the active products Ur X and Th X respectively, the activity of which decayed with the time, seemed at first sight to contradict this. Further observation, however, showed that the total radio-activity of these bodies was not altered by the chemical processes, for it was found that the uranium and thorium from which the active products were removed, spontaneously regained their radio-activity. At any time after removal of the active product, the sum total of the radio-activity of the separated product together with that of the substance from which it has been separated is always equal to that of the original compound before separation. In cases where active products, like Ur X and the radium emanation, decay with time according to an exponential law, this follows at once from the experimental results. If I1 is the activity of the product at any time t after separation, and I₀ the initial value, we know that
At the same time the activity I2 recovered during the same interval t is given by
where λ is the same constant as before. It thus follows that I1 + I2 = I₀, which is an expression of the above result. The same is also true whatever the law of decay of activity of the separated product (see section 200). For example, the activity of Th X after separation from thorium at first increases with the time. At the same time, the activity of the residual thorium compound at first decreases, and at such a rate that the sum of the activities of the thorium and its separated product is always equal to that of the original thorium.
This apparent constancy of the total radiation follows from the general result that the radio-active processes cannot in any way be changed by the action of known forces.