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

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

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

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

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

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

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

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

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

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

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

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

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

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

[25] Muensterberg, Hugo, 'Grundzuege der Psychologie,' Leipzig, 1900, S. 525-561.

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

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

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

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

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

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

* * * * *



TACTUAL ILLUSIONS.

BY CHARLES H. RIEBER.

I.

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

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

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

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

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

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

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

[3] Thiery, A.: Philos. Studien, 1896, Bd. XII., S. 121.

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

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

II.

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

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

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

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

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



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

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

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

TABLE I.

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

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

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

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

TABLE II.

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

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

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

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

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

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

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

TABLE III.

Distances. 4 cm. 6 cm. 12 cm.

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

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

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

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

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

TABLE IV.

4 Centimeters.

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

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

TABLE V.

6 Centimeters.

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

TABLE VI.

8 Centimeters.

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

TABLE VII.

12 Centimeters.

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

TABLE VIII.

18 Centimeters.

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

TABLES IV.-VIII.

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

III.

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

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

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

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

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

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

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

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

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



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

IV.

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

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



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.

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

[7] 'Zeitsinn,' Tuebingen, 1858.

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

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

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

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

[10] Op. citat., p. 98.

V.

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

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

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

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

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

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

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

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

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

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

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

VI.

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

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

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

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

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

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



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

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

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

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

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

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

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

TABLE IX.

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

TABLE X.

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

TABLES IX. AND X.

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

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

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



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

VII.

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



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

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

TABLE XI.

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

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

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

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