Existing observations from ISEE 3 and new observations from Galileo show that when the interplanetary magnetic field (IMF) has a By component, a By component also develops in the Earth's magnetotail, but only in those quadrants in which the addition of the newly opened magnetic flux tubes occurs. The presence of By on the closed field lines (which is in the same direction as the IMF By) is also seen. We suggest that for a positive IMF By, the magnetopause is open only in the north dawn and south dusk quadrants of the magnetotail. The continuity of magnetic field across the open boundary then requires that a By component be present in the magnetosphere in these quadrants but not in the other two quadrants. We present a model of the magnetospheric convection that postulates cross-tail flows in the mantle/lobe system and the plasma sheet. We suggest that shear flows between the northern and the southern halves of the plasma sheet generate a By component on the closed magnetic field lines. The model is consistent with the two-cell ionospheric convection models constructed from electric field observations by Heppner and Maynard [1987>. Results from global MHD simulations confirm the main features of the proposed model. ¿ American Geophysical Union 1996