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Computer models for peculiar forms of interacting galaxies are developed to explain tidal distortions. (WDM)

Very long wavelength universal gravitational waves cannot now produce in clusters of galaxies velocity dispersions greater than that which these systems would possess if they were expanding with the Universe, if the Universe is not younger than $10^{10}$ yr and Hubble's constant is not less than 50 km/sec/ Mpc. A diagram shows that actual velocity dispersions are significantly greater than this limit.

Gaps in the red-shift distribution of quasi-stellar objects and related peculiar galaxies have been studied using 205 sources. The result indicates certain definite trends in the distribution of the gaps but does not suggest any periodicity when the entire sample is considered.

A closed formula for the relation between distance and redshift in an expanding radiation-filled universe is derived for the case of positive cosmological constant and positive space curvature. This formula is then generalized so that it is valid for all values of the cosmological constant and the three possible space curvatures. From this distance redshift formula, a generalized redshift magnitude relation is found. This latter formula is then checked by testing it with the cases expressible in terms of elementary functions.

Galactic evolution may be rapid enough to reconcile the observed magnitude-redshift relation with cosmological models of acceptably great age and low density, in spite of recent evidence to the contrary. Previous treatments of this subject have suffered from use of wrong quantities as the evolutionary correction, and from lack of generality in galactic models. A range of giant elliptical galaxies can be synthesized which are compatible with the available photometry, including Oke and Sandage's (1968) observations of a slow rate of change of color B-V. One such model galaxy is discussed which evolves sufficiently rapidly at short wavelengths to provide an evolutionary correction of several tenths of a magnitude at redshift 0.46.

The observational evidence concerning the nature of the redshifts in quasistellar objects and some peculiar galaxies is reviewed. On balance it seems probable that large intrinsic redshift components are present in some objects.

The analysis by Burbidge and co-workers on the proximity of quasi-stellar objects (QSOs) to bright galaxies is considered within the theory of the generalized gravitational potential. It is shown that in this theory the red-shift data are consistent with a connection hypothesis for three of the four QSO-galaxy systems considered in the statistical analysis.

Distance determinations of the high-redshift galaxy NGC 7319 in Stephan’s Quintet, based on 21-cm line observations, yield a value much smaller than the cosmological distance. At the 98.7% level, a part of the redshift of this galaxy which could amount to 5000 km s−1 is anomalous.

Evidence for non-cosmological redshifts is reviewed. It is shown that all current statistical tests favor association of QSRs with galaxies close by, in distance, to our own. It is possible that all QSRs originate from galaxies of much lower redshift. It is shown that in the four cases where QSRs fall projected closest to bright galaxies, that in all four cases the galaxies show evidence of physical interaction. Evidence for high redshift, compact and peculiar companion galaxies is reviewed. From the individual associations of high redshift QSRs and companions, an empirical continuity of observed characteristics is shown between compactness (youth) and excess redshift. Some theoretical explanations for intrinsic redshifts are mentioned.

A new identification for spectral lines of the N-galaxy 3 C 371 is proposed. The resulting redshift isz=0.40.

The reddening of field galaxies is equal to kz, where k is the linear coefficient in the Kcorrection (z) = kz, and z is the solution to the redshift-magnitude relation log z = 0.2m - 4.630, where m is the apparent magnitude as seen outside the Galaxy, Keorrected for the redshift z. This result holds out to un-K-corrected magnitude (pg). Key words: cosmological reddening - cosmological expansion - redshifts