  We prove a global existence theorem for the $3\times 3$ system of
relativistic Euler equations in one spacial dimension. It is shown that in the
ultra-relativistic limit, there is a family of equations of state that satisfy
the second law of thermodynamics for which solutions exist globally. With this
limit and equation of state, which includes equations of state for both an
ideal gas and one dominated by radiation, the relativistic Euler equations can
be analyzed by a Nishida-type method leading to a large data existence theorem,
including the entropy and particle number evolution, using a Glimm scheme. Our
analysis uses the fact that the equations of state are of the form $p=p(n,S)$,
but whose form simplifies to $p=a^{2}\rho$ when viewed as a function of $\rho$
alone.
