  In this paper R-band photometric and velocity dispersion measurements for a
sample of 452 elliptical and S0 galaxies in 28 clusters are used to construct a
template D_n-sigma relation. This template relation is constructed by combining
the data from the 28 clusters, under the assumption that galaxies in different
clusters have similar properties. The photometric and spectroscopic data used
consist of new as well as published measurements, converted to a common system,
as presented in a accompanying paper. The resulting direct relation, corrected
for incompleteness bias, is log{D_n} =1.203 log{sigma} + 1.406; the zero-point
has been defined by requiring distant clusters to be at rest relative to the
CMB. This zero-point is consistent with the value obtained by using the
distance to Virgo as determined by the Cepheid period-luminosity relation. This
new D_n-sigma relation leads to a peculiar velocity of -72 (\pm 189) km/s for
the Coma cluster. The scatter in the distance relation corresponds to a
distance error of about 20%, comparable to the values obtained for the
Fundamental Plane relation. Correlations between the scatter and residuals of
the D_n-sigma relation with other parameters that characterize the cluster
and/or the galaxy stellar population are also analyzed. The direct and inverse
relations presented here have been used in recent studies of the peculiar
velocity field mapped by the ENEAR all-sky sample.
