  Under the assumption that the gas mass fraction of galaxy clusters estimated
out to an outer hydrostatic radius is constant, it is possible to constrain the
cosmological parameters by using the angular diameter distance relation with
redshift. We applied this to a sample of galaxy clusters from redshifts of 0.1
to 0.94, for which published gas and total masses are available from X-ray
data. After scaling the gas fraction values to the r_500 radius (Evrard,
Metzler & Navarro 1996), we find an apparent decrease in gas fractions at high
redshifts, which can be scaled back to the mean gas fraction value at z ~ 0.1
to 0.2 of (0.060 \pm 0.002) h^{-3/2}, when \Omega_m = 0.55^{+0.35}_{-0.23}
(1-\sigma statistical error, \Omega_m + \Omega_{\Lambda} =1). However, various
sources of systematic errors can contribute to the change in gas mass fraction
from one cluster to another, and we discuss such potential problems in this
method.
