
than there is of ones. I do not see how this could be if the sensation
of two is any more complex than that of one. But if both sensations
are units and all the subject needs to do is to associate the
sensation with an idea, then we should expect that the association he
had made most frequently would be made the most quickly.

If the feeling of twoness or of oneness is anything but an inference,
why is it that a person can perceive two objects on two fingers which
are some distance apart, but perceives the same two objects as one
when the fingers are brought near together and touched in the same
way? It is difficult to see how bringing the fingers together could
make a sensation any less complex, but it would naturally lead a
person to infer one object, because of his previous associations. He
has learned to call that _one_ which seems to occupy one place. If two
contacts are made in succession he will perceive them as two because
they are separated for him by the time interval and he can perceive
that they occupy different places.

When two exactly similar contacts are given and are perceived as one,
we cannot be sure whether the subject feels only one of the contacts
and does not feel the other at all, or feels both contacts and thinks
they are in the same place, which is only another way of saying he
feels both as one. It is true that when asked to locate the point he
often locates it between the two points actually touched, but even
this he might do if he felt but one of the points. To test the matter
of errors of localization I have made a few experiments in the
Columbia University laboratory. In order to be sure that the subject
felt both contacts I took two brass rods about four inches long,
sharpened one end and rounded off the other. The subject sat with the
palm of his right hand on the back of his left and his fingers
interlaced. I stimulated the back of his fingers on the second
phalanges with the sharp end of one rod and the blunt end of the other
and asked him to tell whether the sharp point was to the right or to
the left of the other. I will not give the results in detail here, but
only wish to mention a few things for the purpose of illustrating the
point in question. Many of the answers were wrong. Frequently the
subject would say both were on the same finger, when really they were
on fingers of opposite hands, which, however, in this position were
adjacent fingers. Sometimes when this happened I would ask him which
finger they were on, and after he had answered I would leave the point
on the finger on which he said both points were and move the other
point over to the same finger, then move it back to its original
position, then again over to the finger on which the other point was
resting, and so on, several times. The subject would tell me that I
was raising one point and putting it down again in the same place all
of the time. Often a subject would tell me he felt both points on the
same finger, but that he could not tell to which hand the finger
belonged. When two or more fingers intervened between the fingers
touched no subject ever had any difficulty in telling which was the
sharp and which the blunt point, but when adjacent fingers were
touched it was very common for the subject to say he could not tell
which was which. This cannot be because there is more difference in
the quality of the contacts in one case than in the other. If they
were on the same finger it might be said that they were stimulating
the same general area, but since one is on one hand and one on the
other this is impossible. The subject does not think the two points
are in the same place, because he feels two qualities and hence he
infers two things, and he knows two things cannot be in the same place
at the same time. If the two contacts were of the same quality
probably they would be perceived as one on account of the absence of
difference, for the absence of difference is precisely the quality of
oneness.

These facts, together with those mentioned before, seem to me to
indicate that errors of localization are largely responsible for
judgments which seem to be due to fusion or diffusion of sensations.
But they are responsible only in this way, they prevent the correction
of the first impression. I do not mean that a person never changes his
judgment after having once made it, but a change of judgment is not
necessarily a correction. Often it is just the contrary. But where a
wrong judgment is made and cannot be corrected inability to localize
is a prominent factor. This, however, is only a secondary factor in
the perception of number. The cardinal point seems to me the
following:

Any touch sensation, no matter by how many objects it is produced, is
one, and number is an inference based on a temporal series of
sensations. It may be that we can learn by association to infer number
immediately from the quality of a sensation, but that means only that
we recognize the sensation as one we have had before and have found it
convenient to separate into parts and regard one part after the other,
and we remember into how many parts we separated it. This separating
into parts is a time process. What we shall regard as _one_ is a mere
matter of convenience. Continuity sometimes affords a convenient basis
for unity and sometimes it does not. There is no standard of oneness
in the objective world. We separate things as far as convenience or
time permits and then stop and call that _one_ which our own attitude
has determined shall be one.

That we do associate a sensation with whatever idea we have previously
connected it with, even though that idea be that of the number of
objects producing it, is clearly shown by some experiments which I
performed in the laboratory of Columbia University. I took three
little round pieces of wood and set them in the form of a triangle. I
asked the subject to pass his right hand through a screen and told him
I wanted to train him to perceive one, two, three and four contacts at
a time on the back of his hand, and that I would tell him always how
many I gave him until he learned to do it. When it came to three I
gave him two points near the knuckles and one toward the wrist and
told him that was three. Then I turned the instrument around and gave
him one point near the knuckles and two toward the wrist and told him
that was four. As soon as he was sure he distinguished all of the
points I stopped telling him and asked him to answer the number. I had
four subjects, and each one learned very soon to recognize the four
contacts when three were given in the manner mentioned above. I then
repeated the same thing on the left hand, except that I did not tell
him anything, but merely asked him to answer the number of contacts he
felt. In every case the idea of four was so firmly associated with
that particular kind of a sensation that it was still called four when
given on the hand which had not been trained. I gave each subject a
diagram of his hand and asked him to indicate the position of the
points when three were given and when four were given. This was done
without difficulty. Two subjects said they perceived the four contacts
more distinctly than the three, and two said they perceived the three
more distinctly than the four.

It seems very evident that the sensation produced by three contacts is
no more complex when interpreted as four than when interpreted as
three. If that is true, then it must also be evident that the
sensation produced by one contact is no more complex when interpreted
as two than when interpreted as one. The converse should also be true,
that the sensation produced by two contacts is no less complex when
interpreted as one than when interpreted as two. Difference in number
does not indicate difference in complexity. The sensation of four is
not made up of four sensations of one. It is a unit as much as the
sensation of one is.

There remains but one point to be elaborated. If number is not a
quality of objects, but is merely a matter of attitude of the subject,
we should not expect to find a very clear-cut line of demarcation
between the different numbers except with regard to those things which
we constantly consider in terms of number. Some of our associations
are so firmly established and so uniform that we are likely to regard
them as necessary. It is not so with our associations of number and
touch sensations. We have there only a vague, general notion of what
the sensation of one or two is, because usually it does not make much
difference to us, yet some sensations are so well established in our
minds that we call them one, two or four as the case may be without
hesitation. Other sensations are not so, and it is difficult to tell
to which class they belong. Just so it is easy to tell a pure yellow
color from a pure orange, yet they shade into each other, so that it
is impossible to tell where one leaves off and the other begins. If we
could speak of a one-two sensation as we speak of a yellow-orange
color we might be better able to describe our sensations. It would,
indeed, be convenient if we could call a sensation which seems like
one with a suggestion of two about it a two-one sensation, and one
that seems nearly like two but yet suggests one a one-two sensation.
Since we cannot do this, we must do the best we can and describe a
sensation in terms of the number it most strongly suggests. Subjects
very often, as has been mentioned before, describe a sensation as
'more than one but less than two,' but when pressed for an answer will
say whichever number it most resembles. A person would do the same
thing if he were shown spectral colors from orange to yellow and told
to name each one either orange or yellow. At one end he would be sure
to say orange and at the other yellow, but in the middle of the series
his answers would likely depend upon the order in which the colors
were shown, just as in determining the threshold for the perception of
two points by the method of minimal changes the answers in the
ascending series are not the same as those in the descending series.
The experiments have shown that the sensation produced by two points,
even when they are called one, is not the same as that produced by
only one point, but the difference is not great enough to suggest a
different number.

If the difference between one and two were determined by the distance,
then the substitution of lines for knobs of the æsthesiometer ought to
make no difference. And if the sensations produced by two objects fuse
when near together, then the sensations produced by lines ought to
fuse as easily as those produced by knobs.

In regard to the higher numbers difficulties will arise unless we take
the same point of view and say that number is an inference from a
sensation which is in itself a unit. It has been shown that four
points across the ends of the fingers will be called four or less, and
that four points, one on the end of each alternate finger and one at
the base of each of the others, will be called four or more--usually
more. In either case each contact is on a separate finger, and it is
hardly reasonable to suppose there is no diffusion when they are in a
straight row, but that when they are in irregular shape there is
diffusion. It is more probable that the subject regards the sensation
produced by the irregular arrangement as a novelty, and tries to
separate it into parts. He finds both proximal and distal ends of his
fingers concerned. He may discover that the area covered extends from
his index to his little finger. He naturally infers, judging from past
experience, that it would take a good many points to do that, and
hence he overestimates the number. When a novel arrangement was given,
such as moving some of the weights back on the wrist and scattering
others over the fingers, very little idea of number could be gotten,
yet they were certainly far enough apart to be felt one by one if a
person could ever feel them that way, and the number was not so great
as to be entirely unrecognizable.

       *       *       *       *       *



THE SUBJECTIVE HORIZON.

BY ROBERT MACDOUGALL.


I.


The general nature of the factors which enter into the orientation of
the main axes of our bodies, under normal and abnormal conditions, has
been of much interest to the psychologist in connection with the
problem of the development of space and movement perception. The
special points of attack in this general investigation have comprised,
firstly, the separation of resident, or organic, from transient, or
objective, factors; secondly, the determination of the special organic
factors which enter into the mechanism of judgment and their several
values; and thirdly, within this latter field, the resolution of the
problem of a special mechanism of spatial orientation, the organ of
the static sense.

The special problem with which we are here concerned relates to the
group of factors upon which depends one's judgment that any specified
object within the visual field lies within the horizontal plane of the
eyes, or above or below that plane, and the several functions and
values of these components. The method of procedure has been suggested
by the results of preceding investigations in this general field.

The first aim of the experiments was to separate the factors of
resident and transient sensation, and to determine the part played by
the presence of a diversified visual field. To do so it was necessary
to ascertain, for each member of the experimental group, the location
of the subjective visual horizon, and the range of uncertainty in the
observer's location of points within that plane. Twelve observers in
all took part in the investigation. In the first set of experiments no
attempt was made to change the ordinary surroundings of the observer,
except in a single point, namely, the provision that there should be
no extended object within range of the subject's vision having
horizontal lines on a level with his eyes.

The arrangements for experimentation were as follows: A black wooden
screen, six inches wide and seven feet high, was mounted between two
vertical standards at right angles to the axis of vision of the
observer. Vertically along the center of this screen and over pulleys
at its top and bottom passed a silk cord carrying a disc of white
cardboard, 1 cm. in diameter, which rested against the black surface
of the screen. From the double pulley at the bottom of the frame the
two ends of the cord passed outward to the observer, who, by pulling
one or the other, could adjust the disc to any desired position. On
the opposite side of the screen from the observer was mounted a
vertical scale graduated in millimeters, over which passed a light
index-point attached to the silk cord, by means of which the position
of the cardboard disc in front was read off. The observer was seated
in an adjustable chair with chin and head rests, and a lateral
sighting-tube by which the position of the eyeball could be vertically
and horizontally aligned. The distance from the center of the eyeball
to the surface of the screen opposite was so arranged that, neglecting
the radial deflection, a displacement of 1 mm. in either direction was
equal to a departure of one minute of arc from the plane of the eyes'
horizon.

The observer sat with the light at his back, and by manipulation of
the cords adjusted the position of the white disc freely up and down
the screen until its center was judged to be on a level with the eye.
Its position was then read off the vertical scale by the conductor
(who sat hidden by an interposed screen), and the error of judgment
was recorded in degrees and fractions as a positive (upward) or
negative (downward) displacement. The disc was then displaced
alternately upward and downward, and the judgment repeated. From the
time of signalling that the point had been located until this
displacement the observer sat with closed eyes. These determinations
were made in series of ten, and the individual averages are in general
based upon five such series, which included regularly the results of
sittings on different days. In some cases twice this number of
judgments were taken, and on a few occasions less. The number of
judgments is attached to each series of figures in the tables. In that
which follows the individual values and their general averages are
given as minutes of arc for (_a_) the constant error or position of
the subjective horizon, (_b_) the average deviation from the objective
horizon, and (_c_) the mean variation of the series of judgments.


TABLE I.

  Observer.      Constant Error.   Average Deviation.  Mean Variation.
      _A_  (100)         -19.74         38.78             10.67
      _C_   (90)         -18.18         23.89             10.82
      _D_  (100)         -19.84         33.98              7.95
      _E_   (50)         - 4.28         72.84              6.90
      _F_  (100)         +46.29         46.29              2.05
      _G_   (50)         +14.96         35.40              8.40
      _H_   (50)         -27.22         27.46              5.78
      _I_   (50)         + 6.62         53.34              7.45
      _K_   (50)         + 1.08         30.26              6.59
      _L_   (20)         -56.70         56.70             10.39

  Average:                -7.70         41.89              7.69


The average subjective horizon shows a negative displacement, the
exceptional minority being large. No special facts could be connected
with this characteristic, either in method of judgment or in the past
habits of the reactor. The average constant error is less than an
eighth of a degree, and in neither direction does the extreme reach
the magnitude of a single degree of arc. Since the mean variation is
likewise relatively small, there is indicated in one's ordinary
judgments of this kind a highly refined sense of bodily orientation in
space.


II.


In order to separate the resident organic factors from those presented
by the fixed relations of the external world, an adaptation of the
mechanism was made for the purpose of carrying on the observations in
a darkened room. For the cardboard disc was substituted a light
carriage, riding upon rigid parallel vertical wires and bearing a
miniature ground-glass bulb enclosing an incandescent electric light
of 0.5 c.p. This was encased in a chamber with blackened surfaces,
having at its center an aperture one centimeter in diameter, which was
covered with white tissue paper. The subdued illumination of this
disc presented as nearly as possible the appearance of that used in
the preceding series of experiments. No other object than this spot of
moving light was visible to the observer. Adjustment and record were
made as before. The results for the same set of observers as in the
preceding case are given in the following table:


TABLE II.

  Subject.       Constant Error.  Average Deviation.  Mean Variation.
      _A_   (50)    - 52.76          55.16               30.08
      _C_   (30)    -  7.40          42.00               35.31
      _D_   (50)    - 14.24          38.60               30.98
      _E_   (50)    - 43.12          86.44               30.19
      _F_  (100)    -  2.01          72.33               20.27
      _G_  (100)    - 21.89          47.47               32.83
      _H_   (50)    -  1.62          59.10               29.95
      _I_   (50)    - 32.76          41.60               24.40
      _K_   (50)    - 61.70         100.02               52.44
      _L_   (40)    -128.70         128.90               27.83

   Average:         - 36.62          67.16               31.43


Changes in two directions may be looked for in the results as the
experimental conditions are thus varied. The first is a decrease in
the certainty of judgment due to the simple elimination of certain
factors upon which the judgment depends. The second is the appearance
of definite types of error due to the withdrawal of certain
correctives of organic tendencies which distort the judgment in
specific directions. The loss in accuracy is great; the mean variation
increases from 7.69 to 31.43, or more than 400 per cent. This large
increase must not, however, be understood as indicating a simple
reduction in the observer's capacity to locate points in the
horizontal plane of the eyes. The two series are not directly
comparable; for in the case of the lighted room, since the whole
visual background remained unchanged, each determination must be
conceived to influence the succeeding judgment, which becomes really a
correction of the preceding. To make the two series strictly parallel
the scenery should have been completely changed after each act of
judgment. Nevertheless, a very large increase of uncertainty may
fairly be granted in passing from a field of visual objects to a
single illuminated point in an otherwise dark field. It is probable
that this change is largely due to the elimination of those elements
of sensation depending upon the relation of the sagittal axis to the
plane against which the object is viewed.

The change presented by the constant error can here be interpreted
only speculatively. I believe it is a frequently noted fact that the
lights in a distant house or other familiar illuminated object on
land, and especially the signal lights on a vessel at sea appear
higher than their respective positions by day, to the degree at times
of creating the illusion that they hang suspended above the earth or
water. This falls in with the experimental results set forth in the
preceding table. It cannot be attributed to an uncomplicated tendency
of the eyes of a person seated in such a position to seek a lower
direction than the objective horizon, when freed from the corrective
restraint of a visual field, as will be seen when the results of
judgments made in complete darkness are cited, in which case the
direction of displacement is reversed. The single illuminated spot
which appears in the surrounding region of darkness, and upon which
the eye of the observer is directed as he makes his judgment, in the
former case restricts unconscious wanderings of the eye, and sets up a
process of continuous and effortful fixation which accompanies each
act of determination. I attribute the depression of the eyes to this
process of binocular adjustment. The experience of strain in the act
of fixation increases and decreases with the distance of the object
regarded. In a condition of rest the axes of vision of the eyes tend
to become parallel; and from this point onward the intensity of the
effort accompanying the process of fixation increases until, when the
object has passed the near-point of vision, binocular adjustment is no
longer possible. In the general distribution of objects in the visual
field the nearer, for the human being, is characteristically the
lower, the more distant the higher, as one looks in succession from
the things at his feet to the horizon and _vice versa_. We should,
therefore, expect to find, when the eyes are free to move in
independence of a determinate visual field, that increased convergence
is accompanied by a depression of the line of sight, decreased
convergence by an elevation of it. Here such freedom was permitted,
and though the fixed distance of the point of regard eliminated all
large fluctuations in convergence, yet all the secondary
characteristics of intense convergence were present. Those concerned
in the experiment report that the whole process of visual adjustment
had increased in difficulty, and that the sense of effort was
distinctly greater. To this sharp rise in the general sense of strain,
in coöperation with the absence of a corrective field of objects, I
attribute the large negative displacement of the subjective horizon in
this series of experiments.


III.


In the next set of experiments the room was made completely dark. The
method of experimentation was adapted to these new conditions by
substituting for the wooden screen one of black-surfaced cardboard,
which was perforated at vertical distances of five millimeters by
narrow horizontal slits and circular holes alternately, making a scale
which was distinctly readable at the distance of the observer.
Opposite the end of one of these slits an additional hole was punched,
constituting a fixed point from which distances were reckoned on the
scale. As the whole screen was movable vertically and the observer
knew that displacements were made from time to time, the succession of
judgments afforded no objective criterion of the range of variation in
the series of determinations, nor of the relation of any individual
reaction to the preceding. The method of experimentation was as
follows: The observer sat as before facing the screen, the direction
of which was given at the beginning of each series by a momentary
illumination of the scale. In the darkness which followed the observer
brought the direction of sight, with open eyes, as satisfactorily as
might be into the plane of the horizontal, when, upon a simple signal,
the perforated scale was instantly and noiselessly illuminated by the
pressure of an electrical button, and the location of the point of
regard was read off the vertical scale by the observer himself, in
terms of its distance from the fixed point of origin described above.
The individual and general averages for this set of experiments are
given in the following table:


TABLE III.

  Observer.       Constant Error.  Average Deviation.  Mean Variation.
      _A_   (50)        +  7.75         20.07             19.45
      _C_     "         + 14.41         25.05              2.94
      _D_     "         + 14.42         34.54             29.16
      _E_     "         +108.97        108.97             23.13
      _F_     "         -  5.12         23.00              2.02
      _G_     "         + 20.72         34.80             10.23
      _H_     "         + 35.07         53.60             33.95
      _I_     "         + 25.52         30.68             22.49
      _K_     "         -  8.50         40.65             21.07

  Average:              + 23.69         41.26             17.16


The point at which the eyes rest when seeking the plane of the horizon
in total darkness is above its actual position, the positive
displacement involved being of relatively large amount.

In addition to the removal of the whole diversified visual field there
has now been eliminated the final point of regard toward which, in the
preceding set of experiments, the sight was strained; and the factor
of refined visual adjustment ceases longer to play a part in the
phenomenon. The result of this release is manifested in a tendency of
the eyes to turn unconsciously upward. This is their natural position
when closed in sleep. But this upward roll is not an uncomplicated
movement. There takes place at the same time a relaxation of binocular
convergence, which in sleep may be replaced by a slight divergence.
This tendency of the axes of vision to diverge as the eyes are raised
is undoubtedly connected biologically with the distribution of
distances in the higher and lower parts of the field of vision, of
which mention has already been made. Its persistence is taken
advantage of in the artificial device of assisting the process of
stereoscopic vision without instruments by holding the figures to be
viewed slightly above the primary position, so that the eyes must be
raised in order to look at them and their convergence thereby
decreased. It is by the concomitance of these two variables that the
phenomena of both this and the preceding series of experiments are to
be explained. In the present case the elimination of a fixed point of
regard is followed by a release of the mechanism of convergence, with
a consequent approximation to parallelism in the axes of vision and
its concomitant elevation of the line of sight.

The second fact to be noted is the reduction in amount of the mean
variation. The series of values under the three sets of experimental
conditions hitherto described is as follows: I. 7'.69; II. 31'.42;
III. 17'.16. This increase of regularity I take to be due, as in the
case of the lighted room, to the presence of a factor of constancy
which is not strictly an element in the judgment of horizontality.
This is a system of sensory data, which in the former case were
transient--the vision of familiar objects; and in the latter
resident--the recognition of specific experiences of strain in the
mechanism of the eye. The latter sensations exist under all three sets
of conditions, but they are of secondary importance in those cases
which include the presence of an objective point of regard, while in
the case of judgments made in total darkness the observer depends
solely upon resident experiences. Attention is thus directed
specifically toward these immediate sensational elements of judgment,
and there arises a tendency to reproduce the preceding set of
eye-strains, instead of determining the horizon plane afresh at each
act of judgment upon more general data of body position.

If the act of judgment be based chiefly upon sensory data connected
with the reinstatement of the preceding set of strains, progressions
should appear in these series of judgments, provided a constant factor
of error be incorporated in the process. This deflection should be
most marked under conditions of complete darkness, least in the midst
of full illumination. Such a progression would be shown at once by the
distribution of positive and negative values of the individual
judgments about the indifference point of constant error. As instances
of its occurrence all cases have been counted in which the first half
of the series of ten judgments was uniformly of one sign (four to six
being counted as half) and the second half of the opposite sign. The
percentages of cases in which the series presented such a progression
are as follows: In diffused light, 7.6%; in darkness, point of regard
illuminated, 18.3%; in complete darkness, 26.1%. The element of
constant error upon which such progressions depend is the tendency of
the eye to come to rest under determinate mechanical conditions of
equilibrium of muscular strain.

The relation of the successive judgments of a series to the
reinstatement of specific eye-strains and to the presence of an error
of constant tendency becomes clearer when the distribution of those
series which show progression is analyzed simultaneously with
reference to conditions of light and darkness and to binocular and
monocular vision respectively. Their quantitative relations are
presented in the following table:


TABLE IV.

  Illumination.   Per Cent. Showing Progress.  Binocular.  Monocular.

  In light.                 7.6 %                 50 %        50 %
  In darkness.             18.3                   34.2        65.8


Among judgments made in daylight those series which present
progression are equally distributed between binocular and monocular
vision. When, however, the determinations are of a luminous point in
an otherwise dark field, the preponderance in monocular vision of the
tendency to a progression becomes pronounced. That this is not a
progressive rectification of the judgment, is made evident by the
distribution of the directions of change in the several experimental
conditions shown in the following table:


TABLE V.
                                Light.                 Darkness.
  Direction of Change.  Binocular.   Monocular.  Binocular.  Monocular.
  Upward.                  50 %         100 %      38.4 %      65.0 %
  Downward.                50            00.0      61.6        35.0
  Const. Err.              -7.70        +11.66    -36.62       -3.38


When the visual field is illuminated the occurrence of progression in
binocular vision is accidental, the percentages being equally
distributed between upward and downward directions. In monocular
vision, on the contrary, the movement is uniformly upward and involves
a progressive increase in error. When the illuminated point is exposed
in an otherwise dark field the progression is preponderatingly
downward in binocular vision and upward in vision with the single eye.
The relation of these changes to phenomena of convergence, and the
tendency to upward rotation in the eyeball has already been stated.
There is indicated, then, in these figures the complication of the
process of relocating the ideal horizon by reference to the sense of
general body position with tendencies to reinstate simply the set of
eye-muscle strains which accompanied the preceding judgment, and the
progressive distortion of the latter by a factor of constant error due
to the mechanical conditions of muscular equilibrium in the resting
eye.


IV.


The influence of this factor is also exhibited when judgments made
with both eyes are compared with those made under conditions of
monocular vision. The latter experiments were carried on in alternate
series with those already described. The figures are given in the
following tables:


TABLE VI.

  JUDGMENTS MADE IN DIFFUSED LIGHT.

    Observer.  Constant Error.   Average Deviation.   Mean Variation.
    _A_ (50)     - 28.46                29.04               8.87
    _C_  "       +  7.54                14.86               8.01
    _D_  "       + 39.32                43.28              13.83
    _E_  "       + 50.46                65.26               9.86
    _F_  "       + 62.30                62.30               1.60
    _G_  "          0.00                45.28               9.66
    _H_  "       + 22.92                79.12               5.07
    _I_  "       + 14.36                51.96               8.02
    _K_  "       +  9.26                38.10               9.55
    _L_  "       - 61.10                61.10               6.36
    Average:     + 11.66                49.03               8.18


TABLE VII.

  JUDGMENTS IN ILLUMINATED POINT.

    Observer.  Constant Error.    Average Deviation.   Mean Variation.
    _A_ (50)     - 38.42                 51.96                32.64
    _C_ (30)     - 29.03                 41.23                35.75
    _D_ (20)     - 30.87                 34.07                17.24
    _E_ (50)     + 65.30                 75.86                29.98
    _F_  "       + 50.74                 50.74                 5.89
    _G_  "       + 66.38                 88.10                44.98
    _H_  "       + 65.40                 80.76                42.93
    _I_  "       -  0.02                 80.22                47.53
    _K_  "       - 44.60                 52.56                32.93
    _L_  "       - 71.06                 73.30                31.86
    Average:     - 3.38                  62.88                32.17


The plane of vision in judgments made with the right eye alone is
deflected upward from the true horizon to a greater degree than it is
depressed below it in those made with binocular vision, the respective
values of the constant errors being -7'.70 and +11'.66, a difference
of 19'.36. When the field of vision is darkened except for the single
illuminated disc, a similar reversion of sign takes place in the
constant error. With binocular vision the plane of the subjective
horizon is deflected downward through 36'.62 of arc; with monocular
vision it is elevated 3'.38, a difference of 40'.00, or greater than
in the case of judgments made in the lighted room by 20'.64. This
increase is to be expected in consequence of the elimination of those
corrective criteria which the figured visual field presents. The two
eyes do not, of course, function separately in such a case, and the
difference in the two sets of results is undoubtedly due to the
influence of movements in the closed eye upon that which is open; or
rather, to the difference in binocular functioning caused by shutting
off the visual field from one eye. The former expression is justified
in so far as we conceive that the tendency of the closed eye to turn
slightly upward in its socket affects also the direction of regard in
the open eye by attracting toward itself its plane of vision. But if,
as has been pointed out, this elevation of the line of sight in the
closed eye is accompanied by a characteristic change in the process of
binocular convergence, the result cannot be interpreted as a simple
sympathetic response in the open eye to changes taking place in that
which is closed, but is the consequence of a release of convergence
strain secondarily due to this act of closing the eye.

Several points of comparison between judgments made with binocular and
with monocular vision remain to be stated. In general, the process of
location is more uncertain when one eye only is used than when both
are employed, but this loss in accuracy is very slight and in many
cases disappears. The loss in accuracy is perhaps also indicated by
the range of variation in the two cases, its limits being for
binocular vision +46'.29 to -56'.70, and for monocular +62'.30 to
-61'.10, an increase of 20'.41. In the darkened room similar relations
are presented. The mean variations are as follows: binocular vision,
31'.42; monocular, 32'.17. Its limits in individual judgments are:
binocular, -1'.62 to -128'.70, monocular, +66'.38 to -71'.06, an
increase of 10'.36. In all ways, then, the difference in accuracy
between the two forms of judgment is extremely small, and the
conclusion may be drawn that those significant factors of judgment
which are independent of the figuration of the visual field are not
connected with the stereoscopic functioning of the two eyes, but such
as are afforded by adjustment in the single eye and its results.


VI.


The experimental conditions were next complicated by the introduction
of abnormal positions of the eyes, head and whole body. The results of
tipping the chin sharply upward or downward and keeping it so fixed
during the process of location are given in the following table, which
is complete for only three observers:


TABLE VIII.

  Observer.             Upward Rotation.           Downward Rotation.
                     C.E.     A.D.     M.V.      C.E.     A.D.     M.V.
  _L_ (50)         +43.98    43.98     5.62     +28.32   28.32    5.02
  _K_ (50)         -33.72    33.72    71.33     +19.49   19.49   55.22
  _L_ (20)         -39.10    45.90    33.60     -68.65   69.25   25.20
  Average:         - 9.61    41.20    36.85     -19.94   39.02   28.48
  Normal:          -64.14    67.08    33.51


The results of rotating the whole body backward through forty-five and
ninety degrees are given in the following table:


TABLE IX.

  Observer.              Rotation of 45°.           Rotation of 90°.
                     C.E.     A.D.     M.V.      C.E.     A.D.     M.V.
  _B_ (30)        +  4.10    24.57    18.56
  _D_ (30)        +291.03   291.03    61.86
  _G_ (50)        +266.78   266.78    22.83    +200.16  200.16   11.00
  _F_ (60)        +116.45   116.45    17.14    - 36.06   36.30    6.29
  _J_ (20)        +174.30   174.63    30.94
  Average:        +170.53   174.69    30.66


The errors which appear in these tables are not consistently of the
type presented in the well-known rotation of visual planes
subjectively determined under conditions of abnormal relations of the
head or body in space. When the head is rotated upward on its lateral
horizontal axis the average location of the subjective horizon,
though still depressed below the true objective, is higher than when
rotation takes place in the opposite direction. When the whole body is
rotated backward through 45° a positive displacement of large amount
takes place in the case of all observers. When the rotation extends to
90°, the body now reclining horizontally but with the head supported
in a raised position to allow of free vision, an upward displacement
occurs in the case of one of the two observers, and in that of the
other a displacement in the opposite direction. When change of
position takes place in the head only, the mean variation is decidedly
greater if the rotation be upward than if it be downward, its value in
the former case being above, in the latter below that of the normal.
When the whole body is rotated backward through 45° the mean variation
is but slightly greater than under normal conditions; when the
rotation is through 90° it is much less. A part of this reduction is
probably due to training. In general, it may be said that the
disturbance of the normal body relations affects the location of the
subjective horizon, but the specific nature and extent of this
influence is left obscure by these experiments. The ordinary movements
of eyes and head are largely independent of one another, and even when
closed the movements of the eyes do not always symmetrically follow
those of the head. The variations in the two processes have been
measured by Münsterberg and Campbell[1] in reference to a single
condition, namely, the relation of attention to and interest in the
objects observed to the direction of sight in the closed eyes after
movement of the head. But apart from the influence of such secondary
elements of ideational origin, there is reason to believe that the
mere movement of the head from its normal position on the shoulders up
or down, to one side or the other, is accompanied by compensatory
motion of the eyes in an opposite direction, which tends to keep the
axis of vision nearer to the primary position. When the chin is
elevated or depressed, this negative reflex adjustment is more
pronounced and constant than when the movement is from side to side.
In the majority of cases the retrograde movement of the eyes does not
equal the head movement in extent, especially if the latter be
extreme.

   [1] Münsterberg, H., and Campbell, W.W.: PSYCHOLOGICAL REVIEW,
   I., 1894, p. 441.

The origin of such compensatory reactions is connected with the
permanent relations of the whole bodily organism to the important
objects which surround it. The relations of the body to the landscape
are fairly fixed. The objects which it is important to watch lie in a
belt which is roughly on a horizontal plane with the observing eye.
They move or are moved about over the surface of the ground and do not
undergo any large vertical displacement. It is of high importance,
therefore, that the eye should be capable of continuous observation of
such objects through facile response to the stimulus of their visual
appearance and movements, in independence of the orientation of the
head. There are no such determinate spatial relations between body
position and the world of important visual objects in the case of
those animals which are immersed in a free medium; and in the
organization of the fish and the bird, therefore, one should not
expect the development of such free sensory reflexes of the eye in
independence of head movements as we know to be characteristic of the
higher land vertebrates. In both of the former types the eye is fixed
in its socket, movements of the whole head or body becoming the
mechanism of adjustment to new objects of observation. In the
adjustment of the human eye the reflex determination through sensory
stimuli is so facile as to counteract all ordinary movements of the
head, the gaze remaining fixed upon the object through a series of
minute and rapidly repeated sensory reflexes. When the eyes are closed
and no such visual stimuli are presented, similar reflexes take place
in response to the movements of the head, mediated possibly by
sensations connected with changes in position of the planes of the
semicircular canals.


VII.


If eye-strain be a significant element in the process of determining
the subjective horizon, the induction of a new center of muscular
equilibrium by training the eyes to become accustomed to unusual
positions should result in the appearance of characteristic errors of
displacement. In the case of two observers, _A_ and _H_, the eyes were
sharply raised or lowered for eight seconds before giving judgment as
to the position of the illuminated spot, which was exposed at the
moment when the eyes were brought back to the primary position. The
effect of any such vertical rotation is to stretch the antagonistic
set of muscles. It follows that when the eye is rotated in the
contrary direction the condition of equilibrium appears sooner than in
normal vision. In the case of both observers the subjective horizon
was located higher when judgment was made after keeping the eyes
raised, and lower when the line of sight had been depressed. In the
case of only one observer was a quantitative estimation of the error
made, as follows: With preliminary raising of the eyes the location
was +36'.4; with preliminary lowering, -11'.4.

When the illuminated button is exposed in a darkened room and is
fixated by the observer, it undergoes a variety of changes in apparent
position due to unconscious shifting of the point of regard, the
change in local relations of the retinal stimulation being erroneously
attributed to movements in the object. These movements were not of
frequent enough occurrence to form the basis of conclusions as to the
position at which the eyes tended to come to a state of rest. The
number reported was forty-two, and the movement observed was rather a
wandering than an approximation toward a definite position of
equilibrium. The spot very rarely presented the appearance of sidewise
floating, but this may have been the result of a preconception on the
part of the observer rather than an indication of a lessened liability
to movements in a horizontal plane. Objective movements in the latter
direction the observer knew to be impossible, while vertical
displacements were expected. Any violent movement of the head or eyes
dispelled the impression of floating at once. The phenomenon appeared
only when the illuminated spot had been fixated for an appreciable
period of time. Its occurrence appears to be due to a fatigue process
in consequence of which the mechanism becomes insensible to slight
changes resulting from releases among the tensions upon which constant
fixation depends. When the insensitiveness of fatigue is avoided by a
slow continuous change in the position of the illuminated spot, no
such wandering of the eye from its original point of regard occurs,
and the spot does not float. The rate at which such objective
movements may take place without awareness on the part of the observer
is surprisingly great. Here the fatigue due to sustained fixation is
obviated by the series of rapid and slight sensory reflexes which take
place; these have the effect of keeping unchanged the retinal
relations of the image cast by the illuminated spot, and being
undiscriminated in the consciousness of the observer the position of
the point of regard is apprehended by him as stationary. The
biological importance of such facile and unconscious adjustment of the
mechanism of vision to the moving object needs no emphasis; but the
relation of these obscure movements of the eyes to the process of
determining the plane of the subjective horizon should be pointed out.
The sense of horizontality in the axes of vision is a transient
experience, inner conviction being at its highest in the first moments
of perception and declining so characteristically from this maximum
that in almost every case the individual judgment long dwelt upon is
unsatisfactory to the observer. This change I conceive to be a
secondary phenomenon due to the appearance of the visual wanderings
already described.


VIII.


The influence of sensory reflexes in the eye upon the process of
visual orientation was next taken up in connection with two specific
types of stimulation. At top and bottom of the vertical screen were
arranged dark lanterns consisting of electric bulbs enclosed in
blackened boxes, the fronts of which were covered with a series of
sheets of white tissue-paper, by which the light was decentralized and
reduced in intensity, and of blue glass, by which the yellow quality
of the light was neutralized. Either of these lanterns could be
illuminated at will by the pressure of a button. All other
experimental conditions remained unchanged. The observers were
directed to pay no special regard to these lights, and the reports
show that in almost every case they had no conscious relation to the
judgment. The results are presented in the following table:


TABLE X.

                       Light Below.               Light Above.
  Observer.  Const.Err.  Av.Dev.  M.Var.  Const.Err.  Av.Dev.  M.Var.
  _C_ (40)      +156.37  156.37    19.67   +169.85    169.85   19.22
  _D_ (20)      + 39.30   43.30    17.95   + 46.65     47.35   15.41
  _F_ (30)      + 19.47   19.47     8.83   + 58.37     58.37    7.83
  _G_ (50)      + 66.11  112.76    14.65   +117.86    117.86   13.10
  _H_ (30)      -147.63  147.63    21.07   -105.30    105.30   30.31
  _J_ (20)      +  1.90   31.95    22.33   + 44.40     44.40   20.55
  Average:      + 22.59   85.28    17.42   + 55.30     90.52   17.74


The eye is uniformly attracted toward the light and the location of
the disk correspondingly elevated or depressed. The amount of
displacement which appears is relatively large. It will be found to
vary with the intensity, extent and distance of the illuminated
surfaces introduced. There can be little doubt that the practical
judgments of life are likewise affected by the distribution of light
intensities, and possibly also of significant objects, above and below
the horizon belt. Every brilliant object attracts the eye toward
itself; and the horizon beneath a low sun or moon will be found to be
located higher than in a clouded sky. The upper half of the ordinary
field of view--the clear sky--is undiversified and unimportant; the
lower half is full of objects and has significance. We should probably
be right in attributing to these characteristic differences a share in
the production of the negative error of judgment which appears in
judgments made in daylight. The introduction of such supplementary
stimuli appears to have little effect upon the regularity of the
series of judgments, the values of the mean variations being
relatively low: 17'.42 with light below, 17'.74 with it above.


IX.


In the final series of experiments the influence of limiting visual
planes upon the determination of the subjective horizon was taken up.
It had been noticed by Dr. Münsterberg in the course of travel in hill
country that a curious negative displacement of the subjective horizon
took place when one looked across a downward slope to a distant cliff,
the altitude (in relation to the observer's own standpoint) of
specific points on the wall of rock being largely overestimated.
Attributing the illusion to a reconstruction of the sensory data upon
an erroneous interpretation of the objective relations of the
temporary plane of the landscape, Dr. Münsterberg later made a series
of rough experiments by stretching an inclined cord from the eye
downward to a lower point on an opposite wall and estimating the
height above its termination of that point which appeared to be on a
level with the observing eye. He found an illusion present similar to
the case of an extended slope of country.

The first experiments of this group repeated those just described. The
previous mechanical conditions were varied only by the introduction of
a slender cord which was stretched from just below the eyes to the
bottom of the vertical screen. Full results were obtained from only
two observers, which are given in the following table:


TABLE XI.

   Observer.   Const. Err.  Av. Dev. Mean Var.  Exp. Conds.

  _C_  (30)        +123.92   123.92    11.94  Cord present and
  _G_  (30)         +66.47    66.47    15.56  consciously referred to.
  _C_  (30)        +126.90   126.90     6.31  Cord not present.
  _G_  (30)         +83.20    83.20     6.31
  _C_  (30)        +126.93   126.93     6.39  Cord present but not
  _G_  (30)         +86.63    86.63     9.40  consciously referred to.

  Averages.  I      +95.19    95.19    13.75
     "      II     +105.05   105.05     6.31
     "     III     +106.78   106.78     7.89


The effect of introducing such an objective plane of reference is
twofold: the mean variation is increased, and the plane of the
subjective horizon is displaced downwards. First, then, it acts as a
simple factor of disturbance; it distracts from those habitual
adjustments upon which the accuracy of the judgment depends. Secondly,
it enters as a source of constant error into the determination of the
subjective horizon, which is attracted toward this new objective
plane. In the third section of the table are given the results of
judgments made in the presence of such a plane but without conscious
reference to it.[2] The figures here are of intermediate value in the
case of the mean variation and of slightly greater value than the
first in that of the constant error. In other words, the introduction
of such a plane cannot be wholly overlooked, though it may be greatly
abstracted from.

[2] In the preceding experiments the cord was definitely to be taken
into account in making the judgment. The method of so doing was by
running the eye back and forth over the cord preliminary to
determining the location of the point.

The single cord was next replaced by a plane of blackened wood six
inches wide and extending from the observer to the vertical screen.
This strip was arranged in two ways: first, from the observer's chin
to the bottom of the screen, and secondly, from the feet of the
observer to a point on the screen a short distance below the plane of
the objective horizon. The individual and average results are given in
the following table:


TABLE XII.

   Observer.          Descending Plane.       Ascending Plane.

   _A._ (10)       +18.80  18.80   5.24     +35.10   35.10  8.27
   _E._ (20)       +79.30  79.30  11.56    +131.67  131.67 12.07
   _H._ (10)       -37.50  37.50  16.80     -46.90   46.90  7.90
   _K._ (30)       +71.40  71.40  12.85     +48.05   48.05  5.11
  Average:         +33.00  51.75  11.61     +41.95   65.43  8.34


The introduction of a descending plane lowers the apparent horizon;
that of an ascending plane elevates it. The general disturbance of
judgment appears distinctly greater in the case of a downward than in
that of an upward incline.

The results of a third variation of the experimental conditions may be
presented at once. In it the location of the subjective horizon under
normal conditions was compared with the results of adjustments made
when the screen bearing the white disc was rotated backward from the
observer through an angle of varying magnitude. The averages for each
of the two subjects are as follows:


TABLE XIII.

 Observer          Const. Err.  Av. Dev.  Mean Var.  Rotation.
   _F_    (20)       +130.50      130.50      3.20      20°
    "       "        +115.50      115.50      1.10      50°
   _J_    (20)       +443.10      443.10      9.47      45°


These experiments were carried on in the presence of the definitely
figured visual field of the lighted room, and the observers were
conscious of taking these permanent features into account as
correctives in making their judgments. Before proceeding, this defect
was remedied as far as possible by enclosing the apparatus of
experimentation, including the observer, between two walls of black
fabric. Nothing was to be seen but these two walls, and the inclined
plane which terminated the observer's view. The position of the screen
remained constant at an inclination of 45°. The upper bounding lines
of the enclosing walls, on the contrary, were adjusted in three
different relations to the plane of the gravity horizon. In the first
arrangement these lines were horizontal; in the second the ends next
to the observer were depressed five degrees; while in the final
arrangement these ends were elevated through a like angular distance.

The inclined position of the screen was of course observed by every
reactor, but of the changes in the enclosing walls no subject was
informed, and none discerned them on any occasion. Each observer was
questioned as to alterations in the experimental conditions after the
use of each arrangement, and at the close of the whole series inquiry
was made of each as to the planes of the upper boundaries of the
walls. On various occasions, but not customarily, the observer was
aware of a change of some kind in the whole set of conditions, but the
particular feature altered was not suspected. The results for all
three arrangements are given in the following table; of the sections
of this table the third is incomplete, full results having been
reached in the cases of only three observers:


TABLE XV.

                    Ascending Planes.             Descending Planes.
  Observer     Const. Err. Av. Dev. M. Var. Const. Err.  Av. Dev.  M. V.
  _C_ (50)       -  8.02    11.82     9.47   - 48.14     48.14     9.52
  _F_ (50)       + 78.88    78.88     2.89   + 25.54     25.54     1.98
  _G_ (50)       - 22.56    24.64     6.58   -101.20    101.20     7.39
  _H_ (50)       - 83.84    83.84    11.78   -230.20    230.20    11.88
  _J_ (50)       +315.64   315.64    18.16   +120.12    120.12     9.01
  Average:       + 55.96   102.96     9.78    -44.98    104.84     7.96

                                Horizontal Planes.
  Observer.       Const. Err.    Av. Dev.    Mean Var.
  _C_   (50)       - 27.86         27.86       9.58
  _G_   (50)       - 73.84         73.84       7.59
  _J_   (50)       +243.72        243.72      18.52


For every individual observer, the position of the disc on the screen
has been affected by each change in the direction of these visible
lines. In every case, also, its location when these boundaries lay in
a horizontal plane was intermediate between the other two. The
importance of such relations in the objects of the visual field as
factors in our ordinary determination of the subjective horizon is
made evident by these experimental results. They become construction
lines having assumed permanence in the world of visual-motor
experience. The conception of unchanging spatial relations in the
fundamental lines of perspective vision receives constant
reinforcement from the facts of daily experience. The influence of the
above-described changes in experimental conditions is mediated through
their effect upon the location of the focus of the limiting and
perspective lines of vision. As the plane of the upper boundaries of
the enclosing walls was elevated and depressed the intersection of the
two systems of lines was correspondingly raised and lowered, and in
dependence upon the location of this imaginary point the determination
of the position of the white disc was made, and the plane of
perspective positively or negatively rotated.

Why such perspective lines should enter into the process of judgment
it is not difficult to infer. The plane of perspective for human
beings is characteristically horizontal, in consequence of the
distribution of important objects within the field of visual
perception. Roughly, the belt of the earth's horizon contains the loci
of all human perspective planes. Both natural and artificial
arrangements of lines converge there. The systems of visual objects on
the earth and in the sky are there broken sharply off in virtue of
their practically vast differences in quality and significance for the
observer. The latter perspective probably never extends downward
illusorily to points on the earth's surface; and the former system of
objects is carried continuously upward to skyey points only on
relatively rare occasions, as when one mistakes clouds for mountains
or the upper edge of a fog-belt on the horizon for the rim of sea and
sky. The point of convergence of the fundamental lines of perspective
thus becomes assimilated with the idea of the visual horizon, as that
concept has fused with the notion of a subjective horizon. There can
be little doubt that the disposition of such lines enters constantly
into our bodily orientation in space along with sensations arising
from the general body position and from those organs more specially
concerned with the static sense.

Upon the misinterpretation of such objective planes depends the
illusion of underestimation of the height or incline of a hill one is
breasting, and of the converse overestimation of one seen across a
descending slope or intervening valley. The latter illusion is
especially striking, and in driving over forest roads (in which case
the correction of a wider range of view is excluded) the stretch of
level ground at the foot of a hill one is descending is constantly
mistaken for an opposing rise. This illusion is put into picturesque
words by Stevenson when he describes the world, seen from the summit
of a mountain upon which one stands, as rising about him on every side
as toward the rim of a great cup. The fitness of the image may be
proved by climbing the nearest hill. In all such cases a
reconstruction of the sensory data of judgment takes place, in which
the most significant factor is the plane determined by the positions
of the observing eye and the perspective focus. In these judgments of
spatial relationship, as they follow one another from moment to
moment, this plane becomes a temporary subjective horizon, and
according as it is positively or negatively rotated do corresponding
illusions of perception appear.

       *       *       *       *       *



THE ILLUSION OF RESOLUTION-STRIPES ON THE COLOR-WHEEL.

BY EDWIN B. HOLT.


If a small rod is passed slowly before a rotating disc composed of two
differently colored sectors, the rod appears to leave behind it on the
disc a number of parallel bands of about the width of the rod and of
about the colors, alternately arranged, of the two sectors. These
appear not to move, but gradually to fade away.

This phenomenon was first observed by Münsterberg, and by him shown to
Jastrow,[1] who, with Moorehouse, has printed a study, without,
however, offering an adequate explanation of it.

   [1] Jastrow, J., and Moorehouse, G.W.: 'A Novel Optical
   Illusion,' _Amer. Jour. of Psychology_, 1891, IV., p. 201.


I. APPARATUS FOR PRODUCING THE ILLUSION.


Any form of color-wheel may be used, but preferably one which is
driven by electricity or clock-work, so that a fairly constant speed
is assured. Several pairs of paper discs are needed, of the ordinary
interpenetrating kind which permit a ready readjustment of the ratios
between the two sectors, as follows: one pair consisting of a white
and a black disc, one of a light-and a dark-colored disc (light green
and dark red have been found admirably suited to the purpose), and a
pair of discs distinctly different in color, but equal in luminosity.

The rod should be black and not more than a quarter of an inch broad.
It may be passed before the rotating disc by hand. For the sake of
more careful study, however, the rod should be moved at a constant
rate by some mechanical device, such as the pendulum and works of a
Maelzel metronome removed from their case. The pendulum is fixed just
in front of the color-disc. A further commendable simplification of
the conditions consists in arranging the pendulum and disc to move
concentrically, and attaching to the pendulum an isosceles-triangular
shield, so cut that it forms a true radial sector of the disc behind
it. All the colored bands of the illusion then appear as radial
sectors. The radial shields should be made in several sizes (from 3 to
50 degrees of arc) in black, but the smallest size should also be
prepared in colors matching the several discs. Such a disposition,
then, presents a disc of fused color, rotating at a uniform rate, and
in front of this a radial sector oscillating from side to side
concentrically with the disc, and likewise at a uniform rate. Several
variations of this apparatus will be described as the need and purpose
of them become clear.


II. PREVIOUS DISCUSSION OF THE ILLUSION.


Although Jastrow and Moorehouse (_op. cit._) have published a somewhat
detailed study of these illusion-bands, and cleared up certain points,
they have not explained them. Indeed, no explanation of the bands has
as yet been given. The authors mentioned (_ibid._, p. 204) write of
producing the illusion by another method. "This consists in sliding
two half discs of the same color over one another leaving an open
sector of any desired size up to 180 degrees and rotating this against
a background of a markedly different color, in other words we
substitute for the disc composed of a large amount of one color, which
for brevity we may call the 'majority color,' and a small amount of
another, the 'minority color,' one in which the second color is in the
background and is viewed through an opening in the first. With such an
arrangement we find that we get the series of bands both when the wire
is passed in front of the disc and when passed in back between disc
and background; and further experimentation shows that the time
relations of the two are the same. (There is, of course, no essential
difference between the two methods when the wire is passed in front of
the disc.)" That is true, but it is to be borne in mind that there is
a difference when the wire is passed behind the disc, as these authors
themselves state (_loc. cit._, note):--"The time-relations in the two
cases are the same, but the _color-phenomena_ considerably
_different_." However, "these facts enable us to formulate our first
generalization, viz., that for all purposes here relevant [_i.e._, to
a study of the _time-relations_] the seeing of a wire now against one
background and then immediately against another is the same as its now
appearing and then disappearing; a rapid succession of changed
appearances is equivalent to a rapid alternation of appearance and
disappearance. Why this is so we are unable to say," etc. These
authors now take the first step toward explaining the illusion. In
their words (_op. cit._, p. 205), "the suggestion is natural that we
are dealing with the phenomena of after-images.... If this is the true
explanation of the fact that several rods are seen, then we should,
with different rotation rates of disc and rod, see as many rods as
multiplied by the time of one rotation of the disc would yield a
constant, _i.e._, the time of an after image of the kind under
consideration." For two subjects, J.J. and G.M., the following
tabulation was made.

                                                         J.J.       G.M.
Av. time of rot. of disc when 2 images of rod were seen .0812 sec. .0750 sec.
  "       "        "       "  3    "       "    "    "  .0571  "   .0505  "
  "       "        "       "  4    "       "    "    "  .0450  "   .0357  "
  "       "        "       "  5    "       "    "    "  .0350  "   .0293  "
  "       "        "       "  6    "       "    "    "  .0302  "   .0262  "


"Multiplying the number of rods by the rotation rate we get for J.J.
an average time of after image of .1740 sec. (a little over 1/6 sec.)
with an average deviation of .0057 (3.2%); for G.M. .1492 (a little
over 1/7 sec.) with an average deviation of .0036 (2.6%). An
independent test of the time of after-image of J.J. and G.M. by
observing when a black dot on a rotating white disc just failed to
form a ring resulted in showing in every instance a longer time for
the former than for the latter." That this constant product of the
number of 'rods' seen by the time of one rotation of the disc equals
the duration of after-image of the rod is established, then, only by
inference. More indubitable, since directly measured on two subjects,
is the statement that that person will see more 'rods' whose
after-image persists longer. This result the present writer fully
confirms. What relation the 'constant product' bears to the duration
of after-image will be spoken of later. But aside from all
measurement, a little consideration of the conditions obtaining when
the rod is passed _behind_ the disc will convince any observer that
the bands are indeed after-images somehow dependent on the rod. We may
account it established that _the bands are after-images_.

From this beginning one might have expected to find in the paper of
Jastrow and Moorehouse a complete explanation of the illusion. On
other points, however, these authors are less explicit. The changes in
width of the bands corresponding to different sizes of the sectors and
different rates of movement for the rod and disc, are not explained,
nor yet, what is more important, the color-phenomena. In particular
the fact needs to be explained, that the moving rod analyzes the
apparently homogeneous color of the disc; or, as Jastrow and
Moorehouse state it (_op. cit._, p. 202): "If two rotating discs were
presented to us, the one pure white in color, and the other of ideally
perfect spectral colors in proper proportion, so as to give a
precisely similar white, we could not distinguish between the two; but
by simply passing a rod in front of them and observing in the one case
but not in the other the parallel rows of colored bands, we could at
once pronounce the former to be composite, and the latter simple. In
the indefinitely brief moment during which the rod interrupts the
vision of the disc, the eye obtains an impression sufficient to
analyze to some extent into its elements this rapid mixture of
stimuli." The very question is as to _how_ the eye obtains the
'impression sufficient to analyze' the mixture.

It may be shown at this point that the mistake of these authors lies
in their recognition of but one set of bands, namely (_ibid._, p.
201), 'bands of a color similar to that present in greater proportion'
on the disc. But, on the other hand, it is to be emphasized that those
bands are separated from one another, not by the fused color of the
disc, as one should infer from the article, but by _other bands_,
which are, for their part, of a color similar to that present in
_lesser_ proportion. Thus, bands of the two colors alternate; and
either color of band is with equal ease to be distinguished from the
fused color of the main portion of the disc.

Why our authors make this mistake is also clear. They first studied
the illusion with the smaller sector of the disc open, and the rod
moving behind it; and since in this case the bands are separated by
strips not of the minority but of the fused color, and are of about
the width of the rod itself, these authors came to recognize bands of
but one sort, and to call these 'images of the rod.' But now, with the
rod moving in front of the disc, there appear bands of two colors
alternately disposed, and neither of these colors is the fused color
of the disc. Rather are these two colors approximately the majority
and minority colors of the disc as seen at rest. Thus, the recognition
of but one set of bands and the conclusion (_ibid._, p. 208) that 'the
bands originate during the vision of the minority color,' are wholly
erroneous. The bands originate as well during the vision of the
majority color, and, as will later be shown, the process is
continuous.

Again, it is incorrect, even in the case of those bands seen behind
the open sector, to call the bands 'images of the rod,' for images of
the rod would be of the color of the rod, whereas, as our authors
themselves say (_ibid._, p. 201), the bands 'are of a color similar to
that present in greater proportion' on the disc. Moreover the 'images
of the rod' are of the most diverse widths. In fact, we shall find
that the width of the rod is but one of several factors which
determine the width of its 'images,' the bands.

Prejudiced by the same error is the following statement (_ibid._, p.
208): "With the majority color darker than the minority color the
bands are darker than the resulting mixture, and lighter when the
majority color is the lighter." If this is to be true, one must read
for 'the bands,' 'the narrower bands.'

Another observation found in this article must be criticised. It is
asserted that difference of shade between the two sectors of the disc,
as well as difference of color, is essential to the illusion. To
support this, four cases are given: two in which the sectors were so
similar in luminosity as to bring out the illusion but faintly; two in
which like luminosities yielded no illusion at all. The present writer
agrees that if the two sectors are closely similar in luminosity, the
illusion is fainter. He also selected a red and a green so near each
other in brightness that when a rod 4 mm. broad (which is the largest
rod that Jastrow and Moorehouse mention having used) was passed by
hand before the disc, no trace of a band could be seen. The pendulum,
however, bearing a shield considerably wider than 4 mm. (say of 15
degrees) and moving before the very same red and green shades, mixed
in the same proportions, yielded the illusion with the utmost
clearness. Colors of like luminosities yield the illusion less
strikingly, nevertheless they yield it.

Again (_op. cit._, p. 205), these authors say: "It has been already
observed that the distance between the bands diminishes as the
rotation rate and the rate of movement of the rod increases." But what
had been said before is (_ibid._, p. 203) that 'the bands are
separated by smaller and smaller spaces as the rate of movement of the
rod becomes slower and slower'; and this is equivalent to saying that
the distance between the bands diminishes as the rate of movement of
the rod decreases. The statements are contradictory. But there is no
doubt as to which is the wrong one--it is the first. What these
authors have called 'distance between the bands' has here been shown
to be itself a band. Now, no point about this illusion can be more
readily observed than that the widths of both kinds of band vary
directly with the speed of the rod, inversely, however (as Jastrow and
Moorehouse have noted), with the speed of the disc.

Perhaps least satisfactory of all is their statement (_ibid._, p. 206)
that "A brief acquaintance with the illusion sufficed to convince us
that its appearance was due to contrast of some form, though the
precise nature of this contrast is the most difficult point of all."
The present discussion undertakes to explain with considerable
minuteness every factor of the illusion, yet the writer does not see
how in any essential sense contrast could be said to be involved.

With the other observations of these authors, as that the general
effect of an increase in the width of the interrupting rod was to
render the illusion less distinct and the bands wider, etc., the
observations of the present writer fully coincide. These will
systematically be given later, and we may now drop the discussion of
this paper.

The only other mention to be found of these resolution-bands is one by
Sanford,[2] who says, apparently merely reiterating the results of
Jastrow and Moorehouse, that the illusion is probably produced by the
sudden appearance, by contrast, of the rod as the lighter sector
passes behind it, and by its relative disappearance as the dark sector
comes behind. He thus compares the appearance of several rods to the
appearance of several dots in intermittent illumination of the strobic
wheel. If this were the correct explanation, the bands could not be
seen when both sectors were equal in luminosity; for if both were
dark, the rod could never appear, and if both were light, it could
never disappear. The bands can, however, be seen, as was stated above,
when both the sectors are light or both are dark. Furthermore, this
explanation would make the bands to be of the same color as the rod.
But they are of other colors. Therefore Sanford's explanation cannot
be admitted.

   [2] Sanford, E.C.: 'A Course in Experimental Psychology,'
   Boston, 1898, Part I., p. 167.

And finally, the suggestions toward explanation, whether of Sanford,
or of Jastrow and Moorehouse, are once for all disproved by the
observation that if the moving rod is fairly broad (say three quarters
of an inch) and moves _slowly_, the bands are seen nowhere so well as
_on the rod itself_. One sees the rod vaguely through the bands, as
could scarcely happen if the bands were images of the rod, or
contrast-effects of the rod against the sectors.

The case when the rod is broad and moves slowly is to be accounted a
special case. The following observations, up to No. 8, were made with
a narrow rod about five degrees in width (narrower will do), moved by
a metronome at less than sixty beats per minute.


III. OUTLINE OF THE FACTS OBSERVED.


A careful study of the illusion yields the following points:

1. If the two sectors of the disc are unequal in arc, the bands are
unequal in width, and the narrower bands correspond in color to the
larger sector. Equal sectors give equally broad bands.

2. The faster the rod moves, the broader become the bands, but not in
like proportions; broad bands widen relatively more than narrow ones;
equal bands widen equally. As the bands widen out it necessarily
follows that the alternate bands come to be farther apart.

3. The width of the bands increases if the speed of the revolving disc
decreases, but varies directly, as was before noted, with the speed of
the pendulating rod.

4. Adjacent bands are not sharply separated from each other, the
transition from one color to the other being gradual. The sharpest
definition is obtained when the rod is very narrow. It is appropriate
to name the regions where one band shades over into the next
'transition-bands.' These transition-bands, then, partake of the
colors of both the sectors on the disc. It is extremely difficult to
distinguish in observation between vagueness of the illusion due to
feebleness in the after-image depending on faint illumination,
dark-colored discs or lack of the desirable difference in luminosity
between the sectors (cf. p. 171) and the indefiniteness which is due
to broad transition-bands existing between the (relatively) pure-color
bands. Thus much, however, seems certain (Jastrow and Moorehouse have
reported the same, _op. cit._, p. 203): the wider the rod, the wider
the transition-bands. It is to be noticed, moreover, that, for rather
swift movements of the rod, the bands are more sharply defined if this
movement is contrary to that of the disc than if it is in like
direction with that of the disc. That is, the transition-bands are
broader when rod and disc move in the same, than when in opposite
directions.

5. The total number of bands seen (the two colors being alternately
arranged and with transition-bands between) at any one time is
approximately constant, howsoever the widths of the sectors and the
width and rate of the rod may vary. But the number of bands is
inversely proportional, as Jastrow and Moorehouse have shown (see
above, p. 169), to the time of rotation of the disc; that is, the
faster the disc, the more bands. Wherefore, if the bands are broad
(No. 2), they extend over a large part of the disc; but if narrow,
they cover only a small strip lying immediately behind the rod.

6. The colors of the bands approximate those of the two sectors; the
transition-bands present the adjacent 'pure colors' merging into each
other. But _all_ the bands are modified in favor of the color of the
moving rod. If, now, the rod is itself the same in color as one of the
sectors, the bands which should have been of the _other_ color are not
to be distinguished from the fused color of the disc when no rod moves
before it.

7. The bands are more strikingly visible when the two sectors differ
considerably in luminosity. But Jastrow's observation, that a
difference in luminosity is _necessary_, could not be confirmed.
Rather, on the contrary, sectors of the closest obtainable luminosity
still yielded the illusion, although faintly.

8. A _broad_ but slowly moving rod shows the bands overlying itself.
Other bands can be seen left behind it on the disc.

9. But a case of a rod which is broad, or slowly-moving, or both, is a
special complication which involves several other and _seemingly_
quite contradictory phenomena to those already noted. Since these
suffice to show the principles by which the illusion is to be
explained, enumeration of the special variations is deferred.


IV. THE GEOMETRICAL RELATIONS BETWEEN THE ROD AND THE SECTORS OF THE
DISC.


It should seem that any attempt to explain the illusion-bands ought to
begin with a consideration of the purely geometrical relations holding
between the slowly-moving rod and the swiftly-revolving disc. First of
all, then, it is evident that the rod lies in front of each sector
successively.

Let Fig. 1 represent the upper portion of a color-wheel, with center
at _O_, and with equal sectors _A_ and _B_, in front of which a rod
_P_ oscillates to right and left on the same axis as that of the
wheel. Let the disc rotate clockwise, and let _P_ be observed in its
rightward oscillation. Since the disc moves faster than the rod, the
front of the sector _A_ will at some point come up to and pass behind
the rod _P_, say at _p^{A}. P_ now hides a part of _A_ and both are
moving in the same direction. Since the disc still moves the faster,
the front of _A_ will presently emerge from behind _P_, then more and
more of _A_ will emerge, until finally no part of it is hidden by _P_.
If, now, _P_ were merely a line (having no width) and were not
moving, the last of _A_ would emerge just where its front edge had
gone behind _P_, namely at _p^{A}_. But _P_ has a certain width and a
certain rate of motion, so that _A_ will wholly emerge from behind _P_
at some point to the right, say _p^{B}_. How far to the right this
will be depends on the speed and width of _A_, and on the speed and
width of _P_.

Now, similarly, at _p^{B}_ the sector _B_ has come around and begins
to pass behind _P_. It in turn will emerge at some point to the right,
say _p^{C}_. And so the process will continue. From _p^{A}_ to _p^{B}_
the pendulum covers some part of the sector _A_; from _p^{B}_ to
_p^{C}_ some part of sector _B_; from _p^{C}_ to _P^{D}_ some part of
_A_ again, and so on.

[Illustration: Fig. 1.]

If, now, the eye which watches this process is kept from moving, these
relations will be reproduced on the retina. For the retinal area
corresponding to the triangle _p^{A}Op^{B}_, there will be less
stimulation from the sector _A_ than there would have been if the
pendulum had not partly hidden it. That is, the triangle in question
will not be seen of the fused color of _A_ and _B_, but will lose a
part of its _A_-component. In the same way the triangle _p^{B}OpC_
will lose a part of its _B_-component; and so on alternately. And by
as much as either component is lost, by so much will the color of the
intercepting pendulum (in this case, black) be present to make up the
deficiency.

We see, then, that the purely geometrical relations of disc and
pendulum necessarily involve for vision a certain banded appearance of
the area which is swept by the pendulum, if the eye is held at rest.
We have now to ask, Are these the bands which we set out to study?
Clearly enough these geometrically inevitable bands can be exactly
calculated, and their necessary changes formulated for any given
change in the speed or width of _A_, _B_, or _P_. If it can be shown
that they must always vary just as the bands we set out to study are
_observed_ to vary, it will be certain that the bands of the illusion
have no other cause than the interception of retinal stimulation by
the sectors of the disc, due to the purely geometrical relations
between the sectors and the pendulum which hides them.

And exactly this will be found to be the case. The widths of the bands
of the illusion depend on the speed and widths of the sectors and of
the pendulum used; the colors and intensities of the bands depend on
the colors and intensities of the sectors (and of the pendulum); while
the total number of bands seen at one time depends on all these
factors.


V. GEOMETRICAL DEDUCTION OF THE BANDS.


In the first place, it is to be noted that if the pendulum proceeds
from left to right, for instance, before the disc, that portion of the
latter which lies in front of the advancing rod will as yet not have
been hidden by it, and will therefore be seen of the unmodified, fused
color. Only behind the pendulum, where rotating sectors have been
hidden, can the bands appear. And this accords with the first
observation (p. 167), that "The rod appears to leave behind it on the
disc a number of parallel bands." It is as if the rod, as it passes,
painted them on the disc.

Clearly the bands are not formed simultaneously, but one after another
as the pendulum passes through successive positions. And of course the
newest bands are those which lie immediately behind the pendulum. It
must now be asked, Why, if these bands are produced successively, are
they seen simultaneously? To this, Jastrow and Moorehouse have given
the answer, "We are dealing with the phenomena of after-images." The
bands persist as after-images while new ones are being generated. The
very oldest, however, disappear _pari-passu_ with the generation of
the new. We have already seen (p. 169) how well these authors have
shown this, in proving that the number of bands seen, multiplied by
the rate of rotation of the disc, is a constant bearing some relation
to the duration of a retinal image of similar brightness to the bands.
It is to be noted now, however, that as soon as the rod has produced a
band and passed on, the after-image of that band on the retina is
exposed to the same stimulation from the rotating disc as before, that
is, is exposed to the fused color; and this would tend to obliterate
the after-images. Thus the oldest bands would have to disappear more
quickly than an unmolested after-image of the same original
brightness. We ought, then, to see somewhat fewer bands than the
formula of Jastrow and Moorehouse would indicate. In other words, we
should find on applying the formula that the 'duration of the
after-image' must be decreased by a small amount before the numerical
relations would hold. Since Jastrow and Moorehouse did not determine
the relation of the after-image by an independent measurement, their
work neither confirms nor refutes this conjecture.

What they failed to emphasize is that the real origin of the bands is
not the intermittent appearances of the rod opposite the _lighter_
sector, as they seem to believe, but the successive eclipse by the rod
of _each_ sector in turn.

If, in Fig. 2, we have a disc (composed of a green and a red sector)
and a pendulum, moving to the right, and if _P_ represents the
pendulum at the instant when the green sector _AOB_ is beginning to
pass behind it, it follows that some other position farther to the
right, as _P'_, will represent the pendulum just as the last part of
the sector is passing out from behind it. Some part at least of the
sector has been hidden during the entire interval in which the
pendulum was passing from _P_ to _P'_. Clearly the arc _BA'_ measures
the band _BOA'_, in which the green stimulation from the sector _AOB_
is thus at least partially suppressed, that is, on which a relatively
red band is being produced. If the illusion really depends on the
successive eclipse of the sectors by the pendulum, as has been
described, it will be possible to express BA', that is, the width of
a band, in terms of the widths and rates of movement of the two
sectors and of the pendulum. This expression will be an equation, and
from this it will be possible to derive the phenomena which the bands
of the illusion actually present as the speeds of disc and rod, and
the widths of sectors and rod, are varied.

[Illustration: Fig 2.]

Now in Fig. 2 let the
  width of the band (_i.e._, the arc BA')       = Z
  speed of pendulum                             = r degrees per second;
  speed of disc                                 = r' degrees per second;
  width of sector AOB (_i.e._, the arc AB)      = s degrees of arc;
  width of pendulum (_i.e._, the arc BC)        = p degrees of arc;
  time in which the pendulum moves from P to P' = t seconds.

Now
                       arc CA'
                   t = -------;
                          r

but, since in the same time the green sector AOB moves from _B_ to B',
we know also that
                       arc BB'
                   t = -------;
                         r'
then
                   arc CA'      arc BB'
                   -------  =   -------,
                      r           r'

or, omitting the word "arc" and clearing of fractions,

                   r'(CA') = r(BB').
But now
                   CA' = BA' - BC,
while
                   BA' = Z and BC = p;
therefore
                   CA' = Z-p.
Similarly
                   BB' = BA' + A'B' = Z + s.

Substituting for _CA'_ and _BB'_ their values, we get

                   r'(Z-p) = r(Z+s),
or
                   Z(r' - r) = rs + pr',
or
                   Z = rs + pr' / r' - r.

It is to be remembered that _s_ is the width of the sector which
undergoes eclipse, and that it is the color of that same sector which
is subtracted from the band _Z_ in question. Therefore, whether _Z_
represents a green or a red band, _s_ of the formula must refer to the
_oppositely colored_ sector, _i.e._, the one which is at that time
being hidden.

We have now to take cognizance of an item thus far neglected. When the
green sector has reached the position _A'B'_, that is, is just
emerging wholly from behind the pendulum, the front of the red sector
must already be in eclipse. The generation of a green band (red sector
in eclipse) will have commenced somewhat before the generation of the
red band (green sector in eclipse) has ended. For a moment the
pendulum will lie over parts of both sectors, and while the red band
ends at point _A'_, the green band will have already commenced at a
point somewhat to the left (and, indeed, to the left by a trifle more
than the width of the pendulum). In other words, the two bands
_overlap_.

This area of overlapping may itself be accounted a band, since here
the pendulum hides partly red and partly green, and obviously the
result for sensation will not be the same as for those areas where red
or green alone is hidden. We may call the overlapped area a
'transition-band,' and we must then ask if it corresponds to the
'transition-bands' spoken of in the observations.

Now the formula obtained for Z includes two such transition-bands, one
generated in the vicinity of OB and one near OA'. To find the formula
for a band produced while the pendulum conceals solely one, the
oppositely colored sector (we may call this a 'pure-color' band and
let its width = W), we must find the formula for the width (w) of a
transition-band, multiply it by two, and subtract the product from the
value for Z already found.

The formula for an overlapping or transition-band can be readily found
by considering it to be a band formed by the passage behind P of a
sector whose width is zero. Thus if, in the expression for Z already
found, we substitute zero for s, we shall get w; that is,

              o + pr'      pr'
          w = ------- =  ------
              r' - r     r' - r
Since
          W = Z - 2w,
we have
              rs + pr'       pr'
          W = -------- = 2 ------,
               r' - r      r' - r
or
              rs - pr'
          W = --------            (1)
               r' - r


[Illustration: Fig 3.]

Fig. 3 shows how to derive _W_ directly (as _Z_ was derived) from the
geometrical relations of pendulum and sectors. Let _r, r', s, p_, and
_t_, be as before, but now let

    width of the band (_i.e._, the arc _BA') = W_;

that is, the band, instead of extending as before from where _P_
begins to hide the green sector to where _P_ ceases to hide the same,
is now to extend from the point at which _P_ ceases to hide _any
part_ of the red sector to the point where it _just commences_ again to
hide the same.

Then
                           W + p
                      t = ------- ,
                             r
and
                           W + s
                      t = ------- ,
                             r'

therefore
                 W + p      W + s
                ------- =  ------- ,
                   r          r'

              r'(W + p) = r(W + s) ,

             W (r' - r) = rs - pr' ,
and, again,
                          rs - pr'
                      W = -------- .
                           r' - r

Before asking if this pure-color band _W_ can be identified with the
bands observed in the illusion, we have to remember that the value
which we have found for _W_ is true only if disc and pendulum are
moving in the same direction; whereas the illusion-bands are observed
indifferently as disc and pendulum move in the same or in opposite
directions. Nor is any difference in their width easily observable in
the two cases, although it is to be borne in mind that there may be a
difference too small to be noticed unless some measuring device is
used.

From Fig. 4 we can find the width of a pure-color band (_W_) when
pendulum and disc move in opposite directions. The letters are used as
in the preceding case, and _W_ will include no transition-band.

[Illustration: Fig. 4]

We have

           W + p
       t = -----,
             r
and
           s - W
       t = -----,
             r'

       r'(W + p) = r(s - W) ,

       W(r' + r) = rs - pr' ,

           rs - pr'
       W = -------- .           (2)
            r' + r

Now when pendulum and disc move in the same direction,

            rs - pr'
       W = --------- ,          (1)
            r' - r

so that to include both cases we may say that

           rs - pr'
       W = -------- .           (3)
            r' ± r

The width (W) of the transition-bands can be found, similarly, from
the geometrical relations between pendulum and disc, as shown in Figs.
5 and 6. In Fig. 5 rod and disc are moving in the same direction, and

        w = BB'.

Now
             W - p
        t = ------- ,
              r'

             w
        t = --- ,
             r'

        r'(w-p) = rw ,

        w(r'-r) = pr' ,


                pr'
         w = ------- .          (4)
               r'-r


[Illustration: Fig. 5]

[Illustration: Fig. 6]

In Fig. 6 rod and disc are moving in opposite directions, and

         w = BB',

              p - w
         t = ------- ,
                r

              w
         t = --- ,
              r'

         r'(p - w) = rw ,

         w(r' + r) = pr' ,

                pr'
         w = -------- .
              r' + r            (5)

So that to include both cases (of movement in the same or in opposite
directions), we have that

                pr'
         w = -------- .
              r' ± r            (6)



VI. APPLICATION OF THE FORMULAS TO THE BANDS OF THE ILLUSION.


Will these formulas, now, explain the phenomena which the bands of the
illusion actually present in respect to their width?


1. The first phenomenon noticed (p. 173, No. 1) is that "If the two
sectors of the disc are unequal in arc, the bands are unequal in
width; and the narrower bands correspond in color to the larger
sector. Equal sectors give equally broad bands."

In formula 3, _W_ represents the width of a band, and _s_ the width of
the _oppositely colored_ sector. Therefore, if a disc is composed, for
example, of a red and a green sector, then

                         rs(green) -  pr'
               W(red) = ------------------ ,
                              r' ± r
and
                         rs(red) -  pr'
             W(green) = ------------------ ,
                              r' ± r

therefore, by dividing,

              W(red)     rs(green) -  pr'
            --------- = ------------------- .
             W(green)      rs(red) -  pr'

From this last equation it is clear that unless _s_(green) = _s_(red),
_W_(red) cannot equal _W_(green). That is, if the two sectors are
unequal in width, the bands are also unequal. This was the first
feature of the illusion above noted.

Again, if one sector is larger, the oppositely colored bands will be
larger, that is, the light-colored bands will be narrower; or, in
other words, 'the narrower bands correspond in color to the larger
sector.'

Finally, if the sectors are equal, the bands must also be equal.

So far, then, the bands geometrically deduced present the same
variations as the bands observed in the illusion.


2. Secondly (p. 174, No. 2), "The faster the rod moves the broader
become the bands, but not in like proportions; broad bands widen
relatively more than narrow ones." The speed of the rod or pendulum,
in degrees per second, equals _r_. Now if _W_ increases when _r_
increases, _D_{[tau]}W_ must be positive or greater than zero for all
values of _r_ which lie in question.

Now
                     rs - pr'
                W = --------- ,
                      r' ± r
and
                      (r' ± r)s [±] (rs - pr')
      D_{[tau]}W  = -------------------------- ,
                             (r ± r')

or reduced,
                      r'(s ± p)
                  = -----------
                      (r' ± r)²

Since _r'_ (the speed of the disc) is always positive, and _s_ is
always greater than _p_ (cf. p. 173), and since the denominator is a
square and therefore positive, it follows that

                 D_{[tau]}W > 0

or that _W_ increases if _r_ increases.

Furthermore, if _W_ is a wide band, _s_ is the wider sector. The rate
of increase of _W_ as _r_ increases is

                     r'(s ± p)
       D_{[tau]}W = -----------
                     (r' ± r)²

which is larger if _s_ is larger (_s_ and _r_ being always positive).
That is, as _r_ increases, 'broad bands widen relatively more than
narrow ones.'


3. Thirdly (p. 174, No. 3), "The width of The bands increases if the
speed of the revolving disc decreases." This speed is _r'_. That the
observed fact is equally true of the geometrical bands is clear from
inspection, since in

                    rs - pr'
               W = --------- ,
                     r' ± r

as _r'_ decreases, the denominator of the right-hand member decreases
while the numerator increases.


4. We now come to the transition-bands, where one color shades over
into the other. It was observed (p. 174, No. 4) that, "These partake
of the colors of both the sectors on the disc. The wider the rod the
wider the transition-bands."

We have already seen (p. 180) that at intervals the pendulum conceals
a portion of both the sectors, so that at those points the color of
the band will be found not by deducting either color alone from the
fused color, but by deducting a small amount of both colors in
definite proportions. The locus of the positions where both colors are
to be thus deducted we have provisionally called (in the geometrical
section) 'transition-bands.' Just as for pure-color bands, this locus
is a radial sector, and we have found its width to be (formula 6, p.
184)
                       pr'
               W = --------- ,
                     r' ± r

Now, are these bands of bi-color deduction identical with the
transition-bands observed in the illusion? Since the total concealing
capacity of the pendulum for any given speed is fixed, less of
_either_ color can be deducted for a transition-band than is deducted
of one color for a pure-color band. Therefore, a transition-band will
never be so different from the original fusion-color as will either
'pure-color' band; that is, compared with the pure color-bands, the
transition-bands will 'partake of the colors of both the sectors on
the disc.' Since
                       pr'
               W = --------- ,
                     r' ± r

it is clear that an increase of _p_ will give an increase of _w_;
_i.e._, 'the wider the rod, the wider the transition-bands.'

Since _r_ is the rate of the rod and is always less than _r'_, the
more rapidly the rod moves, the wider will be the transition-bands
when rod and disc move in the same direction, that is, when

                       pr'
               W = --------- ,
                     r' - r

But the contrary will be true when they move in opposite directions,
for then

                       pr'
               W = --------- ,
                     r' + r

that is, the larger _r_ is, the narrower is _w_.

The present writer could not be sure whether or not the width of
transition-bands varied with _r_. He did observe, however (page 174)
that 'the transition-bands are broader when rod and disc move in the
same, than when in opposite directions.' This will be true likewise
for the geometrical bands, for, whatever _r_ (up to and including _r_
= _r'_),

               pr'      pr'
              ----  >  ----
              r'-r     r'+r

In the observation, of course, _r_, the rate of the rod, was never so
large as _r'_, the rate of the disc.


5. We next come to an observation (p. 174, No. 5) concerning the
number of bands seen at any one time. The 'geometrical deduction of
the bands,' it is remembered, was concerned solely with the amount of
color which was to be deducted from the fused color of the disc. _W_
and _w_ represented the widths of the areas whereon such deduction was
to be made. In observation 5 we come on new considerations, _i.e._, as
to the color from which the deduction is to be made, and the fate of
the momentarily hidden area which suffers deduction, _after_ the
pendulum has passed on.

We shall best consider these matters in terms of a concept of which
Marbe[3] has made admirable use: the 'characteristic effect.' The
Talbot-Plateau law states that when two or more periodically
alternating stimulations are given to the retina, there is a certain
minimal rate of alternation required to produce a just constant
sensation. This minimal speed of succession is called the critical
period. Now, Marbe calls the effect on the retina of a light-stimulation
which lasts for the unit of time, the 'photo-chemical unit-effect.'
And he says (_op. cit._, S. 387): "If we call the unit of time
1[sigma], the sensation for each point on the retina in each unit of
time is a function of the simultaneous and the few immediately
preceding unit-effects; this is the characteristic effect."

   [3] 'Marbe, K.: 'Die stroboskopischen Erscheinungen,' _Phil.
   Studien._, 1898, XIV., S. 376.

We may now think of the illusion-bands as being so and so many
different 'characteristic effects' given simultaneously in so and so
many contiguous positions on the retina. But so also may we think of
the geometrical interception-bands, and for these we can deduce a
number of further properties. So far the observed illusion-bands and
the interception-bands have been found identical, that is, in so far
as their widths under various conditions are concerned. We have now to
see if they present further points of identity.

As to the characteristic effects incident to the interception-bands;
in Fig. 7 (Plate V.), let _A'C'_ represent at a given moment _M_, the
total circumference of a color-disc, _A'B'_ represent a green sector
of 90°, and _B'C'_ a red complementary sector of 270°. If the disc is
supposed to rotate from left to right, it is clear that a moment
previous to _M_ the two sectors and their intersection _B_ will have
occupied a position slightly to the left. If distance perpendicularly
above _A'C'_ is conceived to represent time previous to _M_, the
corresponding previous positions of the sectors will be represented by
the oblique bands of the figure. The narrow bands (_GG_, _GG_) are the
loci of the successive positions of the green sector; the broader
bands (_RR_, _RR_), of the red sector.

In the figure, 0.25 mm. vertically = the unit of time = 1[sigma]. The
successive stimulations given to the retina by the disc _A'C'_, say at
a point _A'_, during the interval preceding the moment _M_ will be

  green 10[sigma],
  red   30[sigma],
  green 10[sigma],
  red   30[sigma], etc.

Now a certain number of these stimulations which immediately precede
_M_ will determine the characteristic effect, the fusion color, for
the point _A'_ at the moment _M_. We do not know the number of
unit-stimulations which contribute to this characteristic effect, nor
do we need to, but it will be a constant, and can be represented by a
distance _x_ = _A'A_ above the line _A'C'_. Then _A'A_ will represent
the total stimulus which determines the characteristic effect at _A'_.
Stimuli earlier than _A_ are no longer represented in the after-image.
_AC_ is parallel to _A'C'_, and the characteristic effect for any
point is found by drawing the perpendicular at that point between the
two lines _A'C_ and _AC_.

Just as the movement of the disc, so can that of the concealing
pendulum be represented. The only difference is that the pendulum is
narrower, and moves more slowly. The slower rate is represented by a
steeper locus-band, _PP'_, than those of the swifter sectors.

We are now able to consider geometrically deduced bands as
'characteristic effects,' and we have a graphic representation of the
color-deduction determined by the interception of the pendulum. The
deduction-value of the pendulum is the distance (_xy_) which it
intercepts on a line drawn perpendicular to _A'C'_.

Lines drawn perpendicular to _A'C'_ through the points of intersection
of the locus-band of the pendulum with those of the sectors will give
a 'plot' on _A'C'_ of the deduction-bands. Thus from 1 to 2 the
deduction is red and the band green; from 2 to 3 the deduction is
decreasingly red and increasingly green, a transition-band; from 3 to
4 the deduction is green and the band red; and so forth.

We are now prepared to continue our identification of these
geometrical interception-bands with the bands observed in the
illusion. It is to be noted in passing that this graphic
representation of the interception-bands as characteristic effects
(Fig. 7) is in every way consistent with the previous equational
treatment of the same bands. A little consideration of the figure will
show that variations of the widths and rates of sectors and pendulum
will modify the widths of the bands exactly as has been shown in the
equations.

The observation next at hand (p. 174, No. 5) is that "The total number
of bands seen at any one time is approximately constant, howsoever the
widths of the sectors and the width and rate of the rod may vary. But
the number of bands is inversely proportional (Jastrow and Moorehouse)
to the time of rotation of the disc; that is, the faster the disc, the
more bands."

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT, 17. PLATE V.
               Fig. 7. Fig. 8. Fig. 9.]

This is true, point for point, of the interception-bands of Fig. 7. It
is clear that the number of bands depends on the number of
intersections of _PP'_ with the several locus-bands _RR_, _GG_, _RR_,
etc. Since the two sectors are complementary, having a constant sum of
360°, their relative widths will not affect the number of such
intersections. Nor yet will the width of the rod _P_ affect it. As to
the speed of _P_, if the locus-bands are parallel to the line _A'C'_,
that is, of the disc moved _infinitely_ rapidly, there would be the
same number of intersections, no matter what the rate of _P_, that is,
whatever the obliqueness of _PP'_. But although the disc does not
rotate with infinite speed, it is still true that for a considerable
range of values for the speed of the pendulum the number of
intersections is constant. The observations of Jastrow and Moorehouse
were probably made within such a range of values of _r_. For while
their disc varied in speed from 12 to 33 revolutions per second, that
is, 4,320 to 11,880 degrees per second, the rod was merely passed to
and fro by hand through an excursion of six inches (J. and M., _op.
cit._, pp. 203-5), a method which could have given no speed of the rod
comparable to that of the disc. Indeed, their fastest speed for the
rod, to calculate from certain of their data, was less than 19 inches
per second.

The present writer used about the same rates, except that for the disc
no rate below 24 revolutions per second was employed. This is about
the rate which v. Helmholtz[4] gives as the slowest which will yield
fusion from a bi-sectored disc in good illumination. It is hard to
imagine how, amid the confusing flicker of a disc revolving but 12
times in the second, Jastrow succeeded in taking any reliable
observations at all of the bands. Now if, in Fig. 8 (Plate V.), 0.25
mm. on the base-line equals one degree, and in the vertical direction
equals 1[sigma], the locus-bands of the sectors (here equal to each
other in width), make such an angle with _A'C'_ as represents the disc
to be rotating exactly 36 times in a second. It will be seen that the
speed of the rod may vary from that shown by the locus _P'P_ to that
shown by _P'A_; and the speeds represented are respectively 68.96 and
1,482.64 degrees per second; and throughout this range of speeds the
locus-band of _P_ intercepts the loci of the sectors always the same
number of times. Thus, if the disc revolves 36 times a second, the
pendulum may move anywhere from 69 to 1,483 degrees per second without
changing the number of bands seen at a time.

   [4] v. Helmholtz, H.: 'Handbuch d. physiolog. Optik,' Hamburg
   u. Leipzig, 1896, S. 489.

And from the figure it will be seen that this is true whether the
pendulum moves in the same direction as the disc, or in the opposite
direction. This range of speed is far greater than the concentrically
swinging metronome of the present writer would give. The rate of
Jastrow's rod, of 19 inches per second, cannot of course be exactly
translated into degrees, but it probably did not exceed the limit of
1,483. Therefore, although beyond certain wide limits the rate of the
pendulum will change the total number of deduction-bands seen, yet the
observations were, in all probability (and those of the present
writer, surely), taken within the aforesaid limits. So that as the
observations have it, "The total number of bands seen at any one time
is approximately constant, howsoever ... the rate of the rod may
vary." On this score, also, the illusion-bands and the deduction-bands
present no differences.

But outside of this range it can indeed be _observed_ that the number
of bands does vary with the rate of the rod. If this rate (_r_) is
increased beyond the limits of the previous observations, it will
approach the rate of the disc (_r'_). Let us increase _r_ until _r_ =
_r'_. To observe the resulting bands, we have but to attach the rod or
pendulum to the front of the disc and let both rotate together. No
bands are seen, _i.e._, the number of bands has become zero. And this,
of course, is just what should have been expected from a consideration
of the deduction-bands in Fig. 8.

One other point in regard to the total number of bands seen: it was
observed (page 174, No. 5) that, "The faster the disc, the more
bands." This too would hold of the deduction-bands, for the faster the
disc and sectors move, the narrower and more nearly parallel to _A'C'_
(Fig. 7) will be their locus-bands, and the more of these bands will
be contained within the vertical distance _A'A_ (or _C'C_), which, it
is remembered, represents the age of the oldest after-image which
still contributes to the characteristic effect. _PP'_ will therefore
intercept more loci of sectors, and more deduction-bands will be
generated.


6. "The colors of the bands (page 175, No. 6) approximate those of the
two sectors; the transition-bands present the adjacent 'pure colors'
merging into each other. But _all_ the bands are modified in favor of
the moving rod. If, now, the rod is itself the same in color as one of
the sectors, the bands which should have been of the other color are
not to be distinguished from the fused color of the disc when no rod
moves before it."

These items are equally true of the deduction-bands, since a deduction
of a part of one of the components from a fused color must leave an
approximation to the other component. And clearly, too, by as much as
either color is deducted, by so much must the color of the pendulum
itself be added. So that, if the pendulum is like one of the sectors
in color, whenever that sector is hidden the deduction for concealment
will exactly equal the added allowance for the color of the pendulum,
and there will be no bands of the other color distinguishable from the
fused color of the disc.

It is clear from Fig. 7 why a transition-band shades gradually from
one pure-color band over into the other. Let us consider the
transition-band 2-3 (Fig. 7). Next it on the right is a green band, on
the left a red. Now at the right-hand edge of the transition-band it
is seen that the deduction is mostly red and very little green, a
ratio which changes toward the left to one of mostly green and very
little red. Thus, next to the red band the transition-band will be
mostly red, and it will shade continuously over into green on the side
adjacent to the green band.


7. The next observation given (page 175, No. 7) was that, "The bands
are more strikingly visible when the two sectors differ considerably
in luminosity." This is to be expected, since the greater the
contrast, whether in regard to color, saturation, or intensity,
between the sectors, the greater will be such contrast between the two
deductions, and hence the greater will it be between the resulting
bands. And, therefore, the bands will be more strikingly
distinguishable from each other, that is, 'visible.'


8. "A _broad_ but slowly-moving rod shows the bands lying over itself.
Other bands can also be seen behind it on the disc."

In Fig. 9 (Plate V.) are shown the characteristic effects produced by
a broad and slowly-moving rod. Suppose it to be black. It can be so
broad and move so slowly that for a space the characteristic effect is
largely black (Fig. 9 on both sides of _x_). Specially will this be
true between _x_ and _y_, for here, while the pendulum contributes no
_more_ photo-chemical unit-effects, it will contribute the newer one,
and howsoever many unit-effects go to make up the characteristic
effect, the newer units are undoubtedly the more potent elements in
determining this effect. The old units have partly faded. One may say
that the newest units are 'weighted.'

Black will predominate, then, on both sides of _x_, but specially
between _x_ and _y_. For a space, then, the characteristic effect will
contain enough black to yield a 'perception of the rod.' The width of
this region depends on the width and speed of the rod, but in Fig. 9
it will be roughly coincident with _xy_, though somewhat behind (to
the left of) it. The characteristic will be either wholly black, as
just at _x_, or else largely black with the yet contributory
after-images (shown in the triangle _aby_). Some bands will thus be
seen overlying the rod (1-8), and others lying back of it (9-16).

We have now reviewed all the phenomena so far enumerated of the
illusion-bands, and for every case we have identified these bands with
the bands which must be generated on the retina by the mere
concealment of the rotating sectors by the moving rod. It has been
more feasible thus far to treat these deduction-bands as if possibly
they were other than the bands of the illusion; for although the
former must certainly appear on the retina, yet it was not clear that
the illusion-bands did not involve additional and complicated retinal
or central processes. The showing that the two sets of bands have in
every case identical properties, shows that they are themselves
identical. The illusion-bands are thus explained to be due merely to
the successive concealment of the sectors of the disc as each passes
in turn behind the moving pendulum. The only physiological phenomena
involved in this explanation have been the persistence as after-images
of retinal stimulations, and the summation of these persisting images
into characteristic effects--both familiar phenomena.

From this point on it is permissible to simplify the point of view by
accounting the deduction-bands and the bands of the illusion fully
identified, and by referring to them under either name indifferently.
Figs. 1 to 9, then, are diagrams of the bands which we actually
observe on the rotating disc. We have next briefly to consider a few
special complications produced by a greater breadth or slower movement
of the rod, or by both together. These conditions are called
'complicating' not arbitrarily, but because in fact they yield the
bands in confusing form. If the rod is broad, the bands appear to
overlap; and if the rod moves back and forth, at first rapidly but
with decreasing speed, periods of mere confusion occur which defy
description; but the bands of the minor color may be broader or _may
be narrower_ than those of the other color.


VII. FURTHER COMPLICATIONS OF THE ILLUSION.


9. If the rod is broad and moves slowly, the narrower bands are like
colored, not with the broader, as before, but with the narrower
sector.

The conditions are shown in Fig. 9. From 1 to 2 the deduction is
increasingly green, and yet the remainder of the characteristic effect
is also mostly green at 1, decreasingly so to the right, and at 2 is
preponderantly red; and so on to 8; while a like consideration
necessitates bands from _x_ to 16. All the bands are in a sense
transition-bands, but 1-2 will be mostly green, 2-3 mostly red, and so
forth. Clearly the widths of the bands will be here proportional to
the widths of the like-colored sectors, and not as before to the
oppositely colored.

It may reasonably be objected that there should be here no bands at
all, since the same considerations would give an increasingly red band
from _B'_ to _A'_, whereas by hypothesis the disc rotates so fast as
to give an entirely uniform color. It is true that when the
characteristic effect is _A' A_ entire, the fusion-color is so well
established as to assimilate a fresh stimulus of either of the
component colors, without itself being modified. But on the area from
1 to 16 the case is different, for here the fusion-color is less well
established, a part of the essential colored units having been
replaced by black, the color of the rod; and black is no stimulation.
So that the same increment of component color, before ineffective, is
now able to modify the enfeebled fusion-color.

Observation confirms this interpretation, in that band _y-1_ is not
red, but merely the fusion-color slightly darkened by an increment of
black. Furthermore, if the rod is broad and slow in motion, but white
instead of black, no bands can be seen overlying the rod. For here the
small successive increments which would otherwise produce the bands
1-2, 2-3, etc., have no effect on the remainder of the fusion-color
plus the relatively intense increment of white.

It may be said here that the bands 1-2, 2-3, etc., are less intense
than the bands _x_-9, 9-10, etc., because there the recent or weighted
unit-effects are black, while here they are the respective colors.
Also the bands grow dimmer from _x_-9 to 15-16, that is, as they
become older, for the small increment of one color which would give
band 15-16 is almost wholly overridden by the larger and fresher mass
of stimulation which makes for mere fusion. This last is true of the
bands always, whatever the rate or width of the rod.


10. In general, equal sectors give equal bands, but if one sector is
considerably more intense than the other, the bands of the brighter
color will, for a broad and swiftly-moving rod, be the broader. The
brighter sector, though equal in width to the other, contributes more
toward determining the fusion-color; and this fact is represented by
an intrusion of the stronger color into the transition-bands, at the
expense of the weaker. For in these, even the decreased amount of the
stronger color, on the side next a strong-color band, is yet more
potent than the increased amount of the feebler color. In order to
observe this fact one must have the rod broad, so as to give a broad
transition-band on which the encroachment of the stronger color may be
evident. The process is the same with a narrow rod and narrow
transition-bands, but, being more limited in extent, it is less easily
observed. The rod must also move rapidly, for otherwise the bands
overlap and become obscure, as will be seen in the next paragraph.


11. If the disc consists of a broad and narrow sector, and if the rod
is broad and moves at first rapidly but more slowly with each new
stroke, there are seen at first broad, faint bands of the
minority-color, and narrow bands of the majority-color. The former
grow continuously more intense as the rod moves more slowly, and grow
narrower in width down to zero; whereupon the other bands seem to
overlap, the overlapped part being doubly deep in color, while the
non-overlapped part has come to be more nearly the color of the minor
sector. The overlapped portion grows in width. As the rate of the rod
now further decreases, a confused state ensues which cannot be
described. When, finally, the rod is moving very slowly, the phenomena
described above in paragraph 9 occur.

The successive changes in appearance as the rod moves more and more
slowly, are due to the factors previously mentioned, and to one other
which follows necessarily from the given conditions but has not yet
been considered. This is the last new principle in the illusion which
we shall have to take up. Just as the transition-bands are regions
where two pure-color bands overlap, so, when the rod is broad and
moves slowly, other overlappings occur to produce more complicated
arrangements.

These can be more compactly shown by diagram than by words. Fig. 10,
_a_, _b_ and _c_ (Plate VI.), show successively slower speeds of the
rod, while all the other factors are the same. In practice the
tendency is to perceive the transition-bands as parts of the broad
faint band of the minor color, which lies between them. It can be
seen, then, how the narrow major-color bands grow only slightly wider
(Fig. 10, _a_, _b_) until they overlap (_c_); how the broad
minor-color bands grow very narrow and more intense in color, there
being always more of the major color deducted (in _b_ they are reduced
exactly to zero, _z_, _z_, _z_). In _c_ the major-color bands overlap
(_o_, _o_, _o_) to give a narrow but doubly intense major-color band
since, although with one major, two minor locus-bands are deducted.
The other bands also overlap to give complicated combinations between
the _o_-bands. These mixed bands will be, in part at least,
minor-color bands (_q_, _q_, _q_), since, although a minor locus-band
is here deducted, yet nearly two major locus-bands are also taken,
leaving the minor color to predominate. This corresponds with the
observation above, that, '... the non-overlapped part has come to be
more nearly the color of the minor sector.'

A slightly slower speed of the rod would give an irreducible confusion
of bands, since the order in which they overlap becomes very
complicated. Finally, when the rod comes to move very slowly, as in
Fig. 9, the appearance suffers no further change, except for a gradual
narrowing of all the bands, up to the moment when the rod comes to
rest.

It is clear that this last principle adduced, of the multiple
overlapping of bands when the rod is broad and moves slowly, can give
for varying speeds of the rod the greatest variety of combinations of
the bands. Among these is to be included that of no bands at all, as
will be understood from Fig. 11 (Plate VII). And in fact, a little
practice will enable the observer so to adjust the rate of the (broad)
rod to that of the disc that no bands are observable. But care must be
taken here that the eye is rigidly fixated and not attracted into
movement by the rod, since of course if the eye moves with the rod, no
bands can be seen, whatever the rate of movement may be.

Thus, all the phenomena of these illusion-bands have been explained as
the result solely of the hiding by the rod of successive sectors of
the disc. The only physiological principles involved are those (1) of
the duration of after-images, and (2) of their summation into a
characteristic effect. It may have seemed to the reader tedious and
unnecessary so minutely to study the bands, especially the details
last mentioned; yet it was necessary to show how _all_ the possible
observable phenomena arise from the purely geometrical fact that
sectors are successively hidden. Otherwise the assertions of previous
students of the illusion, that more intricate physiological processes
are involved, could not have been refuted. The present writer does not
assert that no processes like contrast, induction, etc., come into
play to modify somewhat the saturation, etc., of the colors in the
bands. It must be here as in every other case of vision. But it is now
demonstrated that these remoter physiological processes contribute
nothing _essential_ to the illusion. For these could be dispensed with
and the illusion would still remain.

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT, 17. PLATE VI.
               Fig. 10.]

If any reader still suspects that more is involved than the
persistence of after-images, and their summation into a characteristic
effect, he will find it interesting to study the illusion with a
camera. The 'physiological' functions referred to belong as well to
the dry-plate as to the retina, while the former exhibits, presumably,
neither contrast nor induction. The illusion-bands can be easily
photographed in a strong light, if white and black sectors are used in
place of colored ones. It is best to arrange the other variable
factors so as to make the transition-bands as narrow as possible (p.
174, No. 4). The writer has two negatives which show the bands very
well, although so delicately that it is not feasible to try to
reproduce them.


VIII. SOME CONVENIENT DEVICES FOR EXHIBITING THE ILLUSION.


The influence of the width of sector is prettily shown by a special
disc like that shown in Fig. 12 (Plate VII.), where the colors are
dark-red and light-green, the shaded being the darker sector. A narrow
rod passed before such a disc by hand at a moderate rate will give
over the outer ring equally wide green and red bands; but on the inner
rings the red bands grow narrower, the green broader.

The fact that the bands are not 'images of the rod' can be shown by
another disc (Fig. 13, Plate VII.). In all three rings the lighter
(green) sector is 60° wide, but disposed on the disc as shown. The
bands are broken into zigzags. The parts over the outer ring lag
behind those over the middle, and these behind those over the inner
ring--'behind,' that is, farther behind the rod.

Another effective variation is to use rods alike in color with one or
the other of the sectors. Here it is clear that when the rod hides the
oppositely-colored sector, the deduction of that color is replaced
(not by black, as happens if the rod is black) but by the very color
which is already characteristic of that band. But when the rod hides
the sector of its own color, the deduction is replaced by the very
same color. Thus, bands like colored with the rod gain in depth of
tone, while the other pure-color bands present simply the
fusion-color.


IX. A STROBOSCOPE WHICH DEPENDS ON THE SAME PRINCIPLE.


If one produce the illusion by using for rod, not the pendulum of a
metronome, but a black cardboard sector on a second color-mixer placed
in front of the first and rotating concentrically with it, that is,
with the color-disc, one will observe with the higher speeds of the
rod which are now obtainable several further phenomena, all of which
follow simply from the geometrical relations of disc and rod (now a
rotating sector), as discussed above. The color-mixer in front, which
bears the sector (let it still be called a 'rod'), should rotate by
hand and independently of the disc behind, whose two sectors are to
give the bands. The sectors of the disc should now be equal, and the
rod needs to be broader than before, say 50° or 60°, since it is to
revolve very rapidly.

First, let the rod and disc rotate in the same direction, the disc at
its former rate, while the rod begins slowly and moves faster and
faster. At first there is a confused appearance of vague, radial
shadows shuffling to and fro. This is because the rod is broad and
moves slowly (cf. p. 196, paragraph II).

As the velocity of the rod increases, a moment will come when the
confusing shadows will resolve themselves into four (sometimes five)
radial bands of one color with four of the other color and the
appropriate transition-bands between them. The bands of either color
are symmetrically disposed over the disc, that is, they lie at right
angles to one another (if there are five bands they lie at angles of
72°, etc.). But this entire system of bands, instead of lying
motionless over the disc as did the systems hitherto described, itself
rotates rapidly in the opposite direction from disc to rod. As the rod
rotates forward yet faster, no change is seen except that the system
of bands moves backward more and more slowly. Thus, if one rotate the
rod with one's own hand, one has the feeling that the backward
movement of the bands is an inverse function of the increase in
velocity of the rod. And, indeed, as this velocity still increases,
the bands gradually come to rest, although both the disc and the rod
are rotating rapidly.

But the system of bands is at rest for only a particular rate of the
rod. As the latter rotates yet faster, the system of bands now
commences to rotate slowly forward (with the disc and rod), then more
and more rapidly (the velocity of the rod still increasing), until it
finally disintegrates and the bands vanish into the confused flicker
of shadows with which the phenomenon commenced.

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT, 17. PLATE VII.
                        Fig. 11.
               Fig. 12.         Fig. 13.]

This cycle now plays itself off in the reverse order if the speed of
the rod is allowed gradually to decrease. The bands appear first
moving forward, then more slowly till they come to rest, then moving
backward until finally they relapse into confusion.

But let the rate of the rod be not decreased but always steadily
increased. The bands will reappear, this time three of each color with
six transition-bands. As before, the system at first rotates backward,
then lies still, and then moves forward until it is dissolved. As the
rod moves still faster, another system appears, two bands of each
color forming a diameter and the two diameters lying at right angles.
This system goes through the same cycle of movements. When the
increased velocity of the rod destroys this system, another appears
having one band of each color, the two lying on opposite sides of the
center. The system goes through the same phases and is likewise
dissolved. Now, at this point the rod will be found to be rotating at
the same speed as the disc itself.

The explanation of the phenomenon is simple. The bands are not
produced by a single interruption of the vision of a sector by a rod,
but each band is made up of successive superpositions on the retina of
many such single-interruption bands. The overlapping of bands has been
already described (cf. Fig. 10 and pp. 196-198); superposition depends
of course on the same principle.

At the moment when a system of four bands of either color is seen at
rest, the rod is moving just one fifth as rapidly as the disc; so
that, while the rod goes once around, either sector, say the green
one, will have passed behind it exactly four times, and at points
which lie 90° apart. Thus, four red bands are produced which lie at
right angles to one another. But the disc is revolving at least 24
times in a second, the rod therefore at least 4.8 times, so that
within the interval of time during which successive stimuli still
contribute to the characteristic effect the rod will have revolved
several times, and with each revolution four red bands at right angles
to one another will have been formed. And if the rod is moving
_exactly_ one fifth as fast as the disc, each new band will be
generated at exactly that position on the disc where was the
corresponding band of the preceding four. The system of bands thus
appear motionless on the disc.

The movement of the system arises when the rate of the rod is slightly
less or more than one fifth that of the disc. If slightly less, the
bands formed at each rotation of the rod do not lie precisely over
those of the previous rotation, but a little to the rear of them. The
new set still lies mostly superposed on the previous sets, and so
fuses into a regular appearance of bands, but, since each new
increment lags a bit behind, the entire system appears to rotate
backward. The apparatus is actually a cinematograph, but one which
gives so many pictures in the second that they entirely fuse and the
strobic movement has no trace of discontinuity.

If the rod moves a trifle more than one fifth as fast as the disc, it
is clear that the system of bands will rotate forward, since each new
set of bands will lie slightly ahead of the old ones with which it
fuses. The farther the ratio between the rates of rod and disc departs
from exactly 1:5, whether less or greater, the more rapid will the
strobic movement, backward or forward, be; until finally the
divergence is too great, the newly forming bands lie too far ahead or
behind those already formed to fuse with them and so be apperceived as
one system, and so the bands are lost in confusion. Thus the cycle of
movement as observed on the disc is explained. As the rate of the rod
comes up to and passes one fifth that of the disc, the system of four
bands of each color forms in rapid backward rotation. Its movement
grows slower and slower, it comes to rest, then begins to whirl
forward, faster and faster, till it breaks up again.

The same thing happens as the rate of the rod reaches and exceeds just
one fourth that of the disc. The system contains three bands of each
color. The system of two bands of each color corresponds to the ratio
1:3 between the rates, while one band of each color (the two lying
opposite) corresponds to the ratio 1:2.

If the rod and the disc rotate in opposite directions, the phenomena
are changed only in so far as the changed geometrical relations
require. For the ratio 1:3 between the two rates, the strobic system
has four bands of each color; for 1:2, three bands of each color;
while when the two rates are equal, there are two bands of each color,
forming a diameter. As would be expected from the geometrical
conditions, a system of one band of each color cannot be generated
when rod and disc have opposite motions. For of course the rod cannot
now hide two or more times in succession a sector at any given point,
without hiding the same sector just as often at the opposite point,
180° away. Here, too, the cycle of strobic movements is different. It
is reversed. Let the disc be said to rotate forward, then if the rate
of the rod is slightly less than one fourth, etc., that of the disc,
the system will rotate forward; if greater, it will rotate backward.
So that as the rate of the rod increases, any system on its appearance
will move forward, then stand still, and lastly rotate backward. The
reason for this will be seen from an instant's consideration of where
the rod will hide a given sector.

It is clear that if, instead of using as 'rod' a single radial sector,
one were to rotate two or more such sectors disposed at equal angular
intervals about the axis, one would have the same strobic phenomena,
although they would be more complicated. Indeed, a large number of
rather narrow sectors can be used or, what is the same thing, a second
disc with a row of holes at equal intervals about the circumference.
The disc used by the writer had a radius of 11 inches, and a
concentric ring of 64 holes, each 3/8 of an inch in diameter, lying 10
inches from the center. The observer looks through these holes at the
color-disc behind. The two discs need not be placed concentrically.

When produced in this way, the strobic illusion is exceedingly pretty.
Instead of straight, radial bands, one sees a number of brightly
colored balls lying within a curving band of the other color and
whirling backward or forward, or sometimes standing still. Then these
break up and another set forms, perhaps with the two colors changed
about, and this then oscillates one way or the other. A rainbow disc
substituted for the disc of two sectors gives an indescribably
complicated and brilliant effect; but the front disc must rotate more
slowly. This disc should in any case be geared for high speeds and
should be turned by hand for the sake of variations in rate, and
consequently in the strobic movement.

It has been seen that this stroboscope is not different in principle
from the illusion of the resolution-bands which this paper has aimed
to explain. The resolution-bands depend wholly on the purely
geometrical relations between the rod and the disc, whereby as both
move the rod hides one sector after the other. The only physiological
principles involved are the familiar processes by which stimulations
produce after-images, and by which the after-images of rapidly
succeeding stimulations are summed, a certain number at a time, into a
characteristic effect.

       *       *       *       *       *



              STUDIES IN MEMORY.



       *       *       *       *       *



RECALL OF WORDS, OBJECTS AND MOVEMENTS.

BY HARVEY A. PETERSON.


Kirkpatrick,[1] in experimenting with 379 school children and college
students, found that 3-1/3 times as many objects were recalled as
visual words after an interval of three days. The experiment consisted
in showing successively 10 written names of common objects in the one
case and 10 objects in the other at the rate of one every two seconds.
Three days later the persons were asked to recall as many of each
series as possible, putting all of one series together. The averages
thus obtained were 1.89 words, 6.29 objects. The children were not
more dependent on the objects than the college students.

   [1] Kirkpatrick, E.A.: PSYCHOLOGICAL, REVIEW, 1894, Vol. I., p.
   602.

Since the experiment just described was performed without laboratory
facilities, Calkins[2] repeated it with 50 college women, substituting
lantern pictures for objects. She obtained in recall, after two days,
the averages 4.82 words, 7.45 pictures. The figures, however, are the
number of objects or words remembered out of ten, not necessarily
correctly placed. Kirkpatrick's corresponding figures for college
women were 3.22 words, 5.44 objects. The two experiments substantially
agree, Calkins' higher averages being probably due to the shortening
of the interval to two days.

   [2] Calkins, M.W.: PSYCHOLOGICAL, REVIEW, 1898, Vol. V., p.
   451.

Assuming, thus, that objects are better remembered than names in
deferred recall, the question arises whether this holds true when the
objects and names are coupled with strange and arbitrary symbols--a
question which is clearly of great practical interest from the
educational point of view, as it is involved in the pedagogical
problem whether a person seeking to acquire the vocabulary of a
foreign language ought to connect the foreign words with the familiar
words or with the objects themselves. And the further question arises:
what are the facts in the case of movements instead of objects, and
correspondingly in that of verbs instead of nouns. Both questions are
the problems of the following investigation.

As foreign symbols, either the two-figure numbers were used or
nonsense-words of regularly varying length. As familiar material,
nouns, objects, verbs and movements were used. The words were always
concrete, not abstract, by which it is meant that their meaning was
capable of demonstration to the senses. With the exception of a few
later specified series they were monosyllabic words. The nouns might
denote objects of any size perceptible to the eye; the objects,
however, were all of such a size that they could be shown through a
14×12 cm. aperture and still leave a margin. Their size was therefore
limited.

Concerning the verbs and movements it is evident that, while still
being concrete, they might be simple or complicated activities
consuming little or much time, and further, might be movements of
parts of the body merely, or movements employing other objects as
well. In this experiment complicated activities were avoided even in
the verb series. Simple activities which could be easily and quickly
imaged or made were better for the purpose in view.


THE _A_ SET.

The _A_ set contained sixteen series, _A_^{1}, _A_^{2}, _A_^{3}, etc.,
to _A_^{16}. They were divided as follows:

   Numbers and nouns: _A_^{1}, _A_^{5}, _A_^{9}, _A_^{13}.
   Numbers and objects: _A_^{2}, _A_^{6}, _A_^{10}, _A_^{14}.
   Numbers and verbs: _A_^{3}, _A_^{7}, _A_^{11}, _A_^{15}.
   Numbers and movements: _A_^{4}, _A_^{8}, _A_^{12}, _A_^{16}.

The first week _A_^{1-4} were given, the second week _A_^{5-8}, etc.,
so that each week one series of each of the four types was given the
subject.

In place of foreign symbols the numbers from 1 to 99 were used, except
in _A_^{13-15}, in which three-figure numbers were used.

Each series contained seven couplets, except _A_^{13-16}, which, on
account of the greater difficulty of three-figure numbers, contained
five. Each couplet was composed of a number and a noun, object, verb,
or movement.

Certain rules were observed in the composition of the series. Since
the test was for permanence, to avoid confusion no number was used in
more than one couplet. No two numbers of a given series were chosen
from the same decade or contained identical final figures. No word was
used in more than one couplet. Their vowels, and initial and final
consonants were so varied within a single series as to eliminate
phonetic aids, viz., alliteration, rhyme, and assonance. The kind of
assonance avoided was identity of final sounded consonants in
successive words, _e.g._, lane, vine.

The series were composed in the following manner: After the
twenty-eight numbers for four series had been chosen, the words which
entered a given series were selected one from each of a number of
lists of words. These lists were words of like-sounded vowels. After
one word had been chosen from each list, another was taken from the
first list, etc. As a consequence of observing the rules by which
alliteration, rhyme, and assonance were eliminated, the words of a
series usually represented unlike categories of thought, but where two
words naturally tended to suggest each other one of them was rejected
and the next eligible word in the same column was chosen. The
following is a typical series from the _A_ set.

   _A_^{1}. Numbers and Nouns.

    19     42     87     74     11     63     38
   desk   girl   pond   muff   lane   hoop   vine

The apparatus used in the _A_ set and also in all the later sets may
be described as follows: Across the length of a table ran a large,
black cardboard screen in the center of which was an oblong aperture
14 cm. high and 12 cm. wide. The center of the aperture was on a level
with the eyes of the subject, who sat at the table. The aperture was
opened and closed by a pneumatic shutter fastened to the back of the
screen. This shutter consisted of two doors of black cardboard sliding
to either side. By means of a large bulb the length of exposure could
be regulated by the operator, who stood behind the table.

The series--consisting of cards 4×2½ cm., each containing a printed
couplet--was carried on a car which moved on a track behind and
slightly below the aperture. The car was a horizontal board 150 cm.
long and 15 cm. wide, fixed on two four-wheeled trucks. It was divided
by vertical partitions of black cardboard into ten compartments, each
slightly wider than the aperture to correspond with the visual angle.
A curtain fastened to the back of the car afforded a black background
to the compartments. The couplets were supported by being inserted
into a groove running the length of the car, 3 cm. from the front. A
shutter 2 cm. high also running the length of the car in front of the
groove, fastened by hinges whose free arms were extensible, concealed
either the upper or the lower halves of the cards at the will of the
operator; _i.e._, either the foreign symbols or the words,
respectively. A screen 15 cm. high and the same length as the car,
sliding in vertical grooves just behind the cards and in front of the
vertical partitions, shut off the objects when desired, leaving only
the cards in view. Thus the apparatus could be used for all four types
of series.

The method of presentation and the time conditions of the _A_ set were
as follows:--A metronome beating seconds was used. It was kept in a
sound-proof box and its loudness was therefore under control. It was
just clearly audible to both operator and subject. In learning, each
couplet was exposed 3 secs., during about 2 secs. of which the shutter
was fully open and motionless. During this time the subject read the
couplet inaudibly as often as he wished, but usually in time with the
metronome. His object was to associate the terms of the couplet. There
was an interval of 2 secs. after the exposure of each couplet, and
this was required to be filled with repetition of only the
_immediately preceding couplet_. After the series had been presented
once there was an interval of 2 secs. additional, then a second
presentation of it commenced and after that a third. At the completion
of the third presentation there was an interval of 6 secs. additional
instead of the 2, at the expiration of which the test commenced.

_A_^{13-16} had five presentations instead of three. The test
consisted in showing the subject either the numbers or the words in
altered order and requiring him to write as many of the absent terms
as he could. In the object and movement series the objects were also
shown and the movements repeated by the subject if words were the
given terms. The time conditions in the test were,

   Exposure of a term                        3 secs.
   Post-term interval in A^{1-12}            4 secs.
   Post-term interval in A^{13-16}           6 secs.

This allowed the subject 7 secs. for recalling and writing each term
in A^{1-12} and 9 sec. in A^{13-16}. If a word was recalled after that
time it was inserted, but no further insertions were made after the
test of a series had been completed. An interval of 3 min. elapsed
between the end of the test of one series and the beginning of the
next series, during which the subject recorded the English word of any
couplet in which an indirect association had occurred, and also his
success in obtaining visual images if the series was a noun or a verb
series.

As already indicated, four series--a noun, an object, a verb, and a
movement series--given within a half hour, constituted a day's work
throughout the year. Thus variations due to changes in the
physiological condition of the subject had to affect all four types of
series.

Two days later these series were tested for permanence, and in the
same way as the tests for immediate recall, with this exception:

   Post-term interval in A^{13-16}            8 secs.

Thus 11 secs. were allowed for the deferred recall of each term in
A^{13-16}.

In the movement series of this set, to avoid hesitation and confusion,
the operator demonstrated to the subject immediately before the series
began, once for each word, how the movements were to be made.

The _A_ set was given to three subjects. The results of each subject
are arranged separately in the following table. In the tests the words
were required in A^{1-4}, in A^{5-16} the numbers. The figures show
the number of terms correctly recalled out of seven couplets in
A^{1-12} and out of five couplets in A^{13-16}, _exclusive_ of
indirect association couplets. The figures in brackets indicate the
number of correctly recalled couplets per series in which indirect
associations occurred. The total number correctly recalled in any
series is their sum. The figures in the per cent. row give the
percentage of correctly recalled couplets left after discarding both
from the number recalled and from the total number of couplets given
those in which indirect associations occurred. This simply diminished
the subject's number of chances. A discussion of the propriety of this
elimination will be found later. In _A_^{1-12} the absent terms had to
be recalled exactly in order, to be correct, but in _A_^{13-16}, on
account of the greater difficulty of the three-place numbers, any were
considered correct when two of the three figures were recalled, or
when all three figures were correct but two were reversed in position,
_e.g._, 532 instead of 523. _N_ means noun series, _O_ object, _V_
verb, and _M_ movement series. Series _A_^{1}, _A_^{5}, _A_^{9},
_A_^{13} are to be found in the first and third columns, _A_^{2},
_A_^{6}, _A_^{10}, _A_^{14} in the second and fourth, _A_^{3},
_A_^{7}, _A_^{11}, _A_^{15}, in the fifth and seventh, and _A_^{4},
_A_^{8}, _A_^{12}, _A_^{16} in the sixth and eighth columns.


TABLE I.

SHOWING IMMEDIATE RECALL AND RECALL AFTER TWO DAYS.

                              _M_.
   Series.       Im. Rec.   Two Days.     Im. Rec.      Two Days.
                 N.    O.   N.    O.     V.     M.    V.      M.
  A^{1-4}        6     7    3      1     6      7      2      1
  A^{5-8}        5(1)  6    3(1)   6     6(1)   7      5(1)   6
  A^{9-12}       7     7    4      6     7      6(1)   7      6(1)
  A^{13-16}      4     5    2      2     5      3      2      2
  Total.       22(1)  25   12(1)  15    24(1)  23(1)  16(1)  15(1)
  Per cent.    88     96   48     58    96     92     64     66

                              _S_.
   Series.      Im. Rec.   Two Days.     Im. Rec.      Two Days.
                 N.    O.   N.    O.     V.     M.    V.      M.
  A^{1-4}        6(1)  6    0      0     7      7      0      0
  A^{5-8}        6     7    1      3     6      7      0      3
  A^{9-12}       7     6    2      2     5      7      0      0
  A^{13-16}      5     5    0      0     5      5      3      0
  Total.        24(1) 24    3      5    23     26      3      3
  Per cent.     96    92   12     19    88    100     12     12

                              _Hu_.
   Series.      Im. Rec.   Two Days.     Im. Rec.      Two Days.
                 N.    O.   N.    O.     V.     M.    V.      M.
  A^{1-4}        6     7    0      1     5      6(1)   0      2
  A^{5-8}        5(2)  7    1(2)   1     7      7      1      0
  A^{9-12}       6(1)  7    2      2     6      7      0      5
  A^{13-16}      4(1)  4(1) 0      2     5      5      0      1
  Total.        21(4) 25(1) 3(2)   6    23     25(1)   1      8
  Per cent.     95   100   14     24    88    100      4     32


These results will be included in the discussion of the results of the
_B_ set.


THE _B_ SET.


A new material was needed for foreign symbols. After considerable
experimentation nonsense words were found to be the best adapted for
our purpose. The reasons for this are their regularly varying length
and their comparative freedom from indirect associations. An objection
to using nonsense syllables in any work dealing with the permanence of
memory is their sameness. On this account they are not remembered
long. To secure a longer retention of the material, nonsense words
were devised in substantially the same manner as that in which Müller
and Schumann made nonsense syllables, except that these varied
regularly in length from four to six letters. Thus the number of
letters, not the number of syllables was the criterion of variation,
though of course irregular variation in the number of syllables was a
necessary consequence.

When the nonsense words were used it was found that far fewer indirect
associations occurred than with nonsense syllables. By indirect
association I mean the association of a foreign symbol and its word by
means of a third term suggested to the subject by either of the others
and connected at least in _his_ experience with both. Usually this
third term is a word phonetically similar to the foreign symbol and
ideationally suggestive of the word to be associated. It is a very
common form of mnemonic in language material. The following are
examples:

   cax, stone (Caxton);
   teg, bib (get bib);
   laj, girl (large girl);
   xug, pond (noise heard from a pond);
   gan, mud (gander mud).

For both of these reasons nonsense words were the material used as
foreign symbols in the _B_ set.

The nonsense words were composed in the following manner. From a box
containing four of each of the vowels and two of each of the
consonants the letters were chosen by chance for a four-letter, a
five-letter, and a six-letter word in turn. The letters were then
returned to the box, mixed, and three more words were composed. At the
completion of a set of twelve any which were not readily pronounceable
or were words or noticeably suggested words were rejected and others
composed in their places.

The series of the _B_ set were four couplets long. Each series
contained one three-letter, one four-letter, one five-letter, and one
six-letter nonsense word. The position in the series occupied by each
kind was constantly varied. In all other respects the same principles
were followed in constructing the _B_ set as were observed in the _A_
set with the following substitutions:

No two foreign symbols of a series and no two terms of a couplet
contained the same sounded vowel in accented syllables.

The rule for the avoidance of alliteration, rhyme, and assonance was
extended to the foreign symbols, and to the two terms of a couplet.

The English pronounciation was used in the nonsense words. The
subjects were not informed what the nonsense words were. They were
called foreign words.

Free body movements were used in the movement series as in the _A_
set. Rarely an object was involved, _e.g._, the table on which the
subject wrote. The movements were demonstrated to the subject in
advance of learning, as in the _A_ set.

The following are typical _B_ series:

  B2.   Nonsense words and objects.

        quaro       rudv           xem            lihkez
        lid         cent           starch         thorn

  B3.   Nonsense words and verbs.

        dalbva      fomso          bloi           kyvi
        poke        limp           hug            eat

  B4.   Nonsense words and movements.

        ohv         wecolu         uxpa           haymj
        gnash       cross          frown          twist

The time conditions for presenting a series remained practically the
same. In learning, the series was shown three times as before. The
interval between learning and testing was shortened to 4 seconds, and
in the test the post-term interval of _A^{13-16}_ retained (6 secs.).
This allowed the subject 9 secs. for recalling and writing each term.
The only important change was an extension of the number of tests from
two to four. The third test was one week after the second, and the
fourth one week after the third. In these tests the familiar word was
always the term required, as in _A^{1-4}_, on account of the
difficulty of dealing statistically with the nonsense words. The
intervals for testing permanence in the _B_ set may be most easily
understood by giving the time record of one subject.


TIME RECORD OF _Hu_.

  Series.       Im. Rec.     Two Days.     Nine Days.     Sixteen Days.
  B^{1-4}       Feb. 12      Feb. 14       Feb. 21        Feb. 28
  B^{5-8}       Feb. 19      Feb. 21       Feb. 28        Mch. 7
  B^{9-12}      Feb. 26      Feb. 28       Mch. 7         Mch. 14
  B^{13-16}     Mch. 5       Mch. 7        Mch. 14        Mch. 21


The two half-hours in a week during which all the work of one subject
was done fell on approximately the same part of the day. When a number
of groups of 4 series each were to be tested on a given day they were
taken in the order of their recency of learning. Thus on March 7 the
order for _Hu_ was B^{13-16}, B^{9-12}, B^{5-8}.

Henceforth there was also rotation within a given four series. As
there were always sixteen series in a set, the effects of practice and
fatigue within a given half-hour were thus eliminated.

In the following table the results of the _B_ set are given. Its
arrangement is the same as in Table 1., except that the figures
indicate the number of absent terms correctly recalled out of four
couplets instead of seven or five. Where blanks occur, the series was
discontinued on account of lack of recall. As in Table 1., the tables
in the first, third and fifth columns show successive stages of the
same series. Immediate recall is omitted because with rare exceptions
it was perfect, the test being given merely as an aid in learning.


TABLE II.

  SHOWING RECALL AFTER TWO, NINE, AND SIXTEEN DAYS.

      Days.     Two.       Nine.   Sixteen.    Two.        Nine.   Sixteen.
             N.    O.   N.    O.   N.   O.   V.    M.    V.    M.   V.   M.
   Series.                         _M._
  B^{1-4}    2(1)  4    1(1)  2    1(1) 2    4     4     4     2    4    2
  B^{5-8}    3     1    2     1    1    1    2     2     2     1    1    1
  B^{9-12}   2     3    0     3    0    2    3     2     2     0    2    2
  B^{13-16}  2(1)  3    2(1)  0    2(1) 0    1     2     1     0    1    0
  Total      9(2) 11    5(2)  6    4(2) 5   10    10     9     3    8    5
  Per cent. 64    69   36    38   29   31   63    63    56    19   50   31

                                   _S._
  B^{1-4}¹   0     2    0     0              0     1     0     1
  B^{5-8}    0     0                         0     0
  B^{9-12}¹  0     1    0     0              0     1     0     0
  B^{13-16}² 0(2)  1    0(2)  1    0(2) 1    0     0(1)  0     0(1) 0    0(1)
  Total      0(2)  4    0(2)  1    0(2) 1    0     2(1)  0     1(1) 0    0(1)
  Per cent.  0    25    0     6    0    6    0    13     0     7    0    0

                                   _Hu._
  B^{1-4}    1(1)  4    0(1)  1    0(1) 2    1     3     0     2    0    0
  B^{5-8}    0     1(1) 0     0(1) 0    0(1) 0     1     0     1    0    1
  B^{9-12}   0     1    0     0    0    1    0     0     0     1    0    0
  B^{13-16}  0(1)  0    0(1)  0    0(1) 0    0     4     0     0    0    0
  Total      1(2)  6(1) 0(2)  1(1) 0(2) 3(1) 1     8     0     4    0    1
  Per cent.  7    40    0     7    0   20    6    50     0    25    0    6

                                   _B._
  B^{1-4}    1     1(1) 0     0              0     0(1)  0     0
  B^{6-8}    1     2    1     2    1    1    1     0     1     0    1    0
  B^{9-12}   0     2(1) 0     0(1) 0    0(1) 0(1)  2     0     2    0    1
  B^{13-16}  1     3    1     1    1    1    1     2     0     1    0    1
  Total      3     8(2) 2     3(1) 2    2(1) 2(1)  4(1)  1     3    1    2
  Per cent. 19    57   13    21   13   13   13    27     7    20    7   13

                                   _Ho._
  B^{1-4}¹   3     2(1) 2     2(1) 1    0(1) 1(2)  1(2)  1(2)  0(2) 0(2) 0(2)
  B^{6-8}    1     1(1) 1     0(1) 1    0    0     1(1)  1     1    0    1
  B^{9-12}   0(1)  1    0(1)  1    0(1) 0    1     1     1     1    0    0
  B^{13-16}³ 0     0    0     0    0    0    0(1)  4     0(1)  2    0(1) 0
  Total      4(1)  4(2) 3(1)  3(2) 2(1) 0(1) 2(3)  7(3)  3(3)  4(2) 0(3) 1(2)
  Percent.  33    30   25    23   17    0   17    58    25    33    0    8

                                   _Mo._
  B^{1-4}    3     3    3     1    4    1    0     2     0     2    0    2
  B^{5-8}    1     4    1     1    1    2    1     2(2)  1     1(2) 1    1(2)
  B^{9-12}   2     4    2     4    1    4    0(1)  3(1)  1(1)  3(1) 1(1) 2
  B^{13-16}  2(2)  4    2(2)  4    2(2) 2    1     4     1     4    1    4
  Total      8(2) 15    8(2) 10    8(2) 9    2(1) 11(3)  3(1) 10(3) 3(1) 9(2)
  Percent.  57    94   57    63   57   56   13    85    20    79   20   69

   ¹Four presentations in learning.
   ²Five presentations in learning.
   ³Five days' interval instead of two.


In the following summary the recall after two days is combined from
Tables I. and II. for the three subjects _M_, _S_ and _Hu_, there
being no important difference in the conditions of experimentation.
For the three other subjects this summary is merely a résumé of Table
II. The recall after nine and sixteen days in Table II. is omitted,
and will be taken up later. The figures are in all cases based on the
remainders left after those couplets in which indirect associations
occurred were eliminated both from the total number of couplets
learned and from the total number correctly recalled. _E.g._, in the
case of nouns, _M_ learned, in all, 42 couplets in the _A_ and _B_
sets, but since in 3 of them indirect associations occurred, only 39
couplets are left, of which 21 were correctly recalled. This gives 54
per cent.


SUMMARY OF RECALL AFTER TWO DAYS.--FROM TABLES I. AND II.

            N.            O.             V.             M.
  M.   54 per cent.   62 per cent.   63 per cent.   61 per cent.
  S.    8    "        21    "         7    "        12    "
  Hu.  11    "        30    "         5    "        59    "
  B.   19    "        57    "        13    "        27    "
  Ho.  33    "        30    "        17    "        58    "
  Mo.  57    "        94    "        13    "        85    "
  Av.  30 per cent.   49 per cent.   20 per cent.   50 per cent.

  Av. gain in object couplets, 19 per cent.
  "     "  "  movement couplets, 30 per cent.


The first question which occurs in examining the foregoing tables is
concerning the method of treating the indirect associations, _i.e._,
obtaining the per cents. The number of couplets correctly recalled may
be divided into two classes: those in which indirect associations did
not occur, and those in which they did occur. Those in which they did
not occur furnish us exactly what we want, for they are results which
are entirely free from indirect associations. In them, therefore, a
comparison can be made between series using objects and activities and
others using images. On the other hand, those correctly recalled
couplets in which indirect associations _did_ occur are not for our
purposes pure material, for they contain not only the object-image
factor but the indirect association factor also. The solution is to
eliminate these latter couplets, _i.e._, subtract them both from the
number correctly recalled and from the total number of couplets in the
set for a given subject. By so doing and by dividing the first
remainder by the second the per cents, in the tables were obtained.
There is one exception to this treatment. The few couplets in which
indirect associations occurred but which were nevertheless
_incorrectly_ recalled are subtracted only from the total number of
couplets in the set.

The method by which the occurrence of indirect associations was
recorded has been already described. It is considered entirely
trustworthy. There is usually little doubt in the mind of a subject
who comprehends what is meant by an indirect association whether or
not such were present in the particular series which has just been
learned. If none occurred in it the subjects always recorded the fact.
That an indirect association should occasionally be present on one day
and absent on a subsequent one is not strange. That a second term
should effect a union between a first and third and thereafter
disappear from consciousness is not an uncommon phenomenon of
association. There were thirteen such cases out of sixty-eight
indirect associations in the _A_, _B_ and _C_ sets. In the tables they
are given as present because their effects are present. When the
reverse was the case, namely, when an indirect association occurred on
the second, ninth or sixteenth day for the first time, it aided in
later recall and was counted thereafter. There were eight such cases
among the sixty-eight indirect associations.

Is it possible that the occurrence of indirect associations in,
_e.g._, two of the four couplets of a series renders the retention of
the other two easier? This could only be so when the intervals between
two couplets in learning were used for review, but such was never the
case. The subjects were required to fill such intervals with
repetitions of the preceding couplet only.

The elimination of the indirect association couplets and the
acceptance of the remainders as fair portrayals of the influence of
objects and movements on recall is therefore a much nearer approach to
truth than would be the retention of the indirectly associated
couplets.

The following conclusions deal with recall after two days only. The
recall after longer intervals will be discussed after Table III.

The summary from Tables I. and II. shows that when objects and nouns
are coupled each with a foreign symbol, four of the six subjects
recall real objects better than images of objects, while two, _M_ and
_Ho_, show little or no preference. The summary also shows that when
body movements and verbs are coupled each with a foreign symbol, five
of the six subjects recall actual movements better than images of
movements, while one subject, _M_, shows no preference. The same
subject also showed no preference for objects. With the subjects _S_
and _B_ the preference for actual movements is not marked, and has
importance only in the light of later experiments to be reported.

The great difference in the retentive power of different subjects is,
as we should expect, very evident. Roughly, they may be divided into
two groups. _M_ and _Mo_ recall much more than the other four. The
small percentage of recall in the case of these four suggested the
next change in the conditions of experimentation, namely, to shorten
with them the intervals between the tests for permanence. This was
accordingly done in the _C_ set. But before giving an account of the
next set we may supplement these results by results obtained from
other subjects.

It was impossible to repeat this set with the same subjects, and
inconvenient, on account of the scarcity of suitable words, to devise
another set just like it. Accordingly, the _B_ set was repeated with
six new subjects. We may interpolate the results here, and then resume
our experiments with the other subjects. The conditions remained the
same as for the other subjects in all respects except the following.
The tests after nine and sixteen days were omitted, and the remaining
test for deferred recall was given after one day instead of after two.
In learning the series, each series was shown four times instead of
three. The results are summarized in the following table. The figures
in the left half show the number of words out of sixteen which were
correctly recalled. The figures in parentheses separate, as before,
the correctly recalled indirect-association couplets. In the right
half of the table the same results, omitting indirect-association
couplets, are given in per cents, to facilitate comparison with the
summary from Tables I. and II.


TABLE III.

  SHOWING RECALL AFTER ONE DAY.

           N.     O.     V.     M.        N.     O.     V.     M.
  Bur.    6     10(1)   7(1)   5(4)       38     67     44     31
  W.      5(3)  12(1)   6      9          31     75     38     56
  Du.     1     11(1)   8      9           6     69     50     56
  H.      9(1)  14      8     12          56     88     50     75
  Da.     1(3)   7(4)   3(1)   9(3)        7     44     20     56
  R.      7(2)   3(3)   5      5(1)       44     19     31     31
  Total, 29(9)  57(10) 37(2)  49(8)  Av., 30     60     39     51

  Av. gain in object couplets, 30 per cent.
   "    "   " movement couplets, 12 per cent.


The table shows that five subjects recall objects better than images
of objects, while one subject recalls images of objects better.
Similarly, three subjects recall actual movements of the body better
than images of the same, while with three neither type has any
advantage.


THE _C_ SET.


In the _C_ set certain conditions were different from the conditions
of the _A_ and _B_ sets. These changes will be described under three
heads: changes in the material; changes in the time conditions; and
changes in the method of presentation.

For lack of monosyllabic English words the verbs and movements were
dissyllabic words. The nouns and objects were monosyllabic, as before.
All were still concrete, and the movements, whether made or imaged,
were still simple. But the movements employed objects, instead of
being merely movements of the body.

For two of the subjects, _M_ and _Mo_, the time intervals between the
tests remained as in the _A_ and the _B_ sets, namely, two days, nine
days, and sixteen days. With the four other subjects, _S, Hu, B,_ and
_Ho_, the number of tests was reduced to three and the intervals were
as follows:

The I. test, which as before was a part of the learning process, was
not counted. The II. test followed from 4½ to 6½ hours, or an average
of 5-3/8 hours, after the I. test. The III. test was approximately 16
hours after the II. test for all four subjects.

The series were learned between 10 a.m. and 1:30 p.m., the II. test
was the same day between 4:30 and 5:10 p.m., and the III. test was the
following morning between 8:30 and 9:10 a.m. Each subject of course
came at the same hour each week.

Each series was shown three times, as in the _B_ set.

A change had to be made in the length of exposure of each couplet in
the movement series. For, as a rule, movements employing objects
required a longer time to execute than mere movements of the body.
Five seconds was found to be a suitable length of exposure. To keep
the three other types of series comparable with the movement series,
if possible, their exposure was also increased from 3 to 5 secs. The
interval of 2 secs, at the end of a presentation was omitted, and the
interval between learning and testing reduced from 4 secs, in the _B_
set to 2 secs.

In the movement series of the _A_ and _B_ sets, movements of parts of
the body were chosen. But the number of such movements which a person
can conveniently make while reading words shown through an aperture is
limited, and as stated above no single word was ever used in two
couplets. These were now exhausted. In the _C_ set, therefore,
movements employing objects were substituted. The objects lay on the
table in a row in front of the subject, occupying a space about 50 cm.
from left to right, and were covered by a black cambric cloth. They
were thus all exposed at the same moment by the subject who, at a
signal, laid back the cloth immediately before the series began, and
in the same manner covered them at the end of the third presentation.
Thus the objects were or might be all in view at once, and as a result
the subject usually formed a single mental image of the four objects.

With this kind of material it was no longer necessary for the operator
to show the subject in advance of the series what the movements were
in order to avoid hesitation and confusion, for the objects were of
such a nature as obviously to suggest in connection with the words the
proper movements.


TABLE IV.

  SHOWING RECALL AFTER TWO, NINE AND SIXTEEN DAYS FOR TWO SUBJECTS, AND
  AFTER FIVE HOURS AND TWENTY-ONE HOURS FOR FOUR OTHER SUBJECTS.

  Days.      Two.     Nine.   Sixteen     Two.      Nine.    Sixteen
             N.  O.    N.  O.    N.  O.   V.    M.   V.   M.   V.   M.
  Series                             _M._
  C^{1-4}    4   4     4   4     3   2     3     2    2    2    1    1
  C^{5-8}    2   2     2   2     2   1     1     1    1    2    1    0
  C^{9-12}   3   2     3   1     3   0     2     4    3    2    2    1
  C^{13-16}  4   3(1)  4   2(1)  4   2(1)  3     4    2    3    2    3
  Total     13   1(1) 13   9(1) 12   5(1)  9    11    8    9    6    5
  Per cent. 81  73    81  60    75  33    56    69   50   56   38   31

                                     _Mo_
  C^{1-4}    2   4     1   1     1   1     1     4    1    2    1    2
  C^{5-8}    3   2     4   1     3   1     4     3(1) 4    3(1) 2    2(1)
  C^{9-12}   0   1     0   1     0   1     0     3    0    1    0    2
  C^{13-16}  0   0(1)  0   0(1)  0   0(1)  1(1)  4    1(1) 2    0(1) 0
  Total      5   7(1)  5   3(1)  4   3(1)  6(1) 14(1) 6(1) 8(1) 3(1) 6(1)
  Per cent. 31  46    31  20    25  20    40    93   40   53   20   40

  Hours.       Five.          Twenty-one.    Five.          Twenty-one
               N.    O.       N.    O.       V.    M.       V.    M.
  Series                             _S._
  C^{1-4}      1     3        1     1        0     1        0     1
  C^{5-8}      0(1)  3        0     2        0     1        0     1
  C^{9-12}     0(1)  3        0(1)  4        3     4        3     4
  C^{13-16}    1     3        1     3        2     3(1)     3     3(1)
  Total        2(2) 12        2(1) 10        5     9(1)     6     9(1)
  Per cent.   14    75       14    63       33    60       40    60

                                     _Hn._
  C^{1-4}      1     4        1     4        0     4        1     4
  C^{5-8}      0(2)  1        0(2)  1        0(1)  2        1(1)  2(2)
  C^{9-12}     3     4        3     4        2     4        2     4
  C^{13-16}    1     3        3     3        0     3(1)     0     2(1)
  Total        5(2) 12        7(2) 12        2(1) 13(3)     4(1) 12(3)
  Per cent.   36    75       50    75       14   100       29    92

                                     _B._
  C^{1-4}      3     4        3     4        3     4        3     4
  C^{5-8}      3     2        3     3        2     2        2     4
  C^{9-12}     2     4        2     3        2     1        2     2
  C^{13-16}    3     4        3     4        2     4        2     4
  Total       11    14       11    14        9    11        9    14
  Per cent.   69    88       69    88       56    69       56    88

                                     _Ho._
  C^{1-4}      3(1)  2(2)     3(1)  2(2)     0     3(1)     0     1(1)
  C^{5-8}      3(1)  4        3(1)  4        3     3(1)     3     3(1)
  C^{9-12}     1(2)  4        1(2)  4        2(1)  3(1)     2(1)  3(1)
  C^{13-16}    0     2        0     2        2     4        2     4
  Total        7(4) 12(2)     7(4) 12(2)     7(1) 13(3)     7(1) 11(3)
  Per cent.   58    92       58    92       50   100       50    85


The object series were also changed to conform to the movement series.
Formerly the objects had been shown successively through the aperture
and synchronously with their corresponding words; now they were on the
table in front of the subject and all uncovered and covered at once as
in the movement series. The subjects therefore had a single mental
image of these four objects also.

In both the object and the movement series the objects as before were
small and fairly uniform in size and so selected as not to betray to
the subject their presence beneath the cloth in the I. test. In the
II., III. and IV. tests there were no objects on the table.

The previous table shows the results of the _C_ set. The figures give
the number of couplets correct out of four; the figures in brackets
give the number of indirect associations; the total number recalled in
any series is their sum.

In the following summary the recall of _M_ and _Mo_ after two days and
of _S, Hu, B_ and _Ho_ after twenty-one hours are combined.


SUMMARY FROM TABLE IV.

                N.           O.            V.            M.
  _M._        81 per cent.  73 per cent.  56 per cent.  69 per cent.
  _Mo._       31 "          46 "          40 "          93 "
  _S._        14 "          63 "          40 "          60 "
  _Hu._       50 "          75 "          29 "          92 "
  _B._        69 "          88 "          56 "          88 "
  _Ho._       58 "          92 "          50 "          85 "
              -----------   -----------   -----------   -----------
  Av.         51 per cent.  73 per cent.  45 per cent.  81 per cent.

  Av. gain in object couplets, 22 per cent.
  "     "  "  movement couplets, 36 per cent.


Before asking whether the results of the _C_ set confirm the
conclusions already reached, we must compare the conditions of the
three sets to see whether the changes in the conditions in the _C_ set
have rendered it incomparable with the other two. The first change was
the substitution of dissyllabic words in the verb and the movement
series in the place of monosyllabic words. Since the change was made
in both the verb and the movement series their comparability with each
other is not interfered with, and this is the point at issue.
Preliminary tests, however, made it highly probable that simple
concrete dissyllabic words are not more difficult than monosyllabic in
5 secs. exposure. This change is therefore disregarded.

The first important change introduced in the _C_ set was the reduction
of the intervals between the tests for four subjects. The second was
the lengthening of the exposure from 3 to 5 secs. These changes also
do not lessen the comparability of the noun, object, verb and movement
series with one another, since they affected all series of the _C_
set.

The third change in the conditions was the substitution in the
movement series of movements employing objects for movements of the
body alone, and the consequent placing of objects on the table in the
movement and in the object series of which the subject obtained a
single mental image. All of the subjects were of the opinion that this
single mental image was an aid in recall. Each of the objects
contributing to form it was individualized by its spatial order among
the objects on the table. The objects shown through the aperture were
connected merely by temporal contiguity. On this account the object
and the movement series of the _C_ set are not altogether comparable
with those of the _A_ and the _B_ sets. We should expect _a priori_
that the object and the movement series in the _C_ set would be much
better recalled than those of the _A_ and the _B_ sets.

The fourth change was from imaged or made movements of the body alone
to imaged or made movements employing objects. If, as the _A_ and the
_B_ sets have already demonstrated, the presence of objects at all is
an aid to recall, the movement series of the _C_ set should show a
greater gain over their corresponding verb series than the simple
movements of the body in the _A_ and the _B_ sets showed over their
corresponding verb series. For, employing objects in movements is
adding the aid of objects to whatever aid there is in making the
movements.

Turning to the results, we consider the _C_ set by itself with
reference to the effect of the use of objects vs. images in general.
The summary from Table IV. shows that under the conditions given,
after intervals of from slightly less than one day to two days, five
of the six subjects recall object couplets better than noun couplets.
One subject, _M_ recalls noun couplets better. It also shows that
under the conditions and after the intervals mentioned all six
subjects recall movement couplets better than verb couplets. In view
of the small difference here and of his whole record, however, _M_ is
probably to be classed as indifferent in both substantive and action
series.


RECALL AFTER NINE AND SIXTEEN DAYS.


Thus far recall after these longer intervals has not been discussed.
The experiment was originally devised to test recall after two days
only, but it was found that with two of the subjects, _M_ and _Mo_,
recall for greater intervals could be obtained with slight additional
trouble. This was accordingly done in the _B_ and _C_ sets. The
results of the four other subjects in the _B_ set are not so
satisfactory on this point, because not enough was recalled.

The most interesting fact which developed was an apparently slower
rate of forgetting, in many cases, of the nouns and verbs than of the
objects and movements. In the noun-object group of the _B_ set it is
noticeable in three out of the four possible subjects, viz., _B, Ho_,
and _Mo_. _M_ alone does not show it. The two other subjects, _S_ and
_B_, did not recall enough for a comparison. In the verb-movement
group of the _B_ set it is also marked in three out of the four
possible subjects, viz., _M_, _Ho_, and _Mo. B_ alone does not show
it. It is also seen in the _C_ set in the results of _M_ and _Mo_, in
both the noun-object and the verb-movement groups. With the four other
subjects in the _C_ set it could not be noticed, since the series ran
their course in a day. In _M_ (verb-movement group, _C_ set) and _Mo_
(noun-object group, _C_ set) the originally higher object or movement
curves actually fall below their corresponding noun or verb curves.

The results of the tests for recall after nine and sixteen days are
summarized in the following tables. They should be compared with the
recall of these same series after two days given in Tables II. and
IV., nor should it be forgotten that all four types started with
perfect immediate recall. The figures give per cents, correct after
eliminating indirect-association couplets.


TABLE V.

  SHOWING RECALL AFTER NINE AND SIXTEEN DAYS.--SUMMARY FROM _B_ SET.

  Days.        Nine.       Sixteen        Nine.       Sixteen.
               N.  O.      N.  O.         V.  M.      V.  M.
  _M._         36  38      29  31         56  19      50  31
  _S._          0   6       0   6          0   7       0   0
  _Hu._         0   7       0  20          0  25       0   6
  _B._         13  21      13  13          7  20       7  13
  _Ho._        25  23      17   0         25  33       0   8
  _Mo._        57  63      57  56         20  79      20  69
  Av.          22  26      19  21         18  31      13  21


TABLE VI.

  SAME FOR _M_ AND _Mo_.--SUMMARY FROM _C_ SET.

  Days.       Nine.   Sixteen.     Nine.   Sixteen.
              N.  O.   N.  O.      V.  M.   V.  M.
  _M_.        81  60   75  33      50  56   38  31
  _Mo_.       31  20   25  20      40  53   20  40


THE _D_ SET.


A few series of nouns, objects, verbs, and movements dissociated from
foreign symbols were obtained. The material was of the same kind as
the words used in the couplet series, being mostly monosyllabic and
seldom dissyllabic words. They had not been previously used with these
subjects. Each series contained ten words or ten objects. The same
kind of precautions were taken as in the couplet sets to avoid
phonetic aids and the juxtaposition of words which suggest each other.
The apparatus employed in the couplet sets was used. The objects in
the object series were shown through the aperture. Visual images were
required in the noun and in the verb series. The noun and the object
series were exposed at the rate of one word every 2 secs. (or 20 secs.
for the series) for _M_, _S_, and _Hu_, and one every 3 secs. (or 30
secs. for the series) for _B_, _Ho_, and _Mo_. Only one exposure of
the series was given. At its completion the subject at once wrote as
many of the words or objects as he could recall. Two days later at the
same hour he was asked to write without further stimulus as many words
of each series as he could recall, classifying them according to their
type of series.

The verbs were similar to the verbs of the couplet series. There was a
tendency in the verb series among most of the subjects to make a more
or less connected story of the verbs and thus some subjects could
retain all ten words for two days. This was an element not present in
the couplet verb series, according to the subjects, nor in any other
series, and the subjects were, therefore, directed to eliminate it by
imaging each action in a different place and connected with different
persons. The effort was nearly successful, some of the subjects
connecting two or three verbs, and others none. The movements employed
ten objects which were uncovered and covered by the subject as in the
_C_ set. The exposure for the verbs and movements was 5 secs. for each
word, or 50 secs. for the series. The tests were the same as in the
series of ten nouns and ten objects, but in a number of cases (to be
specified in the table) it seemed best to shorten the interval for
deferred recall to one day.

The series were always given in pairs--a noun and an object series, or
a verb and a movement series forming a pair. Only one pair was given
per day and no other series of any kind were given on that day.
Usually several days intervened between the II. test of one pair and
the learning of the next, but in a little less than half of the cases
a new pair was learned on the same day shortly after the II. test of
the preceding pair.

The noun-object pairs and the verb-movement pairs were not given in
any definite order with reference to each other.

The figures in the following table indicate the number of words out of
ten which the subject correctly recalled and placed in their proper
columns. Immediate recall is also given.


TABLE VII.


  Series.     Im. Rec.     Two Days.     Im. Rec.     Two Days.
             N.   O.      N.   O.       V.   M.      V.   M.

                              _M._
  D^{1-4}      8    9       7    7        7   10       4    5
  D^{5-8}      9    7       6    6        8    8       6    6
  D^{9-12}     7    7       5    6        8   10       7    7
  Av.         24   23      18   19       23   28      17   17

                             _Mo_.
  D^{1-4}      6    6       2    1        8   10       0¹   7¹
  D^{5-8}      6    5       0¹   3¹       8    9       2    4
  D^{9-12}     5    7       1¹   6¹      10   10       2    7
  Av.         17   18       3   10       26   29       4   18

                             _S_.
  D^{1-4}      8    9       2    3        9   10       6¹   9¹
  D^{5-8}      8   10       2    4        9   10       4¹   9¹
  D^{9-12}     8   10       2    5        8   10       3¹   7¹
  Av.         24   29       6   12       26   30      13   25

                             _Hu._
  D^{1-4}      6    8       3    7        9   10       4    9
  D^{5-8}      7    9       0    2        9   10       2    7
  D^{9-12}     7    9       4    6        8   10       1    8
  Av.         20   26       7   15       26   30       7   24

                             _Ho._
  D^{1-4}      9    9       3    3       10    9       5    7
  D^{5-8}      9    8       1    6        9    9       6¹   8¹
  D^{9-12}     8    8       5    5       10   10       6¹   7¹
  Av.         26   25       9   14       29   28      17   22

   ¹ One day.


The results of the _D_ set strongly confirm the results of the _A_,
_B_, and _C_ sets. Table VII. shows that after from one to two days'
interval four subjects recall objects better than nouns and movements
better than verbs. One subject, _M._, shows no preference.


CONCLUSIONS.


We are now in a position to answer specifically the problem of this
investigation. The results show: (1) that those five subjects who
recall objects better than nouns (involving images) _when each occurs
alone_, also recall objects better than nouns when each is recalled by
means of an unfamiliar verbal symbol with which it has been coupled;
(2) that the same is true of verbs and movements; (3) that these facts
also receive confirmation on the negative side, viz.: the one subject
who does not recall objects and movements better than nouns and verbs
(involving images) _when they are used alone_, also does not recall
them better _when they are recalled by means of foreign symbols_ with
which they have been coupled.


MINOR QUESTIONS.


The problem proposed at the outset of the investigation having been
answered, two minor questions remain: (1) as to images, (2) indirect
associations.


1. All the subjects were good visualizers. The images became clear
usually during the first of the three presentations, _i.e._, in 1-3
secs., and persisted until the next couplet appeared. In the second
and third presentations the same images recurred, rarely a new one
appeared.

An interesting side light is thrown on M.'s memory by his work in
another experiment in which he was a subject. This experiment required
that the subject look at an object for 10 secs. and then after the
disappearance of its after-image manipulate the memory image. M.
showed unusually persistent after-images. The memory images which
followed were unusually clear in details and also persistent. They
were moreover retained for weeks, as was shown by his surprising
ability to recall the details of an image long past, and separated
from the present one by many subsequent images. His memory was
capacious rather than selective. His eyesight was tested and found to
be normal for the range of the apparatus. Possibly his age (55 yrs.)
is significant, although one of the two subjects who showed the
greatest preference for objects and movements, Mo., was only six yrs.
younger. The ages of the other subjects were S. 36 yrs., Hu. 23 yrs.,
B. 25 yrs., Ho. 27 yrs.

That some if not all of the subjects did not have objective images in
many of the noun and verb couplets if they were left to their own
initiative to obtain them is evident from the image records in the _A_
set, in which the presence of the objective images was optional but
the record obligatory. The same subject might have in one noun or verb
series no visual images and in another he might have one for every
couplet of the series. After the completion of the _A_ set, the effect
of the presence of the objective images in series of 10 nouns alone,
or 10 objects alone after two days' interval, was tested. This was
merely a repetition of similar work by Kirkpatrick after three days'
interval, and yielded similar results. As a matter of fact some of the
subjects were unable wholly to exclude the objective images, but were
compelled to admit and then suppress them as far as possible, so that
it is really a question of degree of prominence and duration of the
images.

The presence of the objective images having been shown to be an aid in
the case of series of nouns, the subjects were henceforth requested to
obtain them in the noun and verb series of the _B_ and _C_ sets, and
the image records show that they were entirely successful in doing so.


2. The total number of couplets in any one or in several sets may be
divided into two classes: (1) Those in which indirect associations did
not occur in the learning, and (2) those in which they did occur. For
reasons already named we may call the first pure material and the
second mixed. We can then ascertain in each the proportion of
correctly recalled couplets after one, two, nine and sixteen days'
interval, and thus see the importance of indirect associations as a
factor in recall. This is what has been done in the following table.

The figures give the number of couplets correctly or incorrectly
recalled out of 64. In the case of the interval of one day the figures
are a tabulation of the III. test (twenty-one hours) of the _C_ set,
which contained 16 series of 4 couplets each. The figures for the
intervals of two, nine and sixteen days are a tabulation of the _B_
set, which also contained 16 series of 4 couplets each. _C_ denotes
correct, _I_ incorrect.


TABLE VIII.

SHOWING GREATER PERMANENCE OF COUPLETS IN WHICH INDIRECT ASSOCIATIONS
OCCURRED.

                  Pure Material.                     Mixed Material.
  Days.     One.     Two.   Nine. Sixteen.   One.   Two.   Nine. Sixteen.
           C   I    C   I   C   I   C   I   C   I   C   I   C   I   C   I
  _M._    40  22   23  39  22  40           2   0   2   0   3   0
  _Mo._   36  22   31  27  29  29           6   0   6   0   5   1
  _S._    27  34    6  55   2  59   1  60   2   1   3   0   3   0   3   0
  _Hu._   35  22   16  45   5  56   4  57   6   1   3   0   3   0   3   0
  _B._    48  16   17  43   9  51   7  53   0   0   4   0   1   3   1   3
  _Ho._   37  15   17  30  13  36   3  46  10   2   9   6   8   7   7   8

  Total: 147  87  132 217  83 268  66 285  18   4  27   6  23  10  21  12
  P'c't.: 63  37   38  62  24  76  19  81  82  18  82  18  70  30  64  36


We see from the table that the likelihood of recalling couplets in
which indirect associations did not occur in learning is 63 per cent.
after one day, and that there is a diminution of 44 per cent. in the
next fifteen days. The fall is greatest during the second day. On the
other hand, the likelihood of recalling couplets in which indirect
associations did occur is 82 per cent. after one day, and there is a
diminution of only 18 per cent. during the next fifteen days. The
fading is also much more gradual.

It is evident, then, that in all investigations dealing with language
material the factor of indirect associations--a largely accidental
factor affecting varying amounts of the total material (in these six
subjects from 3 per cent. to 23 per cent.) is by far the most
influential of all the factors, and any investigations which have
heretofore failed to isolate it are not conclusive as to other
factors.

The practical value of the foregoing investigation will be found in
its bearing upon the acquisition of language. While it is by no means
confined to the acquisition of the vocabulary of a _foreign_ language,
but is also applicable to the acquisition of the vocabulary of the
native language, it is the former bearing which is perhaps more
obvious. If it is important that one become able as speedily as
possible to grasp the meaning of foreign words, the results of the
foregoing investigation indicate the method one should adopt.

       *       *       *       *       *



MUTUAL INHIBITION OF MEMORY IMAGES.

BY FREDERICK MEAKIN.


The results here presented are the record of a preliminary inquiry
rather than a definitive statement of principles.

The effort to construct a satisfactory theory of inhibition has given
rise, in recent years, to a good deal of discussion. Ever since it was
discovered that the reflexes of the spinal cord are normally modified
or restrained by the activity of the brain and Setschenow (1863)
attempted to prove the existence of localized inhibition centers, the
need of such a theory has been felt. The discussion, however, has been
mainly physiological, and we cannot undertake to follow it here. The
psychologist may not be indifferent, of course, to any comprehensive
theory of nervous action. He works, indeed, under a general
presumption which takes for granted a constant and definite relation
between psychical and cerebral processes. But pending the settlement
of the physiological question he may still continue with the study of
facts to which general expression may be given under some theory of
psychical inhibition not inconsistent with the findings of the
physiologist.

A question of definition, however, confronts us here. Can we, it may
be asked, speak of psychical inhibition at all? Does one conscious
state exercise pressure on another, either to induce it, or to expel
it from the field? 'Force' and 'pressure,' however pertinent to
physical inquiries, are surely out of place in an investigation of the
relations between the phenomena of mind. Plainly a distinction has to
be made if we are to carry over the concept of inhibition from the
domain of nervous activity to the conscious domain. Inhibition cannot,
it should seem, have the same sense in both. We find, accordingly,
that Baldwin, who defines nervous inhibition as 'interference with the
normal result of a nervous excitement by an opposing force,' says of
mental inhibition that it 'exists in so far as the occurrence of a
mental process prevents the simultaneous occurrence of other mental
processes which might otherwise take place.'[1]

   [1] Baldwin, J.M.: 'Dictionary of Philosophy and Psychology,'
   New York and London, 1901, Vol. I., article on 'Inhibition.'

Even here, it may be said, there is in the term 'prevents' an
implication of the direct exercise of force. But if we abstract from
any such implication, and conceive of such force as the term
inhibition seems to connote, as restricted to the associated neural or
physiological processes, no unwarranted assumptions need be imported
by the term into the facts, and the definition may, perhaps, suffice.

Some careful work has been done in the general field of psychical
inhibition. In fact, the question of inhibition could hardly be
avoided in any inquiry concerning attention or volition. A. Binet[2]
reports certain experiments in regard to the rivalry of conscious
states. But the states considered were more properly those of
attention and volition than of mere ideation. And the same author
reports later[3] examples of antagonism between images and sensations,
showing how the latter may be affected, and in some respects
inhibited, by the former. But this is inhibition of sensations rather
than of ideas. Again, Binet, in collaboration with Victor Henri,[4]
reports certain inhibitory effects produced in the phenomena of
speech. But here again the material studied was volitional. More
recently, G. Heymans[5] has made elaborate investigation of a certain
phase of 'psychische Hemmung,' and showed how the threshold of
perception may be raised, for the various special senses, by the
interaction of rival sensations, justly contending that this shifting
of the threshold measures the degree in which the original sensation
is inhibited by its rival. But the field of inquiry was in that case
strictly sensational. We find also a discussion by Robert Saxinger,[6]
'Ueber den Einfluss der Gefühle auf die Vorstellungsbewegung.' But the
treatment there, aside from the fact that it deals with the emotions,
is theoretical rather than experimental.

   [2] Binet, A.: _Revue Philosophique_, 1890, XXIX., p. 138.

   [3] Binet, A.: _Revue Philosophique_, 1890, XXX., p. 136.

   [4] Binet, A., et Henri, V.: _Revue Philosophique_, 1894,
   XXXVII., p. 608.

   [5] Heymans, G.: _Zeitschrift f. Psych. u. Physiol. d.
   Sinnesorgane_, 1899, Bd. XXI., S. 321; _Ibid._, 1901, Bd.
   XXVI., S. 305.

   [6] Saxinger, R.: _Zeitschrift f. Psych. u. Physiol. d.
   Sinnesorgane_, 1901, Bd. XXVI., S. 18.

In short, it appears that though much has been said and done upon the
general subject of psychical inhibition, experimental inquiry into the
inhibitory effect of one idea upon another--abstraction made, as far
as possible, of all volitional influence--virtually introduces us to a
new phase of the subject.

The term 'idea,' it should be noted, is here used in its broadest
sense, and includes the memory image. In fact, the memory image and
its behavior in relation to another memory image formed the material
of the first part of the research, which alone is reported here.
Apparatus and method were both very simple.

The ideas to be compared were suggested by geometrical figures cut out
of pasteboard and hung, 25 cm. apart, upon a small black stand placed
on a table in front of the observer, who sat at a distance of four
feet from the stand. The diagrams and descriptions which follow will
show the character of these figures.

Before the figures were placed in position, the subject was asked to
close his eyes. The figures being placed, a few seconds' warning was
given, and at the word 'look' the subject opened his eyes and looked
at the objects, closing his eyes again at the word 'close.' The time
of exposure was five seconds. This time was divided as equally as
possible between the two figures, which were simultaneously exposed,
the observer glancing freely from one to the other as in the common
observation on which our ideas of objects are founded. At the end of
the exposure the subject sat with closed eyes and reported the several
appearances and disappearances of the ideas or mental images of the
objects just presented. The conditions required of him were that he
should await passively the entry of the rival claimants on his
attention, favoring neither and inhibiting neither; that is to say, he
was to remit all volitional activity, save so far as was necessary to
restrict his attention to the general field upon which the ideated
objects might appear, and to note what occurred on the field. The
period of introspection, which followed immediately the disappearance
of such retinal images as remained, after the closing of the eyes to
the external objects, lasted sixty seconds. The reports, like the
signals, were given in a just audible tone. They were in such terms as
'right--left,' 'small--large,' 'circle--star,' terms the simplest that
could be found, or such as seemed, in any given case, most naturally
or automatically associated with the object, and therefore least
likely to disturb the course of the observation. And each report was
noted down by the experimenter at the instant it was given, with the
time of each phase, in seconds, as indicated by a stop-watch under the
experimenter's eye.

It will be remarked that the attitude required of the observer was one
which is not commonly taken. And it may be objected that the results
of an attitude so unusual towards objects so ghostly and attenuated
must be too delicate, or too complex, or influenced by too many alien
suggestions, to be plumply set down in arabic numerals. The subjects,
in fact, did at first find the attitude not easy to assume. A visual
object may hold the attention by controlling the reflexes of the eye.
But an ideational object has ordinarily no sure command of the
conscious field save under the influence of a volitional idea or some
strongly toned affectional state. But with a little practice the
difficulty seemed to disappear. The subject became surer of his
material, and the mental object gradually acquired the same sort of
individuality as the visual object, though the impression it made
might be less intense.

After a few preliminary experiments, figures were devised for the
purpose of testing the effect of mere difference in the complexity of
outline. That is to say, the members of every pair of objects were of
the same uniform color-tone (Bradley's neutral gray No. 2), presented
the same extent of surface (approximately 42 sq. cm.), were exposed
simultaneously for the same length of time (5 seconds), and were in
contour usually of like general character save that the bounding line
in the one was more interrupted and complex than in the other.

In another series the variant was the extent of surface exposed, the
color-tone (neutral gray), outline, and other conditions being the
same for both members of each pair. The smaller figures were of the
same area as those of the preceding series; in the larger figures this
area was doubled. Only one member of each pair is represented in the
diagrams of this and the next series.

In a third series brightness was the variant, one member of each pair
being white and the other gray (Bradley's cool gray No. 2). All other
conditions were for both figures the same.

In still another series strips of granite-gray cardboard half a
centimeter wide were cut out and pasted on black cards, some in
straight and some in broken lines, but all of the same total length
(10 cm.). These were exposed under the same general conditions as
those which have already been described, and were intended to show the
relative effects of the two sorts of lines.


TABLE I.

           1        2        3        4        5      Totals.  Averages.
         L   R    L   R    L   R    L   R    L   R    L    R    L     R
     I. 45  45   25  29   27  27   31  24   36  20   164  145  32.8  29
    II. 20  25   28  28   28  19   31  31   28  14   135  117  27    23.5
   III. 11  12   17  28    0   7    0  15   27  23    55   85  11    17
    IV.  7   6   47  22   17  21   17  45   31  30   119  124  23.8  24.8
     V. 27  33   46  36   40  31   44  31   26  35   183  165  36.6  33.2
    VI. 11  14   32  29   34  21   14  35    0  46    91  145  18.2  29
   VII. 36  33   30  30   50  50   22  22   52  52   190  187  38    37.4
  VIII. 41  44   33  33   45  45   34  44   37  28   190  194  38    38.8
    IX. 45  45   39  46   42  47   47  47   44  44   217  229  43.4  45.8
     X. 40  39   24  25   19  21   21  23   18  25   122  133  24.4  26.6
    XI. 51  53   52  50   42  42   42  42   42  42   229  229  45.8  45.8

       334 349  373 356  344 331  303 359  341 359  1695 1754  30.8 31.9

    The Arabic numerals at the head of the columns refer, in every
    table, to the corresponding numerals designating the objects
    in the diagram accompanying the table.

    _L_: left-hand object.
    _R_: right-hand object.

    The Roman numerals (_I_ to _XI_) indicate the different
    subjects. The same subjects appear in all the experiments, and
    under the same designation. Two of the subjects, _IV_ and
    _VIII_, are women.

    The numbers under _L_ and _R_ denote the number of seconds
    during which the left-hand image and the right-hand image,
    respectively, were present in the period of introspection (60
    seconds).

    General average: _L_, 30.8 sec.; _R_, 31.9 sec.


[Illustration: FIG. 1.]


_Series No. 1._--For the purpose of obtaining something that might
serve as a standard of comparison, a series of observations was made
in which the members of every pair were exact duplicates of each
other, and were presented under exactly the same conditions, spatial
position of course excepted. The records of these observations are for
convenience placed first as Table I.

In treating the facts recorded in the accompanying tables as phenomena
of inhibition no assumption is implied, it may be well to repeat, that
the ideational images are forces struggling with each other for
mastery. Nor is it implied, on the other hand, that they are wholly
unconditioned facts, unrelated to any phenomena in which we are
accustomed to see the expression of energy. Inhibition is meaningless
save as an implication of power lodged somewhere. The implication is
that these changes are conditioned and systematic, and that among the
conditions of our ideas, if not among the ideas themselves, power is
exerted and an inferior yields to a superior force. Such force, in
accordance with our general presupposition, must be neural or
cerebral. Even mental inhibition, therefore, must ultimately refer to
the physical conditions of the psychical fact. But the reference, to
have any scientific value, must be made as definite as the case will
allow. We must at least show what are the conditions under which a
state of consciousness which might otherwise occur does not occur.
When such conditions are pointed out, and then only, we have a case of
what has been called psychical inhibition; and we are justified in
calling it inhibition because these are precisely the conditions under
which physiological inhibition may properly be inferred. And, we may
add, in order that the conditions may be intelligibly stated and
compared they must be referable to some objective, cognizable fact.
Here the accessible facts, the experiential data, to which the
psychical changes observed and the cerebral changes assumed may both
be referred, are visual objects, namely, the figures already
described.

What may occur when these objects are precisely alike, and are seen
under conditions in all respects alike except as to spatial position,
is indicated in Table I. The general average shows that the image
referred to the left-hand object was seen some 30 seconds per minute;
that referred to the right-hand image, some 31 seconds. Sometimes
neither image was present, sometimes both were reported present
together, and the time when both were reported present is included in
the account. In this series it appears, on the whole, that each image
has about the same chance in the ideational rivalry, with a slight
preponderance in favor of the right. Individual variations, which may
be seen at a glance by inspection of the averages, show an occasional
preponderance in favor of the left. But the tendency is, in most
cases, towards what we may call right-handed ideation.

_Series No. II._--In the second series (Table II.) we find that, other
things being equal, _an increase in the relative complexity of the
outline favors the return of the image to consciousness_. Including
the time when both images were reported present at once, the simpler
appears but 27 seconds per minute as against 34 seconds for the more
complex. No attempt was made to arrange the figures on any regularly
increasing scale of complexity so as to reach quantitative results.
The experiment was tentative merely.


TABLE II.

              1            2             3             4
          S     C       S     C       S     C       S      C
     I.  21.5  23.5    14.5  35      22.5  21.5    15     27
    II.  35.5  21.5    32.5  48      32    33.5    32.5  21.5
   III.  27.5  39      20.5  47.5    24.5  46.5     8    22.5
    IV.  31.5  26.5    38    23.5    34.5  22      24    29.5
     V.  48    50      48    39.5    41.5  51.5    51    47.5
    VI.  11.5  35      26.5  28.5    21    33      29    17
   VII.  29.5  35      47    47      10.5  52      29.5  33.5
  VIII.  12.5  41      32    28.5    13    26.5    17    41.5
    IX.  10.5  25.5    27.5  34.5    14.5  44      33    44.5
     X.  24    25.5    20    23      16.5  28      23    21
    XI.  46    46.5    31.5  53.5    18    53.5    27    50.5

        298   369     338   408.5   248.5  412    289   356

                5              6             7               Averages.
          S     C       S     C       S      C              S      C
     I.  20.5  21      14.5  27      7.5    37.5          16.57  27.50
    II.  31.5  32      50    45.5    49.5   39.5          37.64  34.50
   III.  19.5  32.5    13    31      29     18            20.28  33.85
    IV.  40.5  46.5    27    30.5    26     32            31.64  30.07
     V.  47.5  47.5    50.5  48.5    38     38            46.35  46.07
    VI.  14.5  29      14    33      21     28.5          19.64  29.14
   VII.  25.5  43      42.5  30      28     41.5          30.35  40.28
  VIII.   8    34      24    27      33     14.5          19.92  30.42
    IX.  41.5  27      29.5  27.5    29.5   28            26.57  33.00
     X.  10.5  36.5    17    27      18     25            18.42  26.57
    XI.  21.5  53.5    40.5  43.5    30     45            30.64  49.42

        281   402.5   322.5 370.5   309.5  347.5          27.10  34.62

    _S:_ Outline simple.

    _C:_ Outline complex.

    In this and the following tables the numbers in the body of
    the columns represent, in each case, the combined result of
    two observations, in one of which the simpler figure was to
    the left, in the other the more complex. The figures were
    transposed in order to eliminate any possible space error.

    General average: _S_, 27.10 sec.; _C_, 34.62 sec.


Can anything be said, based on the reports, by way of explanation of
the advantage which complexity gives? In the first place, the attitude
of the subject towards his image seems to have been much the same as
his attitude towards an external object: to his observation the image
became, in fact, an object. "When the image was gone," says one, "my
eyes seemed to be in search of something." And occasionally the one
ideated object was felt to exert an influence over the other. "The
complex seemed to affect the form of the simpler figure." "It seemed
that the complex actually had the effect of diminishing the size of
the simpler figure." From time to time the images varied, too, in
distinctness, just as the objects of perception vary, and the superior
distinctness of the more complex was frequently noted by the subjects.
Now the importance of the boundary line in perception is well
understood. It seems to have a corresponding importance here. "What I
notice more in the simple figure," says one observer, "is the mass; in
the complex, the outline." "The simple seemed to lose its form," says
another, "the complex did not; the jagged edge was very distinct." And
it is not improbable, in view of the reports, that irregularities
involving change of direction and increase in extent of outline
contributed mainly to the greater persistence of the more complicated
image, the 'mass' being in both figures approximately the same. Nor
did the advantage of the broken line escape the notice of the subject.
"I found myself," is the comment of one, "following the contour of the
star--exploring. The circle I could go around in a twinkle." Again,
"the points entered the field before the rest of the figure." And
again, "the angle is the last to fade away."

[Illustration: FIG. 2.]

Now this mental exploration involves, of course, changes in the
direction of the attention corresponding in some way to changes in the
direction of the lines. Does this shifting of the attention involve
ideated movements? There can be little doubt that it does. "I felt an
impulse," says one, "to turn in the direction of the image seen." And
the unconscious actual movements, particularly those of the eyes,
which are associated with ideated movements, took place so often that
it is hard to believe they were ever wholly excluded. Such movements,
being slight and automatically executed, were not at first noticed.
The subjects were directed, in fact, to attend in all cases primarily
to the appearance and disappearance of the images, and it was only
after repeated observations and questions were put, that they became
aware of associated movements, and were able, at the close of an
observation, to describe them. After that, it became a common report
that the eyes followed the attention. And as we must assume some
central influence as the cause of this movement, which while the eyes
were closed could have no reflex relation to the stimulus of light, we
must impute it to the character of the ideas, or to their physical
substrates.

The idea, or, as we may call it, in view of the attitude of the
subject, the internal sensory impression, thus seems to bear a double
aspect. It is, in the cases noted, at once sensory and motor, or at
any rate involves motor elements. And the effect of the activity of
such motor elements is both to increase the distinctness of the image
and to prolong the duration of the process by which it is apprehended.
The sensory process thus stands in intimate dependence on the motor.
Nor would failure to move the eyes or any other organ with the
movement of attention, if established, be conclusive as against the
presence of motor elements. A motor impulse or idea does not always
result in apparent peripheral movement. In the suppressed speech,
which is the common language of thought, the possibility of incipient
or incomplete motor innervations is well recognized. But where the
peripheral movement actually occurs it must be accounted for. And as
the cause here must be central, it seems reasonable to impute it to
certain motor innervations which condition the shifting of the mental
attitude and may be incipient merely, but which, if completed, result
in the shifting of the eyes and the changes of bodily attitude which
accompany the scrutiny of an external object. And the sensory process
is, to some extent at least, conditioned by the motor, if, indeed, the
two are anything more than different aspects of one and the same
process.[7]

   [7] Cf. Münsterberg, H.: 'Grundzüge d. Psychologie,' Bd. I.,
   Leipzig, 1900, S. 532.

But where, now, the subject is occupied in mentally tracing the
boundaries of one of his two images he must inhibit all motor
innervations incompatible with the innervations which condition such
tracing: the rival process must cease, and the rival image will fade.
He may, it is true, include both images in the same mental sweep. The
boundary line is not the only possible line of movement. In fact, we
may regard this more comprehensive glance as equivalent to an
enlargement of the boundaries so as to include different mental
objects, instead of different parts of but one. Or, since the
delimitation of our 'objects' varies with our attitude or aim, we may
call it an enlargement of the object. But in any case the mental
tracing of a particular boundary or particular spatial dimensions
seems to condition the sense of the corresponding content, and through
inhibition of inconsistent movements to inhibit the sense of a
different content. No measure of the span of consciousness can, of
course, be found in these reports. The movements of the attention are
subtle and swift, and there was nothing in the form of the experiments
to determine at any precise instant its actual scope. All we need
assume, therefore, when the images are said to be seen together, is
that neither has, for the time being, any advantage over the other in
drawing attention to itself. If in the complete observation, however,
any such advantage appears, we may treat it as a case of inhibition.
By definition, an idea which assumes a place in consciousness which
but for itself, as experiment indicates, another might occupy,
inhibits the other.

[Illustration: FIG. 3.]


TABLE III.

            1           2           3           4           5           6
         S     L     S     L     S     L     S     L     S     L     S    L
     I. 22    24    19.5  23    20    26    21.5  21    21    26    18   31
    II. 31    39    31.5  36    15    32.5  11    22.5  13.5  24.5   7.5 23
   III. 10.5  43.5  12    21.5  13    14.5  19    10.5  18.5  30.5   7   18.5
    IV. 34.5  29.5  29.5  24    40.5  33    30.5  32.5  15    30    26   30
     V. 31.5  30    42    45    39    51    47    49.5  41    37    46   45
    VI. 22    20    20.5  22    23.5  22    25    16    24    20    22   25.5
   VII. 53.5  53.5  23.5  23.5  47.5  47.5  51    52    52.5  53    51   52
  VIII. 34    40.5  23    29    21    22    22    37.5  34.5  35    27.5 28
    IX. 19.5  45    19.5  46    22    23.5  23.5  48    26    45.5  19   44.5
     X. 16    30.5  12    35    21    24.5   8.5  41    15.5  33    19   28
    XI. 38.5  36.5  21    48.5  30    54.5  31    55.5  32    54    12   50

       313   392   254   353.5 292.5 381.5 290   386   293.5 388.5 255  375.5

            7           8           9          10             Averages
         S     L     S     L     S     L     S     L          S      L
     I. 20.5  31.5  21.5  28.5  22.5  28    22.5  26        20.90  26.50
    II. 14.5  17.5  19    20    11     4.5   7    30.5      16.10  25.00
   III. 10    22     8.5  26    17    16     8    16        12.35  21.90
    IV. 27.5  28.5  35    30.5  23.5  46    27.5  49.5      28.95  33.35
     V. 40.5  35    24.5  22.5  21    31    21.5  21.5      35.40  36.75
    VI. 22.5  18.5  11.5  21    20    27    22.5  24        21.35  21.60
   VII. 44.5  46.5  52    51    33.5  49    39.5  50.5      44.85  47.85
  VIII. 19.5  20    21    27    19.5  27.5  18.5  22.5      24.05  29.60
    IX. 18.5  46    13    42    20    42    18.5  43        19.95  44.90
     X. 18.5  24    20.5  21    20.5  22    18.5  28.5      17.00  28.75
    XI. 21    49    32    53.5  38    53.5  34.5  46.5      29.00  50.15

       257.5 338.5 258.5 343   246.5 346.5 238.5 358.5      24.54  33.30

    _L_: large.     _S_: small.

    General average, _S_, 24.54 sec.; _L_, 33.30 sec.


_Series No. III._--In the third series, where the variant is the
extent of (gray) surface exposed, the preponderance is in favor of the
image corresponding to the larger object. This shows an appearance of
some 33 seconds per minute as against 24 for the smaller (Table III.).
Here the most obvious thing in the reports, aside from the relative
durations, is the greater vividness of the favored image. Something,
no doubt, is due to the greater length of boundary line and other
spatial dimensions involved in the greater size. And it is this
superiority, and the ampler movements which it implies, which were
probably felt by the subject who reports 'a feeling of expansion in
the eye which corresponds to the larger image and of contraction in
the other.' But the more general comment is as to the greater
vividness of the larger image. "The larger images seem brighter
whichever side they are on." "The larger is a little more distinct, as
if it were nearer to me." "Large much more vivid than small." Such are
the reports which run through the series. And they point, undoubtedly,
to a cumulative effect, corresponding to a well-known effect in
sensation, in virtue of which greater extension may become the
equivalent of greater intensity. In other words, the larger image made
the stronger impression. Now in external perception the stronger
impression tends to hold the attention more securely; that is, it is
more effective in producing those adjustments of the sensory organs
which perceptive attention implies. So here what was noticed as the
superior brightness and distinctness of the larger image may be
supposed to imply some advantage in the latter in securing those
adjustments of the mental attitude which were favorable to the
apprehension of that image. Advantage means here, again, in part at
least, if the considerations we have urged are sound, inhibition of
those motor processes which would tend to turn attention to a rival.
And here, again, the adjustment may reach no external organ. An
incipient innervation, which is all that we need assume as the
condition of a change of mental attitude, would suffice to block, or
at least to hamper, inconsistent innervations no more complete than
itself.

[Illustration: Fig. 4.]


TABLE IV.

              1            2            3            4
           G     W      G     W      G     W      G     W
     I.   15.5  28.5   21.5  32.5   20    33     21    28.5
    II.   39.5  23     22.5  22.5   19    20.5   35.5  17.5
   III.   13.5  12.5   32     4.5    8.5  10     11.5  11.5
    IV.   30    33.5   38    36.5   36    39.5   37.5  13.5
     V.   33.5  32.5   34.5  32     33    35     45    36.5
    VI.   15    22     21    21     18.5  22     12    22
   VII.   53.5  50     43    46     54.5  55     56    56
  VIII.   15.5  24.5   24    25     20    13     16.5  21
    IX.   17.5  44      9.5  46     18.5  43.5   16    42
     X.   25.5  19     29.5  19     21    20.5   23.5  18
    XI.   35    42.5   13    29.5   18.5  46     16    38
         294   332    288.5 314.5  267.5 338    290.5 304.5

              5             6          7             8
           G     W      G     W      G     W      G     W
     I.   24    26.5   23.5  25     19.5  30.5   21    29
    II.   21    29.5   20    18.5   29    16.5   28.5  14
   III.   20.5   8.5   11    11.5   10    14     23    16.5
    IV.   39.5  28.5   34.5  22.5   23    30.5   33.5  18
     V.   45    53     48    51     45    29     32.5  34.5
    VI.   21.5  28     18    32     20.5  19     21.5  18
   VII.   54.5  56     54.5  54.5   45    46     49    49
  VIII.   24    26.5   23.5  22.5   24    17.5   31    31.5
    IX.   16    44     14    43.5    9    43.5   13    44.5
     X.   24.5  18     24    21.5   25.5  24     22    22.5
    XI.   20.5   8.5   15    36.5   33    23     34    29
         311   327    286   339    283.5 293.5  309   306.5

              9            10           11            12        Averages.
           G     W       G     W      G     W     G     W        G      W
     I.   25    25.5   22.5  21     25    26.5   27    21.5   22.95    27.33
    II.   20    25     15    20     29    32     13.5  20     24.37    21.58
   III.   12    20     12.5  17.5   10.5  21      3    23     14.00    14.25
    IV.   33    19.5   35.5  28     21.5  34.5   25.5  26.5   32.29    27.58
     V.   51    50     35    30.5   40.5  54.5   45.5  52.5   40.70    40.91
    VI.   13    29.5   25    33.5   28.5  23     23.5  27.5   19.83    24.79
   VII.   46.5  39.5   38.5  44.5   43.5  47.5   42.5  34.5   48.41    48.20
  VIII.   17.5  25.5   22    15.5   21    29     22.5  21.5   21.79    22.75
    IX.   13    43.5   12.5  41.5   15    42     11    40     13.75    43.16
     X.   24    24     27    19     25    21.5   23.5  23.5   24.58    20.87
    XI.   13.5  49      2.5  43     14    34     23    22     19.83    33.41
         268.5 351    248   314    273.5 365.5  260.5 312.5   25.61    29.53

   _G:_ Gray.            _W:_ White.

   General average: _G_, 25.61 sec.; _W_, 29.53 sec.


_Series No. IV._--This and the next following series do not suggest
much that differs in principle from what has been stated already. It
should be noted, however, that in the white-gray series (Table IV.)
the persistence of the gray in ideation surprised the subjects
themselves, who confessed to an expectation that the white would
assert itself as affectively in ideation as in perception. But it is
not improbable that affective or æsthetic elements contributed to the
result, which shows as high a figure as 25 seconds for the gray as
against 29 for the white. One subject indeed (IV.) found the gray
restful, and gives accordingly an individual average of 32 for the
gray as against 27 for the white. More than one subject, in fact,
records a slight advantage in favor of the gray. And if we must admit
the possibility of a subjective interest, it seems not unlikely that a
bald blank space, constituting one extreme of the white-black series,
should be poorer in suggestion and perhaps more fatiguing than
intermediate members lying nearer to the general tone of the ordinary
visual field. Probably the true function of the brightness quality in
favoring ideation would be better shown by a comparison of different
grays. The general average shows, it is true, a decided preponderance
in favor of the white, but the individual variations prove it would be
unsafe to conclude directly, without experimental test, from the laws
of perception to the laws of ideation.


_Series No. V._--The fifth series, which was suggested by the second,
presents the problem of the lines in greater simplicity than the
second; and, unlike the earlier series, it shows in all the individual
averages the same sort of preponderance as is shown in the general
average (straight line, 31; broken line, 38). The footings of the
columns, moreover, show an aggregate in favor of the broken line in
the case of every pair of lines that were exposed together. The
results in this case may therefore be regarded as cleaner and more
satisfactory than those reached before, and come nearer, one may say,
to the expression of a general law. The theoretical interpretation,
however, would be in both cases the same.

[Illustration: FIG. 5.]


TABLE V.

             1         2          3          4          5           6
          L    A     L    A     L    A     L    A     L     A     L    A
     I.  28   26.5  24.5 29.5  25   28    26   28.5  26    29.5  25.5 29.5
    II.  35   41.5  42   34.5  31.5 47.5  53   50.5  52    52    48   48
   III.  16.5 19.5  24   29    41   29.5  35.5 29    21    40    39   40
    IV.  40   41.5  37   45    32.5 45.5  36.5 43.5  33.5  38    36.5 43.5
     V.  49   53    45   47    45.5 36.5  32.5 51    37    46    40   51
    VI.  18   31.5  16   45    22.5 30.5  25   25    24.5  37    25   22
   VII.  43   39.5  52   54.5  52.5 53.5  51   54.5  40.5  55    48   48.5
  VIII.  23   23    27   29.5  38   40    34.5 32    23    37    42   38.5
    IX.  23   48    48   47.5  35   46.5  48   35    28.5  48    46.5 34.5
     X.  18   33    19.5 31.5  20.5 30    22   29.5  16.5  35.5  19.5 33
    XI.  22.5 33.5  18   41    26   23    19   35.5   5    38     7   50.5

        316  390.5 353  434   370  410.5 383  414   307.5 456   377   439

            Averages.
          L         A
     I. 25.83     28.58
    II. 43.58     45.66
   III. 29.50     31.16
    IV. 36.00     42.83
     V. 41.50     47.41
    VI. 21.83     31.83
   VII. 47.83     50.91
  VIII. 31.25     33.33
    IX. 38.16     43.25
     X. 19.33     32.08
    XI. 16.25     36.91

        31.91     38.54

    _L_: Line (straight line).     _A_: Angle (broken line).

    General average: _L_, 31.91 sec.; _A_, 38.54 sec.


TABLE VI.

            1           2           3           4           5          6
         P     M     P     M     P     M     P     M     P     M    P     M
     I. 22    32.5  23.5  32    23.5  32    22.5  32.5  23.5  31.5 21    39
    II. 24.5  32.5  31.5  49.5  32    39    36    36    33.5  42   28.5  35
   III.  8.5  23.5   0    36     0    31.5  11.5   5.5   8.5  14    3.5   8.5
    IV. 30    49.5  30.5  42    24    48    27.5  44    28    40.5  43.5 34.5
     V. 55.5  55.5  54.5  54.5  46.5  53    34    36    41.5  47    31   35.5
    VI. 19.5  22.5  19.5  28    19.5  28.5  26.5  27.5  24.5  29.5  18.5 36
   VII. 45    56.5  47.5  55.5  40.5  40    48    54    33.5  50    41   42.5
  VIII. 19.5  24     0    40    27.5  20.5  13.5  23    16    25    23   34.5
    IX. 28    49.5  26.5  48.5  27.5  45    18    45    21.5  48.5  42.5 44.5
     X.  8    43.5  22    29     8.5  43.5   9.5  42.5  16    35    12.5 40.5
    XI.  5.5  42.5   7.5  35.5  16.5  35.5   7.5  41    10    41.5   8   32.5

       24.18 39.27 23.91 40.95 24.18 37.86 23.14 35.18 23.32 36.77 24.82 34.82

     Indiv. Aver.
           P       M
     I. 22.666  33.250
    II. 31.000  39.000
   III.  5.333  19.833
    IV. 30.583  43.083
     V. 43.833  46.916
    VI. 21.333  28.666
   VII. 42.583  49.750
  VIII. 16.583  27.833
    IX. 27.333  46.833
     X. 12.750  39.000
    XI.  9.166  38.083

        23.92   37.48

   _P_: Plain.            _M_: Marked.

   General average: Plain, 23.92 sec.; Marked, 37.48 sec.


Series No. VI._--Both the figures in each pair of this series were of
the same material (granite-gray cardboard) and of the same area and
outline, but the content of one of the two was varied with dark lines
for the most part concentric with the periphery.

The advantage on the side of the figures with a varied content is
marked, the general averages showing a greater difference than is
shown in any of the tables so far considered. And the advantage
appears on the same side both in the individual averages and in the
averages for the different pairs as shown at the foot of the columns.
There can be little doubt, accordingly, that we have here the
expression of a general law.

For the meaning of this law we may consult the notes of the subjects:
'The plain figure became a mere amorphous mass;' 'the inner lines
reinforce the shape, for while previously the number of points in this
star has increased (in ideation), here the number is fixed, and fixed
correctly;' 'my attention traversed the lines of the content, and
seemed to be held by them;' 'the variety of the marked objects was
felt as more interesting;' 'the attention was more active when
considering the marked figures, passing from point to point of the
figure;' 'the surface of the plain figure was attended to as a whole
or mass, without conscious activity;' 'in the plain figure I thought
of the gray, in the marked figure I thought of the lines;' 'part of
the plain figure tended to have lines.'

The part played by the motor elements previously referred to in
sustaining attention and prolonging (internal) sensation is here
unmistakable. We have further evidence, too, of the value of the line
in defining and strengthening the mental attitude. In a mass of
homogeneous elements such as is presented by a uniform gray surface,
the attention is equally engaged by all and definitely held by none.
Monotony therefore means dullness. And the inhibition of incompatible
attitudes being as weak and uncertain as the attitudes actually but
loosely assumed, the latter are readily displaced, and the sensation
to which they correspond as readily disappears. Hence the greater
interest excited by the lined figures. The lines give definiteness and
direction to the attention, and as definitely inhibit incompatible
attitudes. And the shutting out of the latter by the spontaneous
activity of the mind means that it is absorbed or interested in its
present occupation.


TABLE VII.

             1           2           3           4           5           6
          5    10     5    10     5    10     5    10     5    10     5    10
     I. 29.5  23    24.5  21.5  27    18.5  28    26    27    20    25    29.5
    II. 25.5  21    32.5  42.5  19.5  33    27    33.5  26    32    20    28.5
   III.  4.5  18.5  12.5   5.5   0     3.5   7.5  11    10.5  18.5   0     7
    IV. 33    31.5  28    32    42    44    25    45    38.5  43    41    36.5
     V. 35    40.5  35    52.5  28    49.5  43    31    42.5  29    47.5  50.5
    VI. 10.5  34.5  10.5  34.5  23    15    26    26.5  22    27    19.5  34.5
   VII. 27    42    28.5  19    31.5  49    39    45.5  28.5  50.5  49.5  51.5
  VIII. 13.5  21.5  19    15    21.5  18    23    22.5  19.5  18    24.5  21.5
    IX. 33    43.5  36    37.5  35    40    26    45    31.5  44    21.5  43.5
     X. 20.5  23    22.5  23    23    23.5  22    27.5  21.5  29    21    34.5
    XI. 13.5  29    32    16.5   9.5  36.5  40.5   8.5  39.5   8.5  17.5  30.5

        22.32 31.50 25.55 27.23 23.64 30.05 27.91 29.27 27.91 29.05 26.09 33.45

             7           8           9          10          11          12
          5    10     5    10     5    10     5    10     5    10     5    10
     I. 22.5  29    27.5  25.5  26    22    22.5  27.5  25.5  25    22    28
    II. 29    37.5  32.5  28    34    32    26    23    30.5  28    25.5  23
   III. 20.5   8.5  12    16.5  21     9    32     3    21.5  15     8    22
    IV. 31    26    39.5  41.5  37    29.5  28.5  37    36.5  30.5  33    31.5
     V. 38    34    39    46.5  54    40    32.5  46    43.5  46    36.5  50.5
    VI. 30    17    13    25    34.5  26.5  20.5  27    27    35    27.5  33
   VII. 55.5  50    42.5  28    50.5  15.5  49    17.5  43.5  29.5  44    26.5
  VIII. 16.5  21.5  18    17    17.5  21.5  21    22.5  21.5  23.5  23    27.5
    IX. 41    46    45.5  43.5  46.5  33    39    37.5  32    35    33.5  40
     X. 24.5  28.5  26.5  24    28.5  25.5  25.5  25    22    30    24    23.5
    XI. 19.5  26.5  14    30    42.5   2.5  21.5  30    22.5  33    25.5  24

       29.82  29.50 28.18 29.59 35.64 23.36 28.91 26.91 29.64 30.05 27.50 29.96

          Indiv. Aver.
           5       10
     I. 25.58     24.62
    II. 27.33     30.16
   III. 12.50     11.50
    IV. 34.41     35.66
     V. 39.54     43.00
    VI. 22.00     27.95
   VII. 40.75     35.37
  VIII. 19.87     20.83
    IX. 35.04     40.70
     X. 23.45     26.41
    XI. 24.83     22.95

        27.75     29.15

    5: refers to object exposed 5 seconds.
   10: refers to object exposed 10 seconds.

   General average: (5), 27.75 sec.; (10), 29.15 sec.


_Series No. VII._--The object of this series was to determine the
effect in ideation of exposing for unequal lengths of time the two
objects compared. The figures compared were of the same area and
outline, and were distinguished only by their color, one being red and
the other green. These colors were employed, after a preliminary test,
as showing, on the whole, to nearly equal advantage in the individual
choice of colors. The shorter exposure was five seconds and the longer
exposure ten seconds. The color that was to be seen the longer time
was exposed first alone; after five seconds the other was exposed; and
then both were seen for five seconds together, so that neither might
have the advantage of the more recent impression. The two colors were
regularly alternated, and in one half of the series the longer
exposure was to the right, in the other half to the left. The extra
five seconds were thus in each case at the beginning of the
experiment.

The general averages show only a slight advantage in favor of the
color which was exposed the longer time, namely, 29.15 seconds, as
against 27.75 seconds. It is not easy to believe that the advantage of
sole occupancy of the visual field for five seconds, without any
offsetting disadvantage in the next five seconds, should have so
slight an effect on the course of ideation. And it is not improbable
that there was an offsetting disadvantage. In the presence of color
the subject can scarcely remain in the attitude of quiet curiosity
which it is easy to maintain in the observation of colorless objects.
A positive interest is excited. And the appearance of a new color in
the field when there is another color there already seems to be
capable of exciting, by a sort of successive contrast different from
that ordinarily described, an interest which is the stronger from the
fact that the subject has already been interested in a different
color. That is to say, the transition from color to color (only red
and green were employed) seems to be more impressive than the
transition from black to color. And, under the conditions of the
experiment, the advantage of this more impressive transition lay
always with the color which was exposed the shorter time.

Judging from the introspective notes, the outline seems to suffer, in
competition with a colored content, some loss of power to carry the
attention and maintain its place in the ideation. "The colors tend to
diffuse themselves, ignoring the boundary," says one. "The images fade
from the periphery toward the center," says another. On the other
hand, one of the subjects finds that when both images are present the
color tends to fade out. This may perhaps be explained by the remark
of another subject to the effect that there is an alternate shifting
of the attention when both images are present. An attitude of
continued and definite change, we may suppose, is one in which the
color interest must yield to the interest in boundaries and definite
spatial relations.

Other interesting facts come out in the notes. One subject finds the
ideated plane farther away than the objective plane; another conceives
the two as coinciding. The movement of the eyes is by this time
distinctly perceived by the subject. The reports run as follows:
'Eye-movements seem to follow the changes in ideation;' 'I find my
eyes already directed, when an image is ideated, to the corresponding
side, and am sometimes conscious of the movement, but the movement is
not intended or willed;' 'in ideating any particular color I find my
attention almost always directed to the side on which the
corresponding object was seen.' This last observation seems to be true
for the experience of every subject, and, generally speaking, the
images occupy the same relative positions as the objects: the image of
the right object is seen to the right, that of the left object to the
left, and the space between the two remains tolerably constant,
especially for the full-faced figures.

This fact suggested a means of eliminating the disturbing influence of
color, and its contrasts and surprises, by the substitution of gray
figures identical in form and size and distinguished only by their
spatial position. The result appears in the table which follows
(VIII.).

_Series No. VIII._--The object of this experiment was the same as that
of No. VII. Granite-gray figures, however, were substituted, for the
reasons already assigned, in place of the red and green figures. And
here the effect of additional time in the exposure is distinctly
marked, the general averages showing 32.12 seconds for the image of
the object which was exposed 10 seconds, as against 25.42 seconds for
the other.


TABLE VIII.

         1           2           3           4           5       Indiv. Aver.
       5     10    5     10    5     10    5     10    5     10    5     10
   I. 26.5  27    24.5  30.5  26.5  28    27.5  27.5  26.5  29    26.3  28.4
  II. 32.5  38.5  27    36    29    28    17    14.5  37.5  27    28.6  28.8
  III. 4.5  13.5  11     1.5  10    11     7.5  14.5  12.5   8.5   9.1   9.8
  IV. 23.5  40.5  27.5  34    35.5  38    35    28    17    39    27.7  35.9
   V. 41    46    50    51.5  43    42.5  46    35.5  31.5  44    42.3  43.9
  VI.  7.5  27    18    25    21.5  25.5   7    44.5  33.5  19    17.5  28.2
VIII. 24.5  27    34.5  32    36.5  36    34.5  38.5  28    28.5  31.6  32.4
  IX. 17    46    25.5  47.5  44    47    40.5  47.5  48    48    35.0  47.2
   X. 20    29    21    26.5  25.5  24.5  27.5  22    19.5  23.5  22.7  25.1
  XI. 11    41.5   9.5  50     5.5  43.5  15.5  40.5  25.5  32    13.4  41.5
      20.80 33.60 24.85 33.45 27.70 32.40 25.80 31.30 27.95 29.85 25.42 32.12

    VII.--Absent.

     5: refers to object exposed 5 seconds.
    10: refers to object exposed 10 seconds.

    General average: (5), 25.42 sec.; (10), 32.12 sec.


The interpretation of this difference may be made in accordance with
the principles already laid down. The ideated and actual movements
which favor the recurrence and persistence of an idea are, on grounds
generally recognized in psychology, much more likely to occur and
repeat themselves when the corresponding movements, or the same
movements in completer form, have frequently been repeated in
observation of the corresponding object.


TABLE IX.

      1           2           3           4           5          Indiv. Aver.
      1st   2d    1st   2d    1st   2d    1st   2d    1st   2d    1st   2d
   I. 22.5  32.5  27    28    26.5  28    26.5  27.5  26    29    25.7  29.0
  II.  4.5  43     9    29     3.5  38     0    43    17    44.5   6.8  39.5
 III.  0    22     0    20.5   9.5  16.5   0    23.5   3.5   9.5   2.6  18.4
  IV.  0    31     1    35.5   4.5  39    16.5  32.5  16    20.5   7.6  31.7
   V. 24    52.5  41.5  40    12    53.5  22    55    22    50.5  24.3  50.3
 VII.  1.5  52     0    48     0    54.5   0    50.5   0    46.5   0.3  50.3
VIII. 12    26    10    27.5  11.5  23.5  13.5  28.5  15.5  20    12.5  25.1
  IX. 24    43.5  20    42    25    42.5  20.5  44.5  28    42.5  23.5  43.0
   X.  9    45.5  19.5  30    11    33    12    38    14.5  30    13.2  35.3
  XI. 12.5  35    23.5  29.5   1    49     2    44    10.5  52     9.9  41.9
      11.00 38.30 15.15 33.00 10.45 37.75 11.30 38.70 15.30 34.50 12.64 36.45

    VI.--Absent.

    From this point on the place of Miss H. (IV.) is taken by Mr.
    R. The members in each pair of objects in this group were not
    exposed simultaneously.

    1st: refers to object first exposed.
    2d: refers to object last exposed.

    General average: 1st, 12.64 sec.: 2d, 36.45 sec.


What is here called ideated movement--by which is understood the idea
of a change in spatial relations which accompanies a shifting of the
attention or a change in the mental attitude, as distinguished from
the sense of movements actually executed--was recognized as such by
one of the subjects, who says: "When the two objects are before me I
am conscious of what seem to be images of movement, or ideated
movements, not actual movements." The same subject also finds the
image of the object which had the longer exposure not only more vivid
in the quality of the content, but more distinct in outline.


_Series No. IX._--In this experiment the objects, which were of
granite-gray cardboard, were exactly alike, but were exposed at
different times and places. After the first had been exposed five
seconds alone, it was covered by means of a sliding screen, and the
second was then exposed for the same length of time, the interval
between the two exposures being also five seconds. Two observations
were made with each pair, the first exposure being in one case to the
left and in the other case to the right. The object here was, of
course, to determine what, if any, advantage the more recent of the
two locally different impressions would have in the course of
ideation. The table shows that the image of the object last seen had
so far the advantage in the ideational rivalry that it remained in
consciousness, on the average, almost three times as long as the
other, the average being, for the first, 12.64 seconds; for the
second, 36.45 seconds. And both the individual averages and the
averages for the several pairs show, without exception, the same
general tendency.

The notes show, further, that the image of the figure first seen was
not only less persistent but relatively less vivid than the other,
though the latter was not invariably the case. One subject had 'an
impression that the images were farther apart' than in the series
where the exposure of the two objects was simultaneous, though the
distance between the objects was in all cases the same, the time
difference being, apparently, translated into spatial terms and added
to the spatial difference. The sort of antagonism which temporal
distinctions tend, under certain conditions, to set up between ideas
is illustrated by the remark of another subject, who reports that 'the
attention was fairly dragged by the respective images.' And the fact
of such antagonism, or incompatibility, is confirmed by the extremely
low figure which represents the average time when both images were
reported present at the same time. The two images, separated by
processes which the time interval implies, seem to be more entirely
incompatible and mutually inhibitory than the images of objects
simultaneously perceived. For not only does the advantage of a few
seconds give the fresher image a considerable preponderance in its
claim on the attention, but even the earlier image, after it has once
caught the attention, usually succeeds in shutting out the other from
a simultaneous view.


TABLE X.

          1           2           3           4           5      Indiv. Aver.
       V     H     V     H     V     H     V     H     V     H     V     H
   I. 27.5  27    26.5  28    30.5  24.5  27.5  28.5  26    25    27.60 26.60
  II. 45    43.5  37    40    35.5  28.5  19    15.5  30.5  30.5  33.40 31.60
 III. 19    21     0    10.5  19.5  19     9    15     4.5  16    10.40 16.30
  IV. 47.5  39    36    22.5  44.5  41.5  47.5  46    37    36    42.50 37.00
   V. 56.5  46.5  42.5  42.5  48    45.5  48.5  48.5  53    52    49.70 47.00
  VI. 31.5  28.5  30.5  30.5  22    34.5  34.5  28.5  25    26.5  28.70 29.70
 VII. 55    55    55    45.5  38    20    55.5  53.5  56    56    51.90 45.80
VIII. 39.5  47    23.5  23.5  19    18.5  26.5  26.5  26    20.5  26.90 27.20
  IX. 26.5  46    38    42.5  41    44    40.5  46.5  35.5  39    36.30 43.60
   X. 24.5  25    26    25    25.5  23    23.5  28.5  32.5  20.5  26.40 24.40
  XI. 52    52    56.5  54.5  48    49.5  45    47.5  51.5  47.5  50.60 50.20

      38.60 39.14 33.77 33.09 33.77 31.68 34.27 34.95 34.31 33.60 34.94 34.49

   _V_: Vertical.           _H_: Horizontal.

   General average: Vertical, 34.94 sec.; Horizontal, 34.49 sec.


_Series No. X._--The objects used in this experiment were straight
lines, two strips of granite-gray cardboard, each ten centimeters long
and half a centimeter wide, the one being vertical and the other
horizontal. These were pasted on black cards and exposed in alternate
positions, each appearing once to the right and once to the left. The
figures in the columns represent in each case the combined result of
two such observations.

The experiments with these lines were continued at intervals through
a number of weeks, each individual average representing the result of
ten observations, or of five pairs of exposures with alternating
objects.

The striking feature in the observations is the uniformity of the
results as they appear in the general averages and in the averages for
each pair as shown at the foot of the columns. There is some variation
in the individual tendencies, as shown by the individual averages. But
the general average for this group of subjects shows a difference of
less than half a second per minute, and that difference is in favor of
the vertical line.

This series will serve a double purpose. It shows, in the first place,
that on the whole the vertical and the horizontal lines have a nearly
equal chance of recurrence in image or idea. It will serve, in the
second place, as a standard of comparison when we come to consider the
effect of variations in the position and direction of lines.


TABLE XI.

          1           2           3           4           5       Indiv. Av.
       F     O     F     O     F     O     F     O     F     O     F     O
   I. 24    31    26.5  28.5  27    29    22    33.5  27.5  28    25.4  30.0
  II. 53.5  50    52.5  52.5  56.5  55.5  43.5  43.5  56    51.5  52.4  50.6
 III.  3    21.5   4    20    11    17     3.5  27     0    20.5   4.3  21.2
  IV. 26.5  30    11    48.5  12.5  53    12    51    23    51    17.0  46.7
   V. 40.5  56.5  48    56    55.5  55.5  53    55.5  53.5  55.5  50.1  55.58
  VI. 27.5  40.5  23    31.5  24.5  32.5  31    29    27    33.5  26.6  33.4
 VII. 50.5  54    53.5  56.5  53.5  53.5  40.5  52    55    55    50.6  54.2
VIII.  1    33.5  11    27     5    32     7.5  39     4.5  36.5   5.8  33.6
  IX. 35.5  41.5  45.5  47    41.5  41.5  39    44.5  41    41.5  40.5  43.2
   X. 19    30.5  21.5  30.5  21    29.5  16    37.5  22.5  30.5  20.0  31.7
  XI. 11.5  52.5  18    51.5  14.5  50.5  23    50.5  15    52.5  16.4  51.5
      26.59 40.14 28.59 40.86 29.32 40.86 26.45 42.09 29.55 41.45 28.10 41.08

    _F_: Full-faced.         _O_: Outlined.

    General average: full-faced, 28.10 sec.; outlined, 41.08 sec.


_Series No. XI._--In this series full-faced figures were compared with
outline figures of the same dimensions and form. Material,
granite-gray cardboard. The area of the full-faced figures was the
same as that of the figures of similar character employed in the
various series, approximately 42 sq. cm.; the breadth of the lines in
the outline figures was half a centimeter. The objects in each pair
were exposed simultaneously, with the usual instructions to the
subject, namely, to regard each object directly, and to give to each
the same share of attention as to the other.

The form of the experiment was suggested by the results of earlier
experiments with lines. It will be remembered that the express
testimony of the subjects, confirmed by fair inference from the
tabulated record, was to the effect that lines show, in ideation as in
perception, both greater energy and clearer definition than surfaces.
By lines are meant, of course, not mathematical lines, but narrow
surfaces whose longer boundaries are closely parallel. To bring the
superior suggestiveness of the line to a direct test was the object of
this series. And the table fully substantiates the former conclusion.
For the outline figure we have a general average of 41.08 seconds per
minute, as against 28.10 seconds for the full-faced figure.

The notes here may be quoted as corroborative of previous statements.
"I notice," says one, "a tendency of the color in the full-faced
figure to spread over the background"--a remark which bears out what
has been said of the relative vagueness of the subjective processes
excited by a broad homogeneous surface. To this may be added: "The
full-faced figures became finally less distinct than the linear, and
faded from the outside in;" "the areal (full-faced) figure gradually
faded away, while the linear remained." Another comment runs: "I feel
the left (full-faced) striving to come into consciousness, but failing
to arrive. Don't see it; feel it; and yet the feeling is connected
with the eyes." This comment, made, of course, after the close of an
observation, may serve as evidence of processes subsidiary to
ideation, and may be compared, in respect of the motor factors which
the 'striving' implies, with the preparatory stage which Binet found
to be an inseparable and essential part of any given (vocal) motor
reaction.[8]

   [8] Binet, A. et Henri, V.: _op. citat._


_Series No. XII._--Both the figures of each pair in this series were
linear, and presented the same extent of surface (granite-gray) with
the same length of line. In other words, both figures were constituted
of the same elements, and in both the corresponding lines ran in the
same direction; but the lines in the one were connected so as to form
a figure with a continuous boundary, while the lines of the other were
disconnected, _i.e._, did not inclose a space. The total length of
line in each object was twenty centimeters, the breadth of the lines
five millimeters. Both figures were arranged symmetrically with
respect to a perpendicular axis.

[Illustration: FIG. 6.]


TABLE XII.

          1           2           3           4           5       Indiv. Av.
       L     F     L     F     L     F     L     F     L     F     L     F
   I. 31.5  24    30    24.5  23.5  32    25.5  30.5  27    29.5  27.5  28.1
  II. 55    55    56    56    56    56    56.5  56.5  54    54    55.5  55.5
 III. 22     6    26.5   9.5  31.5   1.5  23     5.5  28.5   0    26.3   4.5
  IV. 31    15    46.5  20.5  52     9.5  49     6    55    18    46.7  13.8
   V. 56    54    56    56    56    56    56.5  56.5  55.5  55.5  56.0  55.6
  VI. 33    30    34    39.5  31.5  29.5  26.5  32    26    31.5  30.2  32.5
 VII. 55.5  49.5  56.5  38    54.5  35    57.5  32.5  38    27    52.4  36.4
VIII. 26.5  15.5  21.5  13.5  25    17    25.5  21    15    13.5  22.7  16.1
  IX. 45.5  32.5  44.5  39    42.5  35.5  41.5  37.5  43    40.5  43.4  37.0
   X. 29.5  23    36.5  16    23    28.5  35.5  16.5  29    23    30.7  21.4
  XI. 52     8    49.5  19    45.5  25    43.5  21.5  15    31.5  41.1  21.0
      39.77 28.41 41.77 30.18 40.10 29.60 40.05 28.73 35.10 29.50 39.32 29.26

   L: Interrupted lines.
   F: Figure with continuous boundary. (Figure in outline.)

   General average: Lines, 39.32 sec.; figure, 29.26 sec.


The experiment was devised in further exploration of the effect of the
line in ideation. The result fully bears out, when read in the light
of the introspective notes, what has been said of the importance of
the motor element in ideation. It might have been supposed, in view of
the importance usually attached to unity or wholeness of impression in
arresting and holding the attention in external perception, that the
completed figure would have the more persistent image. The general
averages, however, stand as follows: Interrupted lines, 39.32 seconds
per minute; completed figure, 29.26 seconds per minute. The individual
averages show slight variations from the tendency expressed in these
figures, but the averages for the several pairs are all in harmony
with the general averages.

The notes furnish the key to the situation: "I felt that I was doing
more, and had more to do, when thinking of the broken lines." "The
broken figure seemed more difficult to get, but to attract attention;
continuous figure easy to grasp." "Felt more active when
contemplating the image of the broken figure." "In the broken figure I
had a feeling of jumping from line to line, and each line seemed to be
a separate figure; eye-movement very perceptible." The dominance of
the interrupted lines in ideation is evidently connected with the more
varied and energetic activity which they excited in the contemplating
mind. Apparently the attention cannot be held unless (paradoxical as
it may sound) it is kept moving about its object. Hence, a certain
degree of complexity in an object is necessary to sustain our interest
in it, if we exclude, as we must of course in these experiments,
extraneous grounds of interest. Doubtless there are limits to the
degree of complexity which we find interesting and which compels
attention. A mere confused or disorderly complex, wanting altogether
in unity, could hardly be expected to secure attention, if there is
any truth in the principle, already recognized, that the definite has
in ideation a distinct advantage over the vague. Here again the notes
suggest the method of interpretation. "The broken lines," says one,
"tended to come together, and to take the form of the continuous
figure." Another remarks: "The broken figure suggests a whole
connected figure; the continuous is complete, the broken wants to be."
In virtue of their power to excite and direct the activity of the
attention the interrupted lines seem to have been able to suggest the
unity which is wanting in them as they stand. "The broken lines," says
another, "seemed to run out and unite, and then to separate again"--a
remark which shows a state of brisk and highly suggestive activity in
the processes implied in attention to these lines. And a glance at the
diagram will show how readily the union of the broken lines may be
made. These were arranged symmetrically because the lines of the
completed figures were so arranged, in order to equalize as far as
possible whatever æsthetic advantage a symmetrical arrangement might
be supposed to secure.

It thus appears that, whatever the effect in ideation of unity in the
impression, the effect is much greater when we have complexity in
unity. The advantage of unity is undoubtedly the advantage which goes
with definiteness of impression, which implies definite excitations
and inhibitions, and that concentration of energy and intensity of
effect in which undirected activity is wanting. But a bare unity, it
appears, is less effective than a diversified unity. To what extent
this diversity may be carried we make no attempt to determine; but,
within the limits of our experiment, its value in the ideational
rivalry seems to be indisputable. And the results of the experiment
afford fresh proof of the importance of the motor element in internal
perception.


TABLE XIII.

          1           2           3           4           5       Indiv. Av.
       F     V     F     V     F     V     F     V     F     V     F     V
   I. 25    29    26    29    29.5  26.5  25.5  30    24.5  31    26.1  29.1
  II. 56    56    55    55    54    54.5  47.5  47.5  45    50    51.5  52.6
 III.  2.5   5.5   2.5   8.5   6.5   5    16.5   9.5  17    15     9.0   8.7
  IV. 48    48    31.5  31.5  31    46    51.5  51.5  35    52    39.4  45.8
   V. 54    54    56.5  52    56    56    56    56    54    56    55.3  54.8
  VI. 39    29    30    33.5  35.5  22.5  32.5  34    33.5  24.5  34.1  28.7
 VII. 46    55    54.5  46.5  46.5  50    49.5  54    47    46    48.7  50.3
VIII.  9    14.5  23    20.5  23.5  22    18    14.5  16    17    17.9  17.7
  IX. 43    43    46.5  46.5  45.5  45.5  43.5  43.5  46    47.5  44.9  45.2
   X. 28    26.5  21    29.5  26.5  26.5  21.5  31.5  25    29    24.4  28.6
  XI. 23.5  46    19.5  35.5  20    46    24    47.5  28.5  19.5  23.1  38.9
      34.00 36.95 33.27 35.27 34.05 36.41 35.09 38.14 33.77 35.23 34.03 36.40

   F: Figure (in outline).      V: Vertical lines.

   General average: Figure, 34.03 sec.; vertical lines, 36.40 sec.


_Series No. XIII._--In this series, also, both the figures of each
pair were constituted of the same elements; that is to say, both were
linear, and presented the same extent of surface (granite-gray), with
the same length of line, the total length of the lines in each figure
being twenty centimeters and the breadth of the lines being three
millimeters. But while the lines of one figure were connected so as to
form a continuous boundary, the lines of the other figure were all
vertical, with equal interspaces. And, as in the last preceding
series, the two figures were formed by a different but symmetrical
arrangement of the same lines.

As before, the advantage is on the side of the disconnected lines. In
this case, however, it is very slight, the general averages showing
34.03 seconds for the completed figure, as against 36.40 seconds for
the lines. This reduction in the difference of the averages is
probably to be explained by the reduced complexity in the arrangement
of the lines. So far as they are all parallel they would not be likely
to give rise to great diversity of movement, though one subject does,
indeed, speak of traversing them in all directions. In fact, the
completed figures show greater diversity of direction than the lines,
and in this respect might be supposed to have the advantage of the
lines. The notes suggest a reason why the lines should still prove the
more persistent in ideation. "The lines appealed to me as a group; I
tended always to throw a boundary around the lines," is the comment of
one of the subjects. From this point of view the lines would form a
figure with a content, and we have learned (see Series No. VI.) that a
space with a varied content is more effective in ideation than a
homogeneous space of the same extent and general character. And this
unity of the lines as a group was felt even where no complete boundary
line was distinctly suggested. "I did not throw a boundary around the
lines," says another subject, "but they had a kind of unity." It is
possible also that from the character of their arrangement the lines
reinforced each other by a kind of visual rhythm, a view which is
supported by the comments: 'The lines were a little plainer than the
figure;' 'figure shadowy, lives vivid;' 'the figure grew dimmer
towards the end, the lines retained their vividness.'

On the whole, however, the chances are very nearly equal in the two
cases for the recurrence of the image, and a comparison of this series
with Series No. XII. cannot leave much doubt that the greater
effectiveness of the lines in the latter is due to their greater
complexity. In view, therefore, of the fact that in both series the
objects are all linear, and that the two series differ in no material
respect but in the arrangement of the disconnected lines, the
circumstance that a reduction in the complexity of this arrangement is
attended by a very considerable reduction in the power of the lines to
recur in the image or idea is a striking confirmation of the soundness
of our previous interpretation.


_Series No. XIV._--In this series full-faced figures (granite-gray)
similar in character to those made use of in former experiments, were
employed. The objects were suspended by black silk threads, but while
one of them remained stationary during the exposure the other was
lowered through a distance of six and one half centimeters and was
then drawn up again. The object moved was first that on the right
hand, then that on the left. As the two objects in each case were
exactly alike, the comparative effect of motion and rest in the object
upon the persistence in consciousness of the corresponding image was
obtained. The result shows a distinct preponderance in favor of the
moved object, which has an average of 37.39 seconds per minute as
against 28.88 seconds for the stationary object. The averages for the
pairs, as seen at the foot of the columns, all run the same way, and
only one exception to the general tendency appears among the
individual averages.


TABLE XIV.

          1           2           3           4           5      Indiv. Av.
       S     M     S     M     S     M     S     M     S     M    S      M
   I. 22.5  28.5  25    30.5  24.5  28    28    27.5  25.5  31   25.1   29.6
  II. 47.5  55    53    42    48.5  53.5  34.5  39.5  49    52   46.5   48.4
 III.  3    18     7.5   8.5   0     7.5   0     3.5   0     4    2.1    8.3
  IV. 45    45    33.5  51.5  11    50.5  11    50     8    52.5  21.7  49.9
   V. 54.5  51    53.5  54.5  49    51    30.5  38.5  56    55    48.7  50.0
  VI. 21    32.5  26    33    29.5  37.5  30    35    30    36    27.3  34.8
 VII. 48    55    56.5  49    41.5  54.5  44.5  53    35.5  54    45.2  53.1
VIII. 10.5  20.5  20.5  25     6    33    12.5  29.5  19    18    13.7  25.2
  IX. 37.5  43.5  34.5  45    36    47.5  30    47.5  29    48.5  33.4  46.4
   X. 13    39.5  18    34    19    33.5  19    33    10.5  44    15.9  36.8
  XI. 17.5  43.5  47.5  32    27.5  36    46    16.5  52    16    38.1  28.8

      29.09 39.27 34.14 36.82 26.59 39.55 26.00 33.95 28.59 37.36 28.88 37.39

   S: Refers to figure left stationary.
   M: Refers to figure that was moved during exposure.

   General average: S, 28.88 sec.; M, 37.39 sec.


The effectiveness of a bright light or of a moving object in arresting
attention in external perception is well understood. And the general
testimony of the subjects in this experiment shows that it required
some effort, during the exposure, to give an equal share of attention
to the moving and the resting object. Table IV., however, which
contains the record of the observations in the white-gray series,
shows that we cannot carry over, unmodified, into the field of
ideation all the laws that obtain in the field of perception. The
result of the experiment, accordingly, could not be predicted with
certainty. But the course of ideation, in this case, seems to follow
the same general tendency as the course of perception: the resting
object labors under a great disadvantage. And if there is any force in
the claim that diversity and complexity in an object, with the
relatively greater subjective activity which they imply, tend to hold
the attention to the ideated object about which this activity is
employed, the result could hardly be other than it is. There can be no
question of the presence of a strong motor element where the object
attended to moves, and where the movement is imaged no less than the
qualities of the object. In fact, the object and its movement were
sometimes sharply distinguished. According to one subject, 'the image
was rather the image of the motion than of the object moving.' Again:
'The introspection was disturbed by the idea of motion; I did not get
a clear image of the moving object; imaged the motion rather than the
object.' And a subject, who on one occasion vainly searched the
ideational field for sixty seconds to find an object, reports: 'I had
a feeling of something going up and down, but no object.' Clearly an
important addition was made to the active processes implied in the
ideation of a resting object, and it would be singular if this added
activity carried with it no corresponding advantage in the ideational
rivalry. In one case the ideas of rest and of movement were curiously
associated in the same introspective act. "The figure which moved,"
says the subject, "was imaged as stationary, and yet the idea of
movement was distinctly present."

The reports as to the vividness of the rival images are somewhat
conflicting. Sometimes it is the moving object which was imaged with
the more vivid content, and sometimes the resting object. One report
runs: "The moving object had less color, but was more distinct in
outline than the stationary." Sometimes one of the positions of the
moving object was alone represented in the image, either the initial
position (on a level with the resting object) or a position lower
down. On the other hand, we read: "The image of the moved object
seemed at times a general image that reached clear down, sometimes
like a series of figures, and not very distinct; but sometimes the
series had very distinct outlines." In one case (the circle) the
image of the figure in its upper position remained, while the serial
repetitions referred to extended below. This, as might be supposed, is
the report of an exceptionally strong visualizer. In other cases the
object and its movements were not dissociated: "The moved object was
imaged as moving, and color and outline were retained." And again:
"Twice through the series I could see the image of the moving object
as it moved." "Image of moved object moved all the time."


TABLE XV.

          1           2           3           4           5     Indiv.  Av.
      Gray  Red  Gray  Yellow Gray Green  Gray  Blue Gray Violet Gray Colored.

   I. 26    29    27.5  28.5  26.5  29    21.5  27.5  27.5  26.5  25.8  28.1
  II. 35.5  36.5  45.5  53.5  53.5  53.5  53.5  53.5  55    55    48.6  50.4
 III.  0    11     2.5  19    10.5  16    17.5   8.5   0     9     6.1  12.7
  IV. 45    23.5   8    53.5  48    39    48    52    55.5  35    40.9  40.6
   V. 55.5  55.5  42    53    50    56    52.5  50    44.5  56.5  49.1  54.2
  VI. 22    33.5  29    36.5  28    43.5  26    37.5  39.5  29    28.9  36.0
 VII. 38.5  39    56    56    49.5  54.5  47    47    45.5  50    47.3  49.3
VIII. 15    10.5  15    19.5  23    21    19.5  24    20.5  25    18.6  20.0
  IX. 31.5  49    19    42.5  50    50    35.5  46    48    39    36.8  45.3
   X. 19    33    14.5  37    29.5  23    17    37.5  23    31    20.6  32.3
  XI. 11    49.5   8    51.5   9    43.5  35    43.5  24    47    17.4  47.0
      27.18 33.64 24.27 40.95 34.32 39.00 33.91 38.82 34.82 36.64 30.90 37.81

   General average: Gray, 30.90 sec.; colored, 37.81 sec.


_Series No. XV._--The figures in each pair of this series were
full-faced, and of the same shape and size, but one was gray and the
other colored, the gray being seen first to the left, and then to the
right. The colors used were of Prang's series (Gray, R., Y., G., B.,
V.). In No. 1 the figures were in the form of a six-pointed star, and
gray was compared with red. In No. 2 the figures were elliptical, and
gray was compared with yellow. In No. 3 a broad circular band of gray
was compared with the same figure in green. In No. 4 the figures were
kite-shaped, and gray was compared with blue. In No. 5 a circular
surface of gray was compared with a circular surface of violet. The
objects compared were exposed at the same time, under the usual
conditions.

As might perhaps be expected, the colored surfaces proved to be the
more persistent in ideation, showing a general average of 37.81
seconds per minute as against 30.90 seconds for the gray.

The distinctness of the process of color apprehension is reflected in
the notes: "In the colored images I find the color rather than the
form occupying my attention; the image seems like an area of color, as
though I were close to a wall and could not see the boundary;" and
then we have the significant addition, "yet I feel myself going about
in the colored area." Again: "In the gray the outline was more
distinct than in the colors; the color seems to come up as a shade,
and the outline does not come with it." Or again: "The gray has a more
sharply defined outline than the color." This superior definiteness in
outline of the gray figures is subject to exceptions, and one subject
reports 'the green outline more distinct than the gray.' And even so
brilliant a color as yellow did not always obscure the boundary: "The
yellow seems to burn into my head," says one of the subjects, "but the
outline was distinct." The reports in regard to this color (yellow)
are in fact rather striking, and are sometimes given in terms of
energy, as though the subject were distinctly conscious of an active
process (objectified) set up in the apprehension of this color. The
reports run: "The yellow has an expansive power; there seemed to be no
definite outline." "The yellow seemed to exert a power over the gray
to suppress it; its power was very strong; it seemed to be
aggressive."


TABLE XVI.

              1            2          3           4           5
           a      b     a     b     a     b     a     b     a     b
     I.    0      0     0     0     0     0     0     0     0     0
    II.   43     41    33    51    19    31    32    41    20    18
   III.    0      6     0     0     3    11    13    16     0     0
    IV.   56     28    23    35     0    11    48    56    35    25
     V.   56     55    44    44    57    30    39    32    34    30
    VI.   14      8    12    12    11     5    35    12     9     6
   VII.   52     54    56    56    51    47    56    57    47    26
  VIII.   15      0    18    21    24    39    26    10    23    21
    IX.   28     25    39    31    23    28    26    36    25    17
     X.    0      0     0     0     0     0     0     0     0     0
    XI.   52     45    41    48     7    39    50    36    48    22
          35.11  29.11 29.55 33.11 21.66 26.78 29.55 26.91 21.91 15.00


_Series No. XVI._--The course of experimentation having shown the
superior energy of lines, in comparison with surfaces, in stimulating,
directing, and holding the attention, a series of figures was devised
to test the question whether the direction of the lines would have any
effect upon the length of time during which _both_ images of a pair of
linear figures would be presented together. The materials used were
granite-gray strips half a centimeter wide. The letters (_a_) and
(_b_) at the heads of the columns refer to the same letters in the
diagram, and distinguish the different arrangements of the same pair
of objects. The figures in the body of the columns show only the
length of time during which both images were reported present in
consciousness together. At the foot of the columns are shown the
averages for each pair. No general averages are shown, as the problem
presented by each pair is peculiar to itself.

[Illustration: FIG. 7.]

The maximum is reached in No. 1_a_, where the angle has the arrowhead
form and each angle points to the other. It should be remarked that
the diagram is somewhat misleading in respect to the distance of the
figures, which in this as in the other experiments was 25 cm. The
figures therefore were far enough away from each other to be perceived
and imaged in individual distinctness. But the 'energy' of the lines,
especially where the lines united to form an acute angle, was often
sufficient to overcome the effect of this separation, and either to
bring the figures nearer together or to unite them into a single
object. The notes are very decisive in this regard. A few of them may
be cited: "The angles tended to join points." "The figures showed a
tendency to move in the direction of the apex." "The angles (2_a_)
united to form a cross." "When both figures (4_b_) were in mind I felt
disagreeable strains in the eyeballs; one figure led me to the right
and the other to the left." The effect of the last-named figures
(4_a_) seemed to be different from that of 1_a_ and 2_a_, though the
apex of each angle was turned to that of the other in each of the
three cases. "The two angles," says another subject, speaking of 4_a_,
"appeared antagonistic to each other." It will be observed that they
are less acute than the other angles referred to, and the confluent
lines of each figure are far less distinctly directed towards the
corresponding lines of the opposing figure, so that the attention, so
far as it is determined in direction by the lines, would be less
likely to be carried over from the one image to the other.

On the other hand, when the angles were turned away from each other
the legs of the angles in the two figures compared were brought into
closer relation, so that in 2_b_, for instance, the average is even
higher than in 2_a_. Similarly the average in 3_b_, an obtuse angle,
is higher than in 3_a_. The notes show that in such cases the
contrasted angles tended to close up and coalesce into a single
figure with a continuous boundary. "The ends (2_b_) came together and
formed a diamond." "When the angles were turned away from each other
the lines had an occasional tendency to close up." "There was a
tendency to unite the two images (4_a_) into a triangle." "The two
figures seemed to tug each other, and the images were in fact a little
closer than the objects (4_a_)." "The images (4_a_) formed a
triangle." So with regard to the figures in 5_a_. "When both were in
the field there seemed to be a pulling of the left over to the right,
though no apparent displacement." "The two figures formed a square."

The lowest average--and it is much lower than any other average in the
table--is that of 5_b_, in which the contrasted objects have neither
angles nor incomplete lines directed to any common point between the
objects. In view of the notes, the tabulated record of these two
figures (5_b_) is very significant, and strikingly confirms, by its
negative testimony, what 1_a_ and 2_b_ have to teach us by their
positive testimony. The averages are, in the three cases just cited:
1_a_, 35.11 seconds; 2_b_,33.11 seconds; 5_b_, 15 seconds per minute.

On the whole, then, the power of the line to arrest, direct, and keep
the attention, through the greater energy and definiteness of the
processes which it excites, and thereby to increase the chances of the
recurrence and persistence of its idea in consciousness, is confirmed
by the results of this series. The greatest directive force seems to
lie in the sharply acute angle. Two such angles, pointing one towards
the other, tend very strongly to carry the attention across the gap
which separates them. (And it should be borne in mind that the
distance between the objects exposed was 25 cm.) But the power of two
incomplete lines, similarly situated, is not greatly inferior.

It thus appears that the attention process is in part, at least, a
motor process, which in this case follows the direction of the lines,
acquiring thereby a momentum which is not at once arrested by a break
in the line, but is readily diverted by a change in the direction of
the line. If the lines are so situated that the attention process
excited by the one set is carried away from the other set, the one set
inhibits the other. If, on the other hand, the lines in the one set
are so situated that they can readily take up the overrunning or
unarrested processes excited by the other set, the two figures support
each other by becoming in fact one figure. The great importance of the
motor elements of the attention process in ideation, and thus in the
persistence of the idea, is evident in either phase of the experiment.


RECAPITULATION.

                                          Seconds            Seconds.
  1 Figures alike:          Left          30.8     Right        31.9
  2   "     unlike:         Simple        27.10    Complex      34.62
  3   "       "             Small         24.54    Large        33.30
  4   "       "             Gray          25.61    White        29.53
  5   "       "             Line          31.91    Angle        38.54
  6   "       "             Plain         23.92    Marked       37.48
  7   "       "   (colored) 5 seconds     27.75    10 seconds   29.15
  8   "       "   (gray)    5 seconds     25.42    10    "      32.12
  9   "       "             1st exposure  12.64    2d exposure  36.45
  10  "       "             Vertical line 34.94    Hor. line    34.49
  11  "       "             Full-faced    28.10    Outline      41.08
  12  "       "             Figure        29.26    Int. lines   39.32
  13  "       "             Figure        34.03    Vert. lines  36.40
  14  "       "             Stationary    28.88    Moved        37.39
  15  "       "             Gray          30.90    Colored      37.81
  16 (See Table XVI.)


If we put these results into the form of propositions, we find:

1. That when the objects are similar surfaces, seen under similar
conditions, the chances of the recurrence and persistence of their
images are, on the whole, practically equal.

2. That surfaces bounded by complicated outlines have an advantage in
ideation, other things equal, over surfaces bounded by simple
outlines.

3. That as between two objects of unequal area--color, form, and other
conditions being the same--the larger object has the advantage in the
ideational rivalry.

4. That the image of a white object has a like advantage over the
image of a gray object.

5. That broken or complex lines have in ideation an advantage over
straight or simple lines.

6. That an object with varied content, other conditions remaining the
same, has an advantage over an object with homogeneous surface.

7 and 8. That an increase of the time during which the attention is
given to an object increases the chances for the recurrence of its
image or idea.

9. That of two objects to which attention is directed in succession,
the object last seen has a distinct advantage in the course of
ideation following close on the perception of the objects.

10. That lines of similar appearance and equal length, one of which is
vertical and the other horizontal, have, like surfaces of similar
appearance and form and equal dimensions, practically equal chances of
recurrence and survival in ideation, the slight difference in their
chances being in favor of the vertical line.

11. That as between two figures of similar form and equal dimensions,
one of which has a filled homogeneous content and the other is a mere
outline figure, the latter has a marked advantage in the course of
ideation.

12. That of two linear and symmetrical figures, of which one is an
outline figure with continuous boundary, and the other consists of the
same linear elements, similarly disposed, as the first, but has its
lines disconnected so that it has no continuous boundary, the latter
figure has the advantage in ideation.

13. That if, with material similar to that described in paragraph 12,
the disconnected lines are arranged so as to be vertical and
equidistant, the advantage in ideation still remains with the
disconnected lines, but is much reduced.

14. That if one of two figures, of similar appearance and form and of
equal dimensions, is kept in motion while it is exposed to view, and
the other is left at rest, the image of the moving object is the more
persistent.

15. That, under like conditions, colored objects are more persistent
in ideation than gray objects.

16. That lines and sharp angles, as compared with broad surfaces, have
a strong directive force in the determination of the attention to
their images or ideas; that this directive force is strongest in the
case of very acute angles, the attention being carried forward in the
direction indicated by the apex of the angle; but that uncompleted
lines, especially when two such lines are directed towards each
other, have a similar and not much inferior force in the control of
the course of ideation.

If we should seek now to generalize these experimental results, they
would take some such form as the following:

Abstraction made of all volitional aims and all æsthetic or affective
bias, the tendency of an object to recur and persist in idea depends
(within the limits imposed by the conditions of these experiments)
upon the extent of its surface, the complexity of its form, the
diversity of its contents, the length and recency of the time during
which it occupies the attention, the definiteness of the direction
which it imparts to the attention (as in the case of angles and
lines), its state of motion or of rest, and, finally, its brightness
and its color.

These conditions, however, are for the most part but conditions which
determine the energy, diversity, complexity and definiteness of the
active processes involved in the bestowal of attention upon its
object, and the experiments show that such active processes are as
essential in ideation as in perception. The stability of an image, or
internal sensation, thus depends on the activity of its motor
accompaniments or conditions. And as the presence of an image to the
exclusion of a rival, which but for the effect of these motor
advantages would have as strong a claim as itself to the occupation of
consciousness (cf. Series I., X.), may be treated as a case of
inhibition, the greater the relative persistence of an image or idea
the greater we may say is the 'force' with which it inhibits its
rival. Exclusive possession of the field involves, to the extent to
which such possession is made good, actual exclusion of the rival; and
exclusion is inhibition. Our generalization, accordingly, may take the
following form:--

The inhibitory effect of an idea, apart from volitional or emotional
bias, depends upon the energy, diversity, complexity and definiteness
of the motor conditions of the idea.

       *       *       *       *       *



CONTROL OF THE MEMORY IMAGE.

BY CHARLES S. MOORE.


Since Gallon's classic investigation in the field of mental imagery
several similar investigations have been pursued in the same
direction, chiefly, however, for the purpose of discovering and
classifying types of imagination.

Little has been done in the line of developing and studying the
problems of the memory image proper, and still less, in fact almost
nothing, is to be found bearing on the control of the visual memory
image. The general fact of this control has been presented, with
greater or less detail, based upon returns from questionaries. Gallon
himself, for example, having referred to instances in which the
control was lacking, goes on to say[1]: "Others have complete mastery
over their mental images. They can call up the figure of a friend and
make it sit on a chair or stand up at will; they can make it turn
round and attitudinize in any way, as by mounting it on a bicycle or
compelling it to perform gymnastic feats on a trapeze. They are able
to build up elaborate structures bit by bit in their mind's eye and
add, substract or alter at will and at leisure."

   [1] Gallon, Francis: 'Inquiries into Human Faculty and its
   Development,' London, 1883, p. 109.

More recent writers classify the students, or other persons examined,
according to these persons' own statements with regard to the nature
and degree of control over the mental images which they consider
themselves to possess. An article by Bentley[2] is the only study of a
specific problem of the memory image. After a glance at the literature
with reference to methods pursued in the investigation of problems of
memory in general, Bentley outlines 'a static and genetic account' of
the memory image in particular, and presents details of experiments
'carried on for the special investigation of the visual memory image
and its fidelity to an original presentation.'

   [2] Bentley, I.M.: 'The Memory Image and its Qualitative
   Fidelity,' _Am. Journ. of Psychol._, 1899, XI., pp. 1-48.

Of the many memory problems as yet unattacked, that of the control of
the mental image is one of the most interesting. The visual image
obviously offers itself as the most accessible and the experiments
described in this report were undertaken with the purpose of finding
out something about the processes by which control of this image is
secured and maintained. The report naturally has two aspects, one
numerical and the other subjective, presenting the statements of the
subjects as to their inner experiences.

The term 'suppression' is used as a convenient one to cover the
enforced disappearance of the designated image, whether it be directly
forced out of consciousness (a true suppression) or indirectly caused
to disappear through neglect, or limitation of the attention to the
other image which is to be retained.

As this was an investigation of the control of memory images, the
presence of these images under conditions most favorable to their
vividness and distinctness was desirable. An immediate mental recall
at the end of five seconds of visual stimulation, under favorable
though not unusual conditions of light, position and distance, seemed
most likely to secure this desideratum. Experimentation showed that
five minutes was, on the whole, a suitable period in which to secure
the information needed without developing a fatigue in the subject
which would vitiate the results.

The experiments made in the visual field were restricted to visual
memory images which were called up by the subject during the five
minutes succeeding a five seconds' presentation of one or two objects.
The subject sat, with his eyes closed, about four feet from a wall or
screen, before which the object was placed. At a signal the eyes were
opened, and at a second signal five seconds later they were closed. If
an after-image appeared the subject reported its disappearance, and
then called up the image of the object just presented, and reported as
to its clearness, vividness, persistency and whatever phenomena arose;
and when directed he sought to modify the image in various ways to be
described later.

There were six subjects in experiments conducted during the winter of
1900-1901, and six (five being new ones) in experiments of the fall
of 1901. They were all good visualizers, though they differed in the
readiness with which they visualized respectively form or color.

The experiments of the first few weeks were designed to establish the
fact of control by the subjects over a single visual memory image as
to its position, size, outline, color, movement and presence. In
general it was established that a considerable degree of control in
these particulars existed in these subjects.

Later, two objects were presented at a time, and were such small
articles as a glass ball, a book, a silk purse, an eye-glass case, an
iron hook, and so forth. Still later, colored squares, triangles, or
discs were used exclusively.

The investigation followed these lines: I. Movements of a single
image; II. Changes of color of a single image; III. Movements of two
images in the same and in different directions; IV. Suppression of one
of two images; V. Movements of a single image, the object having been
moved during the exposure.


I. MOVEMENTS OF A SINGLE IMAGE.


The first table gives the time in seconds taken to move voluntarily a
single image (of a colored square or disc) to the right, left, up or
down, and in each case to restore it to its original position. There
were thirty movements of each kind for each of the six subjects,
making one hundred and eighty for each direction and also for each
return, the total of all movements being fourteen hundred and forty.
The distance to which the subjects moved the images was not fixed, but
was in most cases about twelve inches. The time was taken with a
stop-watch, and includes the time between the word of command,
'right,' etc., of the director and the verbal report 'now' of the
subject. It includes, therefore, for each movement two reaction times.
The subject reported 'now' the instant the color reached, or appeared
at, the designated place, not waiting for the completion of the shape
which usually followed. Two of the subjects (H. and K.) took much
longer than the other four, their combined average time being almost
exactly four times the combined average time of the other four.


TABLE I.

  MOVEMENTS OF A SINGLE IMAGE.

  30 Movements of Each Kind for Each Subject Average Time in Seconds.

            To           To
  Subjects  Right Return Left Return Up   Return Down Return Averages
  B.        1.30         1.07        1.06        1.11        1.13
                  0.58        0.73        0.46        0.45        0.55

  G.        1.44         1.15        0.99        0.82        1.10
                  0.92        0.89        0.76        0.57        0.78

  H.        7.12         6.42        5.96        5.85        6.34
                  4.51        4.41        4.36        4.40        4.42

  I.        1.28         1.34        1.62        1.47        1.43
                  0.67        0.62        0.86        0.72        0.72

  J.        1.71         1.42        1.40        1.14        1.50
                  1.34        1.53        0.77        0.74        1.09

  K.        4.81         4.64        3.29        3.28        4.01
                  2.40        2.71        1.91        1.56        2.14

  Averages  2.95         2.67        2.39        2.23        2.59
                  1.72        1.82        1.52        1.41        1.62


NUMERICAL.

The general averages for the different movements show that movement to
the right was hardest, to the left next; while movement downward was
the easiest. A marked exception is seen in I., for whom the upward
movement was the hardest and movement to the right was the easiest. J.
found movement to the left hardest. For the return movements, the
general averages show that the return from the left is the hardest,
from the right next; while from below is the easiest. Here again I.
found the return from above the hardest and from below the next
hardest; while from the left was the easiest.

Arranging the subjects in the order of the average time, taken for all
the movements, including the returns to the original position, we have

  H.  5.35 average time out and back.
  K.  3.07     "     "   "   "    "
  J.  1.29     "     "   "   "    "
  I.  1.07     "     "   "   "    "
  G.   .94     "     "   "   "    "
  B.   .84     "     "   "   "    "


SUBJECTIVE.

All the six subjects whose time records appear in Table I. and also
four others whose time was not recorded reported eye movements, or a
tendency to eye movement. A. and K. reported that when the image was
dim there was accommodation as for long vision and when the image was
vivid there was accommodation as for near vision. B. ideated the new
position and the eye movement occurred automatically. G. reported a
contraction of the scalp muscles and a tendency to cast the eyes up
and locate the image at the back of the head inside; this was an
inveterate habit. He reported also accommodation for the different
distances of the image and an after-feeling of strain in the head. H.
reported a strong tendency in the eyes to return to the center,
_i.e._, the original position, and to carry the image back there. All
the subjects frequently reported a sense of relief in the eye muscles
when the command to return the image to the center was given--also, a
tension in the forehead in the upward movement which was accentuated
(with H.) when there was headache. J. reported, 'always eye strain,'
and noticed that the eyes usually turned as far as the new position,
but sometimes stopped short of it. K. reported first an eye movement,
then an ideation of the image in the new position. E. and H. turned
the head to right and left for movements of the image in those
directions. A., B., E. and F. believed that they could inhibit the eye
movement. Subjects were at times unconscious of eye movements. H.
articulated the names of the colors of the image and found that it
aided the movement of the image to say to himself, for example: "Don't
you see that blue square there?"

All but J. reported a loss in vividness and also, though to a less
degree, in distinctness whenever the image was moved away from the
center. J. found no difference. H. reported that details of the object
which were reproduced in the image when at the center were not
discernible in the image in other positions, also that at the left the
image was more vivid than at the right. B.'s memory image of a watch,
three minutes after it was called up, was still so clear that he read
from it the time. E., who was an experienced photographer, had no
difficulty in recalling outline, light and shade, but had difficulty
in reproducing color. I. frequently lost the form in making the
required improvements.

Under manipulation the memory image usually retained its distinctness
and vividness with no loss or with but slight loss when in its
original position, to the end of the five minutes of the experiment.
The image, also, seldom disappeared except for the momentary
disappearances in passing from one position to another, which are
referred to later. Under passive observation of the memory image
disappearances, though of short duration, were frequent and there was
a noticeable fading away of color and loss of outline.

The memory image almost without exception, when first recalled, was
located in the direction and at the distance of the object presented.

In moving from the center to right and left the image remained in the
same plane with a few exceptions; in moving up and down it moved on an
arc whose center was at the eye. This was especially true of the
downward motion, which was almost always to a greater distance than
any of the other motions.

C., D., F. and H. felt the need of a support for the image in any
except the central position. This was true especially of the position
above the center, but was entirely overcome by practice by C., F. and
H., and partially by D. In movements where time was to be recorded,
the distance was from six to eighteen inches, but the image could be
carried by all the eleven subjects to any part of the room or beyond
the room. Usually the method followed was to fix the attention on the
suggested position and then the image appeared there, sometimes
complete at the outset, but usually in part at first, then developing
instantly to completion. When the subject was requested to trace the
image _in transitu_, this could usually be accomplished, but the time
was much longer. Frequently, in such a case, the image was lost during
the last third or fifth of its journey. J. "felt conscious of a
something that went in the suggested direction but did not develop
details out of this material; had to await development of the image at
the new locality." "At times _forced_ this development out of the
vague something that seemed to go over." G. had 'no feeling of
transition in space.' K. did not perceive the image _in transitu_. I.
perceived the image _in transitu_ when the movement was away from the
center but when the image was to return to the center its passage was
too quick to be followed; 'it came out at the center.'

J. noticed that in moving from the center the image took a curved path
towards himself, and that the position _to_ which the image moved
always seemed further away than the position _from_ which it came, but
the new position seemed to be readjusted when the next movement
occurred.

The return to the center seemed easier to all the subjects except G.,
who was conscious of no difference between the movements with respect
to ease. Several described the return to the center as like the return
of a small ball snapped back by a stretched elastic cord.

With D. a suggestion of weight in the perception of the object was a
hindrance to moving its memory image. Also the image of a short piece
of brass tubing persisted in rolling off the table and along the floor
and could not be held stationary. Other objects rotated rapidly, and
much effort was needed to 'slow down' the rotation and to bring the
objects to rest and keep them at rest.


II. CHANGES OF COLOR OF A SINGLE IMAGE.


Tables II. and III. show the results of experiments in changing the
color of a single image. This was usually a square, sometimes a disc.
The time of optical perception was five seconds. After the
disappearance of after-images, if there were any, eighteen to
twenty-four changes were made in the color of the memory image,
occupying from four and a half to six minutes.

The colors were saturated blue, green, yellow and red, and each one
was changed into each of the other colors and then restored. The order
of change was varied to avoid uniformity of succession. The four
colors were shown to the subjects each day before the experiments
began, to establish a standard. The time was taken with a stop-watch,
and includes the time between the director's word of command, 'green,'
etc., and the subject's report, 'now,' or 'green,' etc. It includes,
therefore, two reaction times. The subject reported 'now' the instant
he secured the desired color, not waiting for the completion of the
shape that usually followed.


TABLE II.

  CHANGES OF COLOR. SINGLE IMAGE. 72 CHANGES OF EACH COLOR.

  [Label 1: Subject.]
  [Label 2: To Green.]
  [Label 3: Return to Blue.]
  [Label 4: To Yellow.]
  [Label 5: Return to Blue.]
  [Label 6: To Red.]
  [Label 7: Return to Blue.]
  [Label 8: To Blue.]
  [Label 9: Return to Green.]
  [Label 10: To Yellow.]
  [Label 11: Return to Green.]
  [Label 12: To Red]
  [Label 13: Return to Green.]

             From Blue.                         From Green.
  [1] [2]  [3]  [4]  [5]  [6]  [7]     [8]  [9]  [10] [11] [12] [13]

  B.  1.72 0.50 1.66 0.38 1.81 0.50    1.23 0.56 1.10 0.65 1.33 0.56
  G.  1.15 0.60 1.10 0.79 0.89 0.65    1.75 0.87 1.04 0.75 1.35 0.71
  H.  4.67 4.25 4.87 4.06 4.81 3.83    5.27 4.50 5.81 4.89 5.37 4.94
  I.  2.27 1.25 1.77 1.19 1.83 1.25    2.15 0.93 1.71 1.04 1.92 1.15
  J.  1.38 0.81 1.29 0.94 1.29 0.95    1.65 1.08 1.15 0.77 1.60 0.81
  K.  2.35 1.71 1.96 1.66 2.10 1.19    2.25 1.25 2.17 1.73 2.44 1.27

  Av. 2.26 1.52 2.11 1.50 2.15 1.39    2.41 1.53 2.15 1.65 2.34 1.57

  [Label 1: Subject.]
  [Label 2: To Blue.]
  [Label 3: Return to Yellow.]
  [Label 4: To Green.]
  [Label 5: Return to Yellow.]
  [Label 6: To Red.]
  [Label 7: Return to Yellow.]
  [Label 8: To Blue.]
  [Label 9: Return to Red.]
  [Label 10: To Green.]
  [Label 11: Return to Red.]
  [Label 12: To Yellow.]
  [Label 13: Return to Red.]

            From Yellow.                         From Red.
  [1] [2]  [3]  [4]  [5]  [6]  [7]     [8]  [9]  [10] [11] [12] [13]

  B.  1.79 1.06 1.35 0.87 1.89 1.10    1.54 0.58 1.71 0.62 1.31 0.71
  G.  1.50 1.10 1.48 0.87 1.31 0.88    1.33 0.92 1.35 0.91 0.77 0.58
  H.  5.02 4.54 5.73 3.91 6.15 4.17    6.35 3.91 5.89 4.69 5.54 4.37
  I.  2.29 1.31 2.54 1.19 2.29 1.27    2.85 1.10 2.50 1.21 1.65 1.31
  J.  1.35 0.98 1.35 0.65 1.27 0.88    1.42 1.04 1.31 1.02 1.25 0.85
  K.  3.02 1.52 3.21 2.04 2.23 1.79    2.54 1.56 2.66 1.60 2.88 1.81

  Av. 2.49 1.76 2.61 1.59 2.52 1.68    2.67 1.51 2.57 1.68 2.23 1.62


TABLE III.

  CHANGES TO THE FOUR COLORS.

  Average time in seconds. 72 changes from and 72 changes to each color.

  [Label 1: To Blue.]
  [Label 2: Return from Blue.]
  [Label 3: To Green.]
  [Label 4: Return from Green.]
  [Label 5: To Yellow.]
  [Label 6: Return from Yellow.]
  [Label 7: To Red.]
  [Label 8: Return from Red.]

               [1]  [2]  [3]  [4]  [5]  [6]  [7]  [8]
  From blue,             2.26 1.52 2.11 1.50 2.12 1.39
    "  green,  2.38 1.53           2.16 1.64 2.33 1.57
    "  yellow, 2.49 1.75 2.61 1.59           2.52 1.68
    "  red,    2.67 1.52 2.58 1.68 2.27 1.62

  Average,     2.52 1.60 2.48 1.59 2.17 1.58 2.33 1.55


  _Changes from_ a presented color.        _Returns to_ a presented color.
            216 movements.                          216 movements.

  _From_ presented      yellow,   2.52    _To_ presented      yellow, 1.67
       "          "     red,      2.49        "         "     red,    1.61
       "          "     green,    2.29        "         "     green,  1.58
       "          "     blue,     2.16        "         "     blue,   1.47

  Average,                        2.37    Average,                    1.58


  _Changes to_ a color _from_    _Returns from_ a color _to_
      a presented color.             a presented color.
      216 movements.                   216 movements.

  _To_ blue,   2.52             _From_ blue,    1.60
     " green,  2.48                  " green,   1.59
     " red,    2.33                  " yellow,  1.58
     " yellow, 2.17                  " red,     1.55

     Average,  2.37                  Average,   1.58


The six subjects fall into two groups--three, H., I., and K., taking
longer than the other three. As in the previous experiment H. was
markedly longer than any of the others.

There were seventeen hundred and twenty-eight changes in all,
including returns to the original color. There were two hundred and
sixteen changes from each of the four colors as presented, to each of
the other three and, of course, the same number of returns to the
presented color.

The change to blue from the other presented colors was the most
difficult and the change to yellow was the easiest.

The averages (216 exp. each) are,

              Sec.
   To blue,   2.55
    " green,  2.48
    " red,    2.33
    " yellow, 2.17

The returns to the presented colors did not differ greatly from each
other, the averages (216 exp. each) being:

                Sec.
   From blue,   1.603
    "   green,  1.597
    "   yellow, 1.589
    "   red,    1.549

From red appears to be the easiest change, and from blue the hardest.

The getting away from a presented blue was the easiest and from a
presented yellow the most difficult, as seen by these averages (216
exp. each):

                Sec.
   From yellow, 2.54
    "   red,    2.49
    "   green,  2.29
    "   blue,   2.16

The returns to the presented colors show that it was hardest to get
back to the presented yellow, easiest to get back to the presented
blue, the averages (216 exp. each), being:

                Sec.
   To yellow,   1.67
    " red,      1.61
    " green,    1.58
    " blue,     1.47

The facts as to blue and yellow shown by these four tables of averages
may be expressed also in this way:

If a blue square was shown, it was easier to change the blue memory
image into the other colors, and also easier to get back the blue
memory image after such changes, than if any other of the three colors
was presented.

If another color than blue was shown it was harder to change the
memory image of that color to blue than to any of the other colors,
and also harder to get back to the memory image of that color from
blue than from any of the other three colors.

If a yellow square was shown, it was harder to change the yellow
memory image into the other colors, and also harder to get back the
yellow memory image after such changes than if any other of the three
colors was presented.

If another color than yellow was shown, it was easier to change the
memory image of that color to yellow than to any of the three other
colors, and also easier to get back to the memory image of that color
from the yellow than from any of the other three colors except red.

If we combine _all_ the changes into a color (both changes from
another presented color and returns to this color previously
presented) we find that changes to green are hardest, to yellow
easiest. The averages (for 432 exp. each) are,

                 Sec.
   To green,     2.03
    " blue,      1.99
    " red,       1.97
    " yellow,    1.92

The changes away from a color (both from this color previously
presented and from this color to the other previously presented
colors) show that it was hardest to get away from yellow, easiest to
get away from blue, the averages (for 432 exp. each) being:

                  Sec.
   From yellow,   2.06
     "  red,      2.02
     "  green,    1.94
     "  blue,     1.88

As for the subjects, all six found yellow the easiest to change into,
one finding red equally easy.


SUBJECTIVE.

For seven of the subjects, mental repetition of the name of the color
(usually accompanied by articulatory movements) tended to bring up the
color, and one other subject occasionally used this method of bringing
about a change that was difficult. With D. the color did not come at
repetition of the name. G. was assisted by auditory recall of the
name. Nine subjects reported a feeling of strain, usually in the eyes
as of focusing, occurring especially when there seemed a difficulty in
producing the desired change. The tension attended almost exclusively
changes of the presented color, not restorations of that color. For D.
this strain was considerable, for G. there was also an after-feeling
of strain in the head. For G. the image was clearest when the feeling
of strain was least, and J. secured the promptest and clearest results
when he could most nearly rid himself of anxiety as to the result. K.
in one instance (a change from green to yellow) became conscious of
the setting of his jaws and motions of feet and body in aid of his
attempt. H. frequently had the feeling of physical fatigue.

In most cases the restoration of the presented color was as a complete
square, triangle, etc. In changes from the presented color the new
color appeared at a corner, or edge, or as a patch at the center. With
E. the "color flashed over the whole field and then had to be
restricted to the figure." B. "held the outline, emptied of the old
color, while it was filled in with the new." D. "had a clear outline,
and the new color came in small blotches inside, and effort spread
them out to cover the whole figure." For I. the "new color came
sliding in from the right side over the old, which, however,
disappeared as if it were moving out of focus." With A. the new color
usually came from either the lower left-hand or the upper right-hand
corner. F. kept a clear outline and the new color came in from the
right.

When E. found it difficult to create at the center the desired color,
he thought of some object (garment, grass, sky, etc.) of that color
and then transferred it to fill in the outline preserved at the
center. B. moved the colored figure aside and in its place put one of
the desired color, moved the new figure up to the old and there
superposed it. With G. the new colors seemed of new material and there
was felt to be an accumulation about the center, of old
color-material. Then he located the square outside of this imaginary
debris and began again. H. found that the colors of his own
experiments, in which he used color squares framed in black, came to
his mind at the names of the desired colors, and the association soon
gave him the figure also. I. located the new colors around the
presented one, first all at the right; then green at the left, red at
the right, yellow above, when presented blue was at the center; then
yellow and green were at the upper left-hand corner, while red came
from behind. The new color 'slid in over the old.' It was found easier
to secure the desired color when its position was known beforehand. J.
also used a similar device. He 'turned towards the places and brought
out the required color and filled the central outline with it.' He
tried to break up this scheme and got red without going after it but
found himself 'at a loss to find the colors.' Later he succeeded so
that the required color simply appeared in the outline of the old
color at the center. K. turned his eyes to corners of the central
outline, then to the center, and found that this aided in developing
the desired color from the corners inward. When difficulty arose, he
experienced muscular tension in body and legs and jaws.

Five of the subjects considered the change from a presented color to
blue the hardest and one found the change to red hardest. Green was
placed second in difficulty by one, and blue second by the one who
found red the hardest. Three reported the change to yellow the easiest
and two the change to red.

The change from red to yellow caused 'an unpleasant sensation' in C.
and the new figure 'had a maroon halo.'

A. in returning from green or blue to yellow passed through a gray;
so, once, in changing from yellow to green, and once, green to red.
With A. blue retinal clouds, which often came, aided changes to blue
and hindered at times changes to other colors. B. had a fusion of
yellow and red in changing from yellow to red. G. had a tendency to
leave uncolored the lower left-hand corner and it 'was wood-colored';
G. had a gray image as the result of fusion of retinal clouds with red
memory image. With H. blue always came in as robin's-egg blue, which
then had to be changed to the standard blue. In one instant the green
memory image seemed to shift into a purple and change to a positive
retinal image which interfered with changes to other colors. J. found
whistling and humming an aid in relaxing an unnatural state of tension
which would hinder the best results. To increase the vividness of the
image he would recall the black background on which the colored
squares had hung. In one experiment K. became 'desperately tired of
yellow,' which was the presented color, so that his 'mind was ready to
jump to any color rather than yellow.' The returns to yellow were, in
this experiment, slower than the changes from yellow.

The images sometimes changed sizes, being at times smaller, but
usually larger than the object. In one experiment of C. the image was
four times the size of the object, which was a green square with sides
of one inch.


III. MOVEMENTS OF TWO IMAGES IN THE SAME AND IN DIFFERENT DIRECTIONS.


Table IV. gives the results of experiments in the movements of two
images, the objects presented being colored squares or discs. Time of
perception was five seconds. After the disappearance of after-images,
if there were any, eighteen to twenty-four movements with returns to
original positions were made, occupying five or six minutes. The
colors were saturated blue, green, yellow and red. Four of the
movements were such as separated the two images, and in four the two
moved uniformly. The first four movements were right and left, left
and right, up and down, down and up; the left-hand object followed the
first direction indicated. The right-and-left movements involved the
crossing of the images. The last four were _both_ to right, to left,
up, down. The time was taken with a stop-watch and includes the time
between the director's word of command and the subject's report,
'now.' It includes, therefore, two reaction times. The subject
reported the instant the colors reached, or appeared at, the suggested
positions.

It is to be noticed that H. was very much slower than any of the
others in making the movements, both out and back; and that K., while
also slower (though much less so than H.) in making the movements
outward, was no slower in making the return movements.


TABLE IV.

  MOVEMENTS OF TWO IMAGES.

  Twenty movements of each kind for each subject. Averages in seconds.

                           In Opposite Directions.

  Subj.   L.-R.   Ret.   R.-L.   Ret.   U.-D.   Ret.   D.-U.   Ret.

     B.    1.82           2.90           2.10           2.27
                  0.86           0.87           0.73           0.86

     G.    3.02           2.86           2.68           2.63
                  1.98           2.25           1.63           2.01

     H.    9.18          10.30           7.50           7.15
                  5.16           6.90           5.36           5.21

     I.    4.17           3.52           3.40           3.37
                  1.26           1.47           1.23           1.31

     J.    2.17           2.90           2.87           2.27
                  1.05           1.63           1.02           1.13

     K.    5.51           6.43           5.16           4.81
                  1.43           1.48           1.20           1.23

   Ave.    4.32           4.82           3.82           3.75
                  1.96           2.43           1.87           1.96

  Average of all movements involving separation (480), 4.18. Returns, 2.06.


                             In Same Direction.

  Subj.     R.    Ret.     L.    Ret.     U.    Ret.     D.    Ret.

     B.    1.31           1.22           1.30           1.11
                  0.72           0.67           0.72           0.85

     G.    2.66           2.35           3.01           2.53
                  2.00           1.86           2.22           1.86

     H.    8.45           7.91           5.66           7.66
                  6.53           5.95           5.96           6.11

     I.    2.57           2.27           2.13           2.05
                  0.97           1.26           1.00           1.13

     J.    1.11           1.16           1.08           11.5
                  0.68           0.90           0.73           0.71

     K.    3.97           3.91           3.60           4.07
                  1.35           1.50           1.75           1.71

   Ave.    3.33           3.14           2.79           3.10
                  2.04           2.02           2.04           2.06

  Average of all movements together (480), 3.09. Returns, 2.04.


NUMERICAL.

There were nineteen hundred and twenty movements in all, including the
returns to the original positions.

In the order of difficulty as shown by the time taken, the movements
stand as follows, the numbers being the averages in seconds for one
hundred and twenty movements of each kind:

   1. Right and left (_i.e._, crossing), 4.82 sec.
   2. Left and right,                    4.32  "
   3. Up and down,                       3.82  "
   4. Down and up,                       3.75  "
   5. Both right,                        3.33  "
   6. Both left,                         3.14  "
   7. Both down,                         3.10  "
   8. Both up,                           3.04  "


SUBJECTIVE.

In the experiments in which the time was recorded, there was no
disappearance of either image except where movements were made
successively. In these cases frequently the image which was awaiting
its turn vanished until the first image was placed, a time varying
from a quarter of a second to three or four seconds. Occasionally the
image already placed would vanish, while the other was _en route_; the
subject's attention in both these cases being centered exclusively on
the image he desired to move. This was especially the case when the
distances to which the images were moved were great, as to the ends of
the room or to ceiling and floor. In other experiments, where, after
the movements took place, the images were held for a short time, there
were disappearances of one image or the other ranging from one quarter
of a second to fifteen seconds, most of the absences, however, being
under five seconds. The absences were more numerous in the latter half
of the five minutes covered by the experiment. Occasionally a noise in
the adjoining room or in the street made the images disappear.

The greater ease of vertical as compared with horizontal movements
recalls an observation of Ladd,[3] in which the idioretinal light was
willed into the shape of a cross. Ladd says: "The vertical bar of the
cross seems much easier to produce and to hold steadily in the field."
This present observation is also in accord with that described above
in the case of movements of a single image.

   [3] Ladd, G.T.: 'Direct Control of the Retinal Field,' PSYCH.
   REV., 1894, L, pp. 351-355.

On several occasions G. reported that the crossing movement was the
easiest, and that the return to the original places was not easier
than the other movements. In one experiment he reported the field at
the center cloudy, so that it was a relief to get away from it. G.'s
time records on these occasions did not support his feeling with
regard to the return to the original places, but they show that the
crossing movements were, in two or three instances, quicker than the
'left-and-right' movement, and the impression of promptness thus made
persisted to the end of the experiment. The four movements in which
both images moved uniformly were easier than the four in which
movements in different directions were involved.

All the subjects were frequently conscious of eye movements, and more
frequently conscious of a tendency to eye movement, which was,
however, inhibited. That the strain in the eyes was practically
constant during all the movements away from the original places, seems
evident from the unanimous reports of a sense of relaxing and relief
in the eyes, attending the movement of returning to the original
places. The distance to which the images were moved was a powerful
factor in producing this sense of strain. When the two images were
moved and held but a few inches apart there was no sense of strain and
no conscious alternation of attention. Practice increased greatly the
distance at which the images could be held apart without conscious
alternation of attention, but the strain of holding them apart and of
inhibiting eye movement increased with the distance.

In the movements for which the time was recorded the distances varied,
according to the subject, from six to eighteen inches, and varied at
times with each subject. In the experiments without time record, A.,
B., C., E., F. and H. reported that they were able to move the images
apart to ceiling and to floor, or to the opposite ends of the room,
and to hold them there both in consciousness at the same time without
either alternation of attention or eye movement, a tendency to which
was felt but was inhibited. I. held them two feet apart without
fluctuation of attention. A. reported: "I tend to turn my body to left
or to right when I move the images in either of these directions." C.,
H. and I. said: "The eyes diverge when one image moves slowly to the
right and one to the left." D. found a slight movement of the eyes
which could be detected by the fingers placed lightly on the lids,
when the attention was alternating between the images. K. had
convergence and divergence of the eyes for crossing and separation
respectively and he was accustomed to run his eye over the outline of
the image. Strain in the scalp muscles was reported by A., B., E., F.
and G. The up-and-down movements were universally characterized by a
feeling as if one eye tended to move up and the other down. C.
unconsciously inclined his head to the left in such movements as if to
make the line of the two eyes parallel with the direction of the
movement.

E., when holding the images two feet apart, had a strong feeling of
difference of accommodation when alternating in observation and so
judged the two to be in different planes.

When the movement seemed difficult the strain was greater, and when an
image became dim the effort to restore its brightness or its
distinctness of outline was accompanied by a feeling of bringing it
nearer by accommodation and near focusing. J. found that the two
images approached each other when he attempted to secure greater
vividness. An analogous instance is that of A.G.C., a subject quoted
in 'Mental Imagery of Students,' by French.[4] In calling up the image
of a die this subject held up his hand as if it held the die. When
there was no sense of strain the hand was fourteen inches from his
face, but when effort was made to image all the sides of the die at
once he unconsciously moved his hand to within four inches of his
eyes. French says in this connection: "Situation depends on the
attention involved and the inference is near that this phenomenon may
be connected with feelings of convergence and accommodation which so
often accompany concentrated visual attention."

   [4] French, F.C.: PSYCH. REVIEW, 1902, IX., p. 40.

The movements were assisted by mentally saying, 'this image is here,
that image is there,' in the case of D., G., H., I. and K.; or, at
times, by articulating the names of the image, or of the color when
the image was of a colored object. I. found it easy to hold outlines,
but in order to retain colors in the movements of separation, he had
to speak the names continually. H. also repeated the names
continually, as, for example, 'violet here, orange there.'

A. represented the line of vision as going to each of the two images,
which seemed connected by a line, thus making a triangle, and then
pictured himself as standing off and seeing himself looking at the
images. When the two objects were solid and the images were to be
crossed, B. carried one image above or below the other, but when the
objects were colored surfaces he conceived them as pure colors so that
there was no sense of impenetrability to interfere with their crossing
and they glided by each other. In the up-and-down movements he moved
one at a time. C. and D. had to construct some support for the images.
In most of the experiments H. first moved the images to a greater
distance away, somewhat higher up and a little farther apart. In this
new position the images appeared smaller and the suggested movements
were made more easily. Sometimes in crossing two colored images he
observed a partial mixture of the colors. J. found that a sharp
movement of the head in the required direction aided materially in
moving the images, and when the objects were colored surfaces fastened
to the same card he found it necessary either to conceive the card as
of rubber or to picture it as cut in two before he could make the
movements of the images.

With A., B., C. and D. there were instances of unwilled movements of
the images, in the experiments where the movements were not timed.
These were much more frequent with D. than with the others, and to
check them required prolonged effort. The more common movements of
this sort were rotation of the image, change of its position,
separation of its parts (if detachable in the object) and change of
shape. E. had a return of the two images of a preceding experiment
which persisted in staying a few seconds and which were as vivid as
the two legitimate occupants of the mental field.

The images were duplicated five times on different days with A., and
once each with C., F. and K.

A.'s cases were these. The 'wraith' of a small box whose image was out
at the right, appeared above the other image off at the left and it
was turned with a corner to the front. Again, at the central position
each image was duplicated, the true pair being of full size, bright
and distinct, the false pair small, dim and on a more distant plane,
_i.e._, behind the others. One of the extra images persisted against
all effort to banish it, for fifty-five seconds. Again, when twelve
inches apart each image was similarly duplicated. In the fourth
instance the images were at the center of the field. In the fifth, the
right image, eight inches from the center, was duplicated, the extra
image being still farther away and above. This second image was very
dark, dim and vague in outline, and came and went slowly. The right
image of C., when seven feet from the center, had a dim double above
it. F. had moved the right-hand image (a violet disc) close to the
left when a blue disc also appeared above it. Though repeating the
word 'violet' he had imaged the violet disc as blue. K. was holding
the two images a foot and a half apart when an extra pair appeared at
the center. Both pairs persisted for sixty seconds and then the outer
pair vanished, and the inner, the false pair, grew brighter.

As was said in the case of a single image, so with double images, the
motion could be traced and often was traced when the movements were
away from the original positions, but on the return to the original
positions the images were not usually seen _in transitu_. For ten of
the subjects, the image moved downward uniformly on an arc whose
center was at the eye; and often the right and left movements were
likewise on an arc. With E. the ends of the arc for motion right and
left were higher also. H., I. and J. reported that all the movements
were in the same plane. The upward movement was always to a less
distance and the downward movement to a greater distance than the
horizontal movements.

In most cases the images were the size of the percepts, in a number of
cases smaller, and in a few cases larger. This was determined by
comparison between the image and the percept immediately on opening
the eyes and seeing the object at the end of the five minutes occupied
by the experiment. A similar mode of comparison showed that, in about
half of the experiments, the images were at the end of five minutes
approximately equal to the percept in clearness and distinctness of
outline. A comparison of these results with those obtained in a series
of experiments involving passive observation of the image seems to
indicate that active manipulation of the image tends to maintain the
qualitative fidelity of the image when at its original position.
During the progress of the experiments the reports were almost
unanimous and constant that at its original position the image was
vivid and distinct, but lost in both respects when away from that
position, the loss being greater the greater the distance to which it
was moved. Frequently there was fluctuation,--a loss of vividness and
then a restoration,--which A. frequently found to be rhythmical, while
in general it was evident that an increase of effort or of attention
was successful in restoring lost vividness and distinctness.

D., after three minutes, read the time in the image of a watch. In
superposing green on yellow, in two instances, the yellow shone
through, making a mixed color, and again, in moving a green disc and a
yellow disc, the green became suffused with yellow, so that the two
discs were one yellow and the other greenish-yellow. For C.,
similarity in the two objects presented tended to make both images
less vivid and distinct and to render more difficult their retention
and manipulation. When one of the two objects partially overlapped the
other it was difficult to separate the two images, and the area of
contact was very vague in the image of the under one, and when the
scrutiny reached that portion the other image returned to its original
overlapping position.


IV. SUPPRESSION OF ONE OF TWO IMAGES.


The next tables (V. and VI.) give the results of experiments in
suppressing one of two images, the objects presented being saturated
color squares, discs, triangles, etc., placed side by side, one above
the other, or a smaller one superposed on a larger. The time of
perception was five seconds. After the disappearance of after-images,
if there were any, the subject was directed to suppress one of the two
memory images, the one to be suppressed being indicated by the
director. The subject reported as soon as the indicated image
disappeared, and reported any return of the suppressed image and its
later disappearance in consequence of his efforts. Also he reported
any disappearance and reappearance of the retained image. Five minutes
was the limit of the time for the experiments with a few exceptions.
The times were recorded, and those given for the first suppression
include the time between the director's command and the subject's
report 'now' or 'gone,' and include, therefore, two reaction times.
The later suppressions include but one reaction time.


TABLE V.

  SUMMARY OF ALL SUPPRESSIONS. AVERAGE TIME IN SECONDS.

  [Label 1: Image Suppressed]
  [Label 2: No of Exper.]
  [Label 3: Time of First Supp.]
  [Label 4: Time of Ab. of Supp. Im.]
  [Label 5: No. of Later Supp.]
  [Label 6: Time of Later Supp.]
  [Label 7: No. of Ab. of Supp. Im.]
  [Label 8: Time of Ab. of Supp. Im.]
  [Label 9: Time of All Supp.]
  [Label 10: Time of All Absence of Supp. Im.]

  [1]       [2]  [3]    [4]  [5]  [6]  [7]  [8]   [9]   [10]
  Right.    46  11.59  82.39 221  8.43 216 35.74  8.94  43.93
  Left.     43  11.89  79.34 175  7.79 173 44.86  8.60  51.26
  Upper.    22  11.67  49.77 150  6.26 147 29.75  6.95  32.35
  Lower.    17  14.23  64     71  7.88  70 46.68  9.11  50.04
  Central.  42  18.24  96.93 357  3.90 352 18.13  5.41  26.54
  Marginal. 20  14.25 181.57  24  8.93  24 78.08 11.35 125.12
  Sundry.    7   8.71 127.21  19 13.34  19 47.27 12.09  68.78
  Averages.     13.48  91.25      6.46     32.14  7.60  41.86


TABLE VI

  SUPPRESSIONS GROUPED BY SUBJECTS. AVERAGE TIME IN SECONDS.

  [Label 1: Subject]
  [Label 2: No. of Exp.]
  [Label 3: Time of First Supp.]
  [Label 4: Time of Ab. of Supp. Im.]
  [Label 5: No. of Later Supp.]
  [Label 6: Time of Later Supp.]
  [Label 7: No. of Ab. of Supp. Im.]
  [Label 8: Time of Ab. of Supp. Im.]
  [Label 9: Time of All Supp.]
  [Label 10: Time of All Ab. of Supp. Im.]

  [1]       [2] [3]   [4]    [5] [6]   [7] [8]    [9]   [10]
  A.        11  28.32  11.29 117 14.90 114  10.35 16.05  10.44
  B.        29   5.79 270.44   5  0.25   5 138.80  4.98 251.08
  C.        18   7.88  43.08  64  3.94  63  67.49  4.81  62.07
  D.        14  23.28 190.07   6 31.66   5 204.60 25.80 193.89
  F.        10  12.67  86.07 230  1.95 230  67.92  2.40  10.09
  G.        21  21.88  20.39 190  9.97 184  19.37 11.15  19.47
  H.        21  15.27  73.27  47 10.30  47  84.48 11.84  81.02
  I.        26   9.77  53.83  96  5.06  94  61.34  6.06  59.72
  J.        26   3.59  32.18 209  1.40 208  31.69  1.64  31.75
  K.        21  21.63  71.90  53 14.75  51  70.04 16.70  31.83
  Averages.     13.48  91.25      6.46      32.14  7.60  41.86

There were ten subjects in most of the experiments, and the marked
differences in the individual records which were evident in the
previous experiments did not exist here except in the case of A., for
whom alone the time required to obtain the suppression exceeded the
time of absence of the suppressed image.

In several experiments the subjects were unable to suppress the
indicated image, which in five cases was the image at the center of a
disc and in two cases the outer portion of the disc. Further, five
failures were by one subject, D., and one each by A. and F. The
statistical report here given includes only the results of the
successful experiments. Forty-four of the one hundred and ninety-seven
were completely successful, as the suppressed image did not return
throughout the entire period. The following table shows the grouping
of the experiments according to the recurrence of the suppressed
image:

   Returned 0  times,          44
      "     1    "             26
      "     2    "             18
      "     3    "             25
      "     4    "             16
      "     5    "             16
      "  6 to 10 "             28
      "  more than 10 times,   24
   Total,                     197

Seventy-three and three fifths per cent. of all the experiments have
five or fewer returns of the suppressed images.

The subjects suppressed the image as soon as possible after each
return, the average time taken to accomplish these later suppressions
being 6.46 sec., while the average time of absence of the suppressed
image was 32.14 sec.

Including the first efforts and the first absences of the suppressed
image, the average time required to suppress the image was 7.60 sec.,
and the average time of absence of the suppressed image was 41.86 sec.

Arranging the subjects according to the average time they required to
accomplish a suppression, we have the following order. J. and F. had
more recurrences of the suppressed image than any of the other
subjects.

    J.    1.64 sec.
    F.    2.40  "
    C.    4.80  "
    B.    4.98  "
    I.    6.06  "
    G.   11.15  "
    H.   11.84  "
    A.   16.05  "
    K.   16.70  "
    D.   25.80  "

Arranging them by the average absence of the suppressed image we have
this order:

    B.  251.08 sec
    D.  193.89  "
    H.   81.02  "
    C.   62.07  "
    I.   59.72  "
    K.   31.83  "
    J.   31.75  "
    G.   19.47  "
    A.   10.44  "
    F.   10.09  "

It is to be remarked, however, that the ability to keep the suppressed
image out of the field increased with practice and that A. and F. had
less than half the number of experiments that the rest had. D., who
had but two thirds as many as most of the other subjects and therefore
had less practice in suppressing the image, stands yet second in
respect to this ability.

If we compare the subjects with regard to _first_ efforts and _first_
absences only, we obtain the following orders:

  According to Ave. Time req.            According to Ave. Absence
   for first Suppression.             of Image after first Suppression.
     J.        3.59 sec.                    B.       270.44 sec.
     B.        5.79  "                      D.       190.07  "
     C.        7.88  "                      F.        86.07  "
     I.        9.77  "                      H.        73.27  "
     F.       12.67  "                      K.        71.90  "
     H.       15.27  "                      I.        53.83  "
     K.       21.63  "                      C.        43.08  "
     G.       21.88  "                      J.        32.18  "
     D.       23.28  "                      G.        20.39  "
     A.       28.32  "                      A.        11.29  "

Arranging the groups of images suppressed according to the average
times of all suppressions and absences we have these orders:

             Suppression.                      Absences.
   Central Images,  5.41       Marginal Images,  125.12
   Upper     "      6.95       Sundry     "       68.78
   Left      "      8.60       Left       "       51.26
   Right     "      8.94       Lower      "       50.04
   Lower     "      9.11       Right      "       43.93
   Marginal  "     11.35       Upper      "       32.35
   Sundry    "     12.09       Central    "       26.54


SUBJECTIVE.

Most of the subjects imaginatively placed the image to be suppressed
behind the screen, in a drawer, in their closed hands, pushed it
forward into the remote distance, sliced up, burned up, or pulverized
and so destroyed it. B. and D. 'thought it away' directly, without
mechanism or device, or got rid of it 'by a pure act of will.'
Superposition was tried, frequently with success, but at times the
under image shone through. When the objects were colored discs one
superposed on the other, the subject spread over the whole surface the
color of the image to be retained, but at times this resulted in there
being two shades of the upper color, and a yellow above a red changed
to an orange. When red was above yellow, the red appeared more highly
illuminated. Associations with objects of the color of the retained
image were found helpful but tended to modify the original color. Such
associations also, at times, by secondary associations brought back
the suppressed image. For example, when thinking of buttercups to
enforce a yellow image, the picture of grass surrounding the flowers
brought back the suppressed green image. Concentration of the
attention on the image to be retained and an ignoring of the other
was, on the whole, the method usually and successfully followed. This
concentration was helped by imagining the image marked off into minute
squares which were carefully counted. Numerous other devices of a
similar character were used. Objects having many details and those
lending themselves readily to suggestions of action (as a china
animal) were the most helpful in enabling the subject to concentrate
his attention on their image to the exclusion of another. Some
subjects conceived themselves as tracing with a pencil the outline and
details of the retained image. Frequently, when the two images were
originally near each other and one alone was being held by close
scrutiny of its parts, when this scrutiny reached the part of the
image which was nearest the position of the suppressed image, the
suppressed image returned. The original association between the two
images was often broken up by change of the position or shape of the
one to be suppressed. But devices soon became 'worn out' and new ones
had to be resorted to.

Motor impulses played a large part in the process of suppression, such
as head and eye movement away from the image to be suppressed,
contraction of the muscles of the forehead and scalp, occasional
'setting' of the teeth, pressure together of the hands when they were
supposed to be holding the image and of the knees under like
circumstances. The eye traced outline and details and the more
actively it could be so employed the more successful was the
suppression. The sensations of accommodation and of focusing
previously referred to were repeated in this series. Enunciation also
was very common.

Frequent comparison of the image with the percept was made at the
close of experiments and showed the utmost diversity in size,
vividness and distinctness. During an experiment when the suppressed
image came back, it was rarely more than a mere blur of color; in two
or three instances the form came without color. Green was found to be
a difficult color to hold. C. had an orange after-image from a
retained yellow image, a red image having been suppressed. Between the
images of a gray disc and an orange disc, three inches apart, he had
a blue disc. J., while suppressing an orange disc and retaining a
green disc, noticed that 'when off the fovea the whole green disc
became bright orange.' There was always a sense of readiness on the
part of the suppressed image to slip back. As C. expressed this, "The
thing suppressed exists in the fringe of consciousness." The recurring
image usually came back at its original position even when the
retained image was being held in a different part of the field. In
such cases the retained image at once resumed its original place.

G. and J. were successful in proportion as they freed themselves from
the nervous strain of anxiety as to the result.


V. MOVEMENTS OF A SINGLE IMAGE, THE OBJECT HAVING BEEN MOVED DURING
THE EXPOSURE.


In an additional series of experiments with five of the same subjects
(B., G., H., I. and K.), the object was moved during the five seconds
of exposure either right, left, up or down, a distance of about six to
eight inches, and back again. In this way the subject was supplied
with further material of a pure memory type and it was believed that
some addition to our knowledge of the nature of the control of the
image might thus be made by securing data contrasting the construction
and the more purely reminiscent work of the imagination.

The question proposed is as follows: Does the fact that a certain
movement of an object was presented to the optical perception give an
advantage in time, or ease, to the mental recall of that object as so
moving, over its recall as moving in other directions? The subjective
experiences during such recalls may be expected to throw light upon
the matter.

The subject, with closed eyes, was requested to move the mental image
of the object in the four directions indicated above, returning it
after each movement to its original position, and the time of each
movement was recorded and, as well, the report of the subject with
regard to his subjective experiences. There were sixteen hundred
movements in all, eight hundred away from the original position of the
image (two hundred in each of the four directions mentioned above) and
eight hundred in returning to the original position.

Besides these experiments, other movements of the object during
exposure were made, such as inversion, rotation, change from the
vertical to the horizontal position and vice versa, rolling, oblique
movements and the subjective phenomena were recorded when the subject
had repeated with the image the designated movements. In all the
experiments the objects were moved by the hand of the conductor of the
experiment.

Table VII. gives the time record in seconds of these experiments for
each subject under each of the four variations: Movement of the object
to right, left, up, down.


TABLE VII.

  MOVEMENTS OF A SINGLE IMAGE, THE OBJECT HAVING BEEN MOVED DURING THE
  TIME OF OPTICAL STIMULATION. AVERAGE TIME IN SECONDS. TEN MOVEMENTS IN
  EACH DIRECTION FOR EACH SUBJECT.

                      _a_.   Object moved to right.

  Subject  R.  Return  L.  Return  Up  Return  Down  Return  Aver.
    B.    0.57        0.75        0.62         0.60          0.64
                0.35        0.42        0.37          0.62   0.44
    G.    0.55        0.60        0.55         0.57          0.57
                0.27        0.25        0.27          0.25   0.26
    H.    6.95        6.90        6.47         6.40          6.65
                5.40        5.55        4.50          5.00   5.11
    I.    2.05        2.10        2.05         2.22          2.10
                1.15        1.35        1.32          1.57   1.35
    K.    2.35        2.97        2.42         2.62          2.59
                1.17        1.20        1.17          1.55   1.28
  Ave.    2.49        2.66        2.02         2.48          2.52
                1.67        1.75        1.53          1.80   1.69

  Ave. to right, 2.49
  Ave. of other movements, 2.52
  Grand average, 2.10

                       _b_. Object moved to left.
    B.    0.72        0.60        0.62         0.60          0.64
                0.52        0.40        0.52          0.42   0.47
    G.    0.67        0.45        0.55         0.67          0.59
                0.42        0.35        0.35          0.37   0.37
    H.    8.22        5.95        6.52         6.42          6.78
                5.82        4.10        4.37          5.55   4.96
    I.    2.40        1.30        2.25         2.72          2.17
                1.97        1.22        0.95          1.47   1.40
    K.    2.45        2.57        2.25         2.00          2.30
                1.70        1.60        1.32          1.35   1.49
  Ave.    2.89        2.17        2.44         2.48          2.50
                2.09        1.53        1.50          1.83   1.74

  Ave. to left, 2.17
  Ave. of other movements, 2.60
  Grand average, 2.12

                      _c_. Object moved up.
    B.    0.75        0.62        0.42         0.57          0.59
                0.32        0.50        0.42          0.37   0.40
    G.    0.65        0.57        0.45         0.47          0.54
                0.35        0.27        0.25          0.27   0.29
    H.    6.77        6.25        6.85         6.15          6.57
                5.27        5.55        5.30          5.30   5.35
    I.    2.47        2.27        1.85         2.65          2.31
                1.25        1.00        0.87          1.10   1.05
    K.    3.40        2.72        1.42         2.20          2.44
                1.50        1.37        1.27          1.17   1.33
  Ave.    2.81        2.49        2.20         2.41          2.48
                1.74        1.74        1.62          1.70   1.69

  Ave. up, 2.20
  Ave. of other movements, 2.57
  Grand average, 2.08

                    _d_. Object moved down.
    B.    0.80        0.72        0.70         0.57          0.70
                0.42        0.42        0.50          0.42   0.44
    G.    0.60        0.60        0.55         0.47          0.55
                0.25        0.25        0.27          0.27   0.26
    H.    6.77        6.80        6.80         8.77          7.29
                5.90        6.35        4.55          5.55   5.59
    I.    2.30        2.20        2.22         1.80          2.13
                1.30        1.20        1.15          1.42   1.27
    K.    3.15        2.75        2.95         2.30          2.79
                1.62        1.57        1.12          1.25   1.39
  Ave.    2.72        2.61        2.64         2.78          2.69
                1.90        1.92        1.52          1.78   1.79

  Ave. down, 2.78
  Ave. of other movements, 2.66
  Grand average, 2.24


NUMERICAL.

As each movement may be compared with three other movements, and as
there were five subjects and four variations in the conditions, there
are sixty opportunities of comparing the time required to move the
image in the direction in which the object was moved with the time
taken to move it in the other directions. In 45 instances the time was
less, in 3 the same, and in 12 greater.

These twelve instances occurred with two subjects, three (to left)
occurring with K. and nine (three each right, up, down) occurring with
H. The cause was the same in all twelve instances, both H. and K.
reporting that (in these cases) they had great difficulty in obtaining
a reasonably vivid and distinct image when directed to move the image
in the direction in which the object had been moved. The attempt to
move the image resulted in a vague image spread continuously over the
entire area that had been covered by the moving object, and the effort
to obtain the image at the desired position only was serious and took
an appreciably longer time than usual. It is to be noted, also, that
the time usually taken by H. is uniformly very much greater than the
time taken by the other subjects. Yet, even with these instances
included, the average time of all movements of the image in the
direction in which the object had been moved is less than the average
time of the other movements, the former being 2.41 seconds, the
latter, 2.59 seconds.


TABLE VIII.

  MOVEMENTS OF A SINGLE IMAGE.

  I., OBJECT PREVIOUSLY MOVED; II., OBJECT NOT MOVED.

  Average Time Given in Seconds.

  Subjects:         B.                    G.                H.
                 I         II        I         II        I      II
  To right,  0.57      1.30      0.55      1.46      6.95      7.15
  Return,         0.35      0.58      0.27      0.92      5.40      4.51
  To left,   0.60      1.06      0.45      1.15      5.95      6.42
  Return,         0.40      0.73      0.35      0.89      4.10      4.41
  Up,        0.42      1.05      0.45      0.99      6.85      5.96
  Return,         0.42      0.46      0.25      0.76      5.30      4.36
  Down,      0.57      1.10      0.47      0.82      8.77      5.85
  Return,         0.42      0.45      0.27      0.06      5.55      4.40
  General    0.54      1.13      0.48      1.10      7.13      6.34
  Averages,       0.40      0.55      0.28      0.66      5.09      4.42


  Subjects:         I.                    K.
                 I         II        I         II
  To right,  2.05      1.28      2.35      4.80
  Return,         1.15      0.67      1.17      2.40
  To left,   1.30      1.34      2.57      4.63
  Retur,          1.22      0.62      1.60      2.73
  Up,        1.85      1.62      1.42      3.29
  Return,         0.87      0.86      1.27      1.90
  Down,      1.80      1.36      2.30      3.27
  Return,         1.42      0.72      1.25      1.56
  General    1.75      1.40      2.16      4.00
  Averages,       1.16       0.72     1.32      2.15


If the record of H. is omitted from Table VII., _a, c, _and _d_, and
that of K. from VII., _b_ (as these are the records of the twelve
exceptions), the former average becomes 1.44 seconds, the latter 1.86
seconds.

The following table affords the means of comparing the time taken in
moving the image in the direction in which the object had been moved
with the time taken in moving the image in the same direction when
there had been no movement of the object. The averages are obtained
from the records of Tables VII. and I.

We have here twenty comparisons each of movements away from the
original positions and movements back to the original positions:

    In the first case, 15 took less time under I., 5 took more
    time under I.

    The 5 cases of more time occurred with two subjects (H., 3 and
    I., 2).

    In the second case, 12 took less time under I., 8 took more
    time under I.

    The 8 cases of more time occurred with three subjects (G., 1;
    H., 3; I., 4).

If we omit H.'s record and take the general averages for each subject,
we find the following advantages in time in form of movements where
the object had been moved;

   B.,       0.59 seconds.
   G.,       0.52    "
   K.,       1.84    "

But I., 0.35 seconds in favor of movements when the object had not
been moved.

Combining these results, we have 0.74 sec. as the average gain in time
for these four subjects.


SUBJECTIVE.

With one exception (G.), the subjects found Movements I., movements in
the direction in which the object had been moved, easier than
Movements II. In Movements II. the eye seemed to construct and compel
the motion, which was not the case with Movements I., in which the eye
followed the motion. The distance to which the image went in Movements
I. seemed predetermined, and these movements seemed exact copies of
the original movement of the object, being purely reminiscent and
reproducing its irregularities when there were any. Also, the image
was usually seen _in transitu_ both out and back, which was never the
case with Movements II. Eye movement and enunciation were much less
frequent and the image was more vivid and distinct in Movements I.

       *       *       *       *       *



        STUDIES IN ÆSTHETIC PROCESSES.



       *       *       *       *       *

Transcriber's Note:

   Rhythmic measures in the first 2 articles of this section are
   transcribed as follows:

   |   delineates measure
   q   quarter note
   q.  dotted quarter note
   e   eighth note
   %   quarter rest

   Major accent of the measure is indicated by a >, either above
   or in front of the beat. Minor accent of the measure is
   indicated by ., used in the same way.

      >   .
    | q q q q | or | >q q .q q | represent the same rhythmic pattern.

       *       *       *       *       *



THE STRUCTURE OF SIMPLE RHYTHM FORMS.

BY ROBERT MACDOUGALL.


I. PROBLEMS AND METHODS OF EXPERIMENTATION.


The investigation of the problems presented by the psychological
phenomena of rhythm has of late years occupied much attention and been
pushed in a variety of different directions. Some researches have been
concerned with an analysis of rhythm as an immediate subjective
experience, involving factors of perception, reaction, memory,
feeling, and the like; others have had to do with the specific
objective conditions under which this experience arises, and the
effect of changes in the relations of these factors; still others have
sought to coördinate the rhythm experience with more general laws of
activity in the organism, as the condition of most effective action,
and to affiliate its complex phenomena upon simpler laws of
physiological activity and repose; while a fourth group has undertaken
a description of that historical process which has resulted in the
establishment of artistic rhythm-types, and has sought to formulate
the laws of their construction.[1]

   [1] Description: (1) Of the psychological factors of the rhythm
   experience: Angell and Pierce, Ettlinger, Hauptmann, Mentz,
   Meumann, Stumpf, Wundt, et al. (2) Of its objective conditions
   and products: Binet et Courtier, Bolton, Ebhardt, Hurst and
   McKay, Meumann, Schumann, Sievers, et al. (3) Of its
   physiological accompaniments: Bolton, Brücke, Dogiel,
   Hausegger, Mach, Mentz, Ribot, Sherrington, Scripture, Smith,
   et al. (4) Of its historical evolution: Bücher, Moritz,
   Scherer, et al.

This differentiation has already made such progress as to constitute
the general topic a field within which specialization is called for,
instead of an attempt to treat the phenomenon as a whole. It is the
purpose of this paper to describe a set of experiments having to do
with the second of these problems, the constitution of objective
rhythm forms. In the determination of such forms it is, of course,
impossible to avoid the employment of terms descriptive of the
immediate experience of rhythm as a psychological process, or to
overlook the constant connection which exists between the two groups
of facts. The rhythm form is not objectively definable as a stable
type of stimulation existing in and for itself; the discrimination of
true and false relations among its elements depends on the immediate
report of the consciousness in which it appears. The artistic form is
such only in virtue of its arousing in the observer that peculiar
quality of feeling expressed in calling the series of sensory stimuli
rhythmically pleasing, or equivalent, or perfect. In no other way than
as thus dependent on the appeal which their impression makes to the
æsthetic consciousness can we conceive of the development and
establishment of fixed forms of combination and sequence among those
types of sensory stimulation which arouse in us the pleasurable
experience of rhythm. The artistic rhythm form cannot be defined as
constituted of periods which are 'chronometrically proportionate,' or
mathematically simple. It is not such in virtue of any physical
relations which may obtain among its constituents, though it may be
dependent on such conditions in consequence of the subordination to
physical laws of the organic activities of the human individual. The
view must be subjectively objective throughout.

The need for simplicity and exactness has led to the very general
employment of material as barely sensorial as could be devised for the
carrying on of experiments upon rhythm. Rich tones and complex
combinations of them are to be avoided, for these qualities are
themselves immediate sources of pleasure, and the introduction of them
into the material of experimentation inevitably confuses the analysis
which the observer is called upon to make of his experience and of the
sources of his pleasure in it. Still more objectionable than the
presence of such complex musical tones in an investigation of rhythm
is the introduction of the symbols of rational speech in concrete
poetical forms. This element can be only a hindrance to the perception
of pure rhythmical relations, in virtue of the immediate interest
which the images called up by the verbal signs possess, and further,
in view of the fact that the connections of significant thought impose
upon the purely rhythmical formulation of the series of stimulations
an unrelated and antagonistic principle of grouping, namely, the
logical relations which the various members of the series bear to one
another.

The demand for a simplification of the material which supports the
rhythm experience, for the purpose of obtaining a more exact control
over the conditions of experimentation, has been met by the invention
of a variety of devices whereby the sequences of music, song and
poetical speech have been replaced by elementary conventional symbols
as the vehicle of the rhythmical impression or expression. On the one
side there has commonly been substituted for musical tones and
rhythmical speech the most simple, sharply limited and controllable
sounds possible, namely, those due to the action of a telephone
receiver, to the vibrations of a tuning-fork placed before the
aperture of a resonator, or to the strokes of metallic hammers falling
on their anvils. On the other side, the form of the reproduced rhythm
has been clarified by the substitution of the finger for the voice in
a series of simple motor reactions beaten out on a more or less
resonant medium; by the use--when the voice is employed--of
conventional verbal symbols instead of the elements of significant
speech; and--where actual verse has been spoken--by a treatment of the
words in formal staccato scansion, or by the beating of time
throughout the utterance. The last of these methods is a halting
between two courses which casts doubt on the results as characteristic
of either type of activity. There is no question that the rhythmic
forms of recitative poetry differ vastly from those of instrumental
music and chanted speech. The measures of spoken verse are elastic and
full of changefulness, while those of music and the chant maintain a
very decided constancy of relations. The latter present determinable
types of grouping and succession, while it is questionable whether the
forms of relationship in spoken verse can ever be considered apart
from the emotion of the moment. In so far as the rhythmic form which
these differing modes of expression embody are to be made the subject
of experimental investigation their characteristic structures should
be kept intact as objects of analysis in independent experiments,
instead of being combined (and modified) in a single process.

The apparatus employed in the course of the present investigation
consisted of four different pieces of mechanism, one affording the
vehicle of expression throughout the series of reproduced rhythms, the
others providing the auditory material of the various rhythms
apperceived but not designedly reproduced. The first of these
consisted of a shallow Marey tambour, placed horizontally upon a table
with its rubber film upwards, and connected by means of rubber-tubing
with a pneumographic pen in contact with the revolving drum of a
kymograph. A Deprez electric marker, aligned with the pneumographic
stylus, afforded a time record in quarter seconds. Upon this tambour,
placed within comfortable reach of the reactor's hand, the various
rhythm types were beaten out. The impact of the finger-tip on the
tense surface of the drum gave forth a faint and pleasing but at the
same time clearly discernible and distinctly limited sound, which
responded with audible variations of intensity to the differing
stresses involved in the process of tapping, and which I have
considered preferable to the short, sharp stroke of the Kraepelin
mouth-key employed by Ebhardt. The rate of revolution in the drum was
so adjusted to the normal range of excursion in the pneumographic pen
as to give sharp definition to every change of direction in the curve,
which hence allowed of exact measurements of temporal and intensive
phases in the successive rhythm groups. These measurements were made
to limits of 1.0 mm. in the latter direction and of 0.5 mm. in the
former.[2]

   [2] Professor Binet's doubt (_L'Année Psychologique_ 1895, p.
   204) that the propulsion of air from the elastic chamber and
   the rebound of the pen might interfere with the significance of
   the graphic record is more serious in connection with the
   application of this method to piano playing than here; since
   its imperfection, as that writer says, was due to the force and
   extreme rapidity of the reactions in the former case. The
   present series involved only light tapping and was carried on
   at a much slower average rate.

The second piece of apparatus consisted of an ordinary metronome
adjusted to beat at rates of 60, 90, and 120 strokes per minute. This
instrument was used in a set of preliminary experiments designed to
test the capacity of the various subjects for keeping time by finger
reaction with a regular series of auditory stimulations.

The third piece of apparatus consisted of an arrangement for producing
a series of sounds and silences, variable at will in absolute rate, in
duration, and, within restricted limits, in intensity, by the
interruptions of an electrical current, into the circuit of which had
been introduced a telephone receiver and a rheostat. Portions of the
periphery of a thin metallic disc were cut away so as to leave at
accurately spaced intervals, larger or smaller extents of the original
boundary. This toothed wheel was then mounted on the driving-shaft of
an Elbs gravity motor and set in motion. Electrical connections and
interruptions were made by contact with the edge of a platinum slip
placed at an inclination to the disc's tangent, and so as to bear
lightly on the passing teeth or surfaces. The changes in form of a
mercury globule, consequent on the adhesion of the liquid to the
passing teeth, made it impossible to use the latter medium. The
absolute rate of succession in the series of sounds was controlled by
varying the magnitudes of the driving weights and the resistance of
the governing fans of the motor. As the relation of sounds and
intervals for any disc was unalterable, a number of such wheels were
prepared corresponding to the various numerical groups and temporal
sequences examined--one, for example, having the relations expressed
in the musical symbol 3/4 | >q e |*; another having that represented in
the symbol 4/4 | >q e e |;* and so on. Variations in intensity were
obtained by mounting a second series of contacts on the same shaft and
in alignment with those already described. The number of these
secondary contacts was less than that of the primary connections,
their teeth corresponding to every second or third of those. The
connections made by these contacts were with a second loop, which also
contained within its circuit the telephone receiver by which the
sounds were produced. The rheostatic resistances introduced into this
second circuit were made to depart more or less from that of the
first, according as it was desired to introduce a greater or slighter
periodic accent into the series. This mechanism was designed for the
purpose of determining the characteristic sequences of long and short
elements in the rhythm group.

  *Transcriber's Note:

   The original article showed "3/4 | q q q |" and "4/4 | q q q q |".
   Applying the erratum after the article (below) resulted in
   fewer beats per measure than indicated by the time signature.
   Other possibilities are "3/4 | >q e q. |" and "4/4 | >q e e q q |".

   "ERRATUM:

   On page 313, line 23, the musical symbols should be a quarter
   note, accented, followed by an eighth note; in the following
   line the symbols should be a quarter note, accented, followed
   by two eighth notes."

The fourth piece of apparatus consisted essentially of a horizontal
steel shaft having rigidly attached to it a series of metallic
anvils, fifteen in number, on which, as the shaft revolved, the
members of a group of steel hammers could be made to fall in
succession from the same or different heights. The various parts of
the mechanism and their connections may be readily understood by
reference to the illustration in Plate VIII. On the right, supported
upon two metal standards and resting in doubly pivoted bearings,
appears the anvil-bearing shaft. On a series of shallow grooves cut
into this shaft are mounted loose brass collars, two of which are
visible on the hither end of the shaft. The anvils, the parts and
attachments of which are shown in the smaller objects lying on the
table at the base of the apparatus, consist of a cylinder of steel
partly immersed in a shallow brass cup and made fast to it by means of
a thumb-screw. This cup carries a threaded bolt, by which it may be
attached to the main shaft at any position on its circumference by
screwing through a hole drilled in the collar. The adjustment of the
anvils about the shaft may be changed in a moment by the simple
movement of loosening and tightening the thumb-screw constituted by
the anvil and its bolt. The device by which the extent of the
hammer-fall is controlled consists of cam-shaped sheets of thin wood
mounted within parallel grooves on opposite sides of the loose collars
and clamped to the anvils by the resistance of two wedge-shaped
flanges of metal carried on the anvil bolt and acting against the
sides of slots cut into the sheets of wood at opposite sides. The
periphery of these sheets of wood--as exhibited by that one lying
beside the loose anvils on the table--is in the form of a spiral which
unfolds in every case from a point on the uniform level of the anvils,
and which, by variations in the grade of ascent, rises in the course
of a revolution about its center to the different altitudes required
for the fall of the hammers. These heights were scaled in inches and
fractions, and the series employed in these experiments was as
follows: 1/8, 2/8, 3/8, 5/8, 7/8, 15/8, 24/8 inch. Upon a
corresponding pair of standards, seen at the left of the illustration,
is mounted a slender steel shaft bearing a series of sections of brass
tubing, on which, in rigid sockets, are carried the shafts of a set of
hammers corresponding in number and position to the anvils of the
main axis. By means of a second shaft borne upon two connected arms
and pivoted at the summit of the standards the whole group of hammers
may at any moment be raised from contact with the cams of the main
shaft and the series of sounds be brought to a close without
interrupting the action of the motor or of the remainder of the
apparatus. By this means phases of acceleration and retardation in the
series, due to initial increase in velocity and its final decrease as
the movement ceases, are avoided. The pairs of vertical guides which
appear on this gearing-shaft and enclose the handles of the several
hammers are designed to prevent injury to the insertions of the hammer
shafts in their sockets in case of accidental dislocations of the
heads in arranging the apparatus. This mechanism was driven by an
electrical motor with an interposed reducing gear.

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT, 17. PLATE VIII.
               Opposite p. 314.]

The intervals between the successive hammer-strokes are controlled in
the following way: on the inner face of the group of pulleys mounted
on the main shaft of the mechanism (this gang of pulleys appears at
the extreme right in the illustration) is made fast a protractor
scaled in half degrees. Upon the frame of the standard supporting
these pulleys is rigidly screwed an index of metal which passes
continuously over the face of the scale as the shaft revolves. The
points of attachment (about the shaft) of the cams are determined by
bringing the point of fall of each cam in succession into alignment
with this fixed index, after the shaft has been turned through the
desired arc of its revolution and made fast by means of the
thumb-screw seen in the illustration at the near end of the shaft.
Thus, if three strokes of uniform intensity are to be given at equal
intervals apart and in continuous succession, the points of fall of
the hammers will be adjusted at equal angular distances from one
another, for example, at 360°, 240°, and 120°; if the temporal
relations desired be in the ratios 2:1:1, the arrangement will be
360°, 180°, 90°; if in the ratios 5:4:3, it will be 360°, 210°, 90°;
and so on. If double this number of hammers be used in a continuous
series the angular distances between the points of fall of the
successive hammers will of course be one half of those given above,
and if nine, twelve, or fifteen hammers be used they will be
proportionately less.

An interruption of any desired relative length may be introduced
between repetitions of the series by restricting the distribution of
angular distances among the cams to the requisite fraction of the
whole revolution. Thus, if an interruption equal to the duration
included between the first and last hammer-falls of the series be
desired, the indices of position in the three cases described above
will become: 360°, 270°, 180°; 360°, 240°, 180°, and 360°, 260°, 180°.
In the case of series in which the heights of fall of the various
hammers are not uniform, a special adjustment must be superimposed
upon the method of distribution just described. The fall of the hammer
occupies an appreciable time, the duration of which varies with the
distance through which the hammer passes. The result, therefore, of an
adjustment of the cams on the basis adopted when the height of fall is
uniform for all would appear in a reduction of the interval following
the sound produced by a hammer falling from a greater height than the
rest, and the amount of this shortening would increase with every
addition to the distance through which the hammer must pass in its
fall. In these experiments such lags were corrected by determining
empirically the angular magnitude of the variation from its calculated
position necessary, in the case of each higher member of the series of
distances, to make the stroke of the hammer on its anvil simultaneous
with that of the shortest fall. These fixed amounts were then added to
the indices of position of the several cams in each arrangement of
intervals employed in the experiments.

This apparatus answers a variety of needs in practical manipulation
very satisfactorily. Changes in adjustment are easily and quickly
made, in regard to intensity, interval and absolute rate. If desired,
the gradation of intensities here employed may be refined to the
threshold of perceptibility, or beyond it.

The possible variations of absolute rate and of relative intervals
within the series were vastly more numerous than the practical
conditions of experimentation called for. In two directions the
adaptability of the mechanism was found to be restricted. The
durations of the sounds could not be varied as were the intervals
between them, and all questions concerning the results of such
changes were therefore put aside; and, secondly, the hammers and
anvils, though fashioned from the same stuff and turned to identical
shapes and weights, could not be made to ring qualitatively alike; and
these differences, though slight, were sufficiently great to become
the basis of discrimination between successive sounds and of the
recognition upon their recurrence of particular hammer-strokes,
thereby constituting new points of unification for the series of
sounds. When the objective differences of intensity were marked, these
minor qualitative variations were unregarded; but when the stresses
introduced were weak, as in a series composed of 3/8-, 2/8-, 2/8-inch
hammer-falls, they became sufficiently great to confuse or transform
the apparent grouping of the rhythmical series; for a qualitative
difference between two sounds, though imperceptible when comparison is
made after a single occurrence of each, may readily become the
subconscious basis for a unification of the pair into a rhythmical
group when several repetitions of them take place.

In such an investigation as this the qualification of the
subject-observer should be an important consideration. The
susceptibility to pleasurable and painful affection by rhythmical and
arrhythmical relations among successive sensory stimuli varies within
wide limits from individual to individual. It is of equal importance
to know how far consonance exists between the experiences of a variety
of individuals. If the objective conditions of the rhythm experience
differ significantly from person to person it is useless to seek for
rhythm forms, or to speak of the laws of rhythmical sequence.
Consensus of opinion among a variety of participators is the only
foundation upon which one can base the determination of objective
forms of any practical value. It is as necessary to have many subjects
as to have good ones. In the investigation here reported on, work
extended over the two academic years of 1898-1900. Fourteen persons in
all took part, whose ages ranged from twenty-three to thirty-nine
years. Of these, five were musically trained, four of whom were also
possessed of good rhythmic perception; of the remaining nine, seven
were good or fair subjects, two rather poor. All of these had had
previous training in experimental science and nine were experienced
subjects in psychological work.


II. THE ELEMENTARY CONDITIONS OF THE APPEARANCE OF THE RHYTHM
IMPRESSION.


The objective conditions necessary to the arousal of an impression of
rhythm are three in number: (_a_) Recurrence; (_b_) Accentuation;
(_c_) Rate.


(_a_) _Recurrence._--The element of repetition is essential; the
impression of rhythm never arises from the presentation of a single
rhythmical unit, however proportioned or perfect. It does appear
adequately and at once with the first recurrence of that unit. If the
rhythm be a complex one, involving the coördination of primary groups
in larger unities, the full apprehension of its form will, of course,
arise only when the largest synthetic group which it contains has been
completed; but an impression of rhythm, though not of the form finally
involved, will have appeared with the first repetition of the simplest
rhythmical unit which enters into the composition. It is conceivable
that the presentation of a single, unrepeated rhythmical unit,
especially if well-defined and familiar, should originate a rhythmical
impression; but in such a case the sensory material which supports the
impression of rhythm is not contained in the objective series but only
suggested by it. The familiar group of sounds initiates a rhythmic
process which depends for its existence on the continued repetition,
in the form of some subjective accentuation, of the unit originally
presented.

The rhythmical form, in all such cases, is adequately and perfectly
apprehended through a single expression of the sequence.[3] It lacks
nothing for its completion; repetition can add no more to it, and is,
indeed, in strict terms, inconceivable; for by its very recurrence it
is differentiated from the initial presentation, and combines
organically with the latter to produce a more highly synthetic form.
And however often this process be repeated, each repetition of the
original sequence will have become an element functionally unique and
locally unalterable in the last and highest synthesis which the whole
series presents.

   [3] When the formal key-note is distinctly given, the
   rhythmical movement arises at once; when it is obscure, the
   emergence of the movement is gradual. This is a salient
   difference, as Bolton, Ettlinger and others have pointed out,
   between subjective rhythms and those objectively supported.

Rhythmical forms are not in themselves rhythms; they must initiate the
factor of movement in order that the impression of rhythm shall arise.
Rhythmical forms are constantly occurring in our perceptional
experience. Wherever a group of homogeneous elements, so related as to
exhibit intensive subordination, is presented under certain temporal
conditions, potential rhythm forms appear. It is a mere accident
whether they are or are not apprehended as actual rhythm forms. If the
sequence be repeated--though but once--during the continuance of a
single attention attitude, its rhythmical quality will ordinarily be
perceived, the rhythmic movement will be started. If the sequence be
not thus repeated, the presentation is unlikely to arouse the process
and initiate the experience of rhythm, but it is quite capable of so
doing. The form of the rhythm is thus wholly independent of the
movement, on which the actual impression of rhythm in every case
depends; and it may be presented apart from any experience of rhythm.

There is properly no repetition of identical sequences in rhythm.
Practically no rhythm to which the æsthetic subject gives expression,
or which he apprehends in a series of stimulations, is constituted of
the unvaried repetition of a single elementary form, the measures,
| >q. q |, or | >q. q q |, for example. Variation, subordination,
synthesis, are present in every rhythmical sequence. The regular
succession is interrupted by variant groups; points of initiation in
the form of redundant syllables, points of finality in the form of
syncopated measures, are introduced periodically, making the rhythm
form a complex one, the full set of relations involved being
represented only by the complete succession of elements contained
between any one such point of initiation and its return.


(_b_) _Accentuation._--The second condition for the appearance of the
rhythm impression is the periodic accentuation of certain elements in
the series of sensory impressions or motor reactions of which that
rhythm is composed. The mechanism of such accentuation is indifferent;
any type of variation in the accented elements from the rest of the
series which induces the characteristic process of rhythmic
accentuation--by subjective emphasis, recurrent waves of attention, or
what not--suffices to produce an impression of rhythm. It is commonly
said that only intensive variations are necessary; but such types of
differentiation are not invariably depended on for the production of
the rhythmic impression. Indeed, though most frequently the basis of
such effects, for sufficient reasons, this type of variation is
neither more nor less constant and essential than other forms of
departure from the line of indifference, which forms are ordinarily
said to be variable and inessential. For the existence of rhythm
depends, not on any particular type of periodical variation in the
sensory series, but on the recurrent accentuation, under special
temporal conditions, of periodic elements within such a series; and
any recurrent change in quality--using this term to describe the total
group of attributes which constitutes the sensorial character of the
elements involved--which suffices to make the element in which it
occurs the recipient of such accentuation, will serve as a basis for
the production of a rhythmical impression. It is the fact of
periodical differentiation, not its particular direction, which is
important. Further, as we know, when such types of variation are
wholly absent from the series, certain elements may receive periodical
accentuation in dependence on phases of the attention process itself,
and a subjective but perfectly real and adequate rhythm arise.

In this sense those who interpret rhythm as fundamentally dependent on
the maintenance of certain temporal relations are correct. The
accentuation must be rhythmically renewed, but the sensory incentives
to such renewals are absolutely indifferent, and any given one of the
several varieties of change ordinarily incorporated into rhythm may be
absent from the series without affecting its perfection as a
rhythmical sequence. In piano playing the accentual points of a
passage may be given by notes struck in the bass register while
unaccented elements are supplied from the upper octaves; in orchestral
compositions a like opposition of heavy to light brasses, of cello to
violin, of cymbals to triangle, is employed to produce rhythmical
effects, the change being one in _timbre_, combined or uncombined
with pitch variations; and in all percussive instruments, such as the
drum and cymbals, the rhythmic impression depends solely on intensive
variations. The peculiar rhythmic function does not lie in these
elements, but in a process to which any one of them indifferently may
give rise. When that process is aroused, or that effect produced, the
rhythmic impression has been made, no matter what the mechanism may
have been.

The single objective condition, then, which is necessary to the
appearance of an impression of rhythm is the maintenance of specific
temporal relations among the elements of the series of sensations
which supports it. It is true that the subjective experience of rhythm
involves always two factors, periodicity and accentuation; the latter,
however, is very readily, and under certain conditions inevitably,
supplied by the apperceptive subject if the former be given, while if
the temporal conditions be not fulfilled (and the subject cannot
create them) no impression of rhythm is possible. The contributed
accent is always a temporally rhythmical one, and if the recurrence of
the elements of the objective series opposes the phases of subjective
accentuation the rhythm absolutely falls to the ground. Of the two
points of view, then, that is the more faithful to the facts which
asserts that rhythm is dependent upon the maintenance of fixed
temporal intervals. These two elements cannot be discriminated as
forming the objective and subjective conditions of rhythm
respectively. Both are involved in the subjective experience and both
find their realization in objective expressions, definable and
measurable.


(_c_) _Rate._--The appearance of the impression of rhythm is
intimately dependent on special conditions of duration in the
intervals separating the successive elements of the series. There
appears in this connection a definite superior limit to the absolute
rate at which the elements may succeed one another, beyond which the
rapidity cannot be increased without either (_a_) destroying
altogether the perception of rhythm in the series or (_b_)
transforming the structure of the rhythmical sequence by the
substitution of composite groups for the single elements of the
original series as units of rhythmic construction; and a less clearly
marked inferior limit, below which the series of stimulations fails
wholly to arouse the impression of rhythm. But the limits imposed by
these conditions, again, are coördinated with certain other variables.
The values of the thresholds are dependent, in the first place, on the
presence or absence of objective accentuation. If such accents be
present in the series, the position of the limits is still a function
of the intensive preponderance of the accented over the unaccented
elements of the group. Further, it is related to the active or passive
attitude of the æsthetic subject on whom the rhythmical impression is
made, and there appear also important individual variations in the
values of the limits.

When the succession falls below a certain rate no impression of rhythm
arises. The successive elements appear isolated; each is apprehended
as a single impression, and the perception of intensive and temporal
relations is gotten by the ordinary process of discrimination involved
when any past experience is compared with a present one. In the
apprehension of rhythm the case is altogether different. There is no
such comparison of a present with a past experience; the whole group
of elements constituting the rhythmic unit is present to consciousness
as a single experience; the first of its elements has never fallen out
of consciousness before the final member appears, and the awareness of
intensive differences and temporal segregation is as immediate a fact
of sensory apprehension as is the perception of the musical qualities
of the sounds themselves.

The absolute value of this lower limit varies from individual to
individual. In the experience of some persons the successive members
of the series may be separated by intervals as great as one and one
half (possibly two) seconds, while yet the impression is distinctly
one of rhythm; in that of others the rhythm dies out before half of
that interval has been reached. With these subjects the apprehension
at this stage is a secondary one, the elements of the successive
groups being held together by means of some conventional symbolism, as
the imagery of beating bells or swinging pendulums. A certain
voluminousness is indispensable to the support of such slow measures.
The limit is reached sooner when the series of sounds is given by the
fall of hammers on their anvils than when a resonant body like a bell
is struck, or a continuous sound is produced upon a pipe or a reed.

In these cases, also, the limit is not sharply defined. The rhythmical
impression gradually dies out, and the point at which it disappears
may be shifted up or down the line, according as the æsthetic subject
is more or less attentive, more or less in the mood to enjoy or create
rhythm, more passive or more active in his attitude toward the series
of stimulations which supports the rhythmical impression. The
attention of the subject counts for much, and this distinction--of
involuntary from voluntary rhythmization--which has been made chiefly
in connection with the phenomenon of subjective rhythm, runs also
through all appreciation of rhythms which depend on actual objective
factors. A series of sounds given with such slowness that at one time,
when passively heard, it fails to produce any impression of rhythm,
may very well support the experience on another occasion, if the
subject try to hold a specific rhythm form in mind and to find it in
the series of sounds. In such cases attention creates the rhythm which
without it would fail to appear. But we must not confuse the nature of
this fact and imagine that the perception that the relations of a
certain succession fulfil the the form of a rhythmical sequence has
created the rhythmical impression for the apperceiving mind. It has
done nothing of the kind. In the case referred to the rhythm appears
because the rhythmical impression is produced, not because the fact of
rhythmical form in the succession is perceived. The capacity of the
will is strictly limited in this regard and the observer is as really
subject to time conditions in his effortful construction as in his
effortless apprehension. The rhythmically constructive attitude does
not destroy the existence of limits to the rate at which the series
must take place, but only displaces their positions.

A similar displacement occurs if the periodic accentuations within the
series be increased or decreased in intensity. The impression of
rhythm from a strongly accented series persists longer, as retardation
of its rate proceeds, than does that of a weakly accented series; the
rhythm of a weakly accented series, longer than that of a uniform
succession. The sensation, in the case of a greater intensive accent,
is not only stronger but also more persistent than in that of a
weaker, so that the members of a series of loud sounds succeeding one
another at any given rate appear to follow in more rapid succession
than when the sounds are faint. But the threshold at which the
intervals between successive sounds become too great to arouse any
impression of rhythm does not depend solely on the absolute loudness
of the sounds involved; it is a function also of the degree of
accentuation which the successive measures possess. The greater the
accentuation the more extended is the temporal series which will hold
together as a single rhythmic group.

This relation appears also in the changes presented in beaten rhythms,
the unit-groups of which undergo a progressive increase in the number
of their components. The temporal values of these groups do not remain
constant, but manifest a slight increase in total duration as the
number of component beats is increased, though this increase is but a
fraction of the proportional time-value of the added beats. Parallel
with this increase in the time-value of the unit-group goes an
increase in the preponderance of the accented element over the
intensity of the other members of the group. Just as, therefore, in
rhythms that are heard, the greatest temporal values of the simple
group are mediated by accents of the highest intensity, so in
expressed rhythms those groups having the greatest time-values are
marked by the strongest accentuation.

Above the superior limit a rhythm impression may persist, but neither
by an increase in the number of elements which the unit group
contains, nor by an increase in the rate at which these units follow
one another in consciousness. The nature of the unit itself is
transformed, and a totally new adjustment is made to the material of
apprehension. When the number of impressions exceeds eight or ten a
second--subject to individual variations--the rhythmical consciousness
is unable longer to follow the individual beats, a period of confusion
ensues, until, as the rate continues to increase, the situation is
suddenly clarified by the appearance of a new rhythm superimposed on
the old, having as its elements the structural units of the preceding
rhythm. The rate at which the elements of this new rhythm succeed one
another, instead of being more rapid than the old, has become
relatively slow, and simple groups replace the previous large and
complex ones. Thus, at twelve beats per second the rhythms heard by
the subjects in these experiments were of either two, three or four
beats, the elements entering into each of these constituent beats
being severally three and four in number, as follows:


TABLE I.

                                           >           >
  Simple Trochaic, four beats per second:  1 2 3, 4 5 6; 7 8 9,10 11 12.
                                           \___/ \___/ \___/ \______/
                                                   >
                                             ________      ___________
                                            /        \    /           \
  Dipodic Trochaic, "     "    "     "     1 2 3, 4 5 6; 7 8 9,10 11 12.
                                            \__/  \__/ \___/ \________/
                                             >>>
  Simple Dactylic, three  "    "     "     1 2 3 4, 5 6 7 8, 9 10 11 12.
                                            \____/   \____/   \_______/


The only impression of rhythm here received was of a trochaic or
dactylic measure, depending upon an accent which characterized a group
and not a single beat, and which recurred only twice or thrice a
second. Sometimes the subjects were wholly unaware that the elements
of the rhythm were not simple, a most significant fact, and frequently
the number reported present was one half of the actual number given.
During the continuance of such a series the rhythm form changes
frequently in the apprehension of the individual subject from one to
another of the types described above.

It cannot be too strongly insisted on that the perception of rhythm is
an _impression_, an immediate affection of consciousness depending on
a particular kind of sensory experience; it is never a construction, a
reflective perception that certain relations of intensity, duration,
or what not, do obtain. If the perception of rhythm in a series of
impressions were dependent on intellectual analysis and
discrimination, the existence of such temporal limits as are actually
found would be inconceivable and absurd. So long as the perception of
the uniformity or proportion of time-relations were possible, together
with the discrimination of the regular recurrence in the series of
points of accentuation, the perception of rhythm should persist,
however great or small might be the absolute intervals which separated
the successive members of the series. If it were the conception of a
certain form of relation, instead of the reception of a particular
impression, which was involved, we should realize a rhythm which
extended over hours or days, or which was comprehended in the fraction
of a second, as readily as those which actually affect us.

The rate at which the elements of a series succeed one another affects
the constitution of the unit groups of which the rhythmical sequence
is composed. The faster the rate, the larger is the number of
impressions which enter into each group. The first to appear in
subjective rhythm, as the rate is increased from a speed too slow for
any impression of rhythm to arise, are invariably groups of two beats;
then come three-beat groups, or a synthesis of the two-beat groups
into four, with major and minor accents; and finally six-and
eight-beat groups appear. When objective accentuation is present a
similar series of changes is manifested, the process here depending on
a composition of the unit-groups into higher orders, and not involving
the serial addition of new elements to the group.

The time relations of such smaller and larger units are dependent on
the relative inertia of the mechanism involved. A definite subjective
rhythm period undoubtedly appears; but its constancy is not maintained
absolutely, either in the process of subjective rhythmization or in
the reproduction of ideal forms. Its manifestation is subject to the
special conditions imposed on it by such apprehension or expression.
The failure to make this distinction is certain to confuse one's
conception of the temporal rhythmic unit and its period. The
variations of this period present different curves in the two cases of
subjective rhythmization and motor expression of definite rhythm
forms. In the former the absolute duration of the unit-group suffers
progressive decrease as the rate of succession among the stimuli is
accelerated; in the latter a series of extensions of its total
duration takes place as the number of elements composing the unit is
increased. The series of relative values for units of from two to
eight constituents which the finger reactions presented in this
investigation is given in the following table:


TABLE II.

    No. of Elements.    Proportional Duration.
       Two,                      1.000
       Three,                    1.109
       Four,                     1.817
       Five,                     1.761
       Six,                      2.196
       Seven,                    2.583
       Eight,                    2.590


This progressive extension of the rhythm period is to be explained by
the mechanical conditions imposed on the expression of rhythm by
processes of muscular contraction and release. Were it possible freely
to increase the rate of such successive innervations, we should expect
to find a much greater constancy in the whole period occupied by the
series of reactions which composes the unit. The comparatively
unsatisfactory quality of these larger series, and the resolution of
them into subgroups described elsewhere in this paper, are due to this
inability to accommodate the series of motor reactions to the
subjective rhythm period.

On the other hand, the temporal value of the unit which appears as the
result of subjective rhythmization undergoes a progressive decrease in
absolute magnitude as the rate of succession among the undifferentiated
stimuli is accelerated. The series of values for units containing from
two to eleven constituents is given in the following table:


TABLE III.

  No. of Elements.    Duration in Seconds.
     Two,                      2.00
     Three,                    1.75
     Four,                     1.66
     Seven,                    1.75
     Nine,                     1.50
     Eleven,                   0.97


If the time-value of the simple rhythm group here depended solely on
the relation of the successive stimuli to the subjective rhythm
period, no progressive diminution should be presented, for in
proportion as the absolute value of the separating intervals decreases
the true nature of this period should be more clearly manifested. It
is scarcely to be doubted that the complexity of its content is
likewise a determinant of the temporal value of this period, and that
to this factor is to be attributed the changes which are here
presented.[4]

   [4] Bolton reports a similar decrease in the temporal value of
   the unit, and gives the following quantitative relations:

       Average length of 2-group, 1.590 secs.
          "      "    "  3-group, 1.380   "
          "      "    "  4-group, 1.228   "
          "      "    "  6-group, 1.014   "
          "      "    "  8-group, 1.160   "

In subjective rhythmization the number of elements which compose the
unit is dependent solely on the relation of the subjective rhythm
period to the rate of succession among such elements. In objective
rhythm, as has been pointed out, a free treatment of the material is
rendered impossible by the determination of specific points of
increased stress, in virtue of which a new unit of change appears,
namely, the whole period elapsing from any one occurrence of
accentuation to its return.

But this is not the sole determinant of the numerical limits of the
simple group in such objective rhythms. The structural unit must
indeed adhere to the scheme given by the period of the recurrent
accentuation; but the point at which simple successions of this figure
give place to complex structures (at which | >q. q q_| is replaced by
| >q. q q;_q. q q_|, for example) may conceivably be hastened or
retarded by other factors than that of the simple rate of succession.
The degrees of segregation and accentuation which characterize the
rhythmic unit are elements which may thus affect the higher synthesis.
Increase in either of these directions gives greater definition to the
rhythmic figure and should tend to preserve the simple group in
consciousness. The latter relation was not made the subject of special
investigation in this research. The former was taken up at a single
point. The sounds were two in number, alternately accented and
unaccented, produced by hammer-falls of 7/8 and 1/8 inch respectively.
These were given at three rates of succession, and three different
degrees of segregation were compared together. In the following table
is given, for six subjects, the average number of elements entering
into the group-form, simple or complex, under which the rhythm was
apprehended:


TABLE IV.

    Ratio of Beat-interval    Value in Seconds of Average Interval,
    to Group-interval.           5/12        3/12          2/12
    1.000: 1.400                  3.5         5.3           9.0
    1.000: 1.000                  4.0         5.4           9.6
    1.000: 0.714                  5.2         8.4          10.8


The quantitative relations presented by these figures are consistent
throughout. For every rate of speed the average rhythmic group is
smallest when the interval separating the successive groups is at its
maximum; it is largest when this interval is at its minimum; while in
each case a median value is presented by the relation of uniformity
among the intervals. In the second as well as the first of the ratios
included in the foregoing table the interval which separates adjacent
groups is felt to be distinctly longer than that internal to the
group; in the third the relative durations of the two intervals are
those which support psychological uniformity. In the latter case, in
consequence of the freer passage from group to group, the continuity
of the rhythmical series is more perfectly preserved than in the
former, and the integration of its elements into higher syntheses more
extended.

The extension of the numerical limits of the rhythm group in
subjective rhythm which appear in consequence of progressive
acceleration in the rate of succession is given for a series of six
different values of the separating intervals in the following table,
the figures of which represent the average for six observers:


TABLE V.

  HIGHEST UNITS WHICH APPEAR.

  Value of interval in secs.:  12/12   7/12   5/12   3/12   2/12   1/12
  No. of el's in rhythm group: 2.5     3.0    4.0    7.0    9.0    11.0
  Average duration of group:   2.500   1.750  1.666  1.750  1.500   0.917

  SIMPLE UNITS.

  No. of els. in simplest group: 2.5    2.3    2.9    3.7    4.7    5.0
  Duration of simplest group:    2.50   1.34   1.21   0.92   0.78   0.41


The rate of increase here presented in the number of elements is not
sufficiently rapid to counterbalance the acceleration of speed and
maintain a constancy in the duration of the group. The greatest value
of this period is coördinated with the slowest rate of succession, the
lowest with the most rapid. As the speed increases, the duration of
the rhythmic unit is shortened. Its average duration for all rates
here included is 1.680 sec., or, without the first of the series
(one-second intervals, at which only two of the observers received the
impression of rhythm), 1.516 sec. These values are not for the
simplest combinations, but for the highest synthetical unit which was
immediately apprehended in the series of stimulations. This
compounding becomes more pronounced as the rate of succession is
accelerated, but even at intervals of 5/12 and 7/12 sec. it is the
characteristic mode of apprehension.

The number of elements in the simple groups of which these higher
units are composed, and their average duration, are also given in the
table. These likewise show a progressive increase in number, but of a
much slower rate than that manifested by the total synthesis of
elements. That is to say, in subjective rhythm as well as in
objectively figured series, subordinate rhythmical differences in the
material sink out of consciousness less rapidly than the inclusion of
fresh elements takes place; in other words, the organic complexity of
the rhythmic unit increases with every acceleration in the rate of
succession. The duration of these simple structural groups, as may be
inferred, decreases with such acceleration, but at a much more rapid
rate than is the case with the total reach of rhythmical apprehension,
the value of that unit which appears in connection with the highest
speed here included being less than half a second. The 'liveliness' of
such rapid measures is thus a resultant of several factors. It is not
a consequence solely of the more rapid rate at which the individual
stimuli succeed one another, but depends also on the shortening of the
periods of both these rhythmical units and on the progressive
divergence of the simple from the complex group.

The influence of the rate of succession on the rhythmical unit is not
confined to its segregation from adjacent groups, but affects the
internal configuration of the measure as well. With every acceleration
in rate the relative preponderance of the interval following the
accented element (in rhythms having initial stress) increases; as the
rate is retarded, smaller and smaller degrees of difference in the
values of accented and unaccented intervals are discriminated. In this
regard the influence of reduction in the absolute value of the
separating intervals is analogous to that of increased accentuation
within the group. In fast tempos and with high degrees of emphasis the
interval following the initial accent is relatively longer, that
following the unaccented relatively shorter, than at slow tempos and
with weak emphasis. This is but another way of expressing the fact
that as the elements of the auditory series succeed one another more
and more slowly the impression of rhythm fades out and that as their
succession increases in rapidity the impression becomes more and more
pronounced. The following table presents these relations in a
quantitative form for trochaic rhythm. The figures represent the
number of times the second, or group interval, was judged to be
greater than, equal to, or less than the first or internal interval of
the group. Three rates were compared together, having average
intervals of 5/12, 3/12 and 2/12 sec. Six observers took part, but
only a small number of judgments was made by each, to which fact is
probably to be attributed the irregularities of form which appear in
the various curves:


TABLE VI.

  Ratio of 1st to 2d       5/12             3/12              2/12
  Interval              +    =    -     +     =     -     +     =     -
  1.000: 1.057        95.0  0.0  5.0  100.0  0.0   0.0 100.0   0.0   0.0
  1.000: 1.000        94.7  5.3  0.0   86.0 10.5   3.5  87.5  12.5   0.0
  1.000: 0.895        40.0 60.0  0.0   46.2 49.6   3.3  74.1  18.5   7.4
  1.000: 0.846        41.0 50.0  9.0   39.4 54.6   6.0  40.0  52.0   8.0
  1.000: 0.800        20.0 60.0 20.0   13.0 70.0  17.0  53.8  46.2   0.0
  1.000: 0.756        29.4 23.5 47.1   21.8 43.4  34.8  28.0  72.0   0.0

  Av. for all ratios, 53.3 33.1 13.5   51.1 38.0  10.8  63.9  33.5   2.6


Within the limits of its appearance, as the figures just presented
indicate, the force, definition and persistency of the rhythmical
impression do not continue uniform. At the lowest rates at which
rhythm appears the integration of the successive groups is weak and
their segregation indistinct. As the rate increases the definition of
the rhythmic form grows more precise, group is separated from group by
greater apparent intervals, and the accentuation of the groups
becomes more pronounced. In subjective rhythmization of an
undifferentiated series, likewise, the impression of segregation and
periodic accentuation grows more forcible and dominating as the rate
increases. The sensitiveness to form and dynamic value in the
successive groups also increases up to a certain point in the process
of acceleration. As expressed in the capacity to discriminate
departures from formal equivalence among the groups, this function
reached its maximum, for those concerned in this investigation, at
rates varying individually from 0.3 sec. to 0.6 sec. in the value of
their intervals.

It is in virtue of its nature as an impression, as opposed to a
construction, that every structural unit, and every rhythmical
sequence into which it enters, possesses a distinct individual
quality, by which it is immediately apprehended and discriminated from
other forms, as the face of an acquaintance is remembered and
identified without detailed knowledge of the character of any feature
it possesses. For what persists from the reception of a rhythm
impression and becomes the basis of future recognition and
reproduction of it, is not the number of beats in a unit or sequence,
nor the absolute or relative intensity of the components of the group;
it is the quality of the groups as individuals, and the form of the
sequence as a whole. The phrase and verse are as vividly conceived as
the unit group; the stanza or the passage is apprehended as
immediately and simply as the bar or the measure. Of the number and
relation of the individual beats constituting a rhythmical sequence
there is no awareness whatever on the part of the æsthetic subject. I
say this without qualification. So long as the rhythmical impression
endures the analytic unit is lost sight of, the synthetic unit, or
group, is apprehended as a simple experience. When the rhythm function
is thoroughly established, when the structural form is well integrated
or familiar, it becomes well-nigh impossible to return to the analytic
attitude and discern the actual temporal and intensive relations which
enter into the rhythm. Even the quality of the organic units may lapse
from distinct consciousness, and only a feeling of the form of the
whole sequence remain. The _Gestaltsqualität_ of the passage or the
stanza is thus frequently appreciated and reproduced without an
awareness of its sequential relations, though with the keenest sense
of what is necessary to, or inconsistent with, its structure; so that
the slightest deviation from its form is remarked and the whole
sequence accurately reproduced.

In order to isolate and exhibit the tendency toward rhythmization in
regularly repeated motor reactions, one should examine series of
similar movements made at different rates both as an accompaniment to
a recurrent auditory stimulus and as free expressions of the motor
impulse independent of such objective control. In the former of these
cases the series of stimuli should be undifferentiated in quality as
well as uniform in time. The rhythm which appears in such a case will
contradict the phases of an objective series which prescribes its
form, and the evidence of its existence, presented under such adverse
conditions, should be indubitable.

As preliminary to their special work the members of the experimental
group were tested in regard to the promptness and regularity of their
reactions (by finger flexion) in accompanying a periodically recurrent
stimulus given by the beating of a metronome; records were taken also
of their capacity to estimate and maintain constant time relations by
freely tapping at intervals of one, two and five seconds. Of the
latter type of reaction the records show that a temporal grouping of
the reactions is presented in every rate of tapping. This, owing to
the large absolute intervals, is uniformly in groups of two, the first
member of which is of shorter, the second of longer duration. There is
likewise an intensive differentiation of the alternate reactions. Thus
a double rhythmical treatment appears, but while with intervals of two
seconds the phases of temporal and intensive rhythm coincide, at rates
of one and five seconds they are opposed, that is, the accentuation
falls on the initial reaction which is followed by the shorter
interval. This doubtlessly marks the emergence of that tendency to
initial accentuation which was subsequently found to prevail in all
expression of rhythm.

The types of reaction which these records afford leave no doubt that a
fuller investigation of the matter would show the constant presence,
in all such forms of activity, of a rhythmical automatization of the
series. The special problems which such an investigation should first
resolve, relate to the dependence of the amount of rhythmical
differentiation on the rate of succession among the reactions; the
relation of the form of this reaction series to factors of attention
and control; and the significance, in connection with the process of
rhythmization, of auditory stimuli produced by and accompanying the
reaction series, that is, the comparison of soundless and sounded
reactions.

In the second set of experiments the reactor was directed simply to
accompany the beating of a metronome by a light tapping with the
forefinger on a rubber-surfaced tambour connected with a pneumographic
registering pen, with which was aligned an electrical time-marker also
actuated by the metronome. Three rates of tapping were adopted, 60, 90
and 120 beats per minute. No specific instructions were given as to
direction or keenness of attention on the part of the reactor; the
most natural and simple accompaniment was desired. Occasionally, for
comparison, the reactor was directed to attend closely to each
successive beat as it occurred.

Certain questions as to the applicability of the material here
interpreted to the point in question, and as to its relation to the
objective conditions of experimentation, must be met at the outset.
The first of these is as to the actual uniformity of the metronome
series. Objective determination of its temporal regularity is
unnecessary (in so far as such a determination looks toward an
explanation of the form of tapping by reference to inequality in the
metronomic intervals). That the rhythmical phases which appear in the
accompaniment are not due to inequality in the stimulation intervals,
is shown by the reversal of relations between the metronome and its
accompaniment which occur in the midst of a continuous series of taps.
To speak roughly, a break occurs every twentieth beat. I do not refer
to minor irregularities occurring within the single group but not
affecting the form of the rhythmical accompaniment. The latter
appeared with surprising rarity, but when found were included in the
continuous calculation of averages. But in every score or so of beats
a stroke out of series would be interpolated, giving the form
| 1 >2 [1] 2 >1 |; the accompaniment being coördinated during the
second portion of the whole series with opposite phases of the
metronome from those with which its elements were connected in the
earlier part. Moreover, the dependence of this grouping of the sounds
on subjective attitudes may readily be made to appear. When attention
is turned keenly on the process its phases of rhythmical
differentiation decline; when the accompaniment becomes mechanical
they mount in value. When the observer tries to mark the ticking as
accurately as possible, not only does the index of his motor reactions
become more constant, but the sounds of the instrument likewise appear
more uniform. The observers report also that at one and the same time
they are aware of the regularity of the metronome and the rhythmical
nature of their tapping, while yet the conviction remains that the
accompaniment has been in time with the beats. Furthermore, if the
phases of ticking in the metronome were temporarily unlike, the motor
accompaniment by a series of observers, if accurate, should reproduce
the time-values of the process, and if inaccurate, should present only
an increase of the mean variation, without altering the characteristic
relations of the two phases. On the other hand, if the series be
uniform and subjectively rhythmized by the hearer, there should be
expected definite perversions of the objective relations, presenting a
series of increasing departures from the original in proportion as the
tendency to rhythmize varied from individual to individual.

On the other hand, a rhythm is already presented in the sounds of the
metronome, occasioned by the qualitative differentiation of the
members of each pair of ticks, a variation which it was impossible to
eliminate and which must be borne in mind in estimating the following
results.

Five reactors took part in the experiment, the results of which are
tabulated in the following pages. The figures are based on series of
one hundred reactions for each subject, fifty accompaniments to each
swing and return of the metronome pendulum. When taken in series of
ten successive pairs of reactions, five repetitions of the series will
be given as the basis of each average. The quantitative results are
stated in Tables VII.-XIV., which present the proportional values of
the time intervals elapsing between the successive reactions of an
accompaniment to the strokes of a metronome beating at the rates of
60, 90 and 120 per minute.


TABLE VII.

  I. AVERAGES ACCORDING TO REACTORS OF ALL RATES FOR BOTH PHASES.

  (_a_) In Series of Ten Successive Pairs of Beats.

  Subject.     I    II   III    IV    V     VI   VII   VIII   IX     X

     J.     1.000 1.005 1.022 1.053 1.044 1.116 1.058 1.061 1.055 1.052
     K.     1.000 1.027 1.057 1.111 1.093 1.086 1.074 1.096 1.093 1.071
     N.     1.000 1.032 1.062 0.990 1.009 0.980 1.019 1.040 1.067 1.040

   Aver.    1.000 1.021 1.047 1.051 1.049 1.061 1.050 1.066 1.072 1.054


TABLE VIII.

  (_b_) First and Second Halves of the Preceding Combined in Series of
  Five.

  Subject.    I    II   III    IV    V
     J.    1.058 1.031 1.041 1.054 1.048
     K.    1.043 1.050 1.076 1.102 1.082
     N.    0.990 1.025 1.051 1.028 1.024

   Aver.   1.030 1.035 1.056 1.061 1.051


TABLE IX.

  AVERAGES OF ALL RATES AND SUBJECTS ACCORDING TO PHASES OF METRONOME.

  (_a_) In Series of Ten Successive Reactions in Accompaniment of Each
  Phase.

  Phase.     I    II    III   IV    V     VI    VII  VIII   IX    X
  First,  1.000 1.055 1.102 1.097 1.082 1.066 1.053 1.123 1.120 1.074
  Second, 1.000 0.988 0.992 1.007 1.016 1.055 1.015 1.009 1.024 1.001


TABLE X.

  (_b_) First and Second Halves of the Preceding Combined in Series of
  Five.

  Phase.     I     II     III    IV      V
  First,  1.033  1.054  1.112  1.108  1.078
  Second, 1.027  1.001  1.000  1.015  1.008


TABLE XI.

  AVERAGES OF ALL SUBJECTS ACCORDING TO RATES AND PHASES OF METRONOME.

  (_a_) First Phase, Series of Ten Successive Reactions.

  Rate. _I     II   III   IV     V    VI    VII  VIII   IX     X_
    60   1.000 1.168 1.239 1.269 1.237 1.209 1.265 1.243 1.237 1.229
    90   1.000 1.048 1.063 1.095 1.086 1.069 1.102 1.127 1.168 1.095
   120   1.000 1.004 0.942 1.043 1.057 0.978 0.949 1.065 1.065 0.967


TABLE XII.

  (_b_) Second Phase, Series of Ten Successive Reactions.

  Rate.   I     II   III    IV    V     VI   VII   VIII   IX    X
   60   1.000 0.963 0.942 0.947 1.009 0.695 0.993 0.995 1.023 0.996
   90   1.000 0.893 0.987 1.018 1.036 1.005 0.995 1.000 0.977 1.000
  120   1.000 1.000 0.990 1.048 1.040 1.007 0.986 1.030 1.037 0.962


TABLE XIII.

  AVERAGES OF ALL SUBJECTS AND BOTH PHASES OF METRONOME ACCORDING TO
  RATES.

  (_a_) In Series of Ten.

  Rate.   I     II   III    IV    V     VI   VII   VIII   IX    X
   60   1.000 1.065 1.140 1.108 1.123 0.952 1.129 1.119 1.130 1.112
   90   1.000 0.970 1.025 1.056 1.061 1.037 1.048 1.063 1.072 1.047
  120   1.000 1.000 0.990 1.048 1.040 1.007 0.986 1.030 1.037 0.962


TABLE XIV.

  (_b_) Above Combined in Series of Five.

  Rate.     I        II      III       IV       V
   60     0.976    1.097    1.129    1.119    1.117
   90     1.018    1.009    1.044    1.059    1.054
  120     1.003    0.993    1.010    1.042    1.001


In the following table (XV.) is presented the average proportional
duration of the intervals separating the successive reactions of these
subjects to the stimulations given by the alternate swing and return
of the pendulum.


TABLE XV.

  Subject.       Rate: 60.       Rate: 90.       Rate: 120.
    B.         0.744 : 1.000   0.870 : 1.000   0.773 : 1.000
    J.         0.730 : 1.000   0.737 : 1.000   0.748 : 1.000
    K.         0.696 : 1.000   0.728 : 1.000   0.737 : 1.000
    N.         0.526 : 1.000   0.844 : 1.000   0.893 : 1.000


The corresponding intensive values, as measured by the excursion of
the recording pen, are as follows:


TABLE XVI.

  Subject.       Rate: 60.       Rate: 90.       Rate: 120.
    B.        (1.066 : 1.000)  0.918 : 1.000  (1.010 : 1.000)
    J.         0.938 : 1.000   0.943 : 1.000   0.946 : 1.000
    K.         0.970 : 1.000   0.949 : 1.000  (1.034 : 1.000)
    N.         0.883 : 1.000   0.900 : 1.000   0.950 : 1.000


These figures present a double process of rhythmic differentiation,
intensively into stronger and weaker beats, and temporally into
longer and shorter intervals. The accentuation of alternate elements
has an objective provocative in the qualitative unlikeness of the
ticks given by the swing and return of the pendulum. This phase is,
however, neither so clearly marked nor so constant as the temporal
grouping of the reactions. In three cases the accent swings over to
the shorter interval, which, according to the report of the subjects,
formed the initial member of the group when such grouping came to
subjective notice. This latter tendency appears most pronounced at the
fastest rate of reaction, and perhaps indicates a tendency at rapid
tempos to prefer trochaic forms of rhythm. In temporal grouping the
coördination of results with the succession of rates presents an
exception only in the case of one subject (XV. B, Rate 120), and the
various observers form a series in which the rhythmizing tendency
becomes more and more pronounced.

Combining the reactions of the various subjects, the average for all
shows an accentuation of the longer interval, as follows:


TABLE XVII.

  Rate.      Temp. Diff.     Intens. Diff.
   60       0.674 : 1.000    0.714 : 1.000
   90       0.795 : 1.000    0.927 : 1.000
  120       0.788 : 1.000    0.985 : 1.000


The rhythmical differentiation of phases is greatest at the slowest
tempo included in the series, namely, one beat per second, and it
declines as the rate of succession increases. It is impossible from
this curve to say, however, that the subjective rhythmization of
uniform material becomes more pronounced in proportion as the
intervals between the successive stimulations increase. Below a
certain rapidity the series of sounds fails wholly to provoke the
rhythmizing tendency; and it is conceivable that a change in the
direction of the curve may occur at a point beyond the limits included
within these data.

The introduction from time to time of a single extra tap, with the
effect of transposing the relations of the motor accompaniment to the
phases of the metronome, has been here interpreted as arising from a
periodically recurring adjustment of the reaction process to the
auditory series which it accompanies, and from which it has gradually
diverged. The departure is in the form of a slow retardation, the
return is a swift acceleration. The retardation does not always
continue until a point is reached at which a beat is dropped from, or
an extra one introduced into, the series. In the course of a set of
reactions which presents no interpolation of extra-serial beats
periodic retardation and acceleration of the tapping take place. This
tertiary rhythm, superimposed on the differentiation of simple phases,
has, as regards the forms involved in the present experiments, a
period of ten single beats or five measures.

From the fact that this rhythm recurs again and again without the
introduction of an extra-serial beat it is possible to infer the
relation of its alternate phases to the actual rate of the metronome.
Since the most rapid succession included was two beats per second, it
is hardly conceivable that the reactor lost count of the beats in the
course of his tapping. If, therefore, the motor series in general
parallels the auditory, the retardations below the actual metronome
rate must be compensated by periods of acceleration above it. Regarded
in this light it becomes questionable if what has been called the
process of readjustment really represents an effort to restore an
equilibrium between motor and auditory processes after an involuntary
divergence. I believe the contrasting phases are fundamental, and that
the changes represent a free, rhythmical accompaniment of the
objective periods, which themselves involve no such recurrent
differentiation.

Of the existence of higher rhythmic forms evidence will be afforded by
a comparison of the total durations of the first and second
five-groups included in the decimal series. Difference of some kind is
of course to be looked for; equivalence between the groups would only
be accidental, and inequality, apart from amount and constancy, is
insignificant. In the results here presented the differentiation is,
in the first place, of considerable value, the average duration of the
first of these groups bearing to the second the relation of
1.000:1.028.

Secondly, this differentiation in the time-values of the respective
groups is constant for all the subjects participating. The ratios in
their several cases are annexed:


TABLE XVIII.

  Subject.          Ratio.
    J.           1.000:1.042
    K.           1.000:1.025
    N.           1.000:1.010


It is perhaps significant that the extent of this differentiation--and
inferably the definition of rhythmical synthesis--corresponds to the
reported musical aptitudes of the subjects; J. is musically trained,
K. is fond of music but little trained, N. is without musical
inclination.

The relations of these larger rhythmical series repeat those of their
constituent groups--the first is shorter, the second longer. The two
sets of ratios are brought together for comparison in the annexed
table:


TABLE XIX.

  Subject.   Unit-Groups.  Five Groups.
     J.      1.000:1.354   1.000:1.042
     K.      1.000:1.388   1.000:1.025
     N.      1.000:1.326   1.000:1.010


It is to be noted here, as in the case of beating out specific
rhythms, that the index of differentiation is greater in simple than
in complex groups, the ratios for all subjects being, in simple
groups, 1.000:1.356, and in series of five, 1.000:1.026.

There is thus present in the process of mechanically accompanying a
series of regularly recurring auditory stimuli a complex rhythmization
in the forms, first, of a differentiation of alternate intervals, and
secondly, of a synthesis of these in larger structures, a process here
traced to the third degree, but which may very well extend to the
composition of still more comprehensive groups. The process of
reaction is permeated through and through by rhythmical
differentiation of phases, in which the feeling for unity and
equivalence must hold fast through really vast periods as the long
slow phases swing back and forth, upon which takes place a swift and
yet swifter oscillation of rhythmical values as the unit groups become
more limited, until the opposition of single elements is reached.


III. THE CHARACTERISTICS OF THE RHYTHMICAL UNIT.


A. _The Number of Elements in the Group and its Limits._

The number of elements which the rhythmical group contains is related,
in the first place, to the rate of succession among the elements of
the sequence. This connection has already been discussed in so far as
it bears on the forms of grouping which appear in an undifferentiated
series of sounds in consequence of variations in the absolute
magnitude of the intervals which separate the successive stimuli. In
such a case the number of elements which enter into the unit depends
solely on the rate of succession. The unit presents a continuous
series of changes from the lowest to the highest number of
constituents which the simple group can possibly contain, and the
synthesis of elements itself changes from a succession of simple forms
to structures involving complex subordination of the third and even
fourth degree, without other change in the objective series than
variations in tempo.

When objectively defined rhythm types are presented, or expression is
given to a rhythm subjectively defined by ideal forms, these simple
relations no longer hold. Acceleration or retardation of speed does
not unconditionally affect the number of elements which the rhythm
group contains. In the rhythmization of an undifferentiated series the
recurrence of accentuation depends solely on subjective conditions,
the temporal relations of which can be displaced only within the
limits of single intervals; for example, if a trochaic rhythm
characterizes a given tempo, the rhythm type persists under conditions
of progressive acceleration only in so far as the total duration of
the two intervals composing the unit approximates more closely to the
subjective rhythm period than does that of three such intervals. When,
in consequence of the continued reduction of the separating intervals,
the latter duration presents the closer approximation, the previous
rhythm form is overthrown, accentuation attaches to every third
instead of to alternate elements, and a dactylic rhythm replaces the
trochaic.

In objective rhythms, on the other hand, the determination of specific
points of increased stress makes it impossible thus to shift the
accentuation back and forth by increments of single intervals. The
unit of displacement becomes the whole period intervening between any
two adjacent points of accentuation. The rhythm form in such cases is
displaced, not by those of proximately greater units, but only by such
as present multiples of its own simple groups. Acceleration of the
speed at which a simple trochaic succession is presented results thus,
first, in a more rapid trochaic tempo, until the duration of two
rhythm groups approaches more nearly to the period of subjective
rhythmization, when--the fundamental trochaism persisting--the
previous simple succession is replaced by a dipodic structure in which
the phases of major and minor accentuation correspond to the
elementary opposition of accented and unaccented phases. In the same
way a triplicated structure replaces the dipodic as the acceleration
still continues; and likewise of the dactylic forms.

We may say, then, that the relations of rate to complexity of
structure present the same fundamental phenomena in subjective
rhythmization and objectively determined types, the unit of change
only differing characteristically in the two cases. The wider range of
subjective adjustment in the latter over the former experience is due
to the increased positive incentive to a rhythmical organic
accompaniment afforded by the periodic reinforcement of the objective
stimulus.

An investigation of the limits of simple rhythmical groups is not
concerned with the solution of the question as to the extent to which
a reactor can carry the process of prolonging the series of elements
integrated through subordination to a single dominant accentuation.
The nature of such limits is not to be determined by the introspective
results of experiments in which the observer has endeavored to hold
together the largest possible number of elements in a simple group.
When such an attempt is made a wholly artificial set of conditions,
and presumably of mechanisms, is introduced, which makes the
experiment valueless in solving the present problem. Both the
direction and the form of attention are adverse to the detection of
rhythmical complications under such conditions. Attention is directed
away from the observation of secondary accents and toward the
realization of a rhythm form having but two simple phases, the first
of which is composed of a single element, while within the latter
fall all the rest of the group. Such conditions are the worst possible
for the determination of the limits of simple rhythm groups; for the
observer is predisposed from the outset to regard the whole group of
elements lying within the second phase as undifferentiated. Thus the
conditions are such as to postpone the recognition of secondary
accents far beyond the point at which they naturally arise.

But further, such an attempt to extend the numerical scope of simple
rhythm groups also tends to transform and disguise the mechanism by
which secondary stresses are produced, and thereby to create the
illusion of an extended simple series which does not exist. For we
have no right to assume that the process of periodic accentuation in
such a series, identical in function though it be, involves always the
same form of differentiation in the rhythmical material. If the
primary accentuation be given through a finger reaction, the fixating
of that specific form of change will predispose toward an overlooking
of secondary emphases depending on minor motor reactions of a
different sort. The variety of such substitutional mechanisms is very
great, and includes variations in the local relations of the finger
reaction, movements of the head, eyes, jaws, throat, tongue, etc.,
local strains produced by simultaneous innervation of flexor and
extensor muscles, counting processes, visual images, and changes in
ideal significance and relation of the various members of the group.
Any one of these may be seized upon to mediate the synthesis of
elements and thus become an unperceived secondary accentuation.

Our problem is to determine at what point formal complication of the
rhythmical unit tends naturally to arise. How large may such a group
become and still remain fundamentally simple, without reduplication of
accentual or temporal differentiation? The determination of such
limits must be made on the basis of quantitative comparison of the
reactions which enter into larger and smaller rhythmical series, on
the one hand, and, on the other, of the types of structure which
appear in subjective rhythmization and the apprehension of objective
rhythms the forms of which are antecedently unknown to the hearer. The
evidence from subjective rhythms is inconclusive. The prevailing
types are of two and three beats. Higher forms appear which are
introspectively simple, but introspection is absolutely unable to
solve the problem as to the possible composite nature of these
extended series. The fact that they are confined to even numbers, the
multiples of two, and to such odd-numbered series as are multiples of
three, without the appearance of the higher primes, indicates the
existence in all these groups of secondary accentuation, and the
resolution of their forms into structures which are fundamentally
complications of units of two and three elements only. The process of
positive accentuation which appears in every higher rhythmical series,
and underlying its secondary changes exhibits the same reduction of
their elementary structure to double and triple groups, has been
described elsewhere in this report. Here it is in place to point out
certain indirect evidence of the same process of resolution as
manifested in the treatment of longer series of elements.

The breaking up of such series into subgroups may not be an explicitly
conscious process, while yet its presence is indispensable in giving
rhythmical form to the material. One indication of such
undiscriminated rhythmical modification is the need of making or
avoiding pauses between adjacent rhythmical groups according as the
number of their constituents varies. Thus, in rhythms having units of
five, seven, and nine beats such a pause was imperative to preserve
the rhythmical form, and the attempt to eliminate it was followed by
confusion in the series; while in the case of rhythms having units of
six, eight, and ten beats such a pause was inadmissible. This is the
consistent report of the subjects engaged in the present
investigation; it is corroborated by the results of a quantitative
comparison of the intervals presented by the various series of
reactions. The values of the intervals separating adjacent groups for
a series of such higher rhythms are given in Table XX. as proportions
of those following the initial, accented reaction.


TABLE XX.

    Rhythm.    Initial Interval.  Final Interval
    Five-Beat,       1.000             1.386
    Six    "         1.000             0.919
    Seven  "         1.000             1.422
    Eight  "         1.000             1.000
    Nine   "         1.000             1.732
    Ten    "         1.000             1.014


The alternate rhythms of this series fall into two distinct groups in
virtue of the sharply contrasted values of their final intervals or
group pauses. The increased length of this interval in the
odd-numbered rhythms is unquestionably due to a subdivision of the
so-called unit into two parts, the first of which is formally
complete, while the latter is syncopated. In the case of five-beat
rhythms, this subdivision is into threes, the first three of the five
beats which compose the so-called unit forming the primary subgroup,
while the final two beats, together with a pause functionally
equivalent to an additional beat and interval, make up the second, the
system being such as is expressed in the following notation:
| .q. q q; >q.  q % |. The pause at the close of the group is
indispensable, because on its presence depends the maintenance of
equivalence between the successive three-groups. On the other hand,
the introduction of a similar pause at the close of a six-beat group
is inadmissible, because the subdivision is into three-beat groups,
each of which is complete, so that the addition of a final pause would
utterly unbalance the first and second members of the composite group,
which would then be represented by the following notation:
| >q. q q; .q. q q % |; that is, a three-group would alternate with a
four-group, the elements of which present the same simple time
relations, and the rhythm, in consequence, would be destroyed. The
same conditions require or prevent the introduction of a final pause
in the case of the remaining rhythm forms.

The progressive increase in the value of the final interval, which
will be observed in both the odd-and even-numbered rhythms, is
probably to be attributed to a gradual decline in the integration of
the successive groups into a well-defined rhythmical sequence.

This subdivision of material into two simple phases penetrates all
rhythmical structuring. The fundamental fact in the constitution of
the rhythmical unit is the antithesis of two phases which we call the
accented and the unaccented. In the three-beat group as in the
two-beat, and in all more complex grouping, the primary analysis of
material is into these two phases. The number of discriminable
elements which enter each phase depends on the whole constitution of
the group, for this duality of aspect is carried onward from its point
of origin in the primary rhythm group throughout the most complex
combination of elements, in which the accented phase may comprise an
indefinitely great number of simple elements, thus:

      ______         __________        ______________
     /      \       /          \      /              \
    >     .         >      .          >>  .
  | q q ; q q |,  | q q q; q q q |, | q q q q; q q q q |,  etc.
    \_/
     >

An indication of this process of differentiation into major and minor
phases appears in the form of rhythm groups containing upwards of four
elements. In these the tendency is, as one observer expresses it, 'to
consider the first two beats as a group by themselves, with the others
trailing off in a monotonous row behind.' As the series of elements
thus bound up as a unit is extended, the number of beats which are
crowded into the primary subgroup also increases. When the attempt was
made to unite eleven or twelve reactions in a single group, the first
four beats were thus taken together, with the rest trailing off as
before. It is evident that the lowest groups with which attention
concerned itself here were composed of four beats, and that the actual
form of the (nominally) unitary series of eleven beats was as follows:

     _______________________
    /                       \
   >>        >        >
  | q q q q; q q q q; q q q q |.
        .        .        .

The subscripts are added in the notation given above because it is to
be doubted if a strictly simple four-beat rhythm is ever met with. Of
the four types producible in such rhythm forms by variation in the
accentual position, three have been found, in the course of the
present investigation, to present a fundamental dichotomy into units
of two beats. Only one, that characterized by secondary accentuation,
has no such discriminable quality of phases. Of this form two things
are to be noted: first, that it is unstable and tends constantly to
revert to that with initial stress, with consequent appearance of
secondary accentuation; and second, that as a permanent form it
presents the relations of a triple rhythm with a grace note prefixed.

The presence of this tendency to break up the four-rhythm into
subgroups of two beats explains a variety of peculiarities in the
records of this investigation. The four-beat rhythm with final accent
is found most pleasant at the close of a rhythmical sequence. The
possibility of including it in a continuous series depends on having
the final interval of 'just the right length.' If one keeps in mind
that a secondary initial accent characterizes this rhythm form, the
value required in this final interval is explained by the resolution
of the whole group into two units of three beats each, the latter of
the two being syncopated. The pause is of 'just the right length' when
it is functionally equal to two unaccented elements with their
succeeding intervals, as follows: | .q. q q; .q  % % |.

Likewise in four-rhythms characterized by initial stress there appears
a tendency to accent the final beat of the group, as well as that to
accent the third. Such a series of four may therefore break up in
either of two ways, into | >q.  q; .q  q | on a basis of two-beat units,
or into | .q. q q; >q % %| on a basis of three-beat units.

The persistence of these simple equivalences appears also in the
treatment of syncopated measures and of supplementary or displaced
accents. Of the form | >q. q >q. | one reactor says, and his
description may stand for all, "This deliberate introduction of a
third accent on the last beat is almost impossible for me to keep. The
single group is easy enough and rather agreeable, but in a succession
of groups the secondarily accented third beat comes against the first
of the next group with a very disagreeable effect." This is the case
where no pause intervenes between the groups, in which case the rhythm
is destroyed by the suppression, in each alternate simple group, of
the unaccented phase; thus, | >q. q >q.  | alone is pleasant, because
it becomes | .q. q; >q % |, but in combination with preceding and
succeeding groups it is disagreeable, because it becomes in reality
| >q. q; .q % |, etc. A long pause between the groups destroys this
disagreeableness, since the lacking phase of the second subgroup is
then restored and the rhythm follows its normal course.

The amphibrachic form, | >q q. q |, is more difficult to maintain than
either the dactylic or the trochaic, and in a continuous series tends
to pass over into one of these, usually the former. 'With sufficient
pause,' the reactors report, 'to allow the attitude to die away,' it
is easily got. The same inability to maintain this form in
consciousness appears when a continuous series of clicks is given,
every third of which is louder than the rest. Even when the beginning
of the series is made coincident with the initial phase of the
amphibrachic group the rhythmic type slips over into the dactylic, in
spite of effort. In this, as in the preceding type of reaction, if the
interval separating adjacent groups be lengthened, the rhythm is
maintained without trouble. The 'dying away' of the attitude lies
really in such an arrangement of the intervals as will formally
complete a phrase made up of simple two-beat units.

The positive evidence which this investigation affords, points to the
existence of factors of composition in all rhythms of more than three
beats; and a variety of peculiarities which the results present can be
explained--and in my estimation explained only--on the basis of such
an assumption. I conclude, therefore, that strictly stated the
numerical limit of simple rhythm groups is very soon reached; that
only two rhythmical units exist, of two and three beats respectively;
that in all longer series a resolution into factors of one of these
types takes place; and, finally, that the subordination of higher
rhythmical quantities of every grade involves these simple relations,
of which, as the scope of the synthesis increases, the opposition of
simple alternate phases tends more and more to predominate over
triplicated structures.

Variation in the number of elements which enter into the rhythmic
unit does not affect the sense of equivalence between successive
groups, so long as the numerical increase does not reach a point at
which it lessens the definiteness of the unit itself. For the purpose
of testing this relation the reactors beat out a series of rhythm
forms from 'one-beat' rhythms to those in which the group consisted of
seven, eight and nine elements, and in which the units were either
identical with one another or were made up of alternately larger and
smaller numbers of elements. Two questions were to be answered in each
case; the manner in which these various changes affected the sense of
rhythmical equivalence in the alternate groups, and the variations in
affective quality which these changes introduced into the experience.
With the former of these problems we are here concerned. From
'one-beat' to four-beat rhythms the increase in number of constituents
in no way affects the sense of rhythmical equivalence. Beyond this
point there is a distinct falling off. 'The first part of the rhythm
begins to fade away before the end of the second,' says one; and
another: 'The series then reverts to a monotonous succession without
feeling of rhythm.' This decline marks those groups composed of an odd
number of elements much earlier and more strongly than those which
contain an even number. The sense of equivalence has fallen off at
five and practically disappears at seven beats, while groups of six
and eight retain a fairly definite value as units in a rhythmical
sequence. This peculiar relation must be due to the subconscious
resolution of the larger symmetrical groups into smaller units of
three and four constituents respectively.

Likewise the introduction of variations in the figure of the
group--that is, in the number of elements which enter into the groups
to be compared, the distribution of time values within them, the
position of accents, rests, and the like--does not in any way affect
the sense of equivalence between the unlike units. Against a group of
two, three, four, or even five elements may be balanced a syncopated
measure which contains but one constituent, with the sense of full
rhythmical equivalence in the functional values of the two types.
Indeed, in the case of five-beat rhythms the definition of values is
greater when such opposition finds place than when the five-beat
group is continuously repeated. This is to be explained doubtlessly by
the more definite integration into a higher rhythmical unity which is
afforded under the former conditions.

The number and the distribution of elements are factors variable at
will, and are so treated in both musical and poetical expression. The
condition which cannot be transgressed is the maintenance of strict
temporal relations in the succession of total groups which constitute
the rhythmical sequence. These relations are, indeed, not invariable
for either the single interval or the duration of the whole group, but
they are fixed functions of the dynamic values of these elements and
units. Two identically figured groups (_e.g._, | >q. q q | >q. q q |
), no more possess rhythmically substitutionary values than does the
opposition of a single beat to an extended series (_e.g._,
| >q. | >q. q q | ), apart from this factor of temporal proportion.
Those groups which are identical in figure must also be uniform in
duration if they are to enter as substitutionary groups into a
rhythmical sequence.[5] When the acatalectic type is alternately
departed from and returned to in the course of the rhythmical
sequence, the metrical equivalents must present total time-values
which, while differing from that of the full measure in direction and
degree, in dependence on the whole form of their structure, maintain
similar fixed relations to the primary type. The changes which these
flexible quantities undergo will here only be indicated. If the
substitutionary groups be of different figures, that which comprises
the larger number of elements will occupy the greater time, that which
contains fewer, the less.

   [5] Theoretically and strictly identical; this abstracts from
   the coördination of such identical groups as major and minor
   components of a higher rhythmical synthesis, which is really
   never absent and in virtue of which the temporal values of the
   groups are also differentiated.

I do not forget the work of other observers, such as Brücke, who finds
that dactyls which appear among trochees are of less duration than the
latter, nor do I impugn their results. The rhythmical measure cannot
be treated as an isolated unit; it must always be considered in its
structural relations to the rhythmical sequence of which it forms a
part. Every non-conforming measure is unquestionably affected by the
prevailing type of the rhythmical sequence in which it occurs. Brücke
points out the converse fact that those trochees and iambs are longest
which appear in dactylic or other four-measures; but this ignores the
complexity of the conditions on which the character of these intrusive
types depends. The time-values of such variants are also dependent on
the numerical preponderance of the typical form in the whole series.
When a single divergent form appears in the sequence the dynamic
relations of the two types is different from that which obtains when
the numbers of the two approach equality, and the effect of the
prevailing form on it is proportionally greater. Secondly, the
character of such variants is dependent on the subordinate
configuration of the sequence in which they appear, and on their
specific functions within such minor rhythmical figures. The relative
value of a single dactyl occurring in an iambic pentameter line cannot
be predicated of cases in which the two forms alternate with each
other throughout the verse. Not only does each type here approximate
the other, but each is affected by its structural relation to the
proximately higher group which the two alternating measures compose.
Thirdly, the quantitative values of these varying forms is related to
their logical significance in the verse and the degree of accentuation
which they receive. Importance and emphasis increase the duration of
the measure; the lack of either shortens it. In this last factor, I
believe, lies the explanation of the extreme brevity of dactyls
appearing in three-rhythms. When a specific rhythm type is departed
from, for the purpose of giving emphasis to a logically or metrically
important measure, the change is characteristically in the direction
of syncopation. Such forms, as has been said elsewhere, mark nodes of
natural accentuation and emphasis. Hence, the dactyl introduced into
an iambic or trochaic verse, which, so far as concerns mere number of
elements, tends to be extended, may, in virtue of its characteristic
lack of accentuation and significance, be contracted below the value
of the prevailing three-rhythm. Conversely the trochee introduced into
a dactylic sequence, in consequence of its natural accentuation or
importance, may exceed in time-value the typical four-rhythm forms
among which it appears. The detailed examination of the relation of
temporal variations to numerical predominance in the series, to
subordinate structural organization, and to logical accentuation, in
our common rhythms, is a matter of importance for the general
investigation which remains still to be carried out. In so far as the
consideration of these factors entered into the experimental work of
the present research, such quantitative time relations are given in
the following table, the two types in all cases occurring in simple
alternation:


TABLE XXI.

  Rhythm.       1st Meas.  2d Meas.  Rhythm.       1st Meas.  2d Meas.

   .     > >                          > >    .
  q q q; q q %    1.000     1.091     q q %; q q q    1.000     1.140
  .      >                            >      .
  q q q; q q %    1.000     1.159     q q %; q q q    1.000     1.021
      .    >                       >       .
  q q q; q q %    1.000     1.025     q q %; q q q    1.000     1.267
  >      .                              .        >
  q q q; q q %    1.000     0.984     q q %; q q q    1.000     1.112
      >  .                          .    >
  q q q; q q %    1.000     0.766     q q %; q q q    1.000     1.119


As the disparity in numerical constitution increases, so will also the
divergence in time-value of the two groups concerned. When
differentiation into major and minor phases is present, the duration
of the former will be greater than that of the latter. Hence, in
consequence of the combination of these two factors--_e.g._, in a
syncopated measure of unusual emphasis--the characteristic time-values
may be inverted, and the briefer duration attach to that unit which
comprises the greater number of elements. Intensive values cannot take
the place of temporal values in rhythm; the time form is fundamental.
Through all variations its equivalences must be adhered to. Stress
makes rhythm only when its recurrence is at regular intervals. The
number of subordinate factors which combine with the accented element
to make the group is quite indifferent. But whether few or many, or
whether that element on which stress falls stands alone (as it may),
the total time values of the successive groups must be sensibly
equivalent. When a secondary element is absent its place must be
supplied by a rest of equivalent time-value. If these proper temporal
conditions be not observed no device of intensive accentuation will
avail to produce the impression of metrical equivalence among the
successive groups.


B. _The Distribution of Elements Within the Group._

(_a_) The Distribution of Intensities.

In the analysis of the internal constitution of the rhythmic unit, as
in other parts of this work, the investigation follows two distinct
lines, involving the relations of rhythm as apprehended, on the one
hand, and the relations of rhythm as expressed, on the other; the
results in the two cases will be presented separately. A word as to
the method of presentation is necessary. The fact that in connection
with each experiment a group of questions was answered gives rise to
some difficulty in planning the statement of results. It is a simple
matter to describe a particular set of experiments and to tell all the
facts which were learned from them; but it is not logical, since one
observation may have concerned the number of elements in the rhythmic
unit, another their internal distribution, and a third their
coalescence in a higher unity. On the other hand, the statement of
each of these in its own proper connection would necessitate the
repetition of some description, however meager, of the conditions of
experimentation in connection with each item. For economy's sake,
therefore, a compromise has been made between reporting results
according to distribution of material and according to distribution of
topics. The evidence of higher grouping, for example, which is
afforded by variations in duration and phases of intensity in
alternate measures, will be found appended to the sections on these
respective classes of material.

In all the following sections the hammer-clang apparatus formed the
mechanism of experimentation in sensory rhythms, while in reactive
rhythms simple finger-tapping was employed.

In comparing the variations in stress which the rhythmical material
presents, the average intensities of reaction for the whole group has
been computed, as well as the intensities of the single reactions
which compose it. This has been done chiefly in view of the unstable
intensive configuration of the group and the small amount of material
on which the figures are based. The term is relative; in ascertaining
the relations of intensity among the several members of the group, at
least ten successive repetitions, and in a large part of the work
fifty, have been averaged. This is sufficient to give a clear
preponderance in the results to those characteristics which are really
permanent tendencies in the rhythmical expression. This is especially
true in virtue of the fact that throughout these experiments the
subject underwent preliminary training until the series of reactions
could be easily carried out, before any record of the process was
taken. But when such material is analyzed in larger and smaller series
of successive groups the number of reactions on which each average is
based becomes reduced by one half, three quarters, and so on. In such
a case the prevailing intensive relations are liable to be interfered
with and transformed by the following factor of variation. When a
wrong intensity has accidentally been given to a particular reaction
there is observable a tendency to compensate the error by increasing
the intensity of the following reaction or reactions. This indicates,
perhaps, the presence of a sense of the intensive value of the whole
group as a unity, and an attempt to maintain its proper relations
unchanged, in spite of the failure to make exact coördination among
the components. But such a process of compensation, the disappearance
of which is to be looked for in any long series, may transpose the
relative values of the accented elements in two adjacent groups when
only a small number of reactions is taken into account, and make that
seem to receive the major stress which should theoretically receive
the minor, and which, moreover, does actually receive such a minor
stress when the value of the whole group is regarded, and not solely
that member which receives the formal accentuation.

The quantitative analysis of intensive relations begins with triple
rhythms, since its original object was to compare the relative
stresses of the unaccented elements of the rhythmic group. These
values for the three forms separately are given in Table XXII., in
which the value of the accented element in each case is represented by
unity.


TABLE XXII.

  Rhythm.         1st Beat.  2d Beat.  3d Beat.

  Dactylic,          1.000     0.436     0.349
  Amphibrachic,      0.488     1.000     0.549
  Anapæstic,         0.479     0.484     1.000


The dactylic form is characterized by a progressive decline in
intensity throughout the series of elements which constitute the
group. The rate of decrease, however, is not continuous. There is a
marked separation into two grades of intensity, the element receiving
accentual stress standing alone, those which possess no accent falling
together in a single natural group, as shown in the following ratios:
first interval to third, 1.000:0.349; second interval to third,
1.000:0.879. One cannot say, therefore, that in such a rhythmic form
there are two quantities present, an accented element and two
undifferentiated elements which are unaccented. For the average is not
based on a confused series of individual records, but is consistently
represented by three out of four subjects, the fourth reversing the
relations of the second and third elements, but approximating more
closely to equivalence than any other reactor (the proportional values
for this subject are 1.000; 0.443; 0.461). Moreover, this reactor was
the only musically trained subject of the group, and one in whom the
capacity for adhering to the logical instructions of the experiment
appears decidedly highest.

In the amphibrachic form the average again shows three degrees of
intensity, three out of four subjects conforming to the same type,
while the fourth reverses the relative values of the first and third
intervals. The initial element is the weakest of the group, and the
final of median intensity, the relation for all subjects being in the
ratio, 1.000:1.124. The amphibrachic measure begins weakly and ends
strongly, and thus approximates, we may say, to the iambic type.

In the anapæstic form the three degrees of intensity are still
maintained, three out of four subjects giving consistent results; and
the order of relative values is the simple converse of the dactylic.
There is presented in each case a single curve; the dactyl moves
continuously away from an initial accent in an unbroken decrescendo,
the anapæst moves continuously toward a final accent in an unbroken
crescendo. But in the anapæstic form as well as in the dactylic there
is a clear duality in the arrangement of elements within the group,
since the two unaccented beats fall, as before, into one natural
group, while the accented element is set apart by its widely
differentiated magnitude. The ratios follow: first interval to second,
1.000:1.009; first interval to third, 1.000:2.084.

The values of the three elements when considered irrespective of
accentual stress are as follows: First, 1.000; second, 1.001; third,
0.995. No characteristic preponderance due to primacy of position
appears as in the case of relative duration. The maximum value is
reached in the second element. This is due to the coöperation of two
factors, namely, the proximity of the accentual stress, which in no
case is separated from this median position by an unaccented element,
and the relative difficulty in giving expression to amphibrachic
rhythms. The absolute values of the reactions in the three forms is of
significance in this connection. Their comparison is rendered possible
by the fact that no change in the apparatus was made in the course of
the experiments. They have the following values: Dactylic, 10.25;
amphibrachic, 12.84; anapæstic, 12.45. The constant tendency, when any
difficulty in coördination is met with, is to increase the force of
the reactions, in the endeavor to control the formal relations of the
successive beats. If such a method of discriminating types be applied
to the present material, then the most easily coördinated--the most
natural--form is the dactyl; the anapæst stands next; the amphibrach
is the most unnatural and difficult to coördinate.

The same method of analysis was next applied to four-beat rhythms. The
proportional intensive values of the successive reactions for the
series of possible accentual positions are given in the following
table:


TABLE XXIII.

  Stress.      1st Beat.  2d Beat.  3d Beat.  4th Beat.

  Initial,        1.000     0.575     0.407      0.432
  Secondary,      0.530     1.000     0.546      0.439
  Tertiary,       0.470     0.407     1.000      0.453
  Final,          0.492     0.445     0.467      1.000


The first and fourth forms follow similar courses, each marked by
initial and final stress; but while this is true throughout in the
fourth form, it results in the first form from the preponderance of
the final interval in a single individual's record, and therefore
cannot be considered typical. The second and third forms are preserved
throughout the individual averages. The second form shows a maximum
from which the curve descends continuously in either direction; in the
third a division of the whole group into pairs is presented, a minor
initial accent occurring symmetrically with the primary accent on the
third element. This division of the third form into subgroups appears
also in its duration aspect. Several inferences may be drawn from this
group of relations. The first and second forms only are composed of
singly accented groups; in the third and fourth forms there is
presented a double accent and hence a composite grouping. This
indicates that the position in which the accent falls is an important
element in the coördination of the rhythmical unit. When the accent is
initial, or occurs early in the group, a larger number of elements can
be held together in a simple rhythmic structure than can be
coördinated if the accent be final or come late in the series. In this
sense the initial position of the accent is the natural one. The first
two of these four-beat forms are dactylic in structure, the former
with a postscript note added, the latter with a grace note prefixed.
In the third and fourth forms the difficulty in coördinating the
unaccented initial elements has resulted in the substitution of a
dipodic division for the anapæstic structure of triple rhythms with
final accent.

The presence of a tendency toward initial accentuation appears when
the average intensities of the four reactions are considered
irrespective of accentual position. Their proportional values are as
follows: First, 1.000; second, 0.999; third, 1.005; fourth, 0.981.
Underlying all changes in accentuation there thus appears a resolution
of the rhythmic structure into units of two beats, which are
primitively trochaic in form.

The influence exerted by the accented element on adjacent members of
the group is manifested in these forms more clearly than heretofore
when the values of the several elements are arranged in order of their
proximity to that accent and irrespective of their positions in the
group. Their proportional values are as follows:


TABLE XXIV.

  2d Remove.  1st Remove.  Accent.  1st Remove.  2d Remove.
    0.442        0.526      1.000     0.514        0.442


This reinforcing influence is greater--according to the figures just
given--in the case of the element preceding the accent than in that of
the reaction which follows it. It may be, therefore, that the position
of maximal stress in the preceding table is due to the close average
relation in which the third position stands to the accented element.
This proximity it of course shares with the second reaction of the
group, but the underlying trochaic tendency depreciates the value of
the second reaction while it exaggerates that of the third. This
reception of the primitive accent the third element of the group
indeed shares with the first, and one might on this basis alone have
expected the maximal value to be reached in the initial position, were
it not for the influence of the accentual stress on adjacent members
of the group, which affects the value of the third reaction to an
extent greater than the first, in the ratio 1.000:0.571.

The average intensity of the reactions in each of the four forms--all
subjects and positions combined--is worthy of note.


TABLE XXV.

  Stress.    Initial.     Secondary.      Tertiary.      Final.
  Value,      1.000         1.211           1.119        1.151


The first and third forms, which involve initial accents--in the
relation of the secondary as well as primary accent to the
subgroups--are both of lower average value than the remaining types,
in which the accents are final, a relation which indicates, on the
assumption already made, a greater ease and naturalness in the former
types. Further, the second form, which according to the subjective
reports was found the most difficult of the group to execute--in so
far as difficulty may be said to be inherent in forms of motor
reaction which were all relatively easy to manipulate--is that which
presents the highest intensive value of the whole series.

In the next group of experiments, the subject was required to execute
a series of reactions in groups of alternating content, the first to
contain two uniform beats, the second to consist of a single reaction.
This second beat with the interval following it constitutes a measure
which was to be made rhythmically equivalent to the two-beat group
with which it alternated. The time-relations of the series were
therefore left to the adjustment of the reactor. The intensive
relations were separated into two groups; in the first the final
reaction was to be kept uniform in strength with those of the
preceding group, in the second it was to be accented.

The absolute and relative intensive values for the two forms are given
in the following table:


TABLE XXVI.

  Rhythm.              1st Beat.  2d Beat.  3d Beat.  Value.

  Syncopated Measures      13.00     15.12     16.50  Absolute.
  Unaccented,               1.000     1.175     1.269 Relative.

  Syncopated Measures      10.95     11.82     16.11  Absolute.
  Accented,                 1.000     1.079     1.471 Relative.


These averages hold for every individual record, and therefore
represent a thoroughly established type. In both forms the reaction of
the syncopated measure receives the greatest stress. In the first
form, while the stress is relatively less than in the second, it is at
the same time absolutely greater. The whole set of values is raised
(the ratio of average intensities in the two forms being 1.147:1.000),
as it has already been found to be raised in other forms difficult to
execute. To this cause the preponderance is undoubtedly to be
attributed, as the reports of every subject describe this form as
unnatural, in consequence of the restraint it imposes on an impulse to
accent the final reaction, _i.e._, the syncopated measure.

In the next set of experiments the series of reactions involved the
alternation of a syncopated measure consisting of a single beat with a
full measure of three beats. The same discrimination into accented and
unaccented forms in the final measure was made as in the preceding
group. The series of absolute and relative values are given in the
following table.


TABLE XXVII.

  Rhythm.            1st Beat.  2d Beat.  3rd Beat.  4th Beat.  Value.

  Syncopated Measures   9.77      8.96       9.61      13.78   Absolute.
  Unaccented,           1.000     0.915      0.983      1.165  Relative.

  Syncopated Measures  11.57     11.07      11.53      21.50   Absolute.
  Accented,             1.000     0.957      0.996      1.858  Relative.


These averages hold for every subject where the syncopated measure
receives accentuation, and for two out of three reactors where it is
unaccented. The latter individual variation shows a progressive
increase in intensity throughout the series.

Here, as in the preceding forms, a well-established type is presented.
Not only when accentuation is consciously introduced, but also when
the attempt is made--and in so far as the introspection of the reactor
goes, successfully made--to maintain a uniformity among the reactions
of the full and syncopated measures, the emphasis on the latter is
unconsciously increased. In the accented form, as before, there is a
clear discrimination into two grades of intensity (ratio of first
three elements to final, 1.000:1.888) while in the unaccented no such
broad separation exists (ratio of first three elements to final,
1.000:1.156).

The type of succession in each of these forms of reaction is a
transformed dactylic, in which group should now be included the simple
four-beat rhythm with final accent, which was found to follow the same
curve. The group begins with a minor stress in both of the present
forms, this stress being greater in the unaccented than in the
accented type. This preponderance I believe to be due to the endeavor
to repress the natural accent on the syncopated measure. In both forms
the intensive value of the second element is less than that of the
third, while the intensity of the initial reaction is greater than
that of either of these subsequent beats. This form of succession I
have called a _transformed dactylic_. It adheres to the dactylic type
in possessing initial accentuation; it departs from the normal
dactylic succession in inverting the values of the second and third
members of the group. This inversion is not inherent in the rhythmic
type. The series of three beats decreasing in intensity represents the
natural dactylic; the distortion actually presented is the result of
the proximity of each of these groups to a syncopated measure which
follows it. This influence I believe to be reducible to more
elementary terms. The syncopated measure is used to mark the close of
a logical sequence, or to attract the hearer's attention to a striking
thought. In both cases it is introduced at significant points in the
rhythmical series and represents natural nodes of accentuation. The
distortion of adjacent measures is to be attributed to the increase in
this elementary factor of stress, rather than to the secondary
significance of the syncopation, for apart from any such change in the
rhythmical structure we have found that the reactions adjacent to that
which receives accentual stress are drawn toward it and increased in
relative intensity.

Further quantitative analysis of rhythmical sequences, involving a
comparison of the forms of successive measures throughout the higher
syntheses of verse, couplet and stanza, will, I believe, confirm this
conception of the mutable character of the relations existing between
the elements of the rhythmical unit, and the dependence of their
quantitative values on fixed points and modes of structural change
occurring within the series. An unbroken sequence of dactyls we shall
expect to find composed of forms in which a progressive decrease of
intensity is presented from beginning to end of the series (unless we
should conceive the whole succession of elements in a verse to take
shape in dependence on the point of finality toward which it is
directed); and when, at any point, a syncopated measure is introduced
we shall look for a distortion of this natural form, at least in the
case of the immediately preceding measure, by an inversion of the
relative values of the second and third elements of the group. This
inversion will unquestionably be found to affect the temporal as well
as the intensive relations of the unit. We should likewise expect the
relations of accented and unaccented elements in the two-beat rhythms
to be similarly affected by the occurrence of syncopated measures, and
indeed to find that their influence penetrates every order of rhythm
and extends to all degrees of synthesis.

To the quantitative analysis of the intensive relations presented by
beaten rhythms must be added the evidence afforded by the apprehension
of auditory types. When a series of sounds temporally and
qualitatively uniform was given by making and breaking an electric
circuit in connection with a telephone receiver, the members of a
group of six observers without exception rhythmized the stimuli in
groups--of two, three and four elements according to rate of
succession--having initial accentuation, however frequently the
series was repeated. When the series of intervals was temporally
differentiated so that every alternate interval, in one case, and
every third in another, stood to the remaining interval or intervals
in the ratio, 2:1, the members of this same group as uniformly
rhythmized the material in measures having final accentuation. In
triple groups the amphibrachic form (in regard to temporal relations
only, as no accentuation was introduced) was never heard under natural
conditions. When the beginning of the series was made to coincide with
the initiation of an amphibrachic group, four of those taking part in
the investigation succeeded in maintaining this form of apprehension
for a time, all but one losing it in the dactylic after a few
repetitions; while the remaining two members were unable to hold the
amphibrachic form in consciousness at all.


(_b_) The Distribution of Durations.

The inquiry concerning this topic took the direction, first, of a
series of experiments on the influence which the introduction of a
louder sound into a series otherwise intensively uniform exerts on the
apparent form of the series within which it occurs. Such a group of
experiments forms the natural preliminary to an investigation of the
relation of accentuation to the form of the rhythm group. The
apparatus employed was the fourth in the series already described. The
sounds which composed the series were six in number; of these, five
were produced by the fall of the hammer through a distance of 2/8
inch; the sixth, louder sound, by a fall through 7/8 inch. In those
cases in which the intensity of this louder sound was itself varied
there was added a third height of fall of two inches. The succession
of sounds was given, in different experiments, at rates of 2.5, 2.2,
and 1.8 sec. for the whole series. The durations of the intervals
following and (in one or two cases) preceding the louder sound were
changed; all the others remained constant. A longer interval
intervened between the close and beginning of the series than between
pairs of successive sounds. After hearing the series the subject
reported the relations which appeared to him to obtain among its
successive elements. As a single hearing very commonly produced but a
confused impression, due to what was reported as a condition of
unpreparedness which made it impossible for the hearer to form any
distinct judgment of such relations, and so defeated the object of the
experiment, the method adopted was to repeat each series before asking
for judgment. The first succession of sounds then formed both a signal
for the appearance of the second repetition and a reinforcement of the
apperception of its material.

In order to define the direction of attention on the part of the
observer it was made known that the factors to be compared were the
durations of the intervals adjacent to the louder sound in relation to
the remaining intervals of the series, and that all other temporal and
intensive values were maintained unchanged from experiment to
experiment. In no instance, on the other hand, did any subject know
the direction or nature of the variation in those quantities
concerning which he was to give judgment. In all, five subjects shared
in the investigation, C., E., F., H. and N. Of these C only had
musical training. In the tables and diagrams the interval preceding
the louder sound is indicated by the letter B, that following it by
the letter A. Totals--judgment or errors--are indicated by the letter
T, and errors by the letter E. The sign '+' indicates that the
interval against which it stands is judged to be greater than the
remaining intervals of the series, the sign '=' that it is judged
equal, and the sign '-' that it is judged less.

The first series of changes consisted in the introduction of
variations in the duration of the interval following the loud sound,
in the form of successive increments. This loud sound was at the third
position in the series. All intensive relations and the duration of
the interval preceding the louder sound remained unchanged. The
results of the experiment are presented in the following table.


TABLE XXVIII.

  Ratio of A to         B           A          Errors   Total   Per cent.
  Other Intervals.  +   =   -   +   =   -    B   A   T  judgts. of errors

  1.000 : 0.625     2   2   2   4   2   0    4   2   6     12      50
  1.000 : 0.666     4   2   0   1   3   2    4   5   9     12      75
  1.009 : 0.714     5   3   0   2   2   4    5   6  11     16      69
  1.000 : 0.770     5   4   0   1   1   7    5   8  13     18      72
  1.000 : 0.833     1   5   0   0   0   6    1   6   7     12      50

    Totals,        17  16   2   8   8  19   19  27  46     70


The value of the interval following the louder sound is correctly
reported eight times out of thirty; that preceding it is correctly
reported sixteen times out of thirty. The influence which such a
change in intensive value introduced at a single point in a series of
sounds exerts on the apparent relation of its adjacent intervals to
those of the remainder of the series is not equally distributed
between that which precedes and that which follows it, but affects the
latter more frequently than the former in a ratio (allowing latitude
for future correction) of 2:1. In the case of interval A the error is
one of underestimation in twenty-seven cases; in none is it an error
of overestimation. In the case of interval B the error is one of
overestimation in seventeen instances, of underestimation in two. The
influence of the introduction of such a louder sound, therefore, is to
cause a decrease in the apparent duration of the interval which
follows it, and an increase in that of the interval which precedes it.
The illusion is more pronounced and invariable in the case of the
interval following the louder sound than of that preceding it, the
proportion of such characteristic misinterpretations to the whole
number of judgments in the two cases being, for A, 77 per cent.; for
B, 54 per cent. The effect on interval A is very strong. In the second
group, where the ratio of this interval to the others of the series is
3:2, it is still judged to be equal to these others in 50 per cent. of
the cases, and less in 35 per cent. Further, these figures do not give
exhaustive expression to the whole number of errors which may be
represented in the judgments recorded, since no account is taken of
greater and less but only of change of sign; and an interval might be
underestimated and still be reported greater than the remaining
intervals of the series in a group of experiments in which the
relation of the interval in question to these remaining intervals
ranged from the neighborhood of equivalent values to that in which one
was double the other. If in a rough way a quantitative valuation of
errors be introduced by making a transference from any one sign to
that adjacent to it (_e.g._, - to =, or = to +) equal to _one_, and
that from one extreme sign to the other equal to _two_, the difference
in the influence exerted on the two intervals will become still more
evident, since the errors will then have the total (quantitative)
values of A 46, and B 19, or ratio of 1.000:0.413.

Next, the position of the louder sound in the series of six was
changed, all other conditions being maintained uniform throughout the
set of experiments. The series of intervals bore the following
relative values: A, 0.900; B, 1.100; all other intervals, 1.000. The
louder sound was produced by a fall of 0.875 inch; all others by a
fall of 0.250 inch. The louder sound occurred successively in the
first, second, third, fourth and fifth positions of the series. In the
first of these forms it must of course be remembered that no interval
B exists. The results of the experiment are shown in the following
table:


TABLE XXIX.

  Position       Apparent Values.     Errors.    % of Errors     Ditto
  in            B              A     B   A   T  in tot. judg.    quant.
  Series    +   =   -    +   =   -                B      A      B     A
  1                      2   6   6   0   12  12         85.7         85.7
  2         2   8   2    1   7   4  10   11  21  83.3   91.6   73.3  91.6
  3         1   9   3    1   8   3  10   11  21  76.9   91.6   71.9  91.6
  4         1   8   4    2   6   5   9   11  20  69.2   84.6   52.8  84.6
  5         0  12   0    0   4   8  12   12  24 100.0  100.0   60.0 100.0
  Totals,   4  37   9    6  31  26  41   57  98  82.3   90.7   64.5  90.7

  Total judgments, 113; Errors (B = 31), A = 57.


The relatively meager results set forth in the preceding section are
corroborated in the present set of experiments. That such a variation
of intensity introduced into an otherwise undifferentiated auditory
series, while it affects the time-values of both preceding and
following intervals, has a much greater influence on the latter than
on the former, is as apparent here as in the previous test. The number
of errors, irrespective of extent, for the two intervals are: B, 82.3
per cent, of total judgments; A, 90.7 per cent. When the mean and
extreme sign displacements are estimated on the quantitative basis
given above these percentages become B, 64.5; A, 90.7, respectively--a
ratio of 0.711:1.000.

The direction of error, likewise, is the same as in the preceding
section. Since the actual values of the two intervals here are
throughout of extreme sign--one always greater, the other always
less--only errors which lie in a single direction are discriminable.
Illusions lying in this direction will be clearly exhibited, since the
differences of interval introduced are in every case above the
threshold of discrimination when the disturbing element of variations
in intensity has been removed and the series of sounds made
intensively uniform. In case of a tendency to underestimate B or
overestimate A, errors would not be shown. This problem, however, is
not to be met here, as the results show; for there is recorded a
proportion of 82.3 per cent. of errors in judgment of interval B, and
of 90.7 per cent. in judgment of interval A, all the former being
errors of overestimation, all of the latter of underestimation.

The influence of position in the series on the effect exerted by such
a change of intensity in a single member can be stated only
tentatively. The number of experiments with the louder sound in
position five was smaller than in the other cases, and the relation
which there appears cannot be absolutely maintained. It may be also
that the number of intervals following that concerning which judgment
is to be given, and with which that interval may be compared, has an
influence on the accuracy of the judgment made. If we abstract from
this last set of results, the tendency which appears is toward an
increase in accuracy of perception of comparative durations from the
beginning to the end of the series, a tendency which appears more
markedly in the relations of the interval preceding the louder sound
than in those of the interval which follows it. This conclusion is
based on the succession of values which the proportion of errors to
total judgments presents, as in the annexed table.


TABLE XXX.

  Percentage of Errors for Each Position.

  Interval.    I    II    III   IV     V
  B.               83.3  76.9  69.2  (100)  Irrespective
  A.         85.7  91.6  91.6  84.6  (100)   of extent.
  B.               73.3  71.9  53.8   (60)    Estimated
  A.         85.7  91.6  91.6  84.6  (100)  quantitatively.


Next, the relation of the amount of increase in intensity introduced
at a single position in such a series to the amount of error thereby
occasioned in the apprehension of the adjacent intervals was taken up.
Two sets of experiments were carried out, in each of which five of
the sounds were of equal intensity, while one, occurring in the midst
of the series, was louder; but in one of the sets this louder sound
was occasioned by a fall of the hammer through a distance of 0.875
inch, while in the other the distance traversed was 2.00 inches. In
both cases the extent of fall in the remaining hammers was uniformly
0.25 inch. The results are given in the following table:


TABLE XXXI.

                     Interval B.¹         Interval A.
  Ratio of Interval 0.875 in. 2.00 in.  0.875 in. 2.00 in.
  B to Interval A.  +  =  -   +  =  -   +  =  -   +  =  -
  1.000 : 1.000     0  6  0   0  4  2   0  5  1   0  0  6
  0.909 : 1.000     2  4  0   0  4  2   0  2  4   2  2  2
  0.833 : 1.000     0  6  0   0  4  2   4  0  2   1  3  2
  0.770 : 1.000     0  6  0   2  2  2   2  4  0   4  0  2
  0.714 : 1.000     0  6  0   1  5  0   6  0  0   2  2  2
  Totals,           2 28      3 19  8  12 11  7   9  7 14
  T.E., T.J.,       2    30  11    30  13    30  21    30
  and per cent.,    6.6%      36.6%      60.0%     70.0%

   ¹Interval B in these experiments is of the same duration as all
   others but that following the louder sound; hence, judgments in
   the second column are correct.


Again the markedly greater influence of increased intensity on the
interval following than on that preceding it appears, the percentage
of errors being, for B (both intensities), 21.6 per cent.; for A, 56.6
per cent. Also, in these latter experiments the direction of error is
more definite in the case of interval A than in that of interval B.

The influence of changes in intensity on the amount of error produced
is striking. Two intensities only were used for comparison, but the
results of subsequent work in various other aspects of the general
investigation show that this correlation holds for all ranges of
intensities tested, and that the amount of underestimation of the
interval following a louder sound introduced into an otherwise uniform
series is a function of the excess of the former over the latter. The
law holds, but not with equal rigor, of the interval preceding the
louder sound. So far as these records go, the influence of such an
increase of intensity is more marked in the case of interval B than in
that of interval A. It is to be noted, however, that the absolute
percentage of errors in the case of A is several times greater than in
that of B. I conclude that A is much more sensitive than B to such
influences, and that there is here presented, in passing from
intensity I. to intensity II., the rise of conditions under which the
influence of the louder sound on B is first distinctly felt--that is,
the appearance of a threshold--and that the rate of change manifested
might not hold for higher intensities.

Lastly, the rate at which the sounds of the series succeeded one
another was varied, in order to determine the relation which the
amount of influence exerted bore to the absolute value of the
intervals which it affected. Three rates were adopted, the whole
series of sounds occupying respectively 2.50 secs., 2.20 secs, and
1.80 secs. The results are summed in the following table:


TABLE XXXII.

                         Rate: 2.5 secs.   Rate: 2.2 secs.   Rate: 1.8 secs.

  Ratio of Interval B    B        A        B        A        B        A
    to Interval A.    +  =  -  +  =  -  +  =  -  +  =  -  +  =  -  +  =  -

  1.000 : 1.000       2  8  0  0  8  2  0  8  2  0  2  8  0  4  0  0  2  2
  0.917 : 1.000       0  8  2  4  6  0  3  8  0  0  8  3  2  2  0  0  2  2
  0.846 : 1.000       1  9  0  5  4  1  3  8  0  3  7  1  6  5  0  1  8  2
  0.786 : 1.000       1 10  0 11  0  0  6  6  0  7  3  4  6  2  2  2  6  2
  0.733 : 1.000                         4  2  0  4  0  2  4  6  0  8  0  2
  0.687 : 1.000                         5  3  1  6  1  2  2  6  0  7  0  1

  Totals              4 35  2 20 18  3 21 35  3 20 21 20 20 25  2 18 18 11*

  *Transcriber's Note: Original "1".

These results are converted into percentages of the total number of
judgments in the following table:


TABLE XXXIII.

  Rate of        B                     A
  Success.   +   =   -   Errors.   +   =   -   Errors.
  2.5 secs   10  85  5     15      49  44   7    51
  2.2  "     36  59  5     41      33  34  33    67
  1.8  "     43  53  4     47      38  38  24    62


In the case of interval A the direction of the curve of error changes
in passing from Rate II. to Rate III. In the case of interval B the
increase is continuous.

This increase in the percentage of error is, further, distinctly in
the direction of an accentuation of the overestimation of the
interval B, as is shown in the percentage of cases in which this
interval appeared greater than the rest of the series for each of the
three rates.

If the three rates be combined in the one set of results, the
difference in the effects produced on the interval following the
louder sound and on that which precedes it becomes again apparent.
This is done in the table below.


TABLE XXXIV.

              B           A             B                A
  Ratio   +   =   -    +  =  -    T.E. T.J.  %     T.E. T.J.  %
    I.     2  20  2    0  12 12     2   24   8.5    12   24  50.0
   II.     5  18  2    4  16  5     5   25  20.0    21   25  84.4
  III.    10  22  0    9  19  4    10   32  31.0    23   32  72.0
   IV.    13  18  2   20   9  8    13   33  39.0    17   37  46.0
    V.     8   8  0   12   0  4     8   16  50.0     4   16  25.0
   VI.     7   9  1   13   1  3     7   17  41.0     4   17  24.0


The overestimation of the interval before the louder sound also tends
to increase in extent with the actual increase in duration of the
interval following that sound over the other intervals of the series.

Thus, the form which the sensible time-relations of such a limited
series of sounds present is found to be intimately dependent on the
intensive preponderance of certain elements within it, on the degree
of increased stress which such elements receive, on their local
position in the series, and on the rate at which the stimulations
succeed one another. The knowledge of these facts prepares us for the
whole series of relations manifested in the special quantitative
investigations reported in the sections which follow. In the first of
these is presented the time-relations obtaining among the successive
reactions of the various rhythm types discussed in the preceding
division of this part, the section, namely, on the distribution of
intensities.

In the first group of reactions the series was not to be consciously
accented, nor to be divided into groups by the introduction of pauses.
The reactor was required only to conceive it as a succession of
two-beat groups continuously repeated, the way in which the groups
should be defined, whether by counting or otherwise, being left to his
own discretion. The experimental group was composed of five subjects.

The following table presents the quantitative results of an analysis
of the material in series of ten successive pairs of reactions, upon
the basis of unity as the value of the first element.


TABLE XXXV.

  Quantities.       I    II    III   IV     V    VI    VII  VIII   IX    X
  Whole Meas.,   1.000 0.894 1.035 0.912 1.000 0.877 1.070 0.877 1.070 0.841
  First Inter.,  1.000 1.142 1.071 1.142 1.000 1.285 1.000 1.214 1.000 1.214
  Second Inter., 1.000 0.837 1.023 0.860 1.000 0.744 1.093 0.767 1.093 0.790


Within the limits of the calculation no progressive change appears,
either of acceleration or of retardation, whether in general or on the
part of individual reactors. In narrower ranges the inconstancy of the
periods is very marked, and their variations of clearly defined
rhythmical character. The duration of the total measures of two beats
is throughout alternately longer and shorter, the average of their
values presenting a ratio of 1.000:0.847. The order of this
arrangement, namely, that the longer period precedes the shorter in
the larger group, is drawn from the fact that measurements
consistently began with the initial reaction of the series.

An analysis of the constituent intervals of the unit group, as shown
in the second and third lines of the table, reveals the existence of a
complex subordinate rhythm. The two components of the rhythmical group
do not increase and decrease concomitantly in temporal value in
composing the alternate long and short measures of the fluent rhythm.
The movement involves a double compensating rhythmical change, in
which the two elements are simultaneously in opposite phases to each
other. A measure which presents a major first interval contains always
a minor second; one introduced by a minor first concludes with a major
second. The ratios of these two series of periodic variations must
themselves manifestly be different. Their values are, for the first
interval of the measure, 1.000:1.214; and for the second interval,
1.000:0.764. The greater rhythmical differentiation marks the second
of the two intervals; on the variations of this second interval,
therefore, depends the appearance of that larger rhythm which
characterizes the series. The ratios of these primary intervals are
less consistently maintained than are those of the rhythmical measures
built out of them. It will be noted that in both intervals there is a
tendency for the value of the difference between those of alternate
groups to increase as the tapping progresses. This change I have
interpreted as indicative of a progressive definition in the process
of rhythmization, depending on an increase in coördination and
differentiation of the reactions as the series advances.

A simple stress on alternate elements was next introduced in the
series, forming a simple trochaic measure repeated without
interruption. The quantitative results follow, arranged as in the
preceding experiment.


TABLE XXXVI.

  Quantity.    I    II    III   IV     V    VI    VII  VIII   IX    X
  Measure,  1.000 1.035 1.070 1.035 1.087 1.070 1.071 1.052 1.070 1.070
  1st Int., 1.000 1.000 1.111 1.000 1.055 1.111 1.166 1.111 1.111 1.111
  2d Int.,  1.000 1.025 1.051 1.051 1.102 1.051 1.025 1.025 1.051 1.051


Here again there is no progressive acceleration or retardation. The
rhythmical differentiation of alternate measures is very slight--the
average ratio of the first to the second being 1.000:0.993--but is of
the same type as in the preceding. The excess in the amount of this
differentiation presented by the first type of reaction over the
second may be due to the presence of a tendency to impart rhythmical
character to such a series of reactions, which, prohibited in one
form--the intensive accent--finds expression through the substitution
for this of a temporal form of differentiation.

In this trochaic rhythm the phases of variation in the constituent
intervals of the measure are concomitant, and their indices of
differentiation almost identical with each other. Their values are,
for the first, 1.000:0.979; and for the second, 1.000:0.995. The
higher index is that of the first interval, that, namely, which
follows the accented beat of the measure, and indicates that the
rhythmical change is due chiefly to a differentiation in the element
which receives the stress.

In iambic measures similarly beaten out there is likewise no
acceleration nor retardation apparent in the progress of the tapping.
The temporal differentiation of alternate measures is of the same
extent as in the preceding group, namely, 1.000:0.991. the
proportional quantitative values of the measure and its constituent
intervals, taken in series of ten successive repetitions, are as
follow:


TABLE XXXVII.

  Quantity     I    II    III   IV     V    VI    VII  VIII   IX    X
  Measure,  1.000 0.979 1.000 0.979 1.020 0.979 0.979 1.020 0.979 0.979
  1st Int., 1.000 0.941 0.941 1.000 1.000 0.941 8.082 0.941 0.941 0.941
  2d Int.,  1.000 1.000 1.032 0.967 1.032 1.000 1.000 1.032 1.000 0.967


The alternation of greater and less duration in the rhythm groups is
due to a variation in the time-value of the second interval only, the
index of average change in the first member being zero. That is, the
greater index of instability again attaches to that element which
receives the stress. Though this holds true throughout these
experiments, the amount of difference here is misleading, since on
account of the smaller absolute value of the first interval the
proportional amount of change within it which passes unrecorded is
greater than in the case of the second interval.

In general, the larger temporal variations of the trochaic and iambic
rhythm forms are too slight to be significant when taken individually.
The evidence of rhythmical treatment in such a series of reactions,
which is strongly marked in the unaccented form, nevertheless receives
reinforcement from these inconsiderable but harmonious results.

The proportional values of the variations in alternate measures for
accented and unaccented elements are given in the following table, in
which the figures for the trochaic and iambic forms are combined:


TABLE XXXVIII.

  Interval     I    II    III   IV    V     VI    VII  VIII   IX    X
  Accented, 1.000 1.000 1.083 1.000 1.041 1.000 1.083 1.000 1.041 1.000
  Unacc.    1.000 1.000 1.000 1.035 1.071 1.000 0.964 1.000 1.000 1.000


It is perhaps worthy of note that in this table a still higher
rhythmical synthesis of regular form appears in the accented elements
if the figures be taken in series of four consecutive pairs of
reactions.

In the group of triple rhythms next taken up--the dactylic, the
amphibrachic and the anapæstic--each type presents an increase in the
duration of the unit group between the beginning and end of the
series, but without any regular curve connecting these terms. Neither
the average results nor those of the individual subjects show anywhere
a decrease of duration in the progress of the tapping. The
proportional results for each of the three rhythm forms, and their
averages, are given in the following table.


TABLE XXXIX.

  Rhythm.      I    II    III   IV    V     VI    VII  VIII   IX    X
  Datyl.,   1.000 1.062 1.062 1.087 1.087 1.075 1.125 1.112 1.125 1.112
  Amphib.,  1.000 1.000 1.000 1.069 1.085 1.046 1.046 1.046 1.046 1.035
  Anapæs.,  1.000 1.012 1.023 1.012 1.037 1.037 1.023 1.059 1.023 1.084

  Average,  1.000 1.024 1.036 1.060 1.060 1.060 1.072 1.072 1.072 1.084


When all types and subjects are thus combined the summation of these
inconstant retardations presents sharply differentiated terms and a
curve uninverted at any point.

A separate analysis of the components of the rhythmical group shows,
for the dactylic form, an important increase in duration in only one
of the three intervals, namely, that following the element which
receives accentual stress. The proportional values for these intervals
follow.


TABLE XL.

Interval.    I    II    III   IV    V     VI    VII  VIII   IX    X
First,    1.000 1.153 1.153 1.153 1.153 1.231 1.193 1.193 1.231 1.231
Second,   1.000 0.917 0.917 1.000 0.917 0.917 0.917 0.917 0.917 0.917
Third     1.000 1.000 1.033 1.066 1.055 1.066 1.133 1.066 1.066 1.066


Since the progressive variation does not penetrate the whole measure,
but affects only a single constituent having a strongly marked
functional character, the process of change becomes unlike that of
true retardation. In such a case, if the increase in duration be
confined to a single element and parallel the changes in a
simultaneous variant of a different order, we should regard them as
functionally connected, and therefore interpret the successively
greater periods of time occupied by the rhythmical measures as
constituting no real slowing of the tempo. The measure of relative
tempo in such a case consists in the ratios of the successive
durations of the rhythmical units after the subtraction of that
element of increase due to this extraneous source. Here, since the
increase is confined to that member of the group which receives
accentual stress, and since the increase of accentuation is typically
accompanied by an extension of the following interval, the changes
presented do fulfil the conditions of a progressively increased
accentuation of the rhythm group, and to this origin I think it is
undoubtedly to be attributed. It is to be noted that the final
interval also undergoes a slight increase, while the median suffers a
similarly slight decrease in duration as the series progresses.

In the amphibrachic form the changes manifested by the constituents of
the unit group are more obscure. No progressive retardation of the
accented element is apparent. In the initial and final intervals the
difference in duration between the first and last members of the
series is small and appears early in the process. If we assume the
general application of the laws of change presented in the preceding
section, there should be here two influences concerned in the
determination of the relations presented, the factors, namely, of
position and accent. The falling of the accentual stress on the median
interval eliminates one of the two factors of progressive reduction in
that element and replaces it by a factor of increase, thereby doing
away with the curve of change; while at the same time it decreases the
changes which occur in the bounding intervals of the group by removing
the accent from the first and by the proximate position of its own
accent tending to reduce the last interval.

Under this same assumption there should be expected in the anapæstic
form of rhythm an exaggeration of the progressive increase in the
final interval, together with a further reduction in the duration of
the initial; since from the falling of the accent on the final
interval two factors of increase combine, while in the initial, which
immediately follows the accented interval in the series, a positive
factor of reduction appears. This is actually the type of change
presented by the quantitative relations, which are given as
proportional values in the following table.


TABLE XLI.

  Interval.    I    II    III   IV    V     VI   VII   VIII   IX    X
  First,    1.000 0.950 1.000 0.950 1.000 0.950 1.000 1.000 1.000 1.050
  Second,   1.000 1.100 1.000 1.050 1.100 1.000 1.000 1.050 1.100 1.000
  Third,    1.000 1.073 1.073 1.024 1.024 1.122 1.098 1.098 1.098 1.146


Between its first and last terms the first interval shows a departure
slightly less than that of the previous rhythm from the rate of change
which characterizes the dactylic type; but if the average values of
the whole series of intervals be taken in each of the three cases, the
progressive reduction will be seen clearly to continue in passing from
the second to the third form. The figures annexed give these averages
as proportions of the first interval in the series.


TABLE XLII.

                      1st      Av. of
    Rhythm.         Interv.   all others.
    Dactylic,        1.000  :  1.188
    Amphibrachic,    1.000  :  1.019
    Anapæstic,       1.000  :  1.000


The relations of the various intervals in the three forms are put
together here for comparison:


TABLE XLIII.

  Rhythm.         1st Interval.      2d Interval.      3d Interval.
  Dactylic,       1.000 : 1.231     1.000 : 1.000     1.000 : 1.066
  Amphibrachic,   1.000 : 1.045     1.000 : 1.000     1.000 : 1.054
  Anapæstic,      1.000 : 1.050     1.000 : 1.000     1.000 : 1.146


An analysis of the factors of accentual stress and of position in the
rhythmical group in isolation from each other, confirms the
assumptions already made as to their influence in defining the form of
the rhythmic unit. Table XLIV. exhibits the series of temporal changes
taking place in accented and unaccented intervals, respectively, for
the three forms combined, and therefore independent of position in the
group.


TABLE XLIV.

  Interval.       I    II    III   IV     V    VI    VII  VIII   IX     X
  Accented.    1.000 1.064 1.064 1.064 1.064 1.094 1.094 1.064 1.094 1.129
  Unaccented,  1.000 1.000 1.000 1.080 1.040 1.040 1.040 1.040 1.040 1.040


Similarly, in Table XLV. are given the proportional values of the
series of intervals in order of their position in the group and
independent of accentual stress:


TABLE XLV.

  Interval.    I    II    III   IV    V     VI    VII  VIII   IX    X
  First,    1.000 1.043 1.087 1.043 1.087 1.043 1.043 1.121 1.043 1.121
  Second,   1.000 1.000 1.000 1.043 1.000 0.956 1.000 0.956 1.000 0.956
  Third,    1.000 1.028 1.028 1.055 1.028 1.083 1.083 1.083 1.083 1.083


The former table makes clear the predominance of the increase in the
accented element over the average of all unaccented elements of the
series; the latter shows the independence of increase in the initial
and final, and of decrease in the median interval, of any relation to
the position of the accentual stress. Both the intensive accentuation
and the demarcation of successive groups thus appear to be factors of
definition in the rhythmic unit. Those types which are either marked
by a more forcible accent or separated by longer pauses are more
distinctly apprehended and more easily held together than those in
which the accent is weaker or the pause relatively less. It would
follow that the general set of changes which these series of reactions
present are factors of a process of definition in the rhythmical
treatment of the tapping, and are not due to any progressive change in
the elementary time relations of the series.

The figures for measures of four beats are incomplete. They show an
increase in the average duration of the group from first to last of
the series in three out of the four forms, namely, those having
initial, secondary and final stress.

Of the relative amounts contributed by the several elements to the
total progressive variation of the measures in the first form, the
least marks those intervals which follow unaccented beats, the
greatest those which follow accented beats; among the latter, that
shows the greater increase which receives the primary accent, that on
which falls the secondary, subconscious accent shows the less; and of
the two subgroups which contain these accents that in which the major
accent occurs contributes much more largely to the progressive change
than does that which contains the minor.

When the phases of accented and unaccented elements are compared,
irrespective of their position in the rhythmic group, the same
functional differences are found to exist as in the case of triple
rhythms. Their quantitative relations are given in the following
table.


TABLE XLVI.

  Phase.       I    II    III   IV    V     VI    VII  VIII   IX    X
  Accented. 1.000 1.103 1.069 1.172 1.241 1.139 1.206 1.310 1.241 1.310
  Unacc.,   1.000 1.083 1.128 1.169 1.159 1.208 1.169 1.250 1.169 1.169


The cause of the apparent retardation lies, as before, in a change
occurring primarily in the accented elements of the rhythm, and this
progressive differentiation, it is inferable from the results cited
above, affects adjacent unaccented elements as well, the whole
constituting a process more naturally interpretable as a functional
accompaniment of progressive definition in the rhythmical treatment of
the material than as a mark of primary temporal retardation.

The contribution of the several intervals according to position in the
series and irrespective of accentual stress is given in the table
following.


TABLE XLVII.

  Interval.    I    II    III   IV    V     VI    VII  VIII   IX    X
  First,    1.000 1.136 1.136 1.182 1.227 1.227 1.227 1.273 1.318 1.318
  Second,   1.000 1.042 1.042 1.125 1.166 1.042 1.042 1.083 1.083 1.166
  Third,    1.000 1.150 1.250 1.250 1.250 1.250 1.400 1.400 1.450 1.450
  Fourth,   1.000 1.059 1.059 1.147 1.179 1.147 1.179 1.294 1.206 1.179


A rhythmical alternation is here presented, the contributions of the
first and third elements being far in advance of those of the second
and fourth. The values of the minor pair are almost equal; of the
major the third exceeds the first. Under the assumption already made
this would indicate the existence at these points of nodes of natural
accentuation, of which the second marks the maximum reached in the
present series.

The determination of relative time-values for accented and unaccented
intervals was next sought by indirect experimentation, in which the
affective aspect of the experience was eliminated from consideration,
and account was taken only of the perception of quantitative
variations in the duration of the successive intervals. Proceeding
from the well-known observation that if every alternate element of a
temporally uniform auditory series receive increased stress, the whole
series will coalesce into successive groups of two elements in which
the louder sound precedes and the weaker follows, while the interval
which succeeds the unaccented sound, and which therefore separates
adjacent groups, will appear of greater duration than that which
follows the accented element, the investigation sought by employing
the method of right and wrong cases with a series of changing
time-values for the two intervals to determine the quantitative
proportion of the two durations necessary to produce the impression of
temporal uniformity in the series.

Two rhythm forms only were tested, the trochaic and dactylic, since
without an actual prolongation of considerable value in the interval
following the louder sound, at the outset, no apprehension of the
series as iambic or anapæstic could be brought about. The stimuli were
given by mechanism number 4, the distance of fall being 2/8 and 7/8
inch respectively for unaccented and accented sounds. The series of
changes included extreme proportional values of 0.714 and 1.769 in
duration of the two intervals. Six persons took part in the
investigation. In the following table is given the percentage of cases
in which the interval following the unaccented element was judged
respectively greater than, equal to, or less than that which followed
the accented element, for each of the series of ratios presented by
the time-values of the intervals in trochaic rhythm.


TABLE XLIX.

  Ration of Unaccented to     Unaccented Interval Judged to be
    Accented Interval.       +                 =              -
     1.000 : 1.769         0.0 per cent.   100.0 per cent   0.0 per cent.
     1.000 : 1.571        12.5    "         50.0    "      37.5    "
     1.000 : 1.400        22.0    "         56.0    "      22.0    "
     1.000 : 1.222        16.0    "         84.0    "
     1.000 : 1.118        26.0    "         74.0    "
     1.000 : 1.000        61.6    "         38.4    "
     1.000 : 0.895       100.0    "
     1.000 : 0.800        88.8    "         11.2    "
     1.000 : 0.714       100.0    "


The anomalous percentage which appears in the first horizontal row
needs explanation. The limit of possible differentiation in the
time-values of accented and unaccented intervals in a rhythmical group
is characteristically manifested, not by the rise of a perception of
the greater duration of the interval following the accented element,
but through an inversion of the rhythmical figure, the original
trochee disappearing and giving place to an iambic form of grouping,
the dactyl being replaced by an anapæst. In the case in question the
inversion had taken place for all subjects but one, in whom the
original trochaic form, together with its typical distribution of
intervals, remained unchanged even with such a great actual disparity
as is here involved.

For this group of observers and for the series of intensities taken
account of in the present experiment, the distribution of time-values
necessary to support psychological uniformity lies near to the ratio
1.400:1.000 for accented and unaccented intervals respectively, since
here the distribution of errors in judgment is arranged symmetrically
about the indifference point. Overestimation of the interval following
the louder sound appears by no means invariable. Under conditions of
objective uniformity the judgment of equality was given in 38.4 per
cent, of all cases. This cannot be baldly interpreted as a persistence
of the capacity for correct estimation of the time values of the two
intervals in the presence of an appreciation of the series as a
rhythmical group. The rhythmic integration of the stimuli is weakest
when the intervals separating them are uniform, and since the question
asked of the observer was invariably as to the apparent relative
duration of the two intervals, it may well be conceived that the
hearers lapsed from a rhythmical apprehension of the stimuli in these
cases, and regarded the successive intervals in isolation from one
another. The illusions of judgment which appear in these experiences
are essentially dependent on an apprehension of the series of sounds
in the form of rhythmical groups. So long as that attitude obtains it
is absolutely impossible to make impartial comparison of the duration
of successive intervals. The group is a unit which cannot be analyzed
while it continues to be apprehended as part of a rhythmical sequence.
We should expect to find, were observation possible, a solution of
continuity in the rhythmical apprehension in every case in which these
distortions of the normal rhythm form are forced on the attention.
This solution appears tardily. If the observer be required to estimate
critically the values of the successive intervals, the attention from
the outset is turned away from the rhythmical grouping and directed
on each interval as it appears. When this attitude prevails very small
differences in duration are recognized (_e.g._, those of 1.000:1.118,
and 1.000:0.895). But when this is not the case, the changes of
relative duration, if not too great for the limits of adaptation, are
absorbed by the rhythmical formula and pass unobserved, while
variations which overstep these limits appear in consciousness only as
the emergence of a new rhythmic figure. Such inversions are not wholly
restricted by the necessity of maintaining the coincidence of
accentuation with objective stress. With the relatively great
differences involved in the present set of experiments, the rhythmical
forms which appeared ignored often the objective accentuation of
single groups and of longer series. Thus, if the second interval of a
dactyl were lengthened the unaccented element which preceded it
received accentuation, while the actual stress on the first sound of
the group passed unobserved; and in a complex series of twelve
hammer-strokes the whole system of accentuation might be transposed in
the hearer's consciousness by variations in the duration of certain
intervals, or even by simple increase or decrease in the rate of
succession.[6]

   [6] Bolton found one subject apperceiving in four-beat groups a
   series of sounds in which increased stress fell only on every
   sixth.

In the experiments on dactylic rhythm the changes introduced affected
the initial and final intervals only, the one being diminished in
proportion as the other was increased, so that the total duration of
the group remained constant. The figures, arranged as in the preceding
table, are given in Table L.

The percentage given in the case of the highest ratio is based on the
reports of two subjects only, one of them the exceptional observer
commented on in connection with two-beat rhythms; for all other
participants the anapæstic form had already replaced the dactylic. The
distribution of values which supports psychological uniformity in this
rhythmic figure lies between the ratios 1.166, 1.000, 0.800, and
1.250, 1.000, 0.755, since in this region the proportion of errors in
judgment on either side becomes inverted. The two rhythmic forms,
therefore, present no important differences[7] in the relations which
support psychological uniformity. A comparison in detail of the
distribution of judgments in the two cases reveals a higher percentage
of plus and minus, and a lower percentage of equality judgments
throughout the changes of relation in the dactylic form than in the
trochaic. This appears to indicate a greater rhythmical integration in
the former case than in the latter. On the one hand, the illusion of
isolation from adjacent groups is greater at every point at which the
intervening interval is actually reduced below the value of either of
the internal intervals in the dactylic than in the trochaic rhythm;
and on the other, the sensitiveness to differences in the whole series
is less in the case of the trochee than in that of the dactyl, if we
may take the higher percentage of cases in which no discrimination has
been made in the former rhythm as a negative index of such
sensibility.

   [7] The ratios of initial to final intervals in the two cases
   are, for trochaic measures, 1.400:1.000, and for dactylic,
   1.400(to 1.666):1.000.


TABLE L.

  Ration of Unaccented        Unaccented Interval Judged to be
  to Accented Interval.      +                =               -
    1.000 : 2.428                                         100.0 per cent
    1.000 : 2.000        20.0 per cent.   33.3 per cent    46.7    "
    1.000 : 1.666        33.2    "        23.9    "        42.9    "
    1.000 : 1.400        39.0    "        46.0    "        15.0    "
    1.000 : 1.182        60.0    "        37.2    "         2.8    "
    1.000 : 1.000        85.4    "        12.2    "         2.4    "
    1.000 : 0.846        89.2    "        10.8    "
    1.000 : 0.714       100.0    "
    1.000 : 0.660        96.0    "         4.0    "


The increase in the number of inverted forms which occur is
coördinated percentually in the following table with the successive
increments of difference between the accented and unaccented intervals
of the group:


TABLE LI.

  Rhythm.  2.428 2.000 1.769 1.666 1.571 1.400 1.222 1.182 1.118 1.000
  Trochaic,             93.7        74.0  44.2  25.0        25.0   2.9
  Datylic,  93.6  54.0        39.4        18.4


These figures are corroborative of the preceding conclusions. The
dactylic figure is maintained in the presence of much greater
differences in the relative durations of accented and unaccented
intervals than is the trochaic. In the latter, inversions not only
appear earlier in the series, but become the (practically) exclusive
mode of apprehension at a point where not fifty per cent, of the
dactyls have suffered transformation. At a certain definite stage in
the process the tendencies toward the two forms of apprehension
balance each other, so that with the slightest change in direction of
attention the rhythmical figure inverts and reverts to the original
form indifferently. These points are defined, in the case of the two
rhythms here reported on, by the following (or intermediate) ratios:
Trochaic-Iambic, (1.400-1.571): 1.000; Dactylic-Anapæstic,
(1.666-2.000): 1.000.

The temporal conditions of such equilibrium are a strict function of
the degree of accentuation which the rhythm group presents. The
location of the indifference point must, therefore be independently
determined for each intensive value through which the accented element
may pass. Its changes are given for five such increments in the
following table, in which the values of the various intervals are
represented as proportions of the absolute magnitudes which appear in
the first, or undifferentiated series.


TABLE LII.

  Intensive Form.   1st Interval.  2d Interval.  3d Interval.
    1/8  1/8  1/8       1.000         1.000          1.000
    3/8  1/8  1/8       1.042         1.010          0.948
    7/8  1/8  1/8       1.142         1.021          0.862
   15/8  1/8  1/8       1.146         1.042          0.808
   24/8  1/8  1/8       1.291         1.000          0.708


IV. THE COMBINATION OF RHYTHMICAL GROUPS IN HIGHER SYNTHESES AND THEIR
EQUIVALENCES.


In the elaboration of higher rhythmical forms the combination of
formally identical groups is rather the rule than the exception, since
in poetical structures the definition of the metrical form and the
maintenance of its proper relations depend on a clear preponderance of
its own particular unit-type over local variants. In the experimental
investigation of composite rhythm forms the temporal relations of
structures presenting such likeness in their constituent groups were
first taken up. In the conduct of the research those differences of
intensity which are actually expressed and apprehended in the
utterance of a rhythmic sequence were uniformly employed. While there
is no doubt that a succession of perfectly identical forms would,
under the requisite temporal conditions, be apprehended as presenting
major and minor phases of accentuation, yet in the expression of
rhythmic relations the subordination of accents is consistently
observed, and all our ordinary apprehension of rhythm, therefore, is
supported by an objective configuration which fulfils already the form
of our own subjective interpretation.

The temporal relations of these major and minor phases cannot be
considered apart from the index of their respective accentuations. As
the distribution of elements within the simple group fluctuates with
the changes in intensive accentuation, so does the form of temporal
succession in larger structures depend on the relations of intensity
in their primary and secondary accentuations. The quantitative values
hereafter given apply, therefore, only to those specific intensities
involved in the experiment. Two types were chosen, the trochee and the
dactyl. The series of sounds was given by successive hammer-falls of
7/8 and 1/8 inch for the major, and 3/8 and 1/8 inch for the minor
phase. The distribution of time-values within each group was made on
the basis of previous experimentation to determine those relations
which support psychological uniformity. These internal relations were
maintained unchanged throughout the series of ratios which the
durations of the two groups presented. Four subjects took part in the
experiment. The quantitative results in the composition of trochaic
forms are given in the following tables (LIII., LIV.), the figures of
which present, in the form of percentages of total judgments, the
apprehension of sensible equality or disparity in the two groups.

In the earlier set of experiments the series of ratios diverged in
both directions from unity; in the later it departed in one only,
since every divergence in the opposite direction had, in the previous
experiments, been remarked at once by the observer. In this second set
the series of differences is more finely graded than in the former;
otherwise the two sets of figures may be considered identical. Using
the equilibrium of errors as an index of sensible equality, the two
trochaic groups are perceptually uniform when the temporal ratio of
major and minor lies between 1.000:0.757 and 1.000:0.779.


TABLE LIII.

  Ratio of Duration           2d Group Judged to be
  of 1st Group to 2d.       +            =             -
  1.000 : 1.250        100 per cent.
  1.000 : 1.116        100 "
  1.000 : 1.057        100 "
  1.000 : 1.000        100 "
  1.000 : 0.895         68 "          22 per cent.
  1.000 : 0.800         25 "          75 "
  1.000 : 0.714                                     100 per cent.


TABLE LIV.

  Ratio of Duration           2d Group Judged to be
  of 1st Group to 2d.         +            =            -
  1.000 : 1.000         100.0 per cent.
  1.000 : 0.973          87.5 "         12.5 per cent.
  1.000 : 0.870          66.6 "         33.3 "
  1.000 : 0.823          33.3 "         22.2 "         44.4 per cent.
  1.000 : 0.777                         50.0 "         50.0 "
  1.000 : 0.735          33.3 "         33.3 "         33.3 "
  1.000 : 0.694                         33.3 "         66.6 "


In the dactylic form, as in the second trochaic series, ratios varying
from unity in one direction only were employed. The results follow:


TABLE LV.

  Ratio of Duration         Second Group Judged to be
  of 1st Group to 2d.        +            =             -
  1.000 : 1.000         100.0 per cent.
  1.000 : 0.946          62.5 "         37.5 per cent.
  1.000 : 0.915          33.3 "         66.6 "
  1.000 : 0.895           8.3 "         33.3 "         58.3 per cent.
  1.000 : 0.800                         40.0 "         60.0 "


As in the preceding case, when relations of equality obtained between
the two subgroups, the secondary period in every instance appeared
longer than the primary. This prolongation was uniformly reported as
displeasing. The distribution of values which here support
psychological uniformity lies between 1.000:0.915 and 1.000:0.895,
that is to say, the difference of phases is less marked than in the
case of the simpler trochaic composite. This is a structural principle
which penetrates all rhythmical forms. The difference in the case of
both of these composites is less than in the opposition of phases
within the simple group, in which for identical intensities and
(practically) the same group of observers these presented the ratio
1.000:0.714. It is evident that the relative differentiation of
accented and unaccented intervals due to specific variations in
intensity is greater than is that of successive groups characterized
by similar differences of accentual stress; and if still more
extensive groups were compared it would unquestionably be found that a
further approximation to equality had taken place.

In the integration of rhythmical groups this subordination of the
intensive accents which characterize them is not the sole mechanism of
higher synthesis with which we are presented. Another mode is the
antithesis of rhythmical quantities through verse catalepsis. Such
variation of the rhythmical figure can take place in two directions
and in two only: by an increase in the number of constituents, giving
what may be called _redundancy_ to the measure, and by a decrease in
their number, or _syncopation_. Each of these forms of departure from
the typical figure fulfils a specific rhythmic function which
determines its temporal and intensive characters, and its local
position in the rhythmical sequence.

(_a_) _Redundant Measures._--The position of such a measure is
uniformly initial. On rare occasions individual observers reported an
inversion of this order in the earlier portion of the series,[8] but
in no case were subjectively formulated series concluded in this way;
and when the objective succession ended with the redundant measure the
experience was rhythmically displeasing. In accentual stress the
redundant measure is of secondary rank, the chief intensity falling
upon the shorter, typical groups. Variation from the type does not,
therefore, unconditionally indicate a point of accentual stress,
though the two are commonly connected.

   [8] This was probably due to beginning the series of
   stimulations with the typical measure. Such beginning was
   always made by chance.

In regard to the relative duration of the redundant measure the
subjective reports indicate a large variability. The dactylic form
appears to be slightly longer than the trochaics among which it
appears; but not infrequently it is shorter.[9] These variations are
probably connected with differences in stress due to the relation
which the measure bears to the accentual initiation of the whole
series; for this accent apparently may fall either within the
redundant measure itself or on the first element of the succeeding
                 ___                _____
               >/   \  >            |   |  >    >
group, thus:  | q q q; q q; |, or | e e e  q q; q q |.
                              \_/

   [9] The only form taken up was the occurrence of dactylic
   measures in trochaic series.

Two rhythm forms were analyzed, the trochaic and the dactylic, the
series of sounds being given by hammer-falls of 7/8 and 1/8 inch for
accented and unaccented elements respectively. In each experiment full
and syncopated measures alternated regularly with each other in
continuous succession, giving the forms

    >     >           >       >
  | q. q; q % | and | q. q q; q. % % |.
    \_____/           \____________/

The initiation of the series was in every case determined by chance.
Six observers took part in the work with trochaic forms, five in that
with dactylic. The quantitative results are given in the following
tables, in each of which the relations of duration, position and
stress are included.


TABLE LVI.

  TROCHAIC FORM.
                                                  Apparent Accentuation
  Ratio of 1st  Second Group Judged to be 2d Group   of Second Group.
  to 2d Group.   +          =         -    Final     +        =       -
  1.000:1.000    55.5%     44.4%            100%     71.5%    28.5%
  1.000:0.946              83.3      16.6%  100      30.0     70.0
  1.000:0.895    66.6      11.1      22.2   100      30.0     60.0   10.0%
  1.000:0.846    16.6      41.6      41.6   100      40.0     60.0
  1.000:0.800    16.6      41.6      41.6   100      40.0     60.0
  1.000:0.756    49.9      24.9      24.9   100      40.0     60.0
  1.000:0.714    16.6      41.6      41.6   100      20.0     80.0


TABLE LVII.

  DACTYLIC FORM.
                                                   Apparent Accentuation
  Ratio of 1st  Second Group Judged to be  2d Group   of Second Group.
  to 2d Group.   +         =         -     Final     +         =       -
  1.000:1.000   100.0%                      100%     40.0%    60.0%
  1.000:0.946             83.3%     16.6%   100      40.0     60.0
  1.000:0.895             66.6      33.3    100      20.0     80.0
  1.000:0.846             37.5      62.5    100      40.0     60.0
  1.000:0.800                      100.0    100      40.0     60.0


The syncopated measure, like the redundant, bears to the acatalectic
group specific relations of duration, accentual stress, and position
in the rhythmical sequence. In position it is final. This relation is
independent of the factor of duration, on which the order of elements
in the simple measure depends. Even the excessive shortening which
occurs in the trochaic form, when the full measure has a duration
almost one and one half times as great as the syncopated, brings about
no inversion of the order.

In duration the syncopated group is a shortened measure. The amount of
reduction necessary to preserve rhythmical proportion with the rest of
the sequence is greater in the trochaic than in the dactylic form, as
in the relation of accented to unaccented elements in the simple
measure it is greater than in the case of the trochaic, a principle of
structure which has already been pointed out.

There is similar evidence in beaten rhythms to show that when a full
measure is elided, the pause which replaces it is of less value than
the duration of a syncopated measure. When trochaic rhythms were
beaten out with a distinct pause after each measure, the relative
values of the two intervals were 1.000:2.046. Such a pause cannot be
equivalent to a suppressed beat and its interval; I regard it as
functionally equal to a whole measure. If that value be allowed for
the second interval which it possesses in the same rhythm type when no
pause is introduced, namely, 1.000:0.920, the first two intervals will
have a value--in terms of linear measurement--of 1.93 + 1.77 or 3.70.
The value of the suppressed measure would therefore be 2.15, a ratio
of acatalectic to elided group of 1.000:0.581.

Iambic rhythm beaten out without separating pauses presents the
following ratio between first and second intervals, 1.000:1.054; on
the introduction of a pause between the measures the ratio becomes
1.000:2.131. The assignment of these proportional values gives 1.68 +
1.77, or 3.45, as the duration of the first two intervals, and 1.81
for the pause, a ratio of 1.00:0.524.

In continuous dactylic tapping, the values of the successive
intervals are 1.000; 0.756; 0.927; with a separating pause their
relations are 1.000; 0.692; 1.346. These being analyzed as before, the
elided measure will have the relative value of 0.419. This shows a
decline in the proportional duration of the elision as the total value
of the measure elided increases. There can be little question that
this principle applies also to the value of elisions of higher
rhythmic structures as well.

In intensity the syncopated measure is a point of increased accentual
stress. This relation is not constantly maintained in the trochaic
form, in which at one ratio the accent appears reduced;[10] in the
dactylic form divergences are all in the direction of an apparent
increase in accentuation. In rhythms beaten out the form of succession
                                 >     .          >     >
was always prescribed (_e.g._, | q. q; q_% | or | q. %; q. q|, but not
                                 \______/         \________/
either at the subjects' preference), so that no material was there
afforded for a determination of the primacy of particular figures; but
the results must of course show any tendency which exists toward an
increased accentuation of the syncopated measure. It needs but a
cursory reference to the statements of these results in Pt. III., B,
of this paper, to observe how constant and pronounced this tendency
is.[11]

   [10] This result is clearly irregular, and is probably due to
   the effect of accidental variations on a meager series of
   judgments. The number of these was three for each observer,
   making eighteen judgments in all the basis of each percentage
   in the table.

   [11] The subjective notes of the observers frequently refer to
   this as an explicitly conscious process, the nature of the
   rhythmical sequence requiring a greater stress at that point
   than elsewhere. Extracts are appended:

   _Trochaic Syncopation._--"There is almost a necessity for an
   accent on the last beat." "... an almost imperative tendency
   to emphasize the final syllable beyond the rest." "The two taps
   were followed by a pause and then a tap with increased
   pressure." "This was not satisfactory with any adjustment of
   time relations so long as the stress of all three beats was the
   same. In attempting to make them all equal I almost
   involuntarily fell into the habit of emphasizing the final
   one."

   _Dactylic Syncopation._--"In this series it was easy to lay
   stress on the last (beat) ... this is the natural grouping; I
   unconsciously make such." "... of these the heavy one
   (accented syncopation) was much more satisfactory." "It was
   constantly my tendency to increase the strength of the last
   tap." "In this it is natural for me to make the final stroke
   heavy. To make the second group balance the first by equalizing
   the time alone is less satisfactory than by introducing
   elements of both time and force." "I felt that the latter part
   of the rhythm (unaccented syncopation) was lacking in force.
   Something seemed continually to be dropped at the end of each
   group."

   The reactors frequently repeated the full measure several times
   before introducing the syncopated measure, which thus brought a
   series to its close. It will probably be found that in the
   actual construction of poetic measures the syncopated or
   partially syncopated foot is systematically introduced
   coincidently with points of rhythmical or logical pause.

Conclusive evidence of the integration of simple rhythm forms in
higher structures is presented by the process of increasing definition
which every rhythmical sequence manifests between its inception and
its close. This process is manifested equally in the facts of sensory
apprehension and those of motor reproduction of rhythm forms. On the
one hand, there is a progressive refinement in the discrimination of
variations from temporal uniformity as the series of stimulations
advances; and correspondingly, the sequence of motor reactions
presents a clearly marked increase in coördination taking place
parallel with its progress. A rhythmical form is thus given to the
whole succession of simple measures which are included within the
limits of the larger series, a form which is no less definite than
that exhibited by the intensive and temporal relations of the
rhythmical unit, and which, there can be little doubt, is even more
important than the latter in determining the character of the rhythm
experience as a whole.

The presentation of experimental results bearing on this point will
follow the lines already laid down. Only that part of the material
which is derived from the apprehension of sensory rhythm forms can be
applied to the determination of this formal curve for the ordinary
metrical types and their complications. The facts of progressive
coördination presented by beaten rhythms are based on the repetition
of simple forms only. The completion of the evidence requires a
quantitative analysis of the temporal relations presented by the whole
sequence of integrated measures which compose the common verse forms:
dimeter, trimeter, etc. This matter was not taken up in the present
investigation.

The perception of variations in the measures of an iambic pentameter
line was first taken up. The series of sounds was produced by the fall
of hammer, the distances traversed being, for the accented elements
0.875 inch, and for the unaccented, 0.250 inch. The series was
followed by a pause equal to one and a half measures, and was repeated
before judgment was made. The time occupied by the series of sounds
was 2.62 seconds. The intervals between the successive sounds were
adjusted on the basis of previous experimentation concerning the most
acceptable relations between the durations of accented and unaccented
intervals. Their values were in the ratio 1.000:0.714 for accented and
unaccented respectively. The variations were introduced in a single
element, namely, the interval following the accented beat of the
group, which, in this form of rhythm, is also the inter-group
interval. This interval was changed by successive increments of one
seventh its original value, or one twelfth the duration of the whole
measure. Four such additions were made, the final value of the
interval standing to its original duration in the ratio 1.000:0.636.
The same series of changes in the duration of the accented interval
was made successively in each measure of the pentameter series. In all
these experiments the subjects were in ignorance of the character and
position of the changes introduced. The results appear in the annexed
table.


TABLE LVIII.

                     Position in Series.    Percentage Values.
  Ratios.             I  II   III  IV       I    II   III    IV
  1.000 : 1.000       0   0    0    0       0     0     0     0
  1.000 : 0.874       4   4    4    7      40    40    40    70
  1.000 : 0.777       6   6    8   10      60    60    80   100
  1.000 : 0.700       6   6   10   10      60    60   100   100
  1.000 : 0.636       6   6   10   10      60    60   100   100


In the five horizontal rows on the left of the table are set down the
number of times, out of a total of ten judgments, the interval in
question was perceived to be greater than the like interval in other
groups, under the original relation of uniformity and for the four
successive increments. On the right these numbers are given as
percentages of the whole number of judgments. These figures show an
increase of discriminative sensibility for such changes as the series
advances. The percentage of correct discrimination, as it stands in
the table, is the same for the first and second positions in the
line, but this coincidence is to be attributed to accident, in
consequence of the relatively small number of judgments on which the
results are based, rather than to a functional indifference in the two
positions. I conclude that fuller experiments would show a curve of
continuous increase in the number of correct judgments for the whole
series of measures here included. If we number the series of ratios
given above from one to five, the thresholds of perceptible change for
this series of positions, expressed in terms of this numerical series,
would be: I., 4.1; II., 4.1; III., 3.9; IV., 3.6.

Secondly, in a series of five trochaic measures, the intervals
separating the groups--which in this case follow the unaccented
beat--were successively lengthened by increments identical with those
employed in the preceding set of experiments. The results are
presented in the table below, arranged similarly to the previous one.


TABLE LIX.

                    Position in Series.         Percentage Values.
  Ratios.             I  II   III  IV         I     II     III    IV
  1.000 : 1.000       0   0    0    0        0.0   10.0    0.0    0.0
  1.000 : 0.874       1   1    3    4       16.5   16.5   50.0   60.0
  1.000 : 0.777       4   4    5    6       66.0   66.0   83.0  100.0
  1.000 : 0.700       6   6    6    6      100.0  100.0  100.0  100.0
  1.000 : 0.636       6   6    6    6      100.0  100.0  100.0  100.0


These results are essentially identical with those of the preceding
section. The sensitiveness to small differences in duration within the
rhythmical series becomes continuously greater as that series
proceeds. The thresholds of perceptible change in terms of the
numerical series of ratios (as in preceding paragraph) are as follows:
I., 4.0; II., 4.0; III., 3.7; IV., 3.6.

Finally, the intensity of the preceding sound was increased as well as
the duration of the interval separating it from the following stroke.
The measure employed was the trochaic, the interval suffering change
was that following the accented beat--in this case, therefore, the
intra-group interval. The relations obtaining among the unchanged
measures were, as to duration of accented and unaccented elements,
1.000:0.714; as to intensity, 0.875:0.250 inch. Instead of a series,
as in the preceding experiments, only one change in each direction
was introduced, namely, an increase in duration of a single accented
element of the series from 1.000 to 1.285, and an increase of the same
element in intensity from 0.875 to 1.875 inch fall. The results are
given in the annexed table:


TABLE LX.

                       Duration.                           Stress.
  Position      Interval Following Louder
  in Series.         Judged to be                      Increased Stress.
                +             =            -        Times Noted.   Not Noted.
    I.     8 per cent.  92 per cent.  0 per cent.   40 per cent.  60 per cent
   II.    42    "       50    "       8    "        42    "       58    "
  III.    57    "       36    "       7    "        54    "       46    "
   IV.    67    "       26    "       7    "        62    "       38    "
    V.    30    "       40    "      40    "        60    "       40    "


The figures show that in regard to the discrimination of changes in
duration occurring in intervals internal to the rhythm group, as well
as in the case of intervals separating adjacent groups, there is a
progressive increase in sensibility to variations as the succession of
sounds advances. This increased sensitiveness is here complicated with
another element, the tendency to underestimate the duration of the
interval following a louder sound introduced into a series. The
influence of this second factor cannot be analyzed in detail, since
the amount of underestimation is not recorded unless it be sufficient
to displace the sign of the interval; but if such a quantitative
method be applied as has already been described, the results show a
continuous decrease in the amount of underestimation of this interval
from the first position to the fourth, or penultimate, which presents
the following relative values: 92, 66, 50, 40. A phase of rapid
increase in the amount of underestimation appears in the fifth or
final position, represented on the above scale of relative values by
120. This falling off at the end of the series, which appeared also in
previous experiments, can be attributed only to an interference with
the functions which the several measures bear in the process of
comparison, and indicates that the accuracy of judgment is dependent
on a comparison of the measure or element in question with those which
follow as well as with those which precede it.

The results presented in the preceding section form the statement of
but one half the evidence of higher rhythmical synthesis afforded by
the material of the present investigation. We turn now to the second
set of results. It deals, in general, with the quantitative relations
of rhythmic forms which find expression through finger reactions.
Portions of this evidence have already been presented, through motives
of economy, in connection with the discussion of the phases of
differentiation in intensity and duration which such beaten rhythms
manifest. The burden of it, however, is contained in the results of an
analysis, form by form, of the proportional mean variations which
characterize these types of rhythmic expression. This method has been
applied to a study (_a_) of the characters of the constituent
intervals of the unit, in their relation to accentuation and position;
(_b_) of the simple group which these elements compose; and (_c_) of
the forms of higher synthesis manifested by the variations in
successive groups. The first of these relations concerns, indeed, only
the internal organization of the simple group, and has no direct
bearing on the combination of such groups in higher syntheses; but,
again for the sake of economy, the items are included with the rest of
the material.

The application of such a method, as in all treatment of material by
mean variations, involves much labor,[12] and on that account alone
the lack of its employment to any considerable extent in previous
investigations may be excused; but to this method, as it seems to me,
must the final appeal be made, as an indisputable means by which all
questions concerning the refined features of rhythmical organization,
the definition of units and the determination of the forms in which
they enter into larger rhythmic quantities, are to be settled.

[12] In connection with this work some 48,000 individual measurements
were made (for the transcription of which I am indebted to the patient
assistance of my wife). Half of these were measurements of the
intensity of the successive reactions; the other half, of the
intervals which separated them. The former series has been employed in
obtaining the averages which appear in the section on the distribution
of intensities; the latter in that on the distribution of durations.
The determination of mean variations was made in connection with the
second series only (24,000). These quantities were combined in series
of single groups, and in series of two, four, eight and ten groups,
and for each of these groupings severally the mean variation of the
series was computed.

Of all the possible forms of rhythmic apprehension or expression, the
material for such a statistical inquiry is most readily obtainable in
the form of a series of finger reactions, and to such material the
application of the method in the present investigation has been
restricted.

In the first experiment of this group the reactor was asked to tap out
a series in which temporal, but not intensive variations were
introduced; the strokes were to be of uniform strength but separated
into groups of two beats. No directions as to length of pause between
the successive groups were given, but the whole form of the groups was
to be kept absolutely constant. The reports of the subjects were
uniformly to the effect that no accent had been introduced. At a
cursory examination no intensive grouping was apparent. These records
were the earliest analyzed, when only time relations were in mind, and
no measurements were made of variations in strength. Only the mean
variations of the intervals, therefore, will here be taken up.

A word first as to the relative value of the two intervals and its
significance. The form of a rhythmical series is determined in every
part by subordination to principles of strict temporal arrangement.
Every suppression of elements in such a series, every rest and
syncopated measure has as positive and well-defined a function as have
the successive reactions and their normal intervals. If such a pause
is made as we find introduced in the present case, its value must be a
fixed function of the system of durations of which it forms a part,
whether it replace an element in a rhythmical unit, or a subgroup in a
higher rhythmical quantity. In general, the value of such a rest is
less than the duration of a corresponding full measure or interval.
For example, the syncopated forms | >q % | and | >q % %_| are
demonstrably of shorter average duration than the corresponding
measures| >q q | and | >q q q_|; and the pause occurring at the close
of a syncopated line--such as that in the middle of a catalectic
trochaic tetrameter--should be found of less value than that of the
regular foot.

In the present instance two reactions are made, a pause follows, then
the reactions take place again, and so on. The intervals separating
successive groups of reactions thus result from the coalescence of two
periods, the interval which would regularly follow the reaction and
the additional pause at its close. The value of the latter I interpret
as functionally equivalent to a group of two beats and not to a single
interval; that is, the rhythm beaten out is essentially quadruple, the
second member of each composite group being suppressed, as follows:
    >
  | q q; % % |.
    \______/

To estimate the proper value of such a rest the average relative
duration of first and second intervals was taken in a continuous
series of two-beat measures, in which the first member was accented
sufficiently to define the rhythmical groups. The ratio was
1.000:0.760. In the present instance the values of the simple initial
interval and the composite interval which follows it are, in terms of
the linear measurement, 1.55 mm. and 3.96 mm. Assuming the above ratio
to hold, the duration of a period which included the second
beat-interval and a group-rest should be 1.16 + 1.55 + 1.16 = 3.87 mm.
This is slightly less than the actual value of the period, whereas it
should be greater. It must be remembered, however, that the disparity
between the two intervals increases with initial accentuation, and in
consequence the proportional amounts here added for the second
interval (1.16 to 1.55) should be greater. This interval is not
rhythmically 'dead' or insensitive. The index of mean variation in all
reactors is greater for the first than for the second interval (or
interval + pause) in the ratio 1.000:0.436, that is, the value of the
latter is more clearly defined than that of the former, and the
reactor doubly sensitive to variations occurring within it.

An analysis of the variations of these intervals separately in series
of four groups reveals a secondary reciprocal rhythm, in which the
changes in value of the mean variation at any moment are in opposite
directions in the two intervals. These values in percentages of the
total duration of the periods are given in the following table.


TABLE LXI.

  Interval.  1st Group.       2d. Group.       3d Group.       4th Group.
  First,    15.4  per cent.  26.4  per cent.  13.8 per cent.  30.3 per cent.
  Second,   12.4     "        7.0     "        9.6    "        7.5    "


Without measurement of their intensive values, interpretation of these
variations is speculative. They indicate that the pairs of beats are
combined in higher groups of four; that the differences of mean
variation in the first interval are functions of an alternating major
and minor accentuation, the former occurring in the second and fourth,
the latter in the first and third; and that the inversely varying
values of the mean variation in the second interval are functions of
the division into minor and major groups, the reduced values of the
second and fourth of these intervals being characteristic of the
greater sensitiveness to variations occurring in the group pause than
to changes occurring within the group.

The fixity of the group is markedly greater than that of the simple
interval. In the one case in which the mean variation of the group is
greater than that of the elementary period the material involved was
meager (five instead of ten repetitions) and the discrepancy therefore
insignificant.

The difference in the mean variation of the first and second intervals
respectively rises to an individual maximum of 3.000:1.000, and
averages for all subjects 2.290:1.000; the fixity, that is to say, of
the inter-group interval in this form of tapping is more than twice as
great as that of the intra-group interval. The fixity of the larger
rhythmical quantities is greater than that of the smaller, whether the
relation be between the elementary interval and the unit group, or
between the synthetic unit and its higher composite. The average mean
variation of the beat intervals exceeds that of the whole group in the
relation of 1.953:1.000. The differentiation of larger and smaller
groups is less clear. When the material is taken in groups of eight
successive beats the mean variation is less in the case of every
subject than when taken in fours, in the ratio 1.000:1.521. The
comparative values for groups of two and four beats is reversed in two
thirds of the cases, yet so that an average for all subjects gives the
ratio 1.000:1.066 between groups of four and two beats. The whole
series of values arranged on the basis of unity for the mean variation
of the beat interval is given in Table LXII.


TABLE LXII.

  Proportional. Single Beat.  2-Beat Group.  4-Beat Group.   8-Beat Group.
     M.V.           1.000          0.512        0.480            0.320


The persons taking part in the investigation were next required to
make a series of reactions composed of unit groups of two beats, in
each of which the first member received accentuation, a simple
trochaic rhythm. In this type the relation of intra-group to
inter-group interval remains unchanged. In all subjects but one the
mean variation of the first interval exceeds that of the second in the
average ratio 1.722:1.000. The amount of difference is less than in
the preceding type of reaction. In the former there is presented not
an intensively uniform series, but an irregularly rhythmical grouping
of intensities, in dependence on the well-defined parallel types of
temporal differentiation; in the latter such intensive differentiation
is fundamental and constant in its form. Assuming the character of the
second interval to remain unchanged, there is in the intensive fixity
of the initial accented element, on the one hand, and the alternate
assertion of the impulse to accentuation and repression of it in the
attempt to preserve uniformity, on the other, an occasion for the
difference in the relation of the mean variation of this interval to
that of the following in the two cases. It is to be expected that
there should be less irregularity in a series of reactions each of
which represents an attempt to produce a definite and constant
rhythmical accent, than in a series in which such an accent is
spasmodically given and repressed.

For a like reason, the difference in value between the mean variations
of the elementary interval and the unit group should be less in the
case of the positive rhythm form than in that of a series which
combines a definite temporal segregation with an attempt to maintain
intensive uniformity. The mean variation of the interval is still of
greater value than that of the unit group, but stands to it in the
reduced ratio 1.000:0.969.

The relations of higher groups present certain departures from the
preceding type. In three cases out of five the unit has a greater
                                       >     .
fixity than its immediate compound ( | q. q; q q |), with an average
                                       \_______/
ratio of 0.969:1.072. The original relation, however, is reëstablished
in the case of the next higher multiple, the eight-beat group, the
whole series of values, arranged on the basis of unity for the simple
interval, being as follows:


TABLE LXIII.

  Proportional  Single Beat  2-Beat Group  4-Beat Group  8-Beat Group
     M.V.          1.000         0.969         1.072        0.859


An analysis of the material in successive pairs of two-beat groups
revealed a pronounced rhythm in the values of the mean variations of
the first and second members of the pair respectively, the fixity of
the second group being much greater than that of the first, the mean
variation having a ratio for all subjects of 0.801:1.000. The
interpretation of this rhythmical variation, as in the preceding
reaction series, must be speculative in the absence of quantitative
measurement of intensive changes, but is still not left in doubt. The
rhythmic material is combined in larger syntheses than the groups of
two beats, alternately accented and unaccented, which were avowedly in
mind. This secondary grouping appears in at least a measure of four
beats, into which the unit group enters as the elementary interval
entered into the composition of that unit. In this larger group the
initial period, or element of stress, is characterized by a greater
mean variation than the unaccented period which follows it. There are
present in this first interval two factors of instability: the factor
of accent, that element which receives the stress, being in general
characterized by a greater mean variation than the unaccented; and the
factor of position, the initial member of a rhythmical group,
independent of accentuation, being marked by a like excess of mean
variation over those which follow it. The interpretation of the latter
fact lies in the direction of a development of uniformity in the motor
habit, which is partially interrupted and reëstablished with the
ending and beginning of each successive group, large or small, in the
series of reactions.

Further, when the material is arranged with four unit groups in each
series, the same relation is found to hold between the first period
composed of two unit groups and the second like period, as obtained
within these pairs themselves. The mean variation of the first period
of four beats is greater than that of the second in the case of all
subjects but one, with an average ratio for all subjects of
1.000:0.745. The analysis was not carried further; there is, however,
nothing which points to a limitation of the process of synthesis to
groups of this magnitude; rather, to judge from the close
approximation in definition of the two orders manifested here, there
is suggested the probability that it is carried into still higher
groupings.

In the next rhythmical type analyzed--the iambic form--that relation
of the first to the second interval holds which was found to obtain in
the preceding forms. The excess of mean variation in the former over
the latter presents the ratio 1.274: 1.000. In amount it is less than
in either of the previous types (2.290:1.000 and 1.722:1.000). For
here, though both elements have constant relations as accented or
unaccented members of the group, the factor of stress has been
transferred from the initial to the final beat. Instead, therefore, of
combining in a single member, the factors of inconstancy due to stress
and to position are distributed between the two elements, and tend to
neutralize each other. That the preponderance of irregularity is still
with the initial interval leads to the inference that position is a
greater factor of inconstancy than accentuation.

Also, the group presents here, as in the preceding forms, a greater
fixity than does the individual interval. This relation holds for all
subjects but one, the average mean variations of the simple interval
and of the unit group having the ratio 1.000:0.824.

In larger groupings irregularities in the relations of higher and
lower again occur, and again the greater constancy obtains between the
first and second orders of higher grouping (in which for only one
subject has the lower group a greater fixity than the higher, and the
averages for all subjects in the two cases are in the ratio
1.149:0.951), and the lesser constancy between the unit group and the
first higher (in which two subjects manifested like relations with
those just given, while three present inverted relations). The whole
series of relations, on the basis of unity for the mean variation of
the simple interval, is given in Table LXIV.


TABLE LXIV.

  Proportional.  Single Beat.  2-Beat Group.  4-Beat Group.  8-Beat Group
      M.V.          1.000          0.824          1.149         0.951


There is also presented here, as in the preceding forms, a synthesis
of the material into groups of four and eight beats, with similar
differences in the fixity of the first and last periods in each. A
single subject, in the case of each order of grouping, diverges from
the type. The ratio of difference in the mean variations of the first
and second members of the groups is, for series of four beats,
1.000:0.657, and for series of eight beats, 1.000:0.770. This
indicates a diminishing definition of rhythmical quantities as the
synthesis proceeds, but a diminution which follows too gradual a curve
to indicate the disappearance of synthesis at the proximate step in
the process.

Three-beat rhythms were next taken up and the same method of analysis
carried out in connection with each of the three accentual forms,
initial, median, and final stress. In these types of rhythm the
intra-group intervals are more than one in number; for the purpose of
comparison with the final, or inter-group interval, the average of the
first and second intervals has been taken in each case.

The results agree with those of the preceding types. The mean
variation of the interval separating the groups is less throughout
than that of the average group-interval. The ratios for the various
rhythm types are as follows:


TABLE LXV.

  Rhythm Form.   Initial Stress.   Median Stress.   Final Stress.
    Ratios,       1.000 : 0.758    1.000 : 0.527    1.000 : 0.658


This relation, true of the average intra-group interval, is also true
of each interval separately. Among these ratios the greatest departure
from unity appears in the second form which all subjects found most
difficult to reproduce, and in which the tendency to revert to the
first form constantly reasserts itself. The difference in value of the
mean variations is least in the first form, that with initial accent,
and of intermediate magnitude in the third form when the accent is
final. The contrary might be expected, since in the first form--as in
the second also--the factors of stress and initial position are both
represented in the average of the first two intervals, while in the
third form the factor of stress affects the final interval and should,
on the assumption already made concerning its significance as a
disturbing element, tend to increase the mean variation of that
interval, and, therefore, to reduce to its lowest degree the index of
difference between the two phases. That it does so tend is evident
from a comparison of the proportional mean variations of this interval
in the three forms, which are in order: initial stress, 4.65 per
cent.; median stress, 4.70 per cent., and final stress, 7.15 per cent.
That the consequent reduction also follows is shown by the individual
records, of which, out of four, three give an average value for this
relation, in forms having final stress, of 1.000:0.968, the least of
the group of three; while the fourth subject departs from this type in
having the mean variation of the initial interval very great, while
that of the final interval is reduced to zero.

If, as has been assumed, the magnitude of the average mean variation
may be taken as an index of the fixity or definition of the rhythm
form, the first of these three types, the ordinary dactylic is the
most clearly defined; the second, or amphibrachic, stands next, and
the third, the anapæstic, has least fixity; for in regard to the final
interval, to the average of the first and second and also to each of
these earlier intervals separately, the amount of mean variation
increases in the order of the accents as follows:


TABLE LXVI.

  Interval.   Initial Stress.   Median Stress.   Final Stress.
  First,      5.82 per cent.    9.95 per cent.   11.95 per cent.
  Second,     6.45     "        7.87     "        9.77     "
  Third,      4.65     "        4.70     "        7.15     "


In these triple rhythms, as in the two-beat forms, the simple interval
is more variable than the unit group, and the lower group likewise
more unstable than the higher. The series of proportional values for
the three forms is given in the table annexed:


TABLE LXVII.

  Rhythm Form.    Single Interval.  3-Beat Group.  6-Beat Group.
  Initial Stress,     1.000            1.214          1.037
  Median   "          1.000            0.422          0.319
  Final    "          1.000            0.686          0.524


A comparison of the second and third columns of the table shows an
excess of mean variation of the smaller group over that of the larger
in each of the three forms. It is true also of the individual subjects
except in two instances, in each of which the two indices are equal.
This proportion is broken in the relation of the primary interval to
the unit group in the dactylic rhythm form. A similar diversity of the
individual records occurred in the two-beat rhythms.

The same indication of higher groupings appears here as in the case of
previous rhythms. Rhythmical variations are presented in the amount of
the mean variations for alternate groups of three beats.
Chronologically in the records, as well as in dependence on
theoretical interpretation, the first member of each higher group is
characterized by the greater instability. The amounts of this
difference in coördination between the first and last halves in series
of six beats is set down for the three rhythm forms in the following
table:


TABLE LXVIII.

  Stress.     First Half.    Second Half
  Initial,      1.000          0.794¹
  Median,       1.000          0.668
  Final,        1.000          0.770

    ¹These figures are made up from the records of three out of
    four subjects. In the exceptional results of the fourth
    subject no mean variation appears in the first half and 6.3
    per cent, in the second, making the average for the whole
    group 1.000:1.023.


There is still other evidence of higher rhythmical grouping than these
oscillations in the amount of the mean variation of alternate groups.
Exactness of coördination between the individual intervals of
successive groups might undergo development without affecting the
relative uniformity of such total groups themselves. But, throughout
these results, an increase in coördination between the periods of the
whole group takes place in passing from the first to the second member
of a composite group. The relation here is not, however, so uniform as
in the preceding case. The series of proportional values is given on
page 403.

TABLE LXIX.

  Stress.    First Half.    Second Half.
  Initial,     1.000          0.846¹
  Median,      1.000          1.064
  Final,       1.000          0.742

    ¹ Here also the records of three subjects only are involved,
    the results of the same reactor as in the preceding cases
    being discarded. Including this, the ratio becomes
    1.000:1.016.

The index of mean variation for the individual elements of the group
also shows a progressive decrease from first to last as follows:


TABLE LXX.

  Stress.     Interval I.      Interval II.    Interval III.
  Initial,   5.82 per cent.   6.45 per cent.  4.65 per cent.
  Median,    9.95    "        7.87    "       4.70    "
  Final,    11.95    "        9.77    "       7.15    "


The relation holds in all cases except that of I. to II. in the rhythm
with initial stress. From this table may be gathered the predominance
of primacy of position as a factor of disturbance over that of stress.
Indeed, in this group of reactions the index of variation for the
accented element, all forms combined, falls below that of the
unaccented in the ratio 6.95 per cent. : 7.91 per cent.

In rhythms of four beats, as in those of three, the estimation of
values is made on the basis of an average of the mean variations for
the three intra-group intervals, which is then compared with the final
or inter-group interval. As in those previous forms, sensitiveness to
variations in duration is greater throughout in the case of the latter
than in that of the former. The proportional values of their several
mean variations are given in the annexed table:


TABLE LXXI.

  Interval.  Initial Stress. Secondary Stress. Tertiary Stress. Final Stress.
  Intra-group,    1.000           1.000            1.000           1.000
  Inter-group,    0.941           0.775            0.725           0.713


This relation, true of the average of all intra-group intervals, is
not, as in the preceding forms, true of each of the three constituent
intervals in every case. In the second and fourth forms, those marked
by secondary and final stress, it holds for each member of the group
of intervals; in the first form it fails for the second and third
intervals, while in the third form it fails for the last of the three.

The proportional amount of this difference in mean variation
continuously increases from beginning to end of the series of
rhythmical forms. This cannot be interpreted as directly indicative of
a corresponding change in the definition which the four forms possess.
The absolute values of the several mean variations must simultaneously
be taken into account. First, then, in regard to the final pause there
is presented the following series of values:


TABLE LXXII.

  Stress. Initial.       Secondary.     Tertiary.      Final.
  M.V.    6.57 per cent. 9.50 per cent. 4.90 per cent. 15.70 per cent.


A very striking rhythmical alternation in the magnitude of the mean
variation thus occurs according as the accents fall on the first
member of the subgroups when its amount is smaller or on the second
member when it is larger. Further, the cases noted above, the second
and fourth forms, in which each of the intra-group intervals is
severally of greater mean variation than the final pause, are just
those in which the index of mean variation in the final pause itself
is at a maximum.

The average mean variations of the earlier intervals thus present
changes which are analogous to and synchronous with those of the final
pause. Their values in proportion to the whole duration of the
intervals are as follows[13]:

   [13] In the second line of figures has been added the series of
   values of the average mean variation for all four intervals of
   the group.


TABLE LXXIII.

  Stress. Initial.       Secondary.      Tertiary.      Final.
  M.V.    6.98 per cent. 12.25 per cent. 6.57 per cent. 22.0 per cent.
  M.V.    6.87     "     11.56     "     6.15     "     20.45    "


Those rhythmical forms having their accentual stress initial, or on
the initial elements of the subgroups, are marked by a sensitiveness
almost twice as great as those in which the stress is final, or on the
final elements of the subgroups.

Finally, if we take the whole series of intervals severally, we shall
find that this rhythmical variation holds true of each element
individually as it does of their average. The whole series of values
is given in the table annexed.


TABLE LXXIV.

  Stress.
  Interval.   Initial.        Secondary.      Tertiary.        Final.

  First,   9.57 per cent. 13.23 per cent. 9.00 per cent. 11.45 per cent.
  Second,  5.53     "     10.60     "     8.70     "      9.00     "
  Third,   5.83     "     12.93     "     2.00     "     12.90     "
  Fourth,  6.57     "      9.50     "     4.90     "      7.85     "


It is an obvious inference from these facts that the position of the
accent in a rhythmical group is of very great significance in relation
to the character of the rhythmical movement. The initial accent gives
incomparably greater coördination and perfection to the forms of
uttered (produced) rhythm than does the final. It is in this sense the
natural position of the accent, because on the success and fluency of
this coördination the æsthetic value of the rhythm depends.

In general, though not so unequivocally, the four-beat rhythms show a
progressive increase of stability in passing from the simple interval
to the group, and from the smaller group to the larger. The series of
values for the four accentual positions follows.


TABLE LXXV.

  Stress.      Single Interval.   4-Beat Group.   2-Beat Group.
  Initial,      7.27 per cent.    8.20 per cent.  8.17 per cent.
  Secondary,   11.60     "        9.60    "       6.25     "
  Tertiary,     3.20     "        3.40    "       2.25     "
  Final,       10.22     "        6.30    "       6.00     "
  Average,      8.07     "        6.87    "       5.67     "


Here, as in the preceding rhythmical forms, the most constant relation
is that of smaller and larger groups, in which no exception occurs to
the excess of mean variation in the former over the latter. The cases
in which this relation is reversed are found, as before, in comparing
the simple interval with the duration of the unit group; and the
exceptional instances are just those, namely the first and third
forms, in which the mean variation of this uncompounded interval is
itself at a minimum. This means that the simple interval presents a
more mobile character than that of the group; and while in general it
is less stable than the latter, it is also the first to show the
influence of increased coördination. Training affects more readily the
single element than the composite measure, and in the most highly
coördinated forms of rhythm the simple interval is itself the most
perfectly integrated unit in the system of reactions.

Here, as in the preceding rhythmical forms, evidence of higher
grouping appears in the alternate increase and decrease of mean
variation as we pass from the first to the second subgroup when the
material is arranged in series of eight beats. The proportional values
of the indices are given in the following table:


TABLE LXXVI.

  Subgroups  Init. Stress   Sec. Stress   Tert. Stress   Fin. Stress
  1st Four,      1.000         1.000          1.000         1.000
  2d Four,       0.950         0.762          0.984         0.790


The first member of the larger group, in the case of every rhythm form
here in question, is less exactly coördinated than the second, the
interpretation of which fact need not here be repeated. Several
additional points, however, are to be noted. The differences in
stability of coördination which are encountered as one passes from the
first to the last of the four rhythm forms, extends, when the
reactions are analyzed in series of eight beats, to both members of
the compound group, but not in equal ratios. The mean variation of the
second and fourth forms is greater, both in the first and second
subgroups, than that of the corresponding subgroups of the first and
third forms; but this increase is greatest in the first member of the
composite group. That is, as the group grows more unstable it does so
mainly through an increase in variation of its initial member; or, in
other words, the difference in variability of the beat intervals of
the first and last subgroups reaches its maximum in those rhythmic
types in which the indices of mean variation for these intervals are
themselves at their maxima.

This process of coördination, with its indication of a higher
rhythmical synthesis, appears also in the transformations in the value
of the mean variations in duration of the total groups, when the
material is treated in series of eight beats, as in table LXXVII.


TABLE LXXVII.

  Subgroups.   Init. Stress.   Sec. Stress.   Tert. Stress.   Final Stress.
  1st Four,         1.000          1.000           1.000           1.000
  2d Four,          0.773          0.768           0.943           0.579


The total initial group, therefore, as well as each of its constituent
intervals, is less stable than the second.

Within the unit group itself the values of the mean variation show
here, as in the preceding forms, a progressive increase in
sensitiveness to temporal variations from first to last of the
component intervals. The proportional values for the four intervals in
order are, 1.000, 0.786, 0.771, 0.666. The distribution of these
relative values, however, is not uniform for all four rhythmical
forms, but falls into two separate types in dependence on the position
of the accents as initial or final, following the discrimination
already made. The figures for the four forms separately are as
follows:


TABLE LXXVIII.

  Stress.     1st Interval.    2d Interval.    3d Interval.    4th Interval.

  Initial,    9.57 per cent.   5.53 per cent.  5.83 per cent.  6.57 per cent.
  Secondary, 13.23    "       10.60    "      12.93    "       9.50    "
  Tertiary,   9.00    "        8.70    "       2.00    "       4.90    "
  Final,     11.45    "        9.00    "      12.60    "       7.85    "


In the first type (Rhythms I. and III.) appear a descending curve
followed by an ascending; in the second type (Rhythms II. and IV.) a
second descending curve follows the first. The changes in the first
type are not coördinated with a similar curve of variation in the
intensive magnitude of the beats. It is to be noted here that the
smallest mean variation presented in this whole set of results is
found in that element of the first form which receives the stress, an
exception to the general rule. The variations in the contrasted type
have their maxima at those points on which the group initiation--
primary or secondary--falls, namely, the first and third.

As in preceding rhythmical forms, while the separation of accentual
stress from primacy in the series tends to increase the mean variation
of that element on which this stress falls and to raise the index of
mean variation for the whole group, yet the mean variation of the
initial element is also raised, and to a still greater degree,
reinforcing the evidence that primacy of position is a more important
factor of instability than the introduction of accentual stress.

In the investigation of mean variations for units (if we may call them
such) of more than four beats only a modicum of material has been
worked up, since the types of relation already discovered are of too
definite a character to leave any doubt as to their significance in
the expression of rhythm. The results of these further experiments
confirm the conclusions of the earlier experiments at every point.

These higher series were treated in two ways. In the first the reactor
beat out a rhythm consisting in the simple succession of groups of
reactions, each of which contained one and only one accent. These
units in each case were marked by initial stress, and were composed of
five, six, seven, eight and ten beats respectively. The results are
given in the following table, which contains the series of mean
variations in duration both for single intervals and for total groups.


TABLE LXXIX.

     No.                  Med. Unac'td
  of Beats.  Acc'td Beat.    Beats.      Final Beat.   Average.   Group.
  Five,         12.2%          6.8%         7.1%         7.9%      6.3%
  Six,           9.2          10.6          6.9          9.7       8.3
  Seven,         7.1           5.2          7.9          5.8       3.6
  Eight,        12.4           9.5          8.8          9.7       8.0
  Ten,           7.5           6.6          7.3          6.8


The averages for the combined, median, unaccented intervals are given
separately from those of the final interval, for the reason that the
mean variation of the latter is greater in three cases out of five
than that of the former, a relation which apparently contradicts what
has already been said concerning the sensitiveness to variations which
marks the intervals separating rhythmical groups. The reason for this
final increase in variation appears when the relative intensities of
the series of reactions are considered. They are given in Table LXXX.


TABLE LXXX.

  No. of Beats.   Acc. Beat.   Av. Unacc.   Final.   Pre-final.
  Five,            1.000        0.543       0.518     0.500
  Six,             1.000        0.623       0.608     0.592
  Seven,           1.000        0.515       0.544     0.437
  Eight,           1.000        0.929       0.949     0.863
  Ten,             1.000        0.621       0.640     0.545


In every case the final element is marked by an increase over that
which precedes it (see last two columns of table) of the average value
for all rhythms of 1.000:0.900; an increase which raises it above the
average value of the whole series of preceding unaccented beats in
three cases out of five. To this final accentuation the increase in
variation is to be attributed. Yet despite the additional element of
disturbance due to this increased final stress the average value of
the mean variation for this final interval is lower than that of the
median unaccented intervals in the ratio (all rhythms combined) of
0.992:1.000.

Turning, then, to Table LXXIX., there is presented, firstly, an excess
of variation in the accented element over that of the average
unaccented elements in every case but one (the six-beat rhythm in
which the values are nearly identical), which for the whole series of
rhythms has a value of 1.000:0.794. Secondly, in every completed case
(part of the figures in the last rhythm are inadvertently lacking),
the average mean variation of the single interval preponderates over
that of the total group.

The second form of rhythmical tapping, in which the longer series were
beaten out as pairs of equal subgroups, was added in order to
determine the quantitative relations of the mean variations for
alternate subgroups when such groups were purposely intended, instead
of appearing in the form of unconscious modifications of the
rhythmical treatment, as heretofore. At the same time the results
present an additional set of figures embodying the relations here in
question. They are as follows:


TABLE LXXXI.
                       Intervals.                  Groups.
  Number                Av.  1st    2d    1st     2d
  of Beats.  Acc.  Unacc.  Half.  Half.  Half.  Half.  Average  Totals
  Six,      27.9%  20.9%   23.4%  23.0%  14.6%  13.3%   13.9%   13.8%
  Eight,     16.6  14.8    13.2   17.3    6.2    3.3     4.7     2.7
  Ten,        7.9   2.6     3.4    4.0    5.9    5.2     5.5     3.1


No exception here occurs to the characteristic predominance in
instability of the accented element. As regards simple intervals, the
relation of first and second groups is reversed, the reason for which
I do not know. It may be connected with the rapid speed at which the
series of reactions was made, and its consequent raising of the
threshold of perceptible variation, proportional to the value of the
whole interval, to which is also due the higher absolute value of the
variations which appear in both tables.

These inversions disappear when we compare the relative stability of
the first and second subgroups, in which the excess of variation in
the former over the latter is not only constant but great, presenting
the ratio for all three rhythms of 1.000:0.816. The characteristic
relation of lower to higher rhythmical syntheses also is here
preserved in regard to the two subgroups and the total which they
compose.

The points here determined are but a few of the problems regarding the
structure of larger rhythmical sequences which are pressing for
examination. Of those proximate to the matter here under
consideration, the material for an analysis of the mean variation in
intensity of a series of rhythmical reactions is contained in the
measurements taken in the course of the present work, and this may at
a future time be presented. The temporal variations having once been
established it becomes a minor point.

Such conclusions, however, are only preliminary to an investigation of
the characteristic structure of the ordinary metrical forms, and to
these attention should next be turned. The configuration of the common
meters should be worked out both in relation to the whole formal
sequence, and to the occurrence within the series of characteristic
variations. There can be no question that each metrical structure, the
iambic trimeter or dactylic tetrameter line, for example, composes a
definite rhythmical melody within which each measure is shortened or
prolonged, subdued or emphasized, according to its position and
connections in the series of relations which constitute the rhythmical
sequence.

These several metrical forms should be explored and the characters of
each measure in the series quantitatively determined. Such an
investigation would include an ascertainment of the proportional
time-value of each successive measure, its average force, and its
sensitiveness to variations, temporal and intensive. It should include
an examination of the configuration of the single measure and the
changes in distribution of accents and intervals which it undergoes as
the rhythmical series advances. For the rhythm group must not be
conceived as a simple unchanging form; both intensively and temporally
it is moulded by its function in the whole sequence, the earlier
iambic of a heroic measure being unlike the later, the dactyl which
precedes a measure of finality different from that which introduces
the series. Such a set of determinations will give the pure
characteristic curves of our common poetical meters.

But these meters are no more simple forms than are their constituent
measures. At every point their structure is subject to modification by
factors which appear in the rhythmic utterance in virtue of its use as
a medium for the free expression of thought and emotion; and the
manner in which the characteristic form is altered by these factors of
variation must be studied. Of these variations the more important are
the effects of the introduction of variants--of spondees among
dactyls, of anapæsts among iambics, and the like--and the occurrence
of points of origin, emphasis, interruption, and finality in special
accentuations, syncopated measures, cæsural pauses and elisions. These
factors influence the structure both of those measures within which
they appear and of those adjacent to them. The nature and extent of
this wave of disturbance and its relation to the configuration of the
whole sequence call for examination.

Finally, this process of investigation should be applied to the larger
structures of the couplet and stanza, that the characteristic
differences in the pair or series of verses involved may be
determined. These characters include the whole time occupied by each
verse of the stanza, the relative values of acatalectic and catalectic
verses occurring within the same stanza structure, differences in
rhythmical melody between the latter forms, the variations of average
intensity in the accentual elements of such lines, and a determination
of the values of rests of higher and lower degrees--mid-line, verse,
and couplet pauses--which appear in the various stanza forms, and
their relation to other structural elements.

       *       *       *       *       *



RHYTHM AND RHYME.

BY R.H. STETSON.


I. INTRODUCTION.


The psychological theory of rhythm has its beginnings in the work of
Herbart,[1] who inaugurated the treatment of rhythm as a species of
time perception and suggested an explanation of its emotional effects.
While Herbart had simply pointed out the effect of a whole rhythmic
series in giving rise to an emotion of expectation, delay, or haste,
Lotze[2] applied the principle severally to each unit group (each
foot) in the rhythm, and made the emotional effect of rhythm depend on
these alternate feelings of strain, expectation, and satisfaction
produced by every repetition of the unit group. Vierordt[3] did the
first experimental work on rhythm, determining the period of greatest
regularity in the tapping of rhythms. But the first important
experiments were carried on by von Brücke.[4] By tapping out rhythms
on a kymograph, he determined the well-known 'Taktgleichheit' of the
feet in scanned verse, and noted a number of facts about the time
relations of the different unit groups. Mach[5] added to the previous
knowledge about rhythm certain observations on the subjective
accentuation of an objectively uniform series, and specially he noted
that the process is involuntary. With a much clearer understanding of
the facts of rhythm than his predecessors had had, he really provided
the foundation for the theories which follow. His most important
contribution, for some time overlooked, was his emphasis of the
essentially motor nature of the phenomena of rhythm, and his motor
theory therefor.

   [1] Herbart, J.F.: 'Psychol. Untersuchungen' (Sämmt. Werk,
   herausgeg. von Hartenstein), Leipzig, 1850-2, Bd. VII., S. 291
   ff.

   [2] Lotze, R.H.: 'Geschichte der Æsthetik,' München, 1863, S.
   487 ff.

   [3] Vierordt, K.: 'Untersuchungen über d. Zeitsinn,' Tübingen,
   1868.

   [4] von Brücke, E.W.: 'Die physiol. Grundlagen d.
   neuhochdeutschen Verskunst,' Wien, 1871.

   [5] Mach, Ernst: 'Unters. ü. d. Zeitsinn d. Ohres,' _Wiener
   Sitz. Ber., mathem. naturw. Classe_, 1865, Bd. 51, II., S. 133.
   _Beiträge zur Physiol. d. Sinnesorgane_, S. 104 ff.

Many of the recent theories of rhythm are based on Wundt's analysis.
The work of Wundt and Dietze,[6] was concerned with rhythmic series;
but it may be noted that the 'span of consciousness' and the
'synthetic activity of consciousness' were the subjects actually under
investigation. Rhythm was considered as a special temporal form of
this 'psychic synthesis.' There are three different elements in a
sound series, declared these writers, which contribute to this
synthesis: qualitative changes, intensive changes and melodic changes.
Of these the intensive changes are the most important. Every increase
in intensity, that is, every beat ('Hebung') is followed by a
decrease, and the next increase which follows is recognized as a
repetition of the preceding beat and as the forerunner of the beat
which is to follow. From this comes the synthetic power of the rhythm.
Just as the simple unit groups are built up by this synthesizing
power, so they in turn are combined into larger phrases and periods.
The motor factor has little place in Wundt's own discussion,[7] the
'mental activity' is the all-important thing. Bolton[8] also made a
very important contribution to the experimental knowledge of rhythm.
His work was based entirely on Wundt's theory. His method of
experimentation was accurate and his observations copious. The
arrangement of his apparatus, however, led him to emphasize objective
uniformity as a condition of rhythmic grouping; so that Meumann's
criticism of his application of this principle to poetry is quite
just. Nevertheless Bolton established the essential facts of
subjective accentuation and apparent temporal displacement. It is
noteworthy that he laid great emphasis on the motor aspect of rhythm,
and made many careful observations on the 'motor accompaniment.' While
inclining strongly to a motor interpretation he did not attempt to cut
loose from the Wundtian 'apperceptive process' as the primary factor.

   [6] Wundt, W.: 'Physiol. Psych.,' 4te Aufl., Leipzig, 1893, Bd.
   II., S. 83.

   [7] Wundt, W.: 'Physiol. Psych.,' 4te Aufl., Leipzig, 1893,
   II., S. 89 ff.

   [8] Bolton, T.L.: _Amer. Jour. of Psych._, 1894, VI., p. 145 et
   seq.

The most elaborate consideration of rhythm yet published is that of
Meumann.[9] He avowedly worked out and defended the theory of Wundt.
The only important difference is the larger place which he gave to the
'motor accompaniment,' although he was always careful to emphasize its
secondary and derived character. He insisted that the 'mental
activity' is always primary, and that without it there can be no
rhythmization; and he opposed vigorously the motor inclinations of
Mach and Bolton. It is certainly unfortunate that rhythm has always
fallen into the hands of the investigators of the 'attention,' or the
'span of consciousness,' or the 'perception of time.' It is but an
incident that judgments of time are often based on rhythms; and
everything that Meumann has said of a 'mental prius,' or a
'synthesizing activity' in the case of rhythms, may just as well be
said in the case of any coördinated act.

   [9] Meumann, E.: _Phil. Stud._, 1894, X., S. 249 ff.

Meumann discussed in detail the characteristics of the rhythm of a
simple series of sounds, of music, and of verse. He assumed that in
the simple sound series we have rhythm in its barest form, and only
the rhythmic synthetic activity is at work; while in music there is a
content which to some extent prescribes unities, and the objective
regularity of the rhythm is broken. In verse we have much more
content, and the rhythmization is no longer regular in its temporal
relations; it is entirely dominated at times by the 'logical unities'
of the 'thought.'

One great difficulty with such a differentiation of the three types of
rhythms presents itself when one inquires into the objective
regularity of the types; the fact is that music is by far the most
regular in its time values, though it has more content than the sound
series; and that just as great irregularities are possible in the bare
sound series as in the rhythm of verse with its rich and definite
content.

Later statements of the facts and theories relating to rhythm have
inclined more and more to an emphasis of the motor aspect, even on the
part of Wundtians. Since Meumann there has been some detailed
laboratory work published, but the amount of accurately measured
rhythmic material is astonishingly small. Meumann established
experimentally the well-known relation between the length of a
rhythmic element and its accent, and corroborated the earlier work on
subjective accentuation. The reports contain the measurements of but
about eighty individual unit groups (iambs, trochees, etc.).
Ebhardt[10] gave the measurements of from 150 to 300 taps from each of
three subjects. But his work is vitiated, as far as any application to
rhythm is concerned, because he based everything on the judgment of
_equality_, which has nothing to do with rhythm.

   [10] Ebhardt, K.: _Zeilschr. f. Psych, u. Physiol. d.
   Sinnesorgane,_1898, Bd. 18, S. 99.

Hurst, McKay and Pringle[11] published measurements of about 600
individual unit groups from three different subjects; in several
cases, the material consists rather too much of records of the
experimenters themselves, but in general their results agree very well
with those of other authors. Scripture[12] published the measurements
of a single stanza of poetry. It is but a single stanza and quite too
little material on which to base any conclusions, but it is notable as
a measurement of freely spoken rhythm. No experiments have been
published which bear on the nature of the rhythmic phrase, of the
period, or of the stanza.

   [11] Hurst, A.S., McKay, J., and Pringle, G.C.F.: _Univ. of
   Toronto Studies,_ 1899, No. 3, p. 157.

   [12] Scripture, E.W.: _Studies from the Yale Psych. Lab.,_
   1899, VII., p. 1.

Our problem is: What part do the recurrent qualitative factors, like
rhyme, play in the grouping of rhythms? They function evidently, in
the main, as factors determining the periods or larger phrases of the
rhythm structure--the verses and stanzas of poetry and nonsense verse.
As no work has been done on the nature of such larger rhythmic
unities, a large share of the investigation was concerned with the
nature of the verse unity.

Two methods of investigation were used: Subjects listened to rhythmic
series, into which various modifications were introduced; and
secondly, rhythms of a prescribed type, produced by the subject, were
recorded and measured.

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT, 17. PLATE IX.
Opposite p. 417]


II. THE PERCEPTION OF A RHYTHMIC SERIES.


Apparatus: A disc (Fig. 1, Plate IX.) about 50 c. in diameter,
rotating on a vertical pivot, was driven by a pulley-cone underneath
mounted on the same spindle (not shown in the figure). On the face of
the disc were four concentric rings of regularly spaced holes, which
received pegs of uniform height and provided with a shoulder.
Corresponding holes of each circle lay on the same radius. On a plate
supported by a bracket were mounted four levers whose heads stood in
line radially to the movable disc. When the disc rotated to the right
under the levers, the pegs forced up the lever heads and made an
electric contact. The dip of the levers was controlled by a screw
adjustment. The apparatus was driven by a motor and reducing gear,
which were isolated in a sound-proof box. The rate of speed was
controllable.

The apparatus was built for use with sounders connected with the
binding-posts, but in this investigation sounders were dispensed with,
and the clicks from the apparatus itself were used, since but one
qualitative difference was introduced. As a rule, the objective accent
of the foot was not given; the subjective accentuation was nearly
always sufficient. Subjects were quite unable to say whether the
accent was objective or not. If necessary, an accentuation was
produced by raising the pegs representing the accentuated part of the
foot. The group elements were represented by single, simple clicks
made by a brass screw on the lever arm striking an iron plate (the
noise of the brass peg striking the lever head was eliminated by
damping with cloth). The rhyme was represented by a compound noise
consisting of a click higher in pitch than the verse element click,
made by the peg striking the lever head, and an almost simultaneous
click lower in pitch than the verse element click, made by the screw
of the lever arm striking another iron plate. The rhyme noise was not
louder than the verse element click, and as a whole gave the
impression of being a lower tone because the first click was very
brief. Subjects did not analyze the rhyme noise, and had no difficulty
in making it represent rhyming syllables. The pauses throughout had
no filling.

The subject was always given a normal series until the type was
clearly established, and when the variations to be judged were
introduced his attention was directed as far as possible to the factor
to be introduced. This seemed the only way to obtain trustworthy
judgments. If the subject waits blindly for some perceptual change in
the whole complicated mass of sensations which the simplest rhythmic
series constitutes, he is apt to fit his attention on some irrelevant
detail, and the change may not be noted until greatly exaggerated, and
he may not judge that particular factor at all.

The subject was always asked to choose a rate of delivery which would
correspond to his natural rate of reading nonsense verse, and the
clicks were always associated with syllables, though not with words.
An effort was made to keep the series as colorless and devoid of
content as possible, to eliminate uncertain association. Beyond
suppressed articulation, the subject was not encouraged to mark the
rhythm with any part of the body, but a number of involuntary
movements of neck, body, hand, or foot were nearly always observed.
Occasionally, when a subject's expression was doubtful, he was asked
to say a nonsense series with the clicks.

The nomenclature to be used in this paper is that of meter, but it is
always subject to the reservation that the material is only analogous
to series of nonsense syllables.

Records were kept in terms of the intervals on the revolving disc; the
time of revolution was also taken, so that the figures may be
translated in time intervals if desired. Thus, 34, 34, 34, 34, 34
represents a series of iambs in which the unaccented click has the
length of three, and the accented click the length of four spaces
between pegs. A uniform verse represented by a digit giving the number
of feet, followed by digits in parenthesis giving the character of the
foot, _e.g._, 4 (34), is an iambic tetrameter.

For convenience, the verse pause is written independently of the last
foot of the verse, _e.g._, 4 (34) p. 7 represents a tetrameter line
having the intervals 34, 34, 34, 37. The interval of the last accented
syllable is counted twice.

Occasionally this is disregarded and vs. p. equals o is written to
indicate that the vs. p. is equal to the foot pause.

The results of the experiments may be grouped under three heads:

1. Why does a synthesizing factor such as rhyme occur at the end of
the verse?

2. What is the relation between the verse pause and the rhyme?

3. What is the relation of rhyme to the cyclic movement of the unit
group and of the verse?


_1. Why the Synthesizing Factor Occurs at the Close of the Verse_.

To determine a possible difference in the sense of rhythm at the
beginning and the close of a verse, pauses ('lags') were introduced
into the earlier and later parts of the verse. These pauses were made
barely perceptible, _i.e._, barely perceptible in any part of the
verse. Usually in iambic verse the barely perceptible lag shows the
following proportions to the other pauses:

  34 _35_ 34 etc., or
  47 _48.5_ 47.

Most of the experiments were performed with iambic tetrameter. The
subject was told to note the lags in the verse: these were introduced
either in both parts of the verse or at its close only. At least three
verses were given, and records were kept of the false judgments. When
lags of identical duration were introduced between the first and
second and between the third and fourth feet, it was found that nearly
always the lag would not be detected in the earlier part of the verse
but would be detected in the later part. Out of eighty-two cases,
there were but six in which the same lag was recognized in the first
as well as in the last position. In two of these cases the subject's
attention had been called to the first part of the verse; and in the
four other cases the lag was still found more marked at the close than
at the beginning.

There were no cases in which a lag detected in the earlier part of the
verse was not also detected in the later part. False judgments, when
they occurred, were made as to a lag in the earlier part of the verse.
One subject falsely located a lag in the first of the verse four
times. Judgments as to the earlier part of the verse were uncertain
and frequently changed.

The maximum lag possible without breaking the unity of the verse was
determined for the earlier and later parts of the verse. The verse
unity was tested by adding enough feet to make a full verse, after the
break, and asking the subject to mark the close of the verse. In every
case this irregularity was introduced into the second verse, and the
first verse was normal, _e.g._ (pentameter),

     I. 5 (34).
    II. 34 lag 34 34 34 34 34.

If the lag does not break the verse, the subject should hear the close
of the verse at the end of the fifth foot in II. If the verse is
broken he should ignore the first foot and make a new verse, ending
with the sixth foot.

    J.     Iamb. tet.      1st pause of verse, max. pos. lag     9
                           3d                                    7
    L.                     1st                                   9
                           3d                                    7
    R.                     1st                                  11
                           3d                                    9
    G.                     1st                                   9
                           3d                                    7
    Mi.                    1st                                  10
                           3d                                    8
    B.                     1st                                   7
    H.                     1st                                  10
                           3d                                    6


Later, in the attempt to determine natural divisions, or nodes in the
verse, the following were determined:


  L. Max. pos. lags in f. p. of iamb. pent. in order  8    13    9     6
  G.                                                 10    11    9     8
  Mi.                                                15    18   17    14
  Me.                                                 7.5  13    9.5   6
  R.                                                  9     9   11     7
  B.                                                 12     8   15     7
  H.                                                  7.5   8   10     7

  B. Max pos. lags in dac. let., cat., in order   12  16   8
  S.                                              10  11   7
  Mc.                                              7  10   6
  G.                                              11  11   7
  L.                                              19  16   7
  H.                                               7   6   4


This shows that an irregularity in the time intervals may be greater
in the earlier than in the later part of the verse. This last table is
further evidence of the increased exactness of the rhythmic perception
at the close of the verse. As far as nodes are concerned, they show
clearly two types: (1) A node after the second foot (L., G., Mi., Mc.)
and (2) a node after the third foot (R., B., H.). For the tetrameter
there is some indication in the cases of B., S. and Mc., but the other
cases are negative and further evidence is needed.

With three of the subjects, Mi., J. and K., it was not always possible
to get records of the maximum lag, since it was impossible to define
the verse unity. When this was unbroken it was the unanimous testimony
of the subjects, corroborated by their unconscious movements, that
there was a feeling of tension during the lag. But the subjects just
referred to got a type of unity, and there was no tension. The lags
were indefinite and very long (35-90). This unity must be of the same
kind as the unity of the stanza, which includes long expressional
pauses, as well as rhythmic verse pauses.

If a subject is asked to fall in at the beginning of a rhythmic series
his first attempts are decidedly incoördinated. His earliest reactions
follow the clicks which they are intended to represent, but presently
the series of motor impulses generated by the sounds and the voluntary
movements which the subject makes fuse into a voluntary type of
reaction in which the cycle has become automatic and definite, and the
clicks take their proper places as coöperating and controlling factors
along with the motor cues of the process itself. The accuracy of the
judgments of time, if such judgments be made, or the estimation of the
likeness of the groups, depends on the definiteness with which
movement sensations follow each other in a regular series.

The following experiments (Table I.) concern the perception of a lag
in different parts not of a verse but of a stanza. It was a question,
namely, whether a lag in the first rhythmic series (first verse) which
establishes the motor cycle in the subject would be detected in the
later rhythmic series (later verses of the stanza) after the motor
cycle in the subject has been inaugurated. This responsive motor cycle
should itself, of course, contain the lag given with the first
rhythmic series.

A stanza of the form of A (Table I.) was clicked out by the
instrument, but the subject had no clue as to the regularity or
irregularity of any verse. The stanza was repeated as often as the
subject wished, but not without a pause of a few moments between each
repetition.


TABLE I.

  THE INFLUENCE OF A LAG IN THE FIRST VERSE ON THE JUDGMENT OF IDENTICAL
  LAGS IN LATER VERSES.

       A. Stanza given:   I. 34  34  35  34   p. 7-9
                         II.  "   "   "   "      "
                        III.  "   "   "   "      "

  In 14 cases the following was reported:

                          I. Lag noted.
                         II.   "   not noted.
                        III.   "    "    "

  In 9 cases the following was reported:

                          I. Lag noted.
                         II.  "    "   but shorter than first.
                        III.  "    "    "     "      "    "

  In 6 cases the following was reported:

                          I. Lag noted.
                         II.  "    "   and equal to first.
                        III.  "    "    "    "    "   "

       B. Stanza given:   I. 35  34  34  34   p. 7-9
                         II.  "   "   "   "      "
                        III.  "   "   "   "      "

    Any pause large enough to be noted in I. was noted in II. and
    III. (This table contains the judgments made on all trials.)


Most of the judgments of the third set are due to the fact that the
subject first attended to the series on the second or third verse. The
large number of cases (83 per cent.) in which the lags in the second
and third verses were concealed by the equal lag in the first verse,
makes it very probable that the type of a verse is somehow altered by
the impression left by the preceding verse.

The method of determining the maximal lags (as previously described)
gave interesting evidence on the point at which the unity of the verse
is actually felt. In the form

    I.    5 (34)
   II.    34 lag 34  34  34  34-34

as the lag increases, a point is reached at which the unity may be
made to include the first foot or to ignore it. Which of these is done
depends on the subject's attitude, or _on the point at which the verse
is brought to a close._ In either case the unity, the 'pentameter
feeling,' is not experienced _until the end of the series unified is
reached._ This is the case with all the subjects.

This development of the feeling of the particular verse form only at
the end of the verse, and the fact that the subject may be uncertain
which form he will hear until the series has actually ceased, shows
that the verse-form movement is not of such a character that the close
of it may not be considerably modified. A form which may fit the
pentameter can be broken off early, and become a satisfactory
tetrameter. The feeling seems to depend on some total effect of the
verse at the close. This effect is probably a blending of the
mass-effect of the impressions received thus far, which have a
definite character and feeling significance, and which form the motor
disposition for the next verse. The essential thing in the
determination of verse unity seems to be the dying out of the
automatism, the cessation of the coördination of the cyclic movement.
The rhyme, it would seem, emphasizes the close of the automatic cycle.
But it is probable that satisfactory phrasing has other
characteristics, and a definite form as a movement whole.


_2. The Relation of the Rhyme to the Verse Pause._

Determinations of the minimal satisfactory verse pause were made with
a view to comparing the minimum in unrhymed with that in rhymed
verses.

The stanza used was of the following form:

    I.   34      34      34      p.
   II.   "       "       "       "
  III.   "       "       "       "

The minimal satisfactory verse pauses were:

                           Without Rhyme.      With Rhyme.
              Subject.  L.      6                  4
                 "      J.      5                  4
                 "      Mc.     6                  4
                 "      R.      7                  4
                 "      B.     6-7                 3.5
                 "      G.      6                  3.5
                 "      Mi.    6-7                 3.25

It thus appears that the minimal pause which is satisfactory, is less
when rhyme is present than when it is not present. Similar
determinations were made for the maximal satisfactory verse pauses, as
follows:

                           Without Rhyme.      With Rhyme.
              Subject.  L.      9-10               11
                 "      J.       8                  9
                 "      Mc.      9                  9
                 "      R.     10-11             10-11
                 "      B.       9                  9
                 "      G.     11-12               11
                 "      Mi.     10                 10

(A few experiments were tried with verse pauses of different length in
the same stanza. A difference of one fourth the value of the pause is
not detected, and unless attention is called to them, the pauses may
vary widely from one another.)

This shows that the rhyme reduces the _necessary_ pause in verse to
the mere foot pause; while at the same time as great a pause is
_possible_ with rhyme as without it. Aside from the table above, a
large number of the records made for other purposes support this
statement: whenever rhyme was introduced, the verse pause was made
equal to the foot pause, or even slightly less than it, and was always
found satisfactory.

Numerous cases of introduction of lags into the verses of rhymed
stanzas go to show that irregularities in such verses do not affect
the length of the pauses.

Two hypotheses suggest themselves in explanation of the striking fact
that the verse pause becomes unnecessary at the close of a rhymed
verse.

The unity is now a new kind of verse unity; the rhyme is a regular
recurrent factor like the accent of a foot, and the series of rhymes
generates a new rhythm. In the rhymed stanza we are to see not a set
of verses, like the verse of blank verse, but a new and enlarged verse
unity.

There are several decided objections to this conception. First, the
verse pause _may_ be eliminated, but its elimination is _not
essential_ to the rhyme effect; the verse pause may still be as long,
if not longer, with rhyme. Secondly, the larger unity into which the
verses enter is not in many cases a unity made up exclusively of
rhymed verses. Verses without rhyme alternate with rhymed verses, and
have the usual verse pause. Thirdly, the rhyme is not merely a
regularly recurring element: it is essentially a recurring element of
which one may say what has been said falsely of the rhythm elements,
that each rhyme is either a repetition of something gone before to
which it refers, or the anticipation of something to which it looks
forward. In most cases, rhymes function in pairs. Such peculiarities
distinguish the rhyme from the accent of the foot. Lastly, the freedom
of the whole stanza structure into which rhyme is introduced is much
greater than that of the single verse; pauses much larger than the
admissible lags of a single verse are possible between the verses, and
there is no tension which persists throughout. There is no feeling of
strain if the series halts at the verse ends.

A second hypothesis is that there is some definite process at the end
of the verse which marks the close of the verse and which takes more
time in the case of blank verse than in the case of rhymed verse. If
we conceive the end of the verse as a point where a dying out of the
tension occurs, we may imagine that the rhyme brings an emphasis, and
becomes a qualitative signal for this release. The slight increase of
intensity on the rhyme contributes to the breaking up of the
coördination, and at the same time exhausts and satisfies the feeling
of tension which the verse embodies. It is at the point for finishing
and releasing the set of strains which constitute the motor image of
the verse. A qualitative change may be supposed to produce the effect
more rapidly than the simple dying out of the tensions, which occurs
in blank verse without a differentiated end accent.


3. _The Relation of the Rhyme to the Cyclic Movement of the Unit Group
and of the Verse_.

A series was arranged in which the accent of an ordinary foot and a
rhyme occurred side by side; the distance between them was gradually
lessened, and the effect on the rhyme and on the ordinary accented
element was noted.

A preliminary set of experiments on the effect of two accents which
approach each other gave some very interesting results. Thus Table II.
shows the effect of gradually eliminating the verse pause from the
couplet.


TABLE II.

  Dactylic, catelectic couplet of the general form:

   ÍII ÍII ÍII Í / ÍII ÍII ÍII Í  Without rhyme.

  Each dactyl (ÍII) is, in terms of spaces between the pegs, 3 2 4;
  or in seconds, .25, .17, .33.

  The pause between the two verses was gradually lessened

  B.
  At 5 (.42 sec.) The verses are normal.
    4.5           The verses are normal, but first accent of II. is fading.
    4             The accent is less and less on first element of II.
    3.3           The accent is almost gone on first element of II.
    3 (.25 sec.)  First foot of II. has quite lost accent. There is now but
                    one verse. 'Amalgamation.'
  Mc.
    7 (.58 sec.)  The verses are normal.
    5.3           Either first element of II. has its normal accent, or
                    it wavers to a secondary accent, and the verses
                    become one.
    5 (.416 sec.) First foot of II. has quite lost accent. Amalgamation.
    3 (.25  sec.) 'Last verse completely spoiled.' Last verse
                            '        '       '       '
                    becomes -- /- -, -- - -, -- - -, -- --.
                    Unsatisfactory.
    2 (.16 sec.)  The II. has become mere 'medley.'
  H.
    6 (.5 sec.)   Normal.
    5             First element of II. attaches to I., and its accent is
                    lessened.
    3 (.25 sec.)  First element of II. has lost its accent; the verses
                            '   '   '   '       '   '   '
                    become  --- --- --- - / - --- --- ---. But one verse.
                     Amalgamation.
  J.
    5 (.42  sec.)  Normal.
    4.6            First element of II. is losing accent.
    3 (.25  sec.)  First two elements of II. 'tumble over each
                               '   '   '   '      '   '   '
                     other.'   --- --- --- - / ---- --- ---.
                     Unsatisfactory.  Amalgamation.
  L.
    5 (.42  sec.)  Normal.
    4              Last element of I. losing accent.
    3.3            Last element of I. and first of II. have completely
                     lost accent. Amalgamation.
  G.
    7  (.58 sec.)  Normal.
                   '   '   '   '           '   '
    3  (.25 sec.)  --- --- --- - / - ----- --- -. Amalgamation.

  Mi.
    4.3(.35 sec.)  Normal.
    4              First two elements of II. equal in accent.
                   '   '   '   '     '  '   '   '
    3  (.25 sec.)  --- --- --- - / - -- --- --- -. Amalgamation.


As soon as the accents are within a certain distance they affect each
other. As a rule the first retains its original intensity and the
second is weakened; rarely the first yields to the second. The table
shows that the distance at which this occurs is about .42 seconds.
Under many conditions it is quite possible for two accents to occur at
that distance, _e.g._, in rapid rhythms, without any 'fusing.' The
subject has a type of rhythm very definitely in mind and the only
hypothesis which will explain the difficulty in observing the type, in
spite of the slight change in time values, is that somehow the cyclic
automatic movement has been affected and can no longer produce the
normal, limiting sensation at the accent. There is not time for the
phase of relaxation before the next, objective, limiting sensation
occurs. We may figure the movement as follows:

[Illustration: FIG. 2.]

_A_ is a curve in which _B_ is the relaxation phase. At _C_ the
tensions are rapidly increasing in anticipation of the next limiting
sensation at _A_. But if the objective factor appears too early, the
tensions will be discharged prematurely, and the second accent will be
weakened. Exactly the obverse of these phenomena is often noticed,
when a slight retardation of the second accent produces a slight
increase in its intensity. When, finally, the second accent has been
moved so near the first accent that it occurs within the phase of the
first, it disappears as an independent accent. At the same time the
objective stimuli immediately following now appear at quite irregular
intervals in the cycle, the coördination is broken up, and chaos
without accentuation for some distance is the result. Occasionally the
process does not right itself before the close of the verse. As this
process eliminates the verse pause, the two verses become one, as the
accents approach each other. In cases where the first accent is lost,
one may suppose that the first accent functions as an anticipatory
stimulus, while the second simply increases the effect (cf. Hofbauer
and Cleghorn), and marks the culmination. The fact that the second
accent is only lost at very close range favors this idea.


TABLE III.

  Dactylic, catalectic couplet of the general form:
  ÍII ÍII ÍII Í / ÍII ÍII ÍII Í (with rhyme).

  Each dactyl (ÍII) is, in terms of spaces between the pegs, 324;
  or, in seconds, .25, .17, .33.

  The pause between the two verses was gradually lessened.

  B.

    At 4  (.33 sec.)  Normal.
       2  (.17 sec.)  First accent of II. is weakening.
       1.3(.21 sec.)  Amalgamation. Rhyme retains the accent.
    Mc.
       5  (.42 sec.)  Normal.
       4              II. has become anapæstic.
       2  (.17 sec.)  Rhyme is lost. Amalgamation.
    J.
       3  (.25 sec.)  Normal.
       2  (.17 sec.)  Accent of rhyme is lost. Amalgamation.
    L.
       4  (.33 sec.)  Normal.
       1.6(.18 sec.)  Rhyme retains accent, first accent of II.
                        is lost. Amalgamation.
    G.
       4  (.33 sec.)  Normal.
       2  (.17 sec.)  Accent of rhyme retained. Amalgamation.
    Mi.
       2  (.17 sec.)  Normal.
       1.6            First foot of II. amphibrachic.
        .4(.03 sec.)  Accent of rhyme retained. Accent of first foot
                         of II. lost. Amalgamation.


When the qualitatively different click representing the rhyme is
introduced, its most striking effect is decidedly to shorten the
possible distance between the two accents. This is in accord with the
notion suggested of the function of rhyme at the verse end. The rhyme
seems greatly to hasten the relaxation phase, as compared with the
time required in the ordinary foot.

There is a variety of forms possible to the unrhymed verse, but that
with the climax at the close is decidedly the most frequent. When the
rhyme is introduced the climax goes with it, and the verse flows down
as it were to the end. When the rhyme is put in the very first of the
verse, however, a secondary or even a primary accent may be developed
at the close of the verse. The natural place for the climax of the
verse movement is apparently at the close, and the fact that not only
is the earlier part of the verse more vague, but also that the end is
the natural, climactic position, makes the synthesizing and delimiting
factor, rhyme, preferable at the close.

The records of the next table were obtained by asking the subjects to
repeat the series with prescribed accents, until they decided whether
or not the rhyme could be felt under the conditions.


TABLE IV.

Rhymes under prescribed accentual conditions: iambic tetrameter.
Heavy accent marked acute (´). Slight accent marked grave (`).
Rhyme indicated by brace.

  Ta ta  ta ta  ta ta  ta dó)
                          gò)
                          dò
                          dò
     Hu. Rhymes imperfectly.
     Mc. Rhymes imperfectly.
     G.  Rhymes imperfectly.
     Ha. Rhymes imperfectly.
     Hy. Rhymes fairly well.

  Ta ta  ta ta  ta ta  ta dò)
                          gó)
                          dò
                          dò
     Hu. Cannot get rhyme.
     Mc. Rhymes imperfectly. 'Produced by some sort of tension.'
     G.  Rhymes imperfectly.

  Ta ta  ta ta  ta ta  ta dò)
                          gò)
                          dó
                          dò
     Hu. Rhymes well.
     Mc. Rhymes well.
     G.  Rhymes well.

  Ta ta  ta ta  ta ta  ta dò
                          gò)
                          dó)
                          dò)
     Hu. Cannot get rhyme.
     Hy. Cannot get rhyme. 'Accent spoils it.'
     G.  Cannot get rhyme. 'Accent breaks it all up.'
     Mc. Rhymes imperfectly.


The table shows that rhymes of syllables which have accents of
strikingly different degrees are difficult to feel. In the last case,
of the rhyming verses separated by a verse having a heavy end accent,
it was practically impossible to hear the rhyme across the break made
by the heavy accent. Somehow the particular condition of the organism
which constitutes the expectation of a rhyme is broken up by a heavy
accent.

The material for the records of Table V. was read to the subjects, the
tones were in every case those of the speaking voice, and intervals
having a definite speech character were chosen. The fifth is the
interval of the rising inflection of the question, the fourth is the
interval of the rising inflection of indifference or negation, and the
single falling slide used is a descending interval of a third or
fourth at the close of the sentence. The fifth appears in the table as
5/, the fourth as 4/, and the single descending interval of finality
as the period (.). Each verse was read on approximately the first tone
of the interval, the rhyming syllable only had the second tone of the
interval.


TABLE V.

  RHYMES UNDER GIVEN PITCH CONDITIONS.

  Iambic tetrameters: two-verse stanzas.

  The body of the verse is omitted; the closing intervals alone are
  indicated. '1' is read 'good rhyme;' '2' is 'poor rhyme'; and '0' is 'no
  rhyme.'

  Couplets:
          --do   5/}  5/}   .}  .}  5/}
          --go    .}  4/}  5/}  .}  5/}
            G.    2    2    0
            S.    0         0   2    1
            R.    2    2    1   2    2
            Mc.   0    0    0   1    1
            Hu.   0    0    ?   1
            Ha.   1         2   1    2

  Iambic tetrameters; four-verse stanzas.

  Rhymes are indicated by 'a' and 'a,' 'b' and 'b.'  Capital* letters are
  read 'poor rhyme;' 'o' is read 'no rhyme.'

        I. II. III. IV. I.  II. III. IV.  I.  II. III. IV.  I.  II. III. IV.
       do, no, go, so.  do, no, go,  so.  do, no, go,  so.  do, no, go,  so.
        5/  .   5/  .    .   5/  .    5/   5/  5/  .    .    5/  5/  .   5/
    G.  a   b   a   b    a   b   a    b    a   a   b    b    a   a   a   o
    R.                   a   b   a    b    a   a   b    b
    Mc. a   b   a   b    a   o   a    o
    Hu. a   b   a   b    a   b   a    b    a   a   b    b    a   a   o   a
    Ha. a   b   a   b    o   o   o    o    a   a   B    B    a   a   o   a

    5/  5/  5/  .    .   .   .    5/   .   .   .    .    .   5/  .    .
    G.  a   a   a    a   a   a   a    o    a   a   a    a    o   o   a    a
    Hu. a   a   a    o   a   a   a    o    a   a   a    a    a   o   a    a
    Ha. a   a   a    o   a   a   A    o    a   a   a    a    a   o   a    a
    Mc. a   a   a    o   a   a   a    o    A   A   A    A    A   o   A    A
    R.  a   a   a    o   a   a   a    o    a   a   a    a    A   o   A    A

        5/  5/  4/   5/  .   .   5/   5/   5/  .   4/   .    5/  .   .    5/
    G.  a   a   o    o  /a   a   b    b   /o   a   o    a    o   o   o    o
                        \a   b   a    b   \A   A   B    B
    R.  A   A   A    A  /o   o   a    a\   a   a   b    b
                        \a   a   o    o/
    Hu. a   a   o    a
    Mc. a   a   o    a   A   A   B    B
    Ha. A   A   B    B   a   a   b    b     o   a   o    a

        4/  4/  4/   .   5/  5/  5/   5/    5/  4/  5/   4/
    G.  a   a   a    a                      o   a   o    a
    Mc. a   a   a    o
    R.  a   a   a    o   a   a   b    b
    Ha.                  A   A   A    A

 *Transcriber's Note: Original used italic lower case letters.


The table shows that there is a decided tendency to prefer rhymes in
which the members of the rhyme have the same interval. The only
exception is in the case of couplets, where two contrasting slides 5/
and . rhyme, whenever the finality interval occurs last. Perhaps the
similarity of pitch of the rhyming syllables is a part of the
'Gestaltqualität' whose recognition brings about the release and
satisfaction of the state which we know as the 'feeling of expecting a
rhyme.' Definite pitch relations in music seem to make rhyme of little
significance. We seldom notice the rhymes in a hymn or in a song of
any musical worth. In comic operas and popular ditties rhyme does now
and then figure. In such cases the pitch of the two or more rhyming
syllables is identical; often the whole phrase is repeated for each
rhyming verse. A few experiments in singing a rhyme to simple
intervals show that when the identical interval is used the two
syllables rhyme well, but if the interval be in the opposite
direction, or in another chord, the rhyme is very uncertain. It seems
that in music we usually have 'feelings of expectation' (_i.e._,
tensions of some sort, central or peripheral), which are adequate to
unite the phrases into larger unities. These tensions are so definite
and vivid that they quite obscure and swallow up the related
condition of rhyme expectation. These experiments on the modification
of the rhyme by the various pitch and accent factors are not at all
exhaustive or conclusive. An extended series of experiments is needed.
The study of sound records for pitch is peculiarly tedious, but it
should reveal some interesting relations between rhyme and speech
melody.


III. THE SPEAKING OF A RHYTHMIC SERIES.


I. _Methods of Making Speech Records._

The study of spoken rhythm is of primary importance. Observations on
what the subject really does are always open to the objections that
subjective factors play a large part, and that the observer's
perception of a rhythm is after all _his_ perception of the rhythm,
not the subject's. The voice is an important indicator of the
activities which generate the rhythms of verse and music, and some
objective method of measuring the sounds made is essential to a study
of the rhythm production.

Methods of recording and studying the tones of the voice are as
numerous as they are unsatisfactory. In the main the work has been
done for purposes of phonetics, and but few of the methods are applied
in the psychological laboratory.

Marage[13] has an excellent summary of the methods with practical
comments on their applicability. Rousselot[14] (Histoire des
applications de phonétique expérimentale, 401-417: objets et
appareils, 1-10 et 669-700) gives a careful history of the methods
from the phonetic point of view. Scripture[15] gives a convenient
English summary of the processes.

   [13] Marage: _l'Année psychologique_, 1898, V., p. 226.

   [14] Rousselot: La Parole, 1899.

   [15] Scripture, E.W.: _Studies from the Yale Psych. Lab._,
   1899, VII., p. I.

A few methods have been devised which avoid the difficulties incident
to the use of a diaphragm, but they are not applicable to the
measurement of rhythm material. The instruments which might be used
for recording spoken rhythms are all modifications of two well-known
forms of apparatus, the phonautograph and the phonograph. The
phonograph record is incised in wax, and presents special difficulties
for study. Boeke, however, has studied the wax record under a
microscope, with special arrangements for illumination. The work is
quite too tedious to permit of its use for material of any length,
though it is fairly satisfactory when applied to single vowels. In
order to enlarge the record, and at the same time to obtain the curves
in the plane of the record surface, Hermann devised an attachment to
the phonograph (cf. Marage, loc. citat.) by which the movements of the
stylus of the phonograph are magnified by a beam of light and recorded
on photographic paper. The measurements of entire words by this method
would be as tedious as by Boeke's.

E.W. Scripture has chosen another type of talking machine from which
to obtain transcribed records. The permanent record of the gramophone
(which makes a record in the plane of the surface, like the
phonautograph) is carefully centered, and a lever attached to a stylus
which follows the furrow of the record transcribes the curve on the
kymographic drum as the plate is slowly revolved. The method has the
advantage of using a record which may be reproduced (_i.e._ the
original gramophone record may be reproduced), and of giving fairly
large and well defined curves for study. It is too laborious to be
applied to extended research on speech rhythms, and has besides
several objections. The investigator is dependent on the manufacturer
for his material, which is necessarily limited, and cannot meet the
needs of various stages of an investigation. He knows nothing of the
conditions under which the record was produced, as to rate, on which
time relations depend, as to tone of voice, or as to muscular
accompaniments. There are also opportunities for error in the long
lever used in the transcription; small errors are necessarily
magnified in the final curve, and the reading for intensity (amplitude
of the curve) is especially open to such error.

The stylus of such a recording apparatus as is used by the gramophone
manufacturers, is subject to certain variations, which may modify the
linear measurements (which determine time relations). The recording
point is necessarily flexible; when such a flexible point is pressed
against the recording surface it is dragged back slightly from its
original position by friction with this surface. When the point is
writing a curve the conditions are changed, and it sways forward to
nearly its original position. This elongates the initial part of the
sound curve. This fact is of little importance in the study of a
single vowel, for the earlier part of the curve may be disregarded,
but if the entire record is to be measured it is a source of error.
Hensen[16] first turned the phonautograph to account for the study of
speech. He used a diaphragm of goldbeater's skin, of conical shape,
with a stylus acting over a fulcrum and writing on a thinly smoked
glass plate. The apparatus was later improved by Pipping, who used a
diamond in place of the steel point. The diamond scratched the record
directly on the glass. The Hensen-Pipping apparatus has the advantage
of taking records directly in the plane of the surface, but it does
not make a record which can be reproduced; in case of doubt as to the
exact thing represented by the curve, there is no means of referring
to the original sounds; and it involves working with a microscope.

   [16] Hensen: Hermann's Handbuch d. Physiol., 1879, Bd. I., Th.
   II., S. 187.

[Illustration: FIG. 3. Diagrammatic section of recording apparatus.
_a_, diaphragm; _s_, stylus; _g_, guide; _p_, section of plate.]

The apparatus which was used in the following experiments consisted
essentially of two recording devices--an ordinary phonograph, and a
recorder of the Hensen type writing on a rotary glass disc (see Fig.
5, Plate X.). Of the phonograph nothing need be said. The Hensen
recorder, seen in cross section in Fig. 3, was of the simplest type. A
diaphragm box of the sort formerly used in the phonograph was modified
for the purpose. The diaphragm was of glass, thin rubber, or
goldbeater's skin. The stylus was attached perpendicularly to the
surface of the diaphragm at its center. The stylus consisted of a
piece of light brass wire bent into a right angle; the longer arm was
perpendicular to the diaphragm; the shorter arm was tipped with a
very fine steel point, which pointed downward and wrote on the disc;
the point was inclined a trifle to the disc, in order that it might
'trail,' and write smoothly on the moving disc. The stylus had no
fulcrum or joint, but recorded directly the vibrations of the
diaphragm. In early experiments, the diaphragm and stylus were used
without any other attachment.

But a flexible point writing on smoked glass is a source of error.
When the disc revolves under the stylus, the flexibility of the
diaphragm and of the stylus permit it to be dragged forward slightly
by the friction of the moving surface. When the diaphragm is set
vibrating the conditions are altered, and the stylus springs back to
nearly its original position. The apparent effect is an elongation of
the earlier part of the curve written, and a corresponding compression
of the last verse written. This error is easily tested by starting the
disc, and without vibrating the diaphragm stopping the disc; the
stylus is now in its forward position; speak into the apparatus and
vibrate the diaphragm, and the stylus will run backward to its
original position, giving an effect in the line like _a_ (Fig. 4). If
the error is eliminated, the stylus will remain in position
throughout, and the trial record will give a sharp line across the
track of the stylus as in _b_.

[Illustration: FIG. 4.]

This source of error was avoided by fixing a polished steel rod or
'guide' at right angles to the vertical part of the stylus, just in
front of the stylus; the stylus trailed against this rod, and could
not spring out of position. The friction of the rod did not modify the
record, and the rod gave much greater certainty to the details of the
sound curve, by fixing the position of the vibrating point. This rod
or guide is shown in Fig. 3 (_g_).

The disc was driven directly from the phonograph by a very simple
method. A fine chain was fixed to the shaft carrying the disc, and
wrapped around a pulley on the shaft. The chain was unwound by the
forward movement of the recording apparatus of the phonograph against
the constant tension of a spring. When the phonograph apparatus was
brought back to the beginning of a record which had been made, the
spring wound up the chain, and the disc revolved back to its original
position.

A T from the speaking-tube near the diaphragm box was connected by a
rubber tube with the phonograph recorder, so that the voice of the
speaker was recorded both on the smoked glass plate and on the
phonograph cylinder. The advantages of such a double record are that
the possible error of a transcription process is eliminated, and yet
there is an original record to which it is possible to refer, and by
which the record measured may be checked.

An important feature in the method was the rate at which the disc
revolved. The disc turned so slowly that the vibrations, instead of
being spread out as a harmonic curve, were closely crowded together.
This had two great advantages; the measurements were not so laborious,
and the intensity changes were much more definitely seen than in the
elongated form of record. Each syllable had an intensity form, as a
'box,' 'spindle,' 'double spindle,' 'truncated cone,' 'cone,' etc.
(cf. p. 446).

The disc was run, as a rule, at a rate of about one revolution in two
minutes. The rate could be varied to suit the purposes of the
experimenter, and it was perfectly possible to procure the usual form
of record when desired. As a result of the low rate, the records were
exceedingly condensed. The records of the 300 stanzas measured are on
two glass discs of about 25 cm. diameter, and as much more could still
be recorded on them.

The diaphragm and the speaking tube were the great sources of error.
For measurements of time values the particular component of the tone
to which the diaphragm happens to vibrate is not important, but the
record of intensities depends on the fidelity with which the diaphragm
responds to a given component, preferably the fundamental, of the
tone. The speaking tube has a resonance of its own which can be but
partly eliminated. For the records here recorded either glass or
goldbeater's skin was used as a diaphragm. Goldbeater's skin has the
advantage of being very sensitive, and it must be used if the subject
has not a resonant voice. It has the great disadvantage of being
extremely variable. It is very sensitive to moisture, even when kept
as loose as possible, and cannot be depended on to give the same
results from day to day. The records marked Hu., Ha. and G. were
usually taken with a glass diaphragm, which has the advantage of being
invariable. As the phonograph records show, glass does not modify the
lower tones of the male voice to any extent.

[Illustration: PSYCHOLOGICAL REVIEW. MONOGRAPH SUPPLEMENT 17. PLATE X.
               Opposite p. 436.
The apparatus is shown arranged for taking parallel records on the
smoked glass disc, and on the cylinder of the graphophone. On the left
is shown the microscope with which the records on the glass disc were
measured. ]

The speaking-tube used was of woven material, not of rubber, and a pad
of felt was kept in the tube near the diaphragm box. As far as
possible more damping was used at the other end of the tube, but this
had to depend on the voices of the subjects.

The best check on the performances of a diaphragm is the number per
second and character of the vibrations. The pitch may be calculated
from the rotation rate of the disc, which is very constant, as it is
driven at a low rate by the well-regulated high-speed motor of the
phonograph. But it is better to place a fork in position to write on
the disc and take a parallel record. All the records were taken with
the vowel 'a' (sound as in father). This vowel has a very
characteristic signature, which is easily seen, even in a very closely
packed curve, and the correctness of this is one of the best
guarantees that the fundamental of the tone is actuating the diaphragm
(though that does not mean that the diaphragm is actually giving the
vibration frequency of that fundamental).

Every record was repeated at least twice, and both records were
measured. In many of the experiments the intensities were fixed by the
conditions of the experiment. There was always the corroborative
testimony of the phonograph diaphragm; for the two were not apt to err
together. It was easy to determine if the actual intensity relations
were preserved in the phonograph (but it could not be taken for
granted). Each record was reproduced on the phonograph immediately
after it had been taken, and both subject and operator listened for
anomalies. In practice it was not hard to get records of the single
vowel used (at a small range of pitch which was never more than a
third or fourth and was nearly always much less) which represented
fairly well the relative intensities. Beside the checks spoken of
above, every record was repeated by a number of subjects, and the
comparison of the results of different voices shows uniformity.

The recording of spoken verse is another matter. It is not difficult
to test a diaphragm carefully through a small range, but to be certain
of its action at all the pitches and qualities of the speaking voice
is impossible. A stable diaphragm, glass or mica, would have to be
used, and careful corrections made for the different vowels.

At best, when the records are satisfactory, nothing can be said for
the measurements of intensity but that they represent relations of
more or less; the diaphragm has a minimum intensity, below which it
does not vibrate, and a maximum intensity, above which the amplitude
of its vibrations does not materially increase without breaking into
partials and 'blasting.'

The disc recorder, which had for a mount a modified microscope stand,
was placed on the shoe of the disc stand and clamped. The wax and disc
records were adjusted at known starting-points and the stylus
carefully lowered, by the rack and pinion adjustment, to the surface
of the disc. After a preliminary trial of the diaphragm the apparatus
was started, and when at full speed at least two satisfactory records
of the material were taken. When the disc had made a single
revolution--a record of some ten or fifteen stanzas--the recorder was
fed inward to a new circle on the disc. After the records were taken,
a microscope with either 2 or 4 Leitz objective and a micrometer
ocular was substituted for the recorder. The phonograph recorder was
raised and drawn back to its starting point, and the disc came back to
its original position. The microscope was focussed, and adjusted by
the screw of the shoe until it had the record line in its field; the
micrometer furnished an object of reference in the field. The
phonograph, now carrying the reproducer--if possible without a horn,
as the tones are truer--was started. At the first syllable of the
record the apparatus was stopped by the device furnished on the
'Commercial' phonograph, and the plate was turned by adjusting the
screw at the phonograph carriage, which changed the length of the
chain connecting the two records, until the record of the first
syllable was at some chosen point in the field. In cases of records
of poetry it was found better to have a set of syllables, say 'one,
two, three' prefixed to the record, for this adjustment. The
phonograph was again started, and the curve-forms representing the
spoken syllables filed past the point as the phonograph repeated each
syllable. The rate was slow enough, with the objective 2, so that
there was no difficulty in observing the passing syllables. After the
conformity of the phonograph record had been noted by the operator,
and the subject had passed judgment on the phonograph as saying
satisfactorily what he had said, the curve-forms were measured with
the micrometer. The record was fed slowly through the field by means
of the chain screw on the phonograph carriage; and measurements of the
lengths of syllables gave their time values. The micrometer was passed
back and forth across the form by the shoe screw, for the measurements
of amplitude (intensity). The micrometer measurements in this case
could be made at least as rapidly as measurements of kymograph curves.
The measurements, with the powers used, are accurate to.01 sec.

The smoked disc records are to be preferred to those scratched with a
diamond, because of the superior legibility of the line, an important
item if thousands of measurements are to be made. The records are
fixed with shellac and preserved, or they may be printed out by a
photographic process and the prints preserved. The parallel set of wax
records is preserved with them. There are several ways in which the
wax records lend themselves to the study of rhythmic questions. It is
easy to change the rate, and thereby get new material for judgment, in
a puzzling case. Consonant qualities are never strong, and it is easy
so to damp the reproducer that only the vowel intensities are heard.
The application in the study of rhyme is obvious.

All the series consisted of regular nonsense syllables. The accented
and unaccented elements were represented by the single syllable 'ta'
('a' as in father). Rhymes were of the form 'da,' 'na,' 'ga' and 'ka.'
In other parts of the work (cf. Table IV.) the vowel o had been used
in rhymes for contrast; but the same vowel, a, was used in these
records, to make the intensity measurements comparable.

The records of the measurements were as complete as possible. The
sonant and the interval of each element were measured, and all the
pauses except the stanza pause were recorded. The intensity of each
syllable was recorded beneath the length of the syllable, and notes
were made both from the appearance of the curve and from the
phonograph record.


_2. The Normal Form of Unrhymed Verse._

To determine the influence of a subordinate factor in rhythm such as
rhyme, it is necessary to know the normal form of verse without this
factor. It is natural to assume that the simplest possible form of
material would be individual feet recorded seriatim. But on trial,
such material turned out to be very complex; the forms changed
gradually, iambs becoming trochees and trochees changing into
spondees. It is very probable that the normal foot occurs only in a
larger whole, the verse.

To corroborate the conclusions from perceived rhythms as to the
existence of variations in earlier and later parts of the verse, a
table of mean variations was prepared from the material recorded and
measured for other purposes.


TABLE VI.

  MEAN VARIATIONS.

  Iambic tetrameters; variations of each element from the average foot
  of the entire stanza.

  [Label 1: Unaccented Element of Foot.]
  [Label 2: Accented Element of Foot.]
  [Label 3: Percentage M.V. of Unac. El.]
  [Label 4: Percentage M.V. of Ac. El.]

  Hu. 8 stanzas            [1]      [2]     [3]   [4]
    M.V. 1st foot          0.9688   1.3125  11.1  7.8
         2d   "            0.8125   0.6563   9.3  3.9
         3d   "            0.8438   1.1875   9.7  7.1
         4th  "            0.9688           11.
  Av. foot of all stanzas  8.69     16.88

  Geo. 10 stanzas, no accents or rhymes within the verse:
    M.V. 1st foot          2.725    2.775   24.6  13.3
         2d  "             1.300    1.325   11.8  6.4
         3d  "             1.400    2.050   12.7  9.8
         4th "             2.750            24.9
  Av. foot of all stanzas 11.05    20.85

  Geo. 8 stanzas, accents and rhymes within the verse:
    M.V. 1st foot          1.4843   2.4687  13.1  11.5
         2d   "            1.4219   2.6875  12.6  12.6
         3d   "            1.7031   2.5312  15.1  11.8
         4th  "            1.8594           16.4
  Av. foot of all stanzas 11.31    21.38

The last element has the 'finality-form' and is not comparable to the
other accented elements and therefore is not given.


Dactylic tetrameters (catalectic); variations of each element from the
average foot of the entire stanza:

  [Label 1: Accented elements of Foot]
  [Label 2: 1st Unaccented element of Foot]
  [Label 3: 2d Unaccented element of Foot]
  [Label 4: Percentage M.V. of Ac. El.]
  [Label 5: Percentage M.V. of 1st Unac. El.]
  [Label 6: Percentage M.V. of 2d Unac. El.]

                         [1]      [2]      [3]     [4]   [5]   [6]
  Me., Ha., 8 stanzas, normal:
     M.V.  1st foot     1.6875   1.2813   1.8125   9.70  9.76  10.5
       "   2d   "       1.0613   1.0613   1.4061   6.1   8.0    8.1
       "   3d   "       1.6875   1.3125   1.3750   9.7   9.9    7.9
     Av. foot          17.38    13.18    17.31

  Geo. 4, stanzas, abnormal type of dactylic foot:
     M.V.  1st foot     1.5000   1.1250   1.2813  11.5  11.0    8.7
       "   2d   "       1.5625   1.1250   1.1250  12.0  11.0    7.6
       "   3d   "       1.3437   1.1873   0.8737  10.3  11.5    5.9
     Av. foot          13.00    10.25    14.75

  Me., Ha., G., Hu., Am., accent on 2d foot, 8 stanzas:
     M.V.  1st foot     2.4688   1.3125   2.2813  12.7  12.7   11.5
       "   2d   "       2.3750   1.1250   3.8438  12.2   8.7   19.3
       "   3d   "       2.9688   1.3750   2.2500  15.5  10.7   11.3
     Av. foot          19.44    12.88    19.88

  Me., Ha., G., Hu., 19 stanzas, normal:
     M.V.  1st foot    1.9474    1.2500   2.2763  10.8   8.6   11.4
       "   2d   "      1.3816    1.2369   1.7766   7.7   8.5    9.3
       "   3d   "      1.3158    1.2105   1.6382   7.3   8.4    8.6
     Av. foot         18.00     14.24    19.05

  Me., Ha., G., 6 stanzas, normal:
     M.V.  1st foot    2.0000    1.2083   1.8750  10.5  10.4   10.7
       "   2d   "      2.6250    1.0416   2.1666  13.8   9.1   12.3
       "   3d   "      2.1250    1.3333   1.3333  11.3  11.4    7.6
     Av. foot         18.92     11.58    17.50
     The last foot (catalectic) is not comparable in these dactylic stanzas.


The mean variations of the table (Table VI.) were calculated as
follows: The average for all the elements of the stanza was obtained
and an average foot constructed (excluding the last sonant and the
pause of the verse). From this average foot the variations of all the
first feet were computed, then the variations of all the second feet,
etc. Then the variations of the first feet of the stanza were averaged
and percentages taken, etc.; it is this last value which goes to the
making up of the tables. In inspecting the averages the corresponding
elements of the feet should be compared. Any increased length due to a
prescribed accent within the verse, etc., appears in the averages as a
corresponding increase in the mean variation at that point, and only
the first and last feet can be compared as to the variations in the
verse as a whole. In making up the tables the material was grouped,
not by combining the records of each subject, but by combining all the
stanzas of a single type, in order to eliminate individual
peculiarities.


TABLE VII.

    Verse pauses in unrhymed stanzas, together with the foot pause
    within the verse. Length of last foot, together with the
    average foot within the verse:

       Average first    Last foot   Average of first   Verse Pause.
      3 feet of verse.  of verse.    3 foot pauses
                                       of verse.
      Iambs:
            36            56.5            24               45.5
            57           122              35              100
            68.5         125              45              102
            63.5         111.5            42               93
            63.5         117.5            39               93.5
            66           135              42              110
            53.5          59              40               45
            60            76              45               61
            56.5          68              41               54
            55.5          56              39               41
            53            53.5            37               41.5
            56            73              34               45
            85            98              56               54
            39            50              26.5             36
            37            43              17               30
            42.5          45              28               30
            38.5          49              26               36
            40            79              26               55
            31            72.5            21               55
            33            66              23               54
            33            76              22               64
      Dactyls, catalectic:
            56            63        (The pauses cannot be
            60            62        compared because of the
            55            66        omission of elements in
            51.5          76        the final foot.)
            37            40
            55            58.5
            53            59.5
            40            73
            38            65
            37.5          56
            37            73


Throughout the series of measurements made the accented element was
nearly always longer, and in no case did the accent fail to increase
the length of the sonant. Ebhardt's suggestion that there are two
significant parts in each foot-element, viz., sonant and pause, does
not seem good. Although the sonant is much longer when accented, the
ratio between the sonant and the following interval is not definite.

An examination of thirty-two stanzas of unrhymed iambic and dactylic
(catalectic) tetrameters (cf. Table VII.) shows that the verse pause
is always at least one fourth larger than the foot pause. In the
unrhymed stanzas the verse pause varies widely, and may be as large as
three times the foot pause. A pause longer than the foot pause is
absolutely essential to the unity of the verse. All sorts of ratios
are presented; evidently the verse pause is not a function of the foot
pause.

The next table (Table VIII.) shows a variety of different dynamic
shadings in the verse. It is noteworthy that in these nonsense verses
the type is uniform throughout the stanza. Representing the
intensities by curves similar to those used by the subjects in
listening to rhythms, we have the forms shown in Fig. 6 (_a_).

The general curve is like that in Fig. 6(_b_).

[Illustration: FIG. 6.]

When a special emphasis is prescribed on some particular accent in the
verse, the type becomes invariable, not only in each stanza, but for
all stanzas of all subjects.

The records show that the accent is produced in a variety of ways.
One, for example, gets the accent by a slight increase in intensity,
but especially by a pause following the sonant.


TABLE VIII.

  THE INTENSITY RELATIONS WITHIN THE TOTAL, UNRHYMED VERSE.

  UNRHYMED IAMBIC TETRAMETERS.
                                     Average
              Intensities.           length      Length
            '      '      '       '  of first    of last
        _   -  _   -  _   -   _   -  3 sonants.  sonant.

  Ha.   2   5  4   5  2   4   3   6        31      31s
        4   4  2   4  2   5   3   7        33      36s
        2   5  3   4  1   5   3   9        32      29s
        2   4  2   5  2   5   3   7        31      22s
        3   5  1   5  3   4   3   5        37      35s
        2   5  2   4  2   4   3   6        35      27s
        2   4  2   4  2   4   2   6        38      22s
        1   4  3   4  1   5   3   6        34      23s
  Hu.   6   6  6   6  6   6   6   5        25      33
        5   5  5   5  5   5   5   6        26      32
        5   5  5   4  5   5   5   5        19      33
        5   5  5   6  8   9   8   9        28      50
        9   9  8   9  9   9   9   8        43      51
        9   7  8   7  7   8   9  10        48      45s
        6   7  7   7  6   7   6   7        43      43s
        6   6  5   6  4   7   7   8        36      50
  G.    9  14  7  14  4  12   6  10        20      25
        7  12  7  14  7  10   6  10        16      26
        7  12  6  11  4  12   5  10        17      26
        6  13  6  11  1   9   7  12        16      26
       10   8  7  30  6  15   7  16        18      25
        7  14  8  12  6  15  10  13        15      28
        7  16  9  15  4  14   7  12        16      25
        7  15  7  13  5  13   6  12        17      25

  In verses marked 's' the last sonant is shorter than the average of
  the preceding sonants.


  UNRHYMED IAMBIC TETRAMETERS: PRESCRIBED ACCENT ON THE THIRD FOOT.

                                            '
                  \/   --   \/   --   \/   --   \/   --
  Mc. Couplets.    4    6    6    7    4    6    4    4
                   5    8    5    6    2   12    8    5
                   4    6    5   10    4   11    5    3
                   4    6    5   10    4   10    4    4
                   7   11    5    9    9   15    5    5
                   5   19   20   22   21   24    6    6
                  12   22   16   22   20   22    8    7
                  12   22   14   31   10   26    6    7
  Ha. Couplets.    4    7    4    8    8    9    5    7
                   5    7    4    6    6    8    2    7
                   2    6    2    6    5    6    3    6
                   2    7    3    6    2   10    3    4
                   3    7    3    7    4    6    4    6
                   4    5    3    6    4    7    2    6
                   5    7    1    6    4    8    2    5
                   2    7    3    5    3    7    2    6


  UNRHYMED IAMBIC TETRAMETERS: PRESCRIBED ACCENT ON THE SECOND FOOT.

                                  '
                  \/   --   \/   --   \/   --   \/   --
   Mc. Couplets.  13   22   22   30   22   18   15   18
                  11   20   22   26   15   19   15   10
                  10   25   20   26   20   24   12   23
                  10   19   17   26   19   11    9   10
                  12   23   18   26   22   17   10   15
                   8   23   20   27   16   22   15   16
                  12   23   26   30   22   21   10   17
                  14   28   26   34   11   28   11   21

   Ha. Couplets.   6    9    4   12    4    5    3
                   4    5    4   12    1    5    2    5
                   3    5    3   12    2    5    2    6
                   1    6    4   15    1    6    2    7
                   -   15    3   12    -    8    -    5
                   -    6    4   12    -    7    -    5
                   -    7    -    7    4   13    -    4
                   -    6    3   13    -    5    -    4

   G. Couplets.    9   19   11   20    4   12    3   10
                   5   13    6   16    5   10    6   11
                   8   16   10   18    5   10    6   11
                   6   12    6   16    6   10    6   10
                   8   16   13   19    5   13    8   12
                   9   17   11   19    3   10    6   12
                   9   16    9   18    6   10    7    9
                   7   15    7   15    5   10    5   10


Frequently the special accent seems to be made by a contrast between
the accented foot and the feet which follow. In most cases the
influence of the special accent is to be seen, not merely within the
accented foot itself, but both before and after the accented foot.
Often the appearance under the microscope is very striking; the
sonants of the feet, both accented and unaccented, increase to the
special accent and then decrease in a regular crescendo--diminuendo
form. Much of this is not shown by the mere measurements.

[Illustration: FIG. 7]

[Illustration: FIG. 8 Iambic Tetrameter Verse
               (with the accent on the second foot)]

In general the special accent may he said to be the climax of the
verse movement. It is the crest of the wave, and, as noted above, the
dynamic shading is not always made by an increase up to the accent,
nor by a stress on a special accent, but by a sharp diminuendo
immediately following the accent. A study of the phonograph record
brings out these forms of shading, especially when the record is
repeated slowly, exaggerating the dynamic variations and giving an
opportunity for more careful observation.

Within the verse the general form of the syllable as it appears in the
mass of closely written vibrations, often varies, but nearly always
shows a square end. Several very common shapes are noticed and appear
in the record as (1) 'truncated cones,' (2) 'boxes,' and (3)
'truncated spindles.' (See Fig. 7.)

With the particular syllable used, 'ta,' the beginning of curve form
was usually square and abrupt (4), and not gradual (5), although a few
of the latter type are found ('spindle').

One syllable form has an especial interest, because of its bearing on
the problem of 'finality' feeling at the close of the verse. At the
close of each verse, whether with or without rhyme, the syllable form
is always a 'cone' (6) (cf. Fig. 8). Of about 600 verses measured not
more than 15 are exceptions to this rule. Of these 15 exceptions 10
are under special conditions and confirm the hypothesis that this form
is related to the finality process. The form very rarely occurs within
the verse, and when it does it is usually before some cæsura, or under
unusual conditions.

This 'cone' form of the closing syllable of the verse indicates a
falling of the intensity of the voice. It is often, though not always,
associated with a fall in the pitch, showing relaxation of the vocal
cords. It seems to be an indication of the dying out of the intensity
factor, a sinking of the tension, at the close of the verse. In the
case of unrhymed verses, with long verse pause, the cone is often very
much elongated, and it is quite impossible to say where the sound
ceases.

Special accentuation of the long syllable of the foot increases the
length of the sonant, of the accented element, and of the entire foot.
There is probably a slight increase of the total length of an
accented verse as compared with the similar unaccented, but no
calculations were made to show that point. This is quite in accord
with other results (Meumann, Ebhardt). This special accentuation is
connected with an increased mean variation of the time values, as
noted above. It is in that sense a 'disturbing factor.'


TABLE IX.

  VERSE PAUSES (INCLUDING FINAL SONANT) TOGETHER WITH THE AVERAGE OF THE
  CORRESPONDING ELEMENT WITHIN THE VERSE.

              Average long   Verse pause   Verse pause   Verse pause
              element of    of 1st verse   of 2d verse   of 3d verse
              first 3 feet.   of stanza.    of stanza.    of stanza.
  End Rhymes.
    Mc.          26              34           104a          35
                 45             _45_a          80b          80a
                 31              33            64a          36
                 41              52a           51b          75a
    Ha.          41             _44_a         _44_          45a
                 43              47a          _43_b         46a
                 39             _41_a          49b          46a
                 43              46a          _45_b        _45_a
                 36              44            41a          53
                 35              44a           58a          38b
                 33              40            73a         ×30
    Hu.          28             ×25a           50           28a

  Feminine Rhymes.
    Hu.          18              21a           37a          19b
                 19             _20_a          22a          16b
                 19             _21_a         _21_a         16b
    Mc.          36              72a           64           51a
                 36             ×32            41a          40
                 22             _22_a          ×18          29a
    Ha.          27              31a           44b         _28_a
                 36              79           ×30           40
                 30              36            79a         _30_b
                 31              38            50a          36
                 32              39a           42           40a
    Am.          34              70            95a          85
                 35              73a           94           89a
                 30              45            47a          86
                 28              54            53a          70
     G.          19              64a           64           79a
                 19              73a           83b          76a
                 21              81            67a          --
                 19              61            83a          79

   The rhymes are marked 'a' and 'b'; _e.g._, couplets a, a, b, b,
   etc. Verse pauses in italics are equal to the foot pause; those
   marked 'x' are _less_ than the foot pause.


3. _Modification of the Normal Form of Verse due to Rhyme._

Verse Pause in Rhymed Material.

There are as wide, isolated variations as in the case of unrhymed
material. As compared with unrhymed verse, the pause is in general
decidedly shorter. The verse pauses of the feminine rhymes are
generally much like those of the end rhymed material. But there are
very few cases of the verse pause being as short as the foot
pause--only four cases in sixty (6.6 per cent.). See Table IX.

This wide variation of the verse pause and its occasional equivalence
to the foot pause in rhymed verses is in accord with the notion that
the rhyme in some way brings the verse to a close by a process more
rapid than that in unrhymed material.

The introduction of rhyme seems to be favorable to the division of a
stanza into two parts by producing an unusually long verse pause after
the second verse. Of 43 unrhymed stanzas there are 19 which show a
decidedly long pause at the close of some one of the verses. But of
these 19 cases, only 8 (18 per cent.) have the break at the close of
the second verse. Of 64 rhymed stanzas, 29 show the division, and of
this 29, 22 (34 per cent.) have the break at the close of the second
verse.


Influence of the Rhymes on Intensities.

The intensities at the close of the verse, without rhyme, may be
slightly greater than within the verse. The dynamic shading of the
verse is elastic, and a variety of forms is possible, a decrescendo at
the close of the verse is not unusual (cf. Table VIII.). But when the
rhyme is introduced the general dynamic form of the verse is fixed,
and in the material measured this is true not only of the verses in a
stanza which contain the rhyme but of other verses in the same stanza.

Of the 32 verses containing rhymes in Table X., but four verses are
exceptions to the rule of an increase of intensity on the rhyme. There
are two cases of double, alternating rhymes where it is doubtful if
the subject actually felt one of the alternating rhymes. This increase
of intensity on the rhyme is not confined to that particular syllable
or foot; often, as indicated by the italics, the influence of the
accent makes itself felt earlier in the verse.


TABLE X.

  INTENSITIES OF IAMBIC TETRAMETER WITH END RHYME (SHOWING INCREASED
  INTENSITY OF THE RHYMING SYLLABLE). ALSO AVERAGE LENGTH OF THE FIRST
  THREE SONANTS, TOGETHER WITH THE LENGTH OF THE LAST SONANT.

               Intensities.          Average length
                                       of first 3    Length of last
                                        sonants.         sonant.
         \/  - \/  - \/  - \/  -
  Mc.    --  5 --  5 --  4 --  5             19            27
         --  4 --  4 --  4 -- _11_a                        34
         --  4 --  4 --  4 --  7                           21
         --  4 --  5 --  3 --  _8_a                        23

         --  6 --  6 --  5 --  6             19            22
         --  8 --  7 --  6 -- _10_a                        34
         --  4 --  3 --  4 --  5                           26
         --  3 --  5 --  4 --  _5_a                        30

          2  3  5  4  4  5  6  _7_a          29            34
          2  3  3  4  2  4  2  _7_b                        48
          1  2  3  2  2  2  1  _4_a                        35
          2  3  3  3  2  3  4  _5_b                        20

         -- -- -- -- -- -- -- --a            25            40
          3  4  4 14  3  4  5  _5_b                        39
          2  3  1  2  2  3  1  _3_a                        25
          1  3  2  2  1  3  3  _5_b                        43

  Ha.     6 15  9 12  3 10  4 16           No increase in length.
          3  5  3  7  3  5  5 15a
          1 15  1  5  4  6  2  9
          4  5  2  5  1  5  2 _14_a

          2  6  4  8  1  6  5 _11_a        No increase in length.
          1  7  5  7  3  6  7 _11_b
          2  5  2  6  2  6  4 _12_a
          1  5  1  5  2  6  3 _15_b          33              38

          4  9  5  9  1  3  6  _9_a          25              33
          2  8  5  6  4  5  5 _10_b          No increase in length.
          2  5  2  5  2  5  5 _11_a
          1  5  2  5  5 10  2 _12_b          32              34


The evidence of an increased intensity on the rhyme is not so positive
in the case of rhymes in the third foot. Among the rhymes in the
second foot there is but one exception. The rhymes in the second and
third feet were never given very satisfactorily by several of the
subjects. The rhymes within the verse determine a climax in the foot
in which they occur, and all the verses follow this well-defined type.
It is interesting to note, in studying the phonographic record, that
in verses in which the accentuation of the rhythm is not very
definite, the accentuation is perceived when the record is repeated at
the normal speed. If the record is repeated more slowly, and
especially at such a distance that the rhyming consonants cannot be
distinguished, then the accentuation seems to disappear. It is
probable that after a verse or stanza type has been established the
voice may deviate from the type, and the accentuation will be supplied
by the hearer.


TABLE XI.

  INTENSITIES OF IAMBIC TETRAMETERS WITH RHYMES IN THE THIRD FOOT
  (SHOWING INCREASE IN INTENSITY OF THE RHYME SYLLABLE).

               '           '            '           '
        \/    --    \/    --    \/     --    \/    --
  Ha.   13    18    10    16    _7_   _9_a     6    12
         9    10     4    11     7   _14_a     4     7
        --    12     5    10     7      9b     6     9
         2    12     5    12     3   _14_b     4     6

         2    12     4    13     7      8a     4     9
         6     8     4    14     4   _15_a     2     9
         2    13    --    12     8      8b    --    --
         5     9     6    10    --      3b     4     6

  Am.   10    10     4    12     6   _14_a     5     5
         4    12     6     9     7      8a     4     4
         5    12     8     9     7   _10_b     3     4
         3     7     5     8     5      7b     2     4

        10    13     5    10     4   _10_a     4     6
         1     9     4     9     3      5a     3     5
         2     8     3     5    --    _8_b     1     5
         1     7     2     7     5    _8_b     2     3

  G.     6    13     6    13     7   _12_a     1    10
         6    10     6     6    _7_   _7_a     1     8
         4     9     7     7    _6_     9b     1     7
         7    12     4    10     2      7b     1     7

        10    12     4    11     6   _10_a    --     8
         5    12     5    11     6   _10_a    --     8
         3     9     6     9    _7_   _9_b     3     8
         2     8     5     9     5      5b     1     6

  D.    10    12    10    10     7      9a     7    11
         5     8     6     9     7      7?     6     6
         5    12     7     9     6   _10_b    --     8
         6     9     7    10     7      7b     5     5

        10    15     5    11     6     9a    --     9
         5     9     4     8     6     6a?    6     7
         7    11     7    11   _11_  _13_b     8    10
         8    11     8    10     7     9b     6     8


  INTENSITIES OF IAMBIC TETRAMETERS WITH RHYMES IN THE SECOND FOOT.

          '           '          '     '
       _  -     _     -       _  -  _  -
  Hu.  5  6     6     6a      5  7  5  6
       5  6     5     4a      5  4  5  6?
       5  6     6     7b      5  6  4  7
       5  6     4     4b      5  7  4  7
       5  7     7     7a      6  7  6  6
       5  7     5     5a      5  6  5  6?
       5  7    _6_    8b      6  7  6  7
       6  7     6     5b      6  7  6  7
  Mc.  5  7     6   _10a_     5  4  3  5
       1  6     6    _8a_     -  6  1  4
       1  6     6   _10b_     1  4  -  4
       -  7     6     5b      3  3  -  3
  Ha. 16 14    _8_  _10a_     6 10  5  9
       5 10     7     8a      5  9  5  7
       2  8     4   _11b_     4  7  2  8
       2  8     4     6b      1  9  4  8
       7 12     7   _10a_     - 10  6 10
       3 10     5     8a      5  8  6 10
       2  8     3   _11b_     3  7  3 10
       -  7     5     9b      4  8  6 12
  Am.  4  9    _9_  _10a_     4  7  4  5
       4  8    _9_   _7a_     5  7  4  6
       1  8     5   _10b_     4  6  3  6
       - 10   _10_    7b_     3  5  2  7
      15 15   _10_   13a_     9 11  - 11
       5 12     7     9a      4 10  4  9
       5  8    _8_   _9b_     4  7  -  6
       7  8     5    _9b_     2  4  -  3
  G.   2  6    _6_   _8a_     1  7  2  3
       - 10    _7_  _12a_     1  9  4  8
       4  9    _6_   _9b_     8  8  2  7
       -  -     -     -b      -  -  -  -
       4  9    _5_ _11_a      -  7  4  6
       -  8     6     7a      2  7  4  5
       -  9    _7_  _6_b      -  7  3  6
       -  7     3     5       -  5  -  3
  D.   -  -     -     -       -  -  -  -
       7 11   _11_  _9_a      7 11  6 10
      11 15    11    11a      8 11  9 14
       6 10   _10_   8b       7  8  7 11
      12 13    10    10a      7  1? 8 11
       6 10     9     8a      5  8  5  9
       9 12    12    13b      8 10  7  9
       7 11   _10_    7b      4  8  4  8

   The values surrounded by '_'s (Transcriber's Note: Original
   italics) show the increase in intensity. Rhymes are indicated
   by 'a' and 'b.'


IV. SUGGESTIONS FOR A MOTOR THEORY OF RHYTHM.


If the basis of rhythm is to be found in muscular sensations, rather
than in the supposed activity of some special 'mental' function, the
nature of the movement cycle involved is of the greatest interest.

In every case where a rhythm comes to peripheral expression, there are
two opposing sets of muscles involved. If a rhythmic movement be
attempted with but a single set of muscles at work, it is very
unsatisfactory and soon ends in the tonic contraction of the muscle
set. One may assume that in all cases of rhythm perception there is a
cycle of movement sensations involved, and that the simplest possible
case of a peripheral rhythmic movement is the type of any rhythm. In
tapping a rhythm with the finger, the flexors which bring the finger
down become the positive muscle set, and the opposing extensor muscles
which raise the finger for the next blow become the negative muscle
set.

In Fig. 9 the upper curve represents the actual movement of the finger
tip, and the heavy lines _a_, _a'_, _a''_ represent the
pressure-tension-sound sensation which we call the 'beat,' and which
is the limiting sensation of the rhythm, and the regulating factor in
the movement cycle of the rhythm. The movement is divided into two
phases; _B_, the phase of relaxation, during which the finger is
raised, and _A_, the phase of contraction, during which the finger
delivers the blow which produces the beat.

The curves below represent the changes in the two opposing sets of
muscles whose interaction brings about the movement cycle. The
contraction of the flexors, the positive muscle set, is represented by
the curve above the base line. It is obvious that during the
contraction phase, the contraction in the positive muscle set is at
its height; it continues at a maximum during the limiting sensation
and then dies away during the relaxation phase. The sensations from
this positive muscle set have the principal place in consciousness
during the rhythm experience. The curve below the base line represents
the contraction of the extensors, the negative muscle set. The
contraction of the negative muscles reaches its climax very soon after
the maximum contraction of the positive muscles, in the contraction
phase. The sharp tension between the two opposing sets of muscles at
the limiting sensation may be made very apparent if the finger beats
the rhythm entirely in the air; in that case the limiting sensation
consists entirely of the feeling of a sudden increase of tension
between the positive and negative muscle sets. During the relaxation
phase the contraction of the negative muscles continues, but the
tension between the two sets grows less and less, for the positive
muscles are rapidly relaxing. At the highest point in the movement
either muscle set is exerting but very little strain; the condition is
represented in the figure by the approach of either curve to the
base-line; the amount of tension between the two sets is figured by
the distance of the two curves from each other.

[Illustration: FIG. 9.]

Assuming such a movement cycle, in which the tension between the two
opposing sets never comes to zero until the close of the series, it is
not difficult to arrange many of the facts of rhythmic perception
under the motor theory.

1. The feeling of rhythm is more definite as we proceed in a verse, or
a series of simple sound sensations. At first the cycle is not
perfectly adjusted and complete automatism established.

2. If an observer is listening to a series, and an unusually long
pause is introduced between two beats, there is always a feeling of
suspense or tension during the 'lag.' As long as the tensions are
maintained there is a rhythmic continuity; the feeling of tension is
the strain of opposition between the opposing muscle sets.

3. The continuity of the rhythmic series, whereby all the beats of a
period seem to belong to a single whole, is due to the continuity of
the muscle sensations involved and the continuous feeling of slight
tension between the positive and negative muscle sets; nowhere within
the period does the feeling of strain die out.

4. But at the close of the period we have a pause which is
demonstrably not a function of any of the intervals of the period.
During this pause the tension between the two sets 'dies out,' and we
have a feeling of finality. This gradual dying out of the tension is
clearly seen in the constant appearance of the cone-shaped final
syllable at the end of each nonsense verse.

5. The period composed of a number of unit groups (the verse, in
nonsense syllables) has a general form which suggests strongly that it
has the unity of a single coördinated movement. There is no more
reason for assuming a transcendental mental activity in the case of a
rhythmic period than in the case of a single act which appears in
consciousness as a unity. Undoubtedly the breathing is correlated with
the rhythmic movements and may be a factor in determining the verse
period. Meumann's principal accent, about which a number of
subordinate accents are grouped, is characteristic not only of poetry
but of the simplest rhythms. At some point in the period there is a
definite climax, a chief accent; the movement 'rises' to that point
and then falls off. This is strikingly seen in nonsense verses spoken
with a heavy accent within the verse. The accent does not stand out
from a dead level, but the verse culminates at that point.

Unfortunately very little is known of the mechanism of so simple a
coördinated muscular activity as that necessary for a simple rhythm.
Sherrington[17] and Hering[18]have pointed out the primary character
of the grouping of the muscles in opposing sets and the reciprocal
nature of almost all muscular activity, but in a review of the work of
coördinated movements Hering denies any simultaneous stimulation of
the two sets and considers the question of the innervation mechanism
of opposing muscle-sets entirely unsettled.

   [17] Sherrington, C.S.: _Proceedings Royal Soc._, 1897, p. 415.

   [18] Hering, H.E.: _Archiv f. d. ges. Physiol._ (Pflüger's),
   1897, Bd. 68, S. 222; _ibid._, 1898, Bd. 70, S. 559.

That the connection between the positive and negative set of muscles
in a rhythmic movement is very close, and that the reaction is of the
circular type, is evident from the automatic character of all rhythmic
movements, and it is evident that the limiting sensation is the
primary cue in the reaction. Anything further is mere hypothesis.
Robert Müller's[19] thorough criticism of the Mosso ergograph throws
great doubt on the present methods of investigation and invalidates
conclusions from the various curves of voluntary movements which have
been obtained.

   [19] Müller, R.: _Phil. Stud._, 1901, Bd. 17, S. 1.

The curve of contraction and relaxation of a simple muscle is well
known and is not affected by Müller's criticism. Its chief
characteristic, with or without opposing tension, is the inequality
of the intervals of the contraction and relaxation phases. As one
might expect, since a single set of muscles dominates in a rhythmic
movement, the typical rhythmic curve has the general character of the
curve of the simple muscle. The average values of the phases of curves
of simple rhythmic movement obtained by A. Cleghorn[20] from a large
number of observations with at least three subjects, are as follows:
phase of contraction, .44 second; phase of relaxation, .54 second. It
is very significant for a motor theory of rhythm that this general
form of the curve of rhythmic movement may easily be altered in all
sorts of fashions by unusual stimuli to the two muscle sets.

   [20] Cleghorn, A.: _Am. Journal of Physiol._, 1898, I., p. 336.

While it is well recognized that a rhythm does not consist necessarily
of sound sensations, the 'rhythmization' of a series of sound
sensations in the ordinary perceived rhythms is a matter of great
interest. Ewald found strong reasons for believing that the ear is
peculiarly connected with the motor apparatus. The experiments of
Hofbauer[21] and Cleghorn[22]show that any strong stimulus to either
eye or ear modifies decidedly the reactions of coördinated muscles.
How shall we assume that the automatic movement cycle necessary to
rhythmic perception is set up when one listens to a series of sounds?

   [21] Hofbauer: _Archiv f. d. ges. Physiol._ (Pflüger's), 1897,
   Bd. 68, S. 553.

   [22] Cleghorn, A.: _op. cit._

It must be assumed that any chance sound sets up a contraction in a
set of muscles, however large or small. If but a single sound occurs,
the phase of contraction in that muscle set is followed by a longer
phase of relaxation, and the musculature is passive as before; it may
be that the stretching of the antagonistic set of muscles weakly
stimulates them, and they then contract during the relaxation phase
and assist in restoring the original condition.

But if a second sound occurs toward the end of the relaxation phase,
before the tension is quite exhausted, the movement will be repeated;
the negative set of muscles will be more definitely stimulated, for
the activity will not have been exhausted when the second sound
occurs. If the sound continues to recur at regular intervals, the
movement cycle thus established will rapidly become coördinated. The
positive set in its vigorous contraction furnishes a limiting
sensation which becomes a cue for its own relaxation and for the
reciprocal contraction of the negative muscle set. The contraction of
the negative muscle set and the resulting changes in tension may
become in turn a cue for the positive set. The reaction is now of the
circular type and the process has become self-regulative, though
constantly reinforced by the recurring sound (which has become a part
of the limiting sensation of the rhythmic movement cycle).

But it is very probable that the second sound may not be timed so as
to come at the close of the relaxation phase in the set of muscles
roused; moreover, in almost all rhythms there are secondary sounds
occurring between the main beats. What happens when a sound occurs out
of place, early in the phase of relaxation, or just before or just
after the climax in the contraction phase? Does it make it impossible
to establish the coördination, or destroy it if already established?

Hofbauer demonstrated that a stimulus which appears in close proximity
to the limiting sensation, _either before or after_, always increases
the force of the reaction, so that such a slight displacement could
not affect the rhythm, which would quickly readjust itself. The
possibility of a stimulus occurring in the relaxation phase is of much
more importance for a motor theory of the initiation of a rhythmic
movement. Cleghorn made the stimulus occur at the beginning of the
relaxation phase. Instead of prolonging or reinstating the contraction
phase, he found that the stimulus _intensified the relaxation process
and shortened its period_. "The stimulated relaxation is not only
quicker than the normal, but also more complete; the end of the normal
relaxation is slow; ... relaxation under the influence of the
stimulus, on the contrary, shows nothing of this, but is a sudden
sharp drop directly to the base line and sometimes below it." A
comparison of the normal phases with the same phases, when the
stimulus occurs within the relaxation phase, follows:


  Normal: Contraction-phase, .44 sec.; relaxation-phase, .54 sec.;
             total, .98 sec.
  With stim.: Contraction-phase, .47 sec.: relaxation-phase, .30 sec.;
             total, .77 sec.


It will be noticed that the total time of the movement cycle is
reduced. One may then assume that a sound which occurs too early to
become a factor in the limiting sensation, functions as a stimulus to
the relaxation process and shortens the interval between the limiting
sensations. Thus the movement cycle would be modified, but not
destroyed. It is impossible to say just how the relaxation process is
affected, and Cleghorn's own conclusions are open to criticism in the
light of Müller's comments on the method. The simplest assumption
would be that the stimulus acted on the negative set of muscles.

E.W. Scripture[23] objects to such a 'tonus theory,' because some
subjects regularly react _before_ the signal. But in no case in the
published records to which he refers is the error more than.05 sec.
either before or after the signal. The investigation of Hofbauer shows
conclusively that in such cases the effect of the external stimulus
simply fuses with the limiting sensation. Scripture overlooks the
automatic character of the rhythmic movement.

   [23] Scripture, E.W.: 'The New Psychology,' London, 1897, p. 182.

There is a striking difference between rhythmic movement from unit
group to unit group within a period, and movement from period to
period (_i.e._, from verse to verse of nonsense syllables). Each foot
is simply the repetition of the movement cycle; all the tensions are
maintained, and each foot is an integral part of a larger act. At the
close of the period (verse) the active tensions die out, either
because of the introduction of some unusual stimulus which causes the
positive muscle set to strike a heavy blow, and abruptly upset the
balanced tensions, or because a pause of indefinite length ensues in
which the tensions die out. This is the process which we call
'finality.'

In the stanza there is evidently a different type of unity from that
in the single verse. When we hear the first verse of the stanza, we do
not know what the verse whole is, until the finality factor or the
verse pause is reached, at its close. Then the verse has a certain
definite cumulative effect, a synthetic effect which results from the
echoes of the various movements and the total effect on the organism.
One may call it the tetrameter feeling. The verse pause may vary
within large limits, but after a few verses there is a definite
scheme, or 'Gestaltqualität,' which represents the verse unity. It is
some sort of a memory image, which functions as a cue to the motor
process. This motor image, set of strains, or whatever it be, is more
than a mere standard by which we judge the present verse. The memory
image fuses in some way with the living motor process. _The preceding
verse affects the character of the following verse._ An irregularity,
easily noted in the first verse, is obscure in the second, and not
detected in the third verse, when the verses are identical.

The experiments of Hofbauer and Cleghorn, and many facts about the
unit groups themselves, make it evident that the function of stimuli,
during the movement cycle, varies with the position of the stimulus in
that cycle. This offers a possible explanation of the striking
peculiarities of the unit groups. The iamb [\/ _'] and the trochee [_'
\/] should be quite alike for a general synthesizing process; but not
only is the experiential character of the two quite unlike, but the
ratio between their intervals is entirely different.

A number of measurements by different observers show that in the
iambic foot the unaccented syllable is proportionately much shorter
than the unaccented syllable in the trochaic foot. It is very easy to
beat a simple up-and-down accompaniment to a series of simple feet of
nonsense syllables; in the accompaniment the bottom of the down
stroke, the limiting sensation of the movement cycle, coincides with
the accented syllable of the foot. It is not an unwarranted assumption
that such a fundamental accompaniment represents the fundamental
movement cycle of that rhythm.

During the present investigation several observers were asked to
determine at just what point in the fundamental movement the
unaccented syllable occurred, when the subject gave a series of
nonsense syllables. In the fundamental accompaniment the excursion of
the hand and arm was at least.4 meter. Four subjects were thus tested,
and the results were uniform in the case of all the simple types of
unit groups.

In the case of the iamb the unaccented syllable occurs at the top of
the movement, at the very beginning of the contraction phase (A, in
Fig. 5).

In the case of the trochee the unaccented syllable occurs in the first
third of the relaxation phase (B).

It is interesting to note that the unaccented element of the trochee
comes at the earlier part of the relaxation phase, where it must
intensify the relaxation process, and tend to shorten the total length
of the cycle. This may be the reason for its peculiar buoyant,
vigorous and non-final character. On the other hand the unaccented
element of the iamb occurs at a point where it may initiate and
intensify the contraction, which gives the limiting sensation; it is,
therefore, more closely bound to the limiting sensation, and has the
character of intensifying the beat. There is a similar contrast in the
cases of the dactyl and anapæst. The accented syllable of the dactyl
is longest, and the second unaccented syllable, the last in the group,
is shortest. The accented syllable of the anapæst is much longer in
proportion than that of the dactyl, and the unaccented syllables are
very short, and hence, very close to the accented syllable, as
compared with the dactyl.

In the case of the dactyl the first unaccented syllable in the
movement cycle occurs at the beginning of the relaxation phase (B), in
the same zone as the unaccented of the trochee. The second unaccented
syllable of the dactyl appears at the beginning of the next
contraction phase (A), in the zone of the unaccented syllable of the
iamb. The group seems a sort of combination of the iamb and trochee,
and has an element in every possible zone of the movement cycle. Like
the trochee the dactyl is a non-final foot.

The unaccented syllables of the anapæst both occur at the beginning of
the contraction phase (A). They are both within the zone of the
unaccented syllable of the iamb. The group seems an iamb with a
duplicated unaccented syllable. It is possible to form a unit group in
nonsense syllables where the unaccented syllable of the iamb shall be
represented not by two syllables, as in the anapæst, but by even
three.

The anapæst and dactyl, if they correspond to this construction,
should show a decided difference as to the possibility of prolonging
the foot pause. The prolongation of the foot pause would make the
dactyl but a modified trochee.

It is significant that in poetry no other types of unit groups are
often recognized. The amphibrach, laid out on this scheme, would
coincide with the dactyl, as there are but three possible zones for
foot elements: the zone of the limiting sensation (always occupied by
the accented syllable), the zone of the contraction phase (occupied by
the unaccented syllables of the iamb and anapæst), and the zone of the
relaxation phase (occupied by the unaccented syllable of the trochee
and the middle syllable of the dactyl).

The simple sound series is fairly regular, because of its cyclic and
automatic character. It is not a matter of time estimation, and the
'Taktgleichheit' is not observed with accuracy. The primary requisite
for the unit groups is that they shall be _alike_, not that they shall
be _equal_. The normal cycle with a heavy accent is longer than the
normal cycle with a lighter accent, for the simple reason that it
takes muscles longer to relax from the tenser condition. Time is not
mysteriously 'lost'; the objective difference is not noticed, simply
because there are no striking differences in the cycles to lead one to
a time judgment. Ebhardt's notion that the motor reaction interferes
with the time judgment, and that a small amount of time is needed in
the rhythmic series in which to make time judgments, is a mere myth.

An unusual irregularity, like a 'lag,' is noted because of the sense
of strain and because other events supervene in the interval. But such
lags may be large without destroying the rhythm; indeed cæsural and
verse pauses are essential to a rhythm, and in no sense
rhythm-destroying. An unbroken series of unit groups is an abstraction
to which most forms of apparatus have helped us. Between the extreme
views of Bolton[24] and Sidney Lanier,[25]who make regularity an
essential of the rhythm of verse, and Meumann, on the other hand, who
makes the meaning predominate over the rhythm, the choice would fall
with Meumann, if one must choose. Bolton comes to the matter after an
investigation in which regularity was a characteristic of all the
series. Lanier's constructions are in musical terms, and for that very
reason open to question. He points out many subtle and interesting
relationships, but that verse can be formulated in terms of music is a
theory which stands or falls by experimental tests.

   [24] Bolton, T.L.: _loc. cit._

   [25] Lanier, S.: 'The Science of English Verse.'


TABLE XII.

  I    saw    a    ship    a    sailing
          50    16  20  13 9 18  32 23-  132
      A    sailing    on    the    sea
      10 16  45       22     8  15  49  -68
  And    it    was    full    of    pretty    things
   8   6 20 6   6  27  37  12  8  7   20   12   41    -34
      For    baby    and    for    me
       14  9  27  37  18 20  14 8  46   --

  Totals of the feet: --/66/60/187
                      26/45/45/117
                      14/59/49/47/75
                      23/64/60/46--

  Who    killed    Cock    Robin
   19      34       23     24 17-77
    I    said    the    sparrow
   45 21  19      3     47   29 --
  With    my    bow    and    arrow
   22     36 25  49 11  38 12 23 33-42
    I    killed    Cock    Robin
    33 12  33   21  22  5  21 16-95

    (The first stanza was measured in the Harvard Laboratory. The
    last is modified from Scripture's measurements of the
    gramophone record (1899). As the scansion of the last is in
    doubt with Scripture, no totals of feet are given.)


In the cases given in the above table there is an irregularity quite
impossible to music.

In the movement cycle of the simple sounds there is a perfect
uniformity of the movements of the positive and negative sets of
muscles from unit group to unit group. But in verse, the movements of
the motor apparatus are very complicated. Certain combinations require
more time for execution; but if this variation in the details of the
movement does not break the series of motor cues, or so delay the
movements as to produce a feeling of strain, the unit groups are felt
to be alike. We have no means of judging their temporal _equality_,
even if we cared to judge of it. It is a mistake, however, to say that
time relations ('quantity') play no part in modern verse, for the
phases of the movement cycle have certain duration relations which can
be varied only within limits.

Extreme caution is necessary in drawing conclusions as to the nature
of verse from work with scanned nonsense syllables or with mechanical
clicks. It is safe to say that verse is rhythmic, and, if rhythm
depends on a certain regularity of movements, that verse will show
such movements. It will of course use the widest variation possible in
the matter of accents, lags, dynamic forms, and lengths of sonant and
element depending on emphasis. The character of the verse as it
appears on the page may not be the character of the verse as it is
actually read. The verses may be arbitrarily united or divided. But in
any simple, rhythmic series, like verse, it seems inevitable that
there shall be a pause at the end of the real verse, unless some such
device as rhyme is used for the larger phrasing.

There is a variety of repetitions in poetry. There may be a vague,
haunting recurrence of a word or phrase, without a definite or
symmetrical place in the structure.

Repetition at once attracts attention and tends to become a structural
element because of its vividness in the total effect. There are two
ways in which it may enter into the rhythmic structure. It may become
a well-defined refrain, usually of more than one word, repeated at
intervals and giving a sense of recognition and possibly of
completeness, or it may be so correlated that the verses are bound
together and occur in groups or pairs. Rhyme is a highly specialized
form of such recurrence.

The introduction of rhyme into verse must affect the verse in two
directions.

It makes one element in the time values, viz., the verse pause, much
more flexible and favors 'run on' form of verses; it is an important
factor in building larger unities; it correlates verses, and
contributes definite 'Gestaltqualitäten' which make possible the
recognition of structure and the control of the larger movements which
determine this structure. Thus it gives plasticity and variety to the
verse.

On the other hand, it limits the verse form in several directions. The
general dynamic relations and the individual accents must conform to
the types possible with rhyme. The expressional changes of pitch,
which constitute the 'melody,' or the 'inflections' of the sentences,
play an important part. The dynamic and melodic phases of spoken verse
which have important relations to the rhyme are not determined by the
mere words. The verses may scan faultlessly, the lines may read
smoothly and be without harsh and difficult combinations, and yet the
total rhythmic effect may be indifferent or unpleasant. When a critic
dilates on his infallible detection of an indefinable somewhat,
independent of material aspects of the verse and traceable to a mystic
charm of 'thought,' it may very well be that the unanalyzed thing lies
in just such dynamic and melodic conditions of rhythm and rhyme.

The most primitive characteristic of music is the _ensemble_. Savage
music is often little else than time-keeping. When the social
consciousness would express itself in speech or movement in unison,
some sort of automatic regulation is necessary. This is the beginning
of music. The free reading of verse easily passes over into singing or
chanting. When this happens, the thing most noticeable in the new form
is its regulated, automatic and somewhat rigid character. It is
stereotyped throughout. Not only are the intervals and accents fixed,
but the pitch and quality changes are now definite, sustained and
recurrent. The whole sum of the motor processes of utterance has
become coördinated and regulated. Along with this precision of all the
movements comes a tendency to beat a new rhythm. This accompanying
rhythm is simpler and broader in character; it is a kind of long swell
on which the speech movements ripple. This second rhythm may express
itself in a new movement of hand, head, foot or body; when it has
become more conscious, as in patting time to a dance or chant, it
develops complicated forms, and a third rhythm may appear beside it,
to mark the main stresses of the two processes. The negro patting time
for a dance beats the third fundamental rhythm with his foot, while
his hands pat an elaborate second rhythm to the primary rhythm of the
dancers.

The essential character of musical rhythm, as contrasted with the
rhythm of both simple sounds and of verse, is just this coördination
of a number of rhythms which move side by side. This is the reason for
the immense complexity and variety of musical rhythms. The processes
check each other and furnish a basis for a precision and elaborateness
of rhythmical movement in the individual parts which is quite
impossible in a simple rhythm.

Even when the concomitant rhythms are not expressed, as in an
unaccompanied solo, an accompaniment of some sort is present in the
motor apparatus, and contributes its effect to the consciousness. This
regulation of the movement by the coincidence of several rhythms is
the cause of the striking regularity of the temporal relations. At
some points in the musical series the several movement cycles may
appear in the same phase, and at these points the same irregularities
as in verse are possible, as in the case of pauses at the ends of
periods and the irregularities of phrasing. It is evident in cases of
expressional variations of tempo that a single broad rhythm is
dominating and serving as a cue for the other more elaborate rhythmic
processes, instead of being regulated by them.

       *       *       *       *       *



STUDIES IN SYMMETRY.[1]

BY ETHEL D. PUFFER.

   [1] SOURCES OF ILLUSTRATIONS.

   Fig. 1 was copied from Reiss u. Stübel, 'Todtenfeld v. Ancou,'
   Berlin, 1880-1887.

   Figs. 2, 3, 4, 5, 6, 7, 8 and 11 were copied from the
   publications of the American Bureau of Ethnology by the kind
   permission of the Direction.

   Fig. 9. was copied from A.C. Haddon, 'The Decorative Art of
   British New Guinea,' Cunningham Memoir, N., Royal Irish
   Academy, 1894.

   Fig. 10 was copied from Franz Boas, 'The Decorative Art of the
   Indians of the North Pacific Coast,' Bulletin of the Am. Mus.
   of Nat. Hist., Vol. IX.


I. THE PROBLEMS OF SYMMETRY.


The problem of æsthetic satisfaction in symmetrical forms is easily
linked with the well-known theory of 'sympathetic reproduction.' If
there exists an instinctive tendency to imitate visual forms by motor
impulses, the impulses suggested by the symmetrical form would seem to
be especially in harmony with the system of energies in our bilateral
organism, and this harmony may be the basis of our pleasure. But we
should then expect that all space arrangements which deviate from
complete symmetry, and thus suggest motor impulses which do not
correspond to the natural bilateral type would fail to give æsthetic
pleasure. Such, however, is not the case. Non-symmetrical arrangements
of space are often extremely pleasing.

This contradiction disappears if we are able to show that the
apparently non-symmetrical arrangement contains a hidden symmetry, and
that all the elements of that arrangement contribute to bring about
just that bilateral type of motor impulses which is characteristic of
geometrical symmetry. The question whether or not this is the fact
makes the leading problem of this paper, and the answer to it must
throw light on the value of the theory itself.

An exhaustive treatment of our question would thus divide itself into
two parts; the first dealing with real (or geometrical) symmetry, the
second with apparent asymmetry; the first seeking to show that there
is a real æsthetic pleasure in geometrical symmetry, and that this
pleasure is indeed based on the harmony of the motor impulses
suggested by symmetry, with the natural motor impulses of the human
organism; the second seeking to show in what manner æsthetically
pleasing but asymmetrical arrangements conform to the same principles.
Within these two groups of problems two general types of investigation
are seen to be required; experiment, and the analysis of æsthetic
objects.

The main question, as stated above, is of course whether the theory
can explain our pleasure in arrangements which are completely or
partly symmetrical. It is, however, an indispensible preliminary to
this question, to decide whether the pleasure in symmetrical
arrangements of space is indeed immediate and original. If it were
shown to be a satisfaction of expectation, bred partly from the
observation of symmetrical forms in nature, partly from the greater
convenience of symmetrical objects in daily use, the whole question of
a psychophysical explanation would have no point. If no original
æsthetic pleasure is felt, the problem would be transformed to a
demand for the explanation of the various ways in which practical
satisfaction is given by symmetrical objects and arrangements. The
logical order, then, for our investigation would be: First, the
appearance of symmetry in the productions of primitive life, as a
(debatable) æsthetic phenomenon emerging from pre-æsthetic conditions;
secondly, the experimental study of real symmetry; thirdly, the
analysis of geometrical symmetry in art, especially in painting and
architecture, by means of which the results of the preceding studies
could be checked and confirmed. Having once established a theory of
the æsthetic significance of real symmetry, we should next have to
examine asymmetrical, beautiful objects with reference to the relation
of their parts to a middle line; to isolate the elements which suggest
motor impulses; to find out how far it is possible to establish a
system of substitution of these psychological factors and how far such
substitution takes place in works of art--_i.e._, to what extent a
substitutional symmetry or balance is found in pleasing arrangements.
These investigations, again, would fall into the two groups of
experiment and analysis. The products of civilized art are too
complicated to admit of the complete analysis and isolation of
elements necessary to establish such a system of substitution of
psychological factors as we seek. From suggestions, however, obtained
from pleasing asymmetrical arrangements, first, isolated elements may
be treated experimentally, and secondly, the results checked and
confirmed by works of art.

With regard to the study of objects without a natural or suggested
middle line, as for instance sculpture, many types of architecture,
landscapes, gardens, room-arrangements, etc., we may fitly consider it
as a corollary to the study of asymmetrical objects with artificial
limits which do suggest a middle. If we find, by the study of them,
that a system of substitution of psychological factors does obtain,
the whole field can be covered by the theory already propounded, and
its application extended to the minutest details. The hypothesis,
having been so far confirmed, may be then easily applied to the field
of asymmetrical objects without a natural middle line.

The set of problems here suggested to the student of symmetry will not
be fully followed out in this paper. The experimental treatment of
geometrical symmetry, the analysis of the completely symmetrical
products of civilized art, and the analysis of all forms of asymmetry
except asymmetry in pictures will be omitted. If, however, the fact of
an original æsthetic feeling for symmetry is established by the study
of primitive art, and the theory of the balance of motor impulses
through the substitution of factors is established by the experimental
treatment of isolated elements, and further confirmed by the analysis
of pictures, the general argument may be taken as sufficiently
supported. This paper, then, will contain three sections: an
introductory one on symmetry in primitive art, and two main sections,
one on experiments in substitutional symmetry, and one on
substitutional symmetry or balance in pictures.


II. SYMMETRY IN PRIMITIVE ART.


The question which this section will attempt to answer is this: Is
there in primitive art an original and immediate æsthetic feeling for
symmetry? This question depends on two others which must precede it:
To what extent does symmetry actually appear in primitive art? and,
How far must its presence be accounted for by other than æsthetic
demands?

For the purpose of this inquiry the word _primitive_ may be taken
broadly as applying to the products of savage and half-savage peoples
of to-day, as well as to those of prehistoric races. The expression
_primitive art_, also, requires a word of explanation. The primitive
man seldom makes purely ornamental objects, but, on the other hand,
most of his articles of daily use have an ornamental character. We
have to consider primitive art, therefore, as represented in the form
and ornamentation of all these objects, constituting practically an
household inventory, with the addition of certain drawings and
paintings which do not appear to serve a definite practical end. These
last, however, constitute only a small proportion of the material.

The method of the following outline treatment will be to deduct from
the object under consideration those symmetrical elements which seem
to be directly traceable to non-æsthetic influences; such elements as
are not thus to be accounted for must be taken as evidence of a direct
pleasure in, and desire for symmetry on the part of primitive man.
These possible non-æsthetic influences may be provisionally suggested
to be the technical conditions of construction, the greater
convenience and hence desirability of symmetrical objects for
practical use, and the symmetrical character of natural forms which
were imitated.

The first great group of objects is given in primitive architecture.
Here is found almost complete unanimity of design, the conical,
hemispherical or beehive form being well-nigh universal. The hut of
the Hottentots, a cattle-herding, half-nomadic people, is a good type
of this. A circle of flexible staves is stuck into the ground, bent
together and fastened at the top, and covered with skins. But this is
the form of shelter constructed with the greatest ease, suitable to
the demands of elastic materials, boughs, twigs, reeds, etc., and
giving the greatest amount of space with the least material. There
are, indeed, a few examples of the rectangular form of dwelling among
various primitive races, but these seem to be more or less open to
explanation by the theory advanced by Mr. V. Mendeleff, of the U.S.
Bureau of Ethnology. "In his opinion the rectangular form of
architecture which succeeds the type under discussion, must have
resulted from the circular form by the bringing together within a
limited area of many houses.... This partition would naturally be
built straight as a two-fold measure of economy."[2] This opinion is
confirmed by Mr. Cushing's observations among the Zuñi villages, where
the pueblos have circular forms on the outskirts. Thus the shape of
the typical primitive dwelling is seen to be fully accounted for as
the product of practical considerations alone. It may therefore be
dismissed as offering no especial points of interest for this inquiry.

   [2] Cushing, F.H.: 'Pueblo Pottery and Zuñi Culture-growth,'
   Rep. of Bur. of Ethnol., 1882-3, p. 473.

Next in the order of primitive development are the arts of binding and
weaving. The stone axe or arrow-head, for example, was bound to a
wooden staff, and had to be lashed with perfect evenness,[3] and when
in time the material and method of fastening changed, the geometrical
forms of this careful binding continued to be engraved at the juncture
of blade and handle of various implements. It should be noted,
however, that these binding-patterns, in spite of their superfluous
character, remained symmetrical.

   [3] Haddon, A.C.: 'Evolution in Art,' London, 1895, pp. 84 ff.

On the great topic of symmetry in weaving, monographs could be
written. Here it is sufficient to recall[4] that the absolutely
necessary technique of weaving in all its various forms of
interlacing, plaiting, netting, embroidering, etc., implies order,
uniformity, and symmetry. The chance introduction of a thread or withe
of a different color, brings out at once an ordered pattern in the
result; the crowding together or pressing apart of elements, a
different alternation of the woof, a change in the order of
intersection, all introduce changes by the natural necessities of
construction which have the effect of purpose. So far, then, as the
simple weaving is concerned, the æsthetic demand for symmetry may be
discounted. While it may be operative, the forms can be explained by
the necessities of construction, and we have no right to assume an
æsthetic motive.

   [4] Holmes, W.H.: 'Textile Art in its Relation to the
   Development of Form and Ornament,' Rep. of Bur. of Ethnol.,
   1884-5, p. 195.

The treatment of human and animal forms in weaving is, however,
indicative of a direct pleasure in symmetry. The human form appears
almost exclusively (much schematized) _en face_. When in profile, as
for instance in Mexican and South American work, it is doubled--that
is, two figures are seen face to face. Animal figures, on the other
hand, are much used as row-ornaments in profile.[5] It would seem that
only the linear conception of the row or band with its suggestions of
movement in one direction, justified the use of profile (_e.g._, in
Peruvian woven stuffs), since it is almost always seen under those
conditions, indicating that a limited rectangular space is felt as
satisfactorily filled only by a symmetrical figure.[6] Moreover, and
still more confirmatory of this theory, even these row-pattern
profiles are immensely distorted toward symmetry, and every
'degradation' of form, to use Professor Haddon's term, is in the
direction of symmetry. (See Fig. 1.)

   [5] Reiss, W., und Stubel, A.: 'Todtenfeld von Ancon,' Berlin,
   1880-7, Bd. II.

   [6] Hein, W.: 'Die Verwendung der Menschen-Gestalt in
   Flechtwerken,' Mitteil. d. Anthrop. Gesellsch. in Wien, Bd.
   XXI.

[Illustration: Fig. 1.]

The shape of primitive pottery is conditioned by the following
influences: The shapes of utensils preceding clay, such as skins,
gourds, shells, etc., which have been imitated, the forms of basket
models, and the conditions of construction (formation by the hands).
For all these reasons, most of these shapes are circular. The only (in
the strict sense) symmetrical shapes found are of unmistakably animal
origin, and it is interesting to notice the gradual return of these to
the eurhythmic form; puma, bird, frog, etc., gradually changing into
head, tail and leg excrescences, and then handles and nodes
(rectangular panels), upon a round bowl or jar L, as shown in the
figures. In fact, in ancient American pottery,[7] at least, all the
symmetrical ornamentations can be traced to the opposition of head and
tail, and the sides between them, of these animal forms. But beyond
this there is no degradation of the broad outline of the design. The
head and tail, and sides, become respectively handles and nodes--but
the symmetry becomes only more and more emphasized. And as in the case
of textiles,