  We study the peculiar velocity field inferred from the Mark III spirals using
a new method of analysis. We estimate optimal values of Tully-Fisher scatter
and zero-point offset, and we derive the 3-dimensional rms peculiar velocity
($\sigma_v$) of the galaxies in the samples analysed. We check our statistical
analysis using mock catalogs derived from numerical simulations of CDM models
considering measurement uncertainties and sampling variations. Our best
determination for the observations is $\sigma_v= (660\pm50) km/s$. We use the
linear theory relation between $\sigma_v$, the density parameter $\Omega$, and
the galaxy correlation function $\xi(r)$ to infer the quantity $\beta
=\Omega^{0.6}/b = 0.60^{+0.13}_{-0.11}$ where $b$ is the linear bias parameter
of optical galaxies and the uncertainties correspond to bootstrap resampling
and an estimated cosmic variance added in quadrature. Our findings are
consistent with the results of cluster abundances and redshift space distortion
of the two-point correlation function. These statistical measurements suggest a
low value of the density parameter $\Omega \sim 0.4$ if optical galaxies are
not strongly biased tracers of mass.
