The transverse 'Fresnel aether drag' experienced when light passes through a refracting medium moving at right angles to the original direction of the light, and confirmed indirectly by Airy's water-filled telescope experiment, has been observed directly. In principle a beam of light is projected through a rotating disk of glass, and the consequent transverse displacement of the beam is measured by using a photoelectric alinement technique in which one grid is imaged on another. The main difficulties in the experiment arise from displacements of the light beam due to other causes: optical inhomogeneities in the disk, skewness in its mounting, and changes in its figure due to centrifugal force. These disturbances are reduced by more than a thousand-fold by making the light traverse the disk twice, by using two observing systems at opposite ends of a diameter, and by an optical correction device for inhomogeneities analogous to the corrector bar on a lead screw. For light traversing a disk of 2.465 cm thickness and refractive index 1.524 at an operating radius of 13.75 cm, when the disk is reversed from +1501.9 to -1501.9 rev/min the displacement observed is 6.175 nm $\pm $ 0.016 nm standard deviation. The displacement (to be expected from the Fresnel aether drag formula is 6.174 nm.