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.