An updated comparison of the $M_{\bullet}$ vs $M_{G}\sigma^2$ relation
  with $M_{\bullet}$ vs $\sigma$ and the problem of the masses of galaxies
  We have studied, in a series of papers, the properties of the $M_{\bullet}$
versus $M_{G}\sigma^2$ relation and we have found that it is useful to describe
the evolution of galaxies in the same way as the HR diagram does for stars and
to predict the masses of Supermassive Black Holes that are difficult to be
guessed using other scaling relations. In this paper, analyzing five samples of
galaxies, we find that this relation has intrinsic scatter similar to the
$M_{\bullet} - \sigma$, but follows the theoretical models much better than the
$M_{\bullet} - \sigma$. Furthermore, we analyze the role of the bulge mass in
the behavior of $M_{\bullet}$ versus $M_{G}\sigma^2$ relation because the
difference with the $M_{\bullet} - \sigma$ is often determined by the choice of
the right sample of galactic masses.
