The local redshift-distance relation and spatial uniformity.

Regrettably, the review of the redshift-distance relation in the review by Salpeter and Hoffman [Salpeter, E. E. & Hoffman, G. L., Jr. (1986) Proc. Natl. Acad. Sci. USA 83, 3056-3063], appears flawed. In particular, the logically inconclusive and uncertain hypothesis of local extragalactic spatial uniformity is used in an essential way. Moreover, even in conjunction with this hypothesis, the Lundmark law fits more closely than the Hubble law, on the basis of the data and criteria of Salpeter and Hoffman, when a rough approximation involved in the estimation of the galaxy luminosity function is eliminated. Specifically, the assumption that all galaxies in the redshift range 500-1700 km.s(-1) are effectively at the redshift 1100 km.s(-1) is made; when this assumption is replaced by a statistically optimal procedure that uses the precise redshifts, the relative fit of the two laws is reversed.