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+Project Gutenberg's Harvard Psychological Studies, Volume 1, by Various
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Harvard Psychological Studies, Volume 1
+       Containing Sixteen Experimental Investigations from the
+       Harvard Psychological Laboratory.
+
+Author: Various
+
+Editor: Hugo Münsterberg
+
+Release Date: July 12, 2005 [EBook #16266]
+
+Language: English
+
+Character set encoding: ISO-8859-1
+
+*** START OF THIS PROJECT GUTENBERG EBOOK PSYCHOLOGICAL STUDIES, VOL 1 ***
+
+
+
+
+Produced by Gallica (http://gallica.bnf.fr/), Clare Boothby,
+Victoria Woosley and the Online Distributed Proofreading
+Team at https://www.pgdp.net.
+
+
+
+
+
+
+
+
+
+                          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 rōle 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 rōle 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 ęsthetic 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 ęsthetic 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 rōle 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 Anęsthesia: 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 ĘSTHETIC 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 Ęsthetics 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 ANĘSTHESIA.
+
+BY EDWIN B. HOLT.
+
+
+I. THE PROBLEM OF ANĘSTHESIA DURING EYE-MOVEMENT.
+
+
+A first suggestion of the possible presence of anęsthesia 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
+anęsthesia 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 anęsthesia, perhaps in the latter case there is
+anęsthesia.
+
+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 anęsthesia 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
+anęsthesia. 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 anęsthesia. 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 anęsthesia.
+
+If by 'anęsthesia' 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 anęsthesia 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 anęsthesia during movement, although the
+functioning of the retina should remain unaltered. Such a central
+anęsthesia 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 anęsthesia 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 anęsthesia 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 anęsthesia 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 anęsthesia could be demonstrated,
+both the feeling of succession and the discontinuity of the
+intensities would be explained (since during the anęsthesia 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 anęsthesia 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 anęsthesia 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 anęsthesia 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 anęsthesia, 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 anęsthesia 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 anęsthesia, 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 anęsthesia 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
+anęsthesia 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
+anęsthesia, 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 anęsthesia
+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 ANĘSTHESIA.
+
+
+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 anęsthesia 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 anęsthesia 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 anęsthesia, 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
+anęsthesia 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 anęsthesia 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 anęsthesia 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 anęsthesia, 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
+anęsthesia_. 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 anęsthesia.
+
+
+V. SUMMARY AND COROLLARIES OF THE EXPERIMENTS, AND A PARTIAL,
+PHYSIOLOGICAL INTERPRETATION OF THE CENTRAL ANĘSTHESIA.
+
+
+We have now to sum up the facts given by the experiments. The fact of
+central anęsthesia during voluntary movement is supported by two
+experimental proofs, aside from a number of random observations which
+seem to require this anęsthesia 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 anęsthesia 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 anęsthesia 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 anęsthesia 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 anęsthesia 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 anęsthesia. 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
+anęsthesia 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 anęsthesia.
+
+We have seen, too, that in reflex eye-or head-movements no anęsthesia
+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 anęsthesia 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 anęsthesia, since no discontinuity of
+vision during voluntary movement is noticeable, although a relatively
+long moment of anęsthesia actually intervenes.
+
+But decidedly the most interesting detail about the anęsthesia 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
+anęsthesia, although beginning later than the movement, is present
+when the eye reaches _O_, while it is between _O_ and _N_, that is,
+during the anęsthetic moment, that the eye is reflexly caught and held
+by the light. This proves again that the anęsthesia 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 anęsthesia? 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 anęsthetic. 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 anęsthesia 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
+anęsthesia, 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 anęsthesia, 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 anęsthesia.
+
+The fact that the anęsthesia commences appreciably later than the
+movement so far favors this interpretation. For if the anęsthesia 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 anęsthesia, 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 anęsthesia 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
+anęsthesia.
+
+       *       *       *       *       *
+
+
+
+
+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 ęsthesiometers, A and B, were arranged in a framework, so that
+uniform stimulations could be given on both arms. The ęsthesiometers
+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 ęsthesiometer could be conveniently adjusted
+by the pins F and H. The shape of the cams was such that the descent
+of the ęsthesiometer 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
+ęsthesiometer 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 ęsthesiometer, 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 ęsthesiometer 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 naļvely 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
+naļve 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 ęsthetic 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 naļvely 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
+ęsthetic 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 ęsthetic 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 ęsthetic 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 ęsthetic
+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
+coėxistence in space. The coėxistence 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 ęsthesiometers. 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
+ęsthesiometer. 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
+ęsthesiometer 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
+ęsthesiometer 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 ęsthesiometer. I
+made an ęsthesiometer 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
+ęsthesiometer 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
+ęsthesiometer. Various methods were tried, but the following was most
+successful. I would tell the subject that I was going to use the
+ęsthesiometer 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 ęsthesiometer 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 ęsthesiometer 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 reėnforcement 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 reėnforcement 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 ęsthesiometer 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 ęsthetic 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 ęsthetic 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 ęsthetic 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 ĘSTHETIC 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
+ęsthetic 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 ęsthetic 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 ęsthetic 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 ęsthetic 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 ęsthetic 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
+  Anapęstic,         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 anapęstic 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 anapęst moves continuously toward a final accent in an unbroken
+crescendo. But in the anapęstic 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; anapęstic, 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 anapęst 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 anapęstic 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 anapęstic--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
+  Anapęs.,  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 anapęstic
+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
+    Anapęstic,       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
+  Anapęstic,      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 anapęstic 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 anapęst. 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 anapęstic 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-Anapęstic,
+(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 reėstablished
+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 reėstablished 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 anapęstic, 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 ęsthetic 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 anapęsts among iambics, and the like--and the occurrence
+of points of origin, emphasis, interruption, and finality in special
+accentuations, syncopated measures, cęsural 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 Ęsthetik,' 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:
+
+   ĶII ĶII ĶII Ķ / ĶII ĶII ĶII Ķ  Without rhyme.
+
+  Each dactyl (ĶII) 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:
+  ĶII ĶII ĶII Ķ / ĶII ĶII ĶII Ķ (with rhyme).
+
+  Each dactyl (ĶII) 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 anapęstic.
+       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)
+                          gņ)
+                          dņ
+                          dņ
+     Hu. Rhymes imperfectly.
+     Mc. Rhymes imperfectly.
+     G.  Rhymes imperfectly.
+     Ha. Rhymes imperfectly.
+     Hy. Rhymes fairly well.
+
+  Ta ta  ta ta  ta ta  ta dņ)
+                          gó)
+                          dņ
+                          dņ
+     Hu. Cannot get rhyme.
+     Mc. Rhymes imperfectly. 'Produced by some sort of tension.'
+     G.  Rhymes imperfectly.
+
+  Ta ta  ta ta  ta ta  ta dņ)
+                          gņ)
+                          dó
+                          dņ
+     Hu. Rhymes well.
+     Mc. Rhymes well.
+     G.  Rhymes well.
+
+  Ta ta  ta ta  ta ta  ta dņ
+                          gņ)
+                          dó)
+                          dņ)
+     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 cęsura, 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 anapęst. 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 anapęst 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 anapęst 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 anapęst, but by even
+three.
+
+The anapęst 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 anapęst), 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 cęsural 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 ęsthetic 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 ęsthetic
+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 ęsthetic 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 ęsthetically
+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 ęsthetic
+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
+ęsthetic 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) ęsthetic phenomenon emerging from pre-ęsthetic 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 ęsthetic 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 ęsthetic 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 ęsthetic 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 ęsthetic
+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-ęsthetic 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-ęsthetic 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 Zuńi 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 Zuńi 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 ęsthetic 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
+ęsthetic 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, the ornaments of the rectangular spaces given by the
+nodes are strikingly symmetrical. Many of these are from animal
+motives, and nearly always heads are turned back over the body, tails
+exaggerated, or either or both doubled, to get a symmetrical effect.
+Although much of the symmetrical ornament, again, is manifestly from
+textile models, its symmetrical character is so carefully preserved
+against the suggestions of the circular form that a direct pleasure in
+its symmetry may be inferred. (See Figs. 2-7.)
+
+   [7] Cushing, F.H.: _op. cit._; Holmes, W.H.: three articles on
+   pottery, Rep. of Bur. of Ethnol., 1882-83, p. 265, p. 367, and
+   p. 443.
+
+[Illustration: Fig. 2]
+
+[Illustration: Fig. 3]
+
+[Illustration: Fig. 4]
+
+The subject of drawing can be here only touched upon, but the results
+of study go to show, in general, two main directions of primitive
+expression: pictorial representation, aiming at truth of life, and
+symbolic ornament. The drawings of Australians, Hottentots and
+Bushmen, and the carvings of the Esquimaux and of the prehistoric men
+of the reindeer period show remarkable vigor and naturalness; while
+the ornamentation of such tribes as the South Sea Islanders has a
+richness and formal beauty that compare favorably with the decoration
+of civilized contemporaries. But these two types of art do not always
+keep pace with each other. The petroglyphs of the North American
+Indians[8] exhibit the greatest irregularity, while their tattooing is
+extremely regular and symmetrical. The Brazilian savage [9] draws
+freehand in a very lively and grotesque manner, but his patterns are
+regular and carefully developed. Again, not all have artistic talents
+in the same direction. Dr. Schurtz, in his 'Ornamentik der Aino,'[10]
+says: "There are people who show a decided impulse for the direct
+imitation of nature, and especially for the representation of events
+of daily life, as dancing, hunting, fishing, etc. It is, however,
+remarkable that a real system of ornamentation is scarcely ever
+developed from pictorial representations of this kind; that, in fact,
+the people who carry out these copies of everyday scenes with especial
+preference, are in general less given to covering their utensils with
+a rich ornamentive decoration."[11] Drawing and ornament, as the
+products of different tendencies, may therefore be considered
+separately.
+
+   [8] Mallery, Garrick: 'Pictographs of the North American
+   Indians,' Rep. of Bur. of Ethnol., 1882-3, p. 13.
+
+   [9] Von den Steinen, Karl: 'Unter den Naturvōlkern
+   Zentral-Brasiliens,' Berlin, 1894.
+
+   [10] _Internal. Archiv s. Ethnog._, Bd. IX.
+
+   [11] Cf. Andrée, Richard: 'Ethnographische Parallelen,' Neue
+   Folge, Leipzig, 1889, S. 59.
+
+The reason for the divergence of drawing and ornament is doubtless the
+original motive of ornamentation, which is found in the clan or totem
+ideas. Either to invoke protection or to mark ownership, the totem
+symbol appears on all instruments and utensils; it has been shown,
+indeed, that practically all primitive ornament is based on totemic
+motives.[12] Now, since a very slight suggestion of the totem given by
+its recognized symbol is sufficient for the initiated, the extreme of
+conventionalization and degradation of patterns is allowable, and is
+observed to take place. The important point to be noted in this
+connection is, however, that all these changes are toward symmetry.
+The most striking examples might be indefinitely multiplied, and are
+to be found in the appended references (see Figs. 8 and 9).
+
+   [12] Haddon, _op. cit._; Frazer, J.G.: 'Totemism,' 1887;
+   Grosse, Ernst: Anfänge der Kunst,' Freiburg i. B. u. Leipzig,
+   1894.
+
+[Illustration: Fig. 5.]
+
+[Illustration: Fig. 6.]
+
+[Illustration: Fig. 7.]
+
+We may distinguish here, also, between the gradual disintegration and
+degradation of pattern toward symmetry, as seen in the examples just
+given, and the deliberate distortion of figures for a special purpose.
+This is strikingly shown in the decorative art of the Indians of the
+North Pacific coast. They systematically represent their totem
+animals--their only decorative motives--as split in symmetrical
+sections, and opened out flat on the surface which is to be
+covered[13] (see Fig. 11). Dr. Boas argues that their purpose is to
+get in all the received symbols, or to show the whole animal, but,
+however this may be, every variation introduces symmetry even where it
+is difficult to do so, as in the case, for instance, of bracelets,
+hat-brims, etc. (Fig. 10). This may in some cases be due to the
+symmetrical suggestions of the human body in tattooing,[14] but it
+must be so in comparatively few.
+
+[13] Boas, Franz: 'Decorative Art of the Indians of the North Pacific
+Coast,' _Bulletin_ of Am. Mus. of Nat. Hist., Vol. IX.
+
+[14] Mallery, G.: _op. cit._; Haddon, A.C.: _op. cit._, p. 257;
+'Decorative Art of British New Guinea,' Cunningham Memoir X., Royal
+Irish Acad., 1894, p. 26.
+
+[Illustration: Fig. 8.]
+
+[Illustration: Fig. 9.]
+
+[Illustration: Fig. 10]
+
+The primitive picture has for its object not only to impart
+information, but to excite the very definite pleasure of recognition
+of a known object. All explorers agree in their accounts of the
+savage's delight in his own naļve efforts at picture making. All such
+drawings show in varying degrees the same characteristics; first of
+all, an entire lack of symmetry. In a really great number of examples,
+including drawings and picture-writing from all over the world, I
+have not found one which showed an attempt at symmetrical arrangement.
+Secondly, great life and movement, particularly in the drawings of
+animals. Thirdly, an emphasis of the typical characteristics, the
+logical marks, amounting sometimes to caricature. The primitive man
+draws to tell a story, as children do. He gives with real power what
+interests him, and puts in what he knows ought to be there, even if it
+is not seen, but he is so engrossed by his interest in the imitated
+object as to neglect entirely its relation to a background.
+
+[Illustration: FIG. 11]
+
+Now, this very antithesis of ornament and picture is enlightening as
+to the dawn of ęsthetic feeling, and the strongest confirmation of our
+hypothesis of an original impulse to symmetry in art. In the
+ornamentation of objects the content or meaning of the design is
+already supplied by the merest hint of the symbol which is the
+practical motive of all ornamentation. The savage artist need,
+therefore, concern himself no more about it, and the form of his
+design is free to take whatever shape is demanded either by the
+conditions of technique and the surface to be ornamented, or by the
+natural ęsthetic impulse. We have found that technical conditions
+account for only a small part of the observed symmetry in pattern, and
+the inference to a natural tendency to symmetry is clear. Pictorial
+representation, on the other hand, is enjoyed by the primitive man
+merely as an imitation, of which he can say, 'This is that animal'--to
+paraphrase Aristotle's Poetics. He is thus constrained to reproduce
+the form as it shows meaning, and to ignore it as form, or as his
+natural motor impulses would make it.
+
+To sum up the conclusions reached by this short survey of the field of
+primitive art, it is clear that much of the symmetry appearing in
+primitive art is due (1) to the conditions of construction, as in the
+form of dwellings, binding-patterns, weaving and textile patterns
+generally; (2) to convenience in use, as in the shapes of spears,
+arrows, knives, two-handled baskets and jars; (3) to the imitation of
+animal forms, as in the shapes of pottery, etc. On the other hand (1)
+a very great deal of symmetrical ornament maintains itself _against_
+the suggestions of the shape to which it is applied, as the ornaments
+of baskets, pottery, and all rounded objects; and (2) all distortion,
+disintegration, degradation of pattern-motives, often so marked as all
+but to destroy their meaning, is in the direction of geometrical
+symmetry. In short it is impossible to account for more than a small
+part of the marked symmetry of primitive art by non-ęsthetic
+influences, and we are therefore forced to conclude an original
+tendency to create symmetry, and to take pleasure in it. A strong
+negative confirmation of this is given, as noted above, by the utter
+lack of symmetry of the only branch of art in which the primitive man
+is fully preoccupied with meaning to the neglect of shape; and by the
+contrast of this with those branches of art in which attention to
+meaning is at its minimum.
+
+The question put at the beginning of this section must thus be
+answered affirmatively. There is evidence of an original ęsthetic
+pleasure in symmetry.
+
+
+III. EXPERIMENTS IN SUBSTITUTIONAL SYMMETRY.
+
+
+_A. Method of Experiment._
+
+A certain degree of original ęsthetic pleasure in symmetry may be
+considered to have been established by the preceding section, and,
+without considering further the problems of real or geometrical
+symmetry, it may now be asked whether the pleasure aroused by the form
+of asymmetrical objects is not at bottom also pleasure in symmetry;
+whether, in other words, a kind of substitution of factors does not
+obtain in such objects, which brings about a psychological state
+similar to that produced by real symmetry.
+
+The question what these substituted factors may be can perhaps be
+approached by a glance at a few pictures which are accepted as
+beautiful in form, although not geometrically symmetrical. Let us
+take, for instance, several simple pictures from among the well-known
+altar-pieces, all representing the same subject, the _Madonna
+Enthroned_ with _Infant Christ_, and all of generally symmetrical
+outline. It seems, then, reasonable to assume that if the variations
+from symmetry show constantly recurring tendencies, they represent the
+chief factors in such a substitutional symmetry or balance, supposing
+it to exist. The following pictures are thus treated in detail, M.
+denoting Madonna; C., Child; and Cn., Central Line. The numbers refer
+to the collection of reproductions used exclusively in this
+investigation, and further described in section IV.
+
+1. 56, Martin Schöngauer: _Madonna in Rose-arbor._ M. is seated
+exactly in Cn., C. on Right, turning to Right. M. turns to Left, and
+her long hair and draperies form one long unbroken line down to Left
+lower corner. All other details symmetrical.
+
+2. 867, Titian: _Madonna_. The picture is wider than it is high. M.
+stands slightly to Right of Cn.; C. on Right. Both turn slightly to
+Left, and the drapery of M. makes a long sweep to Left. Also a deep
+perspective occupies the whole Left field.
+
+3. 248, Raphael: _Madonna_ (The Bridgewater Madonna). M. sits in Cn.,
+turning to Left; C. lies across her lap, head to Left, but his face
+turned up to Right, and all the lines of his body tending sharply down
+to Right.
+
+In 1, all the elements of the picture are symmetrical except the
+position of C. on the Right, and the long flowing line to Left. In 2,
+there is a slightly greater variation. The mass of the figures is to
+Right, and the C. entirely over against the deep perspective and the
+flowing line on the Left, and the direction of both faces toward that
+side. In 3, the greater part of C.'s figure on Left is opposed by the
+direction of his lines and movement to Right. Thus these three
+pictures, whether or not they are considered as presenting a balance,
+at least show several well-defined factors which detach themselves
+from the general symmetrical scheme. (1) Interest in C. is opposed by
+outward-pointing line; (2) greater mass, by outward-pointing line,
+deep vista, and direction of attention; and (3) again interest by
+direction of line and suggestion of movement.
+
+This analysis of several ęsthetically pleasing but asymmetrical
+arrangements of space strongly suggests that the elements of large
+size, deep perspective, suggested movement, and intrinsic interest are
+in some way equivalent in their power to arouse those motor impulses
+which we believe to constitute the basis of ęsthetic response. It is
+the purpose of these experiments to follow up the lines of these
+suggestions, reducing them to their simplest forms and studying them
+under exact conditions.
+
+But before describing the instruments and methods of this experimental
+treatment, I wish to speak of the articles on the 'Ęsthetics of Simple
+Form,' published as Studies from the Harvard Psychological Laboratory,
+by Dr. Edgar Pierce.[15] These articles, sub-entitled 'Symmetry' and
+'The Functions of the Elements' seem at first sight to anticipate the
+discussions of this paper; but a short analysis shows that while they
+point in the same direction, they nevertheless deal with quite
+different questions and in a different manner. In the statement of his
+problem, indeed, Dr. Pierce is apparently treading the same path.
+
+   [15] Pierce E.: PSYCH. REV., 1894, I., p. 483; 1896, III., p.
+   270.
+
+He says: "Can a feeling of symmetry, that is, of ęsthetical equality
+of the two halves, remain where the two sides are not geometrically
+identical; and if so, what are the conditions under which this can
+result--what variations of one side seem ęsthetically equal to the
+variations of the other side?" Some preliminary experiments resulted
+in the conclusion that an unsymmetrical and yet pleasing arrangement
+of a varied content rests on the pleasure in unity, thus shutting out
+the Golden Section choice, which depends on the pleasure in variety.
+That is, the choices made will not in general follow the golden
+section, but 'when the figure consists of two halves, the pleasure
+must be a feeling of ęsthetical symmetry.'
+
+The final experiments were arrangements of lines and simple figures on
+a square, black background in which the center was marked by a white
+vertical line with a blue or a red line on each side. On one side of
+these central lines a line was fixed; and the subject had to place on
+the other side lines and simple figures of different sizes and
+different colors, so as to balance the fixed line. The results showed
+that lines of greater length, or figures of greater area must be put
+nearer the center than shorter or smaller ones--'A short line must be
+farther than a long one, a narrow farther than a wide, a line farther
+than a square; an empty interval must be larger than one filled, and
+so on.' And for colors, "blue, maroon and green, the dark colors, are
+the farthest out; white, red and orange, the bright colors, are
+nearest the center. This means that a dark color must be farther out
+than a bright one to compensate for a form on the other side. The
+brightness of an object is then a constant substitute for its distance
+in satisfying our feeling of symmetry."
+
+Now from these conclusions two things are clear. By his extremely
+emphasized central line, and his explicit question to the subjects,
+'Does this balance?' the author has excluded any other point of view
+than that of mechanical balance. His central fulcrum is quite
+overpowering. Secondly, his inquiry has dealt only with size and
+color, leaving the questions of interest, movement, and perspective
+untouched. But just the purpose of this experimental study is to seek
+for the different and possibly conflicting tendencies in composition,
+and to approximate to the conditions given in pictorial art. It is
+evident, I think, that the two studies on symmetry will not trespass
+on each other's territory. The second paper of Dr. Pierce, on 'The
+Functions of the Elements,' deals entirely with the relation of
+horizontal and vertical positions of the ęsthetic object and of the
+subject to ęsthetic judgments, and has therefore no bearing on this
+paper.
+
+For his apparatus Dr. Pierce used a surface of black cloth stretched
+over black rubber, 1 m. square. Now an investigation which is to deal
+with complicated and varied relations, resembling those of pictures,
+demands an instrument resembling them also in the shape of the
+background. A rectangle 600 mm. broad by 400 mm. high seemed to meet
+this requirement better than the square of Dr. Pierce. Other parts,
+also, of his instrument seemed unfitted for our purpose. The tin, 5
+cm. broad and confined to the slits across the center of the square,
+gave not enough opportunity for movement in a vertical direction,
+while the scale at the back was very inconvenient for reading. To
+supply these lacks, a scale graduated in millimeters was attached on
+the lower edge of the board, between a double track in which ran
+slides, the positions of which could be read on the scale. To the
+slides were attached long strips of tin covered with black cloth. On
+these strips figures glued to small clamps or clasps could be slipped
+up or down; this arrangement of coördinates made it possible to place
+a figure in any spot of the whole surface without bringing the hands
+into the field of view. The experiments were made in a dark room, in
+which the apparatus was lighted by an electric globe veiled by white
+paper and hung above and behind the head of the subject, so as not to
+be seen by him and to cast no shadow: in this soft light of course the
+black movable strips disappeared against the black background. A gray
+paper frame an inch and a half wide was fitted to the black rectangle
+to throw it up against the black depths of the dark room--thus giving
+in all details the background of a picture to be composed.
+
+The differences in method between the two sets of experiments were
+fundamental. In Dr. Pierce's experiments the figures were pulled from
+one side to the other of the half-square in question, and the subject
+was asked to stop them where he liked; in those of the writer the
+subject himself moved the slides back and forth until a position was
+found ęsthetically satisfactory. The subject was never asked, Does
+this balance? He was indeed requested to abstract from the idea of
+balance, but to choose that position which was the most immediately
+pleasing for its own sake, and so far as possible detached from
+associations.
+
+I have said that Dr. Pierce intentionally accentuated the center. The
+conditions of pictorial composition suggest in general the center only
+by the rectangular frame. Most of my experiments were, therefore, made
+without any middle line; some were repeated with a middle line of fine
+white silk thread, for the purpose of ascertaining the effect of the
+enhanced suggestion of the middle line.
+
+But the chief difference came in the different treatment of results.
+Dr. Pierce took averages, whereas the present writer has interpreted
+individual results. Now, suppose that one tendency led the subject to
+place the slide at 50 and another to place it at 130 mm. from the
+center. The average of a large number of such choices would be 90--a
+position very probably disagreeable in every way. For such an
+investigation it was evident that interpretation of individual results
+was the only method possible, except where it could be conclusively
+shown that the subjects took one and only one point of view. They were
+always encouraged to make a second choice if they wished to do so, as
+it often happened that one would say: 'I like both of these ways very
+much.' Of course, individual testimony would be of the highest
+importance, and a general grouping into classes and indication of the
+majority tendency would be the only way to treat the results
+statistically. And indeed in carrying out the experiments this caution
+was found absolutely necessary. In all but one or two of the sections,
+the taking of averages would have made the numerical results
+absolutely unintelligible. Only the careful study of the individual
+case, comparison of various experiments on the same person to find
+personal tendencies, and comparison of the different tendencies, could
+give valuable results for the theory of symmetry.
+
+The first question to be taken up was the influence of right and left
+positions on choice. A long series of experiments was undertaken with
+a line 80×10 mm. on one side and a line 160×10 mm. on the other, in
+which the positions of these were reversed, and each in turn taken as
+fixed and variable, with a view to determining the effect of right and
+left positions. No definite conclusions emerged; and in the following
+experiments, most of which have been made for both right and left
+positions, the results will be treated as if made for one side alone,
+and, where averages are taken, will be considered as indifferently
+left or right.
+
+The experiments of Dr. Pierce were made for only one position of the
+fixed line--at 12 cm. distance from the center. The characteristic of
+the following experiments is their reference to all positions of the
+fixed line. For instance a fixed line, 10 cm. in length at 12 cm.
+distance from the center, might be balanced by a line 5 cm. in length
+at 20 cm. distance. But would the distance be in the same proportion
+for a given distance of the fixed line of say 20 or 25 cm.? It is
+clear that only a progressive series of positions of the fixed line
+would suggest the changes in points of view or tendencies of choice of
+the subject. Accordingly, for all the experiments the fixed line or
+other object was placed successively at distances of 20, 40, 60 mm.,
+etc., from the center; or at 40, 80 mm., etc., according to the
+character of the object, and for each of these fixed points the
+subject made one or two choices. Only an understanding of the
+direction in which the variable series moved gave in many cases an
+explanation for the choice.
+
+Each choice, it should be added, was itself the outcome of a long
+series of trials to find the most pleasing position. Thus, each
+subject made only about ten choices in an hour, each of which, as it
+appears in the tables, represents a large number of approximations.
+
+
+_B. Experiments on Size._
+
+I have said that different tendencies or types of choice in
+arrangement appeared. It will be convenient in the course of
+explaining in detail the method of experiment, to discuss at the same
+time the meaning of these types of choice.
+
+From analysis of the pictures, the simplest suggestion of balance
+appeared in the setting off against each other of objects of different
+sizes;--an apparent equivalence of a large object near the center with
+a small object far from the center; thus inevitably suggesting the
+relations of the mechanical balance, or lever, in which the heavy
+short arm balances the light long arm. This was also the result of
+Dr. Pierce's experiments for one position of his fixed line. The
+experiments which follow, however, differ in some significant points
+from this result. The instrument used was the one described in the
+preceding section. On one side, in the middle of the vertical strip,
+was placed the 'fixed' line, denoted by F., and the subject moved the
+'variable' line, denoted by V., until he found the arrangement
+ęsthetically pleasing. The experimenter alone placed F. at the given
+reading, and read off the position of V. After the choice F. was
+placed at the next interval, V. was again tried in different
+positions, and so on. In the following tables the successive positions
+of F. are given in the left column, reading downward, and the
+corresponding positions of V. in the right column. The different
+choices are placed together, but in case of any preference the second
+choice is indicated. The measurements are always in millimeters. Thus,
+F. 40, V. 60, means that F. is 40 mm. to one side of the center, and
+V. 60 mm. to the opposite side. F. 80×10, V. 160×10, means that the
+white cardboard strips 80 mm.×10 mm., etc., are used. The minus sign
+prefixed to a reading means that the variable was placed on the side
+of the fixed line. An X indicates ęsthetic dislike--refusal to choose.
+An asterisk (*) indicates a second choice.
+
+The following tables are specimen sets made by the subjects _C, O_,
+and _D_.
+
+
+I. (a) F. 80×10, V. 160×10.
+
+  F.                     V.
+         C.            O.                    D.
+
+   40   62, 120       166, 130           28, 24
+   80   70, 110       104, 102           80, 126
+  120   46, X          70, 46           68,--44, 128*
+  160   26, 96         50, 25           85, 196,--88*
+  200   20, X          55, X          --46, 230,* 220,--110*
+
+
+I. (b) F. 160×10, V. 80×10.
+
+  F.                     V.
+         C.            O.                    D.
+
+   40   74, 64         60, 96            27, 34
+   80   76, 65         72, 87            55, 138
+  120   60, 56         48, 82            70, 174
+  160   29, 74         16, 77          --114, 140, 138, 200
+  200   96, 36         25, 36            177,--146,--148, 230
+
+
+Now, on Dr. Pierce's theory, the variable in the first set should be
+nearer the center, since it is twice the size of the fixed line;--but
+the choices V. 120, 166, 130 for F. 40; V. 110, 104, 102, 126 for F.
+80; V. 128 for F. 120; V. 196 for F. 160; V. 230, 220 for F. 200, show
+that other forces are at work. If these variations from the expected
+were slight, or if the presence of second choices did not show a
+certain opposition or contrast between the two positions, they might
+disappear in an average. But the position of F. 40, over against V.
+120, 166, 130, is evidently not a chance variation. Still more
+striking are the variations for I. (_b_). Here we should expect the
+variable, being smaller, to be farther from the center. But for F. 40,
+we have V. 27, 34; for F. 80, all nearer but two; for F. 120, V. 60,
+56, 48, 82, 70; for F. 160, V. 29, 74, 16, 77, 138, and for F. 200, V.
+96, 36, 25, 36, 177--while several positions on the same side of the
+center as the constant show a point of view quite irreconcilable with
+mechanical balance.
+
+
+II. (a) F. 2 LINES 80×10.   V. SINGLE LINK 80×10.
+
+     F.                           V.
+                     C.                O.         P.
+
+   40- 60     58, 114*  138,  20      96, 84     166
+   60- 80     48         40, 138*    100, 56     150
+   80-100     64         70, 162*     47, 87     128
+  100-120     70 to 80   60           53, 53       X
+  120-140     58         82           50, 48      35
+  140-160     74         95 to 100    22, 32      37
+  160-180     72         102           X,  X      42
+  180-200     90         X             X,  X      50
+
+
+Here the variable should supposedly be the farther out; but we have V.
+58, 20 for F. 40-60; V. 48, 40, 56 for F. 60; V. 64, 70, 87 for F. 80;
+no larger choice for F. 100-120; indeed, from this point on everything
+nearer, and very much nearer. We can trace in these cases, more
+clearly perhaps than in the preceding, the presence of definite
+tendencies. _O_ and _P_, from positions in accord with the mechanical
+theory, approach the center rapidly; while _C_ is seldom 'mechanical,'
+but very slowly recedes from the center. The large number of refusals
+to choose assures us that the subjects demand a definitely pleasant
+arrangement--in other words, that every choice is the expression of a
+deliberate judgment.
+
+Taking again the experiments 1. (a) and 1. (b), and grouping the
+results for nine subjects, _C_, _O_, _A_, _S_, _H_, _G_, _D_, and _P_,
+we obtain the following general types of choice. The experiments were
+repeated by each subject, so that we have eighteen records for each
+position. I should note here that preliminary experiments showed that
+near the frame the threshold of difference of position was 10 mm., or
+more, while near the center it was 4 or 5 mm.; that is, arrangements
+were often judged symmetrically equal which really differed by from 4
+to 10 mm., according as they were near to or far from the center. In
+grouping types of choice, therefore, choices lying within these limits
+will be taken as belonging to the same type.
+
+
+   EXP. 1. (a)   F.(80 X 10).   V.(160 X 10).
+
+              1. F. 40.                            V. 40.¹
+
+       Types of Choice for V.
+   (1)  24   24   25   28
+   (2)  40   42   45   45                        40   40   40
+   (3)  62   65
+   (4) 100  105  1O9  120  130  136                  120
+   (5) 166 180                        200  200  200  200  160  160
+
+   ¹This table is obtained by taking from the full list, not given
+   here, of 1. (b) F. (l60 X 10), V. (80 X 10), those positions of
+   160 X 10 where the variable 80 X 10 has been placed at or near
+   40, thus giving the same arrangement as for 1. (a).
+
+
+It might be objected that a group 40-65 (2-3) would not be larger than
+one of 100-136 (4), but the break between 45 and 62 shows the zones
+not continuous. Moreover, as said above, the positions far from the
+center have a very large difference threshold.
+
+    I. (a) 2. F. 80:--(1) 24, (2) 50, (3) 68 70, (4) 80 85 94 95
+    85, (5) 102 104 110 120 124 126 125* 132, (6) 187; also V.
+    80:--(2) 40 40, (4) 80, (5) 120 120, (6) 160 160.
+
+    I. (a) 3. F. 120:--(1) 44 46, (2) 64 48 70 70, (3) 85 95 97
+    91, (4) 113 113 118, (5) 168 169 178;--44, X; also V.
+    120:--(1) 40 40, (3) 80 80 80, (4) 120 120, (5) 160 160.
+
+    I. (a) 4. F. 160:--(1) 25 26, (2) 40 50 57, (3) 82 85 95 100*,
+    (4) 114 115 130, (5) 145 145 156 162, (6) 196,
+    (7)--88*--150*--105.
+
+    I. (a) 5. F. 200:--(1) 20 23 28 36, (2) 55, (3) 108 124 130*,
+    (4) 171 189 199 195, (5) 220 230*, (6)--46--90--110*.
+
+On comparing the different groups, we find that in 1 and 2 there is a
+decided preference for a position somewhat less than half way between
+center and frame--more sharply marked for 1 than for 2. From 3 onward
+there is a decided preference for the mechanical arrangement, which
+would bring the larger strip nearer. Besides this, however, there are
+groups of variations, some very near the center, others approaching to
+symmetry. The maintenance of geometrical symmetry at a pretty constant
+ratio is to be noted; as also the presence of positions on the same
+side of the center as the fixed line. Before discussing the
+significance of these groups we may consider the results of Experiment
+II. (F. double line 80×10, V. single line 80×10) without giving
+complete lists.
+
+We notice therein, first of all, the practical disappearance of the
+symmetrical choice; for F. 40-60, 60-80, 80-100, a tendency,
+decreasing, however, with distance from the center, to the mechanical
+arrangement; for F. 100-120, and all the rest, not one mechanical
+choice, and the positions confined almost entirely to the region
+35-75. In some cases, however, the mechanical choice for (1) 40-80,
+(2) 60-80, was one of two, _e.g._, we have for (1) 20 and 138, for (3)
+70 and 162; in the last two cases the mechanical being the second
+choice.
+
+Now the reversals of the mechanical choice occur for Exp. I. in 1 and
+2 (F. 40 and F. 80); that is, when the small fixed line is near the
+center, the larger variable is distant. For Exp. II. the reversals,
+which are much more marked, occur in all cases _beyond_ F. 40, F. 60
+and F. 80; that is, when the double constant line is far from the
+center, the single variable approaches. If the mechanical theory
+prevailed, we should have in Exp. I. the lines together in the center,
+and in Exp. II. both near the fringe.
+
+From the individual testimony, based both on I. (_a_) and I. (_b_), it
+appears that subject _M_ is perfectly uniform in mechanical choice
+when the fixed line is the small line--_i.e._ when it moves out, the
+larger is placed near the center; but when the conditions of
+mechanical choice would demand that, as the larger fixed line moves
+out, the small variable one should move out farther, he regularly
+chooses the reverse. Nevertheless, he insists that in just these
+cases he has a feeling of equilibrium.
+
+_A_ also takes the mechanical choice as the small fixed line goes
+farther from the center; but when the fixed line is large and leaves
+the center, he reverses the mechanical choice--evidently because it
+would take the small line too far out. As he says, 'he is always
+disturbed by too large a black space in the center.'
+
+_G_ almost always takes the mechanical choice;--in one whole set of
+experiments, in which the fixed line is the large line, he reverses
+regularly.
+
+_H_ takes for F. (80×10) the mechanical choice only for the positions
+F. 160 and F. 200--_i.e._, only when F. is very far from the center
+and he wishes V. (160×10) nearer. For F. (160×10) he makes six such
+choices out of ten, but for positions F. 160 and F. 200 he has V. 44,
+65 and 20.
+
+_S_ takes for F. (160×10) at F. 120, V. 185 and-70; says of V. 185,
+which is also his choice for F. (160×10) at F. 80, 'I cannot go out
+further, because it is so hard to take in the whole field.' For F.
+(160×10) at F. 200, he has V. 130 and 60; says of V. 60, 'Very
+agreeable elements in connection with the relation of the two lines.'
+
+_C_ takes for F. (80×10) only one mechanical choice until it is at F.
+120. Then always mechanical, _i.e._, nearer center; for F. (160×10)
+makes after the position F. 40 no mechanical choice, _i.e._, V. is
+nearer center.
+
+It is evident from the above tables and individual cases that the
+reversals from the mechanical choice occur only when the mechanical
+choice would bring both lines in the center, or both near the edges,
+and the subjective testimony shows from what point of view this
+appears desirable. The subjects wish 'to take in the whole field,'
+they wish 'not to be disturbed by too large a black space in the
+center'; and when, in order to cover in some way the whole space, the
+small line is drawn in or the large one pushed out, they have,
+nevertheless, a feeling of equilibrium in spite of the reversal of
+mechanical balance.
+
+Accepting for the present, without seeking a further psychological
+explanation, the type of 'mechanical balance,' in which amount of
+space is a substitute for weight, as the one most often observed, we
+have to seek some point of view from which this entire reversal is
+intelligible. For even the feeling that 'the whole field must be
+covered' would hardly account for an exact interchanging of positions.
+If size gives 'weight,' why does it not always do so? A simple answer
+would seem to be given by the consideration that we tend to give most
+attention to the center of a circumscribed space, and that any object
+in that center will get proportionately more attention than on the
+outskirts. The small line near the center, therefore, would attract
+attention by virtue of its centrality, and thus balance the large
+line, intrinsically more noticeable but farther away. Moreover, all
+the other moments of ęsthetic pleasure, derived from the even filling
+of the space, would work in favor of this arrangement and against the
+mechanical arrangement, which would leave a large black space in the
+middle.
+
+The hypothesis, then, that the demand for the filling of the whole
+space without large gaps anywhere enters into competition with the
+tendency to mechanical balance, and that this tendency is,
+nevertheless, reconciled with that demand through the power of a
+central position to confer importance, would seem to fit the facts. It
+is, of course, clear that neither 'mechanical balance' nor the balance
+of 'central' with 'intrinsic' importance have been yet accounted for
+on psychological grounds; it is sufficient at this point to have
+established the fact of some kind of balance between elements of
+different qualities, and to have demonstrated that this balance is at
+least not always to be translated into the 'mechanical' metaphor.
+
+
+_C. Experiments on Movement._
+
+In the preceding experiments the element of size was isolated, and it
+was sought to discover, in pleasing combinations of objects of
+different sizes, the presence of some kind of balance and the meaning
+of different tendencies of arrangement. The relative value of the two
+objects was taken as determined on the assumption, supported by common
+sense, that under like conditions a large object is given more
+attention than a small one. If the unequal objects seem to balance
+each other, then the only other condition in which they differ, their
+distance from the center, must be the cause of their balancing. Thus
+the influence of relative position, being the only unknown quantity in
+this balance-equation, is easily made out.
+
+The following experiments will deal with the as yet quite undetermined
+elements of suggested movement, perspective and intrinsic interest. By
+combining objects expressing them, each with another simple object of
+the same size, another equation will be obtained in which there is
+only one unknown quantity, the sizes of the objects being equal and
+the influence of relative position being at least clearly indicated.
+
+
+1. Movement.
+
+The experiments on suggestion of movement were made by _C_, _O_ and
+_P_. Suggestions of movement in pictures are of two kinds--given by
+lines pointing in a direction which the eye of the spectator tends to
+follow, and by movement represented as about to take place and
+therefore interpreted as the product of internal energy. Thus, the
+tapering of a pyramid would give the first kind of suggestion, the
+picture of a runner the second kind. Translated into terms of
+experiment, this distinction would give two classes dealing with (A)
+the direction of a straight line as a whole, and (B) the expression of
+internal energy by a curve or part of a line. In order to be able to
+change the direction of a straight line at a given point, a strip of
+tin two inches long was fastened by a pivot to the usual clasp which
+slipped up and down on the vertical black strip. The tin strip could
+be moved about the pivot by black threads fastened to its perforated
+ends. A strip of cardboard glued upon it would then take its
+direction. The first experiments, made with the usual 80×10 strip,
+proved very disagreeable. The subject was much disturbed by the blunt
+ends of the strip. The variable (pivoted) line was then slightly
+pointed at the upper end, and in the final experiments, in which both
+are oblique, both strips were pointed at each end. In Exp. III. a line
+pointing at an angle from the perpendicular was set over against a
+line of the same dimensions in the ordinary position.
+
+    Exp. III. (_a_) F. (80×10) pointed up toward center at 145°,
+    V. (80×10).
+
+    F. 40:--(1) 39 48 48, (2) 60 66 68, (3) 97 97, (4) 156* 168*.
+
+    F. 60:--(1) 45, (2) 60 62 65 68 90, (3) 90 94, (4) 117 128 152
+    155.
+
+    F. 80:--(1) 50 44*, (2) 74 76 77, (3) 94 100 106 113 115 116,
+    (4) 123 124* 140 165* 169*.
+
+    F. 100:--(1) 36 58 60 65* 65 74 77 80 87, (2) 98 108 118, (3)
+    114* 168 186* 170 136*.
+
+    F. 120:--(1) 40 46 54 60 63 76 96 97 111, (2) 115 120 126*
+    137*, (3) 170 170*.
+
+    F. 140:--(1) 45 52 65 65 76 76 86 90, (2) 109 111, (3) 125
+    140*, (4) 168*.
+
+    F. 160:--(1) 38 50 50 60, (2) 80 90 96 98 98, (3) 176*.
+
+    F. 180:--(1) 21 23, (2) 54 70 84 90, (3) 100 100 108 114 120,
+    (4) 130 145*.
+
+    F. 200:--(1) -2, (2) 33 37 50, (3) 106 110 to 120 115 120 130
+    132 138 142.
+
+The most striking point about these groups is the frequency of
+positions far from the center when F. also is far out. At F. 120, a
+position at which the mechanical choice usually prevails if F. is
+smaller, a very marked preference indeed appears for positions of V.
+nearer the center--in fact, there is only one opposing (first) choice.
+Now, if it is not the wide space otherwise left which pulls the
+variable in,--and we see from a note that the subjects have no feeling
+of a large empty space in the center,--it must be that F. has the same
+effect as if it were really smaller than V., that is, mechanically
+'light.' We see, in fact, that the moment F. has passed the point,
+between 80 and 100, at which both lines close together in the center
+would be disagreeable, the preference is marked for inner positions of
+V., and I repeat that this cannot be for space-filling reasons, from
+the testimony of F. 200 (3).
+
+And this 'lightness' of the line pointed in at 45° is indeed what we
+should have expected _a priori_ since we found that objective
+heaviness is balanced by a movement out from the center on the
+mechanical principle. If movement out and objective heaviness are in
+general alike in effect, then movement in and objective lightness
+should be alike in effect, as we have found to be the case from the
+preceding experiments. The inward-pointed line does not actually move
+in, it is true, but it strongly suggests the completion of the
+movement. It enters into the 'mechanical' equation--it appears to
+balance--as if it had moved.
+
+The point, however, in which this 'lightness' of the inward-pointed
+line differs from that of the small or short line is its space-filling
+quality. It suggests movement in a certain direction, and, while
+giving the mechanical effect of that movement as completed, seems also
+in a sense to cover that space. We see from F. 180 (3), (4), and 200
+(3), that the subject does not shrink from large spaces between the
+lines, and does not, as in Exp. I. (_a_), 4 and 5, bring the variable,
+which in both cases is evidently 'heavier,' to the center. This must
+be from the fact that the empty space does not in this experiment feel
+empty--it is filled with energy of the suggested movement. This view
+is confirmed by the dislike which the subjects show to the position F.
+40; F., being 'lighter,' but the object of attention as close to the
+center, might well balance V. far out. But as if the whole variable
+field would be in that case 'overfilled,' the records show 50 per
+cent. of refusals to choose for this position.
+
+In brief, then, a straight line suggesting movements in a certain
+direction has the effect, in the general scheme of mechanical balance,
+of a static position in which this movement has been carried out, with
+the added suggestion of the filling of the space over which such
+movement is suggested.
+
+A few additional experiments were made with a point on the upper end
+of V. The groups of III. (_a_) are maintained almost exactly: F. 120
+is again strikingly 'mechanical'; after F. 120 there are only two
+mechanical choices out of nineteen; while for F. 40, as in Exp. III.
+(_a_), out of six choices, four are either refusals or question-marked.
+
+Exp. IV. Both lines took oblique directions, and, to get a pleasing
+effect, were pointed at both ends. They were of the usual size, 80×10
+mm., but 1 mm. broader to allow for the effect of length given by the
+points. F. was fixed at 45°, as in III. (_a_), on the points 40, 80,
+120 and 160; V. moved also on fixed points, 60, 100, 140, 180, for
+each position of F., but on each point was adjusted at a pleasing
+angle. Thus, there were four positions of V. to each of F., each with
+one or two angular positions; V. was always in the first quadrant.
+
+The numbers of the table give the angular degrees of V.
+
+
+  F. 40, V. 60:--(1) 10 12 38 44, (2) 50 57* 60, (3) 70.
+     V. 100:--(1) 15 15 30 30, (2) 50 55 50, (3) 69 70*.
+     V. 140:--(1) 12* 14 18 18, (2) 60 60 49, (3) 72.
+     V. 180:--(1) 12 10 38, (2) 60 50, (3) 75.
+        [Many refusals at 140 and 180.]
+
+  F. 80, V. 60:--(1) 11, (2) 25 35 36*, (3) 45 48 55 58 60, (4) 69.
+     V. 100:--(1) 16 15, (2) 24 27 35 40, (3) 52, (4) 62 74*.
+     V. 140:--(1) 10 15 16, (2) 22 28, (3) 40 40 59 59, (4) 70.
+     V. 180:--(1) 14 8, (2) 28, (3) 41 46, (4) 68 79.
+
+  F. 120, V. 60: (1) 28, (2) 42 44 35, (3) 52 58 62 65 65.
+     V. 100:--(1) 9, (2) 23 25, (3) 38 40 40 42 58, (4) 68 70.
+     V. 140:--(1) 10, (2) 20 26 21* 24 29, (3) 34 42 42 44 55*, (4) 75.
+     V. 180:--(1) 17 26, (2) 40 42 46, (3) 62 64 70 70*.
+
+  F. 160, V. 60:--(1) 20 39, (2) 18, (3) 58 60 64 68 70.
+     V. 100:--(1) 23 25 30 38, (2) 44 44 49, (3) 55 58 65.
+     V. 140:--(1) 5, (2) 31 35 40 40 32, (3) 54 55 68.
+     V. 180:--(1) 50 50 58 60, (2) 75.
+
+
+The tendency to mechanical balance would, according to our previous
+analysis, lead the variable to take a direction which, in its
+suggestion of motion inward, should be more or less strong according
+as it were farther from or nearer to the center than the fixed line.
+Such motion inward would, of course, be more strongly suggested by an
+angle less than 45° than by an angle greater than 45°, and it seems
+that the angles chosen are in general in harmony with this
+expectation. For the positions where F. is nearer the center than V.
+there is a preponderance of the angles less than 45° (cf. F. 40 and F.
+80, V. 100 and 140; F. 120, V. 140, 180). When V. passes over to a
+position farther from the center than F. (_e.g._, from F. 80, V. 60,
+to F. 80, V. 100 and from F. 120, V. 60, to F. 120, V. 140) the change
+is marked. In every case where F. is farther from the center than V.
+(_i.e._, F. 80, V. 60; F. 120, V. 60 and V. 100; F. 160, V. 60, V.
+100 and V. 140), there are to be noticed a lack of the very small
+angles and a preponderance of the middle and larger angles. F. 160, V.
+140 and 180 seem to be the only exceptions, which are easily
+explainable by a dislike of the extremely small angle near the edge;
+for it appears from the remarks of the subjects that there is always a
+subconsciousness of the direction suggested by the lower pointed end
+of the line. For the outer positions of both lines, a large angle
+would leave the center empty, and a small one would be disagreeable
+for the reason just given; and so we find, indeed, for F. 160, V. 100,
+140, 160, the middle position the favorite one.
+
+The representation of action may be translated into experimental terms
+by expressing it as a line which changes its direction, thus seeming
+to be animated by some internal energy. The forms chosen were three
+curves 'bulging' from a straight line in differing degrees, and two
+straight lines with projections. _C_ and _O_ were the subjects. The
+results are given in outline.
+
+
+    Exp. V. Curve I. See Fig. 12, I
+
+    (1) Curve out (turned away from center).
+
+    (_a_) F. (80×10), V. Curve.
+
+    About half the positions of V. are farther from the center
+    than F. _O_ at first refuses to choose, then up to F. 120 puts
+    V. farther from the center than F. _C_ has a set of positions
+    of V. nearer the center and several second choices farther
+    than F.
+
+    (_b_) F. Curve, V. (80×10).
+
+    No position of V. nearer center than F. _O_ puts line farther
+    out up to F. 160, then nearer than F. _C_ has a set of nearly
+    symmetrical choices and another where V. is much farther out
+    than F.
+
+    (2) Curve in (turned toward center).
+
+    (_a_) F. (80×10), V. Curve.
+
+    _C_ is absolutely constant in putting V. farther from center
+    than F. _O_, after F. 100, brings it slightly nearer.
+
+    (_b_) F. Curve, V. (80×10).
+
+    _C_, except for F. 40, invariably puts V. nearer center than
+    F. _O_ moves between 90 and 135, putting V. farther to F.
+    100, nearly symmetrical at F. 100 and 120, and after F. 120,
+    from 100 to 135.
+
+[Illustration: FIG. 12]
+
+    Exp. V. Curve II. See Fig. 12, II.
+
+    (1) Curve out.
+
+    (_a_) F. (80×10), V. Curve.
+
+    In every case but one V. is nearer center than F.
+
+    (_b_) F. Curve, V. (80×10).
+
+    _C_ puts V. farther from center than F. _O_ puts V. farther or
+    symmetrical up to F. 120, then nearer than F.
+
+    (2) Curve in.
+
+    (_a_) F. 80×10, V. Curve.
+
+    _C_ has V. always farther from center than F., but a second
+    parallel set, omitting F. 40 (all second choices), of
+    symmetrical positions. _O_ begins with V. farther from center,
+    but from F. 120 has V. always nearer, though gradually
+    receding from the center.
+
+    (_b_) F. Curve. V. (80×10).
+
+    _C_, refusing for F. 40, continues his parallel sets, one with
+    V. always nearer than F., another with symmetrical positions.
+    _O_ begins with V. nearer, changes at F. 120, and continues
+    with V. farther.
+
+
+Recapitulating these results, grouping together the outward and inward
+positions of the curves, and indicating the distance of the line from
+the center by C.-L., and of the curve from the center by C.-Cv., we
+have:
+
+
+_Out_.
+
+Cv. I.  (_a_)  Indeterminate.
+        (_b_)  C.-Cv. < C.-L. (except where large gap would be left).
+
+Cv. II. (_a_)  C.-Cv. < C.-L. (all cases but one).
+        (_b_)  C.-Cv. < C.-L. (except where large gap would be left).
+
+_In._
+
+Cv. I. (_a_)  C.-Cv. > C.-L. (except a few cases to avoid gap).
+       (_b_)  C.-Cv. > C.-L. (more than half of cases).
+
+Cv. II. (_a_)  C.-Cv. > C.-L. (except a few cases to avoid gap).
+        (_b_)  C.-Cv. > C.-L. (except  a few cases to avoid gap).
+
+
+It is evident that in the great majority of cases when the curve turns
+out it is placed nearer the center, when it turns in, farther from the
+center, than the straight line. The numerical differences for choices
+of the same type for the two curves are slight, but regular, and the
+general tendencies are more sharply marked for the line of greater
+curvature. When Curve II. is 'out,' it is usually nearer the center
+than Curve I. for the corresponding positions of the straight line;
+when 'in' it is always farther from the center than Curve I. The
+greater curvature of II. has clearly produced this difference, and the
+effect of the curvature in general is evidently to make its side
+'lighter' when turned toward the center, and 'heavier' when turned
+away. Thus, all but the exceptions already noted seem to belong to the
+mechanically balanced arrangement, in which the suggestion of force
+working in the direction of the curve has the same effect as, in Exp.
+IV., the direction of the line. The exceptions noted, especially
+numerous choices of _O_, seem governed by some fixed law. The evidence
+would seem to be overwhelming that the reversals of the mechanical
+balance occur only where the lines would be crowded together in the
+center or would leave an empty gap there. The remaining
+exceptions--the symmetrical choices mentioned, made by _C_--are
+explained by him as follows. He says there are two ways of regarding
+the curve, (1) as a striving in the direction of the 'bulge,' and (2)
+as the expression of a power that presses together; and that the usual
+choices are the result of the first point of view, the symmetrical
+choices of the second. Naturally, a pressure bending down the line
+would be conceived as working in a vertical direction, and the line
+would be treated as another (80×10)--giving, as is the case,
+symmetrical positions. Thus, we may consider the principle of the
+suggestion of movement by a curve, as giving the same effect as if the
+movement suggested had actually taken place, to have been established,
+the positive evidence being strong, and the exceptions accounted for.
+It is worth noting that the curve-out series are always more
+irregular--the subject repeating that it is always harder to choose
+for that position. Probably the demands of space-filling come into
+sharper conflict with the tendency to mechanical balance, which for
+the outward curve would always widely separate the two lines.
+
+Exp. V. Curve III. See Fig. 12, III.
+
+A series with the upper end turned out from the center was unanimously
+pronounced as ugly. The inward position only appears in the results,
+which are given in full.
+
+
+(_a_) F. (80×10), V. CURVE.
+
+  F.                V.
+             O.               C.
+
+   40     106 126       68  73
+   80     106 128      109 102
+  120     140  88      156 110* 154   72*
+  160     104  66      182  80  136* 130*
+  200       X  52      178 220* 162
+
+
+(_b_) F. CURVE, V. (80×10)
+
+  F.                V.
+              O.              C.
+
+   40     126 122        73  80
+   80     122 128        66 112* 40
+  120      90 116        97 156* 55 105
+  160      65  43       120 182* 87 134
+  200      70  50       148  66
+
+
+This curve exemplifies the same principles as the preceding. _O_ takes
+the natural mechanical choice from (_a_) F. 40 to F. 120, and from
+(_b_) F. 120 to F. 200. A mechanical choice, however, for (_a_) F. 120
+ff., and for (_b_) F. 40 to F. 120, would have brought the lines too
+far apart in (_a_), and too near together in (_b_), hence the
+reversal. _C_ inclines always to the mechanical choice, but recognizes
+the other point of view in his second choices.
+
+Exp. V. Curve IV. See Fig. 12, IV.
+
+    Curve in.
+
+    (_a_) F. (80×10), V. Curve.
+
+    _C_ puts V. always further than F. and, even for F. 200, has
+    V. 230, X. _O_ puts V. farther up to F. 120, then puts it
+    nearer than F., and always refuses to choose for F. 200.
+
+    (_b_) F. Curve, V. (80×10).
+
+    _C_ always puts V. nearer than F. _O_ puts V. farther for F.
+    40 and F. 80, beyond that, nearer than F.; but refuses to
+    choose once each for F. 40, and F. 200.
+
+    The same principles of choice appear. _C_ maintains the
+    mechanical choice, and _O_ reverses it only beyond (_a_) F.
+    120, and up to (_b_) F. 120, to fill space well, showing his
+    preference for the mechanical choice by changing into it at an
+    unusually early point.
+
+Exp. V. Curve V. See Fig. 12, V.
+
+    Curve in.
+
+    (_a_) F. (80×10), V. Curve.
+
+    _C_ puts V. farther than F., except for F. 200, V. 125 and X.
+    _O_ also, changing as usual at F. 120 to V. nearer than F.
+
+    (_b_) F. Curve, V. (80×10).
+
+    _O_ puts V. always farther than F. _O_ has V. farther for F.
+    40 and F. 80, then nearer than F. Refuses to choose for F.
+    200. Results exactly parallel with those of Curve IV.
+
+Comparing all the results of this whole series of experiments on the
+suggestion of movement, we may conclude that movement, whether
+suggested by a whole line or part of a line, produces in terms of
+mechanical balance the same effect that the balanced object would
+produce after the completion of the suggested motion. This tendency to
+balance, it appears, lies at the basis of our preference; it often
+gives way, however, before considerations of space-filling, when the
+figure which on the scheme of mechanical balance is weaker, gains
+interest and so 'heaviness' by being brought nearer the center.
+
+
+_D. Experiments on Interest._
+
+By intrinsic interest is meant the interest which would attach to an
+object quite apart from its place in the space composition. In a
+picture it would be represented by the interest in an important
+person, in an unusual object, or in an especially beautiful object, if
+that beauty were independent of the other forms in the picture--as,
+for instance, a lovely face, or a jeweled goblet, etc. When the
+question of the influence of interest on composition came to be
+discussed, it was found very difficult to abstract the form of the
+object from the content presented; still more difficult to obtain an
+effect of interest at all without the entrance of an element of form
+into the space arrangement. Disembodied intellectual interest was the
+problem, and the device finally adopted seemed to present, in as
+indifferent a form as possible, a content whose low degree of absolute
+interest was compensated for by constant change. Stamps of various
+countries in black and white reproductions and very small outline
+pictures on squares of the same size as the stamps were taken as
+material. The figures were so small in relation to the board that any
+influence on composition of the lines composing them was impossible;
+the outline pictures, indeed, gave to the eye which abstracted from
+their content an impression scarcely stronger than the neighboring
+blank square.
+
+The first set of experiments (VI.) had a small outline picture on the
+side, and on the other a white paper square of the same size. The
+necessary interest was given in the form of novelty by changing the
+picture for every choice. The subjects were _M_, _G_ and _D_. The
+results were of the same type for each subject and could therefore be
+averaged.
+
+Exp. VI. (1).
+
+    _(a)_ F. Picture, V. Blank. Eight choices for each. _M_,
+    Average: V. 17 mm. farther from center. _G_, Average: V. 10
+    mm. farther from center. (Symmetrical position beyond F. 120.)
+    _D_, Average: V. 25.8 mm. farther from center.
+
+   _(b)_ F. Blank, V. Picture. _M_, Average: V. 33 mm. nearer
+   center. _G_, Average: V. 4 mm. nearer center. (Symmetrical
+   beyond F. 120.) _D_, Average: V. 30 mm. nearer center. (But V.
+   farther at F. 40.)
+
+These results are practically unanimous. They show that an object
+which possesses intrinsic interest acts like a mechanically heavy
+object, being placed nearer the center than a blank. Two marked
+deviations from the mechanical choice occur--although they have not
+affected the average sufficiently to destroy the general harmony of
+results. _G_, in both _(a)_ and _(b)_, chooses symmetrical positions
+from F. 120 on. His notes ['_(a)_ F. 140, V. 136, picture
+unimportant'; '_(b)_ F. 120 and ff., loses relation as they separate';
+'_(b)_ F. 160, picture makes no impression'] show clearly that for
+positions wide apart the picture, already a faint outline, becomes
+only a white square like the other and is put into geometrical
+symmetry.
+
+Exp. VI. (2), by _G_ and _D_. A stamp on one side unchanged, took the
+place of the blank; on the other side the stamp was changed for each
+choice.
+
+    _(a)_ F. unchanged stamp; V. changed stamp.
+
+    _D_. Two series, (1) V. always nearer center. (2) Same, except
+    F. 20, V. 52; F. 80, V. 94; F. 140, V. 152; F. 160, V. 175.
+
+    _G_. Two series. (1) V. much farther from center up to F. 140,
+    then nearer. (2) V. farther throughout, except F. 160, V. 121.
+
+    _(b)_ F. changed stamp; V. unchanged stamp.
+
+    _D_. Two series. (1) V. farther up to F. 100, then
+    symmetrical. (2) V. farther up to F. 100, then symmetrical or
+    nearer center.
+
+    _G_. Two series. (1) V. farther up to F. 120, then
+    symmetrical, and beyond F. 140, nearer center. F. 140, V. 63.
+    (2) V. much farther up to F. 120, then nearer center, but more
+    nearly symmetrical than (1). A complete series of second
+    choices beginning at F. 40, V. slightly nearer center than F.
+
+Analyzing results, we find the changed stamp, which has the interest
+of novelty, nearly always nearer the center than the unchanged. This
+would indicate a balance of the mechanical type, in which the interest
+makes an object 'heavier.' The exceptions are in _(a)_ four choices of
+_D_, _G_ to F. 140, and in _(b)_, _D_'s choice beyond F. 200, and
+_G_'s beyond F. 120. The deviations are thus seen to be all of the
+same type: for positions of F. near the center, when a mechanical
+choice would have brought V. still nearer [(_a_)], it is instead put
+farther away; for positions of F. far from the center, when a
+mechanical choice would have put V. still farther away [(_b_)], it is
+instead brought near. The exceptions are thus fully accounted for by
+the demand for space-filling.
+
+
+_E. Experiments on Depth._
+
+The experiments on suggestion of depth in the third dimension were as
+follows. It was desired to contrast two objects differing only with
+respect to the degree to which they expressed the third dimension.
+Those objects that do express the third dimension are, in general,
+views down streets, colonnades, corridors, gates, etc., or, in
+landscape, deep valleys, vistas between trees, distant mountains, etc.
+It is evident that representations of products of human handiwork
+would be less unnatural when isolated for experiment, and two pairs of
+pictures were accordingly prepared as follows: There was drawn on a
+square of 80 mm. the picture of the mouth of a railway tunnel, closed
+tightly by an apparently massive door; and another picture of
+identical form and surroundings, but showing the rails entering at a
+slight curve, the deep blackness within, and the small circle of light
+at the farther end. The second pair consisted of the gateway of a
+baronial castle, with heraldic bearings and closed iron-wrought doors;
+and the same gateway open, showing a flagged pavement and an open
+court with fountain beyond. The perspective effect was heightened by
+all possible means for both pictures, and care was taken to have the
+contrast of black and white the same for each pair, so that to the
+half-shut eye, opened and closed forms seemed to have the same tone.
+
+The subjects were directed to try to _feel_ the third dimension as
+vividly as possible--to project themselves down the vistas, as it
+were--and then to arrange the squares in the most pleasing manner. The
+experiments were made by _A_, _M_, _S_, _H_ and _D_. Not all made the
+same number of repetitions, but as their notes were unusually
+suggestive, I have made use of all the results, and shall quote the
+notes for the most part _verbatim_:
+
+
+Exp. VIII. F. Closed Tunnel. V. Open Tunnel.
+
+                 F.            V.
+  Subject _H_.   40            90
+                 60            57
+                 80            13
+                100            12
+                120            39
+                140           - 1
+                160           -32
+                180           -71, +50
+
+    _Notes._--_H_ finds that he neglects the closed tunnel almost
+    entirely, eye is constantly attracted to open tunnel, F. 180,
+    choice of evils. Position of closed tunnel makes the pictures
+    disagreeable. F. 80, V. 13, closed tunnel grows more
+    uninteresting as it goes out, while the open tunnel seems
+    heavier than ever. F. 140, V.-1, closed tunnel loses force and
+    doesn't gain weight. Open tunnel hangs together with the black
+    field beyond it.
+
+                 F.                     V.
+  Subject _S_.   40            85            95
+                 60           170           195
+                 80           160           180
+                100           185           200
+                120           185          - 35, 200
+                140            85            20
+                160           115           115
+                180                         100
+
+    _Notes._--F. 120, V. 185. After this there is too large a
+    black space between squares, and so a more central position is
+    taken, but there is the necessity of avoiding symmetry, which
+    is displeasing. F. 160, V. 115 is not symmetrical and so is
+    more pleasing. F. 60, V. 195:--the open tunnel holds the eyes,
+    while the other allows them to wander, and so it needs a
+    bigger field on each side. F. 80, V. 180:--a position close
+    together is possible, but it is hard to take them so except as
+    one picture, and that is also difficult. F. 100, V.
+    200:--there is the same objection to any position which seems
+    to be an acknowledgment of similarity; that is, symmetrical
+    position seems to imply that they are alike, and so is
+    disagreeable. F. 120, V.-35, 200:--now they can be close
+    together because the black tunnel harmonizes with the black to
+    the right, and seems to correspond in distance and depth,
+    while the tunnel 'hangs together' with the black to the left.
+    (Cf. _H_, F. 160, V.--32.) F. 140, V. 20:--when they are
+    together it is difficult to apperceive the frame as a whole;
+    but this position is not far apart, and not disagreeable
+    because the larger stretch of black to the right again hangs
+    together with the tunnel. F. 160, V. 115:--when the open
+    tunnel was in the middle, the closed one seemed to have no
+    business at all, therefore the open tunnel had to be moved
+    over. The only position which was not disagreeable.
+
+SUBJECT G.
+
+   F.                 V.
+          (1)     (2)     (3)     (4)¹    (5)¹
+   40      48      31      36      30      23
+   60     105      31      40      51      39
+   80     111      71      60      64      54
+  100     104      63      78      60      86
+  120     123      75      91      62     115
+  140     136      82     111      56     137
+  160     162      93     148      72     156
+  180     107     115     181      83     176
+
+    ¹Second pair (Court).
+
+    _Notes._--(1) All quite unsatisfactory. The arrangement
+    difficult to apperceive as a whole. Each picture taken by
+    itself. (2) The tunnel closed doesn't amount to much. (3) The
+    significance of the tunnel gives it weight. For F. 160, V.
+    148, and F. 180, V. 180, relation difficult. (4) Court closed
+    gets weaker as gets farther from center. (5) At F. 100, begins
+    to lose relation between pictures, as if one were in one room,
+    one in another.
+
+SUBJECT A.
+
+   F.                         V.
+         (1)     (2)     (3)     (4)²   (5)²
+   40     70      66     140      59     130
+   60     80      73     159      62     138
+   80    103      71     120      77     134
+  100    113      94     108      93     100
+  120    119      88      96      96      63
+  140    108      92      60,164  82      43
+  160     92     118      70     109      50
+  180    130     154      78     101      50
+
+     ²Second pair (Court).
+
+    _Notes_.--(1) Difficult to apperceive together. From F. 140,
+    V. 108, depth is more strongly imagined. (3) Tunnel closed has
+    not much value. (5) F. 80, V. 134, taken with reference both
+    to frame and to the other picture--must not be symmetrical nor
+    too far out.
+
+SUBJECT D.
+
+   F.                             V.
+               (1)          (2)          (3)
+   40          100          47            38
+   60           75          60            68
+   80          104          78            80
+  100          148, -12    104           120
+  120          159         166           160
+  140          182         152, 84, 78   168
+  160          193         184, -75      180
+  180          200        - 95, 190      190
+
+    _Note_.--F. 100, V.-12; F. 140, V.-52; F. 160, V. -75: they
+    must be close together when on the same side.
+
+                F.                   V.
+                            (1)           (2)¹
+  Subject M.   40            55            50
+               60            56            74
+               80            64            84
+              100            86           102
+              120            93           111
+              140           124           130
+              160           134           146
+              180           144           178
+
+    ¹Second pair (Court).
+
+    _Note_.--(1) Quite impossible to take both together; necessary
+    to keep turning from one to the other to get perception of
+    depth together with both.
+
+
+The subjects agree in remarking on the lack of interest of the closed
+tunnel, and the attractive power of the open tunnel, and notes which
+emphasize this accompany choices where the open tunnel is put
+uniformly nearer. (Cf. _H_, F. 180, V. 50; F. 80, V. 13; _G_, (2),
+(3), (4), (5); _A_, (3), and F. 140.) As a glance at the results shows
+that the open tunnel is placed on the whole nearer the center, we may
+conclude that these choices represent a mechanical balance, in which
+the open tunnel, or depth in the third dimension, is 'heavier.'
+
+But another point of view asserts itself constantly in the results of
+_S_, and scatteringly in those of the others. Analyzing at first only
+the results of _S_, we find that up to F. 140, with one exception, he
+places the open tunnel much farther out than the other; and from F.
+140 on, nearer. He says, F. 120, V. 185, 'After this there is too
+large a black space'; that is, in bringing the open tunnel in, he is
+evidently filling space. But why does he put the open tunnel so far
+out? It seems that he is governed by the desire for ease in the
+apperception of the two objects. In his note for F. 80, V. 180, this
+point of view comes out clearly. He thinks of the objects as being
+apperceived side by side with the space about each (which apparently
+takes on the character of its object), and then he seems to balance
+these two fields. Cf. F. 60, V. 195: 'The closed tunnel allows the
+eyes to wander, and so it needs a bigger field on each side.'
+Evidently there is an implication here of the idea of balance. Cf.
+also F. 120: 'The black tunnel harmonizes with the black to the right,
+and seems to correspond in distance and depth,' while the closed
+tunnel 'hangs together with the black on the left.' In brief, the view
+of F. seems to be that the closed tunnel is less interesting, and
+partly because it 'allows the eyes to wander,' partly as compensation
+for the greater heaviness of the open tunnel, it takes with it a
+larger space than the open tunnel. It is on the whole better to put
+them apart, because it is more difficult to apperceive them when close
+together, and so the open tunnel in the earlier choices must, of
+course, go farther from the center. When these points conflict with
+the necessity of filling space, the open tunnel comes nearer the
+center. In general, the notes which emphasize the difficulty of
+apperceiving the two pictures as flat and deep together accompany
+choices where the tunnel is put uniformly farther out, or
+symmetrically. Cf. _G_, (1), (5); _A_, (1); _M_, F. 40, etc.
+
+Thus we may continue to separate the two points of view, that of
+mechanical balance and that of another kind of balance, which we have
+known heretofore as 'space-filling,' made possible by the power of the
+center to give 'weight,' but which seems to be now more explicitly
+recognized as a balancing of 'fields.' At this point we need repeat
+only, however, that the suggestion of depth in the third dimension
+seems to confer 'weight,' 'heaviness,' 'balancing power' on its
+object.
+
+Before making a general survey of the results of this chapter, it is
+necessary to consider a type of choice which has been up to this
+point consistently neglected--that in which the variable has been
+placed on the same side of the center as the fixed object. On the
+theory of balance, either in its simple mechanical form or in its
+various disguises, this choice would at first seem to be inexplicable.
+And yet the subjects usually took special pleasure in this choice,
+when they made it at all. These minus choices are confined to three or
+four subjects and to two or three experiments. Exp. I. (a) and (b)
+show the largest number. We have:
+
+
+    EXP. I. (_a_) F. (80×10); V. (160×10).
+     F.                           V.
+    120                   - 44,
+    160                   -150, -105,  -88
+    200                    -94,  -46, -110
+
+        (_b_) F. (160×10); V. (80×10).
+     F.                           V.
+    120                      -70, -80
+    160                     -114
+    200                     -155, -146, -148
+
+
+It will be noticed that, with two exceptions, none of the positions
+chosen are nearer than 70 mm. to the center, and that most of them are
+much farther away. The two lines seem to be more pleasing when they
+are pretty close together on the same side. _S_, in I. (_b_) F. 120,
+V.-70, notes: 'If V. is nearer _O_, there is a tendency to imagine a
+figure by the connection of the ends of the two lines, which is
+disagreeable. 'The only other minus choices were in Exp. VII., by
+_S,_, _H_, and _D_. _S_, F. 120, V.-35, says: 'Now they can be close
+together,' and _H_, F. 140, 160 and 180, V. -1, -32, -71, notes the
+same. So also _D_, F. 100, V. -12; F. 140, V. -52; F. 160, V. -75; F.
+180, V. -95. It is evident from this insistence on the closeness
+together of the objects, and this desire to form no figure, that the
+two are taken as one, and set off against the blackness on the other
+side. It seems as if this were not taken as empty space, but acquired
+a meaning of its own. The association with pictures in which the empty
+space is occupied by a deep vista or an expanse of sky is almost
+irresistible. The case of Exp. VII. seems a little different. _S_, at
+least, separates the two fields as usual, but for him also the black
+space is living, 'corresponds in distance and depth.' It is at least
+certain that there is no subjective feeling of emptiness or of
+unoccupied energies on the empty side. And it would seem that some
+influence from the objects sweeps across the central field and
+vitalizes it. The most natural view would seem to be that the ease of
+apperception of the two objects together, and the tendency of the eye
+movement to begin on the occupied side, and to sweep across to the
+unoccupied, which we think of as deep, combine to give a feeling of
+pleasure and of balance.
+
+       *       *       *       *       *
+
+We have now reached a point from which a backward glance can be cast
+upon the territory traversed. Experiment with the isolated elements in
+pictorial composition has shown that pleasing arrangements of these
+elements can be interpreted by the formula of mechanical balance. This
+principle was obtained by opposing two lines whose relative value
+(corresponding to 'weight' in balance) was known; and it was found
+that their relative positions corresponded to the relation of the arms
+of a balance. Further opposition of lines, of which one was already
+determined in 'weight,' showed the same variations and suggested
+certain valuations of the undetermined lines on the basis of this
+common term of weight. Thus, the line suggesting movement out from the
+center fitted the formula if taken as 'heavy' and _vice versa_, the
+line suggesting movement in, if taken as 'light.' Similarly, objects
+of interest and objects suggesting movement in the third dimension
+were 'heavy' in the same interpretation. But this interpretation, in
+its baldest form, fitted only a majority of the pleasing arrangements;
+the minority, in which the consistent carrying out of the lever
+principle would have left a large unoccupied space in the center,
+exactly reversed it, bringing the 'light' element to the center and
+the 'heavy' to the outer edge. Later experiments showed that this
+choice implied a power in the 'lighter' objects, owing to their
+central position, to cover or infuse with vitality the empty space
+about them, so that the principle of balance seemed to maintain itself
+in one form or another.
+
+All this does not go beyond the proof that all pleasing space
+arrangements can be described in terms of mechanical balance. But
+what is this mechanical balance? A metaphor, no matter how
+consistently carried out, explains nothing. The fact that a small
+object far from the center is usually opposed by a large object near
+the center tells us nothing of the real forces involved. Physical
+balance can be explained by principles of mechanics, but no one will
+maintain that the visual representation of a long line weighs more
+than that of a short one. Moreover, the elements in the balance seem
+utterly heterogeneous. The movement suggested by an idea--the picture
+of a man running--has been treated as if equivalent to the movement
+actually made by the eye in following a long line; the intrinsic
+interest--that is, the ideal interest--of an object insignificant in
+form has been equated to the attractive power of a perspective which
+has, presumably, a merely physiological effect on the visual
+mechanism. What justification can be given either of this
+heterogeneous collection of elements or of the more or less arbitrary
+and external metaphor by which they have been interpreted?
+
+I believe that the required justification of both points of view is
+given in the reduction of all elements to their lowest term--as
+objects for the expenditure of attention. A large object and an
+interesting object are 'heavy' for the same reason, because they call
+out the attention; a deep perspective, because the eye rests in
+it;--why, is another question. And expenditure of effort is
+expenditure of attention; thus, if an object on the outskirts of the
+field of vision requires a wide sweep of the eye to take it in, it
+demands the expenditure of attention, and so is felt as 'heavy.' It
+may be said that involuntary attention is given to the object of
+intrinsic interest, while the uninteresting object far on the
+outskirts needs a voluntary effort to perceive it, and that the two
+attitudes cannot be treated as identical. To this it may be answered
+that an object on the outskirts of a field of view so definitely
+limited calls out of itself a reflex movement of the eye toward it, as
+truly spontaneous as the impulse toward the object of intrinsic
+interest. But what is 'the expenditure of attention' in physiological
+terms? It is nothing more than the measure of the motor impulses
+directed to the object of attention. And whether the motor impulse
+appears as the tendency to fixate an object or as the tendency to
+follow out the suggestions of motion in the object, they reduce to
+the same physiological basis. It may here be objected that our motor
+impulses are, nevertheless, still heterogeneous, inasmuch as some are
+_toward_ the object of interest, and some _along_ the line of
+movement. But it must be said, first, that these are not felt in the
+body, but transferred as values of weight to points in the picture--it
+is the amount and not the direction of excitement that is counted; and
+secondly, that even if it were not so, the suggested movement along a
+line is felt as 'weight' at a particular point.
+
+From this point of view the justification of the metaphor of
+mechanical balance is quite clear. Given two lines, the most pleasing
+arrangement makes the larger near the center, and the smaller far from
+it. This is balanced because the spontaneous impulse of attention to
+the near, large line, equals in amount the involuntary expenditure of
+attention to apprehend the small farther one. And this expenditure of
+motor impulses is pleasing, because it is the type of motor impulses
+most in harmony with our own physical organism.
+
+We may thus think of a space to be composed as a kind of target, in
+which certain spots or territories count more or less, both according
+to their distance from the center and according to what fills them.
+Every element of a picture, in whatever way it gains power to excite
+motor impulses, is felt as expressing that power in the flat pattern.
+A noble vista is understood and enjoyed as a vista, but it is
+_counted_ in the motor equation, our 'balance,' as a spot of so much
+intrinsic value at such and such a distance from the center. The
+skilful artist will fill his target in the way to give the maximum of
+motor impulses with the perfection of balance between them.
+
+
+IV. SYMMETRY IN PICTURES.
+
+
+_A. The Balancing Factors._
+
+The experimental treatment of suggestions as to the elements in
+pictorial composition has furnished an hypothesis for the basis of our
+pleasure in a well-composed picture, and for the particular function
+of each of the several elements. This hypothesis may be expressed as
+follows: (1) The basis of ęsthetic pleasure in composition is a
+_balance of motor impulses_ on the part of the spectator; (2) this
+balance of motor impulses is brought about by means of the elements,
+through the power which they possess of drawing the attention with
+more or less strength towards a certain field. But to the experimental
+working out of an hypothesis must succeed a verification, in its
+application to the masterpieces of civilized art. We have, then, to
+ask whether there is in all great pictures a balance, _i.e._, an equal
+distribution of attention on the two sides of the central line
+suggested by the frame of the picture. It might be, for instance, that
+a picture of pleasing composition would show, when analyzed, all the
+attractions for attention on one side; which would go far to impugn
+either our hypothesis of balance as the basis of pleasure, or our
+attribution of particular functions to the elements. But as this
+second matter may be considered to have been sufficiently determined
+by the results of the preceding section, the first question only
+remains: Is there a balance of attention in a good picture--or rather,
+in the particular good pictures known to the student of art?
+
+This question could only be answered by the examination of a large
+number of pictures of accepted merit, and it was also desirable that
+they should be studied in a form which lent itself to the easy
+comparison of one picture with another. These conditions seemed to be
+best fulfilled by the collection of reproductions in black and white
+known as the _Classischer Bilderschatz_, published by F. Bruckmann, at
+Munich, which contains over a thousand pictures arranged in schools.
+Of these a thousand were taken--substantially the first thousand
+issued, after the frescoes, triptych doors, panels, etc., which are
+evidently parts of a larger whole, had been laid aside. In the
+following discussion the pictures will be designated, when they are
+not further described, by the numbers which they bear in this
+collection.
+
+The equations in the following discussion are based on a system of
+exact measurement, corresponding to that followed in the experimental
+section. This numerical treatment is pre-supposed in all the general
+attributions of balance in the analysis of single pictures. The method
+of measurement was given by the conditions of viewing pictures, which
+are framed and thus isolated from surrounding influences, and
+referred, as compositions, to the middle line suggested by this
+emphasized frame. An adjustable frame of millimeter paper, divided in
+half vertically by a white silk thread, was fitted over the picture to
+be measured, and measurements were made to left and to right of this
+thread-line and, as required, vertically, by reference to the
+millimeter frame divisions.
+
+The main question, of course, to be answered by a statistical
+examination of these thousand pictures refers to the existence of
+balance, but many other problems of symmetry are also seen to be
+closely involved; the relative frequency of the elements in pictures
+of different types, and the result of their employment in producing
+certain emotional effects, also the general types of space arrangement
+as a whole, the feeling-tone belonging to them, and the relation
+between content and shape. The first question will not be treated in
+this paper in the statistical fulness which was necessary to establish
+my conclusions in the investigation itself, inasmuch as the tables
+were very extensive. But examples of the tables, together with the
+full results, will be given, and a sufficient amount of detailed
+discussion to show my methods. The two other subjects, the use of the
+elements and the types of composition, will be briefly treated. I
+expect in other publications to go more closely into statistical
+detail on these matters than is possible in a merely experimental
+thesis.
+
+In the beginning of the proposed statistical analysis a natural
+objection must first be forestalled: it will be said, and truly, that
+color also has its effect in bringing about balance, and that a set of
+black and white reproductions, therefore, ignores an important
+element. To this it may be answered, first, that as a matter of fact
+the color scheme is, as it were, superimposed upon the space-shape,
+and with a balance of its own, all the elements being interdependent;
+and secondly, that the black and white does render the intensity
+contrasts of the colors very well, giving as light and dark, and thus
+as interesting (= attractive) and the reverse, those factors in the
+scheme which are most closely related to the complex of motor
+impulses. After having compared, in European galleries, the originals
+of very many of these reproductions with the equation of balance
+worked out from the black and white, the writer has seldom found an
+essential correction needed.
+
+The pictures were first classified by subjects. This may seem less
+logical than a division by types of arrangement. But it really, for a
+majority, amounted to the same thing, as the historical masterpieces
+of art mostly follow conventional arrangements; thus the altarpieces,
+portraits, genre pictures, etc., were mostly after two or three
+models, and this classification was of great convenience from every
+other point of view. The preliminary classification was as follows:
+(1) Religious, Allegorical and Mythical Pictures; (2) Portraits; (3)
+Genre; (4) Landscape. The historical pictures were so extremely few
+that they were included in the religious, as were also all the
+allegorical pictures containing Biblical persons. Some pictures, of
+which Watteau's are representative, which hovered between genre and
+landscape, were finally classified according as they seemed to owe
+their interest to the figures or to the scenery. A preliminary
+classification of space arrangements, still with reference to content,
+showed three large general types: (1) A single subject or group in the
+middle; (2) the same somewhat on one side, with subordinate elements
+occupying the rest of the space; (3) two objects or groups each
+occupying a well-defined center. These were designated as Single
+Center, Single and Subordinate Center, and Double Center pictures, or
+S.C., S. & S., and D.C. They are in proportions of S.C. 79 per cent.,
+S. & S. 5 percent., D.C. 16 per cent. The D.C. type is evidently
+already explicitly balanced as regards shape and intrinsic interest,
+and is hence of comparative unimportance to our problem. The S.C. will
+show a balance, if at all, in more or less accessory factors; S. & S.,
+broadly, between interest and other factors. As logically more
+important, this last group will be treated more fully. The full
+classification of the thousand pictures by subjects is as follows:
+
+
+                                    S.C.   D.C.   S.S.
+  Altarpieces                 78     70      7      1
+  Madonna & Child             47     47      0      0
+  Holy Family                 67     40     14     13
+  Adorations                  19     19      0      0
+  Crucifixions                23     21      0      2
+  Descents f. Cross           27     26      0      1
+  Annunciations               21      0     21      0
+  Misc. Religious            162     93     55     14
+  Allegorical                 46     36      6      4
+  Genre                       93     63     19     11
+  Landscape                   88     65     22      1
+  Portrait Groups             64     42     17      5
+  Relig. Single Fig.          28     28      0      0
+  Alleg. Single Fig.          12     12      0      0
+  Portrait Single Fig.       207    207      0      0
+  Genre Single Fig.           18     18      0      0
+
+
+Altarpieces.
+
+The pictures of the first group, consisting of the _Madonna_ and
+_Infant Christ_ surrounded by worshippers, and briefly designated as
+Altarpieces, are good for detailed study because they present a simple
+type, and it will be easy to show whether the variations from symmetry
+are in the direction of balance or not. A few examples will make this
+clear. The Madonna in the S.C. pictures is invariably seated holding
+the Christ.
+
+In the following descriptions M. will denote Madonna, C. Child, Cn.
+central line. The elements, Size or Mass, Direction of Motion or
+Attention, Direction of Line, Vista, and Interest, will be set down as
+Ms., D., L., V., and I. A couple of examples will show the method of
+describing and of drawing a conclusion as to balance.
+
+1. 969. Lorenzo Lotto, _Madonna with St. Bernard and St. Onofrius._ C.
+is on one side turning to the same; M. leans far to the other; hence
+interest in C., and direction of C.'s attention are over against Mass
+of M. and direction of M.'s attention; _i.e._, I. + D. = Ms. + D., and
+so far, balance. The surrounding saints are insignificant, and we may
+make the equation I. = Ms.
+
+2. 368. Raffaelino di Francesco, _Madonna Enthroned._ The C. is on
+Right facing front, M. turns away Left, hence interest in C. is over
+against direction of M.'s attention. Moreover, all the saints but one
+turn Left, and of two small vistas behind the throne, the one on the
+Left is deeper. The superior interest we feel in C. is thus balanced
+by the tendency of attention to the opposite side, and we have I. = D.
++ V.
+
+It is clear that the broad characteristics of the composition can be
+symmetrically expressed, so that a classification of the 70 S.C.
+altarpieces can be made on a basis of these constant elements, in the
+order of decreasing balance. Thus: Class 1, below, in which the C. is
+one side of the central line, turned away from the center, the M.
+turned to the other, balances in these broad lines, or I. + D. = D.;
+while in (9), I. + D. + D. = (x), the constant elements work all on
+one side.
+
+
+CLASSIFICATION OF ALTARPIECES.
+
+   1 C. one side turned to same,  M. to other            11
+   2 "     "         "     other, "       "               8
+   3 "     "         "     front, "       "               2
+   4 "     "         "     other, M. front.               9
+   5 "     "         "     facing M.                      6
+   6 "     "         "     front, M. front.               7
+   7 "     "         "       "    M. turned to same.      6
+   8 "     "         "    to same M. turned front.        7
+   9 "     "         "       "    M.     "   to same,    14
+  10 " in middle, turned front.                           0
+
+
+Thus the constant elements, understanding always that C. has more
+interest than M., are as follows: For (1) I. + D. = D.; (2) I. = D. +
+D.; (3) I. = D.; (4) I. = D.; (5) I. + D. = D.; etc. These are in
+order of complete balance, but it will be seen that from (7) on, while
+the factors are constant, the framework is not balanced; _e.g._ in (9)
+both I. and D. work on the same side. For these groups, therefore, the
+variations, if there is balance, will be more striking. Eliminating
+the balancing elements in the framework, the tables for the ten groups
+are:
+
+
+  (1)  I. + D. = D.     (2)  I. = D. + D(M).   (3)  I. = D.
+  969. I. = Ms.           680. I. = D.        1094. Ms. + I. = I. + D.
+  601. I. = Ms.           735. I. = D.          33. I. = I. + D
+   49. I. = Ms. + I.     1121. I. = D.
+  634. I. = Ms. + I.     1035. I. = D.         (4)  I. = D.
+  584. I. = I.            333. I. = I. + D.    775. I. = D.
+  686. I. = I.             80. I. = I. + D.    746. I. = D.
+  794. I. = D.            753. I. = I. + D.   1106. I. = Ms. + D.
+  164. I. = D.           1114. I. = D. + L.    781. I. = Ms. + D.
+  368. I. = D. + V.                           1131. I. = I. + D.
+  927. I. = V.                                 517. I. = I. + D.
+  273. I. = V.                                 327. I. + Ms. = D. + V.
+                                               951. I. + L. = D. + V.
+                                               715. Unbalanced.
+
+  (5)  I. + D. = D.       (6)  I. =                 (7)  I. + D. =
+   43. I. = I.            854. I. = Ms.         725. I. + D. = I. + L.
+  711. I. = I.           1148. I. = I.          206. I. + D. = I. + L.
+  447. I. = Ms.           709. I. = D.          155. I. + D. = D. + L.
+  643. I. = Ms.           907. I. = D.          739. I. + D. = L.
+  777. I. = Ms. + I.      586. I. = Ms. + I.    331. I. + D. = V.
+  637. I. = Ms. + I.      137. I. = Ms. + I.    980. Unbalanced.
+                          187. Unbalanced.
+
+  (8)  I. + D. =           (9)  I. + (D. + D.) =           (10)  0.
+   57. I. + D. = Ms.      835. I. + D. = Ms + I.
+  979. I. + D. = I. + L.  724. I. + D. = Ms + L.
+  134. I. + D. = D.       495. I. + D. = Ms + L.
+  106. I. + D. = D. + V.  182. I. + D. = Ms + V.
+  220. I. + D. = L.       817. I. + D. = I.
+  118. I. + D. = V. + L.  662. I. + D. = I.
+  157. Unbalanced.        806. I. + D. = I.
+                         1136. I. + D. = I. + L.
+                          865. I. + D. = I. +  V.
+                         1023. I. + D. = V.
+                          531. I. + D. = L.
+                          553. I. + D. = L.
+
+
+The most used element is I., in 100 per cent. of cases; the least
+used, V., 13 per cent. D., in 91 per cent. of cases; Ms., 26 per
+cent.; L., 19 per cent. 175, 433, unbalanced.
+
+As seen in the table, a balance of elements is kept, except in four
+cases which will be hereafter considered. In all cases the balance is
+between the interest in C., sometimes plus D., (in the attention of
+the figures to C.), on the one side, and other elements on the other.
+Very seldom are other salient points found on the C. side. When the C.
+side is especially 'heavy,' the number of opposing elements increases,
+and especially takes the form of V. and L. [cf. (7), (8), (9)], which
+were observed in the experimental chapter to be powerful in attracting
+attention. For the fairly well-balancing framework--(i), (2), (3) and
+(4)--Ms., I., and D. are much more often the opposing elements.
+
+The pictures listed as unbalanced are, with one exception, among the
+oldest examples given; conceived in the most slavish geometrical
+symmetry in which, indeed, the geometrical outline almost hides the
+fact that the slight variations are all toward a lack of balance.
+
+There is but one S. & S. case (1054), Titian, _The Madonna of the
+House of Pesaro_. In this, M. and C. are on a high throne on the
+Right, other figures lower down on the Left bearing a flag that leans
+back to the Left. All the lines of the figures and of the massive
+architecture and the general direction of attention bear down so
+strongly to Left that the importance of the Right figures is balanced.
+We should have, then, I. = I. + L. + D. The D.C. cases, seven in
+number, are remarkably alike. Six have a vista separating the two
+groups, in five remarkably deep and beautiful, as if to fix the
+oscillating attention there. In all, M. and C., either in position or
+by the direction of their lines, are nearer the Cn. than the opposing
+figures, which are naturally less interesting, thus giving an instance
+of the mechanical balance. Their general equation, then, would be I. =
+M. or M. + L. Having shown that the small variations from the general
+symmetrical type of altar-pieces are invariably, except in primitive
+examples, in the direction of substitutional symmetry, or balance, we
+may next study the Madonna pictures, using the same classifications
+for purposes of comparison.
+
+
+MADONNA WITH INFANT CHRIST.
+
+  (1)  I. + D. = D.   (2)  I. = D. + D.         (4)  I. = D.
+   56. I. = L.        271. I. = D. + L.         668. I. = D. + Ms.
+  332. I. = L.        867. I. = D. + V. + D.     14. I. = D. + I.
+  633. I. = D.                                   91. I. = D. + V.
+                      (3)  I. = D.             1111. I. = D. + V.
+                      144. I. = D.             1011. I. = D. = L.
+                      521. I. = D.              915. I. = D. = L.
+                                                356. I. = L. + D. + D.
+                                                296. I. + Ms. = V. + L.
+
+             (5)  I. + D. = D.                (6)  I. =
+          51. I. = D.                   596. I. = Ms.
+         581. I. = D.                   892. I. = Ms.
+         829. I. = D. + I.                224. I. = I. + D.
+         159. I. = I. + D.                908. I. = D. + L.
+         683. I. = D. + L.
+        1045. I. = I. + L.                    (7)  I. + D. =
+         745. I. = I. + L.                344. I. + D. = Ms.
+         734. I. = D. + L.                949. I. + D. = Ms. + V. + L.
+         404. I. = D. + L.                608. I. + D. = L.
+         248. I. = L.                   524. I. + D. = L.
+          37. I. = L.
+          97. I. = L.                         (8)  0.
+         363. I. = V. + L.
+         674. I. = V. + L.                    (9)  I. + D. + D. =
+          62. I. = V. + L.                361. I. + D. = L.
+        1142. I. = V. + L.
+        1018. I. = V. + L.                        (10)
+         110. I. + V. = Ms. + L.            538. I. = D.
+         411. I. + V. = Ms. + L.            614. I. + Ms. = V.
+         771. I. + Ms. = V. + L.             34. D. = Ms. + L.
+
+
+Most used element, I., 100 per cent.; least used, Ms., 21 per cent.
+D., 96 per cent.; L., 64 per cent.; V., 27 per cent.
+
+The first thing to be noted, on comparing this table with the
+preceding, is the remarkable frequency of the use of the vista and the
+line. Among the altarpieces, the direction of attention was the
+element most often opposed to the interesting object; and next to
+that, another object of interest. These two elements, however, here
+sink into comparative insignificance. In general, balance is brought
+about through the disposition of form rather than of interests. This
+appears in comparing the numbers; against the use of L. in 19 per
+cent. of the cases among the altarpieces, we have 64 per cent. among
+the Madonna pictures; V. is used in the former cases 13 per cent. of
+the times, in the latter 27 per cent. The reason for this would appear
+to be that the lack of accessories in the person of saints,
+worshippers, etc., and the consequent increase in the size of M. and
+C. in the picture heightens the effect of any given outline, and so
+makes the variations from symmetry greater. This being the case, the
+compensations would be stronger--and as we have learned that V. and L.
+are of this character, we see why they are needed. None of the M. and
+C., S.C. pictures fails to give a complete balance of elements
+according to hypothesis. There are no well-defined cases of S. & S. or
+D.C.
+
+
+Portraits.
+
+A study of the Madonna pictures of all types, then, results in an
+overwhelming confirmation of the hypothesis of substitutional
+symmetry. It may be objected that the generally symmetrical framework
+of these pictures suggests a complete balance, and the next step in
+our analysis would, therefore, be a type of picture which is less
+bound by tradition to the same form. The portrait would seem to
+combine this desideratum with generally large and simple outlines, so
+that the whole surface can be statistically reported with comparative
+ease. A detailed analysis of a couple of portraits may justify the
+classification adopted.
+
+900. Anton Raphael Mengs, _Self-Portrait_. The head of the painter is
+exactly in Cn., but is turned sharply to Right, while his shoulders
+turn Left. His arm and hand are stretched out down to Right, while his
+other hand, holding pencil, rests on his portfolio to Left. Hence, the
+D. of attention plus that of L. on Right, balances I. in implements,
+plus D. of body on Left, or D. + L. = D. + I.
+
+438. B. van der Helst, _Portrait of Paul Potter_. The head of the
+subject is entirely to Left of Cn., his easel on Right. His body is
+turned sharply to Right, and both hands, one holding palette and
+brushes, are stretched down to Right. His full face and frontward
+glance are on Left. Hence, Ms. + I. in person balances I. in
+implements + D. of L., or Ms. + I. = I. + L.
+
+It is seen that the larger elements in these pictures are the
+directions of the head and body, and the position of the head, with
+reference to Cn. The following classification is based on this
+framework.
+
+
+CLASSIFICATION OF PORTRAITS.
+
+            A. Head in Cn.
+    I. Body front, head front,                       6
+   II. Body turned, head turned other way,           7    D. = D.
+  III. Body turned, head front,                     31    D. =
+   IV. Body front, head turned,                      1    D. =
+    V. Body turned, head turned same way,          106    D. + D. =
+
+            B. Head not in Cn.
+   I. Body turned to empty side, head to same,      18    Ms.=D.
+   II. Body turned to empty side, head front,       23    Ms. = D.
+  III. Body turned to empty side, head to other,     3    Ms. + D. = D.
+   IV. Body front, head front,                       2    Ms. =
+    V. Body turned from empty side, head same way,  10    Ms. + D. =
+
+
+This is also in order of less complete balancing of the original
+elements. The principal characteristics of the different divisions are
+as follows:--
+
+A.
+     I. (Symmetrical.) Most used element, L.; least used, V.
+
+    II. (Balanced, D. = D.) Most used element, L.; least used, V.
+
+   III. (D. = .) Most used element, Ms., in 74 per cent, of cases
+        opposed to D.; in 30 per cent, of cases, D. of glance opposed
+        to D. of body; least used, V. (1 per cent.).
+
+    IV. One case only.
+
+    V. (D. = .) Most used element, Ms., in 73 per cent. of cases
+        opposed to D.; in 40 per cent. of cases, D. of glance opposed
+        to D.; in 28 per cent. Ms. + D. of glance opposed to D.; least
+        used element, V. (15 per cent.). I. 39 per cent.; L. 38 per cent.
+
+B.
+     I. (Balanced, Ms. + I. = D.) Most used element (not counting
+        those already included in equation), I., 55 per cent.; least
+        used, V., 2 per cent.; L., 50 per cent. In 44 per cent., D. of
+        glance opposed to D.
+
+    II. (Ms. + I. = D.) Most used element (not in equation), I., 52
+        per cent. Least used, V., 26 per cent. L., 43 per cent. In 21
+        per cent., D. of glance opposed to D.
+
+   III. (Ms. + I. + D. = D.) Three cases. Two cases V. on empty
+        side.
+
+    IV. (Ms. + I. = .) Two cases. One case V. on empty side.
+
+     V. (Ms. + I. + D. = .) Most used element, L., 60 per cent.;
+        least used, V., 10 per cent.; 33-1/3 per cent., D. of glance to
+        empty side.
+
+The portrait class is an especially interesting object for study,
+inasmuch as while its general type is very simple and constant, for
+this very reason the slightest variations are sharply felt, and have
+their very strongest characteristic effect. We shall, therefore, find
+that the five principal factors in composition express themselves very
+clearly. The general type of the portrait composition is, of course,
+the triangle with the head at the apex, and this point is also
+generally in the central line--in 73 per cent. of the whole number of
+cases, as is seen from the table. All cases but one are longer than
+they are wide, most are half-length or more. Nevertheless, great
+richness of effect is brought about by emphasizing variations. For
+instance, the body and head are, in the great majority of cases,
+turned in the same way, giving the strongest possible emphasis to the
+direction of attention--especially powerful, of course, where all the
+interest is in the personality. But it is to be observed that the very
+strongest suggestion of direction is given by the direction of the
+glance; and in no case, when most of the other elements are directed
+in one way, does the glance fail to come backward. (Cf. A. II., V.,
+and B. I., II., V.)
+
+A. It is of especial value for our conclusions that that division in
+which the constant elements are least balanced (V.) is far the most
+numerous. Comparison of this with III. shows that the principal
+element, direction of movement of head or body, is balanced by the
+larger mass of the body or accessories. Very significant, also, is the
+great increase in the use of V. in this most irregular class (15 per
+cent. as against 1 per cent. in III.). Three cases (214, 1087, 154,
+all A.V.,) fail to show substitutional symmetry.
+
+B. With the head on one side of Cn., of course the greatest interest
+is removed to one side, and the element of direction is brought in to
+balance. Again, with this decrease in symmetry, we see the significant
+increase in the use of the especially effective elements, V. and L.
+(Cf. B. I., II., III., IV., and especially V.) In fact, the use of the
+small deep vista is almost confined to the class with heads not in the
+middle. The direction of the glance also plays an important part. It
+is to be noted that in B. I. and II., I. appears as the most
+frequently used element, exclusive of the general equation, which is,
+of course, between the mass of the body and interest of the face, on
+one side, and the direction of suggested movement on the other. This
+means that very often the direction of movement alone is not
+sufficient to balance the powerful Ms. + I. of the other side, and
+that the eye has to be attracted by a definite object of interest.
+This is usually the hand, with or without an implement--like the
+palette, etc., of our first examples--or a jewel, vase, or bit of
+embroidery. This is very characteristic of the portraits of Rembrandt
+and Van Dyck.
+
+In general, it may be said that (1) portraits with the head in the
+center of the frame show a balance between the direction of suggested
+movement on one side, and mass or direction of attention, or both
+together, on the other; while (2) portraits with the head not in the
+center show a balance between mass and interest on one side, and
+direction of attention, or of line, or vista, or combinations of
+these, on the other. The hypothesis of substitutional symmetry is thus
+completely confirmed.
+
+
+Genre.
+
+Still more unsymmetrical in their framework than portraits, in fact
+the most unfettered type of all, are the genre pictures. Being so
+irregular, they admit of no complete classification based on constant
+elements in the framework, such as was possible for the types already
+dealt with. A grouping, based on types of composition, is indeed
+possible, as of triangles, diagonals, etc., but as this begs the
+question of the relative importance of line and direction of
+attention, and assumes that the shape is all-important, it will not be
+made use of here. The broad divisions and the relative use of the
+elements are given as follows:
+
+    S.C. 63. Most frequent form (I. = or I. + D. =). Most used
+    element, I., 89 per cent.; least used, L., 44 per cent.; D.,
+    57 per cent.; Ms., 57 per cent.; V., 46 per cent.
+
+    D.C. 19. Most frequent form (I. + D. = I. + D.) Most used
+    element, I. (all cases); least used, L., 31 per cent.; V., 47
+    per cent.; Ms., 63 per cent.; D., 42 per cent.
+
+    S.&S. 11. Most frequent form (I. or I. + Ms. = V. or V. +).
+    Most used element, I., 100 per cent.; least used, L., 20 per
+    cent.; V., 82 per cent.; Ms., 72 per cent.; D., 27 per cent.
+
+As these are pictures with a human interest, and, therefore full of
+action and particular points of interest, it was to be expected that
+I. would be in all forms the element most frequently appearing. In
+compositions showing great variations from geometrical symmetry, it
+was also to be expected that V. and L., elements which have been
+little used up to this point, should suddenly appear in very high
+percentages; for, as being the most strikingly 'heavy' of the
+elements, they serve to compensate for other variations combined. In
+general, however, the balance is between the interesting side, which
+is also often the most occupied (I. + Ms.), and the direction of
+suggestion to the other side.
+
+For the first time in this investigation the S. & S. and D.C. types
+appear in appreciable numbers. It is of some significance that the
+most irregular type of all, S. & S., in which the weight of interest
+and of mass is overwhelmingly on one side, should be invariably
+balanced by the third dimension (V.). As these somewhat infrequent
+cases are especially enlightening for the theory of substitutional
+symmetry, it is worth while to analyze one in detail.
+
+286. Pieter de Hooch, _The Card-players_, in Buckingham Palace,
+portrays a group completely on the Right of Cn., all facing in to the
+table between them. Directly behind them is a high light window,
+screened, and high on the wall to the extreme Right are a picture and
+hanging cloaks. All goes to emphasize the height, mass and interest of
+the Right side. On the Left, which is otherwise empty, is a door half
+the height of the window, giving on a brightly lighted courtyard, from
+which is entering a woman, also in light clothing. The light streams
+in diagonally across the floor. Thus, with all the 'weight' on the
+Right, the effect of this deep vista on the Left and of its brightness
+is to give a complete balance, while the suggestion of line from
+doorway and light makes, together with the central figure, a roughly
+outlined V, which serves to bind together all the elements. This
+matter of binding together of elements is reserved for further
+discussion--the purpose of this detailed description is only to show
+the extraordinary power of a single element, vista, to balance a whole
+composition of others, and its significance in the tables as an
+increasing accompaniment of increasing variations from symmetry.
+
+The D.C. cases, inasmuch as they always present a balance of interest
+at least, are less valuable for our theory; among the variations the
+larger side, Ms., is often balanced by a vista, or, combining with the
+usual equation for genre pictures, Ms. + I. + D. = V. + I. + D. There
+is only one picture which cannot be schematized (263).
+
+
+Landscape.
+
+The landscape is another type of unfettered composition. As it
+represents no action or single object or group of objects, its parts
+are naturally more or less unconnected. It should, therefore, be said
+that no picture was taken as D.C. unless there was a distinct
+separation of the two sides. The typical examples are analyzed in
+detail.
+
+S.C. 912. J. van Ruysdael, _Forest Landscape_, in the London National
+Gallery. In the Cn. is a stagnant pool, backed on the Right by thick
+woods. A dead tree, white, very prominent in the Right foreground,
+another at its foot sloping down to Cn. On the Left a bank sloping
+down to Cn., a tree at its foot; behind both, and seen also between
+the two central trees, bright sky and clouds. Thus, there is on the
+Right, Mass and Direction to Cn.; on the Left, Vista and Direction to
+Cn.; Ms. + D. = V. + D.
+
+D.C. 642. Hobbema, _The Watermill_, in Buckingham Palace. On the
+Right, a bank sloping upward, a large cluster of trees, a path leading
+down to Right lower corner. On the Left, somewhat lower, the mill, and
+water in front of it, flowing down to Left; clearest sky between mill
+and trees. Thus Mass and Direction out are placed over against
+Interest (in mill) and Direction out, plus possibly a hint of Vista,
+or Ms. + D. = I. + D + V.
+
+S.C. 65. Most frequent form, Ms. + I. = V. + L. Most used element, V.,
+98 per cent.; least used, D., 22 per cent. I. 73 per cent.; Ms. 66 per
+cent.; L. 31 per cent.
+
+S. & S. One case. Ms. + I. + V. = V.
+
+D.C. 22. Most frequent form, Ms. + I. or Ms. = V. or V. + (almost
+invariable). Most used element, V., 100 per cent.; least used, D., per
+cent. Ms. 82 per cent.; I. 73 per cent.; L. 23 per cent.
+
+It was, of course, to be expected that in pictures without action
+there should be little suggestion of attention or of direction of
+movement. What is less evident is the reason for the high percentage
+of I. Of course, figures do appear in many examples, and in most
+pictures some inanimate object is emphasized--as, for instance, the
+mill in our second example. But the most remarkable point of
+difference in these tables from the preceding is the presence of V. in
+practically every example. It is, of course, natural that somewhere in
+almost every picture there should be a break to show the horizon line,
+for the sake of variety, if for nothing else--but what is significant
+is the part played by this break in the balancing of the picture. In
+about two thirds of the examples the vista is enclosed by lines, or
+masses, and when near the center, as being at the same time the
+'heaviest' part of the picture, serves as a fulcrum or center to bind
+the parts--always harder to bring together than in the other types of
+pictures--into a close unity. The most frequent form of this
+arrangement, as seen by the table, is a diagonal, which just saves
+itself by turning up at its far end. Thus the mass, and hence usually
+the special interest of the picture, is on the one side, on the other
+the vista and the sloping line of the diagonal. In very few cases is
+the vista behind an attractive or noticeable part of the picture, the
+fact showing that it acts in opposition to the latter, leading the eye
+away from it, and thus serving at once the variety and richness of the
+picture, and its unity. A pure diagonal would have line and vista both
+working at the extreme outer edge of the picture, and thus too
+strongly--unless, indeed, balanced by very striking elements near the
+other edge.
+
+This function of the vista as a unifying element is of interest in
+connection with the theory of Hildebrand,[16] that the landscape
+should have a narrow foreground and wide background, since that is
+most in conformity with our experience. He adduces Titian's _Sacred
+and Profane Love_ as an example. But of the general principle it may
+be said that not the reproduction of nature, but the production of a
+unified complex of motor impulses, is the aim of composition, and that
+this aim is best reached by focusing the eye by a narrow
+background--_i.e._, vista. No matter how much it wanders, it returns
+to that central spot and is held there, keeping hold on all the other
+elements. Of Hildebrand's example it may be said that the pyramidal
+composition with the dark and tall tree in the center effectually
+accomplishes the binding together of the two figures, so that a vista
+is not needed. A wide background without that tree would leave them
+rather disjointed.
+
+   [16] A. Hildebrand, 'Das Problem der Form in der Bildenden
+   Kunst,' Strassburg, 1897.
+
+Another interesting observation concerns the use of water in
+landscapes. In nearly all appears an expanse of water, and in four
+fifths of the cases it is either on the same side as the vista, or in
+the same line with it. This is no doubt partly due to the
+light-effects which can be got on the water, but it also greatly
+reinforces the peculiar effect of the vista. That effect, as has been
+repeatedly said, is to concentrate, to hold, to fixate vision. The
+same thing is true of the horizontal line, as was shown by some
+preliminary experiments not here reported. The contrast to the
+ordinary trend of lines--particularly in a landscape--together with
+the strong suggestion of quiet and repose, serve to give the same
+concentrating effect to the horizontal lines as to the vista.
+
+In general, it may be said that balance in landscape is effected
+between Mass and Interest on one side and Vista and Line on the other;
+and that unity is given especially by the use of Vista and the
+horizontal lines of water.
+
+A survey of the subject-types remaining on the list of page 514 shows
+that they may quite well be grouped together with those already
+examined; that is, the Holy Families, Adorations, Crucifixions, and
+Annunciations are very symmetrical in type, and present the same
+characteristics as the Altarpieces. The Miscellaneous (mostly
+religious) pictures, the Descents, and the Allegorical are, for the
+most part, freely composed, irregular, full of action, and resemble
+the genre pictures. The Single Figure pictures, Religious, Allegorical
+and Genre, and the Portrait Groups, resemble the portraits. Therefore,
+it may be considered that the existence of a perfect substitutional
+symmetry has been established, inasmuch as it has been shown to be
+almost invariably present in the types examined.
+
+The experimental treatment of the isolated elements determined the
+particular function of each in distributing attention in the field of
+view. The object of large size claims attention, but does not rivet it
+nor draw it out powerfully; the intrinsically interesting object does
+excite it, but limits it to a comparatively small field; the
+suggestion of movement or of attention on the part of pictured objects
+carries the attention through the field of its operation; the vista
+rivets the attention without powerfully exciting it, and the line
+extending in a certain direction carries the attention in the same way
+as does the suggestion of movement. But the preceding statistical
+analysis has shown that while all are possibly operative in a given
+picture, some are given much more importance than others, and that in
+pictures of different types different elements predominate.
+
+The following table gives the distribution of the elements in the
+single-center pictures already examined. The numbers represent the per
+cent. of the whole number of balanced pictures in which the given
+element appears once or more.
+
+
+    S.C.       Ms.    I.    D.    V.    L.
+
+    Alt. p.    26    100    91    13    31
+    Mad.       21    100    96    27    64
+    Port.      80     63    98    17    61
+    Genre      57     89    57    46    44
+    Lands.     66     73    22    98    31
+
+
+It is seen that in those classes with a general symmetrical framework,
+the altar and Madonna pictures, the elements of interest and direction
+of attention are overwhelmingly predominant--which is the more to be
+expected as they appear, of course, as variations in a symmetry which
+has already, so to speak, disposed of mass and line. They give what
+action there is, and when they are very strongly operative, we see by
+page 516, (8) and (9) and note, that they are opposed by salient lines
+and deep vistas, which act more strongly on the attention than mass;
+compare further Mad., V. 27 per cent., L. 64 per cent., as against
+Alt., V. 13 per cent., L. 19 per cent., as confirming the view that
+they are used in the more irregular and active pictures. But I. keeps
+its predominance throughout the types, except in the portraits, where,
+indeed, we should not expect it to be so powerful, since the principal
+object of interest must always be the portrait head, and that is in
+most cases in the Cn., and therefore not counted. Yet I. has a
+respectable representation even in the portrait table, showing that
+such objects as jewels, embroideries, beautiful hands, etc., count
+largely too in composition. Its greatest is in the genre table, where,
+of course, human interests constitute the subject matter.
+
+It is among the portraits that the direction of suggestion is most
+operative. Since these pictures represent no action, it must be given
+by those elements which move and distribute the attention; in
+accordance with which we see that line also is unusually influential.
+As remarked above, the altarpieces and Madonna pictures, also largely
+without action, depend largely for it on D., in the form of direction
+of attention (D. 91 per cent.).
+
+The vista, as said above, rivets and confines the attention. We can,
+therefore, understand how it is that in the genre table it suddenly
+appears very numerous. The active character of these pictures
+naturally requires to be modified, and the vista introduces a powerful
+balancing element, which is yet quiet; or, it might be said, inasmuch
+as energy is certainly expended in plunging down the third dimension,
+the vista introduces an element of action of counterbalancing
+character. In the landscape it introduces the principal element of
+variety. It is always to be found in those parts of the picture which
+are opposed to other powerful elements, and the 'heavier' the other
+side, the deeper the vista. This is especially to be noted in all
+pictures of the S. & S. type, where the one side is very 'heavy' and
+the deep vista practically invariable on the other. Also in D.C.
+pictures it serves as a kind of fulcrum, or unifying element, inasmuch
+as it rivets the attention between the two detached sides. (Cf. D.C.
+among Alt. and Mad.)
+
+The direction of suggestion by means of the indication of a line (L.),
+quite naturally is more frequent in the Madonna-picture and Portrait
+classes. Both these types are of large simple outline, so that L.
+would be expected to tell, but more or less irregular, so that it
+would not appear on both sides, thus neutralizing its action, as often
+in the symmetrical altarpieces. This neutralizing explains why it has
+a comparatively small per cent. in the landscape table, it having
+appeared in minor form all over the field, but less often in large
+salient outline. It is worth noticing that for the D.C. of both genre
+and landscape, the per cent. drops appreciably. As it is, in a decided
+majority of cases, combined with V.--the shape being more or less a
+diagonal slope--it is clear that it acts as a kind of bond between the
+two sides, carrying the attention without a break from one to the
+other.
+
+The element of mass requires less comment. It appears in greatest
+number in those pictures which have little action, portraits and
+landscapes, and which are yet not symmetrical--in which last case mass
+is, of course, already balanced. In fact, it must of necessity exert
+a certain influence in every unsymmetrical picture, and so its
+percentage, even for genre pictures, is large.
+
+Thus we may regard the elements as both attracting attention to a
+certain spot and dispersing it over a field. Those types which are of
+a static character abound in elements which disperse the attention;
+those which are of a dynamic character, in those which make it stable.
+The ideal composition seems to combine the dynamic and static
+elements--to animate, in short, the whole field of view, but in a
+generally bilateral fashion. The elements, in substitutional symmetry,
+are then simply means of introducing variety and action. As a dance in
+which there are complicated steps gives the actor and beholder a
+varied and thus vivified 'balance,' and is thus more beautiful than
+the simple walk, so a picture composed in substitutional symmetry is
+more rich in its suggestions of motor impulse, and thus more
+beautiful, than an example of geometrical symmetry.
+
+
+_B. Principles of Composition._
+
+The particular function of the elements which are substituted for
+geometrical symmetry has been made clear; their presence lends variety
+and richness to the balance of motor impulses. But the natural motor
+response to stimulation has another characteristic which belongs to us
+as individuals. The motor response must be balanced, but also unified.
+In a picture, therefore, there must be a large outline in which all
+the elements are held together, corresponding to this requirement of
+unity. Now this way of holding together, this manner of combination,
+may vary; and I hope to show that it not only varies with the subject
+and purpose of the picture, but bears a very close relation
+thereto--that, in short, it is what determines the whole character of
+the picture. Just what this relation is will appear in the study of
+our material.
+
+Examples of these types of composition may best be found by analyzing
+a few very well-known pictures. We may begin with the class first
+studied, the Altarpiece, choosing a picture by Botticelli, in the
+Florence Academy (746). Under an arch is draped a canopy held up by
+angels; under this, again, sits the M. with the C. on her lap, on a
+throne, at the foot of which, on each side, stand three saints. The
+outline of the whole is markedly pyramidal--in fact, there are,
+broadly speaking, three pyramids; of the arch, the canopy, and the
+grouping. A second, much less symmetrical example of this type, is
+given by another Botticelli in the Academy--_Spring_ (140). Here the
+central female figure, topped by the floating Cupid, is slightly
+raised above the others, which, however, bend slightly inward, so that
+a triangle, or pyramid with very obtuse angle at the apex, is
+suggested; and the whole, which at first glance seems a little
+scattered, is at once felt, when this is grasped, as closely bound
+together.
+
+Closely allied to this is the type of the _Madonna of Burgomaster
+Meyer_, Holbein (725), in the Grand-Ducal Castle, Darmstadt. It is
+true that the same pyramid is given by the head of the M. against the
+shell-like background, and her spreading cloak which envelops the
+kneeling donors. But still more salient is the diamond form given by
+the descending rows of these worshipping figures, especially against
+the dark background of the M.'s dress. A second example, without the
+pyramid backing, is found in Rubens' _Rape of the Daughters of
+Leucippus_ (88), in the Alte Pinakothek at Munich. Here the diamond
+shape formed by the horses and struggling figures is most
+remarkable--an effect of lightness which will be discussed later in
+interpreting the types.
+
+The famous _Bull_ of Paul Potter (149), in the Royal Museum at the
+Hague, furnishes a third type, the diagonal. High on one side are
+grouped the herdsman, leaning on a tree which fills up the sky on that
+side, and his three sheep and cow. The head of the bull is turned
+toward this side, and his back and hind leg slope down to the other
+side, as the ground slopes away to a low distant meadow. The picture
+is thus divided by an irregular diagonal. Somewhat more regular is the
+diagonal of the _Evening Landscape_, by Cuyp (348), in the Buckingham
+Palace, London. High trees and cliffs, horsemen and others, occupy one
+side, and the mountains in the background, the ground and the clouds,
+all slope gradually down to the other side.
+
+It is a natural transition from this type to the V-shape of the
+landscapes by Aart van der Neer, _Dutch Villages_, 245 and 420, in the
+London National Gallery and in the Rudolphinum at Prague,
+respectively. Here are trees and houses on each side, gradually
+sloping to the center to show an open sky and deep vista. Other
+examples, of course, show the opening not exactly in the center.
+
+In the _Concert_ by Giorgione (758), in the Pitti Gallery, Florence,
+is seen the less frequent type of the square. The three figures turned
+toward each other with heads on the same level make almost a square
+space-shape, although it might be said that the central player gives a
+pyramidal foundation. This last may also be said of Verrocchio's
+_Tobias and the Archangels_ in the Florence Academy, for the square,
+or rather rectangle, is again lengthened by the pyramidal shape of the
+two central figures. The unrelieved square, it may here be
+interpolated, is not often found except in somewhat primitive
+examples. Still less often observed is the oval type of _Samson's
+Wedding feast_, Rembrandt (295), in the Royal Gallery, Dresden. Here
+one might, by pressing the interpretation, see an obtuse-angled
+double-pyramid with the figure of Delilah for an apex, but a few very
+irregular pictures seem to fall best under the given classification.
+
+Last of all it must be remarked that the great majority of pictures
+show a combination of two or even three types; but these are usually
+subordinated to one dominant type. Such, for instance, is the case
+with many portraits, which are markedly pyramidal, with the
+double-pyramid suggested by the position of the arms, and the inverted
+pyramid, or V, in the landscape background. The diagonal sometimes
+just passes over into the V, or into the pyramid; or the square is
+combined with both.
+
+It is, of course, not necessary at this point to show how it is that
+such an apparently unsymmetrical shape as the diagonal, alone or in
+combination with other forms, nevertheless produces an effect of
+balance. In all these cases of the diagonal type the mass or interest
+of the one side, or the direction of subordinate lines backward to it,
+balances the impulse of the line descending to the other side. The
+presence of balance or substitutional symmetry is taken for granted
+in this treatment, having been previously established, and only the
+modifications of this symmetry are under consideration.
+
+Now, in order to deal properly with the question of the relation of
+the type of composition to the subject of the picture, complete
+statistical information will be necessary. A table of the pictures,
+classified by subjects and distributed under the heads of the six
+major types, is accordingly subjoined.
+
+
+                       Pyramid.         Double-Pyr.       Diagonal.
+                    S.C. D.C. S.S.    S.C. D.C. S.S.    S.C. D.C. S.S.
+  Altarpieces,       49    0    1      10    4    0       1    0    0
+  Mad. w. C.,        40    0    0       7    0    0       0    0    0
+  Holy Family,       25    0    4       0    0    1       2    2    2
+  Adorations,        19    0    0       0    0    0       0    0    0
+  Crucifixions,      11    0    0       7    0    1       0    0    1
+  Desc. fr. Cross,   12    0    0       3    0    0       1    0    0
+  Annunciations,      0    8    0       0    4    0       0    0    0
+  Misc. Religious,   55   16    3       4    4    0      10    7    5
+  Allegorical,       20    2    1       4    0    0       4    0    2
+  Genre,             25    4    4       5    0    0      18    2    1
+  Landscape,          8    2    1       3    0    0      25    6    0
+  Port. Group,       20    4    2       9    0    0       3    3    2
+  Rel. Single Fig.,  20    0    0       2    0    0       2    0    0
+  Alleg. S.F.,        7    0    0       2    0    0       3    0    0
+  Portrait S.F.,    179    0    0      28    0    0       0    0    0
+  Genre S.F.,        15    0    0       1    0    0       1    0    0
+
+
+                       V-shaped.         Square.             Oval.
+                    S.C. D.C. S.S.    S.C. D.C. S.S.    S.C. D.C. S.S.
+  Altarpieces,        6    1    0       4    1    0       0    1    0
+  Mad. w. C.,         0    0    0       0    0    0       0    0    0
+  Holy Family,       13    3    6       0    0    0       0    0    0
+  Adorations,         0    0    0       0    0    0       0    0    0
+  Crucifixions,       0    0    0       3    0    0       0    0    0
+  Desc. fr. Cross,    5    0    1       3    0    0       2    0    0
+  Annunciations,      0    1    0       0    8    0       0    0    0
+  Misc. Religious,   20   14    2       9   12    1       2    2    3
+  Allegorical,        3    2    1       3    1    0       3    1    0
+  Genre,             10    7    6       4    4    0       1    3    0
+  Landscape,         20   12    0       4    0    0       5    2    0
+  Port. Group,       10    7    1       0    3    0       0    0    0
+  Rel. Single Fig.,   3    0    0       1    0    0       0    0    0
+  Alleg. S.F.,        0    0    0       0    0    0       0    0    0
+  Portrait S.F.,      0    0    0       0    0    0       0    0    0
+  Genre S.F.,         1    0    0       0    0    0       0    0    0
+
+
+What types are characteristic of the different kinds of pictures? In
+order to answer this question we must ask first, What are the
+different kinds of pictures? One answer, at least, is at once
+suggested to the student on a comparison of the pictures with their
+groupings according to subjects. All those which represent the Madonna
+enthroned, with all variations, with or without saints, shepherds or
+Holy Family, are very quiet in their action; that is, it is not really
+an action at all which they represent, but an attitude--the attitude
+of contemplation. This is no less true of the pictures I have called
+'Adorations,' in which, indeed, the contemplative attitude is still
+more marked. On the other hand, such pictures as the 'Descents,' the
+'Annunciations,' and very many of the 'miscellaneous religious,'
+allegorical and genre pictures, portray a definite action or event.
+Taking together, for instance, in two groups of five each, the first
+ten classes in the table, we find that they fall to the six types in
+the following proportion:
+
+
+         P.     D.P.     Dg.     V.      Sq.     Ov.
+   I.    66      13      05      13      03       0
+  II.    43      07      14      20      12       04
+
+
+Inasmuch as II. contains also many 'contemplative' pictures, while I.
+contains no 'active' ones, the contrast between the proportions of the
+groups would really be sharper than the figures indicate. But as it
+is, we see that the pyramid type is characteristic of the
+'contemplative' pictures in a much higher degree. If the closely
+allied double-pyramid type is taken with it, we have 79 per cent of
+the 'contemplative' to 50 per cent, of the 'active' ones. This view is
+confirmed by contrasting the 'Adoration,' the most complete example of
+one group, with the genre pictures, the most complete example of the
+other--and here we see that in the first all are pyramidal, and in the
+second only 26 per cent. A class which might be supposed to suggest
+the same treatment in composition is that of the portraits--absolute
+lack of action being the rule. And we find, indeed, that no single
+type is represented within it except the pyramid and double-pyramid,
+with 86 per cent. of the former. Thus it is evident that for the type
+of picture which expresses the highest degree of quietude,
+contemplation, concentration, the pyramid is the characteristic type
+of composition.
+
+But is it not also characteristic of the 'active' pictures, since, as
+we see, it has the largest representation in that class too? Perhaps
+it might be said that, inasmuch as all pictures are really more
+'quiet' than they are 'active,' so the type _par excellence_ is the
+pyramidal--a suggestion which is certainly borne out by the table as a
+whole. But setting aside for the moment the pyramid and its
+sub-variety, we see that the diagonal V-shaped and square types are
+much more numerous in the roughly outlined 'active' class. Taking,
+again, the genre class as especially representative, we find 23 per
+cent. of the diagonal type, and 25 per cent. of the V-shaped. We have
+seen how closely allied are these two types, and how gradually one
+passes over into the other, so that we may for the nonce take them
+together as making up 47 per cent. of the whole. The type of picture
+which expresses the highest degree of activity, which aims to tell a
+story, has, then, for its characteristic type the V and its varieties.
+
+The landscape picture presents a somewhat different problem. It cannot
+be described as either 'active' or 'passive,' inasmuch as it does not
+express either an attitude or an event. There is no definite idea to
+be set forth, no point of concentration, as with the altarpieces and
+the portraits, for instance; and yet a unity is demanded. An
+examination of the proportions of the types shows at once the
+characteristic type.
+
+
+                  P.    D.P.    Dg.    V.     Sq.    Or.
+  Landscapes,     13     03     35     36     05     08
+
+
+It is now necessary to ask what must be the interpretation of the use
+of these types of composition. Must we consider the pyramid the
+expression of passivity, the diagonal or V, of activity? But the
+greatly predominating use of the second for landscapes would remain
+unexplained, for at least nothing can be more reposeful than the
+latter. It may aid the solution of the problem to remember that the
+composition taken as a whole has to meet the demand for unity, at the
+same time that it allows free play to the natural expression of the
+subject. The altarpiece has to bring about a concentration of
+attention to express or induce a feeling of reverence. This is
+evidently brought about by the suggestion of the converging lines to
+the fixation of the high point in the picture--the small area occupied
+by the Madonna and Child--and by the subordination of the free play of
+other elements. The contrast between the broad base and the apex gives
+a feeling of solidity, of repose; and it seems not unreasonable to
+suppose that the tendency to rest the eyes above the center of the
+picture directly induces the associated mood of reverence or worship.
+Thus the pyramidal form serves two ends; primarily that of giving
+unity; and secondarily, by the peculiarity of its mass, that of
+inducing the feeling-tone appropriate to the subject of the picture.
+
+Applying this principle to the so-called 'active' pictures, we see
+that the natural movement of attention between the different 'actors'
+in the picture must be allowed for, while yet unity is secured. And it
+is clear that the diagonal type is just fitted for this. The attention
+sweeps down from the high side to the low, from which it returns
+through some backward suggestion of lines or interest in the objects
+of the high side. Action and reaction--movement and return of
+attention--is inevitable under the conditions of this type; and this
+it is which allows the free play--which, indeed, _constitutes_ and
+expresses the activity belonging to the subject, just as the fixation
+of the pyramid constitutes the quietude of the religious picture. Thus
+it is that the diagonal composition is particularly suited to portray
+scenes of grandeur, and to induce a feeling of awe in the spectator,
+because only here can the eye rove in one large sweep from side to
+side of the picture, recalled by the mass and interest of the side
+from which it moves. The swing of the pendulum is here widest, so to
+speak, and all the feeling-tones which belong to wide, free movement
+are called into play. If, at the same time, the element of the deep
+vista is introduced, we have the extreme of concentration combined
+with the extreme of movement; and the result is a picture in the
+'grand style'--comparable to high tragedy--in which all the
+feeling-tones which wait on motor impulses are, as it were, while yet
+in the same reciprocal relation, tuned to the highest pitch. Such a
+picture is the _Finding of the Ring_, Paris Bordone (1048), in the
+Venice Academy. All the mass and the interest and the suggestion of
+attention is toward the right--the sweep of the downward lines and of
+the magnificent perspective toward the left--and the effect of the
+whole space-composition is of superb largeness of life and feeling.
+With it may be compared Titian's _Presentation of the Virgin_ (107),
+also in the Academy, Venice. The composition, from the figure moving
+upward to one high on the right, to the downward lines, waiting groups
+and deep vista on the left, is almost identical with that of the
+Bordone. Neither is pure diagonal--that is, it saves itself at last by
+an upward movement. Compare also the two great compositions by
+Veronese, _Martyrdom of St. Mark_, etc. (1091), in the Doge's Palace,
+Venice, and _Esther before Ahasuerus_ (566), in the Uffizi, Florence.
+In both, the mass, direction of interest, movement and attention are
+toward the left, while all the lines tend diagonally to the right,
+where a vista is also suggested--the diagonal making a V just at the
+end. Here, too, the effect is of magnificence and vigor.
+
+If, then, the pyramid belongs to contemplation, the diagonal to
+action, what can be said of the type of landscape? It is without
+action, it is true, and yet does not express that positive quality,
+that _will_ not to act, of the rapt contemplation. The landscape
+uncomposed is negative; and it demands unity. Its type of composition,
+then, must give it something positive besides unity. It lacks both
+concentration and action; but it can gain them both from a space
+composition which shall combine unity with a tendency to movement. And
+this is given by the diagonal and V-shaped type. This type merely
+allows free play to the natural tendency of the 'active' picture; but
+it constrains the neutral, inanimate landscape. The shape itself
+imparts motion to the picture: the sweep of line, the concentration of
+the vista, the unifying power of the inverted triangle between two
+masses, act, as it were, externally to the suggestion of the object
+itself. There is always enough quiet in a landscape--the overwhelming
+suggestion of the horizontal suffices for that; it is movement that is
+needed for richness of effect; and, as I have shown, no type imparts
+the feeling of movement so strongly as the diagonal and V-shaped type
+of composition. It is worth remarking that the perfect V, which is of
+course more regular, concentrated, quiet, than the diagonal, is more
+frequent than the diagonal among the 'Miscellaneous Religious'
+pictures (that is, it is more _needed_), since after all, as has been
+said, the final aim of all space composition is just the attainment of
+repose. But the landscapes need energy, not repression; and so the
+diagonal type is proportionately more numerous.
+
+The square and oval types, as is seen from the table, are far less
+often used. The oval, most infrequent of all, appears only among the
+'active' pictures, with the exception of landscape. It usually serves
+to unite a group of people among whom there is no one especially
+striking--or the object of whose attention is in the center of the
+picture, as in the case of the Descent from the Cross. It imparts a
+certain amount of movement, but an equable and regular one, as the eye
+returns in an even sweep from one side to the other.
+
+The square type, although only three per cent. of the whole number of
+pictures, suggests a point of view which has already been touched on
+in the section on Primitive Art. The examples fall into two classes:
+in the first, the straight lines across the picture are unrelieved by
+the suggestion of any other type; in the second, the pyramid or V is
+suggested in the background with more or less clearness by means of
+architecture or landscape. In the first class are found, almost
+exclusively, early examples of Italian, Dutch and German art; in the
+second, pictures of a later period. The rigid square, in short, is
+found only at an early stage in the development of composition.
+Moreover, all the examples are 'story' pictures, for the most part
+scenes from the lives of the saints, etc. Many of them are
+double-center--square, that is, with a slight break in the middle, the
+grouping purely logical, to bring out the relations of the characters.
+Thus, in the _Dream of Saint Martin_, Simone Martini (325), a fresco
+at Assisi, the saint lies straight across the picture with his head in
+one corner. Behind him on one side, stand the Christ and angels,
+grouped closely together, their heads on the same level. Compare also
+the _Finding of the Cross_, Piero della Francesca (1088), a serial
+picture in two parts, with their respective backgrounds all on the
+same level; and most of the frescoes by Giotto at Assisi--in
+particular _St. Francis before the Sultan_ (1057), in which the actors
+are divided into parties, so to speak.
+
+These are all, of course, in one sense symmetrical--in the weight of
+interest, at least--but they are completely amorphous from an ęsthetic
+point of view. The _forms_, that is, do not count at all--only the
+meanings. The story is told by a clear separation of the parts, and
+as, in most stories, there are two principal actors, it merely happens
+that they fall into the two sides of the picture. Interesting in
+connection with this is the observation that, although the more
+anecdotal the picture the more likely it is to be 'double-centered,'
+the later the picture the less likely it is to be double-centered.
+Thus the square and the double-center composition seem often to be
+found in the same picture and to be, both, characteristic of early
+composition. On the other hand, a rigid geometrical symmetry is also
+characteristic, and these two facts seem to contradict each other. But
+it is to be noted, first, that the rigid geometrical symmetry belongs
+only to the Madonna Enthroned, and general Adoration pieces; and
+secondly, that this very rigidity of symmetry in details can coexist
+with variations which destroy balance. Thus, in the _Madonna
+Enthroned_, Giotto (715), where absolute symmetry in detail is kept,
+the Child sits far out on the right knee of the Madonna. Compare also
+_Madonna_, Vitale di Bologna (157), in which the C. is almost falling
+off M.'s arms to the right, her head is bent to the right, and a monk
+is kneeling at the right lower corner; also _Madonna_, Ottaviano Nelli
+(175)--all very early pictures. Hence, it would seem that the symmetry
+of these early pictures was not dictated by a conscious demand for
+symmetrical arrangement, or rather for real balance, else such
+failures would hardly occur. The presence of geometrical symmetry is
+more easily explained as the product, in large part, of technical
+conditions: of the fact that these pictures were painted as
+altarpieces to fill a space definitely symmetrical in character--often,
+indeed, with architectural elements intruding into it. We may even
+venture to connect the Madonna pictures with the temple images of the
+classic period, to explain why it was natural to paint the object of
+worship seated exactly facing the worshipper. Thus we may separate the
+two classes of pictures, the one giving an object of worship, and thus
+taking naturally, as has been said, the pyramidal, symmetrical shape,
+and being moulded to symmetry by all other suggestions of technique;
+the other aiming at nothing except logical clearness. This antithesis
+of the symbol and the story has a most interesting parallel in the two
+great classes of primitive art--the one symbolic, merely suggestive,
+shaped by the space it had to fill, and so degenerating into the
+slavishly symmetrical, the other descriptive, 'story-telling' and
+without a trace of space composition. On neither side is there
+evidence of direct ęsthetic feeling. Only in the course of artistic
+development do we find the rigid, yet often unbalanced, symmetry
+relaxing into a free substitutional symmetry, and the formless
+narrative crystallizing into a really unified and balanced space form.
+The two antitheses approach each other in the 'balance' of the
+masterpieces of civilized art--in which, for the first time, a real
+feeling for space composition makes itself felt.
+
+       *       *       *       *       *
+
+
+
+
+THE ĘSTHETICS OF UNEQUAL DIVISION.
+
+BY ROSWELL PARKER ANGIER.
+
+
+PART I.
+
+
+The present paper reports the beginnings of an investigation designed
+to throw light on the psychological basis of our ęsthetic pleasure in
+unequal division. It is confined to horizontal division. Owing to the
+prestige of the golden section, that is, of that division of the
+simple line which gives a short part bearing the same ratio to the
+long part that the latter bears to the whole line, experimentation of
+this sort has been fettered. Investigators have confined their efforts
+to statistical records of approximations to, or deviations from, the
+golden section. This exalts it into a possible ęsthetic norm. But such
+a gratuitous supposition, by limiting the inquiry to the verification
+of this norm, distorts the results, tempting one to forget the
+provisional nature of the assumption, and to consider divergence from
+the golden section as an error, instead of another example, merely, of
+unequal division. We have, as a matter of fact, on one hand,
+investigations that do not verify the golden section, and, on the
+other hand, a series of attempts to account for our pleasure in it, as
+if it were, beyond dispute, the norm. In this way the statistical
+inquiries have been narrowed in scope, and interpretation retarded and
+misdirected. Statistically our aim should be to ascertain within how
+wide limits ęsthetically pleasing unequal divisions fall; and an
+interpretative principle must be flexible enough to include persistent
+variations from any hypothetical norm, unless they can be otherwise
+accounted for. If it is not forced on us, we have, in either case,
+nothing to do with the golden section.
+
+Since Fechner, the chief investigation in the ęsthetics of simple
+forms is that of Witmer, in 1893.[1] Only a small part of his work
+relates to horizontal division, but enough to show what seems to me a
+radical defect in statistical method, namely, that of accepting a
+general average of the average judgments of the several subjects, as
+'the most pleasing relation' or 'the most pleasing proportion.'[2]
+Such a total average may fall wholly without the range of judgments of
+every subject concerned, and tells us nothing certain about the
+specific judgments of any one. Even in the case of the individual
+subject, if he shows in the course of long experimentation that he has
+two distinct sets of judgments, it is not valid to say that his real
+norm lies between the two; much less when several subjects are
+concerned. If averages are data to be psychophysically explained, they
+must fall well within actual individual ranges of judgment, else they
+correspond to no empirically determinable psychophysical processes.
+Each individual is a locus of possible ęsthetic satisfactions. Since
+such a locus is our ultimate basis for interpretation, it is inept to
+choose, as 'the most pleasing proportion,' one that may have no
+correspondent empirical reference. The normal or ideal individual,
+which such a norm implies, is not a psychophysical entity which may
+serve as a basis of explanation, but a mathematical construction.
+
+   [1] Witmer, Lightner: 'Zur experimentellen Aesthetik einfacher
+   räumlicher Formverhältnisse,' _Phil. Studien_, 1893, IX., S.
+   96-144, 209-263.
+
+This criticism would apply to judgments of unequal division on either
+side the center of a horizontal line. It would apply all the more to
+any general average of judgments including both sides, for, as we
+shall soon see, the judgments of individuals differ materially on the
+two sides, and this difference itself may demand its explanation. And
+if we should include within this average, judgments above and below
+the center of a vertical line, we should have under one heading four
+distinct sets of averages, each of which, in the individual cases,
+might show important variations from the others, and therefore require
+some variation of explanation. And yet that great leveller, the
+general average, has obliterated these vital differences, and is
+recorded as indicating the 'most pleasing proportion.'[3] That such an
+average falls near the golden section is immaterial. Witmer himself,
+as we shall see,[4] does not set much store by this coincidence as a
+starting point for explanation, since he is averse to any mathematical
+interpretation, but he does consider the average in question
+representative of the most pleasing division.
+
+   [2] _op. cit._, 212-215.
+
+   [3] Witmer: _op. cit._, S. 212-215.
+
+   [4] _op. cit._, S. 262.
+
+I shall now, before proceeding to the details of the experiment to be
+recorded, review, very briefly, former interpretative tendencies.
+Zeising found that the golden section satisfied his demand for unity
+and infinity in the same beautiful object.[5] In the golden section,
+says Wundt,[6] there is a unity involving the whole; it is therefore
+more beautiful than symmetry, according to the ęsthetic principle that
+that unification of spatial forms which occurs without marked effort,
+which, however, embraces the greater manifold, is the more pleasing.
+But to me this manifold, to be ęsthetic, must be a sensible manifold,
+and it is still a question whether the golden section set of relations
+has an actual correlate in sensations. Witmer,[7] however, wrote, at
+the conclusion of his careful researches, that scientific ęsthetics
+allows no more exact statement, in interpretation of the golden
+section, than that it forms 'die rechte Mitte' between a too great and
+a too small variety. Nine years later, in 1902, he says[8] that the
+preference for proportion over symmetry is not a demand for an
+equality of ratios, but merely for greater variety, and that 'the
+amount of unlikeness or variety that is pleasing will depend upon the
+general character of the object, and upon the individual's grade of
+intelligence and ęsthetic taste.' Külpe[9] sees in the golden section
+'a special case of the constancy of the relative sensible
+discrimination, or of Weber's law.' The division of a line at the
+golden section produces 'apparently equal differences' between minor
+and major, and major and whole. It is 'the pleasingness of apparently
+equal differences.'
+
+   [5] Zelsing, A.: 'Aesthetische Forschungen,' 1855, S. 172;
+   'Neue Lehre von den Proportionen des menschlichen Körpera,'
+   1854, S. 133-174.
+
+   [6] Wundt, W.: 'Physiologische Psychologie,' 4te Aufl.,
+   Leipzig, 1893, Bd. II., S. 240 ff.
+
+   [7] _op. cit._, S. 262.
+
+   [8] Witmer, L.: 'Analytical Psychology,' Boston, 1902, p. 74.
+
+   [9] Külpe, O.: 'Outlines of Psychology,' Eng. Trans., London,
+   1895, pp. 253-255.
+
+These citations show, in brief form, the history of the interpretation
+of our pleasure in unequal division. Zeising and Wundt were alike in
+error in taking the golden section as the norm. Zeising used it to
+support a philosophical theory of the beautiful. Wundt and others too
+hastily conclude that the mathematical ratios, intellectually
+discriminated, are also sensibly discriminated, and form thus the
+basis of our ęsthetic pleasure. An extension of this principle would
+make our pleasure in any arrangement of forms depend on the
+mathematical relations of their parts. We should, of course, have no
+special reason for choosing one set of relationships rather than
+another, nor for halting at any intricacy of formulę. But we cannot
+make experimental ęsthetics a branch of applied mathematics. A theory,
+if we are to have psychological explanation at all, must be pertinent
+to actual psychic experience. Witmer, while avoiding and condemning
+mathematical explanation, does not attempt to push interpretation
+beyond the honored category of unity in variety, which is applicable
+to anything, and, in principle, is akin to Zeising's unity and
+infinity. We wish to know what actual psychophysical functionings
+correspond to this unity in variety. Külpe's interpretation is such an
+attempt, but it seems clear that Weber's law cannot be applied to the
+division at the golden section. It would require of us to estimate the
+difference between the long side and the short side to be equal to
+that of the long side and the whole. A glance at the division shows
+that such complex estimation would compare incomparable facts, since
+the short and the long parts are separated, while the long part is
+inclosed in the whole. Besides, such an interpretation could not apply
+to divisions widely variant from the golden section.
+
+This paper, as I said, reports but the beginnings of an investigation
+into unequal division, confined as it is to results obtained from the
+division of a simple horizontal line, and to variations introduced as
+hints towards interpretation. The tests were made in a partially
+darkened room. The apparatus rested on a table of ordinary height, the
+part exposed to the subject consisting of an upright screen, 45 cm.
+high by 61 cm. broad, covered with black cardboard, approximately in
+the center of which was a horizontal opening of considerable size,
+backed by opal glass. Between the glass and the cardboard, flush with
+the edges of the opening so that no stray light could get through, a
+cardboard slide was inserted from behind, into which was cut the
+exposed figure. A covered electric light illuminated the figure with a
+yellowish-white light, so that all the subject saw, besides a dim
+outline of the apparatus and the walls of the room, was the
+illuminated figure. An upright strip of steel, 1½ mm. wide, movable in
+either direction horizontally by means of strings, and controlled by
+the subject, who sat about four feet in front of the table, divided
+the horizontal line at any point. On the line, of course, this
+appeared as a movable dot. The line itself was arbitrarily made 160
+mm. long, and 1½ mm. wide. The subject was asked to divide the line
+unequally at the most pleasing place, moving the divider from one end
+slowly to the other, far enough to pass outside any pleasing range,
+or, perhaps, quite off the line; then, having seen the divider at all
+points of the line, he moved it back to that position which appealed
+to him as most pleasing. Record having been made of this, by means of
+a millimeter scale, the subject, without again going off the line,
+moved to the pleasing position on the other side of the center. He
+then moved the divider wholly off the line, and made two more
+judgments, beginning his movement from the other end of the line.
+These four judgments usually sufficed for the simple line for one
+experiment. In the course of the experimentation each of nine subjects
+gave thirty-six such judgments on either side the center, or
+seventy-two in all.
+
+In Fig. 1, I have represented graphically the results of these
+judgments. The letters at the left, with the exception of _X_, mark
+the subjects. Beginning with the most extreme judgments on either side
+the center, I have erected modes to represent the number of judgments
+made within each ensuing five millimeters, the number in each case
+being denoted by the figure at the top of the mode. The two vertical
+dot-and-dash lines represent the means of the several averages of all
+the subjects, or the total averages. The short lines, dropped from
+each of the horizontals, mark the individual averages of the divisions
+either side the center, and at _X_ these have been concentrated into
+one line. Subject _E_ obviously shows two pretty distinct fields of
+choice, so that it would have been inaccurate to condense them all
+into one average. I have therefore given two on each side the center,
+in each case subsuming the judgments represented by the four end modes
+under one average. In all, sixty judgments were made by _E_ on each
+half the line. Letter _E¹_ represents the first thirty-six; _E²_ the
+full number. A comparison of the two shows how easily averages shift;
+how suddenly judgments may concentrate in one region after having been
+for months fairly uniformly distributed. The introduction of one more
+subject might have varied the total averages by several points. Table
+I. shows the various averages and mean variations in tabular form.
+
+
+TABLE I.
+                         Left.            Right.
+                      Div.  M.V.        Div.   M.V.
+        _A_      54    2.6         50     3.4
+        _B_      46    4.5         49     5.7
+        _C_      75    1.8         71     1.6
+        _D_      62    4.4         56     4.1
+        _E¹_     57   10.7         60     8.7
+        _F_      69    2.6         69     1.6
+        _G_      65    3.7         64     2.7
+        _H_      72    3.8         67     2.1
+        _J_      46    1.9         48     1.3
+                 --    ---         --     ---
+Total            60    3.9         59     3.5
+
+Golden Section = 61.1.
+
+    ¹These are _E_'s general averages on 36 judgments. Fig. 1,
+    however, represents two averages on each side the center, for
+    which the figures are, on the left, 43 with M.V. 3.6; and 66
+    with M.V. 5.3. On the right, 49, M.V. 3.1; and 67, M.V. 2.7.
+    For the full sixty judgments, his total average was 63 on the
+    left, and 65 on the right, with mean variations of 9.8 and 7.1
+    respectively. The four that _E²_ in Fig. 1 shows graphically
+    were, for the left, 43 with M.V. 3.6; and 68, M.V. 5.1. On the
+    right, 49, M.V. 3.1; and 69, M.V. 3.4.
+
+
+[Illustration: FIG. 1.]
+
+Results such as are given in Fig. 1, appear to warrant the criticism
+of former experimentation. Starting with the golden section, we find
+the two lines representing the total averages running surprisingly
+close to it. This line, however, out of a possible eighteen chances,
+only twice (subjects _D_ and _G_) falls wholly within the mode
+representing the maximum number of judgments of any single subject. In
+six cases (_C_ twice, _F_, _H_, _J_ twice) it falls wholly without any
+mode whatever; and in seven (_A_, _B_ twice, _E_, _F_, _G_, _H_)
+within modes very near the minimum. Glancing for a moment at the
+individual averages, we see that none coincides with the total
+(although _D_ is very near), and that out of eighteen, only four (_D_
+twice, _G_ twice) come within five millimeters of the general average,
+while eight (_B_, _C_, _J_ twice each, _F_, _H_) lie between ten and
+fifteen millimeters away. The two total averages (although near the
+golden section), are thus chiefly conspicuous in showing those regions
+of the line that were avoided as not beautiful. Within a range of
+ninety millimeters, divided into eighteen sections of five millimeters
+each, there are ten such sections (50 mm.) each of which represents
+the maximum of some one subject. The range of maximum judgments is
+thus about one third the whole line. From such wide limits it is, I
+think, a methodological error to pick out some single point, and
+maintain that any explanation whatever of the divisions there made
+interprets adequately our pleasure in unequal division. Can, above
+all, the golden section, which in only two cases (_D_, _G_) falls
+within the maximum mode; in five (_A_, _C_, _F_, _J_ twice) entirely
+outside all modes, and in no single instance within the maximum on
+both sides the center--can this seriously play the role of ęsthetic
+norm?
+
+I may state here, briefly, the results of several sets of judgments on
+lines of the same length as the first but wider, and on other lines of
+the same width but shorter. There were not enough judgments in either
+case to make an exact comparison of averages valuable, but in three
+successively shorter lines, only one subject out of eight varied in a
+constant direction, making his divisions, as the line grew shorter,
+absolutely nearer the ends. He himself felt, in fact, that he kept
+about the same absolute position on the line, regardless of the
+successive shortenings, made by covering up the ends. This I found to
+be practically true, and it accounts for the increasing variation
+toward the ends. Further, with all the subjects but one, two out of
+three pairs of averages (one pair for each length of line) bore the
+same relative positions to the center as in the normal line. That is,
+if the average was nearer the center on the left than on the right,
+then the same held true for the smaller lines. Not only this. With one
+exception, the positions of the averages of the various subjects, when
+considered relatively to one another, stood the same in the shorter
+lines, in two cases out of three. In short, not only did the pair of
+averages of each subject on each of the shorter lines retain the same
+relative positions as in the normal line, but the zone of preference
+of any subject bore the same relation to that of any other. Such
+approximations are near enough, perhaps, to warrant the statement that
+the absolute length of line makes no appreciable difference in the
+ęsthetic judgment. In the wider lines the agreement of the judgments
+with those of the normal line was, as might be expected, still closer.
+In these tests only six subjects were used. As in the former case,
+however, _E_ was here the exception, his averages being appreciably
+nearer the center than in the original line. But his judgments of this
+line, taken during the same period, were so much on the central tack
+that a comparison of them with those of the wider lines shows very
+close similarity. The following table will show how _E_'s judgments
+varied constantly towards the center:
+
+                                                            AVERAGE.
+                                                             L.   R.
+  1. Twenty-one judgments (11 on L. and 10 on R.) during
+  experimentation on _I¹, I²_, etc., but not on same days.   64   65
+
+  2. Twenty at different times, but immediately before
+   judging on _I¹, I²_, etc.                                 69   71
+
+  3. Eighteen similar judgments, but immediately after
+  judging on _I¹, I²_, etc.                                  72   71
+
+  4. Twelve taken after all experimentation with _I¹_,
+  _I²_, etc., had ceased.                                    71   69
+
+
+The measurements are always from the ends of the line. It looks as if
+the judgments in (3) were pushed further to the center by being
+immediately preceded by those on the shorter and the wider lines, but
+those in (1) and (2) differ markedly, and yet were under no such
+influences.
+
+From the work on the simple line, with its variations in width and
+length, these conclusions seem to me of interest. (1) The records
+offer no one division that can be validly taken to represent 'the most
+pleasing proportion' and from which interpretation may issue. (2) With
+one exception (_E_) the subjects, while differing widely from one
+another in elasticity of judgment, confined themselves severally to
+pretty constant regions of choice, which hold, relatively, for
+different lengths and widths of line. (3) Towards the extremities
+judgments seldom stray beyond a point that would divide the line into
+fourths, but they approach the center very closely. Most of the
+subjects, however, found a _slight_ remove from the center
+disagreeable. (4) Introspectively the subjects were ordinarily aware
+of a range within which judgments might give equal pleasure, although
+a slight disturbance of any particular judgment would usually be
+recognized as a departure from the point of maximum pleasingness. This
+feeling of potential elasticity of judgment, combined with that of
+certainty in regard to any particular instance, demands--when the
+other results are also kept in mind--an interpretative theory to take
+account of every judgment, and forbids it to seize on an average as
+the basis of explanation for judgments that persist in maintaining
+their ęsthetic autonomy.
+
+I shall now proceed to the interpretative part of the paper. Bilateral
+symmetry has long been recognized as a primary principle in ęsthetic
+composition. We inveterately seek to arrange the elements of a figure
+so as to secure, horizontally, on either side of a central point of
+reference, an objective equivalence of lines and masses. At one
+extreme this may be the rigid mathematical symmetry of geometrically
+similar halves; at the other, an intricate system of compensations in
+which size on one side is balanced by distance on the other,
+elaboration of design by mass, and so on. Physiologically speaking,
+there is here a corresponding equality of muscular innervations, a
+setting free of bilaterally equal organic energies. Introspection will
+localize the basis of these in seemingly equal eye movements, in a
+strain of the head from side to side, as one half the field is
+regarded, or the other, and in the tendency of one half the body
+towards a massed horizontal movement, which is nevertheless held in
+check by a similar impulse, on the part of the other half, in the
+opposite direction, so that equilibrium results. The psychic
+accompaniment is a feeling of balance; the mind is ęsthetically
+satisfied, at rest. And through whatever bewildering variety of
+elements in the figure, it is this simple bilateral equivalence that
+brings us to ęsthetic rest. If, however, the symmetry is not good, if
+we find a gap in design where we expected a filling, the accustomed
+equilibrium of the organism does not result; psychically there is lack
+of balance, and the object is ęsthetically painful. We seem to have,
+then, in symmetry, three aspects. First, the objective quantitative
+equality of sides; second, a corresponding equivalence of bilaterally
+disposed organic energies, brought into equilibrium because acting in
+opposite directions; third, a feeling of balance, which is, in
+symmetry, our ęsthetic satisfaction.
+
+It would be possible, as I have intimated, to arrange a series of
+symmetrical figures in which the first would show simple geometrical
+reduplication of one side by the other, obvious at a glance; and the
+last, such a qualitative variety of compensating elements that only
+painstaking experimentation could make apparent what elements balanced
+others. The second, through its more subtle exemplification of the
+rule of quantitative equivalence, might be called a higher order of
+symmetry. Suppose now that we find given, objects which, ęsthetically
+pleasing, nevertheless present, on one side of a point of reference,
+or center of division, elements that actually have none corresponding
+to them on the other; where there is not, in short, _objective_
+bilateral equivalence, however subtly manifested, but, rather, a
+complete lack of compensation, a striking asymmetry. The simplest,
+most convincing case of this is the horizontal straight line,
+unequally divided. Must we, because of the lack of objective equality
+of sides, also say that the bilaterally equivalent muscular
+innervations are likewise lacking, and that our pleasure consequently
+does not arise from the feeling of balance? A new aspect of
+psychophysical ęsthetics thus presents itself. Must we invoke a new
+principle for horizontal unequal division, or is it but a subtly
+disguised variation of the more familiar symmetry? And in vertical
+unequal division, what principle governs? A further paper will deal
+with vertical division. The present paper, as I have said, offers a
+theory for the horizontal.
+
+To this end, there were introduced, along with the simple line figures
+already described, more varied ones, designed to suggest
+interpretation. One whole class of figures was tried and discarded
+because the variations, being introduced at the ends of the simple
+line, suggested at once the up-and-down balance of the lever about the
+division point as a fulcrum, and became, therefore, instances of
+simple symmetry. The parallel between such figures and the simple line
+failed, also, in the lack of homogeneity on either side the division
+point in the former, so that the figure did not appear to center at,
+or issue from the point of division, but rather to terminate or
+concentrate in the end variations. A class of figures that obviated
+both these difficulties was finally adopted and adhered to throughout
+the work. As exposed, the figures were as long as the simple line, but
+of varying widths. On one side, by means of horizontal parallels, the
+horizontality of the original line was emphasized, while on the other
+there were introduced various patterns (fillings). Each figure was
+movable to the right or the left, behind a stationary opening 160 mm.
+in length, so that one side might be shortened to any desired degree
+and the other at the same time lengthened, the total length remaining
+constant. In this way the division point (the junction of the two
+sides) could be made to occupy any position on the figure. The figures
+were also reversible, in order to present the variety-filling on the
+right or the left.
+
+If it were found that such a filling in one figure varied from one in
+another so that it obviously presented more than the other of some
+clearly distinguishable element, and yielded divisions in which it
+occupied constantly a shorter space than the other, then we could,
+theoretically, shorten the divisions at will by adding to the filling
+in the one respect. If this were true it would be evident that what we
+demand is an equivalence of fillings--a shorter length being made
+equivalent to the longer horizontal parallels by the addition of more
+of the element in which the two short fillings essentially differ. It
+would then be a fair inference that the different lengths allotted by
+the various subjects to the short division of the simple line result
+from varying degrees of substitution of the element, reduced to its
+simplest terms, in which our filling varied. Unequal division would
+thus be an instance of bilateral symmetry.
+
+The thought is plausible. For, in regarding the short part of the line
+with the long still in vision, one would be likely, from the ęsthetic
+tendency to introduce symmetry into the arrangement of objects, to be
+irritated by the discrepant inequality of the two lengths, and, in
+order to obtain the equality, would attribute an added significance to
+the short length. If the assumption of bilateral equivalence
+underlying this is correct, then the repetition, in quantitative
+terms, on one side, of what we have on the other, constitutes the
+unity in the horizontal disposition of ęsthetic elements; a unity
+receptive to an almost infinite variety of actual visual
+forms--quantitative identity in qualitative diversity. If presented
+material resists objective symmetrical arrangement (which gives, with
+the minimum expenditure of energy, the corresponding bilateral
+equivalence of organic energies) we obtain our organic equivalence in
+supplementing the weaker part by a contribution of energies for which
+it presents no obvious visual, or objective, basis. From this there
+results, by reaction, an objective equivalence, for the psychic
+correlate of the additional energies freed is an attribution to the
+weaker part, in order to secure this feeling of balance, of some added
+qualities, which at first it did not appear to have. In the case of
+the simple line the lack of objective symmetry that everywhere meets
+us is represented by an unequal division. The enhanced significance
+acquired by the shorter part, and its psychophysical basis, will
+engage us further in the introspection of the subjects, and in the
+final paragraph of the paper. In general, however, the phenomenon that
+we found in the division of the line--the variety of divisions given
+by any one object, and the variations among the several subjects--is
+easily accounted for by the suggested theory, for the different
+subjects merely exemplify more fixedly the shifting psychophysical
+states of any one subject.
+
+In all, five sets of the corrected figures were used. Only the second,
+however, and the fifth (chronologically speaking) appeared indubitably
+to isolate one element above others, and gave uniform results. But
+time lacked to develop the fifth sufficiently to warrant positive
+statement. Certain uniformities appeared, nevertheless, in all the
+sets, and find due mention in the ensuing discussion. The two figures
+of the second set are shown in Fig. 2. Variation No. III. shows a
+design similar to that of No. II., but with its parts set more closely
+together and offering, therefore, a greater complexity. In Table II.
+are given the average divisions of the nine subjects. The total length
+of the figure was, as usual, 160 mm. Varying numbers of judgments were
+made on the different subjects.
+
+[Illustration: FIG. 2.]
+
+
+TABLE II.
+
+          No. I.   No. II.   No. I. (reversed).  No. II. (reversed).
+          L.  R.    L.  R.         R.  L.              R.  L.
+
+  A       55   0    48   0         59   0              50   0
+  B       59   0    44   0         63   0              52   0
+  C       58   0    56   0         52   0              50   0
+  D       60   0    56   0         60   0              55   0
+  E       74  59    73  65         74  60              75  67
+  F       61  67    60  66         65  64              62  65
+  G       64  64    62  68         63  64              53  67
+  H       76  68    75  64         66  73              67  71
+  J       49   0    41   0         50   0              42   0
+          --  --    --  --         --  --              --  --
+  Total.  61  64    57  65         61  65              54  67
+
+
+With the complex fillings at the left, it will be seen, firstly, that
+in every case the left judgment on No. III. is less than that on No.
+II. With the figures reversed, the right judgments on No. III. are
+less than on No. II., with the exception of subjects _E_ and _H_.
+Secondly, four of the subjects only (_E_, _F_, _G_ and _H_) had
+judgments also on the side which gave the complex filling the larger
+space; to _E_, _F_ and _G_, these were secondary preferences; to _H_
+they were always primary. Thirdly, the judgments on No. III. are less,
+in spite of the fact that the larger component parts of No. II., might
+be taken as additional weight to that side of the line, and given,
+therefore, the shorter space, according to the principle of the lever.
+
+The subjects, then, that appear not to substantiate our suggested
+theory are _E_ and _H_, who in the reversed figures give the shorter
+space to the less complex filling, and _F_ and _G_, who, together with
+_E_ and _H_, have always secondary judgments that allot to either
+complex filling a larger space than to the simple horizontal.
+Consider, first, subjects _E_ and _H_. For each, the difference in
+division of II. and III. is in any case very slight. Further, subject
+_E_, in judgments where the complex filling _exceeds_ the horizontal
+parallels in length, still gives the more complex of the two fillings
+markedly the shorter space, showing, apparently, that its additional
+complexity works there in accord with the theory. There was, according
+to his introspection, another principle at work. As a figure, he
+emphatically preferred II. to III. The filling of II. made up, he
+found, by its greater interest, for lack of length. He here secured a
+balance, in which the interest of the complex material compensated for
+the greater _extent_ of the simpler horizontals. This accounts for its
+small variation from III., and even for its occupying the smaller
+space. But in judgments giving the two complex fillings the larger
+space, the more interesting material _exceeded_ in extent the less
+interesting. In such divisions the balance was no longer uppermost in
+mind, but the desire to get as much as possible of the interesting
+filling. To this end the horizontal parallels were shortened as far as
+they could be without becoming insignificant. But unless some element
+of balance were there (although not present to introspection) each
+complex filling, when up for judgment, would have been pushed to the
+same limit. It, therefore, does seem, in cases where the complex
+fillings occupied a larger space than the horizontals, that the
+subject, not trying consciously to secure a balance of _interests_,
+was influenced more purely by the factor of complexity, and that his
+judgments lend support to our theory.
+
+Subject H was the only subject who consistently _preferred_ to have
+all complex fillings occupy the larger space. Introspection invariably
+revealed the same principle of procedure--he strove to get as much of
+the interesting material as he could. He thought, therefore, that in
+every case he moved the complex filling to that limit of the pleasing
+range that he found on the simple line, which would yield him most of
+the filling. Balance did not appear prominent in his introspection. A
+glance, however, at the results shows that his introspection is
+contradicted. For he maintains approximately the same division on the
+right in all the figures, whether reversed or not, and similarly on
+the left. The average on the right for all four is 67; on the left it
+is 74. Comparing these with the averages on the simple line, we see
+that the right averages coincide exactly, while the left but slightly
+differ. I suspect, indeed, that the fillings did not mean much to _H_,
+except that they were 'interesting' or 'uninteresting'; that aside
+from this he was really abstracting from the filling and making the
+same judgments that he would make on the simple line. Since he was
+continually aware that they fell within the 'pleasing range' on the
+simple line, this conclusion is the more plausible.
+
+Perhaps these remarks account for the respective uniformities of the
+judgments of _E_ and _H_, and their departure from the tendency of the
+other subjects to give the more complex filling constantly the shorter
+space. But subjects _F_ and _G_ also had judgments (secondary with
+both of them) giving to the complex filling a larger extent than to
+the parallels. With them one of two principles, I think, applies: The
+judgments are either instances of abstraction from the filling, as
+with _H_, or one of simpler gravity or vertical balance, as
+distinguished from the horizontal equivalence which I conceive to be
+at the basis of the other divisions. With _F_ it is likely to be the
+latter, since the divisions of the figures under discussion do not
+approach very closely those of the simple line, and because
+introspectively he found that the divisions giving the complex the
+larger space were 'balance' divisions, while the others were
+determined with 'reference to the character of the fillings.' From _G_
+I had no introspection, and the approximation of his judgments to
+those he gave for the simple line make it probable that with him the
+changes in the character of the filling had little significance. The
+average of his judgments in which the complex filling held the greater
+space is 66, while the averages on the simple line were 65 on the
+left, and 64 on the right. And, in general, abstraction from filling
+was easy, and to be guarded against. Subject _C_, in the course of the
+work, confessed to it, quite unsolicited, and corrected himself by
+giving thenceforth _all_ complex fillings much smaller space than
+before. Two others noticed that it was particularly hard not to
+abstract. Further, none of the four subjects mentioned (with that
+possible exception of _E_) showed a sensitiveness similar to that of
+the other five.
+
+With the exception of _H_, and in accord with the constant practice of
+the other five, these subjects, too, occasionally found no pleasing
+division in which the complex filling preponderated in length over the
+horizontals. It was uniformly true, furthermore, in every variation
+introduced in the course of the investigation, involving a complex and
+a simple filling, that all the nine subjects but _H_ _preferred_ the
+complex in the shorter space; that five refused any divisions offering
+it in the larger space; that these five showed more sensitiveness to
+differences in the character of fillings; and that with one exception
+(_C_) the divisions of the simple line which these subjects gave were
+nearer the ends than those of the others. It surely seems plausible
+that those most endowed with ęsthetic sensitiveness would find a
+division near the center more unequal than one nearer the end; for one
+side only slightly shorter than the other would at once seem to mean
+the same thing to them, and yet, because of the obvious difference in
+length, be something markedly different, and they would therefore
+demand a part short enough to give them sharp qualitative difference,
+with, however, in some way, quantitative equivalence. When the short
+part is too long, it is overcharged with significance, it strives to
+be two things at once and yet neither in its fulness.
+
+We thus return to the simple line. I have considered a series of
+judgments on it, and a series on two different figures, varying in the
+degree of complexity presented, in one of their fillings. It remains
+very briefly to see if the introspection on the simple line furnishes
+further warrant for carrying the complexities over into the simple
+line and so giving additional validity to the outlined theory of
+substitution. The following phrases are from introspective notes.
+
+_A_. Sweep wanted over long part. More attention to short.
+Significance of whole in short. Certainly a concentration of interest
+in the short. Short is efficacious. Long means rest; short is the
+center of things. Long, an effortless activity; short, a more
+strenuous activity. When complex fillings are introduced, subject is
+helped out; does not have to put so much into the short division. In
+simple line, subject _introduces_ the concentration. In complex
+figures the concentration is objectified. In _equal_ division subject
+has little to do with it; the _unequal_ depends on the subject--it
+calls for appreciation. Center of references is the division point,
+and the eye movements to right and left begin here, and here return.
+The line centers there. The balance is a horizontal affair.
+
+_B_. Center a more reposing division. Chief attention to division
+point, with side excursions to right and left, when refreshment of
+perception is needed. The balance is horizontal and not vertical.
+
+_C_. A balance with variety, or without symmetry. Centers at division
+point and wants sweep over long part. More concentration on short
+part. Subjective activity there--an introduction of energy. A
+contraction of the muscles used in active attention. Long side easier,
+takes care of itself, self-poised. Line centers at division point.
+Active with short division. Introduces activity, which is equivalent
+to the filling that the complex figures have; in these the introduced
+activity is objectified--made graphic.
+
+_D_. Focal point at division point: wants the interesting things in a
+picture to occupy the left (when short division is also on left).
+Short division the more interesting and means greater complication.
+When the pleasing division is made, eyes move first over long and then
+over short. Division point the center of real reference from which
+movements are made.
+
+_E_. No reference to center in making judgments; hurries over center.
+All portions of simple line of equal interest; but in unequal division
+the short gets a non-apparent importance, for the line is then a
+scheme for the representation of materials of different interest
+values. When the division is too short, the imagination refuses to
+give it the proportionally greater importance that it would demand.
+When too long it is too near equality. In enjoying line, the division
+point is fixed, with shifts of attention from side to side. An
+underlying intellectual assignment of more value to short side, and
+then the sense-pleasure comes; the two sides have then an equality.
+
+_F_. Middle vulgar, common, prosaic; unequal lively. Prefers the
+lively. Eyes rest on division point, moving to the end of long and
+then of short. Ease, simplicity and restfulness are proper to the long
+part of complex figures. Short part of simple line looks wider,
+brighter and more important than long.
+
+_G_. Unequal better than equal. Eye likes movement over long and then
+over short. Subject interested only in division point. Short part
+gives the ęsthetic quality to the line.
+
+_H_. Center not wanted. Division point the center of interest. (No
+further noteworthy introspection from _H_, but concerning complex
+figures he said that he wanted simple or the compact on the short, and
+the interesting on the long.)
+
+These introspective notes were given at different times, and any
+repetitions serve only to show constancy. The subjects were usually
+very certain of their introspection. In general it appears to me to
+warrant these three statements: (1) That the center of interest is the
+division point, whence eye-movements, or innervations involving,
+perhaps, the whole motor system, are made to either side. (2) That
+there is some sort of balance or equivalence obtained (a bilateral
+symmetry), which is not, however, a vertical balance--that is, one of
+weights pulling downwards, according to the principle of the lever.
+All the subjects repudiated the suggestion of vertical balance. (3)
+That the long side means ease and simplicity, and represents
+graphically exactly what it means; that the short side means greater
+intensity, concentration, or complexity, and that this is substituted
+by the subject; the short division, unlike the long, means something
+that it does not graphically represent.
+
+So much for the relation between what is objectively given and the
+significance subjectively attributed to it. There remains still the
+translation into psychophysical terms. The results on the complex
+figures (showing that a division may be shortened by making the
+innervations on that side increasingly more involved) lend
+plausibility to the interpretation that the additional significance
+is, in visual terms, a greater intricacy or difficulty of
+eye-movement, actual or reproduced; or, in more general terms, a
+greater tension of the entire motor system. In such figures the
+psychophysical conditions for our pleasure in the unequal division of
+the simple horizontal line are merely graphically symbolized, not
+necessarily duplicated. On page 553 I roughly suggested what occurs in
+regarding the unequally divided line. More exactly, this: the long
+section of the line gives a free sweep of the eyes from the division
+point, the center, to the end; or again, a free innervation of the
+motor system. The sweep the subject makes sure of. Then, with that as
+standard, the ęsthetic impulse is to secure an equal and similar
+movement, from the center, in the opposite direction. It is checked,
+however, by the end point of the short side. The result is the
+innervation of antagonistic muscles, by which the impression is
+intensified. For any given subject, then, the pleasing unequal
+division is at that point which causes quantitatively equal
+physiological discharges, consisting of the simple movement, on one
+hand, and, on the other, the same kind of movement, compounded with
+the additional innervation of the antagonists resulting from the
+resistance of the end point. Since, when the characteristic movements
+are being made for one side, the other is always in simultaneous
+vision, the sweep receives, by contrast, further accentuation, and the
+innervation of antagonists doubtless begins as soon as movement on the
+short side is begun. The whole of the short movement is, therefore,
+really a resultant of the tendency to sweep and this necessary
+innervation of antagonists. The correlate of the equivalent
+innervations is equal sensations of energy of movement coming from the
+two sides. Hence the feeling of balance. Hence (from the lack of
+unimpeded movement on the short side) the feeling there of
+'intensity,' or 'concentration,' or 'greater significance.' Hence,
+too, the 'ease,' the 'simplicity,' the 'placidity' of the long side.
+
+As in traditional symmetry, the element of unity or identity, in
+unequal division, is a repetition, in quantitative terms, on one side,
+of what is given on the other. In the simple line the _equal_ division
+gives us obviously exact objective repetition, so that the
+psychophysical correlates are more easily inferred, while the
+_unequal_ offers apparently no compensation. But the psychophysical
+contribution of energies is not gratuitous. The function of the
+increment of length on one side, which in the centrally divided line
+makes the divisions equal, is assumed in unequal division by the end
+point of the short side; the uniform motor innervations in the former
+become, in the latter, the additional innervation of antagonists,
+which gives the equality. The two are separated only in degree. The
+latter may truly be called, however, a symmetry of a higher order,
+because objectively the disposition of its elements is not graphically
+obvious, and psychophysically, the quantitative unity is attained
+through a greater variety of processes. Thus, in complex works of art,
+what at first appears to be an unsymmetrical composition, is, if
+beautiful, only a subtle symmetry. There is present, of course, an
+arithmetically unequal division of horizontal extent, aside from the
+filling. But our pleasure in this, _without_ filling, has been seen to
+be also a pleasure in symmetry. We have, then, the symmetry of equally
+divided extents and of unequally divided extents. They have in common
+bilateral equivalence of psychophysical processes; the nature of these
+differs. In both the principle of unity is the same. The variety
+through which it works is different.
+
+       *       *       *       *       *
+
+
+
+
+         STUDIES IN ANIMAL PSYCHOLOGY.
+
+
+
+
+       *       *       *       *       *
+
+
+
+
+HABIT FORMATION IN THE CRAWFISH CAMBARUS AFFINIS.[1]
+
+BY ROBERT M. YERKES AND GURRY E. HUGGINS.
+
+   [1] See also Yerkes, Robert: 'Habit-Formation in the Green
+   Crab, _Carcinus Granulalus_,' _Biological Bulletin_, Vol. III.,
+   1902, pp. 241-244.
+
+
+This paper is an account of some experiments made for the purpose of
+testing the ability of the crawfish to profit by experience. It is
+well known that most vertebrates are able to learn, but of the
+invertebrates there are several classes which have not as yet been
+tested.
+
+The only experimental study of habit formation in a crustacean which
+we have found is that of Albrecht Bethe[2] on the crab, _Carcinus
+maenas_. In his excellent paper on the structure of the nervous system
+of _Carcinus_ Bethe calls attention to a few experiments which he made
+to determine, as he puts it, whether the crab possesses psychic
+processes. The following are the observations made by him. Experiment
+I. A crab was placed in a basin which contained in its darkest corner
+an _Eledone_ (a Cephalopod). The crab at once moved into the dark
+region because of its instinct to hide, and was seized by the
+_Eledone_ and drawn under its mantle. The experimenter then quickly
+freed the crab from its enemy and returned it to the other end of the
+basin. But again the crab returned to the dark and was seized. This
+was repeated with one animal five times and with another six times
+without the least evidence that the crabs profited by their
+experiences with the _Eledone_. Experiment 2. Crabs in an aquarium
+were baited with meat. The experimenter held his hand above the food
+and each time the hungry crab seized it he caught the animal and
+maltreated it, thus trying to teach the crabs that meat meant danger.
+But as in the previous experiment several repetitions of the
+experience failed to teach the crabs that the hand should be avoided.
+From these observations Bethe concludes that _Carcinus_ has no
+'psychic qualities' (_i.e._, is unable to profit by experience), but
+is a reflex machine.
+
+   [2] Bethe, Albrecht: 'Das Centralnervensystem von _Carcinus
+   maenas_,' II. Theil., _Arch. f. mikr. Anat._, Bd. 51, 1898, S.
+   447.
+
+Bethe's first test is unsatisfactory because the crabs have a strong
+tendency to hide from the experimenter in the darkest corner. Hence,
+if an association was formed, there would necessarily be a conflict of
+impulses, and the region in which the animal would remain would depend
+upon the relative strengths of its fear of the experimenter and of the
+_Eledone_. This objection is not so weighty, however, as is that which
+must obviously be made to the number of observations upon which the
+conclusions are based. Five or even twenty-five repetitions of such an
+experiment would be an inadequate basis for the statements made by
+Bethe. At least a hundred trials should have been made. The same
+objection holds in case of the second experiment. In all probability
+Bethe's statements were made in the light of long and close
+observation of the life habits of _Carcinus_; we do not wish,
+therefore, to deny the value of his observations, but before accepting
+his conclusions it is our purpose to make a more thorough test of the
+ability of crustaceans to learn.
+
+[Illustration: FIG. 1. Ground Plan of Labyrinth. _T_, triangular
+compartment from which animal was started; _P_, partition at exit;
+_G_, glass plate closing one exit passage. Scale 1/6.]
+
+For determining whether the crawfish is able to learn a simple form of
+the labyrinth method was employed. A wooden box (Fig. 1) 35 cm. long,
+24 cm. wide and 15 cm. deep, with one end open, and at the other end
+a triangular compartment which communicated with the main portion of
+the box by an opening 5 cm. wide, served as an experiment box. At the
+open end of this box a partition (_P_) 6 cm. long divided the opening
+into two passages of equal width. Either of these passages could be
+closed with a glass plate (_G_), and the subject thus forced to escape
+from the box by the choice of a certain passage. This box, during the
+experiments, was placed in the aquarium in which the animals lived. In
+order to facilitate the movement of the crawfish toward the water, the
+open end was placed on a level with the water in the aquarium, and the
+other end was raised so that the box made an angle of 6° with the
+horizontal.
+
+Experiments were made under uniform conditions, as follows. A subject
+was taken from the aquarium and placed in a dry jar for about five
+minutes, in order to increase the desire to return to the water; it
+was then put into the triangular space of the experiment box and
+allowed to find its way to the aquarium. Only one choice of direction
+was necessary in this, namely, at the opening where one of the
+passages was closed. That the animal should not be disturbed during
+the experiment the observer stood motionless immediately behind the
+box.
+
+Before the glass plate was introduced a preliminary series of tests
+was made to see whether the animals had any tendency to go to one side
+on account of inequality of illumination, of the action of gravity, or
+any other stimulus which might not be apparent to the experimenter.
+Three subjects were used, with the results tabulated.
+
+
+           Exit by       Exit by
+           Right Passage Left Passage.
+    No. 1  6              4
+    No. 2  7              3
+    No. 3  3              7
+          16             14
+
+
+Since there were more cases of exit by the right-hand passage, it was
+closed with the glass plate, and a series of experiments made to
+determine whether the crawfish would learn to avoid the blocked
+passage and escape to the aquarium by the most direct path. Between
+March 13 and April 14 each of the three animals was given sixty
+trials, an average of two a day. In Table I. the results of these
+trials are arranged in groups of ten, according to the choice of
+passages at the exit. Whenever an animal moved beyond the level of the
+partition (_P_) on the side of the closed passage the trial was
+counted in favor of the closed passage, even though the animal turned
+back before touching the glass plate and escaped by the open passage.
+
+
+TABLE I.
+
+HABIT FORMATION IN THE CRAWFISH.¹
+
+ Experiments.  No. 1        No. 2       No. 3       Totals    Per cent
+           Open Closed  Open Closed  Open Closed  Open Closed   Open
+     1-10    8     2      5     5      2     8     15    15     50.0
+    11-20    4     6      8     2      6     4     18    12     60.0
+    21-30    6     3²     8     2      8     2     22     7     75.8
+    31-40    9     1      8     2      8     2     25     5     83.3
+    41-50    8     2      8     2      7     3     23     7     76.6
+    51-60   10     0      8     2      9     1     27     3     90.0
+
+          TEST OF PERMANENCY OF HABIT AFTER 14 DAYS' REST.
+
+    61-70    6     4      8     2      8     2     22     8     73.3
+    (1-10)
+    71-80    6     4      8     2      7     3     21     9     70.0
+   (11-20)
+
+    ¹The experiments of this table were made by F.D. Bosworth.
+
+    ²One trial in which the subject failed to return to the water
+    within thirty minutes.
+
+
+In these experiments there is a gradual increase in the number of
+correct choices (_i.e._, choice of the 'open' passage) from 50 per
+cent. for the first ten trials to 90 per cent. for the last ten
+(trials 51-60). The test of permanency, made after two weeks, shows
+that the habit persisted.
+
+Although the observations just recorded indicate the ability of the
+crawfish to learn a simple habit, it seems desirable to test the
+matter more carefully under somewhat different conditions. For in the
+experiments described the animals were allowed to go through the box
+day after day without any change in the floor over which they passed,
+and as it was noted that they frequently applied their antennae to the
+bottom of the box as they moved along, it is possible that they were
+merely following a path marked by an odor or by moistness due to the
+previous trips. To discover whether this was really the case
+experiments were made in which the box was thoroughly washed out after
+each trip.
+
+The nature of the test in the experiments now to be recorded is the
+same as the preceding, but a new box was used. Fig. 2 is the floor
+plan and side view of this apparatus. It was 44.5 cm. long, 23.5 cm.
+wide and 20 cm. deep. The partition at the exit was 8.5 cm. in length.
+Instead of placing this apparatus in the aquarium, as was done in the
+previous experiments, a tray containing sand and water was used to
+receive the animals as they escaped from the box. The angle of
+inclination was also changed to 7°. For the triangular space in which
+the animals were started in the preceding tests a rectangular box was
+substituted, and from this an opening 8 cm. wide by 5 cm. deep gave
+access to the main compartment of the box.
+
+[Illustration: FIG. 2. Floor Plan and Side View of Labyrinth Number 2.
+_E_, entrance chamber from which animal was started; _C_, cloth
+covering _E_; _M_, mirror; _T_, tray containing sand and water; _G_,
+glass plate; _P_, partition; _R_, right exit passage; _L_, left exit
+passage. Scale 1/8.]
+
+A large healthy crawfish was selected and subjected to tests in this
+apparatus in series of ten experiments given in quick succession. One
+series a day was given. After each test the floor was washed; as a
+result the experiments were separated from one another by a
+three-minute interval, and each series occupied from thirty minutes to
+an hour. Table II. gives in groups of five these series of ten
+observations each. The groups, indicated by Roman numerals, run from
+I. to IX., there being, therefore, 450 experiments in all. Groups I.
+and II., or the first 100 experiments, were made without having either
+of the exit passages closed, in order to see whether the animal would
+develop a habit of going out by one side or the other. It did very
+quickly, as a matter of fact, get into the habit of using the left
+passage (L.). The last sixty experiments (Groups I. and II.) show not
+a single case of escape by the right passage. The left passage was now
+closed. Group III. gives the result. The time column (_i.e._, the
+third column of the table) gives for each series of observations the
+average time in seconds occupied by the animal in escaping from the
+box. It is to be noted that the closing of the Left passage caused an
+increase in the time from 30.9 seconds for the last series of the
+second group to 90 seconds for the first series of the third group. In
+this there is unmistakable evidence of the influence of the change in
+conditions. The animal after a very few experiences under the new
+conditions began going to the Right in most cases; and after 250
+experiences it had ceased to make mistakes. Group VII. indicates only
+one mistake in fifty choices.
+
+
+TABLE II.
+
+  HABIT FORMATION AND THE MODIFICATION OF HABITS IN THE CRAWFISH.
+
+         Results in Series of Ten.   Avs. in Groups of 50.
+        Series  L.  R.  Time. L. R.        L.     R.   Time.
+ Group  I. 1    9   1    45                Per Cent.
+           2    3   7    69
+           3    9   1    20
+           4    4   6    72
+           5   10        31
+               --  --
+               35  15                      70     30   47.4
+
+       II. 1   10        29
+           2   10        30
+           3   10        30
+           4   10        28.8
+           5   10        30.9
+               --        ----
+               50                         100          30
+             ....                        ....
+      III. 1    4   6     90     2
+           2    2   8     89.2   1
+           3    1   9     36.7   1
+           4    2   8     51     2
+           5    1   9     43     2
+               --  --           --
+               10  40            7         20     80    62
+             ....                        ....
+       IV. 1    3   7    124     1
+           2    2   8     44     5
+           3    2   8     37     4
+           4       10     34
+           5    2   8            1
+               --  --           --
+                9  41           11         18     82    60
+             ....                        ....
+        V. 1       10     44     2
+           2       10     35     4
+           3    3   7     76     3
+           4    2   8     50     7
+           5    1   9     50     4
+               --  --           --
+                6  44           20         12     88    51
+             ....                        ....
+       VI. 1    2   8     45     2
+           2       10     41     5
+           3    1   9     41.8   7
+           4       10     32.7   7
+           5       10            8
+               --  --           --
+                3  47           29          6     94    40
+             ....                        ....
+      VII. 1    1   9     39     4
+           2       10     38     7
+           3       10     30.7   3
+           4       10     42     6
+           5       10     48     4
+               --  --           --
+                1  49           24          2     98    39.5
+
+                              R. L.
+                 ....                           ....
+     VIII. 1    8   2    147     1
+           2    9   1     26
+           3    8   2     49     2
+           4    9   1     38     2
+           5    9   1     41
+               --  --           --
+               43   7            5         86     14    60.2
+             ....                        ....
+      IX.  1   1   9      41
+           2   2   8      39     1
+           3      10      29
+           4   1   9      47
+           5   1   9      32     1         10     90    38
+              --  --            --
+               5  45             2
+
+
+The dotted lines at the beginning of groups indicate the closed passage.
+
+
+At the beginning of Group VIII. the Right instead of the Left passage
+was closed in order to test the ability of the animal to change its
+newly formed habit. As a result of this change in the conditions the
+animal almost immediately began going to the Left. What is most
+significant, however, is the fact that in the first trial after the
+change it was completely confused and spent over fifteen minutes
+wandering about, and trying to escape by the old way (Fig. 4
+represents the path taken). At the end of the preceding group the time
+of a trip was about 48 seconds, while for the first ten trips of Group
+VIII. the time increased to 147 seconds. This remarkable increase is
+due almost entirely to the great length of time of the first trip, in
+which the animal thoroughly explored the whole of the box and made
+persistent efforts to get out by the Right passage as it had been
+accustomed to do. It is at the same time noteworthy that the average
+time for the second series of Group VIII. is only 26 seconds.
+
+For Group IX. the conditions were again reversed, this time the Left
+passage being closed. Here the first trial was one of long and careful
+exploration, but thereafter no more mistakes were made in the first
+series, and in the group of fifty tests there were only five wrong
+choices.
+
+The fifth column, R. L. and L. R., of Table II. contains cases in
+which the subject started toward one side and then changed its course
+before reaching the partition. In Group III., for instance, when the
+Left passage was closed, the subject started toward the Left seven
+times, but in each case changed to the Right before reaching the
+partition. This is the best evidence of the importance of vision that
+these experiments furnish.
+
+The first experiments on habit formation proved conclusively that the
+crawfish is able to learn. The observations which have just been
+described prove that the labyrinth habit is not merely the following
+of a path by the senses of smell, taste or touch, but that other
+sensory data, in the absence of those mentioned, direct the animals.
+So far as these experiments go there appear to be at least four
+sensory factors of importance in the formation of a simple labyrinth
+habit: the chemical sense, touch, vision and the muscle sense. That
+the chemical sense and touch are valuable guiding senses is evident
+from even superficial observation, and of the importance of vision and
+the muscle sense we are certain from the experimental evidence at
+hand.
+
+[Illustration: FIG. 3. Path taken by crawfish while being trained to
+avoid the left passage. Marks along the glass plate and partition
+indicate contact by the antennae and chelę.]
+
+Of the significance of the sensations due to the 'direction of
+turning' in these habits the best evidence that is furnished by this
+work is that of the following observations. In case of the tests of
+Table II. the subject was, after 100 preliminary tests, trained by 250
+experiences to escape by the Right-hand passage. Now, in Groups III.
+to VII., the subject's usual manner of getting out of the closed
+passage, when by a wrong choice it happened to get into it, was to
+draw back on the curled abdomen, after the antennae and chelę had
+touched the glass plate, and then move the chelę slowly along the
+Right wall of the partition until it came to the upper end; it would
+then walk around the partition and out by the open passage. Fig. 3
+represents such a course. In Group VIII. the Right passage was closed,
+instead of the Left as previously. The first time the animal tried to
+get out of the box after this change in the conditions it walked
+directly into the Right passage. Finding this closed it at once turned
+to the Right, _as it had been accustomed to do when it came in contact
+with the glass plate_, and moved along the side of the box just as it
+did in trying to get around the end of the partition. The path taken
+by the crawfish in this experiment is represented in Fig. 4. It is
+very complex, for the animal wandered about more than fifteen minutes
+before escaping.
+
+The experiment just described to show the importance of the tendency
+to turn in a certain direction was the first one of the first series
+after the change in conditions. When given its second chance in this
+series the subject escaped directly by the Left passage in 33 seconds,
+and for the three following trips the time was respectively 25, 25 and
+30 seconds.
+
+Upon the experimental evidence presented we base the conclusion that
+crawfish are able to profit by experience in much the same way that
+insects do, but far more slowly.
+
+[Illustration: FIG. 4. Path taken by crawfish which had been trained
+to avoid the Left passage, when the Right passage was closed. Showing
+turning to the right as in Fig. 3.]
+
+It was thought that a study of the way in which crawfish right
+themselves when placed upon their backs on a smooth surface might
+furnish further evidence concerning the ability of the animals to
+profit by experience.
+
+Dearborn[3] from some observations of his concludes that there is no
+one method by which an individual usually rights itself, and,
+furthermore, that the animals cannot be trained to any one method. His
+experiments, like Bethe's, are too few to warrant any conclusions as
+to the possibility of habit formation.
+
+   [3] Dearborn, G.V.N.: 'Notes on the Individual Psychophysiology
+   of the Crayfish,' _Amer. Jour. Physiol._, Vol. 3, 1900, pp.
+   404-433.
+
+For the following experiments the subject was placed on its back on a
+smooth surface in the air and permitted to turn over in any way it
+could. Our purpose was to determine (1) whether there was any marked
+tendency to turn in a certain way, (2) whether if such was not the
+case a tendency could be developed by changing the conditions, and (3)
+how alteration in the conditions of the test would affect the turning.
+
+A great many records were taken, but we shall give in detail only a
+representative series. In Table III., 557 tests made upon four
+subjects have been arranged in four groups for convenience of
+comparison of the conditions at different periods of the training
+process. Each of these groups, if perfect, would contain 40 tests for
+each of the four subjects, but as a result of accidents II., III., and
+IV. are incomplete.
+
+
+TABLE III.
+
+  RE-TURNING OF CRAWFISH.
+
+  Group. Number of    L.    R.   Time in   Tests.
+         Animal.      Per cent.  Seconds.
+  I.       2         22.5  77.5    14.6     40
+           3         42.5  57.5     2.6     40
+           4         52.8  47.2     4.3     38
+          16         44.5  55.5    22.5     45
+          --         ----  ----    ----    ---
+                     40.6  59.4    10.8    163
+
+  Group. Number of    L.    R.   Time in   Tests.
+         Animal.      Per cent.  Seconds.
+  II       2         28    72      50       43
+           3         32    68       6.2     50
+           4         --   100       6.8     40
+          16         31.3  68.7    39.3     42
+          --         ----  ----    ----    ---
+                     22.8  77.2    25.6    175
+
+  Group. Number of    L.    R.   Time in   Tests.
+         Animal.      Per cent.  Seconds.
+  III      2         2.5   97.5    46.5     40
+          --        --     --      --       --
+           4        20     80       5.5     40
+          16        41     59      15       49
+          --         ----  ----    ----    ---
+                    21.2   78.8    22      129
+
+  Group. Number of    L.    R.   Time in   Tests.
+         Animal.      Per cent.  Seconds.
+  IV.      2          2    98      41       50
+          --         --     --      --      --
+           4         32.5  67.5     7.3     40
+          --         ----  ----    ----    ---
+                     17    83      24       90
+
+
+Group I., representing 163 tests, shows 59 per cent. to the right,
+with a time interval of 10.8 seconds (_i.e._, the time occupied in
+turning). Group II. shows 77 per cent. to the right; and so throughout
+the table there is an increase in the number of returnings to the
+right. These figures at first sight seem to indicate the formation of
+a habit, but in such case we would expect, also, a shortening of the
+time of turning. It may be, however, that the animals were gradually
+developing a tendency to turn in the easiest manner, and that at the
+same time they were becoming more accustomed to the unusual position
+and were no longer so strongly stimulated, when placed on their backs,
+to attempt to right themselves.
+
+All the subjects were measured and weighed in order to discover
+whether there were inequalities of the two sides of the body which
+would make it easier to turn to the one side than to the other. The
+chelę were measured from the inner angle of the joint of the
+protopodite to the angle of articulation with the dactylopodite. The
+carapace was measured on each side, from the anterior margin of the
+cephalic groove to the posterior extremity of the lateral edge. The
+median length of the carapace was taken, from the tip of the rostrum
+to the posterior edge, and the length of the abdomen was taken from
+this point to the edge of the telson. These measurements, together
+with the weights of three of the subjects, are given in the
+accompanying table.
+
+
+TABLE IV.
+
+MEASUREMENTS OF CRAWFISH.
+
+              Chelę.           Carapace.      Abdomen.   Weight.
+            Left. Right.  Left. Right. Median.
+
+  No.  2,    9.8  10.0    38.2   38.7   47.3    48.1      29.7
+  No.  4,    7.7   7.7    33.6   33.8   39.4    42.3      17.7
+  No. 16,   12.5  12.4    37.6   37.6   46.4    53.2      36.2
+
+
+Since these measurements indicate slightly greater size on the right
+it is very probable that we have in this fact an explanation of the
+tendency to turn to that side.
+
+To test the effect of a change in the conditions, No. 16 was tried on
+a surface slanted at an angle of 1° 12'. Upon this surface the subject
+was each time so placed that the slant would favor turning to the
+right. Under these conditions No. 16 gave the following results in two
+series of tests. In the first series, consisting of 46 turns, 82.6 per
+cent. were to the right, and the average time for turning was 17.4
+seconds; in the second series, of 41 tests, there were 97.5 per cent,
+to the right, with an average time of 2.5 seconds. We have here an
+immediate change in the animal's method of re-turning caused by a
+slight change in the conditions. The subject was now tested again on
+a level surface, with the result that in 49 tests only 59 per cent.
+were toward the right, and the time was 15 seconds.
+
+
+SUMMARY.
+
+
+1. Experiments with crawfish prove that they are able to learn simple
+labyrinth habits. They profit by experience rather slowly, from fifty
+to one hundred experiences being necessary to cause a perfect
+association.
+
+2. In the crawfish the chief factors in the formation of such habits
+are the chemical sense (probably both smell and taste), touch, sight
+and the muscular sensations resulting from the direction of turning.
+The animals are able to learn a path when the possibility of following
+a scent is excluded.
+
+3. The ease with which a simple labyrinth habit may be modified
+depends upon the number of experiences the animal has had; the more
+familiar the animal is with the situation, the more quickly it changes
+its habits. If the habit is one involving the choice of one of two
+passages, reversal of the conditions confuses the subject much more
+the first time than in subsequent cases.
+
+4. Crawfish right themselves, when placed on their backs, by the
+easiest method; and this is found to depend usually upon the relative
+weight of the two sides of the body. When placed upon a surface which
+is not level they take advantage, after a few experiences, of the
+inclination by turning toward the lower side.
+
+       *       *       *       *       *
+
+
+
+
+THE INSTINCTS, HABITS, AND REACTIONS OF THE FROG.
+
+BY ROBERT MEARNS YERKES.
+
+
+PART I. THE ASSOCIATIVE PROCESSES OF THE GREEN FROG.
+
+
+I. SOME CHARACTERISTICS OF THE GREEN FROG.
+
+The common green frog, _Rana clamitans_, is greenish or brownish in
+color, usually mottled with darker spots. It is much smaller than the
+bull frog, being from two to four inches in length ordinarily, and may
+readily be distinguished from it by the presence of prominent
+glandular folds on the sides of the back. In the bull frog, _Rana
+catesbeana_, these folds are very small and indistinct. The green frog
+is found in large numbers in many of the ponds and streams of the
+eastern United States, and its peculiar rattling croak may be heard
+from early spring until fall. It is more active, and apparently
+quicker in its reactions, than the bull frog, but they are in many
+respects similar in their habits. Like the other water frogs it feeds
+on small water animals, insects which chance to come within reach and,
+in times of famine, on its own and other species of frogs. The prey is
+captured by a sudden spring and the thrusting out of the tongue, which
+is covered with a viscid secretion. Only moving objects are noticed
+and seized; the frog may starve to death in the presence of an
+abundance of food if there is no movement to attract its attention.
+Most green frogs can be fed in captivity by swinging pieces of meat in
+front of them, and those that will not take food in this way can be
+kept in good condition by placing meat in their mouths, for as soon as
+the substance has been tasted swallowing follows.
+
+The animals used for these experiments were kept in the laboratory
+during the whole year in a small wooden tank. The bottom of this tank
+was covered with sand and small stones, and a few plants helped to
+purify the water. An inch or two of water sufficed; as it was not
+convenient to have a constant stream, it was changed at least every
+other day. There was no difficulty whatever in keeping the animals in
+excellent condition.
+
+Of the protective instincts of the green frog which have come to my
+notice during these studies two are of special interest: The
+instinctive inhibition of movement under certain circumstances, and
+the guarding against attack or attempt to escape by 'crouching' and
+'puffing.' In nature the frog ordinarily jumps as soon as a strange or
+startling object comes within its field of vision, but under certain
+conditions of excitement induced by strong stimuli it remains
+perfectly quiet, as do many animals which feign death, until forced to
+move. Whether this is a genuine instinctive reaction, or the result of
+a sort of hypnotic condition produced by strong stimuli, I am not
+prepared to say. The fact that the inhibition of movement is most
+frequently noticed after strong stimulation, would seem to indicate
+that it is due to the action of stimuli upon the nervous system.
+
+What appears to be an instinctive mode of guarding against attack and
+escaping an enemy, is shown whenever the frog is touched about the
+head suddenly, and sometimes when strong stimuli are applied to other
+parts of the body. The animal presses its head to the ground as if
+trying to dive or dodge something, and inflates its body. This kind of
+action is supposed to be a method of guarding against the attack of
+snakes and other enemies which most frequently seize their prey from
+the front. It is obvious that by pressing its head to the ground the
+frog tends to prevent any animal from getting it into its mouth, and
+in the few instants' delay thus gained it is able to jump. This is
+just the movement necessary for diving, and it is probable that the
+action should be interpreted in the light of that instinctive reflex.
+The 'puffing' also would seem to make seizure more difficult. Another
+fact which favors this interpretation is that the response is most
+commonly given to stimuli which seem to come from the front and which
+for this reason could not easily be escaped by a forward jump, while
+if the stimulus is so given that it appears to be from the rear the
+animal usually jumps away immediately. We have here a complex
+protective reaction which may be called a forced movement. It is, so
+far as one can see, very much like many reflexes, although it does not
+occur quite so regularly.
+
+The machine-like accuracy of many of the frog's actions gives a basis
+for the belief that the animal is merely an automaton. Certain it is
+that one is safe in calling almost all the frog's actions reflex or
+instinctive. During months of study of the reaction-time of the frog I
+was constantly impressed with the uniformity of action and surprised
+at the absence of evidences of profiting by experience. In order to
+supplement the casual observations on the associations of the green
+frog made in the course of reaction-time experiments, the tests
+described in this paper were made. They do not give a complete view of
+the associative processes, but rather such a glimpse as will enable us
+to form some conception of the relation of the mental life of the frog
+to that of other animals. This paper presents the outlines of work the
+details of which I hope to give later.
+
+
+II. EXPERIMENTAL STUDY OF HABITS.
+
+
+A. The Chief Problems for which solutions were sought in the following
+experimental study were: (1) Those of associability in general, its
+characteristics, and the rapidity of learning; (2) of discrimination,
+including the parts played in associative processes by the different
+senses, and the delicacy of discrimination in each; (3) of the
+modifiability of associational reactions and general adaptation in the
+frog, and (4) of the permanency of associations.
+
+
+B. Simple Associations, as studied in connection with reaction-time
+work, show that the green frog profits by experience very slowly as
+compared with most vertebrates. The animals have individual
+peculiarities in reaction which enable one in a short time to
+recognize any individual. To these characteristic peculiarities they
+stick tenaciously. One, for instance, always jumps upward when
+strongly stimulated; another has a certain corner of the tank in which
+it prefers to sit. Their habits are remarkably strong and invariable,
+and new ones are slowly formed. While using a large reaction box I
+noticed that the frogs, after having once escaped from an opening
+which could be made by pushing aside a curtain at a certain point in
+the box, tended to return to that place as soon as they were again put
+into the box. This appeared to be evidence of an association; but the
+fact that such stimuli as light and the relation of the opening to the
+place at which the animals were put into the box might in themselves
+be sufficient to direct the animals to this point without the help of
+any associations which had resulted from previous experience, makes it
+unsatisfactory. In addition to the possibility of the action being due
+to specific sensory stimuli of inherent directive value, there is the
+chance of its being nothing more than the well-known phenomenon of
+repetition. Frogs, for some reason, tend to repeat any action which
+has not proved harmful or unpleasant.
+
+For the purpose of more carefully testing this kind of association, a
+small box with an opening 15 cm. by 10 cm. was arranged so that the
+animal could escape from confinement in it through the upper part of
+the opening, the lower portion being closed by a plate of glass 10 cm.
+by 10 cm., leaving a space 5 cm. by 10 cm. at the top. One subject
+placed in this box escaped in 5 minutes 42 seconds. After 5 minutes'
+rest it was given another trial, and this time got out in 2 minutes 40
+seconds. The times for a few subsequent trials were: Third, 1 minute
+22 seconds; fourth, 4 minutes 35 seconds; fifth, 2 minutes 38 seconds;
+sixth, 3 minutes 16 seconds. Although this seems to indicate some
+improvement, later experiments served to prove that the frogs did not
+readily form any associations which helped them to escape. They tended
+to jump toward the opening because it was light, but they did not
+learn with twenty or thirty experiences that there was a glass at the
+bottom to be avoided. Thinking that there might be an insufficient
+motive for escape to effect the formation of an association, I tried
+stimulating the subject with a stick as soon as it was placed in the
+box. This frightened it and caused violent struggles to escape, but
+instead of shortening the time required for escape it greatly
+lengthened it. Here was a case in which the formation of an
+association between the appearance of the upper part of the clear
+space and the satisfaction of escape from danger would have been of
+value to the frog, yet there was no evidence of adaptation to the new
+conditions within a reasonably short time. There can be little doubt
+that continuation of the training would have served to establish the
+habit. This very clearly shows the slowness of adaptation in the frog,
+in contrast with the rapidity of habit formation in the cat or chick;
+and at the same time it lends additional weight to the statement that
+instinctive actions are all-important in the frog's life. A few things
+it is able to do with extreme accuracy and rapidity, but to this list
+new reactions are not readily added. When put within the box
+described, an animal after having once escaped would sometimes make
+for the opening as if it knew perfectly the meaning of the whole
+situation, and yet the very next trial it would wander about for half
+an hour vainly struggling to escape.
+
+A considerable number of simple experiments of this kind were tried
+with results similar to those just given. The frog apparently examines
+its surroundings carefully, and just when the observer thinks it has
+made itself familiar with the situation it reacts in such a way as to
+prove beyond doubt the absence of all adaptation. In all these
+experiments it should be said, for the benefit of any who may be
+trying similar work, that only animals of exceptional activity were
+used. Most green frogs when placed in the experiment box either sit
+still a great part of the time or jump about for only a short time. It
+is very important for studies of this kind, both on account of time
+saving and the obtaining of satisfactory records, to have animals
+which are full of energy and eager to escape when in confinement. By
+choosing such subjects one may pretty certainly avoid all unhealthy
+individuals, and this, it seems to me, counterbalances the
+disadvantage of taking animals which may be unusually quick in
+learning.
+
+
+C. Complex Associations.
+
+1. _Labyrinth Habits_.--A more thorough investigation of the
+associative processes, sensory discrimination and the permanency of
+impressions has been made by the labyrinth method. A wooden box, 72
+cm. long, 28 cm. wide and 28 cm. deep, whose ground plan is
+represented by Fig. 1, served as the framework for a simple labyrinth.
+At one end was a small covered box, _A_, from which the frog was
+allowed to enter the labyrinth. This entrance passage was used in
+order that the animal might not be directed to either side by the
+disturbance caused by placing it in the box. _E_, the entrance, marks
+a point at which a choice of directions was necessary. _P_ is a
+movable partition which could be used to close either the right or the
+left passage. In the figure the right is closed, and in this case if
+the animal went to the right it had to turn back and take the left
+passage in order to get out of the box. A series of interrupted
+electrical circuits, _IC_, covered the bottom of a portion of the
+labyrinth; by closing the key, _K_, the circuit could be made whenever
+a frog rested upon any two wires of the series. When the frog happened
+to get into the wrong passage the key was closed and the animal
+stimulated. This facilitated the experiment by forcing the animal to
+seek some other way of escape, and it also furnished material for an
+association. Having passed through the first open passage, which for
+convenience we may know as the entrance passage, the animal had to
+choose again at the exit. Here one of the passages was closed by a
+plate of glass (in the figure the left) and the other opened into a
+tank containing water. The box was symmetrical and the two sides were
+in all respects the same except for the following variable conditions.
+At the entrance the partition on one side changed the appearance, as
+it was a piece of board which cut off the light. On either side of the
+entrance there were grooves for holding card-boards of any desired
+color. The letters _R, R_ mark sides which in this case were covered
+with red; _W, W_ mark white spaces. These pieces of cardboard could
+easily be removed or shifted at any time. At the exit the glass plate
+alone distinguished the sides, and it is not likely that the animals
+were able to see it clearly. We have thus at the entrance widely
+differing appearances on the two sides, and at the exit similarity.
+The opening from _A_ into the large box was provided with a slide door
+so that the animal could be prevented from returning to _A_ after
+entering the labyrinth. The partitions and the triangular division at
+the entrance extended to the top of the box, 28 cm., so that the
+animals could not readily jump over them.
+
+[Illustration: FIG. 1. Ground Plan of Labyrinth. _A_, small box
+opening into labyrinth; _E_, entrance of labyrinth; _T_, tank
+containing water; _G_, glass plate closing one passage of exit; _P_,
+partition closing one passage at entrance; _IC_, interrupted
+electrical circuit; _C_, cells; _K_, key in circuit; _RR_, red
+cardboard; _WW_, white cardboard. Scale 1/12.]
+
+The experiments were made in series of ten, with ten-minute intervals
+between trials. In no case was more than one series a day taken, and
+wherever a day was missed the fact has been indicated in the tables.
+The only motive of escape from the box depended upon was the animal's
+desire to return to the water of the tank and to escape from
+confinement in the bright light of the room. The tank was one in which
+the frogs had been kept for several months so that they were familiar
+with it, and it was as comfortable a habitat as could conveniently be
+arranged. Usually the animals moved about almost constantly until they
+succeeded in getting out, but now and then one would remain inactive
+for long intervals; for this reason no record of the time taken for
+escape was kept. On account of the great amount of time required by
+experiments of this kind I have been unable to repeat this series of
+experiments _in toto_ on several animals in order to get averages, but
+what is described for a representative individual has been proved
+normal by test observations on other animals. There are very large
+individual differences, and it may well be that the subject of the
+series of experiments herein described was above the average in
+ability to profit by experience. But, however that may be, what is
+demonstrated for one normal frog is thereby proved a racial
+characteristic, although it may be far from the mean condition.
+
+Before beginning training in the labyrinth, preliminary observations
+were made to discover whether the animals had any tendencies to go
+either to the right or to the left. When the colored cardboards were
+removed it was found that there was usually no preference for right or
+left. In Table I. the results of a few preliminary trials with No. 2
+are presented. For these the colors were used, but a tendency to the
+right shows clearly. Trials 1 to 10 show choice of either the right or
+the red throughout; that it was partly both is shown by trials 11 to
+30, for which the colors were reversed. This individual has therefore,
+to begin with, a tendency to the right at the entrance. At the exit it
+went to the right the first time and continued so to do for several
+trials, but later it learned by failure that there was a blocked
+passage as well as an open one. In the tables the records refer to
+choices. It was useless to record time or to lay much stress upon the
+course taken, as it was sometimes very complicated; all that is given,
+therefore, is the action in reference to the passages. _Right_ in
+every case refers to the choice of the open way, and _wrong_ to the
+choice of the blocked passage. The paths taken improved steadily in
+that they became straighter. A few representative courses are given in
+this report. Usually if the animal was not disturbed a few jumps
+served to get it out of the labyrinth.
+
+
+TABLE I.
+
+    PRELIMINARY TRIALS WITH FROG NO. 2.
+
+    Trials.  Red on Right.   White on Left.
+    1 to 10  10 times to red       0
+
+             Red on Left.    White on Right.
+    11 to 20 4 times to red        6
+
+             Red on Left.    White on Right.
+    21 to 30 3 times to red        7
+
+             To Red.  To White.  To Right. To Left.
+    Totals.    17        13         23        7
+
+
+This table indicates in trials 1 to 10 a strong tendency to the red
+cardboard. Trials 21 to 30 prove that there was also a tendency to the
+right.
+
+Training was begun with the labyrinth arranged as shown in Fig. 1,
+that is, with the left entrance passage and the right exit passage
+open, and with red cardboard on the right (red was always on the side
+to be avoided) and white on the left. Table II. contains the results
+of 110 trials with No. 2, arranged according to right and wrong choice
+at the entrance and exit. Examination of this table shows a gradual
+and fairly regular increase in the number of right choices from the
+first series to the last; after 100 experiences there were practically
+no mistakes.
+
+With another subject, No. _6a_, the results of Table III. were
+obtained. In this instance the habit formed more slowly and to all
+appearances less perfectly. Toward the end of the second week of work
+_6a_ showed signs of sickness, and it died within a few weeks, so I do
+not feel that the experiments with it are entirely trustworthy. During
+the experiments it looked as if the animal would get a perfectly
+formed habit very quickly, but when it came to the summing up of
+results it was obvious that there had been little improvement.
+
+[Illustration: FIG. 2. Labyrinth as arranged for experiments. _E_,
+entrance; _R, R_, regions covered with red; _W, W_, regions covered
+with white. The tracing represents the path taken by No. 2 on the
+sixth trial. Dots mark jumps.]
+
+
+TABLE II.
+
+    LABYRINTH HABIT. FROG NO. 2.
+
+              Entrance.        Exit.     Remarks.
+    Trials. Right. Wrong.  Right. Wrong.
+     1- 10    1       9      4       6
+                                         One day rest.
+    11- 20    2       8      5       5
+    21- 30    4       6      7       3
+    31- 40    5       5      6       4
+    41- 50    5       5      6       2
+               (17)    (33)   (30)    (20)
+    51- 60    9       1      8       2
+    61- 70    6       4     10       0
+    71- 80    7       3      9       1
+    81- 90    9       1      8       2
+    91-100    10(50)  0(10) 10(52)   0( 8)
+                 ---    ---    ---     ---
+                 67     43     82      28
+
+
+Other animals which were used gave results so similar to those for
+frog No. 2 that I feel justified in presenting the latter as
+representative of the rapidity with which the green frog profits by
+experience.
+
+
+TABLE III.
+
+    LABYRINTH HABIT. FROG NO. _6a_.
+
+               Entrance.          Exit.        Remarks.
+    Trials   Right.  Wrong.   Right.  Wrong.
+     1- 10     6       4       5        5
+                                               One day rest.
+    11- 20     7       3       4        6
+    21- 30     2       8       1        9
+    31- 40     6       4       1        9
+    41- 50     7       3       8        2
+                (28)    (22)    (19)     (31)
+    51- 60     5       5       7        3
+    61- 70     6       4       4        6
+    71- 80     4       6       3        7
+                                               One day rest.
+    81- 90     5       5       7        3
+    91-100    10(30)   0(20)   8(29)    2(21)
+                ----    ----    ----     ----
+                (58)    (44)   (48)     (52)
+
+                      Preliminary Trials.
+
+                    Red on Left     Partition at Exit on Right
+    1- 5          5 times to Red       4 times to Partition.
+
+                     Red on Right   Partition at Exit on Left
+    6-10          3 times to Red       5 times to Partition.
+
+
+2. _Rapidity of Habit Formation_.--As compared with other vertebrates
+whose rapidity of habit formation is known, the frog learns slowly.
+Experimental studies on the dog, cat, mouse, chick and monkey furnish
+excellent evidence of the ability of these animals to profit quickly
+by experience through the adapting of their actions to new conditions.
+They all show marked improvement after a few trials, and after from
+ten to thirty most of them have acquired perfect habits. But the
+comparison of the frog with animals which are structurally more
+similar to it is of greater interest and value, and we have to inquire
+concerning the relation of habit formation in the frog to that of
+fishes and reptiles. Few experimental studies with these animals have
+been made, and the material for comparison is therefore very
+unsatisfactory. E.L. Thorndike[1] has demonstrated the ability of
+fishes to learn a labyrinth path. In his report no statement of the
+time required for the formation of habit is made, but from personal
+observation I feel safe in saying that they did not learn more quickly
+than did the frogs of these experiments. Norman Triplett[2] states
+that the perch learns to avoid a glass partition in its aquarium after
+repeatedly bumping against it. Triplett repeated Moebius' famous
+experiment, and found that after a half hour's training three times a
+week for about a month, the perch would not attempt to capture minnows
+which during the training periods had been placed in the aquarium with
+the perch, but separated from them by a glass partition. Triplett's
+observations disprove the often repeated statement that fishes do not
+have any associative processes, and at the same time they show that
+the perch, at least, learns rapidly--not so rapidly, it is true, as
+most animals, but more so in all probability than the amphibia.
+
+   [1] Thorndike, Edward: 'A Note on the Psychology of Fishes,'
+   _American Naturalist_. 1899, Vol. XXXIII., pp. 923-925.
+
+   [2] Triplett, Norman: 'The Educability of the Perch,' _Amer.
+   Jour. Psy._, 1901, Vol. XII., pp. 354-360.
+
+The only quantitative study of the associative processes of reptiles
+available is some work of mine on the formation of habits in the
+turtle.[3] In the light of that study I can say that the turtle learns
+much more rapidly than do fishes or frogs. Further observations on
+other species of turtles, as yet unpublished, confirm this conclusion.
+
+   [3] Yerkes, Robert Mearns: 'The Formation of Habits in the
+   Turtle,' _Popular Science Monthly_, 1901, Vol. LVIII., pp.
+   519-535.
+
+For the frog it is necessary to measure and calculate the improvement
+in order to detect it at first, while with the turtle or chick the
+most casual observer cannot fail to note the change after a few
+trials. In connection with the quickness of the formation of
+associations it is of interest to inquire concerning their permanency.
+Do animals which learn slowly retain associations longer? is a
+question to which no answer can as yet be given, but experiments may
+readily be made to settle the matter. I have tested the frog for
+permanency, and also the turtle, but have insufficient data for
+comparison.
+
+
+3. _Sensory Data Contributing to the Associations_.--Among the most
+important of the sensory data concerned in the labyrinth habit are the
+visual impressions received from the different colored walls, the
+slight differences in brightness of illumination due to shadows from
+the partitions and the contrast in form of the two sides of the
+labyrinth resulting from the use of the partitions, and the muscular
+sensations dependent upon the direction of turning. The experiments
+proved beyond question that vision and the direction of turning were
+the all-important factors in the establishment of the habit. At first
+it seemed as if the direction of turning was the chief determinant,
+and only by experimenting with colors under other conditions was I
+able to satisfy myself that the animals did notice differences in the
+appearance of their surroundings and act accordingly. In Table IV.
+some results bearing on this point have been arranged. To begin with,
+the habit of going to the left when the red was on the right at the
+entrance had been established; then, in order to see whether the
+colors influenced the choice, I reversed the conditions, placing the
+red on the left, that is, on the open-passage side. The results as
+tabulated in the upper part of Table IV. show that the animals were
+very much confused by the reversal; at the entrance where there were
+several guiding factors besides the colors there were 50 per cent. of
+mistakes, while at the exit where there were fewer differences by
+which the animal could be directed it failed every time. This work was
+not continued long enough to break up the old habit and replace it by
+a new one, because I wished to make use of the habit already formed
+for further experiments, and also because the animals remained so long
+in the labyrinth trying to find their way out that there was constant
+danger of losing them from too prolonged exposure to the dry air.
+
+
+TABLE IV.
+
+  INFLUENCE OF CHANCES OF CONDITIONS. FROG NO. 2.
+
+     Habit perfectly formed of going to Left (avoiding Red) at
+     entrance and to Right at exit. Conditions now reversed. Red on
+     Left. Partition at Exit on Right.
+
+  Trials.         Entrance.             Exit.         Remarks.
+             Right.     Wrong.     Right.     Wrong.
+   1- 5        3           2         0           5
+   6-10        2           3         0           5
+
+   Discontinued because animal remained so long in labyrinth that
+   there was danger of injuring it for further work. This shows
+   that the habit once formed is hard to change.
+
+   Given 20 trials with conditions as at first in order to
+   establish habit again.
+
+   1-10        9           1         8            2
+  11-20       10           0         9            1
+
+     Colors reversed, no other change. To test influence of colors.
+
+   1-10        6           4        10            0
+
+
+  INFLUENCE OF DISTURBANCE WHEN ANIMAL IS ENTERING BOX.
+
+          No Disturbance.              Animal Touched.
+
+  To Red (Right).  To White (Left).  To Red.   To White.
+        2                 8             5          5
+
+   This was after the tendency to go to the Left at the entrance
+   had been established.
+
+
+These experiments to test the effect of changing colors are also of
+interest in that they show in a remarkable way the influence of the
+direction of turning. The animal after succeeding in getting around
+the first part of the labyrinth failed entirely to escape at the exit.
+Here it should have turned to the left, instead of the right as it was
+accustomed to, but it persisted in turning to the right. Fig. 3
+represents approximately the path taken in the first trial; it shows
+the way in which the animal persisted in trying to get out on the
+right. From this it is clear that both vision and the complex
+sensations of turning are important.
+
+[Illustration: FIG. 3. Labyrinth with Conditions the Reverse of the
+Usual. (Compare with FIG. 2.) The colors as well as the partitions
+have been shifted. The path is, approximately, that taken by No. 2 in
+the first trial after the reversal of conditions.]
+
+The latter part of Table IV. presents further evidence in favor of
+vision. For these tests the colors alone were reversed. Previous to
+the change the animal had been making no mistakes whatever, thereafter
+there were four mistakes at the entrance and none at the exit. Later,
+another experiment under the same conditions was made with the same
+animal, No. 2, with still more pronounced results. In this case the
+animal went to the white, that is, in this instance, into the blind
+alley, and failed to get out; several times it jumped over to the left
+side (the open-passage side) of the box but each time it seemed to be
+attracted back to the white or repelled by the red, more probably the
+latter, as the animal had been trained for weeks to avoid the red.
+Concerning the delicacy of visual discrimination I hope to have
+something to present in a later paper.
+
+The tactual stimuli given by contact with the series of wires used for
+the electrical stimulus also served to guide the frogs. They were
+accustomed to receive an electrical shock whenever they touched the
+wires on the blocked side of the entrance, hence on this side the
+tactual stimulus was the signal for a painful electrical stimulus.
+When the animal chose the open passage it received the tactual
+stimulus just the same, but no shock followed. After a few days'
+experimentation it was noted that No. 2 frequently stopped as soon as
+it touched the wires, whether on the open or the closed side. If on
+the closed side, it would usually turn almost immediately and by
+retracing its path escape by the open passage; if on the open side, it
+would sometimes turn about, but instead of going back over the course
+it had just taken, as on the other side, it would sit still for a few
+seconds, as if taking in the surroundings, then turn again and go on
+its way to the exit. This whole reaction pointed to the formation of
+an association between the peculiar tactual sensation and the painful
+shock which frequently followed it. Whenever the tactual stimulus came
+it was sufficient to check the animal in its course until other
+sensory data determined the next move. When the wrong passage had been
+chosen the visual data gotten from the appearance of the partition
+which blocked the path and other characteristics of this side of the
+labyrinth determined that the organism should respond by turning back.
+When, on the other hand, the open passage had been selected, a
+moment's halt sufficed to give sensory data which determined the
+continuation of the forward movement. Although this reaction did not
+occur in more than one tenth of the trials, it was so definite in its
+phases as to warrant the statements here made. Fig. 4 gives the path
+taken by No. 2 in its 123d trial. In this experiment both choices were
+correctly made, but when the frog touched the wires on the open side
+it stopped short and wheeled around; after a moment it turned toward
+the exit again, but only to reverse its position a second time. Soon
+it turned to the exit again, and this time started forward, taking a
+direct course to the tank. The usual course for animals which had
+thoroughly learned the way to the tank is that chosen in Fig. 5.
+
+[Illustration: FIG. 4. Path of No. 2 for 123d Trial. Showing the
+response to the tactual stimulus from wires.]
+
+An interesting instance of the repetition of a reaction occurred in
+these experiments. A frog would sometimes, when it was first placed in
+the box, by a strong jump get up to the edge; it seldom jumped over,
+but instead caught hold of the edge and balanced itself there until
+exhaustion caused it to fall or until it was taken away. Why an animal
+should repeat an action of the nature of this is not clear, but almost
+invariably the second trial resulted in the same kind of reaction. The
+animal would stop at the same point in the box at which it had
+previously jumped, and if it did not jump, it would look up as if
+preparing to do so. Even after a frog had learned the way to the tank
+such an action as this would now and then occur, and almost always
+there would follow repetition in the manner described.
+
+[Illustration: FIG. 5. Path Usually Taken by Animal Having
+Perfectly-formed Habit.]
+
+
+4. _The Effect of Fear upon Habit Formation._--A certain amount of
+excitement undoubtedly promotes the formation of associations, but
+when the animal is frightened the opposite is true. I have no
+hesitation in stating that, in case of the green frog, any strong
+disturbing stimulus retards the formation of associations. Although
+the frogs gave little evidence of fear by movements after being kept
+in the laboratory for a few weeks, they were really very timid, and
+the presence of any strange object influenced all their reactions.
+Quiescence, it is to be remembered, is as frequently a sign of fear as
+is movement, and one is never safe in saying that the frog is not
+disturbed just because it does not jump. The influence of the
+experimenter's presence in the room with the frogs which were being
+tried in the labyrinth became apparent when the animals were tried in
+a room by themselves. They escaped much more quickly when alone. In
+order to keep records of the experiments it was necessary for me to be
+in the room, but by keeping perfectly quiet it was possible to do this
+without in any objectionable way influencing the results. It may be,
+however, that for this reason the learning is somewhat slower than it
+would have been under perfectly natural conditions. Early in this
+paper reference was made to the fact that the frog did not learn to
+escape from a box with a small opening at some distance from the floor
+if it was prodded with a stick. I do not mean to say that the animal
+would never learn under such conditions, but that they are unfavorable
+for the association of stimuli and retard the process. This conclusion
+is supported by some experiments whose results are tabulated at the
+bottom of Table IV. In these trials the animal had been trained to go
+to the left and to avoid red. At first ten trials were given in which
+the frog was in no way disturbed. The result was eight right choices
+and two wrong ones. For the next ten trials the frog was touched with
+a stick and thus made to enter the labyrinth from the box, _A_. This
+gave five right and five wrong choices, apparently indicating that the
+stimulus interfered with the choice of direction. Several other
+observations of this nature point to the same conclusion, and it may
+therefore be said that fright serves to confuse the frog and to
+prevent it from responding to the stimuli which would ordinarily
+determine its reaction.
+
+
+5. _The Permanency of Associations._--After the labyrinth habit had
+been perfectly formed by No. 2, tests for permanency were made, (1)
+after six days' rest and (2) after thirty days. Table V. contains the
+results of these tests. They show that for at least a month the
+associations persist. And although there are several mistakes in the
+first trials after the intervals of rest, the habit is soon perfected
+again. After the thirty-day interval there were forty per cent. of
+mistakes at the exit for the first series, and only 20 per cent. at
+the entrance. This in all probability is explicable by the fact that
+the colors acted as aids at the entrance, whereas at the exit there
+was no such important associational material.
+
+
+TABLE V.
+
+  PERMANENCY OF ASSOCIATIONS. FROG NO. 2.
+
+  Tests after six days' rest (following the results tabulated in Table
+  III.).
+
+       Trial.               Entrance.               Exit.
+                         Right.    Wrong.     Right.    Wrong
+       1-10                7          3         8         2
+    (110-120)
+      11-20               10          0        10         0
+
+                 Tests after THIRTY days' rest.
+       1-10                8          2         6         4
+      10-20               10          0        10         0
+
+
+D. Association of Stimuli.--In connection with reaction-time work an
+attempt was made to form an association between a strong visual
+stimulus and a painful electrical shock, with negative results. A
+reaction box, having a series of interrupted circuits in the bottom
+like those already described for other experiments, and an opening on
+one side through which a light could be flashed upon the animal,
+served for the experiments. The tests consisted in the placing of a
+frog on the wires and then flashing an electric light upon it: if it
+did not respond to the light by jumping off the wires, an electrical
+stimulus was immediately given. I have arranged in Table VI. the
+results of several weeks' work by this method. In no case is there
+clear evidence of an association; one or two of the frogs reacted to
+the light occasionally, but not often enough to indicate anything more
+than chance responses. At one time it looked as if the reactions
+became shorter with the continuation of the experiment, and it was
+thought that this might be an indication of the beginning of an
+association. Careful attention to this aspect of the results failed to
+furnish any satisfactory proof of such a change, however, and although
+in the table statements are given concerning the relative numbers of
+short and long reactions I do not think they are significant.
+
+
+TABLE VI.
+
+  ASSOCIATION OF ELECTRICAL AND VISUAL STIMULI. FROG No. 1a, 2a, 3a, 4a,
+  5a, A and Z.
+
+  Frog.  Total No.  Days.      Result.
+          Trials.
+
+  No. 1a   180       18     Increase in number of long reaction
+                            toward end. No evidence of association.
+
+  No. 2a   180       17     Increase in number of short reactions
+                            toward end. No evidence of association.
+
+  No. 3a   180       17     Marked increase in the number of
+                            short reactions toward end. No other evidence
+                            of association.
+
+  No. 4a   200       19     Slight increase in the short reactions.
+                            There were a few responses to the light on the
+                            third day.
+
+  No. 5a   200       20     No increase in the number of short reactions.
+                            Few possible responses to light on second and
+                            third days.
+
+  Frog A   250       20     No evidence of association.
+
+  Frog Z   450       28     No evidence of association.
+
+
+To all appearances this is the same kind of an association that was
+formed, in the case of the labyrinth experiments, between the tactual
+and the electrical stimuli. Why it should not have been formed in this
+case is uncertain, but it seems not improbable that the light was too
+strong an excitement and thus inhibited action. There is also the
+probability that the frog was constrained by being placed in a small
+box and having the experimenter near.
+
+
+III. SUMMARY.
+
+
+1. The green frog is very timid and does not respond normally to most
+stimuli when in the presence of any strange object. Fright tends to
+inhibit movement.
+
+2. That it is able to profit by experience has been proved by testing
+it in simple labyrinths. A few experiences suffice for the formation
+of simple associations; but in case of a series of associations from
+fifty to a hundred experiences are needed for the formation of a
+perfect habit.
+
+3. Experiment shows that the frog is able to associate two kinds of
+stimuli, _e.g._, the peculiar tactual stimulus given by a wire and a
+painful electric stimulus which in the experiments followed the
+tactual. In this case the animal learns to jump away, upon receiving
+the tactual stimulus, before the experimenter gives the electric
+stimulus.
+
+4. Vision, touch and the organic sensations (dependent upon direction
+of turning) are the chief sensory factors in the associations. The
+animals discriminate colors to some extent.
+
+5. Perfectly formed habits are hard to change.
+
+6. Fear interferes with the formation of associations.
+
+7. Associations persist for at least a month.
+
+
+PART II. REACTION TIME OF THE GREEN FROG TO ELECTRICAL AND TACTUAL
+STIMULI.
+
+
+IV. THE PROBLEMS AND POSSIBILITIES OF COMPARATIVE REACTION-TIME
+STUDIES.
+
+
+Animal reaction time is at present a new field of research of evident
+importance and full of promise. A great deal of time and energy has
+been devoted to the investigation of various aspects of the time
+relations of human neural processes; a multitude of interesting facts
+have been discovered and a few laws established, but the results seem
+disproportionate to the amount of patient labor expended.
+Physiologists have determined the rate of transmission of the neural
+impulse for a few animals, and rough estimates of the time required
+for certain changes in the nervous system have been made, but this is
+all we have to represent comparative study. Just the path of approach
+which would seem most direct, in case of the time of neural changes,
+has been avoided. Something is known of the ontogenetic aspect of the
+subject, practically nothing of the phylogenetic; yet, in the study of
+function the comparative point of view is certainly as important as it
+is in the study of structure. In calling attention to the importance
+of the study of animal reaction time I would not detract from or
+minimize the significance of human investigations. They are all of
+value, but they need to be supplemented by comparative studies.
+
+It is almost impossible to take up a discussion of the time relations
+of neural processes without having to read of physiological and
+psychological time. The time of nerve transmission, we are told, is
+pure physiological time and has nothing whatever to do with psychic
+processes; the time occupied by the changes in brain centers is, on
+the contrary, psychological time. At the very beginning of my
+discussion of this subject I wish to have it clearly understood that I
+make no such distinction. If one phase of the neural process be called
+physiological time, with as good reason may all be so named. I prefer,
+therefore, to speak of the time relations of the neural process.
+
+Of the value of reaction-time studies, one may well believe that it
+lies chiefly in the way of approach which they open to the
+understanding of the biological significance of the nervous system.
+Certainly they are not important as giving us knowledge of the time of
+perception, cognition, or association, except in so far as we discover
+the relations of these various processes and the conditions under
+which they occur most satisfactorily. To determine how this or that
+factor in the environment influences the activities of the nervous
+system, and in what way system may be adjusted to system or
+part-process to whole, is the task of the reaction-time investigator.
+
+The problems of reaction time naturally fall within three classes:
+Those which deal with (1) nerve transmission rates; (2) the time
+relations of the spinal center activities, and (3) brain processes.
+Within each of these groups there are innumerable special problems for
+the comparative physiologist or psychologist. Under class 1, for
+instance, there is the determining of the rates of impulse
+transmission in the sensory and the motor nerves, (_a_) for a variety
+of stimuli, (_b_) for different strengths of each stimulus, (_c_) for
+different conditions of temperature, moisture, nourishment, fatigue,
+etc., in case of each stimulus, (_d_) and all this for hundreds of
+representative animals. From this it is clear that lines of work are
+not lacking.
+
+Closely related to these problems of rate of transmission are certain
+fundamental problems concerning the nature of the nerve impulse or
+wave. Whether there is a nerve wave, the reaction-time worker has as
+favorable an opportunity to determine as anyone, and we have a right
+to expect him to do something along this line. The relations of the
+form of the nerve impulse to the rhythm of vital action, to fatigue
+and to inhibition are awaiting investigation. Some of the most
+important unsettled points of psychology depend upon those aspects of
+neural activities which we ordinarily refer to as phenomena of
+inhibition, and which the psychologist is helpless to explain so long
+as the physiological basis and conditions are not known.
+
+Then, too, in the study of animals the relation of reaction time to
+instincts, habits, and the surroundings of the subject are to be
+noted. Variability and adaptability offer chances for extended
+biological inquiries; and it is from just such investigations as
+these that biology has reason to expect much. The development of
+activity, the relation of reflex action to instinctive, of impulsive
+to volitional, and the value of all to the organism, should be made
+clear by reaction-time study. Such are a few of the broad lines of
+inquiry which are before the comparative student of animal reaction
+time. It is useless to dwell upon the possibilities and difficulties
+of the work, they will be recognized by all who are familiar with the
+results of human studies.
+
+In the study of the time relations of neural processes Helmholtz was
+the pioneer. By him, in 1850, the rate of transmission of the nerve
+impulse in the sciatic nerve of the frog was found to be about 27
+meters per second[4]. Later Exner[5] studied the time occupied by
+various processes in the nervous system of the frog by stimulating the
+exposed brain in different regions and noting the time which
+intervened before a contraction of the gastrocnemius in each case.
+Further investigation of the frog's reflex reaction time has been made
+by Wundt[6], Krawzoff and Langendorff[7], Wilson[8] and others, but in
+no case has the method of study been that of the psychologist. Most of
+the work has been done by physiologists who relied upon vivisectional
+methods. The general physiology of the nervous system of the frog has
+been very thoroughly worked up and the papers of Sanders-Ezn[9],
+Goltz[10] Steiner[11] Schrader[12] and Merzbacher[13],[14] furnish an
+excellent basis for the interpretation of the results of the
+reaction-time studies.
+
+   [4] Helmholtz, H.: 'Vorläufiger Bericht über die
+   Portpflanzungsgeschwindigkeit der Nervenreizung.' _Arch. f.
+   Anal. u. Physiol._, 1850, S. 71-73.
+
+   [5] Exner, S.: 'Experimentelle Untersuchung der einfachsten
+   psychischen Processe.' _Pflüger's Arch._, Bd. 8. 1874, S.
+   526-537.
+
+   [6] Wundt, W.: 'Untersuchungen zur Mechanik der Nerven und
+   Nervencentren.' Stuttgart, 1876.
+
+   [7] Krawzoff, L., und Langendorff, O.: 'Zur elektrischen
+   Reizung des Froschgehirns.' _Arch. f. Anal. u. Physiol._,
+   Physiol. Abth., 1879, S. 90-94.
+
+   [8] Wilson, W.H.: 'Note on the Time Relations of Stimulation of
+   the Optic Lobes of the Frog.'_Jour. of Physiol._, Vol. XI.,
+   1890, pp. 504-508.
+
+   [9] Sanders-Ezn: 'Vorarbeit für die Erforschung des
+   Reflexmechanismus in Lendentmark des Frosches.' _Berichte über
+   die Verhandlungen der Kgl. sächs. Gesellsch. d. Wissensch. zu
+   Leipzig_, 1867, S. 3.
+
+   [10] Goltz, F.: 'Beiträge zur Lehre von den Functionen der
+   Nervencentren des Frosches.' Berlin, 1869, 130 S.
+
+   [11] Steiner, J.: 'Untersuchungen über die Physiologie des
+   Froschhirns.' Braunschweig, 1885, 127 S.
+
+   [12] Schrader, M.G.: 'Zur Physiologie des Froschgehirns.'
+   _Pflüger's Arch._, Bd. 41, 1887, S. 75-90.
+
+   [13] Merzbacher, L.: 'Ueber die Beziebungen der Sinnesorgane zu
+   den Reflexbewegungen des Frosches.' _Pflüger's Arch._, Bd. 81,
+   1900, S. 223-262.
+
+   [14] Merzbacher, L.: 'Untersuchungen über die Regulation der
+   Bewegungen der Wirbelthiere. I. Beobachtungen an Fröschen.'
+   _Pflüger's Arch._, Bd. 88, 1901, S. 453-474, 11 Text-figuren.
+
+In the present investigation it has been my purpose to study the
+reactions of the normal frog by the reaction-time methods of the
+psychologist. Hitherto the amount of work done, the extent of
+movements or some other change has been taken as a measure of the
+influence of a stimulus. My problem is, What are the time relations of
+all these reactions? With this problem in mind I enter upon the
+following program: (1) Determination of reaction time to electrical
+stimuli: (_a_) qualitative, (_b_) quantitative, (_c_) for different
+strengths of current; (2) Determination of reaction time to tactual
+stimuli (with the same variations); (3) Auditory: (_a_) qualitative,
+(_b_) quantitative, with studies on the sense of hearing; (4) Visual:
+(_a_) qualitative, (_b_) quantitative, with observations concerning
+the importance of this sense in the life of the frog, and (5)
+Olfactory: (_a_) qualitative, (_b_) quantitative.
+
+The present paper presents in rather bare form the results thus far
+obtained on electrical, tactual, and auditory reaction time;
+discussion of them will be deferred until a comparison of the results
+for the five kinds of stimuli can be given.
+
+
+V. METHOD OF STUDY.
+
+
+The measurements of reaction time herein considered were made with the
+Hipp Chronoscope. Cattell's 'Falling Screen' or 'Gravity Chronoscope'
+was used as a control for the Hipp. The Gravity Chronoscope consists
+of a heavy metal plate which slides easily between two vertical posts,
+with electrical connections so arranged that the plate, when released
+from the magnet at the top of the apparatus, in its fall, at a certain
+point breaks an electric circuit and at another point further down
+makes the same circuit. The rate of fall of the plate is so nearly
+constant that this instrument furnishes an accurate standard time with
+which Hipp readings may be compared, and in accordance with which the
+Hipp may be regulated. For, since the rate of a chronoscope varies
+with the strength of the current in use, with the variations in
+temperature and with the positions of the springs on the magnetic bar,
+it is always necessary to have some standard for corrections. In these
+experiments the time of fall of the gravity chronoscope plate, as
+determined by the graphic method with a 500 S.V. electric tuning fork,
+was 125[sigma] (_i.e._, thousandths of a second).
+
+This period, 125[sigma], was taken as a standard, and each hour,
+before the beginning of reaction-time experiments, the time of the
+plate's fall was measured ten times with the Hipp, and for any
+variation of the average thus obtained from 125[sigma], the standard,
+the necessary corrections were made by changing the position of the
+chronoscope springs or the strength of the current.
+
+The standard of comparison, 125[sigma], is shorter than most of the
+reaction times recorded, but since the time measured was always that
+from the breaking to the making of the circuit passing through the
+chronoscope it cannot be urged that there were errors resulting from
+the difference of magnetization which was caused by variations in the
+reaction time. But it is evident that the danger from differences in
+magnetization, if such exists, is not avoided in this way; instead, it
+is transferred from the reaction time proper to the period of
+preparation immediately preceding the reaction; for, from the moment
+the chronoscope is started until the stimulus is given a current is
+necessarily passing through the instrument. At a verbal signal from
+the operator the assistant started the chronoscope; the stimulus was
+then given by the operator, and the instrument recorded the time from
+the breaking of the circuit, effected by the stimulating apparatus, to
+the making of the circuit by the reaction of the animal. Despite
+precautions to prevent it, the period from the starting of the
+chronoscope to the giving of the stimulus was variable, and errors
+were anticipated, but a number of the tests proved that variations of
+even a second did not cause any considerable error.
+
+A fairly constant current for the chronoscope was supplied by a
+six-cell 'gravity battery' in connection with two storage cells, _GB_
+(Fig. 6). This current could be used for two hours at a time without
+any objectionable diminution in its strength. The introduction of
+resistance by means of the rheostat, _R_, was frequently a convenient
+method of correcting the chronoscope.
+
+[Illustration: FIG. 6. General Plan of Apparatus in Diagram. _H_, Hipp
+Chronoscope; _R_, rheostat; _C_, commutator; _SC_, storage cells;
+_GB_, 'Excello' gravity battery; _F_, Cattell's falling screen; _T_,
+reaction table; _RK_, reaction key; _SK_, Stimulating apparatus; _K_,
+key in chronoscope circuit; _S_, stimulus circuit.]
+
+Fig. 6 represents the general plan of the apparatus used in these
+experiments.
+
+The general method of experimentation is in outline as follows:
+
+1. At a 'ready' signal from the operator the assistant makes the
+chronoscope circuit by closing a key, _K_ (Fig. 6), and then
+immediately starts the chronoscope.
+
+2. Stimulus is given by the operator as soon as the chronoscope is
+started, and by this act the chronoscope circuit is broken and the
+record begun.
+
+3. Animal reacts and by its movements turns a key, _RK_ (Fig. 6), thus
+making the chronoscope circuit and stopping the record.
+
+4. Assistant stops chronoscope and takes reading.
+
+[Illustration: FIG. 7. Reaction Key. _l_, lever swung on pivot; _p,
+p_, posts for contacts with platinum plates on base; _b_, upright bar
+for string; _s_, spring for clamping string; _w_, wheel to carry
+string; _c, c_, chronoscope circuit; 1 and 2, points which are brought
+into contact by animal's reaction.]
+
+The steps of this process and the parts of the apparatus concerned in
+each may be clearly conceived by reference to the diagram given in
+Fig. 6. The various forms of stimulating apparatus used and the
+modification of the method will be described in the sections dealing
+with results. The same reaction key was used throughout (see Fig. 7).
+Its essential features are a lever _l_, pivoted in the middle and
+bearing a post at either end, _p, p_. From the middle of this lever
+there projected upward a small metal bar, _b_, through the upper part
+of which a string to the animal ran freely except when it was clamped
+by the spring, _s_. This string, which was attached to the subject's
+leg by means of a light elastic band, after passing through the bar
+ran over a wheel, _w_, and hung tense by reason of a five-gram weight
+attached to the end. Until everything was in readiness for an
+experiment the string was left free to move through the bar so that
+movement of the animal was not hindered, but the instant before the
+ready-signal was given it was clamped by pressure on _s_. The diagram
+shows the apparatus arranged for a reaction. The current is broken,
+since 1 and 2 are not in contact, but a slight movement of the animal
+turns the lever enough to bring 1 against 2, thus making the circuit
+and stopping the chronoscope. When the motor reaction of the subject
+was violent the string pulled out of the clamp so that the animal was
+free from resistance, except such as the string and weight offered.
+The five-gram weight served to give a constant tension and thus
+avoided the danger of error from this source. Between experiments the
+weight was placed on the table in order that there might be no strain
+upon the subject.
+
+That the subject might be brought into a favorable position for an
+experiment without being touched by the operator a special reaction
+box was devised.
+
+The animals used in these studies were specimens of _Rana clamitans_
+which were kept in a tank in the laboratory throughout the year.
+
+
+VI. ELECTRIC REACTION TIME.
+
+
+The reaction time to electrical stimuli was determined first because
+it seemed probable that this form of the pain reaction would be most
+useful for comparison with the auditory, visual, olfactory and tactual
+reactions. In this paper only the electrical and the tactual reaction
+times will be considered. The former will be divided into two groups:
+(1) Those resulting from a stimulus given by touching electrodes to
+the leg of the frog, and (2) those gotten by having the frog resting
+upon wires through which a current could be passed at any time.
+
+_Group 1 of the electrical reactions_ were taken under the following
+conditions. A reaction box about 40 cm. in diameter was used. The mean
+temperature of the experimenting room was about 20° C. In all cases
+the string was attached to the left hind leg of the frog, and the
+stimulus applied to the middle of the gastrocnemius muscle of the
+right hind leg. Reaction times were taken in series of ten, excluding
+those which were imperfect. As the moistness of the skin affects the
+strength of the electric stimulus received, it was necessary to
+moisten the animal occasionally, but as it did not seem advisable to
+disturb it after each experiment this was done at intervals of five
+minutes throughout the series. Were it not for this precaution it
+might be said that lengthening of the reaction times toward the end of
+a series simply indicated the weakening of the stimulus which resulted
+from the gradual drying of the skin. The stimulus in this group was
+applied by means of the stimulating apparatus of Fig. 6. It is merely
+two wire electrodes which could be placed upon the animal, with the
+additional device of a key for the breaking of the chronoscope circuit
+the instant the stimulus was given. The most serious objection to this
+method of stimulating is that there is a tactual as well as an
+electrical stimulus.
+
+Before presenting averages, two representative series of reactions may
+be considered.
+
+
+SERIES I. FROG B. APRIL 9, 1900. 10 A.M.
+
+  Temperature 19° C. String to left hind leg. Stimulus to right hind
+  leg.
+
+  Strength of stimulating current 1.0 volt, .0001 ampčre.
+
+  Number of
+  Experiment.   Hour.    Reaction Time.   Remarks.
+
+       1        10.25                   No reaction.
+       2        10.27                   No reaction.
+       3        10.30        139[sigma]
+       4        10.34        164
+       5        10.35        102
+       6        10.37        169
+       7        10.39        151
+       8        10.40        152
+       9        10.42        144
+      10        10.43        152
+      11        10.45        122
+      12        10.51        179
+      13        10.54                   No reaction.
+
+               Average of 10, 147.4[sigma]
+
+  SERIES 2.   FROG F.  ELECTRICAL STIMULUS.
+
+    No.    Hour.     Reaction Time.      Remarks.     Deviation from Mean.
+
+     1     10.19     35[sigma]      Probable reaction
+                                       to visual stim.
+     2     10.22           173                               4.7
+     3     10.24           161                             - 7.3
+     4     10.25           133                             -35.3
+     5     10.26           199                              30.7
+     6     10.28           130                             -38.3
+     7     10.32           179                              10.7
+     8     10.34           187                              18.7
+     9     10.35            60        Probable reflex.
+    10     10.37           183                              14.7
+    11     10.38           166                             - 2.3
+    12     10.39           172                               3.7
+
+  Average of 10, 168.3[sigma]     Average of first 5, 159.2[sigma]
+  Average Variation, 16.64[sigma] Average of second 5, 177.4[sigma]
+
+
+Both are fairly representative series. They show the extremely large
+variations, in the case of series 1, from 102 to 179[sigma]. In all
+these experiments such variation is unavoidable because it is
+impossible to have the conditions uniform. A very slight difference in
+the frog's position, which could not be detected by the operator,
+might cause considerable difference in the time recorded. Efforts were
+made to get uniform conditions, but the results seem to show that
+there is still much to be desired in this direction.
+
+Tables VII. contains the results of four series of ten reactions each
+for frog _A_. It will be noticed that the time for the first five in
+each series is much shorter than that for the last five; this is
+probably indicative of fatigue.
+
+
+TABLE VII.
+
+  REACTION TIME OF FROG _A_ TO ELECTRICAL STIMULI.
+
+     Series of       Averages     Averages of     Averages of
+  ten reactions.     of series.   first five.     second five.
+         1            163.1[sigma] 134.6[sigma]   191.6[sigma]
+         2            186.2         176.2           196.2
+         3            161.1         125.2           197.0
+         4            158.3         101.6           215.0
+  General averages    167.2[sigma] 134.4[sigma]   199.9[sigma]
+
+
+  TABLE VIII.
+
+  REACTION TIME OF FROG _B_ TO ELECTRICAL STIMULI.
+
+         1            132.7[sigma] 118.2[sigma]   147.4[sigma]
+         2            196.6         167.8           225.4
+         3            147.4         145.5           149.8
+         4            157.5         152.0           163.0
+  General averages    158.6[sigma] 145.9[sigma]   171.4[sigma]
+
+
+TABLE IX.
+
+  NORMAL AND REFLEX REACTION TIME OF SIX ANIMALS TO ELECTRICAL STIMULUS.
+
+                           Normal.                      Reflex.
+              Average for 20               Average for 20
+  Frog.        reactions.     Mean Var.      reactions.     Mean Var.
+  _A_           149.5[sigma] 24.0[sigma]
+  _B_           158.3         16.0           51.5[sigma]    8.0[sigma]
+  _C_           191.0         24.3
+  _D_           167.0         10.1
+  _E_           182.4         28.0           45.1           5.5
+  _F_           176.3         10.2           46.0           4.5
+  General
+  Average.      167.9[sigma] 18.8[sigma]     47.5[sigma]    6.0[sigma]
+
+   For _D_ the average is for ten reactions.
+
+   _B_ and _E_ were males, _F_ a female; the sex of the others was
+   not determined by dissection and is uncertain.
+
+
+Early in the experiments it became evident that there were three
+clearly defined types of reactions: there were a number of reactions
+whose time was shorter than that of the ordinary quick voluntary pain
+reaction, and there were also many whose time was considerably longer.
+The first type it was thought might represent the spinal reflex
+reaction time. For the purpose of determining whether the supposition
+was true, at the end of the series of experiments three of the frogs
+were killed and their reflex reaction time noted. This was done by
+cutting the spinal cord just back of the medulla, placing the animal
+on an experimenting board close to the reaction key with the thread
+from the key fastened to the left leg as in case of the previous work
+and stimulating the gastrocnemius with an induced current by the
+application of wire electrodes.
+
+In Table IX. the reflex reaction times for the three animals are
+given.
+
+The following results obtained with frog _E_ show that the time of
+reaction increases with the increase in the time after death. The
+average of 20 reactions by _E_ taken an hour after the cord had been
+cut was 45.5[sigma]; the average of 20 taken twenty hours later was
+55.85[sigma].
+
+As a rule the reflex reactions were but slightly variable in time as
+is indicated by the accompanying series.
+
+
+  SERIES OF REFLEX REACTIONS OF FROG _F_.
+    Taken at rate of one per minute.
+
+           1                                50[sigma]
+           2                                58
+           3                                55
+           4                                59
+           5                                48
+           6                                46
+           7                                45
+           8                                51
+           9                                42
+          10                                44
+
+
+Throughout these experiments it was noticed that any stimulus might
+cause (1) a twitch in the limb stimulated, or (2) a twitch followed by
+a jump, or (3) a sudden jump previous to which no twitch could be
+detected. And it soon appeared that these types of reaction, as it
+seems proper to call them, would have to be considered in any
+determination of the mean reaction time. As proof of the type theory
+there is given (Fig. 8) a graphic representation of 277 reactions to
+the electrical stimulus.
+
+[Illustration: FIG 8: Distribution of 277 reactions.]
+
+The column of figures at the left indicates the number of reactions at
+any point. Below the base line are the classes. For convenience of
+plotting the reactions have been grouped into classes which are
+separated by 25[sigma]. Class 1 includes all reactions between
+1[sigma] and 25[sigma], class 2 all from 25[sigma] to 50[sigma], and
+so on to 400[sigma], thereafter the classes are separated by
+100[sigma]. It is noticeable that there is one well-marked mode at
+75[sigma]. A second mode occurs at 175[sigma]. This is the primary and
+in our present work the chiefly significant mode, since it is that of
+the quick instinctive reaction to a stimulus. At 500[sigma] there is a
+third mode; but as such this has little meaning, since the reactions
+are usually pretty evenly distributed from 300[sigma] on to
+2000[sigma]; if there is any grouping, however, it appears to be about
+500[sigma] and 800[sigma].
+
+The first mode has already been called the reflex mode. The short
+reactions referred to usually lie between 40[sigma] and 80[sigma], and
+since experiment has shown conclusively that the spinal reflex
+occupies about 50[sigma], there can be little doubt that the first
+mode is that of the reflex reaction time.
+
+The second mode represents those reactions which are the result of
+central activity and control. I should be inclined to argue that they
+are what we usually call the instinctive and impulsive actions. And
+the remaining reactions represent such as are either purely voluntary,
+if any frog action can be so described, or, in other words, depend
+upon such a balancing of forces in the brain as leads to delay and
+gives the appearance of deliberate choice.
+
+Everything points to some such classification of the types as follows:
+(1) Stimuli strong enough to be injurious cause the shortest possible
+reaction by calling the spinal centers into action, or if not spinal
+centers some other reflex centers; (2) slightly weaker stimuli are not
+sufficient to affect the reflex mechanism, but their impulse passes on
+to the brain and quickly discharges the primary center. There is no
+hesitation, but an immediate and only slightly variable reaction; just
+the kind that is described as instinctive. As would be expected, the
+majority of the frog's responses are either of the reflex or of this
+instinctive type. (3) There is that strength of stimulus which is not
+sufficient to discharge the primary center, but may pass to centers of
+higher tension and thus cause a response. This increase in the
+complexity of the process means a slower reaction, and it is such we
+call a deliberate response. Precisely this kind of change in neural
+action and in reaction time is at the basis of voluntary action. And
+(4) finally, the stimulus may be so weak that it will not induce a
+reaction except by repetition. Just above this point lies the
+threshold of sensibility, the determination of which is of
+considerable interest and importance.
+
+_Group 2 of the electrical reactions_ consists of three series taken
+to determine the relation of strength of stimulus to reaction time.
+The conditions of experimentation differed from those for group 1 in
+the following points: (1) The stimulus was applied directly by the
+making of a circuit through wires upon which the subject rested (Fig.
+9); (2) the thread was attached to the right hind leg; (3) the thread,
+instead of being kept at the tension given by the 5-gram weight as in
+the former reactions, was slackened by pushing the upright lever of
+the reaction key one eighth of an inch toward the animal. This was
+done in order to avoid the records given by the slight twitches of the
+legs which precede the motor reaction proper. For this reason the
+reactions of group 2 are not directly comparable with those of group
+1. Fig. 9 is the plan of the bottom of a reaction box 15 cm. at one
+end, 30 cm. at the other, 60 cm. long and 45 cm. deep. On the bottom
+of this, at one end, a series of interrupted circuits were arranged as
+shown in the figure. The wires were 1.2 cm. apart, and an animal
+sitting anywhere on the series necessarily touched two or more, so
+that when the stimulus key, X, was closed the circuit was completed by
+the animal's body; hence, a stimulus resulted. The stimulus key, X,
+was a simple device by which the chronoscope circuit, _c_, _c_, was
+broken at the instant the stimulus circuit, _s_, _c_, was made.
+
+Cells of 'The 1900 Dry Battery' furnished the current used as a
+stimulus. Three different strengths of stimulus whose relative values
+were 1, 2 and 4, were employed in the series 1, 2 and 3. Careful
+measurement by means of one of Weston's direct-reading voltmeters gave
+the following values: 1 cell, 0.2 to 0.5 volt, 0.00001 to 0.00003
+ampčre. This was used as the stimulus for series 1. 2 cells, 0.5 to
+1.0 volt, 0.00003 to 0.00006 ampčre. This was used for series 2. 4
+cells, 1.2 to 1.8 volt, 0.00007 to 0.0001 ampčre. This was used for
+series 3.
+
+[Illustration: Fig. 9. Ground Plan of Reaction Box for Electrical
+Stimuli (Group 2). _IC_, interrupted circuits; _CC_, chronoscope
+circuit; _X_, key for making stimulus circuit and breaking chronoscope
+circuit; _B_, stimulus battery; _S_, string from reaction key to
+animal. Scale 1/2.]
+
+The reactions now under consideration were taken in sets of 24 in
+order to furnish evidence on the problem of fatigue. The stimulus was
+given at intervals of one minute, and the subject was moistened at
+intervals of ten minutes. To obtain 24 satisfactory reactions it was
+usually necessary to give from thirty to forty stimulations. Five
+animals, numbers 1, 2, 4, 5, and 6, served as subjects. They were
+green frogs whose size and sex were as follows:
+
+
+               Length.  Weight.     Sex.
+    Number 1   7.5 cm.  35 grams.  Male.
+    Number 2   7.3  "   37   "     Male.
+    Number 4   8.2  "   50.4 "     Female?
+    Number 5   7.1  "   25   "     Female.
+    Number 6   7.8  "   42   "     Male.
+
+
+For most of these frogs a one-cell stimulus was near the threshold,
+and consequently the reaction time is extremely variable. In Table X.
+an analysis of the reactions according to the number of repetitions of
+the stimulus requisite for a motor reaction has been made. Numbers 1
+and 5 it will be noticed reacted most frequently to the first
+stimulus, and for them 48 satisfactory records were obtained; but in
+case of the others there were fewer responses to the first stimulus,
+and in the tabulation of series 1 (Table XI.) averages are given for
+less than the regular sets of 24 reactions each.
+
+
+TABLE X.
+
+  ANALYSIS OF REACTIONS TO ONE-CELL STIMULUS.
+
+  Frog. Reactions to  To 2d.  To 3d. To 4th. To 5th. More.  Total No.
+       first Stimulus.                                    of Reactions.
+  1          53          2       1      0       0      1        57
+  2          20         12       5      5       4     12        58
+  4          31         15       1      0       2      8        57
+  5          51         11       1      2       0      1        66
+  6          45         15       6      3       1      5        75
+  Totals,   200         55      14     10       7     27       313
+
+
+Table XI. is self-explanatory. In addition to the usual averages,
+there is given the average for each half of the sets, in order that
+the effect of fatigue may be noted. In general, for this series, the
+second half is in its average about one third longer than the first
+half. There is, therefore, marked evidence of tiring. The mean
+reaction time for this strength of stimulus is difficult to determine
+because of the extremely great variations. At one time a subject may
+react immediately, with a time of not over a fifth of a second, and at
+another it may hesitate for as much as a second or two before
+reacting, thus giving a time of unusual length. Just how many and
+which of these delayed responses should be included in a series for
+the obtaining of the mean reaction time to this particular stimulus is
+an extremely troublesome question. It is evident that the mode should
+be considered in this case rather than the mean, or at least that the
+mean should be gotten by reference to the mode. For example, although
+the reaction times for the one-cell stimulus vary all the way from
+150[sigma] to 1000[sigma] or more, the great majority of them lie
+between 200[sigma] and 400[sigma]. The question is, how much deviation
+from the mode should be allowed? Frequently the inclusion of a single
+long reaction will lengthen the mean by 10[sigma] or even 20[sigma].
+What is meant by the modal condition and the deviation therefrom is
+illustrated by the accompanying curve of a series of reaction times
+for the electric stimulus of group I.
+
+
+__________________________________________________________________________
+_8_|______________________________________________________________________
+_7_|_____________________________________|________________________________
+_6_|_____________________________________|________________________________
+_5_|_____________________________________|________________________________
+_4_|________________________________|____|____|___________________________
+_3_|____________|___________________|____|____|___________________________
+_2_|_______|____|____|_________|____|____|____|____|______________________
+_1_|__|____|____|____|_________|____|____|____|____|____|____|____|____|__
+     100  110  120  130  140  150  160  170  180  190  200  210  220  230
+
+
+The column of figures at the left indicates the number of reactions;
+that below the base line gives the reaction times in classes separated
+by 10[sigma]. Of thirty-one reactions, seven are here in the class
+170[sigma]. This is the model class, and the mean gotten by taking the
+average of 31 reactions is 162[sigma]. If the mode had been taken to
+represent the usual reaction time in this case, there would have been
+no considerable error. But suppose now that in the series there had
+occurred a reaction of 800[sigma]. Should it have been used in the
+determination of the mean? If so, it would have made it almost
+30[sigma] greater, thus removing it considerably from the mode. If
+not, on what grounds should it be discarded? The fact that widely
+varying results are gotten in any series of reactions, points, it
+would seem, not so much to the normal variability as to accidental
+differences in conditions; and the best explanation for isolated
+reactions available is that they are due to such disturbing factors as
+would decrease the strength of the stimulus or temporarily inhibit the
+response. During experimentation it was possible to detect many
+reactions which were unsatisfactory because of some defect in the
+method, but occasionally when everything appeared to be all right an
+exceptional result was gotten. There is the possibility of any or all
+such results being due to internal factors whose influence it should
+be one of the objects of reaction-time work to determine; but in view
+of the fact that there were very few of these questionable cases, and
+that in series I, for instance, the inclusion of two or three
+reactions which stood isolated by several tenths of a second from the
+mode would have given a mean so far from the modal condition that the
+results would not have been in any wise comparable with those of other
+series, those reactions which were entirely isolated from the mode and
+removed therefrom by 200[sigma] have been omitted. In series I alone
+was this needful, for in the other series there was comparatively
+little irregularity.
+
+The results of studies of the reaction time for the one-cell electric
+stimulus appear in Table XI. The first column of this table contains
+the average reaction time or mean for each subject. Nos. 2 and 4
+appeared to be much less sensitive to the current than the others, and
+few responses to the first stimulus could be obtained. Their time is
+longer than that of the others, and their variability on the whole
+greater. Individual differences are very prominent in the studies thus
+far made on the frog. The one-cell stimulus is so near the threshold
+that it is no easy matter to get a mean which is significant. Could
+the conditions be as fully controlled as in human reaction time it
+would not be difficult, but in animal work that is impossible. No
+attempt has thus far been made to get the reaction time in case of
+summation effects except in occasional instances, and in so far as
+those are available they indicate no great difference between the
+normal threshold reaction and the summation reaction, but on this
+problem more work is planned.
+
+There are large mean variations in Table XI., as would be anticipated.
+Since the reactions were taken in sets of 24, the means of each set as
+well as that of the total are given, and also, in columns 4 and 5, the
+means of the first half and the last half of each set.
+
+A comparison of Tables XI., XII. and XIII. makes clear the differences
+in reaction time correlated with differences in the strength of an
+electric stimulus. For Table XI., series I, the relative value of the
+stimulus was I; for Table XII., series 2, it was 2, and for Table
+XIII., series 3, it was 4. Throughout the series from I to 3 there is
+a rapid decrease in the reaction time and in the variability of the
+same. The reaction time for stimulus I, the so-called threshold, is
+given as 300.9[sigma]; but of the three it is probably the least
+valuable, for reasons already mentioned. The mean of the second
+series, stimulus 2, is 231.5[sigma] while that of the third, stimulus
+4, is only 103.1[sigma]. This great reduction in reaction time for the
+four-cell stimulus apparently shows the gradual transition from the
+deliberate motor reaction, which occurs only after complex and varied
+central neural activities, and the purely reflex reaction, which takes
+place as soon as the efferent impulse can cause changes in the spinal
+centers and be transmitted as an afferent impulse to the muscular
+system.
+
+
+TABLE XI.
+
+  ELECTRICAL STIMULUS REACTION TIME. SERIES 1.
+
+          Average             Average of   Average   Average   Mean Var
+  Frog.   of all.  Mean Var.    Sets.     of 1st h.  of 2d h.  of Sets.
+
+    1     238.5*     33.3*     216.0*      205.6*     226.7*    33.2*
+                               261.0       248.0      274.1     33.3
+    2     458.0     219.0      458.0       270.4      643.8    219.0
+    4     273.4      59.9      273.4       245.7      301.1     59.9
+    5     263.9      50.5      268.6       244.7      292.5     44.9
+                               259.2       236.0      282.4     56.1
+    6     271.1      65.1      322.6       273.2      372.0     87.9
+                               219.6       208.5      230.6     42.3
+  Gen Av. 300.9      85.5      300.9       244.8      356.8     85.5
+
+                                                               Totals.
+  For No. 1 the averages are for 2 sets of 24 reactions each,    48
+      "   2     "          "    one set of 12      "     "       12
+      "   4     "          "    one set of 24      "     "       24
+      "   5     "          "    two sets of 24     "     "       48
+      "   6     "          "    two sets of 24 and 12 reactions,
+                                    respectively,                36
+
+    *Transcriber's Note: All values in [sigma], 1/1000ths of a second.
+
+
+TABLE XII.
+
+  ELECTRICAL STIMULUS REACTION TIME. SERIES 2.
+
+          Average             Average of   Average   Average   Mean Var
+  Frog.   of all.  Mean Var.    Sets.     of 1st h.  of 2d h.  of Sets.
+
+    1     227.3*     33.7*     229.4*      209.1*     249.6*    25.5*
+                               225.2       207.3      243.0     42.1
+    2     240.1      30.9      239.0       222.3      255.1     29.0
+                               241.3       220.2      262.4     32.8
+    4     270.3      56.5      298.5       285.3      311.4     62.8
+                               242.2       206.0      278.4     50.2
+          198.5      26.2      195.0       197.5      193.0     33.5
+                               202.0       195.2      209.0     18.8
+    6     224.4      24.4      221.6       209.7      233.7     23.6
+                               227.2       213.5      241.0     25.1
+  Gen. Av. 231.5     34.3      231.0       216.6      246.6     34.3
+
+  For No. 5 the averages are for two sets of 18 each; for all the
+  others there are 24 in each set.
+
+    *Transcriber's Note: All values in [sigma], 1/1000ths of a second.
+
+
+TABLE XIII.
+
+  ELECTRICAL STIMULUS REACTION TIME. SERIES 3.
+
+            Average             Average  Average    Average   Mean Var.
+  Frog.     of all.  Mean Var.  of all.  of 1st h.  of 2d h.  of Sets.
+  1          93.6*   13.5*       91.8*    93.2*      90.4*     13.5*
+                                 95.4     91.8       99.0      13.5
+  2          99.9    12.8        92.2     89.4       95.0      17.4
+                                107.5    105.9      109.0       8.2
+  4         125.2    16.3       113.5    106.5      120.5      13.6
+                                136.0    135.7      138.2      19.0
+  5          94.4     8.0        88.6     90.5       88.6       8.2
+                                100.2     97.8      102.7       7.9
+  6         102.5    12.2       104.2     98.6      109.9      12.8
+                                100.9    101.0      108.3      11.6
+  Gen. Avs. 103.1    12.5       103.1    101.0      105.9      12.5
+
+For each animal there are two sets of 24 reactions each.
+
+  *Transcriber's Note: All values in [sigma], 1/1000ths of a second.
+
+The spinal reflex for a decapitated frog, as results previously
+discussed show, is approximately 50[sigma]; and every time the
+four-cell stimulus is given this kind of a reaction results. There is
+a slight twitch of the legs, immediately after which the animal jumps.
+Now for all these series the thread was slackened by one eighth of an
+inch, but the reflex time was determined without this slack.
+Calculation of the lengthening of the reaction time due to the slack
+indicated it to be between 20 and 30[sigma], so if allowance be made
+in case of the reactions to the four-cell stimulus, the mean becomes
+about 70[sigma], or, in other words, nearly the same as the spinal
+reflex. The conclusion seems forced, therefore, that when a stimulus
+reaches a certain intensity it produces the cord response, while until
+that particular point is reached it calls forth central activities
+which result in much longer and more variable reaction times. It was
+said above that the series under consideration gave evidence of the
+gradual transition from the reflex to the volitional in reaction time.
+Is this true, or do we find that there are well-marked types, between
+which reactions are comparatively rare? Examination of the tables
+VII., VIII., IX., XI., XII. and XIII. will show that between 70[sigma]
+and 150[sigma] there is a break. (In tables XI., XII. and XIII.,
+allowance must always be made for the slack in the thread, by
+subtracting 30[sigma].) All the evidence furnished on this problem by
+the electrical reaction-time studies is in favor of the type theory,
+and it appears fairly clear that there is a jump in the reaction time
+from the reflex time of 50-80[sigma], to 140 or 150[sigma], which may
+perhaps be taken as the typical instinctive reaction time. From
+150[sigma] up there appears to be a gradual lengthening of the time as
+the strength of the stimulus is decreased, until finally the threshold
+is reached, and only by summation effect can a response be obtained.
+
+The most important averages for the three series have been arranged in
+Table XIV. for the comparison of the different subjects. Usually the
+reaction time for series 3 is about one half as long as that for
+series 2, and its variability is also not more than half as large. In
+the small variability of series 3 we have additional reason for
+thinking that it represents reflexes, for Table IX. gives the mean
+variation of the reflex as not more than 8[sigma], and the fact that
+the means of this series are in certain cases much larger is fully
+explained by the greater opportunity for variation afforded by the
+slack in the thread.
+
+
+TABLE XIV.
+
+  MEANS, ETC., FOR EACH SUBJECT FOR THE THREE SERIES. (TIME IN [sigma])
+
+                Mean     First    Second      Mean     Frog.
+                         Half.     Half.   Variation.
+  Series 1     238.5     226.8     259.4      33.3
+  Series 2     227.3     208.2     246.3      33.7     No. 1
+  Series 3      93.6      92.5      94.7      13.5
+
+  Series 1     458.0     270.4     643.8     219.0
+  Series 2     240.1     221.2     258.8      30.9     No. 2
+  Series 3      99.9      97.6     102.0      12.8
+
+  Series 1     273.4     245.7     301.1      59.9
+  Series 2     270.3     245.6     294.9      56.5     No. 4
+  Series 3     125.2     121.1     129.3      16.3
+
+  Series 1     263.9     240.4     287.4      50.5
+  Series 2     198.5     196.4     201.0      26.2     No. 5
+  Series 3      94.4      94.2      94.7       8.0
+
+  Series 1     271.1     240.8     301.3      65.1
+  Series 2     224.4     211.6     237.3      24.4     No. 6
+  Series 3     102.5      99.8     109.1      12.2
+
+
+A striking fact is that the averages for the first and last half of
+sets of reactions differ more for the weak than for the strong
+stimulus. One would naturally expect, if the increase were a fatigue
+phenomenon purely, that it would be greatest for the strongest
+stimulus; but the results force us to look for some other conditions
+than fatigue. A stimulus that is sufficiently strong to be painful and
+injurious to an animal forces an immediate response so long as the
+muscular system is not exhausted; but where, as in series 1 and 2 of
+the electrical stimulus, the stimulus is not harmful, the reason for a
+sudden reaction is lacking unless fear enters as an additional cause.
+Just as long as an animal is fresh and unfamiliar with the stimulus
+there is a quick reaction to any stimulus above the threshold, and as
+soon as a few experiences have destroyed this freshness and taught the
+subject that there is no immediate danger the response becomes
+deliberate. In other words, there is a gradual transition from the
+flash-like instinctive reaction, which is of vast importance in the
+life of such an animal as the frog, to the volitional and summation
+responses. The threshold electrical stimulus does not force reactions;
+it is a request for action rather than a demand, and the subject,
+although startled at first, soon becomes accustomed to the experience
+and responds, if at all, in a very leisurely fashion. The reaction
+time to tactual stimuli, soon to be considered, was determined by
+giving a subject only three or four stimulations a day; if more were
+given the responses failed except on repetition or pressure; for this
+reason the data on fatigue, or lengthening of reaction time toward the
+end of a series, are wanting in touch. A few tests for the purpose of
+discovering whether the time would lengthen in a series were made with
+results very similar to those of the threshold electrical stimulus;
+the chief difference lies in the fact that the responses to touch fail
+altogether much sooner than do those to the electrical stimulus. This,
+however, is explicable on the ground that the latter is a stimulus to
+which the animal would not be likely to become accustomed so soon as
+to the tactual.
+
+
+           First Half.         Second Half.      Second % Greater.
+  Series 1  244.8[sigma]        356.8[sigma]         46 per cent
+  Series 2  216.6                246.6               14       "
+  Series 3  101.0                105.9                5       "
+
+
+If pure fatigue, that is, the exhaustion of the nervous or muscular
+system, appears anywhere in this work, it is doubtless in series 3,
+for there we have a stimulus which is so strong as to force response
+on penalty of death; the reaction is necessarily the shortest
+possible, and, as a matter of fact, the motor reaction (jump forward)
+here occupies little more time than the leg-jerk of a decapitated
+frog. This probably indicates that the reaction is a reflex, and that
+the slight increase in its length over that of the spinal reflex is
+due to occasional cerebellar origin; but of this there can be no
+certainly from the evidence herewith presented. At any rate, there is
+no possibility of a voluntary reaction to the strong current, and any
+changes in the general character of the reaction time in a series will
+have to be attributed to fatigue of the nervous or muscular systems.
+The second halves of the sets of series 3 are 5 per cent. longer than
+the first, and unless this is due to the partial exhaustion of the
+nervous system it is hard to find an explanation of the fact. Fatigue
+of the muscles concerned seems out of the question because the
+reactions occur at the rate of only one per minute, and during the
+rest interval any healthy and well-nourished muscle would so far
+recover from the effect of contraction that it would be able to
+continue the rhythmic action for long periods.
+
+To the inquiry, Does fatigue in the experiments mean tiring by the
+exhaustion of nerve energy, or is the lengthening in reaction time
+which would naturally be attributed to tiring due to the fact that
+experience has shown quick reaction to be unnecessary? we shall have
+to reply that there is evidence in favor of both as factors. There can
+be little doubt that in case of the strong stimuli there is genuine
+fatigue which makes quick reaction impossible; but at the same time it
+is certain that the 40 to 50 per cent. increase of the second half of
+sets in series 1 over the first half can not be due to fatigue, for
+the strain is here evidently much less than for series 3. Rather, it
+would seem that habituation instead of exhaustion is the all-important
+cause of the difference in series 1 and 2. It becomes clear from these
+considerations that the repetition of a stimulus can never mean the
+repetition of an effect.
+
+
+VII. TACTUAL REACTION TIME.
+
+
+In the following work on the reactions to tactual stimulation the
+subject was placed in a large reaction box with a thread attached to
+one of its legs and passing to a reaction key, as in the experiments
+already described. The box in which the subject was confined was
+surrounded by movable cloth curtains to prevent the animal's escape
+and at the same time permit the experimenter to work without being
+seen by the frog.
+
+Tactual stimulation was given by means of a hand key[15] similar to
+that used for electrical stimulation which is represented in Fig. 6.
+The touch key ended in a hard-rubber knob which could be brought in
+contact with the skin of the subject. This key was fixed to a handle
+of sufficient length to enable the operator to reach the animal
+wherever it chanced to be sitting in the reaction box. Stimulation was
+given by allowing the rubber point of the touch key to come in contact
+with the skin in the middle region of the subject's back. As soon as
+the point touched the animal the chronoscope circuit was broken by the
+raising of the upper arm of the key.
+
+   [15] This apparatus was essentially the same as Scripture's
+   device for the giving of tactual stimulation.
+
+As a precaution against reactions to visual stimuli, which it might
+well be supposed would appear since the subject could not in every
+case be prevented from seeing the approaching apparatus, the frog was
+always placed with its head away from the experimenter so that the
+eyes could not readily be directed toward the touch apparatus.
+Notwithstanding care in this matter, a reaction occasionally appeared
+which was evidently due to some disturbance preceding the tactual
+stimulus which served as a warning or preparation for the latter. All
+such responses were at once marked as questionable visual reactions
+and were not included in the series of touch reactions proper.
+
+As has been mentioned in connection with the discussion of fatigue, it
+was found absolutely necessary to have the subjects perfectly fresh
+and active, and for this purpose it was advisable to give not more
+than three or four stimulations at any one time. The subject was
+usually kept in the reaction box from 30 to 45 minutes, dependent upon
+the success of the experiments. As the work progressed it became
+evident that the responses to the stimulus were becoming less and less
+certain and slower, that the subjects were becoming accustomed to the
+novel experience and no longer suffered the surprise which had been
+the cause of the prompt reactions at first. It seemed best for this
+reason not to continue the work longer than two weeks, and as a
+consequence it was impossible to base the averages on more than twenty
+reactions for each subject.
+
+So far as the tension of the thread is concerned, the condition for
+the tactual reaction time was the same as that for the first group of
+electrical reaction-time experiments. In comparing the tactual with
+the electrical of series 1, 2 and 3, allowance must be made for the
+slack in the latter cases.
+
+Selection of the tactual reaction times upon which the mean is based,
+has been made with reference to the mode for each set of experiments.
+Inspection of the curves given by the reactions of each subject
+indicated that the great majority of the responses lay between 100 and
+300[sigma], and that those which were beyond these limits were
+isolated and, in all probability, exceptional reactions due to some
+undetected variation in conditions which should throw them out of the
+regular series. On this account it was thought best to use only
+reactions between 100 and 300[sigma].
+
+For convenience of comparison, again, the averages for the electrical
+reaction time of subjects _A_, _B_, _C_, _D_, _E_ and _F_, and the
+same for the tactual reaction time of subjects 1, 2, 3, 4, 5 and 6 are
+herewith given together. All averages are for twenty reactions, except
+for _D_ and 5, for which there are ten.
+
+Besides the usual determination for the tactual reaction-time work on
+the six subjects named, there is given in Table XVI. the electrical
+reaction time of these animals to a two-cell current. Comparison of
+the electrical and tactual results are of interest in this case
+because the mean variation for each is about 34[sigma], being
+34.3[sigma], for the electrical and 33.8[sigma], for the tactual.
+
+
+TABLE XV.
+
+              Average of 20 Electrical           Average of 20 Tactual
+      Frog.          Reactions.          Frog.          Reactions.
+    _A_           149.5[sigma]       1               188.3[sigma]
+    _B_           158.3              2               199.1
+    _C_           191.0              3               212.1
+    _D_           167.0              4               213.0
+    _E_           182.4              5               199.8
+    _F_           176.3              6               221.9
+       Gen. Avs.       167.9                              205.7
+
+
+TABLE XVI.
+
+  REACTION TIME FOR TACTUAL AND ELECTRICAL STIMULI.
+
+            Tactual Reaction Time.       Electrical Reaction Time.
+
+  Frog.     Average. Mean Variation.     Average. Mean Variation.
+
+   1         188.3[sigma]                167.3[sigma]
+   2         199.1                        180.1
+   3         212.1
+   4         213.0                        210.3
+   5¹        199.8                        138.5
+   6         221.9                        164.4
+  Gen. Avs.  205.7      33.8              172.1       34.3
+
+  ¹For 5 the average of ten instead of twenty is given.
+
+
+VIII. EQUAL VARIABILITY AS A CRITERION OF COMPARABILITY OF REACTION
+TIME FOR DIFFERENT KINDS OF STIMULI.
+
+
+Since variability as indicated in the study of the influence of
+different strengths of electrical stimulus becomes less as the
+stimulus increases, parity in variability for different stimuli offers
+a basis for the comparison of reaction times. Certain it is that there
+is no use in comparing the reaction times for different senses or
+different qualities of stimuli unless the relative values of the
+stimuli are taken into consideration; but how are these values to be
+determined unless some such index as variability is available? If the
+reaction time to tactual stimuli as here presented is to be studied in
+its relation to the electrical reaction time, it will mean little
+simply to say that the former is longer than the latter, because the
+electrical reaction time for a one-cell stimulus happens to be
+somewhat less than that for the particular tactual stimulus used. For
+it is clear that this tactual reaction time is really shorter than the
+reaction time to a weak current. In making variability a basis of
+comparison it must be assumed that the strength of stimulus is the
+important factor, and that all other variable conditions are, so far
+as possible, excluded. If, now, on the basis of parity in variability
+we compare the tactual and electrical reaction times, it is apparent
+that the tactual is considerably longer. The tactual average of Table
+XV. is 205.7[sigma], while the electrical reaction time which has
+approximately the same variability is 172.1[sigma]. It may well be
+objected that I have no right to make variability the basis of my
+comparison in these experiments, because the work for the various
+kinds of stimuli was done under different conditions. Admitting the
+force of this objection, and at the same time calling attention to the
+fact that I do not wish to lay any stress on the results of the
+comparisons here made, I take this opportunity to call attention to
+the possibility of this criterion.
+
+The use of variability as a basis of comparison would involve the
+assumptions (1) that a certain intensity of every stimulus which is to
+be considered is capable of producing the shortest possible, or reflex
+reaction, and that this reaction is at the same time the least
+variable; (2) that as the strength of a stimulus decreases the
+variability increases until the threshold is reached.
+
+Suppose, now, it is our desire to compare the results of reactions to
+different intensities of electrical and tactual stimuli; let the
+figures be as follows:
+
+                       Reaction Time.           Variability.
+  Stimulus Strength.  Elect.      Touch.      Elect.    Touch.
+          8            50[sigma] 50[sigma]    10[sigma]  10[sigma].
+          4           130        155          25         30
+          2           175        220          40         40
+          1           300        320          50         60
+
+In the double columns the results for electrical stimuli are given
+first, and in the second column are the tactual. Stimulus 8 is assumed
+to be of sufficient strength to induce what may be designated as
+forced movement, and whatever the quality of the stimulus this
+reaction time is constant. I make this statement theoretically,
+although all the evidence which this work furnishes is in support of
+it. So, likewise, is the variability of this type of reaction time
+small and nearly constant. At the other extreme, stimulus 1 is so weak
+as to be just sufficient to call forth a response; it is the so-called
+threshold stimulus. Whether all qualities of stimulus will give the
+same result here is a question to be settled by experimentation. Wundt
+contends that such is the case, but the observations I have made on
+the electrical and tactual reactions of the frog cause me to doubt
+this assumption. It seems probable that the 'just perceptible stimulus
+reaction time' is by no means the same thing for different qualities
+of stimulus. Those modifications of the vital processes which alone
+enable organisms to survive, make their appearance even in the
+response to the minimal stimulus. In one case the just perceptible
+stimulus may cause nothing more than slight local changes in
+circulation, excretion, muscular action; in another it may produce,
+just because of the particular significance of the stimulus to the
+life of the organism, a violent and sudden motor reaction. But grant,
+if you will, that the threshold reaction time is the same for all
+kinds of stimuli, and suppose that the variability is fairly constant,
+then, between the two extremes of stimuli, there are gradations in
+strength which give reaction times of widely differing variabilities.
+If, now, at some point in the series, as, for instance, to stimulus 2,
+the variability for different kinds of stimuli is the same either with
+reference to the reaction time (ratio) or absolutely, what
+interpretation is to be put upon the fact? Is it to be regarded as
+merely a matter of chance, and unworthy of any special attention, or
+should it be studied with a view to finding out precisely what
+variability itself signifies? It is obvious that any discussion of
+this subject, even of the possible or probable value of variability as
+a criterion for the comparative study of stimuli, can be of little
+value so long as we do not know what are the determining factors of
+variations of this sort. The only suggestion as to the meaning of such
+a condition (_i.e._, equal variability at some point)--and our studies
+seem to show it for touch and electrical stimulation--which I feel
+justified in offering at present, is that parity in variability
+indicates equality in strength of stimuli, that is, the electrical
+stimulus which has a reaction time of the same variability as a
+tactual stimulus has the same effect upon the peripheral nervous
+system as the tactual, it produces the same amplitude and perhaps the
+same form of wave, but the reaction times for the two stimuli differ
+because of the biological significance of the stimuli. The chances are
+that this is wholly dependent upon the central nervous system.
+
+
+IX. SUMMARY.
+
+
+1. This paper gives the results of some experiments on the frog to
+determine its electrical and tactual reaction time. It is the
+beginning of comparative reaction-time studies by which it is hoped
+important information may be gained concerning the significance and
+modes of action of the nervous system. Comparative physiology has
+already made clear that the time relations of neural processes deserve
+careful study.
+
+2. According to the strength of the stimulus, electric stimulation of
+the frog causes three types of reaction: (1) A very weak or threshold
+stimulus results in a deliberate or delayed reaction, the time of
+which may be anywhere from 300[sigma] (thousandths of a second) to
+2,000[sigma]. (2) A very strong stimulus causes a spinal reflex, whose
+time is from 50 to 80[sigma]; and (3) a stimulus of intermediate
+strength causes a quick instinctive reaction of from 150 to 170[sigma]
+in duration.
+
+3. The reaction time for electric stimuli whose relative values were
+1, 2 and 4 were found to be 300.9[sigma], 231.5[sigma] and
+103.1[sigma].
+
+4. The reaction time of the frog to a tactual stimulus (contact of a
+rubber point) is about 200[sigma].
+
+5. The variability of reaction times of the frog is great, and
+increases as the strength of the stimulus decreases.
+
+6. When two kinds of stimuli (_e.g._, electrical and tactual) give
+reaction times of equal variability, I consider them directly
+comparable.
+
+7. According to this criterion of comparability the reaction time to
+electric stimulation which is comparable with that to tactual is
+172.1[sigma]; and it is to be compared with 205.7[sigma]. Both of
+these have a variability of approximately 34[sigma]. On this basis one
+may say that the tactual reaction time is considerably longer than the
+electrical.
+
+
+PART III. AUDITORY REACTIONS OF FROGS.
+
+
+X. HEARING IN THE FROG.
+
+
+A. Influences of Sounds in the Laboratory.
+
+After determining the simple reaction time of the green frog to
+tactual and electrical stimulation, I attempted to do the same in case
+of auditory stimuli. In this I was unsuccessful because of failure to
+get the animal to give a motor response which could be recorded. The
+animal was placed in an experimenting box with a string attached to
+one hind leg as in the experiments described in Part II., and after it
+had become accustomed to the situation a sound was made. A wide range
+of sounds were tried, but to none except the croak of another frog was
+a motor reaction frequently given. Even a loud noise, such as the
+explosion of a large pistol cap, caused a visible motor reaction only
+in rare cases. In fifty trials with this stimulus I succeeded in
+getting three reactions, and since all of them measured between 230
+and 240[sigma] it is perhaps worth while to record the result as
+indicative of the auditory reaction time. As these were the only
+measurements obtained, I have no satisfactory basis for the comparison
+of auditory with other reaction times.
+
+The remarkable inhibition of movement shown by the frog in the
+presence of strong auditory stimulation, at least what is for the
+human being a strong stimulus, led me to inquire concerning the limits
+and delicacy of the sense of hearing in frogs. In the vast quantity of
+literature on the structure and functions of the sense organs of the
+animal I have been able to find only a few casual remarks concerning
+hearing.
+
+In approaching the problem of frog audition we may first examine the
+structure of the ear for the purpose of ascertaining what sounds are
+likely to affect the organ. There is no outer ear, but the membrana
+tympani, or ear drum, covered with skin, appears as a flat disc from 5
+to 10 mm. in diameter on the side of the head just back of the eye and
+a little below it. In the middle ear there is but one bone, the
+columella, forming the connecting link between the tympanum and the
+internal ear. The inner ear, which contains the sense organs,
+consists of a membranous bag, the chief parts of which are the
+utriculus, the sacculus, the lagena, and the three semicircular
+canals. The cavity of this membranous labyrinth is filled with a
+fluid, the endolymph; and within the utriculus, sacculus and lagena
+are masses of inorganic matter called the otoliths. The auditory nerve
+terminates in eight sense organs, which contain hair cells. There is
+no cochlea as in the mammalian ear. The assumption commonly made is
+that vibrations in the water or air by direct contact cause the
+tympanic membrane to vibrate; this in turn causes a movement of the
+columella, which is transmitted to the perilymphatic fluid of the
+inner ear. The sensory hair cells are disturbed by the movements of
+the otoliths in the endolymph, and thus an impulse is originated in
+the auditory nerve which results in a sensation more or less
+resembling our auditory sensation. It is quite probable that the
+frog's sense of hearing is very different from ours, and that it is
+affected only by gross air vibrations. This conclusion the anatomy of
+the ear supports.
+
+Although there does not seem to be a structural basis for a delicate
+sense of hearing, one must examine the physiological facts at hand
+before concluding that frogs do not possess a sense of hearing similar
+to our own. First, the fact that frogs make vocal sounds is evidence
+in favor of the hearing of such sounds at least, since it is difficult
+to explain the origin of the ability to make a sound except through
+its utility to the species. Granting, however, that a frog is able to
+hear the croaks or pain-screams of its own species, the range of the
+sense still remains very small, for although the race of frogs makes a
+great variety of sounds, any one species croaks within a narrow range.
+
+Having satisfied myself that motor reactions for reaction-time
+measurements could not be gotten to any ordinary sounds in the
+laboratory, I tried the effect of the reflex croaking of another frog
+of the same species. In attempting to get frogs to croak regularly, I
+tested the effect of removing the brain. The animals are said to croak
+reflexly after this operation whenever the back is stroked; but for
+some reason I have never been successful in getting the reaction
+uniformly. In many cases I was able to make normal animals croak by
+rubbing the back or flanks, and to this sound the animals under
+observation occasionally responded by taking what looked like an
+attitude of attention. They straightened up and raised the head as if
+listening. In no case have other motor responses been noticed; and the
+above response was so rare that no reaction-time measurements could be
+made.
+
+Again, while working with the green frog on habit formation, I one day
+placed two animals in a labyrinth from which they could escape by
+jumping into a tank of water. Several times when one frog jumped into
+the water I noticed the other one straighten up and hold the
+'listening' or 'attentive' attitude for some seconds. As the animals
+could not see one another this is good evidence of their ability to
+hear the splash made by a frog when it strikes the water.
+
+
+B. Influence of Sounds in Nature.
+
+In order to learn how far fear and artificial conditions were causes
+of the inhibition of response to sounds in the laboratory, and how far
+the phenomenon was indicative of the animal's inability to perceive
+sounds, I observed frogs in their native haunts.
+
+By approaching a pond quietly, it is easy to get within a few yards of
+frogs sitting on the banks. In most cases they will not jump until
+they have evidence of being noticed. Repeatedly I have noted that it
+is never possible to get near to any frogs in the same region after
+one has jumped in. In this we have additional proof that they hear the
+splash-sound. To make sure that sight was not responsible for this
+on-guard condition in which one finds the frogs after one of their
+number has jumped into the water, I made observations on animals that
+were hidden from one another. The results were the same. I therefore
+conclude that the splash of a frog jumping into the water is not only
+perceived by other frogs in the vicinity, but that it is a peculiarly
+significant sound for them, since it is indicative of danger, and
+serves to put them 'on watch.'
+
+A great variety of sounds, ranging in pitch from a low tone in
+imitation of the bull frog's croak to a shrill whistle, and in
+loudness from the fall of a pebble to the report of a pistol, were
+tried for the purpose of testing their effects upon the animals in
+their natural environment. To no sound have I ever seen a motor
+response given. One can approach to within a few feet of a green frog
+or bull frog and make all sorts of noises without causing it to give
+any signs of uneasiness. Just as soon, however, as a quick movement is
+made by the observer the animal jumps. I have repeatedly crept up very
+close to frogs, keeping myself screened from them by bushes or trees,
+and made various sounds, but have never succeeded in scaring an animal
+into a motor response so long as I was invisible. Apparently they
+depend almost entirely upon vision for the avoidance of dangers.
+Sounds like the splash of a plunging frog or the croak or pain-scream
+of another member of the species serve as warnings, but the animals do
+not jump into the water until they see some sign of an unusual or
+dangerous object. On one occasion I was able to walk to a spot where a
+large bull frog was sitting by the edge of the water, after the frogs
+about it had plunged in. This individual, although it seemed to be on
+the alert, let me approach close to it. I then saw that the eye turned
+toward me was injured. The animal sat still, despite the noise I made,
+simply because it was unable to see me; as soon as I brought myself
+within the field of vision of the functional eye the frog was off like
+a flash.
+
+Many observers have told me that frogs could hear the human voice and
+that slight sounds made by a passer-by would cause them to stop
+croaking. In no case, however, have such observers been able to assert
+that the animals were unaffected by visual stimuli at the same time. I
+have myself many times noticed the croaking stop as I approached a
+pond, but could never be certain that none of the frogs had seen me.
+It is a noteworthy fact that when one frog in a pond begins to croak
+the others soon join it. Likewise, when one member of such a chorus is
+frightened and stops the others become silent. This indicates that the
+cessation of croaking is a sign of danger and is imitated just as is
+the croaking. There is in this fact conclusive evidence that the
+animals hear one another, and the probability is very great that they
+hear a wide range of sounds to which they give no motor reactions,
+since they do not depend upon sound for escaping their enemies.
+
+The phenomenon of inhibition of movement in response to sounds which
+we have good reason to think the frogs hear, and to which such an
+animal as a turtle or bird would react by trying to escape, is thus
+shown to be common for frogs in nature as well as in the laboratory.
+This inhibition is in itself not surprising, since many animals
+habitually escape certain of their enemies by remaining motionless,
+but it is an interesting phenomenon for the physiologist. We have to
+inquire, for instance, what effects sounds which stimulate the
+auditory organs and cause the animal to become alert, watchful, yet
+make it remain rigidly motionless, have on the primary organic rhythms
+of the organism, such as the heart-beat, respiration, and peristalsis.
+It is also directly in the line of our investigation to inquire how
+they affect reflex movements, or the reaction time for any other
+stimulus--what happens to the reaction time for an electrical
+stimulus, for example, if a loud noise precede or accompany the
+electrical stimulus.
+
+For the purpose of determining the range of hearing in the frog, I was
+driven to study the influence of sounds upon respiration. Although the
+animals did not make any detectable movement, not even of an eyelid,
+in response to noises, it seemed not improbable that if the sounds
+acted as auditory stimuli at all, they would in some degree modify the
+form or rate of the respiratory movement.
+
+
+C. Influence of Sounds on Respiration.[16]
+
+   [16] For full discussion of the normal respiratory movements of
+   the frog see Martin, _Journal of Physiology,_ Vol. 1., 1878,
+   pp. 131-170.
+
+The method of recording the respiration was the direct transference of
+the movement of the throat by means of a pivoted lever, one end of
+which rested against the throat, while the other served as a marker on
+a revolving drum carrying smoked paper. The frog was put into a small
+box, visual stimuli were, so far as possible, excluded and the lever
+was adjusted carefully; a record was then taken for at least half a
+minute to determine the normal rate of respiration in the absence of
+the stimulus whose effect it was the chief purpose of the experiment
+to discover. Then, as soon as everything was running smoothly, the
+auditory stimulus was given. The following records indicate the
+effects of a few stimuli upon the rate of breathing:
+
+
+1. Stimulus, 100 V. tuning fork.
+
+Number of respirations for 10 cm. _before_ stimulus 18.0, 17.0; number
+of respirations for 10 cm. _after_ stimulus 19.0, 17.3.
+
+The records indicate very little change, and contradict one another.
+For the same stimulus the experiment was tried of taking the normal
+respiration record for a complete revolution of the drum, and then at
+once taking the record for the same length of time (about two minutes)
+with the tuning-fork vibrating close to the frog. The following result
+is typical and proves that the sound has little effect.
+
+Number of respirations in a revolution _before_ stimulus: First rev.
+88; second rev. 88. Number of respirations in a revolution _during_
+stimulus: First rev. 87; second rev. 88.
+
+Concerning the influence of tuning-fork stimuli more will be said
+later in a consideration of the effects of auditory stimuli upon
+reactions to visual stimuli.
+
+
+2. The influence of falling water as an auditory stimulus. Water was
+allowed to fall about two feet in imitation, first, of a plunging
+frog, and second, of water falling over rocks. In representing the
+effect of the stimulus on the rate of respiration, I have given the
+distance on the drum covered by the ten complete respirations just
+preceding the stimulus and the ten following it.
+
+
+             10 Respirations.        10 Respirations.
+           _Before_ Stimulus.  _After_ Stimulus.
+  1st Stim.       13.0 cm.                 11.8 cm.
+  2d Stim.        12.7 cm.                 12.7 cm.
+
+                      With a smaller animal.
+
+  1st Stim.        5.4 cm.                  4.8 cm.
+  2d Stim.         4.9 cm.                  4.7 cm.
+  Average for 5    5.00 cm.                 4.86 cm.
+
+
+_These records show a marked increase in the rate of respiration just
+after the auditory stimulus is given for the first time._ The stimulus
+has less effect when repeated after an interval of one or two minutes,
+and if repeated several times it finally causes no noticeable change.
+On the whole, the sound of falling water seems to arouse the animals
+to fuller life. The stimulus appears to interest them, and it
+certainly accelerates respiration. This is precisely what one would
+expect from a sound which is of special significance in the life of
+the animal.
+
+
+3. In case of a loud shrill whistle inhibition of respiration
+resulted. This probably means that the frogs were frightened by the
+sound. Falling water served rather to excite their natural-habitat
+associations, whereas, the whistle, being an uncommon and unassociated
+sound, caused fear. It is evident to the casual observer that the frog
+sometimes inhibits and sometimes increases its respiratory movements
+when frightened, so the result in this experiment is in no way
+surprising. I am by no means certain, however, that a longer series of
+observations on several individuals would give constant inhibitory
+results. My immediate purpose in the work was to get evidence of
+hearing; the respiratory changes were of secondary importance,
+although of such great interest that I have planned a more thorough
+special study of them for the future.
+
+A few sample results showing the influence of the whistle upon a small
+bull-frog follow:
+
+               Length of 10 Resps.             Length of 10 Resps.
+              _Before_ Stimulus in cm.   _After_ Stimulus in cm.
+  1st Stim.            6.0                             6.7
+  2d    "              5.4                             6.0
+  3d    "              5.9                             5.8
+  1st   "              4.7                             5.4
+  2d    "              4.4                             4.6
+
+
+As a test-check observation for comparison, the influence of a visual
+stimulus upon respiration was noted under the same conditions as for
+the auditory. Effect of turning on electric light over box.
+
+       Length in cm. of 10 Resps.    Length in cm. of 10 Resps.
+        _Before_ Stimulus.      _After_ Stimulus.
+                4.8                           4.4
+                5.3                           4.6
+                4.5                           4.0
+
+These results indicate an increase in the respiration rate due to the
+visual stimulus.
+
+
+4. Of the other auditory stimuli used, the pistol-cap explosion gave
+very irregular results. For one animal it caused acceleration, for
+another inhibition. There is, however, good evidence that the sounds
+were heard.
+
+
+5. The ringing of a bell gave results similer to those for a whistle,
+and the sound of a 500 S.V. tuning fork usually caused a slight
+increase in the rate of breathing. In these experiments I therefore
+have evidence, through their effects upon respiration, of the frog's
+ability to hear sounds ranging from 50 V. to at least 1,000 V.
+
+The croak of the green frog ranges from 100 to 200 V., so far as I
+have been able to determine. That of the bull frog is lower, from 50
+to 75; and in the leopard frog the range is from 80 to 125. The latter
+is very different from the green frog in its croaking, in that it
+croaks whenever disturbed, whereas, the green frog rarely responds in
+that way to a stimulus.
+
+We are now in a position to say that the failure of frogs to give
+motor reactions to strong auditory stimuli is not due to their
+inability to be affected by the stimuli, but is a genuine inhibition
+phenomenon.
+
+
+XI. THE EFFECTS OF AUDITORY STIMULI ON VISUAL REACTIONS.
+
+
+Further experimental evidence of hearing was gotten from some work
+done to test the influence of sounds upon motor reactions to visual
+stimuli. Frogs, like most other amphibians, reptiles and fishes, are
+attracted by any small moving object and usually attempt to seize it.
+They never, so far as I have noticed, feed upon motionless objects,
+but, on the other hand, will take almost anything which moves.
+Apparently the visual stimulus of movement excites a reflex. A very
+surprising thing to those who are unfamiliar with frog habits is the
+fear which small frogs have of large ones. Put some green frogs or
+small bull frogs into a tank with large bull frogs, and the little
+ones will at once show signs of extreme fear; they jump about in the
+most excited manner and try hard to escape. The cause of their fear
+soon appears, since it is usually only a few minutes until the little
+ones are swallowed by their wide-mouthed, cannibalistic fellows.
+
+It is, moreover, well known that a bit of red flannel fastened to a
+hook attracts frogs and is an excellent method of capturing them. Red
+seems to be the color which they most readily notice.
+
+This tendency of the frog to attempt to seize any moving object I made
+use of to test the value of sounds. By placing a frog in a glass
+aquarium which was surrounded by a screen, back of which I could work
+and through a small hole in which I was able to watch the animal
+without being noticed by it, and then moving a bit of red cardboard
+along one side of the aquarium, I could get the frog to jump at it
+repeatedly. In each attempt to get the moving object, the animal
+struck its head forcibly against the glass side of the aquarium. There
+was, therefore, reason to think that a few trials would lead to the
+inhibition of the reaction. Experiment discovered the fact that a
+hungry frog would usually jump at the card as many as twenty times in
+rapid succession.
+
+In this reaction to a visual stimulus there appeared good material for
+testing audition. I therefore arranged a 500 S.V. tuning fork over the
+aquarium and compared the reactions of animals to the visual stimulus
+alone, with that to the visual stimulus when accompanied by an
+auditory stimulus. The tuning-fork sound was chosen because it seemed
+most likely to be significant to the frog. It is similar to the sounds
+made by the insects upon which frogs feed. For this reason one would
+expect that the sight of a moving object and the sound of a
+tuning-fork would tend to reėnforce one another.
+
+The experiments were begun with observations on the effects of moving
+objects on the respiration. In case of a normal rate of 54
+respirations per minute sight of the red object caused an increase to
+58. Then the same determination was made for the auditory stimulus.
+The tuning-fork usually caused an increase in rate. In a typical
+experiment it was from 65 per minute to 76. The observations prove
+conclusively that the 500 S.V. sound is heard. My attention was turned
+to the difference of the environment of the ear in its relation to
+hearing. Apparently frogs hear better when the tympanum is partially
+under water than when it is fully exposed to the air.
+
+Having discovered by repeated trials about how vigorously and
+frequently a frog would react to the moving red card, I tried the
+effect of setting the fork in vibration a half minute before showing
+the card. It was at once evident that the sound put the frog on the
+alert, and, when the object came into view, it jumped at it more
+quickly and a greater number of times than when the visual stimulus
+was given without the auditory. This statement is based on the study
+of only two animals, since I was unable to get any other frogs that
+were in the laboratory at the time to take notice of the red
+cardboard. This was probably because of the season being winter. I
+venture to report the results simply because they were so definite as
+to point clearly to the phenomenon of the reėnforcement of the
+visual-stimulus reaction by an auditory stimulus.
+
+Concerning the influence of this combining of stimuli on the reaction
+time, I am only able to say that the reaction to the moving object
+occurred quicker in the presence of the auditory stimulus. When the
+red card was shown it was often several seconds before the frog would
+notice it and attempt to get it, but when the sound also was given the
+animal usually noticed and jumped toward the moving card almost
+immediately.
+
+Unfortunately I have thus far been unable to get chronoscopic
+measurements of the reaction times in this reėnforcement phenomenon. I
+hope later to be able to follow out the interesting suggestions of
+these few experiments in the study of reėnforcement and inhibition as
+caused by simultaneously given stimuli.
+
+A few observations made in connection with these experiments are of
+general interest. The frog, when it first sees a moving object,
+usually draws the nictitating membrane over the eye two or three times
+as if to clear the surface for clearer vision. Frequently this action
+is the only evidence available that the animal has noticed an object.
+This movement of the eye-lids I have noticed in other amphibians and
+in reptiles under similar conditions, and since it always occurs when
+the animals have need of the clearest possible vision, I think the
+above interpretation of the action is probably correct.
+
+Secondly, the frog after getting a glimpse of an object orients
+itself by turning its head towards the object, and then waits for a
+favorable chance to spring. The aiming is accurate, and as previously
+stated the animal is persistent in its attempts to seize an object.
+
+
+XII. THE PAIN-SCREAM OF FROGS.
+
+
+While making measurements of the frog's reaction time to electrical
+stimulation, I noticed that after a few repetitions of a 2-volt,
+.0001-ampčre stimulus an animal would frequently make a very peculiar
+noise. The sound is a prolonged scream, like that of a child, made by
+opening the mouth widely. The ordinary croak and grunt are made with
+closed or but slightly opened mouth. The cry at once reminds one of
+the sounds made by many animals when they are frightened. The rabbit,
+for example, screams in much the same way when it is caught, as do
+also pigs, dogs, rats, mice and many other animals. The question
+arises, is this scream indicative of pain? While studying reaction
+time I was able to make some observations on the relation of the
+scream to the stimulus.
+
+First, the scream is not given to weak stimuli, even upon many
+repetitions. Second, it is given to such strengths of an electrical
+stimulus as are undoubtedly harmful to the animal. Third, after a frog
+has been stimulated with a strong current (two volts), until the
+scream is given with almost every repetition, it will scream in the
+same way when even a weak stimulus is applied. If, for instance, after
+a two-volt stimulus has been given a few times, the animal be merely
+touched with a stick, it will scream. It thus appears as if the strong
+stimulus increases the irritability of the center for the
+scream-reflex to such an extent that even weak stimuli are sufficient
+to cause the reaction. Are we to say that the weak stimulus is painful
+because of the increased irritability, or may it be concluded that the
+reflex is in this case, like winking or leg-jerk or the head-lowering
+and puffing, simply a forced movement, which is to be explained as an
+hereditary protective action, but not as necessarily indicative of any
+sort of feeling. Clearly if we take this stand it may at once be said
+that there is no reason to believe the scream indicative of pain at
+any time. And it seems not improbable that this is nearer the truth
+than one who hears the scream for the first time is likely to think.
+
+The pain-scream is of interest in this consideration of auditory
+reactions because it increases the range of sounds which we should
+expect frogs to hear if we grant the probability of them hearing their
+own voices.
+
+It may be worth while to recall at this point the fact that a whistle
+from the human lips--the nearest approach to the pain-scream among the
+sounds which were used as stimuli in the experiments on
+respiration--caused marked inhibition of respiration. Perhaps this
+fact may be interpreted in the light of the pain-scream reaction. I
+may add that I have never seen a frog give a motor reaction to the
+pain-scream. Thinking it would certainly alarm the animals and cause
+them to make some movement which would serve for reaction-time
+measurements, I made repeated trials of its effects, but could never
+detect anything except respiratory changes.
+
+       *       *       *       *       *
+
+
+
+
+        STUDIES IN PSYCHOLOGICAL THEORY.
+
+
+
+
+       *       *       *       *       *
+
+
+
+
+THE POSITION OF PSYCHOLOGY IN THE SYSTEM OF KNOWLEDGE.
+
+BY HUGO MÜNSTERBERG.
+
+
+The modern efforts to bring all sciences into a system or at least to
+classify them, from Bacon to Spencer, Wundt and Pearson have never, if
+we abstract here from Hegel, given much attention to those questions
+of principle which are offered by the science of psychology. Of course
+the psychological separation of different mental functions has often
+given the whole scheme for the system, the classification thus being
+too often more psychological than logical. Psychology itself,
+moreover, has had for the most part a dignified position in the
+system; even when it has been fully subordinated to the biological
+sciences, it was on the other hand placed superior to the totality of
+mental and moral sciences, which then usually have found their unity
+under the positivistic heading 'sociology.' And where the independent
+position of psychology is acknowledged and the mental and moral
+sciences are fully accredited, as for instance with Wundt, psychology
+remains the fundamental science of all mental sciences; the objects
+with which philology, history, economics, politics, jurisprudence,
+theology deal are the products of the processes with which psychology
+deals, and philology, history, theology, etc., are thus related to
+psychology, as astronomy, geology, zoölogy are related to physics.
+There is thus nowhere a depreciation of psychology, and yet it is not
+in its right place. Such a position for psychology at the head of all
+'Geisteswissenschaften' may furnish a very simple classification for
+it, but it is one which cannot express the difficult character of
+psychology and the complex relations of the system of mental sciences.
+The historical and philological and theological sciences cannot be
+subordinated to psychology if psychology as science is to be
+coördinated with physics, that is, if it is a science which describes
+and explains the psychical objects in the way in which physics
+describes and explains the physical objects. On the other hand, if it
+means in this central position of mental sciences a science which does
+not consider the inner life as an object, but as subjective activity
+needing to be interpreted and subjectively understood, not as to its
+elements, but as to its meaning, then we should have two kinds of
+psychology, one which explains and one which interprets. They would
+speak of different facts, the one of the inner life as objective
+content of consciousness, as phenomenon, the other of the inner life
+as subjective attitude, as purpose.
+
+The fact is, that these two sciences exist to-day. There are
+psychologists who recognize both and keep them separated, others who
+hold to the one or the other as the only possible view; they are
+phenomenalists or voluntarists. Mostly both views are combined, either
+as psychological voluntarism with interposed concessions to
+phenomenalism or as phenomenalism with the well-known concessions to
+voluntarism at the deciding points. Further, those who claim that
+psychology must be phenomenalistic--and that is the opinion of the
+present writer--do not on that account hold that the propositions of
+voluntarism are wrong. On the contrary: voluntarism, we say, is right
+in every respect except in believing itself to be psychology.
+Voluntarism, we say, is the interpretative account of the real life,
+of immediate experience, whose reality is understood by understanding
+its meaning sympathetically, but we add that in this way an objective
+description can never be reached. Description presupposes
+objectivation; another aspect, not the natural aspect of life, must be
+chosen to fulfill the logical purposes of psychology: the
+voluntaristic inner life must be considered as content of
+consciousness while consciousness is then no longer an active subject
+but a passive spectator. Experience has then no longer any meaning in
+a voluntaristic sense; it is merely a complex of elements. We claim
+that every voluntaristic system as far as it offers descriptions and
+explanations has borrowed them from phenomenalistic psychology and is
+further filled up by fragments of logic, ethics and ęsthetics, all of
+which refer to man in his voluntaristic aspect. We claim, therefore,
+that such a voluntaristic theory has no right to the name psychology,
+while we insist that it gives a more direct account of man's real life
+than psychology can hope to give, and, moreover, that it is the
+voluntaristic man whose purpose creates knowledge and thus creates the
+phenomenalistic aspect of man himself.
+
+We say that the voluntaristic theory, the interpretation of our real
+attitudes, in short teleological knowledge, alone can account for the
+value and right of phenomenalistic psychology and it thus seems unfair
+to raise the objection of 'double bookkeeping.' These two aspects of
+inner life are not ultimately independent and exclusive; the
+subjective purposes of real life necessarily demand the labors of
+objectivistic psychology. The last word is thus not dualistic but
+monistic and the two truths supplement each other. But this
+supplementation must never be misinterpreted as meaning that the two
+sciences divide inner experience, as if, for instance, the
+phenomenalistic study dealt with perceptions and ideas, the
+voluntaristic with feelings and volitions. No, it is really a
+difference of logical purpose of treatment and thus a difference of
+points of view only; the whole experience without exception must be
+possible material for both. There is no feeling and no volition which
+is not for the phenomenalist a content of consciousness and nothing
+else. There is, on the other hand, no perception and no idea which is
+not, or better, ought not to be for the voluntarist a means, an aim, a
+tool, an end, an ideal. In that real life experience of which the
+voluntarist is speaking, every object is the object of will and those
+real objects have not been differentiated into physical things under
+the abstract categories of mechanics on the one hand, and psychical
+ideas of them in consciousness on the other; the voluntarist, if he is
+consistent, knows neither physical nor psychical phenomena.
+Phenomenalist and voluntarist thus do not see anything under the same
+aspect, neither the ideas nor the will.
+
+This difference is wrongly set forth if the antithesis to voluntarism
+is called intellectualism. Intellectualism is based on the category of
+judgment, and judgment too is a ideological attitude. Phenomenalism
+does not presuppose a subject which knows its contents but a subject
+which simply _has_ its contents; the consciousness which has the
+thought as content does not take through that the voluntaristic
+attitude of knowing it and the psychologist has therefore no reason to
+prefer the thought to the volition and thus to play the
+intellectualist. If the psychologist does emphasize the idea and its
+elements, the sensations, it is not because they are vehicles of
+thought but because their relations to physical objects make them
+vehicles of communication. The elements of ideas are negotiable and
+thus through their reference to the common physical world indirectly
+describable; as the elements of ideas are alone in this position, the
+psychologist is obliged to consider all contents of consciousness,
+ideas and volitions alike, as complexes of sensations.
+
+The antithesis is also misinterpreted, or at least wrongly narrowed,
+if it is called voluntarism _versus_ associationism. Recent
+discussions have sufficiently shown that the principle of association
+is not the only possible one for phenomenalistic theories. If
+associationism is identified with objective psychology, all the
+well-founded objections to the monopoly of the somewhat sterile
+principle of association appear as objections to phenomenalism in
+psychology, and voluntaristic theories, especially those which work
+with the teleological category of apperception, are put in its place.
+But without returning to apperceptionism we can overcome the
+one-sidedness of associationism if full use is made of the means which
+the world of phenomena offers to theory. The insufficiency of
+associationism disappears if the content of consciousness is
+considered as variable not only as to quality and intensity but also
+as to vividness. This variation of vividness, on the other hand, is no
+exception from the psychophysical parallelism as soon as the psychical
+process is considered as dependent not only upon the local and
+quantitative differences of the sensory process but also upon the
+motor function of the central physical process. The one-sidedness of
+the physiological sensory theories has been the hidden reason for the
+one-sidedness of associationism. The sensory-motor system must be
+understood as the physical basis of the psychophysical process and the
+variations in the motor discharge then become conditions of those
+psychical variations of vividness which explain objectively all those
+phenomena in whose interest associationism is usually supplemented by
+apperceptionism. The association theory must thus be given up in favor
+of an 'action-theory'[1] which combines the consistency of
+phenomenalistic explanation with a full acknowledgment of the
+so-called apperceptive processes; it avoids thus the deficiency of
+associationism and the logical inconsistency of apperceptionism.
+
+   [1] H. Münsterberg, 'Grundzüge der Psychologie.' Bd. I.,
+   Leipzig, 1900, S. 402-562.
+
+Only if in this way the sciences of voluntaristic type, including all
+historical and normative sciences, are fully separated from
+phenomenalistic psychology, will there appear on the psychological
+side room for a scientific treatment of the phenomena of social life,
+that is, for sociology, social psychology, folk-psychology, psychical
+anthropology and many similar sciences. All of them have been in the
+usual system either crowded out by the fact that history and the other
+mental sciences have taken all the room or have been simply identified
+with the mental sciences themselves. And yet all those sciences exist,
+and a real system of sciences must do justice to all of them. A modern
+classification has perhaps no longer the right as in Bacon's time to
+improve the system by inventing new sciences which have as yet no
+existence, but it has certainly the duty not to ignore important
+departments of knowledge and not to throw together different sciences
+like the descriptive phenomenalistic account of inner life and its
+interpretative voluntaristic account merely because each sometimes
+calls itself psychology. A classification of sciences which is to be
+more than a catalogue fulfills its logical function only by a careful
+disentanglement of logically different functions which are externally
+connected. Psychology and the totality of psychological, philosophical
+and historical sciences offer in that respect far more difficulty than
+the physical sciences, which have absorbed up to this time the chief
+interest of the classifier. It is time to follow up the ramifications
+of knowledge with special interest for these neglected problems. It is
+clear that in such a system sciences which refer to the same objects
+may be widely separated, and sciences whose objects are unlike may be
+grouped together. This is not an objection; it indicates that a
+system is more than a mere pigeon-holing of scholarly work, that it
+determines the logical relations; in this way only can it indeed
+become helpful to the progress of science itself.
+
+The most direct way to our end is clearly that of graphic
+representation wherein the relations are at once apparent. Of course
+such a map is a symbol and not an argument; it indicates the results
+of thought without any effort to justify them. I have given my
+arguments for the fundamental principles of the divisions in my
+'Grundzüge der Psychologie' and have repeated a few points more
+popularly in 'Psychology and Life,' especially in the chapter on
+'Psychology and History.' And yet this graphic appendix to the
+Grundzüge may not be superfluous, as the fulness of a bulky volume
+cannot bring out clearly enough the fundamental relations; the detail
+hides the principles. The parallelism of logical movements in the
+different fields especially becomes more obvious in the graphic form.
+Above all, the book discussed merely those groups which had direct
+relation to psychology; a systematic classification must leave no
+remainder. Of course here too I have not covered the whole field of
+human sciences, as the more detailed ramification offers for our
+purpose no logical interest; to subdivide physics or chemistry, the
+history of nations or of languages, practical jurisprudence or
+theology, engineering or surgery, would be a useless overburdening of
+the diagram without throwing new light on the internal relations of
+knowledge.
+
+Without now entering more fully into any arguments, I may indicate in
+a few words the characteristic features of the graphically presented
+proposition. At the very outset we must make it clear that phenomena
+and voluntaristic attitudes are not coördinated, but that the reality
+of phenomena is logically dependent upon voluntaristic attitudes
+directed towards the ideal of knowledge. And yet it would be
+misleading to place the totality of phenomenalistic sciences as a
+subdivision under the teleological sciences. Possible it would be; we
+might have under the sciences of logical attitudes not only logic and
+mathematics but as a subdivision of these, again, the sciences which
+construct the logical system of a phenomenalistic world--physics
+being in this sense merely mathematics with the conception of
+substance added. And yet we must not forget that the teleological
+attitudes, to become a teleological science, must be also logically
+reconstructed, as they must be teleologically connected, and thus in
+this way the totality of purpose-sciences might be, too, logically
+subordinated to the science of logic. Logic itself would thus become a
+subdivision of logic. We should thus move in a circle, from which the
+only way out is to indicate the teleological character of all sciences
+by starting not with science but with the strictly teleological
+conception of life--life as a system of purposes, felt in immediate
+experience, and not as the object of phenomenalistic knowledge. Life
+as activity divides itself then into different purposes which we
+discriminate not by knowledge but by immediate feeling; one of them is
+knowledge, that is, the effort to make life, its attitudes, its means
+and ends a connected system of overindividual value. In the service of
+this logical task we connect the real attitudes and thus come to the
+knowledge of purposes: and we connect the means and ends--by
+abstracting from our subjective attitudes, considering the objects of
+will as independent phenomena--and thus come to phenomenalistic
+knowledge. At this stage the phenomenalistic sciences are no longer
+dependent upon the teleological ones, but coördinated with them;
+physics, for instance, is a logical purpose of life, but not a branch
+of logic: the only branch of logic in question is the philosophy of
+physics which examines the logical conditions under which physics is
+possible.
+
+One point only may at once be mentioned in this connection. While we
+have coördinated the knowledge of phenomena with the knowledge of
+purposes we have subordinated mathematics to the latter. As a matter
+of course much can be said against such a decision, and the authority
+of most mathematicians would be opposed to it. They would say that the
+mathematical objects are independent realities whose properties we
+study like those of nature, whose relations we 'observe,' whose
+existence we 'discover' and in which we are interested because they
+belong to the real world. All that is true, and yet the objects of the
+mathematician are objects made by the will, by the logical will,
+only, and thus different from all phenomena into which sensation
+enters. The mathematician, of course, does not reflect on the purely
+logical origin of the objects which he studies, but the system of
+knowledge must give to the study of the mathematical objects its place
+in the group where the functions and products of logical thought are
+classified. The arithmetical or geometrical material is a free
+creation, and a creation not only as to the combination of
+elements--that would be the case with many laboratory substances of
+the chemist too--but a creation as to the elements themselves, and the
+value of the creation, its 'mathematical interest,' is to be judged by
+ideals of thought, that is, by logical purposes. No doubt this logical
+purpose is its application in the world of phenomena, and the
+mathematical concept must thus fit the world so absolutely that it can
+be conceived as a description of the world after abstracting not only
+from the will relations, as physics does, but also from the content.
+Mathematics would then be the phenomenalistic science of the form and
+order of the world. In this way mathematics has a claim to places in
+both fields: among the phenomenalistic sciences if we emphasize its
+applicability to the world, and among the teleological sciences if we
+emphasize the free creation of its objects by the logical will. It
+seems to me that a logical system as such has to prefer the latter
+emphasis; we thus group mathematics beside logic and the theory of
+knowledge as a science of objects freely created for purposes of
+thought.
+
+All logical knowledge is divided into Theoretical and Practical. The
+modern classifications have mostly excluded the practical sciences
+from the system, rightly insisting that no facts are known in the
+practical sciences which are not in principle covered by the
+theoretical sciences; it is art which is superadded, but not a new
+kind of knowledge. This is quite true so far as a classification of
+objects of knowledge is in question, but as soon as logical tasks as
+such are to be classified and different aspects count as different
+sciences, then it becomes desirable to discriminate between the
+sciences which take the attitude of theoretical interest and those
+which consider the same facts as related to certain human ends. But we
+may at first consider the theoretical sciences only. They deal either
+with the objectified world, with objects of consciousness which are
+describable and explainable, or with the subjectivistic world of real
+life in which all reality is experienced as will and as object of
+will, in which everything is to be understood by interpretation of its
+meaning. In other words, we deal in one case with phenomena and in the
+other with purposes.
+
+The further subdivision must be the same for both groups--that which
+is merely individual and that which is 'overindividual'; we prefer the
+latter term to the word 'general,' to indicate at once that not a
+numerical but a teleological difference is in question. A phenomenon
+is given to overindividual consciousness if it is experienced with the
+understanding that it can be an object for every one whom we
+acknowledge as subject; and a purpose is given to overindividual will
+in so far as it is conceived as ultimately belonging to every subject
+which we acknowledge. The overindividual phenomena are, of course, the
+physical objects, the individual phenomena the psychical objects, the
+overindividual purposes are the norms, the individual purposes are the
+acts which constitute the historical world. We have thus four
+fundamental groups: the physical, the psychological, the normative and
+the historical sciences.
+
+Whoever denies overindividual reality finds himself in the world of
+phenomena a solipsist and in the world of purposes a sceptic: there is
+no objective physical world, everything is my idea, and there is no
+objective value, no truth, no morality, everything is my individual
+decision. But to deny truth and morality means to contradict the very
+denial, because the denial itself as judgment demands acknowledgment
+of this objective truth and as action demands acknowledgment of the
+moral duty to speak the truth. And if an overindividual purpose cannot
+be denied, it follows that there is a community of individual subjects
+whose phenomena cannot be absolutely different: there must be an
+objective world of overindividual objects.
+
+In each of the four groups of sciences we must consider the facts
+either with regard to the general relations or with regard to the
+special material; the abstract general relations refer to every
+possible material, the concrete facts which fall under them demand
+sciences of their own. In the world of phenomena the general relations
+are causal laws--physical or psychical laws; in the world of purposes
+theories of teleological interrelations--normative or historical; the
+specific concrete facts are in the world of phenomena objects,
+physical or psychical objects, in the world of purposes acts of
+will--specific norms or historical acts. If we turn first to
+phenomena, the laws thereof are expressed in the physical sciences, by
+mechanics, physics, chemistry, and we make mechanics the superior as
+chemistry must become ultimately the mechanics of atoms. In the
+psychological sciences the science of laws is psychology, with the
+side-branch of animal psychology, while human psychology refers to
+individuals and to social groups. Social psychology, as over against
+individual psychology, is thus a science of general laws, the laws of
+those psychological phenomena which result from the mutual influence
+of several individuals.
+
+On the other hand, we have as the special concrete products of the
+laws, the objects themselves, and the most natural grouping of them
+may be from whole to part. In the physical world it means that we
+start from the concrete universe, turning then to the earth, then to
+the objects on the earth, inorganic and organic. There is here no
+logical difficulty. Each one of these objects can be considered in
+three aspects, firstly as to its structure, secondly as to its special
+laws, that is, the special function of the object as related to the
+general sciences of physics and chemistry, and thirdly as to its
+natural development. If we apply these three methods of study to the
+whole universe we have astronomy, astrophysics and cosmology, to the
+whole earth, geography, geophysics, geology, to animals, zoölogy,
+physiology, comparative anatomy, and so on.
+
+The special phenomena in the framework of the psychological sciences
+group themselves in the same logical order, from the whole to the
+part. The psychological totality is empirical mankind, and as we
+select the earth as the one part of the universe which is the habitat
+of man, so our scientific interest must move from the whole psychical
+humanity to those phenomena of human life which are the vehicle of our
+civilization, from mankind to its most important function, the
+association of man; and as we moved from earth to the special objects
+on earth, so we may turn from association to the special phenomena
+which result from association. If we separated further the inorganic
+from the organic, we must here separate the products of
+undifferentiated and of differentiated association. The science of
+mankind is race psychology, the science of the association of man is
+sociology, the science of the results of undifferentiated association
+is Völkerpsychologie, folk psychology. The science of products of
+differentiated association has no special name; its subject matter is
+the whole of historical civilization considered as a psychological
+naturalistic phenomenon. As soon as we follow the ramification still
+further we have to do with the special kinds of these products, that
+is, with the volitions, thoughts, appreciations and beliefs. In the
+undifferentiated associations they give us morals and habits,
+languages and enjoyments and mythological ideas, while the
+individually differentiated association gives political, legal and
+economic life, knowledge, art and religion: all of course merely as
+causal, not as teleological processes, and thus merely as
+psychological and not as historical material. Here, as with the
+physical phenomena, the structure, the special laws and the
+development must be everywhere separated, giving us three sciences in
+every case. For instance, the study of mankind deals with the
+differences of mental structure in psychical anthropology, with the
+special psychical laws in race psychology and with the development in
+comparative psychology. The chief point for us is that social
+psychology, race psychology, sociology, folk psychology, etc., are
+under this system sharply differentiated sciences and that they do not
+at all overlap the real historical sciences. There is no historical
+product of civilization which does not come under their method but it
+must be conceived as a causal phenomenon, not as related to the
+purposes of the real man, and thus even the development means merely a
+growing complication of naturalistic processes and not history in the
+teleological sense.
+
+We turn to the normative sciences. The general theory of the
+overindividual purposes is metaphysics; the special overindividual
+acts are those which constitute the normative volitions, connected in
+the philosophy of morals, the philosophy of state and the philosophy
+of law, those which constitute the normative thoughts and finally
+those which constitute the normative appreciations and beliefs,
+connected in ęsthetics and the philosophy of religion. Especial
+interest belongs to the philosophy of thought. We have discussed the
+reasons why we group mathematics here and not among the
+phenomenalistic sciences. We have thus one science which deals
+critically with the presuppositions of thought, _i.e._ the theory of
+knowledge or epistemology, which can be divided into the philosophy of
+physical sciences, the philosophy of psychological sciences, the
+philosophy of normative sciences and the philosophy of historical
+sciences. We have secondly the science of the processes of thought
+dealing with concepts, judgments and reasoning, _i.e._, logic, and we
+have finally the science of those objects which the thought creates
+freely for its own purposes and which are independent from the content
+of the world, _i.e._, mathematics, which leads to the qualitative
+aspect of general mathematics and the quantitative aspect of concrete
+mathematics. For our purposes it may be sufficient to separate
+externally algebra, arithmetic, analysis and geometry. In this way all
+the philosophical sciences find their natural and necessary place in
+the system, while it has been their usual lot to form an appendix to
+the system, incommensurable with the parts of the system itself, even
+in the case that the other scheme were not preferred, to make ethics,
+logic, ęsthetics, epistemology and metaphysics merely special branches
+of positivistic sociology and thus ultimately of biology.
+
+In the historical sciences the general theory which stands over
+against the special acts has a special claim on our attention. We may
+call it the philosophy of history. That is not identical with the
+philosophy of historical sciences which we mentioned as a part of
+epistemology. The philosophy of historical sciences deals with the
+presuppositions by which historical teleological knowledge becomes
+logically possible. The philosophy of history seeks a theory which
+connects the special historical acts into a unity. It has two
+branches. It is either a theory of the personality, creating a theory
+of real individual life as it enters as ideological factor into
+history, or it seeks the unity of entire humanity. The theory of
+personality shows the teleological interrelation of our purposes; the
+theory of humanity shows the teleological interrelation of all
+nations. The name philosophy of history has been used mostly for the
+theory of humanity only, abstracting from the fact that it has been
+often misused for sociology or for the psychology of history or for
+the philosophy of historical sciences--but the name belongs also to
+the theory of personality. This theory of personality is exactly that
+second kind of 'psychology' which does not describe and does not
+explain but which interprets the inner teleological connections of the
+real man. It is 'voluntaristic psychology' or, as others call it who
+see correctly the relation of this science to history, 'historical
+psychology.' It is practically 'apperceptionistic psychology.' The
+special activities of the historical man divide themselves again into
+volitions, thoughts, appreciations and beliefs, with their realization
+in the state, law, economical systems, knowledge, art and religion.
+Each of these special realizations must allow the same manifoldness in
+treatment which we found with the special physical or psychical
+objects; we can ask as to structure, relation to the general view and
+development. But in accordance with the teleological material the
+study of the structure here means 'interpretation,' the study of the
+general relations here means study of the relation to civilization,
+and the study of the development here means the real history. We have,
+thus, for the state or law or economy or knowledge or art or religion
+always one science which interprets the historical systems of state,
+etc., in a systematic and philological way, one science which deals
+with its function in the historical world and one which studies
+biographically and nationally the history of state, law, economical
+life, science, art or religion.
+
+In the sphere of the practical sciences the divisions of the
+theoretical sciences must repeat themselves. We have thus applied
+physical, applied psychological, applied normative and applied
+historical sciences, and it is again the antithesis of psychological
+and of historical sciences which is of utmost importance and yet too
+often neglected. The application of physical sciences, as in
+engineering, medicine, etc., or the application of normative
+knowledge in the sciences of criticism do not offer logical
+difficulty, but the application of psychological and historical
+knowledge does. Let us take the case of pedagogy or of penology,
+merely as illustrations. Is the application of phenomenalistic
+psychology or the application of teleological voluntarism in question?
+Considering the child, the criminal, any man, as psychophysical
+apparatus which must be objectively changed and treated, we have
+applied psychology; considering him as subject with purposes, as
+bearer of an historical civilization whose personalities must be
+interpreted and understood and appreciated, then we need applied
+historical knowledge. In the first case the science of pedagogy is a
+psycho-technical discipline which makes education mechanical and
+deprives the teacher of the teleological attitude of inner
+understanding; in the second case it is a science of real education
+far removed from psychology. All the sciences which deal with service
+in the system of civilization, service as teacher, as judge, as social
+helper, as artist, as minister, are sciences which apply the
+teleological historical knowledge, and their meaning is lost if they
+are considered as psycho-technical sciences only.
+
+
+LIFE (in its immediate reality, felt as a system of telelogical
+|    experiences, involving the acknowledgement of other subjects of
+|     experiences)
+|
+|-VOLITION (will aiming towards new experiences).
+| |-Individual: _Practical Life._
+| |-Overindividual: _Mortality._
+|
+|-THOUGHT (will acknowledging the connection of experiences).
+| |-Individual: _Judgement_
+| |-Overindividual: TRUTH
+|   |-THEORETICAL KNOWLEDGE (connection of experiences determined by
+|   | |                      pure experience).
+|   | |
+|   | |-KNOWLEDGE OF PHENOMENA (connection of experiences after
+|   | | |                       abstracting their will relations).
+|   | | |-Knowledge of Phenomena Given to Overindividual Consciousness.
+|   | | | |-I. PHYSICAL SCIENCES.
+|   | | |   |-A. GENERAL LAWS.
+|   | | |   | |-Mechanics.
+|   | | |   |   |-Physics.
+|   | | |   |   |-Chemistry.
+|   | | |   |
+|   | | |   |-B. SPECIAL OBJECTS.
+|   | | |     |-1. Universe.
+|   | | |     | |-Astronomy _a, b, c_.
+|   | | |     |
+|   | | |     |-2. Special Parts.
+|   | | |     | |-Geography _a, b, c_.
+|   | | |     |
+|   | | |     |-3. Special Objects on Earth.
+|   | | |       |-Inorganic.
+|   | | |       | |-Mineralogy _a, b, c_.
+|   | | |       |
+|   | | |       |-Organic.
+|   | | |         |-Plants.
+|   | | |         | |-Botany _a, b, c_.
+|   | | |         |
+|   | | |         |-Animals.
+|   | | |           |-Zoology _a, b, c_.
+|   | | |           |-Anthropology _a, b, c_.
+|   | | |
+|   | | |-Knowledge of Phenomena given to Indiviual Consciousness.
+|   | |   |-II. PSYCHOLOGICAL SCIENCES.
+|   | |     |-A. GENERAL LAWS.
+|   | |     | |-PHENOMENALISTIC PSYCHOLOGY
+|   | |     |   |-Animal Psychology.
+|   | |     |   |-Human psychology.
+|   | |     |     |-Individual Ps.
+|   | |     |       |-Normal.
+|   | |     |       | |-Child.
+|   | |     |       | |-Adult.
+|   | |     |       |
+|   | |     |       |-Abnormal.
+|   | |     |
+|   | |     |-B. SPECIAL OBJECTS.
+|   | |       |-1. Mankind.
+|   | |       | |-Race Psychology _a, b, c_.
+|   | |       |-2. Special Functions.
+|   | |       | |-Association of Men.
+|   | |       |   |-Sociology _a, b, c_.
+|   | |       |
+|   | |       |-3. Special Products of Association of Men
+|   | |         |      (considered as natural phenomena).
+|   | |         |-Products of Undiffereniated Association of Men
+|   | |         | |    (Folk Psychology).
+|   | |         | |-Volition.
+|   | |         | | |-Morals _a, b, c_.
+|   | |         | | |-Habits _a, b, c_.
+|   | |         | |
+|   | |         | |-Thoughts.
+|   | |         | | |-Languages _a, b, c_.
+|   | |         | |
+|   | |         | |-Appreciation.
+|   | |         | | |-Enjoyment _a, b, c_.
+|   | |         | |
+|   | |         | |-Belief.
+|   | |         |   |-Mythology _a, b, c_.
+|   | |         |
+|   | |         |-Products of Individual Differentiation
+|   | |           |  (casual phenomenalistic sciences of civilization
+|   | |           |   and its development).
+|   | |           |-Volition.
+|   | |           | |-State _a, b, c_.
+|   | |           | |-Law _a, b, c_.
+|   | |           | |-Economy _a, b, c_.
+|   | |           |
+|   | |           |-Thoughts.
+|   | |           | |-Sciences _a, b, c_.
+|   | |           |
+|   | |           |-Appreciation.
+|   | |           | |-Art _a, b, c_.
+|   | |           |
+|   | |           |-Belief.
+|   | |             |-Religion _a, b, c_.
+|   | |
+|   | |-KNOWLEDGE OF PURPOSES (connection of experiences in their
+|   |   |                      telelogical reality).
+|   |   |
+|   |   |-Knowledge of Purposes of the Overindividual Will.
+|   |   | |-III. NORMATIVE SCIENCES
+|   |   |   |-A. GENERAL THEORY of absolute values.
+|   |   |   | |-Metaphysics.
+|   |   |   |
+|   |   |   |-B. SPECIAL ACTS.
+|   |   |     |-Volition.
+|   |   |     | |-Philosophy of Morals (Ethics).
+|   |   |     | |-Philosophy of Law.
+|   |   |     | |-Philosophy of State.
+|   |   |     |
+|   |   |     |-Thoughts.
+|   |   |     | |-Presuppositions of Thought.
+|   |   |     | | |-Theory of Knowledge.
+|   |   |     | |   |-Phil. of Physics.
+|   |   |     | |   |-Phil. of Psych.
+|   |   |     | |   |-Phil. of Normative Sciences.
+|   |   |     | |   |-Phil. of Historical Sciences.
+|   |   |     | |
+|   |   |     | |-Processes of Thought.
+|   |   |     | | |-Logic.
+|   |   |     | |
+|   |   |     | |-Objects Created by Thought.
+|   |   |     |   |-Mathematics.
+|   |   |     |   |-Algebra.
+|   |   |     |   |-Arithmetic.
+|   |   |     |   |-Analysis.
+|   |   |     |   |-Geometry.
+|   |   |     |
+|   |   |     |-Appreciation.
+|   |   |     | |-Philosophy of Art (Ęsthetics).
+|   |   |     |
+|   |   |     |-Belief.
+|   |   |       |-Philosophy of Religion.
+|   |   |
+|   |   |-Knowledge of Purposes of the Individual Will.
+|   |     |-IV. HISTORICAL SCIENCES.
+|   |       |-A. GENERAL THEORY of real life.
+|   |       | |-Philosophy of History.
+|   |       |   |-Theory of Personality.
+|   |       |   | |-(Theory of selves.)
+|   |       |   | |-("Historical Psychology.")
+|   |       |   | |-("VOLUNTARISTIC Psychology.")
+|   |       |   | |-("Apperceptional Psychology.")
+|   |       |   |-Theory of Humanity.
+|   |       |
+|   |       |-B. SPECIAL ACTS (telelogical interpretative sciences of
+|   |         |                civilization and history.)
+|   |         |-Volition.
+|   |         | |-Politics, _a, b, c_.
+|   |         | |-Law, _a, b, c_.
+|   |         | |-Economy, _a, b, c_.
+|   |         |
+|   |         |-Thoughts.
+|   |         | |-Science, _a, b, c_.
+|   |         |
+|   |         |-Appreciation.
+|   |         | |-Art, _a, b, c_.
+|   |         |
+|   |         |-Belief.
+|   |           |-Religion, _a, b, c_.
+|   |
+|   |-PRACTICAL KNOWLEDGE.
+|     |-APPLIED KNOWLEDGE OF PHENOMENA.
+|     | |-V. APPLIED PHYSICAL SCIENCES.
+|     | | |-Technical Sciences.
+|     | | | |-Applied Physics.
+|     | | | |-Applied Chemistry.
+|     | | | |-Applied Biology.
+|     | | |
+|     | | |-Medicine.
+|     | |
+|     | |-VI. APPLIED PSYCHOLOGICAL SCIENCES.
+|     |   |-Psychotechnical Sciences.
+|     |   | |-Psychological Pedagogy.
+|     |   | |-Psychological Penology.
+|     |   |
+|     |   |-Psychiatry.
+|     |
+|     |-APPLIED KNOWLEDGE OF PURPOSES.
+|       |-VII. APPLIED NORMATIVE SCIENCES.
+|       | |-Volition.
+|       | | |-Politics.
+|       | | | |-Science of Public Service.
+|       | | |
+|       | | |-Law.
+|       | | | |-Science of Legal Service. (Practical Jurisprudence.)
+|       | | |
+|       | | |-Economy.
+|       | |   |-Science of Social Service.
+|       | |
+|       | |-Thoughts.
+|       | | |-Science of Teaching. (Education.)
+|       | |
+|       | |-Appreciation.
+|       | | |-Science of Artistic Production.
+|       | |
+|       | |-Belief.
+|       |   |-Science of Religious Service. (Practical Theology.)
+|       |
+|       |-VIII. APPLIED HISTORICAL SCIENCES.
+|         |-Volition.
+|         | |-Criticism of State.
+|         | |-Criticism of Law.
+|         |
+|         |-Thoughts.
+|         | |-Criticism of Science.
+|         |
+|         |-Appreciation.
+|         | |-Criticism of Art.
+|         |
+|         |-Belief.
+|           |-Criticism of Religion.
+|
+|-APPRECIATION (will resting in isolated experiences).
+| |-Individual: _Enjoyment._
+| |-Overindividual: _Beauty._
+|
+|-BELIEF (will resting in the supplements of experience).
+  |-Individual: _Creed._
+  |-Overindividual: _Religion.
+
+NOTE: The letters _a, b, c_ below the sciences of Special Objects and
+Special Acts indicate the three subdivisions that results from the
+threefold aspects;--of structure(_a_), of relation to the general laws
+or theories(_b_), and of development(_c_). With regards to physical
+phenomena, for instances, we have astronomy(_a_), astrophysics(_b_),
+and cosmology(_c_); or geography(_a_), geophysics(_b_), geology(_c_);
+or botany(_a_), plant physiology(_b_), phylogenetic development of
+plants(_c_). In the same way for psychical objects; for instance:
+structural sociology(_a_), functional sociology(_b_), comparative
+sociology(_c_); or structure (grammar and syntax) of languages(_a_),
+psychology of languages(_b_), comparative study of languages(_c_).
+With regard to the telelogical historical sciences the study of
+structure takes on here the character of intrepretation; the relation
+to the general view is here the dependence on civilization and the
+development is here the real history. We have thus, for instance, the
+intepretation of Roman law(_a_), dependence of Roman law upon
+civilization(_b_), history of Roman law(_c_).
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+End of Project Gutenberg's Harvard Psychological Studies, Volume 1, by Various
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diff --git a/old/16266.txt b/old/16266.txt
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+Project Gutenberg's Harvard Psychological Studies, Volume 1, by Various
+
+This eBook is for the use of anyone anywhere at no cost and with
+almost no restrictions whatsoever.  You may copy it, give it away or
+re-use it under the terms of the Project Gutenberg License included
+with this eBook or online at www.gutenberg.org
+
+
+Title: Harvard Psychological Studies, Volume 1
+       Containing Sixteen Experimental Investigations from the
+       Harvard Psychological Laboratory.
+
+Author: Various
+
+Editor: Hugo Muensterberg
+
+Release Date: July 12, 2005 [EBook #16266]
+
+Language: English
+
+Character set encoding: ASCII
+
+*** START OF THIS PROJECT GUTENBERG EBOOK PSYCHOLOGICAL STUDIES, VOL 1 ***
+
+
+
+
+Produced by Gallica (http://gallica.bnf.fr/), Clare Boothby,
+Victoria Woosley and the Online Distributed Proofreading
+Team at https://www.pgdp.net.
+
+
+
+
+
+
+
+
+
+                          THE
+                   Psychological Review
+
+
+                    _EDITED BY_
+
+
+  J. McKEEN CATTELL     and    J. MARK BALDWIN
+  COLUMBIA UNIVERSITY          PRINCETON UNIVERSITY
+
+
+              _WITH THE CO-OPERATION OF_
+
+       ALFRED BINET, ECOLE DES HAUTES-ETUDES, 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 MUeNSTERBERG, 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 MUeNSTERBERG.
+
+
+               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 'Grundzuege
+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 role 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 role 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 aesthetic 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 aesthetic 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 role 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 cooeperation.
+
+       *       *       *       *       *
+
+
+
+
+CONTENTS.
+
+
+Preface: Hugo Muensterberg ......................................   i
+
+STUDIES IN PERCEPTION.
+
+  Eye-Movement and Central Anaesthesia: 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 AESTHETIC 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 AEsthetics 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 Muensterberg ........................................... 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 ANAESTHESIA.
+
+BY EDWIN B. HOLT.
+
+
+I. THE PROBLEM OF ANAESTHESIA DURING EYE-MOVEMENT.
+
+
+A first suggestion of the possible presence of anaesthesia 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
+anaesthesia 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 anaesthesia, perhaps in the latter case there is
+anaesthesia.
+
+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 Guerber,[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 Loewe; 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 Guerber, 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 Guerber), 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 anaesthesia 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 Serie, V., p.
+   466.
+
+Apart from the experience of the eye watching itself in a glass, Dodge
+(_loc. citat._) found another fact which strongly suggested
+anaesthesia. 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 anaesthesia. 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 anaesthesia.
+
+If by 'anaesthesia' 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 anaesthesia 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 anaesthesia during movement, although the
+functioning of the retina should remain unaltered. Such a central
+anaesthesia 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 deg.' 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 anaesthesia 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 deg., the
+streak jumps with the eye; but if the eye sweeps through a rather
+large arc, say of 40 deg., 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, 'Beitraege 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., _Pflueger'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 anaesthesia 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 anaesthesia 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 deg., and all saw only the correctly localized streak if the arc
+was small, say 5 deg.. 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 deg. 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 deg. 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 anaesthesia could be demonstrated,
+both the feeling of succession and the discontinuity of the
+intensities would be explained (since during the anaesthesia 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 anaesthesia 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 anaesthesia 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 anaesthesia 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 anaesthesia, 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 anaesthesia 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 anaesthesia, 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 anaesthesia 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 deg..
+
+[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 deg. 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 deg. 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 deg.. 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 deg.. 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
+anaesthesia 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
+anaesthesia, 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 anaesthesia
+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 ANAESTHESIA.
+
+
+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 anaesthesia 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 deg.,
+of which the 9-cm. opening _ON_ 9 deg. 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 deg. of its arc,
+the complete swing being therefore 47 deg.. 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 deg. in 11.98[sigma] (since the 9 cm. are 9 deg. 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 deg. 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 deg. 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 deg.. 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 anaesthesia 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 deg., 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 Erklaerung der psychischen Erscheinungen,'
+   Leipzig u. Wien, 1894, S. 128. Mach, Ernst, 'Beitraege 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 deg., 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 deg., 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 anaesthesia, 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
+anaesthesia were carried on, and it is perhaps regrettable that in the
+'empirical' approximation of the natural rate of the eye through 40 deg.
+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 anaesthesia 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, 9x5 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 deg. of its arc: a
+total swing of 19 deg.. 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 deg. 11' of eye-movement, and we saw above that 9 deg. 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 deg.
+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 deg.
+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 deg. 11', of which the nine-centimeter distance of
+exposure is 19 deg. 38'. Now the eye is found to move very well through
+19 deg. 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 deg.. 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 deg. 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 anaesthesia 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 anaesthesia, 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
+anaesthesia_. 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., (Pflueger's) Archiv f. d. gesammte
+   Physiologie, 1869, II., S. 418.
+
+   [23] Guillery, (Pflueger'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 anaesthesia.
+
+
+V. SUMMARY AND COROLLARIES OF THE EXPERIMENTS, AND A PARTIAL,
+PHYSIOLOGICAL INTERPRETATION OF THE CENTRAL ANAESTHESIA.
+
+
+We have now to sum up the facts given by the experiments. The fact of
+central anaesthesia during voluntary movement is supported by two
+experimental proofs, aside from a number of random observations which
+seem to require this anaesthesia 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 anaesthesia 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 deg. or more), the anaesthesia 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 anaesthesia 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 anaesthesia 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 anaesthesia. 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
+anaesthesia correspondingly either brief or discontinuous. Whereas, the
+phenomena are the same when the head moves 90 deg. as when the eyes move
+that amount. It seems probable, then, that voluntary movements of the
+head do equally condition the anaesthesia.
+
+We have seen, too, that in reflex eye-or head-movements no anaesthesia
+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 anaesthesia 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 anaesthesia, since no discontinuity of
+vision during voluntary movement is noticeable, although a relatively
+long moment of anaesthesia actually intervenes.
+
+But decidedly the most interesting detail about the anaesthesia 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
+anaesthesia, although beginning later than the movement, is present
+when the eye reaches _O_, while it is between _O_ and _N_, that is,
+during the anaesthetic moment, that the eye is reflexly caught and held
+by the light. This proves again that the anaesthesia 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
+   Erklaerung 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 anaesthesia? 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 Muensterberg[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] Muensterberg, Hugo, 'Grundzuege 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 anaesthetic. 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 anaesthesia 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
+anaesthesia, 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 anaesthesia, 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 anaesthesia.
+
+The fact that the anaesthesia commences appreciably later than the
+movement so far favors this interpretation. For if the anaesthesia 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 anaesthesia, 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 anaesthesia 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
+anaesthesia.
+
+       *       *       *       *       *
+
+
+
+
+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 cooeperated 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 Thiery,[3] and Dresslar.[4] Thiery 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] Thiery, 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. Muensterberg[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] Muensterberg, H.: 'Beitraege 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 aesthesiometers, A and B, were arranged in a framework, so that
+uniform stimulations could be given on both arms. The aesthesiometers
+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 aesthesiometer could be conveniently adjusted
+by the pins F and H. The shape of the cams was such that the descent
+of the aesthesiometer 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
+aesthesiometer 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 aesthesiometer, 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 aesthesiometer 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,' Tuebingen, 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 Zoellner 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 naively 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
+naive 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 Muensterberg 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 Mueller-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 aesthetic 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 naively 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
+aesthetic 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 Mueller-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 aesthetic 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 aesthetic 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 aesthetic
+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 Muensterberg[19] in
+his studies of movement.
+
+   [18] Delabarre, E.B., 'Ueber Bewegungsempfindungen,' Inaug.
+   Dissert., Freiburg, 1891.
+
+   [19] Muensterberg, H., 'Beitraege 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
+coexistence in space. The coexistence 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,' Tuebingen, 1868.
+
+   [2] Meumann, E.: 'Beitraege 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.: 'Beitraege 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 (1/2 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] squaredx squared}
+
+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. Hoering[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 ueber den Zeitsinn des Ohres,'
+   _Sitzungsber. d. Wiener Akad._, Math.-Nat. Kl., Bd. 51, Abth.
+   2.
+
+   [5] Hoering: 'Versuche ueber das Unterscheidungsvermoegen des
+   Hoersinnes fuer Zeitgroessen,' Tuebingen, 1864.
+
+   [6] Vierordt: _op. cit._
+
+   [7] Kollert, J.: 'Untersuchungen ueber den Zeitsinn,' _Phil.
+   Studien_, I., S. 79.
+
+   [8] Estel, V.: 'Neue Versuche ueber den Zeitsinn,' _Phil.
+   Studien_, II., S. 39.
+
+   [9] Glass R.: 'Kritisches und Experimentelles ueber den
+   Zeitsinn,' _Phil. Studien_, IV., S. 423.
+
+   [10] Mehner, Max: 'Zum Lehre vom Zeitsinn,' _Phil. Studien_,
+   II., S. 546.
+
+   [11] Schumann, F.: 'Ueber die Schaetzung kleiner Zeitgroessen,'
+   _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 aesthesiometers. 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
+aesthesiometer. 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
+aesthesiometer 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
+aesthesiometer 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 aesthesiometer. I
+made an aesthesiometer 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
+aesthesiometer 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
+aesthesiometer. Various methods were tried, but the following was most
+successful. I would tell the subject that I was going to use the
+aesthesiometer 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 aesthesiometer 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 aesthesiometer 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. Brueckner[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 reenforcement 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 reenforcement as
+an indication of fusion.
+
+   [1] Brueckner, A.: 'Die Raumschwelle bei Simultanreizung,'
+   _Zeitschrift fuer 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 Ruecksicht 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 aesthesiometer 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 cooeperation 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 deg..           Rotation of 90 deg..
+                     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 deg. a positive displacement of large amount
+takes place in the case of all observers. When the rotation extends to
+90 deg., 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 deg. the mean variation
+is but slightly greater than under normal conditions; when the
+rotation is through 90 deg. 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 Muensterberg 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] Muensterberg, 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. Muensterberg 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. Muensterberg 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 deg.
+    "       "        +115.50      115.50      1.10      50 deg.
+   _J_    (20)       +443.10      443.10      9.47      45 deg.
+
+
+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 deg.. 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 Muensterberg, 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) squared
+
+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) squared
+
+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 deg., and _B'C'_ a red complementary sector of 270 deg.. 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 deg., 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 deg. 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 deg. or 60 deg., 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 deg., 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 deg. 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 deg. 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
+14x12 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 4x21/2 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 Mueller
+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} squared 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} cubed 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.
+    squaredFive presentations in learning.
+    cubedFive 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 resume 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 41/2 to 61/2 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 Gefuehle 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. Muensterberg, H.: 'Grundzuege 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 aesthetic 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 aesthetic 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 aesthetic 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 AESTHETIC 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 cooerdinate 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, Bruecke, Dogiel,
+   Hausegger, Mach, Mentz, Ribot, Sherrington, Scripture, Smith,
+   et al. (4) Of its historical evolution: Buecher, 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
+aesthetic 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'Annee 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 deg., 240 deg., and 120 deg.; if the temporal
+relations desired be in the ratios 2:1:1, the arrangement will be
+360 deg., 180 deg., 90 deg.; if in the ratios 5:4:3, it will be 360 deg., 210 deg., 90 deg.;
+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 deg., 270 deg., 180 deg.; 360 deg., 240 deg., 180 deg., and 360 deg., 260 deg., 180 deg..
+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 cooerdination 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 aesthetic 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 cooerdinated 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 aesthetic 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 aesthetic 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 cooerdinated 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 aesthetic 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 _Gestaltsqualitaet_ 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 cooerdinated 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
+cooerdination 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 cooerdination 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 Bruecke, 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. Bruecke
+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 cooerdination 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
+  Anapaestic,         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 anapaestic 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 anapaest moves continuously toward a final accent in an unbroken
+crescendo. But in the anapaestic 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 cooeperation 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; anapaestic, 12.45. The constant tendency, when any
+difficulty in cooerdination 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 cooerdinated--the most
+natural--form is the dactyl; the anapaest stands next; the amphibrach
+is the most unnatural and difficult to cooerdinate.
+
+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 cooerdination 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
+cooerdinated 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 cooerdinating the
+unaccented initial elements has resulted in the substitution of a
+dipodic division for the anapaestic 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 cooerdination 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 anapaestic--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
+  Anapaes.,  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 anapaestic
+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
+    Anapaestic,       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
+  Anapaestic,      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 anapaestic 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 anapaest. 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 anapaestic 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
+cooerdinated 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-Anapaestic,
+(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 cooerdination 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
+cooerdination 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 reestablished
+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 reestablished 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 anapaestic, 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 cooerdination 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 cooerdination 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 cooerdination 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 cooerdination 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 cooerdination the aesthetic 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 cooerdination. Training affects more readily the
+single element than the composite measure, and in the most highly
+cooerdinated 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 cooerdinated 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 cooerdination 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 cooerdination, 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 cooerdinated 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 anapaests among iambics, and the like--and the occurrence
+of points of origin, emphasis, interruption, and finality in special
+accentuations, syncopated measures, caesural 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 Bruecke.[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' (Saemmt. Werk,
+   herausgeg. von Hartenstein), Leipzig, 1850-2, Bd. VII., S. 291
+   ff.
+
+   [2] Lotze, R.H.: 'Geschichte der AEsthetik,' Muenchen, 1863, S.
+   487 ff.
+
+   [3] Vierordt, K.: 'Untersuchungen ueber d. Zeitsinn,' Tuebingen,
+   1868.
+
+   [4] von Bruecke, E.W.: 'Die physiol. Grundlagen d.
+   neuhochdeutschen Verskunst,' Wien, 1871.
+
+   [5] Mach, Ernst: 'Unters. ue. d. Zeitsinn d. Ohres,' _Wiener
+   Sitz. Ber., mathem. naturw. Classe_, 1865, Bd. 51, II., S. 133.
+   _Beitraege 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 cooerdinated 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 incooerdinated. 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 cooeperating 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 cooerdination 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
+cooerdination, 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:
+
+   III III III I / III III III I  Without rhyme.
+
+  Each dactyl (III) 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 cooerdination 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:
+  III III III I / III III III I (with rhyme).
+
+  Each dactyl (III) 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 anapaestic.
+       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 do)
+                          go)
+                          do
+                          do
+     Hu. Rhymes imperfectly.
+     Mc. Rhymes imperfectly.
+     G.  Rhymes imperfectly.
+     Ha. Rhymes imperfectly.
+     Hy. Rhymes fairly well.
+
+  Ta ta  ta ta  ta ta  ta do)
+                          go)
+                          do
+                          do
+     Hu. Cannot get rhyme.
+     Mc. Rhymes imperfectly. 'Produced by some sort of tension.'
+     G.  Rhymes imperfectly.
+
+  Ta ta  ta ta  ta ta  ta do)
+                          go)
+                          do
+                          do
+     Hu. Rhymes well.
+     Mc. Rhymes well.
+     G.  Rhymes well.
+
+  Ta ta  ta ta  ta ta  ta do
+                          go)
+                          do)
+                          do)
+     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
+'Gestaltqualitaet' 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 phonetique experimentale, 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'Annee 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 caesura, 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         x30
+    Hu.          28             x25a           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             x32            41a          40
+                 22             _22_a          x18          29a
+    Ha.          27              31a           44b         _28_a
+                 36              79           x30           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 cooerdinated 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
+cooerdinated 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
+cooerdinated 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._ (Pflueger'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 Mueller'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] Mueller, 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 Mueller'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 cooerdinated 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._ (Pflueger'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 cooerdinated. 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 cooerdination, 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 Mueller'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 'Gestaltqualitaet,' 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 anapaest. 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 anapaest 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 anapaest 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 anapaest, but by even
+three.
+
+The anapaest 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 anapaest), 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 caesural 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 'Gestaltqualitaeten' 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 cooerdinated 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 cooerdination
+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. Stuebel, '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 aesthetic 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 aesthetic
+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 aesthetic 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 aesthetically
+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 aesthetic
+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
+aesthetic 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) aesthetic phenomenon emerging from pre-aesthetic 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 aesthetic 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 aesthetic 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 aesthetic 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 aesthetic
+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-aesthetic 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-aesthetic 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 Zuni 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 Zuni 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 aesthetic 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
+aesthetic 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, the ornaments of the rectangular spaces given by the
+nodes are strikingly symmetrical. Many of these are from animal
+motives, and nearly always heads are turned back over the body, tails
+exaggerated, or either or both doubled, to get a symmetrical effect.
+Although much of the symmetrical ornament, again, is manifestly from
+textile models, its symmetrical character is so carefully preserved
+against the suggestions of the circular form that a direct pleasure in
+its symmetry may be inferred. (See Figs. 2-7.)
+
+   [7] Cushing, F.H.: _op. cit._; Holmes, W.H.: three articles on
+   pottery, Rep. of Bur. of Ethnol., 1882-83, p. 265, p. 367, and
+   p. 443.
+
+[Illustration: Fig. 2]
+
+[Illustration: Fig. 3]
+
+[Illustration: Fig. 4]
+
+The subject of drawing can be here only touched upon, but the results
+of study go to show, in general, two main directions of primitive
+expression: pictorial representation, aiming at truth of life, and
+symbolic ornament. The drawings of Australians, Hottentots and
+Bushmen, and the carvings of the Esquimaux and of the prehistoric men
+of the reindeer period show remarkable vigor and naturalness; while
+the ornamentation of such tribes as the South Sea Islanders has a
+richness and formal beauty that compare favorably with the decoration
+of civilized contemporaries. But these two types of art do not always
+keep pace with each other. The petroglyphs of the North American
+Indians[8] exhibit the greatest irregularity, while their tattooing is
+extremely regular and symmetrical. The Brazilian savage [9] draws
+freehand in a very lively and grotesque manner, but his patterns are
+regular and carefully developed. Again, not all have artistic talents
+in the same direction. Dr. Schurtz, in his 'Ornamentik der Aino,'[10]
+says: "There are people who show a decided impulse for the direct
+imitation of nature, and especially for the representation of events
+of daily life, as dancing, hunting, fishing, etc. It is, however,
+remarkable that a real system of ornamentation is scarcely ever
+developed from pictorial representations of this kind; that, in fact,
+the people who carry out these copies of everyday scenes with especial
+preference, are in general less given to covering their utensils with
+a rich ornamentive decoration."[11] Drawing and ornament, as the
+products of different tendencies, may therefore be considered
+separately.
+
+   [8] Mallery, Garrick: 'Pictographs of the North American
+   Indians,' Rep. of Bur. of Ethnol., 1882-3, p. 13.
+
+   [9] Von den Steinen, Karl: 'Unter den Naturvolkern
+   Zentral-Brasiliens,' Berlin, 1894.
+
+   [10] _Internal. Archiv s. Ethnog._, Bd. IX.
+
+   [11] Cf. Andree, Richard: 'Ethnographische Parallelen,' Neue
+   Folge, Leipzig, 1889, S. 59.
+
+The reason for the divergence of drawing and ornament is doubtless the
+original motive of ornamentation, which is found in the clan or totem
+ideas. Either to invoke protection or to mark ownership, the totem
+symbol appears on all instruments and utensils; it has been shown,
+indeed, that practically all primitive ornament is based on totemic
+motives.[12] Now, since a very slight suggestion of the totem given by
+its recognized symbol is sufficient for the initiated, the extreme of
+conventionalization and degradation of patterns is allowable, and is
+observed to take place. The important point to be noted in this
+connection is, however, that all these changes are toward symmetry.
+The most striking examples might be indefinitely multiplied, and are
+to be found in the appended references (see Figs. 8 and 9).
+
+   [12] Haddon, _op. cit._; Frazer, J.G.: 'Totemism,' 1887;
+   Grosse, Ernst: Anfaenge der Kunst,' Freiburg i. B. u. Leipzig,
+   1894.
+
+[Illustration: Fig. 5.]
+
+[Illustration: Fig. 6.]
+
+[Illustration: Fig. 7.]
+
+We may distinguish here, also, between the gradual disintegration and
+degradation of pattern toward symmetry, as seen in the examples just
+given, and the deliberate distortion of figures for a special purpose.
+This is strikingly shown in the decorative art of the Indians of the
+North Pacific coast. They systematically represent their totem
+animals--their only decorative motives--as split in symmetrical
+sections, and opened out flat on the surface which is to be
+covered[13] (see Fig. 11). Dr. Boas argues that their purpose is to
+get in all the received symbols, or to show the whole animal, but,
+however this may be, every variation introduces symmetry even where it
+is difficult to do so, as in the case, for instance, of bracelets,
+hat-brims, etc. (Fig. 10). This may in some cases be due to the
+symmetrical suggestions of the human body in tattooing,[14] but it
+must be so in comparatively few.
+
+[13] Boas, Franz: 'Decorative Art of the Indians of the North Pacific
+Coast,' _Bulletin_ of Am. Mus. of Nat. Hist., Vol. IX.
+
+[14] Mallery, G.: _op. cit._; Haddon, A.C.: _op. cit._, p. 257;
+'Decorative Art of British New Guinea,' Cunningham Memoir X., Royal
+Irish Acad., 1894, p. 26.
+
+[Illustration: Fig. 8.]
+
+[Illustration: Fig. 9.]
+
+[Illustration: Fig. 10]
+
+The primitive picture has for its object not only to impart
+information, but to excite the very definite pleasure of recognition
+of a known object. All explorers agree in their accounts of the
+savage's delight in his own naive efforts at picture making. All such
+drawings show in varying degrees the same characteristics; first of
+all, an entire lack of symmetry. In a really great number of examples,
+including drawings and picture-writing from all over the world, I
+have not found one which showed an attempt at symmetrical arrangement.
+Secondly, great life and movement, particularly in the drawings of
+animals. Thirdly, an emphasis of the typical characteristics, the
+logical marks, amounting sometimes to caricature. The primitive man
+draws to tell a story, as children do. He gives with real power what
+interests him, and puts in what he knows ought to be there, even if it
+is not seen, but he is so engrossed by his interest in the imitated
+object as to neglect entirely its relation to a background.
+
+[Illustration: FIG. 11]
+
+Now, this very antithesis of ornament and picture is enlightening as
+to the dawn of aesthetic feeling, and the strongest confirmation of our
+hypothesis of an original impulse to symmetry in art. In the
+ornamentation of objects the content or meaning of the design is
+already supplied by the merest hint of the symbol which is the
+practical motive of all ornamentation. The savage artist need,
+therefore, concern himself no more about it, and the form of his
+design is free to take whatever shape is demanded either by the
+conditions of technique and the surface to be ornamented, or by the
+natural aesthetic impulse. We have found that technical conditions
+account for only a small part of the observed symmetry in pattern, and
+the inference to a natural tendency to symmetry is clear. Pictorial
+representation, on the other hand, is enjoyed by the primitive man
+merely as an imitation, of which he can say, 'This is that animal'--to
+paraphrase Aristotle's Poetics. He is thus constrained to reproduce
+the form as it shows meaning, and to ignore it as form, or as his
+natural motor impulses would make it.
+
+To sum up the conclusions reached by this short survey of the field of
+primitive art, it is clear that much of the symmetry appearing in
+primitive art is due (1) to the conditions of construction, as in the
+form of dwellings, binding-patterns, weaving and textile patterns
+generally; (2) to convenience in use, as in the shapes of spears,
+arrows, knives, two-handled baskets and jars; (3) to the imitation of
+animal forms, as in the shapes of pottery, etc. On the other hand (1)
+a very great deal of symmetrical ornament maintains itself _against_
+the suggestions of the shape to which it is applied, as the ornaments
+of baskets, pottery, and all rounded objects; and (2) all distortion,
+disintegration, degradation of pattern-motives, often so marked as all
+but to destroy their meaning, is in the direction of geometrical
+symmetry. In short it is impossible to account for more than a small
+part of the marked symmetry of primitive art by non-aesthetic
+influences, and we are therefore forced to conclude an original
+tendency to create symmetry, and to take pleasure in it. A strong
+negative confirmation of this is given, as noted above, by the utter
+lack of symmetry of the only branch of art in which the primitive man
+is fully preoccupied with meaning to the neglect of shape; and by the
+contrast of this with those branches of art in which attention to
+meaning is at its minimum.
+
+The question put at the beginning of this section must thus be
+answered affirmatively. There is evidence of an original aesthetic
+pleasure in symmetry.
+
+
+III. EXPERIMENTS IN SUBSTITUTIONAL SYMMETRY.
+
+
+_A. Method of Experiment._
+
+A certain degree of original aesthetic pleasure in symmetry may be
+considered to have been established by the preceding section, and,
+without considering further the problems of real or geometrical
+symmetry, it may now be asked whether the pleasure aroused by the form
+of asymmetrical objects is not at bottom also pleasure in symmetry;
+whether, in other words, a kind of substitution of factors does not
+obtain in such objects, which brings about a psychological state
+similar to that produced by real symmetry.
+
+The question what these substituted factors may be can perhaps be
+approached by a glance at a few pictures which are accepted as
+beautiful in form, although not geometrically symmetrical. Let us
+take, for instance, several simple pictures from among the well-known
+altar-pieces, all representing the same subject, the _Madonna
+Enthroned_ with _Infant Christ_, and all of generally symmetrical
+outline. It seems, then, reasonable to assume that if the variations
+from symmetry show constantly recurring tendencies, they represent the
+chief factors in such a substitutional symmetry or balance, supposing
+it to exist. The following pictures are thus treated in detail, M.
+denoting Madonna; C., Child; and Cn., Central Line. The numbers refer
+to the collection of reproductions used exclusively in this
+investigation, and further described in section IV.
+
+1. 56, Martin Schoengauer: _Madonna in Rose-arbor._ M. is seated
+exactly in Cn., C. on Right, turning to Right. M. turns to Left, and
+her long hair and draperies form one long unbroken line down to Left
+lower corner. All other details symmetrical.
+
+2. 867, Titian: _Madonna_. The picture is wider than it is high. M.
+stands slightly to Right of Cn.; C. on Right. Both turn slightly to
+Left, and the drapery of M. makes a long sweep to Left. Also a deep
+perspective occupies the whole Left field.
+
+3. 248, Raphael: _Madonna_ (The Bridgewater Madonna). M. sits in Cn.,
+turning to Left; C. lies across her lap, head to Left, but his face
+turned up to Right, and all the lines of his body tending sharply down
+to Right.
+
+In 1, all the elements of the picture are symmetrical except the
+position of C. on the Right, and the long flowing line to Left. In 2,
+there is a slightly greater variation. The mass of the figures is to
+Right, and the C. entirely over against the deep perspective and the
+flowing line on the Left, and the direction of both faces toward that
+side. In 3, the greater part of C.'s figure on Left is opposed by the
+direction of his lines and movement to Right. Thus these three
+pictures, whether or not they are considered as presenting a balance,
+at least show several well-defined factors which detach themselves
+from the general symmetrical scheme. (1) Interest in C. is opposed by
+outward-pointing line; (2) greater mass, by outward-pointing line,
+deep vista, and direction of attention; and (3) again interest by
+direction of line and suggestion of movement.
+
+This analysis of several aesthetically pleasing but asymmetrical
+arrangements of space strongly suggests that the elements of large
+size, deep perspective, suggested movement, and intrinsic interest are
+in some way equivalent in their power to arouse those motor impulses
+which we believe to constitute the basis of aesthetic response. It is
+the purpose of these experiments to follow up the lines of these
+suggestions, reducing them to their simplest forms and studying them
+under exact conditions.
+
+But before describing the instruments and methods of this experimental
+treatment, I wish to speak of the articles on the 'AEsthetics of Simple
+Form,' published as Studies from the Harvard Psychological Laboratory,
+by Dr. Edgar Pierce.[15] These articles, sub-entitled 'Symmetry' and
+'The Functions of the Elements' seem at first sight to anticipate the
+discussions of this paper; but a short analysis shows that while they
+point in the same direction, they nevertheless deal with quite
+different questions and in a different manner. In the statement of his
+problem, indeed, Dr. Pierce is apparently treading the same path.
+
+   [15] Pierce E.: PSYCH. REV., 1894, I., p. 483; 1896, III., p.
+   270.
+
+He says: "Can a feeling of symmetry, that is, of aesthetical equality
+of the two halves, remain where the two sides are not geometrically
+identical; and if so, what are the conditions under which this can
+result--what variations of one side seem aesthetically equal to the
+variations of the other side?" Some preliminary experiments resulted
+in the conclusion that an unsymmetrical and yet pleasing arrangement
+of a varied content rests on the pleasure in unity, thus shutting out
+the Golden Section choice, which depends on the pleasure in variety.
+That is, the choices made will not in general follow the golden
+section, but 'when the figure consists of two halves, the pleasure
+must be a feeling of aesthetical symmetry.'
+
+The final experiments were arrangements of lines and simple figures on
+a square, black background in which the center was marked by a white
+vertical line with a blue or a red line on each side. On one side of
+these central lines a line was fixed; and the subject had to place on
+the other side lines and simple figures of different sizes and
+different colors, so as to balance the fixed line. The results showed
+that lines of greater length, or figures of greater area must be put
+nearer the center than shorter or smaller ones--'A short line must be
+farther than a long one, a narrow farther than a wide, a line farther
+than a square; an empty interval must be larger than one filled, and
+so on.' And for colors, "blue, maroon and green, the dark colors, are
+the farthest out; white, red and orange, the bright colors, are
+nearest the center. This means that a dark color must be farther out
+than a bright one to compensate for a form on the other side. The
+brightness of an object is then a constant substitute for its distance
+in satisfying our feeling of symmetry."
+
+Now from these conclusions two things are clear. By his extremely
+emphasized central line, and his explicit question to the subjects,
+'Does this balance?' the author has excluded any other point of view
+than that of mechanical balance. His central fulcrum is quite
+overpowering. Secondly, his inquiry has dealt only with size and
+color, leaving the questions of interest, movement, and perspective
+untouched. But just the purpose of this experimental study is to seek
+for the different and possibly conflicting tendencies in composition,
+and to approximate to the conditions given in pictorial art. It is
+evident, I think, that the two studies on symmetry will not trespass
+on each other's territory. The second paper of Dr. Pierce, on 'The
+Functions of the Elements,' deals entirely with the relation of
+horizontal and vertical positions of the aesthetic object and of the
+subject to aesthetic judgments, and has therefore no bearing on this
+paper.
+
+For his apparatus Dr. Pierce used a surface of black cloth stretched
+over black rubber, 1 m. square. Now an investigation which is to deal
+with complicated and varied relations, resembling those of pictures,
+demands an instrument resembling them also in the shape of the
+background. A rectangle 600 mm. broad by 400 mm. high seemed to meet
+this requirement better than the square of Dr. Pierce. Other parts,
+also, of his instrument seemed unfitted for our purpose. The tin, 5
+cm. broad and confined to the slits across the center of the square,
+gave not enough opportunity for movement in a vertical direction,
+while the scale at the back was very inconvenient for reading. To
+supply these lacks, a scale graduated in millimeters was attached on
+the lower edge of the board, between a double track in which ran
+slides, the positions of which could be read on the scale. To the
+slides were attached long strips of tin covered with black cloth. On
+these strips figures glued to small clamps or clasps could be slipped
+up or down; this arrangement of cooerdinates made it possible to place
+a figure in any spot of the whole surface without bringing the hands
+into the field of view. The experiments were made in a dark room, in
+which the apparatus was lighted by an electric globe veiled by white
+paper and hung above and behind the head of the subject, so as not to
+be seen by him and to cast no shadow: in this soft light of course the
+black movable strips disappeared against the black background. A gray
+paper frame an inch and a half wide was fitted to the black rectangle
+to throw it up against the black depths of the dark room--thus giving
+in all details the background of a picture to be composed.
+
+The differences in method between the two sets of experiments were
+fundamental. In Dr. Pierce's experiments the figures were pulled from
+one side to the other of the half-square in question, and the subject
+was asked to stop them where he liked; in those of the writer the
+subject himself moved the slides back and forth until a position was
+found aesthetically satisfactory. The subject was never asked, Does
+this balance? He was indeed requested to abstract from the idea of
+balance, but to choose that position which was the most immediately
+pleasing for its own sake, and so far as possible detached from
+associations.
+
+I have said that Dr. Pierce intentionally accentuated the center. The
+conditions of pictorial composition suggest in general the center only
+by the rectangular frame. Most of my experiments were, therefore, made
+without any middle line; some were repeated with a middle line of fine
+white silk thread, for the purpose of ascertaining the effect of the
+enhanced suggestion of the middle line.
+
+But the chief difference came in the different treatment of results.
+Dr. Pierce took averages, whereas the present writer has interpreted
+individual results. Now, suppose that one tendency led the subject to
+place the slide at 50 and another to place it at 130 mm. from the
+center. The average of a large number of such choices would be 90--a
+position very probably disagreeable in every way. For such an
+investigation it was evident that interpretation of individual results
+was the only method possible, except where it could be conclusively
+shown that the subjects took one and only one point of view. They were
+always encouraged to make a second choice if they wished to do so, as
+it often happened that one would say: 'I like both of these ways very
+much.' Of course, individual testimony would be of the highest
+importance, and a general grouping into classes and indication of the
+majority tendency would be the only way to treat the results
+statistically. And indeed in carrying out the experiments this caution
+was found absolutely necessary. In all but one or two of the sections,
+the taking of averages would have made the numerical results
+absolutely unintelligible. Only the careful study of the individual
+case, comparison of various experiments on the same person to find
+personal tendencies, and comparison of the different tendencies, could
+give valuable results for the theory of symmetry.
+
+The first question to be taken up was the influence of right and left
+positions on choice. A long series of experiments was undertaken with
+a line 80x10 mm. on one side and a line 160x10 mm. on the other, in
+which the positions of these were reversed, and each in turn taken as
+fixed and variable, with a view to determining the effect of right and
+left positions. No definite conclusions emerged; and in the following
+experiments, most of which have been made for both right and left
+positions, the results will be treated as if made for one side alone,
+and, where averages are taken, will be considered as indifferently
+left or right.
+
+The experiments of Dr. Pierce were made for only one position of the
+fixed line--at 12 cm. distance from the center. The characteristic of
+the following experiments is their reference to all positions of the
+fixed line. For instance a fixed line, 10 cm. in length at 12 cm.
+distance from the center, might be balanced by a line 5 cm. in length
+at 20 cm. distance. But would the distance be in the same proportion
+for a given distance of the fixed line of say 20 or 25 cm.? It is
+clear that only a progressive series of positions of the fixed line
+would suggest the changes in points of view or tendencies of choice of
+the subject. Accordingly, for all the experiments the fixed line or
+other object was placed successively at distances of 20, 40, 60 mm.,
+etc., from the center; or at 40, 80 mm., etc., according to the
+character of the object, and for each of these fixed points the
+subject made one or two choices. Only an understanding of the
+direction in which the variable series moved gave in many cases an
+explanation for the choice.
+
+Each choice, it should be added, was itself the outcome of a long
+series of trials to find the most pleasing position. Thus, each
+subject made only about ten choices in an hour, each of which, as it
+appears in the tables, represents a large number of approximations.
+
+
+_B. Experiments on Size._
+
+I have said that different tendencies or types of choice in
+arrangement appeared. It will be convenient in the course of
+explaining in detail the method of experiment, to discuss at the same
+time the meaning of these types of choice.
+
+From analysis of the pictures, the simplest suggestion of balance
+appeared in the setting off against each other of objects of different
+sizes;--an apparent equivalence of a large object near the center with
+a small object far from the center; thus inevitably suggesting the
+relations of the mechanical balance, or lever, in which the heavy
+short arm balances the light long arm. This was also the result of
+Dr. Pierce's experiments for one position of his fixed line. The
+experiments which follow, however, differ in some significant points
+from this result. The instrument used was the one described in the
+preceding section. On one side, in the middle of the vertical strip,
+was placed the 'fixed' line, denoted by F., and the subject moved the
+'variable' line, denoted by V., until he found the arrangement
+aesthetically pleasing. The experimenter alone placed F. at the given
+reading, and read off the position of V. After the choice F. was
+placed at the next interval, V. was again tried in different
+positions, and so on. In the following tables the successive positions
+of F. are given in the left column, reading downward, and the
+corresponding positions of V. in the right column. The different
+choices are placed together, but in case of any preference the second
+choice is indicated. The measurements are always in millimeters. Thus,
+F. 40, V. 60, means that F. is 40 mm. to one side of the center, and
+V. 60 mm. to the opposite side. F. 80x10, V. 160x10, means that the
+white cardboard strips 80 mm.x10 mm., etc., are used. The minus sign
+prefixed to a reading means that the variable was placed on the side
+of the fixed line. An X indicates aesthetic dislike--refusal to choose.
+An asterisk (*) indicates a second choice.
+
+The following tables are specimen sets made by the subjects _C, O_,
+and _D_.
+
+
+I. (a) F. 80x10, V. 160x10.
+
+  F.                     V.
+         C.            O.                    D.
+
+   40   62, 120       166, 130           28, 24
+   80   70, 110       104, 102           80, 126
+  120   46, X          70, 46           68,--44, 128*
+  160   26, 96         50, 25           85, 196,--88*
+  200   20, X          55, X          --46, 230,* 220,--110*
+
+
+I. (b) F. 160x10, V. 80x10.
+
+  F.                     V.
+         C.            O.                    D.
+
+   40   74, 64         60, 96            27, 34
+   80   76, 65         72, 87            55, 138
+  120   60, 56         48, 82            70, 174
+  160   29, 74         16, 77          --114, 140, 138, 200
+  200   96, 36         25, 36            177,--146,--148, 230
+
+
+Now, on Dr. Pierce's theory, the variable in the first set should be
+nearer the center, since it is twice the size of the fixed line;--but
+the choices V. 120, 166, 130 for F. 40; V. 110, 104, 102, 126 for F.
+80; V. 128 for F. 120; V. 196 for F. 160; V. 230, 220 for F. 200, show
+that other forces are at work. If these variations from the expected
+were slight, or if the presence of second choices did not show a
+certain opposition or contrast between the two positions, they might
+disappear in an average. But the position of F. 40, over against V.
+120, 166, 130, is evidently not a chance variation. Still more
+striking are the variations for I. (_b_). Here we should expect the
+variable, being smaller, to be farther from the center. But for F. 40,
+we have V. 27, 34; for F. 80, all nearer but two; for F. 120, V. 60,
+56, 48, 82, 70; for F. 160, V. 29, 74, 16, 77, 138, and for F. 200, V.
+96, 36, 25, 36, 177--while several positions on the same side of the
+center as the constant show a point of view quite irreconcilable with
+mechanical balance.
+
+
+II. (a) F. 2 LINES 80x10.   V. SINGLE LINK 80x10.
+
+     F.                           V.
+                     C.                O.         P.
+
+   40- 60     58, 114*  138,  20      96, 84     166
+   60- 80     48         40, 138*    100, 56     150
+   80-100     64         70, 162*     47, 87     128
+  100-120     70 to 80   60           53, 53       X
+  120-140     58         82           50, 48      35
+  140-160     74         95 to 100    22, 32      37
+  160-180     72         102           X,  X      42
+  180-200     90         X             X,  X      50
+
+
+Here the variable should supposedly be the farther out; but we have V.
+58, 20 for F. 40-60; V. 48, 40, 56 for F. 60; V. 64, 70, 87 for F. 80;
+no larger choice for F. 100-120; indeed, from this point on everything
+nearer, and very much nearer. We can trace in these cases, more
+clearly perhaps than in the preceding, the presence of definite
+tendencies. _O_ and _P_, from positions in accord with the mechanical
+theory, approach the center rapidly; while _C_ is seldom 'mechanical,'
+but very slowly recedes from the center. The large number of refusals
+to choose assures us that the subjects demand a definitely pleasant
+arrangement--in other words, that every choice is the expression of a
+deliberate judgment.
+
+Taking again the experiments 1. (a) and 1. (b), and grouping the
+results for nine subjects, _C_, _O_, _A_, _S_, _H_, _G_, _D_, and _P_,
+we obtain the following general types of choice. The experiments were
+repeated by each subject, so that we have eighteen records for each
+position. I should note here that preliminary experiments showed that
+near the frame the threshold of difference of position was 10 mm., or
+more, while near the center it was 4 or 5 mm.; that is, arrangements
+were often judged symmetrically equal which really differed by from 4
+to 10 mm., according as they were near to or far from the center. In
+grouping types of choice, therefore, choices lying within these limits
+will be taken as belonging to the same type.
+
+
+   EXP. 1. (a)   F.(80 X 10).   V.(160 X 10).
+
+              1. F. 40.                            V. 40.¹
+
+       Types of Choice for V.
+   (1)  24   24   25   28
+   (2)  40   42   45   45                        40   40   40
+   (3)  62   65
+   (4) 100  105  1O9  120  130  136                  120
+   (5) 166 180                        200  200  200  200  160  160
+
+   ¹This table is obtained by taking from the full list, not given
+   here, of 1. (b) F. (l60 X 10), V. (80 X 10), those positions of
+   160 X 10 where the variable 80 X 10 has been placed at or near
+   40, thus giving the same arrangement as for 1. (a).
+
+
+It might be objected that a group 40-65 (2-3) would not be larger than
+one of 100-136 (4), but the break between 45 and 62 shows the zones
+not continuous. Moreover, as said above, the positions far from the
+center have a very large difference threshold.
+
+    I. (a) 2. F. 80:--(1) 24, (2) 50, (3) 68 70, (4) 80 85 94 95
+    85, (5) 102 104 110 120 124 126 125* 132, (6) 187; also V.
+    80:--(2) 40 40, (4) 80, (5) 120 120, (6) 160 160.
+
+    I. (a) 3. F. 120:--(1) 44 46, (2) 64 48 70 70, (3) 85 95 97
+    91, (4) 113 113 118, (5) 168 169 178;--44, X; also V.
+    120:--(1) 40 40, (3) 80 80 80, (4) 120 120, (5) 160 160.
+
+    I. (a) 4. F. 160:--(1) 25 26, (2) 40 50 57, (3) 82 85 95 100*,
+    (4) 114 115 130, (5) 145 145 156 162, (6) 196,
+    (7)--88*--150*--105.
+
+    I. (a) 5. F. 200:--(1) 20 23 28 36, (2) 55, (3) 108 124 130*,
+    (4) 171 189 199 195, (5) 220 230*, (6)--46--90--110*.
+
+On comparing the different groups, we find that in 1 and 2 there is a
+decided preference for a position somewhat less than half way between
+center and frame--more sharply marked for 1 than for 2. From 3 onward
+there is a decided preference for the mechanical arrangement, which
+would bring the larger strip nearer. Besides this, however, there are
+groups of variations, some very near the center, others approaching to
+symmetry. The maintenance of geometrical symmetry at a pretty constant
+ratio is to be noted; as also the presence of positions on the same
+side of the center as the fixed line. Before discussing the
+significance of these groups we may consider the results of Experiment
+II. (F. double line 80x10, V. single line 80x10) without giving
+complete lists.
+
+We notice therein, first of all, the practical disappearance of the
+symmetrical choice; for F. 40-60, 60-80, 80-100, a tendency,
+decreasing, however, with distance from the center, to the mechanical
+arrangement; for F. 100-120, and all the rest, not one mechanical
+choice, and the positions confined almost entirely to the region
+35-75. In some cases, however, the mechanical choice for (1) 40-80,
+(2) 60-80, was one of two, _e.g._, we have for (1) 20 and 138, for (3)
+70 and 162; in the last two cases the mechanical being the second
+choice.
+
+Now the reversals of the mechanical choice occur for Exp. I. in 1 and
+2 (F. 40 and F. 80); that is, when the small fixed line is near the
+center, the larger variable is distant. For Exp. II. the reversals,
+which are much more marked, occur in all cases _beyond_ F. 40, F. 60
+and F. 80; that is, when the double constant line is far from the
+center, the single variable approaches. If the mechanical theory
+prevailed, we should have in Exp. I. the lines together in the center,
+and in Exp. II. both near the fringe.
+
+From the individual testimony, based both on I. (_a_) and I. (_b_), it
+appears that subject _M_ is perfectly uniform in mechanical choice
+when the fixed line is the small line--_i.e._ when it moves out, the
+larger is placed near the center; but when the conditions of
+mechanical choice would demand that, as the larger fixed line moves
+out, the small variable one should move out farther, he regularly
+chooses the reverse. Nevertheless, he insists that in just these
+cases he has a feeling of equilibrium.
+
+_A_ also takes the mechanical choice as the small fixed line goes
+farther from the center; but when the fixed line is large and leaves
+the center, he reverses the mechanical choice--evidently because it
+would take the small line too far out. As he says, 'he is always
+disturbed by too large a black space in the center.'
+
+_G_ almost always takes the mechanical choice;--in one whole set of
+experiments, in which the fixed line is the large line, he reverses
+regularly.
+
+_H_ takes for F. (80x10) the mechanical choice only for the positions
+F. 160 and F. 200--_i.e._, only when F. is very far from the center
+and he wishes V. (160x10) nearer. For F. (160x10) he makes six such
+choices out of ten, but for positions F. 160 and F. 200 he has V. 44,
+65 and 20.
+
+_S_ takes for F. (160x10) at F. 120, V. 185 and-70; says of V. 185,
+which is also his choice for F. (160x10) at F. 80, 'I cannot go out
+further, because it is so hard to take in the whole field.' For F.
+(160x10) at F. 200, he has V. 130 and 60; says of V. 60, 'Very
+agreeable elements in connection with the relation of the two lines.'
+
+_C_ takes for F. (80x10) only one mechanical choice until it is at F.
+120. Then always mechanical, _i.e._, nearer center; for F. (160x10)
+makes after the position F. 40 no mechanical choice, _i.e._, V. is
+nearer center.
+
+It is evident from the above tables and individual cases that the
+reversals from the mechanical choice occur only when the mechanical
+choice would bring both lines in the center, or both near the edges,
+and the subjective testimony shows from what point of view this
+appears desirable. The subjects wish 'to take in the whole field,'
+they wish 'not to be disturbed by too large a black space in the
+center'; and when, in order to cover in some way the whole space, the
+small line is drawn in or the large one pushed out, they have,
+nevertheless, a feeling of equilibrium in spite of the reversal of
+mechanical balance.
+
+Accepting for the present, without seeking a further psychological
+explanation, the type of 'mechanical balance,' in which amount of
+space is a substitute for weight, as the one most often observed, we
+have to seek some point of view from which this entire reversal is
+intelligible. For even the feeling that 'the whole field must be
+covered' would hardly account for an exact interchanging of positions.
+If size gives 'weight,' why does it not always do so? A simple answer
+would seem to be given by the consideration that we tend to give most
+attention to the center of a circumscribed space, and that any object
+in that center will get proportionately more attention than on the
+outskirts. The small line near the center, therefore, would attract
+attention by virtue of its centrality, and thus balance the large
+line, intrinsically more noticeable but farther away. Moreover, all
+the other moments of aesthetic pleasure, derived from the even filling
+of the space, would work in favor of this arrangement and against the
+mechanical arrangement, which would leave a large black space in the
+middle.
+
+The hypothesis, then, that the demand for the filling of the whole
+space without large gaps anywhere enters into competition with the
+tendency to mechanical balance, and that this tendency is,
+nevertheless, reconciled with that demand through the power of a
+central position to confer importance, would seem to fit the facts. It
+is, of course, clear that neither 'mechanical balance' nor the balance
+of 'central' with 'intrinsic' importance have been yet accounted for
+on psychological grounds; it is sufficient at this point to have
+established the fact of some kind of balance between elements of
+different qualities, and to have demonstrated that this balance is at
+least not always to be translated into the 'mechanical' metaphor.
+
+
+_C. Experiments on Movement._
+
+In the preceding experiments the element of size was isolated, and it
+was sought to discover, in pleasing combinations of objects of
+different sizes, the presence of some kind of balance and the meaning
+of different tendencies of arrangement. The relative value of the two
+objects was taken as determined on the assumption, supported by common
+sense, that under like conditions a large object is given more
+attention than a small one. If the unequal objects seem to balance
+each other, then the only other condition in which they differ, their
+distance from the center, must be the cause of their balancing. Thus
+the influence of relative position, being the only unknown quantity in
+this balance-equation, is easily made out.
+
+The following experiments will deal with the as yet quite undetermined
+elements of suggested movement, perspective and intrinsic interest. By
+combining objects expressing them, each with another simple object of
+the same size, another equation will be obtained in which there is
+only one unknown quantity, the sizes of the objects being equal and
+the influence of relative position being at least clearly indicated.
+
+
+1. Movement.
+
+The experiments on suggestion of movement were made by _C_, _O_ and
+_P_. Suggestions of movement in pictures are of two kinds--given by
+lines pointing in a direction which the eye of the spectator tends to
+follow, and by movement represented as about to take place and
+therefore interpreted as the product of internal energy. Thus, the
+tapering of a pyramid would give the first kind of suggestion, the
+picture of a runner the second kind. Translated into terms of
+experiment, this distinction would give two classes dealing with (A)
+the direction of a straight line as a whole, and (B) the expression of
+internal energy by a curve or part of a line. In order to be able to
+change the direction of a straight line at a given point, a strip of
+tin two inches long was fastened by a pivot to the usual clasp which
+slipped up and down on the vertical black strip. The tin strip could
+be moved about the pivot by black threads fastened to its perforated
+ends. A strip of cardboard glued upon it would then take its
+direction. The first experiments, made with the usual 80x10 strip,
+proved very disagreeable. The subject was much disturbed by the blunt
+ends of the strip. The variable (pivoted) line was then slightly
+pointed at the upper end, and in the final experiments, in which both
+are oblique, both strips were pointed at each end. In Exp. III. a line
+pointing at an angle from the perpendicular was set over against a
+line of the same dimensions in the ordinary position.
+
+    Exp. III. (_a_) F. (80x10) pointed up toward center at 145 deg.,
+    V. (80x10).
+
+    F. 40:--(1) 39 48 48, (2) 60 66 68, (3) 97 97, (4) 156* 168*.
+
+    F. 60:--(1) 45, (2) 60 62 65 68 90, (3) 90 94, (4) 117 128 152
+    155.
+
+    F. 80:--(1) 50 44*, (2) 74 76 77, (3) 94 100 106 113 115 116,
+    (4) 123 124* 140 165* 169*.
+
+    F. 100:--(1) 36 58 60 65* 65 74 77 80 87, (2) 98 108 118, (3)
+    114* 168 186* 170 136*.
+
+    F. 120:--(1) 40 46 54 60 63 76 96 97 111, (2) 115 120 126*
+    137*, (3) 170 170*.
+
+    F. 140:--(1) 45 52 65 65 76 76 86 90, (2) 109 111, (3) 125
+    140*, (4) 168*.
+
+    F. 160:--(1) 38 50 50 60, (2) 80 90 96 98 98, (3) 176*.
+
+    F. 180:--(1) 21 23, (2) 54 70 84 90, (3) 100 100 108 114 120,
+    (4) 130 145*.
+
+    F. 200:--(1) -2, (2) 33 37 50, (3) 106 110 to 120 115 120 130
+    132 138 142.
+
+The most striking point about these groups is the frequency of
+positions far from the center when F. also is far out. At F. 120, a
+position at which the mechanical choice usually prevails if F. is
+smaller, a very marked preference indeed appears for positions of V.
+nearer the center--in fact, there is only one opposing (first) choice.
+Now, if it is not the wide space otherwise left which pulls the
+variable in,--and we see from a note that the subjects have no feeling
+of a large empty space in the center,--it must be that F. has the same
+effect as if it were really smaller than V., that is, mechanically
+'light.' We see, in fact, that the moment F. has passed the point,
+between 80 and 100, at which both lines close together in the center
+would be disagreeable, the preference is marked for inner positions of
+V., and I repeat that this cannot be for space-filling reasons, from
+the testimony of F. 200 (3).
+
+And this 'lightness' of the line pointed in at 45 deg. is indeed what we
+should have expected _a priori_ since we found that objective
+heaviness is balanced by a movement out from the center on the
+mechanical principle. If movement out and objective heaviness are in
+general alike in effect, then movement in and objective lightness
+should be alike in effect, as we have found to be the case from the
+preceding experiments. The inward-pointed line does not actually move
+in, it is true, but it strongly suggests the completion of the
+movement. It enters into the 'mechanical' equation--it appears to
+balance--as if it had moved.
+
+The point, however, in which this 'lightness' of the inward-pointed
+line differs from that of the small or short line is its space-filling
+quality. It suggests movement in a certain direction, and, while
+giving the mechanical effect of that movement as completed, seems also
+in a sense to cover that space. We see from F. 180 (3), (4), and 200
+(3), that the subject does not shrink from large spaces between the
+lines, and does not, as in Exp. I. (_a_), 4 and 5, bring the variable,
+which in both cases is evidently 'heavier,' to the center. This must
+be from the fact that the empty space does not in this experiment feel
+empty--it is filled with energy of the suggested movement. This view
+is confirmed by the dislike which the subjects show to the position F.
+40; F., being 'lighter,' but the object of attention as close to the
+center, might well balance V. far out. But as if the whole variable
+field would be in that case 'overfilled,' the records show 50 per
+cent. of refusals to choose for this position.
+
+In brief, then, a straight line suggesting movements in a certain
+direction has the effect, in the general scheme of mechanical balance,
+of a static position in which this movement has been carried out, with
+the added suggestion of the filling of the space over which such
+movement is suggested.
+
+A few additional experiments were made with a point on the upper end
+of V. The groups of III. (_a_) are maintained almost exactly: F. 120
+is again strikingly 'mechanical'; after F. 120 there are only two
+mechanical choices out of nineteen; while for F. 40, as in Exp. III.
+(_a_), out of six choices, four are either refusals or question-marked.
+
+Exp. IV. Both lines took oblique directions, and, to get a pleasing
+effect, were pointed at both ends. They were of the usual size, 80x10
+mm., but 1 mm. broader to allow for the effect of length given by the
+points. F. was fixed at 45 deg., as in III. (_a_), on the points 40, 80,
+120 and 160; V. moved also on fixed points, 60, 100, 140, 180, for
+each position of F., but on each point was adjusted at a pleasing
+angle. Thus, there were four positions of V. to each of F., each with
+one or two angular positions; V. was always in the first quadrant.
+
+The numbers of the table give the angular degrees of V.
+
+
+  F. 40, V. 60:--(1) 10 12 38 44, (2) 50 57* 60, (3) 70.
+     V. 100:--(1) 15 15 30 30, (2) 50 55 50, (3) 69 70*.
+     V. 140:--(1) 12* 14 18 18, (2) 60 60 49, (3) 72.
+     V. 180:--(1) 12 10 38, (2) 60 50, (3) 75.
+        [Many refusals at 140 and 180.]
+
+  F. 80, V. 60:--(1) 11, (2) 25 35 36*, (3) 45 48 55 58 60, (4) 69.
+     V. 100:--(1) 16 15, (2) 24 27 35 40, (3) 52, (4) 62 74*.
+     V. 140:--(1) 10 15 16, (2) 22 28, (3) 40 40 59 59, (4) 70.
+     V. 180:--(1) 14 8, (2) 28, (3) 41 46, (4) 68 79.
+
+  F. 120, V. 60: (1) 28, (2) 42 44 35, (3) 52 58 62 65 65.
+     V. 100:--(1) 9, (2) 23 25, (3) 38 40 40 42 58, (4) 68 70.
+     V. 140:--(1) 10, (2) 20 26 21* 24 29, (3) 34 42 42 44 55*, (4) 75.
+     V. 180:--(1) 17 26, (2) 40 42 46, (3) 62 64 70 70*.
+
+  F. 160, V. 60:--(1) 20 39, (2) 18, (3) 58 60 64 68 70.
+     V. 100:--(1) 23 25 30 38, (2) 44 44 49, (3) 55 58 65.
+     V. 140:--(1) 5, (2) 31 35 40 40 32, (3) 54 55 68.
+     V. 180:--(1) 50 50 58 60, (2) 75.
+
+
+The tendency to mechanical balance would, according to our previous
+analysis, lead the variable to take a direction which, in its
+suggestion of motion inward, should be more or less strong according
+as it were farther from or nearer to the center than the fixed line.
+Such motion inward would, of course, be more strongly suggested by an
+angle less than 45 deg. than by an angle greater than 45 deg., and it seems
+that the angles chosen are in general in harmony with this
+expectation. For the positions where F. is nearer the center than V.
+there is a preponderance of the angles less than 45 deg. (cf. F. 40 and F.
+80, V. 100 and 140; F. 120, V. 140, 180). When V. passes over to a
+position farther from the center than F. (_e.g._, from F. 80, V. 60,
+to F. 80, V. 100 and from F. 120, V. 60, to F. 120, V. 140) the change
+is marked. In every case where F. is farther from the center than V.
+(_i.e._, F. 80, V. 60; F. 120, V. 60 and V. 100; F. 160, V. 60, V.
+100 and V. 140), there are to be noticed a lack of the very small
+angles and a preponderance of the middle and larger angles. F. 160, V.
+140 and 180 seem to be the only exceptions, which are easily
+explainable by a dislike of the extremely small angle near the edge;
+for it appears from the remarks of the subjects that there is always a
+subconsciousness of the direction suggested by the lower pointed end
+of the line. For the outer positions of both lines, a large angle
+would leave the center empty, and a small one would be disagreeable
+for the reason just given; and so we find, indeed, for F. 160, V. 100,
+140, 160, the middle position the favorite one.
+
+The representation of action may be translated into experimental terms
+by expressing it as a line which changes its direction, thus seeming
+to be animated by some internal energy. The forms chosen were three
+curves 'bulging' from a straight line in differing degrees, and two
+straight lines with projections. _C_ and _O_ were the subjects. The
+results are given in outline.
+
+
+    Exp. V. Curve I. See Fig. 12, I
+
+    (1) Curve out (turned away from center).
+
+    (_a_) F. (80x10), V. Curve.
+
+    About half the positions of V. are farther from the center
+    than F. _O_ at first refuses to choose, then up to F. 120 puts
+    V. farther from the center than F. _C_ has a set of positions
+    of V. nearer the center and several second choices farther
+    than F.
+
+    (_b_) F. Curve, V. (80x10).
+
+    No position of V. nearer center than F. _O_ puts line farther
+    out up to F. 160, then nearer than F. _C_ has a set of nearly
+    symmetrical choices and another where V. is much farther out
+    than F.
+
+    (2) Curve in (turned toward center).
+
+    (_a_) F. (80x10), V. Curve.
+
+    _C_ is absolutely constant in putting V. farther from center
+    than F. _O_, after F. 100, brings it slightly nearer.
+
+    (_b_) F. Curve, V. (80x10).
+
+    _C_, except for F. 40, invariably puts V. nearer center than
+    F. _O_ moves between 90 and 135, putting V. farther to F.
+    100, nearly symmetrical at F. 100 and 120, and after F. 120,
+    from 100 to 135.
+
+[Illustration: FIG. 12]
+
+    Exp. V. Curve II. See Fig. 12, II.
+
+    (1) Curve out.
+
+    (_a_) F. (80x10), V. Curve.
+
+    In every case but one V. is nearer center than F.
+
+    (_b_) F. Curve, V. (80x10).
+
+    _C_ puts V. farther from center than F. _O_ puts V. farther or
+    symmetrical up to F. 120, then nearer than F.
+
+    (2) Curve in.
+
+    (_a_) F. 80x10, V. Curve.
+
+    _C_ has V. always farther from center than F., but a second
+    parallel set, omitting F. 40 (all second choices), of
+    symmetrical positions. _O_ begins with V. farther from center,
+    but from F. 120 has V. always nearer, though gradually
+    receding from the center.
+
+    (_b_) F. Curve. V. (80x10).
+
+    _C_, refusing for F. 40, continues his parallel sets, one with
+    V. always nearer than F., another with symmetrical positions.
+    _O_ begins with V. nearer, changes at F. 120, and continues
+    with V. farther.
+
+
+Recapitulating these results, grouping together the outward and inward
+positions of the curves, and indicating the distance of the line from
+the center by C.-L., and of the curve from the center by C.-Cv., we
+have:
+
+
+_Out_.
+
+Cv. I.  (_a_)  Indeterminate.
+        (_b_)  C.-Cv. < C.-L. (except where large gap would be left).
+
+Cv. II. (_a_)  C.-Cv. < C.-L. (all cases but one).
+        (_b_)  C.-Cv. < C.-L. (except where large gap would be left).
+
+_In._
+
+Cv. I. (_a_)  C.-Cv. > C.-L. (except a few cases to avoid gap).
+       (_b_)  C.-Cv. > C.-L. (more than half of cases).
+
+Cv. II. (_a_)  C.-Cv. > C.-L. (except a few cases to avoid gap).
+        (_b_)  C.-Cv. > C.-L. (except  a few cases to avoid gap).
+
+
+It is evident that in the great majority of cases when the curve turns
+out it is placed nearer the center, when it turns in, farther from the
+center, than the straight line. The numerical differences for choices
+of the same type for the two curves are slight, but regular, and the
+general tendencies are more sharply marked for the line of greater
+curvature. When Curve II. is 'out,' it is usually nearer the center
+than Curve I. for the corresponding positions of the straight line;
+when 'in' it is always farther from the center than Curve I. The
+greater curvature of II. has clearly produced this difference, and the
+effect of the curvature in general is evidently to make its side
+'lighter' when turned toward the center, and 'heavier' when turned
+away. Thus, all but the exceptions already noted seem to belong to the
+mechanically balanced arrangement, in which the suggestion of force
+working in the direction of the curve has the same effect as, in Exp.
+IV., the direction of the line. The exceptions noted, especially
+numerous choices of _O_, seem governed by some fixed law. The evidence
+would seem to be overwhelming that the reversals of the mechanical
+balance occur only where the lines would be crowded together in the
+center or would leave an empty gap there. The remaining
+exceptions--the symmetrical choices mentioned, made by _C_--are
+explained by him as follows. He says there are two ways of regarding
+the curve, (1) as a striving in the direction of the 'bulge,' and (2)
+as the expression of a power that presses together; and that the usual
+choices are the result of the first point of view, the symmetrical
+choices of the second. Naturally, a pressure bending down the line
+would be conceived as working in a vertical direction, and the line
+would be treated as another (80x10)--giving, as is the case,
+symmetrical positions. Thus, we may consider the principle of the
+suggestion of movement by a curve, as giving the same effect as if the
+movement suggested had actually taken place, to have been established,
+the positive evidence being strong, and the exceptions accounted for.
+It is worth noting that the curve-out series are always more
+irregular--the subject repeating that it is always harder to choose
+for that position. Probably the demands of space-filling come into
+sharper conflict with the tendency to mechanical balance, which for
+the outward curve would always widely separate the two lines.
+
+Exp. V. Curve III. See Fig. 12, III.
+
+A series with the upper end turned out from the center was unanimously
+pronounced as ugly. The inward position only appears in the results,
+which are given in full.
+
+
+(_a_) F. (80x10), V. CURVE.
+
+  F.                V.
+             O.               C.
+
+   40     106 126       68  73
+   80     106 128      109 102
+  120     140  88      156 110* 154   72*
+  160     104  66      182  80  136* 130*
+  200       X  52      178 220* 162
+
+
+(_b_) F. CURVE, V. (80x10)
+
+  F.                V.
+              O.              C.
+
+   40     126 122        73  80
+   80     122 128        66 112* 40
+  120      90 116        97 156* 55 105
+  160      65  43       120 182* 87 134
+  200      70  50       148  66
+
+
+This curve exemplifies the same principles as the preceding. _O_ takes
+the natural mechanical choice from (_a_) F. 40 to F. 120, and from
+(_b_) F. 120 to F. 200. A mechanical choice, however, for (_a_) F. 120
+ff., and for (_b_) F. 40 to F. 120, would have brought the lines too
+far apart in (_a_), and too near together in (_b_), hence the
+reversal. _C_ inclines always to the mechanical choice, but recognizes
+the other point of view in his second choices.
+
+Exp. V. Curve IV. See Fig. 12, IV.
+
+    Curve in.
+
+    (_a_) F. (80x10), V. Curve.
+
+    _C_ puts V. always further than F. and, even for F. 200, has
+    V. 230, X. _O_ puts V. farther up to F. 120, then puts it
+    nearer than F., and always refuses to choose for F. 200.
+
+    (_b_) F. Curve, V. (80x10).
+
+    _C_ always puts V. nearer than F. _O_ puts V. farther for F.
+    40 and F. 80, beyond that, nearer than F.; but refuses to
+    choose once each for F. 40, and F. 200.
+
+    The same principles of choice appear. _C_ maintains the
+    mechanical choice, and _O_ reverses it only beyond (_a_) F.
+    120, and up to (_b_) F. 120, to fill space well, showing his
+    preference for the mechanical choice by changing into it at an
+    unusually early point.
+
+Exp. V. Curve V. See Fig. 12, V.
+
+    Curve in.
+
+    (_a_) F. (80x10), V. Curve.
+
+    _C_ puts V. farther than F., except for F. 200, V. 125 and X.
+    _O_ also, changing as usual at F. 120 to V. nearer than F.
+
+    (_b_) F. Curve, V. (80x10).
+
+    _O_ puts V. always farther than F. _O_ has V. farther for F.
+    40 and F. 80, then nearer than F. Refuses to choose for F.
+    200. Results exactly parallel with those of Curve IV.
+
+Comparing all the results of this whole series of experiments on the
+suggestion of movement, we may conclude that movement, whether
+suggested by a whole line or part of a line, produces in terms of
+mechanical balance the same effect that the balanced object would
+produce after the completion of the suggested motion. This tendency to
+balance, it appears, lies at the basis of our preference; it often
+gives way, however, before considerations of space-filling, when the
+figure which on the scheme of mechanical balance is weaker, gains
+interest and so 'heaviness' by being brought nearer the center.
+
+
+_D. Experiments on Interest._
+
+By intrinsic interest is meant the interest which would attach to an
+object quite apart from its place in the space composition. In a
+picture it would be represented by the interest in an important
+person, in an unusual object, or in an especially beautiful object, if
+that beauty were independent of the other forms in the picture--as,
+for instance, a lovely face, or a jeweled goblet, etc. When the
+question of the influence of interest on composition came to be
+discussed, it was found very difficult to abstract the form of the
+object from the content presented; still more difficult to obtain an
+effect of interest at all without the entrance of an element of form
+into the space arrangement. Disembodied intellectual interest was the
+problem, and the device finally adopted seemed to present, in as
+indifferent a form as possible, a content whose low degree of absolute
+interest was compensated for by constant change. Stamps of various
+countries in black and white reproductions and very small outline
+pictures on squares of the same size as the stamps were taken as
+material. The figures were so small in relation to the board that any
+influence on composition of the lines composing them was impossible;
+the outline pictures, indeed, gave to the eye which abstracted from
+their content an impression scarcely stronger than the neighboring
+blank square.
+
+The first set of experiments (VI.) had a small outline picture on the
+side, and on the other a white paper square of the same size. The
+necessary interest was given in the form of novelty by changing the
+picture for every choice. The subjects were _M_, _G_ and _D_. The
+results were of the same type for each subject and could therefore be
+averaged.
+
+Exp. VI. (1).
+
+    _(a)_ F. Picture, V. Blank. Eight choices for each. _M_,
+    Average: V. 17 mm. farther from center. _G_, Average: V. 10
+    mm. farther from center. (Symmetrical position beyond F. 120.)
+    _D_, Average: V. 25.8 mm. farther from center.
+
+   _(b)_ F. Blank, V. Picture. _M_, Average: V. 33 mm. nearer
+   center. _G_, Average: V. 4 mm. nearer center. (Symmetrical
+   beyond F. 120.) _D_, Average: V. 30 mm. nearer center. (But V.
+   farther at F. 40.)
+
+These results are practically unanimous. They show that an object
+which possesses intrinsic interest acts like a mechanically heavy
+object, being placed nearer the center than a blank. Two marked
+deviations from the mechanical choice occur--although they have not
+affected the average sufficiently to destroy the general harmony of
+results. _G_, in both _(a)_ and _(b)_, chooses symmetrical positions
+from F. 120 on. His notes ['_(a)_ F. 140, V. 136, picture
+unimportant'; '_(b)_ F. 120 and ff., loses relation as they separate';
+'_(b)_ F. 160, picture makes no impression'] show clearly that for
+positions wide apart the picture, already a faint outline, becomes
+only a white square like the other and is put into geometrical
+symmetry.
+
+Exp. VI. (2), by _G_ and _D_. A stamp on one side unchanged, took the
+place of the blank; on the other side the stamp was changed for each
+choice.
+
+    _(a)_ F. unchanged stamp; V. changed stamp.
+
+    _D_. Two series, (1) V. always nearer center. (2) Same, except
+    F. 20, V. 52; F. 80, V. 94; F. 140, V. 152; F. 160, V. 175.
+
+    _G_. Two series. (1) V. much farther from center up to F. 140,
+    then nearer. (2) V. farther throughout, except F. 160, V. 121.
+
+    _(b)_ F. changed stamp; V. unchanged stamp.
+
+    _D_. Two series. (1) V. farther up to F. 100, then
+    symmetrical. (2) V. farther up to F. 100, then symmetrical or
+    nearer center.
+
+    _G_. Two series. (1) V. farther up to F. 120, then
+    symmetrical, and beyond F. 140, nearer center. F. 140, V. 63.
+    (2) V. much farther up to F. 120, then nearer center, but more
+    nearly symmetrical than (1). A complete series of second
+    choices beginning at F. 40, V. slightly nearer center than F.
+
+Analyzing results, we find the changed stamp, which has the interest
+of novelty, nearly always nearer the center than the unchanged. This
+would indicate a balance of the mechanical type, in which the interest
+makes an object 'heavier.' The exceptions are in _(a)_ four choices of
+_D_, _G_ to F. 140, and in _(b)_, _D_'s choice beyond F. 200, and
+_G_'s beyond F. 120. The deviations are thus seen to be all of the
+same type: for positions of F. near the center, when a mechanical
+choice would have brought V. still nearer [(_a_)], it is instead put
+farther away; for positions of F. far from the center, when a
+mechanical choice would have put V. still farther away [(_b_)], it is
+instead brought near. The exceptions are thus fully accounted for by
+the demand for space-filling.
+
+
+_E. Experiments on Depth._
+
+The experiments on suggestion of depth in the third dimension were as
+follows. It was desired to contrast two objects differing only with
+respect to the degree to which they expressed the third dimension.
+Those objects that do express the third dimension are, in general,
+views down streets, colonnades, corridors, gates, etc., or, in
+landscape, deep valleys, vistas between trees, distant mountains, etc.
+It is evident that representations of products of human handiwork
+would be less unnatural when isolated for experiment, and two pairs of
+pictures were accordingly prepared as follows: There was drawn on a
+square of 80 mm. the picture of the mouth of a railway tunnel, closed
+tightly by an apparently massive door; and another picture of
+identical form and surroundings, but showing the rails entering at a
+slight curve, the deep blackness within, and the small circle of light
+at the farther end. The second pair consisted of the gateway of a
+baronial castle, with heraldic bearings and closed iron-wrought doors;
+and the same gateway open, showing a flagged pavement and an open
+court with fountain beyond. The perspective effect was heightened by
+all possible means for both pictures, and care was taken to have the
+contrast of black and white the same for each pair, so that to the
+half-shut eye, opened and closed forms seemed to have the same tone.
+
+The subjects were directed to try to _feel_ the third dimension as
+vividly as possible--to project themselves down the vistas, as it
+were--and then to arrange the squares in the most pleasing manner. The
+experiments were made by _A_, _M_, _S_, _H_ and _D_. Not all made the
+same number of repetitions, but as their notes were unusually
+suggestive, I have made use of all the results, and shall quote the
+notes for the most part _verbatim_:
+
+
+Exp. VIII. F. Closed Tunnel. V. Open Tunnel.
+
+                 F.            V.
+  Subject _H_.   40            90
+                 60            57
+                 80            13
+                100            12
+                120            39
+                140           - 1
+                160           -32
+                180           -71, +50
+
+    _Notes._--_H_ finds that he neglects the closed tunnel almost
+    entirely, eye is constantly attracted to open tunnel, F. 180,
+    choice of evils. Position of closed tunnel makes the pictures
+    disagreeable. F. 80, V. 13, closed tunnel grows more
+    uninteresting as it goes out, while the open tunnel seems
+    heavier than ever. F. 140, V.-1, closed tunnel loses force and
+    doesn't gain weight. Open tunnel hangs together with the black
+    field beyond it.
+
+                 F.                     V.
+  Subject _S_.   40            85            95
+                 60           170           195
+                 80           160           180
+                100           185           200
+                120           185          - 35, 200
+                140            85            20
+                160           115           115
+                180                         100
+
+    _Notes._--F. 120, V. 185. After this there is too large a
+    black space between squares, and so a more central position is
+    taken, but there is the necessity of avoiding symmetry, which
+    is displeasing. F. 160, V. 115 is not symmetrical and so is
+    more pleasing. F. 60, V. 195:--the open tunnel holds the eyes,
+    while the other allows them to wander, and so it needs a
+    bigger field on each side. F. 80, V. 180:--a position close
+    together is possible, but it is hard to take them so except as
+    one picture, and that is also difficult. F. 100, V.
+    200:--there is the same objection to any position which seems
+    to be an acknowledgment of similarity; that is, symmetrical
+    position seems to imply that they are alike, and so is
+    disagreeable. F. 120, V.-35, 200:--now they can be close
+    together because the black tunnel harmonizes with the black to
+    the right, and seems to correspond in distance and depth,
+    while the tunnel 'hangs together' with the black to the left.
+    (Cf. _H_, F. 160, V.--32.) F. 140, V. 20:--when they are
+    together it is difficult to apperceive the frame as a whole;
+    but this position is not far apart, and not disagreeable
+    because the larger stretch of black to the right again hangs
+    together with the tunnel. F. 160, V. 115:--when the open
+    tunnel was in the middle, the closed one seemed to have no
+    business at all, therefore the open tunnel had to be moved
+    over. The only position which was not disagreeable.
+
+SUBJECT G.
+
+   F.                 V.
+          (1)     (2)     (3)     (4)¹    (5)¹
+   40      48      31      36      30      23
+   60     105      31      40      51      39
+   80     111      71      60      64      54
+  100     104      63      78      60      86
+  120     123      75      91      62     115
+  140     136      82     111      56     137
+  160     162      93     148      72     156
+  180     107     115     181      83     176
+
+    ¹Second pair (Court).
+
+    _Notes._--(1) All quite unsatisfactory. The arrangement
+    difficult to apperceive as a whole. Each picture taken by
+    itself. (2) The tunnel closed doesn't amount to much. (3) The
+    significance of the tunnel gives it weight. For F. 160, V.
+    148, and F. 180, V. 180, relation difficult. (4) Court closed
+    gets weaker as gets farther from center. (5) At F. 100, begins
+    to lose relation between pictures, as if one were in one room,
+    one in another.
+
+SUBJECT A.
+
+   F.                         V.
+         (1)     (2)     (3)     (4) squared   (5) squared
+   40     70      66     140      59     130
+   60     80      73     159      62     138
+   80    103      71     120      77     134
+  100    113      94     108      93     100
+  120    119      88      96      96      63
+  140    108      92      60,164  82      43
+  160     92     118      70     109      50
+  180    130     154      78     101      50
+
+      squaredSecond pair (Court).
+
+    _Notes_.--(1) Difficult to apperceive together. From F. 140,
+    V. 108, depth is more strongly imagined. (3) Tunnel closed has
+    not much value. (5) F. 80, V. 134, taken with reference both
+    to frame and to the other picture--must not be symmetrical nor
+    too far out.
+
+SUBJECT D.
+
+   F.                             V.
+               (1)          (2)          (3)
+   40          100          47            38
+   60           75          60            68
+   80          104          78            80
+  100          148, -12    104           120
+  120          159         166           160
+  140          182         152, 84, 78   168
+  160          193         184, -75      180
+  180          200        - 95, 190      190
+
+    _Note_.--F. 100, V.-12; F. 140, V.-52; F. 160, V. -75: they
+    must be close together when on the same side.
+
+                F.                   V.
+                            (1)           (2)¹
+  Subject M.   40            55            50
+               60            56            74
+               80            64            84
+              100            86           102
+              120            93           111
+              140           124           130
+              160           134           146
+              180           144           178
+
+    ¹Second pair (Court).
+
+    _Note_.--(1) Quite impossible to take both together; necessary
+    to keep turning from one to the other to get perception of
+    depth together with both.
+
+
+The subjects agree in remarking on the lack of interest of the closed
+tunnel, and the attractive power of the open tunnel, and notes which
+emphasize this accompany choices where the open tunnel is put
+uniformly nearer. (Cf. _H_, F. 180, V. 50; F. 80, V. 13; _G_, (2),
+(3), (4), (5); _A_, (3), and F. 140.) As a glance at the results shows
+that the open tunnel is placed on the whole nearer the center, we may
+conclude that these choices represent a mechanical balance, in which
+the open tunnel, or depth in the third dimension, is 'heavier.'
+
+But another point of view asserts itself constantly in the results of
+_S_, and scatteringly in those of the others. Analyzing at first only
+the results of _S_, we find that up to F. 140, with one exception, he
+places the open tunnel much farther out than the other; and from F.
+140 on, nearer. He says, F. 120, V. 185, 'After this there is too
+large a black space'; that is, in bringing the open tunnel in, he is
+evidently filling space. But why does he put the open tunnel so far
+out? It seems that he is governed by the desire for ease in the
+apperception of the two objects. In his note for F. 80, V. 180, this
+point of view comes out clearly. He thinks of the objects as being
+apperceived side by side with the space about each (which apparently
+takes on the character of its object), and then he seems to balance
+these two fields. Cf. F. 60, V. 195: 'The closed tunnel allows the
+eyes to wander, and so it needs a bigger field on each side.'
+Evidently there is an implication here of the idea of balance. Cf.
+also F. 120: 'The black tunnel harmonizes with the black to the right,
+and seems to correspond in distance and depth,' while the closed
+tunnel 'hangs together with the black on the left.' In brief, the view
+of F. seems to be that the closed tunnel is less interesting, and
+partly because it 'allows the eyes to wander,' partly as compensation
+for the greater heaviness of the open tunnel, it takes with it a
+larger space than the open tunnel. It is on the whole better to put
+them apart, because it is more difficult to apperceive them when close
+together, and so the open tunnel in the earlier choices must, of
+course, go farther from the center. When these points conflict with
+the necessity of filling space, the open tunnel comes nearer the
+center. In general, the notes which emphasize the difficulty of
+apperceiving the two pictures as flat and deep together accompany
+choices where the tunnel is put uniformly farther out, or
+symmetrically. Cf. _G_, (1), (5); _A_, (1); _M_, F. 40, etc.
+
+Thus we may continue to separate the two points of view, that of
+mechanical balance and that of another kind of balance, which we have
+known heretofore as 'space-filling,' made possible by the power of the
+center to give 'weight,' but which seems to be now more explicitly
+recognized as a balancing of 'fields.' At this point we need repeat
+only, however, that the suggestion of depth in the third dimension
+seems to confer 'weight,' 'heaviness,' 'balancing power' on its
+object.
+
+Before making a general survey of the results of this chapter, it is
+necessary to consider a type of choice which has been up to this
+point consistently neglected--that in which the variable has been
+placed on the same side of the center as the fixed object. On the
+theory of balance, either in its simple mechanical form or in its
+various disguises, this choice would at first seem to be inexplicable.
+And yet the subjects usually took special pleasure in this choice,
+when they made it at all. These minus choices are confined to three or
+four subjects and to two or three experiments. Exp. I. (a) and (b)
+show the largest number. We have:
+
+
+    EXP. I. (_a_) F. (80x10); V. (160x10).
+     F.                           V.
+    120                   - 44,
+    160                   -150, -105,  -88
+    200                    -94,  -46, -110
+
+        (_b_) F. (160x10); V. (80x10).
+     F.                           V.
+    120                      -70, -80
+    160                     -114
+    200                     -155, -146, -148
+
+
+It will be noticed that, with two exceptions, none of the positions
+chosen are nearer than 70 mm. to the center, and that most of them are
+much farther away. The two lines seem to be more pleasing when they
+are pretty close together on the same side. _S_, in I. (_b_) F. 120,
+V.-70, notes: 'If V. is nearer _O_, there is a tendency to imagine a
+figure by the connection of the ends of the two lines, which is
+disagreeable. 'The only other minus choices were in Exp. VII., by
+_S,_, _H_, and _D_. _S_, F. 120, V.-35, says: 'Now they can be close
+together,' and _H_, F. 140, 160 and 180, V. -1, -32, -71, notes the
+same. So also _D_, F. 100, V. -12; F. 140, V. -52; F. 160, V. -75; F.
+180, V. -95. It is evident from this insistence on the closeness
+together of the objects, and this desire to form no figure, that the
+two are taken as one, and set off against the blackness on the other
+side. It seems as if this were not taken as empty space, but acquired
+a meaning of its own. The association with pictures in which the empty
+space is occupied by a deep vista or an expanse of sky is almost
+irresistible. The case of Exp. VII. seems a little different. _S_, at
+least, separates the two fields as usual, but for him also the black
+space is living, 'corresponds in distance and depth.' It is at least
+certain that there is no subjective feeling of emptiness or of
+unoccupied energies on the empty side. And it would seem that some
+influence from the objects sweeps across the central field and
+vitalizes it. The most natural view would seem to be that the ease of
+apperception of the two objects together, and the tendency of the eye
+movement to begin on the occupied side, and to sweep across to the
+unoccupied, which we think of as deep, combine to give a feeling of
+pleasure and of balance.
+
+       *       *       *       *       *
+
+We have now reached a point from which a backward glance can be cast
+upon the territory traversed. Experiment with the isolated elements in
+pictorial composition has shown that pleasing arrangements of these
+elements can be interpreted by the formula of mechanical balance. This
+principle was obtained by opposing two lines whose relative value
+(corresponding to 'weight' in balance) was known; and it was found
+that their relative positions corresponded to the relation of the arms
+of a balance. Further opposition of lines, of which one was already
+determined in 'weight,' showed the same variations and suggested
+certain valuations of the undetermined lines on the basis of this
+common term of weight. Thus, the line suggesting movement out from the
+center fitted the formula if taken as 'heavy' and _vice versa_, the
+line suggesting movement in, if taken as 'light.' Similarly, objects
+of interest and objects suggesting movement in the third dimension
+were 'heavy' in the same interpretation. But this interpretation, in
+its baldest form, fitted only a majority of the pleasing arrangements;
+the minority, in which the consistent carrying out of the lever
+principle would have left a large unoccupied space in the center,
+exactly reversed it, bringing the 'light' element to the center and
+the 'heavy' to the outer edge. Later experiments showed that this
+choice implied a power in the 'lighter' objects, owing to their
+central position, to cover or infuse with vitality the empty space
+about them, so that the principle of balance seemed to maintain itself
+in one form or another.
+
+All this does not go beyond the proof that all pleasing space
+arrangements can be described in terms of mechanical balance. But
+what is this mechanical balance? A metaphor, no matter how
+consistently carried out, explains nothing. The fact that a small
+object far from the center is usually opposed by a large object near
+the center tells us nothing of the real forces involved. Physical
+balance can be explained by principles of mechanics, but no one will
+maintain that the visual representation of a long line weighs more
+than that of a short one. Moreover, the elements in the balance seem
+utterly heterogeneous. The movement suggested by an idea--the picture
+of a man running--has been treated as if equivalent to the movement
+actually made by the eye in following a long line; the intrinsic
+interest--that is, the ideal interest--of an object insignificant in
+form has been equated to the attractive power of a perspective which
+has, presumably, a merely physiological effect on the visual
+mechanism. What justification can be given either of this
+heterogeneous collection of elements or of the more or less arbitrary
+and external metaphor by which they have been interpreted?
+
+I believe that the required justification of both points of view is
+given in the reduction of all elements to their lowest term--as
+objects for the expenditure of attention. A large object and an
+interesting object are 'heavy' for the same reason, because they call
+out the attention; a deep perspective, because the eye rests in
+it;--why, is another question. And expenditure of effort is
+expenditure of attention; thus, if an object on the outskirts of the
+field of vision requires a wide sweep of the eye to take it in, it
+demands the expenditure of attention, and so is felt as 'heavy.' It
+may be said that involuntary attention is given to the object of
+intrinsic interest, while the uninteresting object far on the
+outskirts needs a voluntary effort to perceive it, and that the two
+attitudes cannot be treated as identical. To this it may be answered
+that an object on the outskirts of a field of view so definitely
+limited calls out of itself a reflex movement of the eye toward it, as
+truly spontaneous as the impulse toward the object of intrinsic
+interest. But what is 'the expenditure of attention' in physiological
+terms? It is nothing more than the measure of the motor impulses
+directed to the object of attention. And whether the motor impulse
+appears as the tendency to fixate an object or as the tendency to
+follow out the suggestions of motion in the object, they reduce to
+the same physiological basis. It may here be objected that our motor
+impulses are, nevertheless, still heterogeneous, inasmuch as some are
+_toward_ the object of interest, and some _along_ the line of
+movement. But it must be said, first, that these are not felt in the
+body, but transferred as values of weight to points in the picture--it
+is the amount and not the direction of excitement that is counted; and
+secondly, that even if it were not so, the suggested movement along a
+line is felt as 'weight' at a particular point.
+
+From this point of view the justification of the metaphor of
+mechanical balance is quite clear. Given two lines, the most pleasing
+arrangement makes the larger near the center, and the smaller far from
+it. This is balanced because the spontaneous impulse of attention to
+the near, large line, equals in amount the involuntary expenditure of
+attention to apprehend the small farther one. And this expenditure of
+motor impulses is pleasing, because it is the type of motor impulses
+most in harmony with our own physical organism.
+
+We may thus think of a space to be composed as a kind of target, in
+which certain spots or territories count more or less, both according
+to their distance from the center and according to what fills them.
+Every element of a picture, in whatever way it gains power to excite
+motor impulses, is felt as expressing that power in the flat pattern.
+A noble vista is understood and enjoyed as a vista, but it is
+_counted_ in the motor equation, our 'balance,' as a spot of so much
+intrinsic value at such and such a distance from the center. The
+skilful artist will fill his target in the way to give the maximum of
+motor impulses with the perfection of balance between them.
+
+
+IV. SYMMETRY IN PICTURES.
+
+
+_A. The Balancing Factors._
+
+The experimental treatment of suggestions as to the elements in
+pictorial composition has furnished an hypothesis for the basis of our
+pleasure in a well-composed picture, and for the particular function
+of each of the several elements. This hypothesis may be expressed as
+follows: (1) The basis of aesthetic pleasure in composition is a
+_balance of motor impulses_ on the part of the spectator; (2) this
+balance of motor impulses is brought about by means of the elements,
+through the power which they possess of drawing the attention with
+more or less strength towards a certain field. But to the experimental
+working out of an hypothesis must succeed a verification, in its
+application to the masterpieces of civilized art. We have, then, to
+ask whether there is in all great pictures a balance, _i.e._, an equal
+distribution of attention on the two sides of the central line
+suggested by the frame of the picture. It might be, for instance, that
+a picture of pleasing composition would show, when analyzed, all the
+attractions for attention on one side; which would go far to impugn
+either our hypothesis of balance as the basis of pleasure, or our
+attribution of particular functions to the elements. But as this
+second matter may be considered to have been sufficiently determined
+by the results of the preceding section, the first question only
+remains: Is there a balance of attention in a good picture--or rather,
+in the particular good pictures known to the student of art?
+
+This question could only be answered by the examination of a large
+number of pictures of accepted merit, and it was also desirable that
+they should be studied in a form which lent itself to the easy
+comparison of one picture with another. These conditions seemed to be
+best fulfilled by the collection of reproductions in black and white
+known as the _Classischer Bilderschatz_, published by F. Bruckmann, at
+Munich, which contains over a thousand pictures arranged in schools.
+Of these a thousand were taken--substantially the first thousand
+issued, after the frescoes, triptych doors, panels, etc., which are
+evidently parts of a larger whole, had been laid aside. In the
+following discussion the pictures will be designated, when they are
+not further described, by the numbers which they bear in this
+collection.
+
+The equations in the following discussion are based on a system of
+exact measurement, corresponding to that followed in the experimental
+section. This numerical treatment is pre-supposed in all the general
+attributions of balance in the analysis of single pictures. The method
+of measurement was given by the conditions of viewing pictures, which
+are framed and thus isolated from surrounding influences, and
+referred, as compositions, to the middle line suggested by this
+emphasized frame. An adjustable frame of millimeter paper, divided in
+half vertically by a white silk thread, was fitted over the picture to
+be measured, and measurements were made to left and to right of this
+thread-line and, as required, vertically, by reference to the
+millimeter frame divisions.
+
+The main question, of course, to be answered by a statistical
+examination of these thousand pictures refers to the existence of
+balance, but many other problems of symmetry are also seen to be
+closely involved; the relative frequency of the elements in pictures
+of different types, and the result of their employment in producing
+certain emotional effects, also the general types of space arrangement
+as a whole, the feeling-tone belonging to them, and the relation
+between content and shape. The first question will not be treated in
+this paper in the statistical fulness which was necessary to establish
+my conclusions in the investigation itself, inasmuch as the tables
+were very extensive. But examples of the tables, together with the
+full results, will be given, and a sufficient amount of detailed
+discussion to show my methods. The two other subjects, the use of the
+elements and the types of composition, will be briefly treated. I
+expect in other publications to go more closely into statistical
+detail on these matters than is possible in a merely experimental
+thesis.
+
+In the beginning of the proposed statistical analysis a natural
+objection must first be forestalled: it will be said, and truly, that
+color also has its effect in bringing about balance, and that a set of
+black and white reproductions, therefore, ignores an important
+element. To this it may be answered, first, that as a matter of fact
+the color scheme is, as it were, superimposed upon the space-shape,
+and with a balance of its own, all the elements being interdependent;
+and secondly, that the black and white does render the intensity
+contrasts of the colors very well, giving as light and dark, and thus
+as interesting (= attractive) and the reverse, those factors in the
+scheme which are most closely related to the complex of motor
+impulses. After having compared, in European galleries, the originals
+of very many of these reproductions with the equation of balance
+worked out from the black and white, the writer has seldom found an
+essential correction needed.
+
+The pictures were first classified by subjects. This may seem less
+logical than a division by types of arrangement. But it really, for a
+majority, amounted to the same thing, as the historical masterpieces
+of art mostly follow conventional arrangements; thus the altarpieces,
+portraits, genre pictures, etc., were mostly after two or three
+models, and this classification was of great convenience from every
+other point of view. The preliminary classification was as follows:
+(1) Religious, Allegorical and Mythical Pictures; (2) Portraits; (3)
+Genre; (4) Landscape. The historical pictures were so extremely few
+that they were included in the religious, as were also all the
+allegorical pictures containing Biblical persons. Some pictures, of
+which Watteau's are representative, which hovered between genre and
+landscape, were finally classified according as they seemed to owe
+their interest to the figures or to the scenery. A preliminary
+classification of space arrangements, still with reference to content,
+showed three large general types: (1) A single subject or group in the
+middle; (2) the same somewhat on one side, with subordinate elements
+occupying the rest of the space; (3) two objects or groups each
+occupying a well-defined center. These were designated as Single
+Center, Single and Subordinate Center, and Double Center pictures, or
+S.C., S. & S., and D.C. They are in proportions of S.C. 79 per cent.,
+S. & S. 5 percent., D.C. 16 per cent. The D.C. type is evidently
+already explicitly balanced as regards shape and intrinsic interest,
+and is hence of comparative unimportance to our problem. The S.C. will
+show a balance, if at all, in more or less accessory factors; S. & S.,
+broadly, between interest and other factors. As logically more
+important, this last group will be treated more fully. The full
+classification of the thousand pictures by subjects is as follows:
+
+
+                                    S.C.   D.C.   S.S.
+  Altarpieces                 78     70      7      1
+  Madonna & Child             47     47      0      0
+  Holy Family                 67     40     14     13
+  Adorations                  19     19      0      0
+  Crucifixions                23     21      0      2
+  Descents f. Cross           27     26      0      1
+  Annunciations               21      0     21      0
+  Misc. Religious            162     93     55     14
+  Allegorical                 46     36      6      4
+  Genre                       93     63     19     11
+  Landscape                   88     65     22      1
+  Portrait Groups             64     42     17      5
+  Relig. Single Fig.          28     28      0      0
+  Alleg. Single Fig.          12     12      0      0
+  Portrait Single Fig.       207    207      0      0
+  Genre Single Fig.           18     18      0      0
+
+
+Altarpieces.
+
+The pictures of the first group, consisting of the _Madonna_ and
+_Infant Christ_ surrounded by worshippers, and briefly designated as
+Altarpieces, are good for detailed study because they present a simple
+type, and it will be easy to show whether the variations from symmetry
+are in the direction of balance or not. A few examples will make this
+clear. The Madonna in the S.C. pictures is invariably seated holding
+the Christ.
+
+In the following descriptions M. will denote Madonna, C. Child, Cn.
+central line. The elements, Size or Mass, Direction of Motion or
+Attention, Direction of Line, Vista, and Interest, will be set down as
+Ms., D., L., V., and I. A couple of examples will show the method of
+describing and of drawing a conclusion as to balance.
+
+1. 969. Lorenzo Lotto, _Madonna with St. Bernard and St. Onofrius._ C.
+is on one side turning to the same; M. leans far to the other; hence
+interest in C., and direction of C.'s attention are over against Mass
+of M. and direction of M.'s attention; _i.e._, I. + D. = Ms. + D., and
+so far, balance. The surrounding saints are insignificant, and we may
+make the equation I. = Ms.
+
+2. 368. Raffaelino di Francesco, _Madonna Enthroned._ The C. is on
+Right facing front, M. turns away Left, hence interest in C. is over
+against direction of M.'s attention. Moreover, all the saints but one
+turn Left, and of two small vistas behind the throne, the one on the
+Left is deeper. The superior interest we feel in C. is thus balanced
+by the tendency of attention to the opposite side, and we have I. = D.
++ V.
+
+It is clear that the broad characteristics of the composition can be
+symmetrically expressed, so that a classification of the 70 S.C.
+altarpieces can be made on a basis of these constant elements, in the
+order of decreasing balance. Thus: Class 1, below, in which the C. is
+one side of the central line, turned away from the center, the M.
+turned to the other, balances in these broad lines, or I. + D. = D.;
+while in (9), I. + D. + D. = (x), the constant elements work all on
+one side.
+
+
+CLASSIFICATION OF ALTARPIECES.
+
+   1 C. one side turned to same,  M. to other            11
+   2 "     "         "     other, "       "               8
+   3 "     "         "     front, "       "               2
+   4 "     "         "     other, M. front.               9
+   5 "     "         "     facing M.                      6
+   6 "     "         "     front, M. front.               7
+   7 "     "         "       "    M. turned to same.      6
+   8 "     "         "    to same M. turned front.        7
+   9 "     "         "       "    M.     "   to same,    14
+  10 " in middle, turned front.                           0
+
+
+Thus the constant elements, understanding always that C. has more
+interest than M., are as follows: For (1) I. + D. = D.; (2) I. = D. +
+D.; (3) I. = D.; (4) I. = D.; (5) I. + D. = D.; etc. These are in
+order of complete balance, but it will be seen that from (7) on, while
+the factors are constant, the framework is not balanced; _e.g._ in (9)
+both I. and D. work on the same side. For these groups, therefore, the
+variations, if there is balance, will be more striking. Eliminating
+the balancing elements in the framework, the tables for the ten groups
+are:
+
+
+  (1)  I. + D. = D.     (2)  I. = D. + D(M).   (3)  I. = D.
+  969. I. = Ms.           680. I. = D.        1094. Ms. + I. = I. + D.
+  601. I. = Ms.           735. I. = D.          33. I. = I. + D
+   49. I. = Ms. + I.     1121. I. = D.
+  634. I. = Ms. + I.     1035. I. = D.         (4)  I. = D.
+  584. I. = I.            333. I. = I. + D.    775. I. = D.
+  686. I. = I.             80. I. = I. + D.    746. I. = D.
+  794. I. = D.            753. I. = I. + D.   1106. I. = Ms. + D.
+  164. I. = D.           1114. I. = D. + L.    781. I. = Ms. + D.
+  368. I. = D. + V.                           1131. I. = I. + D.
+  927. I. = V.                                 517. I. = I. + D.
+  273. I. = V.                                 327. I. + Ms. = D. + V.
+                                               951. I. + L. = D. + V.
+                                               715. Unbalanced.
+
+  (5)  I. + D. = D.       (6)  I. =                 (7)  I. + D. =
+   43. I. = I.            854. I. = Ms.         725. I. + D. = I. + L.
+  711. I. = I.           1148. I. = I.          206. I. + D. = I. + L.
+  447. I. = Ms.           709. I. = D.          155. I. + D. = D. + L.
+  643. I. = Ms.           907. I. = D.          739. I. + D. = L.
+  777. I. = Ms. + I.      586. I. = Ms. + I.    331. I. + D. = V.
+  637. I. = Ms. + I.      137. I. = Ms. + I.    980. Unbalanced.
+                          187. Unbalanced.
+
+  (8)  I. + D. =           (9)  I. + (D. + D.) =           (10)  0.
+   57. I. + D. = Ms.      835. I. + D. = Ms + I.
+  979. I. + D. = I. + L.  724. I. + D. = Ms + L.
+  134. I. + D. = D.       495. I. + D. = Ms + L.
+  106. I. + D. = D. + V.  182. I. + D. = Ms + V.
+  220. I. + D. = L.       817. I. + D. = I.
+  118. I. + D. = V. + L.  662. I. + D. = I.
+  157. Unbalanced.        806. I. + D. = I.
+                         1136. I. + D. = I. + L.
+                          865. I. + D. = I. +  V.
+                         1023. I. + D. = V.
+                          531. I. + D. = L.
+                          553. I. + D. = L.
+
+
+The most used element is I., in 100 per cent. of cases; the least
+used, V., 13 per cent. D., in 91 per cent. of cases; Ms., 26 per
+cent.; L., 19 per cent. 175, 433, unbalanced.
+
+As seen in the table, a balance of elements is kept, except in four
+cases which will be hereafter considered. In all cases the balance is
+between the interest in C., sometimes plus D., (in the attention of
+the figures to C.), on the one side, and other elements on the other.
+Very seldom are other salient points found on the C. side. When the C.
+side is especially 'heavy,' the number of opposing elements increases,
+and especially takes the form of V. and L. [cf. (7), (8), (9)], which
+were observed in the experimental chapter to be powerful in attracting
+attention. For the fairly well-balancing framework--(i), (2), (3) and
+(4)--Ms., I., and D. are much more often the opposing elements.
+
+The pictures listed as unbalanced are, with one exception, among the
+oldest examples given; conceived in the most slavish geometrical
+symmetry in which, indeed, the geometrical outline almost hides the
+fact that the slight variations are all toward a lack of balance.
+
+There is but one S. & S. case (1054), Titian, _The Madonna of the
+House of Pesaro_. In this, M. and C. are on a high throne on the
+Right, other figures lower down on the Left bearing a flag that leans
+back to the Left. All the lines of the figures and of the massive
+architecture and the general direction of attention bear down so
+strongly to Left that the importance of the Right figures is balanced.
+We should have, then, I. = I. + L. + D. The D.C. cases, seven in
+number, are remarkably alike. Six have a vista separating the two
+groups, in five remarkably deep and beautiful, as if to fix the
+oscillating attention there. In all, M. and C., either in position or
+by the direction of their lines, are nearer the Cn. than the opposing
+figures, which are naturally less interesting, thus giving an instance
+of the mechanical balance. Their general equation, then, would be I. =
+M. or M. + L. Having shown that the small variations from the general
+symmetrical type of altar-pieces are invariably, except in primitive
+examples, in the direction of substitutional symmetry, or balance, we
+may next study the Madonna pictures, using the same classifications
+for purposes of comparison.
+
+
+MADONNA WITH INFANT CHRIST.
+
+  (1)  I. + D. = D.   (2)  I. = D. + D.         (4)  I. = D.
+   56. I. = L.        271. I. = D. + L.         668. I. = D. + Ms.
+  332. I. = L.        867. I. = D. + V. + D.     14. I. = D. + I.
+  633. I. = D.                                   91. I. = D. + V.
+                      (3)  I. = D.             1111. I. = D. + V.
+                      144. I. = D.             1011. I. = D. = L.
+                      521. I. = D.              915. I. = D. = L.
+                                                356. I. = L. + D. + D.
+                                                296. I. + Ms. = V. + L.
+
+             (5)  I. + D. = D.                (6)  I. =
+          51. I. = D.                   596. I. = Ms.
+         581. I. = D.                   892. I. = Ms.
+         829. I. = D. + I.                224. I. = I. + D.
+         159. I. = I. + D.                908. I. = D. + L.
+         683. I. = D. + L.
+        1045. I. = I. + L.                    (7)  I. + D. =
+         745. I. = I. + L.                344. I. + D. = Ms.
+         734. I. = D. + L.                949. I. + D. = Ms. + V. + L.
+         404. I. = D. + L.                608. I. + D. = L.
+         248. I. = L.                   524. I. + D. = L.
+          37. I. = L.
+          97. I. = L.                         (8)  0.
+         363. I. = V. + L.
+         674. I. = V. + L.                    (9)  I. + D. + D. =
+          62. I. = V. + L.                361. I. + D. = L.
+        1142. I. = V. + L.
+        1018. I. = V. + L.                        (10)
+         110. I. + V. = Ms. + L.            538. I. = D.
+         411. I. + V. = Ms. + L.            614. I. + Ms. = V.
+         771. I. + Ms. = V. + L.             34. D. = Ms. + L.
+
+
+Most used element, I., 100 per cent.; least used, Ms., 21 per cent.
+D., 96 per cent.; L., 64 per cent.; V., 27 per cent.
+
+The first thing to be noted, on comparing this table with the
+preceding, is the remarkable frequency of the use of the vista and the
+line. Among the altarpieces, the direction of attention was the
+element most often opposed to the interesting object; and next to
+that, another object of interest. These two elements, however, here
+sink into comparative insignificance. In general, balance is brought
+about through the disposition of form rather than of interests. This
+appears in comparing the numbers; against the use of L. in 19 per
+cent. of the cases among the altarpieces, we have 64 per cent. among
+the Madonna pictures; V. is used in the former cases 13 per cent. of
+the times, in the latter 27 per cent. The reason for this would appear
+to be that the lack of accessories in the person of saints,
+worshippers, etc., and the consequent increase in the size of M. and
+C. in the picture heightens the effect of any given outline, and so
+makes the variations from symmetry greater. This being the case, the
+compensations would be stronger--and as we have learned that V. and L.
+are of this character, we see why they are needed. None of the M. and
+C., S.C. pictures fails to give a complete balance of elements
+according to hypothesis. There are no well-defined cases of S. & S. or
+D.C.
+
+
+Portraits.
+
+A study of the Madonna pictures of all types, then, results in an
+overwhelming confirmation of the hypothesis of substitutional
+symmetry. It may be objected that the generally symmetrical framework
+of these pictures suggests a complete balance, and the next step in
+our analysis would, therefore, be a type of picture which is less
+bound by tradition to the same form. The portrait would seem to
+combine this desideratum with generally large and simple outlines, so
+that the whole surface can be statistically reported with comparative
+ease. A detailed analysis of a couple of portraits may justify the
+classification adopted.
+
+900. Anton Raphael Mengs, _Self-Portrait_. The head of the painter is
+exactly in Cn., but is turned sharply to Right, while his shoulders
+turn Left. His arm and hand are stretched out down to Right, while his
+other hand, holding pencil, rests on his portfolio to Left. Hence, the
+D. of attention plus that of L. on Right, balances I. in implements,
+plus D. of body on Left, or D. + L. = D. + I.
+
+438. B. van der Helst, _Portrait of Paul Potter_. The head of the
+subject is entirely to Left of Cn., his easel on Right. His body is
+turned sharply to Right, and both hands, one holding palette and
+brushes, are stretched down to Right. His full face and frontward
+glance are on Left. Hence, Ms. + I. in person balances I. in
+implements + D. of L., or Ms. + I. = I. + L.
+
+It is seen that the larger elements in these pictures are the
+directions of the head and body, and the position of the head, with
+reference to Cn. The following classification is based on this
+framework.
+
+
+CLASSIFICATION OF PORTRAITS.
+
+            A. Head in Cn.
+    I. Body front, head front,                       6
+   II. Body turned, head turned other way,           7    D. = D.
+  III. Body turned, head front,                     31    D. =
+   IV. Body front, head turned,                      1    D. =
+    V. Body turned, head turned same way,          106    D. + D. =
+
+            B. Head not in Cn.
+   I. Body turned to empty side, head to same,      18    Ms.=D.
+   II. Body turned to empty side, head front,       23    Ms. = D.
+  III. Body turned to empty side, head to other,     3    Ms. + D. = D.
+   IV. Body front, head front,                       2    Ms. =
+    V. Body turned from empty side, head same way,  10    Ms. + D. =
+
+
+This is also in order of less complete balancing of the original
+elements. The principal characteristics of the different divisions are
+as follows:--
+
+A.
+     I. (Symmetrical.) Most used element, L.; least used, V.
+
+    II. (Balanced, D. = D.) Most used element, L.; least used, V.
+
+   III. (D. = .) Most used element, Ms., in 74 per cent, of cases
+        opposed to D.; in 30 per cent, of cases, D. of glance opposed
+        to D. of body; least used, V. (1 per cent.).
+
+    IV. One case only.
+
+    V. (D. = .) Most used element, Ms., in 73 per cent. of cases
+        opposed to D.; in 40 per cent. of cases, D. of glance opposed
+        to D.; in 28 per cent. Ms. + D. of glance opposed to D.; least
+        used element, V. (15 per cent.). I. 39 per cent.; L. 38 per cent.
+
+B.
+     I. (Balanced, Ms. + I. = D.) Most used element (not counting
+        those already included in equation), I., 55 per cent.; least
+        used, V., 2 per cent.; L., 50 per cent. In 44 per cent., D. of
+        glance opposed to D.
+
+    II. (Ms. + I. = D.) Most used element (not in equation), I., 52
+        per cent. Least used, V., 26 per cent. L., 43 per cent. In 21
+        per cent., D. of glance opposed to D.
+
+   III. (Ms. + I. + D. = D.) Three cases. Two cases V. on empty
+        side.
+
+    IV. (Ms. + I. = .) Two cases. One case V. on empty side.
+
+     V. (Ms. + I. + D. = .) Most used element, L., 60 per cent.;
+        least used, V., 10 per cent.; 33-1/3 per cent., D. of glance to
+        empty side.
+
+The portrait class is an especially interesting object for study,
+inasmuch as while its general type is very simple and constant, for
+this very reason the slightest variations are sharply felt, and have
+their very strongest characteristic effect. We shall, therefore, find
+that the five principal factors in composition express themselves very
+clearly. The general type of the portrait composition is, of course,
+the triangle with the head at the apex, and this point is also
+generally in the central line--in 73 per cent. of the whole number of
+cases, as is seen from the table. All cases but one are longer than
+they are wide, most are half-length or more. Nevertheless, great
+richness of effect is brought about by emphasizing variations. For
+instance, the body and head are, in the great majority of cases,
+turned in the same way, giving the strongest possible emphasis to the
+direction of attention--especially powerful, of course, where all the
+interest is in the personality. But it is to be observed that the very
+strongest suggestion of direction is given by the direction of the
+glance; and in no case, when most of the other elements are directed
+in one way, does the glance fail to come backward. (Cf. A. II., V.,
+and B. I., II., V.)
+
+A. It is of especial value for our conclusions that that division in
+which the constant elements are least balanced (V.) is far the most
+numerous. Comparison of this with III. shows that the principal
+element, direction of movement of head or body, is balanced by the
+larger mass of the body or accessories. Very significant, also, is the
+great increase in the use of V. in this most irregular class (15 per
+cent. as against 1 per cent. in III.). Three cases (214, 1087, 154,
+all A.V.,) fail to show substitutional symmetry.
+
+B. With the head on one side of Cn., of course the greatest interest
+is removed to one side, and the element of direction is brought in to
+balance. Again, with this decrease in symmetry, we see the significant
+increase in the use of the especially effective elements, V. and L.
+(Cf. B. I., II., III., IV., and especially V.) In fact, the use of the
+small deep vista is almost confined to the class with heads not in the
+middle. The direction of the glance also plays an important part. It
+is to be noted that in B. I. and II., I. appears as the most
+frequently used element, exclusive of the general equation, which is,
+of course, between the mass of the body and interest of the face, on
+one side, and the direction of suggested movement on the other. This
+means that very often the direction of movement alone is not
+sufficient to balance the powerful Ms. + I. of the other side, and
+that the eye has to be attracted by a definite object of interest.
+This is usually the hand, with or without an implement--like the
+palette, etc., of our first examples--or a jewel, vase, or bit of
+embroidery. This is very characteristic of the portraits of Rembrandt
+and Van Dyck.
+
+In general, it may be said that (1) portraits with the head in the
+center of the frame show a balance between the direction of suggested
+movement on one side, and mass or direction of attention, or both
+together, on the other; while (2) portraits with the head not in the
+center show a balance between mass and interest on one side, and
+direction of attention, or of line, or vista, or combinations of
+these, on the other. The hypothesis of substitutional symmetry is thus
+completely confirmed.
+
+
+Genre.
+
+Still more unsymmetrical in their framework than portraits, in fact
+the most unfettered type of all, are the genre pictures. Being so
+irregular, they admit of no complete classification based on constant
+elements in the framework, such as was possible for the types already
+dealt with. A grouping, based on types of composition, is indeed
+possible, as of triangles, diagonals, etc., but as this begs the
+question of the relative importance of line and direction of
+attention, and assumes that the shape is all-important, it will not be
+made use of here. The broad divisions and the relative use of the
+elements are given as follows:
+
+    S.C. 63. Most frequent form (I. = or I. + D. =). Most used
+    element, I., 89 per cent.; least used, L., 44 per cent.; D.,
+    57 per cent.; Ms., 57 per cent.; V., 46 per cent.
+
+    D.C. 19. Most frequent form (I. + D. = I. + D.) Most used
+    element, I. (all cases); least used, L., 31 per cent.; V., 47
+    per cent.; Ms., 63 per cent.; D., 42 per cent.
+
+    S.&S. 11. Most frequent form (I. or I. + Ms. = V. or V. +).
+    Most used element, I., 100 per cent.; least used, L., 20 per
+    cent.; V., 82 per cent.; Ms., 72 per cent.; D., 27 per cent.
+
+As these are pictures with a human interest, and, therefore full of
+action and particular points of interest, it was to be expected that
+I. would be in all forms the element most frequently appearing. In
+compositions showing great variations from geometrical symmetry, it
+was also to be expected that V. and L., elements which have been
+little used up to this point, should suddenly appear in very high
+percentages; for, as being the most strikingly 'heavy' of the
+elements, they serve to compensate for other variations combined. In
+general, however, the balance is between the interesting side, which
+is also often the most occupied (I. + Ms.), and the direction of
+suggestion to the other side.
+
+For the first time in this investigation the S. & S. and D.C. types
+appear in appreciable numbers. It is of some significance that the
+most irregular type of all, S. & S., in which the weight of interest
+and of mass is overwhelmingly on one side, should be invariably
+balanced by the third dimension (V.). As these somewhat infrequent
+cases are especially enlightening for the theory of substitutional
+symmetry, it is worth while to analyze one in detail.
+
+286. Pieter de Hooch, _The Card-players_, in Buckingham Palace,
+portrays a group completely on the Right of Cn., all facing in to the
+table between them. Directly behind them is a high light window,
+screened, and high on the wall to the extreme Right are a picture and
+hanging cloaks. All goes to emphasize the height, mass and interest of
+the Right side. On the Left, which is otherwise empty, is a door half
+the height of the window, giving on a brightly lighted courtyard, from
+which is entering a woman, also in light clothing. The light streams
+in diagonally across the floor. Thus, with all the 'weight' on the
+Right, the effect of this deep vista on the Left and of its brightness
+is to give a complete balance, while the suggestion of line from
+doorway and light makes, together with the central figure, a roughly
+outlined V, which serves to bind together all the elements. This
+matter of binding together of elements is reserved for further
+discussion--the purpose of this detailed description is only to show
+the extraordinary power of a single element, vista, to balance a whole
+composition of others, and its significance in the tables as an
+increasing accompaniment of increasing variations from symmetry.
+
+The D.C. cases, inasmuch as they always present a balance of interest
+at least, are less valuable for our theory; among the variations the
+larger side, Ms., is often balanced by a vista, or, combining with the
+usual equation for genre pictures, Ms. + I. + D. = V. + I. + D. There
+is only one picture which cannot be schematized (263).
+
+
+Landscape.
+
+The landscape is another type of unfettered composition. As it
+represents no action or single object or group of objects, its parts
+are naturally more or less unconnected. It should, therefore, be said
+that no picture was taken as D.C. unless there was a distinct
+separation of the two sides. The typical examples are analyzed in
+detail.
+
+S.C. 912. J. van Ruysdael, _Forest Landscape_, in the London National
+Gallery. In the Cn. is a stagnant pool, backed on the Right by thick
+woods. A dead tree, white, very prominent in the Right foreground,
+another at its foot sloping down to Cn. On the Left a bank sloping
+down to Cn., a tree at its foot; behind both, and seen also between
+the two central trees, bright sky and clouds. Thus, there is on the
+Right, Mass and Direction to Cn.; on the Left, Vista and Direction to
+Cn.; Ms. + D. = V. + D.
+
+D.C. 642. Hobbema, _The Watermill_, in Buckingham Palace. On the
+Right, a bank sloping upward, a large cluster of trees, a path leading
+down to Right lower corner. On the Left, somewhat lower, the mill, and
+water in front of it, flowing down to Left; clearest sky between mill
+and trees. Thus Mass and Direction out are placed over against
+Interest (in mill) and Direction out, plus possibly a hint of Vista,
+or Ms. + D. = I. + D + V.
+
+S.C. 65. Most frequent form, Ms. + I. = V. + L. Most used element, V.,
+98 per cent.; least used, D., 22 per cent. I. 73 per cent.; Ms. 66 per
+cent.; L. 31 per cent.
+
+S. & S. One case. Ms. + I. + V. = V.
+
+D.C. 22. Most frequent form, Ms. + I. or Ms. = V. or V. + (almost
+invariable). Most used element, V., 100 per cent.; least used, D., per
+cent. Ms. 82 per cent.; I. 73 per cent.; L. 23 per cent.
+
+It was, of course, to be expected that in pictures without action
+there should be little suggestion of attention or of direction of
+movement. What is less evident is the reason for the high percentage
+of I. Of course, figures do appear in many examples, and in most
+pictures some inanimate object is emphasized--as, for instance, the
+mill in our second example. But the most remarkable point of
+difference in these tables from the preceding is the presence of V. in
+practically every example. It is, of course, natural that somewhere in
+almost every picture there should be a break to show the horizon line,
+for the sake of variety, if for nothing else--but what is significant
+is the part played by this break in the balancing of the picture. In
+about two thirds of the examples the vista is enclosed by lines, or
+masses, and when near the center, as being at the same time the
+'heaviest' part of the picture, serves as a fulcrum or center to bind
+the parts--always harder to bring together than in the other types of
+pictures--into a close unity. The most frequent form of this
+arrangement, as seen by the table, is a diagonal, which just saves
+itself by turning up at its far end. Thus the mass, and hence usually
+the special interest of the picture, is on the one side, on the other
+the vista and the sloping line of the diagonal. In very few cases is
+the vista behind an attractive or noticeable part of the picture, the
+fact showing that it acts in opposition to the latter, leading the eye
+away from it, and thus serving at once the variety and richness of the
+picture, and its unity. A pure diagonal would have line and vista both
+working at the extreme outer edge of the picture, and thus too
+strongly--unless, indeed, balanced by very striking elements near the
+other edge.
+
+This function of the vista as a unifying element is of interest in
+connection with the theory of Hildebrand,[16] that the landscape
+should have a narrow foreground and wide background, since that is
+most in conformity with our experience. He adduces Titian's _Sacred
+and Profane Love_ as an example. But of the general principle it may
+be said that not the reproduction of nature, but the production of a
+unified complex of motor impulses, is the aim of composition, and that
+this aim is best reached by focusing the eye by a narrow
+background--_i.e._, vista. No matter how much it wanders, it returns
+to that central spot and is held there, keeping hold on all the other
+elements. Of Hildebrand's example it may be said that the pyramidal
+composition with the dark and tall tree in the center effectually
+accomplishes the binding together of the two figures, so that a vista
+is not needed. A wide background without that tree would leave them
+rather disjointed.
+
+   [16] A. Hildebrand, 'Das Problem der Form in der Bildenden
+   Kunst,' Strassburg, 1897.
+
+Another interesting observation concerns the use of water in
+landscapes. In nearly all appears an expanse of water, and in four
+fifths of the cases it is either on the same side as the vista, or in
+the same line with it. This is no doubt partly due to the
+light-effects which can be got on the water, but it also greatly
+reinforces the peculiar effect of the vista. That effect, as has been
+repeatedly said, is to concentrate, to hold, to fixate vision. The
+same thing is true of the horizontal line, as was shown by some
+preliminary experiments not here reported. The contrast to the
+ordinary trend of lines--particularly in a landscape--together with
+the strong suggestion of quiet and repose, serve to give the same
+concentrating effect to the horizontal lines as to the vista.
+
+In general, it may be said that balance in landscape is effected
+between Mass and Interest on one side and Vista and Line on the other;
+and that unity is given especially by the use of Vista and the
+horizontal lines of water.
+
+A survey of the subject-types remaining on the list of page 514 shows
+that they may quite well be grouped together with those already
+examined; that is, the Holy Families, Adorations, Crucifixions, and
+Annunciations are very symmetrical in type, and present the same
+characteristics as the Altarpieces. The Miscellaneous (mostly
+religious) pictures, the Descents, and the Allegorical are, for the
+most part, freely composed, irregular, full of action, and resemble
+the genre pictures. The Single Figure pictures, Religious, Allegorical
+and Genre, and the Portrait Groups, resemble the portraits. Therefore,
+it may be considered that the existence of a perfect substitutional
+symmetry has been established, inasmuch as it has been shown to be
+almost invariably present in the types examined.
+
+The experimental treatment of the isolated elements determined the
+particular function of each in distributing attention in the field of
+view. The object of large size claims attention, but does not rivet it
+nor draw it out powerfully; the intrinsically interesting object does
+excite it, but limits it to a comparatively small field; the
+suggestion of movement or of attention on the part of pictured objects
+carries the attention through the field of its operation; the vista
+rivets the attention without powerfully exciting it, and the line
+extending in a certain direction carries the attention in the same way
+as does the suggestion of movement. But the preceding statistical
+analysis has shown that while all are possibly operative in a given
+picture, some are given much more importance than others, and that in
+pictures of different types different elements predominate.
+
+The following table gives the distribution of the elements in the
+single-center pictures already examined. The numbers represent the per
+cent. of the whole number of balanced pictures in which the given
+element appears once or more.
+
+
+    S.C.       Ms.    I.    D.    V.    L.
+
+    Alt. p.    26    100    91    13    31
+    Mad.       21    100    96    27    64
+    Port.      80     63    98    17    61
+    Genre      57     89    57    46    44
+    Lands.     66     73    22    98    31
+
+
+It is seen that in those classes with a general symmetrical framework,
+the altar and Madonna pictures, the elements of interest and direction
+of attention are overwhelmingly predominant--which is the more to be
+expected as they appear, of course, as variations in a symmetry which
+has already, so to speak, disposed of mass and line. They give what
+action there is, and when they are very strongly operative, we see by
+page 516, (8) and (9) and note, that they are opposed by salient lines
+and deep vistas, which act more strongly on the attention than mass;
+compare further Mad., V. 27 per cent., L. 64 per cent., as against
+Alt., V. 13 per cent., L. 19 per cent., as confirming the view that
+they are used in the more irregular and active pictures. But I. keeps
+its predominance throughout the types, except in the portraits, where,
+indeed, we should not expect it to be so powerful, since the principal
+object of interest must always be the portrait head, and that is in
+most cases in the Cn., and therefore not counted. Yet I. has a
+respectable representation even in the portrait table, showing that
+such objects as jewels, embroideries, beautiful hands, etc., count
+largely too in composition. Its greatest is in the genre table, where,
+of course, human interests constitute the subject matter.
+
+It is among the portraits that the direction of suggestion is most
+operative. Since these pictures represent no action, it must be given
+by those elements which move and distribute the attention; in
+accordance with which we see that line also is unusually influential.
+As remarked above, the altarpieces and Madonna pictures, also largely
+without action, depend largely for it on D., in the form of direction
+of attention (D. 91 per cent.).
+
+The vista, as said above, rivets and confines the attention. We can,
+therefore, understand how it is that in the genre table it suddenly
+appears very numerous. The active character of these pictures
+naturally requires to be modified, and the vista introduces a powerful
+balancing element, which is yet quiet; or, it might be said, inasmuch
+as energy is certainly expended in plunging down the third dimension,
+the vista introduces an element of action of counterbalancing
+character. In the landscape it introduces the principal element of
+variety. It is always to be found in those parts of the picture which
+are opposed to other powerful elements, and the 'heavier' the other
+side, the deeper the vista. This is especially to be noted in all
+pictures of the S. & S. type, where the one side is very 'heavy' and
+the deep vista practically invariable on the other. Also in D.C.
+pictures it serves as a kind of fulcrum, or unifying element, inasmuch
+as it rivets the attention between the two detached sides. (Cf. D.C.
+among Alt. and Mad.)
+
+The direction of suggestion by means of the indication of a line (L.),
+quite naturally is more frequent in the Madonna-picture and Portrait
+classes. Both these types are of large simple outline, so that L.
+would be expected to tell, but more or less irregular, so that it
+would not appear on both sides, thus neutralizing its action, as often
+in the symmetrical altarpieces. This neutralizing explains why it has
+a comparatively small per cent. in the landscape table, it having
+appeared in minor form all over the field, but less often in large
+salient outline. It is worth noticing that for the D.C. of both genre
+and landscape, the per cent. drops appreciably. As it is, in a decided
+majority of cases, combined with V.--the shape being more or less a
+diagonal slope--it is clear that it acts as a kind of bond between the
+two sides, carrying the attention without a break from one to the
+other.
+
+The element of mass requires less comment. It appears in greatest
+number in those pictures which have little action, portraits and
+landscapes, and which are yet not symmetrical--in which last case mass
+is, of course, already balanced. In fact, it must of necessity exert
+a certain influence in every unsymmetrical picture, and so its
+percentage, even for genre pictures, is large.
+
+Thus we may regard the elements as both attracting attention to a
+certain spot and dispersing it over a field. Those types which are of
+a static character abound in elements which disperse the attention;
+those which are of a dynamic character, in those which make it stable.
+The ideal composition seems to combine the dynamic and static
+elements--to animate, in short, the whole field of view, but in a
+generally bilateral fashion. The elements, in substitutional symmetry,
+are then simply means of introducing variety and action. As a dance in
+which there are complicated steps gives the actor and beholder a
+varied and thus vivified 'balance,' and is thus more beautiful than
+the simple walk, so a picture composed in substitutional symmetry is
+more rich in its suggestions of motor impulse, and thus more
+beautiful, than an example of geometrical symmetry.
+
+
+_B. Principles of Composition._
+
+The particular function of the elements which are substituted for
+geometrical symmetry has been made clear; their presence lends variety
+and richness to the balance of motor impulses. But the natural motor
+response to stimulation has another characteristic which belongs to us
+as individuals. The motor response must be balanced, but also unified.
+In a picture, therefore, there must be a large outline in which all
+the elements are held together, corresponding to this requirement of
+unity. Now this way of holding together, this manner of combination,
+may vary; and I hope to show that it not only varies with the subject
+and purpose of the picture, but bears a very close relation
+thereto--that, in short, it is what determines the whole character of
+the picture. Just what this relation is will appear in the study of
+our material.
+
+Examples of these types of composition may best be found by analyzing
+a few very well-known pictures. We may begin with the class first
+studied, the Altarpiece, choosing a picture by Botticelli, in the
+Florence Academy (746). Under an arch is draped a canopy held up by
+angels; under this, again, sits the M. with the C. on her lap, on a
+throne, at the foot of which, on each side, stand three saints. The
+outline of the whole is markedly pyramidal--in fact, there are,
+broadly speaking, three pyramids; of the arch, the canopy, and the
+grouping. A second, much less symmetrical example of this type, is
+given by another Botticelli in the Academy--_Spring_ (140). Here the
+central female figure, topped by the floating Cupid, is slightly
+raised above the others, which, however, bend slightly inward, so that
+a triangle, or pyramid with very obtuse angle at the apex, is
+suggested; and the whole, which at first glance seems a little
+scattered, is at once felt, when this is grasped, as closely bound
+together.
+
+Closely allied to this is the type of the _Madonna of Burgomaster
+Meyer_, Holbein (725), in the Grand-Ducal Castle, Darmstadt. It is
+true that the same pyramid is given by the head of the M. against the
+shell-like background, and her spreading cloak which envelops the
+kneeling donors. But still more salient is the diamond form given by
+the descending rows of these worshipping figures, especially against
+the dark background of the M.'s dress. A second example, without the
+pyramid backing, is found in Rubens' _Rape of the Daughters of
+Leucippus_ (88), in the Alte Pinakothek at Munich. Here the diamond
+shape formed by the horses and struggling figures is most
+remarkable--an effect of lightness which will be discussed later in
+interpreting the types.
+
+The famous _Bull_ of Paul Potter (149), in the Royal Museum at the
+Hague, furnishes a third type, the diagonal. High on one side are
+grouped the herdsman, leaning on a tree which fills up the sky on that
+side, and his three sheep and cow. The head of the bull is turned
+toward this side, and his back and hind leg slope down to the other
+side, as the ground slopes away to a low distant meadow. The picture
+is thus divided by an irregular diagonal. Somewhat more regular is the
+diagonal of the _Evening Landscape_, by Cuyp (348), in the Buckingham
+Palace, London. High trees and cliffs, horsemen and others, occupy one
+side, and the mountains in the background, the ground and the clouds,
+all slope gradually down to the other side.
+
+It is a natural transition from this type to the V-shape of the
+landscapes by Aart van der Neer, _Dutch Villages_, 245 and 420, in the
+London National Gallery and in the Rudolphinum at Prague,
+respectively. Here are trees and houses on each side, gradually
+sloping to the center to show an open sky and deep vista. Other
+examples, of course, show the opening not exactly in the center.
+
+In the _Concert_ by Giorgione (758), in the Pitti Gallery, Florence,
+is seen the less frequent type of the square. The three figures turned
+toward each other with heads on the same level make almost a square
+space-shape, although it might be said that the central player gives a
+pyramidal foundation. This last may also be said of Verrocchio's
+_Tobias and the Archangels_ in the Florence Academy, for the square,
+or rather rectangle, is again lengthened by the pyramidal shape of the
+two central figures. The unrelieved square, it may here be
+interpolated, is not often found except in somewhat primitive
+examples. Still less often observed is the oval type of _Samson's
+Wedding feast_, Rembrandt (295), in the Royal Gallery, Dresden. Here
+one might, by pressing the interpretation, see an obtuse-angled
+double-pyramid with the figure of Delilah for an apex, but a few very
+irregular pictures seem to fall best under the given classification.
+
+Last of all it must be remarked that the great majority of pictures
+show a combination of two or even three types; but these are usually
+subordinated to one dominant type. Such, for instance, is the case
+with many portraits, which are markedly pyramidal, with the
+double-pyramid suggested by the position of the arms, and the inverted
+pyramid, or V, in the landscape background. The diagonal sometimes
+just passes over into the V, or into the pyramid; or the square is
+combined with both.
+
+It is, of course, not necessary at this point to show how it is that
+such an apparently unsymmetrical shape as the diagonal, alone or in
+combination with other forms, nevertheless produces an effect of
+balance. In all these cases of the diagonal type the mass or interest
+of the one side, or the direction of subordinate lines backward to it,
+balances the impulse of the line descending to the other side. The
+presence of balance or substitutional symmetry is taken for granted
+in this treatment, having been previously established, and only the
+modifications of this symmetry are under consideration.
+
+Now, in order to deal properly with the question of the relation of
+the type of composition to the subject of the picture, complete
+statistical information will be necessary. A table of the pictures,
+classified by subjects and distributed under the heads of the six
+major types, is accordingly subjoined.
+
+
+                       Pyramid.         Double-Pyr.       Diagonal.
+                    S.C. D.C. S.S.    S.C. D.C. S.S.    S.C. D.C. S.S.
+  Altarpieces,       49    0    1      10    4    0       1    0    0
+  Mad. w. C.,        40    0    0       7    0    0       0    0    0
+  Holy Family,       25    0    4       0    0    1       2    2    2
+  Adorations,        19    0    0       0    0    0       0    0    0
+  Crucifixions,      11    0    0       7    0    1       0    0    1
+  Desc. fr. Cross,   12    0    0       3    0    0       1    0    0
+  Annunciations,      0    8    0       0    4    0       0    0    0
+  Misc. Religious,   55   16    3       4    4    0      10    7    5
+  Allegorical,       20    2    1       4    0    0       4    0    2
+  Genre,             25    4    4       5    0    0      18    2    1
+  Landscape,          8    2    1       3    0    0      25    6    0
+  Port. Group,       20    4    2       9    0    0       3    3    2
+  Rel. Single Fig.,  20    0    0       2    0    0       2    0    0
+  Alleg. S.F.,        7    0    0       2    0    0       3    0    0
+  Portrait S.F.,    179    0    0      28    0    0       0    0    0
+  Genre S.F.,        15    0    0       1    0    0       1    0    0
+
+
+                       V-shaped.         Square.             Oval.
+                    S.C. D.C. S.S.    S.C. D.C. S.S.    S.C. D.C. S.S.
+  Altarpieces,        6    1    0       4    1    0       0    1    0
+  Mad. w. C.,         0    0    0       0    0    0       0    0    0
+  Holy Family,       13    3    6       0    0    0       0    0    0
+  Adorations,         0    0    0       0    0    0       0    0    0
+  Crucifixions,       0    0    0       3    0    0       0    0    0
+  Desc. fr. Cross,    5    0    1       3    0    0       2    0    0
+  Annunciations,      0    1    0       0    8    0       0    0    0
+  Misc. Religious,   20   14    2       9   12    1       2    2    3
+  Allegorical,        3    2    1       3    1    0       3    1    0
+  Genre,             10    7    6       4    4    0       1    3    0
+  Landscape,         20   12    0       4    0    0       5    2    0
+  Port. Group,       10    7    1       0    3    0       0    0    0
+  Rel. Single Fig.,   3    0    0       1    0    0       0    0    0
+  Alleg. S.F.,        0    0    0       0    0    0       0    0    0
+  Portrait S.F.,      0    0    0       0    0    0       0    0    0
+  Genre S.F.,         1    0    0       0    0    0       0    0    0
+
+
+What types are characteristic of the different kinds of pictures? In
+order to answer this question we must ask first, What are the
+different kinds of pictures? One answer, at least, is at once
+suggested to the student on a comparison of the pictures with their
+groupings according to subjects. All those which represent the Madonna
+enthroned, with all variations, with or without saints, shepherds or
+Holy Family, are very quiet in their action; that is, it is not really
+an action at all which they represent, but an attitude--the attitude
+of contemplation. This is no less true of the pictures I have called
+'Adorations,' in which, indeed, the contemplative attitude is still
+more marked. On the other hand, such pictures as the 'Descents,' the
+'Annunciations,' and very many of the 'miscellaneous religious,'
+allegorical and genre pictures, portray a definite action or event.
+Taking together, for instance, in two groups of five each, the first
+ten classes in the table, we find that they fall to the six types in
+the following proportion:
+
+
+         P.     D.P.     Dg.     V.      Sq.     Ov.
+   I.    66      13      05      13      03       0
+  II.    43      07      14      20      12       04
+
+
+Inasmuch as II. contains also many 'contemplative' pictures, while I.
+contains no 'active' ones, the contrast between the proportions of the
+groups would really be sharper than the figures indicate. But as it
+is, we see that the pyramid type is characteristic of the
+'contemplative' pictures in a much higher degree. If the closely
+allied double-pyramid type is taken with it, we have 79 per cent of
+the 'contemplative' to 50 per cent, of the 'active' ones. This view is
+confirmed by contrasting the 'Adoration,' the most complete example of
+one group, with the genre pictures, the most complete example of the
+other--and here we see that in the first all are pyramidal, and in the
+second only 26 per cent. A class which might be supposed to suggest
+the same treatment in composition is that of the portraits--absolute
+lack of action being the rule. And we find, indeed, that no single
+type is represented within it except the pyramid and double-pyramid,
+with 86 per cent. of the former. Thus it is evident that for the type
+of picture which expresses the highest degree of quietude,
+contemplation, concentration, the pyramid is the characteristic type
+of composition.
+
+But is it not also characteristic of the 'active' pictures, since, as
+we see, it has the largest representation in that class too? Perhaps
+it might be said that, inasmuch as all pictures are really more
+'quiet' than they are 'active,' so the type _par excellence_ is the
+pyramidal--a suggestion which is certainly borne out by the table as a
+whole. But setting aside for the moment the pyramid and its
+sub-variety, we see that the diagonal V-shaped and square types are
+much more numerous in the roughly outlined 'active' class. Taking,
+again, the genre class as especially representative, we find 23 per
+cent. of the diagonal type, and 25 per cent. of the V-shaped. We have
+seen how closely allied are these two types, and how gradually one
+passes over into the other, so that we may for the nonce take them
+together as making up 47 per cent. of the whole. The type of picture
+which expresses the highest degree of activity, which aims to tell a
+story, has, then, for its characteristic type the V and its varieties.
+
+The landscape picture presents a somewhat different problem. It cannot
+be described as either 'active' or 'passive,' inasmuch as it does not
+express either an attitude or an event. There is no definite idea to
+be set forth, no point of concentration, as with the altarpieces and
+the portraits, for instance; and yet a unity is demanded. An
+examination of the proportions of the types shows at once the
+characteristic type.
+
+
+                  P.    D.P.    Dg.    V.     Sq.    Or.
+  Landscapes,     13     03     35     36     05     08
+
+
+It is now necessary to ask what must be the interpretation of the use
+of these types of composition. Must we consider the pyramid the
+expression of passivity, the diagonal or V, of activity? But the
+greatly predominating use of the second for landscapes would remain
+unexplained, for at least nothing can be more reposeful than the
+latter. It may aid the solution of the problem to remember that the
+composition taken as a whole has to meet the demand for unity, at the
+same time that it allows free play to the natural expression of the
+subject. The altarpiece has to bring about a concentration of
+attention to express or induce a feeling of reverence. This is
+evidently brought about by the suggestion of the converging lines to
+the fixation of the high point in the picture--the small area occupied
+by the Madonna and Child--and by the subordination of the free play of
+other elements. The contrast between the broad base and the apex gives
+a feeling of solidity, of repose; and it seems not unreasonable to
+suppose that the tendency to rest the eyes above the center of the
+picture directly induces the associated mood of reverence or worship.
+Thus the pyramidal form serves two ends; primarily that of giving
+unity; and secondarily, by the peculiarity of its mass, that of
+inducing the feeling-tone appropriate to the subject of the picture.
+
+Applying this principle to the so-called 'active' pictures, we see
+that the natural movement of attention between the different 'actors'
+in the picture must be allowed for, while yet unity is secured. And it
+is clear that the diagonal type is just fitted for this. The attention
+sweeps down from the high side to the low, from which it returns
+through some backward suggestion of lines or interest in the objects
+of the high side. Action and reaction--movement and return of
+attention--is inevitable under the conditions of this type; and this
+it is which allows the free play--which, indeed, _constitutes_ and
+expresses the activity belonging to the subject, just as the fixation
+of the pyramid constitutes the quietude of the religious picture. Thus
+it is that the diagonal composition is particularly suited to portray
+scenes of grandeur, and to induce a feeling of awe in the spectator,
+because only here can the eye rove in one large sweep from side to
+side of the picture, recalled by the mass and interest of the side
+from which it moves. The swing of the pendulum is here widest, so to
+speak, and all the feeling-tones which belong to wide, free movement
+are called into play. If, at the same time, the element of the deep
+vista is introduced, we have the extreme of concentration combined
+with the extreme of movement; and the result is a picture in the
+'grand style'--comparable to high tragedy--in which all the
+feeling-tones which wait on motor impulses are, as it were, while yet
+in the same reciprocal relation, tuned to the highest pitch. Such a
+picture is the _Finding of the Ring_, Paris Bordone (1048), in the
+Venice Academy. All the mass and the interest and the suggestion of
+attention is toward the right--the sweep of the downward lines and of
+the magnificent perspective toward the left--and the effect of the
+whole space-composition is of superb largeness of life and feeling.
+With it may be compared Titian's _Presentation of the Virgin_ (107),
+also in the Academy, Venice. The composition, from the figure moving
+upward to one high on the right, to the downward lines, waiting groups
+and deep vista on the left, is almost identical with that of the
+Bordone. Neither is pure diagonal--that is, it saves itself at last by
+an upward movement. Compare also the two great compositions by
+Veronese, _Martyrdom of St. Mark_, etc. (1091), in the Doge's Palace,
+Venice, and _Esther before Ahasuerus_ (566), in the Uffizi, Florence.
+In both, the mass, direction of interest, movement and attention are
+toward the left, while all the lines tend diagonally to the right,
+where a vista is also suggested--the diagonal making a V just at the
+end. Here, too, the effect is of magnificence and vigor.
+
+If, then, the pyramid belongs to contemplation, the diagonal to
+action, what can be said of the type of landscape? It is without
+action, it is true, and yet does not express that positive quality,
+that _will_ not to act, of the rapt contemplation. The landscape
+uncomposed is negative; and it demands unity. Its type of composition,
+then, must give it something positive besides unity. It lacks both
+concentration and action; but it can gain them both from a space
+composition which shall combine unity with a tendency to movement. And
+this is given by the diagonal and V-shaped type. This type merely
+allows free play to the natural tendency of the 'active' picture; but
+it constrains the neutral, inanimate landscape. The shape itself
+imparts motion to the picture: the sweep of line, the concentration of
+the vista, the unifying power of the inverted triangle between two
+masses, act, as it were, externally to the suggestion of the object
+itself. There is always enough quiet in a landscape--the overwhelming
+suggestion of the horizontal suffices for that; it is movement that is
+needed for richness of effect; and, as I have shown, no type imparts
+the feeling of movement so strongly as the diagonal and V-shaped type
+of composition. It is worth remarking that the perfect V, which is of
+course more regular, concentrated, quiet, than the diagonal, is more
+frequent than the diagonal among the 'Miscellaneous Religious'
+pictures (that is, it is more _needed_), since after all, as has been
+said, the final aim of all space composition is just the attainment of
+repose. But the landscapes need energy, not repression; and so the
+diagonal type is proportionately more numerous.
+
+The square and oval types, as is seen from the table, are far less
+often used. The oval, most infrequent of all, appears only among the
+'active' pictures, with the exception of landscape. It usually serves
+to unite a group of people among whom there is no one especially
+striking--or the object of whose attention is in the center of the
+picture, as in the case of the Descent from the Cross. It imparts a
+certain amount of movement, but an equable and regular one, as the eye
+returns in an even sweep from one side to the other.
+
+The square type, although only three per cent. of the whole number of
+pictures, suggests a point of view which has already been touched on
+in the section on Primitive Art. The examples fall into two classes:
+in the first, the straight lines across the picture are unrelieved by
+the suggestion of any other type; in the second, the pyramid or V is
+suggested in the background with more or less clearness by means of
+architecture or landscape. In the first class are found, almost
+exclusively, early examples of Italian, Dutch and German art; in the
+second, pictures of a later period. The rigid square, in short, is
+found only at an early stage in the development of composition.
+Moreover, all the examples are 'story' pictures, for the most part
+scenes from the lives of the saints, etc. Many of them are
+double-center--square, that is, with a slight break in the middle, the
+grouping purely logical, to bring out the relations of the characters.
+Thus, in the _Dream of Saint Martin_, Simone Martini (325), a fresco
+at Assisi, the saint lies straight across the picture with his head in
+one corner. Behind him on one side, stand the Christ and angels,
+grouped closely together, their heads on the same level. Compare also
+the _Finding of the Cross_, Piero della Francesca (1088), a serial
+picture in two parts, with their respective backgrounds all on the
+same level; and most of the frescoes by Giotto at Assisi--in
+particular _St. Francis before the Sultan_ (1057), in which the actors
+are divided into parties, so to speak.
+
+These are all, of course, in one sense symmetrical--in the weight of
+interest, at least--but they are completely amorphous from an aesthetic
+point of view. The _forms_, that is, do not count at all--only the
+meanings. The story is told by a clear separation of the parts, and
+as, in most stories, there are two principal actors, it merely happens
+that they fall into the two sides of the picture. Interesting in
+connection with this is the observation that, although the more
+anecdotal the picture the more likely it is to be 'double-centered,'
+the later the picture the less likely it is to be double-centered.
+Thus the square and the double-center composition seem often to be
+found in the same picture and to be, both, characteristic of early
+composition. On the other hand, a rigid geometrical symmetry is also
+characteristic, and these two facts seem to contradict each other. But
+it is to be noted, first, that the rigid geometrical symmetry belongs
+only to the Madonna Enthroned, and general Adoration pieces; and
+secondly, that this very rigidity of symmetry in details can coexist
+with variations which destroy balance. Thus, in the _Madonna
+Enthroned_, Giotto (715), where absolute symmetry in detail is kept,
+the Child sits far out on the right knee of the Madonna. Compare also
+_Madonna_, Vitale di Bologna (157), in which the C. is almost falling
+off M.'s arms to the right, her head is bent to the right, and a monk
+is kneeling at the right lower corner; also _Madonna_, Ottaviano Nelli
+(175)--all very early pictures. Hence, it would seem that the symmetry
+of these early pictures was not dictated by a conscious demand for
+symmetrical arrangement, or rather for real balance, else such
+failures would hardly occur. The presence of geometrical symmetry is
+more easily explained as the product, in large part, of technical
+conditions: of the fact that these pictures were painted as
+altarpieces to fill a space definitely symmetrical in character--often,
+indeed, with architectural elements intruding into it. We may even
+venture to connect the Madonna pictures with the temple images of the
+classic period, to explain why it was natural to paint the object of
+worship seated exactly facing the worshipper. Thus we may separate the
+two classes of pictures, the one giving an object of worship, and thus
+taking naturally, as has been said, the pyramidal, symmetrical shape,
+and being moulded to symmetry by all other suggestions of technique;
+the other aiming at nothing except logical clearness. This antithesis
+of the symbol and the story has a most interesting parallel in the two
+great classes of primitive art--the one symbolic, merely suggestive,
+shaped by the space it had to fill, and so degenerating into the
+slavishly symmetrical, the other descriptive, 'story-telling' and
+without a trace of space composition. On neither side is there
+evidence of direct aesthetic feeling. Only in the course of artistic
+development do we find the rigid, yet often unbalanced, symmetry
+relaxing into a free substitutional symmetry, and the formless
+narrative crystallizing into a really unified and balanced space form.
+The two antitheses approach each other in the 'balance' of the
+masterpieces of civilized art--in which, for the first time, a real
+feeling for space composition makes itself felt.
+
+       *       *       *       *       *
+
+
+
+
+THE AESTHETICS OF UNEQUAL DIVISION.
+
+BY ROSWELL PARKER ANGIER.
+
+
+PART I.
+
+
+The present paper reports the beginnings of an investigation designed
+to throw light on the psychological basis of our aesthetic pleasure in
+unequal division. It is confined to horizontal division. Owing to the
+prestige of the golden section, that is, of that division of the
+simple line which gives a short part bearing the same ratio to the
+long part that the latter bears to the whole line, experimentation of
+this sort has been fettered. Investigators have confined their efforts
+to statistical records of approximations to, or deviations from, the
+golden section. This exalts it into a possible aesthetic norm. But such
+a gratuitous supposition, by limiting the inquiry to the verification
+of this norm, distorts the results, tempting one to forget the
+provisional nature of the assumption, and to consider divergence from
+the golden section as an error, instead of another example, merely, of
+unequal division. We have, as a matter of fact, on one hand,
+investigations that do not verify the golden section, and, on the
+other hand, a series of attempts to account for our pleasure in it, as
+if it were, beyond dispute, the norm. In this way the statistical
+inquiries have been narrowed in scope, and interpretation retarded and
+misdirected. Statistically our aim should be to ascertain within how
+wide limits aesthetically pleasing unequal divisions fall; and an
+interpretative principle must be flexible enough to include persistent
+variations from any hypothetical norm, unless they can be otherwise
+accounted for. If it is not forced on us, we have, in either case,
+nothing to do with the golden section.
+
+Since Fechner, the chief investigation in the aesthetics of simple
+forms is that of Witmer, in 1893.[1] Only a small part of his work
+relates to horizontal division, but enough to show what seems to me a
+radical defect in statistical method, namely, that of accepting a
+general average of the average judgments of the several subjects, as
+'the most pleasing relation' or 'the most pleasing proportion.'[2]
+Such a total average may fall wholly without the range of judgments of
+every subject concerned, and tells us nothing certain about the
+specific judgments of any one. Even in the case of the individual
+subject, if he shows in the course of long experimentation that he has
+two distinct sets of judgments, it is not valid to say that his real
+norm lies between the two; much less when several subjects are
+concerned. If averages are data to be psychophysically explained, they
+must fall well within actual individual ranges of judgment, else they
+correspond to no empirically determinable psychophysical processes.
+Each individual is a locus of possible aesthetic satisfactions. Since
+such a locus is our ultimate basis for interpretation, it is inept to
+choose, as 'the most pleasing proportion,' one that may have no
+correspondent empirical reference. The normal or ideal individual,
+which such a norm implies, is not a psychophysical entity which may
+serve as a basis of explanation, but a mathematical construction.
+
+   [1] Witmer, Lightner: 'Zur experimentellen Aesthetik einfacher
+   raeumlicher Formverhaeltnisse,' _Phil. Studien_, 1893, IX., S.
+   96-144, 209-263.
+
+This criticism would apply to judgments of unequal division on either
+side the center of a horizontal line. It would apply all the more to
+any general average of judgments including both sides, for, as we
+shall soon see, the judgments of individuals differ materially on the
+two sides, and this difference itself may demand its explanation. And
+if we should include within this average, judgments above and below
+the center of a vertical line, we should have under one heading four
+distinct sets of averages, each of which, in the individual cases,
+might show important variations from the others, and therefore require
+some variation of explanation. And yet that great leveller, the
+general average, has obliterated these vital differences, and is
+recorded as indicating the 'most pleasing proportion.'[3] That such an
+average falls near the golden section is immaterial. Witmer himself,
+as we shall see,[4] does not set much store by this coincidence as a
+starting point for explanation, since he is averse to any mathematical
+interpretation, but he does consider the average in question
+representative of the most pleasing division.
+
+   [2] _op. cit._, 212-215.
+
+   [3] Witmer: _op. cit._, S. 212-215.
+
+   [4] _op. cit._, S. 262.
+
+I shall now, before proceeding to the details of the experiment to be
+recorded, review, very briefly, former interpretative tendencies.
+Zeising found that the golden section satisfied his demand for unity
+and infinity in the same beautiful object.[5] In the golden section,
+says Wundt,[6] there is a unity involving the whole; it is therefore
+more beautiful than symmetry, according to the aesthetic principle that
+that unification of spatial forms which occurs without marked effort,
+which, however, embraces the greater manifold, is the more pleasing.
+But to me this manifold, to be aesthetic, must be a sensible manifold,
+and it is still a question whether the golden section set of relations
+has an actual correlate in sensations. Witmer,[7] however, wrote, at
+the conclusion of his careful researches, that scientific aesthetics
+allows no more exact statement, in interpretation of the golden
+section, than that it forms 'die rechte Mitte' between a too great and
+a too small variety. Nine years later, in 1902, he says[8] that the
+preference for proportion over symmetry is not a demand for an
+equality of ratios, but merely for greater variety, and that 'the
+amount of unlikeness or variety that is pleasing will depend upon the
+general character of the object, and upon the individual's grade of
+intelligence and aesthetic taste.' Kuelpe[9] sees in the golden section
+'a special case of the constancy of the relative sensible
+discrimination, or of Weber's law.' The division of a line at the
+golden section produces 'apparently equal differences' between minor
+and major, and major and whole. It is 'the pleasingness of apparently
+equal differences.'
+
+   [5] Zelsing, A.: 'Aesthetische Forschungen,' 1855, S. 172;
+   'Neue Lehre von den Proportionen des menschlichen Koerpera,'
+   1854, S. 133-174.
+
+   [6] Wundt, W.: 'Physiologische Psychologie,' 4te Aufl.,
+   Leipzig, 1893, Bd. II., S. 240 ff.
+
+   [7] _op. cit._, S. 262.
+
+   [8] Witmer, L.: 'Analytical Psychology,' Boston, 1902, p. 74.
+
+   [9] Kuelpe, O.: 'Outlines of Psychology,' Eng. Trans., London,
+   1895, pp. 253-255.
+
+These citations show, in brief form, the history of the interpretation
+of our pleasure in unequal division. Zeising and Wundt were alike in
+error in taking the golden section as the norm. Zeising used it to
+support a philosophical theory of the beautiful. Wundt and others too
+hastily conclude that the mathematical ratios, intellectually
+discriminated, are also sensibly discriminated, and form thus the
+basis of our aesthetic pleasure. An extension of this principle would
+make our pleasure in any arrangement of forms depend on the
+mathematical relations of their parts. We should, of course, have no
+special reason for choosing one set of relationships rather than
+another, nor for halting at any intricacy of formulae. But we cannot
+make experimental aesthetics a branch of applied mathematics. A theory,
+if we are to have psychological explanation at all, must be pertinent
+to actual psychic experience. Witmer, while avoiding and condemning
+mathematical explanation, does not attempt to push interpretation
+beyond the honored category of unity in variety, which is applicable
+to anything, and, in principle, is akin to Zeising's unity and
+infinity. We wish to know what actual psychophysical functionings
+correspond to this unity in variety. Kuelpe's interpretation is such an
+attempt, but it seems clear that Weber's law cannot be applied to the
+division at the golden section. It would require of us to estimate the
+difference between the long side and the short side to be equal to
+that of the long side and the whole. A glance at the division shows
+that such complex estimation would compare incomparable facts, since
+the short and the long parts are separated, while the long part is
+inclosed in the whole. Besides, such an interpretation could not apply
+to divisions widely variant from the golden section.
+
+This paper, as I said, reports but the beginnings of an investigation
+into unequal division, confined as it is to results obtained from the
+division of a simple horizontal line, and to variations introduced as
+hints towards interpretation. The tests were made in a partially
+darkened room. The apparatus rested on a table of ordinary height, the
+part exposed to the subject consisting of an upright screen, 45 cm.
+high by 61 cm. broad, covered with black cardboard, approximately in
+the center of which was a horizontal opening of considerable size,
+backed by opal glass. Between the glass and the cardboard, flush with
+the edges of the opening so that no stray light could get through, a
+cardboard slide was inserted from behind, into which was cut the
+exposed figure. A covered electric light illuminated the figure with a
+yellowish-white light, so that all the subject saw, besides a dim
+outline of the apparatus and the walls of the room, was the
+illuminated figure. An upright strip of steel, 11/2 mm. wide, movable in
+either direction horizontally by means of strings, and controlled by
+the subject, who sat about four feet in front of the table, divided
+the horizontal line at any point. On the line, of course, this
+appeared as a movable dot. The line itself was arbitrarily made 160
+mm. long, and 11/2 mm. wide. The subject was asked to divide the line
+unequally at the most pleasing place, moving the divider from one end
+slowly to the other, far enough to pass outside any pleasing range,
+or, perhaps, quite off the line; then, having seen the divider at all
+points of the line, he moved it back to that position which appealed
+to him as most pleasing. Record having been made of this, by means of
+a millimeter scale, the subject, without again going off the line,
+moved to the pleasing position on the other side of the center. He
+then moved the divider wholly off the line, and made two more
+judgments, beginning his movement from the other end of the line.
+These four judgments usually sufficed for the simple line for one
+experiment. In the course of the experimentation each of nine subjects
+gave thirty-six such judgments on either side the center, or
+seventy-two in all.
+
+In Fig. 1, I have represented graphically the results of these
+judgments. The letters at the left, with the exception of _X_, mark
+the subjects. Beginning with the most extreme judgments on either side
+the center, I have erected modes to represent the number of judgments
+made within each ensuing five millimeters, the number in each case
+being denoted by the figure at the top of the mode. The two vertical
+dot-and-dash lines represent the means of the several averages of all
+the subjects, or the total averages. The short lines, dropped from
+each of the horizontals, mark the individual averages of the divisions
+either side the center, and at _X_ these have been concentrated into
+one line. Subject _E_ obviously shows two pretty distinct fields of
+choice, so that it would have been inaccurate to condense them all
+into one average. I have therefore given two on each side the center,
+in each case subsuming the judgments represented by the four end modes
+under one average. In all, sixty judgments were made by _E_ on each
+half the line. Letter _E¹_ represents the first thirty-six; _E squared_ the
+full number. A comparison of the two shows how easily averages shift;
+how suddenly judgments may concentrate in one region after having been
+for months fairly uniformly distributed. The introduction of one more
+subject might have varied the total averages by several points. Table
+I. shows the various averages and mean variations in tabular form.
+
+
+TABLE I.
+                         Left.            Right.
+                      Div.  M.V.        Div.   M.V.
+        _A_      54    2.6         50     3.4
+        _B_      46    4.5         49     5.7
+        _C_      75    1.8         71     1.6
+        _D_      62    4.4         56     4.1
+        _E¹_     57   10.7         60     8.7
+        _F_      69    2.6         69     1.6
+        _G_      65    3.7         64     2.7
+        _H_      72    3.8         67     2.1
+        _J_      46    1.9         48     1.3
+                 --    ---         --     ---
+Total            60    3.9         59     3.5
+
+Golden Section = 61.1.
+
+    ¹These are _E_'s general averages on 36 judgments. Fig. 1,
+    however, represents two averages on each side the center, for
+    which the figures are, on the left, 43 with M.V. 3.6; and 66
+    with M.V. 5.3. On the right, 49, M.V. 3.1; and 67, M.V. 2.7.
+    For the full sixty judgments, his total average was 63 on the
+    left, and 65 on the right, with mean variations of 9.8 and 7.1
+    respectively. The four that _E squared_ in Fig. 1 shows graphically
+    were, for the left, 43 with M.V. 3.6; and 68, M.V. 5.1. On the
+    right, 49, M.V. 3.1; and 69, M.V. 3.4.
+
+
+[Illustration: FIG. 1.]
+
+Results such as are given in Fig. 1, appear to warrant the criticism
+of former experimentation. Starting with the golden section, we find
+the two lines representing the total averages running surprisingly
+close to it. This line, however, out of a possible eighteen chances,
+only twice (subjects _D_ and _G_) falls wholly within the mode
+representing the maximum number of judgments of any single subject. In
+six cases (_C_ twice, _F_, _H_, _J_ twice) it falls wholly without any
+mode whatever; and in seven (_A_, _B_ twice, _E_, _F_, _G_, _H_)
+within modes very near the minimum. Glancing for a moment at the
+individual averages, we see that none coincides with the total
+(although _D_ is very near), and that out of eighteen, only four (_D_
+twice, _G_ twice) come within five millimeters of the general average,
+while eight (_B_, _C_, _J_ twice each, _F_, _H_) lie between ten and
+fifteen millimeters away. The two total averages (although near the
+golden section), are thus chiefly conspicuous in showing those regions
+of the line that were avoided as not beautiful. Within a range of
+ninety millimeters, divided into eighteen sections of five millimeters
+each, there are ten such sections (50 mm.) each of which represents
+the maximum of some one subject. The range of maximum judgments is
+thus about one third the whole line. From such wide limits it is, I
+think, a methodological error to pick out some single point, and
+maintain that any explanation whatever of the divisions there made
+interprets adequately our pleasure in unequal division. Can, above
+all, the golden section, which in only two cases (_D_, _G_) falls
+within the maximum mode; in five (_A_, _C_, _F_, _J_ twice) entirely
+outside all modes, and in no single instance within the maximum on
+both sides the center--can this seriously play the role of aesthetic
+norm?
+
+I may state here, briefly, the results of several sets of judgments on
+lines of the same length as the first but wider, and on other lines of
+the same width but shorter. There were not enough judgments in either
+case to make an exact comparison of averages valuable, but in three
+successively shorter lines, only one subject out of eight varied in a
+constant direction, making his divisions, as the line grew shorter,
+absolutely nearer the ends. He himself felt, in fact, that he kept
+about the same absolute position on the line, regardless of the
+successive shortenings, made by covering up the ends. This I found to
+be practically true, and it accounts for the increasing variation
+toward the ends. Further, with all the subjects but one, two out of
+three pairs of averages (one pair for each length of line) bore the
+same relative positions to the center as in the normal line. That is,
+if the average was nearer the center on the left than on the right,
+then the same held true for the smaller lines. Not only this. With one
+exception, the positions of the averages of the various subjects, when
+considered relatively to one another, stood the same in the shorter
+lines, in two cases out of three. In short, not only did the pair of
+averages of each subject on each of the shorter lines retain the same
+relative positions as in the normal line, but the zone of preference
+of any subject bore the same relation to that of any other. Such
+approximations are near enough, perhaps, to warrant the statement that
+the absolute length of line makes no appreciable difference in the
+aesthetic judgment. In the wider lines the agreement of the judgments
+with those of the normal line was, as might be expected, still closer.
+In these tests only six subjects were used. As in the former case,
+however, _E_ was here the exception, his averages being appreciably
+nearer the center than in the original line. But his judgments of this
+line, taken during the same period, were so much on the central tack
+that a comparison of them with those of the wider lines shows very
+close similarity. The following table will show how _E_'s judgments
+varied constantly towards the center:
+
+                                                            AVERAGE.
+                                                             L.   R.
+  1. Twenty-one judgments (11 on L. and 10 on R.) during
+  experimentation on _I¹, I squared_, etc., but not on same days.   64   65
+
+  2. Twenty at different times, but immediately before
+   judging on _I¹, I squared_, etc.                                 69   71
+
+  3. Eighteen similar judgments, but immediately after
+  judging on _I¹, I squared_, etc.                                  72   71
+
+  4. Twelve taken after all experimentation with _I¹_,
+  _I squared_, etc., had ceased.                                    71   69
+
+
+The measurements are always from the ends of the line. It looks as if
+the judgments in (3) were pushed further to the center by being
+immediately preceded by those on the shorter and the wider lines, but
+those in (1) and (2) differ markedly, and yet were under no such
+influences.
+
+From the work on the simple line, with its variations in width and
+length, these conclusions seem to me of interest. (1) The records
+offer no one division that can be validly taken to represent 'the most
+pleasing proportion' and from which interpretation may issue. (2) With
+one exception (_E_) the subjects, while differing widely from one
+another in elasticity of judgment, confined themselves severally to
+pretty constant regions of choice, which hold, relatively, for
+different lengths and widths of line. (3) Towards the extremities
+judgments seldom stray beyond a point that would divide the line into
+fourths, but they approach the center very closely. Most of the
+subjects, however, found a _slight_ remove from the center
+disagreeable. (4) Introspectively the subjects were ordinarily aware
+of a range within which judgments might give equal pleasure, although
+a slight disturbance of any particular judgment would usually be
+recognized as a departure from the point of maximum pleasingness. This
+feeling of potential elasticity of judgment, combined with that of
+certainty in regard to any particular instance, demands--when the
+other results are also kept in mind--an interpretative theory to take
+account of every judgment, and forbids it to seize on an average as
+the basis of explanation for judgments that persist in maintaining
+their aesthetic autonomy.
+
+I shall now proceed to the interpretative part of the paper. Bilateral
+symmetry has long been recognized as a primary principle in aesthetic
+composition. We inveterately seek to arrange the elements of a figure
+so as to secure, horizontally, on either side of a central point of
+reference, an objective equivalence of lines and masses. At one
+extreme this may be the rigid mathematical symmetry of geometrically
+similar halves; at the other, an intricate system of compensations in
+which size on one side is balanced by distance on the other,
+elaboration of design by mass, and so on. Physiologically speaking,
+there is here a corresponding equality of muscular innervations, a
+setting free of bilaterally equal organic energies. Introspection will
+localize the basis of these in seemingly equal eye movements, in a
+strain of the head from side to side, as one half the field is
+regarded, or the other, and in the tendency of one half the body
+towards a massed horizontal movement, which is nevertheless held in
+check by a similar impulse, on the part of the other half, in the
+opposite direction, so that equilibrium results. The psychic
+accompaniment is a feeling of balance; the mind is aesthetically
+satisfied, at rest. And through whatever bewildering variety of
+elements in the figure, it is this simple bilateral equivalence that
+brings us to aesthetic rest. If, however, the symmetry is not good, if
+we find a gap in design where we expected a filling, the accustomed
+equilibrium of the organism does not result; psychically there is lack
+of balance, and the object is aesthetically painful. We seem to have,
+then, in symmetry, three aspects. First, the objective quantitative
+equality of sides; second, a corresponding equivalence of bilaterally
+disposed organic energies, brought into equilibrium because acting in
+opposite directions; third, a feeling of balance, which is, in
+symmetry, our aesthetic satisfaction.
+
+It would be possible, as I have intimated, to arrange a series of
+symmetrical figures in which the first would show simple geometrical
+reduplication of one side by the other, obvious at a glance; and the
+last, such a qualitative variety of compensating elements that only
+painstaking experimentation could make apparent what elements balanced
+others. The second, through its more subtle exemplification of the
+rule of quantitative equivalence, might be called a higher order of
+symmetry. Suppose now that we find given, objects which, aesthetically
+pleasing, nevertheless present, on one side of a point of reference,
+or center of division, elements that actually have none corresponding
+to them on the other; where there is not, in short, _objective_
+bilateral equivalence, however subtly manifested, but, rather, a
+complete lack of compensation, a striking asymmetry. The simplest,
+most convincing case of this is the horizontal straight line,
+unequally divided. Must we, because of the lack of objective equality
+of sides, also say that the bilaterally equivalent muscular
+innervations are likewise lacking, and that our pleasure consequently
+does not arise from the feeling of balance? A new aspect of
+psychophysical aesthetics thus presents itself. Must we invoke a new
+principle for horizontal unequal division, or is it but a subtly
+disguised variation of the more familiar symmetry? And in vertical
+unequal division, what principle governs? A further paper will deal
+with vertical division. The present paper, as I have said, offers a
+theory for the horizontal.
+
+To this end, there were introduced, along with the simple line figures
+already described, more varied ones, designed to suggest
+interpretation. One whole class of figures was tried and discarded
+because the variations, being introduced at the ends of the simple
+line, suggested at once the up-and-down balance of the lever about the
+division point as a fulcrum, and became, therefore, instances of
+simple symmetry. The parallel between such figures and the simple line
+failed, also, in the lack of homogeneity on either side the division
+point in the former, so that the figure did not appear to center at,
+or issue from the point of division, but rather to terminate or
+concentrate in the end variations. A class of figures that obviated
+both these difficulties was finally adopted and adhered to throughout
+the work. As exposed, the figures were as long as the simple line, but
+of varying widths. On one side, by means of horizontal parallels, the
+horizontality of the original line was emphasized, while on the other
+there were introduced various patterns (fillings). Each figure was
+movable to the right or the left, behind a stationary opening 160 mm.
+in length, so that one side might be shortened to any desired degree
+and the other at the same time lengthened, the total length remaining
+constant. In this way the division point (the junction of the two
+sides) could be made to occupy any position on the figure. The figures
+were also reversible, in order to present the variety-filling on the
+right or the left.
+
+If it were found that such a filling in one figure varied from one in
+another so that it obviously presented more than the other of some
+clearly distinguishable element, and yielded divisions in which it
+occupied constantly a shorter space than the other, then we could,
+theoretically, shorten the divisions at will by adding to the filling
+in the one respect. If this were true it would be evident that what we
+demand is an equivalence of fillings--a shorter length being made
+equivalent to the longer horizontal parallels by the addition of more
+of the element in which the two short fillings essentially differ. It
+would then be a fair inference that the different lengths allotted by
+the various subjects to the short division of the simple line result
+from varying degrees of substitution of the element, reduced to its
+simplest terms, in which our filling varied. Unequal division would
+thus be an instance of bilateral symmetry.
+
+The thought is plausible. For, in regarding the short part of the line
+with the long still in vision, one would be likely, from the aesthetic
+tendency to introduce symmetry into the arrangement of objects, to be
+irritated by the discrepant inequality of the two lengths, and, in
+order to obtain the equality, would attribute an added significance to
+the short length. If the assumption of bilateral equivalence
+underlying this is correct, then the repetition, in quantitative
+terms, on one side, of what we have on the other, constitutes the
+unity in the horizontal disposition of aesthetic elements; a unity
+receptive to an almost infinite variety of actual visual
+forms--quantitative identity in qualitative diversity. If presented
+material resists objective symmetrical arrangement (which gives, with
+the minimum expenditure of energy, the corresponding bilateral
+equivalence of organic energies) we obtain our organic equivalence in
+supplementing the weaker part by a contribution of energies for which
+it presents no obvious visual, or objective, basis. From this there
+results, by reaction, an objective equivalence, for the psychic
+correlate of the additional energies freed is an attribution to the
+weaker part, in order to secure this feeling of balance, of some added
+qualities, which at first it did not appear to have. In the case of
+the simple line the lack of objective symmetry that everywhere meets
+us is represented by an unequal division. The enhanced significance
+acquired by the shorter part, and its psychophysical basis, will
+engage us further in the introspection of the subjects, and in the
+final paragraph of the paper. In general, however, the phenomenon that
+we found in the division of the line--the variety of divisions given
+by any one object, and the variations among the several subjects--is
+easily accounted for by the suggested theory, for the different
+subjects merely exemplify more fixedly the shifting psychophysical
+states of any one subject.
+
+In all, five sets of the corrected figures were used. Only the second,
+however, and the fifth (chronologically speaking) appeared indubitably
+to isolate one element above others, and gave uniform results. But
+time lacked to develop the fifth sufficiently to warrant positive
+statement. Certain uniformities appeared, nevertheless, in all the
+sets, and find due mention in the ensuing discussion. The two figures
+of the second set are shown in Fig. 2. Variation No. III. shows a
+design similar to that of No. II., but with its parts set more closely
+together and offering, therefore, a greater complexity. In Table II.
+are given the average divisions of the nine subjects. The total length
+of the figure was, as usual, 160 mm. Varying numbers of judgments were
+made on the different subjects.
+
+[Illustration: FIG. 2.]
+
+
+TABLE II.
+
+          No. I.   No. II.   No. I. (reversed).  No. II. (reversed).
+          L.  R.    L.  R.         R.  L.              R.  L.
+
+  A       55   0    48   0         59   0              50   0
+  B       59   0    44   0         63   0              52   0
+  C       58   0    56   0         52   0              50   0
+  D       60   0    56   0         60   0              55   0
+  E       74  59    73  65         74  60              75  67
+  F       61  67    60  66         65  64              62  65
+  G       64  64    62  68         63  64              53  67
+  H       76  68    75  64         66  73              67  71
+  J       49   0    41   0         50   0              42   0
+          --  --    --  --         --  --              --  --
+  Total.  61  64    57  65         61  65              54  67
+
+
+With the complex fillings at the left, it will be seen, firstly, that
+in every case the left judgment on No. III. is less than that on No.
+II. With the figures reversed, the right judgments on No. III. are
+less than on No. II., with the exception of subjects _E_ and _H_.
+Secondly, four of the subjects only (_E_, _F_, _G_ and _H_) had
+judgments also on the side which gave the complex filling the larger
+space; to _E_, _F_ and _G_, these were secondary preferences; to _H_
+they were always primary. Thirdly, the judgments on No. III. are less,
+in spite of the fact that the larger component parts of No. II., might
+be taken as additional weight to that side of the line, and given,
+therefore, the shorter space, according to the principle of the lever.
+
+The subjects, then, that appear not to substantiate our suggested
+theory are _E_ and _H_, who in the reversed figures give the shorter
+space to the less complex filling, and _F_ and _G_, who, together with
+_E_ and _H_, have always secondary judgments that allot to either
+complex filling a larger space than to the simple horizontal.
+Consider, first, subjects _E_ and _H_. For each, the difference in
+division of II. and III. is in any case very slight. Further, subject
+_E_, in judgments where the complex filling _exceeds_ the horizontal
+parallels in length, still gives the more complex of the two fillings
+markedly the shorter space, showing, apparently, that its additional
+complexity works there in accord with the theory. There was, according
+to his introspection, another principle at work. As a figure, he
+emphatically preferred II. to III. The filling of II. made up, he
+found, by its greater interest, for lack of length. He here secured a
+balance, in which the interest of the complex material compensated for
+the greater _extent_ of the simpler horizontals. This accounts for its
+small variation from III., and even for its occupying the smaller
+space. But in judgments giving the two complex fillings the larger
+space, the more interesting material _exceeded_ in extent the less
+interesting. In such divisions the balance was no longer uppermost in
+mind, but the desire to get as much as possible of the interesting
+filling. To this end the horizontal parallels were shortened as far as
+they could be without becoming insignificant. But unless some element
+of balance were there (although not present to introspection) each
+complex filling, when up for judgment, would have been pushed to the
+same limit. It, therefore, does seem, in cases where the complex
+fillings occupied a larger space than the horizontals, that the
+subject, not trying consciously to secure a balance of _interests_,
+was influenced more purely by the factor of complexity, and that his
+judgments lend support to our theory.
+
+Subject H was the only subject who consistently _preferred_ to have
+all complex fillings occupy the larger space. Introspection invariably
+revealed the same principle of procedure--he strove to get as much of
+the interesting material as he could. He thought, therefore, that in
+every case he moved the complex filling to that limit of the pleasing
+range that he found on the simple line, which would yield him most of
+the filling. Balance did not appear prominent in his introspection. A
+glance, however, at the results shows that his introspection is
+contradicted. For he maintains approximately the same division on the
+right in all the figures, whether reversed or not, and similarly on
+the left. The average on the right for all four is 67; on the left it
+is 74. Comparing these with the averages on the simple line, we see
+that the right averages coincide exactly, while the left but slightly
+differ. I suspect, indeed, that the fillings did not mean much to _H_,
+except that they were 'interesting' or 'uninteresting'; that aside
+from this he was really abstracting from the filling and making the
+same judgments that he would make on the simple line. Since he was
+continually aware that they fell within the 'pleasing range' on the
+simple line, this conclusion is the more plausible.
+
+Perhaps these remarks account for the respective uniformities of the
+judgments of _E_ and _H_, and their departure from the tendency of the
+other subjects to give the more complex filling constantly the shorter
+space. But subjects _F_ and _G_ also had judgments (secondary with
+both of them) giving to the complex filling a larger extent than to
+the parallels. With them one of two principles, I think, applies: The
+judgments are either instances of abstraction from the filling, as
+with _H_, or one of simpler gravity or vertical balance, as
+distinguished from the horizontal equivalence which I conceive to be
+at the basis of the other divisions. With _F_ it is likely to be the
+latter, since the divisions of the figures under discussion do not
+approach very closely those of the simple line, and because
+introspectively he found that the divisions giving the complex the
+larger space were 'balance' divisions, while the others were
+determined with 'reference to the character of the fillings.' From _G_
+I had no introspection, and the approximation of his judgments to
+those he gave for the simple line make it probable that with him the
+changes in the character of the filling had little significance. The
+average of his judgments in which the complex filling held the greater
+space is 66, while the averages on the simple line were 65 on the
+left, and 64 on the right. And, in general, abstraction from filling
+was easy, and to be guarded against. Subject _C_, in the course of the
+work, confessed to it, quite unsolicited, and corrected himself by
+giving thenceforth _all_ complex fillings much smaller space than
+before. Two others noticed that it was particularly hard not to
+abstract. Further, none of the four subjects mentioned (with that
+possible exception of _E_) showed a sensitiveness similar to that of
+the other five.
+
+With the exception of _H_, and in accord with the constant practice of
+the other five, these subjects, too, occasionally found no pleasing
+division in which the complex filling preponderated in length over the
+horizontals. It was uniformly true, furthermore, in every variation
+introduced in the course of the investigation, involving a complex and
+a simple filling, that all the nine subjects but _H_ _preferred_ the
+complex in the shorter space; that five refused any divisions offering
+it in the larger space; that these five showed more sensitiveness to
+differences in the character of fillings; and that with one exception
+(_C_) the divisions of the simple line which these subjects gave were
+nearer the ends than those of the others. It surely seems plausible
+that those most endowed with aesthetic sensitiveness would find a
+division near the center more unequal than one nearer the end; for one
+side only slightly shorter than the other would at once seem to mean
+the same thing to them, and yet, because of the obvious difference in
+length, be something markedly different, and they would therefore
+demand a part short enough to give them sharp qualitative difference,
+with, however, in some way, quantitative equivalence. When the short
+part is too long, it is overcharged with significance, it strives to
+be two things at once and yet neither in its fulness.
+
+We thus return to the simple line. I have considered a series of
+judgments on it, and a series on two different figures, varying in the
+degree of complexity presented, in one of their fillings. It remains
+very briefly to see if the introspection on the simple line furnishes
+further warrant for carrying the complexities over into the simple
+line and so giving additional validity to the outlined theory of
+substitution. The following phrases are from introspective notes.
+
+_A_. Sweep wanted over long part. More attention to short.
+Significance of whole in short. Certainly a concentration of interest
+in the short. Short is efficacious. Long means rest; short is the
+center of things. Long, an effortless activity; short, a more
+strenuous activity. When complex fillings are introduced, subject is
+helped out; does not have to put so much into the short division. In
+simple line, subject _introduces_ the concentration. In complex
+figures the concentration is objectified. In _equal_ division subject
+has little to do with it; the _unequal_ depends on the subject--it
+calls for appreciation. Center of references is the division point,
+and the eye movements to right and left begin here, and here return.
+The line centers there. The balance is a horizontal affair.
+
+_B_. Center a more reposing division. Chief attention to division
+point, with side excursions to right and left, when refreshment of
+perception is needed. The balance is horizontal and not vertical.
+
+_C_. A balance with variety, or without symmetry. Centers at division
+point and wants sweep over long part. More concentration on short
+part. Subjective activity there--an introduction of energy. A
+contraction of the muscles used in active attention. Long side easier,
+takes care of itself, self-poised. Line centers at division point.
+Active with short division. Introduces activity, which is equivalent
+to the filling that the complex figures have; in these the introduced
+activity is objectified--made graphic.
+
+_D_. Focal point at division point: wants the interesting things in a
+picture to occupy the left (when short division is also on left).
+Short division the more interesting and means greater complication.
+When the pleasing division is made, eyes move first over long and then
+over short. Division point the center of real reference from which
+movements are made.
+
+_E_. No reference to center in making judgments; hurries over center.
+All portions of simple line of equal interest; but in unequal division
+the short gets a non-apparent importance, for the line is then a
+scheme for the representation of materials of different interest
+values. When the division is too short, the imagination refuses to
+give it the proportionally greater importance that it would demand.
+When too long it is too near equality. In enjoying line, the division
+point is fixed, with shifts of attention from side to side. An
+underlying intellectual assignment of more value to short side, and
+then the sense-pleasure comes; the two sides have then an equality.
+
+_F_. Middle vulgar, common, prosaic; unequal lively. Prefers the
+lively. Eyes rest on division point, moving to the end of long and
+then of short. Ease, simplicity and restfulness are proper to the long
+part of complex figures. Short part of simple line looks wider,
+brighter and more important than long.
+
+_G_. Unequal better than equal. Eye likes movement over long and then
+over short. Subject interested only in division point. Short part
+gives the aesthetic quality to the line.
+
+_H_. Center not wanted. Division point the center of interest. (No
+further noteworthy introspection from _H_, but concerning complex
+figures he said that he wanted simple or the compact on the short, and
+the interesting on the long.)
+
+These introspective notes were given at different times, and any
+repetitions serve only to show constancy. The subjects were usually
+very certain of their introspection. In general it appears to me to
+warrant these three statements: (1) That the center of interest is the
+division point, whence eye-movements, or innervations involving,
+perhaps, the whole motor system, are made to either side. (2) That
+there is some sort of balance or equivalence obtained (a bilateral
+symmetry), which is not, however, a vertical balance--that is, one of
+weights pulling downwards, according to the principle of the lever.
+All the subjects repudiated the suggestion of vertical balance. (3)
+That the long side means ease and simplicity, and represents
+graphically exactly what it means; that the short side means greater
+intensity, concentration, or complexity, and that this is substituted
+by the subject; the short division, unlike the long, means something
+that it does not graphically represent.
+
+So much for the relation between what is objectively given and the
+significance subjectively attributed to it. There remains still the
+translation into psychophysical terms. The results on the complex
+figures (showing that a division may be shortened by making the
+innervations on that side increasingly more involved) lend
+plausibility to the interpretation that the additional significance
+is, in visual terms, a greater intricacy or difficulty of
+eye-movement, actual or reproduced; or, in more general terms, a
+greater tension of the entire motor system. In such figures the
+psychophysical conditions for our pleasure in the unequal division of
+the simple horizontal line are merely graphically symbolized, not
+necessarily duplicated. On page 553 I roughly suggested what occurs in
+regarding the unequally divided line. More exactly, this: the long
+section of the line gives a free sweep of the eyes from the division
+point, the center, to the end; or again, a free innervation of the
+motor system. The sweep the subject makes sure of. Then, with that as
+standard, the aesthetic impulse is to secure an equal and similar
+movement, from the center, in the opposite direction. It is checked,
+however, by the end point of the short side. The result is the
+innervation of antagonistic muscles, by which the impression is
+intensified. For any given subject, then, the pleasing unequal
+division is at that point which causes quantitatively equal
+physiological discharges, consisting of the simple movement, on one
+hand, and, on the other, the same kind of movement, compounded with
+the additional innervation of the antagonists resulting from the
+resistance of the end point. Since, when the characteristic movements
+are being made for one side, the other is always in simultaneous
+vision, the sweep receives, by contrast, further accentuation, and the
+innervation of antagonists doubtless begins as soon as movement on the
+short side is begun. The whole of the short movement is, therefore,
+really a resultant of the tendency to sweep and this necessary
+innervation of antagonists. The correlate of the equivalent
+innervations is equal sensations of energy of movement coming from the
+two sides. Hence the feeling of balance. Hence (from the lack of
+unimpeded movement on the short side) the feeling there of
+'intensity,' or 'concentration,' or 'greater significance.' Hence,
+too, the 'ease,' the 'simplicity,' the 'placidity' of the long side.
+
+As in traditional symmetry, the element of unity or identity, in
+unequal division, is a repetition, in quantitative terms, on one side,
+of what is given on the other. In the simple line the _equal_ division
+gives us obviously exact objective repetition, so that the
+psychophysical correlates are more easily inferred, while the
+_unequal_ offers apparently no compensation. But the psychophysical
+contribution of energies is not gratuitous. The function of the
+increment of length on one side, which in the centrally divided line
+makes the divisions equal, is assumed in unequal division by the end
+point of the short side; the uniform motor innervations in the former
+become, in the latter, the additional innervation of antagonists,
+which gives the equality. The two are separated only in degree. The
+latter may truly be called, however, a symmetry of a higher order,
+because objectively the disposition of its elements is not graphically
+obvious, and psychophysically, the quantitative unity is attained
+through a greater variety of processes. Thus, in complex works of art,
+what at first appears to be an unsymmetrical composition, is, if
+beautiful, only a subtle symmetry. There is present, of course, an
+arithmetically unequal division of horizontal extent, aside from the
+filling. But our pleasure in this, _without_ filling, has been seen to
+be also a pleasure in symmetry. We have, then, the symmetry of equally
+divided extents and of unequally divided extents. They have in common
+bilateral equivalence of psychophysical processes; the nature of these
+differs. In both the principle of unity is the same. The variety
+through which it works is different.
+
+       *       *       *       *       *
+
+
+
+
+         STUDIES IN ANIMAL PSYCHOLOGY.
+
+
+
+
+       *       *       *       *       *
+
+
+
+
+HABIT FORMATION IN THE CRAWFISH CAMBARUS AFFINIS.[1]
+
+BY ROBERT M. YERKES AND GURRY E. HUGGINS.
+
+   [1] See also Yerkes, Robert: 'Habit-Formation in the Green
+   Crab, _Carcinus Granulalus_,' _Biological Bulletin_, Vol. III.,
+   1902, pp. 241-244.
+
+
+This paper is an account of some experiments made for the purpose of
+testing the ability of the crawfish to profit by experience. It is
+well known that most vertebrates are able to learn, but of the
+invertebrates there are several classes which have not as yet been
+tested.
+
+The only experimental study of habit formation in a crustacean which
+we have found is that of Albrecht Bethe[2] on the crab, _Carcinus
+maenas_. In his excellent paper on the structure of the nervous system
+of _Carcinus_ Bethe calls attention to a few experiments which he made
+to determine, as he puts it, whether the crab possesses psychic
+processes. The following are the observations made by him. Experiment
+I. A crab was placed in a basin which contained in its darkest corner
+an _Eledone_ (a Cephalopod). The crab at once moved into the dark
+region because of its instinct to hide, and was seized by the
+_Eledone_ and drawn under its mantle. The experimenter then quickly
+freed the crab from its enemy and returned it to the other end of the
+basin. But again the crab returned to the dark and was seized. This
+was repeated with one animal five times and with another six times
+without the least evidence that the crabs profited by their
+experiences with the _Eledone_. Experiment 2. Crabs in an aquarium
+were baited with meat. The experimenter held his hand above the food
+and each time the hungry crab seized it he caught the animal and
+maltreated it, thus trying to teach the crabs that meat meant danger.
+But as in the previous experiment several repetitions of the
+experience failed to teach the crabs that the hand should be avoided.
+From these observations Bethe concludes that _Carcinus_ has no
+'psychic qualities' (_i.e._, is unable to profit by experience), but
+is a reflex machine.
+
+   [2] Bethe, Albrecht: 'Das Centralnervensystem von _Carcinus
+   maenas_,' II. Theil., _Arch. f. mikr. Anat._, Bd. 51, 1898, S.
+   447.
+
+Bethe's first test is unsatisfactory because the crabs have a strong
+tendency to hide from the experimenter in the darkest corner. Hence,
+if an association was formed, there would necessarily be a conflict of
+impulses, and the region in which the animal would remain would depend
+upon the relative strengths of its fear of the experimenter and of the
+_Eledone_. This objection is not so weighty, however, as is that which
+must obviously be made to the number of observations upon which the
+conclusions are based. Five or even twenty-five repetitions of such an
+experiment would be an inadequate basis for the statements made by
+Bethe. At least a hundred trials should have been made. The same
+objection holds in case of the second experiment. In all probability
+Bethe's statements were made in the light of long and close
+observation of the life habits of _Carcinus_; we do not wish,
+therefore, to deny the value of his observations, but before accepting
+his conclusions it is our purpose to make a more thorough test of the
+ability of crustaceans to learn.
+
+[Illustration: FIG. 1. Ground Plan of Labyrinth. _T_, triangular
+compartment from which animal was started; _P_, partition at exit;
+_G_, glass plate closing one exit passage. Scale 1/6.]
+
+For determining whether the crawfish is able to learn a simple form of
+the labyrinth method was employed. A wooden box (Fig. 1) 35 cm. long,
+24 cm. wide and 15 cm. deep, with one end open, and at the other end
+a triangular compartment which communicated with the main portion of
+the box by an opening 5 cm. wide, served as an experiment box. At the
+open end of this box a partition (_P_) 6 cm. long divided the opening
+into two passages of equal width. Either of these passages could be
+closed with a glass plate (_G_), and the subject thus forced to escape
+from the box by the choice of a certain passage. This box, during the
+experiments, was placed in the aquarium in which the animals lived. In
+order to facilitate the movement of the crawfish toward the water, the
+open end was placed on a level with the water in the aquarium, and the
+other end was raised so that the box made an angle of 6 deg. with the
+horizontal.
+
+Experiments were made under uniform conditions, as follows. A subject
+was taken from the aquarium and placed in a dry jar for about five
+minutes, in order to increase the desire to return to the water; it
+was then put into the triangular space of the experiment box and
+allowed to find its way to the aquarium. Only one choice of direction
+was necessary in this, namely, at the opening where one of the
+passages was closed. That the animal should not be disturbed during
+the experiment the observer stood motionless immediately behind the
+box.
+
+Before the glass plate was introduced a preliminary series of tests
+was made to see whether the animals had any tendency to go to one side
+on account of inequality of illumination, of the action of gravity, or
+any other stimulus which might not be apparent to the experimenter.
+Three subjects were used, with the results tabulated.
+
+
+           Exit by       Exit by
+           Right Passage Left Passage.
+    No. 1  6              4
+    No. 2  7              3
+    No. 3  3              7
+          16             14
+
+
+Since there were more cases of exit by the right-hand passage, it was
+closed with the glass plate, and a series of experiments made to
+determine whether the crawfish would learn to avoid the blocked
+passage and escape to the aquarium by the most direct path. Between
+March 13 and April 14 each of the three animals was given sixty
+trials, an average of two a day. In Table I. the results of these
+trials are arranged in groups of ten, according to the choice of
+passages at the exit. Whenever an animal moved beyond the level of the
+partition (_P_) on the side of the closed passage the trial was
+counted in favor of the closed passage, even though the animal turned
+back before touching the glass plate and escaped by the open passage.
+
+
+TABLE I.
+
+HABIT FORMATION IN THE CRAWFISH.¹
+
+ Experiments.  No. 1        No. 2       No. 3       Totals    Per cent
+           Open Closed  Open Closed  Open Closed  Open Closed   Open
+     1-10    8     2      5     5      2     8     15    15     50.0
+    11-20    4     6      8     2      6     4     18    12     60.0
+    21-30    6     3 squared     8     2      8     2     22     7     75.8
+    31-40    9     1      8     2      8     2     25     5     83.3
+    41-50    8     2      8     2      7     3     23     7     76.6
+    51-60   10     0      8     2      9     1     27     3     90.0
+
+          TEST OF PERMANENCY OF HABIT AFTER 14 DAYS' REST.
+
+    61-70    6     4      8     2      8     2     22     8     73.3
+    (1-10)
+    71-80    6     4      8     2      7     3     21     9     70.0
+   (11-20)
+
+    ¹The experiments of this table were made by F.D. Bosworth.
+
+     squaredOne trial in which the subject failed to return to the water
+    within thirty minutes.
+
+
+In these experiments there is a gradual increase in the number of
+correct choices (_i.e._, choice of the 'open' passage) from 50 per
+cent. for the first ten trials to 90 per cent. for the last ten
+(trials 51-60). The test of permanency, made after two weeks, shows
+that the habit persisted.
+
+Although the observations just recorded indicate the ability of the
+crawfish to learn a simple habit, it seems desirable to test the
+matter more carefully under somewhat different conditions. For in the
+experiments described the animals were allowed to go through the box
+day after day without any change in the floor over which they passed,
+and as it was noted that they frequently applied their antennae to the
+bottom of the box as they moved along, it is possible that they were
+merely following a path marked by an odor or by moistness due to the
+previous trips. To discover whether this was really the case
+experiments were made in which the box was thoroughly washed out after
+each trip.
+
+The nature of the test in the experiments now to be recorded is the
+same as the preceding, but a new box was used. Fig. 2 is the floor
+plan and side view of this apparatus. It was 44.5 cm. long, 23.5 cm.
+wide and 20 cm. deep. The partition at the exit was 8.5 cm. in length.
+Instead of placing this apparatus in the aquarium, as was done in the
+previous experiments, a tray containing sand and water was used to
+receive the animals as they escaped from the box. The angle of
+inclination was also changed to 7 deg.. For the triangular space in which
+the animals were started in the preceding tests a rectangular box was
+substituted, and from this an opening 8 cm. wide by 5 cm. deep gave
+access to the main compartment of the box.
+
+[Illustration: FIG. 2. Floor Plan and Side View of Labyrinth Number 2.
+_E_, entrance chamber from which animal was started; _C_, cloth
+covering _E_; _M_, mirror; _T_, tray containing sand and water; _G_,
+glass plate; _P_, partition; _R_, right exit passage; _L_, left exit
+passage. Scale 1/8.]
+
+A large healthy crawfish was selected and subjected to tests in this
+apparatus in series of ten experiments given in quick succession. One
+series a day was given. After each test the floor was washed; as a
+result the experiments were separated from one another by a
+three-minute interval, and each series occupied from thirty minutes to
+an hour. Table II. gives in groups of five these series of ten
+observations each. The groups, indicated by Roman numerals, run from
+I. to IX., there being, therefore, 450 experiments in all. Groups I.
+and II., or the first 100 experiments, were made without having either
+of the exit passages closed, in order to see whether the animal would
+develop a habit of going out by one side or the other. It did very
+quickly, as a matter of fact, get into the habit of using the left
+passage (L.). The last sixty experiments (Groups I. and II.) show not
+a single case of escape by the right passage. The left passage was now
+closed. Group III. gives the result. The time column (_i.e._, the
+third column of the table) gives for each series of observations the
+average time in seconds occupied by the animal in escaping from the
+box. It is to be noted that the closing of the Left passage caused an
+increase in the time from 30.9 seconds for the last series of the
+second group to 90 seconds for the first series of the third group. In
+this there is unmistakable evidence of the influence of the change in
+conditions. The animal after a very few experiences under the new
+conditions began going to the Right in most cases; and after 250
+experiences it had ceased to make mistakes. Group VII. indicates only
+one mistake in fifty choices.
+
+
+TABLE II.
+
+  HABIT FORMATION AND THE MODIFICATION OF HABITS IN THE CRAWFISH.
+
+         Results in Series of Ten.   Avs. in Groups of 50.
+        Series  L.  R.  Time. L. R.        L.     R.   Time.
+ Group  I. 1    9   1    45                Per Cent.
+           2    3   7    69
+           3    9   1    20
+           4    4   6    72
+           5   10        31
+               --  --
+               35  15                      70     30   47.4
+
+       II. 1   10        29
+           2   10        30
+           3   10        30
+           4   10        28.8
+           5   10        30.9
+               --        ----
+               50                         100          30
+             ....                        ....
+      III. 1    4   6     90     2
+           2    2   8     89.2   1
+           3    1   9     36.7   1
+           4    2   8     51     2
+           5    1   9     43     2
+               --  --           --
+               10  40            7         20     80    62
+             ....                        ....
+       IV. 1    3   7    124     1
+           2    2   8     44     5
+           3    2   8     37     4
+           4       10     34
+           5    2   8            1
+               --  --           --
+                9  41           11         18     82    60
+             ....                        ....
+        V. 1       10     44     2
+           2       10     35     4
+           3    3   7     76     3
+           4    2   8     50     7
+           5    1   9     50     4
+               --  --           --
+                6  44           20         12     88    51
+             ....                        ....
+       VI. 1    2   8     45     2
+           2       10     41     5
+           3    1   9     41.8   7
+           4       10     32.7   7
+           5       10            8
+               --  --           --
+                3  47           29          6     94    40
+             ....                        ....
+      VII. 1    1   9     39     4
+           2       10     38     7
+           3       10     30.7   3
+           4       10     42     6
+           5       10     48     4
+               --  --           --
+                1  49           24          2     98    39.5
+
+                              R. L.
+                 ....                           ....
+     VIII. 1    8   2    147     1
+           2    9   1     26
+           3    8   2     49     2
+           4    9   1     38     2
+           5    9   1     41
+               --  --           --
+               43   7            5         86     14    60.2
+             ....                        ....
+      IX.  1   1   9      41
+           2   2   8      39     1
+           3      10      29
+           4   1   9      47
+           5   1   9      32     1         10     90    38
+              --  --            --
+               5  45             2
+
+
+The dotted lines at the beginning of groups indicate the closed passage.
+
+
+At the beginning of Group VIII. the Right instead of the Left passage
+was closed in order to test the ability of the animal to change its
+newly formed habit. As a result of this change in the conditions the
+animal almost immediately began going to the Left. What is most
+significant, however, is the fact that in the first trial after the
+change it was completely confused and spent over fifteen minutes
+wandering about, and trying to escape by the old way (Fig. 4
+represents the path taken). At the end of the preceding group the time
+of a trip was about 48 seconds, while for the first ten trips of Group
+VIII. the time increased to 147 seconds. This remarkable increase is
+due almost entirely to the great length of time of the first trip, in
+which the animal thoroughly explored the whole of the box and made
+persistent efforts to get out by the Right passage as it had been
+accustomed to do. It is at the same time noteworthy that the average
+time for the second series of Group VIII. is only 26 seconds.
+
+For Group IX. the conditions were again reversed, this time the Left
+passage being closed. Here the first trial was one of long and careful
+exploration, but thereafter no more mistakes were made in the first
+series, and in the group of fifty tests there were only five wrong
+choices.
+
+The fifth column, R. L. and L. R., of Table II. contains cases in
+which the subject started toward one side and then changed its course
+before reaching the partition. In Group III., for instance, when the
+Left passage was closed, the subject started toward the Left seven
+times, but in each case changed to the Right before reaching the
+partition. This is the best evidence of the importance of vision that
+these experiments furnish.
+
+The first experiments on habit formation proved conclusively that the
+crawfish is able to learn. The observations which have just been
+described prove that the labyrinth habit is not merely the following
+of a path by the senses of smell, taste or touch, but that other
+sensory data, in the absence of those mentioned, direct the animals.
+So far as these experiments go there appear to be at least four
+sensory factors of importance in the formation of a simple labyrinth
+habit: the chemical sense, touch, vision and the muscle sense. That
+the chemical sense and touch are valuable guiding senses is evident
+from even superficial observation, and of the importance of vision and
+the muscle sense we are certain from the experimental evidence at
+hand.
+
+[Illustration: FIG. 3. Path taken by crawfish while being trained to
+avoid the left passage. Marks along the glass plate and partition
+indicate contact by the antennae and chelae.]
+
+Of the significance of the sensations due to the 'direction of
+turning' in these habits the best evidence that is furnished by this
+work is that of the following observations. In case of the tests of
+Table II. the subject was, after 100 preliminary tests, trained by 250
+experiences to escape by the Right-hand passage. Now, in Groups III.
+to VII., the subject's usual manner of getting out of the closed
+passage, when by a wrong choice it happened to get into it, was to
+draw back on the curled abdomen, after the antennae and chelae had
+touched the glass plate, and then move the chelae slowly along the
+Right wall of the partition until it came to the upper end; it would
+then walk around the partition and out by the open passage. Fig. 3
+represents such a course. In Group VIII. the Right passage was closed,
+instead of the Left as previously. The first time the animal tried to
+get out of the box after this change in the conditions it walked
+directly into the Right passage. Finding this closed it at once turned
+to the Right, _as it had been accustomed to do when it came in contact
+with the glass plate_, and moved along the side of the box just as it
+did in trying to get around the end of the partition. The path taken
+by the crawfish in this experiment is represented in Fig. 4. It is
+very complex, for the animal wandered about more than fifteen minutes
+before escaping.
+
+The experiment just described to show the importance of the tendency
+to turn in a certain direction was the first one of the first series
+after the change in conditions. When given its second chance in this
+series the subject escaped directly by the Left passage in 33 seconds,
+and for the three following trips the time was respectively 25, 25 and
+30 seconds.
+
+Upon the experimental evidence presented we base the conclusion that
+crawfish are able to profit by experience in much the same way that
+insects do, but far more slowly.
+
+[Illustration: FIG. 4. Path taken by crawfish which had been trained
+to avoid the Left passage, when the Right passage was closed. Showing
+turning to the right as in Fig. 3.]
+
+It was thought that a study of the way in which crawfish right
+themselves when placed upon their backs on a smooth surface might
+furnish further evidence concerning the ability of the animals to
+profit by experience.
+
+Dearborn[3] from some observations of his concludes that there is no
+one method by which an individual usually rights itself, and,
+furthermore, that the animals cannot be trained to any one method. His
+experiments, like Bethe's, are too few to warrant any conclusions as
+to the possibility of habit formation.
+
+   [3] Dearborn, G.V.N.: 'Notes on the Individual Psychophysiology
+   of the Crayfish,' _Amer. Jour. Physiol._, Vol. 3, 1900, pp.
+   404-433.
+
+For the following experiments the subject was placed on its back on a
+smooth surface in the air and permitted to turn over in any way it
+could. Our purpose was to determine (1) whether there was any marked
+tendency to turn in a certain way, (2) whether if such was not the
+case a tendency could be developed by changing the conditions, and (3)
+how alteration in the conditions of the test would affect the turning.
+
+A great many records were taken, but we shall give in detail only a
+representative series. In Table III., 557 tests made upon four
+subjects have been arranged in four groups for convenience of
+comparison of the conditions at different periods of the training
+process. Each of these groups, if perfect, would contain 40 tests for
+each of the four subjects, but as a result of accidents II., III., and
+IV. are incomplete.
+
+
+TABLE III.
+
+  RE-TURNING OF CRAWFISH.
+
+  Group. Number of    L.    R.   Time in   Tests.
+         Animal.      Per cent.  Seconds.
+  I.       2         22.5  77.5    14.6     40
+           3         42.5  57.5     2.6     40
+           4         52.8  47.2     4.3     38
+          16         44.5  55.5    22.5     45
+          --         ----  ----    ----    ---
+                     40.6  59.4    10.8    163
+
+  Group. Number of    L.    R.   Time in   Tests.
+         Animal.      Per cent.  Seconds.
+  II       2         28    72      50       43
+           3         32    68       6.2     50
+           4         --   100       6.8     40
+          16         31.3  68.7    39.3     42
+          --         ----  ----    ----    ---
+                     22.8  77.2    25.6    175
+
+  Group. Number of    L.    R.   Time in   Tests.
+         Animal.      Per cent.  Seconds.
+  III      2         2.5   97.5    46.5     40
+          --        --     --      --       --
+           4        20     80       5.5     40
+          16        41     59      15       49
+          --         ----  ----    ----    ---
+                    21.2   78.8    22      129
+
+  Group. Number of    L.    R.   Time in   Tests.
+         Animal.      Per cent.  Seconds.
+  IV.      2          2    98      41       50
+          --         --     --      --      --
+           4         32.5  67.5     7.3     40
+          --         ----  ----    ----    ---
+                     17    83      24       90
+
+
+Group I., representing 163 tests, shows 59 per cent. to the right,
+with a time interval of 10.8 seconds (_i.e._, the time occupied in
+turning). Group II. shows 77 per cent. to the right; and so throughout
+the table there is an increase in the number of returnings to the
+right. These figures at first sight seem to indicate the formation of
+a habit, but in such case we would expect, also, a shortening of the
+time of turning. It may be, however, that the animals were gradually
+developing a tendency to turn in the easiest manner, and that at the
+same time they were becoming more accustomed to the unusual position
+and were no longer so strongly stimulated, when placed on their backs,
+to attempt to right themselves.
+
+All the subjects were measured and weighed in order to discover
+whether there were inequalities of the two sides of the body which
+would make it easier to turn to the one side than to the other. The
+chelae were measured from the inner angle of the joint of the
+protopodite to the angle of articulation with the dactylopodite. The
+carapace was measured on each side, from the anterior margin of the
+cephalic groove to the posterior extremity of the lateral edge. The
+median length of the carapace was taken, from the tip of the rostrum
+to the posterior edge, and the length of the abdomen was taken from
+this point to the edge of the telson. These measurements, together
+with the weights of three of the subjects, are given in the
+accompanying table.
+
+
+TABLE IV.
+
+MEASUREMENTS OF CRAWFISH.
+
+              Chelae.           Carapace.      Abdomen.   Weight.
+            Left. Right.  Left. Right. Median.
+
+  No.  2,    9.8  10.0    38.2   38.7   47.3    48.1      29.7
+  No.  4,    7.7   7.7    33.6   33.8   39.4    42.3      17.7
+  No. 16,   12.5  12.4    37.6   37.6   46.4    53.2      36.2
+
+
+Since these measurements indicate slightly greater size on the right
+it is very probable that we have in this fact an explanation of the
+tendency to turn to that side.
+
+To test the effect of a change in the conditions, No. 16 was tried on
+a surface slanted at an angle of 1 deg. 12'. Upon this surface the subject
+was each time so placed that the slant would favor turning to the
+right. Under these conditions No. 16 gave the following results in two
+series of tests. In the first series, consisting of 46 turns, 82.6 per
+cent. were to the right, and the average time for turning was 17.4
+seconds; in the second series, of 41 tests, there were 97.5 per cent,
+to the right, with an average time of 2.5 seconds. We have here an
+immediate change in the animal's method of re-turning caused by a
+slight change in the conditions. The subject was now tested again on
+a level surface, with the result that in 49 tests only 59 per cent.
+were toward the right, and the time was 15 seconds.
+
+
+SUMMARY.
+
+
+1. Experiments with crawfish prove that they are able to learn simple
+labyrinth habits. They profit by experience rather slowly, from fifty
+to one hundred experiences being necessary to cause a perfect
+association.
+
+2. In the crawfish the chief factors in the formation of such habits
+are the chemical sense (probably both smell and taste), touch, sight
+and the muscular sensations resulting from the direction of turning.
+The animals are able to learn a path when the possibility of following
+a scent is excluded.
+
+3. The ease with which a simple labyrinth habit may be modified
+depends upon the number of experiences the animal has had; the more
+familiar the animal is with the situation, the more quickly it changes
+its habits. If the habit is one involving the choice of one of two
+passages, reversal of the conditions confuses the subject much more
+the first time than in subsequent cases.
+
+4. Crawfish right themselves, when placed on their backs, by the
+easiest method; and this is found to depend usually upon the relative
+weight of the two sides of the body. When placed upon a surface which
+is not level they take advantage, after a few experiences, of the
+inclination by turning toward the lower side.
+
+       *       *       *       *       *
+
+
+
+
+THE INSTINCTS, HABITS, AND REACTIONS OF THE FROG.
+
+BY ROBERT MEARNS YERKES.
+
+
+PART I. THE ASSOCIATIVE PROCESSES OF THE GREEN FROG.
+
+
+I. SOME CHARACTERISTICS OF THE GREEN FROG.
+
+The common green frog, _Rana clamitans_, is greenish or brownish in
+color, usually mottled with darker spots. It is much smaller than the
+bull frog, being from two to four inches in length ordinarily, and may
+readily be distinguished from it by the presence of prominent
+glandular folds on the sides of the back. In the bull frog, _Rana
+catesbeana_, these folds are very small and indistinct. The green frog
+is found in large numbers in many of the ponds and streams of the
+eastern United States, and its peculiar rattling croak may be heard
+from early spring until fall. It is more active, and apparently
+quicker in its reactions, than the bull frog, but they are in many
+respects similar in their habits. Like the other water frogs it feeds
+on small water animals, insects which chance to come within reach and,
+in times of famine, on its own and other species of frogs. The prey is
+captured by a sudden spring and the thrusting out of the tongue, which
+is covered with a viscid secretion. Only moving objects are noticed
+and seized; the frog may starve to death in the presence of an
+abundance of food if there is no movement to attract its attention.
+Most green frogs can be fed in captivity by swinging pieces of meat in
+front of them, and those that will not take food in this way can be
+kept in good condition by placing meat in their mouths, for as soon as
+the substance has been tasted swallowing follows.
+
+The animals used for these experiments were kept in the laboratory
+during the whole year in a small wooden tank. The bottom of this tank
+was covered with sand and small stones, and a few plants helped to
+purify the water. An inch or two of water sufficed; as it was not
+convenient to have a constant stream, it was changed at least every
+other day. There was no difficulty whatever in keeping the animals in
+excellent condition.
+
+Of the protective instincts of the green frog which have come to my
+notice during these studies two are of special interest: The
+instinctive inhibition of movement under certain circumstances, and
+the guarding against attack or attempt to escape by 'crouching' and
+'puffing.' In nature the frog ordinarily jumps as soon as a strange or
+startling object comes within its field of vision, but under certain
+conditions of excitement induced by strong stimuli it remains
+perfectly quiet, as do many animals which feign death, until forced to
+move. Whether this is a genuine instinctive reaction, or the result of
+a sort of hypnotic condition produced by strong stimuli, I am not
+prepared to say. The fact that the inhibition of movement is most
+frequently noticed after strong stimulation, would seem to indicate
+that it is due to the action of stimuli upon the nervous system.
+
+What appears to be an instinctive mode of guarding against attack and
+escaping an enemy, is shown whenever the frog is touched about the
+head suddenly, and sometimes when strong stimuli are applied to other
+parts of the body. The animal presses its head to the ground as if
+trying to dive or dodge something, and inflates its body. This kind of
+action is supposed to be a method of guarding against the attack of
+snakes and other enemies which most frequently seize their prey from
+the front. It is obvious that by pressing its head to the ground the
+frog tends to prevent any animal from getting it into its mouth, and
+in the few instants' delay thus gained it is able to jump. This is
+just the movement necessary for diving, and it is probable that the
+action should be interpreted in the light of that instinctive reflex.
+The 'puffing' also would seem to make seizure more difficult. Another
+fact which favors this interpretation is that the response is most
+commonly given to stimuli which seem to come from the front and which
+for this reason could not easily be escaped by a forward jump, while
+if the stimulus is so given that it appears to be from the rear the
+animal usually jumps away immediately. We have here a complex
+protective reaction which may be called a forced movement. It is, so
+far as one can see, very much like many reflexes, although it does not
+occur quite so regularly.
+
+The machine-like accuracy of many of the frog's actions gives a basis
+for the belief that the animal is merely an automaton. Certain it is
+that one is safe in calling almost all the frog's actions reflex or
+instinctive. During months of study of the reaction-time of the frog I
+was constantly impressed with the uniformity of action and surprised
+at the absence of evidences of profiting by experience. In order to
+supplement the casual observations on the associations of the green
+frog made in the course of reaction-time experiments, the tests
+described in this paper were made. They do not give a complete view of
+the associative processes, but rather such a glimpse as will enable us
+to form some conception of the relation of the mental life of the frog
+to that of other animals. This paper presents the outlines of work the
+details of which I hope to give later.
+
+
+II. EXPERIMENTAL STUDY OF HABITS.
+
+
+A. The Chief Problems for which solutions were sought in the following
+experimental study were: (1) Those of associability in general, its
+characteristics, and the rapidity of learning; (2) of discrimination,
+including the parts played in associative processes by the different
+senses, and the delicacy of discrimination in each; (3) of the
+modifiability of associational reactions and general adaptation in the
+frog, and (4) of the permanency of associations.
+
+
+B. Simple Associations, as studied in connection with reaction-time
+work, show that the green frog profits by experience very slowly as
+compared with most vertebrates. The animals have individual
+peculiarities in reaction which enable one in a short time to
+recognize any individual. To these characteristic peculiarities they
+stick tenaciously. One, for instance, always jumps upward when
+strongly stimulated; another has a certain corner of the tank in which
+it prefers to sit. Their habits are remarkably strong and invariable,
+and new ones are slowly formed. While using a large reaction box I
+noticed that the frogs, after having once escaped from an opening
+which could be made by pushing aside a curtain at a certain point in
+the box, tended to return to that place as soon as they were again put
+into the box. This appeared to be evidence of an association; but the
+fact that such stimuli as light and the relation of the opening to the
+place at which the animals were put into the box might in themselves
+be sufficient to direct the animals to this point without the help of
+any associations which had resulted from previous experience, makes it
+unsatisfactory. In addition to the possibility of the action being due
+to specific sensory stimuli of inherent directive value, there is the
+chance of its being nothing more than the well-known phenomenon of
+repetition. Frogs, for some reason, tend to repeat any action which
+has not proved harmful or unpleasant.
+
+For the purpose of more carefully testing this kind of association, a
+small box with an opening 15 cm. by 10 cm. was arranged so that the
+animal could escape from confinement in it through the upper part of
+the opening, the lower portion being closed by a plate of glass 10 cm.
+by 10 cm., leaving a space 5 cm. by 10 cm. at the top. One subject
+placed in this box escaped in 5 minutes 42 seconds. After 5 minutes'
+rest it was given another trial, and this time got out in 2 minutes 40
+seconds. The times for a few subsequent trials were: Third, 1 minute
+22 seconds; fourth, 4 minutes 35 seconds; fifth, 2 minutes 38 seconds;
+sixth, 3 minutes 16 seconds. Although this seems to indicate some
+improvement, later experiments served to prove that the frogs did not
+readily form any associations which helped them to escape. They tended
+to jump toward the opening because it was light, but they did not
+learn with twenty or thirty experiences that there was a glass at the
+bottom to be avoided. Thinking that there might be an insufficient
+motive for escape to effect the formation of an association, I tried
+stimulating the subject with a stick as soon as it was placed in the
+box. This frightened it and caused violent struggles to escape, but
+instead of shortening the time required for escape it greatly
+lengthened it. Here was a case in which the formation of an
+association between the appearance of the upper part of the clear
+space and the satisfaction of escape from danger would have been of
+value to the frog, yet there was no evidence of adaptation to the new
+conditions within a reasonably short time. There can be little doubt
+that continuation of the training would have served to establish the
+habit. This very clearly shows the slowness of adaptation in the frog,
+in contrast with the rapidity of habit formation in the cat or chick;
+and at the same time it lends additional weight to the statement that
+instinctive actions are all-important in the frog's life. A few things
+it is able to do with extreme accuracy and rapidity, but to this list
+new reactions are not readily added. When put within the box
+described, an animal after having once escaped would sometimes make
+for the opening as if it knew perfectly the meaning of the whole
+situation, and yet the very next trial it would wander about for half
+an hour vainly struggling to escape.
+
+A considerable number of simple experiments of this kind were tried
+with results similar to those just given. The frog apparently examines
+its surroundings carefully, and just when the observer thinks it has
+made itself familiar with the situation it reacts in such a way as to
+prove beyond doubt the absence of all adaptation. In all these
+experiments it should be said, for the benefit of any who may be
+trying similar work, that only animals of exceptional activity were
+used. Most green frogs when placed in the experiment box either sit
+still a great part of the time or jump about for only a short time. It
+is very important for studies of this kind, both on account of time
+saving and the obtaining of satisfactory records, to have animals
+which are full of energy and eager to escape when in confinement. By
+choosing such subjects one may pretty certainly avoid all unhealthy
+individuals, and this, it seems to me, counterbalances the
+disadvantage of taking animals which may be unusually quick in
+learning.
+
+
+C. Complex Associations.
+
+1. _Labyrinth Habits_.--A more thorough investigation of the
+associative processes, sensory discrimination and the permanency of
+impressions has been made by the labyrinth method. A wooden box, 72
+cm. long, 28 cm. wide and 28 cm. deep, whose ground plan is
+represented by Fig. 1, served as the framework for a simple labyrinth.
+At one end was a small covered box, _A_, from which the frog was
+allowed to enter the labyrinth. This entrance passage was used in
+order that the animal might not be directed to either side by the
+disturbance caused by placing it in the box. _E_, the entrance, marks
+a point at which a choice of directions was necessary. _P_ is a
+movable partition which could be used to close either the right or the
+left passage. In the figure the right is closed, and in this case if
+the animal went to the right it had to turn back and take the left
+passage in order to get out of the box. A series of interrupted
+electrical circuits, _IC_, covered the bottom of a portion of the
+labyrinth; by closing the key, _K_, the circuit could be made whenever
+a frog rested upon any two wires of the series. When the frog happened
+to get into the wrong passage the key was closed and the animal
+stimulated. This facilitated the experiment by forcing the animal to
+seek some other way of escape, and it also furnished material for an
+association. Having passed through the first open passage, which for
+convenience we may know as the entrance passage, the animal had to
+choose again at the exit. Here one of the passages was closed by a
+plate of glass (in the figure the left) and the other opened into a
+tank containing water. The box was symmetrical and the two sides were
+in all respects the same except for the following variable conditions.
+At the entrance the partition on one side changed the appearance, as
+it was a piece of board which cut off the light. On either side of the
+entrance there were grooves for holding card-boards of any desired
+color. The letters _R, R_ mark sides which in this case were covered
+with red; _W, W_ mark white spaces. These pieces of cardboard could
+easily be removed or shifted at any time. At the exit the glass plate
+alone distinguished the sides, and it is not likely that the animals
+were able to see it clearly. We have thus at the entrance widely
+differing appearances on the two sides, and at the exit similarity.
+The opening from _A_ into the large box was provided with a slide door
+so that the animal could be prevented from returning to _A_ after
+entering the labyrinth. The partitions and the triangular division at
+the entrance extended to the top of the box, 28 cm., so that the
+animals could not readily jump over them.
+
+[Illustration: FIG. 1. Ground Plan of Labyrinth. _A_, small box
+opening into labyrinth; _E_, entrance of labyrinth; _T_, tank
+containing water; _G_, glass plate closing one passage of exit; _P_,
+partition closing one passage at entrance; _IC_, interrupted
+electrical circuit; _C_, cells; _K_, key in circuit; _RR_, red
+cardboard; _WW_, white cardboard. Scale 1/12.]
+
+The experiments were made in series of ten, with ten-minute intervals
+between trials. In no case was more than one series a day taken, and
+wherever a day was missed the fact has been indicated in the tables.
+The only motive of escape from the box depended upon was the animal's
+desire to return to the water of the tank and to escape from
+confinement in the bright light of the room. The tank was one in which
+the frogs had been kept for several months so that they were familiar
+with it, and it was as comfortable a habitat as could conveniently be
+arranged. Usually the animals moved about almost constantly until they
+succeeded in getting out, but now and then one would remain inactive
+for long intervals; for this reason no record of the time taken for
+escape was kept. On account of the great amount of time required by
+experiments of this kind I have been unable to repeat this series of
+experiments _in toto_ on several animals in order to get averages, but
+what is described for a representative individual has been proved
+normal by test observations on other animals. There are very large
+individual differences, and it may well be that the subject of the
+series of experiments herein described was above the average in
+ability to profit by experience. But, however that may be, what is
+demonstrated for one normal frog is thereby proved a racial
+characteristic, although it may be far from the mean condition.
+
+Before beginning training in the labyrinth, preliminary observations
+were made to discover whether the animals had any tendencies to go
+either to the right or to the left. When the colored cardboards were
+removed it was found that there was usually no preference for right or
+left. In Table I. the results of a few preliminary trials with No. 2
+are presented. For these the colors were used, but a tendency to the
+right shows clearly. Trials 1 to 10 show choice of either the right or
+the red throughout; that it was partly both is shown by trials 11 to
+30, for which the colors were reversed. This individual has therefore,
+to begin with, a tendency to the right at the entrance. At the exit it
+went to the right the first time and continued so to do for several
+trials, but later it learned by failure that there was a blocked
+passage as well as an open one. In the tables the records refer to
+choices. It was useless to record time or to lay much stress upon the
+course taken, as it was sometimes very complicated; all that is given,
+therefore, is the action in reference to the passages. _Right_ in
+every case refers to the choice of the open way, and _wrong_ to the
+choice of the blocked passage. The paths taken improved steadily in
+that they became straighter. A few representative courses are given in
+this report. Usually if the animal was not disturbed a few jumps
+served to get it out of the labyrinth.
+
+
+TABLE I.
+
+    PRELIMINARY TRIALS WITH FROG NO. 2.
+
+    Trials.  Red on Right.   White on Left.
+    1 to 10  10 times to red       0
+
+             Red on Left.    White on Right.
+    11 to 20 4 times to red        6
+
+             Red on Left.    White on Right.
+    21 to 30 3 times to red        7
+
+             To Red.  To White.  To Right. To Left.
+    Totals.    17        13         23        7
+
+
+This table indicates in trials 1 to 10 a strong tendency to the red
+cardboard. Trials 21 to 30 prove that there was also a tendency to the
+right.
+
+Training was begun with the labyrinth arranged as shown in Fig. 1,
+that is, with the left entrance passage and the right exit passage
+open, and with red cardboard on the right (red was always on the side
+to be avoided) and white on the left. Table II. contains the results
+of 110 trials with No. 2, arranged according to right and wrong choice
+at the entrance and exit. Examination of this table shows a gradual
+and fairly regular increase in the number of right choices from the
+first series to the last; after 100 experiences there were practically
+no mistakes.
+
+With another subject, No. _6a_, the results of Table III. were
+obtained. In this instance the habit formed more slowly and to all
+appearances less perfectly. Toward the end of the second week of work
+_6a_ showed signs of sickness, and it died within a few weeks, so I do
+not feel that the experiments with it are entirely trustworthy. During
+the experiments it looked as if the animal would get a perfectly
+formed habit very quickly, but when it came to the summing up of
+results it was obvious that there had been little improvement.
+
+[Illustration: FIG. 2. Labyrinth as arranged for experiments. _E_,
+entrance; _R, R_, regions covered with red; _W, W_, regions covered
+with white. The tracing represents the path taken by No. 2 on the
+sixth trial. Dots mark jumps.]
+
+
+TABLE II.
+
+    LABYRINTH HABIT. FROG NO. 2.
+
+              Entrance.        Exit.     Remarks.
+    Trials. Right. Wrong.  Right. Wrong.
+     1- 10    1       9      4       6
+                                         One day rest.
+    11- 20    2       8      5       5
+    21- 30    4       6      7       3
+    31- 40    5       5      6       4
+    41- 50    5       5      6       2
+               (17)    (33)   (30)    (20)
+    51- 60    9       1      8       2
+    61- 70    6       4     10       0
+    71- 80    7       3      9       1
+    81- 90    9       1      8       2
+    91-100    10(50)  0(10) 10(52)   0( 8)
+                 ---    ---    ---     ---
+                 67     43     82      28
+
+
+Other animals which were used gave results so similar to those for
+frog No. 2 that I feel justified in presenting the latter as
+representative of the rapidity with which the green frog profits by
+experience.
+
+
+TABLE III.
+
+    LABYRINTH HABIT. FROG NO. _6a_.
+
+               Entrance.          Exit.        Remarks.
+    Trials   Right.  Wrong.   Right.  Wrong.
+     1- 10     6       4       5        5
+                                               One day rest.
+    11- 20     7       3       4        6
+    21- 30     2       8       1        9
+    31- 40     6       4       1        9
+    41- 50     7       3       8        2
+                (28)    (22)    (19)     (31)
+    51- 60     5       5       7        3
+    61- 70     6       4       4        6
+    71- 80     4       6       3        7
+                                               One day rest.
+    81- 90     5       5       7        3
+    91-100    10(30)   0(20)   8(29)    2(21)
+                ----    ----    ----     ----
+                (58)    (44)   (48)     (52)
+
+                      Preliminary Trials.
+
+                    Red on Left     Partition at Exit on Right
+    1- 5          5 times to Red       4 times to Partition.
+
+                     Red on Right   Partition at Exit on Left
+    6-10          3 times to Red       5 times to Partition.
+
+
+2. _Rapidity of Habit Formation_.--As compared with other vertebrates
+whose rapidity of habit formation is known, the frog learns slowly.
+Experimental studies on the dog, cat, mouse, chick and monkey furnish
+excellent evidence of the ability of these animals to profit quickly
+by experience through the adapting of their actions to new conditions.
+They all show marked improvement after a few trials, and after from
+ten to thirty most of them have acquired perfect habits. But the
+comparison of the frog with animals which are structurally more
+similar to it is of greater interest and value, and we have to inquire
+concerning the relation of habit formation in the frog to that of
+fishes and reptiles. Few experimental studies with these animals have
+been made, and the material for comparison is therefore very
+unsatisfactory. E.L. Thorndike[1] has demonstrated the ability of
+fishes to learn a labyrinth path. In his report no statement of the
+time required for the formation of habit is made, but from personal
+observation I feel safe in saying that they did not learn more quickly
+than did the frogs of these experiments. Norman Triplett[2] states
+that the perch learns to avoid a glass partition in its aquarium after
+repeatedly bumping against it. Triplett repeated Moebius' famous
+experiment, and found that after a half hour's training three times a
+week for about a month, the perch would not attempt to capture minnows
+which during the training periods had been placed in the aquarium with
+the perch, but separated from them by a glass partition. Triplett's
+observations disprove the often repeated statement that fishes do not
+have any associative processes, and at the same time they show that
+the perch, at least, learns rapidly--not so rapidly, it is true, as
+most animals, but more so in all probability than the amphibia.
+
+   [1] Thorndike, Edward: 'A Note on the Psychology of Fishes,'
+   _American Naturalist_. 1899, Vol. XXXIII., pp. 923-925.
+
+   [2] Triplett, Norman: 'The Educability of the Perch,' _Amer.
+   Jour. Psy._, 1901, Vol. XII., pp. 354-360.
+
+The only quantitative study of the associative processes of reptiles
+available is some work of mine on the formation of habits in the
+turtle.[3] In the light of that study I can say that the turtle learns
+much more rapidly than do fishes or frogs. Further observations on
+other species of turtles, as yet unpublished, confirm this conclusion.
+
+   [3] Yerkes, Robert Mearns: 'The Formation of Habits in the
+   Turtle,' _Popular Science Monthly_, 1901, Vol. LVIII., pp.
+   519-535.
+
+For the frog it is necessary to measure and calculate the improvement
+in order to detect it at first, while with the turtle or chick the
+most casual observer cannot fail to note the change after a few
+trials. In connection with the quickness of the formation of
+associations it is of interest to inquire concerning their permanency.
+Do animals which learn slowly retain associations longer? is a
+question to which no answer can as yet be given, but experiments may
+readily be made to settle the matter. I have tested the frog for
+permanency, and also the turtle, but have insufficient data for
+comparison.
+
+
+3. _Sensory Data Contributing to the Associations_.--Among the most
+important of the sensory data concerned in the labyrinth habit are the
+visual impressions received from the different colored walls, the
+slight differences in brightness of illumination due to shadows from
+the partitions and the contrast in form of the two sides of the
+labyrinth resulting from the use of the partitions, and the muscular
+sensations dependent upon the direction of turning. The experiments
+proved beyond question that vision and the direction of turning were
+the all-important factors in the establishment of the habit. At first
+it seemed as if the direction of turning was the chief determinant,
+and only by experimenting with colors under other conditions was I
+able to satisfy myself that the animals did notice differences in the
+appearance of their surroundings and act accordingly. In Table IV.
+some results bearing on this point have been arranged. To begin with,
+the habit of going to the left when the red was on the right at the
+entrance had been established; then, in order to see whether the
+colors influenced the choice, I reversed the conditions, placing the
+red on the left, that is, on the open-passage side. The results as
+tabulated in the upper part of Table IV. show that the animals were
+very much confused by the reversal; at the entrance where there were
+several guiding factors besides the colors there were 50 per cent. of
+mistakes, while at the exit where there were fewer differences by
+which the animal could be directed it failed every time. This work was
+not continued long enough to break up the old habit and replace it by
+a new one, because I wished to make use of the habit already formed
+for further experiments, and also because the animals remained so long
+in the labyrinth trying to find their way out that there was constant
+danger of losing them from too prolonged exposure to the dry air.
+
+
+TABLE IV.
+
+  INFLUENCE OF CHANCES OF CONDITIONS. FROG NO. 2.
+
+     Habit perfectly formed of going to Left (avoiding Red) at
+     entrance and to Right at exit. Conditions now reversed. Red on
+     Left. Partition at Exit on Right.
+
+  Trials.         Entrance.             Exit.         Remarks.
+             Right.     Wrong.     Right.     Wrong.
+   1- 5        3           2         0           5
+   6-10        2           3         0           5
+
+   Discontinued because animal remained so long in labyrinth that
+   there was danger of injuring it for further work. This shows
+   that the habit once formed is hard to change.
+
+   Given 20 trials with conditions as at first in order to
+   establish habit again.
+
+   1-10        9           1         8            2
+  11-20       10           0         9            1
+
+     Colors reversed, no other change. To test influence of colors.
+
+   1-10        6           4        10            0
+
+
+  INFLUENCE OF DISTURBANCE WHEN ANIMAL IS ENTERING BOX.
+
+          No Disturbance.              Animal Touched.
+
+  To Red (Right).  To White (Left).  To Red.   To White.
+        2                 8             5          5
+
+   This was after the tendency to go to the Left at the entrance
+   had been established.
+
+
+These experiments to test the effect of changing colors are also of
+interest in that they show in a remarkable way the influence of the
+direction of turning. The animal after succeeding in getting around
+the first part of the labyrinth failed entirely to escape at the exit.
+Here it should have turned to the left, instead of the right as it was
+accustomed to, but it persisted in turning to the right. Fig. 3
+represents approximately the path taken in the first trial; it shows
+the way in which the animal persisted in trying to get out on the
+right. From this it is clear that both vision and the complex
+sensations of turning are important.
+
+[Illustration: FIG. 3. Labyrinth with Conditions the Reverse of the
+Usual. (Compare with FIG. 2.) The colors as well as the partitions
+have been shifted. The path is, approximately, that taken by No. 2 in
+the first trial after the reversal of conditions.]
+
+The latter part of Table IV. presents further evidence in favor of
+vision. For these tests the colors alone were reversed. Previous to
+the change the animal had been making no mistakes whatever, thereafter
+there were four mistakes at the entrance and none at the exit. Later,
+another experiment under the same conditions was made with the same
+animal, No. 2, with still more pronounced results. In this case the
+animal went to the white, that is, in this instance, into the blind
+alley, and failed to get out; several times it jumped over to the left
+side (the open-passage side) of the box but each time it seemed to be
+attracted back to the white or repelled by the red, more probably the
+latter, as the animal had been trained for weeks to avoid the red.
+Concerning the delicacy of visual discrimination I hope to have
+something to present in a later paper.
+
+The tactual stimuli given by contact with the series of wires used for
+the electrical stimulus also served to guide the frogs. They were
+accustomed to receive an electrical shock whenever they touched the
+wires on the blocked side of the entrance, hence on this side the
+tactual stimulus was the signal for a painful electrical stimulus.
+When the animal chose the open passage it received the tactual
+stimulus just the same, but no shock followed. After a few days'
+experimentation it was noted that No. 2 frequently stopped as soon as
+it touched the wires, whether on the open or the closed side. If on
+the closed side, it would usually turn almost immediately and by
+retracing its path escape by the open passage; if on the open side, it
+would sometimes turn about, but instead of going back over the course
+it had just taken, as on the other side, it would sit still for a few
+seconds, as if taking in the surroundings, then turn again and go on
+its way to the exit. This whole reaction pointed to the formation of
+an association between the peculiar tactual sensation and the painful
+shock which frequently followed it. Whenever the tactual stimulus came
+it was sufficient to check the animal in its course until other
+sensory data determined the next move. When the wrong passage had been
+chosen the visual data gotten from the appearance of the partition
+which blocked the path and other characteristics of this side of the
+labyrinth determined that the organism should respond by turning back.
+When, on the other hand, the open passage had been selected, a
+moment's halt sufficed to give sensory data which determined the
+continuation of the forward movement. Although this reaction did not
+occur in more than one tenth of the trials, it was so definite in its
+phases as to warrant the statements here made. Fig. 4 gives the path
+taken by No. 2 in its 123d trial. In this experiment both choices were
+correctly made, but when the frog touched the wires on the open side
+it stopped short and wheeled around; after a moment it turned toward
+the exit again, but only to reverse its position a second time. Soon
+it turned to the exit again, and this time started forward, taking a
+direct course to the tank. The usual course for animals which had
+thoroughly learned the way to the tank is that chosen in Fig. 5.
+
+[Illustration: FIG. 4. Path of No. 2 for 123d Trial. Showing the
+response to the tactual stimulus from wires.]
+
+An interesting instance of the repetition of a reaction occurred in
+these experiments. A frog would sometimes, when it was first placed in
+the box, by a strong jump get up to the edge; it seldom jumped over,
+but instead caught hold of the edge and balanced itself there until
+exhaustion caused it to fall or until it was taken away. Why an animal
+should repeat an action of the nature of this is not clear, but almost
+invariably the second trial resulted in the same kind of reaction. The
+animal would stop at the same point in the box at which it had
+previously jumped, and if it did not jump, it would look up as if
+preparing to do so. Even after a frog had learned the way to the tank
+such an action as this would now and then occur, and almost always
+there would follow repetition in the manner described.
+
+[Illustration: FIG. 5. Path Usually Taken by Animal Having
+Perfectly-formed Habit.]
+
+
+4. _The Effect of Fear upon Habit Formation._--A certain amount of
+excitement undoubtedly promotes the formation of associations, but
+when the animal is frightened the opposite is true. I have no
+hesitation in stating that, in case of the green frog, any strong
+disturbing stimulus retards the formation of associations. Although
+the frogs gave little evidence of fear by movements after being kept
+in the laboratory for a few weeks, they were really very timid, and
+the presence of any strange object influenced all their reactions.
+Quiescence, it is to be remembered, is as frequently a sign of fear as
+is movement, and one is never safe in saying that the frog is not
+disturbed just because it does not jump. The influence of the
+experimenter's presence in the room with the frogs which were being
+tried in the labyrinth became apparent when the animals were tried in
+a room by themselves. They escaped much more quickly when alone. In
+order to keep records of the experiments it was necessary for me to be
+in the room, but by keeping perfectly quiet it was possible to do this
+without in any objectionable way influencing the results. It may be,
+however, that for this reason the learning is somewhat slower than it
+would have been under perfectly natural conditions. Early in this
+paper reference was made to the fact that the frog did not learn to
+escape from a box with a small opening at some distance from the floor
+if it was prodded with a stick. I do not mean to say that the animal
+would never learn under such conditions, but that they are unfavorable
+for the association of stimuli and retard the process. This conclusion
+is supported by some experiments whose results are tabulated at the
+bottom of Table IV. In these trials the animal had been trained to go
+to the left and to avoid red. At first ten trials were given in which
+the frog was in no way disturbed. The result was eight right choices
+and two wrong ones. For the next ten trials the frog was touched with
+a stick and thus made to enter the labyrinth from the box, _A_. This
+gave five right and five wrong choices, apparently indicating that the
+stimulus interfered with the choice of direction. Several other
+observations of this nature point to the same conclusion, and it may
+therefore be said that fright serves to confuse the frog and to
+prevent it from responding to the stimuli which would ordinarily
+determine its reaction.
+
+
+5. _The Permanency of Associations._--After the labyrinth habit had
+been perfectly formed by No. 2, tests for permanency were made, (1)
+after six days' rest and (2) after thirty days. Table V. contains the
+results of these tests. They show that for at least a month the
+associations persist. And although there are several mistakes in the
+first trials after the intervals of rest, the habit is soon perfected
+again. After the thirty-day interval there were forty per cent. of
+mistakes at the exit for the first series, and only 20 per cent. at
+the entrance. This in all probability is explicable by the fact that
+the colors acted as aids at the entrance, whereas at the exit there
+was no such important associational material.
+
+
+TABLE V.
+
+  PERMANENCY OF ASSOCIATIONS. FROG NO. 2.
+
+  Tests after six days' rest (following the results tabulated in Table
+  III.).
+
+       Trial.               Entrance.               Exit.
+                         Right.    Wrong.     Right.    Wrong
+       1-10                7          3         8         2
+    (110-120)
+      11-20               10          0        10         0
+
+                 Tests after THIRTY days' rest.
+       1-10                8          2         6         4
+      10-20               10          0        10         0
+
+
+D. Association of Stimuli.--In connection with reaction-time work an
+attempt was made to form an association between a strong visual
+stimulus and a painful electrical shock, with negative results. A
+reaction box, having a series of interrupted circuits in the bottom
+like those already described for other experiments, and an opening on
+one side through which a light could be flashed upon the animal,
+served for the experiments. The tests consisted in the placing of a
+frog on the wires and then flashing an electric light upon it: if it
+did not respond to the light by jumping off the wires, an electrical
+stimulus was immediately given. I have arranged in Table VI. the
+results of several weeks' work by this method. In no case is there
+clear evidence of an association; one or two of the frogs reacted to
+the light occasionally, but not often enough to indicate anything more
+than chance responses. At one time it looked as if the reactions
+became shorter with the continuation of the experiment, and it was
+thought that this might be an indication of the beginning of an
+association. Careful attention to this aspect of the results failed to
+furnish any satisfactory proof of such a change, however, and although
+in the table statements are given concerning the relative numbers of
+short and long reactions I do not think they are significant.
+
+
+TABLE VI.
+
+  ASSOCIATION OF ELECTRICAL AND VISUAL STIMULI. FROG No. 1a, 2a, 3a, 4a,
+  5a, A and Z.
+
+  Frog.  Total No.  Days.      Result.
+          Trials.
+
+  No. 1a   180       18     Increase in number of long reaction
+                            toward end. No evidence of association.
+
+  No. 2a   180       17     Increase in number of short reactions
+                            toward end. No evidence of association.
+
+  No. 3a   180       17     Marked increase in the number of
+                            short reactions toward end. No other evidence
+                            of association.
+
+  No. 4a   200       19     Slight increase in the short reactions.
+                            There were a few responses to the light on the
+                            third day.
+
+  No. 5a   200       20     No increase in the number of short reactions.
+                            Few possible responses to light on second and
+                            third days.
+
+  Frog A   250       20     No evidence of association.
+
+  Frog Z   450       28     No evidence of association.
+
+
+To all appearances this is the same kind of an association that was
+formed, in the case of the labyrinth experiments, between the tactual
+and the electrical stimuli. Why it should not have been formed in this
+case is uncertain, but it seems not improbable that the light was too
+strong an excitement and thus inhibited action. There is also the
+probability that the frog was constrained by being placed in a small
+box and having the experimenter near.
+
+
+III. SUMMARY.
+
+
+1. The green frog is very timid and does not respond normally to most
+stimuli when in the presence of any strange object. Fright tends to
+inhibit movement.
+
+2. That it is able to profit by experience has been proved by testing
+it in simple labyrinths. A few experiences suffice for the formation
+of simple associations; but in case of a series of associations from
+fifty to a hundred experiences are needed for the formation of a
+perfect habit.
+
+3. Experiment shows that the frog is able to associate two kinds of
+stimuli, _e.g._, the peculiar tactual stimulus given by a wire and a
+painful electric stimulus which in the experiments followed the
+tactual. In this case the animal learns to jump away, upon receiving
+the tactual stimulus, before the experimenter gives the electric
+stimulus.
+
+4. Vision, touch and the organic sensations (dependent upon direction
+of turning) are the chief sensory factors in the associations. The
+animals discriminate colors to some extent.
+
+5. Perfectly formed habits are hard to change.
+
+6. Fear interferes with the formation of associations.
+
+7. Associations persist for at least a month.
+
+
+PART II. REACTION TIME OF THE GREEN FROG TO ELECTRICAL AND TACTUAL
+STIMULI.
+
+
+IV. THE PROBLEMS AND POSSIBILITIES OF COMPARATIVE REACTION-TIME
+STUDIES.
+
+
+Animal reaction time is at present a new field of research of evident
+importance and full of promise. A great deal of time and energy has
+been devoted to the investigation of various aspects of the time
+relations of human neural processes; a multitude of interesting facts
+have been discovered and a few laws established, but the results seem
+disproportionate to the amount of patient labor expended.
+Physiologists have determined the rate of transmission of the neural
+impulse for a few animals, and rough estimates of the time required
+for certain changes in the nervous system have been made, but this is
+all we have to represent comparative study. Just the path of approach
+which would seem most direct, in case of the time of neural changes,
+has been avoided. Something is known of the ontogenetic aspect of the
+subject, practically nothing of the phylogenetic; yet, in the study of
+function the comparative point of view is certainly as important as it
+is in the study of structure. In calling attention to the importance
+of the study of animal reaction time I would not detract from or
+minimize the significance of human investigations. They are all of
+value, but they need to be supplemented by comparative studies.
+
+It is almost impossible to take up a discussion of the time relations
+of neural processes without having to read of physiological and
+psychological time. The time of nerve transmission, we are told, is
+pure physiological time and has nothing whatever to do with psychic
+processes; the time occupied by the changes in brain centers is, on
+the contrary, psychological time. At the very beginning of my
+discussion of this subject I wish to have it clearly understood that I
+make no such distinction. If one phase of the neural process be called
+physiological time, with as good reason may all be so named. I prefer,
+therefore, to speak of the time relations of the neural process.
+
+Of the value of reaction-time studies, one may well believe that it
+lies chiefly in the way of approach which they open to the
+understanding of the biological significance of the nervous system.
+Certainly they are not important as giving us knowledge of the time of
+perception, cognition, or association, except in so far as we discover
+the relations of these various processes and the conditions under
+which they occur most satisfactorily. To determine how this or that
+factor in the environment influences the activities of the nervous
+system, and in what way system may be adjusted to system or
+part-process to whole, is the task of the reaction-time investigator.
+
+The problems of reaction time naturally fall within three classes:
+Those which deal with (1) nerve transmission rates; (2) the time
+relations of the spinal center activities, and (3) brain processes.
+Within each of these groups there are innumerable special problems for
+the comparative physiologist or psychologist. Under class 1, for
+instance, there is the determining of the rates of impulse
+transmission in the sensory and the motor nerves, (_a_) for a variety
+of stimuli, (_b_) for different strengths of each stimulus, (_c_) for
+different conditions of temperature, moisture, nourishment, fatigue,
+etc., in case of each stimulus, (_d_) and all this for hundreds of
+representative animals. From this it is clear that lines of work are
+not lacking.
+
+Closely related to these problems of rate of transmission are certain
+fundamental problems concerning the nature of the nerve impulse or
+wave. Whether there is a nerve wave, the reaction-time worker has as
+favorable an opportunity to determine as anyone, and we have a right
+to expect him to do something along this line. The relations of the
+form of the nerve impulse to the rhythm of vital action, to fatigue
+and to inhibition are awaiting investigation. Some of the most
+important unsettled points of psychology depend upon those aspects of
+neural activities which we ordinarily refer to as phenomena of
+inhibition, and which the psychologist is helpless to explain so long
+as the physiological basis and conditions are not known.
+
+Then, too, in the study of animals the relation of reaction time to
+instincts, habits, and the surroundings of the subject are to be
+noted. Variability and adaptability offer chances for extended
+biological inquiries; and it is from just such investigations as
+these that biology has reason to expect much. The development of
+activity, the relation of reflex action to instinctive, of impulsive
+to volitional, and the value of all to the organism, should be made
+clear by reaction-time study. Such are a few of the broad lines of
+inquiry which are before the comparative student of animal reaction
+time. It is useless to dwell upon the possibilities and difficulties
+of the work, they will be recognized by all who are familiar with the
+results of human studies.
+
+In the study of the time relations of neural processes Helmholtz was
+the pioneer. By him, in 1850, the rate of transmission of the nerve
+impulse in the sciatic nerve of the frog was found to be about 27
+meters per second[4]. Later Exner[5] studied the time occupied by
+various processes in the nervous system of the frog by stimulating the
+exposed brain in different regions and noting the time which
+intervened before a contraction of the gastrocnemius in each case.
+Further investigation of the frog's reflex reaction time has been made
+by Wundt[6], Krawzoff and Langendorff[7], Wilson[8] and others, but in
+no case has the method of study been that of the psychologist. Most of
+the work has been done by physiologists who relied upon vivisectional
+methods. The general physiology of the nervous system of the frog has
+been very thoroughly worked up and the papers of Sanders-Ezn[9],
+Goltz[10] Steiner[11] Schrader[12] and Merzbacher[13],[14] furnish an
+excellent basis for the interpretation of the results of the
+reaction-time studies.
+
+   [4] Helmholtz, H.: 'Vorlaeufiger Bericht ueber die
+   Portpflanzungsgeschwindigkeit der Nervenreizung.' _Arch. f.
+   Anal. u. Physiol._, 1850, S. 71-73.
+
+   [5] Exner, S.: 'Experimentelle Untersuchung der einfachsten
+   psychischen Processe.' _Pflueger's Arch._, Bd. 8. 1874, S.
+   526-537.
+
+   [6] Wundt, W.: 'Untersuchungen zur Mechanik der Nerven und
+   Nervencentren.' Stuttgart, 1876.
+
+   [7] Krawzoff, L., und Langendorff, O.: 'Zur elektrischen
+   Reizung des Froschgehirns.' _Arch. f. Anal. u. Physiol._,
+   Physiol. Abth., 1879, S. 90-94.
+
+   [8] Wilson, W.H.: 'Note on the Time Relations of Stimulation of
+   the Optic Lobes of the Frog.'_Jour. of Physiol._, Vol. XI.,
+   1890, pp. 504-508.
+
+   [9] Sanders-Ezn: 'Vorarbeit fuer die Erforschung des
+   Reflexmechanismus in Lendentmark des Frosches.' _Berichte ueber
+   die Verhandlungen der Kgl. saechs. Gesellsch. d. Wissensch. zu
+   Leipzig_, 1867, S. 3.
+
+   [10] Goltz, F.: 'Beitraege zur Lehre von den Functionen der
+   Nervencentren des Frosches.' Berlin, 1869, 130 S.
+
+   [11] Steiner, J.: 'Untersuchungen ueber die Physiologie des
+   Froschhirns.' Braunschweig, 1885, 127 S.
+
+   [12] Schrader, M.G.: 'Zur Physiologie des Froschgehirns.'
+   _Pflueger's Arch._, Bd. 41, 1887, S. 75-90.
+
+   [13] Merzbacher, L.: 'Ueber die Beziebungen der Sinnesorgane zu
+   den Reflexbewegungen des Frosches.' _Pflueger's Arch._, Bd. 81,
+   1900, S. 223-262.
+
+   [14] Merzbacher, L.: 'Untersuchungen ueber die Regulation der
+   Bewegungen der Wirbelthiere. I. Beobachtungen an Froeschen.'
+   _Pflueger's Arch._, Bd. 88, 1901, S. 453-474, 11 Text-figuren.
+
+In the present investigation it has been my purpose to study the
+reactions of the normal frog by the reaction-time methods of the
+psychologist. Hitherto the amount of work done, the extent of
+movements or some other change has been taken as a measure of the
+influence of a stimulus. My problem is, What are the time relations of
+all these reactions? With this problem in mind I enter upon the
+following program: (1) Determination of reaction time to electrical
+stimuli: (_a_) qualitative, (_b_) quantitative, (_c_) for different
+strengths of current; (2) Determination of reaction time to tactual
+stimuli (with the same variations); (3) Auditory: (_a_) qualitative,
+(_b_) quantitative, with studies on the sense of hearing; (4) Visual:
+(_a_) qualitative, (_b_) quantitative, with observations concerning
+the importance of this sense in the life of the frog, and (5)
+Olfactory: (_a_) qualitative, (_b_) quantitative.
+
+The present paper presents in rather bare form the results thus far
+obtained on electrical, tactual, and auditory reaction time;
+discussion of them will be deferred until a comparison of the results
+for the five kinds of stimuli can be given.
+
+
+V. METHOD OF STUDY.
+
+
+The measurements of reaction time herein considered were made with the
+Hipp Chronoscope. Cattell's 'Falling Screen' or 'Gravity Chronoscope'
+was used as a control for the Hipp. The Gravity Chronoscope consists
+of a heavy metal plate which slides easily between two vertical posts,
+with electrical connections so arranged that the plate, when released
+from the magnet at the top of the apparatus, in its fall, at a certain
+point breaks an electric circuit and at another point further down
+makes the same circuit. The rate of fall of the plate is so nearly
+constant that this instrument furnishes an accurate standard time with
+which Hipp readings may be compared, and in accordance with which the
+Hipp may be regulated. For, since the rate of a chronoscope varies
+with the strength of the current in use, with the variations in
+temperature and with the positions of the springs on the magnetic bar,
+it is always necessary to have some standard for corrections. In these
+experiments the time of fall of the gravity chronoscope plate, as
+determined by the graphic method with a 500 S.V. electric tuning fork,
+was 125[sigma] (_i.e._, thousandths of a second).
+
+This period, 125[sigma], was taken as a standard, and each hour,
+before the beginning of reaction-time experiments, the time of the
+plate's fall was measured ten times with the Hipp, and for any
+variation of the average thus obtained from 125[sigma], the standard,
+the necessary corrections were made by changing the position of the
+chronoscope springs or the strength of the current.
+
+The standard of comparison, 125[sigma], is shorter than most of the
+reaction times recorded, but since the time measured was always that
+from the breaking to the making of the circuit passing through the
+chronoscope it cannot be urged that there were errors resulting from
+the difference of magnetization which was caused by variations in the
+reaction time. But it is evident that the danger from differences in
+magnetization, if such exists, is not avoided in this way; instead, it
+is transferred from the reaction time proper to the period of
+preparation immediately preceding the reaction; for, from the moment
+the chronoscope is started until the stimulus is given a current is
+necessarily passing through the instrument. At a verbal signal from
+the operator the assistant started the chronoscope; the stimulus was
+then given by the operator, and the instrument recorded the time from
+the breaking of the circuit, effected by the stimulating apparatus, to
+the making of the circuit by the reaction of the animal. Despite
+precautions to prevent it, the period from the starting of the
+chronoscope to the giving of the stimulus was variable, and errors
+were anticipated, but a number of the tests proved that variations of
+even a second did not cause any considerable error.
+
+A fairly constant current for the chronoscope was supplied by a
+six-cell 'gravity battery' in connection with two storage cells, _GB_
+(Fig. 6). This current could be used for two hours at a time without
+any objectionable diminution in its strength. The introduction of
+resistance by means of the rheostat, _R_, was frequently a convenient
+method of correcting the chronoscope.
+
+[Illustration: FIG. 6. General Plan of Apparatus in Diagram. _H_, Hipp
+Chronoscope; _R_, rheostat; _C_, commutator; _SC_, storage cells;
+_GB_, 'Excello' gravity battery; _F_, Cattell's falling screen; _T_,
+reaction table; _RK_, reaction key; _SK_, Stimulating apparatus; _K_,
+key in chronoscope circuit; _S_, stimulus circuit.]
+
+Fig. 6 represents the general plan of the apparatus used in these
+experiments.
+
+The general method of experimentation is in outline as follows:
+
+1. At a 'ready' signal from the operator the assistant makes the
+chronoscope circuit by closing a key, _K_ (Fig. 6), and then
+immediately starts the chronoscope.
+
+2. Stimulus is given by the operator as soon as the chronoscope is
+started, and by this act the chronoscope circuit is broken and the
+record begun.
+
+3. Animal reacts and by its movements turns a key, _RK_ (Fig. 6), thus
+making the chronoscope circuit and stopping the record.
+
+4. Assistant stops chronoscope and takes reading.
+
+[Illustration: FIG. 7. Reaction Key. _l_, lever swung on pivot; _p,
+p_, posts for contacts with platinum plates on base; _b_, upright bar
+for string; _s_, spring for clamping string; _w_, wheel to carry
+string; _c, c_, chronoscope circuit; 1 and 2, points which are brought
+into contact by animal's reaction.]
+
+The steps of this process and the parts of the apparatus concerned in
+each may be clearly conceived by reference to the diagram given in
+Fig. 6. The various forms of stimulating apparatus used and the
+modification of the method will be described in the sections dealing
+with results. The same reaction key was used throughout (see Fig. 7).
+Its essential features are a lever _l_, pivoted in the middle and
+bearing a post at either end, _p, p_. From the middle of this lever
+there projected upward a small metal bar, _b_, through the upper part
+of which a string to the animal ran freely except when it was clamped
+by the spring, _s_. This string, which was attached to the subject's
+leg by means of a light elastic band, after passing through the bar
+ran over a wheel, _w_, and hung tense by reason of a five-gram weight
+attached to the end. Until everything was in readiness for an
+experiment the string was left free to move through the bar so that
+movement of the animal was not hindered, but the instant before the
+ready-signal was given it was clamped by pressure on _s_. The diagram
+shows the apparatus arranged for a reaction. The current is broken,
+since 1 and 2 are not in contact, but a slight movement of the animal
+turns the lever enough to bring 1 against 2, thus making the circuit
+and stopping the chronoscope. When the motor reaction of the subject
+was violent the string pulled out of the clamp so that the animal was
+free from resistance, except such as the string and weight offered.
+The five-gram weight served to give a constant tension and thus
+avoided the danger of error from this source. Between experiments the
+weight was placed on the table in order that there might be no strain
+upon the subject.
+
+That the subject might be brought into a favorable position for an
+experiment without being touched by the operator a special reaction
+box was devised.
+
+The animals used in these studies were specimens of _Rana clamitans_
+which were kept in a tank in the laboratory throughout the year.
+
+
+VI. ELECTRIC REACTION TIME.
+
+
+The reaction time to electrical stimuli was determined first because
+it seemed probable that this form of the pain reaction would be most
+useful for comparison with the auditory, visual, olfactory and tactual
+reactions. In this paper only the electrical and the tactual reaction
+times will be considered. The former will be divided into two groups:
+(1) Those resulting from a stimulus given by touching electrodes to
+the leg of the frog, and (2) those gotten by having the frog resting
+upon wires through which a current could be passed at any time.
+
+_Group 1 of the electrical reactions_ were taken under the following
+conditions. A reaction box about 40 cm. in diameter was used. The mean
+temperature of the experimenting room was about 20 deg. C. In all cases
+the string was attached to the left hind leg of the frog, and the
+stimulus applied to the middle of the gastrocnemius muscle of the
+right hind leg. Reaction times were taken in series of ten, excluding
+those which were imperfect. As the moistness of the skin affects the
+strength of the electric stimulus received, it was necessary to
+moisten the animal occasionally, but as it did not seem advisable to
+disturb it after each experiment this was done at intervals of five
+minutes throughout the series. Were it not for this precaution it
+might be said that lengthening of the reaction times toward the end of
+a series simply indicated the weakening of the stimulus which resulted
+from the gradual drying of the skin. The stimulus in this group was
+applied by means of the stimulating apparatus of Fig. 6. It is merely
+two wire electrodes which could be placed upon the animal, with the
+additional device of a key for the breaking of the chronoscope circuit
+the instant the stimulus was given. The most serious objection to this
+method of stimulating is that there is a tactual as well as an
+electrical stimulus.
+
+Before presenting averages, two representative series of reactions may
+be considered.
+
+
+SERIES I. FROG B. APRIL 9, 1900. 10 A.M.
+
+  Temperature 19 deg. C. String to left hind leg. Stimulus to right hind
+  leg.
+
+  Strength of stimulating current 1.0 volt, .0001 ampere.
+
+  Number of
+  Experiment.   Hour.    Reaction Time.   Remarks.
+
+       1        10.25                   No reaction.
+       2        10.27                   No reaction.
+       3        10.30        139[sigma]
+       4        10.34        164
+       5        10.35        102
+       6        10.37        169
+       7        10.39        151
+       8        10.40        152
+       9        10.42        144
+      10        10.43        152
+      11        10.45        122
+      12        10.51        179
+      13        10.54                   No reaction.
+
+               Average of 10, 147.4[sigma]
+
+  SERIES 2.   FROG F.  ELECTRICAL STIMULUS.
+
+    No.    Hour.     Reaction Time.      Remarks.     Deviation from Mean.
+
+     1     10.19     35[sigma]      Probable reaction
+                                       to visual stim.
+     2     10.22           173                               4.7
+     3     10.24           161                             - 7.3
+     4     10.25           133                             -35.3
+     5     10.26           199                              30.7
+     6     10.28           130                             -38.3
+     7     10.32           179                              10.7
+     8     10.34           187                              18.7
+     9     10.35            60        Probable reflex.
+    10     10.37           183                              14.7
+    11     10.38           166                             - 2.3
+    12     10.39           172                               3.7
+
+  Average of 10, 168.3[sigma]     Average of first 5, 159.2[sigma]
+  Average Variation, 16.64[sigma] Average of second 5, 177.4[sigma]
+
+
+Both are fairly representative series. They show the extremely large
+variations, in the case of series 1, from 102 to 179[sigma]. In all
+these experiments such variation is unavoidable because it is
+impossible to have the conditions uniform. A very slight difference in
+the frog's position, which could not be detected by the operator,
+might cause considerable difference in the time recorded. Efforts were
+made to get uniform conditions, but the results seem to show that
+there is still much to be desired in this direction.
+
+Tables VII. contains the results of four series of ten reactions each
+for frog _A_. It will be noticed that the time for the first five in
+each series is much shorter than that for the last five; this is
+probably indicative of fatigue.
+
+
+TABLE VII.
+
+  REACTION TIME OF FROG _A_ TO ELECTRICAL STIMULI.
+
+     Series of       Averages     Averages of     Averages of
+  ten reactions.     of series.   first five.     second five.
+         1            163.1[sigma] 134.6[sigma]   191.6[sigma]
+         2            186.2         176.2           196.2
+         3            161.1         125.2           197.0
+         4            158.3         101.6           215.0
+  General averages    167.2[sigma] 134.4[sigma]   199.9[sigma]
+
+
+  TABLE VIII.
+
+  REACTION TIME OF FROG _B_ TO ELECTRICAL STIMULI.
+
+         1            132.7[sigma] 118.2[sigma]   147.4[sigma]
+         2            196.6         167.8           225.4
+         3            147.4         145.5           149.8
+         4            157.5         152.0           163.0
+  General averages    158.6[sigma] 145.9[sigma]   171.4[sigma]
+
+
+TABLE IX.
+
+  NORMAL AND REFLEX REACTION TIME OF SIX ANIMALS TO ELECTRICAL STIMULUS.
+
+                           Normal.                      Reflex.
+              Average for 20               Average for 20
+  Frog.        reactions.     Mean Var.      reactions.     Mean Var.
+  _A_           149.5[sigma] 24.0[sigma]
+  _B_           158.3         16.0           51.5[sigma]    8.0[sigma]
+  _C_           191.0         24.3
+  _D_           167.0         10.1
+  _E_           182.4         28.0           45.1           5.5
+  _F_           176.3         10.2           46.0           4.5
+  General
+  Average.      167.9[sigma] 18.8[sigma]     47.5[sigma]    6.0[sigma]
+
+   For _D_ the average is for ten reactions.
+
+   _B_ and _E_ were males, _F_ a female; the sex of the others was
+   not determined by dissection and is uncertain.
+
+
+Early in the experiments it became evident that there were three
+clearly defined types of reactions: there were a number of reactions
+whose time was shorter than that of the ordinary quick voluntary pain
+reaction, and there were also many whose time was considerably longer.
+The first type it was thought might represent the spinal reflex
+reaction time. For the purpose of determining whether the supposition
+was true, at the end of the series of experiments three of the frogs
+were killed and their reflex reaction time noted. This was done by
+cutting the spinal cord just back of the medulla, placing the animal
+on an experimenting board close to the reaction key with the thread
+from the key fastened to the left leg as in case of the previous work
+and stimulating the gastrocnemius with an induced current by the
+application of wire electrodes.
+
+In Table IX. the reflex reaction times for the three animals are
+given.
+
+The following results obtained with frog _E_ show that the time of
+reaction increases with the increase in the time after death. The
+average of 20 reactions by _E_ taken an hour after the cord had been
+cut was 45.5[sigma]; the average of 20 taken twenty hours later was
+55.85[sigma].
+
+As a rule the reflex reactions were but slightly variable in time as
+is indicated by the accompanying series.
+
+
+  SERIES OF REFLEX REACTIONS OF FROG _F_.
+    Taken at rate of one per minute.
+
+           1                                50[sigma]
+           2                                58
+           3                                55
+           4                                59
+           5                                48
+           6                                46
+           7                                45
+           8                                51
+           9                                42
+          10                                44
+
+
+Throughout these experiments it was noticed that any stimulus might
+cause (1) a twitch in the limb stimulated, or (2) a twitch followed by
+a jump, or (3) a sudden jump previous to which no twitch could be
+detected. And it soon appeared that these types of reaction, as it
+seems proper to call them, would have to be considered in any
+determination of the mean reaction time. As proof of the type theory
+there is given (Fig. 8) a graphic representation of 277 reactions to
+the electrical stimulus.
+
+[Illustration: FIG 8: Distribution of 277 reactions.]
+
+The column of figures at the left indicates the number of reactions at
+any point. Below the base line are the classes. For convenience of
+plotting the reactions have been grouped into classes which are
+separated by 25[sigma]. Class 1 includes all reactions between
+1[sigma] and 25[sigma], class 2 all from 25[sigma] to 50[sigma], and
+so on to 400[sigma], thereafter the classes are separated by
+100[sigma]. It is noticeable that there is one well-marked mode at
+75[sigma]. A second mode occurs at 175[sigma]. This is the primary and
+in our present work the chiefly significant mode, since it is that of
+the quick instinctive reaction to a stimulus. At 500[sigma] there is a
+third mode; but as such this has little meaning, since the reactions
+are usually pretty evenly distributed from 300[sigma] on to
+2000[sigma]; if there is any grouping, however, it appears to be about
+500[sigma] and 800[sigma].
+
+The first mode has already been called the reflex mode. The short
+reactions referred to usually lie between 40[sigma] and 80[sigma], and
+since experiment has shown conclusively that the spinal reflex
+occupies about 50[sigma], there can be little doubt that the first
+mode is that of the reflex reaction time.
+
+The second mode represents those reactions which are the result of
+central activity and control. I should be inclined to argue that they
+are what we usually call the instinctive and impulsive actions. And
+the remaining reactions represent such as are either purely voluntary,
+if any frog action can be so described, or, in other words, depend
+upon such a balancing of forces in the brain as leads to delay and
+gives the appearance of deliberate choice.
+
+Everything points to some such classification of the types as follows:
+(1) Stimuli strong enough to be injurious cause the shortest possible
+reaction by calling the spinal centers into action, or if not spinal
+centers some other reflex centers; (2) slightly weaker stimuli are not
+sufficient to affect the reflex mechanism, but their impulse passes on
+to the brain and quickly discharges the primary center. There is no
+hesitation, but an immediate and only slightly variable reaction; just
+the kind that is described as instinctive. As would be expected, the
+majority of the frog's responses are either of the reflex or of this
+instinctive type. (3) There is that strength of stimulus which is not
+sufficient to discharge the primary center, but may pass to centers of
+higher tension and thus cause a response. This increase in the
+complexity of the process means a slower reaction, and it is such we
+call a deliberate response. Precisely this kind of change in neural
+action and in reaction time is at the basis of voluntary action. And
+(4) finally, the stimulus may be so weak that it will not induce a
+reaction except by repetition. Just above this point lies the
+threshold of sensibility, the determination of which is of
+considerable interest and importance.
+
+_Group 2 of the electrical reactions_ consists of three series taken
+to determine the relation of strength of stimulus to reaction time.
+The conditions of experimentation differed from those for group 1 in
+the following points: (1) The stimulus was applied directly by the
+making of a circuit through wires upon which the subject rested (Fig.
+9); (2) the thread was attached to the right hind leg; (3) the thread,
+instead of being kept at the tension given by the 5-gram weight as in
+the former reactions, was slackened by pushing the upright lever of
+the reaction key one eighth of an inch toward the animal. This was
+done in order to avoid the records given by the slight twitches of the
+legs which precede the motor reaction proper. For this reason the
+reactions of group 2 are not directly comparable with those of group
+1. Fig. 9 is the plan of the bottom of a reaction box 15 cm. at one
+end, 30 cm. at the other, 60 cm. long and 45 cm. deep. On the bottom
+of this, at one end, a series of interrupted circuits were arranged as
+shown in the figure. The wires were 1.2 cm. apart, and an animal
+sitting anywhere on the series necessarily touched two or more, so
+that when the stimulus key, X, was closed the circuit was completed by
+the animal's body; hence, a stimulus resulted. The stimulus key, X,
+was a simple device by which the chronoscope circuit, _c_, _c_, was
+broken at the instant the stimulus circuit, _s_, _c_, was made.
+
+Cells of 'The 1900 Dry Battery' furnished the current used as a
+stimulus. Three different strengths of stimulus whose relative values
+were 1, 2 and 4, were employed in the series 1, 2 and 3. Careful
+measurement by means of one of Weston's direct-reading voltmeters gave
+the following values: 1 cell, 0.2 to 0.5 volt, 0.00001 to 0.00003
+ampere. This was used as the stimulus for series 1. 2 cells, 0.5 to
+1.0 volt, 0.00003 to 0.00006 ampere. This was used for series 2. 4
+cells, 1.2 to 1.8 volt, 0.00007 to 0.0001 ampere. This was used for
+series 3.
+
+[Illustration: Fig. 9. Ground Plan of Reaction Box for Electrical
+Stimuli (Group 2). _IC_, interrupted circuits; _CC_, chronoscope
+circuit; _X_, key for making stimulus circuit and breaking chronoscope
+circuit; _B_, stimulus battery; _S_, string from reaction key to
+animal. Scale 1/2.]
+
+The reactions now under consideration were taken in sets of 24 in
+order to furnish evidence on the problem of fatigue. The stimulus was
+given at intervals of one minute, and the subject was moistened at
+intervals of ten minutes. To obtain 24 satisfactory reactions it was
+usually necessary to give from thirty to forty stimulations. Five
+animals, numbers 1, 2, 4, 5, and 6, served as subjects. They were
+green frogs whose size and sex were as follows:
+
+
+               Length.  Weight.     Sex.
+    Number 1   7.5 cm.  35 grams.  Male.
+    Number 2   7.3  "   37   "     Male.
+    Number 4   8.2  "   50.4 "     Female?
+    Number 5   7.1  "   25   "     Female.
+    Number 6   7.8  "   42   "     Male.
+
+
+For most of these frogs a one-cell stimulus was near the threshold,
+and consequently the reaction time is extremely variable. In Table X.
+an analysis of the reactions according to the number of repetitions of
+the stimulus requisite for a motor reaction has been made. Numbers 1
+and 5 it will be noticed reacted most frequently to the first
+stimulus, and for them 48 satisfactory records were obtained; but in
+case of the others there were fewer responses to the first stimulus,
+and in the tabulation of series 1 (Table XI.) averages are given for
+less than the regular sets of 24 reactions each.
+
+
+TABLE X.
+
+  ANALYSIS OF REACTIONS TO ONE-CELL STIMULUS.
+
+  Frog. Reactions to  To 2d.  To 3d. To 4th. To 5th. More.  Total No.
+       first Stimulus.                                    of Reactions.
+  1          53          2       1      0       0      1        57
+  2          20         12       5      5       4     12        58
+  4          31         15       1      0       2      8        57
+  5          51         11       1      2       0      1        66
+  6          45         15       6      3       1      5        75
+  Totals,   200         55      14     10       7     27       313
+
+
+Table XI. is self-explanatory. In addition to the usual averages,
+there is given the average for each half of the sets, in order that
+the effect of fatigue may be noted. In general, for this series, the
+second half is in its average about one third longer than the first
+half. There is, therefore, marked evidence of tiring. The mean
+reaction time for this strength of stimulus is difficult to determine
+because of the extremely great variations. At one time a subject may
+react immediately, with a time of not over a fifth of a second, and at
+another it may hesitate for as much as a second or two before
+reacting, thus giving a time of unusual length. Just how many and
+which of these delayed responses should be included in a series for
+the obtaining of the mean reaction time to this particular stimulus is
+an extremely troublesome question. It is evident that the mode should
+be considered in this case rather than the mean, or at least that the
+mean should be gotten by reference to the mode. For example, although
+the reaction times for the one-cell stimulus vary all the way from
+150[sigma] to 1000[sigma] or more, the great majority of them lie
+between 200[sigma] and 400[sigma]. The question is, how much deviation
+from the mode should be allowed? Frequently the inclusion of a single
+long reaction will lengthen the mean by 10[sigma] or even 20[sigma].
+What is meant by the modal condition and the deviation therefrom is
+illustrated by the accompanying curve of a series of reaction times
+for the electric stimulus of group I.
+
+
+__________________________________________________________________________
+_8_|______________________________________________________________________
+_7_|_____________________________________|________________________________
+_6_|_____________________________________|________________________________
+_5_|_____________________________________|________________________________
+_4_|________________________________|____|____|___________________________
+_3_|____________|___________________|____|____|___________________________
+_2_|_______|____|____|_________|____|____|____|____|______________________
+_1_|__|____|____|____|_________|____|____|____|____|____|____|____|____|__
+     100  110  120  130  140  150  160  170  180  190  200  210  220  230
+
+
+The column of figures at the left indicates the number of reactions;
+that below the base line gives the reaction times in classes separated
+by 10[sigma]. Of thirty-one reactions, seven are here in the class
+170[sigma]. This is the model class, and the mean gotten by taking the
+average of 31 reactions is 162[sigma]. If the mode had been taken to
+represent the usual reaction time in this case, there would have been
+no considerable error. But suppose now that in the series there had
+occurred a reaction of 800[sigma]. Should it have been used in the
+determination of the mean? If so, it would have made it almost
+30[sigma] greater, thus removing it considerably from the mode. If
+not, on what grounds should it be discarded? The fact that widely
+varying results are gotten in any series of reactions, points, it
+would seem, not so much to the normal variability as to accidental
+differences in conditions; and the best explanation for isolated
+reactions available is that they are due to such disturbing factors as
+would decrease the strength of the stimulus or temporarily inhibit the
+response. During experimentation it was possible to detect many
+reactions which were unsatisfactory because of some defect in the
+method, but occasionally when everything appeared to be all right an
+exceptional result was gotten. There is the possibility of any or all
+such results being due to internal factors whose influence it should
+be one of the objects of reaction-time work to determine; but in view
+of the fact that there were very few of these questionable cases, and
+that in series I, for instance, the inclusion of two or three
+reactions which stood isolated by several tenths of a second from the
+mode would have given a mean so far from the modal condition that the
+results would not have been in any wise comparable with those of other
+series, those reactions which were entirely isolated from the mode and
+removed therefrom by 200[sigma] have been omitted. In series I alone
+was this needful, for in the other series there was comparatively
+little irregularity.
+
+The results of studies of the reaction time for the one-cell electric
+stimulus appear in Table XI. The first column of this table contains
+the average reaction time or mean for each subject. Nos. 2 and 4
+appeared to be much less sensitive to the current than the others, and
+few responses to the first stimulus could be obtained. Their time is
+longer than that of the others, and their variability on the whole
+greater. Individual differences are very prominent in the studies thus
+far made on the frog. The one-cell stimulus is so near the threshold
+that it is no easy matter to get a mean which is significant. Could
+the conditions be as fully controlled as in human reaction time it
+would not be difficult, but in animal work that is impossible. No
+attempt has thus far been made to get the reaction time in case of
+summation effects except in occasional instances, and in so far as
+those are available they indicate no great difference between the
+normal threshold reaction and the summation reaction, but on this
+problem more work is planned.
+
+There are large mean variations in Table XI., as would be anticipated.
+Since the reactions were taken in sets of 24, the means of each set as
+well as that of the total are given, and also, in columns 4 and 5, the
+means of the first half and the last half of each set.
+
+A comparison of Tables XI., XII. and XIII. makes clear the differences
+in reaction time correlated with differences in the strength of an
+electric stimulus. For Table XI., series I, the relative value of the
+stimulus was I; for Table XII., series 2, it was 2, and for Table
+XIII., series 3, it was 4. Throughout the series from I to 3 there is
+a rapid decrease in the reaction time and in the variability of the
+same. The reaction time for stimulus I, the so-called threshold, is
+given as 300.9[sigma]; but of the three it is probably the least
+valuable, for reasons already mentioned. The mean of the second
+series, stimulus 2, is 231.5[sigma] while that of the third, stimulus
+4, is only 103.1[sigma]. This great reduction in reaction time for the
+four-cell stimulus apparently shows the gradual transition from the
+deliberate motor reaction, which occurs only after complex and varied
+central neural activities, and the purely reflex reaction, which takes
+place as soon as the efferent impulse can cause changes in the spinal
+centers and be transmitted as an afferent impulse to the muscular
+system.
+
+
+TABLE XI.
+
+  ELECTRICAL STIMULUS REACTION TIME. SERIES 1.
+
+          Average             Average of   Average   Average   Mean Var
+  Frog.   of all.  Mean Var.    Sets.     of 1st h.  of 2d h.  of Sets.
+
+    1     238.5*     33.3*     216.0*      205.6*     226.7*    33.2*
+                               261.0       248.0      274.1     33.3
+    2     458.0     219.0      458.0       270.4      643.8    219.0
+    4     273.4      59.9      273.4       245.7      301.1     59.9
+    5     263.9      50.5      268.6       244.7      292.5     44.9
+                               259.2       236.0      282.4     56.1
+    6     271.1      65.1      322.6       273.2      372.0     87.9
+                               219.6       208.5      230.6     42.3
+  Gen Av. 300.9      85.5      300.9       244.8      356.8     85.5
+
+                                                               Totals.
+  For No. 1 the averages are for 2 sets of 24 reactions each,    48
+      "   2     "          "    one set of 12      "     "       12
+      "   4     "          "    one set of 24      "     "       24
+      "   5     "          "    two sets of 24     "     "       48
+      "   6     "          "    two sets of 24 and 12 reactions,
+                                    respectively,                36
+
+    *Transcriber's Note: All values in [sigma], 1/1000ths of a second.
+
+
+TABLE XII.
+
+  ELECTRICAL STIMULUS REACTION TIME. SERIES 2.
+
+          Average             Average of   Average   Average   Mean Var
+  Frog.   of all.  Mean Var.    Sets.     of 1st h.  of 2d h.  of Sets.
+
+    1     227.3*     33.7*     229.4*      209.1*     249.6*    25.5*
+                               225.2       207.3      243.0     42.1
+    2     240.1      30.9      239.0       222.3      255.1     29.0
+                               241.3       220.2      262.4     32.8
+    4     270.3      56.5      298.5       285.3      311.4     62.8
+                               242.2       206.0      278.4     50.2
+          198.5      26.2      195.0       197.5      193.0     33.5
+                               202.0       195.2      209.0     18.8
+    6     224.4      24.4      221.6       209.7      233.7     23.6
+                               227.2       213.5      241.0     25.1
+  Gen. Av. 231.5     34.3      231.0       216.6      246.6     34.3
+
+  For No. 5 the averages are for two sets of 18 each; for all the
+  others there are 24 in each set.
+
+    *Transcriber's Note: All values in [sigma], 1/1000ths of a second.
+
+
+TABLE XIII.
+
+  ELECTRICAL STIMULUS REACTION TIME. SERIES 3.
+
+            Average             Average  Average    Average   Mean Var.
+  Frog.     of all.  Mean Var.  of all.  of 1st h.  of 2d h.  of Sets.
+  1          93.6*   13.5*       91.8*    93.2*      90.4*     13.5*
+                                 95.4     91.8       99.0      13.5
+  2          99.9    12.8        92.2     89.4       95.0      17.4
+                                107.5    105.9      109.0       8.2
+  4         125.2    16.3       113.5    106.5      120.5      13.6
+                                136.0    135.7      138.2      19.0
+  5          94.4     8.0        88.6     90.5       88.6       8.2
+                                100.2     97.8      102.7       7.9
+  6         102.5    12.2       104.2     98.6      109.9      12.8
+                                100.9    101.0      108.3      11.6
+  Gen. Avs. 103.1    12.5       103.1    101.0      105.9      12.5
+
+For each animal there are two sets of 24 reactions each.
+
+  *Transcriber's Note: All values in [sigma], 1/1000ths of a second.
+
+The spinal reflex for a decapitated frog, as results previously
+discussed show, is approximately 50[sigma]; and every time the
+four-cell stimulus is given this kind of a reaction results. There is
+a slight twitch of the legs, immediately after which the animal jumps.
+Now for all these series the thread was slackened by one eighth of an
+inch, but the reflex time was determined without this slack.
+Calculation of the lengthening of the reaction time due to the slack
+indicated it to be between 20 and 30[sigma], so if allowance be made
+in case of the reactions to the four-cell stimulus, the mean becomes
+about 70[sigma], or, in other words, nearly the same as the spinal
+reflex. The conclusion seems forced, therefore, that when a stimulus
+reaches a certain intensity it produces the cord response, while until
+that particular point is reached it calls forth central activities
+which result in much longer and more variable reaction times. It was
+said above that the series under consideration gave evidence of the
+gradual transition from the reflex to the volitional in reaction time.
+Is this true, or do we find that there are well-marked types, between
+which reactions are comparatively rare? Examination of the tables
+VII., VIII., IX., XI., XII. and XIII. will show that between 70[sigma]
+and 150[sigma] there is a break. (In tables XI., XII. and XIII.,
+allowance must always be made for the slack in the thread, by
+subtracting 30[sigma].) All the evidence furnished on this problem by
+the electrical reaction-time studies is in favor of the type theory,
+and it appears fairly clear that there is a jump in the reaction time
+from the reflex time of 50-80[sigma], to 140 or 150[sigma], which may
+perhaps be taken as the typical instinctive reaction time. From
+150[sigma] up there appears to be a gradual lengthening of the time as
+the strength of the stimulus is decreased, until finally the threshold
+is reached, and only by summation effect can a response be obtained.
+
+The most important averages for the three series have been arranged in
+Table XIV. for the comparison of the different subjects. Usually the
+reaction time for series 3 is about one half as long as that for
+series 2, and its variability is also not more than half as large. In
+the small variability of series 3 we have additional reason for
+thinking that it represents reflexes, for Table IX. gives the mean
+variation of the reflex as not more than 8[sigma], and the fact that
+the means of this series are in certain cases much larger is fully
+explained by the greater opportunity for variation afforded by the
+slack in the thread.
+
+
+TABLE XIV.
+
+  MEANS, ETC., FOR EACH SUBJECT FOR THE THREE SERIES. (TIME IN [sigma])
+
+                Mean     First    Second      Mean     Frog.
+                         Half.     Half.   Variation.
+  Series 1     238.5     226.8     259.4      33.3
+  Series 2     227.3     208.2     246.3      33.7     No. 1
+  Series 3      93.6      92.5      94.7      13.5
+
+  Series 1     458.0     270.4     643.8     219.0
+  Series 2     240.1     221.2     258.8      30.9     No. 2
+  Series 3      99.9      97.6     102.0      12.8
+
+  Series 1     273.4     245.7     301.1      59.9
+  Series 2     270.3     245.6     294.9      56.5     No. 4
+  Series 3     125.2     121.1     129.3      16.3
+
+  Series 1     263.9     240.4     287.4      50.5
+  Series 2     198.5     196.4     201.0      26.2     No. 5
+  Series 3      94.4      94.2      94.7       8.0
+
+  Series 1     271.1     240.8     301.3      65.1
+  Series 2     224.4     211.6     237.3      24.4     No. 6
+  Series 3     102.5      99.8     109.1      12.2
+
+
+A striking fact is that the averages for the first and last half of
+sets of reactions differ more for the weak than for the strong
+stimulus. One would naturally expect, if the increase were a fatigue
+phenomenon purely, that it would be greatest for the strongest
+stimulus; but the results force us to look for some other conditions
+than fatigue. A stimulus that is sufficiently strong to be painful and
+injurious to an animal forces an immediate response so long as the
+muscular system is not exhausted; but where, as in series 1 and 2 of
+the electrical stimulus, the stimulus is not harmful, the reason for a
+sudden reaction is lacking unless fear enters as an additional cause.
+Just as long as an animal is fresh and unfamiliar with the stimulus
+there is a quick reaction to any stimulus above the threshold, and as
+soon as a few experiences have destroyed this freshness and taught the
+subject that there is no immediate danger the response becomes
+deliberate. In other words, there is a gradual transition from the
+flash-like instinctive reaction, which is of vast importance in the
+life of such an animal as the frog, to the volitional and summation
+responses. The threshold electrical stimulus does not force reactions;
+it is a request for action rather than a demand, and the subject,
+although startled at first, soon becomes accustomed to the experience
+and responds, if at all, in a very leisurely fashion. The reaction
+time to tactual stimuli, soon to be considered, was determined by
+giving a subject only three or four stimulations a day; if more were
+given the responses failed except on repetition or pressure; for this
+reason the data on fatigue, or lengthening of reaction time toward the
+end of a series, are wanting in touch. A few tests for the purpose of
+discovering whether the time would lengthen in a series were made with
+results very similar to those of the threshold electrical stimulus;
+the chief difference lies in the fact that the responses to touch fail
+altogether much sooner than do those to the electrical stimulus. This,
+however, is explicable on the ground that the latter is a stimulus to
+which the animal would not be likely to become accustomed so soon as
+to the tactual.
+
+
+           First Half.         Second Half.      Second % Greater.
+  Series 1  244.8[sigma]        356.8[sigma]         46 per cent
+  Series 2  216.6                246.6               14       "
+  Series 3  101.0                105.9                5       "
+
+
+If pure fatigue, that is, the exhaustion of the nervous or muscular
+system, appears anywhere in this work, it is doubtless in series 3,
+for there we have a stimulus which is so strong as to force response
+on penalty of death; the reaction is necessarily the shortest
+possible, and, as a matter of fact, the motor reaction (jump forward)
+here occupies little more time than the leg-jerk of a decapitated
+frog. This probably indicates that the reaction is a reflex, and that
+the slight increase in its length over that of the spinal reflex is
+due to occasional cerebellar origin; but of this there can be no
+certainly from the evidence herewith presented. At any rate, there is
+no possibility of a voluntary reaction to the strong current, and any
+changes in the general character of the reaction time in a series will
+have to be attributed to fatigue of the nervous or muscular systems.
+The second halves of the sets of series 3 are 5 per cent. longer than
+the first, and unless this is due to the partial exhaustion of the
+nervous system it is hard to find an explanation of the fact. Fatigue
+of the muscles concerned seems out of the question because the
+reactions occur at the rate of only one per minute, and during the
+rest interval any healthy and well-nourished muscle would so far
+recover from the effect of contraction that it would be able to
+continue the rhythmic action for long periods.
+
+To the inquiry, Does fatigue in the experiments mean tiring by the
+exhaustion of nerve energy, or is the lengthening in reaction time
+which would naturally be attributed to tiring due to the fact that
+experience has shown quick reaction to be unnecessary? we shall have
+to reply that there is evidence in favor of both as factors. There can
+be little doubt that in case of the strong stimuli there is genuine
+fatigue which makes quick reaction impossible; but at the same time it
+is certain that the 40 to 50 per cent. increase of the second half of
+sets in series 1 over the first half can not be due to fatigue, for
+the strain is here evidently much less than for series 3. Rather, it
+would seem that habituation instead of exhaustion is the all-important
+cause of the difference in series 1 and 2. It becomes clear from these
+considerations that the repetition of a stimulus can never mean the
+repetition of an effect.
+
+
+VII. TACTUAL REACTION TIME.
+
+
+In the following work on the reactions to tactual stimulation the
+subject was placed in a large reaction box with a thread attached to
+one of its legs and passing to a reaction key, as in the experiments
+already described. The box in which the subject was confined was
+surrounded by movable cloth curtains to prevent the animal's escape
+and at the same time permit the experimenter to work without being
+seen by the frog.
+
+Tactual stimulation was given by means of a hand key[15] similar to
+that used for electrical stimulation which is represented in Fig. 6.
+The touch key ended in a hard-rubber knob which could be brought in
+contact with the skin of the subject. This key was fixed to a handle
+of sufficient length to enable the operator to reach the animal
+wherever it chanced to be sitting in the reaction box. Stimulation was
+given by allowing the rubber point of the touch key to come in contact
+with the skin in the middle region of the subject's back. As soon as
+the point touched the animal the chronoscope circuit was broken by the
+raising of the upper arm of the key.
+
+   [15] This apparatus was essentially the same as Scripture's
+   device for the giving of tactual stimulation.
+
+As a precaution against reactions to visual stimuli, which it might
+well be supposed would appear since the subject could not in every
+case be prevented from seeing the approaching apparatus, the frog was
+always placed with its head away from the experimenter so that the
+eyes could not readily be directed toward the touch apparatus.
+Notwithstanding care in this matter, a reaction occasionally appeared
+which was evidently due to some disturbance preceding the tactual
+stimulus which served as a warning or preparation for the latter. All
+such responses were at once marked as questionable visual reactions
+and were not included in the series of touch reactions proper.
+
+As has been mentioned in connection with the discussion of fatigue, it
+was found absolutely necessary to have the subjects perfectly fresh
+and active, and for this purpose it was advisable to give not more
+than three or four stimulations at any one time. The subject was
+usually kept in the reaction box from 30 to 45 minutes, dependent upon
+the success of the experiments. As the work progressed it became
+evident that the responses to the stimulus were becoming less and less
+certain and slower, that the subjects were becoming accustomed to the
+novel experience and no longer suffered the surprise which had been
+the cause of the prompt reactions at first. It seemed best for this
+reason not to continue the work longer than two weeks, and as a
+consequence it was impossible to base the averages on more than twenty
+reactions for each subject.
+
+So far as the tension of the thread is concerned, the condition for
+the tactual reaction time was the same as that for the first group of
+electrical reaction-time experiments. In comparing the tactual with
+the electrical of series 1, 2 and 3, allowance must be made for the
+slack in the latter cases.
+
+Selection of the tactual reaction times upon which the mean is based,
+has been made with reference to the mode for each set of experiments.
+Inspection of the curves given by the reactions of each subject
+indicated that the great majority of the responses lay between 100 and
+300[sigma], and that those which were beyond these limits were
+isolated and, in all probability, exceptional reactions due to some
+undetected variation in conditions which should throw them out of the
+regular series. On this account it was thought best to use only
+reactions between 100 and 300[sigma].
+
+For convenience of comparison, again, the averages for the electrical
+reaction time of subjects _A_, _B_, _C_, _D_, _E_ and _F_, and the
+same for the tactual reaction time of subjects 1, 2, 3, 4, 5 and 6 are
+herewith given together. All averages are for twenty reactions, except
+for _D_ and 5, for which there are ten.
+
+Besides the usual determination for the tactual reaction-time work on
+the six subjects named, there is given in Table XVI. the electrical
+reaction time of these animals to a two-cell current. Comparison of
+the electrical and tactual results are of interest in this case
+because the mean variation for each is about 34[sigma], being
+34.3[sigma], for the electrical and 33.8[sigma], for the tactual.
+
+
+TABLE XV.
+
+              Average of 20 Electrical           Average of 20 Tactual
+      Frog.          Reactions.          Frog.          Reactions.
+    _A_           149.5[sigma]       1               188.3[sigma]
+    _B_           158.3              2               199.1
+    _C_           191.0              3               212.1
+    _D_           167.0              4               213.0
+    _E_           182.4              5               199.8
+    _F_           176.3              6               221.9
+       Gen. Avs.       167.9                              205.7
+
+
+TABLE XVI.
+
+  REACTION TIME FOR TACTUAL AND ELECTRICAL STIMULI.
+
+            Tactual Reaction Time.       Electrical Reaction Time.
+
+  Frog.     Average. Mean Variation.     Average. Mean Variation.
+
+   1         188.3[sigma]                167.3[sigma]
+   2         199.1                        180.1
+   3         212.1
+   4         213.0                        210.3
+   5¹        199.8                        138.5
+   6         221.9                        164.4
+  Gen. Avs.  205.7      33.8              172.1       34.3
+
+  ¹For 5 the average of ten instead of twenty is given.
+
+
+VIII. EQUAL VARIABILITY AS A CRITERION OF COMPARABILITY OF REACTION
+TIME FOR DIFFERENT KINDS OF STIMULI.
+
+
+Since variability as indicated in the study of the influence of
+different strengths of electrical stimulus becomes less as the
+stimulus increases, parity in variability for different stimuli offers
+a basis for the comparison of reaction times. Certain it is that there
+is no use in comparing the reaction times for different senses or
+different qualities of stimuli unless the relative values of the
+stimuli are taken into consideration; but how are these values to be
+determined unless some such index as variability is available? If the
+reaction time to tactual stimuli as here presented is to be studied in
+its relation to the electrical reaction time, it will mean little
+simply to say that the former is longer than the latter, because the
+electrical reaction time for a one-cell stimulus happens to be
+somewhat less than that for the particular tactual stimulus used. For
+it is clear that this tactual reaction time is really shorter than the
+reaction time to a weak current. In making variability a basis of
+comparison it must be assumed that the strength of stimulus is the
+important factor, and that all other variable conditions are, so far
+as possible, excluded. If, now, on the basis of parity in variability
+we compare the tactual and electrical reaction times, it is apparent
+that the tactual is considerably longer. The tactual average of Table
+XV. is 205.7[sigma], while the electrical reaction time which has
+approximately the same variability is 172.1[sigma]. It may well be
+objected that I have no right to make variability the basis of my
+comparison in these experiments, because the work for the various
+kinds of stimuli was done under different conditions. Admitting the
+force of this objection, and at the same time calling attention to the
+fact that I do not wish to lay any stress on the results of the
+comparisons here made, I take this opportunity to call attention to
+the possibility of this criterion.
+
+The use of variability as a basis of comparison would involve the
+assumptions (1) that a certain intensity of every stimulus which is to
+be considered is capable of producing the shortest possible, or reflex
+reaction, and that this reaction is at the same time the least
+variable; (2) that as the strength of a stimulus decreases the
+variability increases until the threshold is reached.
+
+Suppose, now, it is our desire to compare the results of reactions to
+different intensities of electrical and tactual stimuli; let the
+figures be as follows:
+
+                       Reaction Time.           Variability.
+  Stimulus Strength.  Elect.      Touch.      Elect.    Touch.
+          8            50[sigma] 50[sigma]    10[sigma]  10[sigma].
+          4           130        155          25         30
+          2           175        220          40         40
+          1           300        320          50         60
+
+In the double columns the results for electrical stimuli are given
+first, and in the second column are the tactual. Stimulus 8 is assumed
+to be of sufficient strength to induce what may be designated as
+forced movement, and whatever the quality of the stimulus this
+reaction time is constant. I make this statement theoretically,
+although all the evidence which this work furnishes is in support of
+it. So, likewise, is the variability of this type of reaction time
+small and nearly constant. At the other extreme, stimulus 1 is so weak
+as to be just sufficient to call forth a response; it is the so-called
+threshold stimulus. Whether all qualities of stimulus will give the
+same result here is a question to be settled by experimentation. Wundt
+contends that such is the case, but the observations I have made on
+the electrical and tactual reactions of the frog cause me to doubt
+this assumption. It seems probable that the 'just perceptible stimulus
+reaction time' is by no means the same thing for different qualities
+of stimulus. Those modifications of the vital processes which alone
+enable organisms to survive, make their appearance even in the
+response to the minimal stimulus. In one case the just perceptible
+stimulus may cause nothing more than slight local changes in
+circulation, excretion, muscular action; in another it may produce,
+just because of the particular significance of the stimulus to the
+life of the organism, a violent and sudden motor reaction. But grant,
+if you will, that the threshold reaction time is the same for all
+kinds of stimuli, and suppose that the variability is fairly constant,
+then, between the two extremes of stimuli, there are gradations in
+strength which give reaction times of widely differing variabilities.
+If, now, at some point in the series, as, for instance, to stimulus 2,
+the variability for different kinds of stimuli is the same either with
+reference to the reaction time (ratio) or absolutely, what
+interpretation is to be put upon the fact? Is it to be regarded as
+merely a matter of chance, and unworthy of any special attention, or
+should it be studied with a view to finding out precisely what
+variability itself signifies? It is obvious that any discussion of
+this subject, even of the possible or probable value of variability as
+a criterion for the comparative study of stimuli, can be of little
+value so long as we do not know what are the determining factors of
+variations of this sort. The only suggestion as to the meaning of such
+a condition (_i.e._, equal variability at some point)--and our studies
+seem to show it for touch and electrical stimulation--which I feel
+justified in offering at present, is that parity in variability
+indicates equality in strength of stimuli, that is, the electrical
+stimulus which has a reaction time of the same variability as a
+tactual stimulus has the same effect upon the peripheral nervous
+system as the tactual, it produces the same amplitude and perhaps the
+same form of wave, but the reaction times for the two stimuli differ
+because of the biological significance of the stimuli. The chances are
+that this is wholly dependent upon the central nervous system.
+
+
+IX. SUMMARY.
+
+
+1. This paper gives the results of some experiments on the frog to
+determine its electrical and tactual reaction time. It is the
+beginning of comparative reaction-time studies by which it is hoped
+important information may be gained concerning the significance and
+modes of action of the nervous system. Comparative physiology has
+already made clear that the time relations of neural processes deserve
+careful study.
+
+2. According to the strength of the stimulus, electric stimulation of
+the frog causes three types of reaction: (1) A very weak or threshold
+stimulus results in a deliberate or delayed reaction, the time of
+which may be anywhere from 300[sigma] (thousandths of a second) to
+2,000[sigma]. (2) A very strong stimulus causes a spinal reflex, whose
+time is from 50 to 80[sigma]; and (3) a stimulus of intermediate
+strength causes a quick instinctive reaction of from 150 to 170[sigma]
+in duration.
+
+3. The reaction time for electric stimuli whose relative values were
+1, 2 and 4 were found to be 300.9[sigma], 231.5[sigma] and
+103.1[sigma].
+
+4. The reaction time of the frog to a tactual stimulus (contact of a
+rubber point) is about 200[sigma].
+
+5. The variability of reaction times of the frog is great, and
+increases as the strength of the stimulus decreases.
+
+6. When two kinds of stimuli (_e.g._, electrical and tactual) give
+reaction times of equal variability, I consider them directly
+comparable.
+
+7. According to this criterion of comparability the reaction time to
+electric stimulation which is comparable with that to tactual is
+172.1[sigma]; and it is to be compared with 205.7[sigma]. Both of
+these have a variability of approximately 34[sigma]. On this basis one
+may say that the tactual reaction time is considerably longer than the
+electrical.
+
+
+PART III. AUDITORY REACTIONS OF FROGS.
+
+
+X. HEARING IN THE FROG.
+
+
+A. Influences of Sounds in the Laboratory.
+
+After determining the simple reaction time of the green frog to
+tactual and electrical stimulation, I attempted to do the same in case
+of auditory stimuli. In this I was unsuccessful because of failure to
+get the animal to give a motor response which could be recorded. The
+animal was placed in an experimenting box with a string attached to
+one hind leg as in the experiments described in Part II., and after it
+had become accustomed to the situation a sound was made. A wide range
+of sounds were tried, but to none except the croak of another frog was
+a motor reaction frequently given. Even a loud noise, such as the
+explosion of a large pistol cap, caused a visible motor reaction only
+in rare cases. In fifty trials with this stimulus I succeeded in
+getting three reactions, and since all of them measured between 230
+and 240[sigma] it is perhaps worth while to record the result as
+indicative of the auditory reaction time. As these were the only
+measurements obtained, I have no satisfactory basis for the comparison
+of auditory with other reaction times.
+
+The remarkable inhibition of movement shown by the frog in the
+presence of strong auditory stimulation, at least what is for the
+human being a strong stimulus, led me to inquire concerning the limits
+and delicacy of the sense of hearing in frogs. In the vast quantity of
+literature on the structure and functions of the sense organs of the
+animal I have been able to find only a few casual remarks concerning
+hearing.
+
+In approaching the problem of frog audition we may first examine the
+structure of the ear for the purpose of ascertaining what sounds are
+likely to affect the organ. There is no outer ear, but the membrana
+tympani, or ear drum, covered with skin, appears as a flat disc from 5
+to 10 mm. in diameter on the side of the head just back of the eye and
+a little below it. In the middle ear there is but one bone, the
+columella, forming the connecting link between the tympanum and the
+internal ear. The inner ear, which contains the sense organs,
+consists of a membranous bag, the chief parts of which are the
+utriculus, the sacculus, the lagena, and the three semicircular
+canals. The cavity of this membranous labyrinth is filled with a
+fluid, the endolymph; and within the utriculus, sacculus and lagena
+are masses of inorganic matter called the otoliths. The auditory nerve
+terminates in eight sense organs, which contain hair cells. There is
+no cochlea as in the mammalian ear. The assumption commonly made is
+that vibrations in the water or air by direct contact cause the
+tympanic membrane to vibrate; this in turn causes a movement of the
+columella, which is transmitted to the perilymphatic fluid of the
+inner ear. The sensory hair cells are disturbed by the movements of
+the otoliths in the endolymph, and thus an impulse is originated in
+the auditory nerve which results in a sensation more or less
+resembling our auditory sensation. It is quite probable that the
+frog's sense of hearing is very different from ours, and that it is
+affected only by gross air vibrations. This conclusion the anatomy of
+the ear supports.
+
+Although there does not seem to be a structural basis for a delicate
+sense of hearing, one must examine the physiological facts at hand
+before concluding that frogs do not possess a sense of hearing similar
+to our own. First, the fact that frogs make vocal sounds is evidence
+in favor of the hearing of such sounds at least, since it is difficult
+to explain the origin of the ability to make a sound except through
+its utility to the species. Granting, however, that a frog is able to
+hear the croaks or pain-screams of its own species, the range of the
+sense still remains very small, for although the race of frogs makes a
+great variety of sounds, any one species croaks within a narrow range.
+
+Having satisfied myself that motor reactions for reaction-time
+measurements could not be gotten to any ordinary sounds in the
+laboratory, I tried the effect of the reflex croaking of another frog
+of the same species. In attempting to get frogs to croak regularly, I
+tested the effect of removing the brain. The animals are said to croak
+reflexly after this operation whenever the back is stroked; but for
+some reason I have never been successful in getting the reaction
+uniformly. In many cases I was able to make normal animals croak by
+rubbing the back or flanks, and to this sound the animals under
+observation occasionally responded by taking what looked like an
+attitude of attention. They straightened up and raised the head as if
+listening. In no case have other motor responses been noticed; and the
+above response was so rare that no reaction-time measurements could be
+made.
+
+Again, while working with the green frog on habit formation, I one day
+placed two animals in a labyrinth from which they could escape by
+jumping into a tank of water. Several times when one frog jumped into
+the water I noticed the other one straighten up and hold the
+'listening' or 'attentive' attitude for some seconds. As the animals
+could not see one another this is good evidence of their ability to
+hear the splash made by a frog when it strikes the water.
+
+
+B. Influence of Sounds in Nature.
+
+In order to learn how far fear and artificial conditions were causes
+of the inhibition of response to sounds in the laboratory, and how far
+the phenomenon was indicative of the animal's inability to perceive
+sounds, I observed frogs in their native haunts.
+
+By approaching a pond quietly, it is easy to get within a few yards of
+frogs sitting on the banks. In most cases they will not jump until
+they have evidence of being noticed. Repeatedly I have noted that it
+is never possible to get near to any frogs in the same region after
+one has jumped in. In this we have additional proof that they hear the
+splash-sound. To make sure that sight was not responsible for this
+on-guard condition in which one finds the frogs after one of their
+number has jumped into the water, I made observations on animals that
+were hidden from one another. The results were the same. I therefore
+conclude that the splash of a frog jumping into the water is not only
+perceived by other frogs in the vicinity, but that it is a peculiarly
+significant sound for them, since it is indicative of danger, and
+serves to put them 'on watch.'
+
+A great variety of sounds, ranging in pitch from a low tone in
+imitation of the bull frog's croak to a shrill whistle, and in
+loudness from the fall of a pebble to the report of a pistol, were
+tried for the purpose of testing their effects upon the animals in
+their natural environment. To no sound have I ever seen a motor
+response given. One can approach to within a few feet of a green frog
+or bull frog and make all sorts of noises without causing it to give
+any signs of uneasiness. Just as soon, however, as a quick movement is
+made by the observer the animal jumps. I have repeatedly crept up very
+close to frogs, keeping myself screened from them by bushes or trees,
+and made various sounds, but have never succeeded in scaring an animal
+into a motor response so long as I was invisible. Apparently they
+depend almost entirely upon vision for the avoidance of dangers.
+Sounds like the splash of a plunging frog or the croak or pain-scream
+of another member of the species serve as warnings, but the animals do
+not jump into the water until they see some sign of an unusual or
+dangerous object. On one occasion I was able to walk to a spot where a
+large bull frog was sitting by the edge of the water, after the frogs
+about it had plunged in. This individual, although it seemed to be on
+the alert, let me approach close to it. I then saw that the eye turned
+toward me was injured. The animal sat still, despite the noise I made,
+simply because it was unable to see me; as soon as I brought myself
+within the field of vision of the functional eye the frog was off like
+a flash.
+
+Many observers have told me that frogs could hear the human voice and
+that slight sounds made by a passer-by would cause them to stop
+croaking. In no case, however, have such observers been able to assert
+that the animals were unaffected by visual stimuli at the same time. I
+have myself many times noticed the croaking stop as I approached a
+pond, but could never be certain that none of the frogs had seen me.
+It is a noteworthy fact that when one frog in a pond begins to croak
+the others soon join it. Likewise, when one member of such a chorus is
+frightened and stops the others become silent. This indicates that the
+cessation of croaking is a sign of danger and is imitated just as is
+the croaking. There is in this fact conclusive evidence that the
+animals hear one another, and the probability is very great that they
+hear a wide range of sounds to which they give no motor reactions,
+since they do not depend upon sound for escaping their enemies.
+
+The phenomenon of inhibition of movement in response to sounds which
+we have good reason to think the frogs hear, and to which such an
+animal as a turtle or bird would react by trying to escape, is thus
+shown to be common for frogs in nature as well as in the laboratory.
+This inhibition is in itself not surprising, since many animals
+habitually escape certain of their enemies by remaining motionless,
+but it is an interesting phenomenon for the physiologist. We have to
+inquire, for instance, what effects sounds which stimulate the
+auditory organs and cause the animal to become alert, watchful, yet
+make it remain rigidly motionless, have on the primary organic rhythms
+of the organism, such as the heart-beat, respiration, and peristalsis.
+It is also directly in the line of our investigation to inquire how
+they affect reflex movements, or the reaction time for any other
+stimulus--what happens to the reaction time for an electrical
+stimulus, for example, if a loud noise precede or accompany the
+electrical stimulus.
+
+For the purpose of determining the range of hearing in the frog, I was
+driven to study the influence of sounds upon respiration. Although the
+animals did not make any detectable movement, not even of an eyelid,
+in response to noises, it seemed not improbable that if the sounds
+acted as auditory stimuli at all, they would in some degree modify the
+form or rate of the respiratory movement.
+
+
+C. Influence of Sounds on Respiration.[16]
+
+   [16] For full discussion of the normal respiratory movements of
+   the frog see Martin, _Journal of Physiology,_ Vol. 1., 1878,
+   pp. 131-170.
+
+The method of recording the respiration was the direct transference of
+the movement of the throat by means of a pivoted lever, one end of
+which rested against the throat, while the other served as a marker on
+a revolving drum carrying smoked paper. The frog was put into a small
+box, visual stimuli were, so far as possible, excluded and the lever
+was adjusted carefully; a record was then taken for at least half a
+minute to determine the normal rate of respiration in the absence of
+the stimulus whose effect it was the chief purpose of the experiment
+to discover. Then, as soon as everything was running smoothly, the
+auditory stimulus was given. The following records indicate the
+effects of a few stimuli upon the rate of breathing:
+
+
+1. Stimulus, 100 V. tuning fork.
+
+Number of respirations for 10 cm. _before_ stimulus 18.0, 17.0; number
+of respirations for 10 cm. _after_ stimulus 19.0, 17.3.
+
+The records indicate very little change, and contradict one another.
+For the same stimulus the experiment was tried of taking the normal
+respiration record for a complete revolution of the drum, and then at
+once taking the record for the same length of time (about two minutes)
+with the tuning-fork vibrating close to the frog. The following result
+is typical and proves that the sound has little effect.
+
+Number of respirations in a revolution _before_ stimulus: First rev.
+88; second rev. 88. Number of respirations in a revolution _during_
+stimulus: First rev. 87; second rev. 88.
+
+Concerning the influence of tuning-fork stimuli more will be said
+later in a consideration of the effects of auditory stimuli upon
+reactions to visual stimuli.
+
+
+2. The influence of falling water as an auditory stimulus. Water was
+allowed to fall about two feet in imitation, first, of a plunging
+frog, and second, of water falling over rocks. In representing the
+effect of the stimulus on the rate of respiration, I have given the
+distance on the drum covered by the ten complete respirations just
+preceding the stimulus and the ten following it.
+
+
+             10 Respirations.        10 Respirations.
+           _Before_ Stimulus.  _After_ Stimulus.
+  1st Stim.       13.0 cm.                 11.8 cm.
+  2d Stim.        12.7 cm.                 12.7 cm.
+
+                      With a smaller animal.
+
+  1st Stim.        5.4 cm.                  4.8 cm.
+  2d Stim.         4.9 cm.                  4.7 cm.
+  Average for 5    5.00 cm.                 4.86 cm.
+
+
+_These records show a marked increase in the rate of respiration just
+after the auditory stimulus is given for the first time._ The stimulus
+has less effect when repeated after an interval of one or two minutes,
+and if repeated several times it finally causes no noticeable change.
+On the whole, the sound of falling water seems to arouse the animals
+to fuller life. The stimulus appears to interest them, and it
+certainly accelerates respiration. This is precisely what one would
+expect from a sound which is of special significance in the life of
+the animal.
+
+
+3. In case of a loud shrill whistle inhibition of respiration
+resulted. This probably means that the frogs were frightened by the
+sound. Falling water served rather to excite their natural-habitat
+associations, whereas, the whistle, being an uncommon and unassociated
+sound, caused fear. It is evident to the casual observer that the frog
+sometimes inhibits and sometimes increases its respiratory movements
+when frightened, so the result in this experiment is in no way
+surprising. I am by no means certain, however, that a longer series of
+observations on several individuals would give constant inhibitory
+results. My immediate purpose in the work was to get evidence of
+hearing; the respiratory changes were of secondary importance,
+although of such great interest that I have planned a more thorough
+special study of them for the future.
+
+A few sample results showing the influence of the whistle upon a small
+bull-frog follow:
+
+               Length of 10 Resps.             Length of 10 Resps.
+              _Before_ Stimulus in cm.   _After_ Stimulus in cm.
+  1st Stim.            6.0                             6.7
+  2d    "              5.4                             6.0
+  3d    "              5.9                             5.8
+  1st   "              4.7                             5.4
+  2d    "              4.4                             4.6
+
+
+As a test-check observation for comparison, the influence of a visual
+stimulus upon respiration was noted under the same conditions as for
+the auditory. Effect of turning on electric light over box.
+
+       Length in cm. of 10 Resps.    Length in cm. of 10 Resps.
+        _Before_ Stimulus.      _After_ Stimulus.
+                4.8                           4.4
+                5.3                           4.6
+                4.5                           4.0
+
+These results indicate an increase in the respiration rate due to the
+visual stimulus.
+
+
+4. Of the other auditory stimuli used, the pistol-cap explosion gave
+very irregular results. For one animal it caused acceleration, for
+another inhibition. There is, however, good evidence that the sounds
+were heard.
+
+
+5. The ringing of a bell gave results similer to those for a whistle,
+and the sound of a 500 S.V. tuning fork usually caused a slight
+increase in the rate of breathing. In these experiments I therefore
+have evidence, through their effects upon respiration, of the frog's
+ability to hear sounds ranging from 50 V. to at least 1,000 V.
+
+The croak of the green frog ranges from 100 to 200 V., so far as I
+have been able to determine. That of the bull frog is lower, from 50
+to 75; and in the leopard frog the range is from 80 to 125. The latter
+is very different from the green frog in its croaking, in that it
+croaks whenever disturbed, whereas, the green frog rarely responds in
+that way to a stimulus.
+
+We are now in a position to say that the failure of frogs to give
+motor reactions to strong auditory stimuli is not due to their
+inability to be affected by the stimuli, but is a genuine inhibition
+phenomenon.
+
+
+XI. THE EFFECTS OF AUDITORY STIMULI ON VISUAL REACTIONS.
+
+
+Further experimental evidence of hearing was gotten from some work
+done to test the influence of sounds upon motor reactions to visual
+stimuli. Frogs, like most other amphibians, reptiles and fishes, are
+attracted by any small moving object and usually attempt to seize it.
+They never, so far as I have noticed, feed upon motionless objects,
+but, on the other hand, will take almost anything which moves.
+Apparently the visual stimulus of movement excites a reflex. A very
+surprising thing to those who are unfamiliar with frog habits is the
+fear which small frogs have of large ones. Put some green frogs or
+small bull frogs into a tank with large bull frogs, and the little
+ones will at once show signs of extreme fear; they jump about in the
+most excited manner and try hard to escape. The cause of their fear
+soon appears, since it is usually only a few minutes until the little
+ones are swallowed by their wide-mouthed, cannibalistic fellows.
+
+It is, moreover, well known that a bit of red flannel fastened to a
+hook attracts frogs and is an excellent method of capturing them. Red
+seems to be the color which they most readily notice.
+
+This tendency of the frog to attempt to seize any moving object I made
+use of to test the value of sounds. By placing a frog in a glass
+aquarium which was surrounded by a screen, back of which I could work
+and through a small hole in which I was able to watch the animal
+without being noticed by it, and then moving a bit of red cardboard
+along one side of the aquarium, I could get the frog to jump at it
+repeatedly. In each attempt to get the moving object, the animal
+struck its head forcibly against the glass side of the aquarium. There
+was, therefore, reason to think that a few trials would lead to the
+inhibition of the reaction. Experiment discovered the fact that a
+hungry frog would usually jump at the card as many as twenty times in
+rapid succession.
+
+In this reaction to a visual stimulus there appeared good material for
+testing audition. I therefore arranged a 500 S.V. tuning fork over the
+aquarium and compared the reactions of animals to the visual stimulus
+alone, with that to the visual stimulus when accompanied by an
+auditory stimulus. The tuning-fork sound was chosen because it seemed
+most likely to be significant to the frog. It is similar to the sounds
+made by the insects upon which frogs feed. For this reason one would
+expect that the sight of a moving object and the sound of a
+tuning-fork would tend to reenforce one another.
+
+The experiments were begun with observations on the effects of moving
+objects on the respiration. In case of a normal rate of 54
+respirations per minute sight of the red object caused an increase to
+58. Then the same determination was made for the auditory stimulus.
+The tuning-fork usually caused an increase in rate. In a typical
+experiment it was from 65 per minute to 76. The observations prove
+conclusively that the 500 S.V. sound is heard. My attention was turned
+to the difference of the environment of the ear in its relation to
+hearing. Apparently frogs hear better when the tympanum is partially
+under water than when it is fully exposed to the air.
+
+Having discovered by repeated trials about how vigorously and
+frequently a frog would react to the moving red card, I tried the
+effect of setting the fork in vibration a half minute before showing
+the card. It was at once evident that the sound put the frog on the
+alert, and, when the object came into view, it jumped at it more
+quickly and a greater number of times than when the visual stimulus
+was given without the auditory. This statement is based on the study
+of only two animals, since I was unable to get any other frogs that
+were in the laboratory at the time to take notice of the red
+cardboard. This was probably because of the season being winter. I
+venture to report the results simply because they were so definite as
+to point clearly to the phenomenon of the reenforcement of the
+visual-stimulus reaction by an auditory stimulus.
+
+Concerning the influence of this combining of stimuli on the reaction
+time, I am only able to say that the reaction to the moving object
+occurred quicker in the presence of the auditory stimulus. When the
+red card was shown it was often several seconds before the frog would
+notice it and attempt to get it, but when the sound also was given the
+animal usually noticed and jumped toward the moving card almost
+immediately.
+
+Unfortunately I have thus far been unable to get chronoscopic
+measurements of the reaction times in this reenforcement phenomenon. I
+hope later to be able to follow out the interesting suggestions of
+these few experiments in the study of reenforcement and inhibition as
+caused by simultaneously given stimuli.
+
+A few observations made in connection with these experiments are of
+general interest. The frog, when it first sees a moving object,
+usually draws the nictitating membrane over the eye two or three times
+as if to clear the surface for clearer vision. Frequently this action
+is the only evidence available that the animal has noticed an object.
+This movement of the eye-lids I have noticed in other amphibians and
+in reptiles under similar conditions, and since it always occurs when
+the animals have need of the clearest possible vision, I think the
+above interpretation of the action is probably correct.
+
+Secondly, the frog after getting a glimpse of an object orients
+itself by turning its head towards the object, and then waits for a
+favorable chance to spring. The aiming is accurate, and as previously
+stated the animal is persistent in its attempts to seize an object.
+
+
+XII. THE PAIN-SCREAM OF FROGS.
+
+
+While making measurements of the frog's reaction time to electrical
+stimulation, I noticed that after a few repetitions of a 2-volt,
+.0001-ampere stimulus an animal would frequently make a very peculiar
+noise. The sound is a prolonged scream, like that of a child, made by
+opening the mouth widely. The ordinary croak and grunt are made with
+closed or but slightly opened mouth. The cry at once reminds one of
+the sounds made by many animals when they are frightened. The rabbit,
+for example, screams in much the same way when it is caught, as do
+also pigs, dogs, rats, mice and many other animals. The question
+arises, is this scream indicative of pain? While studying reaction
+time I was able to make some observations on the relation of the
+scream to the stimulus.
+
+First, the scream is not given to weak stimuli, even upon many
+repetitions. Second, it is given to such strengths of an electrical
+stimulus as are undoubtedly harmful to the animal. Third, after a frog
+has been stimulated with a strong current (two volts), until the
+scream is given with almost every repetition, it will scream in the
+same way when even a weak stimulus is applied. If, for instance, after
+a two-volt stimulus has been given a few times, the animal be merely
+touched with a stick, it will scream. It thus appears as if the strong
+stimulus increases the irritability of the center for the
+scream-reflex to such an extent that even weak stimuli are sufficient
+to cause the reaction. Are we to say that the weak stimulus is painful
+because of the increased irritability, or may it be concluded that the
+reflex is in this case, like winking or leg-jerk or the head-lowering
+and puffing, simply a forced movement, which is to be explained as an
+hereditary protective action, but not as necessarily indicative of any
+sort of feeling. Clearly if we take this stand it may at once be said
+that there is no reason to believe the scream indicative of pain at
+any time. And it seems not improbable that this is nearer the truth
+than one who hears the scream for the first time is likely to think.
+
+The pain-scream is of interest in this consideration of auditory
+reactions because it increases the range of sounds which we should
+expect frogs to hear if we grant the probability of them hearing their
+own voices.
+
+It may be worth while to recall at this point the fact that a whistle
+from the human lips--the nearest approach to the pain-scream among the
+sounds which were used as stimuli in the experiments on
+respiration--caused marked inhibition of respiration. Perhaps this
+fact may be interpreted in the light of the pain-scream reaction. I
+may add that I have never seen a frog give a motor reaction to the
+pain-scream. Thinking it would certainly alarm the animals and cause
+them to make some movement which would serve for reaction-time
+measurements, I made repeated trials of its effects, but could never
+detect anything except respiratory changes.
+
+       *       *       *       *       *
+
+
+
+
+        STUDIES IN PSYCHOLOGICAL THEORY.
+
+
+
+
+       *       *       *       *       *
+
+
+
+
+THE POSITION OF PSYCHOLOGY IN THE SYSTEM OF KNOWLEDGE.
+
+BY HUGO MUeNSTERBERG.
+
+
+The modern efforts to bring all sciences into a system or at least to
+classify them, from Bacon to Spencer, Wundt and Pearson have never, if
+we abstract here from Hegel, given much attention to those questions
+of principle which are offered by the science of psychology. Of course
+the psychological separation of different mental functions has often
+given the whole scheme for the system, the classification thus being
+too often more psychological than logical. Psychology itself,
+moreover, has had for the most part a dignified position in the
+system; even when it has been fully subordinated to the biological
+sciences, it was on the other hand placed superior to the totality of
+mental and moral sciences, which then usually have found their unity
+under the positivistic heading 'sociology.' And where the independent
+position of psychology is acknowledged and the mental and moral
+sciences are fully accredited, as for instance with Wundt, psychology
+remains the fundamental science of all mental sciences; the objects
+with which philology, history, economics, politics, jurisprudence,
+theology deal are the products of the processes with which psychology
+deals, and philology, history, theology, etc., are thus related to
+psychology, as astronomy, geology, zooelogy are related to physics.
+There is thus nowhere a depreciation of psychology, and yet it is not
+in its right place. Such a position for psychology at the head of all
+'Geisteswissenschaften' may furnish a very simple classification for
+it, but it is one which cannot express the difficult character of
+psychology and the complex relations of the system of mental sciences.
+The historical and philological and theological sciences cannot be
+subordinated to psychology if psychology as science is to be
+cooerdinated with physics, that is, if it is a science which describes
+and explains the psychical objects in the way in which physics
+describes and explains the physical objects. On the other hand, if it
+means in this central position of mental sciences a science which does
+not consider the inner life as an object, but as subjective activity
+needing to be interpreted and subjectively understood, not as to its
+elements, but as to its meaning, then we should have two kinds of
+psychology, one which explains and one which interprets. They would
+speak of different facts, the one of the inner life as objective
+content of consciousness, as phenomenon, the other of the inner life
+as subjective attitude, as purpose.
+
+The fact is, that these two sciences exist to-day. There are
+psychologists who recognize both and keep them separated, others who
+hold to the one or the other as the only possible view; they are
+phenomenalists or voluntarists. Mostly both views are combined, either
+as psychological voluntarism with interposed concessions to
+phenomenalism or as phenomenalism with the well-known concessions to
+voluntarism at the deciding points. Further, those who claim that
+psychology must be phenomenalistic--and that is the opinion of the
+present writer--do not on that account hold that the propositions of
+voluntarism are wrong. On the contrary: voluntarism, we say, is right
+in every respect except in believing itself to be psychology.
+Voluntarism, we say, is the interpretative account of the real life,
+of immediate experience, whose reality is understood by understanding
+its meaning sympathetically, but we add that in this way an objective
+description can never be reached. Description presupposes
+objectivation; another aspect, not the natural aspect of life, must be
+chosen to fulfill the logical purposes of psychology: the
+voluntaristic inner life must be considered as content of
+consciousness while consciousness is then no longer an active subject
+but a passive spectator. Experience has then no longer any meaning in
+a voluntaristic sense; it is merely a complex of elements. We claim
+that every voluntaristic system as far as it offers descriptions and
+explanations has borrowed them from phenomenalistic psychology and is
+further filled up by fragments of logic, ethics and aesthetics, all of
+which refer to man in his voluntaristic aspect. We claim, therefore,
+that such a voluntaristic theory has no right to the name psychology,
+while we insist that it gives a more direct account of man's real life
+than psychology can hope to give, and, moreover, that it is the
+voluntaristic man whose purpose creates knowledge and thus creates the
+phenomenalistic aspect of man himself.
+
+We say that the voluntaristic theory, the interpretation of our real
+attitudes, in short teleological knowledge, alone can account for the
+value and right of phenomenalistic psychology and it thus seems unfair
+to raise the objection of 'double bookkeeping.' These two aspects of
+inner life are not ultimately independent and exclusive; the
+subjective purposes of real life necessarily demand the labors of
+objectivistic psychology. The last word is thus not dualistic but
+monistic and the two truths supplement each other. But this
+supplementation must never be misinterpreted as meaning that the two
+sciences divide inner experience, as if, for instance, the
+phenomenalistic study dealt with perceptions and ideas, the
+voluntaristic with feelings and volitions. No, it is really a
+difference of logical purpose of treatment and thus a difference of
+points of view only; the whole experience without exception must be
+possible material for both. There is no feeling and no volition which
+is not for the phenomenalist a content of consciousness and nothing
+else. There is, on the other hand, no perception and no idea which is
+not, or better, ought not to be for the voluntarist a means, an aim, a
+tool, an end, an ideal. In that real life experience of which the
+voluntarist is speaking, every object is the object of will and those
+real objects have not been differentiated into physical things under
+the abstract categories of mechanics on the one hand, and psychical
+ideas of them in consciousness on the other; the voluntarist, if he is
+consistent, knows neither physical nor psychical phenomena.
+Phenomenalist and voluntarist thus do not see anything under the same
+aspect, neither the ideas nor the will.
+
+This difference is wrongly set forth if the antithesis to voluntarism
+is called intellectualism. Intellectualism is based on the category of
+judgment, and judgment too is a ideological attitude. Phenomenalism
+does not presuppose a subject which knows its contents but a subject
+which simply _has_ its contents; the consciousness which has the
+thought as content does not take through that the voluntaristic
+attitude of knowing it and the psychologist has therefore no reason to
+prefer the thought to the volition and thus to play the
+intellectualist. If the psychologist does emphasize the idea and its
+elements, the sensations, it is not because they are vehicles of
+thought but because their relations to physical objects make them
+vehicles of communication. The elements of ideas are negotiable and
+thus through their reference to the common physical world indirectly
+describable; as the elements of ideas are alone in this position, the
+psychologist is obliged to consider all contents of consciousness,
+ideas and volitions alike, as complexes of sensations.
+
+The antithesis is also misinterpreted, or at least wrongly narrowed,
+if it is called voluntarism _versus_ associationism. Recent
+discussions have sufficiently shown that the principle of association
+is not the only possible one for phenomenalistic theories. If
+associationism is identified with objective psychology, all the
+well-founded objections to the monopoly of the somewhat sterile
+principle of association appear as objections to phenomenalism in
+psychology, and voluntaristic theories, especially those which work
+with the teleological category of apperception, are put in its place.
+But without returning to apperceptionism we can overcome the
+one-sidedness of associationism if full use is made of the means which
+the world of phenomena offers to theory. The insufficiency of
+associationism disappears if the content of consciousness is
+considered as variable not only as to quality and intensity but also
+as to vividness. This variation of vividness, on the other hand, is no
+exception from the psychophysical parallelism as soon as the psychical
+process is considered as dependent not only upon the local and
+quantitative differences of the sensory process but also upon the
+motor function of the central physical process. The one-sidedness of
+the physiological sensory theories has been the hidden reason for the
+one-sidedness of associationism. The sensory-motor system must be
+understood as the physical basis of the psychophysical process and the
+variations in the motor discharge then become conditions of those
+psychical variations of vividness which explain objectively all those
+phenomena in whose interest associationism is usually supplemented by
+apperceptionism. The association theory must thus be given up in favor
+of an 'action-theory'[1] which combines the consistency of
+phenomenalistic explanation with a full acknowledgment of the
+so-called apperceptive processes; it avoids thus the deficiency of
+associationism and the logical inconsistency of apperceptionism.
+
+   [1] H. Muensterberg, 'Grundzuege der Psychologie.' Bd. I.,
+   Leipzig, 1900, S. 402-562.
+
+Only if in this way the sciences of voluntaristic type, including all
+historical and normative sciences, are fully separated from
+phenomenalistic psychology, will there appear on the psychological
+side room for a scientific treatment of the phenomena of social life,
+that is, for sociology, social psychology, folk-psychology, psychical
+anthropology and many similar sciences. All of them have been in the
+usual system either crowded out by the fact that history and the other
+mental sciences have taken all the room or have been simply identified
+with the mental sciences themselves. And yet all those sciences exist,
+and a real system of sciences must do justice to all of them. A modern
+classification has perhaps no longer the right as in Bacon's time to
+improve the system by inventing new sciences which have as yet no
+existence, but it has certainly the duty not to ignore important
+departments of knowledge and not to throw together different sciences
+like the descriptive phenomenalistic account of inner life and its
+interpretative voluntaristic account merely because each sometimes
+calls itself psychology. A classification of sciences which is to be
+more than a catalogue fulfills its logical function only by a careful
+disentanglement of logically different functions which are externally
+connected. Psychology and the totality of psychological, philosophical
+and historical sciences offer in that respect far more difficulty than
+the physical sciences, which have absorbed up to this time the chief
+interest of the classifier. It is time to follow up the ramifications
+of knowledge with special interest for these neglected problems. It is
+clear that in such a system sciences which refer to the same objects
+may be widely separated, and sciences whose objects are unlike may be
+grouped together. This is not an objection; it indicates that a
+system is more than a mere pigeon-holing of scholarly work, that it
+determines the logical relations; in this way only can it indeed
+become helpful to the progress of science itself.
+
+The most direct way to our end is clearly that of graphic
+representation wherein the relations are at once apparent. Of course
+such a map is a symbol and not an argument; it indicates the results
+of thought without any effort to justify them. I have given my
+arguments for the fundamental principles of the divisions in my
+'Grundzuege der Psychologie' and have repeated a few points more
+popularly in 'Psychology and Life,' especially in the chapter on
+'Psychology and History.' And yet this graphic appendix to the
+Grundzuege may not be superfluous, as the fulness of a bulky volume
+cannot bring out clearly enough the fundamental relations; the detail
+hides the principles. The parallelism of logical movements in the
+different fields especially becomes more obvious in the graphic form.
+Above all, the book discussed merely those groups which had direct
+relation to psychology; a systematic classification must leave no
+remainder. Of course here too I have not covered the whole field of
+human sciences, as the more detailed ramification offers for our
+purpose no logical interest; to subdivide physics or chemistry, the
+history of nations or of languages, practical jurisprudence or
+theology, engineering or surgery, would be a useless overburdening of
+the diagram without throwing new light on the internal relations of
+knowledge.
+
+Without now entering more fully into any arguments, I may indicate in
+a few words the characteristic features of the graphically presented
+proposition. At the very outset we must make it clear that phenomena
+and voluntaristic attitudes are not cooerdinated, but that the reality
+of phenomena is logically dependent upon voluntaristic attitudes
+directed towards the ideal of knowledge. And yet it would be
+misleading to place the totality of phenomenalistic sciences as a
+subdivision under the teleological sciences. Possible it would be; we
+might have under the sciences of logical attitudes not only logic and
+mathematics but as a subdivision of these, again, the sciences which
+construct the logical system of a phenomenalistic world--physics
+being in this sense merely mathematics with the conception of
+substance added. And yet we must not forget that the teleological
+attitudes, to become a teleological science, must be also logically
+reconstructed, as they must be teleologically connected, and thus in
+this way the totality of purpose-sciences might be, too, logically
+subordinated to the science of logic. Logic itself would thus become a
+subdivision of logic. We should thus move in a circle, from which the
+only way out is to indicate the teleological character of all sciences
+by starting not with science but with the strictly teleological
+conception of life--life as a system of purposes, felt in immediate
+experience, and not as the object of phenomenalistic knowledge. Life
+as activity divides itself then into different purposes which we
+discriminate not by knowledge but by immediate feeling; one of them is
+knowledge, that is, the effort to make life, its attitudes, its means
+and ends a connected system of overindividual value. In the service of
+this logical task we connect the real attitudes and thus come to the
+knowledge of purposes: and we connect the means and ends--by
+abstracting from our subjective attitudes, considering the objects of
+will as independent phenomena--and thus come to phenomenalistic
+knowledge. At this stage the phenomenalistic sciences are no longer
+dependent upon the teleological ones, but cooerdinated with them;
+physics, for instance, is a logical purpose of life, but not a branch
+of logic: the only branch of logic in question is the philosophy of
+physics which examines the logical conditions under which physics is
+possible.
+
+One point only may at once be mentioned in this connection. While we
+have cooerdinated the knowledge of phenomena with the knowledge of
+purposes we have subordinated mathematics to the latter. As a matter
+of course much can be said against such a decision, and the authority
+of most mathematicians would be opposed to it. They would say that the
+mathematical objects are independent realities whose properties we
+study like those of nature, whose relations we 'observe,' whose
+existence we 'discover' and in which we are interested because they
+belong to the real world. All that is true, and yet the objects of the
+mathematician are objects made by the will, by the logical will,
+only, and thus different from all phenomena into which sensation
+enters. The mathematician, of course, does not reflect on the purely
+logical origin of the objects which he studies, but the system of
+knowledge must give to the study of the mathematical objects its place
+in the group where the functions and products of logical thought are
+classified. The arithmetical or geometrical material is a free
+creation, and a creation not only as to the combination of
+elements--that would be the case with many laboratory substances of
+the chemist too--but a creation as to the elements themselves, and the
+value of the creation, its 'mathematical interest,' is to be judged by
+ideals of thought, that is, by logical purposes. No doubt this logical
+purpose is its application in the world of phenomena, and the
+mathematical concept must thus fit the world so absolutely that it can
+be conceived as a description of the world after abstracting not only
+from the will relations, as physics does, but also from the content.
+Mathematics would then be the phenomenalistic science of the form and
+order of the world. In this way mathematics has a claim to places in
+both fields: among the phenomenalistic sciences if we emphasize its
+applicability to the world, and among the teleological sciences if we
+emphasize the free creation of its objects by the logical will. It
+seems to me that a logical system as such has to prefer the latter
+emphasis; we thus group mathematics beside logic and the theory of
+knowledge as a science of objects freely created for purposes of
+thought.
+
+All logical knowledge is divided into Theoretical and Practical. The
+modern classifications have mostly excluded the practical sciences
+from the system, rightly insisting that no facts are known in the
+practical sciences which are not in principle covered by the
+theoretical sciences; it is art which is superadded, but not a new
+kind of knowledge. This is quite true so far as a classification of
+objects of knowledge is in question, but as soon as logical tasks as
+such are to be classified and different aspects count as different
+sciences, then it becomes desirable to discriminate between the
+sciences which take the attitude of theoretical interest and those
+which consider the same facts as related to certain human ends. But we
+may at first consider the theoretical sciences only. They deal either
+with the objectified world, with objects of consciousness which are
+describable and explainable, or with the subjectivistic world of real
+life in which all reality is experienced as will and as object of
+will, in which everything is to be understood by interpretation of its
+meaning. In other words, we deal in one case with phenomena and in the
+other with purposes.
+
+The further subdivision must be the same for both groups--that which
+is merely individual and that which is 'overindividual'; we prefer the
+latter term to the word 'general,' to indicate at once that not a
+numerical but a teleological difference is in question. A phenomenon
+is given to overindividual consciousness if it is experienced with the
+understanding that it can be an object for every one whom we
+acknowledge as subject; and a purpose is given to overindividual will
+in so far as it is conceived as ultimately belonging to every subject
+which we acknowledge. The overindividual phenomena are, of course, the
+physical objects, the individual phenomena the psychical objects, the
+overindividual purposes are the norms, the individual purposes are the
+acts which constitute the historical world. We have thus four
+fundamental groups: the physical, the psychological, the normative and
+the historical sciences.
+
+Whoever denies overindividual reality finds himself in the world of
+phenomena a solipsist and in the world of purposes a sceptic: there is
+no objective physical world, everything is my idea, and there is no
+objective value, no truth, no morality, everything is my individual
+decision. But to deny truth and morality means to contradict the very
+denial, because the denial itself as judgment demands acknowledgment
+of this objective truth and as action demands acknowledgment of the
+moral duty to speak the truth. And if an overindividual purpose cannot
+be denied, it follows that there is a community of individual subjects
+whose phenomena cannot be absolutely different: there must be an
+objective world of overindividual objects.
+
+In each of the four groups of sciences we must consider the facts
+either with regard to the general relations or with regard to the
+special material; the abstract general relations refer to every
+possible material, the concrete facts which fall under them demand
+sciences of their own. In the world of phenomena the general relations
+are causal laws--physical or psychical laws; in the world of purposes
+theories of teleological interrelations--normative or historical; the
+specific concrete facts are in the world of phenomena objects,
+physical or psychical objects, in the world of purposes acts of
+will--specific norms or historical acts. If we turn first to
+phenomena, the laws thereof are expressed in the physical sciences, by
+mechanics, physics, chemistry, and we make mechanics the superior as
+chemistry must become ultimately the mechanics of atoms. In the
+psychological sciences the science of laws is psychology, with the
+side-branch of animal psychology, while human psychology refers to
+individuals and to social groups. Social psychology, as over against
+individual psychology, is thus a science of general laws, the laws of
+those psychological phenomena which result from the mutual influence
+of several individuals.
+
+On the other hand, we have as the special concrete products of the
+laws, the objects themselves, and the most natural grouping of them
+may be from whole to part. In the physical world it means that we
+start from the concrete universe, turning then to the earth, then to
+the objects on the earth, inorganic and organic. There is here no
+logical difficulty. Each one of these objects can be considered in
+three aspects, firstly as to its structure, secondly as to its special
+laws, that is, the special function of the object as related to the
+general sciences of physics and chemistry, and thirdly as to its
+natural development. If we apply these three methods of study to the
+whole universe we have astronomy, astrophysics and cosmology, to the
+whole earth, geography, geophysics, geology, to animals, zooelogy,
+physiology, comparative anatomy, and so on.
+
+The special phenomena in the framework of the psychological sciences
+group themselves in the same logical order, from the whole to the
+part. The psychological totality is empirical mankind, and as we
+select the earth as the one part of the universe which is the habitat
+of man, so our scientific interest must move from the whole psychical
+humanity to those phenomena of human life which are the vehicle of our
+civilization, from mankind to its most important function, the
+association of man; and as we moved from earth to the special objects
+on earth, so we may turn from association to the special phenomena
+which result from association. If we separated further the inorganic
+from the organic, we must here separate the products of
+undifferentiated and of differentiated association. The science of
+mankind is race psychology, the science of the association of man is
+sociology, the science of the results of undifferentiated association
+is Voelkerpsychologie, folk psychology. The science of products of
+differentiated association has no special name; its subject matter is
+the whole of historical civilization considered as a psychological
+naturalistic phenomenon. As soon as we follow the ramification still
+further we have to do with the special kinds of these products, that
+is, with the volitions, thoughts, appreciations and beliefs. In the
+undifferentiated associations they give us morals and habits,
+languages and enjoyments and mythological ideas, while the
+individually differentiated association gives political, legal and
+economic life, knowledge, art and religion: all of course merely as
+causal, not as teleological processes, and thus merely as
+psychological and not as historical material. Here, as with the
+physical phenomena, the structure, the special laws and the
+development must be everywhere separated, giving us three sciences in
+every case. For instance, the study of mankind deals with the
+differences of mental structure in psychical anthropology, with the
+special psychical laws in race psychology and with the development in
+comparative psychology. The chief point for us is that social
+psychology, race psychology, sociology, folk psychology, etc., are
+under this system sharply differentiated sciences and that they do not
+at all overlap the real historical sciences. There is no historical
+product of civilization which does not come under their method but it
+must be conceived as a causal phenomenon, not as related to the
+purposes of the real man, and thus even the development means merely a
+growing complication of naturalistic processes and not history in the
+teleological sense.
+
+We turn to the normative sciences. The general theory of the
+overindividual purposes is metaphysics; the special overindividual
+acts are those which constitute the normative volitions, connected in
+the philosophy of morals, the philosophy of state and the philosophy
+of law, those which constitute the normative thoughts and finally
+those which constitute the normative appreciations and beliefs,
+connected in aesthetics and the philosophy of religion. Especial
+interest belongs to the philosophy of thought. We have discussed the
+reasons why we group mathematics here and not among the
+phenomenalistic sciences. We have thus one science which deals
+critically with the presuppositions of thought, _i.e._ the theory of
+knowledge or epistemology, which can be divided into the philosophy of
+physical sciences, the philosophy of psychological sciences, the
+philosophy of normative sciences and the philosophy of historical
+sciences. We have secondly the science of the processes of thought
+dealing with concepts, judgments and reasoning, _i.e._, logic, and we
+have finally the science of those objects which the thought creates
+freely for its own purposes and which are independent from the content
+of the world, _i.e._, mathematics, which leads to the qualitative
+aspect of general mathematics and the quantitative aspect of concrete
+mathematics. For our purposes it may be sufficient to separate
+externally algebra, arithmetic, analysis and geometry. In this way all
+the philosophical sciences find their natural and necessary place in
+the system, while it has been their usual lot to form an appendix to
+the system, incommensurable with the parts of the system itself, even
+in the case that the other scheme were not preferred, to make ethics,
+logic, aesthetics, epistemology and metaphysics merely special branches
+of positivistic sociology and thus ultimately of biology.
+
+In the historical sciences the general theory which stands over
+against the special acts has a special claim on our attention. We may
+call it the philosophy of history. That is not identical with the
+philosophy of historical sciences which we mentioned as a part of
+epistemology. The philosophy of historical sciences deals with the
+presuppositions by which historical teleological knowledge becomes
+logically possible. The philosophy of history seeks a theory which
+connects the special historical acts into a unity. It has two
+branches. It is either a theory of the personality, creating a theory
+of real individual life as it enters as ideological factor into
+history, or it seeks the unity of entire humanity. The theory of
+personality shows the teleological interrelation of our purposes; the
+theory of humanity shows the teleological interrelation of all
+nations. The name philosophy of history has been used mostly for the
+theory of humanity only, abstracting from the fact that it has been
+often misused for sociology or for the psychology of history or for
+the philosophy of historical sciences--but the name belongs also to
+the theory of personality. This theory of personality is exactly that
+second kind of 'psychology' which does not describe and does not
+explain but which interprets the inner teleological connections of the
+real man. It is 'voluntaristic psychology' or, as others call it who
+see correctly the relation of this science to history, 'historical
+psychology.' It is practically 'apperceptionistic psychology.' The
+special activities of the historical man divide themselves again into
+volitions, thoughts, appreciations and beliefs, with their realization
+in the state, law, economical systems, knowledge, art and religion.
+Each of these special realizations must allow the same manifoldness in
+treatment which we found with the special physical or psychical
+objects; we can ask as to structure, relation to the general view and
+development. But in accordance with the teleological material the
+study of the structure here means 'interpretation,' the study of the
+general relations here means study of the relation to civilization,
+and the study of the development here means the real history. We have,
+thus, for the state or law or economy or knowledge or art or religion
+always one science which interprets the historical systems of state,
+etc., in a systematic and philological way, one science which deals
+with its function in the historical world and one which studies
+biographically and nationally the history of state, law, economical
+life, science, art or religion.
+
+In the sphere of the practical sciences the divisions of the
+theoretical sciences must repeat themselves. We have thus applied
+physical, applied psychological, applied normative and applied
+historical sciences, and it is again the antithesis of psychological
+and of historical sciences which is of utmost importance and yet too
+often neglected. The application of physical sciences, as in
+engineering, medicine, etc., or the application of normative
+knowledge in the sciences of criticism do not offer logical
+difficulty, but the application of psychological and historical
+knowledge does. Let us take the case of pedagogy or of penology,
+merely as illustrations. Is the application of phenomenalistic
+psychology or the application of teleological voluntarism in question?
+Considering the child, the criminal, any man, as psychophysical
+apparatus which must be objectively changed and treated, we have
+applied psychology; considering him as subject with purposes, as
+bearer of an historical civilization whose personalities must be
+interpreted and understood and appreciated, then we need applied
+historical knowledge. In the first case the science of pedagogy is a
+psycho-technical discipline which makes education mechanical and
+deprives the teacher of the teleological attitude of inner
+understanding; in the second case it is a science of real education
+far removed from psychology. All the sciences which deal with service
+in the system of civilization, service as teacher, as judge, as social
+helper, as artist, as minister, are sciences which apply the
+teleological historical knowledge, and their meaning is lost if they
+are considered as psycho-technical sciences only.
+
+
+LIFE (in its immediate reality, felt as a system of telelogical
+|    experiences, involving the acknowledgement of other subjects of
+|     experiences)
+|
+|-VOLITION (will aiming towards new experiences).
+| |-Individual: _Practical Life._
+| |-Overindividual: _Mortality._
+|
+|-THOUGHT (will acknowledging the connection of experiences).
+| |-Individual: _Judgement_
+| |-Overindividual: TRUTH
+|   |-THEORETICAL KNOWLEDGE (connection of experiences determined by
+|   | |                      pure experience).
+|   | |
+|   | |-KNOWLEDGE OF PHENOMENA (connection of experiences after
+|   | | |                       abstracting their will relations).
+|   | | |-Knowledge of Phenomena Given to Overindividual Consciousness.
+|   | | | |-I. PHYSICAL SCIENCES.
+|   | | |   |-A. GENERAL LAWS.
+|   | | |   | |-Mechanics.
+|   | | |   |   |-Physics.
+|   | | |   |   |-Chemistry.
+|   | | |   |
+|   | | |   |-B. SPECIAL OBJECTS.
+|   | | |     |-1. Universe.
+|   | | |     | |-Astronomy _a, b, c_.
+|   | | |     |
+|   | | |     |-2. Special Parts.
+|   | | |     | |-Geography _a, b, c_.
+|   | | |     |
+|   | | |     |-3. Special Objects on Earth.
+|   | | |       |-Inorganic.
+|   | | |       | |-Mineralogy _a, b, c_.
+|   | | |       |
+|   | | |       |-Organic.
+|   | | |         |-Plants.
+|   | | |         | |-Botany _a, b, c_.
+|   | | |         |
+|   | | |         |-Animals.
+|   | | |           |-Zoology _a, b, c_.
+|   | | |           |-Anthropology _a, b, c_.
+|   | | |
+|   | | |-Knowledge of Phenomena given to Indiviual Consciousness.
+|   | |   |-II. PSYCHOLOGICAL SCIENCES.
+|   | |     |-A. GENERAL LAWS.
+|   | |     | |-PHENOMENALISTIC PSYCHOLOGY
+|   | |     |   |-Animal Psychology.
+|   | |     |   |-Human psychology.
+|   | |     |     |-Individual Ps.
+|   | |     |       |-Normal.
+|   | |     |       | |-Child.
+|   | |     |       | |-Adult.
+|   | |     |       |
+|   | |     |       |-Abnormal.
+|   | |     |
+|   | |     |-B. SPECIAL OBJECTS.
+|   | |       |-1. Mankind.
+|   | |       | |-Race Psychology _a, b, c_.
+|   | |       |-2. Special Functions.
+|   | |       | |-Association of Men.
+|   | |       |   |-Sociology _a, b, c_.
+|   | |       |
+|   | |       |-3. Special Products of Association of Men
+|   | |         |      (considered as natural phenomena).
+|   | |         |-Products of Undiffereniated Association of Men
+|   | |         | |    (Folk Psychology).
+|   | |         | |-Volition.
+|   | |         | | |-Morals _a, b, c_.
+|   | |         | | |-Habits _a, b, c_.
+|   | |         | |
+|   | |         | |-Thoughts.
+|   | |         | | |-Languages _a, b, c_.
+|   | |         | |
+|   | |         | |-Appreciation.
+|   | |         | | |-Enjoyment _a, b, c_.
+|   | |         | |
+|   | |         | |-Belief.
+|   | |         |   |-Mythology _a, b, c_.
+|   | |         |
+|   | |         |-Products of Individual Differentiation
+|   | |           |  (casual phenomenalistic sciences of civilization
+|   | |           |   and its development).
+|   | |           |-Volition.
+|   | |           | |-State _a, b, c_.
+|   | |           | |-Law _a, b, c_.
+|   | |           | |-Economy _a, b, c_.
+|   | |           |
+|   | |           |-Thoughts.
+|   | |           | |-Sciences _a, b, c_.
+|   | |           |
+|   | |           |-Appreciation.
+|   | |           | |-Art _a, b, c_.
+|   | |           |
+|   | |           |-Belief.
+|   | |             |-Religion _a, b, c_.
+|   | |
+|   | |-KNOWLEDGE OF PURPOSES (connection of experiences in their
+|   |   |                      telelogical reality).
+|   |   |
+|   |   |-Knowledge of Purposes of the Overindividual Will.
+|   |   | |-III. NORMATIVE SCIENCES
+|   |   |   |-A. GENERAL THEORY of absolute values.
+|   |   |   | |-Metaphysics.
+|   |   |   |
+|   |   |   |-B. SPECIAL ACTS.
+|   |   |     |-Volition.
+|   |   |     | |-Philosophy of Morals (Ethics).
+|   |   |     | |-Philosophy of Law.
+|   |   |     | |-Philosophy of State.
+|   |   |     |
+|   |   |     |-Thoughts.
+|   |   |     | |-Presuppositions of Thought.
+|   |   |     | | |-Theory of Knowledge.
+|   |   |     | |   |-Phil. of Physics.
+|   |   |     | |   |-Phil. of Psych.
+|   |   |     | |   |-Phil. of Normative Sciences.
+|   |   |     | |   |-Phil. of Historical Sciences.
+|   |   |     | |
+|   |   |     | |-Processes of Thought.
+|   |   |     | | |-Logic.
+|   |   |     | |
+|   |   |     | |-Objects Created by Thought.
+|   |   |     |   |-Mathematics.
+|   |   |     |   |-Algebra.
+|   |   |     |   |-Arithmetic.
+|   |   |     |   |-Analysis.
+|   |   |     |   |-Geometry.
+|   |   |     |
+|   |   |     |-Appreciation.
+|   |   |     | |-Philosophy of Art (AEsthetics).
+|   |   |     |
+|   |   |     |-Belief.
+|   |   |       |-Philosophy of Religion.
+|   |   |
+|   |   |-Knowledge of Purposes of the Individual Will.
+|   |     |-IV. HISTORICAL SCIENCES.
+|   |       |-A. GENERAL THEORY of real life.
+|   |       | |-Philosophy of History.
+|   |       |   |-Theory of Personality.
+|   |       |   | |-(Theory of selves.)
+|   |       |   | |-("Historical Psychology.")
+|   |       |   | |-("VOLUNTARISTIC Psychology.")
+|   |       |   | |-("Apperceptional Psychology.")
+|   |       |   |-Theory of Humanity.
+|   |       |
+|   |       |-B. SPECIAL ACTS (telelogical interpretative sciences of
+|   |         |                civilization and history.)
+|   |         |-Volition.
+|   |         | |-Politics, _a, b, c_.
+|   |         | |-Law, _a, b, c_.
+|   |         | |-Economy, _a, b, c_.
+|   |         |
+|   |         |-Thoughts.
+|   |         | |-Science, _a, b, c_.
+|   |         |
+|   |         |-Appreciation.
+|   |         | |-Art, _a, b, c_.
+|   |         |
+|   |         |-Belief.
+|   |           |-Religion, _a, b, c_.
+|   |
+|   |-PRACTICAL KNOWLEDGE.
+|     |-APPLIED KNOWLEDGE OF PHENOMENA.
+|     | |-V. APPLIED PHYSICAL SCIENCES.
+|     | | |-Technical Sciences.
+|     | | | |-Applied Physics.
+|     | | | |-Applied Chemistry.
+|     | | | |-Applied Biology.
+|     | | |
+|     | | |-Medicine.
+|     | |
+|     | |-VI. APPLIED PSYCHOLOGICAL SCIENCES.
+|     |   |-Psychotechnical Sciences.
+|     |   | |-Psychological Pedagogy.
+|     |   | |-Psychological Penology.
+|     |   |
+|     |   |-Psychiatry.
+|     |
+|     |-APPLIED KNOWLEDGE OF PURPOSES.
+|       |-VII. APPLIED NORMATIVE SCIENCES.
+|       | |-Volition.
+|       | | |-Politics.
+|       | | | |-Science of Public Service.
+|       | | |
+|       | | |-Law.
+|       | | | |-Science of Legal Service. (Practical Jurisprudence.)
+|       | | |
+|       | | |-Economy.
+|       | |   |-Science of Social Service.
+|       | |
+|       | |-Thoughts.
+|       | | |-Science of Teaching. (Education.)
+|       | |
+|       | |-Appreciation.
+|       | | |-Science of Artistic Production.
+|       | |
+|       | |-Belief.
+|       |   |-Science of Religious Service. (Practical Theology.)
+|       |
+|       |-VIII. APPLIED HISTORICAL SCIENCES.
+|         |-Volition.
+|         | |-Criticism of State.
+|         | |-Criticism of Law.
+|         |
+|         |-Thoughts.
+|         | |-Criticism of Science.
+|         |
+|         |-Appreciation.
+|         | |-Criticism of Art.
+|         |
+|         |-Belief.
+|           |-Criticism of Religion.
+|
+|-APPRECIATION (will resting in isolated experiences).
+| |-Individual: _Enjoyment._
+| |-Overindividual: _Beauty._
+|
+|-BELIEF (will resting in the supplements of experience).
+  |-Individual: _Creed._
+  |-Overindividual: _Religion.
+
+NOTE: The letters _a, b, c_ below the sciences of Special Objects and
+Special Acts indicate the three subdivisions that results from the
+threefold aspects;--of structure(_a_), of relation to the general laws
+or theories(_b_), and of development(_c_). With regards to physical
+phenomena, for instances, we have astronomy(_a_), astrophysics(_b_),
+and cosmology(_c_); or geography(_a_), geophysics(_b_), geology(_c_);
+or botany(_a_), plant physiology(_b_), phylogenetic development of
+plants(_c_). In the same way for psychical objects; for instance:
+structural sociology(_a_), functional sociology(_b_), comparative
+sociology(_c_); or structure (grammar and syntax) of languages(_a_),
+psychology of languages(_b_), comparative study of languages(_c_).
+With regard to the telelogical historical sciences the study of
+structure takes on here the character of intrepretation; the relation
+to the general view is here the dependence on civilization and the
+development is here the real history. We have thus, for instance, the
+intepretation of Roman law(_a_), dependence of Roman law upon
+civilization(_b_), history of Roman law(_c_).
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+End of Project Gutenberg's Harvard Psychological Studies, Volume 1, by Various
+
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