Fully relativistic calculations of radiative rates and electron impact excitation cross sections for Fe X are used to derive theoretical emission-line ratios involving transitions in the 174-366 A wavelength range. A comparison of these with solar active region observations obtained during the 1989 and 1995 flights of the Solar Extreme-ultraviolet Research Telescope and Spectrograph (SERTS) reveals generally very good agreement between theory and experiment. Several Fe X emission features are detected for the first time in SERTS spectra, while the transition at 195.32 A is identified for the first time (to our knowledge) in an astronomical source. The most useful Fe X electron density diagnostic line ratios are assessed to be 175.27/174.53 and 175.27/177.24, which both involve lines close in wavelength and free from blends, vary by factors of 13 between Ne = 1E8 and 1E13 cm-3, and yet show little temperature sensitivity. Should these lines not be available, then the 257.25/345.74 ratio may be employed to determine Ne, although this requires an accurate evaluation of the instrument intensity calibration over a relatively large wavelength range. However, if the weak 324.73 A line of Fe X is reliably detected, the use of 324.73/345.74 or 257.25/324.73 is recommended over 257.25/345.74.
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