DE MOIVEE. 193 



Thus by the aid of Stirling's Theorem the value of Bernoulli's 

 Theorem is largely increased. 



De Moivre adverts to the controversy between Nicolas Ber- 

 noulli and Dr Arbuthnot, respecting the inferences to be drawn 

 from the observed fact of the nearly constant ratio of the number 

 of births of boys to the number of births of girls ; see Art. 223. 

 De Moivre shews that Nicolas Bernoulli's remarks were not re- 

 levant to the argument really advanced by Dr Arbuthnot. 



886. Thus we have seen that the principal contributions to 

 our subject from De Moivre are his investigations respecting the 

 Duration of Play, his Theory of Recurring Series, and his extension 

 of the value of Bernoulli's Theorem by the aid of Stirling's Theorem. 

 Our obligations to De Moivre would have been still gi-eater if he 

 had not concealed the demonstrations of the important results 

 which we have noticed in Art. 306 ; but it will not be doubted 

 that the Theory of Probability owes more to him than to any 

 other mathematician, with the sole exception of Laplace. 



13 



