Beilby’s ball, n. — Green’s Dictionary of Slang

Beilby’s ball n.

[ety. unknown; the identity of Mr Beilby is unknown but a number of suggestions exist. The most obvious is that Beilby was a well-known sheriff; a second is that Beilby is a mispronunciation of Old Bailey, the court in which so many villains were sentenced to death. The third, and that espoused by Partridge, is that Beilby refers to the bilbo, a long iron bar, furnished with sliding shackles to confine the ankles of prisoners and a lock by which to fix one end of the bar to the floor or ground. Bilbo comes from the Spanish town of Bilbao, where these fetters were invented]

the reification of judicial hanging.

In phrases

dance at Beilby’s ball (v.)

to be hanged; also ext. with ...where the sheriff plays the music or ...where the sheriff pays the fiddlers.

1785, 1788, 1796		Grose Classical Dict. of the Vulgar Tongue n.p.: Beilby’s ball, he will dance at Beilby’s ball, where the sheriff plays the musick: he will be hanged. Who Mr Beilby was, or why that ceremony was so called, remains with the quadrature of the circle, the discovery of the philosopher’s stone and divers other desiderata as yet undiscovered.
1811		Lex. Balatronicum.
1823		Egan Grose’s Classical Dict. of the Vulgar Tongue.

shake one’s trotters at Beilby’s ball (v.) (also shake one’s trotters at Bilby’s ball, shiver… ) [trotter n. (1)]

to be hanged.

1747		Life and Character of Moll King 12: He doss in a Pad of mine! No, Boy, if I was to grapple him, he must shiver his Trotters at Bilby’s Ball.
1754		G. Stevens ‘A Cant Song’ Muses Delight 177: I can but shake trotters at fam’d Bilby’s ball, / And go off like a bowman that’s quiddish.
1785, 1788, 1796		Grose Classical Dict. of the Vulgar Tongue n.p.: To shake one’s trotters at Bilby’s ball, where the sheriff pays the fiddlers; perhaps the Bilboes ball, i.e. the ball of fetters: fetters and stocks were anciently called the bilboes.
1811		Lex. Balatronicum [as cit. 1785].
1823		Egan Grose’s Classical Dict. of the Vulgar Tongue.