1] IONIZATION THEORY OF GASES 31 
Although the variation of the current with voltage depends 
only on the velocity of the ions and their rate of recombination, 
the full mathematical analysis is intricate, and the equations, 
expressing the relation between current and voltage, are only 
integrable for the case of uniform ionization. The question is com- 
plicated by the inequality in the velocity of the ions and by the 
disturbance of the potential gradient between the plates by the 
movement of the ions. J. J. Thomson! has worked out the case 
for uniform production of ions between two parallel plates, and has 
found that the relation between the current 7 and the potential 
difference V applied is expressed by 
Av?+ Bi=V 
where A and & are constants for a definite intensity of radiation 
and a definite distance between the plates. 
In certain cases of unsymmetrical ionization, which arise in the 
study of the radiations from active bodies, the relation between 
current and voltage is very different from that expressed by 







Current 


i} 
Saturation Curve 
Radium, activity 1,000 
plates 4-5 cms. apart 








0 100 200 300 400 500 600 700 
Volts 
Fig. 3. 
1 Phil. Mag. 47, p. 253, 1899. J.J. Thomson, Conduction of Electricity through 
Gases, p. 73, 1903. 
