$$ \frac {I_t} {I_T} = \frac {e^{–λ_3 t} − e^{–λ_2 t}} {e^{–λ_3 T} − e^{–λ_2 T}} $$, where _I_{T}_ is the maximum activity observed, which is reached after an interval _T_. Since the activity finally decays according to an exponential law (half value in 28 minutes), one of the values of λ is equal to 4·13 × 10⁻⁴. As in the case of thorium and actinium, the experimental curves do not allow us to settle whether this value of λ is to be given to λ₂ or λ₃. From other data (see section 226) it will be shown later that it must refer to λ₃. Thus λ₃ = 4·13 × 10⁻⁴ (sec)⁻¹. The experimental curve agrees very closely with theory if λ₂ = 5·38 × 10⁻⁴ (sec)⁻¹. The agreement between theory and experiment is shown by the table given below. The maximum value _I_{T}_ (which is taken as 100) is reached at a time _T_ = 36 minutes. In order to obtain the β-ray curve, the following procedure was adopted. A layer of thin aluminium was placed inside a glass tube, which was then exhausted. A large quantity of radium emanation was then suddenly introduced by opening a stop-cock communicating with the emanation vessel, which was at atmospheric pressure. The emanation was left in the tube for 1·5 minutes and then was rapidly swept out by a current of air. The aluminium was then removed and was placed under an electroscope, such as is shown in Fig. 12. The α rays from the aluminium were cut off by an interposed screen of aluminium ·1 mm. thick. The time was reckoned from a period of 45 seconds after the introduction of the emanation. Time in Theoretical Observed minutes value of value of activity activity 0 0 0 10 58·1 55 20 88·6 86 30 97·3 97 36 100 100 40 99·8 99·5 50 93·4 92 60 83·4 82 80 63·7 61·5 100 44·8 42·5 120 30·8 29 There is thus a good agreement between the calculated and observed values of the activity measured by the β rays. The results are satisfactorily explained if it is supposed:— (1) That the change B into C (half transformed in 21 minutes) does not give rise to β rays; (2) That the change C into D (half transformed in 28 minutes) gives rise to β rays. =222.= These conclusions are very strongly supported by observations of the decay measured by the β rays for a long exposure. The curve of decay is shown in Fig. 88 and Fig. 89, curve I. [Illustration: Fig. 89.]