  We show how the use of the normal projection of the Einstein tensor as a set
of boundary conditions relates to the propagation of the constraints, for two
representations of the Einstein equations with vanishing shift vector: the ADM
formulation, which is ill posed, and the Einstein-Christoffel formulation,
which is symmetric hyperbolic. Essentially, the components of the normal
projection of the Einstein tensor that act as non-trivial boundary conditions
are linear combinations of the evolution equations with the constraints that
are not preserved at the boundary, in both cases. In the process, the
relationship of the normal projection of the Einstein tensor to the recently
introduced ``constraint-preserving'' boundary conditions becomes apparent.
