Abstract; Masses and radii of degenerate stars were calculated using a pressure function which significantly deviates from the usual one based on the Fermi energy of free electrons. Assuming only a central number density ranging from 10³⁰cm^-3to 10³⁶ cm^{^-3}, the calculations yield masses between those of Jupiter and the sun. The masses were found to be a function of the composition of the elements. The maximum masses and the cosmic abundance of the elements are correlated. The radii come close to those of pulsars at high central densities, while at low densities they are equal to those of white dwarfs. (Formerly added: The period lengths of shock waves in dense stars are calculated, the results being in agreement with the observed period-lengths of pulsars. A proposal for interpreting quasi-stellar objects is made assuming matter compised if electrons and positrons.)