Humboldt State University

Richard A. Paselk

The Torquetum

Torquetum icon
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.


The first known accounts of the torquetum are those of Bernardus de Virduno (Bernard of Verdun) in the Tractus super totum astrologium3 and Franco de Polonia (Franco of Poland). It is not possible to ascribe priority to either since the date of Bernard's account is unknown. Franco Torquetum iconThe earliest known manuscript of Franco's account is dated at 1284.4 Franco does appear to be the main disseminator of the instrument, since manuscript versions of his account are much more common, and other descriptions, up to the late fifteenth century, are based on Franco's work. A mid-fourteenth century manuscript at the Ashmolean Library of Oxford, based on Franco's tract,5 includes labeled construction diagrams, as well as a diagram and description of the semis.6 Semis icon A number of observations using the torquetum have been recorded, beginning in the thirteenth century. Peter of Limoges used one to measure the initial position of the comet of 1299 in the eighteenth degree of Taurus.7 Jean de Murs, a Parisian astronomer famous for introducing the Alphonsine tables to Medieval astronomy, and exceptional in his time for his record of astronomical observations made between c. 1318 and 1344, recorded the entry of the Sun into Aries on March 12, 1318 using a torquetum. For this observation he invoked the the authority of Alphonse X, thus becoming one of the earliest advocates of these tables.8
In the late fifteenth and early sixteenth centuries Franco's description was superseded by a number of new accounts, among the best known being those of Regiomontanus and Apian. Regiomontanus Torquetum iconJohannes Regiomontanus (Johann Müller, 1436-76) was a German astronomer famous for his tables of planetary motion as well as his important celestial observations. In 1472 he made scientific observations of what later became known as Halley's comet.9 Reisch Torquetum iconRegiomontanus instrument, as depicted in 1472, included a variety of scales (like those found on an astrolabe) allowing the determination of time, the position of the sun in the zodiac on a given day etc., as does the instrument depicted by Gregor Reisch.
Perhaps the best known account, and certainly the most commonly Apian Torquetum iconreproduced image of a torquetum, is that of Peter Apian (1495-1552) published in 1532.10 Apian depicts a "back-to-basics" instrument made of wood with just the required observational scales. This instrument is also set for a fixed latitude. Apian Comet observations iconAn illustration of comet observation published by Apian in 1532 includes a torquetum, collapsed into the horizon configuration, and a cross-staff.11 In 1540 Apian published his second major work, the Astronomicum Caesarium, including his pioneering observations on comets. This was the first scientific description of comets other than their positions in the sky, describing the appearances of five comets (including Halley's) and the fact that their tails always point away from the sun.12 A late observation in which a torquetum was involved was the observation of Spica in 1575 by Landgrave William IV working with Tycho Brahe.13
Despite this late example of its usage as an observational instrument, most scholars seem to consider its popularity in the sixteenth century to be do to its other uses: 1) as a device to demonstrate the various coordinate systems of Ptolomaic astronomy, 2) as an analog computer to inter-convert measurements between coordinate systems without the use of tedious calculations, and 3) as a demonstration of the owners astronomical expertise and sophistication (the torquetum is, after all a very impressive instrument). The most famous example of this last usage is in the painting The French Ambassadors by Hans Holbien the Younger (1533).14
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 Gillespie, Charles Coulston (ed.). Dictionary of Scientific Biography Charles Scribner's Sons, New York (1970-80) II p 24.
4 Hudson, p 624.
5 Giles Hudson, personal communication.
6 Gunther, R. T. Early Science in Oxford: v. II, Astronomy. Oxford University Press, Oxford (1923) pp 35-7. The images here are from Gunther, apparently redrawn from the original manuscript.
7 Hudson, p 624.
8 Gillespie, VII p 129, 130.
9 Azimov, Issac. Azimov's Biographical Encyclopedia of Science and Technology 2nd ed. Doubleday & Company, Inc. Garden City (1982) p 70.
10 Apian's Astronomicum Caesarium is now available on-line. The RARE BOOK ROOM site from the Bodleian Library at the University of Oxford has the book at The torquetum, including construction diagrams, is shown on thumbnails 61-62 (November 2010). The entire book may also be downloaded as a pdf from the Vienna University Observatory rare book collection at: (December 2007).
11 Wolfschmidt, Gudrun. Planeten, Kometen, Finsternisse - Peter Apian als Astronom und Instrumentenbauer in Peter Apian: Astronomie, Kosmographie und Mathematik am Beginn der Neuzeit. Polygon-Verlag Buxheim, Eichstätt (1995) p 101.
12 Gillespie, I p 179.
13 Ibid, II p 404.
14 Images of this painting are avaialble on a variety of sites. One with very high quality images and closeups is the Web Gallery of Art site (December 2007). Click here to see an example of a closeup of the torquetum from this painting.

Description and Usage

Labeled Torquetum iconThe major components of the torquetum are shown in the photograph.14 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.15 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.
14 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.
15 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.


The instrument pictured was made in 1999 from brass and "mahogany" (an unknown tropical hardwood recovered from a pallet). The "mahogany" base measures 14 3/4 x 12 1/4 x 1/2 inches. The diameters of the brass circles for the crista, basilica, and tabula orbis signorum, are each 9 1/4 inches with a thickness of 1/8 inch. The brass hour circle on the tabula equinoctialis is 10 1/4 inches in diameter. The overall height of the instrument when set up for ecliptic observations at about 45° latitude is about 40 cm. All of the metal parts were fabricated from sheet or round stock with the exception of three commercial 5/16" brass washers. Nearly all of the materials were salvage, e.g. the heavy brass sheet was obtained as 4" diameter pipe, cut, annealed, and flattened with hammers, while the light sheet was from a door kick plate. The various rods and turned items were also fabricated from salvaged red or yellow round stock picked up at garage sales etc. Some construction notes follow.

Labeled Torquetum icon Base (tabula orizontis and tabula equinoctialis): The base was made from three 4 x 1/2" pallet slats, edge-planed and glued up with aliphatic glue using 1/4" dowel pins for alignment. The resulting plank was then hand-planed flat on both sides and sanded smooth with a random-orbital sander. It was then cut into two pieces: a 15" x 12 1/4" piece for the tabula orizontis and an 11 1/4" square for the tabula equinoctialis.

Torquetum base iconThe equatorial circle on the tabula equinoctialis was graduated on a thin (< 1/16") red brass circle. This circle was first laid out with a large wing divider, then cut from red brass sheet (from a door kick-plate) with a band saw, and filed to shape. The dividers were then used to scribe three circles creating two bands for graduating in hours and degrees, respectively. Next 30° and 15° intervals were marked off on the middle circle with the dividers to serve as checks in the final graduation process (follow this link for graduation methods). The outer band was then graduated at one hour (15°) intervals and numbered with 1/8" stamps (1-12 & 1-12), while the inner band was graduated at 1° intervals, numbering every 10° (0-360°) with 1/16" stamps. The finished circle was then centered on the tabula equinoctialis and fixed with four bronze nails. A 5/16" diameter hole was then drilled through both the circle and tabula for the pin which will hold the basilica.

Torquetum ecliptic plate  iconBasilica/tabula orbis signorum: The circles for the basilica and tabula were each scribed on sheets of heavy (1/8" thick) yellow brass with large wing dividers, then cut out with a bandsaw using a blade for non-ferrous metals. The edges where then finished with a file. Dividers and a straightedge were used to scribe graduations at 15° intervals around the outer edge of the basilica as noted above. These graduations were left unlabeled. The tabula orbis signorem (top view at right) was scribed with five circles giving, from the outside in, two narrow bands for division into single degree and five degree intervals (0, 5, ..30 for each zodiac sign), respectively, then a wide band labeled with the names of the zodiac signs (and with room to add symbols or icons later), then another narrow band divided at five degree intervals and labeled inside the circle every 30°, going eastward from zero (at the first point of Aries) to 360°.

Torquetum ecliptic mechanism iconThe folding mechanism is based on two parallel brass strips (1/8" x 3/8" cross-section x 7" long) silver soldered onto the bottom of the tabula (after its graduation) parallel to the Cancer-Capricorn meridian and spaced 4" apart. (Due to the large mass of brass involved, a large torch was necessary to achieve sufficient heat, even with "extra-easy" silver solder.) Holes (1/8" dia) were drilled through the ends of both strips. On the end toward Capricorn 1/8" dia pins attached the strips to a brass block (1/2" x 1/4" cross-section) screwed onto the basilica to make a hinge. (The block was attached with screws to allow disassembly/reassembly in trying different arrangements.) On the end toward Cancer a brass U-bracket fabricated from 1/8" x 1/2" brass stock was riveted to the basilica. A brass "H" was then fabricated from two strips of 1/16" x 3/8" of proper length to support the tabula at 23.5° when perpendicular to the basilica and a 4" length of 3/16" round stock soldered into holes in the strips to make the "H." The "H" was then attached to the parallel strips on the tabula using a length of 1/8" rod through holes in the ends to make a hinge. A second rod with a turned handle of 1/4" brass soldered on one end is used to attach the "H" to the U-bracket to hold the tabula in the ecliptic position, or alternatively this rod fits through a second set of holes in the parallel strips and the holes in the U-bracket to lock the tabula in the flattened position.

A note on the folding arrangements: Hinging the tabula to the basilica to allow the tabula to reside in the plane of the basilica or at 23.5° relative to this plane (the angle of the ecliptic to the equator) turned out to be one of the more challenging design problems of the instrument. Initially I designed a simple, reinforcing hinge with a folding prop which allowed the tabula to be raised to 23.5° or alternately folded flat, both positions maintained by the force of gravity. However, in testing the instrument for the low latitudes found in the contiguous United States (25-48°) or in particular at my home in Arcata, California (42°) it was found that the instrument was unstable. The center of gravity of the tabula and crista etc. caused the assembly to open up when the equatorial and ecliptic angles were additive, and in fact for lower latitudes the assembly was unstable even with the ecliptic angle closed. Thus it was necessary to redesign the prop as a locking assembly. With the locking device it turned out that at low latitudes the tabula equinoctialis was also unstable when the two angles were additive, and thus the stylus also had to be designed as a locking device. It is apparent from the photograph of the torquetum of Martin Bylica1 and the period diagrams of torquetums that this was not a consideration in their construction. This is a result of their intended use at the higher latitudes of northern Europe, a situation I found to be true of my instrument as well - at latitudes of 50° and above locking is not required.

Torquetum head & crista iconCrista/Turnus:The outline circle for the crista was scribed on a rectangular sheet of heavy (1/8" thick) yellow brass with large wing dividers. Additional circles were scribed at 3/16", 3/8", 3/4", and 1 3/4" in from the edge. The sigmoid curves of the neck were also laid out with dividers set to large radii. The resultant head and neck was then cut out with a bandsaw using a blade for non-ferrous metals, using multiple cuts to follow the complex curves of the neck. The edges where then shaped with the roller portion of a belt sander and finished with flat and curved files. Heavy lines were scribed across the entire diameter.formed between the outer diameter of the crista and the outermost circle was then divided at 5° intervals and the band formed by the two outermost scribed circle was divided at 1° intervals with a 'dividing engine.' The divisions were numbered at 10° intervals in quarters with the horizontal axis at 0°, 0° and the vertical axis 90°, 90°.

The bottom of the crista was carefully squared off perpendicular to the vertical axis, filed flat and square, and then silver-soldered to a 2 1/2" square of 1/8" brass plate. Four decorative holes were also drilled and countersunk in the neck. Finally, two twisted strips of 1/8" brass were formed into diagonal braces and riveted with copper rivets (home-made from 12 gauge electrical wire) onto the plate and the neck to provide additional support.

The Turnus was cut from a 4" x 9 1/2" rectangle of 16 gauge yellow brass. First a 4" diameter circle was laid out on the with a dividers. A straight line was then carefully scribed through the center point along the long axis - line is critical as it will form the rule edges of the alidade for measuring angles. Two parallel lines were then laid out at 5/8" on either side of the axis to define the outside rule edges of the turnus. A small dividers was then used to layout small arcs to create an ogee at each end of the turnus. The turnus was next cut out with the bandsaw as above and carefully finished with files. The rule edges required particular attention to bring them into precise alignment with the axis of the turnus as initially laid out. Last, a bevel was filed on each rule edge to make reading graduations easier, and to improve the appearance. Two 1 1/4" x 1" rectangles of 1/8" yellow brass plate were next prepared for sights. A line was carefully scribed down the center of each parallel to the 1" edge. A 1/16" hole was then drilled 3/4" from the bottom carefully centered on this line, and a triangular notch was filed on the top exactly centered on the line. Each plates was then clamped with the line exactly aligned with the rule edge of the turnus and in contact with an end ogee and silver soldered. A 5/16" hole was now drilled through the exact center of the turnus for a pin to attach it to the basilica.

Torquetum head  iconFinally, four 1/8" diameter holes were drilled in the turnus and the base plate of the crista such that the crista would be centered and aligned with the rule edges of the turnus. The holes were counter-sunk on the bottom of the turnus and the top of the crista base to allow expansion of rivet heads. Four 1 3/8" lengths of 3/8" brass rod were then prepared, and a 1/8" diameter hole bored through the length of each. Four 1 9/16" lengths of 1/8" brass rod were next cut for use as rivets, placed in the aligned turnus, rods and crista and flattened out on each end with a small ball-pein hammer.

Alidada circuli magna:The alidada was laid out and fabricated just like the turnus above, but with a smaller central circle. The sights of the alidada were based on the same dimensions as for the turnus, except that 1" extensions were laid out on the bottom of each to give arms for suspending the semis.

Semis: For the semis a 7 1/2" dia semicircle was laid out on 16 gauge red brass sheet and cut out with a bandsaw as above. A series of circles was then scribed with dividers to form 1/4", 1/2" and 1" bands for graduations at 1°, 5°, and 10° intervals. The graduations were then numbered 90° - 0° - 90° at the 10° graduations in the 5° band. Small brass pins were then silver soldered at the two ends of the horizontal (90° - 90°) edge for suspension from the alidada sights. A small brass plumb bob, turned from 1/2" yellow brass round stock, was suspended from the central hole to finish the zenith indicator.

The Cabinet

Torquetum case icon

Torquetum case, open, iconTorquetum case, open, iconIn the Spring of 2000 I determined to construct a cabinet for the storage and transport of the Torquetum. The walls of the cabinet were cut from 3/4" rich-grained red "Philipine Mahogony" recycled from speaker cabinets I had made in 1969. The corners are finger-jointed (box-jointed) for strength. The top and bottom were cut from high quality 1/4" Teak veneer paneling recovered from an LA law office by my brother's construction firm. The interior pine mounts were all cut from 3/4" pine recovered from a "pine-box coffin" I had built years ago as a prop for a retirement party. The various pine pieces are cut to accomodate and fit the crista, semis, and alidada such that no movement is possible once the various tabs are turned into place. The base of the torquetum lies on top of the pine frame and is held in place by three heavy bronze brackets modified from some brackets salvaged from discarded physics apparatus. The interior lid of the cabinet is lined with a fitted bit of 1/4" polyethylene packing foam wrapped with red velvet left over from one of my wife's costume projects. The carry-handle for the cabinet is made from two modified bronze brackets drilled to fit the knocker of a salvaged brass door knocker. The hinges and latch are quite standard, of the sort available at any US hardware store. The cabinet with the torquetum on display is shown below:

Torquetum mounted in case icon

Instruments Medieval Astronomer iconMedieval Science & Scientific Instruments


© R. Paselk
Last modified 17 November 2010