Scottish National Dictionary (1700–)
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First published 1974 (SND Vol. IX).
This entry has not been updated since then but may contain minor corrections and revisions.
TUILLIE'S MILL, n.comb. A kind of mob-law punishment in which the delinquent was forced to run the gauntlet, in phr. to gie or gae um Tuillie's Mill (Rxb. 1927 E. C. Smith Braid Haaick 11).
[Poss. a pun on tuillie, Tulyie, n., or an altered form of tulyie-mulyie s.v.]