with the first point of the new distance.  The lever was not used in the present experiment; but in later experiments, where the points were moved under the finger tip, which was held stationary, this lever was very useful in producing different rates of speed.  In one series of experiments with this apparatus the filled spaces were presented first, and in another series the open spaces were presented first.  In the previous experiments, so far as I have reported them, the filled spaces were always presented first.

[Illustration:  FIG. 10.]

In order to enable the subject to make proper connections with the first point in the filled space, when the open space was presented first, a slight depression was put in the smooth surface.  This depression amounted merely to the suggestion of a groove, but it sufficed to guide the finger.

The general results of the first series of experiments with this apparatus were similar to those already given, but were based on a very much larger number of judgments.  They show at once that the short filled spaces are overestimated, while the longer spaces are underestimated.  The uniformity of this law has seemed to me one of the most significant results of this entire investigation.  In the results already reported from the experiments with the former apparatus, I have mentioned the fact that the judgments upon the distances fluctuate more widely when one is filled and the other open, than when both are open.  This fluctuation appeared again in a pronounced way in the present experiments.  I now set about to discover the cause of this variation, which was so evidently outside of the limits of Weber’s law.

TABLE XI.

I.                        II. 
Subjects.      R.      B.      A.        R.      B.       A.
2=      3.1     3.2     3.7       2.7     2.5      3.1
3=      4.5     4.4     4.1       4.1     4.0      3.6
4=      5.3     5.0     4.3       4.2     4.6      4.6
5=      6.0     5.1     5.8       5.9     5.2      4.3
6=      6.8     5.6     6.2       6.9     5.3      6.0
7=      7.4     7.2     6.9       7.6     7.3      6.8
8=      8.1     8.4     7.3       8.3     9.7      7.8
9=      9.3     9.0     8.5       9.5     8.9      8.7
Filled    10=     10.1    10.0     8.1      10.3    10.0      9.2
Spaces.   11=     10.5     9.3     9.7      10.6     8.7      9.6
12=     11.7    10.6    10.6      11.8     9.7     10.2
13=     12.3    10.9    10.9      11.1    10.2      9.6
14=     12.2    11.5    12.2      10.4     9.6     11.3
15=     13.6    12.3    11.9      13.1    10.1      9.6
16=     14.1    13.5    14.1      12.3    13.2     13.3
17=     14.9    12.9    14.6      14.1    12.6     13.7
18=     15.0    15.3    14.9      15.0    15.3     13.8
19=     15.2    14.6    15.2      14.1    13.9     14.2
20=     17.1    16.5    15.7      16.1    16.4     14.7

The first line of group I. reads: