CHAP/XVII.] GENERAL METHOD IN PROBABILITIES. 257 



which our knowledge of that connexion is to be employed is in- 

 dependent of the nature of the source from which such know- 

 ledge has been derived. 



The practical importance of the above principle consists 

 in the circumstance^ that whatever may be the nature of the 

 events whose probabilities are given, whatever the nature of 

 the event whose probability is sought, we are always able, by an 

 application of the Calculus of Logic, to determine the expression 

 of the latter event as a definite combination of the former events, 

 and definitely to assign the whole of the implied relations con- 

 necting the former events with each other. In other words, we 

 can determine what that combination of the given events is whose 

 probability is required, and what combinations of them are alone 

 possible. It follows then from the above principle, that we can 

 reason upon those events as if they were simple events, whose 

 conditions of possible combination had been directly given by 

 experience, and of which the probability of some definite combi- 

 nation is sought. The possibility of a general method in proba- 

 bilities depends upon this reduction. 



6. As the investigations upon which we are about to enter 

 are based upon the employment of the Calculus of Logic, it is 

 necessary to explain certain terms and modes of expression which 

 are derived from this application. 



By the event #, I mean that event of which the proposition 

 which affirms the occurrence is symbolically expressed by the 



equation 



x = 1. 



By the event $ (x, y, z, . .), I mean that event of which the 

 occurrence is expressed by the equation 



Such an event may be termed a compound event, in relation to 

 the simple events x, y, z, which its conception involves. Thus, 

 if x represent the event " It rains," y the event " It thunders," 

 the separate occurrences of those events being expressed by the 

 logical equations 



*=!> /=!> 



then will x(\-y)+y(\-x) represent the event or state of 



s 



