156 



MR. J. S. TOWNSENI) ON THE DIFFUSION OF IONS INTO GAsi;s 



S, 2 is the distance between the centres of the molecules at collision in centimetres. 

 V is the " velocity of mean square " of a molecule of hydrogen at C. 



V = \/(3p/p) = 186000 centims. per second. 



N is the number of molecules in a cubic centimetre at and 7GO millims. pressure. 

 Taking the value of N, which we have found, 2 X 10 19 , we see that 



If the carrier of the charge is large compared with the molecule, S 12 will be the 

 radius of the carrier and l/w 2 will be small compared with 1/u;,. 



Letting D 12 = '156, the coefficient of diffusion of ions into hydrogen, ?, = 1, we 

 obtain for the radius of the ion in hydrogen 



A. similar calculation shows that the radius of an ion in oxygen is 



9'2 X 10-*. 



Adopting the second theory which we have proposed to account for the slowness 

 of the rates of diffusion of the ions, and applying the same formulae, the values of S 

 will be greater than the above values by the factor \/2, since the terms 1/Wj and l/w t 

 are of the same order. 



The values obtained in this way for S 12 would denote the distance that a molecule 

 of the gas must approach an ion in order that the electric force should appreciably 

 alter its motion. 



RECOMBINATION. 



The results of the experiments which were made to determine the rate of recombina- 

 tion are given in the following table. T is the time, in seconds, in which the conduc- 

 tivity falls from N 2 to Nj, and V is the volume, in cub. centims., of gas which was 

 used in each experiment. 



TABLE VI. 



