prevent any direct action of the electric field in abstracting ions from the neighbourhood of T.
If the electric field is sufficiently strong, all the ions travel in to the electrodes at A, and no current is observed at the electrode B. If the current is observed successively at different distances along the tube, all the electrodes except the one under consideration being connected to earth, it is found that the current diminishes with the distance from the active body. If the tube is of fairly wide bore, the loss of the ions due to diffusion is small, and the decrease in conductivity of the gas is due to recombination of the ions alone.
On the ionization theory, the number dn of ions per unit volume which recombine in the time dt is proportional to the square of the number present. Thus
where α is a constant.
Integrating this equation,
if N is the initial number of ions, and n the number after a time t.
The experimental results obtained8 have been shown to agree very well with this equation.
In an experiment similar to that illustrated in Fig. 6, using uranium oxide as a source of ionization, it was found that half the number of ions present in the gas recombined in 2·4 seconds, and that at the end of 8 seconds one-fourth of the ions were still uncombined.
Since the rate of recombination is proportional to the square of the number present, the time taken for half of the ions present in the gas to recombine decreases very rapidly with the intensity of the ionization. If radium is used, the ionization is so intense that the rate of recombination is extremely rapid. It is on account of this rapidity of recombination that large voltages are necessary to produce saturation in the gases exposed to very active preparations of radium.
The value of α, which may be termed the coefficient of recombination, has been determined in absolute measure by Townsend9, McClung10 and Langevin11 by different experimental methods but with very concordant results. Suppose, for example, with the apparatus of Fig. 6, the time T, taken for half the ions to recombine after passing by the electrode A, has been determined experimentally. Then
where N is the number of ions per c.c. present at A. If the saturation current i is determined