240 Imperial Instltitle of Ft a/ice, 



EEPORT OF TIIK PROCEKDINGS OF THE IMPERIAL INSTI- 

 TUTE OF FRANCE* DURING THE YEAR 1811. 



Mathematical Department, 



(Drawn up by M. Delambre, Perpetual Secretary.) 



JSJethadsJhr definite integrals, and their application to prO' 

 bal'iiities, and par lieu Uirly to the investigation of the mean 

 which must he fixed upon, among the results of observa- 

 tiofis. By Count Laplace. 



The theory of ProbabiHtics is one of those to which M. 

 Laplace has directed his attention since his entrance upon 

 his career as an analytical philosopher, and to which at 

 diflercnt periods he has made many valuable additions. Be- 

 sides several important memoirs, which l)e has published 

 in the volumes of the Academy of Sciences, or of the In- 

 stitute, he has elucidated the subject also in his lectures at 

 the Normal school, in his Syslnne dii Monde, &c. 



Thus bv extending his information, and by the clear ac- 

 count which he has given, he has enabled every person to 

 form an idea of the most profound part of the mathemati- 

 cal sciences. 



The publication to which we now refer is particularly 

 adapted to geometricians who are sufficiently advanced in 

 that science to understand count Laplace's Analyse Sa- 

 vante. It is a sufficient eulogium on tliat work to mention 

 that the Academy of Sciences announced its title, but left 

 its merits to be determined by those who peruse it ; and we 

 are under the necessity of following their example. Of 

 the two branches which distinguish this new work of count 

 Laplace, the first is merely a short historical introduction, 

 from which no abbreviation can be made without rendering 

 it obscure and incomplete : in this part we find some novel 

 observations respecting the existence of difierent branches- 

 of the modern analysis, especially the passages relating to 

 finite and infinite, and also to real and imaginary quan- 

 tities. 



The second division of the work shows that all analytical 

 researches are easier unravelled than extracted. 



The author confesses that he has reserved various demon- 

 strations on the subject for a work wliich it is his inten- 

 tion to publish very soon, on Probabilities, We cannot 



* This is ihe title bo'.y assumed by ihe French Natiinsl Institute. — 



do 



