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tions and distances traversed by the rays will be altered thus:— The ray sa is reflected along ab, fig. 2; the angle bab/ being equal to the aberration =a, is returned along ban (aba, =2a), and goes to the focus of the telescope, whose direction is unaltered. The transmitted ray goes along ac, is returned along ca/} and is reflected at an making cap equal 90—-a, and therefore still coinciding with the first ray. It may be remarked that the rays ba, and can do not now meet exactly in the same point an though the difference is of the second order; this does not affect the validity of the reasoning. Let it now be required to find the difference in the two paths aban and acar Let Y= velocity of light.
v—velocity of the earth in its orbit.
D=distance ab or ac, fig. 1.
T=time light occupies to pass from a to c.
T7=time light occupies to return from c to an (fig. 2.)
Then T=^^-, T==r—. The whole time of going and com* V-vJ ' V+ v G °
ing is T+T,=2D anc^ the distance traveled in this time
Y3 / v\
is 2Dya 2D/ 1 + yA neglecting terms of the fourth order.
The length of the other path is evidently 2Dy^ or to the
same degree of accuracy, 2D^l+^^j. The difference is thereto3
fore D^. If now the whole apparatus be turned through 90°,
the difference will be in the opposite direction, hence the dis-
placement of the interference fringes should be 2D^. Considering only the velocity of the earth in its orbit, this would be 2DxlO"8. If, as was the case in the first experiment, D = 2xl08 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 reflection, 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 meter square and 0*3 meter thick. It rests on an annular wooden float bb, 1*5 meter outside diameter, 0*7 meter inside diameter, and 0*25 meter thick. The float rests on mercury contained in the cast-iron trough cc, 1*5 centimeter thick, and of such dimensions as to leave a clearance of about one centimeter around the float. A pin d, guided by arms gggg, fits into a socket e attached to the float. Th$ pin may be pushed into the socket or be withdrawn, by a lever pivoted at / 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 center 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 partr reflected to d,\ the two pencils followed the paths indicated in the figure, bdedbf and bdfitdpf respectively, and were observed by the telescope /. Both / and a revolved witfi the stone. The mirrors were of speculum metal carefully worked to optically plane surfaces five centimeters in diameter, and the glasses b and c were plane-parallel and of the same thickness, 1*25 centimeter;