  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 <I>_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, <1000km/s. The zero
point of the FP must therefore be quite stable. The residuals from the
Mg_2-sigma relation may be used to flag galaxies with deviant populations, and
possibly to correct the distance determinations for the deviations.
