38 IONIZATION THEORY OF GASES [CH. 
Integrating this equation, 
al 
ey See 
n N ae 
if V is the initial number of ions, and n the number after a time ¢. 
The experimental results obtained! 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 1s 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 a, which may be termed the coefficient of recom- 
bination, has been determined in absolute measure by Townsend?, 
M°Clung* and Langevin‘ by different experimental methods but 
with very concordant results. Suppose, for example, with the 
apparatus of Fig. 6, the time 7’, taken for half the ions to recombine 
after passing by the electrode A, has been determined experi-— 
mentally. Then — aT, where WV is the number of ions per c.c. 
present at A. If the saturation current 7 is determined at the 
electrode A, i= Ve where e is the charge on an ion and JV is the 
volume of uniformly ionized gas carried by the electrode A per 
second. Then a= a 
The following table shows the value of a obtamed for different 
gase 
NM 
. 
1 Rutherford, Phil. Mag. Nov. 1897, p. 144, Jan. 1899. 
* Phil. Trans. Roy. Soc. A, p. 157, 1899. 3 Phil. Mag. p. 283, March, 1902. 
4 Thése présentée & la Faculté des Sciences, p. 151, Paris, 1902. 

