The first element may be an obsolete Gaelic word án ‘driving’ or aon ‘one’. The second element -struther likely denotes an obsolete word sruthair ‘stream’, related to the current word sruth ‘stream. The water-course in question is possibly the Dreel Burn which flows through Anstruther (locally pronounced ‘Ainster’).
A type of lobster-fishing boat called ‘the Anstruther’ was popular in the Hebrides and was called in Gaelic An Eanstrach ‘the one from Anstruther’. On the coast of Coigach in Ross-shire is a place called Port na h-Eanstraich ‘the port of the Anstruther boat’. The sail was so big it was often used as a point of comparison: Cha robh uinneag ann nach robh cho mòr ‘s cho leathann ri seòl-toisich Eanstraich ‘there wasn’t a single window that wasn’t as big or as wide as an Anstruther foresail’.
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