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[76] XVII. On Fresnel's Theory of the Aberration of Light. By, M.A., Fellow of Pembroke College, Cambridge.

HE theory of the aberration of light, and of the absence of any influence of the motion of the earth on the laws of refraction, &c., given by Fresnel in the ninth volume of the Annales de Chimie, p. 57, is really very remarkable. If we suppose the diminished velocity of propagation of light within refracting media to arise solely from the greater density of the æther within them, the elastic force being the same as without, the density which it is necessary to suppose the æther within a medium of refractive index $$\mu$$ to have is $$\mu^2$$, the density in vacuum being taken for unity. Fresnel supposes that the earth passes through the æther without disturbing it, the æther penetrating the earth quite freely. He supposes that a refracting medium moving with the earth carries with it a quantity of æther, of density $$\mu^{2}-1$$, which constitutes the excess of density of the æther within it over the density of the æther in vacuum. He supposes that light is propagated through this æther, of which part is moving with the earth, and part is at rest in space, as it would be if the whole were moving with the velocity of the centre of gravity of any portion of it, that is, with a velocity $$\left(1-\tfrac{1}{\mu^{2}}\right)v$$, $$v$$ being the velocity of the earth. It may be observed however that the result would be the same if we supposed the whole of the æther within the earth to move together, the æther entering the earth in front, and being immediately condensed, and issuing from it behind, where it is immediately rarefied, undergoing likewise sudden condensation or rarefaction in passing from one refracting medium to another. On this supposition, the evident condition that a mass $$v$$ of the æther must pass in a unit of time across a plane of area unity, drawn anywhere within the earth in a direction perpendicular to that of the earth's motion, gives $$\left(1-\tfrac{1}{\mu^{2}}\right)v$$ for the velocity of the æther within a refracting medium. As this idea is rather simpler than Fresnel's, I shall adopt it in considering his theory. Also, instead of considering the earth as in motion and the æther outside it as at rest, it will be simpler to conceive a velocity equal and opposite to that of the earth impressed both on the earth and on the æther. On this supposition the earth will be at rest; the æther outside it will be moving with a velocity $$v$$, and the æther in a refracting medium with a velocity