Chase.] ^76 [April 17, 



4 

 of revolution ; the ratio of ms viva is, therefore, — = .405285, and we 



have J? : ^• :: 1.405285 : 1. 



In 1877, Preston ( P. Mag., iii, 453 ; iv. 209), showed "that a physical 

 relation exists between the velocity of the particles of a medium consti- 

 tuted according to the kinetic theory, and the velocity of propagation of 

 a wave in the medium." . Maxwell calculated the numerical value of this 

 relation at V f, which represents Chase's ratio of relative vis viva; but he 

 did not give the method by which he reached that result, and no record 

 of it was found among his papers. The following thermodynamic demon- 

 stration may, therefore, be satisfactory to those who have found any diflS- 

 culty in accepting the more simple and more general photodynamic proof, 

 which is furnished by reference to oscillatory centres. 



nm 

 If we represent the density of a gas, — , by p, the fundamental equa- 

 tion of pressure becomes 



^'='r=t "' 



Alexander Naumann, iAnn. Pharm., 1867, 142, 267 ; J. B., 1867, 62) 

 showed that 



^ = Ur'-r) •- (2) 



IJ- being the heat of molecular motion, or mean vis viva of a perfect gas ; 

 Y', the specific heat under constant pressure ; y, the specific heat under 

 constant volume ; y' — y, the heat of expansion, or vis viva of mean velo- 

 city. The total specific heat is, therefore, 



O^fiJ^y'-y^l^l, (3) 



Hence, Pg : p„ : : 5 : 9 (4) 



«^ : »„ : : ;/5 : 3 (5) 



Prof. d'Auria, in a special investigation relating to the dynamics of 



direct-acting pumping engines, not yet published, has found, by analogy, 



that 



6v 

 /. = -^ ^ . 607927^ (6) 



Substituting this value in eq. (2) we get Chase's result : 



y' — y= .405285;- (7) 



yi = 1.405285^ (8; 



The exactness of agreement between this a priori value and the one 

 which was found by Rontgen (1.4053 ; Pogg, 1873, 148, 603), is very re- 

 markable. 



