624 Mr. Rankine on the Centrifugal Theory of Elasticity, 

 the following equations : 



=c»'*(^-^0 



> 



(17) 



Me' Zm( T ,\ 



and if Q represent the quantity of heat in unity 

 of weight f 



^"M""2^ " 2\CnfjL ) J 



(19.) The real)specific heat of a given substance is found by- 

 taking the differential coefficient of the quantity of heat with 

 respect to the temperature. Hence it is expressed in various 



forms by the following equations, in which the coefficient r is 



supposed not to vaiy sensibly with the temperature. 



Real specific heat of one atom, 



dr ~~ 2Cnfju ' 

 real specific heat of unity of weight, 

 £?Q __ Sk 

 dr " 2Cnfju ' ^. . . . (18) 



real specific heat of so much of a perfect gas 

 as occupies unity of volume under unity of 

 pressure at the temperature of melting ice, 



dq_ SAM 



The coefficient , representing the ratio of the total vis viva 



of the motions of the molecular atmospheres to the portion of 

 vis viva which produces elasticity, multiplied by the ratio of the 

 total mass of the atom to that of its atmospheric part, is the 

 specific factor in the capacity of an atom for heat. The view 

 which I have stated as probable in article 13, — that the first 

 factor of this coefficient is, like the second, a function of some 

 permanent peculiarity in the nature of the atom, — is confirmed 

 by the laws discovered by Dulong : that the specific heats of all 

 simple atoms bear to each other veiy simple ratios, and generally 

 that of equality; that the same property is possessed by the 

 specific heats of certain groups of similarly constituted compound 

 atoms ; and that the specific heats of equal volumes of all simple 

 gases, at the same temperature and pressure, are equal. 



