engage in tacking, changing bearing repeatedly. How does it return to its intended course? This is where the rule of marteloio came in. The traverse problem The rule of marteloio addressed the problem of changing bearing at sea. More specifically, it helped a navigator plot the traverse from one navigational course to another. For example, suppose a ship was to sail from Corsica to Genoa, a course bearing straight north ("Tramontana") for some 130 miles. But the winds are not cooperative, and the ship was forced to sail northwest ("Maestro") for some 70 miles. How does it return to its original route? Re-setting its bearing to northeast ("Greco") seems sensible enough, but how long should it sail on that bearing? How would a navigator know when the ship had reached its old route and should turn north again? How to avoid overshooting or undershooting the old course? This is a mathematical problem of solving a triangle. If a navigator knows how long the ship has sailed on the erroneous course, he can calculate its current distance from its intended course, and estimate how long it must sail back on a new bearing until it recovers its old course. In the Corsica-to-Genoa example, there is an implied triangle ACD, with one side given (AC = 70 miles on actual NW course), a 45° angle at A (angle of difference between actual course NW and intended course N) and another angle of 90° at C (angle of difference between actual course NW and return course NE). The challenge to the navigator is to find how long one must sail on the NE return course (the length of side CD, what is called the ritorno) and how far one has advanced on the intended course by the time one straightens out (the length of the hypotenuse AD, or what is called the total avanzo). This is elementary trigonometry, solving for two sides given one side (70) and two angles (45° and 90°). This is quickly done by applying the law of sines: yielding up the solutions ritorno = 70 miles and total avanzo = 98.99 miles. This means that if the ship bears NE from its current position (C), it will reach its original intended course after 70 miles of sailing on the NE bearing. By the time it reaches its junction point (D), it will have covered 98.99 miles of its original