CHAP. XVII.] GENERAL METHOD IN PROBABILITIES. 271 



It is understood in this case that X, Y, W, Z may be any 

 compound events whatsoever. The expressions X Y and WZ 

 represent the products of the symbolical expressions of X and Y 

 and of Wand. Z, formed according to the rules of the Calculus of 

 Logic. 



The determination of the single constant c may in certain 

 cases be resolved into, or replaced by, the determination of a series 

 of arbitrary constants c 1? c 2 . . according to convenience, as pre- 

 viously explained. '. t, 



18. It has been stated (I. 12) that there exist two distinct de- 

 finitions, or modes of conception, upon which the theory of pro- 

 babilities may be made to depend, one of them being connected 

 more immediately with Number, the other more directly with 

 Logic. We have now considered the consequences which flow 

 from the numerical definition, and have shown how it conducts 

 us to a point in which the necessity of a connexion with Logic 

 obviously suggests itself. We have seen to some extent what 

 is the nature of that connexion ; and further, in what manner the 

 peculiar processes of Logic, and the more familiar ones of quanti- 

 tative Algebra, are involved in the same general method of solu- 

 tion, each of these so accomplishing its own object that the two 

 processes may be regarded as supplementary to each other. It 

 remains to institute the reverse order of investigation, and, setting 

 out from a definition of probability in which the logical relation 

 is more immediately involved, to show how the numerical defini- 

 tion would thence arise, and how the same general method, 

 equally dependent upon both elements, would finally, but by a 

 different order of procedure, be established. 



That between the symbolical expressions of the logical cal- 

 culus and those of Algebra there exists a close analogy, is a fact 

 to which attention has frequently been directed in the course of 

 the present treatise. It might even be said that they possess a 

 community of forms, and, to a very considerable degree, a com- 

 munity of laws. With a single exception in the latter respect, 

 their difference is only one of interpretation. Thus the same 

 expression admits of a logical or of a quantitative interpretation, 

 according to the particular meaning which we attach to the sym- 



