183 



The Vakiation iisr the Ratio of the Specific Heats of a 

 Gas at the Temperature of Liquid Air. 



By C. M. Smith. 



Introduction. — The value of the ratio of the specific heat of a gas at 



Q 



constant pressure, to the specific heat at constant volume, ^ = — ^ ^^s 



G y 



occupied the attention of physicists since the time of Newton. It was well 

 understood by him that the values for the velocity of sound in a gas as 



calculated from his formula V = . elasticity ^ ^gj.g ^^^ -^^ accord 



\) density 



with observed values, and being impressed by this discordance he was 

 moved to make certain violent assumptions concerning the relative magni- 

 tudes of the gas molecules and the inrer-molecular spaces, together with 

 the relative velocities of sound in each. The true explanation of the 

 discordance was first suggested by LaGrange, who pointed out that the 

 elasticity of a gas might be augmented faster than its density, under com- 

 pression, although it remained for LaPlace, in 1816, to develop the complete 

 theory, and elucidate the necessity for regarding the adiabitic changes in 



volume, the modified equation being V . | ^^'^^^'^^l^V x k, where k is 



4 



density 



the ratio of the adiabatic and isothermal elasticities, likewise the ratio of 

 the specific heats. Since that time more tlian a score of investigators have 

 occupied themselves with the determination of the value of 7c\ under the 

 various conditions of temperature and pressure, and ihe importance at- 

 tached to the determination of k will be apparent from the following 

 considerations. 



With a value of k assumed as known, its use in Newton's equation 

 is convenient for studying various physical constants of a gas, and in 

 small quantities of the gas, values of the velocity of sound and specific 

 heats may be determined or compared. Furthermore a knowledge of the 



^ For an exhaustive review of the history of the problem, see Maneuvrier, Jour, 

 dfc Physique, 4, J 895. 



