  We present a new determination of the mass function of galaxy clusters, based
on optical virial mass estimates for a large sample of 152 nearby (z\le0.15)
Abell-ACO clusters, as provided by Girardi et al. (1998). This sample includes
both data from the literature and the new ENACS data. The resulting mass
function is reliably estimated for masses larger than M_{lim}\simeq 4\times
10^{14} \msun, while it is affected by sample incompleteness at smaller masses.
We find N(>M_{lim})=(6.3\pm 1.2) 10^{-6} (h^{-1} Mpc)^{-3} for cluster masses
estimated within a 1.5 h^{-1} radius. Our mass function is intermediate between
the two previous estimates by Bahcall & Cen (1993) and by Biviano et al.
(1993). Based on the Press-Schechter approach, we use this mass function to
constrain the amplitude of the fluctuation power spectrum at the cluster scale.
After suitably convolving the PS predictions with observational errors on
cluster masses and COBE-normalizing the fluctuation power spectrum, we find
sigma_8=(0.60\pm 0.04) Omega_0^{-0.46+0.09 Omega_0} for flat low-density models
and sigma_8=(0.60\pm 0.04) Omega_0^{-0.48+0.17 Omega_0} for open models (at the
90% c.l.).
