212 Mr. 0. Klein on Scattered Radiation from 



Consequently 



r 



-kx 



i 



dx=K{h)- ' f v^ fe[*[l+«)]. (U) 

 <&>=$(*)-«-**0[£(l + «)]. . . (15) 



J. (1 + *)- 



For ?7i = l we get 



1 + 



So we have reduced all the integrals of this form. There 

 remains only 



J* * J** * 



This one is immediately reduced by the relation (10), 

 which gives 



'"* °° - far 



\ e — r dx = e- kz ^>(hz). 

 By effecting all these reductions of K, we finally get : 



K = 2iog~ +2e~^(kz) 

 l + z 



+ (2-2*+y-J)(*(*)-«- fa *[*(l+*)]) 



~1^^ 2 + 6 ^"^l + ^V 3j + 3(l+*)V 



+ i^ + l(fli7 + l(i^ +2C -K 2 -|)- ^ 



For 2 equal to oo , i. e. @=-~, this expression is trans- 

 formed to 



K. /2 =21ogJ + (2-2i+J-| 3 )^,(i)+2C--^(2-|).(17) 



This value must be used in order to calculate the scattered 

 radiation entering the ionization-chamber, when the plate is 

 quite close to its opening. It now remains to show how 

 <£(X) is connected with known tabulated functions. This is 

 extremely simple and follows from (10). Then the function 



%J 00 



,-t 

 — dt 



is found in the tables of Jancke and Emde under the desig- 

 nation Ei(X). (10) gives 



<£(X) = --e A E;(-X) (18) 



