Molecular Thermodynamics. 629 



constant will be that of the pure solvent, corresponding to 

 the statistical temperature. In centinormal aqueous solution 

 of KG, for instance, there are about 3000 solvent molecules 

 (" dihydrol ") to every molecule of electrolyte. 



But quite apart from this, it is far from clear how the 

 kinetic energies of particular ions can enter into the question 

 of the electrostatic forces in which those particular ions are 

 concerned. The logical force of the above quotation does 

 not seem at all obvious. 



Thus Milner's calculation of %%r<f)(r) appears to rest 

 on a stricter basis than he himself has claimed, though his 

 application of it in the form of the Virial theorem seems 

 altogether doubtful theoretically. 



The calculation proved to be complex, and the form in 

 which the final approximation was cast 



RTA£(A) 



depends on a tabulated function <j>(7i). 



In an inconspicuous footnote *, Milner remarks that " It 

 may be shown as an approximation, and when li is very 

 small " that 



</>(/*) = - v|7rA C 77 ) 



Now in dilute conducting solutions li is small, and owing 

 to the rather striking result to which it will lead, one is very 

 interested to find, on examining the values for Ihcjytfi) given 

 by Milner in the later paper, that up to centinormal (or even 

 higher concentrations) we shall not be very far out in 

 applying this approximation (77), which, since h is of the 

 form A'c%, means that XXrcj)(r) is of the form 



Acz per gram-molecule (78) 



This gives for the general energy term 



nRu'c*, (79) 



instead of the expression nRu'c^ used in (66), and we shall 

 obviously obtain 



^ = M o (<£ M + 2Rc)+2w(0-Rlogc)-RM o <£'ci, . (80) 

 whence 



>, • • (81) 



|*=2{0-R(logc + if c )*}J 

 * Loc. cit. xxiii. p. 575. 



