steady state until 2k[alpha]t is large, that is until t is large
compared with 1/2k[alpha] or with 1/2[root](q[alpha]). We may thus
take 1/2[root](q[alpha]) as a measure of the time taken by the gas to
reach a steady state when exposed to an ionizing agent; as this time
varies inversely as [root]q we see that when the ionization is feeble
it may take a very considerable time for the gas to reach a steady
state. Thus in the case of our atmosphere where the production of ions
is only at the rate of about 30 per cubic centimetre per second, and
where, as we shall see, [alpha] is about 10^-6, it would take some
minutes for the ionization in the air to get into a steady state if
the ionizing agent were suddenly applied.

We may use equation (1) to determine the rate at which the ions
disappear when the ionizing agent is removed. Putting q=0 in that
equation we get dn/[alpha]t = -[alpha]n^2.

Hence n = n0/(1 + n0[alpha]t) (3),

where n0 is the number of ions when t = 0. Thus the number of ions
falls to one-half its initial value in the time 1/n0[alpha]. The
quantity [alpha] is called the _coefficient of recombination_, and its
value for different gases has been determined by Rutherford (_Phil.
Mag._ 1897 [5], 44, p. 422), Townsend (_Phil. Trans._, 1900, 193, p.
129), McClung (_Phil. Mag._, 1902 [6], 3, p. 283), Langevin (_Ann.
chim. phys._ [7], 28, p. 289), Retschinsky (_Ann. d. Phys._, 1905, 17,
p. 518), Hendred (_Phys. Rev._, 1905, 21, p. 314). The values of
[alpha]/e, e being the charge on an ion in electrostatic measure as
determined by these observers for different gases, is given in the
following table:--

+-----+----------+----------+----------+------------+----------+
| | Townsend.| McClung. | Langevin.|Retschinsky.| Hendred. |
+-----+----------+----------+----------+------------+----------+
| Air | 3420 | 3380 | 3200 | 4140 | 3500 |
| O2 | 3380 | | | | |
| CO2 | 3500 | 3490 | 3400 | | |
| H2 | 3020 | 2940 | | | |
+-----+----------+----------+----------+------------+----------+

The gases in these experiments were carefully dried and free from
dust; the apparent value of [alpha] is much increased when dust or
small drops of water are present in the gas, for then the ions get
caugh