20 EXCITED RADIO-ACTIVITY [CH. 
change, but the number which has undergone the first but not the 
second change at the time 7 after removal is given by 
Onur OF) Gikk. 
The number q of particles which have undergone the first of 
the two changes at a time 7’ after removal is thus given by 
i 
V= ine | Qe tS) Gli 
: 0 
Ay N 
a= Si pai 
wee (e Gast 
Now the number of these particles breaking up in unit time is 
proportional to A,qg, and is a measure of the radiation accompany- 
ing the change (section 124). 
If kK is the ratio of the ionization produced in the second 
change to that produced in the first change, the saturation current 
I, resulting from the two successive changes is given by 
of = Ange M+ Pog = e-iT Hr, 
vf Ai N% NS oe Ne 
FO at Fy ett 
Ne — vy Ne — Ny 5) 

(e-%eT — e-h7) 
where J, is the initial value of the saturation current. 
This equation will be applied later with satisfactory results 
in section 190, to explain the rise of activity of Th X after its 
separation. 
176. On examination of the curve shown in Fig. 50, which 
shows the rise of activity of a rod exposed for ten minutes in the 
presence of the thorium emanation, it is seen that the curve C, 
showing a rise to a maximum, is roughly similar to the curves of 
recovery of uranium and thorium when the UrX and Th X 
respectively have been removed. If the curve is produced back- 
wards, it 1s seen to pass very nearly through the origin. The 
abscissae measure the time from the moment the rod was intro- 
duced into the emanation vessel. 
If the increase of activity with time is due to a secondary 
change of the type already considered, it follows at once that the 
