  We investigate the dependence of the luminosity-diameter relation of galaxies
on the environment. This study is based on a comparison between the 80 galaxies
in the Shapley-Ames Catalog that are located within a distance of 10 Mpc, and
the luminosity-diameter relation for galaxies in great clusters such as Virgo
and Coma. A relatively tight linear correlation is observed between the
absolute magnitudes and the logarithms of the linear diameters of galaxies
located within 10 Mpc. Surprisingly this observed power-law relationship
appears to be almost independent of environment and local mass density as
defined by Karachentsev & Malakov. However, at a given luminosity, early-type
galaxies are (on average) slightly more compact than are objects of a later
type. Unexpectedly the present results appear to indicate that the
luminosity-diameter relation for the galaxies within 10 Mpc is
indistinguishable from what is observed in the much denser Virgo cluster.
Galaxies appear to form an almost one-dimensional family in parameter space. It
remains a mystery why the luminosity-diameter relation for galaxies is so
insensitive to environment.
