TREMBLEY. 427 



791. The memoir refers to that of Daniel Bernoulli on the 

 same subject which we have noticed in Art. 412. Trembley ob- 

 tains results agreeing with those of Daniel Bernoulli so far as the 

 latter was rigorous in his investigations ; but Trembley urges ob- 

 jections against some of the results obtained by the use of the 

 infinitesimal calculus, and which were only presented as aiDproxi- 

 mate by Daniel Bernoulli. 



792. As is usual with Trembley, the formula which occur 

 are not demonstrated, but only obtained by induction from some 

 simple cases. Thus he spends three pages in arriving at the re- 

 sult which we have given in Art. 410 from Daniel Bernoulli ; he 

 examines in succession the five most simple cases, for which 

 m = 1, 2, 3, 4, 5, and then infers the general formula by analogy. 



793. . For another example of his formulae we take the follow- 

 ing question. Suppose n men marry n women at the same time ; 

 if w out of the 2n die^ required the chance that m marriages are 

 dissolved. 



[^ 

 We may take m pairs out of n in j ways. In each 



7?2 



n — in 



of the m pairs only one person must die ; this can happen in 2'" 

 ways. Thus the whole number of cases favourable to the result 



is , = — . But the whole number of cases is the whole 



\m 



n — m 



number of ways in which 77i persons out of 2n may die ; that is 



\2n ^ ^ 



. Hence the required chance is 



in 



2n — 7n 



2'" [^ I 2?i — m 



2 II 



n — in 



Trembley spends two pages on this problem, and then does 

 not demonstrate the result. 



794. Trembley makes some api^lications of his formulae to the 

 subject of annuities for widows. He refers to a work by Karstens, 

 entitled Theorie von Wittwencassen, Halle, 1784; and also names 

 Tetens. On the other hand, he names Michelsen as a writer who 



