A previous paper (Hollweg, 1974a) discussed a new physical mechanism for accelerating &agr; particles in the solar wind, via their interaction with Alfv¿n waves. This paper presents numerical calculations of a simple three-fluid solar wind model, which incorporates the new physical process. The principal result is that the Alfv¿n wave do effect an important additional coupling between protons and &agr; particles, which tends to equalize their flow speeds at 1 AU. This is in sharp contrast to previous calculations, which gave va/vp=0.7--0.8 at 1 AU. But the model calculations still contain two important problems: (1) we do not obtain va?vp at 1 AU, as is frequently observed; and (2) the model calculations give values of va which are unreasonably low near the sun. Thus we conclude that the new physical mechanism is probably sufficiently important to warrant its inclusion in future solar wind models but also that there must be other physical processes working, which still remain to be discovered.