  The stellar ejection rate and the rates of change of the binary semimajor
axis and eccentricity are derived from scattering experiments for the
restricted three-body problem. They are used to study the evolution of binaries
in simple models for galactic nuclei, starting soon after the black holes
become bound and continuing until the evolution is dominated by the emission of
gravitational radiation, or until the ejected mass is too large for the galaxy
to be considered fixed. The eccentricity growth is found to be unimportant
unless the binary forms with a large eccentricity. The scattering results are
compared with predictions from Chandrasekhar's dynamical-friction formula and
with previous work on the capture and scattering of comets by planetary
systems. They suggest that a binary with masses $m_1\geq m_2$ should not be
considered hard until its orbital velocity exceeds the background velocity
dispersion by a factor that scales as $(1+m_1/m_2)^{1/2}$.
