183 
THe VARIATION IN THE Ratio oF THE SpeciFiIc HEATS oF A 
Gas AT THE TEMPERATURE OF LiquiIp AIR. 
By C. M. SMITH. 
INTRODUCTION.—The value of the ratio of the specific heat of a gas at 
constant pressure, to the specific heat at constant volume, ;— —” has 
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 
ealeulated from his formula V — \ elasticity , were not in 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 inter-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 zas 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 adiabatic changes in 
volume, the modified equation being V - elasticity < k, where k is 
density 
the ratio of the adiabatic and isothermal elasticities, likewise the ratio of 
the specific heats. Since that time more than a score of investigators have 
occupied themselves with the determination of the value of k*, under the 
various conditions of temperature and pressure, and the 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 physica! constants of a gas, and in 
small quantities of the gas, values of the velocity of sound and specific 
heats may be determined cr compared. Furthermore a knowledge of the 
1 For an exhaustive review of the history of the problem, see Maneuvrier, Jour. 
de Physique, 4, 1895. 
