Green’s Dictionary of Slang

ballarat n.2

[joc. use of proper name Ballarat, the last stop on the railway line from Melbourne]

the erect penis; also as v., to have an erection.

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[UK]Roger’s Profanisaurus in Viz 87 Dec. n.p.: Ballarat Aus. n. A fully erect penis. As in ‘How are you gettin’ on Bruce?’ ‘Bleedin’ marvellous Sheila. I’m nearly at Ballarat.’ See also Lake Wendouree.