Ne = (3 × 10^8u_{1})/K electrostatic units,
where u_{1} is the velocity for 1 volt (i.e. 1/300 E. S. unit) per cm.
It is known that one absolute electromagnetic unit of electricity in passing through water liberates 1·23 c.c. of hydrogen at a temperature of 15° C. and standard pressure. The number of atoms in this volume is 2·46N, and, if e´ is the charge on the hydrogen atom in the electrolysis of water,
2·46Ne´ = 3 × 10^{10} E. S. units,
Ne´ = 1·22 × 10^{10} E. S. units.
Thus e/e´ = 2·46 × 10^{-2}(u_{1}/K).
For example, substituting the values of u_{1} and K determined in moist air for the positive ion,
e/e´ = (2·46/100) × (1·37/·032) = 1·04.
Values of this ratio, not very different from unity, are obtained for the positive and negative ions of the gases hydrogen, oxygen, and carbon dioxide. Taking into consideration the uncertainty in the experimental values of u_{1} and K, these results indicate that the charge carried by an ion in all gases is the same and is equal to that carried by the hydrogen ion in the electrolysis of liquids.
39. Number of the ions. We have seen that, from experimental
data, Townsend has found that N, the number of molecules
present in 1 c.c. of gas at 15° C. and standard pressure, is given by
Ne = 1·22 × 10^{10}.
Now e, the charge on an ion, is equal to 3·4 × 10^{-10} E. S. units;
thus N = 3·6 × 10^{19}.
If I is the saturation current through a gas, and q the total rate of production of ions in the gas,
q = I/e.
