The consequences arising from the consideration of geostrophy in a rotating barotropic fluid are re-examined. It is shown that geostrophy implies that the horizontal divergence must vanish. A simple case of a fluid flow that is not geostrophic is also investigated, showing that the potential vorticity (defined in terms of variables parallel to the axis of rotation) is conserved. The approximations involved in transforming this conservation principle to one having terms of locally normal variables are then investigated....