Are polar rings self-gravitating?

In a number of S0 galaxies, rings of gas, dust and stars are observed to lie roughly perpendicular to the galactic disc. These polar rings appear nearly flat, and undisturbed by differential precession in the gravitational field of the galaxy. It is shown here that a self-gravitating polar ring may precess uniformly as a solid body about an axisymmetric galaxy, if the ring is sufficiently massive and its tilt varies suitably with radius. Both stable and unstable equilibria exist. A stable, nearly polar ring bends towards the pole at the outer edge; this is in contrast to the stable warped discs that may exist in triaxial galaxies, which turn towards the equator. The required masses are comparable to those observed in neutral hydrogen. An initially unstable ring may break into a number of independently precessing sub-rings, so that a multiple ring system can result from capturing a single gas cloud.