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Time resolved X-ray spectroscopy of thermonuclear bursts observed from lowmass X-ray binaries offer a unique tool to measure neutron star masses andradii. In this paper, we continue our systematic analysis of all the X-raybursts observed with RXTE from X-ray binaries. We determine the events whichshow clear evidence for photospheric radius expansion and measure the Eddingtonlimits for these accreting neutron stars using the bolometric fluxes attainedat the touchdown moments of each X-ray burst. We employ a Bayesian technique toinvestigate the degree to which the Eddington limit for each source remainsconstant between bursts. We find that for sources with a large number of radiusexpansion bursts, systematic uncertainties are at a 5-10% level. Moreover, insix sources with only pairs of Eddington-limited bursts, the distribution offluxes is consistent with a ~10% fractional dispersion. This indicates that thespectroscopic measurements of neutron star masses and radii using thermonuclearX-ray bursts can reach the level of accuracy required to distinguish betweendifferent neutron star equations of state, provided that uncertainties relatedto the overall flux calibration of X-ray detectors are of comparable magnitude.

Systematic Uncertainties in the Spectroscopic Measurements of Neutron-Star Masses and Radii from Thermonuclear X-ray Bursts. II. Eddington Limit