The heat capacity of "^He adsorbed on graphite has been precisely measured over a fine grid of coverages for temperatures extending down to 100 mK and for coverages up to five atomic layers. The data indicate that the two-dimensional liquid is self-bound in each of the first three layers with an areal density of about 0.04 atom/A^. There is also evidence suggesting that this liquid undergoes a KosterlitzThouless transition.PACS numbers: 67.70.+n, 67.40.Kh The submonolayer phase diagrams of ^He and "^He adsorbed on graphite appear remarkably similar [1] for areal densities greater than that corresponding to the VJ registered phase R, At lower coverages, however, the generally accepted "^He diagram [1-3] differs substantially from that recently proposed [4,5] for ^He. Here ^He heat-capacity data [4] indicate that this system exists as a two-dimensional (2D) fluid F, down to presumably absolute zero, although there is evidence suggesting some type of phase transition near 3 mK. In contrast, low-coverage heat-capacity data for "^He exhibit a rounded maximum near 1 K which has been ascribed to many different phenomena [6]. At present, the consensus appears to be that this "peak" corresponds to the crossing of a phase boundary separating 2D vapor at high temperature and a vapor condensed-phase coexistence region at lower temperature. Although this condensed phase was once thought to be the 2D liquid state [7,8], it is now usually taken to be the R phase; see Fig. 1 (a) [9]. The low-coverage "^He system at temperatures less than 1 K is thus expected to be in a two-phase region bounded by the pure 2D gas phase near zero coverage and by the pure R phase at PR (0.0637 atom/A^) even though there is no convincing evidence from either scattering or thermodynamic experiments to substantiate this belief. However, given the quantitative similarities between the ^He and "^He phase diagrams in the vicinity of the registered phase, the recent heatcapacity results for ^He raise several questions and doubts about the interpretation of the "^He phase diagram. The very-low-temperature ^He data show unambiguously that this system enters into a two-phase region only near PR and that the broad portion of the phase diagram associated with the registered phase is actually an F'R coexistence region. In the "^He picture the corresponding region of the phase diagram is thought to be the registered phase existing with as much as 30% vacancies [2].In this Letter we present new low-temperature heatcapacity data for "^He/graphite which contradict the current view and indicate a two-phase region involving the R phase which is restricted, as for submonolayer ^He, to 0.04;Sp;Sp/?; see Fig. 1(b). At lower coverages there is a coexistence of the 2D gas and the liquid which is believed to be superfluid. We also have evidence at much higher coverages suggesting that each of the next several atomic layers undergoes a similar evolution with increasing layer density. The new results are based on precise heat-capacity measurements which extend to lower tempe...