Velocity dispersions of low luminosity ellipticals - L approximately equal to sigma-cubed

A complete sample of elliptical galaxies in the core of the Virgo cluster is used to derive a relation between stellar velocity dispersion and luminosity. L is found to approximately equal sigma to the nth power, where n = 3.2 + or - 0.2 over two decades of luminosity, with a scatter of 0.38 mag. The possibility of curvature in the relation or rotational support of the galaxies is examined, and a derivation of a law of slope 3 is presented and compared with the derivation for a slope of 4. It is concluded that the lack of increased scatter as the points deviate from a slope of 4 implies that rotation is not important.