law, but the change is not accompanied by any ionizing rays. In other words, the change from A to B is a "rayless" change. On the other hand, B breaks up into C with the accompaniment of all three kinds of rays. On this view the activity of the active deposit at any time represents the amount of the substance B present, since C is inactive or active to a very minute extent.
If the variation of the activity imparted to a body exposed for a short interval in the presence of the thorium emanation, is due to the fact that there are two successive changes in the deposited matter A, the first of which is a "rayless" change, the activity I_{t} at any time t after removal should be proportional to the number Q_{t} of particles of the matter B present at that time. Now, from equation (4) section 197, it has been shown that
Q_{t} = (λ_{1}n/(λ_{1} - λ_{2}))(e^{-λ_{2}t} - e^{-λ_{1}t}).
The value of Q_{t} passes through a maximum Q_{T} at the time T when
λ_{2}/λ_{1} = e^{-(λ_{1}-λ_{2})T}.
The maximum activity I_{T} is proportional to Q_{T} and
I_{t}/I_{T} = Q_{t}/Q_{T} = (e^{-λ_{2}t} - e^{-λ_{1}t})/(e^{-λ_{2}T} - e^{-λ_{1}T}).
It will be shown later that the variation with time of the activity, imparted to a body by a short exposure, is expressed by an equation of the above form. It thus remains to fix the values of λ_{1}, λ_{2}. Since the above equation is symmetrical with regard to λ_{1}, λ_{2}, it is not possible to settle from the agreement of the theoretical and experimental curve which value of λ refers to the first change. The curve of variation of activity with time is unaltered if the values of λ_{1} and λ_{2} are interchanged.
It is found experimentally that the activity 5 or 6 hours after removal decays very approximately according to an exponential law with the time, falling to half value in 11 hours. This is the normal rate of decay of thorium for all times of exposure, provided measurements are not begun until several hours after the removal of the active body from the emanation.
