  The Langevin theory of the polarization of a dilute collection of dipoles by
an external field is often included in introductory solid state physics and
physical chemistry curricula. The average polarization is calculated assuming
the dipoles are in thermal equilibrium with a heat bath. The heart of the
polarization calculation is a derivation of the average dipole-field
projection, whose dependence on the external field is given by the Langevin
function. The Langevin problem is revisited, here, and the average projection
of any given dipole onto any other dipole from the collection is derived in
terms of the Langevin function. A simple expression is obtained for the
underlying dipole-dipole angular distribution function.
