A previous measurement of the Fresnel "aether drag" in a transversely moving medium (Jones 1972) has been repeated with improved accuracy to find whether the original Fresnel formula should be modified by a dispersion term as was shown by Lorentz and Zeeman for the longitudinal drag. A formula derived by M.A. Player and by G.L. Rogers gives the transverse displacement of a beam of light passing through a medium of thickness t moving with transverse velocity \upsilon as \upsilon t(ng - nφ-1)/c rather than \upsilon t(ng - nφ-1)/c as given by the original Fresnel formula, where nφ is the phase refractive index and ng is the 'group refractive index.' The present experiment gives results in accordance with the Player-Rogers formula rather than with the Fresnel formula or one in which the group refractive index alone is involved; it parallels what Zeeman found for the longitudinal case. The main improvement in experimental accuracy has come from recognition of errors in the method of calibration by optical micrometry.