628 Mr. Bernard Oavanagh on 



comparing (70) and (74) we see that this requirement in- 

 volves also that 



[K' + J^']=0, (76) 



as in the hypothetical perfect gaseous state (extremely hot 

 and rarefied) conceived for the determination of the integra- 

 tion constants in the entropy function (see section I.). 



This reveals the impossibility of even an approximate fulfil- 

 ment of the above requirement, such as might rashly be 



assumed on the grounds that ^^ (in (75)) will probably 

 not be large. " 



For consider firstly that u' depends directly on the Dielectric- 

 constant of the solvent, which would suffer an enormous total 

 change during this transition to the gaseous state, and secondly 

 that since c is n/M , u' depends also on p Q the density of the 

 solvent, whose variation (total) is perhaps even more obvious. 



It is clear that if the validity of the general method of 

 this paper is conceded, Milner's use of the Yirial theorem 

 cannot possibly be justified on theoretical grounds. 



But if we thus reject his application of the Virial theorem, 

 the true value of Milner s calculation of S2^<£( ?1 ) ^ s i n no 

 way diminished, as the opening of this section will have 

 indicated. 



The Application of Milner' s Calculation. 



As he fully realizes, Milner's assumptions limit him to 

 fairly dilute solution where, in addition to the satisfaction of 

 certain requirements involved in the probability considera- 

 tions, the ions may be regarded as point charges, and the 

 solvent is present in such large excess that its dielectric 

 constant K may be used with accuracy in calculating the 

 forces between the ions. 



But Milner states in a footnote * that, involved in the 

 calculation of IXr^r) is the implicit assumption that K is 

 independent of the temperature, saying that "if it were not 

 constant, the electrical force between two ions would depend 

 on their kinetic energies as well as on their positions." 



There appears to be some mistake here. 



The electrostatic force between two ions will depend on 

 the effective dielectric constant of the intervening medium. 

 In dilute solution — to which Milner is limited — the laroe 

 majority of the ions will be separated by many molecules of 

 solvent, so that, on the average, the effective dielectric 



* Loc. cit. xxv. p. 748. 



