122 EULOGY ON AMPERE. 



Hiero, Kiug of Syracuse, suspecting the honesty of a goldsmith, and 

 desiring, without injuring his crown, to determine the purity of the 

 gold, applied to Archimedes, who thus, through his instrumentality, 

 discovered the fundamental principle of hydrostatics, one of the most 

 brilliant discoveries of antiquity. 



The curioso who asked, after having observed the seven bridges be- 

 tween the two branches of the river Pregel and the island of Kueiphof, 

 whether it were possible to cross them successively without passing 

 twice over the same, and he who wished to know how the knight could 

 move over the sixty-four squares of the chess-board without returning 

 twice to the same square, became involved in that geometry of 2)osiUon, 

 (glanced at by Leibnitz,) which never makes use of the magnitudes of 

 quantities. 



Finally, the speculations of a gambler, belonging to the aristocratic 

 circles, the Chevalier de Mere, first suggested, in the reigu of Louis 

 XIV, the calculation of probabilities, or at least directed toward it 

 the attention of Pascal and Perm at, two of the most wonderful 

 geniuses of whom France is so deservedly proud. 



This last branch of applied mathematics, although called, by an illus- 

 trious geometer, " common sense reduced to calculation^^'' was not received 

 without opposition. 



Even now public opinion will scarcely admit that analytical formulas 

 are capable of determining the secret of judiciary decisions ; or of giv- 

 ing the comparative values of judgments pronounced by tribunals dif- 

 ferently constituted ; it unwillingly adopts, also, the numerical limits in 

 which have been included the mean result of several series of distinct 

 and more or less concordant observations. When there is a question 

 of an order of problems less subtile, all understanding play require 

 but the most ordinary intelligence to see at a glance that the aid of 

 algebra can here be satisfactorily called in, but even here are met, 

 in the details and applications, real difficulties, requiring the skill of 

 professional men. 



Every one readily understands the danger, the stakes being equal, 

 of playing when the conditions of the game give to one greater chances 

 of winning ; every one sees, too, at the first glance, tbat if the chances of 

 the two players are unequal, the stakes should be so too; that if the chances 

 of one, for example, are tenfold those of his adversary, the respective 

 stakes, the sums risked upon the game, should be in the proportion of 

 ten to one ; that this exact proportionality of the stakes to the chances 

 is the necessary and characteristic rule, sufficient for all fair play. 

 There are cases, however, where, in spite of the observance of these 

 mathematical conditions, a prudent man would decline to play. Who, 

 for instance, with a million of chances against one in his favor, would 

 risk a million to gain one franc? 



In order to explain this anomaly, this disagreement between the re- 

 sults of calculation and the inspirations of common sense, Buftbu found 



