When a thorium compound is in a state of radio-active equilibrium, the series of changes in which Th X, the emanation, and thorium A and B are produced, go on simultaneously. Since a state of equilibrium has been reached for each of these products, the amount of each product changing in unit time is equal to the amount of that product supplied from the preceding change in unit time. Now the matter Th X is soluble in ammonia, while thorium A and B are not. The Th X is thus removed from the thorium by precipitation with ammonia, but A and B are left behind with the thorium. Since the active deposit is produced from the emanation, which in turn arises from Th X, on the removal of the parent matter Th X, the radiation due to this active deposit will decay, since the rate of production of fresh matter no longer balances its own rate of change. Disregarding the initial irregularity in the decay curve of the active deposit, its activity will have decayed to half value in about 11 hours, and to one quarter value at the end of 22 hours. As soon, however, as the Th X has been separated, new Th X is produced in the thorium compound. The activity of this new Th X is not, however, sufficient to compensate at first for the loss of activity due to the change in the active deposit, so that, as a whole, the activity will at first _decrease_, then pass through a minimum, then increase again. The correctness of this point of view has been tested by Rutherford and Soddy[307] as follows: If the precipitated thorium hydroxide after the removal of Th X is put through a series of precipitations with ammonia at short intervals, the Th X is removed almost as fast as it is formed, and, at the same time, the activity of thorium B in the thorium decays. The following table indicates the results obtained. A portion of the precipitated hydroxide was removed after each series of precipitations and its activity tested in the usual way. Activity of hydroxide per cent. After 1 precipitation 46 After 3 precipitations at 39 intervals of 24 hours After 3 more precipitations at 22 intervals of 24 hours and 3 at intervals of 8 hours After 3 more each of 8 hours 24 After 6 more each of 4 hours 25 [Illustration: Fig. 79.]