Backarapper is Birmingham and Midlands slang for a kind of firework. A post on the OxfordWords blog about Gandalf's Particularly excellent fireworks includes:
A colleague has pointed that the backarapper isn’t only confined to Middle Earth. They’re described in a glossary of the Warwickshire dialect from 1896 as ‘a firework so folded that the charges in the folds detonate in succession’. You can read all about them, Tolkien’s other vocabulary, and his time on the Oxford English Dictionary, in Peter Gilliver, Jeremy Marshall, and Edmund Weiner’s The Ring of Words: Tolkien and the Oxford English Dictionary (OUP, 2006).
I found some citations earlier than G.F. Northall’s Warwickshire Word-book (1896).
The Christian World Magazine of November, 1866 describes Guy Fawkes' night of 20-30 years earlier, such fireworks not being allowed at the time of writing:
It is scarely necessary to remark that the fifth of November commemorates the well-known "Gunpowder Plot"... Years ago, the observances of this day were of far more importance than now they are... Then came the grand display fireworks at night, for which all the little ones say up, and the "letting off" of which was the grand achievement of the evening; -- wheels, squibs, serpents, rockets, and Roman candles, to say nothing of back-rappers that leaped, about like fiery dragons, to the infinite satisfaction of the lads, and the discomfiture, real or pretended, of the girls. Twenty or thirty years ago even, children used to look forward with eager delight to the fifth of November: now the ancient festivities are discontinued by the authorities, it being forbidden under certain penalties to let of fireworks or make bonfires in any public place.
A July 1860 entry in Visit of His Royal Highness the Prince of Wales to the British North American Provines and United States in the Year 1860. Compiled from the Public Journals by Robert Cellem (1861) says:
As on the previous evening, the juvenile portion of the population indulged themselves ad libitum in the use of crackers, back-rappers, serpents, and squibs. How so many got into Newfoundland is a problem no one I have questioned is able to solve.
Here's some more recent citations.
Two years after Northall's dictionary, Joseph Wright's The English Dialect Dictionary (1898) includes:
The cited Roger Ploughman's Second Visit to London is really Roger Plowman's Second Excursion to London and c.1878.
A 1948 snippet of Queen's Medical Magazine, Volumes 41-45, by Birmingham Medical and Dental Schools includes:
Then there is Number 12's "hollow" cough, which is like a hand grenade gone off in the depths of Wookey Hole. Number l's stock in trade is a low moaning cough reminding one of the haunted church at midnight. There is also the "loose" cough, the "dry" cough, the "acking corf," the "backarapper" cough and several others.