  Adopting two independent approaches (a) Lorentz-invariance of physical laws
and (b) local phase invariance of quantum field theory applied to the Dirac
Lagrangian for massive electrically neutral Dirac particles, we rediscovered
the fundamental field equations of Heaviside Gravity (HG) of 1893 and
Maxwellian Gravity (MG), which look different from each other due to a sign
difference in some terms of their respective field equations. However, they are
shown to represent two mathematical representations of a single physical theory
of vector gravity that we name here as Heaviside-Maxwellian Gravity (HMG), in
which the speed of gravitational waves in vacuum is uniquely found to be equal
to the speed of light in vacuum. We also corrected a sign error in Heaviside's
speculative gravitational analogue of the Lorentz force law. This spin-1 HMG is
shown to produce attractive force between like masses under static condition,
contrary to the prevalent view of field theorists. Galileo's law of
universality of free fall is a consequence of HMG, without any initial
assumption of the equality of gravitational mass with velocity-dependent mass.
We also note a new set of Lorentz-Maxwell's equations having the same physical
effects as the standard set - a byproduct of our present study.
