Page:MillerTheory.djvu/2

 He develops expressions for angles of reflexion, for wave-length after reflexion, and for the conditions which determine the network of parallelograms formed by the two systems of wave-fronts. The diagonals of these parallelograms are alternately lines of maximum and minimum disturbance in the æther, so that they define the interference phenomena. These expressions are not only rigorous, but also general, applying to any adjustment whatever of the optical parts of the apparatus, and form a welcome contribution to the thorough understanding of the theory of the Michelson and Morley experiment.

In one passage he says that a term added by him "may entirely modify the nature of the changes produced as the direction of the drift alters"; and some appear to think that the inference from the earlier experiment is involved in doubt by this discussion. It is therefore well to examine again the theory.

Let D, Pl. IX. fig. 1, be a plane-parallel glass plate, silvered so thinly that equal quantities of light are transmitted and reflected. S being a source of light, part of the light passes through D, moves on to the plane mirror II, where it is reflected back to D; here, part is transmitted and lost, part is reflected to the observer at T. The other part of the entering light is reflected at the first surface of D, reflected again by the mirror I, is in part reflected by D, and lost, in part transmitted through D, and proceeds towards T. If distances and angles are suitable, the reunited rays between D and T will produce interference phenomena. If distances are equal, we may obtain interference phenomena in white light. In one of the usual adjustments of distances and angles, parallel fringes are seen when the eye or the telescope is made to give distinct vision of one of the mirrors I or II. The fringes apparently coincide with these surfaces. A central fringe is black; on either side are coloured fringes, less and less distinct till they fade away into uniform illumination. If the path of either ray is shortened, the fringes move rapidly to one side. If we engrave a scale on I or II, we can, after any alteration of one of the paths, restore with great accuracy and ease the former relations by bringing the central dark fringe to its original place on this scale. If the motion of the earth through the æther were the cause of this change of path, we could measure the amount of change by measuring the displacement.

Suppose, fig. 2, that the apparatus moves in the direction of the arrow through the stationary æther. While the ray of light moves from D to I and returns to D, the mirror D