106 THE PRINCIPLES OF SCIENCE. 



problem it is best to form, in the first place, a complete 

 series of all the combinations of terms involved in it. 

 If there be two terms A and B, the utmost variety of 

 combinations in which they can appear are 



* KB 



Kb 



aB 



ab. 



The term A appears in the first and second ; B in the 

 first and third ; a in the third and fourth ; and b in the 

 second and fourth. . Now if we have any premise, say 



A = B, 



we must ascertain which of these combinations would be 

 rendered self-contradictory by substitution ; the second 

 and third would have to be struck out, and there would 



remain 



AB 



ab. 



Hence we draw the following inferences 



A = AB, B = AB, a = ab, b = ab. 

 Exactly the same method must be followed where a 



question involves a greater number of terms. Thus by 



the Law of Duality the three terms A, B, C, give rise to 



eight conceivable combinations, namely 



ABC . () 



ABc (0) 



A6C (7) 



Abe (S) 



aBC (e) 



abC fa) 



abc. (0) 



The development of the term A is formed by the first four 

 of these ; for B we must select (a), (/8), (e), () ; C consists 

 of (a), ( ? ), (e) (,) ; b of (7), (J), (), (6), and so on. 



