180 Prof. E. Rutherford on Radio activity 



Let q be the rate of increase of the intensity due to the 

 steady supply o£ radio-active material. Then 



dl T 



or 



\og e (q — LI) = — L^ + A. 



But 1 = when t=0. 

 Therefore 



Therefore 



or 



A=- r \og e q. 



, q — LI T 



loo>^ =— Jjt 



1=4(1-,-*). 



L 



When L£ is very large, the maximum value of the intensity 

 I is given by 



I =|- and ^=1—6 



■ u 



or the equation representing the rise of intensity of the 

 radiation is the same as the rise of an electric current in a 

 circuit of constant self-induction. 



The curve which is shown in fig. 8 is in rough agreement 

 with this equation. For example, the intensity of the 

 radiation has risen to half its value in about twelve hours. 

 Now e~ u =l when f = 11 hours, i.e., according to theory, 

 the current should have reached half its value in about eleven 

 hours. 



There is a divergence between the theoretical and observed 

 results in the first part of the curve. The rate of increase 

 of intensity is slower at first than the theory would suggest. 

 Tt is probable, however, that the rate of supply of radio-active 

 material does not reach a steady value for a considerable 

 time after the exposure of the plate, and such a cause would 

 account for the results observed. Other results obtained, 

 under different conditions, all show too small a value of the 

 intensity for the first few hours of exposure. 



We have so far assumed that the radio-active particles 

 were conveyed to the surface under the influence of an 

 electric field. The equations which have been given will, 

 however, apply equally well to the case of diffusion. If no 

 electromotive forces are acting, the radio-active particles 



