440 PHILOSOI'HICAL TRANSACTIONS. [aNNO \6Qg. 



same maDtier, if the proportion of certainty be set at -f^Jj^, it will come to a half 

 from the 70th hand: and if at -f^^i, from the 6Q5ih hand. 



Prop. II. Concerning Concurrent Testifications. — If two concurrent reporters 

 have, each of them, as |-ths of certainty ; they will both give me an assurance 

 of fiths, or of 35 to one : if three, an assurance of j-f^, or of -2 15 to one. 

 For if one of them gives a certainty for 12001. as of fths ; there remains but an 

 assurance of ith, or of 200l. wanting to me, for the whole. And towards 

 that the second attester contributes according to his proportion of credibility, 

 that is to 4ths of certainty, before had, he adds -f-ths of the -i-th which was 

 wanting ; so that there is now wanting but -^th of a ^th, that is -^ ; and con- 

 sequently I have from them both -f^ths of certainty. So from three, 



That is, if the first witness gives me of certainty, and there is wanting 



of it — — ; the second attester will add — ; — of that ; and consequently 



a + c a + c a + c l J 



leave nothing wanting but — -- of that — ; — r= -=-. In like manner 



the third attester adds his — of that ., and leaves wanting only 



a + c a + c\ ° ^ 



=^', &c. 



a + c|3 



Carol. — Hence it follows, that if a single witness should be only so far credi- 

 ble as to give me the half of a full certainly ; a second of the same credibility 

 would, joined with the first, give me ^ths ; a third -i-ths ; &c. : so that the 

 co-attestation of a tenth would give me 4-J}-|4ths of certainty ; and the co-attes- 

 tation of a twentieth 4a|_6^|.9 ths, 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 six particulars of a narrative equally remarkable : if he to whom the 

 report is given, has -f-ths of certainty for the wliole, or sum of them, he has 35 

 to one against the failure in any one certain particular. For he has 5 to I there 

 will be no failure at all : and if there be, he has yet another 5 to 1, that it falls 

 not on that single particular of the 6. That is, he has f ths of a certainty for 

 the whole ; and of the ^th wanting, he has likewise ^ths or VVths of the whole, 

 more ; and therefore, that there will be no failure in that single particular, he 

 has ^ths and -s-Vths of certainty, or ffths of it. 



In general, if —— be the proportion of certainty for the whole ; and — ^ 



be the chance of the rest of the particular articles m, against some one or more 



