  An attempt is made to compare statistical properties of self-diffusion of
particles constituting gases in infinite volume and on torus. In this second
part, derivation, from BBGKY equations, of roughened model of self-diffusion is
revised as applied to finite $N$-particle gas under micro-canonical ensemble.
The model confirms existence of characteristic time $\approx N$, in units of
free flight time, for cross-over between non-Gaussian and Gaussian regimes of
diffusion, but then loses its legacy.
