210 Mr. 0. Klein on Scattered Radiation from 



I commence by examining the integral 



u=f*(l--^ ' W 



Jo \ x L + Xj 



We may write 



Jo V * ~l-rx) w X \ * i + v) 



and 

 But 



is equal to the constant of Euler : 



lim ( 1 +- + + +... + log m) . 



Besides, this may be proved without difficulty by starting 

 from the ordinary integral form of 0, which in the manner 

 known may be directly derived from the above-mentioned 

 definition, i. e. 



<4'ks>-v> 



If we take the difference between the two integrals and 

 exchange the limits and co for t and T, we obtain by 

 effecting the integration : 



log(l + T) +log(l-<r T )-logT 



-log (1 + — log(l-e-<) + log*. 



The limit value of this expression when t goes to and 

 T to g© will evidently be 0. The other part of U may be 

 written as follows : 



r (i=£? _ i ) dx = r (i _ i ) *_ r ^i dx 



Jz \ % 1+^7 Jz \x 1 + xJ J z X 



±+z i °° *?-* x 



= log 1 ^. 



Z J z X 



Consequently 



U = C + log* + log-4-_+t e —dx. . . (6) 



