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this can be achieved by means of a hypothesis, which I already have spoken out some time ago,^[1] and to which, as I found out later, also Fitzgerald arrived.^[2] Of which the hypothesis consists, shall be shown in the next §.

§ 90. For simplification we want to assume, that we would work with an instrument as that during the first experiments, and that with respect to one main-position, the arm P coincides exactly with the direction of Earth's motion. Let ${\mathfrak {p}}$ be the velocity of this motion, and L the length of every arm, thus 2L the path of the light rays. Then by the theory ^[3], the translation causes that the time, in which one light-beam travels forth and back along P, is longer by

$L\cdot {\frac {{\mathfrak {p}}^{2}}{V^{3}}}$

than the time, in which the other beam completes its path. Exactly this difference would also exist, when (without that the translation would have an influence) arm P would be longer by

$L\cdot {\frac {{\mathfrak {p}}^{2}}{2V^{2}}}$

than arm Q. Similar things are true for the second main-position.

Thus we see, that the phase difference expected by the theory could also arise, when (during the rotation of the apparatus) sometimes one, sometimes the other arm would have the greater length. From that if follows, that they can be compensated by

1. Lorentz. Zittingsverslagen der Akad. v Wet. te Amsterdam, 1893—93, p. 74.
2. As Fitzgerald was so friendly to tell me, that he dealt with this hypothesis already for a longer time in his lectures. In the literature, I only found it mentioned by Lodge, in the treatise „Aberration problems" (London Phil. Trans, Vol. 184, A, p. 727, 1893). I allow myself, to also add at his place, that this treatise, besides some theoretical considerations, also contains the description of very interesting experiments, in which two discs of metal (Diameter 1 Yard) perpendicularly fixed on that axis, were rotated with great velocity. By means of a certain interference method it was investigated, whether the aether that was present between the discs, was co-rotating; the result was negative, even though the number of rotations in a second was increased up to 20 or more. Lodge concludes, that the discs haven't communicated to the aether the 800th part of their velocity.
3. see Lorentz, Arch. néerl., T. 21, pp. 168—176, 1887.