> http://www.physicsinsights.org/sagnac_1.html

You might also be interested in

http://www.atomicprecision.com/new/a45thpaper.pdf

which describes the Sagnac effect in terms of general, rather than special, 
relativity. Special relativity is not applicable because it is not concerned 
with acceleration.

For background info on the theory used, see

http://www.aias.us

Rob

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