  We study the limiting case of the Krichever construction of orthogonal
curvilinear coordinate systems when the spectral curve becomes singular. We
show that the case when the curve is reducible and all its irreducible
components are rational curves the construction procedure reduces to solving
systems of linear equations and simple computations with elementary functions.
Therewith we demonstrate how such well-known coordinate systems as the polar
coordinates, the cylindrical coordinates in the three-space, and the spherical
coordinates in the Euclidean spaces fit in this scheme.
