  A `polydisperse' system has an infinite number of conserved densities. We
give a rational procedure for projecting its infinite-dimensional free energy
surface onto a subspace comprising a finite number of linear combinations of
densities (`moments'), in which the phase behavior is then found as usual. If
the excess free energy of the system depends only on the moments used, exact
cloud, shadow and spinodal curves result; two- and multi-phase regions are
approximate, but refinable indefinitely by adding extra moments. The approach
is computationally robust and gives new geometrical insights into the
thermodynamics of polydispersity.
