  We have determined the cluster X-ray temperature function from two flux- and
redshift-limited samples of clusters. The first sample is comprised of 25
clusters with average redshift 0.05. The local temperature function derived
from it supercedes the one we previously published. Fourteen clusters with
average redshift 0.38 comprise the second sample. We perform maximum likelihood
fits of cluster evolution models to these data in order to constrain
cosmological parameters. For an open model with zero cosmological constant we
find that the density parameter is Omega_0 = 0.49+/-0.12, the rms mass density
fluctuation averaged over 8 h-1 Mpc spheres is sigma_8 = 0.72+/-0.10, and the
effective index of the mass density fluctuation spectrum on cluster scales is n
= -(1.72+/-0.34) where all errors are symmetrized at 68% confidence. The
corresponding results for the case where a cosmological constant produces a
flat universe are : 0.44+/-0.12, 0.77+/-0.15, and -(1.68+/-0.38). These results
agree with those determined from a variety of different independent methods,
including supernovae, galaxy-galaxy correlations, fluctuations in the microwave
background, gravitational lens statistics, and cluster peculiar velocities.
