A Nonhomogeneous Cosmological Model.

Various theories about the extragalactic red shift are considered. It is concluded that actual recessional motion is the most plausible explanation of the observed red shifts. To avoid the well-known difficulties of the homogeneous cosmological models, a group of relativistic, nonstatic, nonhomogeneous, cosmological models which have spherical symmetry, zero pressure, and co-moving co-ordinates are considered. As a first approximation the observer is assumed to be near the center of symmetry. Then, following the general procedures of Hubble and Tolman, we can derive the necessary relations between the theoretical model and the astronomical observations. The average density of matter in the neighborhood of the observer at the present time is assumed to be 1O~ gm/cc. The cosmological constant is taken to be 8.78 X 1019 (1ight-years)~. For the radius of curvature in the neighborhood of the observer we assign 1/R2 = - 1O~0 (light-years)~. Then the total time elapsed in the neighborhood of the observer since the beginning of the expansion would be 3.64 X 1O~ years. The calculated red shifts agree with the observed red shifts given by Hubble to within 0.1 mag., except for the two Ursa Major clusters, for which the observational data are unreliable. The calculated values of log N, where N is the nebular count per square degree, depart from the observed values pre- sented by Hubble by 0.002 or less. The expansion in this model does not begin simultaneously every- where, but begins at progressively later epochs for those spatial regions which have larger radial co- ordinates. This suggests a possible explanation of the red excesses observed by Stebbins and Whitford for the E nebulae in the clusters. The hypothetical nature of the model must be emphasized, since the theoretical assumptions have been oversimplified and the observational data are not too reliable. The chief value of the model possibly lies in showing that currently accepted astronomical data can be treated by accepted physical principles without the necessity of introducing new physical hypotheses