We have made X-ray observations of the radio galaxy 3C 388 with the ROSAT H
RI, resolving the thermal gas that confines the lobes of this powerful (FR
II) radio source. The gas pressure is substantially higher than the minimum
pressures in the radio lobes, implying that the latter is an underestimate
by an order of magnitude or more. We discuss how this can be reconciled wi
th recent observations that find inverse-Compton emission from radio lobes
at the level predicted from conventional minimum-energy arguments. We sugge
st that the excess pressure is due to low-energy electrons and positrons an
d/or protons, so that magnetic field strengths are below equipartition. If
this calibration of minimum-energy arguments applies to radio lobes in gene
ral, the power of radio jets has been underestimated by the same factor, im
plying that jet kinetic energy flux is close to or exceeds bolometric lumin
osity in radio-loud active galactic nuclei (AGNs). Most of the X-rays from
3C 388 are emitted by the thermal gas, which is well centered on the host c
D galaxy, itself the center of a small cluster. This component is well fitt
ed by a standard beta model. The ends of the radio lobes are beyond the app
roximate to 33 kpc core radius, so the density is declining roughly as a po
wer law with rho proportional to R-1.6. On most models, this is not a fast
enough decline to allow a constant expansion speed for the source. A compac
t X-ray source with 0.1-2.4 keV luminosity of 5 x 10(35) W lies at the cent
er. This is probably the AGN, although a galaxy-scale "cooling-flow" core c
annot be ruled out.