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1888, Australian, New Zealand, and South African slang for "English immigrant;" U.S. use is attested from 1918, originally "British sailor, British warship," short for lime-juicer (1857), in derisive reference to the British Navy's policy (begun 1795) of issuing lime (n.2) juice on ships to prevent scurvy among sailors. In U.S., extended to "any Englishman" by 1924.
Midway Signs Limey Prof to Dope Yank Talk ["Chicago Tribune" headline, Oct. 18, 1924]
[fr the ration of lime juice given to British sailors as an antiscorbutic; the dated use for the first sense is strictly ''an English immigrant to the Antipodes''; the generalized term probably reflects the US use, ''English sailor or soldier,'' found by 1918]