302 RADIO-ACTIVE PROCESSES [CH. 
is thus analogous to the curves of recovery of uranium and thorium 
which have been freed from the active products Ur X and Th X 
respectively. The intensity J, of the recovered activity at any 
I, 
ve, 
the radio-active constant of the emanation. The decay and recovery 
curves are complementary to one another. 
Knowing the rate of decay of activity of the radium emanation, 
the recovery curve of the activity of radium can thus at once be 
deduced, provided all of the emanation formed is occluded in the 
radium compound. 
time is given by — =1—e~’, where J, is the final value, and X is 
When the emanation is removed from a radium compound by 
solution or heating, the activity measured by the B rays falls 
almost to zero, but increases in the course of a month to its 
original value. The curve showing the rise of 8 rays with time 
is practically identical with the curve, Fig. 58, showing the re- 
covery of the lost activity of radium measured by the a rays. The 
explanation of this result les in the fact that the 8 rays from 
radium only arise from emanation X, and that the non-separable 
activity of radium gives out only a rays. On removal of the 
emanation, the activity of the emanation X decays nearly to 
zero, and in consequence the 8 rays almost disappear. When 
the radium is allowed to stand, the emanation begins to ac- 
cumulate, and produces in turn emanation X, which gives rise to 
B rays. The amount of @ rays (allowing for a period of retarda- 
tion of a few hours) will then increase at the same rate as the - 
activity of the emanation, which is continuously produced from 
the radium. 
192. If the radium allows some of the emanation produced to 
escape into the air, the curves of recovery will be different from 
that shown in Fig. 58. For example, suppose that the radium 
compound allows a constant fraction a of the amount of emana- 
tion, present in the compound at any time, to escape per second. 
If n is the number of emanation particles present in the com- 
pound at the time ¢, the number of emanation particles changing 
in the time dt is Andt, where X is the constant of decay of activity 
of the emanation. If qg is the rate of production of emanation 
