x] RADIO-ACTIVE PROCESSES 297 
of the separated Th X had increased about 15 per cent. at the 
end of 24 hours, and then steadily decayed, falling to half value in 
about four days. 
This peculiarity of the Th X curve follows, of necessity, from the 
considerations already advanced to explain the drop in the recovery 
curve. As soon as the Th X is separated, it at once produces from 
itself the emanation, and this in turn produces the emanation X. The 
activity due to the emanation X at first more than compensates 
for the decay of activity of the Th X itself. The total activity 
100 



80 




(o)) 
(o) 

Activity 

g 













0 4 38 12 16 20 
Time in Days 
Fig. 56. 
thus increases to a maximum, and then slowly decays to zero 
according to an exponential law with the time. The curve ex- 
pressing the variation of the activity of the separated Th X with 
time can be deduced from the theory of successive changes already 
considered in section 175. In the present case there are three 
successive changes occurring at the same time, viz. the change of 
Th X into the emanation, of the emanation into emanation X, and 
the final changes giving rise to the activity of emanation X. Since, 
however, the change of the emanation into emanation X (about 
half changed in one minute) is far more rapid than the changes 
occurring in Th X or emanation X, for the purposes of calculation 
it may be assumed without serious error that the Th X changes at 
