If the perturbation of the zonal wind component and the Coriolis term which arises in the zonal equation of motion as a result of vertical motions are neglected, the linearized vorticity equation and the continuity equation (when written in pressure coordinates) become a complete set for the meridional wind and vertical motion perturbations. This set is solved for a class of easterly waves which reach their maximum intensity at the equator and dampen poleward. The theoretical streamlines and the theoretical field of divergence both agree quite well with their empirical counterparts. On the other hand, the theoretical isotachs are somewhat distorted and the theoretical phase speed is a bit low.