Page:The principle of relativity (1920).djvu/22

 of ether by moving medium is possible. Thus Fresnelian convection compensation can have no possible application in this case. Yet some marvellous compensation has evidently taken place which has completely masked the "absolute" velocity of the earth.

In Michelson and Morley's experiment, the distance travelled by the beam along 0A[P3: OA or 0A?] (that is, in a direction parallel to the motion of the platform) is 2l β^2, while the distance travelled by the beam along 0B, perpendicular to the direction of motion of the platform, is 2lβ. Yet the most careful experiments showed, as Eddington says, "that both parts of the beam took the same time as tested by the interference bands produced. It would seem that 0A and 0B could not really have been of the same length; and if 0B was of length l, 0A must have been of length l/β. The apparatus was now rotated through 90°, so that 0B became the up-stream. The time for the two journeys was again the same, so that 0B must now be the shorter length. The plain meaning of the experiment is that both arms have a length l when placed along 0y (perpendicular to the direction of motion), and automatically contract to a length l/β, when placed along 0x (parallel to the direction of motion). This explanation was first given by Fitz-Gerald."

This Fitz-Gerald contraction, startling enough in itself, does not suffice. Assuming this contraction to be a real one, the distance travelled with respect to the ether is 2lβ and the time taken for this journey is 2lβ/c. But the distance travelled with respect to the platform is always 2l. Hence the velocity of light with respect to the platform is 2l/(2lβ/c) = c/β, a variable quantity depending on the "absolute" velocity of the platform. But no trace of such an effect has ever been found. The velocity of light is always found to be quite independent of the velocity