  It is proven that a class of Gegenbauer tau approximations to a 4th order
differential eigenvalue problem of hydrodynamic type provide real, negative and
distinct eigenvalues, as is the case for the exact solutions. This class of
Gegenbauer tau methods includes Chebyshev and Legendre Galerkin and `inviscid'
Galerkin but does not include Chebyshev and Legendre tau. Rigorous and
numerical results show that the results are sharp: positive or complex
eigenvalues arise outside of this class. The widely used modified tau approach
is proved to be equivalent to the Galerkin method.
