150 A^ CLIMATOLOGY 



Chapter 3 shows that the bending, ti,o, of the radio wave between any 

 two points in the atmosphere is given by 



ri.2 = ^ + (01 - e,), (4.27) 



where di,2 is the distance between the two points 1 and 2 (see fig. 4.42) 

 projected along the earth's surface, a is the radius of the earth, and 6i 

 and 62 are the angles in radians the ray makes with the horizontal at points 

 1 and 2 respectively. As described in chapter 3, Schulkin [43] obtained 

 Ti,2 in radians as 



r,,, = ^^^ 7 ^^^ for < 00 < 10° (4.28) 



where Arii = rii — 1, A/io = no — 1, d^ = {Si + 02)/2. In terms of refrac- 

 tivity, (4.28) becomes 



{N, - N2) X 10-^ AN X 10-^ ., ^Q. 



Tl.2 = a = a • (4.29) 



Considering now the case of the half-length, dht, (4.27) becomes 



ri.2 = ^ + e„ (4.30) 



since 02 = at the top of the duct, and di = 6p. Now substituting (4.29) 

 in (4.30), 



^^q^i^ = ^-' + 0„ (4.31) 



since here dm = 0p/2. Rearranging (4.31) 



dht = a 

 Since 



'2AN X 10~' 

 _ dp (rad) 



+ dp (rad) . (4.32) 



dp = cos-^ ^^^ ^ J2[aN X 10-^ - ^'^ ~ ^h . (4.33) 

 (rad) 



