The Michelson--Morley experiment yielded a null result, indicating equal light travel times in the longitudinal and transverse arms of an interferometer, traditionally interpreted as evidence for the absence of a light-propagating medium. This paper analyzes the experiment in the reference frame of a hypothetical medium, modeled as a property of space or a field, without assuming its absence. We introduce longitudinal and transverse dilation/contraction factors and derive their relationship to reproduce the null result. This generalizes the Lorentz contraction and provides a framework for alternative medium-based interpretations consistent with the experimental outcome. The analysis is extended to show that the derived relationship remains valid when comparing arbitrary inertial frames in motion relative to the medium, demonstrating the internal consistency of a medium-based approach.