Does anyone know the origins of the expression "to do something on the fly"?

The Oxford English Dictionary's oldest quotation containing this phrase is from a book in 1851, reporting it as an expression used among working-class people in London, so it is at least as old as that. It's a pretty obvious metaphor, meaning "in motion," "in passing," etc.

In the quoted example it has to do with beggars who would meet passers-by "on the fly" (as they were walking down the street) and ask them for money.