  Recent work has shown that the addition of an appropriate covariant boundary
term to the gravitational action yields a well-defined variational principle
for asymptotically flat spacetimes and thus leads to a natural definition of
conserved quantities at spatial infinity. Here we connect such results to other
formalisms by showing explicitly i) that for spacetime dimension $d \ge 4$ the
canonical form of the above-mentioned covariant action is precisely the ADM
action, with the familiar ADM boundary terms and ii) that for $d=4$ the
conserved quantities defined by counter-term methods agree precisely with the
Ashtekar-Hansen conserved charges at spatial infinity.
