The dispersions of the isolated disc scale with the square root of its surface density (Eqs. 19 and 20), but the process of embedding the disc in a dark halo modifies the disper- sions. BG97 find that embedding the isolated disc in the halo allowed the settling process at the beginning of the N − body simulations to rearrange the dispersions itself. 3 The result is an initial central outflow in the simulations, leading to a decrease in the dispersions, more- or-less naturally accounting for the observed disc dispersion of NGC 6503. BG97 find that their two lightest discs remain stable to bars, but are unable to reproduce the σ − drop. Visible on Fig. 8 are the points corresponding to the models used by BG97. They are located well above the 2 σ confidence interval. The discrepancy occurs because Q is obtained from the radial dispersion σ$_{R}$ , which, in BG97’s models, is directly coupled to the surface density (cf. Eqs. 19 and 20). Thus, BG97’s σ$_{R}$ is determined by the disc surface density, which is not the case for the GalactICS model. Their Fig. 9 shows that, after settling, their minimum Q − values decline so that they fall in line with our PDF in Fig. 8. Thus, their M$_{d}$ − Q$_{min}$ data points are consistent with our M$_{d}$ − Q$_{min}$ PDF. However, their discs do not display bar formation, while ours do; there are two possible reasons for this. First, from Fig. 10, most of our models only develop a bar after ∼ 2 Gyr, while BG97 evolved their simulations for ∼ 1 . 3 Gyr. Second, and more importantly, it is now known that live halos can trigger bar formation (Athanassoula 2002); BG97 used rigid halo potentials for their simulations, so this bar formation trigger is not in play. We evolved one of our bar unstable models in exactly the way described in § 5, except the number of disc particles was reduced to 40K. We found that the bar formation in this model was delayed by ∼ 1 − 2 Gyr, suggesting that sufficient numerical resolution is needed to capture the correct evolution. This is consistent with halo-triggered bar formation, because inadequate numerical resolution will fail to resolve the resonant interactions required for this mechanism. $^{3}$BG97 attempted to account for the embedding: σ z can be modified by a factor F ( ϵ ) accounting for the relative halo contribution, where The result is that when ϵ is less than 0 (as it could be near the centre where ∂ $_{∂R}$v 2 c is very large) the dispersion can decrease upon embedding, while large values of ϵ cause the dispersions to increase. BG97 dropped this factor for the models discussed in that paper and used the isolated disc dispersions (Bottema, private communication). 25 ϵ = ( ρ z =0 halo − 1 4 πR ∂ ( v 2 $_{C}$) ∂R ) / ( ρ z =0 disc ) . (23)