  It has been shown that the canonical structure of the first order
Einstein-Hilbert (1EH) action involves three generations of constraints and
that these can be used to find the generator of a gauge transformation which
leaves the action invariant; this transformation is a diffeomorphism with
field-dependent gauge function while on shell. In this paper we examine the
relationship between the canonical structure of this action and that of the
first order spin-2 (1S2) action, which is the weak field limit of the
Einstein-Hilbert action. We find that the weak field limit of the Possion
Brackets (PB) algebra of first class constraints associated with the 1EH action
is not that of the 1S2 action.
