36 BELL SYSTEM TECHNICAL JOURNAL 



wave. In Part Two of this paper it is shown that a plane electro- 

 magnetic wave, polarized with the electric vector in the plane of 

 incidence and in the wave front, impinging on a plane solid at nearly 

 grazing incidence produces a total field in which the horizontal elec- 

 tric field near the solid has very nearly the same ratio to the vertical 

 electric field as in the Zenneck surface wave. In Part Three of this 

 paper it is shown that the wave tilt near the ground at a great distance 

 from a vertical dipole is almost the same as that found for the plane 

 wave at nearly grazing incidence. 



Part One — The Evidence Against the Surface Wave 



The following discussion centers around the surface wave wave- 

 function P and the series (5), (6), (8) and (9) of paper 3 in the 

 bibliography.* These series and P follow 



P = - j!^^H,^'Ksr)e"^',] (12) 



(2i + P/2 = -„T-^ i: ^n(- xY, (5) 



r\ - t'- 



n=0 



1 t2/,X2 00 



Q, + P/2 = -^Y^ ^ ^"(- ^2)"' (6) 



^1 ''■ n=0 



1 



1 _ ^1 



n=l 



Q, = Q, + P ~ - j-^ry2 T. CnX~\ (8) 



(2i~^r^'^^"^2-", (9) 



where r = horizontal distance, x = — ik\r, x^ = — ik2.r, r = kilk^, 

 S = ^i/Vl + T^, k^ = €//aj2 — 4:Tr(TfJLia}, ki^ = kr (e — ilcXcr), ki « 2x/X 

 in air, a = 7^(1 + r^), a^ = 1/(1 + t^), 



Ao = I, Ai = y[a tanh""'Va, A2 = Ai — a, 

 Ar, = {{In - 3)^„_i - o^„_2]/(w - \)\ 



5o = 1, -Si = Va2 tanh"^Va2, Bi = Bx — ai, 

 Br, = l{2n - 3)5„_x - 025„_2]/(w - 1)2, 

 Ci = - l/a, C2 = - 3/^2 + l/a, 

 C„ = l(2n - l)C„_i - (« - iyCn-2']la, 

 Di = — 1/^2, Di = — 3/a2^ + l/<22, 

 D„ = l(2n - l)Z)„_i - (n- lyD^-il/a^. 

 * Sommerfeld's time factor e"*"' which was used in paper 3 has been replaced by 



t z, the height above ground, is zero in paper 3. 



