When I add new extended-Regency-era country dance tune books to my collection of photos and scans, one of the things I do is quickly skim through the figures looking for anything out of the ordinary.  And while heys (or reels) are quite common figures for country dances in the late eighteenth and early nineteenth centuries (indeed, all the way back to the seventeenth century!), in this period, they are almost always heys for three.  Figures like "hey your own sides", "hey contrary sides and hey your own sides", "hey top and bottom" (where one dancer in a couple goes up and one goes down the set), and the corner-formation heys where the lady heys with two gentlemen and the gentleman with two ladies are all very common.  But these are all heys for three dancers.  A "right and left" quite round is technically a circular hey for four, but a classic, Scotch reel-style hey for four dancers in a line is not listed as a standard figure and doesn't really turn up.  

Until, of course, it does....[two dance figures behind the cut]