We have completed a torsional oscillator study of superfluidity in thi
n films of He-4 adsorbed on the basal plane of graphite for coverages
above one atomic layer. In this report we focus on the details of the
superfluid dissipation. For coverages above 2 1/4 layers we resolve a
dissipation peak at the superfluid transition. The evolution of this p
eak with increasing coverage is distinct from the behavior observed on
heterogeneous substrates such as mylar. In particular, we observe two
coverage regions, in the third and fourth layers, where the temperatu
re of the dissipation maximum is nearly independent of the coverage.