4 RUSS, Note on Radio-active Recoil. 



where Q, = number of Radium B particles produced after 

 a time t, Aj and A2 being the radio-active constants of 

 Radium A and Radium B respectivel)% and ;/ being con- 

 sidered constant during the time of exposure. 



The number of Radium B particles supplied to the 

 disc will be a fraction of this, depending on the solid 

 angle subtended by the disc, which will be considered 

 later. 



At any time T after removal 



As Radium V> is supplied to the disc it immediately 

 begins to form Radium C, the rate of increase of which 

 may be denoted thus : — 



. .Ji, = — n[i - ae - + />e ■ | 



K X., 



where rt = \ — hr and fi = 



A, -A. K.-K 



For a definite time of exposure the quantity within 

 the brackets is determinate, and may be replaced by AI, 

 whence 



K 



Since the decay curves were measured by means of 

 the alpha rays, we require to know the quantity of 

 Radium C on the disc at any time T after removal. 



The quantity of C may be considered as made of two 

 part.s — 



(i) That actually on the disc at the moment of 

 removal, which at any subsequent time T will be 



— n Me '-^ . 

 A,, 



