  We have used an electron beam ion trap to measure electron-density-diagnostic
line-intensity ratios for extreme ultraviolet lines from F XII, XIII, and XIV
at wavelengths of 185-205 255-276 Angstroms. These ratios can be used as
density diagnostics for astrophysical spectra and are especially relevant to
solar physics. We found that density diagnostics using the Fe XIII
196.53/202.04 and the Fe XIV 264.79/274.21 and 270.52A/274.21 line ratios are
reliable using the atomic data calculated with the Flexible Atomic Code. On the
other hand, we found a large discrepancy between the FAC theory and experiment
for the commonly used Fe XII (186.85 + 186.88)/195.12 line ratio. These FAC
theory calculations give similar results to the data tabulated in CHIANTI,
which are commonly used to analyze solar observations. Our results suggest that
the discrepancies seen between solar coronal density measurements using the Fe
XII (186.85 + 186.88)/195.12 and Fe XIII 196.54/202.04 line ratios are likely
due to issues with the atomic calculations for Fe XII.
