210 PIERCE. 



the time average of cos^ ) IT ^'^^ ~~ ^^■^ ( '^ ^/^' '^^^^ time average of 

 current square at the base of the antenna, by (1) is ~ P sin" -^ = 

 - P sin^ f J Whence the radiation resistance becomes in ohms 



-Rfl = j-T \ Ri — Ri cos q — Rz sin g /■ , (44) 



sm^ I- 



in which i?i, i?2, R3 and g have the values given in (41) and (42). 



We shall later give tables of Ri, R2, and R^, that will reduce the 

 calculations of R to very simple operations, and shall compare the 

 results with calculations on the doublet hypothesis and with observa- 

 tions. 



We shall, however, first investigate theoretically the radiation from 

 the horizontal part of the antenna. This is a problem of considerable 

 mathematical difficulty but is capable of solution. 



