Page:WitteSagnac2.djvu/3

756 the light ray which is following the same direction of the rotation, experiences a path-elongation corresponding to the factor $$\left(1+\tfrac{v}{c}\right)$$, yet also a velocity increase corresponding to the same factor $$\left(1+\tfrac{v}{c}\right)$$, which is canceling each other; the same arises at the oppositely moving ray $$\left(1-\tfrac{v}{c}\right)$$; there, $$v$$ is the orbit velocity of ($$O$$), $$c$$ is the speed of light.

With finite number of edges (Fig. 2), a path elongation and velocity change is given according to the factor $$\left(1+\tfrac{v}{c}\cdot\cos\tfrac{\vartheta}{2}\right)$$ at first approximation. Conservation of velocity is assumed in a known way at the reflecting points, because the mirrors are moving in their plane. However, there it is presupposed, that the process of reflection as such, exerts no disturbing influence of observable order of magnitude.

, Technische Hochschule.