  (Abridged) Axisymmetric models of the Milky Way exhibit strong interrelations
between the Galactic constants (R_0 and T_0), the stellar columndensity (S_*)
and the shape of the dark matter (DM) halo. Here we present analytical
relations that can be used to investigate the effects of the uncertain gaseous
velocity dispersion on the HI flaring constraints. The contribution of cosmic
rays and magnetic fields to the pressure gradients is small. A significantly
flattened dark matter halo is only possible if R_0 <~ 6.8 kpc.
  If R_0 is larger than ~7 kpc, or T_0 >~ 170 km/s, we can rule out two DM
candidates that require a highly flattened DM halo: 1) decaying massive
neutrinos; and 2) a disk of cold molecular hydrogen.
  It is only possible to construct self-consistent models of the Galaxy based
on the IAU-recommended values for the Galactic constants in the unlikely case
that the the stellar columndensity is smaller than ~18 M_sun/pc^2. If we assume
that the halo is oblate and S_* = 35 +/- 5 M_sun/pc^2, R_0 <~ 8 kpc and T_0 <~
200 km/s.
  Combining the best kinematical and star-count estimates of S_*, we conclude
that: 25 <~ S_* <~ 45 M_sun/pc^2. Kuijken & Gilmore's (1991) determination of
the columndensity of matter with |z|<=1.1 kpc is robust and valid over a wide
range of Galactic constants.
  Our mass models show that the DM density in the Galactic centre is uncertain
by a factor 1000. In the Solar neighbourhood we find: rho_DM ~0.42 GeV/c^2/cm^3
or (11 +/- 5) mM_sun/pc^3 -- roughly 15% of rho_tot.
