the Litminiferoiis ^Ether. 393 



retain more than two or three figures to the left hand of the 

 tens ; and we will write such expressions as if they were the 

 exact results of the computations. 



If V be the velocity of a wave in an elastic medium whose 

 coefficient of elasticity, or, in other words, its tension, is e 

 and density S, both for the same unit, we have the well-known 

 relation 



/de 



And for gases we have 



ft 



e = fc, 



where 7 = 1*4; and the differential of the latter substituted in 

 the former gives 



=\/i <*> 



V ... f 



The tension of a gas varies directly as the kinetic energy of 

 its molecules per unit of volume. If v 2 be the mean square 

 of the molecules of a self-agitated gas, we have 



eozSv 2 , or t; 2 = ^^-, (3) 



where x is a factor to be determined. Equations (2) and (3) 

 give 



v 2 =-Y 2 (4) 



7 



Assuming, with Clausius, that the heat-energy of a molecule 

 due to the action of its constituent atoms, whether of rotation 

 or otherwise, is a multiple of its energy of translation, we 

 have for the energy in a unit of volume producing heat, 



where y is a factor to be determined. If c be the specific 

 heat of a gas, w its weight per cubic foot at the place where 

 (7 = 32*2, J Joule's mechanical equivalent, r its absolute tem- 

 perature ; then the essential energy of a cubic foot of the 

 medium will be cwtJ; and observing that w=gS, we have 



i^ = cgSrJ, (5) 



which, reduced by (4), gives 



•^^ • W 



the second member of which is constant for a given gas. To 



