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.