Royal Societv. 419 
Corollary. Hence it follows, that if a fingle witnefs /hould be 
only fo far credible, as to give me the half of a full certainty; a 
fecond of the fame credibility would, joined with the firft, give 
me I J a third j, ^c. fo that the co-atteflation of a tenth, would 
give me i^H of certainty 5 and the co-attcftation of a twentieth 
t^fyl^a or above two millions to one, ^c 
'Prop. III. concerning the credit of a reporter for a particular 
article of that narrative, for the whole of which he is credible in 
a certain degree. 
Let there be fix particulars of a narrative equally remarkable ; 
if he to whom the report is given has ^ of certainty for the 
whole, or fum of them, he has ? 5 to one, againfl the failure in 
any one certain particular : For if he has 5 to i there will be no 
failure at all, and if there be, he has yet another 5 to i, that it 
does not fall upon that fingle particular of the fix ; that is, he 
has § of certainty for the whole, and of the # wanting, he has 
likewile # or f 5 of the whole, more 5 and therefore that there 
will be no failure in that fingle particular, he has f and |^^ of 
certainty, or |J of it : In general, if — f— he the proportion 
of certainty for the whole, and ~ — be the chance of the rell 
•' m -\- n 
of the particular articles m, againft fome one, or more of them 
n-j there will be nothing wanting to an abfolute certainty, againfl 
the not failing in the article or articles n but only — -. . 
'Prop. IV. concerning the truth of either oral, or written tra- 
dition, in whole or in part, fucceffively tranfmitted, and alfo co- 
attefted by feveral fucceffions of tranfmittcnts. 
I. Suppofing the tranfmiffion of an oral narrative to be fo per- , 
formed by a fucceffion of fingle men, or joined in companies, as 
that each tranfmiffion, after the narrative has been kept for 20 
years, impairs the credit of it a 12th part 5 and that confe- 
quently at the 12th hand, or at the end of 240 years, its cer- 
tainty is reduced to a half; and there grows then an even lay 
(by the corollary of the 2d propofition) againft the truth of the 
relation ; yet if we further fuppofe, that the fame relation is co- 
attefted by 9 other feveral fucceffions, tranfmitting alike each of 
them, the credibility of it, when they are all found to agree, will 
(by the corollary of the firfl: prop.) be as Tofi of certainty, or 
above a thoufand to one ; and if we fuppofe a co-atteftation of 
I5>, the credibility of it will be above two millions to one. 
G g g 2 i. la 
