196 BAPvBEYRAC. ARBUTHNOT. 



TlCu 



It is easily seen that the limit, when n is infinite, is j— ^ , that 



IS 



ah 



The above is substantially the method of Nicolas Bernoulli. 



341. Nicolas BernouUi has a very curious mode of estimating 

 the probability of innocence of an accused person. He assumes 

 that any single evidence against the accused person is twice as 

 likely to be false as true. Suppose we denote by ii^ the probability 

 of innocence when there are n different evidences against him ; 

 there are two chances out of three that the n*^' evidence is false, 

 and then the accused prisoner is reduced to the state in which there 

 are n — 1 evidences against him ; and there is one chance out of 

 three that the evidence is true and his innocence therefore impos- 

 sible. Thus 



_ 2w„_,jf0 _ 2 





. n 



Hence ^"~ (sj * 



This is not the notation of Nicolas ; but it is his method and 

 result. 



842. In the correspondence between Montmort and Nicolas 

 Bernoulli allusion was made to a work by Barbeyrac, entitled 

 Traits dii Jeu; see Art. 212. I have not seen the book myself. 

 It appears to be a dissertation to shew that religion and morality 

 do not prohibit the use of games in general, or of games of chance 

 in particular. It is stated that there are two editions of the work, 

 published respectively in 1709 and 1744. 



Barbeyrac is also said to have published a discourse Sur la 

 nature du Sort 



See the English Cyclopoidia, and the Biographie Universelle, 

 under the head Barbeyrac. 



343. We have next to notice a memoir by Arbuthnot to whom 

 we have already assigned an elementary work on our subject ; 

 see Art. 79. 



The memoir is entitled A7i Argument for Divine Providence, 



