Rate of Recombination of Ions in Gases. 149 



where a is the distance between the centre of a positive and that 



of a negative ion, when in contact, and I F{p)dp is the work 



J a 

 done when two ions recombine. On comparing this with the 

 equation given by Professors Thomson and Rutherford*, which for 

 the case of unequal numbers of the two ions takes the form 



dt dt ai ^ ~' 



we see that the coefficient of recombination a is equal to 



va* A /l + ^fl x jl + — ^ f F(p)dp\. 



It is evident from this expression that a is independent of the 

 pressure of the gas, as has been found to be the case by 

 Mr McClungf. 



In order to make further deductions from the formula we 



require to know the value of I F(p)dp the work done on an ion 



during recombination. We shall assume that this is equal to the 



energy necessary to ionize a molecule. It is evident that even 



if the two things are not identical they must at any rate be of the 



same order of magnitude. Now Professor Townsend| has shown 



that the energy required to ionize a molecule in air is equal to 



that acquired by a corpuscle in falling through a potential 



f 00 . 5e 



difference of five volts. Thus the value of I F(p)dp is ^— 



where e is the charge on an ion in electrostatic units. If we 

 substitute the following numerical values, viz., 



(1) fur the number of molecules in a cubic centimetre of a gas 

 at 0° C. and 760 mm. n = 2x 10 19 , 



(2) for the charge on an ion e = 6*5 x 10~ 10 electrostatic units, 



(3) for the mean velocity square for a hydrogen molecule 



a" = 3 - 24 x 10 10 (cms. per sec.) 2 , 

 we find 



- J ^F (p)dp = 14,8; 



additional te 

 with unity. 



so that the additional term due to the attraction is large compared 



* Phil. Mag., Nov. 1898. 

 t Phil. Mag., March, 1902. 

 + Phil. Mag. 6. i. 198. 



