  The persistent, second order, anomalous signal found in the Brillet and Hall
experiment is derived by applying 4D differential geometry in the rotating
earth frame. By incorporating the off diagonal time-space components of the
rotating frame metric directly into the analysis, rather than arbitrarily
transforming them away, one finds a signal dependence on the surface speed of
the earth due to rotation about its axis. This leads to a Brillet-Hall signal
prediction in remarkably close agreement with experiment. No signal is
predicted from the speed of the earth in solar or galactic orbit, as the
associated metric for gravitational orbit has no off diagonal component. To
corroborate this result, a repetition by other experimentalists of the
Brillet-Hall experiment, in which the test apparatus turns with respect to the
earth surface, is urged.
