However, before I began this second series, in which one of the chief variations was to be in the weights of the different points, I made a brief preliminary series of experiments to determine in a general way the influence of pressure on judgments of point distances.  Only three distances were employed, four, six and twelve centimeters, and three weights, twelve, twenty and forty grams.  Table III. shows that, for three men who were to serve as subjects in the main experiments that are to follow, an increase in the weight of the points was almost always accompanied by an increase in the apparent distance.

TABLE III.

  Distances. 4 cm. 6 cm. 12 cm.

   Weights
   (Grams). 12 20 40 12 20 40 12 20 40

R.        3.9  3.2  3.0    6.2  5.6  5.3    11.4  10.4   9.3
F.        4.3  4.0  3.6    6.1  5.3  5.5    12.3  11.6  10.8
B.        4.1  3.6  3.1    6.0  5.7  5.8    12.0  10.2   9.4
P.        4.3  4.1  3.7    5.9  5.6  5.6    13.1  11.9  10.7

In the standard distances the points were each weighted to 6 grams.  The first three figures signify that a two-point distance of 4 cm., each point weighing 6 grams, was judged equal to 3.9 cm. when each point weighed 12 grams. 3.2 cm. when each point weighed 20 grams, etc.  Each figure is the average of five judgments.

Now the application of this principle in my criticism of Parrish’s experiments, and as anticipating the direction which the following experiments will take, is this:  if we take a block such as Parrish used, with only two points in it, and weight it with forty grams in applying it to the skin, it is plain that each point will receive one half of the whole pressure, or twenty grams.  But if we put a pressure of forty grams upon a block of eight points, each point will receive only one eighth of the forty, or five grams.  Thus, in the case of the filled space, the end points, which play the most important part in the judgment of the distance, have each only five grams’ pressure, while the points in the open space have each twenty grams.  We should, therefore, naturally expect that the open space would be overestimated, because of the decided increase of pressure at these significant points.  Parrish should have subjected the blocks, not to the same pressure, but to a pressure proportional to the number of points in each block.  With my apparatus, I was easily able to prove the correctness of my position here.  It will be seen in Tables IV. to VIII. that, when the sum of the weights of the two end points in the open space was only just equal to the sum of the weights of all the points in the filled space, the filled space was underestimated just as Parrish has reported.  But when the points were all of the same weight, both in the filled and the open space, the filled space was judged longer in all but the very short distances.  For this latter exception I shall offer an explanation presently.