
182 CONTINUOUS PRODUCTION OF RADIO-ACTIVE MATTER  [CH. 
half its activity. This time in each case is about four days. The 
percentage proportion of the activity regained by the thorium, over 
any given interval, is approximately equal to the precentage pro- 
portion of the activity lost by the Th X during the same interval. 
If the recovery curve is produced backwards in the normal 
direction to meet the vertical axis, it does so at a minimum of 
25 per cent., and the above conclusions hold more accurately, if the 
recovery is assumed to start from this minimum. This is clearly 
shown by Fig. 35, where the percentages of activity recovered, 
reckoned from the 25 per cent. minimum, are plotted as ordinates. 
In the same figure the decay curve, after the second day, is shown 
on the same scale. The activity of the Th X decays with the time 
according to an exponential law, falling to half value in about 
four days. If J, is the initial activity and J; is the activity after 
a time ¢, then 
Ly 
is 
ene, 
where X is a constant and e the natural base of logarithms. The 
experimental curve of the rise of activity from a minimum to a 
maximum value is therefore expressed by the equation 
[, 
| —e-*t 
if ane 
where J, is the amount of activity recovered when the state of 
constant activity is reached, and J; the activity recovered after 
a time ¢, and X is the same constant as before. 
120. Uranium X. Similar results were obtained when 
uranium was examined. The Ur X was separated by Becquerel’s 
method of successive precipitations with barium. The decay of 
the separated activity and the recovery of the lost activity are 
shown graphically in Fig. 36. A more detailed discussion of this 
experiment is given in section 189. 
The curves of decay and recovery exhibit the same peculiarities 
and can be expressed by the same equations as in the case of 
thorium. The time-rate of decay and recovery is, however, much 
slower than for thorium, the activity of the Ur X falling to half its 
value in about 22 days. 
