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of density within the medium proportional to the square of its index and being convected in proportion to this excess of density, which would give an apparent velocity to the ether of $\left(1-\mu ^{-2}\right)\nu$, instead of the velocity of the earth. Stokes suggested, as a simpler idea, that we suppose the ether is not convected but passes freely through the earth, being condensed as it passes into a body in the ratio of 1 to μ² , so that its velocity within the refracting medium becomes $\left(1-\mu ^{-2}\right)\nu$, from the law of continuity.^[1]

Babinet in the second-century period attempted to test Fresnel's theory by examining the interference of two rays traversing a piece of glass, the one in the direction of the earth's motion and the other in the opposite direction. Stokes showed that a negative result was not contrary to the theory of aberration, since the retardation would be the same as if the earth were at rest.

He showed further, what Fresnel had not proven to be true in general, that on Fresnel's theory the laws of reflection and refraction for single refracting media are uninfluenced by the motion of the earth. In fact, Rayleigh has shown that, in using terrestrial sources, no optical effect can be produced by any system of reflecting or refracting optical surfaces moving as a rigidly connected system relatively to the ether, if we take into account the Doppler "effect," and neglect quantities of the second order of the aberration. Since, as Stokes says, the theory of a quiescent ether may be dispensed with, and as there is no good evidence that the ether moves quite freely through the solid mass of the earth, he proposes to explain the phenomenon of aberration on the undulation theory of light, upon the supposition that the earth and the planets carry a portion of the ether along with them, so that the ether close to their surfaces is at rest relatively to those surfaces and diminishes in velocity till at no great distance in space there is no motion. Cauchy had previously discussed the theory of a mobile ether, and had proposed to explain aberration by a shearing of the wave-fronts due to the translatory motion of the medium, but he did not develop his method sufficiently to explain how much the aberration would be.

On the other hand Stokes has specifically indicated his assumptions and formulated his conclusions. He examines the displacements of a wave-front in its passage from the ether at rest, across the region of transition to the ether in the neighborhood of the observer, which is at rest relatively to him. Adopting the same method which is used in the case of an ether at rest in determining the wave-front at any future time from that of a given one at any instant, he shows,

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1. If x is the velocity of the ether relative to the moving matter, and the density of ether within it is μ², the density of free ether being unity, we have from the law of continuity $\nu =(\nu -x)\mu ^{2}$ and hence,

   $x{\frac {\nu \mu ^{2}-\nu }{\mu ^{2}}}=(1+\mu ^{-2})\nu$