Green’s Dictionary of Slang

a silk handkerchief with a green base and white spots.

1839		W.A. Miles Poverty, Mendicity and Crime; Report 115: The new term for handkerchiefs is a Billy, for which pickpockets have peculiar terms known only in the trade. [...] randlesman, green, with white spots, 2s.
1847		G.W.M. Reynolds Mysteries of London III 85/1: Two belchers, a cream fancy, a randlesman and a blue billy .
1859, 1860		Hotten Dict. of Modern Sl. etc.
1864, 1867, 1870		Hotten Sl. Dict.
1873		Sl. Dict.