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¿1014 cm-3 K (log Pe=14.2). ¿ 1999 American Geophysical Union