  The Dirac constraint formalism is used to analyze the first order form of the
Einstein-Hilbert action in d > 2 dimensions. Unlike previous treatments, this
is done without eliminating fields at the outset by solving equations of motion
that are independent of time derivatives when they correspond to first class
constraints. As anticipated by the way in which the affine connection
transforms under a diffeomorphism, not only primary and secondary but also
tertiary first class constraints arise. These leave d(d - 3) degrees of freedom
in phase space. The gauge invariance of the action is discussed, with special
attention being paid to the gauge generators of Henneaux, Teitelboim and
Zanelli and of Castellani.
