C[iii]{}\]$\lambda1909$ set an upper limit on the density $n_{\rm H} \la 10^{9.5}$ [@Davidson79]. Since $L \propto Q({\rm H})$, this naturally led to the prediction that the BLR radius would scale with luminosity as $R \propto L^{1/2}$. Unfortunately, best-estimate values for $Q({\rm
H})$ and $n_{\rm H}$ led to a significant overestimate of the BLR radius [@Peterson85] as a consequence of the simple but erroneous assumption that all the broad lines arise cospatially (i.e., models employed a single representative BLR cloud).

With the advent of reverberation mapping [hereafter RM; @Blandford82; @Peterson93], direct measurements of $R$ enabled improved black hole mass determinations. Attempts to estimate black hole masses based on early RM results and the $R \propto L^{1/2}$ prediction included those of [@Padovani88], [@Koratkar91], and [@Laor98]. The first multiwavelength RM campaigns demonstrated ionization stratification of the BLR [@Clavel91; @Krolik91; @Peterson91] and this eventually led to identification of the virial relationship, $R \propto V^{-2}$ [@PetersonWandel99; @PetersonWandel00; @Onken02; @Kollatschny03; @Bentz10], that gave reverberation-based mass measurements higher levels of credibility. Of course, the virial relationship demonstrates only that the central force has a $R^{-2}$ dependence, which is also characteristic of radiation pressure; whether or not radiation pressure from the continuum source is important has not been 