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The whole time of going and coming is
and the distance travelled in this time is
neglecting terms of the fourth order. The length of the other path is evidentlyor to the same degree
of accuracy, The difference is therefore
If now the whole apparatus be turned through 90°,
the difference will be in the opposite direction, hence the
displacement of the interference-fringes should be
Considering only the velocity of the earth in its orbit, this would be 2D × 10–8. If, as was the case in the first experiment, D = 2 × 106 waves of yellow light, the displacement to be expected would be 0. 04 of the distance between the interference-fringes.
In the first experiment, one of the principal difficulties encountered was that of revolving the apparatus without producing distortion; and another was its extreme sensitiveness to vibration. This was so great that it was impossible to see the interference-fringes except at brief intervals when working in the city, even at two o'clock in the morning. Finally, as before remarked, the quantity to be observed, namely, a displacement of something less than a twentieth of the distance between the interference-fringes, may have been too small to be detected when masked by experimental errors.
The first-named difficulties were entirely overcome by mounting the apparatus on a massive stone floating on mercury; and the second by increasing, by repeated reflexion, the path of the light to about ten times its former value.
The apparatus is represented in perspective in fig. 3, in plan in fig. 4, and in vertical section in fig. 5. The stone a (fig. 5) is about 1. 5 metre square and 0. 3 metre thick. It rests on an annular wooden float bb, 1. 5 metre outside diameter, 0. 7 metre inside diameter, and 0. 25 metre thick. The float rests on mercury contained in the cast-iron trough cc, 1. 5 centi-
metre thick, and of such dimensions as to leave a clearance of about one centimetre around the float. A pin d, guided by arms g g g g, fits into a socket e attached to the float. The pin may be pushed into the socket or be withdrawn, by a lever pivoted at f. This pin keeps the float concentric with the trough, but does not bear any part of the weight of the stone. The annular iron trough rests on a bed of cement on a low brick pier built in the form of a hollow octagon.
At each corner of the stone were placed four mirrors dd ee, fig. 4. Near the centre of the stone was a plane parallel glass b. These were so disposed that light from an argand burner a, passing through a lens, fell on b so as to be in part reflected to d/; the two pencils followed the paths indicated in the figure, bdedbf and bd/e/d/bf respectively, and were observed by the telescope f. Both f and a revolved with the stone. The mirrors were of speculum metal carefully worked to optically plane surfaces five centimetres in diameter, and the glasses b and c were plane parallel of the same thickness, 1. 25 centimetre; their surfaces measured 5.0 by 7.5 centimetres. The second of these was placed in the path of one of the pencils to compensate for the passage of the other through the same thickness of glass. The whole of the optical portion of the apparatus was kept covered with a wooden cover to prevent air-currents and rapid changes of temperature.
The adjustment was effected as follows: —The mirrors having been adjusted by screws in the castings which held the