In order to discover whether Weber's law holds in the case of the brightness vision of the dancer it was necessary for me to determine the just perceivable difference between the standard and the variable lights for two or more standard values. I chose to work with three values, 5, 20, and 80 hefners, and I was able to discover with a fair degree of accuracy how much less than 5, 20, or 80 hefners, as the case might be, the variable light had to be in order that it should be discriminable from the other. For the work with the 5 hefner standard I used 2-candle-power lamps,[1] for the 20, 4-candle-power, and for the 80, 16-candle-power.
[Footnote 1: I give merely the commercial markings of the lamps. They had been photometered carefully by two observers by means of a Lummer-Brodhun photometer and a Hefner amyl acetate lamp previous to their use in the experiment. For the photometric measurements in connection with the Weber's law tests I made use of the Hefner lamp with the hope of attaining greater accuracy than had been possible with a standard paraffine candle, in the case of measurements which I had made in connection with the experiments on color vision that are reported in Chapters IX and X. The Hefner unit is the amount of light produced by an amyl acetate lamp at a flame height of 40 mm. (See Stine's "Photometrical Measurements.") A paraffine candle at a flame height of 50 mm. is equal to 1.2 Hefner units.]
For reasons which will soon appear, Weber's law tests were made with only one dancer. This individual, No. 51, had been thoroughly trained in white- black discrimination previous to the experiments in the apparatus which is represented in Figure 17. Having given No. 51 more than two hundred preliminary tests in the Weber's law apparatus with the electric-boxes sufficiently different in brightness to enable her to discriminate readily, I began my experiments by trying to ascertain how much less the value of the illumination of one electric-box must be in order that it should be discriminable from a value of 20 hefners in the other electric- box. In recording the several series of tests and their results hereafter, I shall state in Hefner units the value of the fixed or standard light and the value of the variable light, the difference between the two in terms of the former, and the average number of wrong choices in per cent.
With the lamps so placed that the difference in the illumination of the two electric-boxes was .53 of the value of the standard, that is about one half, No. 51 made twenty wrong choices in one hundred, or 20 per cent. When the difference was reduced to .36 (one third) the number of errors increased to 36 per cent, and with an intermediate difference of .48 there were 26 per cent of errors (see Table 14).
Are these results indicative of discrimination, or are the errors in choice too numerous to justify the statement that the dancer was able to distinguish the boxes by their difference in brightness? Evidently this question cannot be answered satisfactorily until we have decided what the percentage of correct choices should be in order that it be accepted as evidence of ability to discriminate, or, to put it in terms of errors, what percentage of wrong choices is indicative of the point of just perceivable difference in brightness. Theoretically, there should be as many mistakes as right choices, 50 per cent of each, when the two electric-boxes are equally illuminated (indiscriminable), but in practice this does not prove to be the case because the dancer tends to return to that electric-box through which in the previous test it passed safely, whereas it does not tend in similar fashion to reënter the box in which it has just received an electric shock. The result is that the percentage of right choices, especially in the case of series which have the right box in the same position two, three, or four times in succession, rises as high as 60 or 70, even when the visual conditions are indiscriminable. Abundant evidence in support of this statement is presented in Chapters VII and IX, but at this point I may further call attention to the results of an experiment in the Weber's law apparatus which was made especially to test the matter. The results appear under the date of May 27 in Table 14. In this experiment, despite the fact that both boxes were illuminated by 80 hefners, the mouse chose the standard (the illumination in which it was not shocked) 59 times in 100. In other words the percentage of error was 41 instead of 50. It is evident, therefore, that as low a percentage of errors as 40 is not necessarily indicative of discrimination. Anything below 40 per cent is likely, however, to be the result of ability to distinguish the brighter from the darker box. To be on the safe side we may agree to consider 25 wrong choices per 100 as indicative of a just perceivable difference in illumination. Fewer mistakes we shall consider indicative of a difference in illumination which is readily perceivable, and more as indicative of a difference which the mouse cannot detect. The reader will bear in mind as he examines Table 14 that 25 per cent of wrong choices indicates the point of just perceivable difference in brightness.
TABLE 14
RESULTS OF WEBER'S LAW EXPERIMENTS
Brightness vision
DATE NUMBER STANDARD VARIABLE DIFFERENCE % OF ERRORS OF TESTS LIGHT LIGHT
May 13 100 20 9.4 .53 20
15 100 20 12.8 .36 36
16 100 20 10.8 .46 26
20 50 80 37.6 .53 6
21 50 80 51.3 .36 10
22 100 80 71.1 .11 35
24 100 80 60.0 .25 21
25 100 80 65.0 .19 25
27 100 80 80 0 41
28 50 5 2.5 .50 18
29 50 5 4.0 .20 14
29 100 5 4.5 .10 25
31 50 5 4.25 .15 20
June 1 50 5 4.85 .03 48
2 50 20 15.0 .25 16
3 50 20 17.4 .13 22
3 100 20 18.0 .10 22
4 100 80 72.0 .10 18
5 100 5 4.5 .10 12
7 100 5 4.67 .067 46
8 50 80 74.67 .067 56
9 50 20 18.67 .067 44
If we apply this rule to the results of the first tests, reported above, it appears that a standard of 20 hefners was distinguished from a variable of 9.4 hefners (.53 difference), for the percentage of errors was only 20. But in the case of a difference of .36 in the illuminations lack of discrimination is indicated by 36 per cent of errors. A difference of .46 gave a frequency of error so close to the required 25 (26 per cent) that I accepted the result as a satisfactory determination of the just perceivable difference for the 20 hefner standard and proceeded to experiment with another standard value.