Page:WitteSagnac1.djvu/6

 Now, $$r\cdot\cos\tfrac{\vartheta}{2}$$ is equal to the length of the perpendicular $$\varrho$$ from the center of the circle upon the polygon side, $$U\cdot\varrho$$ is furthermore the double of area $$F$$ of the polygon; thus one obtains the end result:

Due to reasons of measurement, causes the apparatus to turn in one sense first, then in the other sense, thus he measures $$4\cdot x$$, and his end formula therefore reads:

By this formula 6), calculates the fringe displacement to be expected; that the effect is indeed of first order $$\left(\tfrac{v}{c}\right)$$ shows variation 4) of the same formula.

As it was said, then the observed value agrees quite satisfactorily with the calculated one.

The circle diameter $$2r$$ amounts to 50 cm; the rotating number $$N$$ is of order of magnitude 1 or 2 rotations per second; the interference images are made in a photographic way; the photographic plate, the light source, etc., share the rotation.

5. It is now the question, whether 's conclusion that the effect is deciding the alternative "aether or relativity principle", namely that it decides against the relativity principle and in favor of the aether, is necessary.

The following representation seems possible to me:

a) That the effect comes about, doesn't follow from the translatory velocity of observing point $$O$$, but from the rotational motion of the whole system (and by that of course also point $$O$$).