  We consider a classical system of point particles interacting by means of a
short range potential. We prove that, in the low--density (Boltzmann--Grad)
limit, the system behaves, for short times, as predicted by the associated
Boltzmann equation. This is a revisitation and an extension of the thesis of
King (unpublished), appeared after the well known result of Lanford for hard
spheres, and of a recent paper by Gallagher et al (arXiv: 1208.5753v1). Our
analysis applies to any stable and smooth potential. In the case of repulsive
potentials (with no attractive parts), we estimate explicitly the rate of
convergence.
