376 I*rof. Thomson, On the theory of the motion 



If the absolute temperature is d 



\mu^ = ol6, 



where a does not depend upon the nature of the ion or of the gas. 

 Thus the mobility will be 



i.e. it will not depend upon the mass of the ion except in so far as 

 mass is an indication of size, and since Xo diminishes on this view 

 as the size of the ion increases, \ would depend to some extent on 

 the value of m. 



It must be confessed however that in this as in many other 

 problems the methods founded on the mean free path leave much 

 to be desired, and are far less satisfactory than the method 

 introduced by Maxwell when he replaced the idea of collisions 

 between hard elastic spheres by that of the effects produced by 

 forces exerted by one molecule on another. Maxwell gave a 

 complete solution when these forces are repulsions varying in- 

 versely as the fifth power of the distance. It happens that on 

 the simplest view we can take of the forces between a charged 

 ion and a neutral molecule, i.e. that these forces are due to the 

 attraction between the electric charge on the ion and the dis- 

 tribution of electricity induced by this charge on the molecules 

 regarded as conducting spheres, these forces will vary inversely as 

 the fifth power of the distance unless the ion gets close to the 

 molecule. For the attraction between an electric charge e and an 

 unelectrified conducting sphere of radius a is equal to 



(see Thomson's Electricity and Magnetism, 4th edition, p. 154), 

 where f is the distance between the charge and the centre of the 

 molecule ; when / is a considerable multiple of a, this expression is 

 approximately 



2e^a^ 



and thus varies inversely as the fifth power of the distance between 

 the ion and the molecule. In this case the force is an attraction 

 while Maxwell considers the case of a repulsion. Maxwell's 

 investigation can be applied to the case when the force is attractive 

 with hardly any modification, the only change that is required 

 is in the numerical constants which Maxwell denotes by -4i, A^^; 

 these have not the same values for repulsion as for attractive 

 forces, since they depend on the magnitude of the apsidal 

 distance ; with this exception Maxwell's results can be applied 



