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BELL SYSTEM TECHNICAL JOURNAL 



excellent transmission at very low frequencies, where there is no phase 

 shift due either to reflection or to path difference, from the excellent 

 transmission at very high frequencies {e.g., 2000 mc.) where large phase 

 shifts due to these two causes nullify each other. 



In those cases in which calculations of this sort indicate a very 

 weak resultant field, these estimates may be considerably in error due 

 to neglect of terms which are usually unimportant. 



It may be of interest to note that two of the experiments described 

 have given an inverse square of distance variation. In both cases the 

 antennas were near the surface of the earth. It can easily be shown 

 that this should be expected when total reflection occurs with reversal 



10 20 50 100 200 500 1000 2000 5000 10000 

 FREQUENCY MEGACYCLES 



Fig. 14 — Above: Profile of a hypothetical path. Below: Calculated frequency 

 characteristics for various conditions. Curves are shown for vertical polarization 

 over sea water (o- = 20 X 10~i''^ 'e.m.u., e = 80 e.s.u.), for vertical polarization over 

 land (o- = 5 X 10~" e.m.u., e = 15 e.s.u.), and for horizontal polarization over 

 either (ground constants not important in this case). 



of phase provided that the difference in path length is smaller than 

 one sixth of a wave-length. Thus, in Fig. 9 the signal received at R 

 will tend to be zero or very small, except as the phase relation is 

 altered by the difference in the path lengths TOR and TSR. The 

 corresponding phase difference in radians is 4:irH^ID\, if H is small. 

 Since the differences of two vectors of equal magnitude are equal to 

 the product of their phase difference, if small, and their magnitude, 

 the resultant field is equal to 4TrKH^J\D'^. One of the inverse distance 

 factors is due to the phase angle and the other is due to the fact that the 

 amplitude, KjD, of the direct wave itself varies inversely with the 

 distance. Under these conditions, therefore, the signal would vary 

 inversely as the square of the distance, D, directly as the square of 

 elevation, H, and inversely as the wave-length. Qualitatively, at 

 least, all of these tendencies have been observed experimentally. 



