  Type Ia supernovae (SNe Ia), produced by the thermonuclear explosion of white
dwarf (WD) stars, are used here to derive extragalactic distances and an
estimate of the Hubble constant from their emission signatures at late phases
({\it Nebular SNe Ia Method}, NSM). The method, first developed in
Ruiz--Lapuente \& Lucy (1992), makes use here of an improved modeling of the
forbidden line emission at late phases. Hydrodynamic models of the explosion of
WDs of different masses, both sub--Chandrasekhar and Chandrasekhar, provide the
basis for comparison with the observations. It is shown that it is possible to
probe the overall density structure of the ejecta and the mass of the exploding
WD by the effect that the electron density profile has in shaping the forbidden
line emission of the iron ions, and that a robust diagnostic of the mass of the
exploding WD can be obtained. Cosmic distance scale can thus be related to
basic diagnostics of excitation of iron lines. Once the most adequate model is
selected, comparison of the predicted line emission at these phases with the
observed spectra gives an internal estimate of both the reddening and the
distance to the SNe Ia. The results presented here favor denser models than
those corresponding to sub--Chandrasekhar explosions. From a sample of seven
SNe Ia in Leo, Virgo, Fornax and beyond, a value of the Hubble constant $H_{0}
= 68 \ \pm 6\ (stat) \pm 7\ (syst)\ km\ s^{-1}\ Mpc^{-1}$ is derived. The depth
of the Virgo cluster is found to be large, ranging from 13 to 23 Mpc at least.
If NGC 4526 traces well the core of the Virgo Cluster, then the latter is
located at $16\pm 2 \ Mpc$. The galaxy NGC 3267 in Leo appears to be located at
9.8 $\pm$ 1.5 Mpc.
