A catalogue is prepared of 2712 rich clusters of galaxies found on the National Geographic Society--Palomar Observatory Sky Survey. From the catalogue, 1682 clusters are selected which meet specific criteria for inclusion in a homogeneous statistical sample. An investigation of the sample leads to the following conclusions: (i) The distribution function of clusters according to richness, N(n) increases rapidly as n decreases. (ii) The data allow no significant decision that the spatial density of cluster centers varies with distance. (iii) Galactic obscuration of the order of a few tenths of a magnitude (photored) exists at high northern galactic latitudes around galactic longitude 300°. (iv) There is a highly significant nonrandom distribution of clusters in direction, both when clusters at all distances and when clusters at various distances are considered. An analysis of the distribution yields strong evidence for the existence of second-order clusters, that is clusters of clusters of galaxies. A statistical test shows the observed distribution to be compatible with the assumption of complete second-order clustering of galaxies.