  We determine X-ray temperatures and abundances for elliptical galaxies drawn
from a complete, optically selected sample. The optical magnitude-limited
sample consists of 43 galaxies, complete to a (corrected) B magnitude of
m_B^o=11.36. Of these, 30 have enough X-ray spectral counts to allow
temperature determinations. We find that the temperatures of the X-ray emitting
gas in these ellipticals are correlated with the central stellar velocity
dispersions: T ~ sigma^1.45; this is a shallower trend than the simple thermal
relation T ~ sigma^2. The diffuse gas is substantially hotter than the kinetic
temperature of the luminous stars, since kT > mu m_p sigma^2 for all galaxies
with measurable temperatures. This strongly indicates that dark matter halos
are characterized by velocity dispersions which exceed those of the luminous
stars. We see no evidence of emission from X-ray binaries becoming
progressively more dominant in lower luminosity ellipticals. We find that
so-called "supersoft" sources adhere to the observed kT-sigma relation, so they
are no softer than expected for their velocity dispersions. We also find that
ISM temperatures and abundances are correlated, with the gas in hotter systems
being more enriched than in cooler galaxies. However, no correlation is found
between gaseous abundances and stellar abundances, as inferred from Mg_2
indices.
