LAPLACE. 4G5 



and the subject itself; we shall not give any account of his investi- 

 gations, but confine ourselves to the part of his memoir which 

 relates to the Theory of Probability. 



863. Laplace considers three problems in our subject. The 

 first is the problem of the Duration of Play, supposing two players 

 of unequal skill and unequal capital ; Laplace, however, rather 

 shews how the j)i"oblem may be solved than actually solves it. He 

 begins with the case of equal skill and equal caj^ital, and then 

 passes on to the case of unequal skill. He proceeds so far as to 

 obtain an equation in Finite Differences with one independent 

 variable which would present no difficulty in solving. He does 

 not actually discuss the case of unequal capital, but intimates that 

 there will be no obstacle except the length of the process. 



The problem is solved completely in the Theorie...des Proh. 

 pages 225—238 ; see Art. 588. 



8GL The next problem is that connected with a lottery which 

 appears in the Theorie...des Proh. pages 191 — 201. The mode of 

 solution is nearly the same in the two places, but it is easier to 

 follow in the Theorie...des Proh. The memoir does not contain 

 any of the approximate calculation which forms a large part of the 

 diiicussion in the Theorie,..des Proh. ^Ye have already given the 

 history of the problem; see Arts. -11:8, 775. 



865. The third problem is the following : Out of a heap of 

 counters a number is taken at random ; find the chances that this 

 number will be odd or even respectively. Laplace obtains what we 

 should now call the ordinary results ; his method however is more 

 elaborate than is necessary, for he uses Finite Differences : in the 

 Tlieorie...des Proh. page 201, he gives a more simj^le solution. 

 We have already sjDoken of the problem in Art. 350. 



866. The next memoir is entitled Memoire sur la Prohahilite 

 des causes par les echiemens ; it occupies pages 621 — QoQ of the 

 volume cited in Art. 861. 



The memoir commences thus : 



La Theorie des hasarda est une dcs parties les plus curieuses et les 



30 



