Humboldt State University ® Department of Chemistry

Richard A. Paselk

The Torquetum



Brass, "mahogony"

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.2 Certainly 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

Labeled Torquetum iconThe 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 crista corresponds 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:
Alt-Azimuth Torquetum icon
In 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 basilica oriented 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.
Equatorial Torquetum icon
The positions of celestial objects are now given in right ascension (in hours, minutes, and seconds) indicated by the almuri on the hour circle, and declination (in degrees) on the crista. Note the two reference points used in this coordinate system: the zero for right ascension is defined as the vernal equinox, while the zero for declination is still the equator, making the north pole equal to 90°. In this instance the torquetum resembles a modern equatorially mounted telescope, with the alidada circuli magni replacing the telescope.
In the third, most commonly illustrated configuration, the tabula orbis signorum is set to the obliquity of the ecliptic, giving ecliptic coordinates.
Ecliptic Torquetum icon
Positions of celestial objects are now measured in celestial latitude and celestial longitude. The celestial latitude (sometimes designated as b) of an object is north of (above) the ecliptic if it is positive, while if below it is negative (the division of the crista, 90-0-90 on both sides of the vertical, makes this measurement easy). Celestial longitude (sometimes designated as l) is measured by two conventions. Today it is usually measured in degrees (0-360) eastward along the ecliptic from the vernal equinox. But from ancient times it was common to divide the ecliptic into the twelve signs of the zodiac of 30° each. Since the vernal equinox is defined as the first point of the Ram, 0° = Ram 0°, 26° = Ram 26°, 35° = Bull 5°, etc. In similar fashion a difference in celestial longitude of 65° would be expressed as 2 signs 5°, 90° would be 3 signs, etc.
Why bother with these three systems? Convenience for particular observations. Thus the altazimuth setup is very easy, but it is specific to a place - observations at different locations and /or times will measure different values for the same object. For stars equatorial coordinates are the most useful - they revolve with the stars. It is as if they were "painted on the heavens." On the other hand, ecliptic coordinates are very convenient for planetary observations, since all of the planets (including the moon) follow paths within a few degree of the ecliptic.
1 One of these instruments (c. 1487, made of brass, attributed to Hans Dorn), made for Martin Bylica of Olkusz. is illustrated in Turner, Anthony. Early Scientific Instruments: Europe 1400-1800. Sotheby's Publications (1987) p 17. The other, dated 1444, was owned by Nicolas of Cues. See Turner and/or Hudson, Giles M. Torquetum, in Instruments of Science: An Historical Encyclopedia. (Bud, Robert and Warner, Deborah Jean, eds.) Garland Publishing, Inc. New York (1998) p 624..
2 See Hudson, Giles M. Torquetum, in Instruments of Science: An Historical Encyclopedia. (Bud, Robert and Warner, Deborah Jean, eds.) Garland Publishing, Inc. New York (1998) p 626.
3 The Latin nomenclature is taken from Hudson, Giles M. Torquetum, in Instruments of Science: An Historical Encyclopedia. (Bud, Robert and Warner, Deborah Jean, eds.) Garland Publishing, Inc. New York (1998) pp 623-6.
4 For a discussion of coordinate systems and their use in ancient and modern times see Evans, James. The History & Practice of Ancient Astronomy. Oxford University Press, Oxford (1998). pp 99-104.

I would like to thank Giles Hudson of the Museum of the History of Science, Oxford, for aiding me in researching the torquetum, providing contacts to others, and for his generous aid in providing information about the instrument and sources regarding it.

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© R. Paselk
Last modified 7 August 2015