sin pt,
then if d is the distance between the plates, the electric intensity
is equal to a sin pt/d; if we suppose the velocity of the ion is
proportional to the electric intensity, and if u is the velocity for
unit electric intensity, the velocity of the negative ion will be ua
sin pt/d. Hence if x represent the distance of the ion from AB

dx ua
--- = --- sin pt
dT d

ua
x = ----(1 - cos pt), if x = 0 when t = 0.
pd

Thus the greatest distance the ion can get from the plate is equal to
2au/pd, and if the distance between the plates is gradually reduced to
this value, the plate AB will begin to lose a negative charge; hence
when this happens

d = 2au/pd, or u = pd^2/2a,

an equation by means of which we can find u.

In this form the method is not applicable when ions of both signs are
present. Franck and Pohl (_Verh. deutsch. physik. Gesell._ 1907, 9, p.
69) have by a slight modification removed this restriction. The
modification consists in confining the ionization to a layer of gas
below the gauze EF. If the velocity of the positive ions is to be
determined, these ions are forced through the gauze by applying to the
ionized gas a small constant electric force acting upwards; if
negative ions are required, the constant force is reversed. After
passing through the gauze the ions are acted upon by alternating
forces as in Rutherford's method.

Langevin (_Ann. chim. phys._, 1903, 28, p. 289) devised a method of
measuring the velocity of the ions which has been extensively used; it
has the advantage of not requiring the rate of ionization to remain
uniform. The general idea is as follows. Suppose that we expose the
gas between two parallel plates A, B to Rontgen rays or some other
ionizing agent, then stop the rays and apply a uniform electric field
to the region between the plates. If the force on the positive ion is
from A to B, the plate B will receive a positive charge of
electricity. After the electric force has acted for a time T reverse
it. B will now begin to receive negative electricity and will go on
doing so until the supply of negative ions is exhausted. Let us
consider how the quantity of positive electricity received by B will
vary with T. To fix our ideas, suppose the positive ions move more
slowly than the negative; let T2 and T1 be respectively the times
taken by the positive and