138 BELL SYSTEM TECHNICAL JOURNAL 



When a hill is interposed as shown in Fig. 10-5, elements such as E, 

 below the profile of the hill, are prevented from contributing to the 

 signal at R, while elements such as E', above the profile, contribute as 

 before. This is the simple concept as used in optics and will be used 

 without essential modification in the explanation of non-rectilinear 

 radio transmission. 



Refraction 



Besides reflection and diffraction, a third optical concept, atmos- 

 pheric refraction, must be considered in this study. ^'^ It is a well- 

 known fact that a star, appearing to be exactly on the horizon, is 

 really 35 minutes below it. It is obvious that the " image " of an ultra- 

 short wave transmitting antenna will be elevated above its true 

 direction by this same means. The only question is whether the 

 effect is appreciable or not. The answer, obtained theoretically, is 

 that refraction must be taken into account. Unfortunately, we so 

 far do not have quantitative measurements which show the effect of 

 refraction of ultra-short waves in an unmistakable way. Those that 

 we do have, however, appear to be consistent with expectations based 

 on the theory which will now be presented. 



The physical picture to be assumed is one in which the dielectric 

 constant of the atmosphere decreases with height above sea level and 

 is not a function of horizontal dimensions. In other words, the phase 

 velocity of a wave in this medium becomes greater as the distance from 

 the center of the earth increases. In the case of ultra-short waves, 

 we are almost always interested in waves traveling in a substantially 

 horizontal direction. The wave-front, therefore, lies in a plane which 

 is nearly vertical and since the upper portions travel faster than the 

 lower, there is a tendency for the ray to bend slowly back toward 

 the earth. 



This phenomenon, in its general aspects, is the same as that which 



is commonly assumed to explain the bending of longer waves about 



the earth. There is an important difference, however, in regard to 



the part of the atmosphere which is important. In the case of these 



longer waves (for example, one having a wave-length of 15 meters or 



a frequency of 20 mc), the ionization in the atmosphere 100 to 400 km. 



above the earth is the cause of the refraction which makes long distance 



signaling possible. In the case of ultra-short waves, however (for 



example, one having a wave-length of 1.5 meters or a frequency of 



200 mc), this upper region is of no importance but it is the region 



1* Jouaust {L'Onde Eleclrique, 9, 5-17, Jan. 1930) has pointed out the importance 

 of refraction in the propagation of ultra-short waves. The authors believe, however, 

 that he has overemphasized its importance. 



