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 j) 



« = — cos 

 2c 



^^|(c^-ro)| 



2 + 2^,_4+^^,^6^^, 



3!2 



5! 4 



7!6 



( 2^+2^-4 ,, , 4^ + 2^-6 ,, 

 + co^q\ ^t:^ ^'^+ F77 ^' 



3! 2 



62 + 2« - 8 



+ sm q\ 



7!6 

 32+2^-5 



k' + 



514 

 82+28— 10 



413 



72 + 2" - 9 

 8!7 



B + 



918 



52 + 2^-7 

 6!5 



¥- 



P- 



02 _j_ 09 — 11 

 '^ + 10!9 ^ 



(39) 



Equation {39) gives the total power radiated by the vertical portion of 

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

 tion, the current factor / 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 powder into watts, which can be done by multiplying the right 

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

 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 cos2 \ — (ct 



ro) 



jRi — i?2 cos q — Ri sin q 



(40) 



where 



