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Assuming a gravitational origin for the Fe III$\lambda\lambda$2039-2113redshift and using microlensing based estimates of the size of the regionemitting this feature, we obtain individual measurements of the virial factor,$f$, in 10 quasars. The average values for the Balmer lines, $\langlef_{H\beta}\rangle={\bf 0.43\pm 0.20}$ and $\langle f_{H\alpha}\rangle={\bf0.50\pm 0.24}$, are in good agreement with the results of previous studies forobjects with lines of comparable widths. In the case of Mg II, consistentresults, $f_{Mg II} \sim {\bf 0.44}$, can be also obtained accepting areasonable scaling for the size of the emitting region. The modeling of thecumulative histograms of individual measurements, $CDF(f)$, indicates a{relatively} high value for the ratio between isotropic and cylindricalmotions, $a\sim {\bf 0.4}-0.7$. On the contrary, we find very large values ofthe virial factor associated to the Fe III$\lambda\lambda$2039-2113 blend,$f_{FeIII}=14.3\pm2.4$, which can be explained if this feature arises from aflattened nearly face-on structure, similar to the accretion disk.

Individual Estimates of the Virial Factor in 10 Quasars: Implications on the Kinematics of the Broad Line Region