Not only do the curves of variation of the excited activity after removal depend upon the time of exposure to the emanation, but they also depend upon whether the α or β and γ rays are used as a means of measurement. The curves obtained for the γ rays are identical with those from the β rays, showing that these two types of rays always occur together and in the same proportion. The curves measured by the β rays are very different, especially for the case of a short exposure to the emanation. This is clearly shown in Fig. 68, which gives the β and γ ray curves for exposures of 10 minutes, 40 minutes, and 1 hour, and also the limiting case of an exposure of 24 hours. [Illustration: Fig. 67.] [Illustration: Fig. 68.] About 25 minutes after removal, the activity decays approximately at the same rate in each case. For convenience of representation, the ordinates of the curves were adjusted so that they all passed through a common point. We shall see later (chapter XI) that the rates of decay are not identically the same until several hours after removal; but, in the above figure, it is difficult to represent the slight variations. It will be observed that for the short exposure of 10 minutes the activity measured by the β rays is small at first but rises to a maximum in about 22 minutes, and then dies away with the time. The curve of decay of activity, measured by the β rays for a long exposure, does not show the rapid initial drop which occurs in all the α ray curves. Curie and Danne[276] made an investigation of the curves of decay of excited activity for different times of exposure to the radium emanation, but apparently did not take into account the fact that measurements made by the α and β rays give quite different curves of decay. Some of the family of curves, given in their paper, refer to the α rays and others to the β rays. They showed, however, the important fact that the curve of decay obtained by them for a long exposure (which is identical with the β ray curve) could be empirically expressed by an equation of the form $$ \frac {I_t} {I₀} = ae^{–λ_1 t} − (a − 1) e^{–λ_2 t} $$, where _I₀_ is the initial intensity and _I__{_t_} the intensity after any time _t_; λ₁ = ¹⁄₂₄₂₀, λ₂ = ¹⁄₁₈₆₀. The numerical constant _a_ = 4·20. After an interval of 2·5 hours, the logarithmic decay curve is nearly a straight line, that is, the activity falls off according to an exponential law with the time, decreasing to half value in about 28 minutes. The full explanation of this equation, and of the peculiarities of the various decay curves of the excited activity of radium, will be discussed in detail in chapter XI.