The cross-staff is a navigational instrument, an early form of which is thought to have been invented in around 400 BCE in Chaldea (an ancient land bordering the upper end of the Persian Gulf), although its use for navigation does not appear to have occurred until the fourteenth century CE. The main component is a long wooden rod or staff, usually about thirty-six inches long, having a square cross-section and a graduated scale marked along its length on each of the four sides. The other components consist of much shorter vanes (cross-pieces) that are designed to slide back and forth along the length of the main staff. Each vane (of which there are usually four in number) is unique in terms of both its length and how it is graduated. When the cross-staff is in use, only one vane is used at a time, each being intended for use with the markings on a different side of the main staff.
A reproduction of the 1720 Jochem Hasebroek Cross-staff
A full description of the reproduction 1720 Jochem Hasebroek cross-staff illustrated above, together with many other navigational instruments of historical interest, can be found at the website of Nicolàs de Hilster (http://www.dehilster.info). The website features a number of reproductions created by him, together with some very useful background information. The cross-staff gets its name from its cruciform appearance (it may also be occasionally referred to as a Jacob's staff or Jacob staff, although this name is also sometimes used to refer to other types of apparatus, so we will stick with the name cross-staff).
The cross-staff as we know it today was first described the Jewish mathematician Levi ben Gerson of Provence, France (1288-1344), although its invention is credited by some sources to Jewish astronomer and physician Jacob ben Makir ibn Tibbon (1236-1312) who also lived in Provence during the same period. The instrument has been variously used for astronomical observations, for surveying, and for navigation. It can be used to measure the angular height of an object relative to the user, or to measure the angular distance between two objects in the night sky.
The use of the cross-staff for navigation is believed to have first been suggested in 1514 by the German mathematician Johannes Werner (1468-1522). It was typically used to measure the elevation of the Sun at mid-day in order to find the current latitude of the observer. Each vane (or cross-piece) is used to measure a different range of angles. The user holds one end of the cross-staff close to one cheek in order to sight along its length, and slides the vane along the main staff until its lower edge lines up with the horizon and its upper edge lines up with the Sun. The vane is then held in place and lowered so that its position in relation to the markings on the main staff can be read. The reading gives the altitude (usually in degrees) of the Sun above the horizon.
A cross-staff in use (image credit: Canadian Museum of History)
In some ways, the cross-staff was ideal for use at sea as a navigational instrument. It was light, portable and relatively simple to make. On the other hand, it did suffer from some limitations. The instrument relied on the ability of the observer to accurately line up two different points simultaneously. However, the human eye is not actually capable of focusing on two different points at the same time, which meant that there was always the possibility of errors being made, particularly if the user was inexperienced. The margin of error is usually relatively small if the angle being measured is greater than or equal to twenty degrees (20°) and less than or equal to sixty degrees (60°). The further the angle falls outside this range, the greater the likelihood of error.
There was also the small matter of having to look directly into the Sun whilst measuring its altitude - never a particularly good idea, although the use of smoked glass provided a partial solution. The problem of having to look directly into the sun was eventually solved by the introduction of an instrument called the back-staff. This instrument measured the altitude of the Sun by allowing it to cast the shadow of a vane (called the shadow vane) onto another vane (the horizon vane) mounted at the front of the instrument. The user stood with their back to the Sun, and sighted the horizon through slits in the sighting vane (mounted at the rear of the instrument) and the horizon vane. The shadow vane would be moved along the forward arc until its shadow fell on the horizon vane, and its position on the arc then recorded. Easier to use than the cross-staff (although according to some sources less accurate), the back-staff gradually became more widely used. Eventually, both instruments would be superseded by the octant.
An 18th century back-staff (image credit: National Museum of American History)
The back-staff illustrated above is typical of those that had evolved by the mid-seventeenth century from the instrument originally designed by English navigator and explorer Captain John Davis (1550-1605) in 1594. The version designed by Davis, which became known as the Davis Quadrant, was a significant improvement on existing versions of the back-staff. It also overcame some of the shortcomings of other navigational instruments in use at the time, including the cross-staff, astrolabe and quadrant.