﻿Molecular Thermodynamics. 231 



however, that the masses of the components are together with 

 temperature and pressure the independent variables, we see 

 that there may be a limit, for it must be theoretically possible 

 to alter temperature and pressure so quickly that the 

 numbers present of these complexes which we are admitting 

 as components remain sensibly unaltered during the change. 

 According to the view put forward in the previous section, 

 it involves us in a definite postulate bearing upon the nature 

 of molecules and of chemical change, when we say that the 

 limit is reached ichen and only ivhen every molecular species 

 which can be formed in the system has taken its place in the 

 list of ' ; components.''' 



Proceeding in theory to this limit, we obtain the general 

 expression for -fy which is referred to in the sequel as the 

 ".molecular expression for ty" and as Planck showed, we can 

 determine it completely when it is linear by " connecting-up " 

 with the known properties of the low-pressure gaseous 

 mixture. 



When the expression is not linear, the higher or " general " 

 terms are subject only to a single limitation inherent in 

 Planck's method, as pointed out in the previous paper *. 

 Observing that the " general " terms in the corresponding 

 expression for U f do not involve " chemical" energy, the 

 present author also suggested and illustrated J the interesting- 

 possibility of employing ordinary dynamical theory, at least 

 as a valuable aid, in determining and interpreting the form 

 of these " general " terms. 



This "molecular expression for yfr," however, will clearly 

 not in general correspond with our experiments carried out 

 under ordinary conditions. They will correspond with an 

 expression of the "general thermodynamic" type in which 

 the components are appropriate to the conditions of ex- 

 periment. 



The theoretical problem then presents itself of connecting 

 this " experimental" expression for -\jr, in a manner at once 

 rigorous — that is trustworthy — and practically effective, with 

 the "molecular" expression and its possibilities of theoretical 

 interpretation. 



The treatment of two important problems of this kind has 

 been attempted. 



Planck pointed out that when a single molecular species 



* Phil. Mag. xliii. p. 606 (1922). 



t Entirely analogous considerations apply to V, but ordinarily owing 

 to the low pressures used, V figures relatively negligibly in the determi- 

 nation of ^ [c/. footnote, p. 630, Phil. Mag. xliii. (1922)]. 



X Loc. cit. p. 62"). 



