  We introduce a modified divergence law for the energy-momentum tensor in the
theory of unimodular relativity. Consequently, an additional equation for the
measure field follows from the divergence of the field equations. The equations
of motion are derived and the weak-field, low-velocity limit is investigated.
It is found that the gravitational acceleration acquires a term that is
proportional to the gradient of the mass density. We show that this term can
provide the additional acceleration observed on astrophysical scales without
the need for dark matter.
