10 TECHNICAL SURVEY 
This applies when the heights h; and hz 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 done in Figures 
12 and 13. 
The series (27), though simple in external appear- 
ance, still proves extremely difficult to evaluate. 
Burrows and Gray,?? 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. 
