  The relationship between the magnetic field and the circular polarization of
astrophysical maser radiation due to the Zeeman effect under idealized
conditions is investigated when the Zeeman splitting is much smaller than the
spectral linebreadth and when radiative saturation is significant. The
description of the circular polarization, as well as inferences about the
magnetic field from the observations, are clearest when the rate for stimulated
emission is much less than the Zeeman splitting. The calculations here are
performed in this regime, which is relevant for some (if not most) observations
of astrophysical masers. We demonstrate that Stokes-$V$ is proportional to the
Zeeman splitting and the fractional linear polarization is independent of the
Zeeman splitting when the ratio of the Zeeman splitting to the spectral line
breadth is small---less than about 0.1. In contrast to its behavior for
ordinary spectral lines, the circular polarization for masers that are at least
partially saturated does not decrease with increasing angle between the
magnetic field and the line-of-sight until they are nearly perpendicular.
