on the observed properties of the broad [H$\alpha$]{} line (namely [$L_{\mathrm{H{\alpha}}}$]{} and [$\mathrm{FWHM}_\mathrm{H{\alpha}}$]{}, derived from a single-epoch spectrum), without incurring appreciable additional uncertainty.

We begin by rederiving the radius-luminosity relation of Kaspi et al. (2000), using the more recent [H$\beta$]{} lags (derived from the cross-correlation centroid) and [$L_{5100}$]{} luminosities listed in Peterson et al. (2004), corrected to our adopted cosmology. The data points that Peterson et al. deem to be uncertain are omitted. We calculate symmetric error bars using the mean of the quoted upper and lower uncertainties, and use the weighted average of all available lag measurements. Using an ordinary least-squares fit with uncertainties in both parameters, we obtain

$${\ensuremath{R_{\mathrm{BLR}}}}= (30.2 \pm 1.4)~\left( \frac{{\ensuremath{L_{5100}}}}{10^{44}~{\rm erg~
s^{-1}}} \right)^{0.64 \pm 0.02} \ \ \ {\rm lt-days} .$$

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Note that the slope of the radius-luminosity relation, $0.64 \pm
0.02$, is somewhat shallower than that originally published by Kaspi et al. (2000), $0.700 \pm 0.033$, although it is consistent with the value of $0.67 \pm 0.07$ recently rederived by Kaspi [et al.]{} (2005). For $v = \frac{\sqrt{3}}{2}~v_{\mathrm{FWHM}}$, appropriate for random orbits, and using $v_{\mathrm{FWHM}}$ = [$\mathrm{FWHM}_\mathrm{H{\beta}}$]{} for consistency with Kaspi [et al.]{} (2000), the virial formula[^4] for BH mass is

$$\begin{aligned}
{\ensuremath{M_\mathrm{BH}}}&=& 