J 02 MONTMORT. 



...the Solution of Mr Nicolas Bernoulli beiog very much crouded 

 with Symbols, and the verbal Explication of them too scanty, I own 

 I did not understand it thoroughly, which obliged me to consider Mr. 

 de Monimort^s Solution with very great attention : I found indeed that 

 he was very plain, but to my great surpriza I found him very erroneous; 

 still in my Doctrine of Chances I printed that Solution, but rectified 

 and ascribed it to Mr. de Monmort, without the least intimation of any 

 alterations made by me ; but as I had no thanks for so doing, I resume 

 my right, and now print it as my own — 



Doctrine of Chances; second edition page 181, third edition, page 211. 



The language of De Moivre in his second and third editions 

 would seem to imply that the solutions of Nicolas Bernoulli and 

 Montmort are different ; but they are really coincident, as De 

 Moivre had himself stated in his first edition. The statement that 

 Montmort's solution is very erroneous, is unjustly severe ; Mont- 

 mort has given his formula without proper precaution, but his 

 example which immediately follows shews that he was right him- 

 self and would serve to guide his readers. The second edition of 

 the Doctrine of Chances appeared nearly twenty years after the 

 death of Montmort ; and the change in De Moivre's language 

 respecting him seems therefore especially ungenerous. 



182. We shall not here give Montmort's general solution of 

 the Problem of the Duration of Play ; we shall have a better 

 opportunity of noticing it in connexion with De Moivre's investiga- 

 tions. We will make three remarks which may be of service to 

 any student who examines Montmort's own work. 



Montmort's general ^statement on his pages 2G8, 269, might 

 easily mislead ; the example at the end of page 269 is a safer 

 guide. If the statement were literally followed, the second line in 

 the example would consist of as many terms as the first line, the 

 fourth of as many terms as the third, and the sixth of as many 

 terms as the fifth; but this would be wrong, shewing that the 

 general statement is not literally accurate. 



Montmort's explanation at the end of his page 270, and the be- 

 ginning of his page 271, is not satisfactory. It is not true as he 

 intimates, that the four letters a and the eleven letters h must be 



