The torquetum or turquet is a complex and sophisticated instrument characteristic of Medieval astronomy and the Ptolemaic tradition. It was a product of Christian Europe in the late 13th century. It could be used to make measurements in the three sets of astronomical coordinates: horizon (alt-azimuthal), equatorial, and ecliptic. It also provided a mechanical means to interconvert between these sets of coordinates without the use of calculations (it served as an analog computer), and to demonstrate the relationships of these coordinate sets.

Modern scholars attribute the torquetum's use largely for demonstration purposes and "conspicuous intellectual consumption," which was probably true for the majority of the surviving examples: two late Medieval instruments from the 15th century¹, and eight known from the 16th century.²Certainly the demands of 16th century astronomy were beyond the precision attainable with so complex an instrument given the technology available at that time - the best observations required stable instruments of large radius.

Description and Usage

The major components of the torquetum are shown in the photograph.³ The various plates and circles model the circles of the Celestial sphere. Thus the base of the instrument, Franco's tabula orizontis,represents the horizon. A second plate, the tabula equinoctialis, hinged to the base and held at the complement to the observers latitude by a prop, the stilus, represents the celestial equator. A circle on this plate is graduated in hours. The basilica rotates over the tabula equinoctialis on a pin representing the axis of the Earth. Attached to the basilica is the tabula orbis signorum, which may be locked at an angle of 23.5° to represent the plane of the ecliptic. A zodical calendar and degree scales are inscribed on the tabula orbis signorum. A pointer, the almuri, is attached to the basilica beneath the zero point of Capricorn. Rotating around the axis of the ecliptic circle is the turnus which doubles as an alidade and as the stand for a vertical circle divided to degrees, the crista. When the ecliptic circle is folded flat, the cristacorresponds to the meridians of the celestial sphere. An alidade, the alidada circuli magni, rotates over the crista. Finally, suspended from two arms on the alidada circuli magni, is the semis, a half-circle divided in degrees (90-0-90). A plumb-line and bob, the perpendiculum, is suspended from its center, fixing the zenith.

The torquetum can be used for observations in three different coordinate systems.⁴ In the first configuration, giving horizon coordinates, all of the tables are folded flat as shown below:

n this configuration the alidade on the crista measures altitude (with the plane of the horizon at zero and the zenith at 90°), while with the basilicaoriented so that the zero degree mark is north, the turnus indicates the azimuth (measuring eastward 0-360° as on a compass). Here the instrument is essentially identical to the altazimuth theodolite.

In the second configuration, giving equatorial coordinate, the tabula equinoctialis is set with the stilus to the co-latitude (90°-latitude) and its axis aligned with the north pole.