Precise heat-capacity results are presented for

{}^{3}{He}

adsorbed on graphite. The temperature range of the data is from 2 to 200 mK, while the coverages span from somewhat below monolayer completion up through five atomic layers. Promotion of atoms into the second, third, and fourth layers is clearly observed. Nuclear-spin exchange energies of the order of a few tenths of a mK are found for the submonolayer incommensurate solid phase. These values differ significantly from those recently inferred from NMR experiments. Data for the second-layer fluid yield

{}^{3}{He}

quasiparticle effective masses that agree well with the corresponding first-layer values and range from one to five times the bare

{}^{3}{He}

mass. Prior to third-layer promotion, the second layer undergoes a first-order phase transition. By comparison with the phase diagram for the first layer, the new phase in the second layer is assumed to be a registered solid. Registry is now with respect to the first

{}^{3}{He}

layer, which continues to exist as a triangular-lattice solid incommensurate with the graphite substrate. The registered phase exhibits a large, sharp heat-capacity anomaly at 2.5 mK.

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