  We present multi-frequency VLA observations of the two radio galaxies 3C 129
and 3C 129.1 embedded in a luminous X-ray cluster. These radio observations
reveal a substantial difference in the Faraday Rotation Measures (RMs) toward
3C 129.1 at the cluster center and 3C 129 at the cluster periphery. After
deriving the density profile from available X-ray data, we find that the RM
structure of both radio galaxies can be fit by a tangled cluster magnetic field
with strength 6 microGauss extending at least 3 core radii (450 kpc) from the
cluster center. The magnetic field makes up a small contribution to the total
pressure (5%) in the central regions of the cluster. The radio morphology of 3C
129.1 appears disturbed on the southern side, perhaps by the higher pressure
environment. In contrast with earlier claims for the presence of a moderately
strong cooling flow in the 3C 129 cluster, our analysis of the X-ray data
places a limit on the mass deposition rate from any such flow of <1.2 Msun/yr.
