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dìg f. [d̥ʲiːɡ̊ʲ], gen. -e [ə], also dìge [d̥ʲiːɡ̊ʲə] and dìog [d̥ʲiːɡ̊] ‘ditch, channel, trench; marsh; dyke, stone fence or wall’. The sense ‘trench’ is found across the Hebrides, mainland Argyllshire and the north of Scotland, although the sense ‘marsh’ also occurs less commonly in the Hebrides; the sense ‘wall’ is found across the mainland from Easter Ross to Kintyre (where there is an overlap with ‘trench’). The principal form is dìg; dìge is largely confined to the mainland, but seems incidental; dìog is found in Easter Ross, Sutherland, Kintyre, South Uist, Benbecula and Lewis, but appears to be being superseded by dìg.
A ‘ditch, i.e. channel, trench’
(i) dìog: Lewis (LASID IV, 250, Item 183: [ḋ̲´iːġ]), Benbecula (ibid., 230, Item 183: [d´ʒiːg]), Sutherland (ibid., 274, Item 183: [ḋ´iːġ̲]; cf. Armstrong (1825); written diog in Shaw (1780);
(ii) dìg: Outer Hebrides: Lewis, 
Written in an unconventional orthography, dik (Christiansen 1938, 5, 24: Lewis) no doubt represents dìg.
(iii) dìge: Wester Ross (Wentworth 2003, s.v. ditch: [d̥’iːɡ̊’ə]), Argyllshire (MacDomhnuill 1741: díge), ?South Uist (Faclan bhon t-Sluagh˄); cf. Armstrong (1825).
B ‘marsh, bog’
dìg: Harris, Skye (Faclan bhon t-Sluagh˄).
C ‘dyke, i.e. stone fence or wall; embankment’
(i) dìog: Kintyre (LASID IV, 213, Item 182: [d̲ʒiːg̲]), Easter Ross (Watson 2022: /d´iːɡ/); cf. Armstrong (1825);
(ii) dìg: Sutherland (Faclan bhon t-Sluagh˄: [dʹʒıːɡʹ]; Grannd 2013), Glengarry (Dieckhoff 1932, s.v. dig: [dˈjiːg]); cf. Armstrong (1825); HSS (1828), Cameron (in MacBain 1894a, 628); MacBain (1911); Dwelly (1911);
(iii) dìge: Armstrong (1825).
MacBain (1911) derives dìg in the sense ‘wall’ from Scots dyke; Christiansen (1938, 24: dik) derives dìg in the sense ‘trench’ from ON díki nt.; Cameron (in MacBain 1894a, 628: dig) derives dìg in both senses from ON díki; McDonald (2009, 349) considers the loan uncertain.
ON díki has the senses ‘marsh’ and ‘trench’ (NO), but not ‘wall’.
So also Old and Modern Icelandic díki, which Cleasby (1874) and Zoëga (1910) unhelpfully translate as ‘dike, ditch’.
EScots (c.1375–c.1450) dyke (< OEng. dīc) had both the senses ‘trench’ and ‘wall’, and this was also the case for MScots dyke (c.1450–c.1700) until perhaps the 17th century, by which time it may have come to mean exclusively ‘wall’, as it certainly seems to have done by the 18th century and the onset of the modern Scots period (DOST˄, SND˄, s.v. dyke).
OEng. dīc ‘trench’ yields northerly Eng. dike (hence Scots dyke) and southerly Eng. ditch, 
For the development, cf. northerly breek ~ southerly breech (s.v. briogais).
EG díc occurs in both the senses ‘trench’ and ‘earthern rampart’, the editors of eDIL˄ suggesting the former was probably the earlier meaning, which is the sense of modern Ir. díog 
Recorded in Lhuyd 1707: diog.
Stokes (1892, 78) proposes Early Modern Irish díog derives from Fr. digue (if not Old English), but a French provenance seems unlikely as Fr. dique applies exclusively to ‘seawalls, breakwaters etc.’ (CNTRL˄, s.v. digue) and is a loan from MDut. dijc ‘idem’ (Verdam 1964 and Valkhoff 1931, 108–09, cited in ibid.). Risk (1970, 633–34; 1974, 78) acknowledges OEng. dīc as a possible source, but prefers a derivation from AN dike, digue ‘trench’.
So also Vendryes (1996), while eDIL˄ suggests either an Anglo-Norman or an Old English provenance.
EG díc ‘trench’, then, may derive from OEng. dīc ‘trench’, ultimately yielding Ir. díog etc., Mx jeeig, jeeigey and SG dìg etc., all in the sense ‘trench’. The sense ‘earthern rampart’ is absent from Ir. díog and Mx jeeig, and appears to have developed in EG díc only temporarily.
Cf. EG claḋ ‘trench’ and ‘earthern rampart’, where the former is probably the earlier meaning (eDIL˄).
Henderson (1910, 351) derives the Skye village name (Eng.) Digg NG464695 from ON dík (sic) ‘trench’, but Eng. Digg is a loan-name from SG An Dìg ‘the trench’ (Taylor 2011, s.v. Digg; Robertson, in King 2019, 196), which consists of the Scottish Gaelic article + SG dìg.
EG díc yields Ir. díog directly, while Ir. díg represents a normalised dative form of díc as an ā-stem; Ir. díoga, on the other hand, is a reflex of díc as a dental stem (< díogaidh). The pronunciation of Mx jeeig ([d´ʒiːg]) aligns with Ir. díog, cf. Mx sheeig [ʃiːg] ‘stack of sheaves’ (Broderick ibid.), Ir. síog (EG síc), although the orthography may indicate the pronunciation was earlier *[d´ʒiːg´]; 
For the alternation /ɡ´/ ~ /ɡ/ in Manx, see Broderick 1984 III, 12. (Besides jeeigey, Kelly (1991˄) gives both jeeig and jeeg.)
Before diphthongisation in Middle Scots (Aitken 2002, 152; Macafee 2003, 140).
Cf. MEng. prīs ‘price’ > SG prìs /pðiːʃ/ ~ Eng. piece > SG pìos /piːs/ (Oftedal 1956, 67).