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A society of gentlemen, eminent for wit and learning, who in the reign of queen Anne and George I. met at a house kept by one Christopher Cat. The portraits of most of the members of this society were painted by Sir Godfrey Kneller, of one size; thence still called the kit-cat size.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Kit * Kitchen PhysicNathan 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.