Fizeau tested that straightforward consequence of this theory which is known as Fresnel's Law, and ascertained by experiment that a beam of light was accelerated or retarded by a stream of water, according as it travelled with or against the stream. And he found the magnitude of the effect precisely in accordance with the ratio of the locomotive portion of the ether to the whole,—the fraction (μ²−1)/μ² of the speed of the water being added to or subtracted from the velocity of light, when a beam was sent down or up the stream.
But even if another mode of expression be adopted, the result to be anticipated from this experiment would be the same.
For instead of saying that a modified portion of the ether is moving with the full velocity of the body while the rest is stationary, it is permissible for some purposes to treat the whole internal ether as moving with a fraction of the velocity of the body.
On this method of statement the ether outside a moving body is still absolutely stationary, but, as the body advances, ether may be thought of as continually condensing in front, and, as it were, evaporating behind; while, inside, it is streaming through the body in its condensed condition at a pace such that what is equivalent to the normal quantity of ether in space may remain absolutely stationary. To this end its speed backwards relative to the body must be u/μ² and accordingly its speed forward in space must be u(1 − 1/μ²).
For consider a slab of matter moving flatways with velocity u; let its internal etherial density be μ², and let the external ether of density 1 be stationary. Let the forward speed of the internal ether through space be xu, so that a beam of light therein would be hurried forward with this velocity. Then consider two imaginary parallel planes moving with the slab, one in advance of it and the other inside it, and express the fact that the amount of ether between those two planes must continue constant. The amount streaming relatively backwards through the first plane as it moves will be measured by u times the external density, while the amount similarly streaming backwards through the second plane will be (u − xu) times the internal density. But this latter amount must equal the former amount. In other words,
u × 1 must equal (u − xu) × μ².
Consequently x comes out x = (μ² − 1) / μ²; which is Fresnel's incontrovertible law for the convective effect of moving transparent matter on light inside it.
The whole subject, however, may be treated more generally, and for every direction of the ray, on the lines of Chapter [X], thus:—
Inside a transparent body light travels at a speed V/μ; and the ether, which outside drifts at velocity v, making an angle θ with the ray, inside may be drifting with velocity v´ and angle θ´.
Hence the equation to a ray inside such matter is