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II. Note on the Significance of the Chemical Constant and its 

 Relation to the Behaviour of Gases at Low Temperatures. 

 By F. A. LiNDEMANN, Professor of Experimental Philo- 

 sophy, Oxford *. 



THE general equation for the vapour pressure of a solid, 

 derived try integrating the Glausius-Clapeyron equation, 

 is of the form 



r T x p\ -f T cdT+f T CdT 



l°gP = \ R ^T-fO = J J ° ^ T2 Jo p . dT + C. 



Here X is the latent heat, \ the same at the absolute zero, 

 c p and C p the molecular heats of solid and gas at constant 

 pressure, H the gas constant and C the chemical constant. 



^ The object of this note is to examine the question of the 

 dimensions of somewhat more in detail than is usually 

 done, since it may be shown that this question is intimately 

 bound up with the problem of the degradation of perfect 

 gases. As will appear, the evidence of the chemical con- 

 stants seems to be against the degradation theory if the 

 above equation is accepted, and, moreover, the physical 

 significance of the chemical constant appears in quite a new 

 light when examined on these lines. 



In the text-books two different statements are found, 

 namely, that the chemical constant has the dimensions of the 

 logarithm of a pressure, e.g. Jellinck, Phys. Chem. d. Gas- 

 reaktionen, p. 765, or that it has the dimensions of the 

 logarithm of a pressure divided by a temperature to the 

 power 5/2, e. g. Lewis, ' System of Physical Chemistry/ 

 vol. iii. p. 190. The first statement, which at first sight 



appears to be justified by the fact that p^dTisapure 



number, really entails the assumption that the atomic heat of 

 the gas becomes equal to that of the solid at the absolute zero. 

 The second view is arrived at by assuming the gas laws to 

 hold down to the lowest temperatures. The question may be 

 stated generally as follows. If c p and Cp are analytic func- 

 tions of T one may write 



i T ,ylT = a + a l T-{-a 2 T 2 + ... 



and 





C p dT = b -j-b l T-]-b 2 T+.. 



Communicated by the Author. 



