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.
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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
I_{t}/I_{T} = (e^{-λ_{2}t} - e^{-λ_{1}t})/(e^{-λ_{2}T} - e^{-λ_{1}T}),
where λ_{1} and λ_{2} are two constants, and I_{T} the maximum activity reached after an interval T. After 20 minutes the activity decreased exponentially with the time, falling to half value in 35·7 minutes. This gives the value λ_{1} = ·0194 (min.)^{-1}. By comparison with the curve, the value of λ_{2} was found to be ·317 (min.)^{-1}. This corresponds to a change in which half the matter is transformed in 2·15 minutes. Exactly as in the analogous curve for thorium, it can be shown that the matter initially deposited undergoes two changes, the first of which is a rayless one. The same difficulty arises in fixing which of the values of λ refers to
