two horizontal plates which could be maintained at different
potentials. The charged drops between the plates were acted upon by a
uniform vertical force which affected their rate of fall. Let X be the
vertical electric force, e the charge on the drop, v1 the rate of fall
of the drop when this force acts, and v the rate of fall due to
gravity alone. Then since the rate of fall is proportionate to the
force on the drop, if a is the radius of the drop, and [rho] its
density, then

Xe + (4/3)[pi][rho]ga^3 v1
---------------------- = ---,
4/3[pi][rho]ga^3 v

or Xe = (4/3)[pi][rho]ga^3(v1 - v)/v.

But v = 2/9ga^2[rho]/[mu],

so that

/ / [mu]^3 v^(3/2)(v1 - v)
Xe = \/ 2.9[pi] - / ------ . ---------------.
\/ g[rho] v

Thus if X, v, v1 are known e can be determined. Wilson by this method
found that e was 3.1 X 10^-10 electrostatic units. A few of the ions
carried charges 2e or 3e.

Townsend has used the following method to compare the charge carried
by a gaseous ion with that carried by an atom of hydrogen in the
electrolysis of solution. We have

u/D = Ne/[Pi],

where D is the coefficient of diffusion of the ions through the gas, u
the velocity of the ion in the same gas when acted on by unit electric
force, N the number of molecules in a cubic centimetre of the gas when
the pressure is [Pi] dynes per square centimetre, and e the charge in
electrostatic units. This relation is obtained on the hypothesis that
N ions in a cubic centimetre produce the same pressure as N uncharged
molecules.

We know the value of D from Townsend's experiments and the values of u
from those of Zeleny. We get the following values for Ne X 10^-10:--

+---------------+---------------------+---------------------+
| | Moist Gas. | Moist Gas. |
+---------------+----------+----------+----------+----------+
| Gas. | Positive | Negative | Positive | Negative |
| | Ions. | Ions. | Ions. | Ions. |
+---------------+----------+----------+----------+----------+
| Air | 1.28 | 1.29 | 1.46 | 1.31 |
| Oxygen | 1.34 | 1.27 | 1.63 | 1.36 |
| Carbonic acid | 1.01 | .87 | .99 | .93 |
| Hydrogen | 1.24 | 1.18 | 1.63 | 1.25