, where
is the index of refraction. These two hypotheses give a complete and satisfactory explanation of aberration. The second hypothesis, notwithstanding its seeming improbability, must be considered as fully proved, first, by the celebrated experiment of Fizeau,[3] and secondly, by the ample confirmation of our own work.[4]. The experimental trial of the first hypothesis forms the subject of the present paper.
If the earth were a transparent body, it might perhaps be conceded, in view of the experiments just cited, that the inter-molecular æther was at rest in space, notwithstanding the motion of the earth in its orbit; but we have no right to extend the conclusion from these experiments to opaque bodies. But there can hardly be question that the æther can and does pass through metals. Lorentz cites the illustration of a metallic barometer tube. When the tube is inclined the æther in the space above the mercury is certainly forced out, for it is imcompressible.[5]. But again we have no right to assume that it makes its escape with perfect freedom, and if there be any resistance, however slight, we certainly could not assume an opaque body such as the whole earth to offer free passage through its entire mass. But as Lorentz aptly remarks: "Quoi qu'il en soit, on fera bien, à mon avis, de ne pas se laisser guider, dans une question aussi importante, par des considérations sur le degré de probabilité ou de simplicité de l'une ou de l'autre hypothèse, mais de s'addresser a l'expérience pour apprendre à connaitre l'état, de repos ou de mouvement, dans lequel se trouve l'æther à la surface terrestre."[6]
In April, 1881, a method was proposed and carried out for testing the question experimentally.[7]
In deducing the formula for the quantity to be measured, the effect of the motion of the earth through the æther on the path of the ray at right angles to this motion was overlooked.[8] The discussion of this oversight and of the entire experiment forms the subject of a very searching analysis by H. A. Lorentz,[9], 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
, fig. 1, be a ray of light which is partly reflected in
