208 



PIERCE, 



If now we add together the terms multiphed by sin q and those 

 multiplied by cos q, and those not involving q, we have (on factoring 

 out the I) 



p = - cos 



- -; — (cf — ro) 



I X 



2 + 2 



(L) 3!2 



k-" - 



'^'k^+'^k^ 



o!4 



7!6 



+ cos 9 -^ — 



+ sin q \ — 



22+2 



4 4^+2^-6 



3!2 '^^ 5!4 ^ 



6'- + 2« - 8 8- + 2^ - 10 



7!6 



32 + 2^-5 



4!3 



7^+2^-9 

 8!7 



9!8 



52 _j_ 25 — 7 



k' + 



6!5 



92 + 2^ - 11 

 10!9 



k^ - 



(39) 



Equation (39) gives the total poicer radiated by the vertical portion of 

 the antenna into the hemisphere above the earth's surface. In this equa- 

 tion, the current factor I is in absolute c. g. s. electrostatic units, and 

 the power p is in ergs per second. 



It is convenient to change the current factor into amperes and the 

 radiated power into watts, which can be done by multiplying the right 

 hand side of (39) by 30 c. This is done, and the equation is rewi*itten 

 in the next section. 



10. Result of the Integration for Power Radiated from the 

 Vertical Part of the Antenna. — By equation (39), when reduced to 

 practical units, the total power radiated into the aerial hemisphere 

 from the vertical part of the antenna may be written 



p = P cos^ \ — (ct 



- ro) 



Ri — Ri cos q — R3 sin q 



(40) 



where 



