Irrotational Motion in General.-Liquid originally at rest in a singly-connected space cannot be set in motion by a field of force due to a single-valued potential function; any motion set up in the liquid must be due to a movement of the boundary, and the motion will be irrotational; for any small spherical element of the liquid may be considered a smooth solid sphere for a moment, and the normal pressure of the surrounding liquid cannot impart to it any rotation.
If this relation is true along all paths, the velocity of the aether must be of irrotational type, like that of frictionless fluid.
Moreover, this is precisely the condition for the absence of interference between the component of a split beam; because, the time of passage being to the first order fds/V f(udx+vdy+wdz)V2, the second term will then be independent of the path (43 being a single valued function) and therefore the same for the paths of both the interfering beams. If therefore the aether can be put into motion, we conclude (with Stokes) that such motion, in free space, must be of strictly irrotational type.
But the aether at a great distance must in any case be at rest; while the facts of astronomical aberration require that the motion of that medium must be irrotational.