  Recent progress in the measurement of relative distances to galaxies has been
quite substantial, and catalogs of 3000 galaxies with distances are soon to
become available. The peculiar {\it velocity} field (deviations from Hubble
flow) derivable from these catalogs, when compared to the peculiar {\it
gravity} field derived from all sky redshift surveys of galaxies such as the
1.2Jy IRAS survey, leads to a unique and extremely powerful test of the density
parameter $\beta \equiv \Omega^{0.6}/b_I$, where $b_I$ is the possible linear
bias of the IRAS selected galaxies relative to the mass fluctuations. We review
the status of these large scale flow measurements and present a new methodology
to describe the two fields by means of an expansion in a set of orthogonalized
functions describing a general potential flow to any chosen resolution. The
parameters of the flow can be estimated by minimization of the $\chi^2$
describing the scatter of observed versus predicted linewidths from an inverse
Tully-Fisher relation. By this method one can intercompare the gravity and
velocity fields coefficient by coefficient, deriving a precise fit for the
density parameter and an assessment of the degree of coherence between the
fields. The present situation is transitory-- different analyses of the same
data are not yielding consistent results. Until this embarassment is untangled,
estimates of $\beta$ should be taken with a large grain of salt.
