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Old English elles "other, otherwise, different," from Proto-Germanic *aljaz (cf. Gothic aljis "other," Old High German eli-lenti, Old English el-lende, both meaning "in a foreign land;" see also Alsace), an adverbial genitive of the neuter of PIE root *al- "beyond" (cf. Greek allos "other," Latin alius; see alias). Synonym of other, the nuances of usage are often arbitrary.
Productive of a number of handy compounds that somehow never got traction or have been suffered to fall from use: elsehow (1660s) "somehow or other;" elsewards (adv.), 1882, "somewhere else;" Old English elsewhat (pron.) " something else, anything else;" elsewhen (adv.), early 15c., "at another time; elsewhence (c.1600); elsewho (1540s). Among the survivors are elsewhere, elsewise.