SECT. 8.] The Rule of Succession. 197 



bag which contains any number, we know not what, of 

 balls each of which is white or black, find the chance of 

 the next drawing also yielding a white ball. The answer is 



m+ 1 



m+2 



Thus far mathematics. Then comes in the physical 

 assumption that the universe may be likened to such a bag 

 as the above, in the sense that the above rule may be 

 applied to solve this question : an event has been observed 

 to happen m times in a certain way, find the chance that 

 it will happen in that way next time. Laplace, for instance, 

 has pointed out that at the date of the writing of his Essai 

 Philosophique, the odds in favour of the sun s rising again 

 (on the old assumption as to the age of the world) were 

 1,826,214 to 1. De Morgan says that a man who standing 

 on the bank of a river has seen ten ships pass by with flags 

 should judge it to be 11 to 1 that the next ship will also 

 carry a flag. 



8. It is hard to take such a rule as this seriously, for 

 there does not seem to be even that moderate confirmation 

 of it which we shall find to hold good in the case of the 

 application of abstract formulae to the estimation of the 

 evidence of witnesses. If however its validity is to be dis 

 cussed there appear to be two very distinct lines of enquiry 

 along which we may be led. 



(1) In the first place we may take it for what it pro 

 fesses to be, and for what it is commonly understood to 

 be, viz. a rule which assigns the measure of expectation 

 we ought to entertain of the recurrence of the event under 

 the circumstances in question. Of course, on the view 

 adopted in this work, we insist on enquiring whether it is 

 really true that on the average events do thus repeat their 

 performance in accordance with this law. Thus tested, no 



