Non-time-orthogonality and Tests of Special Relativity
  An intriguing, and possibly significant, anomalous signal in the Brillet and Hall experiment is contrasted with a simple first order test of special relativity subsequently performed to discount that signal as spurious. Analysis of the non-time-orthogonal nature of the rotating earth frame leads to the conclusion that the latter test needed second order accuracy in order to detect the effect sought, and hence was not sufficient to discount the potential cause of the anomalous signal. The analysis also explains the results found in Sagnac type experiments wherein different media were placed in the path of the light beams. 
Robert D. Klauber