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BELL SYSTEM TECHNICAL JOURNAL 



3. The velocity of propagation, of electromagnetic waves in a gas, 

 3 X W 



is given by y = 



v« 



, and the radius of curvature of the ray, in 



the plane of " /r," is, 



V 2e 



R = 



IM 



dv 

 dh 



de 

 dh 



K Tp 



62370 



d(Kp) 

 dh 



dh 



From the linear addition theorem, the " K '' of a composite gas 

 like moist air will be 



or 



lOOi^ 



K 



(100 - a)211 + a(182( 1 +-^) 



X 10- 



211 + a( ^^ - 0.293 



X io-«, 



where " a " is the percentage of water vapor, in the air, by volume. 



Hence 



M X 10« 1 



R = - 



31185 



dh 



211 + a { ^^ - 0.293 



where " M " is the molecular weight of the gas involved, and " p," 

 " a," and " T " are to be determined as functions of " ^," the alti- 

 tude above the earth. 



4. From Humphrey's " Physics of the Air " we obtain the following 

 data: 



On page 38 average summer and winter temperature versus height 

 curves are given. For the first two kilometers a good fit to the 

 summer curve is given by the equation, 



T = - 6.l9h + 288 where " h " is in miles. 



On page 72, average summer and winter air and water vapor 

 pressure, and total density tables, as a function of the height, are given. 

 For the first two kilometers the density is given by the equation, 



- 0.000185/i + 0.001224 



