  We have used an NMR technique to measure the short-time, three-dimensional
displacement of grains in a system of mustard seeds vibrated vertically at 15g.
The technique averages over a time interval in which the grains move
ballistically, giving a direct measurement of the granular temperature profile.
The dense, lower portion of the sample is well described by a recent
hydrodynamic theory for inelastic hard spheres. Near the free upper surface the
mean free path is longer than the particle diameter and the hydrodynamic
description fails.
