150 Mr Richardson, The Theory of the 



As an illustration I have used the above formula to calculate 

 the coefficient of recombination on the assumption that the 

 negative ions are corpuscles and the positive ions gas molecules 

 each possessing a charge equal to that of a corpuscle. Assuming 

 Townsend's result that the mean free path of a corpuscle is four 

 times that of a gas molecule, the only other physical quantities 

 required for the calculation are 



(1) the collision frequency of a molecule of the gas, 



(2) the electrochemical equivalent of hydrogen, and 



(3) the mean velocities of agitation of a corpuscle and a gas 

 molecule. 



The value of the coefficient of recombination found in this way 

 is 114 x 10~ 6 . Very little stress can be laid on the agreement of 

 this number with the value (2 - 2 x 10~ 6 ) which has been found 

 experimentally ; for a large number of results have been obtained 

 which indicate that X-ray ions in air have a far more complex 

 structure than that assumed in this calculation. 



Since the value of — ~- \ F(p)dp is great compared with 



unity we may write a very approximately in the form 



v* 



Sa/1 + ^o* 



From this we see that for the same gas a varies inversely as the 

 square root of the absolute temperature ; the coefficient of re- 

 combination should therefore diminish slowly as the temperature 

 increases. If the effect of the attraction between the ions were 

 negligible compared with their velocities of agitation a would 

 have been directly proportional to the square root of the absolute 

 temperature. 



If we apply this method to the calculation of the mean free 

 path (X) of an ion in air — a quantity required for the computation 

 of the velocity (v) of an ion under unit field, according to the 



1 e \ 

 formula v = ■= — ~ we are placed in difficulties owing to our 



ignorance of the attraction between an ion and a molecule. 

 Moreover, on this view, for very high velocities the number of 

 collisions made by an ion with the molecules of a gas, in going 

 through one centimetre of it, becomes independent of the velocity 

 of the ion. This result is, at any rate, open to criticism, since it 

 is probable that an ion makes fewer and fewer collisions the 

 greater its velocity. 



If we assume that an ion and a molecule act on one another 

 purely as centres of force varying as a power of the distance 



