- 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
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:
- 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
- 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.
- 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
- In the third, most commonly illustrated configuration,
the tabula orbis signorum is set to the obliquity of the
ecliptic, giving ecliptic coordinates.
- 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
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,
- 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.
- © R. Paselk
- Last modified 7 August 2015