Page:Elektrische und Optische Erscheinungen (Lorentz) 122.jpg

 this can be achieved by means of a hypothesis, which I already have spoken out some time ago, and to which, as I found out later, also arrived. 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, the translation causes that the time, in which one light-beam travels forth and back along P, is longer by

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

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