The Electrical Oscillations of a Perfectly Conducting Prolate Spheroid

The forced oscillations of a perfectly‐conducting prolate spheroid of eccentricity nearly unity are shown to be decomposable into ``harmonics'' corresponding to different modes of vibration, each harmonic being quantitatively connected with a certain portion of the impressed electric field which drives the antenna. The harmonics contribute additively to the current and field of the spheroid; each offers a characteristic impedance to the driving field, and the properties of the antenna are a composite depending upon the proportions of the various harmonics present. The behavior of the harmonics with frequency is discussed qualitatatively; analytical expressions obtained are useful chiefly at the resonant frequencies of the antenna, where the most important harmonic becomes sinusoidal in character.