THE REDSHIFT DISTANCE RELATION

Key predictions of the Hubble law are inconsistent with direct observa tions on equitable complete samples of extragalactic sources in the op tical, infrared, and x-ray wave bands-e.g., the predicted dispersion i n apparent magnitude is persistently greatly in excess of its observed value, precluding an explanation via hypothetical perturbations or ir regularities. In contrast, the predictions of the Lundmark (homogeneou s quadratic) law are consistent with the observations. The Lundmark la w moreover predicts the deviations between Hubble law predictions and observation with statistical consistency, while the Hubble law provide s no explanation for the close fit of the Lundmark law. The flux-redsh ift law F is-proportional-to (1 + z)/z appears consistent with observa tions on equitable complete samples in the entire observed redshift ra nge, when due account is taken of flux limits by an optimal statistica l method. Under the theoretical assumption that space is a fixed spher e, as in the Einstein universe, this law implies the redshift-distance relation z = tan2(r/2R), where R is the radius of the spherical space . This relation coincides with the prediction of chronometric cosmolog y, which estimates R as 160 +/- 40 Mpc (1 parsec = 3.09 x 10(16) m) fr om the proper motion to redshift relation of superluminal sources. Tan gential aspects, including statistical methodology, fundamental physic al theory, bright cluster galaxy samples, and proposed luminosity evol ution, are briefly considered.