The theory of the resistive evolution of an axisymmetric toroidal plasma hinges on calculating self-consistent conditions on the plasma velocity. These conditions ensure that the plasma proceeds along a sequence of equilibrium states, and at finite aspect ratio involve computing the averages of certain equilibrium quantities around flux surfaces at every time step. The authors utilize the established representation of a large aspect ratio Tokamak equilibrium to show that for this case the flux-surface averages can be evaluated analytically. The resulting transport equations, which can be developed to high order in inverse aspect ratio, are explicitly 1-D while containing effects of both toroidicity and shaping.