M‘Cievttanp—The Energy of Secondary Radiation. 21 
Let the total downward flow of energy at depth # through unit area in 
unit time be &, and let the upward flow at same depth be +. 
R is made up partly of unabsorbed primary radiation, and partly of secondary 
radiations, including under the term secondary not only true secondary radiation, 
but also tertiary and all successive radiations. The upward flow 7 is composed 
entirely of secondary radiations. Further, let ~ denote what the coefficient of 
absorption would be if there were no secondary radiations, and let «x denote 
the ratio of the energy of the secondary radiation given out by the layer 
dz to the incident energy absorbed by this layer. 
With this notation we have 
oe =— Rt Se eo 
The first term on the right-hand side results from the absorption of primary 
radiation; the second term expresses that x times the energy absorbed is set 
free again as secondary radiation, of which, as au approximation, half may 
be taken as travelling upwards and half downwards. The third term results 
from the fact that, in the layer considered, the quantity 7 of the upward flow 
is absorbed with a corresponding generation of secondary. The coefficient p is 
taken to be the same for all the radiations primary and secondary. 
In exactly the same way we have 
Lipa Ore Ha. HE 
= Be TTP gy Pe 
or 
o. = aR + by (1) 
and | 
o = ar = bR (2) 
where 
sali «\ 
oeplind 
and 
ee Es 
ut 2 
From (1) and (2) we get 
2 
a =(¢—08)R 
and 
2h 
eae (a — b’)r. 
