  We find the Hamiltonian expression in the York basis of canonical ADM tetrad
gravity of the 4-Weyl tensor of the asymptotically Minkowskian space-time. Like
for the 4-Riemann tensor we find a radar tensor (whose components are 4-scalars
due to the use of radar 4-coordinates), which coincides with the 4-Weyl tensor
on-shell on the solutions of Einstein's equations. Then, by using the
Hamiltonian null tetrads, we find the Hamiltonian expression of the Weyl
scalars of the Newman-Perose approach and of the four eigenvalues of the 4-Weyl
tensor.
  After having introduced the Dirac observables of canonical gravity, whose
determination requires the solution of the super-Hamiltonian and super-momentum
constraints, we discuss the connection of the Dirac observables with the notion
of 4-scalar Bergmann observables. Due to the use of radar 4-coordinates these
two types of observables coincide in our formulation of canonical ADM tetrad
gravity. However, contrary to Bergmann proposal, the Weyl eigenvalues are shown
not to be Bergmann observables, so that their relevance is only in their use
(first suggested by Bergmann and Komar) for giving a physical identification as
point-events of the mathematical points of the space-time 4-manifold.
  Finally we give the expression of the Weyl scalars in the Hamiltonian
Post-Minkowskian linearization of canonical ADM tetrad gravity in the family of
(non-harmonic) 3-orthogonal Schwinger time gauges.
