This is the third paper in a series which aims to identify the acceleration mechanisms acting on the ionized gas in the narrow line region (NLR) of Seyfert galaxies. Using the sample and approach described in Papers I and II, galaxy luminosity, M(tot), and bulge luminosity, M(bul), are taken as the principal parameters describing nuclear virial speeds, while radio luminosity and morphology are used to track possible nuclear perturbations. The fundamental conclusions from Paper II are confirmed. Plots of [O III] FWHM versus M(tot) or M(bul) show strong correlations (R approximately 0.6, P(null) approximately 10(-8) indicating that gravity plays a key role in defining the NLR velocity field. However, Seyfert galaxies with linear radio morphology and high radio luminosity (L1415 greater-than-or-equal-to 10(22.5) W Hz-1) have systematically broader lines, suggesting that acceleration of NLR gas by outflowing jets is also important in some Seyferts. For Seyfert galaxies without linear radio sources, [O III] FWHM is more fundamentally related to M(bul) than M(tot). Indeed, the scatter in the M(tot) versus [O III] FWHM relation has a Hubble-type dependence which is identical to the Hubble-type dependence of the bulge/total ratio used in the evaluation of M(bul) from M(tot). This agreement between photometrically defined bulge/total ratio for normal spirals and kinematically defined bulge/total ratio for Seyfert galaxies lends powerful support to the argument that M(bul) is playing the fundamental role. A fit to the M(bul) versus [O III] FWHM relation of the form L(bul) is-proportional-to (FWHM)n gives gradient n congruent-to 2.2, zero point FWHM20 congruent-to 250 km s-1 (where FWHM20 = FWHM at M(bul) = -20), and approximately 1 mag scatter. This is compared to the Faber-Jackson relation for normal galaxies, L(bul) is-proportional-to (FWHM(stars))n, where n congruent-to 3.2 and FWHM20 congruent-to 360 km s-1. The overall similarity of these two relations supports the virial origin of [O III] FWHM. In detail, however, the Seyferts appear offset from the Faber-Jackson relation. The offset may be viewed in two ways. Either FWHM[O III] congruent-to 0.7 x FWHM(stars), or Seyfert galaxies are approximately 1 mag more luminous than normal spirals for a given bulge (or total) mass The possibility that Seyfert galaxies are overluminous is investigated using the Tully-Fisher relation, M(tot) versus DELTA-V(rot)c. There is some indication that Seyfert galaxies, particularly those of early type, are offset, although the effect is confused by the underlying Hubble-type dependence of the Tully-Fisher relation. The situation is clarified using a normalized Tully-Fisher plot in which this type dependence is removed. It seems that Seyfert galaxies are indeed offset relative to normal spirals (P(null) approximately 0.04), implying M/L ratios lower by a factor approximately 1.5-2.0. Both the Faber-Jackson and Tully-Fisher offsets for Seyfert galaxies are compared to similar offsets found previously for peculiar radio galaxies and spirals in compact groups. It is possible that enhanced star formation causes lower M/L ratios in Seyfert galaxies, although the absence of a correlation between offset and galaxy color excess fails to support this possibility. Offsets on the M(bul) versus [O III] FWHM plot are further analyzed by introducing additional variables. There is no dependence on Seyfert type, inclination, Hubble type, or redshift. Unbarred Seyfert galaxies show a tighter correlation than barred Seyfert galaxies (P(null) approximately 0.04) suggesting that bars can modify the NLR velocity field. The strongest result, however, is that disturbed and interacting Seyfert galaxies have significantly broader lines (P(null) approximately 10(-4)), showing that external perturbations can influence nuclear gas. A plot of Faber-Jackson offsets against perturbation class (a 1-6 ranking scale based on Dahari's IAC parameter) shows a positive correlation which converges on zero offset for maximally disturbed galaxies. If offsets reflect dissipational settling of gas into a soft nuclear potential, then external perturbations may act to reestablish overall virial equilibrium. The historically significant correlations between [O III] FWHM and radio luminosity, L1415, and [O III] luminosity, L5007, are reanalyzed in the light of jet perturbations and the virial relations. Although the [O III] FWHM versus L1415 correlation is very strong (R approximately 0.6, P(null) approximately 10(-10)), removing the luminous linear radio sources merely weakens the correlation but does not destroy it. The remaining correlation is indirect and exists principally because L1415 is itself tied to the virial parameter M(bul) in a relation of the form L(radio) is-proportional-to L(bul)2.6 (R approximately 0.6, P(null) approximately 10(-7)). Interestingly, similar correlations with M(tot) or M(disk) are significantly weaker, suggesting that development of the nuclear radio source depends on the bulge potential, although the origin of this dependence is not yet clear. The relation between [O III] FWHM and [O III] luminosity (R approximately 0.4, P(null) approximately 10(-6)) is probably of indirect origin, since L5007 correlates very strongly with L1415 (L5007 (5007 is-proportional-to L1415(1.1), R approximately 0.7, P(null) approximately 10(-16) and also with M(bul) (L5007 is-proportional-to L(bul)2.5, R approximately 0.5, P(null) approximately 10(-7) - both of which share direct causal ties to [O III] FWHM. Interestingly, the correlation between L5007 and M(bul) is stronger than with either M(tot) or M(disk). This reinforces the suggestion that the spheroidal mass plays an important role in defining not only NLR kinematics but also NLR luminosities, both radio and emission line.
