140 DE MOIVRE. 



250. The sixteenth and seventeenth problems relate to the 

 game of bowls ; see Art. 177. These problems are reproduced in 

 a more general form in the Doctrine of Chances, pages 117 — 123. 

 Respecting these two problems Montmort says, on his page 366, 



Les Problemes 16 et 17 ne sont que deux cas tres simples d'un 

 meme Probleme, c'est presque le seul qui m'ait echape de tous ceux que 

 je trouve dans ce Livre. 



251. The eighteenth and nineteenth problems are Problems 

 XXXIX. and XL. of the Doctrine of Chances, where we shall find 

 it more convenient to notice them. 



252. The remaining seven problems of the memoir form 

 a distinct section on the Duration of Play. They occur as 

 Problems LViii, LX, LXi, LXii, LXiii, Lxv, LXVI, of the Doctrine 

 of Chances; and we shall recur to them. 



253. It will be obvious from what we have here given that the 

 memoir De Mensura Sortis deserves especial notice in the history 

 of our subject. Many important results were here first published 

 by De Moivre, although it is true that these results already existed 

 in manuscript in the Ars Conjectandi and the correspondence 

 between Montmort and the Bernoullis. 



We proceed to the Doctrine of Chances. 



254. The second edition of the Doctrine of Chances contains 

 an Advertisement relating to the additions and improvements 

 effected in the work ; this is not reprinted in the third edition. 

 The second edition has at the end a Table of Contents which 

 neither of the others has. The third edition has the following 

 Advertisement : 



The Author of this Work, by the failure of his Eye-sight in extreme 

 old age, was obUged to entrust the Care of a new Edition of it to one of 

 his Eriends ; to whom he gave a Copy of the former, with some marginal 

 Corrections and Additions, in his own hand writing. To these the 

 Editor has added a few more, where they were thought necessary : and 

 has disposed the whole in better Order; by restoring to their proper 

 places some things that had been accidentally misplaced, and by putting 

 all the Problems concerning Aymuities together; as they stand in the 

 late imj-yroved edition of the Treatise on that Subject. An A'ppendix 



