  The measured rotation velocity profiles of mature spiral galaxies are
successfully described with a gravitational model consisting of a thin
axisymmetric disk of finte radius. The disk is assumed uniformly thin but with
variable radial mass density. The governing integral equation is based on
mechanical balance between Newtonian gravitational and centrifugal forces (due
to galaxy rotation) at each and every point in a finite set of concentric
rings. The nondimensionalized mathematical system contains a dimensionless
parameter we call ``galactic rotation parameter'' which concisely crystallizes
perspective. Computational solutions are obtained for the radial mass
distributions that satisfy the measured rotational velocity profiles. Together
with a constraint equation for mass conservation, the galactic rotational
parameter is also determined from which the total galactic mass is calculated
from measured galactic radii and maximum rotation velocities. These calculated
total galactic masses are in good agreement with data. Our deduced
exponentially decreasing mass distributions in the central galactic core are in
agreement with almost all others. However our mass distributions differ toward
the galactic periphery with more ordinary baryonic mass in these outer disk
regions which are cooler with lower opactiy/emissivity (and thus darker).
