362 



BELL SYSTEM TECHNICAL JOURNAL 



Symbol Definition 



F' The horizontal component of the electric wave in medium 1. 



(Positive direction in the direction of propagation along the 



interface.) 

 E' The vertical component of the electric wave in medium 1. 



(Positive direction downward.) 

 PI Specific resistivity of medium 1. 



Pi Specific resistivity of medium 2. 



ki Dielectric constant of medium 1 and equal to unity for a 



vacuum. 

 ki Dielectric constant of medium 2. 

 / Frequency 



Unit 

 volts per 

 kilometer 



volts per 



kilometer 



ohms per 



centimeter 



cube 



ohms per 



centimeter 



cube 



numeric 



numeric 

 cycles per 

 second 



27r/ 



Our primary interest is in the case where the first medium is air, 

 and the second medium is the earth beneath an antenna system. 

 In this case the constants of the media may be given the values: 



(air), 

 (earth), 

 (air), 

 (earth). 



Substituting these values into the general equation (301) 



pi = 00 



P2 = P 



k^ = 1 



k2 = k 



F' 1 



— i=r7 = e-'* tan T = -^ 



fkp 



18 X 10" 



1 + 



fkf 



18 X 10" 



gj(l/2tan-i(18XlOiV/trt!, (302) 



At this point it is desirable to indicate the significance of the term 

 "quasi-tilt angle" as applied to T. It is seen that (tan T) is the 

 absolute magnitude of the ratio of the horizontal and vertical com- 

 ponents of the electric field. In the case that the time phase between 

 the two components of the field is zero (i.e., 8 = 0), T would represent 

 the angle of forward inclination of the propagated wave front. In 

 general, 8 is unequal to zero and hence the angle of inclination of the 

 major axis of the ellipse traced by the electiic vector is less than T, 

 but it still remains convenient to express the ratio of the magnitudes 

 of the two components of the field as the tangent of an angle. This 

 angle cannot be called the wave tilt, however, but the term "quasi-tilt 

 angle" may safely be applied to it. 



