d'alembeht. 263 



bility would be quite willing to accept D'Alembert's reference to 

 experiment ; for relying on the theorem of James Bernoulli, they 

 would have no doubt that experiment would confirm their calcula- 

 tions. It is however curious that D'Alembert proceeds in his 

 very next paragraph to make a remark which is quite inconsistent 

 with his appeal to experiment. For he says that if head has 

 arrived three times in succession, it is more likely that the next 

 arrival will be tail than head. He says that the oftener head 

 has arrived in succession the more likely it is that tail will 

 arrive at the next throw. He considers that this is obvious, and 

 that it furnishes another example of the defects of the ordinary 

 theory. In the Opuscules, Vol. iv. pages 90 — 92, D'Alembert 

 notices the charge of inconsistency which may be urged against 

 him, and attempts to reply to it. 



475. D'Alembert then proceeds to another example, which, 

 as he intimates, he had already given in the Encyclopedie, under 

 the titles Croix ou Pile and Gageure ; see Art. 463. The question 

 is this : required the probability of throwing a head with a coin 

 in two trials. 



D'Alembert came to the conclusion in the Encyclopedie that 



2 3 



the chance ought to be ^ instead of -r . In the Opuscides how- 



ever he does not insist very strongly on the correctness of the 



2 

 result ^ , but seems to be content with saying that the reasoning 

 o 



3 



which jDroduces j is unsound. 



D'Alembert urges his objections against the ordinary theory 

 with great pertinacity ; and any person who wishes to see all that 

 a gi'eat mathematician could produce on the wrong side of a 

 question should consult the original memoir. But we agree with 

 every other ^^Titer on the subject in thinking that there is no 

 real force in D'Alembert's objections. 



476. The folloAving extract will shew that D'Alembert no 



2 

 longer insisted on the absolute accuracy of the result ^ : 



