The Born-Green equation is used to clarify and estimate the error introduced into Monte Carlo and molecular dynamics simulations of dense fluids by the use of periodic boundary conditions. This theory is applied to the Lennard-Jones fluid and the theoretical predictions are found to be in reasonable agreement with experiment. The implications for size dependence of pressure, for anisotropy of the radial distribution function, for size dependence of the supercooling limit for crystal nucleation, and for the orientations of nucleated crystals are discussed.