  We propose a method for measuring the cosmological density parameter $\Omega$
from the statistics of the divergence field, $\theta \equiv H^{-1} \div v$, the
divergence of peculiar velocity, expressed in units of the Hubble constant, $H
\equiv 100 h km/s/Mpc$. The velocity field is spatially smoothed over $\sim 10
h^{-1} Mpc$ to remove strongly nonlinear effects. Assuming weakly-nonlinear
gravitational evolution from Gaussian initial fluctuations, and using
second-order perturbative analysis, we show that $ <\theta^3> \propto
-\Omega^{-0.6} <\theta^2>^2$. The constant of proportionality depends on the
smoothing window. For a top-hat of radius R and volume-weighted smoothing, this
constant is $26/7-\gamma$, where $\gamma=-d\log <\theta^2> / d\log R$. If the
power spectrum is a power law, $P(k)\propto k^n$, then $\gamma=3+n$. A Gaussian
window yields similar results. The resulting method for measuring $\Omega$ is
independent of any assumed biasing relation between galaxies and mass.
  The method has been successfully tested with numerical simulations. A
preliminary application to real data, provided by the POTENT recovery procedure
from observed velocities favors $\Omega \sim 1$. However, because of an
uncertain sampling error, this result should be treated as an assessment of the
feasibility of our method rather than a definitive measurement of $\Omega$.
