53 MOLECULAR AND ATOMIC ENERGY 117 



unity, and therefore the mass of the gas given by the 

 density p, the heat needed is 



cp, 



where c is the specific heat of the gas at constant volume. 

 If J is the value of the mechanical equivalent of heat, the 

 equivalent of this amount of heat in terms of mechanical 

 energy is 



H = Jcp. 



With this value of the whole amount of energy in unit 

 volume of the gas we have to compare the value 



*-**. 



which we obtained in 16 for the kinetic energy of mole- 

 cular motion contained in the same unit volume. 



Since in regard to the latter magnitude we know that in 

 correspondence with Gay-Lussac's law it increases pro- 

 portionally to the absolute temperature when heat is added, 

 we see at once that both H and K are proportional to the 

 absolute temperature . Their ratio is therefore a constant 

 number independent of the temperature of the gas, constant 

 at least if the assumption founded on Eegnault's obser- 

 vations for atmospheric air is in general true, viz. that the 

 specific heat c at constant volume does not alter with the 

 temperature. Since also both magnitudes are proportional 

 to the density p, we have with that supposition the proposi- 

 tion : In a perfect gas the kinetic energy of the molecule 

 stands in a constant ratio to the total energy contained in 

 the QOS. 



The formulae given are sufficient to determine the 

 numerical value of this ratio. But the proceeding employed 

 by Clausius, 1 of first reducing to the same units the two 

 magnitudes to be compared, and of giving them as nearly 

 as possible the same form, is more to be recommended. 

 This was done by Clausius in the same way as J. E. 

 Mayer 2 determined the value of the mechanical equivalent, 



1 Pogg. Ann. c. 1857, p. 377 ; AbhandL iiber Warmetheorie, 2. Abth. p. 256 ; 

 Mech. Warmetheorie, iii. 1889-91, p. 35; transl. Phil. Mag. [4] xiv. 1857, 

 p. 108. 



2 Ann. Chem. Pharm. xlii. 1842, p. 239 ; Mechanik der Wdrme, 1867, p. 28- 



