. BSTJ 1: 1. July 1922: Transmission Characteristics of the Submarine Cable. (Carson, John R.; Gilbert, ). r dr r- 9<£2 - 4tt\hPIE = 0, the solution of which is a Fourier-Bessel expansion, E = AoK0 (ra) -Mi #i (ra) cos + A2K2 (ra) cos 20 + . . +, r and being referred to the axis of the particular wire. Assuming that the current distribution in the core conductor isindependent of the angle , that is, neglecting the individual char-acter of the armor wires only in their effect on the current distribu-tion in the core, the effect due to the current in the core is represented Wave Propagati
. BSTJ 1: 1. July 1922: Transmission Characteristics of the Submarine Cable. (Carson, John R.; Gilbert, ). r dr r- 9<£2 - 4tt\hPIE = 0, the solution of which is a Fourier-Bessel expansion, E = AoK0 (ra) -Mi #i (ra) cos + A2K2 (ra) cos 20 + . . +, r and being referred to the axis of the particular wire. Assuming that the current distribution in the core conductor isindependent of the angle , that is, neglecting the individual char-acter of the armor wires only in their effect on the current distribu-tion in the core, the effect due to the current in the core is represented Wave Propagation over Parallel Wires; The Proximity Effect. John , Phil. Mai-., vol. xli, p. 607 (1921). 102 BELL SYSTEM TECHNICAL JOURNAL by the first term of such a series, and the total field intensity may bewritten N — 1 pa E = AK0 (m) + 22 BsKs (apj) COS s<fo (3i) J = o s = o pj and ty being referred to the axis of wire j, as shown in Fig. 5. Thatis, the resultant field is expressible as a set of waves centered on theaxis of the cable and the axes of the N armor Fig. 5 In the neighborhood of the armor wires the arguments of the Besselfunctions are sufficiently small3 to permit of the approximations where and K0 (ap) = K - log p, K = log—,a Ks (ap) = (- apy 3 See Note I at end of paper. TRANSMISSION OVER SUBMARINE CABLES 103 The series (34) can, therefore, be written E - A(K - log,) + B0(NK - ]Tlogp,-) + ]r JT Bs -^^, (35) j = O J = O 5 = i * in which Bs has absorbed the constant quantities. From this, the magnetic intensity in the sea water can be obtained by differentiation. Inside any armor wire, at the surface, the field intensities are E = C0J0(lt) + &M& cos 4> + . . + C„J„($) cos tuf> + . . + , (36)ff* = ^[o/0(*)+Ci/i(£)cos4+ • • • + CHJn(t)cosn4>+ ... + ](37) where £ = ais/iTrXupi, X and n being the electrical conductivity and the magnetic perme-ability, respectively, of the material of the armor wire. The quan-tities a and 0 ar
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Keywords: ., bookcentury1900, bookdecade1920, booksubjectarmor, bookyear1922
