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pofuioa that tlicy are concurrent, will be determined in the fame 

 manner, that is, will be as that power of the number of chances 

 of their telling truth, whofe index' is the number of witncffes, to 

 unity. 



The feries of antecedents whofe common confequent is unity, 

 which exprefs the ratio of the probability of the truth and falihood 

 of the concurring reporters, being the fucccifive pov/ers of a given 

 number greater than unity, encreafe in geometrical progreflion, 

 and therefore will at length exceed any number however great. 

 And if concurring reporters be all of equal credibility, their number 

 may be fo far encreafed as to produce a probability greater than 

 any that can be affigned. 



a 

 For let any propofed degree of probability be = , : and let 



the probability that a given witnefs tells truth be expreffed by the 



b 

 fraction r-r — -, b being lefs than a -, take fuch a power b" of b as 



that it fhall exceed «, and let « be the number of witneffes, then 

 will the probability of the veracity of the concurrent witnefTes be 



expreffed by the fradlion >— ; — , which is greater than the fraction 



a 

 — _j— ■; becaufe unity, the given difference of the numerators and 



denominators bears a lefs proportion to the greater quantity b", and 



therefore 



