We report the first direct investigation of the spatial properties of flux transfer events (FTEs) at the Earth's dayside magnetopause. Simultaneous magnetometer and plasma data from the ISEE 1 and 2 satellites are combined to show that magnetosheath FTEs can have a scale size of order an Earth radius in the magnetopause normal direction. We confirm that the magnetic field within the events appers to be twisted, this twisting corresponding to a core field-aligned current of magnitude a few x 105 A. We also show evidence for plasma vorticity in FTEs. The transverse flow and field perturbations accompanying the three events studied obey approximately the Wal¿n relation for a propagating Alfv¿n wave.