Despite many decades of study, the kinematics of the broad-line region of 3C~273 are still poorly understood. We report a new, high signal-to-noise, reverberation mapping campaign carried out from November 2008 to March 2018 that allows the determination of time lags between emission lines and the variable continuum with high precision. The time lag of variations in H$beta$ relative to those of the 5100 Angstrom continuum is $146.8_{-12.1}^{+8.3}$ days in the rest frame, which agrees very well with the Paschen-$alpha$ region measured by the GRAVITY at The Very Large Telescope Interferometer. The time lag of the H$gamma$ emission line is found to be nearly the same as for H$beta$. The lag of the Fe II emission is $322.0_{-57.9}^{+55.5}$ days, longer by a factor of $sim$2 than that of the Balmer lines. The velocity-resolved lag measurements of the H$beta$ line show a complex structure which can be possibly explained by a rotation-dominated disk with some inflowing radial velocity in the H$beta$-emitting region. Taking the virial factor of $f_{rm BLR} = 1.3$, we derive a BH mass of $M_{bullet} = 4.1_{-0.4}^{+0.3} times 10^8 M_{odot}$ and an accretion rate of $9.3,L_{rm Edd},c^{-2}$ from the H$beta$ line. The decomposition of its $HST$ images yields a host stellar mass of $M_* = 10^{11.3 pm 0.7} M_odot$, and a ratio of $M_{bullet}/M_*approx 2.0times 10^{-3}$ in agreement with the Magorrian relation. In the near future, it is expected to compare the geometrically-thick BLR discovered by the GRAVITY in 3C 273 with its spatially-resolved torus in order to understand the potential connection between the BLR and the torus.
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