  We present first data on event-by-event fluctuations in the average
transverse momentum of charged particles produced in Pb+Pb collisions at the
CERN SPS. This measurement provides previously unavailable information allowing
sensitive tests of microscopic and thermodynamic collision models and to search
for fluctuations expected to occur in the vicinity of the predicted QCD phase
transition. We find that the observed variance of the event-by-event average
transverse momentum is consistent with independent particle production modified
by the known two-particle correlations due to quantum statistics and final
state interactions and folded with the resolution of the NA49 apparatus. For
two specific models of non-statistical fluctuations in transverse momentum
limits are derived in terms of fluctuation amplitude. We show that a
significant part of the parameter space for a model of isospin fluctuations
predicted as a consequence of chiral symmetry restoration in a non-equilibrium
scenario is excluded by our measurement.
