438 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1954 



indication of the errors introduced by the approximations used in the 

 derivation of (2.10) and its analogue. 



3. RADIO PROPOGATION OVER A SUCCESSION OF RIDGES ON THE EARTH's 

 SURFACE 



The results mentioned in Section 1 concerning propagation over a 

 succession of ridges may be obtained from the expressions and curves of 

 Section 2 as follows: Consider the situation shown in Fig. 3.1. Let a 

 radio wave start out from a transmitter at T. We assume that by the 

 time it arrives at the first ridge at P it has become equivalent to a 

 plane wave of amplitude K/t traveling in the direction TP, where A is 

 a constant depending on the strength of the transmitter. For the sake 

 of simplicity the waves reflected from the ground are neglected. In a 

 more careful study they would have to be included.* 



In order to calculate the strength of the wave at the second ridge, 

 we assume it to be a crest wave coming from P. Let G denote the value 

 of I ^ I (we assume the case of horizontal polarization since the reflection 

 coefficient of physical materials approaches — 1 for almost grazing in- 

 cidence) at Q corresponding to a plane wave of unit amplitude incident 

 on P. From Fig. 3.1 we see that the values of ^ and p to be used in com- 

 puting G are ^1/ ^ —i/R, p = 27r^/X, X = wavelength, R = radius of 

 earth. The value of h depends upon the radius of curvature of the ridge: 

 2h = 2t (radius of curvature)/X. 







Fig. 3.1 — Diagram showing ridges at P and Q which diffract the radio wave 

 starting from T so that a portion of it is received at *S. 



A method for doing this (for one hill) is given in Reference 1, page 417. 



