THE ELECTROMAGNETIC I'IKIJ) 



41 



Elach of the terms which compose (lie sum (27) 

 is called a mode. The coefficients jT,„ arc complex con- 

 stants with their real parts positive. They represent 

 therefore an exponential decrease of the field strength 

 with distance. The real part of f m is the attenuation 

 [actor of the nith mode expressed in nepers per unit 

 distance. The height-gain functions U m arc found to 

 increase with height above the ground. The increase 

 is first slow but eventually becomes exponential and 

 remains that way for large heights. 



The real part of f„„ the attenuation factor, in- 

 creases with increasing mode number; hence, if the 

 receiver is far enough from the transmitter, all 

 modes except the first one become very small and 

 the sum in equation (27) reduces to its first term 

 which can be computed without much difficulty. 

 This applies when the heights hi and hi are fairly 

 small. The height-gain functions increase with height 

 the more rapidly the higher their order, and as one 

 approaches the line of sight the number of modes 

 that contribute to the field strength becomes large. 

 It is true that the series (27) converges everywhere, 



but above the line of sight the number of terms re- 

 quired for a good approximation is so large that the 

 expression is useless for numerical work. Here the 

 methods of ray optics become applicable. It is 

 usually found that, at a given distance d, the field 

 in the lower part of the diffraction zone can be 

 computed by using one or a few terms of the series 

 (27). At large heights above the line of sight 

 the field is determined by the methods of ray 

 optics, and the two curves can be joined with a 

 good degree of accuracy by graphical means on 

 a decibel diagram. This has been clone in Figures 

 12 and 13. 



The series (27) , though simple in external appear- 

 ance, still proves extremely difficult to evaluate. 

 Burrows and Gray, 23 however, have simplified the 

 mechanics of evaluation to such a degree that nu- 

 merical data can be obtained by means of a small 

 number of graphs. The detailed procedures employed 

 in computing field strength and contour diagrams by 

 the method of modes are summarized and collected 

 in Volume 3. 



