Rayleigh's electrified water drops

Abstract

Theoretical investigations into the stability of electrified liquid drops take as their starting point a result due to Rayleigh. It was felt that this result is important enough to warrant a more complete derivation than that originally given by Rayleigh in the reference which is usually quoted. A literature search revealed a second paper of Rayleigh's which is never quoted, but which contains important steps, not given elsewhere, towards his original calculation. Even when both papers are taken together, however, the calculation still seems incomplete. For this reason the entire calculation is presented using a modern formalism which in particular recognises the effects of electrostriction. To complement this the complete calculation as originally conceived by Rayleigh is presented in an appendix.