Queer, quaint, old-fashioned. This word was first applied to Roman Catholic priests, and subsequently to other clergymen. Thus Swift speaks of “a rabble of tenants and rusty dull rums” (country parsons). As these “rusty dull rums” were old-fashioned and quaint, a “rum fellow” came to signify one as odd as a “rusty dull rum.”
Professor De Morgan thought that the most probable derivation was from booksellers trading with the West Indies. It is said that in the eighteenth century they bartered books for rum, but set aside chiefly such books as would not sell in England.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
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