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The MHD slow mode wave has application to coronal seismology, MHD turbulence,and the solar wind where it can be produced by parametric instabilities. Weconsider analytically how a drifting ion species (e.g. He$^{++}$) affects thelinear slow mode wave in a mainly electron-proton plasma, with potentialconsequences for the aforementioned applications. Our main conclusions are: 1.For wavevectors highly oblique to the magnetic field, we find solutions thatare characterized by very small perturbations of total pressure. Thus, ourresults may help to distinguish the MHD slow mode from kinetic Alfv\'en wavesand non-propagating pressure-balanced structures, which can also have verysmall total pressure perturbations. 2. For small ion concentrations, there aresolutions that are similar to the usual slow mode in an electron-proton plasma,and solutions that are dominated by the drifting ions, but for small drifts thewave modes cannot be simply characterized. 3. Even with zero ion drift, thestandard dispersion relation for the highly oblique slow mode cannot be usedwith the Alfv\'en speed computed using the summed proton and ion densities, andwith the sound speed computed from the summed pressures and densities of allspecies. 4. The ions can drive a non-resonant instability under certaincircumstances. For low plasma beta, the threshold drift can be less than thatrequired to destabilize electromagnetic modes, but damping from the Landauresonance can eliminate this instability altogether, unless $T_{\mathrme}/T_{\mathrm p}\gg1$.

Magnetohydrodynamic Slow Mode with Drifting He$^{++}$: Implications for Coronal Seismology and the Solar Wind