Enskog kinetic theory is applied to the calculation of the Miesowicz viscosities and the Leslie coefficients of a nematic liquid crystal comprised of hard ellipsoidal particles. The anisotropies in the calculated viscosities are consistent with those derived from computer simulation, affine transformation theory and from experiment. When the Miesowicz viscosities are combined with the diffusion coefficients for a nematic, approximate Stokes-Einstein relations are found.