In 1953 G.I. Taylor showed that longitudinal dispersion of matter in a pip can be represented y a one-dimensional dispersion equation and derived the magnitude of a coefficient to represent the effect of the shear flow. Taylor's analysis is extended to a shear folow in which the velocity vector rotates with depth but is horizontally homogeneous. We show that horizontal dispersion can be represented by a two-dimensional equation in which a tensor coefficient represents the effect of the vertical shea. The terms in the tensor are derived for an approximation to the mean flow on the Middle Atlantic Bight of the U.S. Atlantic continental shelf.