A current crossing the interface between a ferromagnetic layer F-1 and a normal layer N induces a magnetization in the conduction-electron gas near the interface. This ''spin-injection'' manifests itself as a DC voltage between N and a second ferromagnetic layer F-2 deposited on N. We treat the case where the magnetizations of F-1 and F-2 are perpendicular. The spin [(s) over bar] of injected conduction electrons precesses around the exchange field present in F-2. As a result, the direction of the local conduction-electron spin density in F-2 is a function of the distance from the N-F-2 interface.