  Measurements of the temperature and density structure of the solar corona
provide critical constraints on theories of coronal heating. Unfortunately, the
complexity of the solar atmosphere, observational uncertainties, and the
limitations of current atomic calculations, particularly those for Fe, all
conspire to make this task very difficult. A critical assessment of plasma
diagnostics in the corona is essential to making progress on the coronal
heating problem. In this paper we present an analysis of temperature and
density measurements above the limb in the quiet corona using new observations
from the EUV Imaging Spectrometer (EIS) on \textit{Hinode}. By comparing the Si
and Fe emission observed with EIS we are able to identify emission lines that
yield consistent emission measure distributions. With these data we find that
the distribution of temperatures in the quiet corona above the limb is strongly
peaked near 1 MK, consistent with previous studies. We also find, however, that
there is a tail in the emission measure distribution that extends to higher
temperatures. EIS density measurements from several density sensitive line
ratios are found to be generally consistent with each other and with previous
measurements in the quiet corona. Our analysis, however, also indicates that a
significant fraction of the weaker emission lines observed in the EIS
wavelength ranges cannot be understood with current atomic data.

Solar and Stellar Astrophysics