30 McCretuanp ann Hackerr—Secondary Radiation from Compounds. 
of the energy emitted as secondary £ particles by any small volume of the 
substance to the energy of the primary radiation absorbed by that volume. 
The relation between these two constants was shown to be 
4p 
~ (@* Ip 
and from the observed values of p, the values of « were calculated by this equation. 
Consider now the absorption of a compound, and the emission of secondary 
radiation from it. 
If we let & denote the energy passing per unit time through unit area of a 
surface at depth x in the compound, the part of this energy absorbed in a 
thickness dz is wRdzx, and the corresponding amount of energy set free again as 
secondary $ rays from the layer is wxRdz, where p is the true coefficient of 
absorption of the compound for the radiation, and « is the transformation-constant 
of the compound as defined above. 
If now the absorption and emission of secondary rays are atomic properties, 
we can consider the total absorption and emission as the sum of the absorptions 
and emissions of the separate atoms, the atoms of different types having different 
values for » and x. 
If there are m, atoms of any class in unit volume, and if the average absorption 
produced by each atom of this class is q, we have therefore 
pe = Sy a, 
and pK = yHkK; 
Ny K 
and therefore oe 
>A 
Again, we have obviously 
1 
eat! 
N, 
where p, is the true coefficient of absorption of an elementary substance composed 
of atoms of the class to which a refers, and JV, is the number of atoms in unit- 
volume of this element. 
Further, if d, denote the density of this elementary substance, and @, its 
atomic mass, we have 
ING, S Che 
v 
Therefore a, = Ma" 
ant 
