Topsails are the second sails up. To reef a sail is to draw part of it up to the yard to reduce the area of sail exposed to the wind. Topsails have three and sometimes four reef-bands running across the upper half, where there are short lengths of rope that can be used to tie the sail to the rope or cable along the bottom of a yard. To double-reef them is to haul them up as far as the second reef-band.