  I show that solutions of the SU(infinity) Toda field equation generating a
fixed Einstein-Weyl space are governed by a linear equation on the
Einstein-Weyl space. From this, obstructions to the existence of Toda solutions
generating a given Einstein-Weyl space are found. I also give a classification
of Einstein-Weyl spaces arising from the Toda equation in more than one way.
This classification coincides with a class of spaces found by Ward and hence
clarifies some of their properties. I end by discussing the simplest examples.
