The Electrical Oscillations of a Prolate Spheroid. Paper I

Differential equation. Solutions in spheroidal coordinates of the differential equation of the electromagnetic field are obtained which are valid all the way from the surface of a prolate spheroid of eccentricity unity to infinity. Free oscillations. The wave-length $\lambda$ and logarithmic decrement $\delta$ of the fundamental free oscillations are computed for all eccentricities. Forced oscillations. The wave-length $\lambda$, current $I$, and phase $\phi$ at resonance are computed for six eccentricities near unity for an antenna stimulated by a uniform field varying sinusoidally with the time. Three resonance curves are computed, the radiation resistance at resonance is calculated for six eccentricities and off resonance for two. Expressions for the entire field at all points are given, and reduced to explicit form for the radiation field. An expression is obtained for the mean rate of radiation.