We have made third sound velocity measurements via the time-of-flight technique for 4He films adsorbed on the surface of a single leaf of highly oriented pyrolytic graphite between 1.0 and 1.3 K. Our results are in qualitative agreement with an earlier experiment involving third sound on Grafoil foam. As a function of film thickness, the third sound velocity shows oscillatory variation with a period roughly equal to one atomic layer. This novel effect is not seen with other substrates. The third sound velocity determined in this experiment suffers relatively little path-length correction. This is a condition not met in the foam experiment.
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