The space-time metric is derived by following the classical treatment in which the universe is regarded as a static continuous fluid of densityϱ and pressurep. It was necessary to make the assumption thatp+c2ϱ=0 so that the effects of a finite density could be considered. The metric contains a time dilation coefficient which produces a redshift proportional to the density and to the square of the distance between source and observer. Observational data are not inconsistent with a square law within a distance of 30 Mpc. The mean densityϱ may be sufficient to account for the observed redshift even though the system of galaxies is stationary. The density required for a non-expanding interpretation is 6.6·10−27 g cm−3 if the absolute magnitude of the average field galaxy is −20.07.