The extended Rayleigh theory of the oscillation of liquid droplets

The Rayleigh theory of oscillation of liquid drops has been extended to include the case in which the drop is immersed in a uniform electric field. The resonant frequencies of the modes of the drop are shown to be shifted by the electric field. The magnitude and the direction of the shift are dependent on the dielectric constant of the drop. The condition for instability of drops in large electric fields is given and found to differ from that found by previous workers. This difference is attributed to the assumptions by previous workers that the drops, under the influence of an electric field, distorted into ellipsoids of revolution about the field direction. The dynamical equations are derived, and the solution for small oscillation is given.