  Accurate measurements of electron density are critical for determination of
the plasma properties in the solar corona. We compare the electron densities
diagnosed from Fe XIII lines observed by the Extreme-Ultraviolet Imaging
Spectrometer (EIS) onboard the Hinode mission with the near infra-red (NIR)
measurements provided by the ground-based Coronal Multichannel Polarimeter
(COMP). To do that, the emissivity-ratio method based on all available observed
lines of Fe XIII is used for both EIS and CoMP. The EIS diagnostics is further
supplemented by the results from Fe XII lines. We find excellent agreement,
within 10%, between the electron densities measured from both EUV and NIR
lines. In the five regions selected for detailed analysis, we obtain electron
densities of log(Ne [cm-3]) = 8.2-8.6. Where available, the background
subtraction has a significant impact on the diagnostics, especially on the NIR
lines, where the loop contributes less than a quarter of the intensity measured
along the line of sight. For the NIR lines, we find that the line center
intensities are not affected by stray light within the instrument, and
recommend using these for density diagnostics. The measurements of the Fe XIII
NIR lines represent a viable method for density diagnostics using ground-based
instrumentation.
