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 moves to the new position D2. The angle of reflexion from D is no longer equal to the angle of incidence. The ray moving from D towards II finds the latter in the position II2, returns to D2, and is reflected from D2 nearly in the same direction with the ray from I. In four azimuths of the apparatus the coincidence is exact; for all others, the ray I and the ray II are inclined at a small angle which, at its maximum, is numerically equal to $$v^2 /\mathrm{V}^2$$, v and V being the velocities of the apparatus and of light. Since the angle, the total aberration, cannot be observed, being annulled by the motion of the observing telescope at T, we can hope to detect merely this aberration of the second degree, namely, the small angle between the emergent rays I and II.

With the adjustments just supposed, there are four methods of measuring interference phenomena which in turn measure the angle sought. We may use a micrometer in the telescope, or a scale engraved on I or on II; we may use mechanical compensation to return a displaced fringe to its marked position, or we may use optical compensation.

In another adjustment the fringes are made infinitely broad. We are then limited to the last pair of methods. This pair, especially the last method, is capable of very great precision. When Michelson and Morley set up the first apparatus in which they utilized this method, the mean error of a setting, in which the observer did not himself see the reading, was less than the two-hundredth part of a wave-length. Since the theory of the apparatus in this special case is simpler, the discussion will assume this adjustment.

Accordingly, let the angles I B D, II B D, fig. 3 (PI. IX.), be equal to each other and to 45°. Let the three planes intersect in a common point B. For brevity, imagine that the mirrors themselves are produced so as to intersect in this point. Assume that the system is moving through the æther in a direction making an angle of 67½° with the direction of the light entering the telescope, as indicated in fig. 2. The velocities of the apparatus and of light being denoted by v, V, assume that $$v/\mathrm{V}\ =\ 1/5$$.

A certain wave-front enters the apparatus, making with II an angle which is to be specified. If some given ray enters the apparatus so as to pass axially through the telescope, rays making an angle of 5 minutes on either side of it will pass through our actual apparatus. Almost any ray, wisely selected, may be used to determine what we desire to know about the whole pencil. For instance, we might select the ray which, after reflexion from II, shall