The value of Qt passes through a maximum QT at the time T when
The maximum activity IT is proportional to QT and
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 λ1, λ2. Since the above equation is symmetrical with regard to λ1, λ2, 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 λ1 and λ2 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.
This fixes the value of the constants of one of the changes. Let us assume for the moment that this gives the value of λ1.
Since the maximum activity is reached after an interval T = 220 minutes (see Fig. 65), substituting the values of λ1 and T in the equation, the value of λ2 comes out to be
This value of λ2 corresponds to a change in which half the matter is transformed in 55 minutes.
Substituting now the values of λ1, λ2, T, the equation reduces to
