  We report here multi-epoch, multi-frequency observations of the circular
polarization in Sagittarius A*, the compact radio source in the Galactic
Center. Data taken from the VLA archive indicate that the fractional circular
polarization at 4.8 GHz was -0.31% with an rms scatter of 0.13% from 1981 to
1998, in spite of a factor of 2 change in the total intensity. The sign
remained negative over the entire time range, indicating a stable magnetic
field polarity. In the Summer of 1999 we obtained 13 epochs of VLA A-array
observations at 1.4, 4.8, 8.4 and 15 GHz. In May, September and October of 1999
we obtained 11 epochs of Australia Telescope Compact Array observations at 4.8
and 8.5 GHz. In all three of the data sets, we find no evidence for linear
polarization greater than 0.1% in spite of strong circular polarization
detections. Both VLA and ATCA data sets support three conclusions regarding the
fractional circular polarization: the average spectrum is inverted with a
spectral index ~0.5 +/- 0.2; the degree of variability is roughly constant on
timescales of days to years; and, the degree of variability increases with
frequency. We also observed that the largest increase in fractional circular
polarization was coincident with the brightest flare in total intensity.
Significant variability in the total intensity and fractional circular
polarization on a timescale of 1 hour was observed during this flare,
indicating an upper limit to the size of 70 AU at 15 GHz. The fractional
circular polarization at 15 GHz reached -1.1% and the spectral index is
strongly inverted during this flare. We conclude that the spectrum has two
components that match the high and low frequency total intensity components.
(abridged)
