Subjects      P      R      F      Rr
2=     3.8    3.6    2.9     2.8
3=     4.1    4.1    4.2     3.9
4=     4.7    5.1    4.3     4.3
Filled     5=     5.2    5.6    5.8     6.0
Spaces.    6=     6.0    6.3    6.4     5.2
7=     6.8    6.5    6.6     7.0
8=     7.5    7.6    7.2     7.4
9=     8.3    8.1    8.2     8.6
10=     8.9    9.1    8.7     8.5

TABLE X.

Subjects      P      R      F      Rr
2=     4.0    3.8    3.2     2.6
3=     4.3    4.2    4.4     3.6
4=     4.6    5.6    4.6     4.8
Filled     5=     5.4    6.1    5.6     5.7
Spaces.    6=     6.2    6.4    6.8     6.9
7=     7.3    6.8    7.9     7.2
8=     7.8    7.4    7.3     7.8
9=     8.6    8.0    7.9     8.9
10=     9.3    9.1    8.9     8.5

TABLES IX.  AND X.

First line reads:  ’When the finger-tip was drawn over a filled distance of 2 cm., the subject P measured off 3.8 on the open surface, the subject R 3.6, etc.’  Each number is the average of five judgments.  In Table IX. the points were set at regular intervals.  In Table X. the filling was made irregular by having some points rougher than the others and set at different intervals.

I can give here only a very brief summary of the results with this apparatus.  In Tables IX. and X. I give a few of the figures which will show the tendency of the experiments.  In these tests a different length and a different filling were given for each judgment.  The result of the experiments of this group is, first, that the shorter filled spaces are judged longer and the longer spaces shorter than they really were.  Second, that an increase in the number of points in the filled space causes no perceptible change in the apparent length.  Third, that when the filling is so arranged as to produce a tactual rhythm by changing the position or size of every third point, the apparent length of the space is increased.  It will be noticed, also, that this is just the reverse of the result that was obtained for passive touch.  These facts, which were completely borne out by several other experiments with different apparatus which I shall describe later, furnish again a reason why different investigators have hitherto reported the illusion to exist, now in one direction, now in the other.  Dresslar drew the conclusion from his experiments that the filled spaces are always overestimated, but at the same time his figures show an increasing tendency towards an underestimation of the filled spaces as the distances increased in length.  I shall later, in connection with similar results from other experiments on this illusion, endeavor to explain these anomalous facts.