206 DE. T. J. I'A. BKOMWICH ON THE SCATTERING OF PLANE ELECTRIC WAVES, ETC. 

 Our result accordingly becomes 



(7'69) X = e- MT \ e "'( 1 + c05 ) 008< ''J ( K a sin sin tf) sin tf cos tf dtf. 



IT Jo 



An exact evaluation of the integral would be troublesome ; but it can be trans- 

 formed by integration by parts. This process leads to a series of which the first 

 term is 



/ 7 - 7 \ x _ <*?_ e -r Ji (*CT sin 0) 



^ ' r Ka sin 6 



The formula (77) will represent (7 '6 9) sufficiently accurately if (l 4- cos 0)/sin 9 = cot %0 

 is regarded as small ; and this is the correct assumption here, since 9 is supposed to 

 be nearly equal to -w. 



In the special cases Ka 9, 10 it appears that the approximation (7'7) represents 

 the scattered wave sufficiently well within a cone extending to about 10 from the . 

 axis. 



