In
navigation the instrument is also called a
cross-staff and was used to determine angles, for instance the angle between the horizon and
Polaris or the
sun to determine a vessel's
latitude, or the angle between the top and bottom of an object to determine the distance to said object if its height is known, or the height of the object if its distance is known, or the horizontal angle between two visible locations to determine one's point on a map. The Jacob's staff, when used for astronomical observations, was also referred to as a
radius astronomicus. With the demise of the cross-staff, in the modern era the name "Jacob's staff" is applied primarily to the device used to provide support for surveyor's instruments.
History The original Jacob's staff was developed as a single pole device, in the 14th century, that was used in making astronomical measurements. It was first described by the French-Jewish mathematician
Levi ben Gerson of
Provence, in his "Book of the Wars of the Lord" (translated in Latin as well as Hebrew). He used a Hebrew name for the staff that translates to "Revealer of Profundities", while the term "Jacob's staff" was used by his Christian contemporaries. Its invention was likely due to fellow French-Jewish astronomer
Jacob ben Makir, who also lived in Provence in the same period. is less likely, because Purbach was not born until 1423. (Such attributions may refer to a different instrument with the same name.) Its origins may be traced to the
Chaldeans around 400 BCE. Although it has become quite accepted that ben Gerson first described Jacob's staff, the British Sinologist
Joseph Needham theorizes that the
Song dynasty Chinese scientist
Shen Kuo (1031–1095), in his
Dream Pool Essays of 1088, described a Jacob's staff. Shen was an
antiquarian interested in ancient objects; after he unearthed an ancient crossbow-like device from a home's garden in
Jiangsu, he realized it had a sight with a graduated scale that could be used to measure the heights of distant mountains, likening it to how mathematicians measure heights by using right-angle triangles.
Construction s'
Practical Navigation (1672) In the original form of the cross-staff, the pole or main staff was marked with
graduations for length. The cross-piece (
BC in the drawing to the right), also called the
transom or
transversal, slides up and down on the main staff. On older instruments, the ends of the transom were cut straight across. Newer instruments had
brass fittings on the ends, with holes in the brass for observation. (In
marine archaeology, these fittings are often the only components of a cross-staff that survive.) It was common to provide several transoms, each with a different range of angles it would measure; three transoms were common. In later instruments, separate transoms were switched in favour of just one with pegs to indicate the ends. These pegs were mounted in one of several pairs of holes symmetrically located on either side of the transom. This provided the same capability with fewer parts.
Johannes Werner suggested the cross-staff be used at sea in 1514 The cross-staff was difficult to use. In order to get consistent results, the observer had to position the end of the pole precisely against his cheek. He had to observe the horizon and a star in two different directions while not moving the instrument when he shifted his gaze from one to the other. In addition, observations of the sun required the navigator to look directly at the sun. This could be a uncomfortable exercise and made it difficult to obtain an accurate
altitude for the sun. Mariners took to mounting
smoked-glass to the ends of the transoms to reduce the glare of the sun. , above the sailor. This seal dates from 1915, though a cross-staff is depicted in 17th century versions. As a navigational tool, this instrument was eventually replaced, first by the
backstaff or
quadrant, neither of which required the user to stare directly into the sun, and later by the
octant and the
sextant. Perhaps influenced by the backstaff, some navigators modified the cross-staff to operate more like the former. Vanes were added to the ends of the longest cross-piece and another to the end of the main staff. The instrument was reversed so that the shadow of the upper vane on the cross piece fell on the vane at the end of the staff. The navigator held the instrument so that he would view the horizon lined up with the lower vane and the vane at the end of the staff. By aligning the horizon with the shadow of the sun on the vane at the end of the staff, the elevation of the sun could be determined. This actually increased the accuracy of the instrument, as the navigator no longer had to position the end of the staff precisely on his cheek. Another variant of the cross-staff was a
spiegelboog, invented in 1660 by the Dutchman, Joost van Breen. Ultimately, the cross-staff could not compete with the backstaff in many countries. In terms of handling, the backstaff was found to be easier to use. However, it has been proven by several authors that in terms of accuracy, the cross-staff was superior to the backstaff. Backstaves were no longer allowed on board
Dutch East India Company vessels as per 1731, with octants not permitted until 1748. ==In surveying==