Radioactivity from Thorium, Radium, and Actinium. 375 
At a time ¢, after removal the corresponding number is 
no f (t)dt+noi f (t+dt)}dt+ ..... +nof ¢+t,)dt 
ttt; 
={ no f ()dt. 
Since the radiation arises only from the second change, 
and is proportional to the value of q, the ratio of the current 
r at a time ft, after removal to the initial current is given’ by 
— e—Agt ied — p—Ait 
ere): 
SSR 
2 
Te Tee 
Ss Ay 
Let ane =A, Be GUOH ber abil 
and ——e™ =B. tides iyi Linco 
eee | pais Eien: sahil 63} 
When a plate has been exposed for an interval of only a 
few minutes, it may be assumed that only a small proportion 
of the radioactive matter deposited has undergone the first 
change at the time of removal; thus the curve of decay for 
such an exposure will be approximately that of particles all 
deposited simultaneously. From such a curve the values of 
A, and A, can be obtained. The curve of decay for an ex- 
posure of ten minutes shows that half the matter undergoes 
the first change in about fifty-five minutes. Substituting this 
value in the equation = =e¢- the value A, =°00021 is ob- 
0 
tained, t being expressed in seconds. ‘The rate of the second 
change i is a decay to half value in about eleven hours, which 
gives A,="0000175. By substituting these values in (1) and 
(2), A and B and A—B can be determined for different 
2C 2 
