214 



PIERCE. 



this is to be neglected even in the phase angle, because its value is 

 absolutelv small. We have then 



dE^ = dH^ 



4x7 sin ^P . Az . )2Tr , .] 



r sin — ■ sin K -^ (ct — ro + x cos yp) > 



TqcK To l \ ) 



\ 2 tt/Xo a I 



(50) 



This equation may be shortened up by writing 



and 



(51) 

 (52) 



To obtain the total electric and magnetic intensities due to the 

 flat-top, the equation (50) must be integrated for all the doublets 

 and their images between the limits 



x' = and x' = h 



where h is the length of the flat-top. This integration is expressed 

 in the following equation. 



4x7 sin lA . Az n . ( 2irx' . . 



tj, = Hx = ; sin — I sin r H r — cos \p sin 



rocX roJ V X 



B - ^^) dx'. (53) 



To perform the integration let us introduce a change of variable 

 by putting 



s = B- 



2irx 



then dx = — ^ ds 



and the limits of integration become 



for .r' = 0, s = B, for x' = h, 5 = 0. 



Equation (53) then becomes 



