Page:Philosophical Transactions of the Royal Society A - Volume 184.djvu/829

is meant by "moving medium" seems necessary before we can adequately test the question whether electromagnetic waves in It move with it or lag behind.

I suppose that it must be desirable to examine substances other than water, especially those with a much higher refractive index. I hope to do this, though it may be noted that the value of $n$ which would make Fresnel's and Thomson's theories exactly agree, is $1\cdot 4142$, and that the available range of refractive indices of liquids and solids affords but a narrow margin for discrimination between the two hypotheses.

The balance of evidence is at present strongly in favour of Fresnel's hypothesis, and I propose ordinarily to assume its truth. I cannot, indeed, understand the possibility of Thomson's theory, though I detect no flaw in his work, for it seems to require a distinction between the case of source or receiver moving through a medium, and the case of medium flowing past source or receiver; that is, it seems to demand a knowledge of absolute velocity.

Fresnel's Law.

7. The statement of Fresnel's law can be thrown almost into the form of hypothesis (b), § 3, and at the same time its apparent licence of language about "free" and "bound" ether can be lessened, by supposing that the "modification" induced by the encroachment of matter on the ether is really a condensation, in the ratio $1:n^{2}$; no motion in the ether other than what is necessarily involved in that act being postulated. On this method of statement the ether outside a moving body is absolutely stationary, but, as the body advances, ether is 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 relatively to the body must be $v/n^{2}$, and accordingly its speed in space must be $v\left(1-1/n^{2}\right)$.

Thus, instead of saying that a portion of the ether is moving with the full velocity of the body while the rest is stationary, it is probably preferable to say that the whole internal ether is moving with a fraction of the velocity of the body.

One or other form of statement is absolutely involved in the Fresnellian idea of increased ethereal density, as may be rigorously shown (vide Lord Rayleigh, 'Nature' March, 1892; vide also Eisenlohr), thus:—

Consider a slab moving forward flatways with velocity $v$, let its internal ethereal density be $n^{2}$, and let the external ether, of density 1, be stationary. Let the speed of the internal ether through space be $xv$, and consider that the amount of ether enclosed between two planes moving with the slab, one outside and one inside, must be constant; it follows at once that

$v=n^{2}\left(v-xv\right)$