EULOGY ON AMPERE. 123 



it would be necessary to add a new condition to the principles which 

 had seemed to satisfy all but himself. He referred to moral considera- 

 tions. He remarked that we could not, unless by instinct, prevent our- 

 selves from acknowledging the effects, the loss or i)rofit attached to the 

 proposed games would have on our social position and habits ; he ob- 

 served that an advantage derived from a benefit could not be measured 

 by the absolute value of that benefit, separated from the fortune to 

 which it was about to be added. The geometrical relation of the increase 

 of fortune to the primitive fortune seemed to him to lead to considera- 

 tions much more in accordance with our mode of life. By adopting 

 this rule you understand at once, for example, that with a million of favor- 

 able chances against one single adverse chance, no man, in the full 

 possession of his senses, would consent to play a million francs against 

 one. 



The introduction of moral considerations into the mathematical theory 

 of play has undoubtedly detracted from its importance, its clearness, and 

 vigor. It should be regretted, then, that Buffon has used them to reach 

 the conclusion, given in these words : "A long series of chances, is a 

 fatal chain: whose prolongation leads to misery," in less i)oetical terms, 

 a professional player ends in certain ruin? 



This proposition is of the highest social importance, and Ampere was 

 anxious to demonstrate it without borrowing the conditions used by 

 the distinguished naturalist, and the not less celebrated Daniel Bernoulli. 

 Such was the principal object of the work, which appeared in Lyons in 

 1802, with the modest title of ^^Considerations sur la theorie mathemati- 

 que du jcu^'' — "Eeflections on the mathematical theory of chances," in 

 which the author proves himself an ingenious and jiracticed calculator. 

 His formulas, full of elegance, lead to pm-ely algebraic demonstrations 

 of theorems, seeming to require the aijplicatiou of the differential 

 analysis. The principal question, moreover, is found completely solved. 

 The course followed by Ampere is clear, methodical, and faultless. 

 He first established that, betw^een two persons, equally rich, the mathe- 

 matical principle of Pascal and Fermat, the proportionality of the 

 stakes to the favorable chances should inevitably be the rule of the 

 game 5 that inequality of fortunes should give rise to no change in this 

 general rule when the players have decided to play but a limited num- 

 ber of games, so few that neither shall be exposed to the total loss of 

 all his fortune; that the question is changed if there should be an in- 

 definite number of games, and a possibility of continuing the play a 

 longer time, thus giving to the richer player an incontestable advant- 

 age, which rapidly increases, in iiroportion to the difference of fortunes. 



The disadvantage of one of the players becomes immense if his ad- 

 versary be very much richer than he, which is always, and very evi- 

 dently, the case of the professional player, who plays with every one. 

 The whole number of players against whom he plays is to be considered 

 as one single individual endowed with an immense fortune. In games 



