608 Mr. Bernard Cavanagh on 



Now for a change of total Entropy while all the n's remain 

 unchanged, 



1CI dJJ-\-pdV ^ diii+pdvi _* duj 4- pdv x ' , N 



«k = rf — =2wi Tjf — +n*2 ^ fx(pic 2 • • •) 



= 2wid$i + W*2(d* JC ')/ c (c 1 C s . . . .) . . . -. . . ' . (3) 



Integrating, 



^> = tn l (s 1 +k 1 ) + n t t(s x '-i-Jc x ')f x {c ] c 2 ) (4) 



The integration constants are determined by conceiving the 

 system, by an ideal process of raising the temperature and 

 diminishing the pressure, to pass into the perfect gaseous 

 state, the number of the various molecules remaining 

 unchanged. 



It is not necessary that this should be practicable. The 

 ideal process of " rushing " the system over the intervening- 

 unstable states, to exist, at least momentarily in the perfect 

 gaseous state, all without appreciable change in the numbers 

 of the various molecular species, is conceivable. It is not 

 intrinsically impossible, or incompatible with our more 

 limited experience, and that is all that is required. 



For then, however momentarily, the entropy of the system 

 will be expressible both by the integrated expression (4) and 

 by the known expression for the entropy of a perfect gaseous 

 mixture : 



S = Sm [>!_+*! -R log Cl ], 



which gives us 



h = h— B log c u 



kx == $x ? 



the latter sj corresponding to the ideal limiting state so that 

 Ici (etc.) like l x (etc.) and unlike k x (etc.), are independent 

 of concentrations. 



Returning now to our solution under ordinary conditions, 



S=2?i 1 (s 1 -r-Z 1 — U log d) + w*2(**' + fe'j f^c^ ....), 

 and so 



^.=(S-^±^) = « 1 (f , + t-B log <:,) 



+,n t Z{f x ' + k x ')f : ,(c lCl .. .), 



where yfr is the thermodynamic potential (of the dimensions 

 of Entropy) used by Planck, which will be called simply 

 u potential '' throughout this paper. 



