MR. J. S. TOWNSEND ON THE DIFFUSION OF IONS INTO GASES. 145 



front of Ej 3 centims. from the window in A 2 . The gratings in front of the electrodes, 

 being in metallic connection with the tubes A, and A 2 , prevent the fields of force 

 from extending up the tubes, so that when ions are produced in a stream of gas they 

 are not acted upon by any force till they cross the grating. 



A stream of gas is passed through the tube A, and the rays allowed to fall upon 

 it for 20 seconds. The positive ions are collected on the electrode as before, and 

 a deflection N, is obtained on the electrometer scale (it is not necessary in this M9 

 to make a similar experiment with the negative ions). The apparatus is then moved 

 so as to bring the window W 2 over the bulb, and the stream of gas is sent through 

 the tube A 2 , and the deflection N 2 , which is greater than N,, is obtained when the 

 same experiment is made with the electrode E 2 joined to the electrometer. If d i and 

 dt are the distances of the gratings from the windows W, and W 2 , we see that the 

 conductivity falls from N, to N,, while the gas travels the distance (c/, rf,). This 

 reduction in conductivity is nearly entirely due to recombination, since the tubing is 

 so wide that the loss due to diffusion to the sides is inappreciable. The mean time 

 T that the gas takes to traverse the distance d t d? can be found from the rate at 

 which the gas escapes from the gasometer. It is important that this rate of escape 

 should be the same as the rate of escape in the experiments in which , and 2 were 

 determined, so that the ions should be distributed throughout the same volume 

 of gas. 



If cN is the number of ions in a gas in which no new ions are being produced, 

 then the rate at which N varies with the time is given by the formula : 



dN/dt = - aN*,* 



when no other influences except recombination contribute to the reduction in N. 

 Hence, by integration, 



where T is the time in which the conductivity falls from N 2 to N, due to recom- 

 bination. The value of a can therefore be determined by substituting the olerved 

 values of N,, N 2 , and T in this equation. 



Returning to the case where the gas passes along the fine tubes, the conductivity 

 falls from 71, to n, while the gas passes along the last nine centims. of T,. Let 6 be 

 the average time that any portion of the gas takes to traverse these nine centims. 

 The amount of iouization per cub. centim. of gas can easily be reduced so that the 

 loss of conductivity due to recombination is only - a ^th of that due to diffusion to the 

 sides. 



From formula 10, Section I., we see that the conductivity n at any section of the 

 tubes T, is given approximately by the formula : 



* J. J. THOMSON and RUTHERFORD, ' Phil. Mag.,' November, 1896. 

 VOL. CXCIII. A. U 



