maximum variation of the size of BLR of 3C390.3 calculated through the variations of the line width should be $(\frac{\sigma_{max}}{\sigma_{min}})^2=(\frac{\sim100{\rm \AA}}{\sim92{\rm \AA}})^2\sim1.18$, which is consistent with the results above $\frac{R_{BLR,max}}{R_{BLR,min}}\frac{\sim715{\rm R_G}}{\sim596{\rm R_G}}\sim1.19$.

The results above indicate that the virialization assumption is still available for the double-peaked emitter 3C390.3. However, the common empirical relation $R_{BLR}\propto L^{\sim0.5}$ is not available to show the properties of [**time-varying**]{} size of BLRs of 3C390.3. In other words, based on the [**mean**]{} continuum luminosity (broad line luminosity) in one long period, the [**mean**]{} size of BLR can be estimated by the empirical relation $R_{BLR}\propto L^{\sim0.5}$, however, the time-varying size of BLR is decreasing with the line luminosity increasing.

Previous Results
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Besides the well-known double-peaked emitter 3C390.3, there are several other double-peaked emitters, of which the double-peaked broad line profiles have been studied and reported. Some simple results about correlation between peak separation (in some literature, peak separation was used as substitute for line width) and line flux (continuum emission) can be found.

In Figure 4 of Shapovalova et al. (2001), we can find one rough negative correlation between peak separation and line flux (continuum emission) for the double-peaked broad H$\beta$ of 3C390.3 observed from 1995 