THE PLANE ASTROLABE AND THE ANAPHORIC CLOCK

by

A. G. Drachmann

The history of the plane astrolabe after say + 1100 is well known; we have specimens of the instruments and texts describing their use. F. Nau in 1899 would have it to be an invention by Eudoxos, about -350, on the strength of the word arachne in Vitruvius; H. Michel, on the other hand, writing in 1947, takes the astrolabe to have been invented in the 6th century A.D.

In 1950, 0. Neugebaue? collected in the Isis all the material for the earlier history of the astrolabe, and found the following: Arachne and conarachne in Vitruvius refer to sundials only and have no relation to the plane astrolabe. The mathematical basis of the construction of the astrolabe, the planispheric projection of a star map, is known to have been used first by Hipparchos, about -150, as related by Synesios,' writing about +400; Ptolemaios4 gives us, about + 150, the mathematical theory for the planispheric projection and uses the word aranea in the same sense as the later writers. Neugebauer calls attention to the connexion between the astrolabe and the anaphoric clock, and by comparing the descriptions of Philoponos (+550) and Sebokht (+660) he reconstructs the contents of a lost treatise by Theon (+400). There can now be no doubt that the plane astrolabe was invented during antiquity, probably by Hipparchos, and certainly before Ptolemaios.

But it seems to me that it might be possible so to interpret the evidence collected by Neugebauer that we get a clearer picture of what happened and how it happened.

The anaphoric clock is described by Vitruviuss. It consisted of a metal disk with a planispheric projection of the stars of the Northern hemisphere

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Fig. 1. The network placed before the rotating star map in the anaphoric clock. The concentric circles represent the months; the short arcs indicate the hours of the day or the

watches of the night, according as they are placed above or below the horizon.

and as many as are found between the equator and the tropic of the Capricorn; indeed this tropic formed the outer limit of the disk. The circle representing the Zodiac was provided with 365 holes, in which could be placed a small disk representing the sun. The great disk was made to turn on a horizontal axle, one revolution from sunrise to sunrise, by means of a klepsydra. Before it was placed a network of bronze wires. A vertical wire represented the meridian, three concentric wires the two tropics and the equator, and between the tropics other circles represented the Zodiacal months two and two. (It is true that Vitruvius lived after Caesar's calendar reform; but the description of the clock seems to show that it was invented before the reform. A fragment of a disk found at Salzburg5, and dated about f250, showed on its back side both Zodiacal and Caesarean months.) Across all the circles was an arc representing the horizon for the place where the clock belonged, and the concentric circles were divided into hours, twelve for each day, twelve for each night, above and below the horizon respectively. Fig. 1.

When the image of the sun was placed in the hole corresponding to

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the current day, and the clock was started at sunrise, the sun would mark the hours of the day and the watches of the night; every day the clock was “wound”, and the sun was moved to its proper place. In this way the unequal local hours were marked though the disk always turned at the same speed. In my work on Ktesibios, Philon and Heron’ I ascribed the invention

of this clock to Hipparchos, without having anything to show for it. The work by Synesios quoted by Neugebauer supports this hypothesis strongly.

The plane astrolabe, as we know it from Philopono~~, the oldest description extant, consisted of a disk of brass, like a very large and very flat watch. It had a triangular lug with a suspension ring, so that it could be held vertically, and its back side had two engraved lines at right angles, one vertical, the other horizontal, when it was so held. One of the upper quadrants was divided into 90 degrees, and a small diopter or alhidade was placed on a stud in the middle of the disk. This was the real “astro- labe”, the star-catcher, by means of which it was possible to find the height above the horizon for any visible star or the sun or the moon, and read its height above the horizon on the scale. On the other side the disk had a narrow raised rim divided into 360 degrees, beginning right below the suspension ring. Inside the rim there was room for several flat disks, one for each climate. These disks were engraved with lines showing in planispheric projection the tropic of Cancer and the equator as con- centric circles, while. the edge of the disk corresponded to the tropic of the Capricorn. A vertical line represented the meridian, while an arc represented the horizon for the climate in question. Below the horizon the meridian and five short curves on either side of it represented the hour lines ; above the horizon were almucantaras, curves representing parallels to the horizon, 90 in all in the big astrolabes, if we let the point represent- ing the zenith be designed as a curve. In the smaller instruments only every other or every third curve was traced. Philoponos says that it was Ptolemaios who decided not to have hour lines on the upper part of the disk, since it would become too crowded. Later on many more curves were added both to the back and the face of the instrument; but here I follow Philoponos as the first known work. Fig. 2.

On top of this disc was placed the aranea, the spider, so called, says Sebokhta, because it looked like the animal. The spider contains the planispheric projection of the sky; but because it is necessary to see as much as possible of the plate beneath it, the map is reduced to a sort of skeleton. This part of the astrolabe has tempted the artists very much;

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Fig. 2. The disk for the horizon of 36". for a plane astrolabe. The large, concentric circles are the tropic of Capricorn, the equator, and the tropic of Cancer; the short arcs on the lower part are hour lines; the circles and arcs on the upper part are almucantaras, with

the horizon as the lowest arc.

many beautiful shapes are seen but they all seem to be derived from a pattern found in the earliest specimens, a form that corresponds to the description of Philoponos. The Zodiac is always a full cricle, divided into the twelve Signs, each of them subdivided more or less according to the size of the instrument. Capricorn touches the rim, which represents its tropic, Cancer touches its own tropic on the climate beneath it, and Aries and Libra follow the equator, when the spider is turned. The middle of the spider is solid, to fit a stud in the middle of the instrument; its rim, representing the tropic of the Capricorn, is some three quarters of a circle, being open only to allow the Zodiac to have its periphery un- disturbed round Capricorn. There is a quarter circle for the equator out- side the Zodiac, connected with the tropic of Capricorn by radii, and an East-West line connecting the tropic of Capricorn, the Zodiac, and the middle. From all these curves, except the outer circumference of the Zodiac, are sprouting small pointers, whose points mark the position of some bright star. Fig. 3.

To use the astrolabe it is necessary first to find, by means of the alhidade

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Fig. 3. The “spider”, that is the skeleton star map for a plane astrolabe. The full circle is the Zodiac; the large, three quarter circle is the tropic of Capricorn; the quarter circle is

part of the equator. Each of the 15 pointers indicate some bright star.

on the back, the height of the sun or some bright star; then the spider is moved until the star touches the height curve, almucantara, in question, and you have the position of the sky for the moment of the observation. You can tell which sign is rising, culminating or setting, you can find the hour by noting the time curve reached by the place of the sun in the Zodiac, and find an answer to many other questions of the same kind. If the sun is observed, the sun’s place in the Zodiac is made to reach its almucantara, and the time is found from the part of the Zodiac opposite the sun.

If we compare these two instruments, the anaphoric clock and the astrolabe, their similarity is unmistakable; all writers agree that they are two expressions of the same idea. The general opinion seems to be that the anaphoric clock was made after the pattern of the astrolabe. But it seems to me that it is much more likely that it is the other way about. The first person to make a planispheric projection of the sky would certainly not hit upon the idea of making a skeleton “spider”; he would have made a solid map of all the stars and constellations north of the

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tropic of the Capricorn. The next step would be to make the map rotate and make the stars rise and set in their proper order. A vertical wire would give us the meridian, for the upper and lower culmination; a horizontal line would represent the horizon of the sphaera recta, that is the sky seen from somewhere on the equator. But by an application of the planispheric projection to the lines placed before the map it would be possible to represent our own horizon, or any other horizon, by its proper arc, and now the unequal, local hours could be fitted in. Still, the map lacked something: there was no sun. There was the Zodiac, of course; the sun had to be somewhere there, in a different place every day. By adding the tropic of Cancer, the equator and the parallels for the zodiacal months it was possible to follow the sun during the turning of the map by watching the part of the Zodiac moving between or on these circles.

And now I think that the two instruments were differentiated: the clock, in which the map was turned by water, and the sun had its place assigned by means of 365 holes, one for each day; and the astrolabe, in which the place of the sun was indicated by a graduated circle, divided into signs, each subdivided by 30 degrees. For the first attempt it seems the most obvious way to make the map of the sky solid, and to cover it by an open network of lines.

That is how I imagine the first astrolabe, the astrolabe of Hipparchos. But as time went on, and the astrolabe was used more and more, more

and more lines had to be added: almucantaras, for determining the height of the sun or of the stars. And now the thickness of the wires began to make itself felt. In the clock it did not matter; the bulla representing the sun would be broader than the wires, and you could see quite clearly when its centre passed the hour lines or the horizon; also no almucantaras were necessary. But in the astrolabe either the wire would hide the star, or you had to decide on one side of the wire only to represent the line. And even then the other lines would hide other stars just as you wanted to see them.

Then someone had the inspiration to change the places of the map and the lines. Lines engraved in an polished plate can be made as thin as anyone would wish; and of the whole starry sky you only wanted the Zodiac and a few selected stars; some 14 or sixteen in all. These could be shown by slender pointers, arranged so as to interfere as little as possible with the Zodiac and with each other, but still far more robust than the network of wires; and the different climates would be solid and probably much cheaper to make than when they had to consist of thin

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wires. And so we have the second astrolabe, the astrolabe of Ptolemaios, to give it a name; for Ptolemaios4 tells us that the spider contains the projection of the sky with its stars.

So far this is only guess-work, a hypothesis built on the probabilities of how the clock and the astrolabe might have come into existence. But in the material assembled by Neugebauer there seem to be two indications that this reconstruction of events may be true.

The first bit of proof comes from the use of the word “spider”. Sebokhts says that the sliding part is called “spider” because it looks like a spider. With all respect for the most reverend bishop of Qenserin I must say that I fail to see the slightest resemblance between the “spider” of the ordinary astrolabe and the living animal. But if we assume, as surely we must, that the arachne of Vitruvius was named from the spiders’ web, there is no difficulty at all: the network of lines in the astrolabe of Hipparchos was called the spider’s web; and when the astrolabe was changed, so that the lines came behind, and the star map in front, the sliding part simply retained its name. It is not very likely that all astrolabes were changed during the same night by imperial decree, so we must imagine that both constructions were in use for many years, until the latter form, Ptole- maios’s form, gaining ground more and more, at last was the only one in use.

So far it is still just hypothesis, although it seems to me quite probable. But there is one piece of direct evidence that an astrolabe of the Hipparchic type has existed, and that is found in the passage from Synesios’. He seems to have made the star map the background, and the horizon, the hour lines, and almucantaras in the shape of a network moving across it. And he tells us expressly that he has gone back to Hipparchos in his studies, and has disregarded Ptolemaios and his followers in his construction.

R E F E R E N C E S

1. A. G. Drachmann: Ktesibios, Philon and Heron. Acta histor. Scient. natur. mathem. 4, 1948. p. 26.

2. Neugebauer, 0. Isis 1949: 40: 240-256. 3. Philoponus. Rhein. Museum Philol., 1839: 6: 127-171. 4. Ptolemaios: Planisphaerium cap. 14. In: Opera quae exstant omnia, Vol. 2. ed.

J. L. Heiberg. Lpz. 1907, p. 249: 19-23. 5. Salzburg Fragment. 0. Benndorf, E. Weiss und A. Rehm: Jahreshefte Bsterr. archSol.

Institutes Wien 1903: 6: 32-49. 6. Sebokht. Journal asiatique 1899: 13: 56101, 238-303. 7. Synesios: Migne: Patrologia graeca 66: 1577-1588. 9. Vitruvius 9: 8.