After standing several hours to make temperature conditions steady, the slide was opened, and the emanation began to diffuse into the tube B. The current through the tubes A and B was measured at regular intervals by an electrometer, with a suitable capacity in parallel. Initially there is no current in B, but after the opening of the slide, the amount in A decreased and the amount in B steadily increased. After several hours the amount in each half is nearly the same, showing that the emanation is nearly uniformly diffused throughout the cylinder.
It can readily be shown[1] that if
K = coefficient of diffusion of the emanation into air,
t = duration of diffusion experiments in secs.,
a = total length of cylinder,
S_{1} = partial pressure of emanation in tube A at end of diffusion,
S_{2} = partial pressure of emanation in tube B at end of diffusion,
then
(S_{1} - S_{2})/(S_{1} + S_{2}) = (8/π^2)(e^{-(π^2Kt)/a^2} + (1/9)e^{-(9π^2Kt)/a^2} + . . .).
Now the values of S_{1} and S_{2} are proportional to the saturation ionization currents due to the emanations in the two halves of the cylinder. From this equation K can be determined, if the relative values of S_{1} and S_{2} are observed after diffusion has been in progress for a definite interval t.
The determination of S_{1} and S_{2} is complicated by the excited activity produced on the walls of the vessel. The ionization due to this must be subtracted from the total ionization observed in each half of the cylinder, for the excited activity is produced from the material composing the emanation, and is removed to the electrodes in an electric field. The ratio of the current due to excited activity to the current due to the emanation depends on the time of exposure to the emanation, and is only proportional to it for exposures of several hours.
The method generally adopted in the experiments was to open the slide for a definite interval, ranging in the experiments from 15 to 120 minutes. The slide was then closed and the currents in each half determined at once. The central rods, which had
- ↑ See Stefan, Sitzungsber. d. Wien. Akad. 63, II. p. 82, 1871.
