Propagation of Radio Waves over a Plane Earth

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 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.