Precession and Trepidation in Indian Astronomy before A.D. 1200

I have used the edition of both the Yājua (with Somākara Śeṣa's Bhāý) and the Ārca recensions, prepared by Sudhākara Dvivedin , The Pandit , NS xxix (1907, repr. Benares, 1907); and the edition by Shamasastry R. (Mysore, 1936). The standard article on precession and trepidation in India remains that written by Colebrooke H. T. a century and a half ago (“On the Notion of the Hindu Astronomers concerning the Precession of the Equinoxes and Motions of the Planets”, Asiatic researches , xii (1816), 209–50, reprinted in his Miscellaneous essays , ii (London, 1837), 374–416). This was used by Martin T.-H. , Mémoire sur celte question: La précession des équinoxes a-t-elle été connue des égyptiens ou de quelque autre peuple avant Hipparque? (Paris, 1869), 179–88; Martin is misunderstood by Duhem P. , Le système du monde , ii (Paris, 1914), 212–14 and 223–6. Later articles on the subject do not really advance our knowledge of the history of precession and trepidation in India; they represent a continuation of the misunderstanding of the implications of Vedic literature that, as this paper attempts to demonstrate, originated in about the fifth century a.d. Nonetheless, it may not be useless to mention the more significant of these: Mookerjee D. N. , “Notes on Indian Astronomy”, Journal of the Department of Letters, University of Calcutta , v (1921), 277–302; Ghatak J. , “The Conception of the Indian Astronomers Concerning the Precession of the Equinoxes”, Journal of the Asiatic Society of Bengal , NS xix (1923), 311–21; Das S. K. , “Precession and Libration of the Equinoxes in Hindu Astronomy”, Journal of the Asiatic Society of Bengal , NS xxiii (1927), 403–13; Krishnamurthy R. , “Precession or Ayanamsa”, The mathematics student , xiii (1945), 77–81; and Abhyankar K. V. , “The Precession of the Equinoxes and its Discovery in India”, Acharya Dhruva Smaraka Grantha (Ahmadabad, 1946), iii, 155–64.

I have used the edition of the Brhatsamhitā with the Vivrti of Utpala prepared by Sudhākara Dvivedin, Vizianagram Sanskrit series , xii (Benares, 1895–97).

It is to this zodiac, whose beginning lies in the vicinity of the star ζ Piscium, that I hereafter refer with the adjective “fixed”; in it the nakṣatras are equal arcs of 13;20° each. In the zodiac of the Vedāñgajyotiṣa the nakṣatras are also equal arcs of 13;20° each, but the initial point of the system is not known to us. In the Vedic texts the nakṣatras are individual stars or groups of stars whose identity is not certain. Much confusion is introduced into the history of Indian astronomy by reading all texts as though they refer to the fixed zodiac; the specific parameters used for the limits of trepidation in Indian astronomy also result from this misunderstanding on the part of Indian astronomers in the fifth and sixth centuries a.d.

I have used the edition of Neugebauer O. Pingree D. , Det Kongelige Danske Videnskabernes Selskab , Hist.-Filos. Skr., vi, 1 (Copenhagen, 1970).

Unfortunately still unpublished, though an edition is promised by Śukla K. S. of Lucknow. I cite this quotation from Kuppanna T. S. Sastri's edition of Bhāskara's Mahābhāskarīya , (with the Bhāý of Govindasvāmin and the Siddhāntadīpikā of Parameśvara), Madras Government oriental series , cxxx (Madras, 1957), p. XXVI.

Maṇindha is the prevalent South Indian orthography for Maịttha, which represents the Greek Manethōn. Maịttha's work was known to Varāhamihira, and so must have been written in the fourth or fifth century. The opinion is also ascribed to Maịttha by Nilakaṇtha (on Āryabhaīya , Kālakriyā 10; see below, ref. 17).

I have used transcripts of MS 3166 in the Mysore Government Oriental Library and of MS D 11498 in the Sarasvati Mahal Library in Tanjore.

This verse is not found in his Grahacāranibandhana edited by Sarma K. V. , Journal of oriental research, Madras , xxiii (1953/54, repr. Madras, 1954).

For this method see, for instance, Parameśvara (a.d. 1443) in his second Goladīpikā (4, 85–90), ed. Sarma K. V. , Brahmavidyā , xx (1956), 119–86 and xxi (1957), 87–144; repr. as Adyar library series Paper 32 (Madras, 1957).

For the possible connection see Dumbarton Oaks papers , xviii (1964), 138.

I have used the editions by Hall F.-E. Bāpū Deva Śāstrin with the Gūḥārthaprakāśaka of Rañganātha, Bibliotheca Indica , xxv (Calcutta, 1854–58); by Sudhākara Dvivedin , Bibliotheca Indica , clxxiii (Calcutta, 1910–11, repr. Calcutta, 1925); and by Ssukla K. S. (with the Vivaraṣa of Parameśvara) (Lucknow, 1957). An apparent misunderstanding of this passage is found in Bhāskara's Siddhāntaśiromaṣi (see ref. 27), and Sumatiharṣa (a.d. 1619) in his commentary on Bhāskara's Karạakutūhala (2, 17; see below, ref. 24), ignoring 3, 9c-d, interprets Sūryasiddhānta 3, 9a-b to refer to a trepidation over an arc 60° (30° on either side of Aries 0°) at a rate of 0;1° per year. One complete oscillation, then, takes 7200 years as it should, but the rate of precession is that of Govindasvāmin's second school. Sumatiharṣa ascribes this interpretation to a Lkā on the Sūryasiddhānta. See also below, ref. 25.

Both of these texts are Edited by Dvidevin V. P. , Jyautiṣasiddhāntasañgraha, Benares Sanskrit series , 2 fasc. (Benares, 1912).

I have used the edition of the Khaṇḍakhādyaka (with the Vāsanābhāý of Āmarāja) prepared by Babua Miśra (Calcutta, 1925).

The Uttarakhaṇḍakhādyaka is apparently by Brahmagupta himself. In his Brāhmasphuạsiddhānta (11, 54; I have used the edition of Sudhākara Dvivedin (Benares, 1902)), written in a.d. 628, he denies a motion of the solstices; see also Bhāskara's Vāsanābhāý (on Siddhāntaśiromaṣi, Golādhyāya 7, 17–18; see below, ref. 27). But the Uttarakhaṇḍakhādyaka was written almost 40 years later.

See below, ref. 24.

I have used the edition of Sudhākara Dvivedin , Benares Sanskrit series , cxlviii-cl, 3 fasc. (Benares, 1910), and the edition of the Pūrvagaịta by Sarma S. R. (2 vols., Marburg, 1966). Munīśvara (b. a.d. 1603) in his Marīcī on the Siddhāntaśiromaṣi (Golādhyāya 7, 17–19) refers to this Āryabhaṣa, not to the author of the Āryabhaīya as imagined by Colebrooke.

There is no mention of a motion of the equinoxes in the Āryabhaīya; I have used the editions of Kern H. (with the Bhaṣadīpikā of Parameśvara) (Leiden, 1874), and of Saāstrī Sāmbaśiva K. (1 and 2) and Pillai Kunjan Suranad (3) (with the Bhāý of Nīlakaṇṭha), Trivandrum Sanskrit series , ci, cx and clxxxv (3 vols., Trivandrum, 1930, 1931, and 1957).

See, e.g., the texts collected by Sarma K. V. in his edition of Haridatta's Grahacāranibandhana (see above, ref. 8), pp. V–VI.

I have used the edition of Śarman G. L. Śarman G. (Bambaī Saṣ. 2008, Śāka 1873 (a.d. 1951)).

I do not find this in Prthüdakasvāmin's Vivaraṣa, with the Khaṇḍakhādyaka by Sengupta P. C. (Calcutta, 1941); but only the beginning of his commentary on the Uttarakhaṇḍakhādyaka is preserved.

Apparently in his lost Brhanmānasa; it is quoted by the commentators on his extant Laghumānasa (1, 2), e.g., by Praśastadhara (a.d. 958) as quoted in Majumdar's edition, p. 5, and by Parameśvara, and was noted by al-Bīrünī ( India (ed. Hyderabad, 1958), 308; trans. Sachau E. C. (London, 1910), i, 366–7) as occurring in the Laghumānasa. For the Laghumānasa I have used the editions of Majumdar N. K. (Calcutta, 1951), and of Āpaṣe B. D. , Ānandāśrama Sanskrit series , cxxiii (Poona, 1952). For another opinion attributed to Muñjāla by Bhāskara see below, ref. 27.

Quoted by Babuāji Miśra in his edition of Śrīpati's Siddhāntaśekhara (2 vols., Calcutta, 1932–47), i, 12.

I have used the edition of Ṣikārāma Dhanañjaya (Benares, n.d.).

I have used the edition (with the Gaṣakakumudakaumudī of Sumatiharṣa) (Bambaī Sa. 1958, Śaka 1823 (a.d. 1901)).

Another possible interpretation would be: One should add 4217 to the lapsed years (since the epoch of the work) and divide (the result) by 61. One would then assume that the initial year of the Kaliyuga (—3101) was a year of coincidence, that the annual rate of trepidational motion is 0;1,1°, and that the limit of trepidation is 30° from fixed Aries 0° as in the case of Sumatiharṣa's interpretation of the Sūryasiddhānta (see above, ref. 11). Then the motion in 4217 years would be about 70°, so that the actual position of the vernal point relative to fixed Aries 0° would be —10°.

I have used MS Sanskrit 2769 of the India Office Library, London; see also the Pañcasiddhāntikā , i, 8.

I have used the edition of Dattātreya Āpaṣe (with Bhāskara's own Vāsanābhāý and Munīśvara's Marīcī), Ānandāśrama Sanskrit series , cxxii (2 vols., Poona, 1943–52).

See Munīśvara's Marīcī, ad loc. , and Colebrooke's summary thereof.