  We support, with new fitting instruments and the analysis of more recent
experimental data, the proposal of a relationship between the mass of a
Supermassive Black Hole (SMBH) and the kinetic energy of random motions in the
host elliptical galaxy. The first results obtained in a previous paper with 13
elliptical galaxies are now confirmed by the new data and an enlarged sample.
We find $M_{BH} \propto (M_{G} \sigma^{2}/c^2)^\beta$ with $0.8 \leq \beta \leq
1$ depending on the different fitting methods and samples used. The meaningful
case $\beta = 1$ is carefully analyzed. Furthermore, we test the robustness of
our relationship including in the sample also lenticular and spiral galaxies
and we show that the result does not change. Finally we find a stronger
correlation between the mass of the galaxy and the corresponding velocity
dispersion that allows to connect our relationship to the $M_{BH} \propto
\sigma^\alpha$ law. With respect to this law, our relationship has the
advantage to have a smaller scatter.

Astrophysics