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Cosmo Graphical Mapping | Celestial Mappings

Mathomathis would like to present an article on Cosmo Graphical Mapping by JOSEPH E. SCHWARTZBERG. The following article would start a conversation on a topic called as: Celestial Mappings

To speak of celestial mapping as a part of the cosmographical tradition of traditional Hindu culture is perhaps to extend the meaning of “mapping” beyond its customary limits. Nevertheless, attempts have been made, since ancient times, to present orderly graphic portrayals of portions of the heavens in painting, sculpture, and architecture. The relevant literature is extensive. It derives on the one hand from art historians and on the other from historians of astronomy, and author have studied and understood only a small portion of the total corpus and none of it from primary sources in Sanskrit and other Indian languages. Thus, in what follows author can do no more than to provide a brief sketch of a few of the means and forms by which attempts at celestial mapping, broadly conceived, have been carried out and to indicate something of the emergence on Indian soil of certain centers of observational astronomy that sought to arrive at more objective and accurate views of the heavens than those that sufficed for most religious purposes.

The development in India of anthropomorphic icons to represent heavenly bodies may be traced back to the time of the Kusanas (first century A.D.) in the case of Surya, the sun-god; to the mid-second century in the case of the planetary deities (grahas), including the sun and moon; and at least to the sixth and seventh centuries, respectively, in the cases of Rahu and Ketu, the deities associated with eclipses. These “planetary deities,” nine  in all, were designated by the Sanskrit term navagrahas and were customarily portrayed in a fixed order, beginning with the seven that in turn exercised their lordship over the days of the week (sun, moon, Mars, Mercury, Jupiter, Venus, and Saturn) and ending with Rahu and Ketu. They so appear in innumerable sculptures (especially on the lintels over the portals of temples), in paintings, and in other forms. Although their early manifestations would hardly be described as maps, we do find in later cosmographies, some of which are described below, the maintenance of both the icons and the order established in ancient times. Iconographic portrayals of astronomical phenomena were not confined to the navagrahas. “In some interesting paintings of the schools of Rajasthan and of Deccan we can see personifications of the lunar days (tithi), of the hours of good auspices (muhurta), of the days of the week (dina, vara), of the months (masa), of the years (varsa), of the stars (naksatra), of the signs of the zodiac (rasi), etc. These are based on iconographic texts often reproduced in the same pictures.” Plate 27 provides a characteristic example of the way naksatras (groups of stars near the plane of the ecliptic separating various lunar mansions) have been portrayed in Rajasthan in recent centuries.

Not all symbols used to represent astronomical features in painted cosmographies were pictorial. As Tantric Hinduism developed, its use of essentially geometric astronomical (and astrological) charting came to be quite important. This esoteric tradition has given rise to numerous rather varied and often complex astronomical drawings, many of which have recently found their way into semipopular art books. Author, have not found it possible to study the original sources, which are never cited in the works  he has seen. Nor  author have been able to translate the abundant text or interpret the mathematical formulas that characteristically accompany the published drawings. Author have referred above to a pair of huge cosmographic paintings in Minaksi temple in the south Indian city of Madurai, both recent (1963 and 1966) replacements for accidentally destroyed works that were originally executed in 1568. One of this pair, entitled Bhugolam (the earth) has already been described. The other (Figure 1), several meters to the left of it and of the same size (about 4.25 X 4.25 m), is designated Khagolam (the celestial dome). Although there is a bit of hindrance for explaining the details of the painting with confidence, He suggests that, much of it could correspond fairly well to the following summation, by Pingree, of a portion of the cosmological sections of various Puranas.

Figure 1: Khagolam (The celestial Dome)
Figure 1: Khagolam (The celestial Dome)

[About Figure 1: This oil painting on canvas is in the waiting hall of Minaksi temple, Madurai, Tamil Nadu. It is a repainting (1966) of an original dated 1568. This diagram is believed to represent, among other things, the twelve zodiacal months; the paths of the sun, moon, and five known planets; and presumably the ties of the celestial deities Rahu and Ketu to other heavenly bodies. Size of the original: approx. 4 X 4.5 m. Photograph by Joseph E. Schwartzberg.]

Above the earth’s surface and parallel to its base are a series of wheels the centers of which lie on the vertical axis of Meru, at the tip of which is located the North Polestar, Dhruva. The wheels, bearing the celestial bodies, are rotated by Brahma by means of bonds made of wind. The order of the celestial bodies varies; the earliest seems to be sun, moon, naksatras, and Saptarishis (Ursa Major). Some Puranas place the grahas (planets) between the moon and the naksatras; in others, interpolated verses add Mercury, Venus, Mars, Jupiter, and Saturn (in that order) between the naksatras and the Saptarishis.

Which of the many concentric circles shown in figure 1 represent the orbits (wheels) noted in the previous

description is uncertain. But it seems safe to assume that the male and female figures seated in the center of the painting represent the sun and the moon, respectively, and that the wheels for the planets occupy the relatively light space between the more central and more peripheral groups of concentric rings. Radiating outward from the center of the diagram are twelve spokes that may be described as like hour divisions of a clock. Presumably these are the divisions between the twelve zodiacal months. The spokes vary in color. Those at 1, 2, 4, 8, 10, and 11 o’clock are yellow, those at 5 and 7 o’clock white, and those at 3, 9, and 12 o’clock purple, blue, and red. Distributed over much of the painting are arabic numerals (in their Western form), which very likely indicate (as on Jain cosmographies to be discussed below) the dimensions of various portions of the cosmos or their distance from its central axis.

The snakelike figure extending upward from the center and somewhat to the left to just beyond the outermost planetary ring I take to be Rahu, the causer of eclipses. Its open jaws appear about to swallow up the sun and the moon. Also extending upward from the center, through the light field of nine encompassing rings and slightly to the right, is a thick band that looks like a river, which perhaps represents Ketu. Rahu’s tail is tethered by seven (count not certain) fine lines (not discernible on the photograph), connected to various wheels (grahas?). All but one of these lines terminate in the upper half of the painting. One might suppose they are somehow associated with the “celestial bodies … rotated by … bonds made of wind” cited in the quotation from Pingree, but their tie to Rahu, rather than Brahma, argues against such a conjecture. A final feature of note in this exceedingly complex cosmography is a gold pavilion at the very top of the wheel, possibly the abode from which Brahma observes his creation and regulates the mechanics of the entire cosmos. Despite marked differences in their appearance, author does suggest a fairly close correspondence between many of the conceptions embodied in the diagram just described and in the upper, astronomical portion of the south Indian cosmography described in the previous articles. Not only are Indian temples repositories for astronomical paintings and sculpture, but in some instances the temple itself may be regarded as an astronomical artifact. Although a number of so-called astronomical temples are known to exist in India, which in various ways provide architectural reflections of a portion of the heavens, regrettably their analysis is beyond the scope of this study.

Nevertheless, such instruments had been in use in India, mainly by Muslims, for centuries before the creation of most of the Hindu artifacts to which author have focused a bit more attention to the topic. Despite opposition from some Brahman astronomers, however, Hindus did ultimately begin to construct and utilize astrolabes and celestial globes to some extent; but those instruments differed from their Islamic counterparts in little more than script and nomenclature. Author does not mean to suggest, of course, that astronomical instruments were of no concern to Indians before the advent of the Muslims, but they were of relatively little importance and their nature is not well known despite references to them in numerous surviving texts. Space precludes discussing them further. The earliest-known reference to an Indian observatory relates to one that apparently existed in what is now Kerala about A.D. 860. Its existence is implied by a commentary by Sankaranarayana text known as the Laghubhaskariyavivarana. Author does quote the translation in full:

(To the King): Oh Ravivarmadeva, now deign to tell us quickly, reading off from the armillary sphere installed (at the observatory) in Mahodayapura, duly fitted with all the relevant circles and with the Sign (-degree-minute) markings, the time of the rising point of the ecliptic (lagna) when the Sun is at 10° in the Sign of Capricorn, and also when the Sun is at the end of the Sign Libra, which I have noted. Then again-Oh, Ravi, deign to tell us immediately, reading off from the armillary sphere, by means of the reverse vilagna method, the time for offering the daily oblations, when the Sun, shrouded under thick clouds, is 10° in the Sign Leo and also when it is the middle (i.e. 15°) in the Sign Sagittarius.

But this quotation, if taken as proof that an observatory did indeed exist, may be no more than the exception that proves the rule in regard to observational astronomy; for we know of no additional Indian citation of a Hindu observatory until 1866, when, in his work Manamandira, Bapudeva refers to the observatory constructed in Varanasi, approximately a century and a half earlier, by the celebrated polymath Raja Sawai Jai Singh II, whose astronomical achievements we shall now consider. Numerous studies have been written about Sawai Jai Singh (1686-1743) and his diversified scientific endeavors. For details about the physical characteristics of the four of his five observatories that have survived into the twentieth century, Kaye, despite being somewhat dated, remains an indispensable source, as is Blanpied’s admirable critical historiographic analysis. Given these and other works, many of them illustrated, it will not be necessary to touch on more than a few highlights to establish Jai Singh’s place in the history of celestial mapping in South Asia. Nominally a vassal of the Mughal emperor, and governor at times of the Mughal provinces of Agra and Malwa, Jai Singh was in effect a powerful and independent monarch in his own right. His mathematical and scientific bent became evident at a very early age, and his lifelong quest for knowledge, especially in astronomy and mathematics, was not constrained by barriers of culture. “Thus, although [he] was a Hindu who… subscribed publicly to Hindu cosmology, his emphasis on observational rather than on calculational astronomy, as well as a number of textual references, suggest that his observational program was influenced more by Islamic than by Hindu astronomy.”

Over the period from about 1722 to 1739, drawing upon his considerable influence and wealth, he supervised the construction and staffing of observatories at the Mughal capital of Delhi; his own new capital, Jaipur; Varanasi; Ujjain; and Mathura. The precise dates of construction of none of these are known, but there seems little doubt that the so-called Jantar Mantar (a corruption of yantra and mantra) in Delhi was first and Jaipur second. Of the five, that of Mathura is a total ruin and the one at Ujjain is in serious disrepair. The remaining three have undergone varying degrees of restoration. Jai Singh modeled his observatories largely on the one constructed in Samarkand in 1428 by his great Timurid predecessor Ulugh Beg, but the instruments installed in them, mainly masonry constructions, were hardly limited to those used in the fifteenth century. In fact, some of the most accurate and ingenious of the instruments were of Jai Singh’s own design. The massive scale of many of Jai Singh’s instruments is attributable to his conviction that small instruments could not possibly yield satisfactory accuracy. In the preface to his Zij-i Muhammad Shahi (New tables of Muhammad Shah [named for the then ruling Mughal emperor; hereafter referred to as the Zij]), Jai Singh expresses himself (writing in the third person) on this and related points as follows:

But finding that brass instruments did not come up to the ideas which he had formed of accuracy, because of the smallness of their size, the want of division into minutes, the shaking and wearing of their axes, the displacement of the centres of the circles, and the shifting of the planes of the instruments: he [Jai Singh] concluded that the reason why the determinations of the ancients, such as HIPPARCHUS and PTOLEMY proved inaccurate, must have been of this kind; therefore he constructed in … Shah-Jehanabad [Delhi], which is the seat of empire and prosperity, instruments of his own invention, such as Jey-pergas [Light of Jai, a hemispheric dial, to be explained below] and Ramjunter [a circular instrument for measuring altitudes and azimuths] and Semrat-junter [Emperor of Instruments, an equinoctial sundial, Jai Singh’s chief instrument], the semi-diameter of which is of eighteen cubits, and one minute on it is a barley-corn and a half; of stone and lime, of perfect stability, with attention to the rules of geometry, and adjustment to the meridian, and to the latitude of the place, and with care in the measuring and fixing of them: so that the inaccuracies, from the shaking of the circles, and the wearing of their axes, and displacement of their centres, and the inequality of the minutes, might be corrected. Thus, an accurate method of constructing an observatory was established; and the difference which had existed between the computed and observed places of the fixed stars and planets, by means of observing their mean motions and aberrations with such instruments, was removed.

A point of this account that warrants particular note is that Jai Singh was most concerned with providing stability for his instruments. It is therefore hardly surprising that in four of his five observatories he had the ground leveled and carefully prepared for the instruments to be placed there. Only Varanasi, where the observatory was built on the roof of a palace built by Jai Singh’s grandfather, Man Singh, was an exception. Although this proves nothing, it does lend circumstantial support to Gurjar’s conjecture that this relatively small observatory was simply added onto another of even more modest proportions that was already in existence there. Since the Jaipur observatory contains a wider array of extant instruments than any of the others, author provides in figure 2 a copy of the plan of it.

Figure 2: Plan of the Jaipur Observatory
Figure 2: Plan of the Jaipur Observatory

[About Figure 2: Built by Maharaja Sawai Jai Singh II of Jaipur between 1728 and 1739, this observatory, the largest of five he constructed, contained numerous massive fixed masonry astronomical instruments as well as other smaller mobile metal instruments. Most of the former survive and are shown in this diagram. After George Rusby Kaye, The Astronomical Observatories of Jai Singh (Calcutta: Superintendent Government Printing, India, 1918; reprinted Varanasi: Indological Book House, 1973)]

Space precludes discussing these instruments in more detail, but a simple inventory will convey the sense of their diversity and of the uses they were put to. Author list’s them below in the order in which they are discussed by Kaye:

  •  Samrat Yantra, the largest instrument ever constructed by Jai Singh. It is an equinoctial dial consisting of a triangular gnomon, oriented along the local meridian, its hypotenuse is parallel to the earth’s surface, with two attached quadrants. It measures nearly 90 feet high and 147 feet long, and its quadrants have radii of 49 feet, 10 inches. Though it is graduated to read to seconds, “this is impossible in practice, owing to the ill-defined shadow (due to the size of the penumbra).
  • Sastamsa Yantra, a sextant with a convex arc of 60° and 28 feet, 4 inches in radius. Two pairs of such arcs are built into the masonry at the eastern and western ends of the Samrat Yantra.
  • Rasivalaya Yantra, an ecliptic instrument consisting of a collection of twelve dials on a platform, one for each sign of the zodiac, each of the same design as the Samrat Yantra, but with quadrants in the plane of the ecliptic when that sign is on the horizon and not on the plane of the equator.
  • Jai Prakasa, a pair of hemispheric dials, 17 feet, 10 inches in diameter (fig. 16.21); their use will be explained in some detail below.
  • Kapali, a smaller pair of hemispheric dials, 11 feet, 4 inches in diameter, one with the plane of its upper edge representing the horizon, the other with that plane representing the solstitial colure. This instrument is found only in Jaipur.
  • Rama Yantra, a cylindrical astrolabe employing an orthographic projection with a pillar at its center and a floor and walls graduated for altitude and azimuth observations. The four such instruments at Jaipur (not all of which appear on Kaye’s plan) were actually built long after Jai Singh’s death, but according to the same general specifications as larger instruments of the same type that he had constructed in Delhi. The larger of two pairs have diameters of 23 feet, 11 inches.
  •  Digamsa Yantra, a simple azimuth instrument consisting of a pillar and two surrounding circular walls, a lower inner wall of the same height as the pillar (about 4 feet), on which an observer can walk, and an outer wall twice the height of the former over which the observer with a movable sighting string can look. In effect, this is a circular protractor.
  • Nari Valaya Yantra, a masonry cylinder about 10 feet in diameter with a horizontal axis in the plane of the meridian and parallel dial faces in the plane of the equator. The dials are graduated into ghatis (one-sixtieth of a day, i.e., twenty-four minutes) and palas (one-sixtieth of a ghati).
  • Dakshinavrtti Yantra, a simple mural instrument used for taking meridian altitudes. On its east face are two intersecting quadrants 20 feet in radius and on the west a semicircle of 19 feet, 10 inches.
  •  Yantra Raja, two large, fixed metal single-disk astrolabes, 7 feet in diameter, one made of about sixty sheets of iron riveted together, the other of brass. It is likely that Jai Singh brought these from Delhi to Jaipur.
  • Unnatamsa Yantra, a graduated brass circle, 17 feet, 6 inches in diameter, suspended so as to revolve about a vertical axis and used to measure altitude. This was possibly of Jai Singh’s own design.
  • Chakra Yantra, an equatorial, of which there are two identical examples at Jaipur. Each consists of a metal disk, 6 feet in diameter, fixed so as to revolve about an axis parallel to that of the earth, with a separate graduated hour circle at the southern end of the axis and a pointer on the axis to indicate the hour angle, and with an index  and a sighter on the main circle.
  • Krantivrtti Yantra, an instrument of rather limited accuracy used to measure celestial latitude and longitude, consisting of two brass circles, pivoted so that one moves in the equatorial plane and the other in the plane of the ecliptic. Though the one now at Jaipur is quite modem, masonry work still exists to support a much larger instrument of the same type, presumably from Jai Singh’s time. Among the instruments cited above, the Jai Prakasa (figs. 3 and 4) “is perhaps the most ingenious and original of Jai Singh’s inventions.” Hence author quote’s in full Blanpied’s description of it:
Figure 3: Jai Prakash Light of victory
Figure 3: Jai Prakash Light of victory
Figure 4: Schematic Diagram of Jai Prakasha
Figure 4: Schematic Diagram of Jai Prakasha

[About Figure 3: This astronomical instrument, designed by Maharaja Sawai Jai Singh II and constructed by him at the Jantar Mantar observatory in Jaipur, was used to determine the stellar coordinates of celestial bodies. It comprises two sunken concave hemispheres onto whose complementary surfaces lines of sight from the observed bodies could be projected. Other instruments appear in the background. Photograph courtesy of Robert Harding Picture Library, London.]

[About Figure 4: This diagram shows how the Jai Prakasa were used to fix the position of the North Pole and the stellar coordinates of an observed heavenly body. After William A. Blanpied, “The Astronomical Program of Raja Sawai Jai Singh II and Its Historical Context,” Japanese Studies in the History of Science, no. 13 (1974): 87-126, esp. fig. 2 (p.99).]

Each instrument consists of a pair of hemispherical bowls which, at the Delhi observatory, are about 4.2 meters in radius. The surfaces of these bowls are inscribed with the celestial coordinates and oriented such that the positions of celestial objects can be mapped directly onto them [fig. 4]. Two straight wires in the horizontal plane, one oriented north and south and one east and west, intersect at what would be the center of the complete sphere. In essence celestial bodies are mapped onto the concave hemisphere by an observer inside the bowl who sights them through the intersection point. For example, the straight line which passes through this point and is inclined at the latitude angle A. to the horizontal defines a line of sight to the north celestial pole. Therefore, the pole of the instrument is inscribed at the intersection of that line with the concrete surface. Likewise, the plane perpendicular to the aforementioned line which passes through the east-west wire is parallel to the earth’s equator and would, if extended, intersect the celestial equator. A great circle is inscribed on the masonry surface at its intersection with this plane, and defines the instrument’s equator. Circles of celestial longitude and azimuth were inscribed on the instrument by following an analogous set of prescriptions. In practice, nighttime measurements seem to have been made by fixing one end of a taut string to the intersection of two horizontal wires. The observer stood at the bottom of the concave bowl and moved about until by fixing the free end of the string he could sight the particular star or planet along it. The intersection of the string and the coordinates inscribed on the hemisphere then gave the celestial coordinates of the planet or star. In order to facilitate such measurements, passages with stairways were cut into the hemispherical bowls. These enabled the observer to move around easily and to stand at a lower level than the graduated surface. For this reason each Jai Prakash consists of two complementary hemispheres. Positions of the access passages on one are positions of gradations on the other, and vice versa.

Daytime measurements could be made simply and directly with the Jai Prakash. Since the parallel rays of the sun are equivalent to lines of sight, the shadow cast upon the concave hemisphere by the intersection of the two horizontal wires falls upon the inscribed lines defining its celestial coordinates. Additional circles of zodiacal signs were inscribed on the surface in such a way that the particular circle on which the shadow of the intersection point falls determines the sign which is then on the meridian.

The impressive scale of some of the instruments of Jai Singh described above is evident in figure 3, which shows a portion of the Jaipur observatory complex popularly known as the Jantar Mantar. That the accuracy of the data obtained from Jai Singh’s observatories far surpassed that of any of his Indian predecessors’ cannot be doubted. The Samrat Yantra, for example, “could be used by a skilled observer to read solar time to a precision of 15 seconds, … [and] also should have been capable of yielding the solar altitude to within 2 minutes of arc … [and] the Jai Prakash and the Ram Yantra seem also to have been capable of precision of about this order.” How the data yielded by these and other instruments compared with the data of contemporaneous European astronomy is debatable, however. Before Mercier’s recent translation of the Persian tables forming the body of Jai Singh’s Zij, evidently compiled over about 1730-38, commentators on the subject based their judgments mainly on the observations made by various European assessments of the instruments employed and on Jai Singh’s criticisms of the findings of the astronomical tables of Philippe de La Hire, transmitted to him in 1730 by the Portuguese Jesuit missionary Emmanuel de Figuerda. Jai Singh professed, for example, to have found an error of half a degree in La Hire’s assignment of the place of the moon, and for this and other reasons he implied in the preface to the Zij that he had nothing to learn from the astronomy of Europe. Nevertheless, he remained in contact with European missionary and lay astronomers, either by correspondence or by direct discussion with those resident in Jaipur, especially the French Jesuits Claude Boudier and Pierre Pons, who journeyed all the way from Chandernagore in 1734 at the raja’s invitation.IDS Since Mercier’s study of the Zif; is the most thorough and recent available, it is in order that I quote here, virtually in its entirety, the abstract of that work:

The [tables of the] Zij-i-Muhammad Shahi . .. are usually represented as embodying the observational work done at the observatories of Delhi and Jaipur, under the direction of Jai Singh and [his chief astronomer] Jagannatha. In this paper these Persian tables are analysed thoroughly, and their various components are identified with earlier sources. In fact no new observational results are to be found apart from a new determination of the obliquity. Instead, the tables of the Sun, Moon, and Planets are all identical with those of La Hire (1727), apart from a mere change of meridian from Paris to Delhi. There are worked examples for the time of a solar eclipse of A.D. 1734 May 3, which was total in central India. The tables and text of Book II on basic spherical astronomy are taken without alteration from the Zij of Ulugh Beg, except that those functions which depend on the obliquity have been recalculated. The star table is taken from Ulugh Beg. The long geographical table includes those of Ulugh Beg and La Hire, as well as some 240 sites (many in India) from unidentified sources. The Vrttasastamsa of Delhi and Jaipur is a sextant totally enclosed by walls in which the Sun’s image is formed as in a camera obscura. It is certainly the only instrument in those observatories susceptible of real accuracy, and it was used in determining the obliquity and the latitude. A number of accounts of its design and use are given, including those of Jagannatha and the Jesuits.

Assuming that Mercier’s conclusions are correct, we must ask ourselves when and how Jai Singh decided, despite the claims he made for the accuracy of his own instruments, to copy so many not only of the findings of La Hire, but also of those made in the fifteenth century by Ulugh Beg. One possible explanation is that the preface to the Zij; was written before a sufficient body of data had been amassed to establish the tables included there, and in the anticipation that those data would embody a degree of accuracy that they failed to realize. The instruments employed may well have been capable of achieving the sought-for level of accuracy, but the observers using them may have been deficient in their concern for careful measurement, thereby confounding Jai Singh’s hopes and expectations.  Author know of no written source that might throw additional light on this line of speculation. A related issue is Jai Singh’s failure to make use of the telescope, of which he almost certainly had knowledge. “Perhaps,” suggests Blanpied, one of the Jesuit missions to Jaipur did convince him that the new European observational techniques had already made even the grandest naked eye instruments obsolete, and convinced him of that fact after seven years of labor with his great instruments at Delhi, instruments erected a bare five kilometers from the throne of the Moghul emperor who had allegedly commissioned them. In that case the most intrepid of scholars might well have become discouraged with the observational program he had devised.

No One may also wonder why there is no mention in the Zij of the dynamics of planetary motion and why Jai Singh seemingly displayed little or no interest in the Copernican heliocentric conception of the solar system, though he appears to have been informed of it. One intriguing possibility is that Jai Singh may also have learned from the Jesuits of the havoc being caused in Europe by the Copernican revolution and that he may therefore have decided to suppress the idea in India even though he may have been personally convinced of the correctness of Copernican views in regard to heliocentricity and the elliptical orbits of the planets. What, we may ask in conclusion, were Jai Singh’s underlying motives in carrying out his ambitious astronomical program? Apart from the intellectual curiosity for which he was justifiably acclaimed, one primary object, one can argue, “was to provide solar data on which to base a reformed calendar” to replace the centuries- old Hindu sidereal calendar based on the Suryasiddhanta. This is in keeping with the fact that Jai Singh lavished much greater care on the task of improving the Samrat Yantra, which was primarily used for solar observations, than he devoted to his other instruments. One can only speculate on the course Indian astronomy might have taken had the intrusion of European power been delayed by one or more generations. Although Jai Singh failed to achieve all his ambitious astronomical goals and seems not to have even attempted to establish a new school of astronomy, his astronomical tables, whatever their ultimate sources may have been, were used in northern India throughout the eighteenth century and were then considered among the best available. And the grandeur of his astronomical conceptions, whatever the shortcomings in their realization, command admiration and set him apart from his less scientifically minded Indian contemporaries.

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