We have studied a sample of 81 E and SO galaxies (taken mostly from the literature) that were observed with the Einstein Observatory. Fifty–five galaxies are detected in X–rays, most of which come from a hot interstellar medium. It is possible that discrete sources make a significant contribution to the X–ray emission for 21 of the detected galaxies with the lowest X–ray luminosity, LX
, for a given optical luminosity, LB. We examine the LX
distribution (see Figure 1), and derive approximate values of the central electron density, central cooling time and total mass in gas for the sample. Typical values are ~ 0.1cm−3, ~ 5 × 106 yr and 5 × 109
⊙, respectively. The short cooling times suggest the presence of cooling flows, and we consider heating by supernovae and by gravitational processes. Supernovae at the accepted rate would overproduce the observed X–ray luminosity: either the true rate is many times lower or the supernova energy is not well coupled to the hot gas. There are also difficulties in explaining the suppression of a strong galactic wind if supernova heating dominates, unless an external pressure confines the gas. Gravitational heating gives LX
σ2, where σ is the line–of–sight velocity dispersion in the galaxy, and we find that this is roughly the case. Gravitational heating exceeds the mean observed Lx
by a factor of ~ 3 — 4 if one uses the accepted rate of stellar mass loss and assumes that the gas falls all the way to the center of the galaxy. This could be reconciled if the mass injection rate were lower or if matter drops out of the flow at all radii. The sample properties provide no additional information about the presence or absence of heavy halos in early type galaxies.