The Astronomical Observatories of Jai Singh c6.s1: The Astrolabe

The Astronomical Observatories of Jai Singh c6.s1

Language: English

c6.s1.t1 The Tablets (Ṣafāiḥ) — 90 parts

The Astrolabe

c6.s1.1

9. Of these metal instruments the astrolabe appears to have played the most important part in Jai Singh's work. Indeed in the middle ages the astrolabe was one of the chief astronomical instruments. The Arabs perfected it at a very early date and it remained one of the principal astronomical instruments until about the 17th century, and is still used in the East for astrological purposes. It was usually of brass¹ and varied in diameter from a couple of inches to several feet. The mariner's astrolabe (as used by Columbus) was adapted from that of the astronomers about A.D. 1480, but was superseded by Hadley's Quadrant of 1731. The famous scholar Gerbet, who afterwards became Pope Sylvester II, had such skill in making astrolabes, etc., that he was supposed to have sold his soul to the devil. There are many references in mediæval literature to the astrolabe. More than three centuries before Jai Singh, Chaucer wrote his Treatise on the Astrolabe. "Trust well," he says, "that alle the conclusions that have be founde, or else possibly might be founde in so noble an instrument as is an Astrolabe been unknowe parfitly to any mortal man in this regioun, as I suppose."

c6.s1.2

¹ Gower refers to one of gold "With him his astrolabe he name, which was of fine gold precious, with points and circles marvellous." The Granada astrolabe described by H. S. Cooper (JRAS 1904, 53f) has silver knobs on each pointer of the *‘ankabūt*; in the British Museum are several inlaid with silver; and others evidently had some sort of jewel fixed in the *kursi* (see fig. 12). Gilt instruments are not uncommon.

c6.s1.3

10. The type of astrolabe principally used by Jai Singh was the flat astrolabe or *astrolabium planisphaerum*, in Arabic called *Zāt al-Ṣafā’iḥ* (‘Consisting of tablets’) like ‘Jaipur A’ and ‘Jaipur B,’ to which the following description particularly applies.

c6.s1.4

The *corpus astrolabii* is a circular disc with a raised edge into which fit the several parts of the instrument:

c6.s1.5

(i) The containing disc is termed the *mater*² (Ar. *umm*) and the inner part of this is the *venter*,³ while the raised edge is called the *kuffa* or rim.⁴ The *venter* is often inscribed with latitudes and longitudes of important cities. (Figures 13, 14, 15.)

c6.s1.6

² Moder, mother, rotula.

c6.s1.7

³ Also *wajh* or face.

c6.s1.8

⁴ Also called Margillabrum or Limpbus, Hajra (side) etc.

c6.s1.9

(ii) The ‘ankabūt or aranea’¹ is an open-work disc marked with the ecliptic, the signs of the zodiac and a number of stars. It is placed in the venter and can be revolved. The branches on which the names of the stars are written and the points of which indicate the positions of the stars are termed shazāyā or ‘splinters.’² The pointer at the top of the ‘ankabūt at the first point of Capricorn is termed the muri or index.³ (Figures 5, 6, 9 and 10.)

c6.s1.10

¹ Also shabakah, net, rete; Alancabuth; Volvellum, etc.

c6.s1.11

² Ibr al-Kawākib, needles of the stars, etc.

c6.s1.12

³ Muri rās al-jadi (index of the head of Capricorn); Almury, Ostensor, Denticle, etc. “Thin Almury is cleped the Denticle of Capricorne. This same almury sit fix in the hed of capricorne.” Chaucer, I, 23.

c6.s1.13

(iii) Several thin discs or tablets,⁴ marked with almucantarats,⁵ azimuth circles, hour circles, etc., for various latitudes, etc., fit into the body of the astrolabe. (Figures 17 and 18.)

c6.s1.14

⁴ Ar. Ṣifā’iḥ, Saphiahs, Tympana, Tabulæ regionum, etc.

c6.s1.15

⁵ Circuli progressionum (Ar. maganṭarāt).

c6.s1.16

(iv) The alhidade or⁶ sighter revolves round the centre on the back of the mater. Each arm has a perforated libna⁷ or ‘tile,’ which is sometimes hinged on to the alhidade. European astrolabes sometimes had another marker or label⁸ without sights for use on the front of the instrument. (Figure 7.)

c6.s1.17

⁶ Ar. ‘iẓādah, ‘door post’; Dioptra, Mediclinium, Verticulum, Alidade, etc. Tanner (1587) describes the alhidade thus: “Altriada or mediclinium, in which are put two little pins or tables to take the height of the sun in the day and of the stars at night, of which one side goeth through the centre of the astrolabe is called the line of trust, because it bringeth credit of things practised there.”

c6.s1.18

⁷ Tabella, Pinna, Pinnula; ḥadaf, dafa.

c6.s1.19

⁸ Ostensor, index, petite roue, etc.

c6.s1.20

(v) The tablets and alhidade, etc., are fixed together by a pin (Ar. quṭb⁹) which is fastened by a wedge termed by the Arabs faras or ‘horse,’ and often fashioned into some resemblance of a horse’s head.¹⁰ (Figure 24.)

c6.s1.21

⁹ Axis, clavus, exiltre, alchitot, cavilla, etc.; miḥwar (axis), watad (stake).

c6.s1.22

¹⁰ See D and E (fig. 24). The former (D) is from the India Office Persian astrolabe, and E is taken from the British Museum MS. of Mās-shā Allah’s work. See also page 63 and figure 68; and Nallino, al Battāni I, 319.

c6.s1.23

(vi) The whole is suspended by a ring (Ar. ḥalqa) joined to the ‘urwah or handle, which in its turn is riveted to the projecting part, kursi or throne, of the mater. To the ḥalqa was sometimes attached a cord (Ar. ‘ilāqa).

c6.s1.24

(vii) The back of the astrolabe (Ẓahr al-asṭurlāb) in all cases has an outer graduated scale, two upper quadrants and certain shadow scales. It is often inscribed with tables of use to the astrologer and geographer: the details vary greatly. (Figures 7, 8, 11 and 12.)

c6.s1.25

The sighter and graduated circle (fig. 7) on the back of the astrolabe form the part of the instrument used in actual observation; while the ‘tablets’ and the ‘ankabūt (which rotates) and the graduated circle on the raised edge (kuffa) of the mater form a very efficient calculating machine.

The Tablets (Ṣafāiḥ)

c6.s1.t1.1

11. The ordinary disc or ‘tablet’ is marked on each side with stereographical projections of the horizon and almucantarats, azimuth and hour circles for a particular latitude and also the equator and tropics.

c6.s1.t1.2

Fig 13. VENTER OF ASTROLABE (JAIPUR B).

c6.s1.t1.3

Fig 14. VENTER OF ASTROLABE (JAIPUR D).

c6.s1.t1.4

Fig 15. VENTER OF ASTROLABE (HERAT C).

c6.s1.t1.5

Fig 16. TABLET OF HORIZONS (HERAT C).

c6.s1.t1.6

The almucantarats are circles of altitude,¹ the almucantarat of zero altitude being the horizon (*EHW* in plate V). In the diagram almucantarats are drawn for 60°, 40°, 20° (as well as the horizon, 0°) and are marked *a*₆₀, *a*₄₀, *a*₂₀. The number of almucantarats varies in different astrolabes: if there is one for each degree of altitude, the instrument is called *tāmm* or ‘complete’; if for every other degree, it is termed *niṣfi*, ‘bipartite’ and so on. Jaipur A and B (figures 5 and 6) are *tāmm* or ‘complete’; Herāt C (figures 17 and 18) is *niṣfi*; while ‘Jaipur D’ (figure 10) is *sudsi* or sexpartite.

c6.s1.t1.7

¹ *Let ABCD* (Plate V) represent the tropic of Capricorn and *CA* the meridian, and let the arc *AF* measure the obliquity of the ecliptic, then the point *S* on the intersection of *BF* and *AC* is on the equator and *SENW* represents the equator, *E* being the eastern point. Similarly by drawing *Os* parallel to *OF* we get *s*, the southern point of the tropic of Cancer and *Cs* the diameter of the ecliptic. The angles *SL* and *WL* measure the latitude (φ) of the place, and by joining *LE* and *L*₁*E* we get *Z*, the zenith, and *H*, the meridian point on the horizon. The opposite point on the horizon is *H*₁ where *El*₁ (=φ) meets the meridian line *NS* produced. To obtain a circle (almucantarat) for altitude *a*, mark off angles (φ±*a* 90°) from *S*, the south point of the equator, (positive direction *S W*) and join both these points to *E*, the east point on the equator: the distance between the points intersepted on the meridian line *NS* is the diameter of the circle of altitude *a*.

c6.s1.t1.8

Azimuth lines are drawn at right angles to the almucantarats.² These are seen in figures 17 and 18, and in plate V portions of certain azimuth circles *Z*₅₆, *Z*₄₂, etc., are drawn. In some tablets these azimuths are continued below (to the north of) the horizon.

c6.s1.t1.9

² In the diagram *NL*=*SL*=φ, the latitude of the place, and *El*₁ cuts the meridian line *NS* in the nadir *n*. The horizon is graduated by joining the zenith *Z*, and the graduations on the equator, and each azimuth circle passes through the zenith, nadir and the point on the horizon to which it pertains, while the centres of the azimuth circles lie on the line parallel to *EW* and bisecting *Zn*.

c6.s1.t1.10

Temporal hours.—The temporal or unequal or planetary hour lines are shown in figures 17 and 18, and in plate V by the broken lines *t*₁, *t*₂, etc.³ They divide the time between sun-rise and sunset into twelve equal portions and therefore vary in length from day to day. These divisions of time gradually fell into disuse (see page 87), and equal or equinoctial hours were introduced. These are shown in figures 18 (but not in figure 17) and in plate V they are marked *e*₁, *e*₂, etc.

c6.s1.t1.11

³ To draw the temporary hour circles, divide the day portion (that is the portion below the horizon in the diagram) of each of the three circles—the tropic of Capricorn, the equator, and the tropic of Cancer—into twelve equal parts and draw circles *t*₁, *t*₂, etc., through each trio of corresponding parts. For the equal hours draw through *X*, the centre of the circle of the horizon, a circle concentric with the equator and tropics. Graduate this circle at intervals of 15 degrees starting from the south point and proceeding westwards. With the south point and in succession the other points of graduation as centres, and radius equal to the radius (*XH*) of the horizon draw arcs *e*₁, *e*₂, etc., from the circle of Capricorn to that of Cancer. (These arcs will pass through the equal divisions of the equator, already marked for temporal hours.) The result of this construction is that any point on the ecliptic, as the ‘ankabūt is rotated, passes from one equal hour line to another in one twenty-fourth of a revolution.

c6.s1.t1.12

Houses.—The tablet is sometimes divided into twelve astrological ‘houses.’⁴ The boundary lines of these are seen in figure 17 and in plate V are marked *h*₁, *H*₇, *h*₂, *H*₈, etc. (See appendix B.)

c6.s1.t1.13

⁴ The lines that divide the houses pass through *H* and *H*₇, the points common to the horizon and meridian, and points on the Equator at intervals of 30 degrees starting from the East and West line. Their centres lie on the line that passes through *X* (the centre of the circle of the horizon) and is parallel to the East and West line. The points of intersection of these house lines with the Ecliptic are termed cusp. (For further details, see p. 120 and STOFLER, *Elucidatio fabricæ ususque astrolabii* 1524.)

c6.s1.t1.14

Longest days and latitudes.—The latitude for the particular tablet is generally written just below the *ufk* or oblique horizon, *EWH*, on the right of the meridian line; while, in the corresponding place on the left of the meridian the length of the longest day of the year for the particular latitude is generally given. In figure 18, for example, we have

c6.s1.t1.15

| Hours | Latitude |
| 13 47 | 28 |

c6.s1.t1.16

In some cases the name of a city is also given. For example ‘Delhi R’ has “Avamtikayām 22” and “Amadāvād 23.”

c6.s1.t1.17

(vii) *Special Tablets.*—In the ordinary astrolabe the number of tablets varies to as many as nine—not counting the ‘ankabūt. Generally one is a special disc for horizons on one side and celestial co-ordinates on the other and occasionally there are other special tablets: the rest are the ordinary tablets, already described for several latitudes.

c6.s1.t1.18

*Horizons.*—The tablet of the horizons (*al-Ṣafīḥat al-āfāqiyah*) is shown in figure 16. The horizons are arranged in four sets—one set in each quadrant consisting of six or seven horizons—and below each of these sets are two scales termed *al-mail al-kullī* (*shamālī* or *janūbī*) or the total obliquity (northern or southern).

c6.s1.t1.19

*Ankabut co-ordinates.*—On the other side of the ‘tablet of the horizons’ is generally the ‘tablet of the latitude of the complement of the total obliquity.’ This really gives the celestial co-ordinates (longitude and latitude) and by its aid the positions of the stars on the ‘ankabūt can be at once read off. Morley seems to have thought ² that this was an ordinary tablet for latitude 66½° N, but it is quite rightly described as *Ṣafīḥah mīzān al-‘ankabūt*, ‘the tablet of the measure of the ‘ankabūt.’ It occurs in most of the astrolabes I have examined.

c6.s1.t1.20

² Morley says: “These last two mentioned *Ṣafīḥahs* appear to have been used as models for the construction of the ordinary tablets,” but he is not altogether right in the second case.

c6.s1.t1.21

(ix) The Lahore Museum astrolabe has a tablet for the latitude of the equator. Here the oblique and straight horizons coincide and this line is marked *al-maghrib al-‘ard lah* ‘the west—no latitude’ and *al-mashriq al-‘ard lah*, ‘the east no latitude.’ Below the horizon are concentric semicircles which appear to be circles of declination: a similar tablet is in the ‘Delhi Q’ instrument.³ Another curious tablet belongs to the Jaipur Hindu *niṣfi* astrolabe (described below p. 31) and is for latitude 72° North. It has engraved upon it only the three circles and the almucantarats (none being numbered—the only number inscribed being ‘72’). The India Office Hindu astrolabe contains a similar projection, but more complete and is marked *amśa* 72, *horā* 23.

c6.s1.t1.22

¹ Avamti is Ujjain, the latitude of which is roughly 23° 10′. The latitude of Ahmedabad is approximately 23° 6′.

c6.s1.t1.23

³ Morley (pp. 12–13) describes three tablets for ‘no latitude’ and gives diagrams (XX, 17, 18 and 19). One belongs to the India Office Persian astrolabe, another to the Vaux astrolabe, the third to the India Office Hindu astrolabe.

c6.s1.t1.24

CONSTRUCTIONS FOR ASTROLABE TABLET.

c6.s1.t1.25

In an astrolabe (Delhi Q) that was shown to me in Delhi there are two other types: (i) a tablet with co-ordinates for latitudes 30° (13ʰ 56ᵐ) and 28° (13ʰ 46ᵐ) engraved on the same side, and a similar one for latitudes 40 (14ʰ 51ᵐ) and 62°; (ii) a tablet split into two halves along the meridian, for latitudes 32° (14ʰ 6ᵐ) and 36° (14ʰ 26ᵐ).

c6.s1.t1.26

12. *Ankabūt* (aranea) or *shabakah* (rete). The *‘ankabūt* or ‘spider’ is an open work tablet so arranged that the one below it may be conveniently seen (Figures 5, 6, 9 and 10). It exhibits a graduated ecliptic circle¹ with the signs of the zodiac and a number of the more important northerly stars. The points (*shazāyā*) of the net work indicate the positions of the stars, the names of which are engraved on the branches. The number of stars varies with the size, etc., of the instrument. The small Jaipur astrolabe (*D*) has 25, the Shāh Ḥusain instrument has 63, etc.

c6.s1.t1.27

¹ The diameter of the ecliptic is the distance *Cs* or *At* (Plate V) between the intersections on the meridian line N S of the tropics of Capricorn and Cancer. The graduations of the ecliptic lie on the line joining the pole of the ecliptic to the corresponding graduations on the equator. The pole of the equator is, of course, at the centre of the disc, while the pole of the ecliptic is at a distance from the pole of the equator equal to the maximum declination (approximately 23½°). It is sometimes marked *Quṭb al-burūj*.

c6.s1.t1.28

The *‘ankabūt* is generally the most ornamental part of the instrument: it is sometimes inlaid with silver; Jaipur A shows the forms of the constellation animals, etc. The *‘ankabūt* is not used in a fixed position like the other tablets, but can be rotated and thus is employed, in combination with the tablet placed below, for finding the position of any star at a given time, the ascendant or ‘horoscope,’ the time and length of the day, etc., etc.

c6.s1.t1.29

13. *Back of the Astrolabe (Zahr al-Aṣṭurlāb).*

c6.s1.t1.30

The back of the astrolabe is usually covered with a great deal of information, useful principally to the geographer and astrologer. The several instruments differ in detail, but the general arrangement is much the same. The contents may be roughly classified thus:—

c6.s1.t1.31

(a) The upper half of the periphery is graduated into degrees, etc.
(b) The South East quadrant² consists of a graphic table of sines.
(c) The South West quadrant² is inscribed with declination graphs, etc.
(d) Shadow scales (lower periphery and central rectangle).
(e) Tables of signs, mansions, planets, terms, faces, etc.; generally contained in the inner semi-circles of the lower half of the disc.

c6.s1.t1.32

² The south point is at the top of the disc.

c6.s1.t1.33

Special tables contained in rectangles such as:

c6.s1.t1.34

(f) The times of the rising of the signs (In the centre of figure 8).
(g) Trigons or triplicates and their regents (In the centre of figure 12 and right of figure 7).
(h) Table of climates (Lower part of figure 7).
(i) Differences between true and nominal years (Left of figure 7).

c6.s1.t1.35

(a) The periphery of each of the upper quadrants is graduated into degrees commencing from the east and west points. In ‘Jaipur A’ (figure 7) the degrees are divided into quarters. In conjunction with the alhidade or sighter these graduations were used for measuring altitudes and other angles.

c6.s1.t1.36

(b) The ‘quadrant of sines’ occupies the south-east quadrant and occurs in most instruments. In some instruments the vertical radius is divided into sixty equal parts, and lines parallel to the other radius are drawn to the circumference from each point of division (figure 12); in others, both radii are so divided and horizontal and vertical lines are drawn from each point of division (figure 8); in others, horizontal lines are drawn from each degree on the quadrant. The vertical and horizontal scales indicate the sines and cosines of the corresponding angles. In the description of the Zarqālī astrolabe below (p. 29) the use of these scales is explained in more detail. In some instruments arcs for 23½°, 30°, etc., are described.

c6.s1.t1.37

(c) The south-west quadrant in most instruments exhibits a sort of yearly calendar. The horizontal and vertical radii are divided into six equal divisions¹ (figures 7, 8). From the points of division arcs are described and the names or numbers (figure 11) of the signs are written in the spaces, six on the horizontal radius and six on the vertical, in the following order:—

c6.s1.t1.38

¹ In the Herāt (figure 12) and the Shāh Ḥusain instruments the main divisions are not equal but proportional to the sun's declination.

c6.s1.t1.39

| | | 3 | 4 | 5 | 6 | 7 | 8 |
| Vertical | . | Cancer | Leo | Virgo | Libra | Scorpio | Sagittarius |
| Horizontal | . | Gemini | Taurus | Aries | Pisces | Aquarius | Capricornus |
| | | 2 | 1 | 0 | 11 | 10 | 9 |

c6.s1.t1.40

This division, combined with the graduated circumference, forms a scale of circular and angular co-ordinates, and on this scale are traced various kinds of graphs² showing, for example—

c6.s1.t1.41

² Figure 37 shows how the curve (i) is constructed for latitude 27 N. For each pair of signs, radii marking the angle of the meridian altitude of the sun are drawn, and the points of intersection of these radii with the corresponding arcs of the signs are joined. To make the graph perfectly correct, intermediate points must, of course, also be fixed. Figure 11 shows the unequal hour curves. According to Delambre (Astronomie du Moyen Age, p. 243) this is first described in a small work by Sacrobosco (circa A.D. 1250). It occurs on many old astrolabes, but it gives only roughly approximate results. To construct these hour lines the arc of the quadrant is divided into six equal parts and a semi-circle erected on one of the bounding radii. This is the sixth hour line and the others are arcs of circles of which the centres are on the same radius, but at points equidistant from the centre of the quadrant and from the successive points of division on the arc of the quadrant.

c6.s1.t1.42

(i) The relation between the sun's right ascension and meridian altitude (figures 7, 8 and 37);

c6.s1.t1.43

(ii) The meridian altitudes for certain latitudes (figure 12);

c6.s1.t1.44

(iii) The altitude of the sun when it traverses the azimuthal circle of the Ka'bah at Mecca;

c6.s1.t1.45

(iv) The temporal or unequal hours (figure 11).

c6.s1.t1.46

(d) There are generally four sets of shadow scales³ two on the periphery of the lower half of the disc and two in the central rectangle. In the Zarqālī instrument, however, the latter are replaced by a pair of central circular shadow scales (figure 19). Given the length of the shadow in terms of its gnomon—by the aid of the shadow scale and the alhidade the degree of altitude of the sun and the time can be found.

c6.s1.t1.47

³ Figure 23 shows how these scales are constructed. There are generally two kinds of scales—one for a 7-unit gnomon and the other for a 12-unit gnomon. The semi-circle a c e is bisected at c, and ac and ce are bisected at b and d. The line bd, which is bisected at c¹, is the basis for both scales: the part bc¹ is divided into 12 equal divisions and c¹d into 7 equal divisions and these graduations are continued on their respective sides, as far as is convenient. Lines joining the points of division with the centre cut the arcs and the small central rectangle, and form on them the shadow scales. On most astrolabes the 12-unit scales are on a b c and e g, etc.; and the 7-unit scales on c e and i l. The Zarqālī astrolabe has, however, in place of the central rectangle, the smaller semi-circle, fj, graduated. Variations occur, e.g., the basis line (b c¹) may be placed vertically through b, and then graduated.

c6.s1.t1.48

(e) In most of the instruments the inner semi-circles of the lower half of the disc give lists of the signs, manzils, terms, faces, etc. These tables are generally for astrological purposes, and they are explained in some detail in a note on astrology appended to this volume (appendix B).

c6.s1.t1.49

Some of the special tables are of great interest. The following are taken from A, B, and C (figures 7, 8 and 12).

c6.s1.t1.50

(f) A table of rising signs is given in the central rectangle of ‘Jaipur B.’

c6.s1.t1.51

*Table of times of rising of the signs for the latitudes of certain cities in India.*

c6.s1.t1.52

| | 39 | 38 | 37 | 36 | 35 | 34 | 33 | 32 | 31 | 30 | 29 | 28 | 27 | 26 | 25 | 24 | 23 | 22 | 21 | 20 | LATITUDES. | |
| | H. | M. | H. | M. | H. | M. | H. | M. | H. | M. | H. | M. | H. | M. | H. | M. | H. | M. | H. | M. | H. | M. | H. | M. | H. | M. | H. | M. | H. | M. | H. | M. | H. | M. | H. | M. | H. | M. | H. | M. | SIGNS. | |
| t₁ | 1 | 14 | 1 | 15 | 1 | 16 | 1 | 18 | 1 | 19 | 1 | 20 | 1 | 21 | 1 | 22 | 1 | 24 | 1 | 25 | 1 | 26 | 1 | 27 | 1 | 28 | 1 | 29 | 1 | 30 | 1 | 31 | 1 | 32 | 1 | 33 | 1 | 34 | 1 | 35 | Pisces | Aries. |
| t₂ | 1 | 28 | 1 | 29 | 1 | 31 | 1 | 32 | 1 | 33 | 1 | 34 | 1 | 35 | 1 | 36 | 1 | 37 | 1 | 38 | 1 | 38 | 1 | 39 | 1 | 40 | 1 | 41 | 1 | 42 | 1 | 43 | 1 | 44 | 1 | 44 | 1 | 45 | 1 | 46 | Aquarius | Taurus. |
| t₃ | 1 | 56 | 1 | 57 | 1 | 57 | 1 | 57 | 1 | 57 | 1 | 58 | 1 | 58 | 1 | 58 | 1 | 59 | 2 | 0 | 2 | 0 | 2 | 0 | 2 | 1 | 2 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 2 | 3 | 2 | 3 | Capricornus | Gemini. |
| t₄ | 2 | 22 | 2 | 21 | 2 | 21 | 2 | 20 | 2 | 20 | 2 | 20 | 2 | 19 | 2 | 19 | 2 | 18 | 2 | 18 | 2 | 17 | 2 | 17 | 2 | 16 | 2 | 16 | 2 | 16 | 2 | 15 | 2 | 15 | 2 | 15 | 2 | 14 | 2 | 14 | Sagittarius | Cancer. |
| t₅ | 2 | 31 | 2 | 30 | 2 | 29 | 2 | 28 | 2 | 27 | 2 | 26 | 2 | 25 | 2 | 24 | 2 | 22 | 2 | 22 | 2 | 22 | 2 | 21 | 2 | 20 | 2 | 19 | 2 | 18 | 2 | 17 | 2 | 17 | 2 | 16 | 2 | 16 | 2 | 14 | Scorpio | Leo. |
| t₆ | 2 | 30 | 2 | 28 | 2 | 27 | 2 | 26 | 2 | 22 | 2 | 23 | 2 | 22 | 2 | 21 | 2 | 20 | 2 | 19 | 2 | 18 | 2 | 16 | 2 | 15 | 2 | 14 | 2 | 13 | 2 | 12 | 2 | 11 | 2 | 10 | 2 | 10 | 2 | 9 | Libra | Virgo. |

c6.s1.t1.53

This table and the rule on which it is based played a very important part in mediæval astronomy and astrology.¹

c6.s1.t1.54

¹ See Book ii of the Almagest; al-Battānī, Opus Astronomicum, 2nd Part, p. 65f; the Sūrya Siddhānta, ii, 60f. etc.; also the note on astrology (Appendix B). From the formula Sin a₁ = tan φ . tan δ, where φ is the latitude and δ the declination, the so-called ascensional differences are calculated; then from sin b₁ = sin 30°. cos ω / cos δ₁, sin (b₁ + b₂) = sin 60°. cos ω / cos δ₂, sin (b₁ + b₂ b₃) = 1 the values of b are calculated; and finally t₁ = b₁ - a₁, t₂ = b₂ - a₂ + a₁, t₃ = b₃ - a₃ + a₂, t₄ = b₄ - a₄ + a₃ = b₄ + a₃ - a₂ and so on, since b₄ = b₂, b₅ = b₁, b₆ = b₁, and a₅ = a₅ = a₁.

c6.s1.t1.55

(g) Trigons.—On the right of the lower half of ‘Jaipur B’ (figure 8) and in the centre of C (figure 12) is a table showing the regents of the trigons, etc.

c6.s1.t1.56

*Nature of the Trigons and their Regents or Lords.*

c6.s1.t1.57

| Nature of the Triplicities. | | Fiery. | | Earthy. | | Airy. | | Wat ry. |
| Day Lords | . | Sun | . | Jupiter | . | Saturn | . | Venus | . | Moon | . | Mars | . | Saturn | . | Mercury | . | Jupiter | . | Venus | . | Mars | . | Moons. |
| Triplicities | . | Aries | . | Leo | . | Sagittarius | Taurus | . | Virgo | . | Capric-ornus | . | Gemini | . | Libra | . | Aquarius | Cancer | . | Scorpio | . | Pisces. |
| Night Lords | . | Jupiter | . | Sun | . | Saturn | . | Moon | . | Venus | . | Mars | . | Mercury | . | Saturn | . | Jupiter | . | Mars | . | Venus | . | Moon |

c6.s1.t1.58

The triplicities, or trigons, are groups of three signs, each of which is situated 120 degrees from the other two. It will be noticed that Saturn, Mars, Jupiter and the Moon occur in their respective triplicities both as day and night regents and they are sometimes therefore termed ‘common regents.’ (See Appendix B.)

c6.s1.t1.59

(*h*) **Climates.**—The table of climates occurs only on Jaipur A (*figure 7*), towards the bottom of the lower half of the disc.

c6.s1.t1.60

Table of climates.

c6.s1.t1.61

| Climates. | First. | Second. | Third. | Fourth. | Fifth. | Sixth. | Seventh. |
| Beginnings (*b*)and middles (*m*) | b m | b m | b m | b m | b m | b m | b m |
| Latitudes . . . | 12⁴¹ 16⁴⁴ | 20²¹ 24¹⁰ | 27³⁴ 30⁴⁶ | 33⁴³ 36²⁸ | 39¹ 41²¹ | 43²⁰ 45³⁹ | 47²⁸ 48⁵⁹ |
| Hours . . . | 12⁴⁵ 13⁰ | 13¹⁵ 13³⁰ | 13⁴⁵ 14⁰ | 14¹⁵ 14³⁰ | 14⁴⁵ 15⁰ | 15¹⁵ 15³⁰ | 15⁴⁵ 16⁰ |

c6.s1.t1.62

This topic of ‘ Climates ’ recalls a most interesting chapter in the history of civilization. It exercised the attention of such astronomers and astrologers as Eudoxus, Eratosthenes, Hipparchus, Manilius, Ptolemy, Dorothea of Sidon, etc., etc. The subject presented difficulties. The number of climates assumed varied, but generally a chorographic system, which applied the seven planets to the seven zones or climates, prevailed. Also, according to Paul of Alexandria, “ each sign corresponds to a climate or parallel, and by virtue of its Trigon to each quarter.” For the mathematicians, the problem was to find a progression corresponding to ascensional differences. They took the length of the day as the measure,¹ and progressed from one climate to another by half hour steps. (See appendix C.)

c6.s1.t1.63

¹ The measure of the longest day is (180° + 2h)/15 where sin h = tan φ. tan ω.

c6.s1.t1.64

(*i*) **The year.**—The rectangular table to the left in Jaipur A (*figure 7*) shows multiples of the differences between the approximately correct length of the tropical year and 365 days, thus :

c6.s1.t1.65

| 67¹⁶ | 340²⁴ | 252⁵² | 165¹⁹ | 77⁴⁵ | 350¹² | 262³⁹ | 175 ⁶ | 87³³ |
| 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |
| 90 | 80 | 70 | 60 | 50 | 40 | 30 | 20 | 10 |
| 319³⁸ | 164 ⁸ | 0 8³⁷ | 213 ⁶ | 57³⁵ | 262⁴ | 106²³ | 11² | 155³¹ |

c6.s1.t1.66

The table gives *n*(87° 33′ 6″)—*a*.360° where *n* ranges from 1 to 9 and from 10 to 90 and *a* is a whole number.² Now 87° 33′ 6″, expressed in time, is 5 hours 50 minutes 12·4 seconds, and the length of the tropical year was supposed to be 365 days 5 hours 50 minutes 12·4 seconds.³ 14. The face.—(*Wajh* or Venter).—The inside surface (*venter*) of most of the astrolabes is engraved with a list of cities and their latitudes and longitudes and, sometimes, their position relative to Mecca.¹ The last is indicated by the *inḥirāf* or ‘inclination’ and the *masāfat* or ‘distance’ and *jihat* (side or point of the compass). The *inḥirāf* is the arc of the horizon intercepted between the meridian of the place and the vertical circle passing through the zenith of Mecca.² The Masāfat is the distance of Mecca measured along a great circle, and the *jihat* is the quarter of the horizon in which Mecca lies.

c6.s1.t1.67

² For example 106° 33′ = 30 (87° 33′ 6″)—*a*.360 = 2626° 33′—*a*.360° = 106° 33′—*a*.360° and *a*=7.

c6.s1.t1.68

³ A British Museum astrolabe dated A.H. 1070 (=A.D. 1659-60), by Muḥammad Muqīm of Lahore, gives the same table. Al-Battānī gives 86° 36′ and Nallino gives the following note: “ Ḥabash in suo astronomiæ libro narrat partem excedentem revolutionis (*fazl al-daur*), scilicet quantitatem (gradibus expressam) qua Solis totus ambitus 365 dies excedit, inventam esse ab astronomis khalifae al-Ma’mūn :— In specula al-Shammāsiyyah . . . . . 86° 43′ 39ⁱⁱ 36ⁱⁱⁱ 47ⁱᵛ Damasci in urbe . . . . . . 86° 41′ 25ⁱⁱ 14ⁱⁱⁱ 9ⁱᵛ a Yaḥy'a ibn Abī Manṣūr . . . . . 86° 35′ 13ⁱⁱ 46ⁱⁱⁱ In tabulis suis Habash primam quantitatem recepit, rotunde scribens 86° 43′ 39ⁱⁱ 37ⁱⁱⁱ, vel, gradibus in tempus conversis, 5ʰ 46ᵐ 54ˢ 36ᵗ etc.” *Opus Astronomica*, i. pp. 42 & 211. The present length of the tropical year expressed in mean time is 365 days 5 hours 48 minutes 45·5 seconds. or 365·2422 days nearly.

c6.s1.t1.69

¹ See the excellent little book *Paraphrase de l'astrolabe* written in A.D. 1555 by Jaques Focard de Monipeltier, who terms the venter ‘Miroer du Monde’ and gives on it an actual map of the world (i. 136-7).

c6.s1.t1.70

² The *angulus positionis* of the old geographers. See al-Battānī i. 136-7; L. A. Sédillot’s *Mémoire*, 97f.; the *Nuzhat al-Qulūb* (Ed. 9, le Strange) p. 26; &c. &c.

c6.s1.t1.71

Fig 17. TABLET FOR LATITUDE 32.

c6.s1.t1.72

Fig 18. TABLET FOR LATITUDE 28.

c6.s1.t1.73

Fig 19. ZARQALI ASTROLABE (OBVERSE).

c6.s1.t1.74

Fig 20. ZARQALI ASTROLABE (REVERSE).

c6.s1.t1.75

Jaipur B (figure 13) gives the longitude and latitude of 210 places, and also the districts in which they are situated, but does not give the *inḥirāf* etc.; Jaipur D gives 36 towns; the Herāt astrolabe (C) gives 44 places with the *inḥirāf* and *jihat*; the Shāh Ḥusain instrument gives 103 places with latitude, longitude, *inḥirāf*, *masāfat* and *jihat*; the Lahore astrolabe gives also 36 places, with latitudes and longitudes only. A selection from these astrolabe gazetteers is given in an appendix (pp. 127-8).

c6.s1.t1.76

The longitude is in all cases reckoned from the ‘Fortunate Islands.’ Compared with a modern atlas the differences for a few selected³ places are—

c6.s1.t1.77

³ The values given on all the instruments examined for these six places are the same: at Marāghah, Baghdād and Nishāpūr were important observatories.

c6.s1.t1.78

| | Longitude difference. | Latitude difference. |
| Marāghah | 35° 43′ | 0° 1′ |
| Baghdād | 35° 22′ | 0° 4′ |
| Shīrāz | 35° 20′ | 0° 6′ |
| Nishāpūr | 33° 50′ | 0° 13′ |
| Yezd | 34° 30′ | 0° 22′ |
| Isfahān | 34° 56′ | 0° 14′ |

c6.s1.t1.79

The difference in latitude may be taken as some criterion of the accuracy of the determinations, but it must be remembered that the precise localities of the observations (old and new) are not known.⁴

c6.s1.t1.80

⁴ One second of longitude at Delhi is roughly equivalent to about 30 yards; very roughly a mile to a minute of arc. (At latitude 30° N. one degree of longitude=96489 metres=59.97 miles)

c6.s1.t1.81

The longitude differences point to some place about 35 degrees west of Greenwich as the point of origin. The zero meridian therefore passed through the Azores. In this matter the Muhammadans copied the Greeks, who fixed upon the ‘Fortunate Isles,’ possibly, as the western end of the world. These ‘Fortunate Isles’ were originally imaginary islands where the souls of the good were made happy, but later the name became attached to the Canary Islands. In the *Āīn-i-Akbarī*⁵ we read: “The Greeks commence their reckoning from Khālidāt, which are six islands in the western ocean, which in ancient times were inhabited, but now are inundated, etc.”

c6.s1.t1.82

⁵ Ed. Gladwin, ii. 351.

c6.s1.t1.83

The longitude values are somewhat irregular and illustrate the inherent difficulty in the determination. The errors for Jerusalem and Cairo and Mecca seem to be traditional. The list of names on ‘Jaipur B’ (figure 13) is interesting as being copied from Ulugh Beg’s table.¹ The number of towns is the same, but the astrolabe designer left out some of the western places [*e.g.*, those in the country of Rūm and some of those of Shām (Syria) ], and added some extra towns for India. Otherwise the names, the order and the latitudes and longitudes are the same.

c6.s1.t1.84

¹ See L. P. E. A. Sédillot, *Prolégomènes des tables astronomiques d’ Oloug-Beg*. 1853, p. 257 f. Compare also al-Battānī’s list (*Opus Astronomicum* ii, 33–54).

c6.s1.t1.85

15. The Alhidade (*‘iḍāḍah*) or Sighter.—In all old oriental astrolabes the alhidade is of the type attached to Jaipur A and shown in figure 7. It is fixed on the centre pin so that its graduated edge lies on a diameter of the circle. Half of the bevelled edge (the right upper edge in figure 7) is divided into 60 equal divisions, every third division being numbered. The left upper edge is divided into six equal divisions, corresponding to the divisions for the signs of the zodiac in the south-west quadrant, and each division is marked with its two proper signs and divided into 15 parts. The right lower edge is divided into six divisions numbered 1 and 12, 2 and 11, etc. Near to each end is fixed a sighting tablet, each having two holes, the upper pair generally being the larger. On modern Hindu instruments is another type of revolving index. It has no sighters and is the length of the radius only. In mediaeval European instruments we often find such a marker or ‘label,’ as it was called,² used on the front of the astrolabe. (Figure 24.)

Linked texts (1)

Sūryasiddhānta — Maya, Sanskrit

The Astronomical Observatories of Jai Singh c6.s1: The Astrolabe

Contents

The Astrolabe

The Tablets (Ṣafāiḥ)

Linked texts (1)