Since its publication in 1882, Rayleigh's work on electrically charged conducting drops has been widely quoted, but its rigorous derivation has not been given in the literature. By means of the domain perturbation technique, this work presents a rigorous derivation of Rayleigh's results, following his approach with Lagrange's equation. With the systematic procedure, it becomes explicit that the first-order surface deformations result in a deviation of the drop surface potential of only

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... der significance. Besides providing mathematical details, this work also reveals an apparent error in Rayleigh's original result for two-dimensional (cylindrical) drops. Introduction. An electrically charged conducting drop is subjected to two opposing forces at its surface. One comes from the uniform surface tension, which tends to maintain the drop shape spherical or, in other words, to keep the surface area minimum for a given amount of liquid mass. The other force results from electrical repulsion from the charge, which tends to tear the drop apart. As the amount of charge increases to a critical value, the drop becomes unstable and disruption of the surface ensues. This phenomenon was first investigated in 1882 by Lord Rayleigh [1], who derived the characteristic frequencies of charged drop oscillations for both three-dimensional (spherical) and two-dimensional (cylindrical) configurations and established the amount of charge necessary to induce disruption of the drop surface. Like many of his works, Rayleigh's results for charged drops have been widely quoted in the literature and have found many important applications. Although the physical phenomena associated with such charged drops are generally regarded as well known, serious students as well as researchers were often frustrated by the overabundance of omitted steps in Rayleigh's original work. To alleviate this awkward situation, Hendricks and Schneider [2] provided a detailed derivation for a nearly spherical drop in 1963. Although their final results are correct, their derivation was not presented in a rigorous mathematical fashion with clear tracking of terms