PREVOST AND LHUILIER. 459 



in Art. 851 from Laplace. The memoir is divided into four 

 sections. 



853. The first section is on the lUility of the principle. It is 

 asserted that before the epoch when this principle was laid down 

 many errors had occurred in the waiters on Probability. 



The following paragraph is given : 



Dans I'appreciation de la valeur dii temoignage de deux tenioias 

 simultanes, il paroit que, jusqu'a Lambert, on n'a point use d'un autre 

 artifice, que de prendre le comjDlement de la formule employee pour le 

 temoignage successif. On suivoit ^ cet egard la trace de I'appreciation 

 des argumens conspirans, telle que I'avoit faite Jac. Bernoulli. Si I'on 

 avoit connu la vraie methode de I'estimation des causes, on n'auroit pas 

 manque d' examiner avant tout si ce cas s'y rapportoit ; et Ton auroit vu 

 que I'accord entre les temoins est un evenement posterieur k la cause 

 quelconque qui a determine les depositions : en sorte qu'il s'agit ici 

 d'estimer la cause par I'efiet. On seroit ainsi retorabe tout naturelle- 

 ment et sans effort dans la methode que Lambert a trouvee par un 

 effet de cette sagacite rare qui caracterisoit son genie. 



854. The authors of the memoir illustrate this section by 

 quoting from a French translation, published in Paris in 1786, of 

 a w^ork by Haygarth on the small-pox. Haygarth obtained from a 

 mathematical friend the following remark. Assuming that out 

 of tAventy persons exjDosed to the contagion of the small-jDox 

 only one escapes, then, however violent the small-pox mav 

 be in a town if an infant has not taken the disease we may 

 infer that it is 19 to 1 that he has not been exposed to the 

 contagion ; if two in a family have escaped the probability that 

 both have not been exposed to the contagion is more than 400 to 1 ; 

 if three it is more than 8000 to 1. 



With respect to this statement the memoir says that M. de la 

 Roche the French translator has shewn that it is ^ATong by a judi- 

 cious discussion. The end of the translator's note is quoted ; the 

 chief part of this quotation is the following sentence : 



Si Ton a observe que sur vingt persounes qui pontent a une table de 

 pharaon il y en a dix-neuf qui se ruinent, on ne pourra pas en deduire 

 qu'il y a un a parier centre dix-neuf que tout homme dont la foi-tune 



