360 HISTORY OF ACOUSTICS. 



now before us as a prize-question 4 : "To give the 

 mathematical theory of the vibrations of elastic 

 surfaces, and to compare it with experiment." Only 

 one memoir was sent in as a candidate for the 

 prize ; and this was not crowned, though honour- 

 able mention was made of it 5 . The formulae of 

 James Bernoulli were, according to M. Poisson's 

 statement, defective, in consequence of his not tak- 

 ing into account the normal force which acts at the 

 exterior boundary of the plate 6 . The author of the 

 anonymous memoir corrected this errour, and cal- 

 culated the note corresponding to various figures of 

 the nodal lines; and he found an agreement with 

 experiment sufficient to justify his theory. He had 

 not, however, proved his fundamental equation, 

 which M. Poisson demonstrated in a Memoir, read 

 in 1814 7 . At a more recent period also, MM. Pois- 

 son and Cauchy (as well as a lady, Mile. Sophie 

 Germain,) have applied to this problem the artifices 

 of the most improved analysis. M. Poisson 8 deter- 

 mined the relation of the notes given by the longi- 

 tudinal and the transverse vibrations of a rod ; and 

 solved the problem of vibrating circular plates 

 when the nodal lines are concentric circles. In 

 both these cases, the numerical agreement of his 

 results with experience, seemed to confirm the jus- 

 tice of his fundamental views 9 . He proceeds upon 



4 See Chladni,p.357. 5 Poisson's Mem. in Ac. Sc. 1812, p. 169. 

 c Ib. p. 220. 7 Ib. 1812, p. 2. * Ib. t. viii. 1829. 



9 An. Ckim. torn, xxxvi. 1827, p. 90. 



