  Two Hamiltonian formulations of General Relativity, due to Pirani, Schild and
Skinner (Phys. Rev. 87, 452, 1952) and Dirac (Proc. Roy. Soc. A 246, 333,
1958), are considered. Both formulations, despite having different expressions
for constraints, allow one to derive four-dimensional diffeomorphism
invariance. The relation between these two formulations at all stages of the
Dirac approach to the constrained Hamiltonian systems is analyzed. It is shown
that the complete sets of their phase-space variables are related by a
transformation which satisfies the ordinary condition of canonicity known for
unconstrained Hamiltonians and, in addition, converts one total Hamiltonian
into another, thus preserving form-invariance of generalized Hamiltonian
equations for constrained systems.
