TREMBLEY. 421 



r Acad.... Berlin; the date of publication is 1799: tlie memoir 

 occupies pages 69 — 108 of tlie mathematical portion of the volume. 

 The problem discussed is that which we have noticed in Art. 44:8. 



776. Trembley refers in the course of his memoir to what had 

 been done by De Moivre, Laplace and Euler. He says, 



L'analyse dont M. Euler fait usage dans ce. Memoire est tres-inge- 

 nieuse et digne de ce grand geometre, mais comme elle est un peu 

 iudirecte et qu'il ne seroit pas aise de I'appliquer au probleme general 

 dont celui-ci n'est qu'un cas particulier, j'ai entrepris de traiter la chose 

 directement d'apres la doctrine des combinaisons, et de donner a la 

 question toute I'etendue dont elle est susceptible. 



777. The problem in the degree of generality which Trembley 

 gives to it had already engaged the attention of De Moivre ; see 

 ilrt. 293. De Moivre begins with the simpler case in his Pro- 

 blem XXXIX, and then briefly indicates how the more general 

 question in his Problem XLI. is to be treated. Trembley takes the 

 contrary order, beginning Vvdth the general question and then 

 deducing the simpler case. 



When he has obtained the results of his problem Trembley 

 modifies them so as to obtain the results of the problem discussed 

 by Laplace and Euler. This he does very briefly in the manner 

 we have indicated in Aii. 453. 



778. Trembley gives a numerical example. Suppose that a 

 lottery consists of 90 tickets, and that 5 are drawn at each time ; 

 then he obtains 74102 as the approximate value of the probability 

 that all the numbers mil have been drawn in 100 drawings. 

 Euler had obtained the result -7419 in the work which we have 

 cited in Art. 456. 



779. Trembley's memoir adds little to what had been given 

 before. In fact the only novelty which it contains is the investi- 

 gation of the probability that n-1 kinds of faces at least should 

 come up, or that n-2 kinds of faces at least, or n - 3, and so on. 

 The result is analogous to that which had been given by Euler and 

 which we have quoted in Ai^t. 458. Nor do Trembley's methods 

 present any thing of importance ; they are in fact such as would 

 naturally occur to a reader of De Moivre's book if he wished to 



