Electron densities derived from Si III, Ne VII, Mg VIII, Si VIII, and Mg IX line ratios observed above the limb of a polar coronal hole with the Solar Ultraviolet Measurements of Emitted Radiation (SUMER) spectrometer on the Solar and Heliospheric Observatory (SoHO) are presented. The electron densities are consistent with a constant pressure of 1.6 × 1014cm−3 K (logPe = 14.2).