  We prove results towards the equidistribution of certain families of periodic
torus orbits on homogeneous spaces, with particular focus on the case of the
diagonal torus acting on quotients of $\PGL_n(\R)$. After attaching to each
periodic orbit an integral invariant (the discriminant) our results have the
following flavour: certain standard conjectures about the distribution of such
orbits hold up to exceptional sets of at most $O(\Delta ^{\epsilon})$ orbits of
discriminant $\leq \Delta$. The proof relies on the well-separatedness of
periodic orbits together with measure rigidity for torus actions. We also give
examples of sequences of periodic orbits of this action that fail to become
equidistributed, even in higher rank.
  We give an application of our results to sharpen a theorem of Minkowski on
ideal classes in totally real number fields of cubic and higher degrees.
