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Theory of the Aberration of Light.

${\tfrac {v}{\mu ^{2}}}$, 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 æther at rest. Then ${\tfrac {V}{\mu }}$ would be the velocity with which light would traverse the glass if the æther were at rest; but the æther moving with a velocity ${\tfrac {v}{\mu ^{2}}}$, the light traverses the glass with a velocity ${\tfrac {V}{\mu }}\pm {\tfrac {v}{\mu ^{2}}}$, and therefore in a time

$T\div \left({\frac {V}{\mu }}\pm {\frac {v}{\mu ^{2}}}\right)={\frac {\mu T}{V}}\left(1\pm {\frac {v}{\mu V}}\right)$

But if the glass were away, the light, travelling with a velocity $V\pm v$, would pass over the space $T$ in the time

$T\div (V\pm v)={\frac {T}{V}}\left(1\pm {\frac {v}{V}}\right)$

Hence the retardation, expressed in time, $=(\mu -1){\tfrac {T}{V}}$, 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