  A careful study of the induced transformations on spatial quantities due to
4-dimensional spacetime diffeomorphisms in the canonical formulation of general
relativity is undertaken. Use of a general formalism, which indicates the role
of the embedding variables in a transparent manner, allows us to analyse the
effect of 4-dimensional diffeomorphisms more generally than is possible in the
standard ADM approach. This analysis clearly indicates the assumptions which
are necessary in order to obtain the ADM-Dirac constraints, and furthermore
shows that there are choices, other than the ADM hamiltonian constraint, that
one can make for the deformations in the ``timelike'' direction. In particular
an abelian generator closely related to true time evolution appears very
naturally in this framework. This generator, its relation to other abelian
scalars discovered recently, and the possibilities it provides for a group
theoretic quantisation of gravity are discussed.
