Is the velocity-distance relation for galaxies linear?

Diameters of ScI galaxies, the luminosities of supernovae of type Ia at maximum light, and the brightness of central galaxies in rich clusters are examined as potential yardsticks or standard candles for study of the velocity-distance relationship. Both supergiant ScI galaxies and supernovae Ia (which have luminosities that differ by up to a factor of approximately 10) are found to be unsuitable for such a study. The remarkably small luminosity dispersion of first-ranked cluster galaxies (which is not yet understood physically) suggests that deviations from a linear velocity-distance relationship are less, approximately 20% out to red shifts of approximately 40,000 km.s-1.