442 Dr. J. P. V. Madsen on 



The remainder represented by the fraction (1 — q) are 

 turned into j3 rays at once. Let i = ql \e~ Kx dx. 



As a result of scattering in a direction inclined to the 

 original at an angle #, let (qFO represent the number of 

 particles per sec. which cross the unit area of a spherical 

 surface of unit radius described with centre at the point 

 where scattering occurs ; then the number of scattered rays 

 which emerge per sec. from the fiat plate of thickness L 



T "" 



= " 2tt sin 6 . F0 . qI o \e-^e-W- x)seod d0 dx. 



o - ~ 



In addition to these rays we have emerging per sec. a 

 number I e~ x]j which have suffered no scattering. 



We are not at present able to evaluate the expression given 

 above, from want of knowledge regarding ¥0. However, we 

 may proceed to make an approximate calculation of the effect 

 which might be expected in such a case as we have investi- 

 gated in fig. 1. 



Considering as before a fine pencil of homogeneous 7 rays 

 falling normally upon a plate of thickness L, we may express 

 the emergence radiation as — 



e -\z e -a\'<J>-*)dx=£^(e-n^e-<*' 1 ') 







where k is a constant, X the coefficient of absorption of the 

 primary set of rays, \' a similar coefficient for the secondarv 

 rays, and a a constant obliquity factor, which in the present 

 case is taken as 2, a value obtained by considering the 

 geometrical arrangement of the radiators in fig. 1 with 

 regard to the ionization-chamber. 



Let us now apply this result to the case of a Pb radiator ; 

 the values of A, and V are '32 and 1*3 respectively. The 

 curve corresponding to e~' 32Ij —e~ 2 ' 6Jj is shown by the dotted 

 line in fig. 2, the maximum having been adjusted to the 

 same value as for the experimental curve. 



The agreement between the theoretical and the actual 

 curve is very good. 



The maximum value is reached for about the same 

 thickness of radiator, and for thicknesses of radiator greater 

 than that required to give the maximum effect the curves 

 slope away to about the same extent. This, taken in con- 

 junction with previous experiments, seems to show that 



