42 Mr. J. J. E. Durack on Lenard Rays, 



by Prof. J. J. Thomson some time ago at a meeting of the 

 Cavendish Physical Society. 



Suppose a force to act between an ion and a molecule 

 when the former approaches the latter, the force varying 

 inversely as the square of the distance. 



Let r be the radius of the sphere of action of a molecule, 

 that is, an ionizing collision will just occur when an ion 

 comes within this distance from its centre. 



Let an ion carrying a charge e and of mass m be projected 

 from an infinite distance with velocity v in the direction of 

 the molecule. 



The initial kinetic energy of the ion is 



\mv 2 . 



The work done by the forces when the ion is distant r from 



. e 2 

 the centre of the molecule is — . 



r 



Now the projected ion will just have sufficient energy to 



produce a pair of ions when 



e 2 



Hence collisions just occur when 



2e 2 



r= 2- 



But the number of collisions in unit distance is propor- 

 tional to r 2 . 



tt 2 4^ 4 



Hence a p =cr 2 = — 5-j, 



or a p varies inversely as the fourth power of the velocity. 



On comparison of my experiments with those of Prof. 

 Townsend, a p does not appear to decrease so fast as is given 

 by the inverse fourth power of velocity. However, this 

 depends on the law of force assumed to act between an ion 

 and a molecule ; the argument is the same if we assume (as 

 Maxwell did for the law of force between molecules) the 

 inverse fifth power, in which case a v varies inversely as 

 the velocity. As far as one can estimate from Townsend's 

 results and my own, this seems not improbable. 



I have tried to give an explanation of the variation of a p 

 with velocity based on the consideration of the induced charge 

 on a molecule when an ion passes close to it. 



Let us assume that a molecule is a sphere, capable of 

 having a charge induced on it. 



