DISCUSSION

Our ``complete" sample of bright QSOs (Table ) contains 29 objects brighter than B = 16.16 ($O_{\rm APS} <$ 16.00), three of them (indicated by a ``N" in the last column of Table ) are not within the PG area. The area common to the PG and FBS surveys at |b| > 30$^\circ$ ($\sim$2250 deg²) contains 26 bright QSOs (13 PG QSOs and 13 others) (but there are 17 PG QSOs with $B_{\rm PG} <$ 16.16 in the area; this larger number is probably due to the Eddington (1940) effect, the PG magnitudes being affected by relatively large errors, $\sigma \sim$ 0.37 mag). From these data, we derive a surface density of 0.012 deg^-2, which is to be compared with the original value of the PG survey: 0.0064 deg^-2, implying a maximum completeness of 53$\pm$10% for the PG survey.

Grazian et al. (2000) have cross-correlated the RASS with photometric databases in an 8164 deg² area of the northern sky at |b|> 30$^\circ$, selecting all coincidences brighter than $R \sim$ 15.4; from this, they derive a surface density of bright (B < 15.5) QSOs (defined as AGNs with M_B< -23.0) of 10$\pm$2 10^-3 deg^-2 and conclude that the true surface density of such objects is about three times larger than that derived from the PG survey. However, they do not specify how the B magnitude of their objects was derived. Their sample contains 46 QSOs; 15 of them have z > 0.20; we have extracted from the APS catalogue the O magnitudes for 12 of them (for the three others, these magnitudes are unavailable); it turns out that only one (J172320.5+341756) has O < 15.34, corresponding to B < 15.5, suggesting that the O magnitudes used by Grazian et al. are underestimated and, consequently, the surface density overestimated.

Lamontagne et al. (2000) claim that they found a surface density of bright QSOs three times larger than the PG value. They have searched for UV-excess stellar-like objects with B < 16.5 and U - B < -0.6 in a 840 deg² area covering the south Galactic cap; the errors in the B magnitudes are estimated to be 0.30 mag rms. They have found 228 such objects which have all been spectroscopically identified; 32 are AGNs, out of which only eleven are brighter than B = 16.16 and M_B = -24.0 (including 0117-2837 which, according to Grupe et al. (1999), has a redshift of 0.349 rather than 0.055). We derive a surface density or 0.013 deg^-2, in agreement with our value and only twice the PG value.