not seen completely edge-on. This is consistent with the observed stellar disc from Paper IV, where we measured $i=86.8^\circ$ (Table 2 of Paper IV). We have attempted to correct for this by lowering the observed thickness by 30%, but will treat the results are uncertain in view of this inclination issue. The noise in this galaxy was too high for the velocity dispersion to be measure, so we keep this fixed at $\sigma=10$km/s.

The results for the optically thin and the self-absorbing [ <span style="font-variant:small-caps;">HI</span> ]{}models are shown in Figure \[fig:ESO138decomposition\]. The cross-correlation diagram of the optically thin model is shown in Figure \[fig:ESO138-crosscorr\] (left), while the one for the self-absorption model is shown in Figure \[fig:ESO138-crosscorr\] (right). In both cases, the rotation curve and the vertical force gradient have been successfully fitted. Only at the larger radii do observed and theoretical curves of the vertical force gradient start to deviate.

The optically thin model produces a halo core density $\rho_{0,\textrm{halo}}$ of $0.261^{+0.002}_{-0.003}$ M$_\odot$/pc$^3$ and a scale-length of $R_c =0.70^{+0.02}_{-0.01}$kpc. The halo is distinctly prolate, with the optimal solution located at the boundary condition of $q =2.0^{+0.1}_{-0.2}$. The stellar disc is very bright, with $M_*/L_R=0.50^{+0.02}_{-0.01}$.

Compared to this, the self-absorbing 