  The matter content of jets in active galactic nuclei is examined in a new
way. We model the dynamical expansion of its cocoon embedded in the
intra-cluster medium (ICM). By comparing the observed shape of the cocoon with
that expected from the theoretical model, we estimate the total pressure
($P_{\rm c}$) and electron temperature ($T_{e}$) of the cocoon. The number
density of the total electrons ($n_{e^{-}}$) is constrained by using the
non-thermal spectrum of the hot spot and the analysis of the momentum balance
between the jet thrust and the rum pressure of ICM. Together with the obtained
$P_{\rm c}$, $T_{e}$ and $n_{e^{-}}$, we constrain the matter content in the
jets. We find that, in the case of Cygnus A, the ratio of number density of
protons to that of electrons is of order of $10^{-3}$ . This implies the
existence of a large number of positron in the jet.
