[Illustration:  FIG. 2.  Back of hand.]

[Illustration:  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.

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.]