﻿to maintain a Current in a Gas at Low Pressures. 217 



of accuracy. Curve C> for instance, being an average of 

 eight separate curves, the greatest variation from the mean 

 being 4 per cent., the error for the most part being very much 

 less, and in none of the other curves does it rise to more than 

 2 per cent. In all cases the general form for the same 

 pressure was the same, the only difference being in the 

 steepness of the curve. Fig. 2 (see above) shows the average 

 number of readings taken for each set, and may serve to 

 indicate the regular nature of all curves obtained. 



Thus we clearly see that there are two distinct cases de- 

 pending on the pressure. Above the critical pressure, the 

 potential to maintain the current drops below the sparking 

 potential, and tends towards a limiting value which may 

 perhaps be independent of the current. Below the critical 

 pressure, the maintaining potential rise- more or less rapidly 

 above the sparking potential. 



Discussion of Result*. 



The first condition of affairs observed, that above the critical 

 pressure, falls in exactly with Professor Townsend's theories 

 previously advanced. Sparking will take place when 



a-{3e(«-V d =.Q; 



where a. is the number of the new ions produced by a negative 

 ion in going across a centimetre of the gas, ft is the corre- 

 sponding number produced by a positive ion, and d is the 

 distance apart of the electrodes. 



Knowing a and ft, the sparking potential X<7 can then be 

 calculated for a given pressure. This has been found to be 

 in accurate agreement compared with the sparking potential 

 determined experimentally *. The sparking potential deter- 

 mined experimentally may consequently be used in the 

 determination of a and ft. The quantity a. has been already 

 determined over a large range of pressures and forces. The 

 same has not yet, however, been done for ft. It has been 



shown that the value of - bears a constant relation to — , 



P P 



where X is the electric force and p is the pressure : conse- 

 quently from the curve connecting these two ratios the value 



J. S. Townsend, Phil. Mag. vi. p. 598 (1903). 



