For increase of the time of exposure from 1 minute to 24 hours the curves obtained are intermediate in shape between the two representative limiting curves, Figs. 87 and 88. Some of these curves have already been shown in Fig. 68. [Illustration: Fig. 88.] =220. Explanation of the curves.= It has been pointed out that the rapid initial drop for curves _A_ and _B_, Fig. 86, is due to a change giving rise to α rays, in which half of the matter is transformed in about 3 minutes. The absence of the drop in the corresponding curves, when measured by the β rays, shows that the first 3-minute change does not give rise to β rays; for if it gave rise to β rays, the activity should fall off at the same rate as the corresponding α-ray curve. It has been shown that the activity several hours after removal decays in all cases according to an exponential law with the time, falling to half value in about 28 minutes. This is the case whether for a short or long exposure, or whether the activity is measured by the α, β, or γ rays. This indicates that the final 28-minute change gives rise to all three types of rays. It will be shown that these results can be completely explained on the supposition that three successive changes occur in the deposited matter of the following character[315]:— (1) A change of the matter A initially deposited in which half is transformed in about 3 minutes. This gives rise only to α rays. (2) A second “rayless” change in which half the matter B is transformed in 21 minutes. (3) A third change in which half the matter C is transformed in 28 minutes. This gives rise to α, β, and γ rays. =221. Analysis of the β-ray curves=. The analysis of the changes is much simplified by temporarily disregarding the first 3-minute change. In the course of 6 minutes after removal, three quarters of the matter A has been transformed into B and 20 minutes after removal all but 1 per cent. has been transformed. The variation of the amount of matter B or C present at any time agrees more closely with the theory, if the first change is disregarded altogether. A discussion of this important point is given later (section 228). The explanation of the β-ray curves (see Figs. 87 and 88), obtained for different times of exposure, will be first considered. For a very short exposure, the activity measured by the β rays is small at first, passes through a maximum about 36 minutes later, and then decays steadily with the time. The curve shown in Fig. 87 is very similar in general shape to the corresponding thorium and actinium curves. It is thus necessary to suppose that the change of the matter B into C does not give rise to β rays, while the change of C into D does. In such a case the activity (measured by the β rays) is proportional to the amount of C present. Disregarding the first rapid change, the activity _I_{t}_ at any time _t_ should be given by an equation of the same form (section 207) as for thorium and actinium, viz.,