Our index τ_HB as a function of cluster ages obtained from different authors. Top: cluster ages from VandenBerg et al. (2013), Leaman et al. (2013). The error bar in the lower left corner shows the conservative ±0.5 Gyr error on the GGC ages. Bottom: ages from Salaris & Weiss (2002) based on the metallicity scale provided by Carretta & Gratton (1997). In both panels red squares are the same second parameter clusters shown in Fig. 16 and discussed in this section. Red lines determine the best-fit to each data sample, blue lines the ±1σ levels.