  The stellar velocity fields of elliptical galaxies hold clues to their
dynamical structure and origin. The construction of velocity field models is
greatly simplified by assuming an approximate geometrical form for the
streamlines of the mean stellar motions. We test the conjecture that confocal
streamlines are a valid approximation for realistic triaxial systems. We
numerically integrate orbits in Schwarzschild's logarithmic potential, and fit
confocal streamlines to their mean velocity fields by minimizing the RMS
magnitude of the cross product between the velocity vectors and the
streamlines. We find that most orbits at a given energy can be fitted by nearly
identical confocal systems. There are statistically significant differences
between the streamline parameters obtained for different orbit families, but
the differences are small. The fitted parameters reproduce, to high accuracy,
the boundary between short axis and outer long axis tubes, which is a direct
measure of the triaxiality of the potential. These results strongly support
efforts to obtain accurate statistical measurements of triaxiality from
kinematic observations and reasonably simple velocity field models.
