  An `effective' quasi-local energy expression, motivated by the
(relativistically corrected) Newtonian theory, is introduced in exact GR as the
volume integral of all the source terms in the field equation for the Newtonian
potential in static spacetimes. In particular, we exhibit a new post-Newtonian
correction in the source term in the field equation for the Newtonian
gravitational potential. In asymptotically flat spacetimes this expression
tends to the ADM energy at the spatial infinity as a {\em monotonically
decreasing} set function. We prove its positivity in spherically symmetric
spacetimes under certain energy conditions, and that its vanishing
characterizes flatness. We argue that any physically acceptable quasi-local
energy expression should behave qualitatively like this `effective' energy
expression in this limit.
