  One can associate to many of the well known algebraically integrable systems
of Jacobians (generalized Hitchin systems, Sklyanin) a ruled surface which
encodes much of its geometry. If one looks at the classification of such
surfaces, there is one case of a ruled surface that does not seem to be
covered. This is the case of projective bundle associated to the first jet
bundle of a topologically nontrivial line bundle. We give the integrable system
corresponding to this surface; it turns out to be a deformation of the Hitchin
system.
