[ ^o6 ] 



fradion can never be equal tu unity; that is, no finite number of 

 concurrent reporters can produce abfolute certainty. 



By this unlimited encreafe is to be underftood the adual, not 

 fenfible probability ; for the indefinitely little defed from certainty is 

 capable of mathematical computation, as well as the greatefl quantity, 

 though it be imperceptible by the human mind. We are therefore 

 juftified in concluding, that the evidence of human teftimony effec- 

 tually attains its maximum, becaufe it arrives at fuch a degree, as that 

 any further increafe of it is imperceptible. And the like takes place 

 iry extenfion ; fuppofe a yard to be encreafed by the hundred 

 thoufandth part of an inch, and by half that quantity, and by the 

 J-, and -J^- &c. ad infinitum; the increment of this line would be 

 imperceptible, and yet the line would never attain its maximum. 



If the chances for the truth and falfhood of the report of each 

 of any concurrent witneffes be equal, no number whatever of fuch 

 witneffes can render an event probable, by their teflimony. Becaufe 

 the number of chances of their coincidence in falfhood encreafes in 

 the fame proportion with the number of chances for their telling 

 truth. Let their number = », fince the probability that each 

 \yitnefs tells truth is = ^, the meafure of the probability of the 

 concurrent witneffes will be = - = i. 



271 



If it be improbable that each witnefs tells truth, that is, if the 

 number of chances that each tells falfhood, be to the number 



of 



