﻿678 The Charges on Ions. 



the pressure, and if that process alone were acting, the ratio 

 of the charge acquired by the disk to the total charge coming- 

 through the aperture would depend only on the product 

 N . e . X. In the particular form of apparatus which I 

 used and which was also used by Mr. Pomeroy, the disk 

 should receive one half the number of ions coming through 

 the aperture when X=k1*4 volts per centimetre and N . e 

 has the normal value 1*23 X 10 10 . As the plate A was at a 

 distance of 7 centimetres from the electrodes B and C, the 

 potential difference between the plate and the electrodes is 

 in this case about 10 volts. A smaller voltage would be 

 necessary if the disk receives a smaller proportion of the 

 charge. 



The effect of self-repulsion acts according to different 

 lawSj it increases with the pressure of the gas and also with 

 the density ot ionization. It is easy to see that if p is the 

 charge per cubic centimetre of a distribution of ions at a 

 point moving with the ions, the density p diminishes with 

 the time t according to the formula 



P s 1 



p 1 + Airkpot ' 



p being the initial value of p and k the velocity of the ions 

 under unit electrostatic force* An approximate estimate of 

 the effect of self-repulsion in expanding the section of the 

 stream may be obtained from this formula. Let Q be the 

 charge coining through the aperture per second, s the area 

 of the aperture, the charge p per cubic centimetre of the 

 gas is /> =eQ /s »& * E, E being the force in electrostatic 

 units in the space between the plate A and the electrodes. 

 The ratio of the charge received by the disk to the charge 

 coming through the aperture is p/p , and in the time t the 

 ions travel 7 centimetres under the force X so that t^7/kE. 

 Hence 



Mp t=±M .-^o . * s 28 ^o . 



This quantity must be small as compared with unity in 

 order that the effect of diffusion may be the predominating 

 factor in expanding the stream when the value of E is of the 

 order 1*4/300* To secure this condition at atmospheric 

 pressure where k is the velocity due to unit force,, it would be 

 necessary to reduce Q to such a small value that it would be 

 very difficult to detect the charges acquired by the electrodes 

 unless the observations extended over some hours. At a 

 pressure of 10 millimetres, 76 times as great a charge can 



