IV AVE PROPAGATION 551 



where, as before 



x' ^xy/a 



g' = \/a limes the depth below the surface of the ground. 



The integral can undoubtedly be evaluated in somewhat the same way 

 as (29) and can in any case be numerically computed without much 

 difficulty. Owing, however, to the secondary technical interest in the 

 electric intensity below the surface of the earth, the detailed solution 

 has not been undertaken, nor has the magnetic field been worked out. 



V 



The practical utility of the preceding theory and formulas will now 

 be illustrated by a brief sketch of their application to two important 

 transmission problems. 



The Wave Antenna 



When a transmission line with "ground return" is employed as a 

 radio receiving antenna it is called a wave antenna. The theory and 

 design of such an antenna requires a knowledge of the transmission 

 characteristics of the ground return circuit, which are calculable, as 

 shown above, from the geometry and constants of the overhead wire, 

 together with Z' = 4co/, which may be termed the "ground return" 

 impedance. 



We assume that the wire is approximately 30 ft. above the ground 

 (/? = 10^) and that the frequency is 5.10^ c.p.s. corresponding to the 

 frequency employed in Trans-Atlantic radio communication. The 

 ground conductivity X is exceedingly variable, depending on the 

 locality and weather conditions. Calculations of Z' will therefore 

 be made for two extreme cases, X = 10"'- and X = 10~" which should 

 cover the range of variation encountered in practice. 



ForX = 10-'2, 

 \/«=a/4^i^ = 2.10-3 

 and for \ = lQ-^\ 

 a = 2.10-". 



