  We examine the plasma composition of relativistic jets in four FRII radio
galaxies by analyzing the total cocoon pressure in terms of partial pressures
of thermal and non-thermal electrons/positrons and protons. The total cocoon
pressure is determined by cocoon dynamics via comparison of theoretical model
with the observed cocoon shape. By inserting the observed number density of
non-thermal electrons/positrons and the upper limit of thermal
electron/positron number density into the equation of state, the number density
of protons is constrained. We apply this method to four FRII radio galaxies
(Cygnus A, 3C 219, 3C 223 and 3C 284), for which the total cocoon pressures
have been already evaluated. We find that the positron-free plasma comprising
of protons and electrons is ruled out, when we consider plausible particle
distribution functions. In other words, the mixture of positrons is required
for all four FRII radio galaxies; the number density ratio of
electrons/positrons to protons is larger than two. Thus, we find that the
plasma composition is independent of the jet power and the size of cocoons. We
also investigate the additional contribution of thermal electrons/positrons and
protons on the cocoon dynamics. When thermal electrons/positrons are absent,
the cocoon is supported by the electron/ proton plasma pressure, while both
electron/positron pressure supported and electron/proton plasma pressure
supported cocoons are allowed if the number density of thermal
electrons/positrons is about 10 times larger than that of non-thermal ones.
