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BELL SYSTEM TECHNICAL JOURNAL 



A and B at constant tan 4>. Thus, for any distance of the plane, we 

 can read from the curves the values of A, B, and tan $, and can 

 calculate the path difference (^2 — ri) by equation (2). 



In this manner, the theoretical reception curves, which are given in 

 Figs. 15 to 20 (dotted curves), were calculated for flights at 8000, 5000, 

 2500, and 1000 feet. The ordinate "Relative Signal Strength — 

 Decibels," is 20 login Eo/Er, and gives the received signal strength in 

 decibels below the field strength in free space at a distance of one mile 

 from the transmitter. 



10 20 30 40 60 60 70 80 90 100 110 120 130 140 150 



MILES 



Fig. 23 — Sample curve for calculating airplane results. 



Since the scale of the observed reception curves is unknown, they 

 are superimposed upon the calculated ones by causing the maxima of 

 the observed curves to coincide at some point with the theoretical loci 

 of maxima (see for example, the points marked ".x" in Figs. 16 and 18). 



In the limit, as grazing incidence is approached, the theoretical 

 reception approaches zero. In equation (1), -K^ becomes unity and Q 

 becomes 180 degrees and the path length difference {fi. — r\) becomes 

 zero. The observed field at distances greater than those required for 

 grazing incidence is a diffraction one. 



Appendix II 

 Diffraction Calculations 

 In Fig. 25 the data of Fig. 17 for the 5000-foot airplane flight are 

 compared with a theoretical curve which has been corrected from that 

 of Fig. 17 by considering a possible diffraction around Mt. Cushetunk. 

 This hill, 650 feet high, is 36 miles from Beer's Hill along the line of 

 flight, and is the first major obstruction to an optical path at the 

 greater airplane distances. For this calculation the points of reflection, 

 angles of incidence, and path length differences are determined in the 

 manner described in Appendix I, just as if the hill were absent. The 



