  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 $3.5\pm 0.6$ \AA for In and $5.5\pm 0.4$ \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.
