We explore the incorporation of the cosmically abundant species O, C, N, Mg, Si, Fe, and S into interstellar dust. Column densities based on Goddard High Resolution Spectrograph 3.5 km/s resolution measurements from the literature for eight individual absorbing regions toward five lines of sight are used. Corrections are applied as needed in order to account for recent improvements in oscillator strengths. In order to acquire the most accurate column densities, and check on the accuracy of the oscillator strengths, we compare column densities based on the very strong Lorentzian damped lines of C II, O I, N I, and Mg II with results for the weak lines of these species, and confirm the previously determined f-values for O I lambda 1335, C II lambda 2325, and N I lambda lambda 1159, 1160. New empirical f-values of 1.25 x 10(exp -3) and 6.25 x 10(exp -4), respectively, are derived for the Mg II weak doublet at 1239 and 1240 A. Assuming a cosmic reference abundance based on solar and B star values, we derive depletions and dust-phase abundances which suggest that more than 70% of the available Mg and Fe is incorporated into dust-grain cores, whereas only 35% of the silicon is. This implies that oxides are important constituents of the grain core population. Mg and Fe atoms are mantled onto grain cores in a ratio of 1.8 to 1, whereas approximately 4.0 Si atoms are in the mantle per Fe atom. Since Si is not expected to accrete onto silicate or graphite grains, other grain cores, perhaps oxides and/or metallic Fe, may provide mantling sites for this species. The abundances of Fe and Mg in mantles would imply that graphite grains must have a substantial coating unless oxides provide significant mantling sites for these species. The abundance of O and N in the dust phase as implied by the solar reference abundance values are difficult to reconcile with the fact that these elements are not expected to participate in mantle formation, and the 3.1 micrometer H2O ice feature is not seen in absorption toward stars similar to those studied. The B star reference abundances for O and N, however, imply that no mantling of these species has occurred. The dust-phase abundance for C implied by solar reference abundances agrees with predictions for the number of graphite grains needed to produce the 2175 A bump. B star reference abundances, however, suggest that the abundance of C in the dust phase is not always sufficient to produce the bump.