80 34·2 34·8 100 22·7 23·2 120 14·9 15·2 This is shown by the agreement of the numbers in the above table. The first column in the table above gives the theoretical values of the activity deduced from the equation $$ \frac {I_t} {I₀} = \frac {λ_2} {λ_2 − λ_3} e^{–λ_3 t} − \frac {λ_3} {λ_2 − λ_3} e^{–λ_2 t} $$ for the values of λ₂, λ₃ previously employed. The second column gives the observed values of the activity deduced from the decay curve _LL_. The close agreement of the curve _LL_ with the theoretical curve deduced on the assumption that there are two changes, the first of which does not emit rays, shows that the change of radium B into C does not emit α rays. In a similar way, as in the curve I, Fig. 89, the curve _LL_ may be analysed into its two components represented by the two curves _CC_ and _BB_. The curve _CC_ represents the activity supplied by the matter C present at the moment of removal. The curve _BB_ represents the activity resulting from the change of B into C and is identical with the corresponding curve in Fig. 89. Using the same line of reasoning as before, we may thus conclude that the change of B into C is not accompanied by α rays. It has already been shown that it does not give rise to β rays, and the identity of the β and γ-ray curves shows that it does not give rise to γ rays. The change of B into C is thus a “rayless” change, while the change of C into D gives rise to all three kinds of rays. An analysis of the decay of the excited activity of radium thus shows that three distinct rapid changes occur in the matter deposited, viz.:— (1) The matter A, derived from the change in the emanation, is half transformed in 3 minutes and is accompanied by α rays alone; (2) The matter B is half transformed in 21 minutes and gives rise to no ionizing rays; (3) The matter C is half transformed in 28 minutes and is accompanied by α, β, and γ rays; (4) A fourth very slow change will be discussed later. =224. Equations representing the activity curves.= The equations representing the variation of activity with time are for convenience collected below, where λ₁ = 3·8 × 10⁻³, λ₂ = 5·38 × 10⁻⁴, λ₃ = 4·13 × 10⁻⁴:— (1) Short exposure: activity measured by β rays, $$ \frac {I_t} {I_T} = 10\cdot3 (e^{–λ_3 t} − e^{–λ_2 t}) $$ where _I_{T}_ is the maximum value of the activity; (2) Long exposure: activity measured by β rays, $$ \frac {I_t} {I₀} = 4\cdot3 (e^{–λ_3 t} − 3\cdot3 e^{–λ_2 t}) $$, where _I₀_ is the initial value; (3) Any time of exposure _T_: activity measured by the β rays, $$ \frac {I_t} {I₀} = \frac {ae^{–λ_3 t} − be^{–λ_2 t}} {a − b} $$, where $$ a = \frac {1 − e^{–λ_3 T}} {λ_3} $$, $$ b = \frac {1 − e^{–λ_2 T}} {λ_2} $$; (4) Activity measured by α rays: long time of exposure,