  The Vlasov-Poisson system describes interacting systems of collisionless
particles. For solutions with small initial data in three dimensions it is
known that the spatial density of particles decays like $t^{-3}$ at late times.
In this paper this statement is refined to show that each derivative of the
density which is taken leads to an extra power of decay so that in $N$
dimensions for $N\ge 3$ the derivative of the density of order $k$ decays like
$t^{-N-k}$. An asymptotic formula for the solution at late times is also
obtained.
