Asymptotic Dipole Radiation Formulas

HE analysis of the radiation from dipoles as given by Sommerfeld and by von Hoerschelmann is deficient in one respect: it does not give the true 1 asymptotic expressions for the radiation leaving at a considerable angle from the horizontal. The correct asymptotic formulas have already been easily supplied by an appeal to the Reciprocal Theorem; lately M. J. O. S t r u t t 2 has got them directly from the boundary conditions and H. W e y l 3 has 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.