144 Mr Richardson, The Theory of the 



The Theory of the Rate of Recombination of Ions in Gases. By 

 O. W. Richardson, B.A., Coutts Trotter Student, Trinity College. 



[Received 17 June 1902.] 



The object of the present paper is to calculate the rate of 

 recombination of ions in gases. Recombination is supposed to 

 take place when the ions collide, the number of collisions being 

 increased by the mutual attraction of the ions. In a paper on the 

 " Viscosity of Gases and Molecular Force," Mr Sutherland* has 

 given a method for calculating the increase produced by molecular 

 attraction, in the number of collisions of two gaseous molecules of 

 equal mass, when the molecules are moving with a given relative 

 velocity. Mr Sutherland's mode of calculation when applied to 

 two molecules of unequal mass yields an absurd result. This is 

 due to the fact that he takes as his uniformly moving origin one 

 of the moving molecules which is really accelerated. The proper 

 assumption to make is that, whatever be the nature of the action 

 between the molecules, it cannot affect the motion of their centre 

 of gravity. I have therefore calculated on this assumption the 

 number of collisions which take place between two molecules of 

 different masses whose relative velocity is r. From this I have 

 obtained the total number of collisions which take place, by inte- 

 grating over all values of r which occur according to the Max- 

 wellian distribution. Finally the formulae so obtained have been 

 applied to calculate the coefficient of recombination of X-ray ions 

 in gases. 



In what follows it will be assumed that a molecule may be 

 represented with sufficient accuracy as a hard sphere. A collision 

 would then ensue when two such spheres come in contact, and 

 the average number of collisions made by a molecule per second 

 would be V27r$ 2 X2iV where S is the diameter of a molecule, D, is 

 the mean speed, and N the number of molecules in a cubic centi- 

 metre. In this case the number of collisions is the same as the 

 number of molecules whose centres lie within the volume 

 described by a sphere of radius J2S moving with the molecule ; 

 if the molecules attract one another, then the number of collisions 

 will be greater than this, the effect of the attractive forces being 



* Phil. Mag. xxxvi. 507. 



