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The top side the other way; i.e. the wrong side upwards; some explain it, the top side turf ways, turf being always laid the wrong side upwards.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
Topping Man * TorcheculNathan 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.