It will be shown that a vortex element has the following image system in a rigid sphere immersed in incompressible fluid: (i) A transverse vortex element at the inverse point, equal in strength to minus the transverse resultant of the given vortex element, divided by the ratio of its distance from the centre to the radius of the sphere. (ii) A radial vortex element at the inverse point, equal in strength to plus the radial resultant of the given vortex element, divided by the same ratio. (iii) A uniform line vortex stretching from the inverse point to the centre of the sphere, equal and opposite in total strength to the radial vortex element at the inverse point.
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M. J. Lighthill (1956) studied this question.