Like the original Michelson-Morley experiment, the Michelson-Gale-Pearson version compared the light from a single source (carbon arc) after travelling in two directions.
The major change was to replace the two "arms" of the original MM version with two rectangles, one much larger than the other.
Light was sent into the rectangles, reflecting off mirrors at the corners, and returned to the starting point.
The expected fringe shift in accordance with the stationary aether and special relativity was given by Michelson as: where
In other words, this experiment was aimed to detect the Sagnac effect due to Earth's rotation.
The ring interferometer of the Michelson-Gale experiment was not calibrated by comparison with an outside reference (which was not possible, because the setup was fixed to the Earth).
Those two results are not incompatible per se, but in the absence of a model to reconcile them, they are more ad hoc than the explanation of both experiments within special relativity.
Today, Sagnac type effects due to Earth's rotation are routinely incorporated into GPS.