Having now given an account of the results of this digression into experiments to determine the influence of pressure upon point distances, I shall pa.s.s to the second series of experiments on the illusion in question. In this series, as has been already stated, the filled s.p.a.ce 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 s.p.a.ce gradually decreases until in the case of the filled distance of 18 cm. the judgments pa.s.s over into p.r.o.nounced 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 s.p.a.ce. 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 s.p.a.ces 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 s.p.a.ces were made up of 4, 5 and 6 points, respectively. The total weight of the filled s.p.a.ce in _A_, _B_ and _C_ was always just equal to the weight of the two points in the open s.p.a.ce, 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 s.p.a.ce consisted of four points, but here the weight of each point was 10 gr., making a total weight of 40 gr. for the filled s.p.a.ce, as against 20 gr.

for the open s.p.a.ce. In _E_ the weight of each was 20 gr., making the total weight of the filled s.p.a.ce 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 s.p.a.ce 4 cm., total weight 20 gr., with a filled s.p.a.ce of 4 points, total weight also 20 gr., the filled s.p.a.ce 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 s.p.a.ces are underestimated, that long s.p.a.ces 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 p.r.o.nounced 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 s.p.a.ce 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 s.p.a.ces. 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 s.p.a.ce. 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 s.p.a.ces 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 s.p.a.ces was very much lessened, and with some subjects the tendency pa.s.sed 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 s.p.a.ce 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 p.r.o.nounced, 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 p.r.o.nounced 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.

[Ill.u.s.tration: FIG. 2. Back of hand.]

[Ill.u.s.tration: FIG. 3. Forearm.]

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

[Ill.u.s.tration: 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 s.p.a.ces, 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 s.p.a.ce. 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 ma.s.sed 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 s.p.a.ce 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 s.p.a.ce, 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.

[Ill.u.s.tration: Fig. 5.]

[Ill.u.s.tration: Fig. 6.]