210 PIERCE. 



the time average of cos^ ] — (et — ro) [■ is 1/2. The time average of 

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

 P sin^ ( ^ 1 Whence the radiation resistance becomes in ohms 



2 V2 



Ra = ITT \ Ri — Ri cos q — Rssinq > , (44) 



''-' if) ' 



in which Ri, R2, Rz and q have the values given in (41) and (42). 



We shall later give tables of Ri, R2, and R3, 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. 



