  Let $q_1,q_2,...,q_N$ be the coordinates of $N$ particles on the circle,
interacting with the integrable potential $\sum_{j<k}^N\wp(q_j-q_k)$, where
$\wp$ is the Weierstrass elliptic function. We show that every symmetric
elliptic function in $q_1,q_2,...,q_N$ is a meromorphic function in time. We
give explicit formulae for these functions in terms of genus $N-1$ theta
functions.
