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 motion of the solid be progressive and not oscillatory. This appears to be due to two causes; first, the motion considered would probably be unstable in the part of the fluid behind the solid; and secondly, a tangential force is called into play by the sliding of one portion of fluid along another; and this force is altogether neglected in the common equations of hydrodynamics, from which equations the motion considered is deduced. If, instead of supposing the solid to move continueously, we supposed it first to be in motion for a very small interval of time, then to be at rest for another equal interval, then to be in motion for a third interval equal to the former, and so on alternately, theoretically the fluid ought to be at rest at the expiration of the first, third, &c. intervals, but practically a very slight motion would remain at the end of the first interval, would last through the second and third, and would be combined with a slight motion of the same kind, which would have been left at the end of the third interval, even if the fluid immediately before the commencement of it had been at rest; and the accumulation of these small motions would soon become sensible.

Let us now return to the æther. We know that the transversal vibrations constituting light are propagated with a velocity about 10,000 times as great as the velocity of the earth; and Mr. Green has shown that the velocity of propagation of normal vibrations is in all probability incomparably greater than that of transversal vibrations (Cambridge Philosophical Transactions, vol. vii. p. 2). Consequently, in considering the motion of the æther due to the motion of the earth, we may regard the æther as perfectly incompressible. To explain dynamically the phænomena of light, it seems necessary to suppose the motion of the æther subject to the same laws as the motion of an elastic solid. If the views which I have explained at the end of a paper On the Friction of Fluids, &c. (Cambridge Philosophical Transactions, vol. viii. part 3) be correct, it is only for extremely small vibratory motions that this is the case, while if the motion be progressive, or not very small, the æther will behave like an ordinary fluid. According to these views, therefore, the earth will set the æther in motion in the same way as a solid would set an ordinary incompressible fluid in motion.

Instead of supposing the earth to move continuously, let us first suppose it to move discontinuously, in the same manner as the solid considered above, the æther being at rest just before the commencement of the first small interval of time. By what precedes, the æther will move during the first interval in the same, or nearly the same, manner as an incompressible