222 DANIEL BERNOULLI. 



1 



rg-, that is to 2 "9 approximately; and Cramer considers 



(2 — V2) 



this to be nearer the comm.on notion on the subject than his former 

 value 13. 



892. It is obvious that Cramer's suppositions are entirely 

 arbitrary, and that such suppositions might be multiplied to any 

 extent. Montucla alludes on his page 403 to an attempt made by 

 M. Fontaine to explain the paradox. This attempt seems to con- 

 sist in limiting the game to 20 throws at most, instead of allowing 

 it theoretically to extend to infinity. But the opponents of the 

 mathematical theory would assert that for the game as thus under- 

 stood the value of the expectation assigned by the theory is still 

 far larger than common sense can admit. 



393. The Petersburg Problem will come under our notice 

 again as we advance with the subject. We may remark that 

 Laplace adopts Daniel Bernoulli's view ; Theorie . . . des Proh. 

 page 439. Poisson prefers to reconcile mathematical theory with 

 common sense by the consideration that the fortune of the person 

 whom we represent by B is necessarily finite so that he cannot pay 

 more than a certain sum ; this in result practically coincides with 

 the first of Cramer's two suppositions ; see Poisson, RechercJies 

 sur la Proh... page 73; Cournot, Exposition de la Theorie des 

 Chances... page 108. 



894. We pass to another memoir by Daniel Bernoulli. The 

 Academy of Sciences of Paris proposed the following question as a 

 prize subject for 1732, 



Quelle est la cause physique de rinclinaison des Plans des Orbites 

 des Planetes par rapport au plan de I'Equateur de la revolution du 

 Soleil autour de son axe; Et d'oii vient que les inclinaisons de ces 

 Orbites sont differentes entre elles. 



None of the memoirs sent in appeared to the judges to be 

 worthy of the prize. The Academy then proposed the subject 

 again for 1734, with a double prize. The prize was divided be- 

 tween Daniel Bernoulli and his father John BernoulH. The 

 memoirs of both are contained in the Recueil des pieces qui ont 

 remporte le prix de VAcademie Roy ale des Sciences, Tom. 3, 1734. 



