The fundamental plane for cluster E and S0 galaxies

We have analyzed the Fundamental Plane (FP) for a sample of 226 E and S0 galaxies in ten clusters of galaxies. For photometry in Gunn r the best fitting plane is log r_e=1.24 log sigma - 0.82 log _e + cst. The scatter is 0.084 in log r_e. The slope of the FP is not significantly different from cluster to cluster. The residuals of the FP correlate weakly with the velocity dispersion and the surface brightness. Thus, to avoid biases of derived distances the galaxies need to be selected in a homogeneous way. The FP has significant intrinsic scatter. No other structural parameters like ellipticity or isophotal shape can reduce the scatter significantly. The Mg_2-sigma relation differs slightly from cluster to cluster. Galaxies in clusters with lower velocity dispersions have systematically lower Mg_2. With the current stellar population models, it is in best agreement with our results regarding the FP if the offsets are mainly caused by differences in metallicity. Most of the distances that we derive from the FP imply small peculiar motions,