2 Mr Wellisch, The Laws of Mohility and Diffusion 



An ion is regarded as involving two distinct elements: 



(i) a mass (independent of the charge). Considering this 

 element alone, let us represent the ion as a nucleus surrounded 

 by a sphere of force of radius \s'. 



(ii) a charge e (electrostatic units). During motion of the 

 ion through the gas the effect of this charge is (as will be shown) 

 to increase the radius of the force sphere of the ion without 

 altering the mass. 



A collision occurs between any two molecules when the distance 

 between their centres is equal to the sum of the radii of their 

 force spheres. 



As the ion moves through the gas the charge associated with 

 it attracts the neutral molecules ; there results an increase in the 

 mean collision frequency of the ion and consequently a diminution 

 in its mean free path. 



Expression for the ionic mean free path. 



Consider the motion of an ion and a molecule regarded in the 

 light of two interacting free particles. Let R denote the potential 

 due to the polarisation of the molecule by the charge on the ion*, 

 so that the force, taken as wholly radial, between the ion and the 



molecule is given by -j- at a distance r. Let us reduce the 



molecule to rest and consider the relative motion as the ion 

 approaches it so that the velocity at infinity was U. The 

 interacting forces must now be considered as being derived from 



a potential R, m denoting the mass of the molecule. 



■^ m 



The shortest distance r to which the ion and the molecule 



approach is given by the equations : 



hU = ru, 



^ ^ ^ m 



where u denotes the velocity of the ion in this position and 

 b is the length of the perpendicular from the molecule to the 

 rectilineal path of the ion. 

 We deduce 



I 1 Mm I . 

 [ 2M+m \ 



* The polarisation of the molecule by the electric field is regarded as negligible 

 in comparison with that due to the ionic charge. 



