  The photon-scattering winds of M-giants absorb parts of the chromospheric
emission lines and produce self-reversed spectral features in high resolution
{\it HST}/GHRS spectra. These spectra provide an opportunity to assess
fundamental parameters of the wind, including flow and turbulent velocities,
the optical depth of the wind above the region of photon creation, and the
star's mass-loss rate. This paper is the last paper in the series `GHRS
Observations of Cool, Low-Gravity Stars'; the last several have compared
empirical measurements of spectral emission lines with models of the winds and
mass-loss of K-giant and supergiants. We have used the Sobolev with Exact
Integration (SEI) radiative transfer code, along with simple models of the
outer atmosphere and wind, to determine and compare the wind characteristics of
the two M-giant stars, $\gamma$~Cru (M3.5III) and $\mu$~Gem (M3IIIab), with
previously derived values for low-gravity K-stars. The analysis specifies the
wind parameters and calculates line profiles for the \ion{Mg}{2} resonance
lines, in addition to a range of unblended \ion{Fe}{2} lines. Our line sample
covers a large range of wind opacities and, therefore, probes a range of
heights in the atmosphere.
  Our results show that $\mu$~Gem has a slower and more turbulent wind then
$\gamma$~Cru. Also, $\mu$~Gem has weaker chromosphere, in terms of surface
flux, with respect to $\gamma$~Cru. This suggests that $\mu$~Gem is more
evolved than $\gamma$~Cru. Comparing the two M-giants in this work with
previously studied K-giant and supergiant stars ($\alpha$~Tau, $\gamma$~Dra,
$\lambda$~Vel) reveals that the M-giants have slower winds than the earlier
giants, but exhibit higher mass-loss rates. Our results are interpreted in the
context of the winds being driven by Alfv\'{e}n waves.
