at once when the velocities and coefficients of diffusion of the ions are known. Townsend (loc. cit.) has shown that the equation of their motion is expressed by the formula
where e is the charge on an ion,
and u is the velocity due to the electric force X in the direction of the axis of x. When a steady state is reached,
Let N be the number of molecules in a cubic centimetre of gas at the pressure P and at the temperature 15° C., for which the values of u and K have been determined. Then N/P may be substituted for n/p, and, since P at atmospheric pressure is 106,
then
where u1 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,
For example, substituting the values of u1 and K determined in moist air for the positive ion,
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 u1 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
Now e, the charge on an ion, is equal to 3·4 × 10-10 E. S. units;
If I is the saturation current through a gas, and q the total rate of production of ions in the gas,
The saturation current through air was found to be 1·2 × 10 -8 ampères, i.e. 36 E.S. units, for parallel plates 4·5 cms. apart, when ·45 gramme of radium of activity 1000 times that of uranium was spread over an area