effect of sufficient magnitude to be detected in measurements of the activity due to the succeeding changes. The question is of great interest, for it involves the important theoretical point whether the substances A and B are produced independently of one another, or whether A is the parent of B. In the latter case, the matter A which is present changes into B, and, in consequence, the amount of B present after A is transformed should be somewhat greater than if B were produced independently. Since the change of A is fairly rapid, the effect should be most marked in the early part of the curve.
In order to examine this point experimentally, the curve of rise of activity, measured by the β rays, was determined immediately after the introduction of a large quantity of the radium emanation into a closed vessel. The curve of decay of activity on a body for a long exposure after removal of the emanation, and the rise of activity after the introduction of the emanation, are in all cases complementary to one another. While, however, it is difficult to measure with certainty whether the activity has fallen in a given time, for example, from 100 to 99 or 98·5, it is easy to be sure whether the corresponding rise of activity in the converse experiment is 1 or 1·5 per cent. of the final amount. Fig. 92, curve I, shows the rise of activity (measured by the β rays) obtained for an interval of 20 minutes after the introduction of the emanation. The ordinates represent the percentage amount of the final activity regained at any time.
Curve III shows the theoretical curve obtained on the assumption that A is a parent of B. This curve is calculated from equation (9) discussed in section 198, and λ_{1}, λ_{2}, λ_{3} are the values previously found.
Curve II gives the theoretical activity at any time on the assumption that the substances A and B arise independently. This is calculated from an equation of the same form as (8), section 198.
It is seen that the experimental results agree best with the view that A and B arise independently. Such a conclusion, however, is of too great importance to be accepted before examining closely whether the theoretical conditions are fulfilled in the experiments. In the first place, it is assumed that the
