star as freed from aberration, or to its apparent direction as affected ly aberration? The question whether rays coming from the stars are refracted differently from rays originating in terrestrial sources had been raised originally by Michell[1]; and Robison and Wilson[2] had asserted that the focal length of an achromatic telescope should be increased when it is directed to a star towards which the earth is moving, owing to the change in the relative velocity of light. Arago[3] submitted the matter to the test of experiment, and concluded that the light coming from any star behaves in all cases of reflexion and 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; so that the apparent refraction in a moving prism is equal to the absolute refraction in a fixed prism. Fresnel now set out to provide a theory capable of explaining Arago's result. To this end he adopted Young's suggestion, that the refractive powers of transparent bodies depend on the concentration of aether within them; and made it more precise by assuming that the aethereal density in any body is proportional to the square of the refractive index, Thus, if c denote the velocity of light in vacuo, and if c1 denote its velocity in a given material body at rest, so that μ = c/σ1 is the refractive index, then the densities ρ and ρ1 of the aether in interplanetary space and in the body respectively will be connected by the relation
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Fresnel further assumed that, when a body is in motion, part of the aether within it is carried along-namely, that part which constitutes the excess of its density over the density of aether in vacuo; while the rest of the aether within the space occupied by the body is stationary. Thus the density of aether carried
