﻿Problems in Radioactivity. 243 



If, then, we have a mass of radioactive matter enclosed by 

 a surface S, the intensity of the primary radiations which 

 reach P can be easily calculated, as in the corresponding 

 optical case *. The intensity at P due to contributions from 



the mass cut out by a small cone PAB of solid angle d£l is 

 given by 



dl = ^sdn e-^i i * e-'i'—ri) dr, 



where N is the number of radioactive molecules per unit 

 volume, X the coefficient of absorption for air, /c that for the 

 radioactive mass itself, while r, — PA, r 2 = PB, and r = Ys. 



The total intensity as measured by the ionization per unit 

 volume in an electroscope at P i; 



given by 



I^f^-x^jf^-^-nWpn, 



(3) 



the integral being taken so as to include contributions from 

 all the elements of the radioactive mass, 



We notice that if the radioactive molecules are distributed 

 uniformly in the mass S and if S is homogeneous we have 



Ns f 



{i 



.«(. 



,)) da. 



(4) 



In this form (4) leads to a curious reciprocal relation 

 which may be stated as follows : — The ionization per unit- 

 volume at P due to a distribution of N molecules per unit 

 volume throughout a mass occupying a surface 8, is equal to 

 the total ionization throughout S due to N molecules ot 

 radioactive matter concentrated at P. 





• King, "' Note on the Cosine Law of Radiation," supra, p. - 



