Now let Δ be the evolution of the emanation by radium, a quantity which I will assume constant. Let us consider what would occur if no emanation were escaping to the exterior. The emanation generated would then be completely utilised by the radium for the production of the radiation. We have from Formula 1—
and consequently, in the state of equilibrium, the radium would contain a certain quantity of emanation, Q, such that—
and the radiation of the radium would then be proportional to Q.
Let us suppose the radium placed in the circumstances under which it gives off the emanation to the exterior; this is obtained by dissolving the radium compound or by heating it. The equilibrium will be disturbed, and the activity of the radium diminished. But as soon as the cause of the loss of emanation has been abolished (the body being restored to the solid state or the heating having ceased), the emanation is accumulated afresh in the radium and we have a period during which the evolution, Δ, surpasses the velocity of destruction, q/θ. We then have—
from which—
(d/dt)(Q – q) = –(Q – q)/θ,
Q – q = (Q – q0)e–t/θ 3,