  A systematic construction of a Lax pair and an infinite set of conservation
laws for the Ernst equation is described. The matrix form of this equation is
rewritten as a differential ideal of gl(2,R)-valued differential forms, and its
symmetry condition is expressed as an exterior equation which is linear in the
symmetry characteristic and has the form of a conservation law. By means of a
recursive process, an infinite collection of such laws is then obtained, and
the conserved "charges" are used to derive a linear exterior equation whose
components constitute a Lax pair.
