LIMITS TO PRESSURE IN STARS AND VELOCITY DISPERSIONS IN STELLAR-SYSTEMS

New, rigorous, upper and lower limits to pressure in outer layers of s pherically symmetric mass distributions in hydrostatic equilibrium are presented. Upper and lower limits to general integrals of stellar var iables are obtained and illustrated. The pressure inequalities transla te into rigorous, upper and lower limits for velocity dispersion in is otropic, spherically symmetric stellar systems. They set lower limits to gravitational masses of galaxies in terms of the X-ray temperatures of the gas they contain.