for a correction in the Theory of Sound, 105 



partial differential equations in their applications to physical 

 questions." 



Since Dr. Le Conte attributes misconception of the physical 

 theory of M. Laplace's correction in the problem of sound to 

 others, he of course challenges examination with respect to his 

 own conception of it. Now the original suggestion of M. Laplace 

 was made to M. Biot, who put it into what he considered a ma- 

 thematical form*. This solution, from the intimacy between 

 them, very probably received the assent of Laplace before it was 

 published, and would therefore be his first solution, and would 

 embody his original views. It was several years later that M. 

 Poisson showed the solution to be erroneous f, and gave the 

 mathematical form of the expression for the elasticity of an 

 elastic fluid in a state of vibratory motion which was required 

 for the solution of the problem. After many years again (in 

 1816), Laplace adopts Poisson' s solution J in another form, and 

 finally, in the Mecanique Celeste, admits that they are the same 

 solution, and claims them to have originated from his suggestion. 



We have here two points to consider, namely, Laplace's sug- 

 gestion to Biot, and Poisson' s solution of the problem. "With 

 respect to Laplace's popular suggestion, the objections are un- 

 questionably valid, that a consideration of cold developed in 

 rarefactions might be applied to account for a smaller velocity 

 than the Newtonian one, as reasonably as a development of heat 

 in condensations to account for a greater one, and have never 

 been answered. Dr. Le Conte, like others, diverts the argument 

 to Poisson's solution, which is quite another matter. 



M. Poisson found that, in order to obtain a strict mathema- 

 tical solution, it was necessary to assume the formula 



in the expression for the pressure (p) in the disturbed fluid, 



p=gmh(l+s+tr); 



and cr = /3s 3 , a = (Ss b , &c, or the product of /3 with any other 

 odd power of s would satisfy the conditions, but a — (3s would 

 alone furnish the required solution. It was required also that 

 the temperature of the gas should rise 1° Centigrade for a con- 

 densation T^th part, and this also simultaneously with the con- 

 densation. 



Now these were assumptions; and Dr. Le Conte says rightly, 

 t( in problems of this character, no deduction from analysis is 

 worthy of confidence which does not admit of a rational physical 



* Journal de Physique, vol. lv., for 1802. 



t Journal de I'Ecole Poly technique, vol. vii. cahier 14 for 1807. 



X Annates de Chimie et de Physique, vol. iii. p. 238. 



