  Multi-frequency radio observations of the radio bridge of a powerful
classical double radio source can be used to determine: the beam power of the
jets emanating from the AGN; the total time the source will actively produce
jets that power large-scale radio emission; the thermal pressure of the medium
in the vicinity of the radio source; and the total mass, including dark matter,
of the galaxy or cluster of galaxies traced by the ambient gas that surrounds
the radio source. Empirical determinations of each of these quantities are
obtained and analyzed for 22 radio sources. Typical beam powers are about
$10^{45} {erg s}^{-1}$. The characteristic or total time the AGN will actively
produce a collimated outflow is estimated. Typical total lifetimes are $\sim
(10^7$ to $10^8$) years. Total masses, and mass-density profiles, similar to
those of low-redshift clusters of galaxies are obtained. Thus, some clusters of
galaxies, or cores of clusters, exist at redshifts of one to two.
  A new method of estimating the thermal pressure of the ambient gas in the
vicinity of a powerful classical double radio source is presented. This new
estimate is independent of synchrotron and inverse Compton aging arguments, and
depends only upon the properties of the radio lobe and the shape of the radio
bridge. Thermal pressures on the order of $10^{-10} {dyne cm}^{-2}$, typical of
gas in low-redshift clusters of galaxies, are found for the environments of the
sources studied here. It is shown that appreciable amounts of cosmic microwave
background diminution (the Sunyaev-Zel'dovich effect) are expected from many of
these clusters. This could be detected at high frequency where the emission
from the radio sources is weak.
