[529] Mach, Wiener Sitzungsb., li, 2. 133 (1865); Estel, loc. cit. p. 65; Mehner, loc. cit. p. 586; Buccola, op. cit. p. 378. Fechner labors to prove that his law is only overlaid by other interfering laws in the figures recorded by these experimenters; but his case seems to me to be one of desperate infatuation with a hobby. (See Wundt's Philosphische Studien iii, 1.)
[530] Curious discrepancies exist between the German and the American observers with respect to the direction of the error below and above the point of indifference—differences perhaps due the fatigue involved in the American method. The Germans lengthened intervals below it and shortened those above. With seven Americans experimented on by Stevens this was exactly reversed. The German method was to passively listen to the intervals, then judge; the American was to reproduce them actively by movements of the hand. In Mehner's experiments there was found a second indifference point at about 5 seconds, beyond which times were judged again too long. Glass, whose work on the subject is the latest (Philos. Studien, iv, 423) found (when corrections were allowed for) that all times except 0.8 sec. were estimated too short. He found a series of points of greatest relative accuracy, viz. at 1.5, 2.5, 3.75, 5, 6.25, etc., seconds respectively, and thought that his observations roughly corroborated Weber's law. As 'maximum' and 'minimum' are printed interchangeably in Glass's article it is hard to follow.
[531] With Vierordt and his pupils the indifference point lay as high as from 1.5 sec to 4.9 sec, according to the observer (cf. Der Zeitsinn, 1868, p. 112). In most of these experiments the time heard was actively reproduced, after a short pause, by movements of the hand, which were recorded. Wundt gives good reasons (Physiol. Psych., ii, 289, 290) for rejecting Vierordt's figures as erroneous. Vierordt's book, it should be said, is full of important matter, nevertheless.
[532] Physiol. Psych., ii, 286, 290.
[533] Philosophische Studien, i, 86.
[534] Mind, xi, 400.
[535] Loc cit. p. 144.
[536] Op. cit. p. 376. Mach's and Buccola's figures, it will be observed, are about one half of the rest—sub-multiples, therefore. It ought to be observed, however, that Buccola's figure has little value, his observations not being well fitted to show this particular point.
[537] Estel's figures led him to think that all the multiples enjoyed this privilege; with Mehner, on the other hand, only the odd multiples showed diminution of the average error; thus, 0.71, 2.15, 3.55, 5, 6.4, 7.8, 9.3, and 10.65 second were respectively registered with the least error. Cf. Phil. Studien, ii, pp. 57, 562-5.
[538] Cf. especially pp. 558-561.