VOL. XXI.] PHILOSOPHICAL TRANSACTIONS. 430 



confidence, as that I would not give above one in six to be insured of the truth 

 of what he says, shall inform me as above, concerning J200l. I may then 

 reckon that I have as good as the absolute certainty of lOOOl. or five-sixths of 

 absolute certainty for the whole sum. 



The credibility of any reporter is to be rated, 1. By his integrity or fidelity; 

 and 1. By his ability : and a double ability is to be considered ; both that of ap- 

 prehending what is delivered ; and also of retaining it afterwards, till it be 

 transmitted. 



" What follows concerning the degrees of credibility, is divided into four 

 propositions. The first two respect the reporters of the narrative, as they 

 either transmit successively, or attest concurrently ; the third the subject of it, 

 as it may consist of several articles; and the fourth joins those three considera- 

 tions together, exemplifying them in oral and in written tradition." 



Prop. I. — Concerning the Credibility of a Report made by Single Successive 

 Reporters, who are equally credible. — Let their reports have each of them -|ths 

 of certainty ; and let the first reporter give me a certainty of lOOOl. in 12001. ; 

 it is plain that the second reporter, who delivers that report, will give me the 

 certainty but of ^ths of that lOOOl., or the -|-lhs of fths of the full certainty 

 for the whole 1200l. And so a third reporter, who has it from the second, will 

 transmit to me but -§-ths of that degree of certainty the second would have de- 

 livered me, &c. That is, if a be put for the share of assurance a single re- 

 porter gives me ; and c for that which is wanting to make that assurance com- 

 plete ; and I therefore supposed to have of certainty from the first re- 

 porter ; I shall have from the second, ; from the third, =^-=r- ; &c. 



And accordingly, if a be = 100, and c =. Q, (the number of pounds that lOOl. 

 put out to interest, brings at the year's end,) and consequently my share of cer- 

 tainty from one reporter be = -HtIj which is the present value of any sum to be 

 paid a year hence: ihe proportion of certainty coming to me from a second, will 

 be -i-g-§- multiplied by -f-g-o (which is the present value of money to be paid after 

 2 years ;) and that from a third-hand reporter = -f-g^l- thrice multiplied into itself; 

 (the value of money payable at the end of 3 years,) &c. 



Corollary. — And therefore, as at the rate of 6 per cent, interest, the present 

 value of any sum payable after 12 years is but half the sum ; so if the proba- 

 bility, or proportion of certitude transmitted by each reporter, be J-S-g-, the pro- 

 portion of certainty after 12 such transmissions, will be but as a half; and it 

 will be by that time an equal lay, whether the report be true or not. In the 



