McCietianp AND Hackutr—The Absorption of B Radiuwn Rays by Matter, 41 
Using the equation (1) above, viz. : 
aR 
ada 
and remembering that =O when xw=d, we get 
= = Gh db br, 
(A — @)) Tg = A’\(A+ a)er@ + (0 - Cua 
and 
IBy = 1B QA a A'(e™@ el emma) 
Eliminating A’ we get 
Ry _ (At aje™ + (A—aj)e™™ 
1 Bye 2r 
But un = grt 
Ra Y 
ent — af ren + a)e™ + (N— ae 
2d ? 
or 
GY = GO =(G= l)e™, (3) 
where 
a K 
guste VA teat ane ( =) 
~ By ~— BWSR = 2/1 =k 
C can be calculated for any substance from the values of « given in Table I. 
in the previous paper referred to above. From this investigation it is evident 
that the coefficient \’ as usually determined is not an accurate coefficient of 
absorption of the total radiation passing through a plate of the substance 
under examination; this coefficient is the quantity \, and \’ =X only when the 
thickness d is great; for very small values of d, \’ is greater than \, and the 
difference is serious for substances for which « is large. For example, when 
Cis calculated for lead, it is found that the maximum value of 2’ is 1°64). 
The method employed in this paper consists in calculating \ from suitably 
observed values of \’, employing the previously determined values of x. We 
have then an accurate coefficient of absorption (A) of the total radiation, 
primary and secondary, passing through the substance. We can then, if 
desired, calculate the ¢rue coefficient of absorption (#) of a definite set of 
particles by using the relation 
= tJ ll = fe 
This ¢rue coefficient is, as stated above, what the coefficient of absorption would 
be if there were no secondary radiation. 
