The Quadrant

The quadrant is an instrument for measuring both the altitude of celestial objects and the angular distance between them. It is similar in in its basic functionality to the astrolabe, although somewhat less sophisticated and simpler in construction. It is believed to have first appeared around 150 CE following a design proposed by Claudius Ptolemy (circa 90 - circa 168 CE), an Egyptian-born Greek mathematician and astronomer (among other things). Ptolemy lived in Alexandria, and was a citizen of the Roman Empire. The quadrant is (as its name suggests) in the shape of a quarter-circle, and can be used to measure angles up to ninety degrees. In larger versions of the instrument, a moveable arm called a radius is attached to the apex of the quadrant, and is used to measure angles.

The illustration above is an early 18th century copperplate engraving on paper attributed to Philipp Florinus von Pfalz-Sulzbach (1630-1703), and shows astronomers at work. One of them is using a large quadrant, probably to measure the angles between various stars and planets. Like the astrolabe, the quadrant has been used for many different purposes, and many different types of quadrant have been created. Early versions of the so-called mural quadrant were created by drawing the outline of the quadrant on a suitable wall. Later versions were created by constructing a wooden or metal framework, which was then attached to a wall.

Other large quadrants were housed in their own frame. The frame-based quadrant shown below is one of the artifacts that can be seen in the pretelescopic Beijing Ancient Observatory in China, and was constructed in 1673. Mural and frame-based instruments were typically used to measure the altitude of, and angular distances between, celestial objects.

In gunnery, the quadrant was often used to measure the angle of elevation of the barrel of a cannon or other form of artillery. Quadrants of various types could also be used to determine the time. Other types of quadrant were used for surveying and navigation. The mariner's quadrant shown below (also known as a geometric quadrant) is part of a collection of nautical instruments housed at the National Maritime Museum, Greenwich, London, and dates from around 1725. It is made from brass, and the scale marked around the circumference (the limb) goes from zero to ninety degrees (0°-90°) in thirty second (30′) intervals. Note the sights at the top and bottom end of the right-hand edge of the quadrant, which form a simple alidade (an alidade is a device that allows an observer to determine the line of site between themselves and some distant object). As you can see, a plumb bob is suspended from a pin affixed to the apex of the quadrant.

In order to measure the altitude of some celestial object such as a star, the observer must hold the quadrant upright (i.e. in the vertical plane) and establish a line of sight to the object using the sights of the alidade. The idea is that you should be able to see the star (or whatever object you are interested in finding the altitude of) through both sights of the alidade. The plumb bob is allowed to hang down vertically, and the point at which it crosses the limb is read to give the angle of elevation. It could be quite difficult to maintain the instrument in the correct position and check the position of the plumb bob at the same time. Often, one person established a line of sight using the quadrant, while a second person recorded the position of the plumb bob. The accuracy of the instrument was limited by its size (smaller instruments tended to be less accurate than their larger counterparts). Accuracy was also rather dependent on the conditions in which the instrument was being used. High winds and heavy seas, for example, would have made accurate observations almost impossible.