﻿236 Mr. Bernard Cavanaffh 



i=> 



on 



Then we have 



but again remembering 



Sj£dta=0, (13) 



O n oi 



and so from (8) 



'^ffr*jXpn(~Bdlogg$fe) + fw«V 



(15) 



c=o c=o 



= <£ M + R(idlog(l+mC-t- jScoirfGoi. ■ (16) 



(17) 



c=o c=o 



Now (6) with (8) gives 



\B^/Mo L \<Wn J, ft H-mO 



And if we write (16) in the form 



^^M+nfirfi.og (i+mC)+a M , . (is) 



*c=o 

 it is at once clear that the " general " terms thus adopted 

 (and therefore, of course, the " linear " terms similarly) are 

 connected by the Gibbs fundamental relation [see note at 



end of this paper], for (M G') being a function of n 0l 



^i , homogeneous and of the first degree, 



Z>ioidG ol ' +2n s dG s ' = ; 



i-e. -M Zc 01 dG Q1 ' + Xn s dG s ' = 0, 



i-e. Mo^Gm 4-2n,dG,' = 0*, . . , (19) 



which means that [M G M + %nJ3t s '} or (say) M G is, as a 



* The Gibbs relation might indeed have been used to obtain (16) direct 

 from (17), <j) M appearing as the integration constant. The above treat- 

 ment [(12) to (16)] appeared, however, to be more interesting, and to 

 introduce M in a more natural and illuminating manner, in its relation 

 to the original " molecular " expression for ^r. 



