MONTMORT. 131 



the question of the ratio of male infants to female infants. We 

 have already stated that Nicolas Bernoulli had refused to see any 

 argument for Divine Providence in the fact of the nearly constant 

 ratio. He assumes that the ])rohahility of the hiHh of a male is to 

 the probability of the birth of a female as IS to 17 ; he then shews 

 that the chances are 43 to 1 that out of 14,000 infants the males 

 will lie between 7037 and 7363. His investigation involves a 

 general demonstration of the theorem of his uncle James called 

 Bernoulli's Theorem. The investigation requires the summation 

 of terms of a binomial series ; this is effected approximately by a 

 process which is commenced in these words : Or comme ces termes 

 sont furieusement grands, il faut un artifice singulier pour trouver 

 ce rapport : voici comment je m'y suis pris. 



The whole investigation bears some resemblance to that of 

 James Bernoulli and may have been suggested by it, for Nicolas 

 Bernoulli says at the end of it, Je me souviens que feu mon Oncle 

 a demontre une sembla])le chose dans son Traits De Arte Con- 

 jectandi, qui s'imprime a present a Bale, . . . 



226. TJie next letter is from Montmort to Nicolas Bernoulli ; 

 it occupies pages 395 — 400. Montmort records the death of the 

 Duchesse d'Angouleme, which caused him both grief and trouble ; 

 he says he cannot discuss geometrical matters, but will confine 

 himself to literary intelligence. 



He mentions a work entitled Pr emotion Physique ^ ou Action 

 de Dieu sur les Creatures demontree par raisonnement The 

 anonymous author pretended to follow the method of mathe- 

 maticians, and on every page were to be found such great words 

 as Definition, Axiom, Theorem, Demonstration, Corollary, &c. 



Montmort asks for the opinion of Nicolas Bernoulli and his 

 uncle respecting the famous Commerciiim Epistolicum which he 

 says M™ de la Societe Royale ont fait imprimer pour assurer a 

 M. Newton la gloire d'avoir invente le premier et seul les nou- 

 velles methodes. 



Montmort speaks with approbation of a little treatise which 

 had just appeared under the title of Mechanique du Feu. 



Montmort expresses his strong admiration of two investigations 

 which he had received from Nicolas Bernoulli ; one of these was 



9—2 



