  In the first paper in this series, a class of observables that generalized
the gravitational wave memory effect were introduced and given the name
"persistent gravitational wave observables." These observables are all nonlocal
in time, nonzero in spacetimes with gravitational radiation, and have an
observable effect that persists after the gravitational waves have passed. In
this paper, we focus on the persistent observable known as "curve deviation,"
and we compute the observable using the Bondi-Sachs approach to asymptotically
flat spacetimes at the leading, nontrivial order in inverse Bondi radius. The
curve deviation is related to the final separation of two observers who have an
initial separation, initial relative velocity, and relative acceleration. The
displacement gravitational wave memory effect is the part of the curve
deviation that depends on the initial separation and is the entire contribution
for initially comoving, inertial observers at large Bondi radius. The spin and
center-of-mass memory effects are contained within the dependence of the curve
deviation on the initial relative velocity, and the dependence of the curve
deviation on relative acceleration contains observables distinct from these
known memory effects. We find that the full curve deviation observable can be
written in terms of differences in nonradiative data before and after the
radiation (which we call the "charge" contribution), along with a nonlinear
"flux" contribution that vanishes in the absence of gravitational radiation.
This splitting generalizes the notion of "ordinary" and "null" memory that
exists for the displacement, spin, and center-of-mass gravitational wave memory
effects to the full curve deviation observable.
