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.¹

4 Centimeters.

A           B              D            E
less = gr.  less = gr.     less = gr.   less = gr. 
R. (a)  7  2  1     8  1  1        6  2  2      5  1  4
(b)  7  3  0     7  1  2        6  2  2      6  1  3
F. (a)  6  3  1     7  1  2        7  0  3      6  0  4
(b)  7  0  3     9  1  0        6  1  3      5  2  3
-------    --------       --------     --------
27  8  5    31  4  5       25  5 10     22  4 14

¹In columns A, B, and C the filled spaces were made up of 4, 5 and 6 points, respectively.  The total weight of the filled space in A, B and C was always just equal to the weight of the two points in the open space, 20 gr.  In (a) the filled distance was given on the right arm first, in (b) on the left arm.  It will be observed that this reversal made practically no difference in the judgments and therefore was sometimes omitted.  In D the filled space consisted of four points, but here the weight of each point was 10 gr., making a total weight of 40 gr. for the filled space, as against 20 gr. for the open space.  In E the weight of each was 20 gr., making the total weight of the filled space 80 gr.

TABLE V.