124 MONTMORT. 



211. Althougli the earliest iiotice of the problem occurs in 

 the letter of Montmort's which we are now examining, yet the 

 earliest piiblicatioyi of it is due to De Moivre ; it is Problem XV. 

 of the De Mensura Sortis. We shall however speak of it as 

 Waldegraves Problem, from the person whose name we have found 

 first associated with it. 



The problem is discussed by Laplace, Theorie . . . des Froh. 

 page 238, and we shall therefore have to recur to it. 



212. Montmort refers on page 320 to a book entitled Traite 

 dii Jeu, which he says he had lately received from Paris. He says 

 it is un Livre de morale. He praises the author, but considers 

 him to be wrong sometimes in his calculation of chances, and 

 gives an example. Nicolas Bernoulli in reply says that the 

 author of the book is Mr Barbeyrac. Nicolas Bernoulli agrees 

 with Montmort in his general opinion respecting the book, but 

 in the example in question he thinks Barbeyrac right and Mont- 

 mort wrong. The difference in result arises from a difference in 

 the way of understanding the rules of the game. Montmort 

 briefly replied ; see pages 332, 3-i6. 



Montmort complains of a dearth of mathematical memoirs ; he 

 says, page 322, 



Je suis etonne de voir les Journeaux de Lei23sic si degarnis de 

 morceaux de Matliematiques : ils doivent en partie leur reputation aux 

 excellens Memoires que Messieurs vos Oiicles y envoyoient souveiit : les 

 Geometres n'y trouvent plus depuis cinq ou six ans les memes ricliesses 

 qu' autrefois, faites-en des reproches a M. votre Oncle, et permettcs-nioi 

 de vous en faire aussi, Luceat lux vestra coram hominihus. 



213. The next letter is from Nicolas Bernoulli to Montmort ; 

 it occupies pages 323 — 337. It chiefly relates to matters which 

 we have already sufficiently noticed, namely, the games of Treize, 

 Her, and Tas, and Waldcgrave's Problem. Nicolas Bernoulli ad- 

 verts to the letter by his uncle James on the game of Tennis, 

 which was afterwards published at the end of the Ars Conjectandi, 

 and he proposes for solution four of the problems which are con- 

 sidered in the letter in order to see if Montmort's results will 

 agree with those of James Bernoulli. 



