where I₀ is the amount of activity recovered when the state of constant activity is reached, It the activity recovered after a time t, and λ is the same constant as before.
129. Uranium X. Similar results were obtained when uranium was examined. The Ur X was separated by Becquerel’s method of successive precipitations with barium. The decay of the separated activity and the recovery of the lost activity are shown graphically in Fig. 49. A more detailed discussion of this experiment is given in section 205.
The curves of decay and recovery exhibit the same peculiarities and can be expressed by the same equations as in the case of thorium. The time-rate of decay and recovery is, however, much slower than for thorium, the activity of the Ur X falling to half its value in about 22 days.
A large number of results of a similar character have been obtained from other radio-active products, separated from the radio-elements, but the cases of thorium and uranium will suffice for the present to form a basis for the discussion of the processes that are taking place in radio-active bodies.
130. Theory of the phenomena. These processes of decay and recovery go on at exactly the same rate if the substances are removed from the neighbourhood of one another, or enclosed in lead, or placed in a vacuum tube. It is at first sight a remarkable phenomenon that the processes of decay and recovery should be so intimately connected, although there is no possibility of mutual interaction between them. These results, however, receive a complete explanation on the following hypotheses:
(1) That there is a constant rate of production of fresh radio-active matter by the radio-active body;
(2) That the activity of the matter so formed decreases according to an exponential law with the time from the moment of its formation.