  We consider integrable systems that are connected with orthogonal separation
of variables in complex Riemannian spaces of constant curvature. An isomorphism
with the hyperbolic Gaudin magnet, previously pointed out by one of us, extends
to coordinates of this type. The complete classification of these separable
coordinate systems is provided by means of the corresponding $L$-matrices for
the Gaudin magnet. The limiting procedures (or $\epsilon $ calculus) which
relate various degenerate orthogonal coordinate systems play a crucial result
in the classification of all such systems.
