THE THEOR Y OF PROBABILITIES. 9 



ace is thrown. Here is a complex event. We resolve it into, 

 (1) the tossing of the die ; (2) the coming up of the ace. The 

 first constitutes the 'trial,' on which different possible results 

 might have occurred ; the second is the particular result which 

 actually did occur. They are in fact related as genus and 

 differentia. Besides both, there are many circumstances of the 

 event ; as how the die was tossed, by whom, at what time, 

 rejected as irrelevant. 



This applies in every case of probability. Take the case of 

 a vessel sailing up a river. The vessel has a flag. What was 

 the a priori probability of this? Before any answer can by 

 possibility be given to the enquiry, we must know (1) what cir- 

 cumstances the person who makes it rejects as irrelevant. Such 

 as, e.g. the colour of which the vessel is painted, whether it is 

 sailing on a wind, &c. &c. ; (2) what circumstances constitute in 

 his mind the ' trial ;' the experiment which is to lead to the 

 result of flag or no flag; must the vessel have three masts? 

 must it be square rigged? (3) What idea he forms to himself 

 of a flag. Is a pendant a flag ? Must the flag have a particular 

 form and colour ? Is it matter of indifference whether it is at the 

 peak or the main ? Unless all such points were clearly under- 

 stood, the most perfect acquaintance with the nature of the case 

 would not enable us to say what was the a priori probability of 

 the event : for this depends, not only on the event, but also on 

 the mind which contemplates it. 



The assertion therefore that f is the probability that any 

 observed event had on an a priori probability greater than -J, or 

 that three out of four observed events had such an & priori 

 probability, seems totally to want precision. A priori proba- 

 bility to what mind? In relation to what way of looking at 

 them? 



16. Let us see if this will throw any light on the ques- 

 tion. Let h be a large number. And suppose we took h trials 

 and that the probability of a certain event from each (considered 



in a determinate manner) was ; let us take a second set of h 



m 



trials for which the same quantity is : and so on to - 



77? m 



and 1. 



