The analysis of the radiation from dipoles as given hy Sommerfeld and by von Hoerschelmann is deficient in one respect: it does not give the true1asymptotic expressions for the radiation leaving at a considerable angle from the horizontal. The correct asymptotic formulas have already heen easily supplied by an appeal to the Reciprocal Theorem; lately M. J. O. Strutt2has got them directly from the boundary conditions and H. Weyl3has derived the correct asymptotic formula for a vertical dipole at the surface of the earth by a method quite different from Sommerfeld's. In the present paper it is shown how they can be got by merely improving the rigor of Sommerfeld's analysis.
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W. Howard Wise (1929) studied this question.