After separation of actinium X, the activity, whether measured by the α or β rays, increases about 15 per cent. during the first day, and afterwards decays exponentially with the time, falling to half value in 10·2 days. The activity of the separated actinium was small at first but steadily increased with the time, reaching a practical maximum after an interval of sixty days. After the first day, the decay and recovery curves of activity are complementary to one another. The curves of rise and decay are shown graphically in Fig. 82, curves I and II respectively. Godlewski observed that a solution of actinium, freed from actinium X, gave out very little emanation, while a solution of actinium X gave off the emanation in large quantity. The amount of emanation from the solution was measured by observing the activity produced in a testing vessel, similar to that shown in Fig. 51, when a constant current of air was passed through the solution. The emanating power of actinium X decreased exponentially with the time at the same rate as that at which the actinium X lost its activity. At the same time the actinium solution increased in emanating power, reaching its original value after about 60 days. The behaviour of actinium and thorium is thus quite analogous, and the explanation advanced to explain the decay and recovery curves of thorium applies equally well to the corresponding curves of actinium. [Illustration: Fig. 82.] The actinium X is produced at a constant rate from the parent matter actinium, and is transformed according to an exponential law with the time. The constant of change λ = ·068 (day)⁻¹, and this value is characteristic of the product actinium X. As in the case of thorium, the above experiments show that the emanation does not arise from actinium itself but from actinium X. The emanation in turn breaks up and gives rise to an active deposit on the surface of bodies. =212. Analysis of the active deposit from the emanation.= Debierne[312] observed that the excited activity produced by actinium decayed to half value in about 41 minutes. Miss Brooks[313] showed that the curves of decay of the excited activity after removal depended upon the duration of exposure to the emanation. The curves for different times of exposure have already been shown in Fig. 69. Bronson, using the direct deflection method described in section 69, accurately determined the activity curve corresponding to a short exposure to the actinium emanation. The curve obtained is shown in Fig. 83. [Illustration: Fig. 83.] This curve is similar in shape to the corresponding curve obtained for the active deposit from thorium, and is explained in a similar way. The activity _I_{t}_ at any time _t_ is given by $$ \frac {I_t} {I_T} = \frac {e^{–λ_2 t} − e^{–λ_1 t}} {e^{–λ_2 T} − e^{–λ_1 T}} $$,