  This paper is the third in a series reporting on a study of carbon abundances
in a carefully chosen sample of planetary nebulae representing a large range in
progenitor mass and metallicity. We make use of the IUE Final Archive database
containing consistently-reduced spectra to measure line strengths of C III]
1909 along with numerous other UV lines for the planetary nebulae DDDM1, IC
3568, IC 4593, NGC 6210, NGC 6720, NGC 6826, & NGC 7009. We combine the IUE
data with line strengths from optical spectra obtained specifically to match
the IUE slit positions as closely as possible, to determine values for the
abundance ratios He/H, O/H, C/O, N/O, and Ne/O. The ratio of C III] 1909/C II
4267 is found to be effective for merging UV and optical spectra when He II
1640/4686 is unavailable. Our abundance determination method includes a 5-level
program whose results are fine-tuned by corrections derived from detailed
photoionization models constrained by the same set of emission lines. All
objects appear to have subsolar levels of O/H, and all but one show N/O levels
above solar. In addition, the seven planetary nebulae span a broad range in C/O
values. We infer that many of our objects are matter bounded, and thus the
standard ionization correction factor for N/O may be inappropriate for these
PNe. Finally, we estimate C/O using both collisionally-excited and
recombination lines associated with C+2 and find the well established result
that abundances from recombination lines usually exceed those from
collisionally-excited lines by several times.
