nsity, F the
resultant force on the ions between A and B is vertical and equal to
_ _ _
/ / /
| | | Z[rho]dxdydz.
_/_/_/

Let us suppose that the velocity of the ion is proportional to the
electric intensity, so that if w is the vertical velocity of the ions,
which are supposed all to be of one sign, w = RZ.

Substituting this value of Z, the vertical force on the ions between A
and B is equal to
_ _ _
1 / / /
- | | | w[rho]dxdydz.
R _/_/_/

But [integral][integral]w[rho]dxdy = [iota], where [iota] is the
current streaming from the point. This current, which can be easily
measured by putting a galvanometer in series with the discharging
point, is independent of z, the vertical distance of a plane between A
and B below the charging point. Hence we have
_
[iota] / [iota]
F = ------ | dz = ------.z.
R _/ R

This force must be counterbalanced by the difference of gaseous
pressures over the planes A and B; hence if pB and pA denote
respectively the pressures over B and A, we have

[iota]
pB - pA = ------ z.
R

Hence by the measurement of these pressures we can determine R, and
hence the velocity with which an ion moves under a given electric
intensity.

There are other methods of determining the velocities of the ions, but
as these depend on the theory of the conduction of electricity through
a gas containing charged ions, we shall consider them in our
discussion of that theory.

By the use of these methods it has been shown that the velocities of
the ions in a given gas are the same whether the ionization is
produced by Rontgen rays, radioactive substances, ultra-violet light,
or by the discharge of electricity from points. When the ionization is
produced by chemical action the ions are very much less mobile, moving
in the same electric field with a velocity less than one-thousandth
part of the velocity of the first kind of ions. On the other hand, as
we shall see later, the velocity of the negative ions in flames is
enormously greater than that of even the first kind of ion under
similar electric fields and at the same pressure. But when these
negative ions get into the cold part of the flame, they move
sluggishly with velocities of the order of those possessed by the
second kind. The results of the various