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A very small bottle; short measure being among the many means used by the keepers of those houses, to gain what they call an honest livelihood: indeed this is one of the least reprehensible; the less they give a man of their infernal beverages for his money, the kinder they behave to him.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
See also the definition in Nathan Bailey's 1736 dictionary of canting and thieving slang.
Bawdy Basket * Bay FeverNathan 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.