A wide variety of physical-chemical phenomena depend on the behavior of the polymer at solid-liquid interfaces. The feature that distinguishes such phenomena from their small-molecule counterparts is the long-chain structure of the polymer molecules. Just as in solution and the bulk, the conformational statistics of the polymer molecules in the interface is an important determinant of interfacial properties. Conformational statistics of interfacial polymer is expressed in terms a function called the polymer density profile phi(Z), which is just the volume fraction of polymer as a function of Z, the distance from the solid surface out into the continuum liquid. There is only one experimental technique that is purported to be able to determine polymer density profiles of polymers confined to the interface between finely divided substrate and dispersant, and that technique is small-angle neutron scattering (SANS). In this paper we present a protocol for the analysis of SANS data on spherical particles with adsorbed polymer for the determination of phi(Z). We give an example for nearly-monodisperse chains of poly(n-butyl methacrylate) with a molecular weight of 45,000 tethered to silica spheres with a diameter of 2150 Angstrom. The polymer density profile demonstrates a deep depletion layer next to the surface with a maximum in phi(Z) of about 0.7 at about Z = 40 Angstrom. Our experimental phi(Z) is compared with various theoretical predictions.