﻿522 Prof. J. A. Pollock on the 



so for low pressures a'\p' may be neglected in comparison 

 with ajp, and as a first approximation we have here 



At all pressures it would appear, then, that if the adsorbed 

 fluid is in the liquid state, it has a latent heat and a density 

 very little different from those of water. 



It must be mentioned that the preceding thermodynamic 

 argument was first applied in this connexion by Trouton in 

 the earlier of his papers quoted ; I use it here, however, in 

 the converse form to that in which it was employed by him. 



The large ion, then, may be considered as a rigid core 

 surrounded by a film of water rather than by a dense atmo- 

 sphere of water molecules, though of course the transition 

 layer from water to vapour must be an important feature. 



An estimate of the diameter of the ion may be made, in 

 the light of a knowledge of the mobility, by considering the 

 resistance which the molecules of the surrounding gas offer 

 to the motion of the ion in an electric field; but, on account 

 of the assumptions which are involved in any such application 

 of the principles of the kinetic theory as outline 1 below, the- 

 result of the calculation must be taken as giving merely the 

 order of magnitude. 



According to the work of Langevin * in this connexion, 

 amended by H. A. Wilson t, the velocity of an ion in a field 

 of unit intensity is given by the expression 



w=l*4^Z ] /?n 1 ?? 1 , 



where e is the ionic charge, l x the mean free path of the ion, 

 m 1 its mass, and i\ its mean velocity of thermal agitation. 

 The size of an ion, however, cannot be calculated merely 

 from a knowledge of the mobility, and we are forced to 

 follow the converse method of assuming size and mass and 

 calculating mobility. To obtain a suitable expression for 

 this purpose, let sy be the diameter of the ion, s 2 that of the 

 air molecule, and in general let the subscripts 1 and 2 refer 

 to ionic and molecular quantities respectively. 

 From the kinetic theory we have J 



i - 1= ™/£l+!,)l/ 1+ « 1 ( 1+ ^) j 



V 2 /V m 2 \ m 2 v 2 / 



* Lang-evii), Ann. de Chim. et de Phys. vii. p. 335 (1903). 

 + H. A. Wilson, Phil. Mag. xx. p. 385 (1910). 



1 See Wellisch, Phil. Trans. A. ccix. p. 272 (1009^ ; also Lusbv 5 PhiL 

 Mac?, xxii. p. 784 (1911). 



