  [Background] Besides its intrinsic value as a fundamental nuclear-structure
observable, the weak-charge density of 208Pb - a quantity that is closely
related to its neutron distribution - is of fundamental importance in
constraining the equation of state of neutron-rich matter.
  [Purpose] To assess the impact that a second electroweak measurement of the
weak-charge form factor of 208Pb may have on the determination of its overall
weak-charge density.
  [Methods] Using the two putative experimental values of the form factor,
together with a simple implementation of Bayes' theorem, we calibrate a
theoretically sound - yet surprisingly little known - symmetrized Fermi
function, that is characterized by a density and form factor that are both
known exactly in closed form.
  [Results] Using the charge form factor of 208Pb as a proxy for its
weak-charge form factor, we demonstrate that using only two experimental points
to calibrate the symmetrized Fermi function is sufficient to accurately
reproduce the experimental charge form factor over a significant range of
momentum transfers.
  [Conclusions] It is demonstrated that a second measurement of the weak-charge
form factor of 208Pb supplemented by a robust theoretical input in the form of
the symmetrized Fermi function, would place significant constraints on the
neutron distribution of 208Pb and, ultimately, on the equation of state of
neutron-rich matter.
