6 Centimeters.

A B C D E
less = gr. less = gr. less = gr. less = gr. less = gr. 
R. (a) 10 8 2 12 0 8 14 6 0 9 6 5 8 2 10
F. (a) 12 4 4 12 6 2 12 4 4 8 3 9 6 3 11
K. (a) 10 2 8 12 6 2 14 2 4 6 4 10 7 2 11
-------- -------- -------- -------- --------
32 14 14 36 12 12 40 12 8 23 13 24 21 7 32

TABLE VI.

8 Centimeters.

A B C D E
less = gr. less = gr. less = gr. less = gr. less = gr. 
R. (a) 4 1 5 5 1 4 7 0 3 4 0 6 3 0 7
(b) 4 0 6 5 1 4 6 1 3 4 1 5 2 1 7
F. (a) 5 0 5 5 0 5 6 0 4 3 0 7 4 0 6
(b) 5 1 4 6 1 3 8 0 2 4 1 5 2 3 5
K. (a) 4 1 5 6 1 3 7 1 2 3 2 5 1 3 6
(b) 4 0 6 7 0 3 6 1 3 4 0 6 3 0 7
------- ------- ------- ------- -------
26 3 31 34 4 22 40 3 17 22 4 34 15 7 38

TABLE VII.

12 Centimeters.

A B C D E
less = gr. less = gr. less = gr. less = gr. less = gr. 
R. (a) 3 6 16 8 3 14 10 8 7 6 3 16 3 4 18
F. (a) 5 7 13 10 5 10 9 6 10 6 4 15 5 1 19
K. (a) 8 2 15 8 4 13 13 9 3 3 7 15 3 0 22
-------- -------- ------- -------- ---------
16 15 44 26 12 37 32 23 20 15 14 46 11 5 59

TABLE VIII.

18 Centimeters.

A B C D E
less = gr. less = gr. less = gr. less = gr. less = gr. 
R. (a) 2 0 23 0 0 25 4 4 17 3 1 21 0 1 24
(b) 3 1 21 1 0 24 5 3 17 1 6 18 0 2 23
F. (a) 1 4 20 3 0 22 8 6 11 0 5 20 2 0 23
(b) 2 3 20 2 1 22 6 7 12 1 4 20 0 3 22
K. (a) 4 2 19 4 0 21 2 7 16 0 7 18 0 0 25
(b) 1 0 24 2 6 17 8 0 17 2 6 17 1 0 24
-------- -------- -------- -------- --------
13 10 127 12 7 131 33 27 90 7 29 114 3 6 141

TABLES IV.-VIII.

The first line in column A (Table IV.) signifies that out of 10 judgments, comparing an open space 4 cm., total weight 20 gr., with a filled space of 4 points, total weight also 20 gr., the filled space was judged less 7 times, equal 2 times, and greater once.

III.

The results of the investigation, thus far, point to the conclusion that short filled spaces are underestimated, that long spaces are overestimated, and that between the two there lies what might be called an ‘indifference zone.’  This unexpected outcome explains, I think, the divergent opinions of the earlier investigators of this problem.  Each theory is right in what it affirms, but wrong in what it implicitly or openly denies.