[ I03 ] 



fpecific event admitting only of one of them, the former is capablc- 

 of indefinitely furpaffing the latter.. 



In order to prove this, we muft confider the law which the- 

 evidence of concurring witneffes follows, according to the number 

 of the witneffes. 



Let there be two dies, of the fame kind, in each of which the 

 number of white faces is m, each alfo having but one black face; 

 and fuppofe, that thefe dies being thrown together, it be required 

 to determine, what is the proportion of the number of chances - 

 that two white faces will turn up to the number of chances that 

 two black faces will turn up together. The number of combina- 

 tions of two white faces is the fquare of m; and the number of 

 combinations of black faces is unity. Therefore the odds that 

 two white faces will turn up rather than two black faces, is as 

 fn^ to I. The cafes where a black and a white face turn up to- 

 gether are excluded by the nature of the queftion, becaufe the 

 witneffes are fuppofed to be concurrent, that is, that the faces of 

 thedies are of the fame colour. In like manner, if there be three 

 dies of the fame kind as before, the odds that three white faces 

 will turn up together rather than three black faces, will he m^ 

 to I ; and fo on, the index of tn being always equal to the num- 

 ber of dies. 



Now if the number of chances that any witneffes refpeilively 

 tell truth, to the number of chances of their telling fahhood be as 

 m \.o I ; the odds, that they tell truth rather than falfhood, on fup- 



pofition. 



