  We show that the kinematics of the shells seen around some elliptical
galaxies provide a new, independent means for measuring the gravitational
potentials of elliptical galaxies out to large radii. A numerical simulation of
a set of shells formed in the merger between an elliptical and a smaller galaxy
reveals that the shells have a characteristic observable kinematic structure,
with the maximum line-of-sight velocity increasing linearly as one moves inward
from a shell edge. A simple analytic calculation shows that this structure
provides a direct measure of the gradient of the gravitational potential at the
shell radius. In order to extract this information from attainable data, we
have also derived the complete distribution of line-of-sight velocities for
material within a shell; comparing the observed spectra of a shell to a stellar
template convolved with this distribution will enable us to measure the
gradient of the potential at this radius. Repeating the analysis for a whole
series of nested shells in a galaxy allows the complete form of the
gravitational potential as a function of radius to be mapped out. The requisite
observations lie within reach of the up-coming generation of large telescopes.
