Chapter ix
of Buccola's book, Le Legge del tempo, etc., gives a full account of the subject.
[438] If so, the reactions upon the spark would have to be slower than those upon the touch. The investigation was abandoned because it was found impossible to narrow down the difference between the conditions of the sight-series and those of the touch-series, to nothing more than the possible presence in the latter of the intervening motor-idea. Other disparities could not be excluded.
[439] Tischer gives figures from quite unpractised individuals, which I have not quoted. The discrimination-time of one of them is 22 times longer than Tischer's own! (Psychol. Studien, i, 527.)
[440] Compare Lipps's excellent passage to the same critical effect in his Grundtatsachen des Seelenlebens, pp. 390-393.--I leave my text just as it was written before the publication of Lange's and Münsterberg's results cited on pp. 92 and 432. Their 'shortened' or 'muscular' times, got when the expectant attention was addressed to the possible reactions rather than to the stimulus, constitute the minimal reaction-time of which I speak, and all that I say in the text falls beautifully into line with their results.
[441] Cf. Sully: Mind, x, 494-5; Bradley: _ibid._ xi, 83; Bosanquet: _ibid._ xi, 405.
[442] The judgment becomes easier if the two couples of terms have one member in common, if _a--b_ and _b--c_, for example, are compared. This, as Stumpf says (Tonpsychologie, i, 131), is probably because the introduction of the fourth term brings involuntary cross-comparisons with it, _a_ and _b_ with _d, b_ with _c_, etc., which confuses us by withdrawing our attention from the relations we ought alone to be estimating.
[443] J. Delbœuf: Éléments de Psychophysique (Paris, 1883), p. 64. Plateau in Stumpf, Tonpsych., i, 125. I have noticed a curious enlargement of certain 'distances' of difference under the influence of chloroform. The jingling of the bells on the horses of a horse-car passing the door, for example, and the rumbling of the vehicle itself, which to our ordinary hearing merge together very readily into a _quasi_-continuous body of sound, have seemed so far apart as to require a sort of mental facing in opposite directions to get from one to the other, as if they belonged in different worlds. I am inclined to suspect, from certain data, that the ultimate philosophy of difference and likeness will have to be built upon experiences of intoxication, especially by nitrous oxide gas, which lets us into intuitions the subtlety whereof is denied to the waking state. Cf. B. P. Blood: The Anæsthetic Revelation, and the Gist of Philosophy (Amsterdam, N. Y., 1874). Cf. also Mind, vii, 200.
[444] _Op. cit._ p. 126 ff.
[445] Stumpf, pp. 111-121.
[446] Stumpf, pp. 116-7. I have omitted, so as not to make my text too intricate, an extremely acute and conclusive paragraph, which I reproduce here: "We may generalize: Wherever a number of sensible impressions are apprehended _as a series_, there in the last instance must perceptions of simple likeness be found. _Proof:_ Assume that all the terms of a series, e.g. the qualities of tone, _c d e f g_, have something in common,--_no matter what it is_, call it _X_; then I say that the differing parts of each of these terms must not only be differently constituted in each, but must _themselves form a series_, whose existence is the ground for our apprehending the original terms in serial form. We thus get instead of the original series _a b c d ef_ ... the equivalent series _Xɑ, Xβ, Xɣ_,... etc. What is gained? The question immediately arises: How is _ɑ β ɣ_ known as a series? According to the theory, these elements must themselves be made up of a
## part common to all, and of parts differing in each, which latter parts
form a new series, and so on _ad infinitum_, which is absurd."
[447] The most important ameliorations of Fechner's formula are Delbœuf's in his Recherches sur la Mesure des Sensations (1873), p. 35, and Elsas's in his pamphlet Über die Psychophysik (1886) p. 16.
[448] Reversing the order is for the sake of letting the opposite accidental errors due to 'contrast' neutralize each other.
[449] Theoretically it would seem that it ought to be equal to the sum of all the additions which we judge to be increases divided by the total number of judgments made.
[450] J. Delbœuf, Éléments de Psychophysique (1883), p. 9.
[451] Philos. Studien, iv, 588.
[452] Berlin Acad. Sitzungsberichte, 1888, p. 917. Other observers (Dobrowolsky, Lamausky) found great differences in different colors.
[453] See Merkel's tables, _loc. cit._ p. 568.
[454] American Journal of Psychology, i, 125. The rate of decrease is small but steady, and I cannot well understand what Professor J. means by saying that his figures verify Weber's law.
[455] Philosophische Studien, v, 514-5.
[456] Cf. G. E. Müller: Zur Grundlegung der Psychophysik, §§ 68-70.
[457] Philosophische Studien, v, 287 ff.
[458] American J. of Psychology, iii, 44-7.
[459] Cf. Stumpf, Tonpsychologie, pp. 397-9. "One sensation cannot be a multiple of another. If it could, we ought to be able to subtract the one from the other, and to feel the remainder by itself. Every sensation presents itself as an indivisible unit." Professor von Kries, in the Viertejahrschrift für wiss. Philosophie, vi, 257 ff., shows very clearly the absurdity of supposing that our stronger sensations contain our weaker ones as parts. They differ as qualitative units. Compare also J. Tannery in Delbœuf's Éléments de Psychophysique (1883), p. 134 ff.; J. Ward in Mind, i, 464: Lotze, Metaphysik, § 258.
[460] F Brentano, Psychologie, i, 9, 88 ff.--Merkel thinks that his results with the method of equal-appearing intervals show that we compare considerable intervals with each other by a different law from that by which we notice barely perceptible intervals. The stimuli form an arithmetical series (a pretty wild one according to his figures) in the former case, a geometrical one in the latter--at least so I understand this valiant experimenter but somewhat obscure if acute writer.
[461] This is the formula which Merkel thinks he has verified (if I understand him aright) by his experiments by method 4.
[462] Elsas: Ueber die Psychophysik (1856), p. 41. When the pans of a balance are already loaded, but in equilibrium, it takes a proportionally larger weight added to one of them to incline the beam.
## CHAPTER XIV .[463]
ASSOCIATION.
After discrimination, association! Already in the last