  We report in this paper the progresses on the determination of the Boltzmann
constant using the acoustic gas thermometer (AGT) of fixed-length cylindrical
cavities. First, we present the comparison of the molar masses of pure argon
gases through comparing speeds of sound of gases. The procedure is independent
from the methodology by Gas Chromatography-Mass Spectrometry (GC-MS). The
experimental results show good agreement between both methods. The comparison
offers an independent inspection of the analytical results by GC-MS. Second, we
present the principle of the novel differential-cylindrical procedure based on
the AGT of two fixed-length cavities. The deletion mechanism for some major
perturbations is analyzed for the new procedure. The experimental results of
the differential-cylindrical procedure demonstrate some major improvements on
the first, second acoustic and third virial coefficients, and the excess
half-widths. The three acoustic virial coefficients agree well with the
stated-of-the-art experimental and theoretical (the ab initio calculation)
results. The new method is characterized by much less correction-dependence.
The differential-cylindrical procedure results in the preliminary determination
of the Boltzmann constant of 1.380 650 6*10^-23 with the relative standard
uncertainty of 2.3*10^-6. The new value is in 1.3*10^-6 above the adjusted
Boltzmann constant given in CODATA 2010. The resultant gas constant R =8.314
473 J/mol/K with the same the relative standard uncertainty.
