The gravitational potential used in an earlier paper with the same title does not correspond to circular rings with infinitesimal thickness, but to a distribution of matter extending to infinity with axial symmetry. In the present paper the correct expression for the gravitational potential of a circular ring is obtained. It is shown that if the area density of the ring is expressed as a Bessel function (as in the earlier paper) plus an infinite integral, but numerically the integral is much smaller than the single Bessel function term. Therefore the numerical results of the earlier paper on the stability analysis of the motion of the ring are expected to be only slightly affected by using the correct expression for the potential and this is verified numerically.