
34 IONIZATION THEORY OF GASES [CH. 
theory, which is of utility in interpreting the experimental results, 
can however be simply deduced if the disturbance of the potential 
gradient is disregarded, and the ionization assumed uniform be- 
tween the plates. 
_ Suppose that the ions are produced at a constant rate q per 
cubic centimetre per second in the gas between parallel plates 
distant / cms. from each other. When no electric field is applied, 
the number WV present per c.c., when there is equilibrium between 
the rates of production and recombination, is given by q=al?, 
where 4 is a constant. 
If a small potential difference V is applied, which gives only a 
small fraction of the maximum current, and consequently has not 
much effect on the value of NV, the current 7 per sq. cm. of the 
plate, is given by 
NeuwV 
Tee 

where wu is the sum of the velocity of the ions for unit potential 
: VE 
gradient, and e is the charge carried by an ion. “* is the velocity 
l 
- 
of the ions in the electric field of strength a E 
The number of ions produced per second in a prism of length / 
and unit area of cross-section is gl. The maximum or saturation 
current J per sq. cm. of the plate is obtamed when all of these 
ions are removed to the electrodes before any recombination has | 
occurred. 
Thus PV UG. 
As NS uV 
Lis git ab Vagal 
This equation expresses the fact previously noted that, for small 
voltages, the current 71s proportional to V. 
and 

Let 7 = p, 
then 
y _ p-PN qa 
U 
