As a celestial navigation teacher, I have long been interested in the tool that Arab seafarers used for crossings of the Indian Ocean. To measure the altitude of celestial bodies above the horizon (as a means of determining latitude), they developed a simple tool called the kamal or "guide."
The kamal consists of a small parallelogram made of horn or wood, usually one inch by two inches, with one or more strings inserted through its center. This string is knotted at different points along its length.
The kamal was used in conjunction with a technique called latitude sailing: one sailed south or north until one reached the latitude of one’s destination and then sailed east or west to the desired port. A kamal provided an Arab navigator with knowledge of latitude.
To take a sight with the kamal, one of the knots was clenched in the teeth, and the kamal was held at arm’s length. When the upper and lower edges of the device became coincident with the pole star and the horizon, the navigator knew his latitude was correct. The latitude of different ports corresponded to the position of particular knots on the string.
The string on the kamal was marked off into divisions called isba (a measurement based on a finger’s width, or 1 degree 36 minutes) that were used on kamals in lieu of degrees and minutes. A kamal had markings that ranged from 1 to 16 isba.
Since the pole star is several degrees from the celestial pole, some correction must be made to get an accurate latitude; it isn’t known how Arab navigators made this correction. Twice in each revolution, the pole star stands at the altitude of the celestial pole, and these points can be determined by noting the position of Kochab and its fellow star at the dipper end of the little dipper (these stars were called "the guards" by Europeans). A rule based on this relationship was taught to European sailors in the late 15th century, but it’s not known if Arab navigators knew of it. Col. Warren Davis, a celestial navigator and sailor, has used many ancient tools for navigation on passages. It is his belief that the Arab navigators would have had a small collection of kamals, each one properly labeled and with its string knotted for the labeled port or headland. He questions whether the kamal was actually constructed by mathematical plan or design. "I believe," he writes, "that the mariners, in the course of their apprenticeship, visited many ports. At each port they could make a kamal and mark it to the right knotted string length by actual observation."
David Berson is a sailor and navigation instructor in New York City.