ULTRA-SHORT WAVE PROPAGATION 



157 



(f is velocity of light and « the refractive index, which is assumed 

 approximately equal to one at point a). But by Pedersen's equation 9' 



7ir sin <p = To cos \{/. f3) 



Hence 



dt = 



n^r 



tqc cos \{/ 



dd. 



(4) 



Now, Eccles ^^ has shown that when the dielectric constant varies 

 with r (distance to center of earth) as follows: 



n = 



«+i 



(5) 



Fig. 17 

 the solution for the path of the ray is 



ro' cos (sd — \p) ^ r' cos \p. (6) 



Here 5 is a constant and ro is the distance to the center of the earth 

 from a, the arbitrarily fixed point of reference in the path, ro is there- 

 fore not very different in our case from the radius of the earth. 

 By combining (5) with (6) we find that 



nr = 



/'o cos xf/ 



cos {sd — xp) ' 

 which when substituted in (4) gives 



fo cos xp dd 



dt = 



c 



^0 Electrician, 71, 969-970 (1913). 



cos^ {sd — yp) ' 



(7) 



(8) 



