A simple example problem is constructed for which the continuous primitive equations are shown to have a solution. The model is then discretized in the vertical in a manner equivalent to that used in the NMC global spectral model. It is shown that, in general, the discretized version of the problem has no solution. The vertical discretization schemes used in NMC and many other atmospheric circulation models are therefore inconsistent with the continuous equations. Conditions for design of a vertical differencing scheme that does not have this limitation are suggested.