  Within a hydrodynamical approach we investigate the sensitivity of single
inclusive momentum spectra of hadrons in 158A GeV Pb+Pb collisions to three
different equations of state of nuclear matter. Two of the equations of state
are based on lattice QCD results and include a phase transition to a
quark-gluon plasma. The third equation of state has been extracted from the
microscopic transport code RQMD under the assumption of complete local
thermalization. All three equations of state provide reasonable fits to data
taken by the NA44 and NA49 Collaborations. The initial conditions before the
evolution of the fireballs and the space-time evolution pictures differ
dramatically for the three equations of state when the same freeze-out
temperature is used in all calculations. However, the softest of the equations
of state results in transverse mass spectra that are too steep in the central
rapidity region. We conclude that the transverse particle momenta are
determined by the effective softness of the equation of state during the
fireball expansion.
