XII. On Stokes’s current function

Abstract

In Maxwell’s ‘Electricity and Magnetism’ a view is put forward, in accordance with which we may regard any irrotational motion in a perfect liquid, for which the velocity potential is a solid zonal harmonic, as due to the juxtaposition at the origin, and upon the axis of symmetry, of sinks and sources. But, in a liquid, any irrotational motion which is symmetrical with respect to an axis gives a velocity potential which may be expressed as a sum of a series of solid zonal harmonics, their common axis being the axis of symmetry, and their origin arbitrary, provided it is excluded from the region to which the expressions apply. The position of the origin upon the axis is arbitrary, since, by a transference formula, we may pass from one origin to another.