fluid would; and when, at the end of this interval, the earth is reduced to rest, the whole of the æther will be reduced to rest, except as regards an extremely small motion, of the same nature as that already considered in the case of an ordinary fluid. But in the present case this small motion will be propagated into space with the velocity of light; so that just before the commencement of the third interval the æther may be considered as at rest, and everything will be the same as before. Supposing now the number of intervals of time to be indefinitely increased, and their magnitude indefinitely diminished, we pass to the case in which the earth is supposed to move continuously.
It appears then, from these views of the constitution of the æther, that (a.) must be an exact differential, if it be not prevented from being so by the action of the air on the æther. We know too little about the mutual action of the æther and material particles to enable us to draw any very probable conclusion respecting this matter; I would merely hazard the following conjecture. Conceive a portion of the æther to be filled with a great number of solid bodies, placed at intervals, and suppose these bodies to move with a velocity which is very small compared with the velocity of light, then the motion of the æther between the bodies will still be such that (a.) is an exact differential. But if these bodies are sufficiently close and numerous, they must impress either the whole, or a considerable portion of their own velocity on the æther between them. Now the molecules of air may act the part of these solid bodies. It may thus come to pass that (a.) is an exact differential, and yet the æther close to the surface of the earth is at rest relatively to the earth. The latter of these conditions is however not necessary for the explanation of aberration.
There is one curious consequence of the theory contained in my paper of last July, which I did not at the time observe. On referring to this paper, it will be seen that if the motion of the æther is such that (a.) is an exact differential, the change in the direction of the normal to a wave of light, as the wave passes from a part of space where the disturbance of the æther due to the motion of the earth is insensible to another part where the disturbance is sensible, is given by the equation
which is what (6.) becomes when and are each put equal to zero; and the plane passing through the direction of the
