208 Hacxertr—The Secondary Radiation excited by y Rays. 
determining the radiation from different substances. The more complete dis- 
cussion, later in the paper, affords an explanation of the actual differences 
between the amounts of radiation from the various elements. 
If these physical ideas are translated into mathematical language, the same 
result is obtained, but in a more precise form. The treatment already given by 
McClelland in his papers on secondary radiation due to 6 rays is easily adapted 
to the case of y rays. He assumed that a certain fraction « of the energy of the 
8 rays absorbed in each element of volume is re-emitted as secondary 8 rays. As 
a first approximation, half of the secondary rays may be taken as travelling in the 
same direction, and half in the opposite direction. This has been found sufficient 
in discussing all the experimental facts. It will be noticed that this manner of 
looking at this type of secondary radiation of 8 particles covers equally well all 
the hypotheses—(1) that they are scattered 6 particles of the primary stream, 
then « is the coefficient of scattering; (2) that they are electrons expelled from 
the atom; (8) that they consist of a mixture of both. 
In the case of y rays, we can assume, according to Bragg, that the emission of 
secondary radiation of 6 particles takes place in the same direction as the 
exciting radiation; but this is not a special consequence of Bragg’s theory ; it is 
equally possible on an ether-pulse theory. Such an effect might possibly exist in 
the case of B rays; but it would be obscured by the effect of scattering of the 
rays, which makes it difficult to distinguish even the true secondary radiations, as 
a whole, from the total scattering. 
On the other hand, the same approximation as for 6 rays may be adopted, 
that half of the secondary goes initially in the same direction as the primary, and 
half in the opposite direction. This has been done for symmetry below. It is 
easy afterwards to deduce the result of assuming that it all goes initially in 
one direction. 
Let the energy of y rays incident normally per unit area ona plate AB be 
denoted by &, and the energy passing down through unit area of a depth be R. 
If », be the coefficient of absorption of y rays, the amount of energy absorbed in 
the layer dz is p, Rdz. The amount of secondary radiation generated in the 
layer will be «yu, Rdv, if we assume that the energy of the emitted secondary 
rays bears a constant ratio (x,) to the energy absorbed. Let the downward flow 
of secondary radiation be S, and the upward flow s. This secondary radiation of 
B rays excites a tertiary radiation in each element of volume through which it 
passes. If pu, be the true coefficient of absorption of B rays, this effect at a 
depth z is represented by two terms, each similar to that for y rays paka[S + 8]. 
The total energy set free as secondary radiation in the layer dz per unit area is 
(u,k,R + ek S + s])dz. According to what has been said above, half may be 
taken as travelling upwards, and half downwards. 
