IV.

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

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

[Illustration: Fig. 4.]

I need hardly say that here, and in all my other experiments, the subjects were kept as far as possible in complete ignorance of the object of the experiment. This and the other recognized laboratory precautions were carefully observed throughout this work. Four distances were used, 4, 8, 12 and 16 cm. At frequent intervals throughout the tests the contact was made with only one of the points instead of four. In this way there came to light again the interesting fact which we have already seen in the last section, which is of great significance for my theory--that the end points are located differently when given alone than when they are presented simultaneously with the other points. I give a graphic representation of the results obtained from a large number of judgments in Figs. 4, 5 and 6. These experiments with filled spaces, like the earlier experiments, were made on the volar side of the forearm beginning near the wrist. In each distance four points were used, equally distributed over the space. The shaded curve, as in the previous figures, represents the results of the attempts to localize the points when all four were given simultaneously. In the dotted curves, the end points were given alone. The height of the curve at any place is determined by the number of times a point was located immediately underneath that

## particular part of the curve. In Fig. 4 the curve which was determined

by the localization of the four points when given simultaneously, shows by its shape how the points appear massed towards the center. In Fig. 5 the curve _AB_ shows, by its crests at _A_ and _B_, that the end points tended to free themselves from the rest in the judgments. But if the distance _AB_ be taken to represent the average of the judgments upon the filled space 1, 2, 3, 4, it will be seen to be shorter than what may be regarded as the average of the judgments upon the corresponding open space, namely, the distance _A'B'_, determined by the localizations of the end points alone. The comparative regularity of the curve indicates that the subject was unable to discriminate among the points of the filling with any degree of certainty. The localizations were scattered quite uniformly along the line. In these short distances the subject often judged four points as two, or even one.

[Illustration: Fig. 5.]

[Illustration: Fig. 6.]

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

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

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

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

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

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

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

[7] 'Zeitsinn,' Tübingen, 1858.

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

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

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

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

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