Integrating this equation,
1/n - 1/N = αt,
if N is the initial number of ions, and n the number after a time t.
The experimental results obtained[1] 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 Townsend[2], M^cClung[3] and Langevin[4] 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 1/N = αT, where N is the number of ions per c.c. present at A. If the saturation current i is determined at the electrode A, i = NVe, where e is the charge on an ion and V is the volume of uniformly ionized gas carried by the electrode A per second. Then α = Ve/(iT).
The following table shows the value of α obtained for different gases.
