336 PROF. W. STANLEY JEVONS ON 



ing whether or not the magnitude of a class is determined 

 or not^ or in indicating what further hypotheses or data 

 are required. It will appear^ too^ that where an exact 

 result is not determinable we may yet assign limits 

 within which an unknown quantity must lie. 



11. Let us suppose, as an instance, that in a certain 

 statistical investigation, among lOO A^s there are found 

 45 B^s and 53 C^s ; that is to say, in 45 out of one hundi^ed 

 cases where A occurs B also occurs, and in 53 cases C 

 occurs. Suppose it to be also known that wherever B is, 

 C also necessarily exists. The data then are as follows : — 



Numerical equations 



'(A) = ioo (i) 



^ (B)= 45 (2) 



^(C)= 53 (3) 



Logical equation . . B =BC. 



Let it be required to determine 



(i) The number of cases where C exists without B. 



(2) The number of cases where neither B nor C exists. 

 The logical equation asserts that the class B is identical 

 with the class B C, which is the true mode of asserting 

 that all B^s are C^s. Two distinct results follow from 

 this, namely : — ist, that the number of the class BC is iden- 

 tical with the number of the class B ; and, 2nd, that there 

 are no such things as B^s which are not C's. 



The logical equation is thus exactly equivalent to two 

 additional numerical equations, namely, 



(B) = (BC) (4) 



(Bc)= o (5) 



We have now full means of solving the problem ; for, by 

 the law of duality, 



(C) = (BC) + {bC) 

 By (4) 



= (B) +(^C), 



