DISCEIMINATION AND COMPARISON. 647 



that in most sensations a new kind of feeling invariably ac- 

 companies our judgment of an increased impression ; and 

 this is a fact which Fechner's formula disregards.* 



But apart from these a priori difficulties, and even sup- 

 posing that sensations did consist of added units, Fechner's 

 assumption that all equally perceptible additions are equally 

 great additions is entirely arbitrary. Why might not a 

 small addition to a small sensation be as perceptible as a 

 large addition to a large one ? In this case Weber's law 

 would apply not to the additions themselves, but only to 

 their perceptibility. Our noticing of a difference of units in 

 two sensations would depend on the latter being in a fixed 

 ratio. But the difference itself would depend directly on 

 that between their respective stimuli. So many units added 

 to the stimulus, so many added to the sensation, and if 

 the stimulus grew in a certain ratio, in exactly the same 

 ratio would the sensation also grow, though its perceptibility 

 grew according to the logarithmic law.t 



If A stand for the smallest difi'erence which ive perceive, 



then we should have, instead of the formula As = const.. 



As 

 which is Fechner's, the formula - — = const., a formula 



,9 



which interprets all the /ads of Weber's law, in an entirely 

 different theoretic way from that adopted by Fechner.^ 

 The entire superstructure which Fechner rears upon the 



* Cf. Stumpf, Tonpsycliologie, 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 pre- 

 sents itself as an indivisible unit." Professor von Kries, in the Viertel- 

 jahrschrift fiir wiss. Philosophic, vi. 257 &., shows very clearly the ab- 

 surdity of supposing that our stronger sensations contain our weaker ones 

 as parts. They differ as qualitative units. Compare also J. Tannery in 

 DelbcBuf'sElementsdePsychophy.sique(1883), p. 134ff.; J. Ward in Mind, 

 I. 464: Lotze, Metaph\^sik, § 258. 



f F. Brentano, Psychologic, i. 9, 88 ff.— Merkel thinks that his results 

 with the method of equal-appearing intervals show that we compare con- 

 siderable 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 experi- 

 menter but somewhat obscure if acute writer. 



i This is the formula which Merkel thinks he has verified (if 1 under- 

 stand him aright) by his experiments by method 4. 



