It will be shown later that the variation with time of the activity, imparted to a body by a short exposure, is expressed by an equation of the above form. It thus remains to fix the values of λ₁, λ₂. Since the above equation is symmetrical with regard to λ₁, λ₂, it is not possible to settle from the agreement of the theoretical and experimental curve which value of λ refers to the first change. The curve of variation of activity with time is unaltered if the values of λ₁ and λ₂ are interchanged. It is found experimentally that the activity 5 or 6 hours after removal decays very approximately according to an exponential law with the time, falling to half value in 11 hours. This is the normal rate of decay of thorium for all times of exposure, provided measurements are not begun until several hours after the removal of the active body from the emanation. This fixes the value of the constants of one of the changes. Let us assume for the moment that this gives the value of λ₁. Then λ₁ = 1·75 × 10⁻⁵ (sec)⁻¹. Since the maximum activity is reached after an interval _T_ = 220 minutes (see Fig. 65), substituting the values of λ₁ and _T_ in the equation, the value of λ₂ comes out to be λ₂ = 2·08 × 10⁻⁴ (sec)⁻¹. This value of λ₂ corresponds to a change in which half the matter is transformed in 55 minutes. Substituting now the values of λ₁, λ₂, _T_, the equation reduces to $$ \frac {I_t} {I_T} = 1\cdot37 (e^{–λ_2 t} − e^{–λ_2 t}) $$ . The agreement between the results of the theoretical equation and the observed values is shown in the following table: Time in Theoretical Observed value minutes value of of _I_{t}_/_I_{T}_ _I_{t}_/_I_{T}_ 15 ·22 ·23 30 ·38 ·37 60 ·64 ·63 120 ·90 ·91 220 1·00 1·00 305 ·97 ·96 After 5 hours the activity decreased nearly exponentially with the time, falling to half value in 11 hours. It is thus seen that the curve of rise of activity for a short exposure is explained very satisfactorily on the supposition that two changes occur in the deposited matter, of which the first is a rayless change.