JAMES BERNOULLI. 77 



Thus the contest is either decided in an even number of games, 

 or else in an odd number of games in which the victor is at least 

 three games in advance of his adversary : in the last case no ad- 

 vantage or disadvantage will accrue to either player if they play 

 one more game and count it in. Thus the contest may be con- 

 ducted without any change of probabilities under the following 

 laws: the number of games shall be even, and the victor gain not 

 less than n and be at least two in advance of his adversary. But 

 since the number of games is to be even we see that the two 

 players are on an equal footing. 



135. Gouraud has given the following summary of the merits 

 of the A7^s Conjectandi ; see his page 28 : 



Tel est ce livre de YArs conjectandi, livre qui, si Ton considere le 

 temps ou il fut compose, I'origiualite, Fetendue et la penetration 

 d'esprit qu'y montra son autenr, la fecondite etonnante de la constitution 

 scientifique qu'il donna au Calcul des probabilites, I'influence enfin qu'il 

 devait exercer sur deux siecles d'analyse, pourra sans exageration etre 

 regarde comme un des monuments les plus importants de I'histoire des 

 matliematiques. II a place a jamais le nom de Jacques Bernoulli parmi 

 les noms de ces inventeurs, a qui la posterite reconnaissante rejiorte tou- 

 jours et a bon droit, le plus pur merite des decouvertes, que sans leur 

 premier effort, elle n'aurait jamais su faire. 



Tliis 2^aneg}Tic, however, seems to neglect the simple fact r.f 

 the date of inihlication of the Ars Conjectandi, which was really 

 subsequent to the first appearance of Montmort and De Moivre in 

 this field of mathematical investigation. The researches of James 

 Bernoulli were doubtless the earlier in existence, but they were 

 the later in appearance before the world ; and thus the influence 

 which they might have exercised had been already produced. The 

 problems in the first three parts of the Ars Conjectandi cannot be 

 considered equal in importance or difliculty to those which we 

 find investigated by Montmort and De Moivre ; but the memorable 

 theorem in the fourth part, which justly bears its author's name, 

 will ensure him a permanent \)\'d.cQ in the history of the Theory of 

 Probability. 



