Harvard Psychological Studies, Volume 1, Edited

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while up to this time the results of our investigations have been scattered in various places, and have often remained unpublished through lack of space, henceforth, we hope to have in these STUDIES the opportunity to publish the researches of the Harvard Laboratory more fully and in one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

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

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

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

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

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

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

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

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

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

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."

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.

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.

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

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

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. Ostwald7 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.

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

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

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

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

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

This phenomenon was probably first described by Mach, in 1886.8 His view is essentially as follows: It is clear that in whatever direction the eye moves, away from its luminous fixation point, the streak described on the retina by the luminous image will lie on the same part of the retina as it would have lain on had the eye remained at rest but the object moved in the opposite direction. Thus, if the eye moves to the right, we should expect the streak to appear to dart to the left. If, however, the streak has not faded by the time the eye has come to rest on a new fixation point (by supposition to the right of the old), we should expect the streak to be localized to the left of this, that is, to the right of the former fixation-point. In order to be projected, a retinal image has to be localized with reference to some point, generally the fixation-point of the eyes; and it is therefore clear that when two such fixation-points are involved, the localization will be ambiguous if for any reason the central apparatus does not clearly determine which shall be the point of reference. With regard to the oppositely moving streak Mach says:9 "The streak is, of course, an after-image, which comes to consciousness only on, or shortly before, the completion of the eye-movement, nevertheless with positional values which correspond, remarkably enough, not to the later but to the earlier position and innervation of the eyes." Mach does not further attempt to explain the phenomenon.

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.

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.

Cornelius11 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.

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. Schwarz16 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 I.). 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°.

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

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

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

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

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

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

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

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

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

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.

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

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.

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 110σ19. If the eye sweeps from O to N in the same time, it will be moving at an angular velocity of 1° in 11.98σ (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 99.9σ, which is an average of only 2.49σ 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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 275σ.

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 110σ 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 275σ. 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 275σ, although, again, this is much more than a proportionate part of the total time (99.9σ) given by Dodge and Cline for a movement of the eye through 40°. The eye is in this case also moving slowly. As before, it is permissible to let the pendulum run down till it swings too slowly for the eye to move with it; since any lessened speed of the pendulum only makes the reddish-orange phase more prominent.

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

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

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

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

The possible appearances to the moving eye are closely analogous to those in the dumb-bell experiment. If the eye moves too soon or too late, so that it is at rest during the exposure, the image is like T itself (Fig. 8) but somewhat fainter and localized midway between the points P and P'. If the eye moves reflexly at the rate of the pendulum, the image is of the shape i and shows the two phases (3 followed by 5). It is localized in the middle and appears to move across the nine-centimeter opening.

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

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

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

The frequent and unmistakable appearance of this band of straw-yellow on a non-elongated green field without the previous phase in which the band is reddish-orange, although this latter was unmistakable when the same stimulation was given to the eye at rest, is authenticated by eight subjects. This appearance, together with that of the handleless dumb-bell, is submitted as a demonstration that during voluntary movements of the eyes, and probably of the head as well, there is a moment in which stimulations are not transmitted from the retina to the cerebral cortex, that is, a moment of central anæsthesia. The reason for saying 'and probably of the head as well,' is that although the phenomena described are gotten equally well from movements of the head, yet it is not perfectly certain that when the head moves the eyes do not also move slightly within the head, even when the attempt is made to keep them fixed.

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

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

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

Finally, the method of making judgments on after-images is not new in psychology. Lamansky's well-known determination of the rate of eye-movements22 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 Guillery23 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.

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

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

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

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

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

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

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

But decidedly the most interesting detail about the anæsthesia is that shown by the extreme liability of the eye to stop reflexly on the red or the green light, in the second experiment with the pendulum. Suppose the eye to be moving from P to P' (Fig. 5); the anæsthesia, although beginning later than the movement, is present when the eye reaches O, while it is between O and N, that is, during the anæsthetic moment, that the eye is reflexly caught and held by the light. This proves again that the anæsthesia is not retinal, but it proves very much more; namely, that the retinal stimulation is transmitted to those lower centers which mediate reflex movements, at the very instant during which it is cut off from the higher, conscious centers. The great frequency with which the eye would stop midway in its movements, both in the second pendulum-experiment and in the repetition of Dodge's perimeter-test, was very annoying at the time, and the observation cannot be questioned. The fact of the habitual reflex regulation of voluntary movements is otherwise undisputed. Exner24 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.

But shall we suppose that the 'connection' between the retina and the conscious centers is cut off during the central anæsthesia? All that the facts prove is that the centers are at that time not conscious. It would be at present an unwarrantable assumption to make, that these centers are therefore disconnected from the retina, at the optic thalami, the superior quadrigeminal bodies, or wheresoever. On broad psychological grounds the action-theory of Münsterberg25 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.

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

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

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

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

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

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

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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. James1 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.

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.

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. Münsterberg5 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.

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.

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

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

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

TABLE I.

TABLE II.

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.

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.

TABLE V.

6 Centimeters.

TABLE VI.

8 Centimeters.

TABLE VII.

12 Centimeters.

TABLE VIII.

18 Centimeters.

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

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

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

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

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

At this stage in the inquiry as to the cause of the underestimation of short distances, I began some auxiliary experiments on the problem of the localization of cutaneous impressions, which I hoped would throw light on the way in which the fusion or displacement that I have just described takes place. These studies in the localization of touch sensations were made partly with a modification of the Jastrow æsthesiometer and partly with an attachment to the apparatus before described (Fig. 1). In the first case, the arm upon which the impressions were given was screened from the subject's view, and he made a record of his judgments on a drawing of the arm. The criticism made by Pillsbury6 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.

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

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

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.

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.

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.

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.

Vierordt7 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. Fechner8 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.

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 Donaldson9 discovered, that an increase in the pressure of a moving point diminishes the apparent distance.

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

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. Auerbach11 says, in his investigation of the quantitative variations of the illusion, that concentration of attention diminishes the illusion. In the Zöllner figure, for instance, I have been able to notice the illusion fluctuate through a wide range, without eye-movements and without definitely attending to any point, during the fluctuation of the attention. My experiments with the tactual illusion have led me to the conclusion that it fluctuates even more than the optical illusion. Any deliberation in the judgment causes the apparent size of the filled space to shrink. The judgments that are given most rapidly and naïvely exhibit the strongest tendency to overestimation; and yet these judgments are so consistent as to exclude them from the category of guesses.

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

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

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

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

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 Dresslar12 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."

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.

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.

TABLE X.

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.

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

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.

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.

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

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

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

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

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

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

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

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

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

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

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

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. James14 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.

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.

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.

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

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

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

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

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

The failure to recognize the importance of these inwardly initiated sensations is the chief defect in Dresslar's reasoning. He has endeavored to make our judgments in the illusion in question depend entirely on the sensations of external origin. He insists also that the illusion varies according to the variations in quantity of these external sensations. Now my experiments have shown, I think, very clearly that it is not the numerical or quantitative extent of the objective sensations which disturbs the judgment of distance, but the sensation of inner origin which we set over against these outer sensations. The piece of plush, because of the disagreeable sensations which it gives, is judged shorter than the space filled with closely crowded tacks. Dresslar seems to have overlooked entirely the fact that the feelings and emotions can be sources of illusions in the amount of movement, and hence in our judgments of space. The importance of this element has been pointed out by Münsterberg19 in his studies of movement.

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 Stumpf20 has formulated against Bain's genetic space-theory. Stumpf's famous criticism applies not only to Bain, but also to the other English empiricists and to Wundt. Bain says: "When with the hand we grasp something moving and move with it, we have a sensation of one unchanged contact and pressure, and the sensation is imbedded in a movement. This is one experience. When we move the hand over a fixed surface, we have with the feelings of movement a succession of feelings of touch; if the surface is a variable one, the sensations are constantly changing, so that we can be under no mistake as to our passing through a series of tactual impressions. This is another experience, and differs from the first not in the sense of power, but in the tactile accompaniment. The difference, however, is of vital importance. In the one case, we have an object moving and measuring time and continuous, in the other case we have coëxistence in space. The coëxistence is still further made apparent by our reversing the movement, and thereby meeting the tactile series in the inverse order. Moreover, the serial order is unchanged by the rapidity of our movements."21

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. Henri22 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.

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.

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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.

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.

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.

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.

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^-γ2x2

and, assuming two points (x₁ y₁) and (x₂ y₂) on the curve, we deduce the formula

where D = x₁ ± x₂, and k = value of y when x = 0.

x₁ and x₂ 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, y₁ and y₂ which we may select from the table, we know the value of x₁ ± x₂, we can compute the value of x₁, 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.

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. Mach4 found no constant error. Höring5 found that intervals over 0.5 sec. were overestimated. Vierordt,6 Kollert,7 Estel8 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. Mehner10 found underestimation from 0.7 to 5.0 and overestimation above 5.0. Schumann11 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. Stevens12 found underestimation of small intervals and overestimation of longer ones, placing the indifference point between 0.53 and 0.87.

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.

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 Mehner13 thought results gotten without a maximum of practice are worthless, while Meumann14 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.

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.

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.

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.

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.

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.

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.

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.

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.

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 Meumann15 in investigating the effects of intensity changes upon auditory time, and also with the results obtained by Schumann16 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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

So far as the primary object of this part of the experiment is concerned the results are negative, but incidentally the process of training brought out some facts of a more positive nature. It was early noticed that some groups of four were much more readily recognized than others, and that some of them were either judged correctly or underestimated while others were either judged correctly or overestimated. For convenience the fingers were indicated by the letters A B C D, A being the index finger. The thumb was not used. Two weights were over each finger. The one near the base was called 1, the one toward the end 2. Thus A12 B1 C2 means two contacts on the index finger, one near the base of the second finger, and one near the end of the third finger. The possible arrangements of four may be divided into three types: (1) Two weights on each of two fingers, as A12 B12, C12 D12, etc., (2) four in a line across the fingers, A1 B1 C1 D1 or A2 B2 C2 D2, (3) unsymmetrical arrangements, as A1 B2 C1 D2, etc. Arrangements of the first type were practically never overestimated. B12 C12 was overestimated once and B12 D12 was overestimated once, but these two isolated cases need hardly be taken into account. Arrangements of the second type were but rarely overestimated—A2 B2 C2 D2 practically never, A1 B1 C1 D1 a few times. Once the latter was called eight. Apparently the subject perceived the line across the hand and thought there were two weights on each finger instead of one. Arrangements of the third type were practically never underestimated, but were overestimated in 68 per cent. of the cases.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

If the only fact we had to explain was that two points are often thought to be one when they are near together, 'fusion' might be a good hypothesis, but we have other facts to consider. If this one is explained by fusion, then the mistaking of one point for two must be due to diffusion of sensations. Even that might be admissible if the Vexirfehler were the only phenomenon of this class which we met. But it is also true that several contacts are often judged to be more than they actually are, and that hypothesis will not explain why certain arrangements of the stimulating objects are more likely to bring about that result than others. Still more conclusive evidence against fusion, it seems to me, is found in the fact that two points, one on each hand, may be perceived as one when the hands are brought together. Another argument against fusion is the fact that two points pressed lightly may be perceived as one, and when the pressure is increased they are perceived as two. Strong pressures should fuse better than weak ones, and therefore fusion would imply the opposite results. Brückner1 has found that two sensations, each too weak to be perceived by itself, may be perceived when the two are given simultaneously and sufficiently near together. This reënforcement of sensations he attributes to fusion. But we have a similar phenomenon in vision when a group of small dots is perceived, though each dot by itself is imperceptible. No one, I think, would say this is due to fusion. It does not seem to me that we need to regard reënforcement as an indication of fusion.

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 observers3 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.

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

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

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

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

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

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

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

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

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

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

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

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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.

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.

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.

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.

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.

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.

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.

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.

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.

TABLE VII.

JUDGMENTS IN ILLUMINATED POINT.

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.

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.

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

TABLE IX.

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 Campbell1 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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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.

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.

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.

"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.

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.

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.

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.

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^AOp^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^BOpC 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.

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.

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

but, since in the same time the green sector AOB moves from B to B', we know also that

then

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

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,

Since

W = Z - 2w,

we have

or

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

and

therefore

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

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

and, again,

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.

We have

and

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

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

Now when pendulum and disc move in the same direction,

so that to include both cases we may say that

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

r'(w-p) = rw,

w (r'-r) = pr',

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

w = BB',

r'(p - w) = rw ,

w(r' + r) = pr' ,

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

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

and

therefore, by dividing,

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_τW must be positive or greater than zero for all values of r which lie in question.

Now

and

or reduced,

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_τW > 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

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

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)

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

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

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

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'),

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 Marbe3 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 1σ, 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."

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 = 1σ. 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

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."

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. Helmholtz4 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 1σ, 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.

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.

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.

If any reader still suspects that more is involved than the persistence 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.

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.

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.

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.

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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.

Since the experiment just described was performed without laboratory facilities, Calkins2 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.

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 contained sixteen series, A¹, A², A³, etc., to A¹⁶. They were divided as follows:

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.

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,

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:

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 A¹, A⁵, A⁹, A¹³ are to be found in the first and third columns, A², A⁶, A¹⁰, A¹⁴ in the second and fourth, A³, A⁷, A¹¹, A¹⁵, in the fifth and seventh, and A⁴, A⁸, A¹², A¹⁶ in the sixth and eighth columns.

TABLE I.

SHOWING IMMEDIATE RECALL AND RECALL AFTER TWO DAYS.

These results will be included in the discussion of the results of 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:

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:

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.

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.

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.

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.

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.

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.

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.

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.

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.

TABLE VI.

SAME FOR M AND Mo.—SUMMARY FROM C 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.

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.

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.

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.

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.

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