﻿in Air and Hydrogen at Atmospheric Pressure. 175 



the electrometer. In the above C 1? V l5 C 2 , and V 2 are the 

 capacities and potentials of* the system first connected to the 

 electrometer and of the whole system respectively. 



A uniform field in the chamber K was maintained in the 



following way : — A series of flat brass rings B, C, I 



were placed 1 cm. apart and connected by equal high resist- 

 ances. B was raised to a potential V and I was earthed. 



A was raised to a potential V higher than V and of the 

 same si on. The rino- r and the disk c were cut from the 

 same sheet of brass so as to avoid any chance of contact 

 potential between them and their potential in no case differed 

 much from zero. 



A theory for the distribution of the ions has been worked 

 out by Townsend * from Maxwell's equations for the diffusion 

 of one gas into another. An outline of this is given below. 

 In this theory it is assumed that the partial pressure of the 

 ions is not appreciably greater than that of an equal number 

 of molecules, but in Townsend's experiments the distribution 

 was found to fit in with the theory except for negative ions 

 where the pressure was low and the g;is very dry, and in the 

 present experiments it was found that no correction need be 

 made in any case. 



When a uniform stream is passing through the aperture 0, 

 the partial pressure (p) of the ions at any point in the field 

 of uniform force Z is given by the equation, 



N^Z dp 



where N is the number of molecules per cubic centimetre in 

 a gas at atmospheric pressure \i and a temperature equal to 

 that of the gas in the experiments. 



The solution of this equation is given by p=f(N.e.Z), 

 but where the assumption made above is correct and n = the 

 number of ions per c.c. p = Tln/]$. Whence n = <j>(N . e . Z), 

 in which all the constants are functions of the coordinates of 

 the position of the point, i. e. of r and z. 



In the experiments z — h, and therefore 



Qc 



i 



rn dr 



'o 



rn dr 



where a and b are the radii of the disk and ring respectively, 

 * J. S. Townsend, Roy. Soc. Proc. A. vol. 80, p. 207. 



