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cases, in which likewise the plijsical cause is not perceived, in 

 which liowever by chance a judgment is emitted, though this 

 time a correct one. These facts being dependent on circumstances 

 beyond our will, the chances are equal that either a wrong or a 

 right judgment may be given. If therefore we had v false cases, we 

 may reasonably admit the existence of v cases, in which practically 

 the physical cause has not been perceived, and where yet a judgment, 

 this time a correct one, has been given. These v cases however have 

 been recorded amongst the true cases, though they cannot be 

 admitted as cases of correct perception: it is only in ?ü—z; cases that 

 we may suppose the physical cause to have been really and correctly 

 perceived ; in all other cases, in 2t> + i cases therefore, there has 

 been no perception of the real difference of the stimuli. 



In this way we have only to consider two possibilities, constitu- 

 ting the perceived and non-perceived cases, the number of which 

 I will indicate by § and /. The supposition tliat we may apply 

 the principles of the calculus of probability to them, is justified a 

 priori. 



This supposition is changed into a certainty, if we apply the 

 mathematical relations, stated by Fechner to exist between the 

 numbers of true and false cases. 



As is well known, Fechner added to the number of true cases, 

 obtained by the experiment, one half of the dubious cases: he 

 used therefore in his calculation a rectified number of true cases 

 10^ =z w -\- \ t. In the same manner he corrected the number of false 

 cases by adding to them likewise one half of the dubious cases : 

 v'=:v-\-\L 



In calculating the number of my perceived cases, I get § = iv — v, 

 whilst the number of non-perceived cases is represented by x = ^ + 2v. 

 Evidently I may also express the number of perceived cases by 



As Fechner has given for the relative value of the corrected 

 number of true cases the expression : 



Dh 

 



and for the corrected relative number of false cases the expression 



Dh 



Dh 



