670 BELL SYSTEM TECHNICAL JOURNAL 



Returning to equation (15) 



Ey"^ -^-co^r^-^Tn.-- r~^U- fl~l^^^ \ /o(rp)g-''-^r^rl 

 dydx\_ Jq m+l\ koH+ki^m/ ^ ^ J 



a^ 



— 7-0) 



dydx 



(y^r^n,"" -k^r'-V) 



'^ —l(Xi cos C^;r COS 



1 + 



i-|^(i+i?0 



giA-i2a cos 6; 





(20) 



Usually one cares only for it^'' at ^ = 7r/2 and E^'' and E^'' are of 

 no particular interest. Figs. 2, 3 and 4 are polar diagrams in the 



0.25 



0.50 



0.75 



Fig. 4 — Polar diagrams of the vertical fields of horizontal dipoles computed for 

 X = 6 meters, « = 9, ju =1 and a = 10"^^ 



vertical plane of equations (13), (14) and (19). Assuming the con- 

 ductivity of the air to be zero and the dielectric constant to be unity 



^i = k,\e + i2c\a), ki = 2t/\, 



where e is the dielectric constant of the ground referred to air as 

 unity and a is the conductivity of the ground in electromagnetic units. 

 The values of e and a used in computing the polar diagrams are 

 generally supposed to be somewhere in the neighborhood of their 



