The Sūrya-siddhānta and the Pañcasiddhāntikā

By David Reigle on May 15, 2012 at 6:09 am

The Sūrya-siddhānta is by far the most widely used Sanskrit text on astronomy. It has been held in great esteem in India. Its opening verses say that an incarnation of the sun taught it to the great asura named Maya at the end of the last kṛta-yuga, or age of perfection. According to the information given in its first chapter on the lengths of the yugas and how many of these ages have passed in this kalpa or world-period, this would have been more than two million years ago. If so, the Sūrya-siddhānta has undergone a lot of change since then. Based solely on what can be seen in the last 1,500 years, material has been deleted from it, material has been added to it, and its arrangement has frequently been altered.

Six verses from the Sūrya-siddhānta that are not found in the now available version (as published with the commentary by Raṅganātha) were quoted by Bhaṭṭotpala in his commentary on Varāha-mihira’s Bṛhat-saṃhitā, chapters 4 and 5. This was first pointed out by Shankar Balakrishna Dikshit in his 1896 Marathi language book, Bharatiya Jyotish Sastra (English translation, vol. 2, 1981, pp. 38-39), where these six verses are quoted and translated. Then, a block of verses after chapter 2, verse 14, of the Sūrya-siddhānta gives the same series of numbers for trigonometry sines that the Āryabhaṭīya gives, and so on. They interrupt an older theory, which resumes in verse 52. Prabodh Chandra Sengupta, who pointed this out in his new Introduction to the 1935 Calcutta reprint of the 1860 Ebenezer Burgess translation (p. xix), therefore thinks that this material was copied from the Āryabhaṭīya and interpolated into the Sūrya-siddhānta. Raṅganātha in his commentary on the Sūrya-siddhānta, completed in 1603 C.E., had centuries earlier pointed out interpolated verses (see Dikshit, op. cit., p. 43). Bimalā Prasāda Siddhānta Sarasvatī’s 1894 or 1896 edition of the Sūrya-siddhānta in Bengali script has twenty-one additional verses in chapter 14 between verses 23 and 24 (see Sengupta, op. cit., p. xxx). David Pingree, who has catalogued all known Sanskrit astronomy manuscripts (Census of the Exact Sciences in Sanskrit, Series A, 5 vols., 1970-1994, unfinished), tells us about the Sūrya-siddhānta that: “Virtually every commentator, however, has rearranged the text, adding and subtracting verses ad libitum” (David Pingree, Jyotiḥśāstra: Astral and Mathematical Literature, 1981, p. 23).

What has shown convincingly that we do not have the original Sūrya-siddhānta intact, and that even its astronomical constants have been somewhat altered, was the publication in 1889 of the Pañcasiddhāntikā by Varāha-mihira (circa 550 C.E.). As its name implies, the Pañca-siddhāntikā is a summary of five (pañca) astronomical treatises (siddhānta), all very old, including the Sūrya-siddhānta. While the summary given in the Pañcasiddhāntikā of the Sūrya-siddhānta shows “that the treatise of that name known to Varāha Mihira agreed with the modern Sūrya Siddhānta in its fundamental features,” yet “we cannot fail to notice that in certain points the teaching of the old Sūrya Siddhānta must have differed from the correspondent doctrines of its modern representative” (G. Thibaut and Sudhākara Dvivedī, The Pañchasiddhāntikā, 1889, reprint 1968, p. xii; on this see pp. xii-xx). These differences appear in the astronomical constants given for the various planets, etc., and the calculations made from them. The astronomical constants found in the older Sūrya-siddhānta as summarized in the Pañcasiddhāntikā differ somewhat from those given in the now extant Sūrya-siddhānta.

The Pañcasiddhāntikā is a karaṇa text, as opposed to a siddhānta text, such as the Sūrya-siddhānta. While a siddhānta gives the full astronomical theory, a karaṇa is a more brief manual for practical use, giving only what is required for making calculations from the latest astronomical epoch in use. Based on this fact, Sudhi Kant Bharadwaj attempted to show that the differences in astronomical constants between the old and the modern Sūrya-siddhānta are due only to the brief karaṇa version abbreviating the numbers given in the full siddhānta version (Sūryasiddhānta: An Astro-Linguistic Study, 1991, pp. 24-33). Thibaut had considered this possibility, and gave reasons for rejecting it in his 1889 “Introduction” (op. cit., pp. xii-xx). Prabodh Chandra Sengupta in his 1935 “Introduction” tabulated the differences between the astronomical constants given in the two versions (op. cit., pp. ix-xii). He showed that the astronomical constants given in the old Sūrya-siddhānta mostly agree with those given in Brahmagupta’s Khaṇḍa-khādyaka (first Sanskrit edition published in 1925). Sengupta showed in a 1930 paper (“Aryabhata’s Lost Work”) that the astronomical constants found in the Khaṇḍa-khādyaka were taken from a lost work by Āryabhaṭa I, author of the Āryabhaṭīya. After the discovery of the Mahābhāskarīya (announced in Bibhutibhusan Datta’s 1930 article, “The Two Bhāskaras”), it was found that these same astronomical constants taken from a lost work by Āryabhaṭa I are preserved in the Mahābhāskarīya, chapter 7 (first Sanskrit edition published in 1945). The agreement with this old set of astronomical constants has convinced most researchers that the astronomical constants given in the old Sūrya-siddhānta accord with a specific system, and are not mere abbreviations of those given in the now extant Sūrya-siddhānta.

In addition to this, Sengupta then described differences in the methods of calculation used in the two versions of the Sūrya-siddhānta (pp. xx-xxvi). He showed that methods used in the modern Sūrya-siddhānta agree with methods used by Āryabhaṭa I and Brahmagupta. This means that someone after the time of Varāha-mihira’s summary of the old Sūrya-siddhānta in the Pañcasiddhāntikā introduced these methods into the Sūrya-siddhānta that we now have. Not only was the modern Sūrya-siddhānta revised by someone, Sengupta believed that Varāha-mihira revised the previous Sūrya-siddhānta. So even the old Sūrya-siddhānta as summarized in the Pañcasiddhāntikā is a revision of a yet older Sūrya-siddhānta. Bina Chatterjee, in her 1970 Sanskrit edition and English translation of Brahmagupta’s Khaṇḍakhādyaka, agreed with Sengupta, and provided further evidence for this, with further charts of comparison (vol. 1, pp. 279-285). Kripa Shankar Shukla did not agree with Sengupta on this particular point, but he agreed that not only the astronomical constants but also the methods vary between the two versions of the Sūrya-siddhānta. He gave another helpful set of charts comparing the two versions, adding variants from the modern version as preserved in two different sets of commentaries, in his English introduction to his 1957 Sanskrit edition of The Sūrya-siddhānta with the Commentary of Paramesvara (pp. 15-27).

The Pañcasiddhāntikā, our sole source on the old version of the Sūrya-siddhānta, was itself long lost. It was recovered from two very faulty manuscripts in the 1889 Sanskrit edition and English translation by G. Thibaut and Sudhākara Dvivedī. So the Sanskrit text as found in the best of these two manuscripts was given alongside a heavily emended text. The extensive and sometimes extreme emendations were justified by the need to make sense of an otherwise partly incomprehensible text. Eighty years later, a new attempt to make sense of this text was made by O. Neugebauer and D. Pingree in their Sanskrit edition and English translation (The Pañcasiddhāntikā of Varāhamihira, 2 vols., 1970, 1971). The few additional manuscripts discovered since the first two were copies of the same faulty exemplars. From these highly respected scholars we expected to get as careful and accurate an edition as could be made from the available materials. But as said about the Neugebauer-Pingree edition by K. V. Sarma in his “Introduction” to yet a third Sanskrit edition and English translation: “Often the emendations are wilder than those of Thibaut-Sudhakar Dvivedi” (Pañcasiddhāntikā of Varāhamihira, trans. by T. S. Kuppanna Sastry, ed. by K. V. Sarma, 1993, p. xviii).

A prime example of the wild and unwarranted emendations to the Pañcasiddhāntikā is its often-quoted verse 4 of chapter 1. Thibaut and Sudhākara Dvivedī emended the word tithi (or tithaḥ) to kṛtaḥ and translated: “The Siddhānta made by Pauliśa is accurate, near to it stands the Siddhānta proclaimed by Romaka; more accurate is the Sāvitra (Saura); the two remaining ones are far from the truth.” Neugebauer and Pingree emended the word tithi (or tithaḥ) to stvatha and translated: “The Pauliśa is accurate; that which was pronounced by Romaka is near it; the Sāvitra (i.e. the Sūryasiddhānta) is more accurate; the remaining two have strayed far away (from the truth).” Thus, through this often-quoted verse, everyone was led to believe that the accuracy of the Paitāmaha-siddhānta and the Vāsiṣṭha-siddhānta was disparaged by Varāha-mihira. But Kuppanna Sastry and Sarma did not emend the word tithi, and translated: “The tithi resulting from the Pauliśa is tolerably accurate and that of the Romaka approximate to that. The tithi of the Saura is very accurate. But that of the remaining two (viz. the Vāsiṣṭha and the Paitāmaha) have slipped far away (from the real).” In other words, it was only the accuracy of their calculation of the tithi or lunar day that was disparaged, not their overall accuracy. Thus, anyone using the Pañcasiddhāntikā today should use only the Kuppanna Sastry-Sarma edition/translation, because the remaining two, the Thibaut-Sudhākara Dvivedī and the Neugebauer-Pingree editions/translations, have strayed far away from the truth.

For the extant Sūrya-siddhānta, only three different English translations have been published so far. All of these are more than a century old. The first of these was made by Rev. Ebenezer Burgess, revised by William Dwight Whitney, and published in 1860. The second of these was made by Bāpū Deva Śāstrī independently of the Burgess translation, and published in 1861. The third of these was made by Bimalā Prasāda Siddhānta Sarasvatī from Sanskrit to Bengali and published in 1894 or 1896, and then translated from Bengali to English and published in 2007. All three translations utilized the commentary by Raṅganātha to interpret the verses of the Sūrya-siddhānta. The Burgess translation was reprinted in Calcutta in 1935, edited by Phanindralal Gangooly. This was again reprinted in India more recently, and is sometimes listed under the name of the editor, even though it is the translation by Burgess. A 2001 book, The Sūryasiddhānta (The Astronomical Principles of the Text), by A. K. Chakravarty, includes a rearranged translation. It has adopted the translation by Burgess.

Sometimes students are inclined to distrust a translation of a Sanskrit text by a Christian missionary, and to trust a translation made by an Indian pandit. The present case, however, is a little different. My impression is that all three translations are good, but the Burgess/Whitney translation is more literally accurate in comparison with the Sanskrit than the other two. Bāpū Deva Śāstrī used a somewhat interpretive style of translation, as was common at that time. The translation by Bimalā Prasāda Siddhānta Sarasvatī is a translation of a translation, so for that reason alone it is less literally accurate in comparison with the Sanskrit. This does not mean, in either case, that their translations are inaccurate. It means that for someone trying to follow the Sanskrit, the Burgess/Whitney translation will be more helpful. The Burgess/Whitney translation also provides extensive notes and examples of calculations, while the other two translations do not.

An example of the difference between the three translations may be seen in chap. 1, verse 3, stating what the asura Maya asked the sun about. He wanted to know the jyotiṣāṃ gati-kāraṇam, the cause (kāraṇam) of the motion (gati) of the heavenly bodies (jyotiṣām). The Burgess/Whitney translation is literally accurate, adding only “namely” to this phrase; thus Maya is “desirous to know . . . the cause, namely, of the motion of the heavenly bodies.” In the Bāpū Deva Śāstrī translation, this phrase is interpreted, and becomes simply “Astronomy”; that is, Maya is “desirous of obtaining . . . knowledge of Astronomy.” In the Bimalā Prasāda Siddhānta Sarasvatī translation of a translation, “cause” becomes transformed into “information”; thus what Maya desires to acquire is knowledge that is complete with “the information about the motion of the heavenly bodies.” The latter two translations give the general idea accurately enough, but the Burgess/Whitney translation gives the exact idea.

Rev. Ebenezer Burgess went to India as a missionary in 1839. He diligently applied himself to the study of Indian astronomy and its primary text, the Sūrya-siddhānta, throughout his years in India, in order to produce a textbook on astronomy in the Marathi language. He writes in his “Introductory Note” to the translation of the Sūrya-siddhānta that: “My first rough draft of the translation and notes was made while I was still in India, with the aid of Brahmans who were familiar with the Sanskrit and well versed in Hindu astronomical science.” When he returned to the United States, he turned it over to William Dwight Whitney, a brilliant linguist and competent Sanskrit scholar. Whitney’s touch is evident throughout, in two ways. First, he made the translation follow the Sanskrit closely; that is, he made it literally accurate. Only few errors have been noted by later scholars and pandits. Second, sharing the prejudices of his time, he made comments in the notes showing the superiority of Western knowledge and the inferiority of Indian knowledge. These did not, however, affect the translation.

The translation by Burgess/Whitney was highly enough regarded in India that it was reprinted by the University of Calcutta in 1935. The “Note” that introduces this reprint says: “Owing to the time, thought and patient diligence that he and his colleagues devoted to the task, this translation stands out as a model of research work in the field of Hindu astronomy.” This reprint included a new 45-page Introduction by eminent Indian scholar of Hindu astronomy, Prabodh Chandra Sengupta. Sengupta there concludes (p. li): “Burgess’s translation, indeed, gives a very clear and complete exposition and discussion of every rule that it contains together with illustrations also.” Moreover, Sengupta adds that “his views about the originality of Hindu astronomy are the sanest.” Sengupta is referring to Burgess’s view that the astronomy of the Sūrya-siddhānta was original to India (see “Concluding Note by the Translator”), in disagreement with Whitney, who thought that astronomy came to India from Greece. The Burgess/Whitney translation was originally published in the Journal of the American Oriental Society, vol. 6, 1860, pp. 141-498. This is now available from JSTOR, as part of their free “Early Journal Content” offering, at: It had been reprinted in 1978 by Wizards Bookshelf in the Secret Doctrine Reference Series.

The Sanskrit text of the Sūrya-siddhānta was first published, along with the commentary by Raṅganātha, in 1859 in the Bibliotheca Indica series, Calcutta. It was edited by Fitzedward Hall, known for his care and accuracy, just as Indian printing is known for its many typographical errors. This resulted in a long list of errata given at the back of this book, something done by Hall but skipped by many others. The Sūrya-siddhānta with the commentary by Raṅganātha was again printed in Calcutta in 1871, with no editor statement. It appears by its format to be a re-typeset reprint of Hall’s edition. The Sūrya-siddhānta with the commentary by Raṅganātha was once again printed in Calcutta in 1891, edited by Jībānanda Vidyāsāgara. This says dvitīya-saṃskaraṇam, “second edition,” allowing us to think that perhaps he was responsible for the 1871 edition as well.

The Sūrya-siddhānta with a modern Sanskrit commentary by Sudhākara Dvivedī was published in Calcutta in 1911 in the Bibliotheca Indica series. The Sūrya-siddhānta with a modern Sanskrit commentary by Kapileśwara Chaudhary was published in Varanasi in 1946 in the Kashi Sanskrit Series. The Sūrya-siddhānta with the traditional Sanskrit commentary by Parameśvara, edited by Kripa Shankar Shukla, was published in 1957 by the University of Lucknow. The Sūrya-siddhānta with the traditional Sanskrit commentary by Kamalākara Bhaṭṭa, edited by Śrīcandra Pāṇḍeya, was published in 1991 by the Sampurnanand Sanskrit University. There are a few other Sanskrit editions of the Sūrya-siddhānta, apparently secondary or derivative, that I have not seen.

The Sanskrit text of the Sūrya-siddhānta is included in the 2007 English translation of Bimalā Prasāda Siddhānta Sarasvatī, but in Bengali script rather than devanāgarī, and also in Roman script (but with so many errors that it cannot be relied on). The Sanskrit text of the Sūrya-siddhānta in Roman script is also included as an appendix in A. K. Chakravarty’s 2001 book, The Sūryasiddhānta (The Astronomical Principles of the Text). Several of these Sanskrit editions and English translations are now available at the Digital Library of India.

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