  The interpretation, due to T. Mabuchi, of the classical Futaki invariant of
Fano toric manifolds is extended to the case of the Generalized Futaki
invariant, introduced by W. Ding and G. Tian, of almost Fano toric varieties.
As an application it is shown that the real part of the Generalized Futaki
invariant is positive for all degenerations of the Fano manifold V_{38},
obtained by intersection of the Veronese embedding of ${\bf P}^3\times{\bf P}^2
\subset {\bf P}^{11}$ with codimension-two hyperplanes.
