  We study the action for the three-space formalism of General Relativity,
better known as the BF\'O (Barbour--Foster--\'O Murchadha) action, which is a
square-root BSW (Baierlein--Sharp--Wheeler) action. In particular, we explore
the (pre)symplectic structure by pulling it back via a Legendre map to the
tangent bundle of the configuration space of this action. With it we attain the
canonical Lagrangian vector field which generates the gauge transformations
(3-diffeomorphisms) and the true physical evolution of the system. This vector
field encapsulates all the dynamics of the system. We also discuss briefly the
observables and perennials for this theory. We then present a symplectic
reduction of the constrained phase space.
