length l, OA being placed up-stream. Let c be the velocity of light. The time for the double journey along OA and back is
t_{1} = l/(c - u) + l/(c + u) = 2lc/(c^2 - u^2) = (2l/c)β^2
where β = (1 - u^2/c^2)^{-1/2}. a factor greater than unity.
For the transverse journey the light must have a component velocity n up-stream (relative to the ether) in order to avoid being carried below OB: and since its total velocity is c, its component across-stream must be [sqrt](c^2 - u^2), the time for the double journey OB is accordingly
t_{2} = (2a/[sqrt](c^2 - u^2)) = (2a/c)β, so that t_{1} > t_{2}.
But when the experiment was tried, it was found that both parts of the beam took the same time, as tested by the interference bands produced."
After a most careful series of observations, Michelson and Morley failed to detect the slightest trace of any effect due to earth's motion through ether.
The Michelson-Morley experiment seems to show that there is no relative motion of ether and matter. Fresnel's stagnant ether requires a relative velocity of—u. Thus Michelson and Morley themselves thought at first that their experiment confirmed Stokes' viscous ether, in which no relative motion can ensue on account of the absence of slipping of ether at the surface of separation. But even on Stokes' theory this viscous flow of ether would fall off at a very rapid rate as we recede from the surface of separation. Michelson and Morley repeated their experiment at different heights from the surface of the earth, but invariably obtained the same negative results, thus failing to confirm Stokes' theory of viscous flow.
