* 



4 Prof. J. Le Conte on the Discrepancy between the Computed 



cesses which have been employed, others have assailed t\\z phy- 

 sical aspects of his explanation, and attempted to show that it is 

 entirely inadequate to account for the discordance between theory 

 and observation. /^ 



It appears to me that the obscurity which marks many of the 

 discussions relating to this problem arises from two distinct causes : 

 namely, first, from a misconception of the physical theory of 

 Laplace and that of Poisson, which is substantially the same ; 

 and secondly, from the difficulties and obscurities which invest the 

 mathematical theory of partial differential equations in their appli- 

 cations to physical questions. I shall consider each of these 

 causes separately. 



1. Under the first head may be included the speculations of 

 Winter, of Tredgold, of Farey, of Galbraith, and, more recently, of 

 Blake, on the supposed correction for the modulus of elasticity of 

 air, and on the presumed influence of barometric pressure and lati- 

 tude on the velocity of sound*. It is certainly a curious illustration 

 of physical misconception, that it was not clearly perceived, as a 

 simple corollary from the investigations of Newton, as well as 

 those of Lagrange, Euler, Laplace, and. Poisson, that, ceteris 

 paribus, neither the density of the air nor the intensity of gravity 

 have any influence on the theoretic velocity of sound. For, 

 according to the Newtonian formula, the velocity of sound in air 

 — y/gh, — g being the velocity generated by terrestrial gravity in 

 a mean solar second, and h the height of a homogeneous atmo- 

 sphere. Now, as the value of h depends on the ratio of the den- 

 sity of mercury to the density of air, and as the latter varies, 

 according to Mariotte's law, as the height of the barometric 

 column, it is obvious that h remains constant, or is independent 

 of barometric fluctuations. Again, as the value of g increases, 

 the magnitude of h diminishes, and vice versa; so that the value 

 of gh remains constant in all latitudes, at all altitudes in the atmo- 

 sphere, and consequently under all barometric pressures, provided 

 there is no change of temperature^ . Even MM. Moll and Van 



* Winter, in Phil. Mag. S. 1. vol. xliii. p. 201 (1814). Tredgold, ibid, 

 vol. lii. p. 214 (1818). Farey, ibid. vol. lxiv. p. 178 (1824). Galbraith, 

 ibid. vol. lxvi. p. 109 (1825); also vol. lxviii. p. 219 (1826). Blake, in 

 Silliman's American Journal of Science, 2nd series, vol. v. p. 372. 



\ The same result may be reached by algebraic reasoning. Let 

 D = density of mercury, d = density of air, and b the height of mercury in 



bV 

 the barometric column. We have k= — r. Hence 



Now (D being constant), by Mariotte's law, of varies directly as b; hence 



