2.1.1 Clusters of galaxies
The term cluster is not uniquely defined. Hubble (1934) wrote:
``The usage of the term ``cluster'' is quite arbitrary, ranging from the conservative practice which applies the name only to the great conspicuous examples to the other extreme in which almost any grouping is glorified by the title.''
Shapley (1934) summarizes his experience from a sample of 43,000 galaxies as follows:
``Even with the appropriate correction for `optical doubling' the physical association of galaxies is found to be very common. Multiple systems are not rare, and groups and clusters of individual galaxies throughout the Metagalaxy appear to be analogous in nature and frequency to the grouping and clustering of stars in the galactic system. As for the open star clusters of the Milky Way, so also for loose groupings among the galaxies, no sharp line can be drawn between irregularities in distribution and coarse clustering. Lundmark speaks of hundreds of recognized `metagalactic clusters' whereas Hubble lists but a few rich objects as clusters of galaxies.''
For criticism on the concept of clusters in contrast to clustering see Carpenter (Sect. 2.3.1.).
The first quantitative definition of rich clusters was given by Abell (Sect. 1.5).
Zwicky (1938) stated explicitly that clusters of galaxies are not the exception but the rule. He wrote:
``a) Practically all nebulae are bunched in more or less regular clusters and clouds of nebulae if the general physical conditions of the universe are of a stationary character.
b) In a typical cluster the number of nebulae per unit volume as a function of the distance from the center may be derived from Emden's theory of the radial distribution of mass in an isothermal gravitational gas sphere.
c) The process of clustering results in a segregation of nebular types inasmuch as the most massive nebulae exhibit the greatest tendency toward clustering.''
Recently, observational evidence has accumulated that members of massive cluster galaxies serve as gravitational lenses which make more distant clusters visible (Soucail et al. 1987). The following is a reminder to the origin of this concept.
Fifty years ago, Zwicky (1937a, b) published two brief communications:
``Einstein recently  published some calculations concerning a suggestion made by R.W. Mandl, namely, that a star B may act as a `gravitational lens' for light coming from another star A which lies closely enough on the line of sight behind B. As Einstein remarks the chance to observe this effect for stars is extremely small. Last summer Dr. V.K. Zworykin (to whom the same ideas had been suggested by Mr. Mandl) mentioned to me the possibility of an image formation through the action of gravitational fields. As a consequence I made some calculations which show that extragalactic nebulae offer a much better chance than stars for the observation of gravitational lens effects.''
In his second communication Zwicky includes an interesting footnote:
``Dr. G. Strömberg of the Mt. Wilson Observatory kindly informs me that the idea of stars as gravitational lenses is really an old one. Among others, E.B. Frost, late director of the Yerkes Observatory, as early as 1923 outlined a program for the search of such lens effects among stars.''
Zwicky pointed out again:
``The problem in question, however, takes on a radically different aspect, if, instead of stars we think in terms of extragalactic nebulae. Provided that our present estimates of the masses of cluster nebulae are correct, the probability that nebulae which act as gravitational lenses will be found becomes practically a certainty''.