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The discusssion of this oversight and of the entire experiment forms the subject of a very searching analysis by H. A. Lorentz,* who finds that this effect can by no means be disregarded. In consequence, the quantity to be measured had in fact but one-half the value supposed, and as it was already barely beyond the limits of errors of experiment, the conclusion drawn from the result of the experiment might well be questioned; since, however, the main portion of the theory remains unquestioned, it was decided to repeat the experiment with such modifications as would insure a theoretical result much too large to be masked by experimental errors. The theory of the method may be briefly stated as follows:
Let sa, fig. 1, be a ray of light which is partly reflected in ah, and partly transmitted in a<?, being returned by the mirrors b and c, along ba and ca. ba is partly transmitted along ad,
and ca is partly reflected along ad. If then the paths ab and ac are equal, the two rays interfere along ad. Suppose now, the ether being at rest, that the whole apparatus moves in the direction sc, with the velocity of the earth in its orbit, the direc-
* De l’lnfluence du M.ouvement de la Terre sur lea Phen. Lum. Archives N6er-landaises, xxi, 2m® livr., 1886.
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.