We report x-ray reflectivity (XR) and small angle off-specular diffuse scattering (DS) measurements from the surface of liquid Indium close to its melting point of $156^circ$C. From the XR measurements we extract the surface structure factor convolved with fluctuations in the height of the liquid surface. We present a model to describe DS that takes into account the surface structure factor, thermally excited capillary waves and the experimental resolution. The experimentally determined DS follows this model with no adjustable parameters, allowing the surface structure factor to be deconvolved from the thermally excited height fluctuations. The resulting local electron density profile displays exponentially decaying surface induced layering similar to that previously reported for Ga and Hg. We compare the details of the local electron density profiles of liquid In, which is a nearly free electron metal, and liquid Ga, which is considerably more covalent and shows directional bonding in the melt. The oscillatory density profiles have comparable amplitudes in both metals, but surface layering decays over a length scale of $3.5pm 0.6$ AA for In and $5.5pm 0.4$ AA for Ga. Upon controlled exposure to oxygen, no oxide monolayer is formed on the liquid In surface, unlike the passivating film formed on liquid Gallium.
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