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One reeling, and ready to fall at the least touch; also the childish amusement of riding upon the two ends of a plank, poised upon the prop underneath its centre, called also see-saw. Perhaps tatter is a rustic pronunciation of totter.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
To Titter * Tittle-tattleNathan 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.