The 1878 edition of The Globe Encyclopaedia of Universal Information describes a loxodrome line as:
Loxodrom′ic Line is a curve which cuts every member of a system of lines of curvature of a given surface at the same angle. A ship sailing towards the same point of the compass describes such a line which cuts all the meridians at the same angle. In Mercator's Projection (q.v.) the Loxodromic lines are evidently straight.