28 |
| 200 | | 3.4 | 2.8 | 1.6 | .5 |
| 240 | 2.45 | 3.8 | 4.0 | 2.35 | .99 |
| 320 | 2.7 | 4.5 | 5.5 | 4.0 | 2.1 |
| 400 | | 5.0 | 6.8 | 6.0 | 3.6 |
| 480 | 3.15 | 5.4 | 8.0 | 7.8 | 5.3 |
| 560 | | 5.8 | 9.3 | 9.4 | 7.1 |
| 640 | 3.25 | 6.2 | 10.6 | 10.8 | 8.9 |
+---------+----------+----------+----------+----------+----------+

We see from this table that for a given value of X, [alpha] for small
pressures increases as the pressure increases; it attains a maximum at
a particular pressure, and then diminishes as the pressure increases.
The increase in the pressure increases the number of collisions, but
diminishes the energy acquired by the corpuscle in the electric field,
and thus diminishes the change of any one collision resulting in
ionization. If we suppose the field is so strong that at some
particular pressure the energy acquired by the corpuscle is well above
the value required to ionize at each collision, then it is evident
that increasing the number of collisions will increase the amount of
ionization, and therefore [alpha], and [alpha] cannot begin to
diminish until the pressure has increased to such an extent that the
mean free path of a corpuscle is so small that the energy acquired by
the corpuscle from the electric field falls below the value when each
collision results in ionization.

The value of p, when X is given, for which [alpha] is a maximum, is
proportional to X; this follows at once from the fact that [alpha] is
of the form X.F(X/p). The value of X/p for which F(X/p) is a maximum is
seen from the preceding table to be about 420, when X is expressed in
volts per centimetre and p in millimetres of mercury. The maximum value
of F(X/p) is about 1/60. Since the current passing between two planes
at a distance l apart is i0[epsilon]^{[alpha]l} or
i0[epsilon]^{XlF(X/p)}, and since the force between the plates is
supposed to be uniform, Xl is equal to V, the potential between the
plates; hence the current between the plates is i0[epsilon]^{VlF(X/p)},
and the greatest value it can have is i0[epsilon]^{V/60}. Thus the
ratio between the current between the plates when there is ionization
and when there is none