NUMERICALLY DEFINITE REASONING. 335 



the terms A and B may consist of, it is necessarily true, 

 according to this law, that 



A is B or not B ; 

 in symbols 



A = AB'\'Ab, 



If any third term C enters into a problem, it is equally 

 certain that 



A=AC-I-Ac; 



and combining these two developments, we have 

 A=ABC'\'ABc\'AbC'\'Abc, 



The same process of subdivision can be carried on ad 

 infinitum with respect to any terms that occur ; and this 

 Indirect Method of Inference, which I have described in 

 the books mentioned, consists in determining the possible 

 existence of the various alternatives thus produced. The 

 nature and procedure of this method will, as far as pos- 

 sible, be rendered apparent in the mode of treating numer- 

 ical questions. It has also been partially explained to the 

 Society, in connexion with the logical abacus, in which the 

 working of the method is mechanically represented (Pro- 

 ceedings of the Manch. Lit. and Phil. Soc. April 3rd 1866, 

 p. 161 ; see also Philosophical Transactions, 1870, p. 497). 



10. The data of any problem in numerically definite 

 logic will be of two kinds : — 



1. The logical conditions governing the combinations 

 of certain qualities or classes of things, expressed 

 in propositions. 



2. The numbers of individuals in certain logical classes 

 existing under those conditions. 



The qucesitum of the problem will be to determine the 

 numbers of individuals in certain other logical classes ex- 

 isting under the same logical conditions, so far as such 

 numbers are rendered determinable by the data. The 

 usefulness of the method will, indeed, often consist in show- 



