Let me first call attention to some obvious criticisms on Parrish’s experiments.  They were all made with one distance, namely, 6.4 centimeters; and on only one region, the forearm.  Furthermore, in these experiments no attempt was made to control the factor of pressure by any mechanical device.  The experimenter relied entirely on the facility acquired by practice to give a uniform pressure to the stimuli.  The number of judgments is also relatively small.  Again, the open and filled spaces were always given successively.  This, of course, involves the comparison of a present impression with the memory of a somewhat remote past impression, which difficulty can not be completely obviated by simply reversing the order of presentation.  In the optical illusion, the two spaces are presented simultaneously, and they lie adjacent to each other.  It is still a debated question whether this illusion would exist at all if the two spaces were not given simultaneously and adjacent.  Muensterberg[5] says of the optical illusion for the open and filled spaces, “I have the decided impression that the illusion does not arise from the fact of our comparing one half with the other, but from the fact that we grasp the line as a whole.  As soon as an interval is inserted, so that the perception of the whole line as constituted of two halves vanishes, the illusion also disappears.”  This is an important consideration, to which I shall return again.

   [5] Muensterberg, H.:  ‘Beitraege zur Exper.  Psy.,’ Freiburg i.B.,
   1889, Heft II., S. 171.

Now, in my experiments, I endeavored to guard against all of these objections.  In the first place, I made a far greater number of tests.  Then my apparatus enabled me, firstly, to use a very wide range of distances.  Where the points are set in a solid block, the experiments with long distances are practically impossible.  Secondly, the apparatus enabled me to control accurately the pressure of each point.  Thirdly, the contacts could be made simultaneously or successively with much precision.  This apparatus (Fig. 1) was planned and made in the Harvard Laboratory, and was employed not only in our study of this particular illusion, but also for the investigation of a number of allied problems.

[Illustration:  FIG. 1.]

Two aesthesiometers, A and B, were arranged in a framework, so that uniform stimulations could be given on both arms.  The aesthesiometers were raised or lowered by means of the crank, C, and the cams, D and E. The contacts were made either simultaneously or successively, with any interval between them according to the position of the cams on the crank.  The height of the aesthesiometer could be conveniently adjusted by the pins F and H. The shape of the cams was such that the descent of the aesthesiometer was as uniform as the ascent, so that the contacts were not made by a drop motion unless that was desired.  The sliding rules, of which there were several forms and lengths, could be easily