ULTRA-SIIORT-WAVE TRjINSMISSION PHENOMENA 



223 



hill is then intioducx'd in the picture and, considering it as a straight 

 edge, its effect on both direct and reflected rays is calculated. (See 

 Fig. 24.) 



BEERS HILL 



MT. CUSHETUNK SEA LEVEL 



Fig. 24 — Diffraction by Mount Cushetunk. 



The resultant field at the receiver is then. 



Er = 



Eo 



[/Tj -|- i^7r2gt[27r/X(r2-r,) + e+^,-0,]-] 



(4) 



{a + b) 

 where, 



Fi = amplitude change in the direct ray due to diffraction 

 Fi = amplitude change in the reflected ray due to diffraction 

 /3i = phase change of the direct ray produced by diffraction 

 182 = phase change of the reflected ray produced by diffraction 

 K = amplitude change due to reflection at the ground 

 6 = phase change at reflection 

 £0 = free space field strength at distance of one mile. 

 The amplitude factors Fi and F2 and the phase changes /Si and ^2 

 may be calculated from the Fresnel integrals to the parameter "v" 

 (see note at end), where 



(5) 



"hi" and "/za" are the heights of the direct and reflected rays above the 

 straight edge. 



"a" and "6" are distances from the straight edge to transmitter 

 and receiver. 



A comparison of Figs. 17 and 25 shows that by taking account of 

 diffraction around Mt. Cushetunk better agreement of calculated and 

 observed curves is obtained. However, at grazing incidence this 

 simple theory is inadequate; in this case Fi = Fi, /3i = 182, K = 1, 



