French IStaiional Injlilute. 1 83 



With a fealed note, containing, befides the motto, the name 

 and addrefs of the author. This note will not be opened 

 but in cafe the paper fliall have been found entitled to the 

 prize. The prize will be paid, without any formality, to the 

 bearer of an order for that purpofe, which will be delivered 

 by the fecretary. 



FRENCH NATIONAL INSTITUTE. 



The following is an account of the labours of the Clafa 

 of the Mathematical and Phyfical Sciences during the third 

 <|uarter of the year 8, as read by J. B. S. Delambre, fecretary i 



Among the memoirs of which we have to give an account, 

 there are fonie, and thefe form the greater number, that can- 

 not be appreciated but by thofe who have particularly ap* 

 plied to the objedls on which they treat. As they would 

 require all the attention of the moft experienced mathema- 

 ticiafts, they are not very fufceptible of abridgement. Such, 

 in general, are all the memoirs on pure analyfis and the 

 higher parts of geometry. We muft be excufed, therefore, 

 if we do not take fo much notice of thefe works as ^heir 

 importance would require. We fhall content ourfelves with 

 announcing only, by their titles, a memoir of C. Niewport 

 on the immediate integrability of differential equations to any 

 number of variable ones ; and two memoirs of Biot contain- 

 ing analytical refearches, one on partial differential equa- 

 tions, and the other on vibrating furfaces. 



We fhall pay a little more attention to a memoir on me- 

 chanics, by C. Coulomb, which contains, befides the ana- 

 lytical part, a feries of experiments, of which we can at leafl 

 give the refults. The fubjeft is, the refiftance of fluids when 

 the motion is ven,' flow. If a body impels on a fluid, or 

 v/hen it is impelled by the latter with a very fmall velocity, 

 fuch, for example, as 0*3 yard, per fecond, it will be found 

 hy experiment that the refifiance is in proportion to the 

 fquare of the velocity : but where the motion is exceedingly 

 finall, for example, below o'Oi yard per fecond, the refift- 

 ance is not merely proportioned to the fquare, but to a com- 

 plex funftion of the velocity. Suppofing the velocity very 

 fmall, the quantity which reprefenls the refiftance will allb 



be 



