 where "θ" is the angle of difference between the two routes.Using Lull's example, a ship that intended to sail southeast ("Exaloch" is Catalan for "Scirocco") but was instead forced to sail east ("Levant"), then the angle of difference is "θ" = 45°.After 100 miles on the erroneous route, the "miliaria" on the intended route is 100 × cos 45° = 70.71.