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
uninfluenced by the motion of the earth. The method which I employ will, I hope, be found simpler than Fresnel’s; besides it applies easily to the most general case. Fresnel has not given the calculation for reflexion, but has merely stated the result; and with respect to refraction, he has only considered the case in which the course of the light within the refracting medium is in the direction of the earth’s motion. This might still leave some doubt on the mind, as to whether the result would be the same in the most general case.
If the aether were at rest, the direction of light would be that of a normal to the surfaces of the waves. When the motion of the aether is considered, it is most convenient to define the direction of light to be that of the line along which the same portion of a wave moves relatively to the earth. For this is in all cases the direction which is ultimately observed with a telescope furnished with cross wires. Hence, if A is any point in a wave of light, and if we draw AB normal to
the wave, and proportional to V oraccording as the light
is passing through vacuum or through a refracting medium, and if we draw BC in the direction of the motion of the aether,
and proportional to v or and join A C, this line will give
the direction of the ray.Of course, we might equally have drawn A D equal and parallel to B C and in the opposite direction, when D B would have given the direction of the ray.
Let a plane P be drawn perpendicular to the reflecting or refracting surface and to the waves of incident light, which in this investigation may be supposed plane. Let the velocity v of the aether in vacuum be resolved into p perpendicular to the plane P, and q in that plane; then the resolved parts of
the velocityof the aether within a refracting medium will
beLet us first consider the effect of the velocity p.
It is easy to see that, as far as regards this resolved part of the velocity of the aether, the directions of the refracted and reflected waves will be the same as if the aether were at rest. Let BAC (fig. 1) be the intersection of the refracting surface and the plane P; DAE a normal to the refracting surface; AF, AG, A H normals to the incident, reflected and refracted waves. Hence A F, A G, A H will be in the plane P, and ∠GAD = FAD, μ sin HAE = sin FAD.
Take AG = AF,