  Elaborated calculations of the shear and the bulk viscosities in the hadron
gas, using the ultrarelativistic quantum molecular dynamics (UrQMD) model cross
sections, are made. These cross sections are analyzed and improved. A special
treatment of the resonances is implemented additionally. All this allows for
better hydrodynamical description of the experimental data. The previously
considered approximation of one constant cross section for all hadrons is
justified. It's found that the bulk viscosity of the hadron gas is much larger
than the bulk viscosity of the pion gas while the shear viscosity is found to
be less sensitive to the hadronic mass spectrum. The maximum of the bulk
viscosity of the hadron gas is expected to be approximately in the temperature
range ${T=150 190 MeV}$ with zero chemical potentials. This range covers the
critical temperature values found from lattice calculations. We comment on some
important aspects of calculations of the bulk viscosity, which were not taken
into account or were not analyzed well previously. Doing this, a generalized
Chapman-Enskog procedure, taking into account deviations from the chemical
equilibrium, is outlined. Some general properties, features, the physical
meaning of the bulk viscosity and some other comments on the deviations from
the chemical equilibrium supplement this discussion. Analytical closed-form
expressions for the transport coefficients and some related quantities within a
quite large class of cross sections can be obtained. Some examples are
explicitly considered. Comparisons with some previous calculations of the
viscosities in the hadron gas and the pion gas are done.
