In the weak field approximation, the nonsymmetric gravitational theory
(NGT) has, in addition to the Newtonian gravitational potential, a Yu
kawa-like potential produced by the exchange of a spin 1(+) boson betw
een fermions. If the range r(0) = mu(-1) is 25 kpc, then this addition
al potential due to the interaction with matter in the halos of galaxi
es can explain the flat rotation curves of galaxies and the Tully-Fish
er law (L similar to upsilon(4)) without the dark matter hypothesis. P
ossible fits to clusters of galaxies and gravitational lensing observa
tions are discussed. The results are based on a linear approximation t
o a new perturbatively consistent version of the NGT field equations,
which does not violate the weak equivalence principle.