Propagation of Radio Waves over a Plane Earth

Abstract

THE purpose of this letter is to point out an error in sign in Prof. A. Sommerfeld's original paper (1909) on the attenuation of radio waves¹. This error in sign has recently been reflected in Bruno Rolf's graphs² of the Sommerfeld formula, predicting dips to zero in the field intensity at finite distances from a radio transmitter and other anomalous phenomena. This error in sign has been corrected in Prof. Sommerfeld's 1926 papers³ and also does not occur in the derivation by B. van der Pol and K. F. Niessen⁴. In this latter paper an exact expression is given for the potential of a vertical infinitesimal dipole (equation 21). After expanding this expression, I found that most of the terms are negligibly small at moderately low frequencies for distances from the source greater than a wave-length, giving for the potential function of a vertical dipole over a plane earth: where ϵ is the dielectric constant of the ground referred to air as unity, is the conductivity of the ground in electromagnetic units, c is the velocity of light in cm. per sec., is the wave-length in cm. and r is the distance in cm.