the Theory of Probabilities. 441 



s (quantitative) = probability,, before the nexus, of the event s, 

 t (quantitative) = probabiUty, before the nexus, of the event t, 



and so on. And hence V, V^, V<, &c. quantitative, representing 

 what the same expressions logical become when we change, as 

 above, the signification of 5, t, &c., we have the following derived 

 probabilities (Principle I.). 



Probabilities before the nexus : — 



V (quantitative) = probability of the drawing of a ball not of 



the species D. 

 V^ (quantitative) = probability of the drawing of a ball of the 



species s but not of the species D. 

 V^(quantitative) = probability of the drawing of a ball of the 



species t but not of the species J), 

 A (quantitative) = probability of the drawing of a ball of the 



species A. 



Now, after the nextis, the probability of the drawing of a ball 

 of the species s is obviously the same as the probability before 

 the nexus, that if a ball not of the species D be drawn, it will be 

 of the species s. Hence 



Prob. (before nexus) of s not D 



pzrz ^ 



^ Prob. (before nexus) of not D 

 V 

 =Y- (^) 



And thus we form the series of quantitative equations, 



Y=P' r =?'&<= (9) 



Again, the probability after the nexus, of the event A, is equal 

 to the probability before the nexus, that if a ball not of the species 

 D be drawn it will be of the species A, 



_ Prob. (before nexus) of A not B 

 " Prob. (before nexus) of not D 

 __ Prob. (before nexus) of A 

 ~~ Prob. (before nexus) of not D* 

 Since the events A and D are mutually exclusive, 



A 



Hence representing Prob. w by u, we have 



u = ^. ....... (10) 



The solution of the problem is now completed. The values of 

 phil. Mag, S. 4. Vol, 8. No. 54. Dec. 1854. 2 G 



