180 PROFESSOR BOOLE S MATHEMATICAL THEORY 



processes of a mathematical aspect to deny that these are very 

 remarkable principles. Bj way of instance, we select from the work 

 under review the following problem, in which two premises are given. 

 Let it be granted, first, that the annelida are soft-bodied, and either 

 naked or enclosed in a tube ; and, next, that they consist of all inver- 

 tebrate animals having red blood in a double system of circulating 

 vessels. Put 



A = annelida, s = soft-bodied animals, 



n = naked, t = enclosed in a tube, 



i = invertebrate, r = having red blood in &c. 



Then the given premises are 



A = vs {n (1—0 -f- ^ (1 —n)\,......(25) 



A=ir (26) 



Suppose the problem then to be : to find the relation in which 

 soft bodied animals enclosed in tubes stand to the following elements, 

 viz., the possession of red blood, of an external covering, and of a 

 vertebral column. Professor Boole would doubtless have granted 

 that this problem admits of being solved by what he calls the ordi- 

 nary logic ; but he would probably have contended that the ordinary 

 logic does not possess any definite and invariable method of solution. 

 A skilful thinker may be able to find out how syllogisms may be 

 formed so as ultimately to give him the relation which soft bodied 

 animals enclosed in tubes bear to the elements specified ; but what 

 of thinkers who are not very skilful ? How are they to proceed ? 

 In Professor Boole's system, the process is as determinate, and as 

 certain of leading to the desired result, as the rules for solving a 

 group of simple equations in Algebra. Eliminate v, the symbol of 

 indefinite quantity, from (25). Reduce (25), thus modified, and (26), 

 to a single equation, by the method described in a previous paragraph. 

 The equation is 



A \ I -sn{l — — st{l — n)\ + A{1 -ir) + ir(l -A) +nt =0. 

 Then, since the annelida are not to appear in the conclusion, we must 

 eliminate A, by (22), from this equation. This will be found to give 

 us 



ir \ I — sn {I — t) — St (1 - n) \ + nt = 0. 

 And ultimately we get 



St = ir {I - n) + %i{l^ r) (I ~ n) + % {I - i) (1 - n) ; 

 the interpretation of which is : Soft bodied animals enclosed in tubes 



