214 PIERCE. 



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

 absolutely small. We have then 



,T^ ITT AtI sin xp . Az . \2-K, , , ,.) 



dE^ = dtix = 7 sm — • sin < -^- (ct — ^o + x cos \p) > 



roc\ r-o X ) 



■ . \ 2 tt/Xo a / , ; 



(50) 



This equation may be shortened up by writing 



(51) 



and 



9^ /\„ \ 9^/i 



(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 .A . Az n . ( . 2ttx' \ . 



Ej, = H^ = r sm — / sin r H r — cos \p sm 



(b - ^^) dx'. (53) 



To perform the integration let us introduce a change of variable 

 by putting 



s = B — ~ — then dx = — p— ds 



X 2ir 



and the limits of integration become 



for .r' = 0, s = B, for.r' = b, s = 0. 



Equation (53) then becomes 



