156 THE PRINCIPLES OF SCIENCE. 



We therefore restrict our attention to those cases which 

 may be represented in natural phenomena where at least 

 two combinations are present, and which correspond to 

 those columns of the table in which each of A, a, B, b 

 appears. These cases are shown in the columns marked 

 with an asterisk. 



We find that seven cases remain for examination, thus 

 characterised 



Four cases exhibiting three combinations, 

 Two cases exhibiting two combinations, 

 One case exhibiting four combinations. 

 It has already been pointed out that a proposition of the 

 form A = AB destroys one combination Ah, so that this 

 is the form of law applying to the twelfth case. But 

 by changing one or more of the terms in A = AB into 

 its negative, or by interchanging A and B, a and b, we 

 obtain no less than eight different varieties of the one form ; 

 thus 



1 2th case. 8th case. i5th case. i4th case. 



A = AB A = A6 a = aE a = ab 



b = ab B = aB b = A.b B = AB. 



But the reader of the preceding sections will at once 

 see that each proposition in the lower line is logically equi- 

 valent to, and is in fact the contrapositive of, that above 

 it (p. 98). Thus the propositions A = A& and B = aB 

 both give the same combinations, shown in the eighth 

 column of the table, and trial shows that the twelfth, 

 eighth, fifteenth and fourteenth cases are thus fully ac- 

 counted for. We come to this conclusion then The 

 general form of proposition A = AB admits of four 

 logically distinct varieties, each capable of expression in 

 two different modes. 



In two columns of the table, namely the seventh and 

 tenth, we observe that two combinations are missing. Now 

 a simple identity A = B renders impossible both A.b and aB, 



