  The low frequency quantum transport properties of a three-probe mesoscopic
conductor are studied using B\"uttiker's AC transport formalism. The static
transmission coefficients and emittance matrix of the system were computed by
explicitly evaluating the various partial density of states (PDOS). We have
investigated the finite size effect of the scattering volume on the global
PDOS. By increasing the scattering volume we observed a gradual improvement in
the agreement of the total DOS as computed externally or locally. Our numerical
data permits a particular fitting form of the finite size effect.
