EFFECTIVE EARTH'S RADIUS 57 



combining (3.15) and (3.17), the familiar equation, 



i=-^f^, (3.18) 



p n dp 



is obtained. If the ray path makes an angle 6 with the surface of constant 

 refractive index 



dr = dp cos d (3.19) 



and 



1 = _ i ^ cos e. (3.20) 



p n dr 



If the curvature of the effective earth is defined as 



tte a p 

 then 



(3.21) 



and 



Ue = ka ^ .. ^ .. (3.22) 



1/a — 1/p 



k = ^ . (3.23) 



a dn 



1 + — 77 cos d 



n dn 



For the small values of 6 normally used in tropospheric propagation, cos 6 

 may be set equal to unity. Further, by setting 



I - - fa ^'-'^^ 



one obtains the familiar value of k = 4/3 for the effective earth's radius 

 factor. By assuming that the gradient of 7i is constant, a linear model 

 of N versus height has been adopted. 

 For this model, the bending 



ri.2 = — / cot d dn (3.25) 



is written 



-'=£'1^'* (3.26) 



