  We derive the baryon mass function for a complete sample of low-redshift
clusters and argue that it is an excellent proxy for the total mass function if
the ratio f_b=M_b/M_tot in all clusters is close to its universal value,
Omega_b/Omega_M. Under this assumption, the baryon mass function can be used to
constrain the amplitude and slope of the density fluctuations power spectrum on
cluster scales. This method does not use observational determinations of the
total mass and thus bypasses major uncertainties in the traditional analyses
based on the X-ray temperature function. However, it is sensitive to possible
systematic variations of the baryon fraction as a function of cluster mass.
Adapting a weak dependence f_b(M) suggested by observations and numerical
simulations by Bialek et al., we derive sigma_8=0.72+-0.04 and the shape
parameter Omega_M*h=0.13+-0.07, in good agreement with a number of independent
methods. We discuss the sensitivity of these values to other cosmological
parameters and to different assumptions about variations in f_b.
