I may say in advance of the account of my experiments, that I have here also found a ground of reconciliation for these two divergent opinions.  Just as in the case of the illusion for passive touch, there are here also certain conditions under which the filled space seems longer, and other conditions under which it appears shorter than the open space.  I feel warranted, therefore, in giving in some detail my research on this illusion, which again has been an extended one.  I think that the results of this study are equally important with those for passive touch, because of the further light which they throw on the way in which our touch sense functions in the perception of the geometrical illusions.  Dresslar’s experiments, like those of James, were made with cards in which one half was filled with punctures.  The number of punctures in each centimeter varied with the different cards.  Dresslar’s conclusion was not only that the filled space is overestimated, but also that the overestimation varies, in a general way, with the number of punctures in the filling.  Up to a certain point, the more holes there are in the card, the longer the space appears.

I had at the onset of the present experiment the same feeling about Dresslar’s work that I had about Parrish’s work, which I have already criticised, namely, that a large number of experiments, in which many variations were introduced, would bring to light facts that would explain the variety of opinion that had hitherto been expressed.  I was confident, however, that what was most needed was a quantitative determination of the illusion.  Then, too, inasmuch as the illusion, whatever direction it takes, is certainly due to some sort of qualitative differences in the two kinds of touch sensations, those from the punctured, and those from the smooth half, it seemed especially desirable to introduce as many changes into the nature of the filling as possible.  The punctured cards I found very unsatisfactory, because they rapidly wear off, and thus change the quality of the sensations, even from judgment to judgment.

[Illustration:  FIG. 7.]

The first piece of apparatus that I used in the investigation of the illusion for open and filled space with active touch is shown in Fig. 7.  A thimble A, in which the finger was carried, moved freely along the rod B.  The filled spaces were produced by rows of tacks on the roller C.  By turning the roller, different kinds of fillings were brought into contact with the finger-tip.  The paper D, on which the judgments were recorded by the subject, could be slowly advanced under the roller E.  Underneath the thimble carrier there was a pin so arranged that, by a slight depression of the finger, a mark was made on the record paper beneath.  A typical judgment was made as follows; the subject inserted his finger in the thimble, slightly depressed the carrier to record the starting points, then brought