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Published 01/10/24
àrainn f. [ˈaːɾiɲ], gen. àrainne -[ə], rarely fàrainn, 
MacLeod 1978, 482, 496.
is derived by Mackay (1897, 95: arainn) from Ice. arinn m. ‘hearth’ and by Henderson (1910, 113: àirinn), de Vries (1962) and McDonald (2009, 338) from the Old Norse cognate. Ice./ON arinn has a short stressed vowel, although a variant árinn is found (Cleasby 1874 and NO). In spite of Mackay’s form arainn (which in the sense ‘hearth’ has been copied by Dwelly 1911, 
Dwelly attributes the usage to Sutherland: Mackay (the Rev. Neil Mackay) was from Ardgay in Sutherland.
An Stòr-Dàta 1993 and Am Faclair Beag), àrainn has a long stressed vowel, and, in spite of Henderson’s form àirinn, the word is generally found with a non-palatal r. The word is probably best translated as ‘vicinity, neighbourhood’ and is commonly found in the phrase air àrainn, e.g. air àrainn an taighe ‘in the vicinity of the house’, cha tig mi air t’ àrainn ‘I will not come near you, I will have nothing to do with you’ (Watson 1932, 339). Semantically and probably phonetically preferrable derivations are oblique forms of EG *árann < aḋ- + rann- ‘share’ in the sense ‘allotment, apportionment’ (Watson, ibid., who cites Meyer’s (1906, 25) EG aḋ-rannaim ‘I portion out, divide’) and EG *aḋrand < aḋ- + rind- ‘cut’ in the sense ‘limit, bounds, enclosure’ (O’Rahilly 1927, 16).