  Orbits in triaxial ellipsoidal potentials precess about either the major or
minor axis of the ellipsoid. In standard perturbation theory it can be shown
that a circular orbit will precess about the minor axis if its angular momentum
vector lies in a region bounded by two great circles which pass through the
intermediate axis and which are inclined with minimum separation $i_T$ from the
minor axis. We test the accuracy of the standard formula for $i_T$ by
performing orbit integrations to determine $i_S$, the simulated turnover angle
corresponding to $i_T$. We reach two principal conclusions: (i) $i_S$ is
usually greater than $i_T$, by as much as 12 degrees even for moderate
triaxialities, $A/1.2<B<C/0.8$. This reduces the expected frequency of polar
rings. (ii) $i_S$ is not a single, well-defined number but can vary by a few
degrees depending upon the initial phase of the orbit. This means that there is
a reasonable probability for capture of gas onto orbits which precess about
both axes. Interactions can then lead to substantial loss of angular momentum
and subsequent infall to the galactic centre.
