An old dance to a quick movement. See Cotton, in his Virgil Travesti; where, speaking of Eolus he has these lines,
Bounce cry the port-holes, out they fly,
And make the world dance Barnaby.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Barn * BarnacleNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes