CAIN OF DIRECTIVE ANTENNAS 89 



This integration has been carried out by R. M. F'oster who has very 

 kindly placed the results at the writer's disposal. Only the final 

 result is given herewith: 



T = -4Tr + -^/'S' (" - ^y cos {2irkb)'Q{2-Kka, 0) 



+ -1^/e {N - K) • cos (2TKB)-Q(2TrKA, 0> 

 ni\ ly K=i 



+ ^^^2 e| (N-K)- cos {2irKB) • (2(0. 2tKA) 

 + -^"E e\« - ^)(iV - K)- cos (2x2^5) 



11 I\ I\ i=l A'=l 



cos (27rkb)-Q(2w^kW + XM2, 0) 



K)(N - K)- cos (27rir5) 

 cos {2irKB)-Q{2TrKA, 2tKA) 



,N - K)- cos (27ry^6) 



cos {2TvKB)-Q{2Trka, 2TrKA) 



+ -tItf/I:' e' (A^ - X)(iV - ^). cos {2^KB) 

 ni\^I\^ K=i K=i 



+ -tI^oE' E' (« - ^)(iV - ^)- cos (2Tkb) 



I 2 n-l x-1 A^-l 



+ -TTT^2 L Z E (« - -^)(A^ - X)(A^ - iC) 



• cos (2 7ry^6)- cos (I ttKB)- cos (2x^5) 



• Q{2Uk'-a' + X2^2^ 2T;;:i4). (25) 



Where the function 



'2(-^'' 3') = (^2 _^ yj3/2 sin (V.x-2 + /) + ^^, ^ ^3^, cos (Vx2 + /) 



^.2 2-1/2 



- (^iiqr^lpsin (Vx2 + /). (25a) 

 In particular 



and 



sin a: , cos x sin .t 

 (2(x, 0) = — — + —-. -r- (25b) 



„,_ , 2 cos X , 2 sin x ,r.- s 



(2(0, .r) = - --^- + -— - • (2^c) 



Special Cases 



(1) If we assume n = 2, a = \, h = — \ and 5 = 5 = 0, the test 

 ratio is given by 



