This changing of the apparent temperature of the end points has, it must be admitted, introduced another factor; and it might be objected that it was not so much the prevention of fusion as the change in the temperature that caused the judgments to drift towards overestimation. I have statistics to show that this observation is in a way just. Extremes in temperature, whether hot or cold, are interpreted as an increase in the amount of space. This conclusion has also been reported from a number of other laboratories. My contention at this point is simply that there are certain conditions under which these distances will be overestimated and that these are the very conditions which bring the phenomenon into closer correspondence with the optical illusion, both as to the stimuli and the subjective experience. Then, aside from this, such an objection will be seen to be quite irrelevant if we bear in mind that when the end points in the filled distance were replaced by metallic points, metallic points were also employed in the open distance. The temperature factor, therefore, entered into both spaces alike. By approaching the problem from still another point of view, I obtained even more conclusive evidence that it is the fusion of the end points with the adjacent points in the short distances that leads to the underestimation of these. I have several series in which the end points were prevented from fusing into the filling, by raising or lowering them in the apparatus, so that they came in contact with the skin just after or before the intermediate points. When the contacts were arranged in this way, the tendency to underestimate the filled spaces was very much lessened, and with some subjects the tendency passed over into a decided overestimation. This, it will be seen, is a confirmation of the results in Table II.
I have already stated that the two series of experiments reported in Section II. throughout point to the conclusion that an increase of pressure is taken to mean an increase in the distance. I now carried on some further experiments with short filled distances, making variations in the place at which the pressure was increased. I found a maximum tendency to underestimate when the central points in the filled space were weighted more than the end points. A strong drift in the opposite direction was noticed when the end points were heavier than the intermediate ones. It is not so much the pressure as a whole, as the place at which it is applied, that causes the variations in the judgments of length. In these experiments the total weights of the points were the same in both cases. An increase of the weight on the end points with an equivalent diminution of the weights on the intervening points gave the end points greater distinctness apparently and rendered them less likely to disappear from the judgments.
At this stage in the inquiry as to the cause of the underestimation of short distances, I began some auxiliary experiments on the problem of the localization of cutaneous impressions, which I hoped would throw light on the way in which the fusion or displacement that I have just described takes place. These studies in the localization of touch sensations were made partly with a modification of the Jastrow æsthesiometer and partly with an attachment to the apparatus before described (Fig. 1). In the first case, the arm upon which the impressions were given was screened from the subject's view, and he made a record of his judgments on a drawing of the arm. The criticism made by 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.
The results from these two methods were practically the same. But the second method, although it obviously permitted the determination of the displacements in one dimension only, was in the end regarded as the more reliable method. With this apparatus I could be more certain that the contacts were made simultaneously, which was soon seen to be of the utmost importance for these particular experiments. Then, too, by means of this æsthesiometer, all movement of the points after the contact was made was prevented. This also was an advantage in the use of this apparatus, here and elsewhere, which can hardly be overestimated. With any æsthesiometer that is operated directly by the hand, it is impossible to avoid imparting a slight motion to the points and thus changing altogether the character of the impression. The importance of this consideration for my work was brought forcibly to my attention in this way. One of the results of these tests was that when two simultaneous contacts are made differing in weight, if only one is recognized it is invariably located in the region of the contact with the heavier point. But now if, while the points were in contact with the skin and before the judgment was pronounced, I gave the lighter point a slight jar, its presence and location were thereby revealed to the subject. Then, too, it was found to be an advantage that the judgments were thus confined to the longitudinal displacement only; for, as I have before insisted, it was the relative, not the absolute position that I wished to determine, since my object in all these experiments in localization was to determine what connection, if any, exists between judgments upon cutaneous distances made indirectly by means of localization, and judgments that are pronounced directly upon the subjective experience of the distance.
In the first of these experiments, in which two points of different weight were used, the points were always taken safely outside of the threshold for the discrimination between two points in the particular region of the skin operated on. An inspection of the results shown in Figs. 2 and 3 will indicate the marked tendency of the heavier point to attract the lighter. In Figs. 2 and 3 the heavy curves were plotted from judgments where both heavy and light points were given together. The dotted curve represents the localization of each point when given alone. The height of the curves at any particular point is determined by the number of times a contact was judged to be directly under that point. The fact that the curves are higher over the heavy points shows that, when two points were taken as one, this one was localized in the vicinity of the heavier point. When points were near the threshold for any region, it will be observed that the two points were attracted to each other. But when the points were altogether outside the threshold, they seemed strangely to have repelled each other. As this problem lay somewhat away from my main interest here, I did not undertake to investigate this peculiar fluctuation exhaustively. My chief purpose was satisfied when I found that the lighter point is displaced toward the heavier, in short distances. A further explanation of these figures will be given in connection with similar figures in the next section.
Fig. 2. Back of hand.
Fig. 3. Forearm.
This attraction of the heavier for the lighter points is, I think, a sufficient explanation for the variations in judgments upon filled distances where changes are made in the place at which the pressure is applied. I furthermore believe that an extension of this principle offers an explanation for the underestimation of cutaneous line-distances, which has been frequently reported from various laboratories. Such a straight line gives a subjective impression of being heavier at the center. I found that if the line is slightly concave at the center, so as to give the ends greater prominence and thereby leave the subjective impression that the line is uniform throughout its entire length, the line will be overestimated in comparison with a point distance. Out of one hundred judgments on the relative length of two hard-rubber lines of 5 cm. when pressed against the skin, one of which was slightly concave, the concave line was overestimated eighty-four times. For sight, a line in which the shaded part is concentrated at the center appears longer than an objectively equal line with the shading massed towards the ends.