Redshift-distance survey of early-type galaxies.: II.: The Dn-σ relation

R-band photometric and velocity dispersion measurements for a sample of 452 elliptical and SO 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 arid spectroscopic data used consist of new as well as published measurements, converted to a common system, as presented in an 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 cosmic microwave background. 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 +/- 189 km s(-1) 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.