Abstract: A chain of quantum particles on a line interacting through the
sinh^{-2}(x) pair potential is considered. The spectral density
of the Lax matrix L in the classical and thermodynamical limit
is shown to satisfy the integral equation conjectured by
Sutherland. The proof is based on the analytic properties of
elliptic functions. The work was done together with V. I. Inozemtsev.
