  As the largest gravitationally bound objects in the universe, clusters of
galaxies may contain a fair sample of the baryonic mass fraction of the
universe. Since the gas mass fraction from the hot ICM is believed to be
constant in time, the value of the cosmological deceleration parameter $q_0$
can be determined by comparing the calculated gas mass fraction in nearby and
distant clusters (Pen 1997). To test the potential of this method, we compare
the gas fractions derived for a sample of luminous ($L_X > 10^{45} $erg
s$^{-1}$), nearby clusters with those calculated for eight luminous, distant
($0.3 < z < 0.6$) clusters using ASCA and ROSAT observations. For consistency,
we evaluate the gas mass fraction at a fixed physical radius of 1 $h_{50}^{-1}$
Mpc (assuming $q_0=0.0$). We find a best fit value of $q_0 = 0.07$ with -0.47 <
q_0 < 0.67 at 95% confidence. We also determine the gas fraction using the
method of Evrard, Metzler, & Navarro (1997) to find the total mass within
$r_{500}$, the radius where the mean overdensity of matter is 500 times the
critical density. In simulations, this method reduces the scatter in the
determination of gravitational mass without biasing the mean. We find that it
also reduces the scatter in actual observations for nearby clusters, but not as
much as simulations suggest. Using this method, the best fit value is $q_0 =
0.04$ with -0.50 < q_0 < 0.64. The excellent agreement between these two
methods suggests that this may be a useful technique for determining $q_0$. The
constraints on $q_0$ should improve as more distant clusters are studied and
precise temperature profiles are measured to large radii.
