234 French National Institute. 



dements of the planetary'orbits ; they give with the same 

 t'acilitv the two inequalities of the lunar motion in lonei- 

 luUe and latitude, which depend on the flattening or the 

 earth, formerly determined by M. La PI ic:e. 

 ^ The results are therefore perfectly identical with those 

 found bv M. Lagrange by a totally different way. They 

 would be mutualTv confirmed if occasion required, and if 

 the two methods did not carry their demonstration along 

 with them. The most remarkable diflerence c<uisists \\\ 

 M. La Place hatving adroitlv avoided a very great analytical 

 difficulty, and capable of impeding the progress of a less 

 eminent geometrician ; while on the other hand M. La- 

 grange has overcome the difficulty ; and by giving, like 

 M. La Place, the theorem, so imptutant to astronomers, of 

 the invarialjility of motions, he has furnished analysts at 

 the same time with formulas remarkable lor their clegance.- 

 But it is not less curious to observe with what facility, by 

 a simple transformation, JNL La Place has eliciicd these new 

 truths from the formulae in which they were contained. 



The secretary of the Institute then, proceeded to give a 

 detailed account of the works composed during the year 

 1808 by members of the class. 



Physics. — At the commencement of the year the class 

 had the honour to present to the emperor ihe History of 

 the Sciences since the year 1 789, which his majesty ordered 

 to be printed. The editors of this work, in profiting by 

 the materials furnished by nsembcrs of the class, and by 

 foreigners, have endeavoured to trace, -vvith truth and sim- 

 plicity, the immense progress which the human mind has 

 made in the knowledge of nature during these twenty years, 

 when war, intestine dissensions, and extravagant passions, 

 which alternately visited all states and empires, seemed to 

 have interrupted all useful inquiries and discoveries. 



This historical sketch will now serve as our point of 

 departure, and our annual reports in future will be so many 

 continuations. 



We ought, it is true, in our analyses, to treat only of 

 the subjects which have been discussed at our ifteetings : 

 but in the active relations in which we find ourselves with 

 the majority of those who cultivate the sciences, it is verv 

 unlikely that any important discovery will be made through- 

 out Europe, which will not speedily be heard of within the 

 walls of the Institute, and excite its members to smiilar 

 pursuits. 



Chemistry, in the decomposition of the alkalis, has this 

 year presented a striking exainple of the emidation which 



animalci 



