412 TREMBLE Y. 



carried into effect in a memoir in the next volume of the Gottin- 

 gen Commentationes. The present memoir discusses nine problems, 

 most of which are to be found in De Moivre's Doctrine of Chances. 

 To this work Trembley accordingly often refers, and his references 

 obviously shew that he used the second edition of De Moivre's 

 work ; we shall change these references into the corresponding 

 references to the third edition. 



In this and other memoirs Trembley proposes to give elemen- 

 tary investigations of theorems which had been previously treated 

 by more difficult methods ; but as we shall see he frequently leaves 

 his results really undemonstrated. 



7o7. The first problem is, to find the chance that an event 

 shall happen exactly h times in a trials, the chance of its haj)peniug 

 in a single trial being p. Trembley obtains the well known result, 



a 



p^ (1 — i^Y ' ^® ^^^^^ ^li® modern method ; see Art. 257. 



a 



-h 



758. The second problem is to find the chance that the event 

 shall happen at least h times. Trembley gives and demonstrates 

 independently both the formulae to which we have already drawn 

 attention ; see Art. 172. He says, longum et taediosum foret has 

 formulas inter se comparare a priori; but as we have seen in 

 Art. 174 the comparison of the formulae is not really difficult. 



759. The third problem consists of an application of the second 

 problem to the Problem of Poiyits, in the case of tw^o players ; the 

 fourth problem is that of Points in the case of three players ; and 

 the fifth problem is that of Points in the case of four players. The 

 results coincide with those of De Moivre; see Art. 267. 



760. Trembley's next three problems are on the Duration of 

 Play. He begins with De Moivre's Problem LXV, which in effect 

 supposes one of the players to have an unlimited capital ; see 

 Arts. 807, 309. Trembley gives De Moivre's second mode of 

 solution, but his investigation is unsatisfactory ; for after havino- 

 found in succession the first six terms of the series in brackets, he 

 says Perspicua nunc est lex progressionis, and accordingly writes 

 down the general term of the series. Trembley thus leaves the 

 main difficulty quite untouched. 



