428 TREMBLE Y. 



had represented the calculations of mathematicians on such sub- 

 jects as destitute of foundation. 



Trembley intimates his intention of continuing his investi- 

 gations in another memoir, which I presume never appeared. 



795. The next memoir is entitled Observations sur la metJiode 

 de prendre les milieux entre les observations. 



This memoir is published in the volume for 1801 of the 

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

 volume is 1804 : the memoir occupies pages 29 — 58 of the mathe- 

 matical portion of the volume. 



796. The memoir commences thus : 



La maniere la plus avantagense de prendre les milieux entre les 

 observations a ete detaillee par de grands geometres. M. Daniel Ber- 

 noidli, M. Lambert, M. de la Place, M. de la Grange s'en sont occupes. 

 Le dernier a donne la-dessus un tres-beau memoire dans le Tome v. des 

 Memoires de Turin. II a employe pour cela le calcul integral. Mon 

 dessein dans ce memoire est de montrer comment on peut parvenir aux 

 niemes resultats par un simple usage de la doctrine des combinaisons. 



797. The preceding extract shews the object of the memoir. 

 We observe however that although Lagrange does employ the 

 Integral Calculus, yet it is only in the latter part of his memoir, 

 on wdiich Trembley does not touch ; see Arts. 570 — 575. In the 

 other portions of his memoir, Lagrange uses the Differential Cal- 

 culus ; but it was quite unnecessary for him to do so ; see 

 Art. 564. 



Trembley's memoir appears to be of no value whatever. The 

 method is laborious, obscure, and imperfect, while Lagrange's is 

 simple, clear, and decisive. Trembley begins with De Moivre's 

 problem, quoting from him ; see Art. 149. He considers De 

 Moivre's demonstration indirect and gives another. Trembley's 

 demonstration occupies eight pages, and a reader would probably 

 find it necessary to fill up many parts with more detail, if he were 

 scrupulous about exactness. 



After discussing De Moivre's problem in this manner, Trem- 

 bley proceeds to inflict similar treatment on Lagrange's problems. 



We may remark that Trembley copies a formula from La- 



