Determination of the Hamiltonian in the Presence of Constraints

The ambiguity in the Hamiltonian for systems with constraints is discussed, and a counter example is provided to a conjecture of Dirac, which has led previously to the identification of the system Hamiltonian as the extended Hamiltonian, HE. The conjecture fails and HE also generates the wrong canonical equations; Dirac's test for identifying the Hamiltonian, however, leads to correct results for the example.