XVII. On Fresnel's Theory of the Aberration of Light, By G. G. Stokes, M.A., Fellow of Pembroke College, Cambridge *.
THE 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 aether within them, the elastic force being the same as without, the density which it is necessary to suppose the aether within a medium of refractive index μ to have is μ2, the density in vacuum being taken for unity. Fresnel supposes that the earth passes through the aether without disturbing it, the aether penetrating the earth quite freely. He supposes that a refracting medium moving with the earth carries with it a quantity of aether, of density μ2 − 1, which constitutes the excess of density of the aether within it over the density of the aether in vacuum. He supposes that light is propagated through this aether, 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 velocityv 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 aether within the earth to move together, the aether 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 aether 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, givesfor the velocity of the aether
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 aether 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 aether. On this supposition the earth will be at rest; the aether outside it will be moving with a velocity v, and the aether in a refracting medium with a velocity * Communicated by the Author.
in a direction contrary to that of the earth’s real motion.
On account of the smallness of the coefficient of aberration, we may also neglect the square of the ratio of the earth’s velocity to that of light; and if we resolve the earth’s velocity in different directions, we may consider the effect of each resolved part separately.
In the ninth volume of the Comptes Rendus of the Academy of Sciences, p. 774, there is a short notice of a memoir by M. Babinet, giving an account of an experiment which seemed to present a difficulty in its explanation. M. Babinet found that when two pieces of glass of equal thickness were placed across two streams of light which interfered and exhibited fringes, in such a manner that one piece was traversed by the light in the direction of the earth’s motion, and the other in the contrary direction, the fringes were not in the least displaced. This result, as M. Babinet asserts, is contrary to the theory of aberration contained in a memoir read by him before the Academy in 1829, as well as to the other received theories on the subject. I have not been able to meet with this memoir, but it is easy to show that the result of M. Babinet’s experiment is in perfect accordance with Fresnel’s theory.
Let T be the thickness of one of the glass plates, V the velocity of propagation of light in vacuum, supposing the aether
at rest. Thenwould be the velocity with which light would
traverse the glass if the aether were at rest; but the aether
moving with a velocitythe light traverses the glass with a
velocityand therefore in a time
But if the glass were away, the light, travelling with a velocity V ± v would pass over the space T in the time
Hence the retardation, expressed in time,the
same as if the earth were at rest. But in this case no effect would be produced on the fringes, and therefore none will be produced in the actual case.
I shall now show that, according to Fresnel’s theory, the laws of reflexion and refraction in singly refracting media are