$$ \frac {I_t} {I₀} = \frac {1}{2} e^{–λ_1 t} + \frac {1}{2} (4\cdot3 e^{–λ_3 t} − 3\cdot3 e^{–λ_2 t}) $$ . The equations for the α rays for any time of exposure can be readily deduced, but the expressions are somewhat complicated. [Illustration: Fig. 91.] =225. Equations of rise of excited activity.= The curves expressing the gradual increase to a maximum of the excited activity produced on a body exposed in the presence of a constant amount of emanation are complementary to the curves of decay for a long exposure. The sum of the ordinates of the rise and decay curves is at any time a constant. This follows necessarily from the theory and can also be deduced simply from _à priori_ considerations. (See section 200.) The curves of rise and decay of the excited activity for both the α and β rays are shown graphically in Fig. 91. The thick line curves are for the α rays. The difference between the shapes of the decay curves when measured by the α or β rays is clearly brought out in the figure. The equations representing the rise of activity to a maximum are given below. For the β and γ rays, $$ \frac {I_t} {I_{max}} = 1 − (4\cdot3 e^{–λ_3 t} − 3\cdot3 e^{–λ_2 t}) $$ . For the α rays, $$ \frac {I_t} {I_{max}} = 1 − \frac {1}{2} e^{–λ_1 t} − \frac {1}{2} (4\cdot3 e^{–λ_3 t} − 3\cdot3 e^{–λ_2 t}) $$ . =226. Effect of temperature.= We have so far not considered the evidence on which the 28-minute rather than the 21-minute change is supposed to take place in the matter C. This evidence has been supplied by some recent important experiments of P. Curie and Danne[316] on the volatilization of the active matter deposited by the emanation. Miss Gates[317] showed that this active matter was volatilized from a platinum wire above a red heat and deposited on the surface of a cold cylinder surrounding the wire. Curie and Danne extended these results by subjecting an active platinum wire _for a short time_ to the action of temperatures varying between 15° C. and 1350° C., and then examining at room temperatures the decay curves not only for the active matter remaining on the wire, but also for the volatilized part. They found that the activity of the distilled part always increased after removal, passed through a maximum, and finally decayed according to an exponential law to half value in 28 minutes. At a temperature of about 630° C. the active matter left behind on the wire decayed at once according to an exponential law, falling to half value in 28 minutes. P. Curie and Danne showed that the matter B is much more volatile than C. The former is completely volatilized at about 600° C., while the latter is not completely volatilized even at a temperature of 1300° C. The fact that the matter C, left behind when B is completely volatilized, decays at once to half value in 28 minutes shows that the matter C itself and not B is half transformed in 28 minutes.