The stratification with optical depth of the line-of-sight (LOS) velocity o
f a simple, isolated, round sunspot observed with the Advanced Stokes Polar
imeter (ASP; Elmore et al.) presented here completes this series of papers
that investigates the stratification in optical depths of such a typical su
nspot. These results have been obtained through the use of the SIR techniqu
e (Stokes Inversion based on Response functions of Ruiz Cobo & del Toro Ini
esta). From these data we have confirmed that there are strong downflowing
velocities at log tau (5) = 0 that coincide spatially with the places where
the magnetic field points downward (Westendorp Plaza et al.). Further conf
irmation is obtained by the application of the same method on a different s
unspot, already analyzed with the Milne-Eddington inversion technique (Stan
chDeld, Thomas, & Lites). These downflows reconcile observations that have
detected Evershed velocities outside sunspots together with suggestions of
the possible return of the flow within the penumbra. The Evershed flow seem
s to be concentrated in elevated channels not thicker than 1 or 2 scale hei
ghts that are mostly located in the space between magnetic spines, i.e., in
places where the magnetic field is more inclined, weaker in the inner-midd
le penumbra, and stronger in the outer penumbra and beyond the visible limi
ts of the sunspot. This conclusion is based upon the tight correlation foun
d between LOS velocities and the (reported in the second paper of this seri
es) magnetic field strength and zenith angle. The upstreaming material is s
een in the inner penumbra and the downstreaming in the outer penumbra. A st
rong increase with optical depth has been obtained for the LOS velocities t
hat provides indications of the superposition of Evershed channels along th
e LOS. The differential opacity effect between the center-side and the limb
-side penumbra, already reported in the second paper in this series, is als
o seen in the velocity maps and has suggested the comparison of the vertica
l mass flux through the upstreaming zones (mostly seen in the center side)
and the downstreaming zones (mostly seen in the limb side), obtaining a fai
rly good balance between the two.