http://mathpages.com/rr/s2-07/2-07.htm

extract:

Despite the ease and clarity with which special relativity accounts for the Sagnac effect, one occasionally sees claims that this effect entails aconflictwith the principles of special relativity. The usual claim is that the Sagnac effect somehow falsifies the invariance of light speed with respect to all inertial coordinate systems. Of course, it does no such thing, as is obvious from the fact that the simple description of an arbitrary Sagnac device given above is based on isotropic light speed with respect to one particular system of inertial coordinates, and all other inertial coordinate systems are related to this one by Lorentz transformations, which are defined as the transformations that preserve light speed. Hence no description of a Sagnac device in terms of any system of inertial coordinates can possibly entail non-isotropic light speed, nor can any such description yield physically observable results different from those derived above (which are known to agree with experiment).

So the mathematics say

But what of the PRACTICAL

**arbitrary Sagnac device**

The experiment by Sagnac was a real experiment

The experiment by Sagnac was a real experiment