Green’s Dictionary of Slang

a euph. for the vagina; thus show one’s agility v., of a woman, to reveal one’s vagina inadvertently.

1812		Spirit of Irish Wit 118: [headline] agility. The lady taking a morning canter [...] around Dublin, her horse stumbled and pitched her ladyship over his head [...] ‘John, did you see my agility?’ ‘Faith, I did my lady sure enough [...] but I never heard it called by that name, before’ .
1846		Swell’s Night Guide 107/1: Agility, see prat, quim, and c--t.
1890–1904		Farmer & Henley Sl. and Its Analogues.
1890		Music Hall & Theatre Rev. 24 May 9/2: nellie navette showed her agility in another form on Sunday last in connection with the coach escapade. I am told her somersault was very neatly executed.
1895		Harrington & LeBrunn [perf. Marie Lloyd] The Wrong Girl 🎵 ‘The day your gee-gee stumbled there / And threw you off, you know. / But you were up and on again / As agile as can be’ / I said, ‘Excuse me, sir, you’ve not / Seen my agility’.
[c.1900		Little Tich ‘The girl Got Off at Clapham’ 🎵 When she went on the ice she caused a great sensation / Her heels went up and she went down, and she showd her indignation].