LAPLACE. 501 



geomtStriqiie. Des t^moiiis attestent qu'ils tieunent de la Divinite meme, 

 qu'en se conformant k telle chose, on jouira, non pas d'une ou de deux, 

 mais d'une infinite de vies heureuses. Quelque faible que soit la proba- 

 bilite des temoignages, pourvu quelle ne soit pas infiniment petite; 11 

 est clair que I'avantage de ceux qui se conforment a la chose prescrite, 

 est infini, puisqu'il est le produit de cette probabilite par un bien 

 infiDi; on ne doit done point balancer a se procurer cet avantage. 



See also the Athenceum for Jan. 14tli, 1865, page oo. 



942. The next section is entitled, Des clioix et des decisions 

 des assemhUes; it occupies four pages: results are stated re- 

 specting voting on subjects and for candidates which are obtained 

 at the end of Chapter ii. of the Theorie...des Proh. 



The next section is entitled, De la probabilite des Jugemens 

 des tiibunaux; it occupies five pages: results are stated which 

 are obtained in the first supplement to the Theo7'ie...des Prob. 

 This section is nearly all new in the third edition of the 

 Theorie. . . des Prob. 



The next section is entitled, Des Tables de mortalite, et des 

 durees moyennes de la vie, des mariages et des associations quel- 

 conques; it occupies six pages : results are stated which are ob- 

 tained in Chapter VIIL of the Theorie... des Prob. 



The next section is entitled, Des benefices des etablissemens qui 

 dependent de la probabilite des evenemens; it occupies five pages. 

 This section relates to insurances : results are given which are ob- 

 tained in Chapter ix. of the Theorie... des Prob. 



943. The next section is entitled, Des illusions dans Vesti- 

 mation des Probabilites ; this important section occupies pages 

 cii — cxxviii: in the second edition of the Theorie... des Prob. the 

 corresponding section occupied little more than seven pages. 



The illusions which Laplace notices are of various kinds. One 

 of the principal amounts to imagining that past events influence 

 future events when they are really unconnected. This is illus- 

 trated from the example of lotteries, and by some remarks on 

 page CIV. relating to the birth of a son, which are new in the 

 third edition. Another illusion is the notion of a kind of fatality 

 which gamblers often adopt. 



Laplace considers that one of the great advantages of the 



