Theoretical electron-density-sensitive C III emission line ratios are presented for R1 = I(2s2p 3P - 2p2 3P)/I(2s2p 1P - 2p2 1S) = I(1176 angstrom)/I(1247 angstrom), R2 = I(2s2p 3P - 2p2 3P)/I(2s2 1S - 2s2p P-3(1)) = I(1176 angstrom/I(1908 angstrom), and R3 = I(2s2p 1P - 2p2 1S)/I(2S2 1S - 2s2p P-3(1)) = I(1247 angstrom)/I(1908 angstrom). These are significantly different from those deduced previously, principally due to the adoption of improved electron impact excitation rates in the present analysis. Electron densities deduced from the present theoretical line ratios, in conjunction with observed values of R1, R2, and R3 measured from solar spectra obtained by the Naval Research Laboratory's S082B instrument on board Skylab, are found to be generally compatible. In contrast, previous diagnostic calculations imply electron densities from R1, R2, and R3 that differ by up to two orders of magnitude. These results provide observational support for the accuracy of the atomic physics adopted in the present calculations, and the methods employed in the derivation of the theoretical line ratios.