  We present calculations of the spin-down of a neutron star atmosphere due to
hydrostatic expansion during a Type I X-ray burst. We show that (i) Cumming and
Bildsten overestimated the spin-down of rigidly-rotating atmospheres by a
factor of two, and (ii) general relativity has a small (5-10%) effect on the
angular momentum conservation law. We rescale our results to different neutron
star masses, rotation rates and equations of state, and present some detailed
rotational profiles. Comparing with recent observations of large frequency
shifts in MXB 1658-298 and 4U 1916-053, we find that the spin-down expected if
the atmosphere rotates rigidly is a factor of two to three less than the
observed values. If differential rotation is allowed to persist, we find that
the upper layers of the atmosphere spin down by an amount comparable to the
observed values; however, there is no compelling reason to expect the observed
spin frequency to be that of only the outermost layers. We conclude that
hydrostatic expansion and angular momentum conservation alone cannot account
for the largest frequency shifts observed during Type I bursts.
