274 MR. E. M. WELLISCH ON THE MOBILITIES OF THE 



Expression for the Potential R due to the Polarisation of the Molecule by the Ionic 

 Charge. If the molecules of a gas are polarised by an electric field of intensity X, 



XT' _ 1 



the electric moment per cubic centimetre is - X, where K denotes the dielectric 



4?r 



jr _ i 



constant of the gas. The electric moment (u.) of a molecule is therefore - X. 



47m 



The mechanical force 011 the molecule is u -= , which is equal to -- = . The 



dr 8im dr 



potential is therefore given by 



R = ~ ~ 



- 

 8Trn 8-irn ' r 4 ' 



when the molecule is polarised by the field due to the ionic charge. 



This expression for R assumes that the polarising field is uniform throughout the 

 volume of the molecule. L ANGEVIN (loc. cit., p. 317) has obtained the general 

 expression for R in the case of a spherical molecule and finds it to be given by a series 

 of which the above is the most important term. 



Expression for the Mobility of the Ion. Let 17 denote the coefficient of viscosity of 

 the gas, p its density, p the pressure in dynes per square centimetre, and I the 

 molecular . mean free path. Let n 1; p 1} p lt Kj denote the values of n, p, p, K respec- 

 tively corresponding to a temperature of C. and a pressure of 760 mm. of mercury. 



The charge e carried by the ion is taken as equal to that (E) on the monovalent 

 ion in the electrolysis of solutions. This equality was established from measurements 

 of the mobility and rate of diffusion of gaseous ions.* The exact value of the ionic 

 charge is not required in the present treatment, inasmuch as e only enters in the 

 expression n^e = WjE, which has been shown from experiments in electrolysis to have 

 the value l'30x!0 10 ,t E being measured in electrostatic units. The product n t E is 

 denoted by A. 



The gas is regarded throughout as being at a temperature of C. 



We have the following equations : 



k = eL/MV, 77 = 



I- 1 = Tr\/2ns\ 



m mv 



where <r = 



Srm 



MV 2 = mv 2 (equipartition of energy), 

 e = E, p = nm, 



jE = A, p = 



* Fide J. J. THOMSON, ' Conduction of Electricity through Gases,' 2nd edition, Art. 39. 

 t The electro-chemical equivalent of hydrogen was taken as - 00001035 gram/coulomb. 



