(Abstract of the paper) We have acquired redshifts for a complete sample of 351 Abell clusters with tenth-ranked galaxy magnitudes (m_10_) less than or equal to 16.5, including 115 entirely new cluster redshifts. The survey includes all such clusters which lie north of {delta}=-27deg30arcmin and is the largest magnitude-limited redshift survey of rich clusters to date. Analysis of the spatial distribution of these clusters reveals no clustering on scales larger than 75h^-1^Mpc; we do not detect the large supercluster complexes reported by Tully. The correlation length is 20.0(+/-4.3)h^-1^Mpc, consistent with the results from other surveys. The frequency of voids with radii of order 60h^-1^Mpc or less is consistent with the form and amplitude of the observed two-point correlation function. There is no significant difference between the clustering properties of RC = O and RC >= 1 clusters. A percolation analysis yields 23 superclusters, 17 of which are new. The superclusters are not significantly elongated in the radial direction; large-scale peculiar motions are of order 1000 km s^-1^ or less. Dramatically new constraints on the large-scale cluster distribution will require surveys an order of magnitude larger.