. The Bell System technical journal . this is to note that equation (10) might justas well have been obtained directly from V instead of from Qi. Substituting equation (11) in equation (4) we get whence ^ ^ k2 cos 0. - h^k2^ - k{^ sin^ ^_.^..,(^.-^, ) e^-^ ^ ^j^) £/ = -ico( n/ + ;fei-2^n. ^2^ cos dz + ki-\k2^ — jfei^ sin^ dz a^ i?i where - ioi sin2 ^,(1 + i?igi^i2«cos9.)_^^ (13) i?l = ^2^ COS 02 — ki-^ki^ — ki^ sin^ 62 k2^ cos ^z + ^iV^2^ — ^1^ sin^ dzSubstituting equation (11) in equation (2) and adding £2°° we get Ez ~ - iw cos d:, cos ^^(1 - i?igi*)^ (14) i?i is the coefficient of
. The Bell System technical journal . this is to note that equation (10) might justas well have been obtained directly from V instead of from Qi. Substituting equation (11) in equation (4) we get whence ^ ^ k2 cos 0. - h^k2^ - k{^ sin^ ^_.^..,(^.-^, ) e^-^ ^ ^j^) £/ = -ico( n/ + ;fei-2^n. ^2^ cos dz + ki-\k2^ — jfei^ sin^ dz a^ i?i where - ioi sin2 ^,(1 + i?igi^i2«cos9.)_^^ (13) i?l = ^2^ COS 02 — ki-^ki^ — ki^ sin^ 62 k2^ cos ^z + ^iV^2^ — ^1^ sin^ dzSubstituting equation (11) in equation (2) and adding £2°° we get Ez ~ - iw cos d:, cos ^^(1 - i?igi*)^ (14) i?i is the coefficient of reflection for a plane wave polarized in theplane of incidence. The horizontal fields of a horizontal dipole are aj \ dx dy dz and = — ico n^ dx~ ^ Riemann-Webers Differentialglcichungen dcr Physik, p. 556. 668 BELL SYSTEM TECHNICAL JOURNAL -)] = - zo;(n,=° + n/) + cot ipEy^; (16) _•, E/ = EJ sin if - Ey^ cos <p ^ - iw sin <p(nx°° + n/). (17) Evidently the procedure which yielded the true asymptotic expres-. p:„ 2—Vertical dipole polar diagrams computed for X =6 meters,£ = 9, M = 1. and cr = 10-1=* sion for V will do the same for H/. The details are not result is n. 2k\ cos dz , ikiRi ki cos d, + -ylki^ - ki sin2 d, ^2 (18) ASYMPTOTIC DI POLE RADIATION FORMULASSubstituting equation (18) in equation (17) we get £/ 1- io) sin .^(1 - i?oei^i2<zcos0.) ___^ 669 (19) ^here Ro = ^k^^ — kr sin- ds — ki cos g;■yjko - ki^ sin- 6, + ki cos 0, i?o is the coefficient of reflection for a plane wave polarized perpen-dicular to the plane of incidence. Formulas (13), (14) and (19) are just what one would get by applying
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