1814.] Imperial Institute of France. 231 



IMPERIAL INSTITUTE OP FRANCE. 



Account of the Labours of the Class of Mathematical and Physical 

 Sciences of the Impeiial Institute of France during the Year 1813. 



I. Mathematical Department.— By M. le Chevalier De- 

 lambre, Perpetual Secretary. 



Meinoirs of M. Laplace on the Variations of the pla?ietary Ele- 

 ments, ami on the Comets. 



The most interesting article of this notice of the labours of the 

 scientific class ought to be the announcement of the Mechanicjue 

 Analylique of M. le Conite Lagrange. The printing of the second 

 volume had commenced about the beginning of January. The 

 ardour with which the illustrious author devoted himself to this 

 labour gave us the hope of soon reaping the fruits of it. His death, 

 which at all times would have been a misfortune for the sciences, 

 has been the more sensibly felt because it delayed,' or perhaps 

 destroyed altogether, the expectations which appeared so well 

 founded : but the influence of a great man is not confined to the 

 limited period of his existence. The domains which he has added 

 to science will be cultivated and fertilized by his successors. In the 

 success which they may obtain we shall see tlic result of his own 

 happy labours. Thus when we read the memoirs with which 

 Comte Laplace has enriched the collection of this year, we shall 

 recollect that one of the first. labours of M. Lagrange had for its 

 object the theory which constitutes the foundation of the calculus 

 of probabilities, which he afterwards treated in a manner so new 

 and so remarkable. It will be recollected also, that in the last 

 memoir which he read to the Institute he had simplified and gene- 

 ralized with the same sriiperiority tlic calculus of the variations of 

 the elements of the planetary orbits. 



These are the two subjects to which M. Lagrange, who had 

 likewise treated of them in his own vvay, has just added new devc- 

 lopements. We shall satisfy our-elves at present with a simple 

 armounce of the last of his memoirs, which we merely heard once 

 read over. We can give a more complete notion of the first memoir, 

 which h<is been just published. 



M. le Comte Laplace, wiio gave us last year a complete work on 

 Probabilities, has applied his theory to one of the most difficult 

 questions which physical astionomy prc'icnts : namely, the origin of 

 comets, and the nature of their orliits. 



Herschd's opinion on this subject will he recollected, who per- 

 ceiving almost every where in the celestial spaces a n)atter feel)ly 

 luminous, in which lie observed disseminated certain points that 

 appearcfl tij him more dense and more luminous, conceived that in 

 time universal attraction might unite round these centres the nebu- 

 lous matter with wliich they are siirroiuided ; that in consequence of 

 their mutual attraction two or more of these centres might accjuire a 

 inoveincntj that this motion might carry them to the surface of th« 



