Limits on the Local Deviation of the Universe from a Homogeneous Model.

If the Hubble constant is determined by some means in the redshift range 4000 <cz < 15, 000 km s-, are corrections needed to obtain an "asymptotic" value which has a global significance? The size of such a correction depends on the effect of departures from homogeneity on the velocity field. We have set limits on this effect and on departures from spatial homogeneity in two ways. 1. Analysis of perturbations on the velocity field of 30 local (cz < 10, 000 km s ') clusters of galaxies was made by testing departures of the slope A of the redshift-magnitude relation rn = A log cz B from the value of 5. The departure was less than 1 g for all solutions. Using a dynamical model by Haggerty and Wertz, we are able to set limits on the density contrast. We are puzzled by our cluster result compared with different results by de Vaucouleurs for field galaxies, and we believe the problem remains open. Because of the obvious local clumping of matter on a scale of 20 Mpc, such lack of perturbation, if correct, could require that q0 0. In any case, the agreement of the cluster data with the prediction from the homogeneous model, in the z 0 limit, requires that no correction to H6 should be made. 2. New data on galaxy counts in the CataThgue of Galaxies and of Galaxies were obtained, and are tabulated for the north and south polar caps to = 15. 7. These data, together with the galaxy counts of Mayall, Shane and Wirtanen, and Hubble put limits on any systematic deviation from largescale homogeneity. Following Wertz, if a systematic deviation is characterized by N (r), the limit on 0 is 0 = -0. 115 + 0. 030, which does not differ significantly from 0 = 0. A hierarchical model suggested by de Vaucouleurs with 0 = 1. 7 is not confirmed. The result is the same as that which was obtained from the deep surveys of Hubble and Mayall.