98 THE ROYAL SOCIETY OF CANADA 
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 dQ is given by 
To 
al = Ws 9e if e— *(1—") dr 
" 
where N is the number of radioactive molecules per unit volume, À the 
co-efficient of absorption for air, « that for the radioactive mass itself, 
while. 7, ‘PA, 7, PB and n= Ps: 
The total intensity as measured by the ionization per unit volume 
in an electroscope at P is given by 
Ns ins 
lee rat ee do...) 
K 
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 uni- 
formly in the mass S, and if S is homogenous we have 
a Ns — M, f Sie = ro. | 
I= —*fe le RCE (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 dis- 
tribution of N molecules per unit volume throughout a mass occupying 
‘a surface S, is equal to the total ionization throughout S due to N mole- 
cules of radioactive matter concentrated at P. 
Absorption in Flat Plates. 
2. In most cases (4) leads to integrals which are difficult to evalu- 
ate numerically. A case of considerable interest and one.for which the 
integrals reduce to tabulated functions is afforded by considering the 
y-radiation from a homogeneous distribution of radioactive matter 
throughout an infinite slab of thickness À . 
Let z be the height of P above the surface of the plate, ¢ the angle 
which PA makes with the perpendicular from P, y the azimuth angle 
* King: Note on the Cosine Law of Radiation. See p. 89 of the present volume. 
