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 kms ^ { -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 .