﻿244 Mr. L. Y. King on Absorption 



§ 2. Absorption in Flat Plates. 



In most cases (4) leads to integrals which are difficult to 

 evaluate numerically. A case of considerable interest and 

 one for which the integrals reduce to tabulated functions is 

 afforded by considering the 7-radiation from a homogeneous 

 distribution of radioactive matter throughout an infinite slab 

 of thickness h. 



YlZ. 2. 



Let z be the height of P above the surface of the plate, 

 <f> the angle which PA makes with the perpendicular from P 5 

 -^r the azimuth angle which the plane through PA and the 

 perpendicular makes with a fixed direction in the plane 

 of the slab. AYe then have r z — r 1 = AB = Ji/ cos </>, 

 ri = PA = z\ cos 0, and dfl = sin (/> dcf) dyjr. 



Thus (4) gives on integrating with respect to yfr between 

 and 27r, 



I = ?^( 1 ^-X^sec^ 1 _^_ i:Asec ^ sec ,^ f (5) 



K Jo 



We note that the integral 



J' 



2 ™* . . ,. i "e-udu 



e -* sec <t>smcf>dcf) = .v J 



u> > 



by the transformation cos 0= -; integrating by parts, 



I e -xsec(p g i n (k dd> = e~ x —x \ . 



Jo r J x u 



The last integral 



C"e-"du = _ C~ x ^du 

 J, u .! u 



