Consider the number of particles n₀dt of the matter A produced during the interval dt. At any later time t, the number of particles dQ of the matter B, which result from the change in A, is given (see equation 4) by
After a time of exposure T, the number of particles QT of the matter B present is readily seen to be given by
If the body is removed from the emanation after an exposure T, at any later time t the number of particles of B is in the same way given by
It will be noted that the method of deduction of QT and Q is independent of the particular form of the function f(t).
Substituting the particular value of f(t) given in equation (10) and integrating, it can readily be deduced that
where
