We report. on a homogeneous dynamical analysis of a sample of 21 round (17
E0/E1, 4 E2) elliptical galaxies. We present new kinematic data for eight o
f these galaxies and new photometry for one object. The remaining kinematic
and photometric data and the required distance information are taken from
the literature. The analysis uses non-parametric spherical models and takes
into account line profile information as well as velocity dispersions. We
present model fits to the kinematic data and the derived radial profiles of
orbital anisotropy and B-band mass-to-light ratio, including confidence in
tervals. The circular velocity curves resulting from our model fits are all
consistent with being flat outside R approximate to 0.3 R-e. Generally, th
e M/L ratio profiles show an outward increase, although models based on lum
inous matter are ruled out at 95% confidence only for three galaxies (NGC 2
434, NGC 7507, NGC 7626). For NGC 1399, NGC 4472, NGC 4486, and NGC 4636, w
here X-ray observations are available, the mass profiles of the best fit mo
dels match the ones derived from the X-ray analysis. The best models for mo
st galaxies are isotropic to slightly radially anisotropic, with typical be
ta less than or similar to 0.3, in a few cases beta less than or similar to
0.5 at R-e/2. We discuss the generally small effects of flattening along t
he line-of-sight (the expected < c/a > = 0.79 for this sample of luminous e
llipticals) and of small embedded disks. Our results suggest that elliptica
l galaxies have surprisingly uniform dynamical properties.