Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/137

along is (ρ₁-ρ) or (μ² - 1)ρ, while a quantity of aether of density ρ remains at rest. The velocity with which the centre of gravity of the aether within the body moves forward in the direction of propagation is therefore

${\frac {\mu ^{2}-1}{\mu ^{2}}}\omega$

where ω denotes the component of the velocity of the body in this direction. This is to be added to the velocity of propagation of the light-waves within the body, so that in the moving body the absolute velocity of light is

$c_{1}+{\frac {\mu ^{2}-1}{\mu ^{2}}}\omega$

Many years afterwards Stokes^[1] put the same supposition in a slightly different form. Suppose the whole of the aether within the body to move together, the aether entering the body in front, and being immediately condensed, and issuing from it behind, where it is immediately rarefied. On this assumption a mass ρω of aether must pass in unit time across a plane of area unity, drawn anywhere within the body in a direction at right angles to the body's motion; and therefore the aether within the body has a drift-velocity - ω_ρ/ρ₁, relative to the body: sa the velocity of light relative to the body will be c₁ - ω_ρ/ρ₁, and the absolute velocity of light in the moving body will be

$c_{1}+\omega -{\frac {\omega _{\rho }}{\rho _{1}}}$

or$c_{1}+{\frac {\mu ^{2}-1}{\mu ^{2}}}\omega$,      as before.

This formula was experimentally confirmed in 1851 by H. Fizeau^[2] who measured the displacement of interference fringes formed by light which had passed through a column of moving water.

1. Phil. Mag. xxviii (1846) p. 76.
2. Annales de Chimie, lvii (1859), p. 385. Algo by A. A. Michelson and E. W. Morley, Am. Journ. Science, xxxi (1886), p. 377.