42G TREMBLEY. 



mortalite....(i'C.; it occurs on pages 80 — 82 of the mathematical 

 portion of the vokime. 



Trembley corrects some misprints in the memoir, and he says : 



Au reste, je dois avertir que la metliode d' approximation que j'ai 

 donn^e dans ce memoire comme un essai, en attendant que des obser- 

 vations plus detaillees nous missent en etat de proceder avec plus de 

 regularite, que cette methode, dis-je, ne vaut absolument rien, et je dois 

 des excuses au public pour la lui avoir presentee. 



He then shews how a more accurate calculation may be made ; 

 and he says that he has found that the values of n instead of 

 remaining nearly constant really varied enormously. 



789. The next memoir is entitled Essai sur la maniere de 

 trouver le teime general des series r^currentes. 



This memoir is published in the volume for 1797 of the Me- 

 moires de V Acad.... Berlin ; the date of publication is 1800, The 

 pages 97 — 105 of the memoir are devoted to the solution of a pro- 

 blem which had been solved by Laplace in Vol. vii. of the 

 Me moires... par divers Savans ; Trembley refers to Laplace. 



The problem is as follows : Suppose a solid having n equal 

 faces numbered 1, 2, 3 ...jy, required the probability that in the 

 course of n throws the faces will appear in the order 1, 2, 8, ...p. 



This problem is very nearly the same as that of De Moivre on 

 the run of luck ; see Art. 325. Instead of the equation 



'^«+i =Un+ 0-- Un_p) ha^, 

 we shall now have 



^^«+i = '^^n + (1 — Wn_") «^' ; and a=-. 



V 



Trembley solves the problem in his usual incomplete manner ; 

 he discusses in succession the cases in which p = 2, 3, 4 ; and then 

 he asssumes that the law which holds in these cases will hold 

 generally. 



790. The next memoir is entitled Ohservations sur les calculs 

 relatifs a la dur^e des mariages et au nornhre des dpoux suhsistans. 



This memoir is published in the volume for 1799 — 1800 of 

 the Memoir es de T Acad... Berlin ; the date of publication is 1803; 

 the memoir occupies pages 110 — 130 of the mathematical portion 

 of the volume. 



