The small-scale motion of a liquid surface is discussed in terms of the behavior of Gaussian local modes when the discrete molecular structure of the surface becomes important. The observed enhancement of surface roughness as the scale of observation approaches molecular dimensions is attributed to the transition from purely harmonic motion, with restoring force parallel to the surface, to anharmonic motion, with restoring force at right angles to the surface. Calculations based on this model, with no adjustable parameters, give results in excellent agreement with experimental data for the initial decrease and subsequent increase of the apparent surface tension with increasing wave vector, and for the variation of surface tension versus wave vector plots with the nature of the liquid. Because the important intermolecular interactions in the model occur at short range, there is very little difference between the results predicted for l/r(3) and l/r(6) potentials. The increase in apparent surface tension as the wave vector approaches its upper limit is the consequence of thermally excited motion on this scale frequently exceeding the potential barriers that otherwise would prevent either evaporation of the molecules involved or their accommodation into the bulk liquid, with the result that such large-amplitude motions do not contribute to the time-averaged surface roughness.