258 BELL SYSTEM TECHNICAL JOURNAL 



Except in the immediate proximity of the transmitter this angle is 

 small and the resultant field is 



E ='Eo(^Trhih2/\d), (3) 



where £o is the free space field. Since ^ 



60TrHI ... 



the resultant field becomes 



E = 240TrH-II}Hh2/\-d\ (5) 



Equation (5) shows that the field over level terrain is inversely pro- 

 portional to the square of the distance from the source.^ 



Data presented in Fig. 8 of reference 1 show that at a frequency of 

 69 megacycles per second the field strength variation with distance 

 follows approximately the inverse-square relationship for a range of 

 from two to ninety kilometers.^ In fact, the best straight line through 

 these data agrees with the numerical values obtained from equation (5) 

 well within the accuracy of the experimental data. Experiments 

 designed to test the validity of this equation now are being conducted 

 at Deal, New Jersey and data obtained to date confirm it both as to 

 absolute value and variation with terminal heights and wave-length 

 for horizontal polarization within the range 2 < //i < 25, 2 < /?2 < 25, 

 2 < X < 17, d = 9,420 and 26,300, all measured in meters. The 

 experimental confirmation of this formula for these distances indicates 

 that the effect of the earth's curvature is secondary to the negative 

 reflection effect upon which this formula is based. This might be 

 expected in view of the fact that both diffraction and refraction tend 

 to mitigate the additional attenuation that would be caused by re- 

 flection from a plane tangent to the earth's surface at the point of 

 geometric reflection. 



Mf 7 is in amperes, d in meters, and H the effective height of the antenna, and X 

 the wave-length in the same units, Eo is given in voUs per meter. 



* Since distance appears in this equation only as a factor and not as an exponent, 

 the reduction with distance of the field strength of ultra-short waves over level 

 terrain is independent of wave-length, polarization, dielectric constant, etc., as all 

 of these quantities cancel in the ratio of the field strength at one point to that at 

 another. The absolute magnitude of the field strength is proportional to the fre- 

 quency for the same radiated power and antenna heights. If the antenna heights are 

 sufficiently low, the field is also dependent upon the polarization and ground constants 

 as indicated by expressions (a) and (b) of footnote 6. 



^ While undoubtedly at the greater distances the field suffers additional attenuation 

 above that shown by equation (5) due to the curvature of the earth, such additional 

 attenuation evidently takes place at distances beyond those emjiloyed in any of the 

 authors' experiments. 



