4G6 LAPLACE. 



plus del'cates de I'analyse, par la finesse dcs comblnaisons qu'elle exige 

 et par la difficulte de les soumettre au calcul ; celui qui paroit I'avoir 

 traitee avec le pins de succcs estM. Moivre, dans un excellent Oiivrage 

 qui a pour titre, Theory of Chances ; nous devons a cet habile Geometre 

 les premieres rocherches que Ton ait faites sur Fintegration des equa- 

 tions differencielles aux differences finies ; ... 



867. Laplace then refers to Lagrange's researches on the 

 theory of equations in Finite Differences, and also to two of his 

 own memoirs, namely that which we have just examined, and one 

 wdiich was about to appear in the volume of the Academy for 

 1773. But his present object, he says, is very different, and is 

 thus stated : 



...je me propose de determiner la probabilite des causes par les 

 evenemens, maticre neuve a bicn des egards et qui merite d'autant plus 

 d'etre cultivee que c'est principalement sous ce point de vue que la 

 science des hasards pent etre utile dans la vie civile. 



868. This memoir is remarkable in the history of the subject, 

 as being the first which distinctly enunciated the principle for 

 estimating the probabilities of the causes by which an observed 

 event may have been produced. Bayes must have had a notion of 

 the principle, and Laplace refers to him in the Theorie...des Proh. 

 page cxxxvii. though Bayes is not named in the memoir. See 

 Arts. 539, 696. 



869. Laplace states the general principle which he assumes in 

 the follow^ing words : 



Si un evenement peut etre produit par un nombre n de causes dif- 

 ferentes, les probabilites de I'existence de ces causes prises de I'evene- 

 ment, sent entre elles comme les probabilites de I'evenement prises de 

 ces causes, et la probabilite de I'existence de cliacune d'elles, est egale 

 a la probabilite de I'evenement prise de cette cause, divisee par la somme 

 de toutes les probabilites de Tevenement prises de chacune de ces 

 causes. 



870. Laplace first takes tlie standard problem in this part of 

 our subject : Suppose that an urn contains an infinite number of 

 white tickets and black tickets in an unknown ratio ; ^ + </ tickets 



