246 



GUIDED PROPAGATION IN NONHOMOGENEOUS ATMOSPHERE 



in equation (3) is found to be 64 rather than 65. 

 The great advantage of the variational method 

 lies in the fact that, if we wish, we can increase the 

 number of parameters in the approximating func- 

 tion. For example, we can assume 



E(h) = sin 



sin exp 



< h < H 



h - H 



H 



h> H , (9) 



without specifying that 6 = \p = 3x/4 as we did 

 in obtaining the curve in Figure 1. We should then 

 calculate H, d, and ^ from 



7 = 0-^ = 0^ = 



(10) 



However, aside from the labor of solving these 

 equations and having to deal with more complicated 



results, we shall lose the advantage inherent in a 

 description of the field in terms of only one easily 

 understood parameter. The most we could hope for 

 from an analysis of these equations is a somewhat 

 better choice of the master curve for the type of 

 atmospheric conditions which are the most likely 

 to occur. 



The obvious general conclusion from equations 

 (7) and (8) is this: if MQi) is multiplied by a con- 

 stant factor, the effect on H is the same as that- 

 obtained if we divide X by the square root of this 

 factor. If M is proportional to h n , then H is propor- 

 tional to X 2/< w) . Since the gain of the guided wave 

 over a free space wave is proportional to Xp/ff 2 , 

 where p is the distance from the transmitter, the 

 gain is independent of the wavelength when M (h) 

 is proportional to /i 2 . For a uniform lapse rate the 

 gain varies inversely as one-third power of the 

 wavelength. 



