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Rogues who make it their business to defraud young apprentices, or errand-boys, of goods committed to their charge, by prevailing on them to execute some trifling message, pretending to take care of their parcels till they come back; these are, in cant terms, said to be on the kid lay.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
To Kid * KidderNathan 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.