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Theory of the Aberration of Light. On substituting these values in equations (A), and observing that in the terms multiplied by $$q$$ we may put $$\phi_{'}=\phi,\ \mu\sin\phi'=\sin\phi$$, the small terms destroy each other, and we have $$\sin\phi_{'}=\sin\phi,\ \mu\sin\phi'=\sin\phi$$. Hence the laws of reflexion and refraction at the surface of a refracting medium will not be affected by the motion of the æther.

In the preceding investigation it has been supposed that the refraction is out of vacuum into a refracting medium. But the result is the same in the general case of refraction out of one medium into another, and reflexion at the common surface. For all the preceding reasoning applies to this case if we merely substitute $$\tfrac{p}{\mu'^{2}},\tfrac{q}{\mu'^{2}}$$ for $$p,q,\tfrac{V}{\mu'}$$ for $$V$$, and $$\tfrac{\mu}{\mu'}$$ for $$\mu$$, $$\mu'$$ being the refractive index of the first medium. Of course refraction out of a medium into vacuum is included as a particular case.

It follows from the theory just explained, that the light coming from any star will behave in all cases of reflexion and ordinary refraction precisely as it would if the star were situated in the place which it appears to occupy in consequence of aberration, and the earth were at rest. It is, of course, immaterial whether the star is observed with an ordinary telescope, or with a telescope having its tube filled with fluid. It follows also that terrestrial objects are referred to their true places. All these results would follow immediately from the theory of aberration which I proposed in the July number of this Magazine; nor have I been able to obtain any result, admitting of being compared with experiment, which would be different according to which theory we adopted. This affords a curious instance of two totally different theories running parallel to each other in the explanation of phænomena. I do not suppose that many would be disposed to maintain Fresnel's theory, when it is shown that it may be dispensed with, inasmuch as we would not be disposed to believe, without good evidence, that the æther moved quite freely through the solid mass of the earth. Still it would have been satisfactory, if it had been possible, to have put the two theories to the test of some decisive experiment.