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To run up a score, which in alehouses is commonly recorded with chalk on the walls of the bar.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Walking the Plank * WallNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes
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Francis Grose was independently wealthy, having inherited money from his father, a jeweller. Finding himself overspending, he published a number of books; his Provincial Glossary seems to have been the starting-point for the Vulgar Tongue reproduced here.