  We define here a standard candle to determine the distance of clusters of
galaxies and to investigate their peculiar velocities by using the n^{th} rank
galaxy (magnitude m$_n$). We address the question of the universality of the
luminosity function for a sample of 28 rich clusters of galaxies ($cz \simeq
20000 km/s$) in order to model the influence on $m_n$ of cluster richness. This
luminosity function is found to be universal and the fit of a Schechter profile
gives $\alpha = -1.50 \pm 0.11$ and $M_{bj}* = -19.91 \pm 0.21$ in the range
[-21,-17]. The uncorrected distance indicator $m_n$ is more efficient for the
first ranks n. With n=5, we have a dispersion of 0.61 magnitude for the
(m$_n$,5log(cz)) relation. When we correct for the richness effect and subtract
the background galaxies we reduce the uncertainty to 0.21 magnitude with n=15.
Simulations show that a large part of this dispersion originates from the
intrinsic scatter of the standard candle itself. These provide upper bounds on
the amplitude $\sigma_v$ of cluster radial peculiar motions. At a confidence
level of 90%, the dispersion is 0.13 magnitude and $\sigma_v$ is limited to
1200 km/s for our sample of clusters.
