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He is down in the black book, i.e. has a stain in his character. A black book is keep in most regiments, wherein the names of all persons sentenced to punishment are recorded.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Black A-se * Black BoxNathan 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.