Coronal cavities are common features of the solar corona that appear as darkened regions at the base of coronal helmet streamers in coronagraph images. Their darkened appearance indicates that they are regions of lowered density embedded within the comparatively higher density helmet streamer. Despite interfering projection effects of the surrounding helmet streamer (which we refer to as the cavity rim), Fuller et al. have shown that under certain conditions it is possible to use a Van de Hulst inversion of white-light polarized brightness (pB) data to calculate the electron density of both the cavity and cavity rim plasma. In this article, we apply minor modifications to the methods of Fuller et al. in order to improve the accuracy and versatility of the inversion process, and use the new methods to calculate density profiles for both the cavity and cavity rim in 24 cavity systems. We also examine trends in cavity morphology and how departures from the model geometry affect our density calculations. The density calculations reveal that in all 24 cases the cavity plasma has a flatter density profile than the plasma of the cavity rim, meaning that the cavity has a larger density depletion at low altitudes than it does at high altitudes. We find that the mean cavity density is over four times greater than that of a coronal hole at an altitude of 1.2 R_☉ and that every cavity in the sample is over twice as dense as a coronal hole at this altitude. Furthermore, we find that different cavity systems near solar maximum span a greater range in density at 1.2 R_☉ than do cavity systems near solar minimum, with a slight trend toward higher densities for systems nearer to solar maximum. Finally, we found no significant correlation of cavity density properties with cavity height—indeed, cavities show remarkably similar density depletions—except for the two smallest cavities that show significantly greater depletion