  Suppose we have a natural Hamiltonian $H$ of $n$ particles on the line,
centre of mass momentum $P$ and a further independent quantity $Q$, cubic in
the momenta. If these are each $S_{n}$ invariant and mutually Poisson commute
we have the Calogero-Moser system with potential $V={1/6}\sum\limits_{i\neq
j}\wp(q_{i}-q_{j}) +const$.
