his finger-tip into contact with the first point in the filled space.  The subject was, of course, all the while ignorant of the length or character of the filling over which he was about to pass.  The finger-tip was then drawn along the points, and out over the smooth surface of the roller, until the open space passed over was judged equal to the filled space.  Another slight depression of the finger registered the judgment on the paper below.  The paper was then moved forward by turning the roller E, and, if desired, a different row of pins was put in place for judgment by revolving the roller C.  The dividing line between the open and filled spaces was continuously recorded on the paper from below by a pin not shown in the illustration.

The rollers, of which I had three, were easily removed or turned about, so that the open space was presented first.  In one of the distances on each roller both spaces were unfilled.  This was used at frequent intervals in each series and served somewhat the same purpose as reversing the order in which the open and filled spaces were presented.  With some subjects this was the only safe way of securing accurate results.  The absolute distances measured off were not always a sure criterion as to whether the filled space was under-or overestimated.  For example, one rather erratic subject, who was, however, very constant in his erratic judgments, as an average of fifty judgments declared a filled space of 4 cm. to be equal to an open space of 3.7 cm.  This would seem, on the surface, to mean that the filled space had been underestimated.  But with these fifty judgments there were alternated judgments on two open spaces, in which the first open space was judged equal to the second open space of 3.2 cm.  From this it is obvious that the effect of the filling was to cause an overestimation—­not underestimation as seemed at first sight to be the case.

In another instance, this same subject judged a filled space of 12.0 cm. to be equal to an open space of 12.9 cm., which would seem to indicate an overestimation of the filled space.  But an average of the judgments on two open spaces that were given in alternation shows that an equivalence was set up between the two at 13.7 cm. for the second open space.  This would show that the filling of a space really produced an underestimation.

The same results were obtained from other subjects.  In my experiments on the illusion for passive touch, I pointed out that it is unsafe to draw any conclusion from a judgment of comparison between open and filled cutaneous spaces, unless we had previously determined what might be called a standard judgment of comparison between two open spaces.  The parts of our muscular space are quite as unsymmetrical as the parts of our skin space.  The difficulties arising from this lack of symmetry can best be eliminated by introducing at frequent intervals judgments on two open spaces.  As I shall try to show later, the psychological character of the judgment is entirely changed by reversing the order in which the spaces are presented, and we cannot in this way eliminate the errors due to fluctuations of the attention.