  Starting from a careful analysis of the coupled Langevin equations for two
interacting Brownian particles, we derive a method for extracting the binary
friction tensor from the correlation function matrix of the instantaneous
forces exerted by the bath particles on the fixed Brownian particles, and from
the relaxation of the total momentum of the bath in a {\it finite} system. The
general methodology, which circumvents the pitfalls associated with the
inversion of the thermodynamic and long time limits, is applied to the case of
two Brownian hard spheres in a bath of light spheres.
