ONlwSG

baghan m. [ˈb̥əɣan], 

Cf. /bɤɣan/ (AFB^˄).

gen. baghain -[æɲ], -[ɛɲ], ‘stomach, paunch’ 

Also written badhan (McDonald 1972, s.v.) and baoghan (MacBain 1911, s.v. baghan).

is recorded in Gairloch (Wentworth 2003, s.v. paunch: [b̥ɤɣɑn]) and South Uist (McDonald 1972, s.v. badhan), while the form maghan 

/mɤɣan/ (AFB^˄).

is recorded in Sutherland (Mackay 1897, 95; MacBain ibid.; Dwelly 1911).

The form maghan appears to have been known in South Uist also (McDonald 1972, s.v. badhan).

Both SG baghan and maghan appear to derive from ON maga, obl. form of magi m. ‘stomach’, 

Cf. (baghan) Stewart (2004, 408); McDonald (2009, 385); (maghan) Mackay (1897, 95: Ice. magi); MacBain (1911, s.v. maghan); McDonald (2009, 385); while MacBain (ibid. s.v. baghan) merely compares ON magi, Germ. Magen and Eng. maw, and MacLennan (1925) ON magi, OHGerm. mago and Eng. maw.

with the addition of the native suffix -an. While Old Norse g [ɣ] in magi yields a plosive in Scots muggy, mogi ‘stomach’ (SND^˄), the fricative is retained in SG maghan, which in turn yields baghan, presumably via back-formation after the article: (rad.) am maghan > am baghan, (dat.) a’ mhaghan > a’ bhaghan.