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.

Having now given an account of the results of this digression into
experiments to determine the influence of pressure upon point
distances, I shall pass to the second series of experiments on the
illusion in question. In this series, as has been already stated, the
filled space was taken on one arm and the open on the other, and then
the process was reversed in order to eliminate any error arising from
a lack of symmetry between the two regions. Without, for the present,
going into a detailed explanation of the statistics of this second
series of experiments, which are recorded in Tables IV., V., VI.,
VII. and VIII., I may summarize the salient results into these general
conclusions: First, the short filled distance is underestimated;