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[Proceedings of the Royal Society, A, Vol. LXXXVIII. pp. 103110, 1913.]
SOME interesting problems in electric wave propagation are suggested by an experiment of Hertz*. In its original form waves of the simplest kind travel in the positive direction (fig. 1), outside an infinitely thin conducting cylindrical shell, AA, which comes to an end, say, at the plane #=0. Co-axial with the cylinder a rod or wire BE (of less diameter) extends to infinity in both directions. The conductors being supposed perfect, it is required to determine the waves propagated onwards beyond the cylinder on the positive side of zt as well as those reflected back outside the cylinder and in the annular space between the cylinder and the rod.
IB -iA
Fig. 1.
So stated, the problem, even if mathematically definite, is probably intractable; but if we modify it by introducing an external co-axial conducting sheath CO (fig. 2), extending to infinity in both directions, and if we further suppose that the diameter of this sheath is small in comparison with the wave-length (A,) of the vibrations, we shall bring it within the scope of approximate methods. It is under this limitation that I propose here to
* "Ueber die Fortleitung electrischer "Wellen durch Drahte," Wied. Ann. 1889, Vol. xxxvii. p., que la compressibility de 1'air est ne'gligeable et que la visco cinematique est absolument constante. Si les resultats de 1'experience sont pas completement d'accord avec la theorie, on devra examiner hypotheses de plus pres.