2gS French National Injlilutc, 



fervations before he can make the neo.cflarv corrections. Tn 

 the calculation of this oppolition, C. Lalande junior and 

 Burckhardt from three obfervations of the fun which agreed 

 very well, diminiihed by n" the longitude of this planet 

 given by the tables. 



Mathematics applied to Philosophy. — Remarks 

 on the Difference between the Velocity of Sound deduced 

 from Theory and that given by Obfer-vation. New Demon- 

 Jirations of the principal Theorems in regard to the Attrac- 

 tion exercifed by Spheroids ; fpecial Determination of the 

 Conditmis of the Equilibrium of a Body made to balance 

 freely on a Flexible Wire or on a Fluid. 



The refult found by Newton for the velocity with which 

 found is propagated in the atmofpheric air, and fince con- 

 firmed by various analytical refearches of fucceeding geome- 

 tricians, differs however about a ninth from that given bv 

 experiment : the former is only 297*3 metres, and thelecond is 

 comprehended between 337*2 metres and 350*8. This point 

 of philofophy being one of thofe to which analyfis applies wiili 

 the greated rigour, it was impoflible to afcribe to the errors 

 or imperfection of calculation, the difference between theory 

 and obfervation. Newton therefore himfelf and fome of the 

 philofophers who wrote after him on this fubject have formed 

 different hypothefes, in regard to the constitution of the at- 

 mofphere, in order to account for the difference in queftion. 

 But as none of thefe hypothefes, which explained the fact 

 only in a very vague manner, could accord with the difcove- 

 ries of the modern chemiitiy, refpecling the nature of the 

 air, it has fince been afcribed to the influence which the va- 

 riations of the tci-nperature that accompany the dilatation and 

 condenfation of the air refulting from its vibrations may have 

 on the velocity of found. 



C. Biot, affociate, has endeavoured to determine by cal- 

 culation, the effect Which thefe vibrations that cannot be 

 doubted, produce on the velocity of found. He has proved 

 that it might he very fenfible, and even iufficient to carry the 

 velocity pi found beyond the term fixed by experiment. For 

 this purpofe he fet out from fome experiments on the dilata- 

 tion of the air, and of gas, made under the direction of 

 Berthollet, by C. Guy-Luflac, and he has combined them 

 with a plaufibie hypothecs on the quantity of caloric di (en- 

 gaged by the compreflion of the air, viz. that this fluid, 

 under thefe circumftances, abandons as much of it as is ne- 

 ceffary to he taken from it by fimple cooling in order to re- 

 duce it to the bulk it is made to occupy. 



As 



