PROPAGATION OF PERIODIC CURRENTS 



533 



In its simplest form, as here contemplated, the wave antenna con- 

 sists of a long straight horizontal wire terminated at each end in its 

 characteristic impedance K, as represented by Fig. 12a, which gives 



f(x,e) 



FCx,e) 



Positive 

 ,, directions 



K,r 



K 



Fig. 12a 







Fig. 12& 



an elevation view. This is seen to be the same as Fig. 1 when 

 Zo = Zg = K\ and 7 is now the propagation constant, per unit length, 

 of the wave antenna regarded as a transmission line. Hence formulas 

 (46), • • • (54), pertaining to Fig. 1, are immediately applicable for 

 calculating the current at any point x in the wave antenna of Fig. 12a, 

 after the appropriate formulation of the functions f{x) and F{x) — 

 namely the impressed axial electric force and the impressed potential, 

 respectively, at any point x in the wave antenna. 



These functions can be evaluated by aid of Fig. 126, which gives a 

 plan view representing a train of plane radio waves (whose magnetic 

 component is horizontal) incident on the wave antenna at an arbitrary 

 angle 6 measured horizontally from the wave antenna to the direction 

 of propagation of the wave train along the earth's surface. By the 

 'direction of propagation' is here meant the horizontally specified 

 direction of a vertical plane which is normal to the plane of the wave 

 front, /(x, d) denotes the horizontal component of electric force in 

 the impressed waves at any point x of the wave antenna, and F{x, 6) 

 the potential of the impressed waves there.^^ Then the axial electric 



-^ The presence of 6 in the functional symbols is of course to allow for a possible 



