  The conductance of a normal-metal mesoscopic system in proximity to
superconducting electrode(s) is calculated. The normal-metal part may have a
general geometry, and is described as a ``circuit'' with ``leads'' and
``junctions''. The junctions are each ascribed a scattering matrix which is
averaged over the circular orthogonal ensemble, using recently-developed
techniques. The results for the electrical conductance reproduce and extend
Nazarov's circuit theory, thus bridging between the scattering and the bulk
approaches. The method is also applied to the heat conductance.
