210 Hacxert—The Secondary Radiation excited by y Rays. 
The value of S is identical with the value which would be obtained for a 
radio-active substance emitting only B rays, whose intensity of radiation was 
Rye'v4,«, per unit volume, when secondary effects are considered. The 
approximation p,/Ag=0 is equivalent to considering the intensity of the rays 
constant in the layer from which the 6 rays come, and writing e“s*=0, to 
considering only a small thickness on one side of the plate important. 
The expression for the secondary radiation emerging from that side of the 
plate on which the rays are incident will be obtained from the above by the 
omission of e“y%. It is clear that it should be the same fraction of the intensity 
of the primary passing through the surface layer in both cases. 
2p aly eee 
Sy = Oa n jit) [B] 
If we assume that all the secondary radiation excited by y rays goes initially 
in the direction of the primary rays, then we have the equations :— 
dR 
aa Gare BR, 
ds 
dv = be ar Zeepk eS ate s| ag Bk, R, 
ds 
~ a = = [Bp or 2hakaS + 3]; 
or 
vit = Roe eats 
a — aS + bs + 2ck, 
_ = =- as + bS. 
A solution of these equations is given by 
S = Ae™*s* + Bet*s* + 2eMRye-"r*. 
bs = (a — \,) Ae™*s* + (a + d,) Be**s* + 2chye-"y* [Ma - p,) - 1], 
where 
Ag = Pal mena) 
_ at 
ds = fey 
Proceeding exactly as before, we obtain for S, and s, the expressions 
Siz = Rye? 2, [C] 
Xa 
K 
Lo=—,)il Sp 
So — R, [easy 2 = Ry Py 2, [D] 
Neg Xe 
