58 MOLECULAR AND ATOMIC ENERGY 133 



admissible. But we can with more ease and exactness 

 determine the other specific heat, that at constant pressure, 

 and infer from the behaviour of the one that of the other. 

 For this the ratio of the two magnitudes need not be 

 known if the gas in question obeys with exactness the 

 laws of Boyle and Gay-Lussac. For the equation 



p = p x const, 



which is the mathematical expression of these laws when, 

 as before, p represents the pressure, p the density, and 

 the absolute temperature, in connection with the formula 

 that we have already used several times, viz. 



p=J(C- c)p, 



in which J is the mechanical equivalent of heat, immediately 

 gives the law that the difference C c of the two specific 

 heats is a constant independent of both pressure and 

 temperature. This law, which was first given by S. Carnot, 

 leads at once to the conclusion that, for those gases whose 

 specific heat C at constant pressure does not alter with 

 the temperature and pressure, the specific heat c at constant 

 volume has also a constant magnitude. 



Now Kegnault 1 has experimentally shown for air 

 and hydrogen, and Eilhard Wiedemann 2 for carbon 

 monoxide, that the specific heat C at constant pressure / 

 does not depend on the temperature. From this we may 

 probably assume that all gases whose molecules contain 

 two atoms will exhibit the same behaviour if they obey 

 Boyle's and Gay-Lussac's laws exactly. In this case, 

 therefore, there would be no doubt as to the ratio of the 

 atomic energy (5- to the molecular energy E having a 

 constant value. 



For other gases, on the contrary, whose molecules are 

 composed of more than two atoms, it has been observed 

 that C is by no means constant. Eegnault found with 

 carbonic acid, and E. Wiedemann with carbonic acid, 

 ethylene, nitrous oxide, and ammonia, an unmistakable 



1 M6m. de VAcad. de Paris, xxvi. 



2 Habilitationsschrift, Leipzig 1875 ; Pogg. Ann. clvii. 1876, p. 1. 



