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To take off one’s hat or cap. To cap the quadrangle; a lesson of humility, or rather servility, taught undergraduates at the university, where they are obliged to cross the area of the college cap in hand, in reverence to the fellows who sometimes walk there. The same ceremony is observed on coming on the quarter deck of ships of war, although no officer should be on it.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
To Cap * To Cap-2Nathan 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.