  We address a question raised in the work of Gallagher, Saint-Raymond and
Texier (From Newton to Boltzmann: Hard Spheres and Short-range Potentials,
Z\"urich Lectures in Advanced Mathematics, EMS, 2013) that concerns the
convergence of soft-potential dynamics to hard sphere dynamics. In the case of
two particles, we establish that hard sphere dynamics is the limit of soft
sphere dynamics in the weak-star topology of BV. We view our result as
establishing a topological method by which to construct weak solutions to the
ODE of hard sphere motion.
