538 PSYCHOLOGY. 



when the stimulus is increased, we can just barely perceive 

 to be added. The total number of units which any given 

 sensation contains will consist of the total number of such 

 increments which may be perceived in passing from no 

 sensation of the kind to a sensation of the present amount. 

 We cannot get at this number directly, but we can, now 

 that we know Weber's law, get at it by means of the physi- 

 cal stimulus of which it is a function. For if we know how 

 much of the stimulus it will take to give a barely percep- 

 tible sensation, and then what percentage of addition to 

 the stimulus will constantly give a barely perceptible incre- 

 ment to the sensation, it is at bottom only a question of 

 compound interest to compute, out of the total amount of 

 stimulus which we may be employing at any moment, the 

 number of such increments, or, in other words, of sensa- 

 tional units to which it may give rise. This number bears 

 the same relation to the total stimulus which the time 

 elapsed bears to the capital plus the compound interest 

 accrued. 



To take an example : If stimulus A just falls short of 

 producing a sensation, and if r be the percentage of itself 

 which must be added to it to get a sensation which is 

 barely perceptible — call this sensation 1 — then we should 

 have the series of sensation-numbers corresponding to 

 their several stimuli as follows : 



Sensation = stimulus A ; 



« 1 = " A (1 + r) ; 



2= " A(l + r)2; 



3= " A(lH-r)3; 



" n= " A (1 + rf. 



The sensations here form an arithmetical series, and 

 the stimuli a geometrical series, and the two series corre- 

 spond term for term. Now, of two series corresponding in 

 this way, the terms of the arithmetical one are called the 

 logarithms of the terms corresponding in rank to them in 

 the geometrical series. A conventional arithmetical series 

 beginning with zero has been formed in the ordinary log- 

 arithmic tables, so that we may truly say (assuming our 



