58 



TROPOSPHERIC REFRACTION 



since 



and 



N = No - ^ 10 

 4a 



dn = dN X 10-' = - ? 

 4a 



(3.27) 



(3.28) 



Further, for the case hi = ho ^ 0, and 



< 00 < 10°, 



where do is the initial elevation angle of a ray, (3.26) may be approximated 

 by 



TO,h — 



dli 

 4ad ' 



The angle 6 may be determined from 



7. - )dl-h 2{N - No) +l(h- ho) • 10' 



1/2 



u-iir 



For the case when ^o = 0, (3.29) becomes 



1 I" dh 



TO.h 



2\/6a '^'^ Vh VQ 

 1 



To.h — 



Vq 



1 Ih 



Vh/a. 



Now, from the geometrical relationship, 



To.h = ' h (do ~- Oh), 



(3.29) 



(3.30) 

 (3.31) 



(3.32) 



(3.33) 



(3.34) 



one finds, for do = 0, 



do.h ~ a(ro,/i + dh), 



(3.35) 



