In expressing the results of particle size analysis from micrographs, i t is customary to report statistics of the distribution such as mean diameter and standard deviation, together with various weighted average diameters. Each of these values represents one or more moments of the distribution, as do the various average particle sizes which are determined by different experimental methods. An analogous situation prevails in the reporting of molecular weights of heterogeneous polymers. During recent extensive work in this laboratory on lattices of very narrow-size distributions, correlations among the various statistics became apparent; this led us to consider the narrow distribution as a special limiting case.