RADIATION' CHARACTERISTICS OF AN ANTENNA. 231 



Jo 1 — sin^ d cos^ (j> 



-~^r\~ 



sin^ d cos^ <^ 



by reasoning similar to the above. Expanding the denominator by 

 {93a), we have 



W 



= 4 / d(t> cos2 <^ j 1 + sin2 ^ cos^ <t> + sin" d cos" + 

 = 2.|^ + ^sin^.+ if|sin".+ ----[- 



\ 



(96) 



(If we need it, this integral can be obtained by direct integration in 

 the form 



W=^.^ ^ \ 



I cos 0(1 + cos 0) ) 



but the expanded form is more useful for our purpose). 

 Now substituting (95) and (96) in (89) we obtain 



2/2 fT/2 

 C Jo 



— sin B cos 6 sin (A cos 6) — cos G 

 "1 



dd sin 6 sin (A cos 6) ■( cos B cos (A cos 6) 



f 



^{B -s\nB)sine 



+ ~(B-f,-smB]smH 

 ^lJ^(B-^-,^-.inB]sirfe 



2-4-6 



3! ' 5: 



+ 



(97) 



To evaluate this expression we must obtain the following integrals: 



T 



de sin"^ e 



sin (2A cos 0) 



c?0 sin" d cos sin2 (^ cos 6), 



(98) 

 (99) 



