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The photon-scattering winds of M-giants absorb parts of the chromosphericemission lines and produce self-reversed spectral features in high resolution{\it HST}/GHRS spectra. These spectra provide an opportunity to assessfundamental parameters of the wind, including flow and turbulent velocities,the optical depth of the wind above the region of photon creation, and thestar's mass-loss rate. This paper is the last paper in the series `GHRSObservations of Cool, Low-Gravity Stars'; the last several have comparedempirical measurements of spectral emission lines with models of the winds andmass-loss of K-giant and supergiants. We have used the Sobolev with ExactIntegration (SEI) radiative transfer code, along with simple models of theouter atmosphere and wind, to determine and compare the wind characteristics ofthe two M-giant stars, $\gamma$~Cru (M3.5III) and $\mu$~Gem (M3IIIab), withpreviously derived values for low-gravity K-stars. The analysis specifies thewind parameters and calculates line profiles for the \ion{Mg}{2} resonancelines, in addition to a range of unblended \ion{Fe}{2} lines. Our line samplecovers a large range of wind opacities and, therefore, probes a range ofheights 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 surfaceflux, with respect to $\gamma$~Cru. This suggests that $\mu$~Gem is moreevolved than $\gamma$~Cru. Comparing the two M-giants in this work withpreviously studied K-giant and supergiant stars ($\alpha$~Tau, $\gamma$~Dra,$\lambda$~Vel) reveals that the M-giants have slower winds than the earliergiants, but exhibit higher mass-loss rates. Our results are interpreted in thecontext of the winds being driven by Alfv\'{e}n waves.

GHRS Observations of Cool, Low-Gravity Stars. VI Mass-Loss Rates and Wind Parameters for M Giants