On Tubes of Force in a special class of electromagnetic fields

Extract

Professor Whittaker, in a paper entitled “On Tubes of Electromagnetic Force” {see Proceedings of the Royal Society of Edinburgh, Vol. XLII., Part I. (No 1)}, introduces certain surfaces, which he names calamoids, in connection with an electromagnetic field in the four-dimensional world of space-time. The calamoids consist of “a convariant family of surfaces which when the field is purely electrostatic or purely magnetostatic reduce to the ordinary Faraday tubes of force.” Professor Whittaker, in the paper referred to, also introduces two sets of surfaces, each a covariant family of ∞² surfaces, one of them named the electropotential surfaces, and the other family the magnetopotential surfaces of the electromagnetic field. The electropotential surfaces and the magnetopotential surfaces are shown to be everywhere absolutely orthogonal. (One member of each family meeting at a point, any line from this point in the one family is orthogonal to every line through the point in the other family). Moreover, a “calamoid, at every one of its points, is half-parallel and half-orthogonal to the electropotential surface which passes through the point, and is also half-parallel and half-orthogonal to the magnetopotential surface which passes through the point.”