96 MONTMORT. 



168. The fourth part of Montmort's book occupies pages 

 216 — 282 ; it contains the solution of various problems respecting 

 chances, and in particular of the five proposed by Huygens in 

 1657 ; see Art. 35. This part of the work extends to about double 

 the length of the corresponding part in the first edition. 



169. Montmort's solution of Hujgens's first problem is similar 

 to that given by James Bernoulli. The first few lines of Mont- 

 mort's Remarque on his page 217 are not in his first edition ; they 

 strongly resemble some lines in the Ars Coiijectandi, page 51. 

 But Montmort does not refer to the latter work, either in his 

 preface or elsewhere, although it appeared before his own second 

 edition; the interval however between the two publications may 

 have been very small, and so perhaps Montmort had not seen the 

 Ars Conjectandi until after his own work had been completely 

 printed. 



The solution of Huygens's fifth problem is very laborious, and 

 inferior to that given by James Bernoulli ; and Montmort him- 

 self admits that he had not adopted the best method ; see his 

 page 223. 



The solutions of Huygens's problems which Montmort gave 

 in his first edition received the benefit of some observations by 

 John Bernoulli ; these are printed in Montmort's fifth part, 

 pages 292 — 294, and by the aid of them the solutions in the second 

 edition were improved : but Montmort's discussions of the pro- 

 blems remain still far less elaborate than those of James Bernoulli. 



170. Montmort next takes two problems which amount to 

 finding the value of an annuity, allowing compound interest. 

 Then he proceeds to the problem of which a particular example 

 is to find in how many throws with a single die it will be an 

 even chance to throw a six. 



171. Montmort now devotes his pages 232 — 248 to the Pro- 

 blem of Points. He reprints Pascal's letter of August 14th, 1654, 

 to which we have alluded in Art. 16, and then he adds, page 241, 



Le respect que nous avons pour la reputation et pour la memoire de 

 M. Pascal, ne nous permet pas de faire remarquer ici en detiiil toutes 



