A cross staff is a mechanical device used to measure the angle between two objects. Historically, the cross staff was famously used in navigation to help sailors orient themselves, and it was also used by astronomers studying the sky, and by surveyors who wanted to be able to take accurate measurements. This device appears to have been invented first by the Chinese, with Europeans beginning to use it around the 14th century; like many devices, it was probably invented independently in several different locations, which means that several people and nations probably deserve the credit.
Also known as a Jacob's Staff, the cross staff consists of a long pole with a series of markings, and a sliding bar known as a transom or transversal which is mounted at a perpendicular angle. Many staffs have a set of transoms, so that people can select the length which would be more appropriate; this allows the staff itself to be relatively short, making it easier and more convenient to use.
To use a cross staff, the navigator positions the end of the pole on the cheek just below the eye, and picks two objects to sight, such as the horizon and the sun. He or she slides the transom along the staff until one end lines up with one object, and the opposite end lines up with the other object. While this sounds simple, it is actually quite complicated, as the user needs to look in two directions at once without allowing the staff to slip or wobble, and that can be even harder on board a swaying ship.
Once the transom is in position, the marking covered by the transom indicates the angle between the two objects, which can be used to calculate latitude and to collect other information. One of the big disadvantages to using a cross staff is the need to look directly into the sun for sightings during the day; later models of the device featured filters which allowed sailors to look more comfortably. Furthermore, cloudiness could obscure sightings at night using various stars or sightings during the day in very heavy cloud cover, which could mean that people might be forced to go several days without taking a navigational siting, making it difficult to stay on course.
Cross staffs are sometimes used in classroom exercises to introduce students to the math behind the staff, or to the history of navigation. These devices have since been supplanted by global positioning satellites and other navigation devices which are highly accurate and very easy to use.