DISCRIMINATION AND COMPARISON. 639 



facts to be correct so far) tliat the sensations vary in the 

 same proportion as the logarithms of their respective stimuli. 

 And we can thereupon proceed to compute the number of 

 units in any given sensation (considering the unit of sen- 

 sation to be equal to the just perceptible increment above 

 zero, and the unit of stimulus to be equal to the increment 

 of stimulus r, which brings this about) by multiplying the 

 logaritlim of the stimulus by a constant factor which must 

 vary with the particular kind of sensation in question. If 

 we call the stimulus R, and the constant factor C, we get 

 the formula 



S = C log R, 



which is what Fechner calls the psychophysischer Maas- 

 formel. This, in brief, is Fechner's reasoning, as I under- 

 stand it. 



The Maasformd admits of mathematical development 

 in various directions, and has given rise to arduous discus- 

 sions into which I am glad to be exempted from entering 

 here, since their interest is mathematical and metaphysical 

 and not primarily psychological at all.* I must say a word 

 about them metaphysically a few pages later on. Mean- 

 while it should be understood that no human being, in any 

 investigation into which sensations entered, has ever used 

 the numbers computed in this or any other way in order to 

 test a theory or to reach a new result. The whole notion 

 of measuring sensations numerically, remains in short a 

 mere mathematical speculation about possibilities, which 

 has never been applied to practice. Incidentally to the 

 discussion of it, however, a great many particular facts 

 have been discovered about discrimination which merit a 

 place in this chapter. 



In the first place it is found, when the difference of two 

 sensations approaches the limit of discernibility, that at 

 one moment we discern it and at the next we do not. There 

 are accidental fluctuations in our inner sensibility which 

 make it impossible to tell just what the least discernible 



* The most important ameliorations of Fechner's formula are Delboeuf s 

 Id his Keclierclies sur la Mesure des Sensations (1873), p. 35, and Elsas's in 

 his pamphlet Uber die Psychophysik (1886), p. 16. 



