Using new close-coupling excitation rates for the C-like ion Si IX, density-diagnostic ratios based on Si IX lines have been re-evaluated and applied to a sequence of CDS observations taken above a polar coronal hole. The derived electron densities are in excellent agreement with previous values of N_{e} estimated from the N-like ion Si VIII for another coronal hole. The confirmed trend is for a fall-off of one order of magnitude within the first 0.3R\odot above the limb. These densities are well fitted with an analytic formulae for the density profile out to at least 8R\odot, by which stage the electron density has fallen to ~ 4 10^{3} cm^{-3}, from 1.5 10^{8} cm^{-3} at 1.0R\odot.