Category Archives: Exercise 1 – volvelles & astrolabes

Early Modern volvelles from the Bodleian (part I)

First page of a 15th-century guidebook on constructing volvelles, and some Early Modern ones, reproduced here with the kind permission of The Bodleian Libraries, The University of Oxford.

You may click on any one of the images to view a slideshow with further information, including the manuscript and folio numbers. As these are simple snapshots I took of the manuscripts, you are encouraged to contact the Imaging Services of the Bodleian Libraries directly to obtain professional reproductions.

Please note that MS Savile 100, f.8r has also been reproduced on the LUNA site of the Bodleian Libraries. See also the late 15th-century brass equatorium and astrolabe at the Museum of the History of Science at Oxford (inventory #49847).

Yelda Nasifoglu

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Early Modern volvelles from the Bodleian (part II)

Illustrations from a late 14th century manuscript by Nicholas of Lynn, reproduced here with the kind permission of The Bodleian Libraries, The University of Oxford.

You may click on any one of the images to view a slideshow with further information, including the manuscript and folio numbers. As these are simple snapshots I took of the manuscripts, you are encouraged to contact the Imaging Services of the Bodleian Libraries directly to obtain professional reproductions. 

Please note that MS Ashmole 789 f.365r has also been produced on the LUNA site of the Bodleian Libraries.

Select sources on Nicholas of Lynn:

Other sources:

Yelda Nasifoglu

Holbein’s instruments

Holbein’s Double Portrait of Jean de Dinteville, the Bailly of Troyes and Georges de Selve, Bishop of Lavaur, or ‘the Ambassadors’ (1533), famous for the anamorphic skull at the bottom of the painting,

but some of you might be interested in the instruments depicted:

See also the article by Elly Dekker and Kristen Lippincott, “The Scientific Instruments in Holbein’s Ambassadors: A Re-Examination,” Journal of the Warburg and Courtauld Institutes, Vol. 62, 1999, pp. 93-125. [Subscription-based site (JSTOR); accesible via McGill]

 

Guillaume’s Astrolabe

Présentation et fonctionnement d’un Astrolabe

L’astrolabe est avant tout un instrument destiné à lire l’heure solaire ou stellaire en un endroit donné. La version présentée est volontairement simplifiée.

Sur la Mater sont gravées des lignes qui représentent la projection stéréographique (une sphère sur un plan) de la Terre, uniquement valides pour une latitude géographique donnée. Autrefois, les voyageurs devaient donc transporter avec eux autant de Maters que de lieux où ils se rendaient. Sur cette grille de coor- données tourne l’Araignée, un cadre avec des points représentant les étoiles fixes. Enfin, une règle, l’index est au dessus et fonctionne comme une aiguille.

Au verso, la Mater indique les degrés des angles déterminés par l’Alidade.

Tous les éléments tournent autour d’un axe central.

heure stellaire:
On vise une étoile à l’aide de l’Alidade en tenant l’instrument par le crochet prévu à cet effet de manière à ne pas fausser les valeurs relevées. Alignée sur une étoile, l’Alidade indique un angle sur la Mater. On tourne alors l’instrument pour reporter cette valeur. En tournant l’Araignée où se trouvent les principales étoiles, on aligne l’étoile en question sur le cercle correspondant. On positionne l’Index sur la date du jour de l’observation sur l’Araignée, La pointe de l’Index indique l’heure sur la Mater.

heure solaire:
De jour, on ne vise évidemment pas le Soleil. Il suffit alors que les extrémités de l’Alidade marque une seule et même ombre. On lit l’angle sur la Mater. On place sur le verso de l’instrument, l’araignée de façon à placer la date du jour avec le degré correspondant. Aligné sur ce même point, l’index indique l’heure sur la Mater.

Planispheric Astrolabe

This is a paper reconstruction of one of the four brass planispheric astrolabe by well known 15th century German astronomer, Georg Hartmann. It was originally made in 1532 in Nuremberg, Germany (49°27’0” N 11°5’0” E) to which this astrolabe had been calibrated to. The original astrolabe is currently in the permanent collection of British Museum.

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Operational Guide

  • Telling the position and visibility of stars for a given night at a given time

First you set up ant the back of the mater by using the alidade to point at the date on the calendar scale (at the inner most ring). Once aligned read the matching zodiac on the zodiac on the zodiac scale, which gives the position of the sun on that given day. Turn to the front of the astrolabe and locate the position of the star on the ecliptic ring on the rete then use the ruler to align with that point. Now as if the rete and the ruler are both fixed together, turn the ruler so it points to a time of interest for that given night. Once in position, the entire astrolabe is done setting and ready for observation. Every star pointer that lies within horizon line, indicated on the climate (with the stereographic projection of the entire night sky relative to the viewer’s zenith), is visible at that particular day and time.

  • Using the position of the Sun or star to tell time

First one finds the start of interest in the sky. Hang the astrolabe by its throne so aligns itself relatively perpendicular to the ground. Use the calendar scale and zodiac scale at the back of the ring to convert the given date to zodiac. Then use the alidade to point towards the star or sun using the two sights so that their sight hole aligns (note use the shadow of the sights to align in the case of sun). Once they align record the altitude using the elevation scale at the outer most rings. Now flip to the front. Locate the star of interest on the star pointer as a reference point. Rotate the rete so that this reference point intersects with the altitude (as recorded previously) on the stereographic projection on the climate. Once set, rotate the ruler so it points to the zodiac on the ecliptic ring on the rete. At the other end of this ruler indicates the time.

  • Measuring height or depth of objects using the shadow square.

Measure the distance between where the astrolabe is set and the object(such as a building) to measure. Hang the astrolabe at its throne so it falls relatively perpendicular to the ground. Then uses the alidade at the back of the astrolabe to sight the top of the building. Take the value pointed by the alidade on the Umbra Recta on the shadow square and divide by 12. Take one over that result and multiply by the distance between the astrolabe and the object of interest. The result gives the height of the object.

Mark L.

Saphea Arzachelis

L’astrolabe est daté de 1551 et est signé par Antoine Mestrel, à Paris.  Il est fabriqué en laiton, et son diamètre fait 257 millimètres.  Le plateau principal contient cinq échelles différentes (de l’intérieur vers l’extérieur): les heures, les signes du zodiaque, le carré d’ombre et un diagramme qui sert à convertir deux différents systèmes d’heures (appelés UNEQUALES).  Les étoiles sont également inscrites selon leurs positions dans le zodiaque.

Cet astrolabe n’est pas dessiné pour une latitude spécifique puisqu’il est dit universel, (lat. Saphea Arzachelis).  Sa construction fut probablement influencée par le mathématicien espagnol Juan de Rojas puisque ce dernier a publié la même année un livre traitant de la projection orthographique et certains détails sont fortement similaires, comme le trône décoratif.

Il est marquée d’une échelle allant de 0 à 90 avec des hachures à chaque unité d’angle.  Les lignes d’ascension entre l’arctique et l’antarctique (POLVS ARCTICUS et POLVS ARTARCTICVS) sont divisés en 4 minutes par des traits.  Entre les tropiques, des lignes sont à chaque 2 degrés et illustent la position du soleil dans l’ecliptique.  Des signes du zodiaque sont dessinés le long du diamètre vertical.  Au-dessus de HOROE ANTE MERIDIEM et HORAE POST MERIDIEM des heures sont inscrites (de 1 à 12).  Quelques étoiles sont positionnées et marquées.

La règle, ou l’aiguille est une échelle de minutes, allant de 0 à 360.  La façon de l’utiliser est de la rotationner dans le sens contraire des aiguilles d’une montre à l’angle de la co-latitude (90 degrés moins la latitude locale).  Cela peut déterminer la position des étoiles à minuit, au solstice d’été.  Il est possible ensuite de calculer la position des étoiles sachant qu’elles se trouvent à la même position deux heures plus tard à chaque mois précédant.  La trajectoire d’une étoile peut être suivie selon l’arc parallèle la plus près.  La deuxième fonction de l’astrolabe est de déterminer la position du selon l’heure et la date, en déterminant la position du lever et coucher du soleil ainsi que le crépuscule.  Il suffit de trouver la position du soleil sur le zodiac et ensuite sur la ligne écliptique (la ligne diagonale).

Le modèle ci-construit est à l’échelle 1:1 de l’original, dessiné à la main au crayon de mine HB sur un carton.  Cet astrolabe fait actuellement partie de la collection du Musée d’histoire et de science à Oxford.

The astrolabe is dated of 1551 and is signed by Antoine Mestrel, in Paris.  It is made of brass, and has a diameter of 257 mm.  The plate contains five scales (from exterior to interior) : the hours, the zodiac signs, a calendar, a shadow square and a diagram for converting time between different systems of hours (called UNEQUALES).  The stars are named according to their position.

The astrolab is not designed for a specific latitude, because this one is universal (lat. Saphea Arzachelis).  This model of astrolabe was probably influenced by the mathematician Juan de Rojas because he has published the same year a book that tells about the orthographic projection of the sky and contains a lot of resemblances like the decorative throne with a head and other technical elements.

It is scaled from 0 to 90 with hatching for every angle.  Ascension lines are drawn for every twelve minutes between the arctic and the antarctic (POLVS ARCTICUS and POLVS ARTARCTICVS) and they are divided in four minutes by little lines.   Between the tropics, lines are at every two degrees and this illustrate the sun position in the ecliptic.  Zodiacal symbols are drawn on the vertical diameter.  Above HOROE ANTE MERIDIEM and HORAE POST MERIDIEM the hours are marked (1 to 12).  Some stars are positioned and marked.

The rule is a scale of minutes (0 to 360). The way to use it is to rotate it anti-clockwise to the angle of the co-latitude (90 degrees minus the latitude).  It can determine the position of the stars at midnight at the summer solstice.  Then it his possible to calculate the other positions of the stars knowing that they are at the same position two hours later for each month earlier.  The track of a star is along the (nearest) parallel arc on the plate.  The second use is to determine the position of the sun at any time and date, with the sunrise, sunset and twilight.  By finding the position of the sun on the zodiac and then on the ecliptic line (the diagonal line).

The present model is at a 1:1 scale of the original and is drawn by hand with a HB pencil on a cardboard.  The astrolabe is presently in the collection of the Museum of history and science in Oxford.

Émélie DT

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Paper Astrolabe

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Astrolabe designed for an android application – location Ottawa, Canada (developer: Robin Davies)

Some of the possible calculations with the astrolabe:
1) tell the time
2) tell what time the sun will rise the next morning
3) calculate how many hours of darkness for a given date

1) – set current calendar date on the back of the base plate with the help of the alidade
– convert to the corresponding astrological date by looking at the intersection or the alidade on the astological dates scale on the back of the base plate
– use the alidade to find the altitude of the brighest known star in the sky (outer scale of the back of the base plate)
– locate the specific star of which you have measured the altitude on the rete (front of astrolabe)
– rotate the rete to align the star with the altitude line that crosses the meridian
– the astrolabe is now set for the specific date
– rotate the rule on the rete according to the astrological date found in the first step
– follow the opposite side of the rule to determine the time of day in solar time

2) – convert the calendar date to the astrological date on the back of the base plate
– on the front of the astrolabe, rotate the rete so that the astrological date intersects the horizon
– determine the time by aligning the rule with the astrological date and follow it to the time scale

3) – convert the calendar date to the astrological date on the back of the base plate
– on the front of the astrolabe, rotate the rete so that the astrological date intersects the horizon
– align the rule to find the time (like opt 2) at each intersection of the rete on the horizon
– determine at what time the sun will rise and set and calculate remaining hours of the day to know how many hours of darkness there will be