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Persons slightly acquainted, or only so far as mutually to salute with the hat on meeting. A woman who endeavours to attract the notice of any particular man, is said to set her cap at him.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
To Cap-2 * Caper MerchantNathan 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.