We present multifrequency VLA observations of the two radio galaxies 3C 129
and 3C 129.1 embedded in a luminous X-ray cluster. These radio observation
s reveal a substantial difference in the Faraday Rotation Measures (RMs) to
ward 3C 129.1 at the cluster centre and 3C 129 at the cluster periphery. Af
ter deriving the density profile from available X-ray data, we find that th
e RM structure of both radio galaxies can be fitted by a tangled cluster ma
gnetic field with strength 6 muG extending at least 3 core radii (450 kpc)
from the cluster centre. The magnetic field makes up a small contribution t
o the total pressure (5 per cent) in the central regions of the cluster. Th
e radio morphology of 3C 129.1 appears disturbed on the southern side, perh
aps by the higher pressure environment. In contrast with earlier claims for
the presence of a moderately strong cooling flow in the 3C 129 cluster, ou
r analysis of the X-ray data places a limit on the mass deposition rate fro
m any such flow of < 1.2 M-. yr(-1).