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II. On the Constitution of the Luminiferous Æther, viewed with reference to the phænomenon of the Aberration of Light. By G. G. Stokes, M.A., Fellow of Pembroke College, Cambridge^[1].

In a former communication to this Magazine (July 1845), I showed that the phænomenon of aberration might be explained on the undulatory theory of light, without making the startling supposition that the earth in its motion round the sun offers no resistance to the æther. It appeared that the phænomenon was fully accounted for, provided we supposed the motion of the æther such as to make

$udx+vdy+wdz$

(a.)

an exact differential, where $u,v,w$ are the resolved parts, along three rectangular axes, of the velocity of the particle of æther whose co-ordinates are $x,y,z$. It appeared moreover that it was necessary to make this supposition in order to account in this way for the phænomenon of aberration. I did not in that paper enter into any speculations as to the physical causes in consequence of which (a.) might be an exact differential. The object of the present communication is to consider this question.

The inquiry naturally divides itself into two parts: — First, In what manner does one portion of æther act on another beyond the limits of the earth's atmosphere? Secondly, What takes place in consequence of the mutual action of the air and the æther?

In order to separate these two questions, let us first conceive the earth to be destitute of an atmosphere. Before considering the motion of the earth and the æther, let us take the case of a solid moving in an ordinary incompressible fluid, which may be supposed to be infinitely extended in all directions about the solid. If we suppose the solid and fluid to be at first at rest, and the solid to be then moved in any manner, it follows from the three first integrals of the ordinary equations of fluid motion, obtained by M. Cauchy, that the motion of the fluid at any time will be such that (a.) is an exact differential. From this it may be easily proved, that if at any instant the solid be reduced to rest, the whole of the fluid will be reduced to rest likewise; and that the motion of the fluid is the same as it would have been if the solid had received by direct impact the motion which it has at that instant. Practically however the motion of the fluid after some time would differ widely from what would be thus obtained, at least if the

1. Communicated by the Author.