RADIATION CHARACTERISTICS OF AN ANTENNA. 



199 



replaced by tq, which can be done without appreciable error for large 



values of r. The same substitution cannot be 



made in the argument of/ in (10), for there r 



determines the phase of the oscillation, and this 



phase changes through an angle of t for a half 



wavelength, independent of the distance from the 



origin. 



dz 



.. e, 



7. Expression of the Field in Terms of 

 Current. — We shall next express the moment 

 of the doublet and the intensities of the field in 

 terms of the current i at the point z'. To do 

 this we shall think of the current as delivering a 

 charge + e to one end of the element of length 

 dz' and a change — e to the other end of dz' in a 

 certain time. A neighboring doublet has a differ- 

 ent current and delivers different charges + ei 

 and — ei partly counteracting the charges of the 

 given doublet, and leaving just the charge e — ei that actually occurs 

 on the wire. This is represented in Figure 5. 



With this view of the case 



Figure 5. 



and 



I = e, 



f it) = e dz' = I dz'. 



(12) 



Whence, by substituting the value of i from equation (1) into equation 

 (12) we shall have, in view of (7) and (9) 



dEe = dH^ = 



2t I sin d 2x , 



r cos ^:- (ct 



Acro X 



ro — z cos d) 

 27r Ao 



sin 



^(|»-/)rf.'. (m 



By integrating this expression from 2' = to 2' = a, we obtain the 

 electric and magnetic intensities at the point P due to direct trans- 

 mission from the vertical portion of the antenna. Indicating this 

 integration, we have 



