  We give a complete proof of the result stated in an earlier article, that the
general Einstein metric with a symmetry, an anti-self-dual Weyl tensor and
nonzero scalar curvature is determined by a solution of the $SU(\infty)$-Toda
field equation. We consider the two canonical forms found for solutions to the
same problem by Przanowski (J.Math.Phys. 32(1991) 1004-1010) and show that his
Class A will reduce to the Toda equation with respect to a second complex
structure, different from that in which the metric is first given.
