14 RADIO REFRACTIVE INDEX OF AIR 



Thus k is defined by 



1 + iT" COS 6 



n an 



which, for rays tangential to the earth (60 = 0) and assuming n in unity, 

 is approximated by 



^ - 1 + a dn/dh ' ^^-^^^ 



It is customary to set 



dn/dh = - 7- , (1-30) 



and thus obtain k = 4/3. Since l/4a is close to the observed gradients 

 of n, this represents a "standard atmosphere" gradient and one may re- 

 move the "standard" decrease of N with height by adding a quantity, 8N 



m = {h/4a) 10' (1.31) 



to N{h) thus obtaining the "B unit" or 



B(h) = [(n - 1) + h/ia] lO' = N(h) + (/i/4a) lO'. (1.32) 



This method of presenting refractive index profiles has been shown to 

 be very useful in emphasizing the departure from standard of the atmos- 

 phere over southern California [22]. The principal advantage of the 

 B unit is that any departure from a vertical line, and thus constant n 

 gradient of dn/dh = — l/4a, equals a departure in refractive bending from 

 that in the effective earth's radius atmosphere with k = 4/3. 



A very similar approach is used to aid in the study of extended ranges 

 of radio waves. The most pronounced case of this phenomena occurs 

 when dn/dh = — (1/a) which, from (1.29), gives k = 00 or an effective 

 earth of infinite radius. This then implies, for radio purposes, the earth is 

 flat and comnmnication is between "radio-visible" terminals. For this 

 special study the modified index of refraction, M, is defined by 



M{h) = [{n - 1) + h/a] lO' = N(h) + (h/a) lO'. (1.33) 



A gradient of dM/dh = implies that A = oc and also implies a theo- 

 retically infinite range of radio signals. M units were used to present the 



