  Eddington-limited X-ray bursts from neutron stars can be used in conjunction
with other spectroscopic observations to measure neutron star masses, radii,
and distances. In order to quantify some of the uncertainties in the
determination of the Eddington limit, we analysed a large sample of
photospheric radius-expansion thermonuclear bursts observed with the Rossi
X-ray Timing Explorer. We identified the instant at which the expanded
photosphere "touches down" back onto the surface of the neutron star and
compared the corresponding touchdown flux to the peak flux of each burst. We
found that for the majority of sources, the ratio of these fluxes is smaller
than 1.6, which is the maximum value expected from the changing gravitational
redshift during the radius expansion episodes (for a 2M_sun neutron star). The
only sources for which this ratio is larger than 1.6 are high inclination
sources that include dippers and Cyg X-2. We discuss two possible geometric
interpretations of this effect and show that the inferred masses and radii of
neutron stars are not affected by this bias. On the other hand, systematic
uncertainties as large as ~50% may be introduced to the distance determination.
