  We reconsider the study of persistent currents in a disordered
one-dimensional ring threaded by a magnetic flux, using he one-band
tight-binding model for a ring of N-sites with random site energies. The
secular equation for the eigenenergies expressed in terms of transfer matrices
in the site representation is solved exactly to second order in a perturbation
theory for weak disorder and fluxes differing from half-integer multiples of
the elementary flux quantum. From the equilibrium currents associated with the
one-electron eigenstates we derive closed analytic expressions for the disorder
averaged persistent current for even and odd numbers, Ne, of electrons in the
ground state. Explicit discussion for the half-filled band case confirms that
the persistent current is flux periodic as in the absence of disorder, and that
its amplitude is generally suppressed by the effect of the disorder. In
comparison to previous results, based on an approximate analysis of the secular
equation, the current suppression by disorder is strongly enhanced by a new
flux-dependent factor.
