  We show that the spatial correlation function of a flux-limited sample of
X-ray selected clusters of galaxies will exhibit a correlation scale that is
smaller than the correlation scale of a volume-limited, richness-limited sample
of comparable apparent spatial density. The flux-limited sample contains
clusters of different richnesses at different distances: poor groups are found
nearby and rich clusters at greater distances. Since the cluster correlation
strength is known to increase with richness, the flux-limited sample averages
over the correlations of poor and rich clusters. On the other hand, a
volume-limited, richness-limited sample has a minimum richness threshold, and a
constant mixture of richnesses with redshift. Using the observed correlation
scale for rich ($R\ge 1$) clusters, $r_o (R\ge 1) = 21\pm 2 h^{-1}$Mpc that was
determined from previous volume-limited studies, we derive for the ROSAT
flux-limited X-ray cluster sample $r_o({\rm flux}{\rm -}{\rm limited}) \approx
14h^{-1}$Mpc, in agreement with the recently observed value of $13.7\pm 2.3
h^{-1}$Mpc.
