  We present x-ray reflectivity and diffuse scattering measurements from the
liquid surface of pure potassium. They strongly suggest the existence of atomic
layering at the free surface of a pure liquid metal with low surface tension.
Prior to this study, layering was observed only for metals like Ga, In and Hg,
the surface tensions of which are 5-7 fold higher than that of potassium, and
hence closer to inducing an ideal "hard wall" boundary condition. The
experimental result requires quantitative analysis of the contribution to the
surface scattering from thermally excited capillary waves. Our measurements
confirm the predicted form for the differential cross section for diffuse
scattering, $d\sigma /d\Omega \sim 1/q_{xy}^{2-\eta}$ where $\eta = k_BT
q_z^2/2\pi \gamma $, over a range of $\eta$ and $q_{xy}$ that is larger than
any previous measurement. The partial measure of the surface structure factor
that we obtained agrees with computer simulations and theoretical predictions.
