540 PSYCHOL007. 



increment of the sensation is witliout taking tlie average o\ 

 a large number of appreciations. These accidental errors 

 are as likely to increase as to diminish our sensibility, 

 and are eliminated in such an average, for those above 

 and those below the line then neutralize each other in the 

 sum, and the normal sensibility, if there be one (that is, the 

 sensibility due to constant causes as distinguished from 

 these accidental ones), stands revealed. The best way of 

 getting at the average sensibility has been very minutely 

 worked over. Fechner discussed three methods, as follows : 



(1) The Metliod of just-discernible Differences. Take a 

 standard sensation S, and add to it until you distinctly feel the 

 addition d ; then subtract from S -\-d until you distinctly 

 feel the effect of the subtraction ; * call the difference here 



d'. The least discernible difference sought is — '—■ — ; and 



A 



the ratio of this quantity to the original S (or rather to 

 ^ -|- '^^ ~ ^^ i^ what Fechner calls the difference-threshold. 

 Tliis difference-threshold should be a constant fraction (no 

 matter what is the size oi S) if Weber's laiu holds universally 

 true. The difficulty in applying this method is that we are 

 so often in doubt whether anything has been added to *S' or 

 not. Furthermore, if we simply take the smallest d about 

 which we are never in doubt or in error, we certainly get 

 our least discernible difference larger than it ought theo- 

 retically to be.f 



Of course the sensibility is small when the least dis- 

 cernible difference is large, and vice versa ; in other words, 

 it and the difference-threshold are inversely related to each 

 other. 



(2) The Method of True and False Cases. A sensation 

 which is barely greater than another will, on account of 

 accidental errors in a long series of experiments, sometimes 

 be judged equal, and sometimes smaller ; i.e., we shall 

 make a certain number of false and a certain number of 



* Reversing the order is for the sake of letting the opposite accidental 

 errors due to ' contrast ' neutralize each other. 



+ Theoretically it would seem that it ought to be equal to the sum of 

 ail the additions which we judge to be increases divided by the total num- 

 ber of judgments made. 



