The rule of marteloio is a medieval technique of navigational computation that uses compass direction, distance and a simple trigonometric table known as the toleta de marteloio. The rule told mariners how to plot the traverse between two different navigation courses by means of resolving triangles with the help of the Toleta and basic arithmetic. Those uncomfortable with manipulating numbers could resort to the visual tondo e quadro (circle-and-square) and achieve their answer with dividers. The rule of marteloio was commonly used by Mediterranean navigators during the 14th and 15th centuries, before the development of astronomical navigation.
Etymology The etymology comes from the Venetian language. In his 1436 atlas, Venetian captain and cartographer Andrea Bianco introduced a table of numbers which he called the toleta de marteloio ("table of marteloio"), and the method of using it as the raxon de marteloio ("reason of marteloio"). The meaning of marteloio itself is uncertain. The most widely accepted hypothesis, first forwarded by A.E. Nordenskiöld, is that marteloio relates to "hammer" ("martelo" in Venetian), referring to the small hammer that was used to hit the on-board ship's bell to mark the passage of time. It has been suggested that the -oio suffix implies that marteloio meant not quite the hammer itself nor the hammerer, but rather "the hammering", intending to indicate "the hammering, the din, the racket" from the change of the watch every four hours. As there were many hands on deck during a change of the watch, it would be an opportune moment for the ship's pilot to order a change in bearing (if necessary). Alternative hypotheses (not nearly as accepted) are that "marteloio" is a corruption of mari logio (meaning "rule of the sea"), or from mare tela (meaning "sea network"), or that it derives from the Greek homartologium (όμαρτόλογίον, meaning "companion piece"), or from the Greek imeralogium (ήμερόλογίον, meaning "daily calculation") or that it might be from the northern French matelot, which in turn comes from Breton martolod (meaning "sailors").
Purpose
The "rule of marteloio" was used in European navigation in the Middle Ages, most notably in the Mediterranean Sea between the 14th and 16th centuries, although it may have older roots. It was an integral part of navigation by "compass and chart", before the advent of geographical coordinates and the development of celestial navigation in Europe. Medieval navigation relied on two parameters, direction and distance. On board ship, direction was determined by the mariner's compass (which emerged around 1300). Distance was measured by dead reckoning, (i.e., distance = speed × time), where time was measured by a half-hour-glass, and speed readings were taken with by some form of a chip log (the archaic method, used in the 14th and 15th centuries, involved heaving a piece of wood or flotsam overboard; the crew engaged in a rhythmic chant to mark the time it took for the chip to float past the length of the ship).
Plotting a course required knowing the compass direction and distance between point A and point B. Knowledge of where ports lay relative to each other was acquired by navigators by long experience at sea. This information was sometimes collected and written down in a pilot's handbook, known as a portolano ("port book", in Italian, equivalent to the Greek periplus, the Portuguese roteiro and the English rutter). These handbooks were used to construct a class of nautical maps known as portolan charts. Portolan charts began being produced in Genoa in the late 13th century, and soon spread to Venice and Majorca. Portolan charts were not gridded by longitude and latitude lines, but rather by a web of compass rhumb lines, giving mariners an idea of only the distance and direction between places.
By a handbook or a portolan chart, a navigator could see immediately that, for example, Pisa lay 85 miles southeast ("Scirocco" in the traditional compass rose nomenclature) of Genoa, and so a ship that set out from Genoa to Pisa would simply maintain that bearing for that distance. However, most sailing courses were not nearly that neat. A mariner wishing to sail from Majorca to Naples could tell the latter was due east ("Levante") by some 600 miles – but the island of Sardinia lies in the way, therefore the ship's bearing must be changed along the route. This is easier said than done, as geographical coordinates did not exist during this era. The only way to determine the exact position of the ship at sea would be to calculate via past bearing and distance travelled. Islands were a predictable obstacle – circumventing Sardinia would be simply a matter of sailing southeast for a set distance then changing the bearing to northeast ("Greco") for the remainder. More problematic is if the ship were blown off its intended route by fitful winds, or had to engage in tacking, changing bearing repeatedly. In order to return to its intended course, the rule of marteloio would then be utilized.
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?
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