JAMES BEENOULLT. 59 



of various problems relating to games of chance. The fourth part 

 proposed to apply the Theory of Probability to questions of interest 

 in morals and economical science. 



We may observe that instead of the ordinary symbol of 

 equality, = James Bernoulli uses x, which Wallis ascribes to Des 

 Cartes; see Walliss Algebra, 1693, page 138. 



99. A French translation of the first part of the Ars Con- 

 jectandi was published in 1801, under the title of LArt de 



Conjecturer, Tradidt du Latin de Jacques Bernoulli; Avec des 

 Observations, Eclair cissemens et Additions. Far L. G. F. Vastel,... 

 Caen. 1801. 



The second part of the Ars Conjectandi is included in the 

 volume of reprints which we have cited in Art. 47; Maseres in 

 the same volume gave an English translation of this part. 



100. The first part of the Ars Conjectandi occupies pages 

 1 — 71 ; with respect to this part we may observe that the com- 

 mentary by James Bernoulli is of more value than the original 

 treatise by Huygens. The commentary supplies other proofs of 

 the fundamental propositions and other investigations of the pro- 

 blems; also in some cases it extends them. We will notice the 

 most important additions made by James Bernoulli. 



101. In the Problem of Points with two players, James 

 Bernoulli gives a table which furnishes the chances of the two 

 players when one of them wants any number of points not 

 exceeding nine, and the other wants any number of points not 

 exceeding seven ; and, as he remarks, this table may be j^rolonged 

 to any extent; see his page 16. 



102. James Bernoulli gives a long note on the subject of 

 the various throws which can be made with two or more dice, 

 and the number of cases favourable to each throw. And we may 

 especially remark that he constructs a large table which is equi- 

 valent to the theorem we now express thus : the number of ways 

 in which ni can be obtained by throwing n dice is equal to the 

 co-efficient of ^'" in the development of {x + x^ -{- x^ -\- x^ ^ x° -\- x^ 

 in a series of powers of x. See his page 21;. 



