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the effect of the motion of the earth through the aether on the path of the ray at right angles to this motion was overlooked*. The discussion 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 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 ab, and partly transmitted in ac, 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 aether being at rest, that the whole apparatus moves in the direction sc, with the velocity of the earth in its orbit, the directions and distances traversed by the rays will be altered thus: —The ray sa is reflected along ab, fig. 2;
* It may be mentioned here that the error was pointed out to the author of the former paper by M. A. Potier, of Paris, in the winter of 1881.
† “De l'lnfluence du Mouvement do la Terre sur les Phen. Lum. ”
Archives Néerlandaiscs. xxi. 2me livr. (1886).
2 H 2
the angle bab/ being equal to the aberration = α, is returned along ba/, (aba/=2α), 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 a/ making ca/e equal 90 – α, and therefore still coinciding with the first
ray. It may be remarked that the rays ba/ and ca/ do not now meet exactly in the same point a/, 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 aba/ and aca/.
Let V=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.
T/=time light occupies to return from c to a/ (fig. 2).