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The Collaborative International Dictionary
To sail on a rhumb

Rhumb \Rhumb\, n. [F. rumb, Sp. rumbo, or Pg. rumbo, rumo, probably fr. Gr. ??? a magic wheel, a whirling motion, hence applied to a point of the compass. See Rhomb.] (Navigation) A line which crosses successive meridians at a constant angle; -- called also rhumb line, and loxodromic curve. See Loxodromic.

To sail on a rhumb, to sail continuously on one course, following a rhumb line.