A survey of galaxy redshifts. III. The density field and the induced gravity field.

The observed luminosity distribution function of the north and south samples is displayed, showing them to be quite similar and moderately well fitted by a Schechter luminosity function. The determined luminosity function is used to compare a plot of the observed velocity distribution of the sample with what would be expected in a homogeneous universe. The presence of a large hole behind the foreground Virgo cluster is strikingly apparent. It is considered surprising, however, that the average number and luminosity density for the north and for the south agree remarkably well. Also derived is the average overdensity of the Virgo supercluster interior to the radius of the Local Group of galaxies. It is shown that, given a luminosity function and radial shell counts, it is possible, using linear perturbation theory, to derive the peculiar gravity caused by the inhomogeneous matter distribution on large scales and the expected velocity of the Local Group of galaxies.