RADIATION CHARACTERISTICS OF AN ANTENNA. 203^ 



p = -7- cos^ 1 ~^ (c^ — '"o) } cos^ B j ^ — 



c I \ ) \_ Jo sin 6 



de_ 



sine 

 '""/^ cos 6 sin (^-1 cos d) cos (.4 cos e) dQ 



, . „ „ T'^/^ cos2 sin2 (^ cos 0) rfe , , ^, r''/2 



+ sin- B I ; — h cos- u I 



Jo sm0 Jo s 



/ 



Jo Sin 9 



r'^/2 cos (A cos 0) (f 



— 2 sin fi cos B 



— 2 cos B cos 6' 



sine 



, ^ • 71 n r cos d sm {A cos d) dd^ ,^,. 



+ 2 sm 5 cos G I ^-, — • (24) 



Jo sin d J 



This equation when integrated gives the power radiated from the 

 vertical part of the antenna. The integration is a tedious operation, 

 and is given in the next section, which may be omitted by readers 

 not interested in the mathematical processes involved. The result 

 of the integration is found in Section 10. 



9. The Integration of Equation (24) . — By the use of such trigo- 

 nometric equations as 



1 + cos 2a: 



cos^ X = 



sin^ X 



2 



1 — cos 2x 

 2 



the squares of sines and cosines in the integrands of (24) may be 

 avoided, and equation (24) written 



2/2 .( 2x . . .) rn . O.A n de 



, cos 2 5 r'^/2 cos (2 A cos d) dd sin^ B T-/^ . ^ ,^ 



H ^ — / —^-Z ^— / sin d dd 



2 Jo smo I Jo 



s\xC-B C'^''^ 

 H -— / sin Q cos (2 .4 cos Q) dQ 



-' Jo 



'/2 cos Q sin (2 A cos Q) dd 



sm2B p 

 2 Jo 



— 2 cos B cos G 



r-/2cos_y_ 



Jo si 



sin 9 



cos 6) dd 



sin 6 



: o • » n T''^^ cos d sin (A cos 9) dd ~\ , . 



+ 2 sin iJ cos G I : — • (25> 



Jo sin 9 J 



