280 THE PRINCIPLES OF SCIENCE. 



process we arrive at the conclusion that the actual pro- 

 bability of C, being the cause is 



p t + p, + P 3 

 and the similar probabilities of the existence of C 3 and 



C 3 are, p p 



and ^ 



p. + p, + P3 Pt + p,+ p 3 



The sum of these three fractions amounts to unity, which 

 correctly expresses the certainty that one cause or other 

 must be in o*peration. 



We may thus state the result in general language. 

 If it is certain that one or other of the supposed causes 

 exists, the probability that any one does exist is the 

 probability that if it exists the event happens, divided by 

 the sum of all the similar probabilities. There may seem 

 to be an intricacy in this subject which may prove dis- 

 tasteful to some readers ; but this intricacy is essential 

 to the subject in hand. No one can possibly understand 

 the principles of inductive reasoning, unless he will take 

 the trouble to master the meaning of this rule, by which 

 we recede from an event to the probability of each of its 

 possible causes. 



This rule or principle of the indirect method is that 

 which common sense leads us to adopt almost instinctively, 

 before we have any comprehension of the principle in its 

 general form. It is easy to see, too, that it is the rule 

 which will, out of a great multitude of cases, lead us most 

 often to the truth, since the most probable cause of an 

 event really means that cause which in the greatest 

 number of cases produces the event. But I have only 

 met with one attempt at a general demonstration of the 

 principle. Poisson imagines each possible cause of an 

 event to be represented by a distinct ballot-box, containing 

 black and white balls, in such ratio that the probability of 

 a white ball being drawn is equal to that of the event 



