154 BELL SYSTEM TECHNICAL JOURNAL 



For angles near grazing incidence, both {\ — K) and i/' are pro- 

 portional to ^. 



^ = b^, U -> 0], 



where a and b are now both independent of ^. li K = 1, the ratio 

 of the resultant of the direct and reflected waves to the direct wave 

 becomes 2 sin (7/2). If in addition 7 is small, this ratio becomes 

 simply 7. 



For angles near normal incidence, both K and ip are independent of ^. 



^-'i-^^:- f^-'^/^i' 



^ = tan-(^J, \X 



■^12], 



where a, b, and c are now independent of ^. 



For good conductivity, g{= lajj) » e > r(= e - cos- ^) ; a = i 

 = V2g; c = g for vertical polarization. For horizontal polarization 



a = — b = \'2/5, c = 1/q. _ 



For poor conductivity, $(= 2(r//) «r(= e - cos^ ^) < e;a = 2e/Vr, 

 ^ = 0; c = eV^; lA = when ^ < cot~' \€, and \p = it when ^ > cot-^ Ve 

 for vertical polarization. For horizontal polarization a = 2/Vr, 6 = 0, 

 c = 1/r, V' = 0. 



Appendix II — Refractive Index and Curvature of Rays 



The dielectric constant, e, of dry air is given by the expression 



€ - 1 = 210 X lO-^p/K, 



where p is the pressure in millimeters of mercury and K is the tem- 

 perature in degrees absolute. 



When water is present, however, an appreciable change is produced 

 in the dielectric constant and doubtful points arise. Such , for example, 

 are the effect of association of water molecules with each other or with 

 other molecules, and the effect of adsorption on the surface of the plate 

 of the test condenser. The work of Zahn -^ seems to have clarified 



^^Phys. Rev., 27, 329, March, 1926. 



