480 BELL SYSTEM TECHNICAL JOURNAL 



In obtaining the solution for the propagation of radio waves over 

 the surface of the earth, besides assuming the earth to be a perfect 

 conductor, Watson assumed that the electromagnetic properties of 

 the air were independent of the height above the earth's surface. 

 Data to be presented later indicate that neglecting refraction in the 

 lower atmosphere introduces the greater error for certain frequencies. 

 Fortunately in such cases, it is simpler to extend the solution to take 

 into account atmospheric refraction than the imperfect conductivity 

 of the earth. 



It is known ^ that for electromagnetic waves propagated along the 

 surface of the earth, the optical effect of the existing changes in refrac- 

 tivity with height in the lower atmosphere is the same as the effect 

 that would be produced if the earth's radius were increased. If this 

 " effective radius " is substituted for the actual radius in equation (5) 

 the resulting equation for the ratio of the field to that received over a 

 perfectly conducting plane becomes 



f{y) = 0. 1 136 V3; Y\ —V- e-^-^'^-i-' y, (7) 



where 



y = x/^Y^ = d/yl^^' (8) 



and K is the ratio of the effective radius of the earth to the actual 

 radius. 



From this it can be seen that the effect of refraction is to multiply 

 the distance at which a given reduction in the field due to the earth's 

 curvature occurs by a factor which is equal to the two-thirds power of 

 the ratio of effective to actual radius of the earth. The analysis of 

 the available meteorological data in the aforementioned article " 

 indicates that this radius ratio is about 4/3 on the average. This 

 results in an increase of 1.21 times in the distance at which the reduc- 

 tions in fields occur.® 



The ratio of the field received over perfectly conducting spherical 

 earth with refraction by the lower atmosphere to that which would 

 be received over a perfectly conducting plane is shown in Fig. 2. 



Watson ^ has pointed out the relation of the empirical Austin-Cohen 



^ T- C. Schelleng, C. R. Burrows and E. B. Ferrell, "Ultra-Short-Wave Propaga- 

 tion," Proc. I.R.E. 21, 427-4:63, March, 1933 and Bell Svs. Tech. Jour. 12, 125-161, 

 April, 1933. 



" The increase in range is not as great as this due to the inverse distance factor. 



This advantage would not be realized for waves greater than a certain length. This 

 Hniit occurs when that part of the atmosphere for which the refractive index no 

 longer decreases at the assumed rate becomes important in the propagation of the 

 waves. 



' G. N. Watson, "The Transmission of Electric Waves Arounil the Earth," 

 Proc. Roy. Soc. {London) APS, 546-563, July 15, 1919. 



