You were linked one of the experiments, there are others:
http://www.conspiracyoflight.com/Sagnac/SagnacEarth.html

In this series of experiments we were successful in detecting earth's diurnal rotational motion using a purely optical method. The resolution is quite reasonable considering the low cost design and implementation. The device demonstrates that the speed of light is not constant in the Sagnac interferometer from the perspective of the laboratory observer, even though both the observer and the interferometer are not moving in the laboratory frame. When the device is angled at 45 degrees with the z-axis facing north, the clockwise beam travels faster than the counter-clockwise beam, leading to a phase shift between the two beams at the photodetector. Because the clockwise beam is faster, according to C=fl, the wavelength of the clockwise beam appears longer than the counter-clockwise beam when measured in the laboratory frame. The difference in the velocities of the two beams amounts to the angular velocity of the loop with respect to the pole of the earth (the ECI frame). This is approximately 3.6 E -5 m/s. This amounts to a fringe shift of only 4.2 E -5 between the two beams. However, due to the high amplification used in this system, we are able to detect fringe shifts on the order of 0.7 E -6 of a fringe per mV.