We show how to recover the distribution function f(E, L^2^) of an equilibrium population in a spherical stellar system, as well as the gravitational potential {PHI}(r) in which that population orbits, given its joint distribution of apparent positions and line-of-sight velocities. No assumptions are made about the variation with radius of the mass-to-light ratio or the form of f Practical nonparametric algorithms are presented for the case of continuous data, as derived from integrated stellar spectra, and discrete data, in the form of individual radial velocities. Ruling out a constant mass-to-light ratio model for any early-type galaxy with a dark halo is shown to require accurate measurement of the line-of-sight velocity distribution at radii extending well beyond the effective radius. In the case of discrete data sets, it is shown that estimates of {PHI}(r) from samples containing only a few hundred velocities can be rather strongly dependent on presumptions about the smoothness of f.
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David Merritt (1993) studied this question.