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6. All of the discussions which follow are based on HUBBLE'S old distance scale, corresponding to a symbolic velocity of recession (universal redshift) equal to Vs = 550 km/sec per million parsecs. The investigations by TH. PAGE and E. HOLMBERG, mentioned in the following, use Vs = 526 km/sec per million parsecs.

Various values for the masses of individual galaxies have been obtained from the study of their absolute luminosities, from internal motions and rotations, from the velocity dispersion in clusters of galaxies and from the differences in radial velocities of the components of double galaxies. Radio astronomy and the possible future discovery of gravitational lens effects promise to offer further approaches to the masses of galaxies.

The masses of individual galaxies were originally derived from either absolute luminosities [11], assuming that these masses are, in solar units, equal to a few times the luminosities of these galaxies, also measured in solar units. This approach is thus based on the assumption that the mass-luminosity ratio for a whole galaxy is, in order of magnitude, the same as the corresponding ratio averaged over all of the known stars in the solar neighborhood. This of course disregards the possibility of large masses being concentrated in dark bodies, gases and dust. The masses of even the most luminous galaxies, on these assumptions, are only a few billion times that of the Sun (109 Msun).

ZWICKY, in 1933, made the first determination of masses of galaxies on the basis of the virial theorem and the velocity dispersion in clusters of galaxies [17]. For instance, for the six hundred brightest galaxies in the Coma cluster he derived an average value for the individual masses of about 2 x 1011 Msun, or several hundred times the value estimated from luminosities. Although it was later found that clusters of galaxies contain very many dwarf galaxies and probably much dark dispersed intergalactic matter, such as gases and dust [9], the whole discrepancy probably cannot be entirely described to the existence of these components. This conclusion is strengthened by the results of PAGE and HOLMBERG on the masses of the components of double galaxies. PAGE [14], from the investigation of 35 double systems, obtained a mean mass of 8 x 1010 Msun for the component galaxies and a mass luminosity ratio of 348 in the above mentioned solar units. E. HOLMBERG, in his most recent studies [18], derived for the components of 26 double galaxies a mean mass of 6.5 x 1010 Msun and a mass luminosity ratio equal to 127. Although these investigations are subject to rather large errors of both observational and theoretical origin, they nevertheless indicate, in confirmation of the results derived from the velocity dispersions in clusters, that the masses of galaxies are very much larger than could be inferred from their luminosities. The methods used by PAGE and HOLMBERG can be strengthened, if more accurate differences in radial velocities of multiple galaxies are obtained, and if not only average differences are used but the whole fields of the radial velocities over the full extent of the galaxies involved are studied. Furthermore, one must make sure that one does not deal with optical doubles or with galaxies which are clearly escaping from one another. Also, it will be necessary to obtain accurate distances of the double galaxies studied.

The requirements mentioned for trustworthy determinations of the masses of the components of double galaxies are obviously severe and not easily satisfied. Independent approaches are therefore most desirable. Unfortunately, the determination of the mass of a galaxy from its rotation and its internal motions is beset by equally severe difficulties [9]. On the other hand, the discovery of gravitational lens effects among galaxies would do away with most of the uncertainties [17], [9]. For details on the theory of gravitational lenses the reader is referred to "Morphological Astronomy", by F. ZWICKY, Springer Verlag 1957.

What features of multiple galaxies reflect phenomena which took place during the creation of stars and galaxies and what other features are due to evolution or to the effects of rather recent encounters is a most fascinating problem. Far too little, however, is known at the present time about these subjects to permit us to make any statements here, lest we wish to run the danger of indulging in idle speculations. We only recommend that, an attack on multiple galaxies with all of the means at our disposal should certainly prove most fruitful to unravel the mysteries surrounding the origin and the evolution of the large scale aggregates of matter in the universe.

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