  In this article, we present a universal relationship between the glass
transition temperature $T_g$ and the local glass structure. The derivation of
the simplest expression of this relationship and some comparisons with
experimental $T_g$ values have already been reported in a recent letter. We
give here the analytical expression of the parameter $\beta$ of the Gibbs-Di
Marzio equation and also new experimental probes for the validity of the
relationship, especially in low modified binary glasses.
