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Jyotihshastra: Astral and Mathematical Literature c4.s6: Yantra

Jyotiḥśāstra: Astral and Mathematical Literature c4.s6

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English

Yantra

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The earliest observational instrument in use in India was the śaṅku or gnomon, employed to find the cardinal directions in the Śulbasūtras. Since the fourth century B.C. both the śaṅku and the nāḍikā or outflowing water-clock have been used (with linear zig-zag functions) to determine time within the solar year and within any period of daylight. More elaborate uses of the śaṅku as an instrument for measuring local time and terrestrial latitude are given in every siddhānta and karaṇa in the chapter on tripraśna; eventually the noon equinoctial shadow cast by the śaṅku was used to characterize the latitude of localities mentioned in late medieval geographical lists.²⁷²

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²⁷² SATIUS 73a–75b and SATE 53–55.

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Besides the simple śaṅku vertical to the plane of the horizon, Varāhamihira (PS 14)²⁷³ describes a hemispherical sun dial, a perforated ring, and a perforated sphere (in each of the last two instruments perforations 180° apart serve as a diopter). Other instruments mentioned in the siddhāntas are basically illustrative, or are elaborate toys; illustrative are the rotating wooden model of the celestial sphere mentioned by Āryabhaṭa (A. Gola 22–23) or the three-dimensional scale models of the Sines of the planets’ azimuths and altitudes described also by the same astronomer,²⁷⁴ while his clepsydras in fanciful shapes are examples of toys.²⁷⁵ Many later authors of siddhāntas describe these or similar instruments, sometimes in the middle of the text (e.g., MB 3, 56–50), but more often in separate chapters on yantras (e.g., BSS 22; ŚDV II 8; SŚŚ 19; and SŚB II 11). The most significant new instrument introduced in these texts composed before the introduction of the astrolabe into India seems to be the phalaka or board of Bhāskara (SŚB II, 16–27), which is basically a dial with a gnomon suspended vertically in the plane of the Sun’s altitude circle.

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²⁷³ See also Āryabhaṭa in K. S. SHUKLA in Gaṇita 18 (1967), 97–100, and in IJHS 12 (1977), 185.

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²⁷⁴ IJHS 12 (1977), 183–184.

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²⁷⁵ Gaṇita 18 (1967), 100–101, and IJHS 12 (1977), 185–186.

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The first text to describe the construction and use of the yantrarāja or astrolabe in Sanskrit was the Yantrarāja²⁷⁶ composed by Mahendra Sūri,²⁷⁷ a Jaina from Bhṛgupura, for Fīrūz Shāh in 1370. A commentary was composed by Mahendra’s pupil, Malayendu Sūri,²⁷⁸ in about 1382, and another, the Vilāsavatī, by Gopirāja²⁷⁹ in 1540. Mahendra has taken from an unidentified Arabic source not only the rules relating directly to the construction and use of the astrolabe (including a Ptolemaic star-catalogue adjusted for precession), but also a Sine table in which R = 3600 or 1, 0, 0 sexagesimally; a declination table in which ε = 23;35°; a list of cities (including a number in Islamic lands outside of India) with their latitudes expressed in degrees; and shadow tables for twelve and seven digit gnomons.

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²⁷⁶ Edited with the ṭīkā of Malayendu by S. DVIVEDIN and L. SARMA, Benares 1882, and by K. K. RAIKVA, Mumbayī 1936.

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²⁷⁷ CESS A 4.

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²⁷⁸ CESS A 4.

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²⁷⁹ CESS A 2, 133a–133b; cf. Gopinātha in CESS A 2, 132b.

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After Mahendra a number of other texts describing traditional Indian instruments were composed in Sanskrit, almost all of them in Gujarāt and Rājasthān, but the astrolabe was generally neglected. The earliest of these is the Yantraratnāvalī composed in about 1400 by Padmanābha, whom we have mentioned earlier as the author of a commentary of Brahmagupta’s Kh. The Yantraratnāvalī contains two chapters, each of which describes the construction and use of a single instrument. The first, on the diksādhana, is not available to me, but I have been able to consult a manuscript of the second, the dhruvabhramaṇa,²⁸⁰ on which Padmanābha himself wrote a commentary. This instrument appears to be an elaboration of Bhāskara’s phalaka, and is not derived from the Islamic tradition.

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²⁸⁰ BM Add. 14,365 l.

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A treatise describing a semicircular instrument also derived from the native Indian tradition is the Yantracintāmaṇi²⁸¹ composed by Cakradhara,²⁸² probably in the late fifteenth or early sixteenth century; Cakradhara himself wrote a commentary on this, as did also Rāma (Yantradīpikā) in 1625. In the same Indian tradition are the works on yantras composed in the sixteenth century by Gaṇeśa, the author of the GL, at Nandigrāma in Gujarāt; these are the Cābukayantra, of which no copy is available to me, and the Pratodayantra,²⁸³ which is a special form of Sun dial.

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²⁸¹ I have used BM Add. 14,365k and Bodleian Library, CS d. 751 (5) and d. 774 (3); I have not seen the editions with Cakradhara’s own vivṛti and Rāma’s Yantradīpikā by B. SARMAN, Benares 1883, nor that with Hindī and Saṃskṛta ṭīkās by S. SARMAN, Mathurā 1898.

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²⁸² CESS A 3, 36b—37b, and A 4.

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²⁸³ I have used ff. 15—16 of IO 1989.

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Interest in the astrolabe was reawakened in north India in the Mughal period. The Risālat al-uṣṭurlāb of the great thirteenth century Persian polymath, Naṣīr al-Dīn Muḥammad al-Ṭūsī,²⁸⁴ was translated into Sanskrit at some time during this period. In 1615 at Jambūsara in Gujarāt Viśrāma wrote a Yantracintāmaṇi²⁸⁵ in which he describes the astrolabe, the gnomon, the water-clock, the quadrant, and several other instruments. Incidentally, he presents several elements borrowed from Islamic astronomy in addition to the astrolabe: tables of the Sine and Cosine functions at intervals of 1° with R = 120; a declination table with ε = 23;35°; and the goal year periods of the planets.²⁸⁶

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²⁸⁴ CESS A 3, 145a, and A 4.

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²⁸⁵ Edited by K. K. RAIKVA on pp. 83—117 of his edition of Mahendra’s Yantrarāja.

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²⁸⁶ D. PINGREE in JHAS 2 (1978), 319—320.

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A more significant adaptation of Islamic instruments was that by Savāi Jayasiṃha in the 1720’s and 1730’s, the Mahārāja and founder of Jayapura whom we have previously mentioned as the author of a koṣṭhaka. His monumental stone observatories erected at Jayapura, Ujjayinī, Delhi, Mathurā, and Vārāṇasī in imitation of Ulugh Beg’s at Samarqand have often been described, though first by his learned paṇḍita, Jagannātha.²⁸⁷ He also wrote a prose treatise on the construction and use of the astrolabe, the Yantrarājaracanā;²⁸⁸ there is a versification of this, the Yantraprabhā²⁸⁹ of Śrīnātha. Though a number of Sanskrit astrolabes made in north India in the eighteenth and nineteenth centuries survive, the only other extant Sanskrit texts on instruments written after 1500 are the yantrādhyāyas of the SSJ (II 5), the SR (II 3), and the SSBM (II 2). The topic of the development of Indian astronomical instruments is one worthy of much fuller scholarly investigation than has hitherto been devoted to it.

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²⁸⁷ See his Yantrādhyāya in R. S. SHARMA’s edition of the Siddhāntasamrāṭ, vol. 2, pp. 1031–1048.

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²⁸⁸ Edited by KEDARNATH, “Śrīmanmahārājādhirājaśrījayasimhaviracitā Yantrarājakārikā,” The Pandit (Jaipur) 1, 1924, art. 2, with, as art. 3, the English translation published originally by A. H. GARRETT and C. GULERI in their The Jaipur Observatory and its Builder, Allahabad 1902; and edited with the Yantraprabhā of Śrīnātha by KEDARNATH, RPG 5, Jayapura 1953.

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²⁸⁹ Edited by KEDARNATH on pp. 17–19 of his edition of the Yantrarājaracanā.

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