of the total observed double-peaked broad H$\alpha$ can be re-written as (Zhang 2011b) $$\sigma^2 = R \times \sigma_1^2 + (1-R) \times \sigma_2^2$$ where $R$ is the flux ratio of $R = f_{1/2}/f_{all}$. The equation above can be easily proved by definition of second moment (Equation 3). Based on the mean disk parameters shown in our paper I (Zhang 2011a), we have $\sigma_1\sim109{\rm \AA}$ and $\sigma_2\sim69{\rm \AA}$. Through the equation above, in order to obtain the measured line width of the double-peaked broad H$\alpha$ varying from $\sim92$Å to $\sim100$Å(minimum and maximum values for the second moment of broad H$\alpha$ of 3C390.3), the parameter of $R$ should be varying from $\sim0.53$ to $\sim0.73$, which is consistent with the shown results about R in Figure \[fr\] and in Table 1.

The results above indicate that the unexpected positive correlation shown in Figure \[fj\_3c390\] for 3C390.3 can be naturally explained by the proposed accretion disk origination of the double-peaked broad H$\alpha$. Certainly, here we do not consider effects from probable ’external’ ionizing source for the double-peaked emitter 3C390.3, which will be discussed in detail in subsection 3.4.

Virialization Assumption
------------------------

As the most convenient method to estimate central black hole masses of broad line 