  We report an experimental study of \nco, a Mott insulator containing chains
of edge-sharing CuO$_4$ plaquettes, by polarized x-ray absorption spectroscopy
(XAS), resonant magnetic x-ray scattering (RMXS), magnetic susceptibility, and
pyroelectric current measurements. The XAS data show that the valence holes
reside exclusively on the Cu$^{2+}$ sites within the copper-oxide spin chains
and populate a $d$-orbital polarized within the CuO$_4$ plaquettes. The RMXS
measurements confirm the presence of incommensurate magnetic order below a
N\'eel temperature of $T_N = 11.5$ K, which was previously inferred from
neutron powder diffraction and nuclear magnetic resonance data. In conjunction
with the magnetic susceptibility and XAS data, they also demonstrate a new
"orbital" selection rule for RMXS that is of general relevance for magnetic
structure determinations by this technique. Dielectric property measurements
reveal the absence of significant ferroelectric polarization below $T_N$, which
is in striking contrast to corresponding observations on the isostructural
compound \lco. The results are discussed in the context of current theories of
multiferroicity.
