  We prove Archimedes' principle for a macroscopic ball in ideal gas consisting
of point particles with non-zero mass. The main result is an asymptotic
theorem, as the number of point particles goes to infinity and their total mass
remains constant. We also show that, asymptotically, the gas has an exponential
density as a function of height. We find the asymptotic inverse temperature of
the gas. We derive an accurate estimate of the volume of the phase space using
the local central limit theorem.
