7.2. The ratio of velocity dispersions 7.3. The relationship between asymmetric drift, stability and cusp value The ratio σ$_{z}$/σ$_{R}$ = 0 . 6 is an observation of the solar neighbourhood. Should this ratio hold at all radii in a general disc galaxy? Gerssen et al. (1997) and Gerssen et al. (2000) find that the ratio is closer to 0.7 for NGC 488 and to 0.85 for NGC 2985, and Westfall et al. (2007) find that the ratio is also high for NGC 3949 and NGC 3982 (the latter’s vertical dispersion is larger than its radial dispersion). Theoretical studies of the dispersion ratio have been carried out by Ida et al. (1993) and Shiidsuka & Ida (1999), who find that σ$_{R}$/σ$_{z}$ ∼ 0 . 6 is roughly correct provided that κ/ Ω ≲ 1 . 5; higher values of κ/ Ω imply higher σ$_{z}$ values. This condition is probably satisfied in the centres of galaxies, and it would therefore be unreasonable to extend a fixed ratio of velocity dispersions across the entire disc. In fact, one might surmise that the reason for the central outflow in BG97’s heavier discs is the incorrect ratio of velocity dispersions there. To examine the velocity dispersion ratio for NGC 6503, we took the fiducial best fit model for NGC 6503 (that is, the means from Table 2) and all models used to test bar stability and calculated the ratio as a function of radius. The results are found in Fig. 21. NGC 6503’s dispersion ratio depends critically on the assumed model – scenario K exhibits a nearly linear decline with radius in which σ$_{z}$/σ$_{R}$ > 0 . 6 within two disc scale lengths. There is no indication of flattening that would justify adopting a single value over the entire disc, and very little scatter. Scenarios E, KL and KG display considerably more scatter, although only scenario KG displays anything close to a relatively constant ratio of 0.6 over a significant range; models from scenario KG appear to converge to σ$_{z}$/σ$_{R}$ ∼ 0 . 6 at small radii, but the scatter increases at larger radii. The shape and slope of the curve is critically dependent on the choice of R$_{d}$ and R$_{σ}$ ; in scenario K, R$_{d}$ ≪ R$_{σ}$ , which drags down the dispersion ratio at outer radii. If we set R$_{σ}$ to be 50% of the fiducial value, the ratio would fall less rapidly with radius but would still not be constant. Note that when R$_{d}$ = R$_{σ}$ the ratio is constant by Eqs. 19 and 20, although this may not hold in an embedded disc. Overall, we find that a constant dispersion ratio does not apply for this galaxy. The issues of cusps, asymmetric drift and stability are intertwined because all hinge on the reliability of rotation curve data and all depend on a full accounting of effects that alter the interpretation of the rotation curve. As already indicated, it is inappropriate to assume that the gas rotation traces the gravitational potential, implying that: (1) the difference between the gas and stellar rotation curves is not a measure of the asymmetric drift; (2) the gas rotation cannot be used to assess the cusp value; and (3) the proper choice of rotation 26