SUCCESSION OF CHANGES IN RADIOACTIVE BODIES. 185 



If the body is removed from the emanation after an exposure T, at any time t later 

 the number of particles of B is in the same way given by 



Q = * 



It will be noted that the method of deduction of Q T and Q is independent of the 

 particular form of the function f (t). 



Substituting the particular value of f (t) given in equation (10) and integrating, it 

 can readily be deduced that 



Q," a-b 



where 



1 - e-* , 1 - e- A ' T 



" X, ' b = Xl ' 



In a similar way, the number of particles R of the matter C present at any time 

 can be deduced by substitution of the value of f (t) in equation (5). These equations 

 are, however, too complicated in form for simple application to experiment, and will 

 be omitted. 



13. Changes in the Active Deposit from Thorium. If the variation of the activity, 

 imparted to a body exposed for a short interval in the presence of the thorium 

 emanation, is due to the fact that there are two successive changes in the deposited 

 matter A, the first of which is a ' rayless ' change, the activity I< at any time t after 

 removal should be proportional to the number Q/ of particles of the matter B present 

 at that time. Now, from equation (4), it has been shown that 



Q, = (e-* - e~). 



The value of Q/ passes through a maximum Q T at the time T when 



The maximum activity I T is proportional to Q T and 



t ._ Q/ ._ e-* - e- A " 

 IT "" Or ~ *-* ~ e-^ ' 



It will be shown later that the variation with time of the activity, imparted to a 

 body by a short exposure, is expressed by an equation of the above form. It thus 

 remains to fix the values of X,, X..,. Since the above equation is symmetrical with 

 regard to X,, A.,, it is not possible to settle from the agreement of the theoretical and 

 experimental curve which value of X refers to the first change. The curve of 

 variation of activity with time is unaltered if the values of Xj and X, are interchanged. 



VOL. ccjv. A, 2 B 



