Long before the era of extragalactic astronomy it was recognized that the small-scale distribution of "nebulae" in space is not random. Even the small sample of the 35 Messier objects now recognized as galaxies exhibits this nonrandomness; nearly half of these objects are in the vicinity of the Virgo cluster. Plots of the distribution on the sky of "nebulae" listed in John Herschel's General Catalogue, or in Dreyer's New General Catalogue and Index Catalogue, reveal several pronounced concentrations now recognized as nearby clusters of galaxies. Two of these, the Perseus cluster and the Coma cluster, were described in some detail by Wolf (1902, 1906) early in the century. Also, Wirtz (1923, 1924a, b), who supplemented the distribution of NGC and IC objects with data from the surveys of Fath, Curtis, and himself, called attention to several conspicuous well-defined centers of clustering.
Following Hubble's demonstration of the nature of galaxies in 1924, several systematic surveys of the distribution of galaxies were made. Among these are the extensive surveys by Shapley and his co-workers at Harvard in the two decades following 1930. At least four distinct clusters - the Virgo cluster, the Ursa Major cloud, and two clusters in Fornax - are apparent in the distribution of the bright galaxies in the Shapley-Ames catalog (1932). Shapley himself (1933) catalogued and described 25 individual clusters. The Harvard surveys to faint limiting magnitudes in the southern hemisphere with the Bruce telescope revealed still greater clustering, and Shapley (e.g., 1957) has called attention to a major unevenness in surface distribution, which apparently cannot be described as local clustering but which suggests "metagalactic structure" or superclustering.
Hubble's (1934) fundamental investigation of the distribution of galaxies over the sky provided further information on the clustering tendency. The survey was conducted on 1283 small selected regions of the sky which were intentionally chosen to avoid most of the well-known clusters; nevertheless, from the scanty evidence available to him, Hubble estimated there to be one great cluster (with hundreds of member galaxies) for every 50 square degrees of the sky. He estimated that if the great clusters averaged 500 members each, they would account for about 1 percent of the total number of observed galaxies. Even after omitting the great clusters from his investigation, however, Hubble found the galaxian distribution to be nonrandom; he interpreted a skewness in the frequency distribution of the numbers of fields with various numbers of counted galaxies as a tendency toward small-scale clustering (see Hubble 1936a). According to Hubble, the groups and clusters could not be merely superposed on a random distribution of isolated galaxies; either condensations in the general field produced the clusters, or evaporation of galaxies from clusters populated the general field.
Meanwhile, additional individual clusters were discovered, often by accident. Tombaugh (1937) described three at low galactic latitudes. Zwicky discovered several new clusters with the 18-inch Schmidt telescope on Palomar Mountain, and investigated these and other clusters with that instrument, and later with the 48-inch Schmidt and 200-inch telescopes (for the best summary, see Zwicky 1957). The general prevalence of clustering led him (Zwicky 1938) to propose that all galaxies belong to clusters and that the Universe can be regarded as divided into cluster "cells" with a mean diameter of about 7.5 × 106 pc. (Zwicky's estimate was based on the old distance scale; for the Hubble constant H = 50 km s-1, the diameter of a "cluster cell" would be about 7.5 × 107 pc.)
Since World War II, two photographic surveys of the sky have demonstrated conclusively that clusters of galaxies are extremely numerous - far more so than most investigators had believed; these are the Lick 20-inch Astrographic Survey and the National Geographic Society-Palomar Observatory Sky Survey. From counts of galaxy images on the Lick photographs, Shane and his collaborators (Shane and Wirtanen 1954; Shane 1956a; Shane, Wirtanen, and Steinlin 1959; Shane and Wirtanen 1967) have prepared catalogs and charts of the surface density of galaxies (per square degree). They have called attention to many striking clusters and clouds of galaxies, and even to apparent superclusters. The Lick counts have been analyzed statistically under the direction of Scott and Neyman at the Berkeley Statistical Laboratory (Neyman and Scott 1952; Neyman, Scott, and Shane 1953, 1954; Scott, Shane, and Swanson 1954). It was found that the serial correlation between counts in 1° × 1° squares persists to square separations of about 4°, and that it has almost the same value in both galactic polar caps. From the shape of the quasi-correlation function, the statisticians derived parameters that describe the scale and amplitude of the clustering. They then applied these parameters to the manufacture of a "synthetic" field of galaxy images based on a model that assumes that all galaxies are in clusters. Comparison of the synthetic field with fields plotted from actual plates showed a striking similarity between the prediction of the model and the observed distribution of galaxies; if anything, the actual fields displayed a slightly greater clustering tendency than the synthetic one. Neyman, Scott, et al. found typical clusters to have populations of the order 102 and diameters of a few million parsecs.
Limber (1953, 1954) also investigated the distribution of galaxies from Shane and Wirtanen's counts on the Lick plates and fitted it to a model in which the spatial density of galaxies is a smoothly varying function of position in space. Limber thereby derived an independent estimate of the scale of clustering. Although his procedure was criticized by Neyman and Scott (1955) on the grounds that the discrete nature of galaxies is incompatible with a smoothly varying function describing their distribution among volume cells in space, Limber's results are in qualitative agreement with those of Neyman, Scott, et al. A model which takes account of the discrete fluctuations that arise because of the discrete character of the distribution of galaxies as well as those that arise from clustering, and which also applies to a distribution that exhibits clustering but that does not consist entirely of discrete and independent clusters, has been suggested by Layzer (1956).
Tens of thousands of discrete groups and clusters of galaxies are easily identified on the Palomar Sky Survey photographs. The writer (Abell 1958) has catalogued 2712 of the very richest of these, and has analyzed the distribution of 1682 clusters that comprise a more or less homogeneous sample chosen from the catalog. Also from the Palomar plates, Zwicky and his associates have prepared a far more extensive Catalogue of Galaxies and Clusters of Galaxies (Zwicky, Herzog, Wild, Karpowicz, and Kowal 1961-68). Some statistics on the sizes of the largest of these clusters and on the area of the sky coveted by them have been published (Zwicky and Rudnicki 1963, 1966; Zwicky and Berger 1965; Zwicky and Karpowicz 1965, 1966). Finally, Klemola (1969) and Snow (1970) list an additional 78 groups and clusters of southern-hemisphere galaxies discovered on plates taken for the Yale-Columbia proper-motion survey.
Thus it is recognized today that clustering of galaxies is a dominant tendency, and may be fundamental. It is, in fact, not impossible that all or nearly all galaxies belong to clusters, or at least that they were originally formed in clusters. We speak of the general "field" or "background" of noncluster galaxies, but the extent to which such a "field" has physical significance is not known at present. As was shown by the Berkeley statistical investigation of the Lick counts, the impression of a field of noncluster objects can be created by many clusters and groups (in many of which only the one or two brightest members may be visible) seen overlapping in projection. Only those systems that stand out conspicuously against the field (whatever its nature), either because they are unusually rich aggregates or because their members lie in very close proximity to each other in comparison to intergalactic distances, will be recognized as discrete groups or clusters. Obviously small groups will not be identified unless they are relatively nearby. Even rich clusters are increasingly difficult to distinguish from the field at increasing distances. Our knowledge about clusters, therefore, tends to be biased toward the richest systems, and even for them it is never possible to say with certainty which galaxies (except statistically) are cluster members.
The very definition of a cluster or group of galaxies, therefore, is not a trivial matter. Such properties as total sizes, total populations, distributions of member galaxies, and luminosity functions depend very critically on how the clusters are defined and how their members are distinguished from the field. Several investigators (e.g., Zwicky and Abell) have given rather specific operational definitions of clusters for the purposes of their respective studies. Many of the differences in opinion among them concerning the nature of clusters stem from the fact that they have defined clusters in different ways. It is beyond the scope of this review to attempt to provide a definitive definition of a cluster of galaxies. We shall, however, try to be specific about the definitions and assumptions on which the results discussed depend.