According to Stokes' rule an integration of angular velocity Ω over an area A is substituted by an integration of tangential component of translational velocity v along the closed line of length L limiting the given area:
Now, apply Stokes' theorem to this interferometer (center of rotation does not coincide anymore with its geometrical center):
We already know the formula which is proportional to the area of the interferometer:
4AωsinΦ/c
2This simplifies to:
4Aω/c
2Ask yourself this very important question now: what is the form/nature of the SAGNAC FORMULA which, according to Stokes' theorem, is proportional to the translational velocity v along the closed line of length L limiting the given area?
V = radius of earth x angular velocity, of course
Obviously, it must be of the form:
Δt = 2vL/c
2A SAGNAC INTERFEROMETER WILL ALWAYS RECORD/REGISTER BOTH THE CORIOLIS EFFECT AND THE SAGNAC EFFECT, if the Earth is rotating around its own axis. This is the huge omission which Michelson, perhaps intentionally, forgot to mention in his 1925 paper (MGX).
So, according to Stokes' theorem, you must have TWO formulas for each interferometer: one is proportional to the area, the other one is proportional to the velocity.