| Xe = √ 2 · 9π√ | μ3 | · | v32(v1 − v) | . |
| g ρ | v |
Thus if X, v, v1 are known e can be determined. Wilson by this method found that e was 3.1×10-10 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/Π,
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 Π 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×10-10:—
| Gas. | Moist Gas. | Moist Gas. | ||
| Positive Ions. | Positive Ions. | Positive Ions. | Positive 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 |
| Mean | 1.22 | 1.15 | 1.43 | 1.21 |
Since 1.22 cubic centimetres of hydrogen at the temperature 15° C. and pressure 760 mm. of mercury are liberated by the passage through acidulated water of one electromagnetic unit of electricity or 3×1010 electrostatic units, and since in one cubic centimetre of the gas there are 2.46 N atoms of hydrogen, we have, if E is the charge in electrostatic units, on the atom of hydrogen in the electrolysis of solutions
2.46NE = 3×1010,