Hacxertr—The Secondary Radiation exerted by y Rays. 209 
With this notation we have the following equations :— 
a7 ag pf. 
ds 1 
Oo) Oa tiaheme Gea 
ds 
— FT He + 4[p,K,R + peka(S + s)]5 
or 
18, = Lie By 
d. 
DS —_ _ aS). Big & IBS = Ss ARIS OR, 
dz dz 
A solution of these equations is given by 
S = Ae*s* + Be**s* + cLR,e-"y*, 
where 
Ag = Hp ll — Key 
ih = Mp ats a. 
: ; 
M's —~ By 
The constants A and B have yet to be determined by the conditions 
S=0 when 2=0; s=0 when xw=d where d = thickness of plate. The 
expressions obtained are complicated for the general case, but assume a simple 
form for the particular case to which the observations apply. McClelland* 
has shown that d, isthe apparent coefficient of absorption of B rays, so that 
if plates thick enough to absorb 8 rays falling on the upper side are used, 
e*s?=0, and also p,/\, may be neglected in comparison with the other 
terms. 
We find 
Aes — olhi, Aor = U; 
B= 0, Bet? = - cL L(a = Hy) = 1] Rey’. 
a+ Xz 
Inserting these values, we obtain for S,, the secondary radiation emerging on 
the same side of the plate as the y rays, 
S,= Ren"? Evy Esty A 
So ONE =r) ie 
The term R,e-"y%#,«, is the amount of secondary radiation excited per unit 
volume in the surface layer. 
* J. A. McClelland, Trans. Roy. Dub. Soc., vol. ix., part iv., 1907. 
TRANS. ROY, DUB. SOC., N.S., VOL. IX., PART IX, 2 
