Maxwell's equations in a rotating medium: Is there a problem?

In 1908 Einstein and Laub used special relativity to predict that a moving magnetic dipole develops an electric dipole moment. The classic 1913 experiment of Wilson and Wilson on a polarizable, permeable medium rotating in an external magnetic field has long been cited as verifying this prediction. We argue that since the experiment involved rotation rather than uniform translation, it did not test special relativity. The analysis should properly be done in a rotating coordinate system. The field equations for a rotating object are well known and the analysis is straightforward, but the result disagrees with the Wilson experiment. After carefully examining all steps in the derivation, we conclude that either the experiment is wrong or the theoretical analysis must be modified. One possible resolution of the conflict is the hypothesis that the dielectric constant ɛ and permeability μ are well defined only in a frame in which the medium is at rest and time and space are orthogonal coordinates.