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This paper is the third in a series reporting on a study of carbon abundancesin a carefully chosen sample of planetary nebulae representing a large range inprogenitor mass and metallicity. We make use of the IUE Final Archive databasecontaining consistently-reduced spectra to measure line strengths of C III]1909 along with numerous other UV lines for the planetary nebulae DDDM1, IC3568, IC 4593, NGC 6210, NGC 6720, NGC 6826, & NGC 7009. We combine the IUEdata with line strengths from optical spectra obtained specifically to matchthe IUE slit positions as closely as possible, to determine values for theabundance ratios He/H, O/H, C/O, N/O, and Ne/O. The ratio of C III] 1909/C II4267 is found to be effective for merging UV and optical spectra when He II1640/4686 is unavailable. Our abundance determination method includes a 5-levelprogram whose results are fine-tuned by corrections derived from detailedphotoionization models constrained by the same set of emission lines. Allobjects appear to have subsolar levels of O/H, and all but one show N/O levelsabove solar. In addition, the seven planetary nebulae span a broad range in C/Ovalues. We infer that many of our objects are matter bounded, and thus thestandard ionization correction factor for N/O may be inappropriate for thesePNe. Finally, we estimate C/O using both collisionally-excited andrecombination lines associated with C+2 and find the well established resultthat abundances from recombination lines usually exceed those fromcollisionally-excited lines by several times.Comment: 36 pages, 7 tables, 2 figures, latex. Tables and figures supplied as  two separate postscript files. Accepted for publication in Ap

A New Look at Carbon Abundances in Planetary Nebulae. III. DDDM1, IC 3568, IC 4593, NGC 6210, NGC 6720, NGC 6826, and NGC 7009