RADIATION CHARACTERISTICS OF AN ANTENNA. 217 



E^,e = E^ cos a 



H^,e = Nicosia — ^j = Hs sin a. 



and for the ^-components 



E^,^ = E^ cos f -^ ^ ) ~ — E^ sin a 



Hz,<p = H-s: cos a. 



Adding these quantities to the corresponding components of the 

 intensities due to the vertical part of the antenna, we obtain for the 

 total intensities, which are designated by primes, the values 



E'e = Ee + E^ cos a, 

 E'^ = — E^ sin a, 

 H'g = H^ sin a 

 H'^ = H^-\- H2, cos a. 



All of these intensities are perpendicular to tq. To get the power 

 radiated through an element of surface dS perpendicular to Tq, we may 

 make use of Poynting's vector, in the form 



rfj, = ^^(E'xH')rfS 



where the cross between the vectors means the vector-product. Tliis 

 vector-product, expanded, gives 



dp 



= J- ( E'g H'^ — E'^ H'g j dS 



= —{EgH^-\- E^H-2, cos^ a-\- H^E^ cos a-\- EbHj: cos a -\- 



E^ H^ sin a j c?S 



= ~(EgH^+E^H^-\-2cosaEeH.j,]dS. (56) 



We have already found the first term of this power and have ob- 

 tained its integral all over the aerial hemisphere. This integral we 



