spanning a wide range of [H$\alpha$]{}luminosity from $\sim 10^{40}$ to $10^{44}$ erg s$^{-1}$. He showed that [$L_{\mathrm{H{\alpha}}}$]{} traces the optical continuum luminosity with a slope of $1.05 \pm 0.03$, consistent with unity and very similar to the slope found here ($1.157 \pm 0.005$). Similarly, from an analysis of AGNs ranging from nearby low-luminosity Seyferts to quasars, Ho & Peng (2001) found that the luminosity of the broad [H$\beta$]{} line, from $\sim
10^{38}$ to $10^{44}$ erg s$^{-1}$, correlates strongly with the $B$-band continuum luminosity, roughly of the form [$L_{\mathrm{H{\beta}}}$]{}$\propto
L_B^{0.9}$. While this slope is formally shallower than that found in our sample ($1.133 \pm 0.005$), the measurements for the low-luminosity sources in the sample of Ho & Peng are also considerably more uncertain, making it difficult to judge the significance of the apparent discrepancy. Our study, based on a large, uniform, and modern data set, provides an important confirmation of the earlier results.

The correlation between the luminosity of the Balmer lines and the optical continuum arises naturally if the latter traces the low-energy tail of a featureless continuum that extends into the far-ultraviolet, which powers the line emission through photoionization. Indeed, quite early on this simple picture provided a natural 