On the Existence of a Surface Wave in Dipole Radiation over a Plane Earth

In a paper published in 1909, Sommerfeld stated the existence of a surface-type wave in the radiation of a vertical Hertzian dipole over a plane earth. Weyl, in 1919, objected to this solution. Despite a great number of papers on this problem, it had not been definitively settled so far. Its solution is given in the present paper by proving in a quite general way that this surface wave cannot be included in the said dipole radiation and by pointing out a thusfar hidden error in Sommerfeld's computation.