  With new Chandra observations of the cluster containing the two radio
galaxies 3C129 and 3C129.1, we have made a fit to the X-ray surface brightness
to obtain thermal pressures. VLA data at 1.4 GHz have been obtained to
complement previous maps at 0.33 GHz and at 5 and 8 GHz. From these radio data,
we are able to derive the minimum non-thermal pressure of various emitting
volumes along the tail of 3C129 and in the lobes of 3C129.1. Under the
assumption that the non-thermal plasma excludes significant thermal plasma, we
may expect pressure balance for most features since ram pressure should be
important only close to the cores of the galaxies. Since we find that the
minimum non-thermal pressures are generally only a factor of a few below
estimates of the ambient thermal pressure, we conclude that it is unlikely that
relativistic protons contribute significantly to the total pressure. Reasonable
contributions from low energy electrons and filling factors in the range 0.1 to
1 suffice to achieve pressure balance. Although we do not find strong
signatures for the exclusion of hot gas from the radio structures, we find soft
features near the cores of both galaxies suggestive of cool gas stripping and
hard features associated with radio jets and possibly a leading bow shock.
