  This paper studies representation stability in the sense of Church and Farb
for representations of the symmetric group $S_n$ on the cohomology of the
configuration space of $n$ ordered points in $\mathbf{R}^d$. This cohomology is
known to vanish outside of dimensions divisible by $d-1$; it is shown here that
the $S_n$-representation on the $i(d-1)^{st}$ cohomology stabilizes sharply at
$n=3i$ (resp. $n=3i+1$) when $d$ is odd (resp. even).
  The result comes from analyzing $S_n$-representations known to control the
cohomology: the Whitney homology of set partition lattices for $d$ even, and
the higher Lie representations for $d$ odd. A similar analysis shows that the
homology of any rank-selected subposet in the partition lattice stabilizes by
$n\geq 4i$, where $i$ is the maximum rank selected.
  Further properties of the Whitney homology and more refined stability
statements for $S_n$-isotypic components are also proven, including conjectures
of J. Wiltshire-Gordon.
