the volume of the gas. Another method which answers the same purpose
is due to Langevin (_Ann. Chim. Phys._, 1903, 28, p. 289); it is as
follows. Let A and B be two parallel planes immersed in a gas, and let
a slab of the gas bounded by the planes a, b parallel to A and B be
ionized by an instantaneous flash of Rontgen rays. If A and B are at
different electric potentials, then all the positive ions produced by
the rays will be attracted by the negative plate and all the negative
ions by the positive, if the electric field were exceedingly large
they would reach these plates before they had time to recombine, so
that each plate would receive N0 ions if the flash of Rontgen rays
produced N0 positive and N0 negative ions. With weaker fields the
number of ions received by the plates will be less as some of them
will recombine before they can reach the plates. We can find the
number of ions which reach the plates in this case in the following
way:--In consequence of the movement of the ions the slab of ionized
gas will broaden out and will consist of three portions, one in which
there are nothing but positive ions,--this is on the side of the
negative plate,--another on the side of the positive plate in which
there are nothing but negative ions, and a portion between these in
which there are both positive and negative ions; it is in this layer
that recombination takes place, and here if n is the number of
positive or negative ions at the time t after the flash of Rontgen
rays,

n = n0/(1 + [alpha]n0t).

With the same notation as before, the breadth of either of the outer
layers will in time dt increase by X(k1 + k2)dt, and the number of ions
in it by X(k1 + k2)ndt; these ions will reach the plate, the outer
layers will receive fresh ions until the middle one disappears, which
it will do after a time l/X(k1 + k2), where l is the thickness of the
slab ab of ionized gas; hence N, the number of ions reaching either
plate, is given by the equation
_
/ l/X(k1+k2) n0X(k1 + k2) X(k1 + k2) / n0[alpha]l \
N = | --------------dt = ---------- log( 1 + ---------- ).
_/ 0 1 + n0[alpha]t [alpha] \ X(k1 + k2) /

If Q is the charge received by the plate,

X / Q0[epsilon]\
Q = Ne = -------------- log ( 1 + ----------- ),
4[pi][epsilon] \