176 DE MOIVRE. 



Laplace are correct. The misapprehension may have arisen from 

 reading only a part of De Moivre's page 205, and so assuming a 

 law of a series to hold universally, which he distinctly says breaks 

 off after a certain number of terms. 



The just reputation of Dr Oettinger renders it necessary for me 

 to notice his criticisms, and to record my dissent from them. 



812. De Moivre's Problems Lxvi. and LXVii. are easy deduc- 

 tions from his preceding results ; they are thus enunciated : 



LXVI. To find what Probability there is that in a given number 

 of Games A may be a winner of a certain number q of Stakes, and at 

 some other time B may likewise be winner of the number p of Stakes, 

 so that both circumstances may happen. 



LXVII. To find what Probability there is, that in a given number 

 of Games A may win the number q of Stakes ; with this farther con- 

 dition, that £ during that whole number of Games may never have 

 been winner of the number j^ of Stakes. 



813. De Moivre now proceeds to express his results relating 

 to the Duration of Play in another form. He says, page 215, 



The Pules hitherto given for the Solution of Problems relating to 

 the Duration of Play are easily practicable, if the number of Games 

 given is but small ; but if that number is large, the work will be very 

 tedious, and sometimes swell to that degree as to be in some manner 

 impracticable : to remedy which inconveniency, I shall here give an 

 Extract of a paper by me produced before the Poyal Society, wherein 

 was contained a Method of solving very expeditiously the chief Pro- 

 blems relating to that matter, by the help of a Table of Sines, of which 

 I had before given a hint in the first Edition of my Doctrine of Chances, 

 pag. 149, and 150. 



The paper produced before the Poyal Society does not appear 

 to have been published in the Philosophical Transactions; pro- 

 bably we have the substance of it in the Docty^ine of Chances. 



De Moivre proceeds according to the announcement in the 

 above extract, to express his results relating to the Duration of 

 Play by the help of Trigonometrical Tables; in Problem LXVIII. he 

 supposes the players to have equal skill, and in Problem LXix. he 

 supposes them to have unequal skill. 



