The use of the tensor virial theorem (TVT) as a diagnostic of anisotropic
velocity distributions in galaxies is revisited. The TVT provides a rigorous
global link between velocity anisotropy, rotation and shape, but the quantities
appearing in it are not easily estimated observationally. Traditionally use has
been made of a centrally averaged velocity dispersion and the peak rotation
velocity. Although this procedure cannot be rigorously justified, tests on
model galaxies show that it works surprisingly well. With the advent of
integral-field spectroscopy it is now possible to establish a rigorous
connection between the TVT and observations. The TVT is reformulated in terms
of sky-averages, and the new formulation is tested on model galaxies.Comment: 6 pages submitted to MNRA