SUCCESSION OF niAMiKS IN RAniOACTTTR BODIES. 183 



matter A deposited, l>eing taken jis 100. The amount of matter B is initially aero, 

 passes through a maximum about 10 minutes later, and then diminishes with the, 

 time. In a similar way, the amount of C passes through a maximum uhout 37 minutes 

 after removal. After an interval of several hours the amount of both B and C 

 diminishes very approximately according to an exponential law with the time, falling 

 to half value after intervals of 21 and 28 minutes respectively. 



11. Long Exposure. The exposure is supposed to be so long that a state 01 

 equilibrium is reached between the emanation and the successive products resulting 

 from it. In this case the number 7*0 of particles of A, deposited per second from the 

 emanation, is equal to the number of particles of A which change into B per second, 

 and of B into C, and so on. This requires the relation 



...... (6), 



where P , QQ, R,, are the maximum numbers of particles of the matter A, B, and C 

 when a steady state is reached. 



The values of P, Q, R at any time t after removal from a long exposure are given 

 by equations of the same form as (3) and '(5) for a short exposure. Remembering the 

 condition that initially 



p = P = WO/A,, 



it can readily be shown that 



Q = Qo = 



R = RO = 



P =-*'' .............. (7), 



A i 



R = n (cur*-' + be~ + ce-*) (9), 



where 



a = 



^: 



(A, - A,) (A, - A 3 ) ' "(A,-A 2 )(A 2 -A 3 )' ' X, (A, - A,) (A, - A,) 



The relative numbers of atoms of P, Q, R existing at any time are shown graphically 

 in fig. 9, curves A, B, and C respectively. The number of atoms R,, is taken as 100 for 

 comparison, and values of A,, Aj, Ag are taken corresponding to the 3, 21, and 28- 

 minute changes in the active deposit of radium. A comparison with fig. 8 for a short 

 exposure brings out very clearly the variation in the relative amounts of P, Q, R in 

 the two cases. The amount of R initially decreases very slowly. This is due to the 

 fact that the supply of C due to breaking up of B at first, nearly compensates for 

 the breaking up of C. The values of Q and R after several hours decrease 

 exponentially, reaching half value every 28 minutes. 



