Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/432

 when transmitting light: the orientation of the wave-fronts of the light will consequently in general be altered; and the direction in which a heavenly body is seen, being normal to the wavefronts will thereby be allected. But if the aethereal motion is irrotational, so that the elements of the aether do not rotate, it is easily seen that the direction of propagation of the light in space is unaffected; the luminous disturbance is still propagated in straight lines from the star, while the normal to the wave-front at any point deviates from this line of propagation by the small angle, where denotes the component of the aethereal velocity at the point, resolved at right angles to the line of propagation, and  denotes the velocity of light. If it be supposed that the aether near the earth is at rest relatively to the earth's surface, the star will appear to be displaced towards the direction in which the earth is moving, through an angle measured by the ratio of the velocity of the earth to the velocity of light, multiplied by the sine of the angle between the direction of the earth's motion and the line joining the earth and star. This is precisely the law of aberration.

An objection to Stokes's theory has been pointed out by several writers, amongst others by H. A. Lorentz. This is, that the irrotational motion of an incompressible fluid is completely determinate when the normal component of the velocity at its boundary is given: so that if the aether were supposed to have the same normal component of velocity as the earth, it would not have the same tangential component of velocity. It follows that no motion will in general exist which satisfies Stokes's conditions; and the difficulty is not solved in any very satisfactory fashion by either of the suggestions which, have been proposed to meet it. One of those is to suppose that the moving earth does generate a rotational disturbance, which, however, being radiated away with the velocity of light, does not affect the steadier irrotational motion; the other, which was