to suggest that the increase may not be as great.

A stretch of the Erb and Pettini velocity widths of $\alpha(req)=2.64$ gives the best fit to the predicted distribution of $V_{c7}$, as shown in Figure 1. It is noticeable that the predicted distribution of $V_{c7}$ is rather narrow, compared to the broad distribution of $\sigma$. We consider this point again later.

Modelling observational effects and selection cuts to determine [$\alpha(obs)$]{}
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The principle of measuring $\alpha(obs)$, accounting for observational effects and selection cuts, is illustrated in Figure \[fig:lbg\_cumf\], and is explained as follows. For galaxies of specified circular velocity radial profile, and luminosity radial profile, it is possible to predict the observed distribution of the ratio $V_r/V_{c7}$, for any given observing conditions – defined by the seeing, the slit width and the selection criteria. Since $\alpha=V_{c7}/\sigma$ we can stretch our model distribution of $V_r/V_{c7}$ by a factor $\alpha$ to match the observed distribution of $V_r/\sigma$. This best fit stretch factor is $\alpha(obs)$. If the massive–halo model is correct $\alpha(obs)$ will be consistent with $\alpha(req)$. As regards the slit width, since two observational set–ups were used, with 0.76arcsec (NIRSPEC) and 1.00arcsec (ISAAC) slits, we model both cases, and weight the results 