642 Prof. E. Rutherford on Slow 
3 
e t . e e,e A 
given by N. =e-*, where Nj is the amount initially present, 
4 IN 
E = aie € ft 
and 2 is the constant of change. Differentiating, ay oe —rN;, 
or the rate of change is always proportional to the amount 
present. 
Suppose that Po, particles of the product radium D are 
deposited during the time of exposure to the emanation. 
This time is supposed to be so short that theamount of change 
of radium D during the time of exposure is very small. 
Yiet P=number of particles of matter radium D present at 
any time. 
Q=number of particles of radium E present at any 
time. 
,=constant of change of radium D. 
A, =constant of change of radium H. 
Then P=P,e*. 
As the matter D changes into EH, the value of Q at first 
increases. The increase dQ in the time dt is given by the 
difference between the number of particles of HE (A,P) sup- 
plied by the change of D into E and the number of E (A,Q) 
which change into F. 
Then dQ= 2, Pdt—r,Qdt, 
and d 
= = Ay Poet — Ag. 
The solution of the equation is of the form 
Q= ae! ber, 
Since (Q=0 when t=0, we have 
Xr 
skits deal ae Po 
and ( 
MP, —A,t —Aot 
() = A 3 a (e é ys 
For small values of ¢, Q=2,P).¢; i. e., the value of @ 
increases proportionately with the time. The value of 
Q passes through a maximum at a time T, given by 
Xr. . . 
gr Alt 4 , and then decreases with the time. 
1 
The initial increase of the « ray activity with the time is 
thus in agreement with the view that radium E (which emits 
only « rays) is produced from radium D. The time of obser- 
vation (two months) has not yet been long enough to obtain 
