Gadrooning is a decorative motif which reminds me of flower petals lined up in one direction. On furniture, they are often an ornamental motif of uniform or tapering concave or convex shapes that often flank both sides of a central motif, such as the band on the Berkey and Gay piece, below.
Gadrooning may also elongate with a decorative motif place don top of the gadrooning, such as in the Italian cassone, below. It was extremely popular in the Italian Renaissance, and 18th and early 19th century design, both in furniture and in architecture. the paisley-like motif is sometimes seen spiraling up a classical column.