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BELL SYSTEM TECHNICAL JOURNAL 



If the refractive index of the air varies as a power of the distance to 

 the earth's center, it has been shown ^ that the actual state of affairs 

 can be duplicated by a homogeneous atmosphere over an earth, the 

 radius of curvature of which is greater than that of the actual earth 

 and is calculable from the exponent of the height variation function. 

 With this "effective" earth radius, the formulae already mentioned 

 become usable. If the air refractive index does not vary as a power of 

 the distance to the center of the earth we must take that exponent 

 which gives the best first order fit over the height covering the re- 

 fracted wave front, the alternative being a prohibitive complication of 

 the theory. 



A plausible physical picture of the fading mechanism can now be 

 set up. If we lump the four boundary reflected components in one, 

 and plot as a function of the distance, we have curves "yl " of Fig. 15. 



REFLECTING BOUNDARY 



Fig. 14 — Drawing illustrating the four components of a single reflection 

 at an air boundary. 



Curves "5" are the Wwedensky ^ * and Gray ^ theories. These are 

 for our Highlands-East Moriches circuit with the average effective 

 earth radius of 8500 kilometers and a 1500-meter boundary height. 

 If we now imagine a receiver moving away from the transmitter we 

 shall first traverse the zone of high "5" amplitude with no fading 

 present. The signal amplitude will, for any given near-by point, and 

 for any given antenna ampere-meters, depend on the height of the 

 antenna above the ground and the ground constants. As the distance 

 to the transmitter increases, the falling "5" curve approaches the 

 rising "^" curve in ordinate and we enter a disturbed region where, 

 for any instability of the boundary, more or less complete interference 

 can result and fading will occur. (One such instability occurs when 



* There is an error in the formula, as given by Wwedensky. It is corrected here. 

 See appendix II. 



