  In this paper, we investigate the influences of two continuum radiation
pressures of the central engines on the black hole mass estimates for 40 active
galactic nuclei (AGNs) with high accretion rates. The two continuum radiation
pressure forces, usually believed negligible or not considered, are from the
free electron Thomson scattering, and the recombination and re-ionization of
hydrogen ions that continue to absorb ionizing photons to compensate for the
recombination. The masses counteracted by the two radiation pressures
$M_{\rm{RP}}$ depend sensitively on the percent of ionized hydrogen in the
clouds $\beta$, and are not ignorable compared to the black hole virial masses
$M_{\rm{RM}}$, estimated from the reverberation mapping method, for these AGNs.
As $\beta$ increases, $M_{\rm{RP}}$ also does. The black hole masses
$M_{\rm{\bullet}}$ could be underestimated at least by a factor of 30--40
percent for some AGNs accreting around the Eddington limit, regardless of
redshifts of sources $z$. Some AGNs at $z < 0.3$ and quasars at $z \ga 6.0$
have the same behaviors in the plots of $M_{\rm{RP}}$ versus $M_{\rm{RM}}$. The
complete radiation pressures will be added as AGNs match $M_{\rm{RP}}\ga 0.3
M_{\rm{RM}}$ due to the two continuum radiation pressures. Compared to
$M_{\rm{RM}}$, $M_{\rm{\bullet}}$ might be extremely underestimated if
considering the complete radiation pressures for the AGNs accreting around the
Eddington limit.
