1x] EXCITED RADIO-ACTIVITY 267 
If N is the number of ions produced immediately after removal, 
t+t, 
x, |, foae 
7 eee 5 
3 [ sat 
0 
.! 

The decay curve for any time of exposure can thus also be 
deduced from the curve of decay for a short exposure. For a very 
long interval of exposure the value JN, at a time ¢ after removal is 
given by 
: Sond NE culeyedt 
Now the curve of rise =} is given by 
0 
N 
7" [fo dt 
eT ES as 

Thus ] —-—~= 
Thus the decay and rise curves are very simply connected, 
whatever the law of decay of the radiations. This relation may 
be expressed as follows: For a long exposure, the percentage actiwity 
lost after removal for a time t is equal to the percentage of the final 
activity gained by a body exposed during the same interval. 
This result, which has already been shown to apply to the 
decay and recovery curves of Ur X, Th X, and other radio-active 
products, is of general application to all cases of radio-active 
change when the rate of supply is a constant. The connection 
between the decay curves of radium and thorium excited activity, 
for different times of exposure, can also be shown to hold equally 
for all types of active products. 
The relation that holds between the decay and recovery curves 
can easily be deduced from @ priori considerations. 
