We have reanalyzed SUMER observations of a parcel of coronal gas using new collisional ionization equilibrium ( CIE ) calculations . These improved CIE fractional abundances were calculated using state-of-the-art electron-ion recombination data for K-shell , L-shell , Na-like , and Mg-like ions of all elements from H through Zn and , additionally , Al- through Ar-like ions of Fe . They also incorporate the latest recommended electron impact ionization data for all ions of H through Zn . Improved CIE calculations based on these recombination and ionization data are presented here . We have also developed a new systematic method for determining the average emission measure ( EM ) and electron temperature ( T _ { e } ) of an isothermal plasma . With our new CIE data and our new approach for determining average EM and T _ { e } , we have reanalyzed SUMER observations of the solar corona . We have compared our results with those of previous studies and found some significant differences for the derived EM and T _ { e } . We have also calculated the enhancement of coronal elemental abundances compared to their photospheric abundances , using the SUMER observations themselves to determine the abundance enhancement factor for each of the emitting elements . Our observationally derived first ionization potential ( FIP ) factors are in reasonable agreement with the theoretical model of Laming ( 31 ) .