  We continue the study of the time evolution of a system consisting of a
piston in a cubical container of large size $L$ filled with an ideal gas. The
piston has mass $M\sim L^2$ and undergoes elastic collisions with $N\sim L^3$
gas particles of mass $m$. In a previous paper, Lebowitz, Piasecki and Sinai
considered a scaling regime, with time and space scaled by $L$, in which they
argued heuristically that the motion of the piston and the one particle
distribution of the gas satisfy autonomous coupled differential equations. Here
we state exact results and sketch proofs for this behavior.
