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;
second, this underestimation of the filled space gradually decreases
until in the case of the filled distance of 18 cm. the judgments pass
over into pronounced overestimations; third, an increase in the number
of points of contact in the shorter distances increases the
underestimation, while an increase in the number of points in the
longer distance increases the overestimation; fourth, an increase of
pressure causes an invariable increase in the apparent length of
space. If a general average were made of the results given in Tables
IV., V., VI., VII. and VIII., there would be a preponderance of
evidence for the conclusion that the filled spaces are overestimated.
But we cannot ignore the marked tendencies in the opposite direction
for the long and the short distances. These anomalous results, which,
it will be remembered, were also found in our first series, call for
explanation. Several hypotheses were framed to explain these
fluctuations in the illusion, and then some shorter series of
experiments were made in different directions with as large a number
of variations in the conditions as possible, in the hope of
discovering the disturbing factors.

TABLE IV.