  We present an exact formulation of the physics of Barnett relaxation. Our
formulation is based on a realistic kinetic model of the relaxation mechanism
which includes the alignment of the grain angular momentum in body coordinates
by Barnett dissipation, disalignment by thermal fluctuations, and coupling of
the angular momentum to the gas via gas damping. We solve the Fokker-Planck
equation for the measure of internal alignment using numerical integration of
the equivalent Langevin equation for Brownian rotation. The accuracy of our
results is calibrated by comparing our numerical solutions with exact analytic
results obtained for special cases.We describe an analytic approximation for
the measure of alignment which fits our numerical results for cases of
practical interest.
