[ I05 ] 



therefore the quantities ^'' and i5" + i are more nearly equal than 



a 



the numerator and denominator of the fradion -• 



It is manii'eft, that where the credibih'ty of each witnefs is very- 

 great, a very few witneffes will be fufHcient to overcome the pro- 

 bability derived from the nature of the fad. Thus fuppofe the 



6560 

 latter probability = TTr' '■> ^""^ '^^ us fuppofe that each witnefs tells 



truth only nine times for once that he tells falfhood ; that is, let the 



probability of the truth of his report be equal only to — ; then 



10 



four fueh concurring witneffes will be fufficient to produce belief, 



/ 



After a certain number of concurring witneffes have given 

 their teftimony in confirmation of the truth of a fad, any farther 

 encreafe of their number is fuperfluous; becaufe the difference 

 between unity and the fradion expreffing the probability, which is ' 

 the refult of their concurrent tefiimony, is indefinitely little ; and 

 all that an indefinite encreafe of the number of witneffes could do, 

 would be to diminifh that indefinitely little defed. 



Yet that probability, in cafes of teftimony, admits of an un- 

 limited encreafe, is evident ; beqaufe the limit of probability is cer- 

 tainty, but the denominator of the fradion, which expreffes pro- 

 bability, always exceeds the numerator by unity; therefore the 



Vol. VII. O fradion 



