RADIATION CHARACTERISTICS OF AN ANTENNA. 



219 



P 



\ 



- COS- B + cos^ xl/ sin- 5+1—2 cos B cos (5 cos \p) 

 sin i/' 1_ ( 



_ 7^ r^ # 



'live Jo •:- 



— 2 cos ^p sin B sin (5 cos i/^) / c?2 [sin^ (^ sin yp cos S)] /• 



+7r/2 



2 I 



r/2 



(60) 



We shall first perform the integration with respect to 2 



,r/2 



/ (GjsinM^sini/'CosS)} 



"^-x/2 



= / 



T ( 



\ 1 — cos (2 A sin i/' cos 2)) 



TT 1 T" 



= - — - / cos (2 yl sin i/' cos 2) dl,. 



2 2 



7r/2 



- / cos (2 yl sin i/' cos 2) c?2 — - I cos (2 ^ sin yp cos S)cG 

 2 t/_ X 2 «yo 



2 (61) 



TT 1 Tt 



= - — - I cos (2 .4 sin ^ cos 2) c^2 

 Z 2 »/ o 



(62) 



This last step consists in changing the variable of the first integral 

 of the right-hand side of (61) by putting 



2' = TT + 2, 



TT 



which makes the limits - and tt without any other change, except 



the change of 2 to 2'. But since this is the variable of integration, 

 the prime may be omitted, and the terms of (61) added, giving (62). 



Equation (62) may now be integrated by Formula (11) Art. 121 

 of Byerly's Fourier's Series and Spherical Harmonics giving for the 

 integral of (62) 



