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Published online by Cambridge University Press: 14 August 2015
Under the assumption that the inverse square central force law is a good approximation to the gravitational force, at least for large distances, the different possibilities for the evolution of the Universe are sketched. Several of the possibilities lead naturally to a dynamical classification of clusters of galaxies in an expanding universe. In one of the classifications the galaxies must define configurations which are functions of the masses. The virial theorem approach of determining masses of galaxies in a cluster is briefly examined. Some tentative statements concerning a dynamical explanation of the local hypothesis for quasars are advanced. Finally, the role of mathematical probability in predicting the behavior of the Universe is discussed.