CEAIG. 55 



by adopting a different law of diminution concluded that faith 

 would expire in 1789. 



See Montmort, page XXXVIII. ; also the Athenceum for Nov, 7th, 

 1863, page Gil. 



91. A Calctdation of the C^'edihility of Human Testimony is 

 contained in Vol. xxi. of the Philosophical Transactions; it is the 

 volume for 1699 : the essay occupies pages 359 — 365. The essay 

 is anonymous ; Lubbock and Drinkwater suggest that it may be 

 by Craig. 



The views do not agree with those now received. 



First suppose we have successive witnesses. Let a report be 

 transmitted through a series of n witnesses, whose credibilities are 

 Pi' P^y-'Pn' the essay takes the jDroduct j^^j^g '"Pn ^s representing 

 the resulting probability. 



Next, suppose we have concurrent witnesses. Let there be two 

 witnesses ; the first witness is supposed to leave an amount of un- 

 certainty represented by 1 —p{, of this the second witness removes 

 the fraction p^, and therefore leaves the fraction (1 —p^ (1 — p^ : 

 thus the resulting probability is ^ — 0- — 2\) 0- ~2^2)- Sii^^iiarly 

 if tliere are three concurrent testimonies the resulting probability 

 is 1 — (1 —2\) (1 — i^a). 0- —P^) '} ^^^^ s^ 0^ ^^^' '^ greater number. 



The theory of this essay is adopted in the article Prohahilite 

 of the original French Encyclopedie, which is reproduced in the 

 Encyclopedie Methodique: the article is unsigned, so that we must 

 apparently ascribe it to Diderot. The same theory is adopted by 

 Bicquillcy in his work Bu Calcul des Frohahilites. 



