  We explore the use of tidal streams from Galactic satellites to recover the
potential of the Milky Way. Our study is motivated both by the discovery of the
first lengthy stellar stream in the halo (\cite{it98}) and by the prospect of
measuring proper motions of stars brighter than 20th magnitude in such a stream
with an accuracy of $\sim 4\mu as/$yr, as will be possible with the Space
Interferometry Mission (SIM). We assume that the heliocentric radial velocities
of these stars can be determined from supporting ground-based spectroscopic
surveys, and that the mass and phase-space coordinates of the Galactic
satellite with which they are associated will also be known to SIM accuracy.
Using results from numerical simulations as trial data sets, we find that, if
we assume the correct form for the Galactic potential, we can predict the
distances to the stars as a consequence of the narrow distribution of energy
expected along the streams. We develop an algorithm to evaluate the accuracy of
any adopted potential by requiring that the satellite and stars recombine
within a Galactic lifetime when their current phase-space coordinates are
integrated backwards. When applied to a four-dimensional grid of triaxial
logarithmic potentials, with varying circular velocities, axis ratios and
orientation of the major-axis in the disk plane, the algorithm can recover the
parameters used for the Milky Way in a simulated data set to within a few
percent using only 100 stars in a tidal stream.
