is thus about 5000 times greater for the former change.
Taking into consideration the early part of the curves, the current does not reach a practical maximum as soon as would be expected on the simple ionization theory. It seems probable that the slow increase with the large voltages is due either to an action of the electric field on the rate of production of ions, or to the difficulty of removing the ions produced near the surface of the uranium before recombination. It is possible that the presence of a strong electric field may assist in the separation of ions which otherwise would not initially escape from the sphere of one another’s attraction. From the data obtained by Townsend for the conditions of production of fresh ions at low pressures by the movement of ions through the gas, it seems that the increase of current cannot be ascribed to an action of the moving ions in the further ionization of the gas.
28. The equation expressing the relation between the current and the voltage is very complicated even in the case of a uniform rate of production of ions between the plates. An approximate 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 between 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 l cms. from each other. When no electric field is applied, the number N present per c.c., when there is equilibrium between the rates of production and recombination, is given by
where α 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 N, the current i per sq. cm. of the plate, is given by
where u is the sum of the velocity of the ions for unit potential gradient, and e is the charge carried by an ion.
is the velocity of the ions in the electric field of strength
The number of ions produced per second in a prism of length l and unit area of cross-section is ql. The maximum or saturation current I per sq. cm. of the plate is obtained when all