MR. J. S. TOWNSEND ON THE DIFFUSION OF IONS INTO OASES. 157 



The numbers N, and N, are the electrometer deflections obtained in the manner 

 described above. In the first three gases the electrode E, was at a distance V2 centims. 

 from the window W,, and the electrode E, at a distance 3 centims. from the window 

 Wf The conductivity therefore fell from N 2 to N, while the gas passed through 

 9 centims. of the tube A^ 



The position of the electrodes had to be altered for hydrogen, as this gas would 

 have lost about 1 G per cent, of its conductivity, due to diffusion to the sides alone, in 

 passing along 9 centims. of the wide tubing. The electrodes were therefore put at 

 distances 3 and G centims. from the windows, and the strength of the ionization was 

 increased. 



The correction given in the tables is to compensate for the loss of conductivity 

 arising from diffusion. 



The electrometer was standardised, and it was found that each division corresponded 

 to a charge of '0042 electrostatic unit. If c is the charge on the ion, the number of 



.. . NX -0042 , . . ... 



ions in a cub. centim. is -- = , which we will denote by v. 



From the theory of recombination we have 



dv/dt = ftv\ or - - = T. 



f, , 



From the numbers given in Table VI. we can obtain the values of ft for the different 

 gases. We thus find that for air, oxygen, carbonic acid, and hydrogen the values of 

 ft are, 3420 X e, 3380 X e, 3500 X e, and 3020 X e. 



The rates of recombination in air, oxygen, and carbonic acid tire practically the 

 same, and about 1 5 per cent, greater than the recombination in hydrogen. 



Substituting for e its value, we obtain for the first three gases ft = 2 X 10~*, q.p. 



We can now find how near two ions of opposite sign must approach each other in 

 nnler to recombine. If there are v positive ions, and v negative ions, in a cub. centim., 

 the number that recombine in a time 8t is w'ft&t. 



The number of negative ions that approach within a distance S of positive ions in 

 the same time can be found from the kinetic theory of gases. 



MAXWELL has shown* how to calculate the number of times per second a molecule 

 of one gas will come within a distance R of the molecules of another gas. 



This number is 



2n / 



where n is the number of molecules per cub. centim. of the second gas, a* = f v?, 

 f? = | v\, v\ and v\ are the mean squares of the velocities of agitation of the two 

 gases. 



We will suppose that an ion has the same mass as a molecule of the gas in which 



* ' Phil. Mag.,' January and July, 1860. 



