  Pandres has developed a theory which extends the geometrical structure of a
real four-dimensional space-time via a field of orthonormal tetrads with an
enlarged covariance group. This new group, called the conservation group,
contains the group of diffeomorphisms as a proper subgroup and we hypothesize
that it is the foundational group for quantum geometry. Using the curvature
vector, $C_\mu$, we find a free-field Lagrangian density $C^\mu C_\mu
\sqrt{-g}\,$. When massive objects are present a source term is added to this
Lagrangian density. Spherically symmetric solutions for both the free field and
the field with sources have been derived. The field equations require nonzero
stress-energy tensors in regions where no source is present and thus may bring
in dark matter and dark energy in a natural way. A simple model for a galaxy is
given which satisfies our field equations. This model includes flat rotation
curves. In this paper we compare our results with recently reported results of
McGaugh, Lelli and Schombert which exhibit a new law between the observed
radial acceleration and the baryonic radial acceleration. We find a slightly
different model which relates these accelerations. In conjunction with our
model, the McGaugh, Lelli and Schombert relation imply a new critical baryonic
acceleration. When applied to bulge-dominated galaxies, this critical baryonic
acceleration may be used to predict the radial velocity curve value by using
the radius of the bulge.
