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The mass discrepancy in clusters of galaxies was found by Zwicky (1933). He measured redshifts of galaxies in the Coma cluster and found that the total mass of the cluster calculated from the velocity dispersion using the virial theorem exceeds the sum of masses of visible galaxies more than tenfolds. He concluded that the cluster contains large amounts of invisible dark matter.

For some reasons the work of Zwicky escaped the attention of the astronomical community. The next step in the study of mass of systems of galaxies was made by Kahn and Woltjer (1959). They paid attention to the fact that most galaxies have positive redshifts as a result of the expansion of the Universe, only the Andromeda galaxy M31 has a negative redshift of about 120 km/s. This fact can be explained, if both galaxies, M31 and our Galaxy, form a physical system. A negative radial velocity indicates that these galaxies have already passed the apogalacticon of their relative orbit and are presently approaching each other. From the approaching velocity, mutual distance and time since passing the perigalacticon (taken equal to the present age of the Universe) the authors calculated the total mass of the double system. They found that Mtot geq 1.8 × 1012 Msun. The conventional mass of the Galaxy and M31 is of the order of 2 × 1011 Msun, in other words, the authors found evidence for the presence of additional mass in the Local Group of galaxies. The authors suggested that the extra mass is probably in the form of hot ionised gas; most of the paper was devoted to the analysis of the physical state of the gas. Using modern data Einasto & Lynden-Bell (1982) made a new estimate of the total mass of the Local Group, the result was 4.5 ± 0.5 × 1012 Msun for present age of the Universe 14 Gyr. This estimate is in good agreement with new determinations of total masses of M31 and the Galaxy including their dark halos (see below).

The conventional approach for the mass determination of pairs and groups of galaxies is statistical. The method is based on the virial theorem and is almost identical to the procedure used to calculate masses of clusters of galaxies. Instead of a single pair or group a synthetic group is used consisting of a number of individual pairs or groups. These determinations yield for the mass-to-luminosity (in blue light) ratio the values M / LB = 1...20 for spiral galaxy dominated pairs and M / LB = 5...90 for elliptical galaxy dominated pairs (Page 1960, Burbidge & Burbidge 1961, van den Bergh 1961, Karachentsev 1976, Faber & Gallagher 1979).

The stability of clusters of galaxies was discussed in a special meeting during the IAU General Assembly (Neyman, Page & Scott 1961). Here the hypothesis of Ambartsumian on the expansion of clusters was discussed in detail. Van den Bergh (1961) drew attention to the fact that the dominating population in elliptical galaxies is the bulge consisting of old stars, indicating that cluster galaxies are old. It is very difficult to imagine how old cluster galaxies could form an instable and expanding system. These remarks did not find attention and the problem of the age and stability of clusters remained open.

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