  The alignment of interstellar dust grains is described by the joint
distribution function for certain ``internal'' and ``external'' variables,
where the former describe the orientation of a grain's axes with respect to its
angular momentum, J, and the latter describe the orientation of J relative to
the interstellar magnetic field. I show how the large disparity between the
dynamical timescales of the internal and external variables--- which is
typically 2--3 orders of magnitude--- can be exploited to greatly simplify
calculations of the required distribution. The method is based on an
``adiabatic approximation'' which closely resembles the Born-Oppenheimer
approximation in quantum mechanics. The adiabatic approximation prescribes an
analytic distribution function for the ``fast'' dynamical variables and a
simplified Fokker-Planck equation for the ``slow'' variables which can be
solved straightforwardly using various techniques. These solutions are accurate
to order epsilon, where epsilon is the ratio of the fast and slow dynamical
timescales. As a simple illustration of the method, I derive an analytic
solution for the joint distribution established when Barnett relaxation acts in
concert with gas damping. The statistics of the analytic solution agree with
the results of laborious numerical calculations which do not exploit the
adiabatic approximation.
