The results of an experimental study using torsional oscillators of th
e superfluidity of He-4 films adsorbed on hydrogen plated graphite are
reported. The evolution of superfluidity with the growth of the film
shows considerable structure arising from the atomic layering of the f
ilm. There is evidence that the superfluidity of a single fluid layer
is strongly suppressed, possibly due to the influence of the periodic
potential arising from the underlying solid layer. The behavior of two
fluid layers is quite distinct, but shows similarities to that of thi
cker films on heterogeneous substrates; we suggest that the usual theo
ry of the superfluidity of two-dimensional 4He should be extended to a
ccount for superfluid onset temperatures in such a film. (C) 1997 Amer
ican Institute of Physics.