REFERENCES 87 



whence 



riiri co.s di = ti2r2 cos do, (3.68) 



which is Snell's law for polar coordinates, (3.1). 

 In figure 3.20, it can be seen that 



PF dr 

 '^"'=QF = 7d-^- (3.69) 



where </> is the angle at the earth's center between r and COZ. Substitut- 

 ing (3.69) in (3.67) 



dn 

 tan dd(f) -\ tan Odd = 0, 



n 



or 



dn 

 id4> - dd) tan = - — . (3.70) 



Since, by considering (3.61) for infinitesimal angles, 



dr = d<t) - de, 



or, in (3.70) 



or 



dr tan 6 = — — 



n 



dti 



dr = -cote — . (3.71) 



n 



Integration of (3.71) yields (3.2). 



3.13. References 



[1] Smart, W. M. (1931), Book, Spherical Astronomy, Ch. 3 (Cambridge Univ. 

 Press, London, England). 



[2] Bean, B. R., and G. D. Thayer (May 1959), On models of the atmospheric re- 

 fractive index, Proc. IRE 47. No. 5, 740-755. 



[3] Booker, H. G., and W. Walkinshaw (1947), The mode theory of tropospheric 

 refraction and its relation to wave guides and diffraction, Book, Meteorological 

 Factors in Radio-Wave Propagation, pp. 80-127 (The Physical Society, 

 London, England). 



[4] Freehafer, John E. (1951), Tropospheric refraction. Book, Propagation of Short 

 Radio Waves, pp. 9-22 (McGraw-Hill Book Co., Inc. New York, N.Y.). 



[5] Bean, B. R., and B. A. Cahoon (Nov. 1957), The use of surface weather observa- 

 tions to predict the total atmospheric bending of radio waves at small elevation 

 angles, Proc. IRE, 45, 1545-1546. 



