^ k THE INDIAN CALENDAR THE INDIAN CALENDAR WITH TABLES FOR THE CONVERSION OF HINDU AND MUHAMMADAN INTO A.D. DATES, AND VICE VERSA ROBERT SEWELL Late of Her Majesty's Indian Civil Service, SANKARA BALKRISHNA DIKSHIT Traitiing College, Poona. WITH TABLES OF ECLIPSES VISIBLE IN INDIA BY Dr. ROBERT SCHRAM Of Vienna. LONDON SWAN SONNENSCHEIN & Co., Ltd. Paternoster Square ^ENTlt.'X Printed al the Motley J^ess, Amsterdam. ; PREFACE. This Volume is designed for the use, not only of those engaged in the decypherment of Indian inscriptions and the compilation of Indian history, but also of Judicial Courts and Government Ofifices in India. Documents bearing dates prior to those given in any existing almanack are often produced before Courts of Justice as evidence of title ; and since forgeries, many of them of great antiquity, abound, it is necessary to have at hand means for testing and verifying the authenticity of these exhibits. Within the last ten years much light has been thrown on the subject of the Indian methods of time-reckoning by the pubHcations of Professor Jacobi, Dr. Schram, Professor Kielhorn, Dr. Fleet, Pandit Sahkara Balkrishna Dikshit, and others but these, having appeared only in scientific periodicals, are not readily accessible to officials in India. The Government of Madras, therefore, desiring to have a summary of the subject with Tables for ready reference, requested me to undertake the work. In process of time the scheme was widened, and in its present shape it embraces the whole of British India, receiving in that capacity the recognition of the Secretary of State for India. Besides containing a full explanation of the Indian chronological system, with the necessary tables, the volume is enriched by a set of Tables of Eclipses most kindly sent to me by Dr. Robert Schram of Vienna. In the earher stages of my labours I had the advantage of receiving much support and assistance from Dr. J. Burgess (late Director-General of the Arch.-eological Survey of India) to whom I desire to express my sincere thanks. After completing a large part of the calculations necessary for determining the elements of Table I., and drawing up the draft of an introductory treatise, I entered into correspondence with Mr. Sankara Balkrishna Dikshit, with the result that, after^a short interval, we agreed to complete the work as joint authors. The introductory treatise is mainly his, but I have added to it several explanatory paragraphs, amongst others those relating to astronomical phenomena. Tables XIV. and XV. were prepared by Mr. T. Lakshmiah Naidu of Madras. It is impossible to over-estimate the value of the work done by Dr. Schram, which renders it now for the first time easy for anyone to ascertain the incidence, in time and place, of every solar eclipse occurring in India during the past 1600 years, but while thus briefly noting his services in the cause of science, I cannot neglect this opportunity of expressing to him my gratitude for his kindness to myself. S38499 I must also tender my warm thanks for much invaluable help to Mr. 11. 11. Turner, Savilian Professor of Astronomy at Oxford, to Professor Kiclhorn, CLE., of Gottingen, and to Professor Jacobi. The Tables have been tested and re-tested, and we believe that they may be safely relied on for accuracy. No pains have been spared to secure this object. R. SEWELL. II. It was only in September, 1893, that I became acquainted with Mr. R. Sewell, after he had already made much progress in the calculations necessary for the principal articles of Table I. of this work, and had almost finished a large portion of them. The idea then occurred to me that by inserting the a, h, c figures (cols. 23, 24, and 25 of Table I.) which Mr. Sewell had already worked out for the initial days of the luni-solar years, but had not proposed to print in full, and by adding some of Professor Jacobi's Tables published in the Indian Antiquary, not only could the exact moment of the beginning and end of all luni- solar tithis be calculated, but also the beginning and ending moments of the nakshatra, yoga, and karana for any day of any year; and again, that by giving the exact moment of the Mesha sankranti for each solar year the exact European equivalent for every solar date could also be determined. I therefore proceeded to work out the details for the Mesha sankrantis, and then framed rules and examples for the exact calculation of the required dates, for this purpose extending and modifying Professor Jacobi's Tables to suit my methods. Full explanation of the mode of calculation is given in the Text. The general scheme was originally propounded by M. Largeteau, but we have to thank Professor Jacobi for his publications which have formed the foundation on which we have built. My calculation for the moments of Mesha sankrantis, of mean intercalations of months (Mr. Sewell worked out the true intercalations), and of the samvatsaras of the cycle of Jupiter were carried out by simple methods of my own. Mr. Sewell had prepared the rough draft of a treatise giving an account of the Hindu and Muhammadan systems of reckoning, and collecting much of the information now embodied in the Text. But I found it necessary to re-write this, and to add a quantity of new matter. I am responsible for all information given in this work which is either new to European scholars, or which differs from that generally received by them. All points regarding which any difference of opinion seems possible are printed in footnotes, and not in the Text. They are not, of course, fully discussed as this is not a controversial work. Every precaution has been taken to avoid error, but all corrections of mistakes which may have crept in, as well as all suggestions for improvement in the future, will be gladly and thankfully received. S. BALKRISHNA DIKSHIT. TABLE OF CONTENTS. PART I. The Hindu Calendar. Art. I. Introductory I Elciitents and Definitions. Art. 4. The panchahga 2 „ 5. The vara, or week day 2 Days of the week 2 ,, 6. Time divisions 2 Subdivisions of the day 2 „ 7. The tithi, amavasya, purnima 3 „ 8. The nakshatra 3 „ 9. The yoga 3 ,, 10. The karana 3 „ II. The paksha • 4 „ 12. Lunar months 4 „ 13. Amanta and purnimanta systems 4 ,, 14. Luni-solar month names 5 „ 15. The solar year, tropical, sidereal, and anomalistic 5 „ 16. The Kalpa. Mahayuga. Yuga. Julian Period 6 ,, 17. Siddlianta year-measurement 6 „ 1 8. Siddhantas now used for the same 7 The Siddhantas a7id other Astronomical Works. Art. 19. Siddhantas, Karanas, bija, Hindu schools of astronomers ... 7 „ 20. Note on the Siddhantas, and their authors and dates .... 7 ,, 21. Authorities at present accepted by Hindus 9 Further details. Contents of the Pahchaiiga. Art. 22. The Indian Zodiac, rasi, ariisa 9 ,, 23. The Sankrantis. Names given to solar months 9 Length of months .10 ,, 24. Duration of solar months. Table 10 ,, 25. Adhika masas. Calendar used il ,, 26. True and mean sankrantis. Sodhya 11 TABLE OF CONTENTS. Page Art. 28. The beginning of a solar month 12 Rule I. (a) The midnight Rule (Bengal). ,, 1. (li) The any-time Rule (Orissa). „ II. (a) The sunset Rule (Tamil). „ II. (l>) The afternoon Rule (Malabar). „ 29. Paiichangs, tithis 13 „ 30. Extract from an actual pafichanga 13 The Ahargana 16 „ 31. Correspondence of tithis and solar days 16 Performance of religious ceremonies, sraddhas, vratas 17 „ 32. Adhika and kshaya tithis 17 „ 34. Variation on account of longitude 18 „ 35. Examples of the same 19 „ 36. True and mean time 19 Mean sun, mean moon, true and mean sunrise 19 „ 37. Basis of calculation for the Tables 20 Elements of uncertainty 20 „ 38. Nakshatras 21 Yoga-taras. Equal and unequal space systems. Garga and Brahma Siddlianta systems 21 Table. Longitude of Ending-points of Nakshatras 22 ,, 39. Auspicious Yogas 22 „ 40. Karanas 23 ,, 40fl. Eclipses 23 Oppolzer's Canon. Note by Professor Jacobi 23 „ 41 Lunar months and their names 24 Season-names, star-names 24 „ 42—44. Modern names of, derived from the nakshatras 24 Table shewing this derivation 25 ,, 45. Adhika and kshaya masas. Rules 25 Table 26 ,, 46. Their names. Rules 26 ,, 47. Their determination according to true and mean systems .... 27 Change of practice about A.U. 1 100 .......... 27 Sripati. Bhaskaracharya 28 „ 48. Rules given in another form . • 28 „ 49. Different results by different Siddkantas 29 ,, 50. Some peculiarities in the occurrence of adhika and kshaya masas . 29 ,, 51. Intercalation of months by purnimiinta scheme 30 Years and Cycles. „ 52. The Hindu New Year's Day in solar and luni-solar reckoning . 31 When the first month is intercalary 32 Differs in different tracts 32 ,, 53. The si.\ty-year cycle of Jupiter 32 TABLE OF CONTENTS. Page 33 Art. 54— 55. Kshaya samvatsaras samvatsaras 33 56— 57. Variations in expunction of Jyotislia-tattva Rule 33 samvatsara 34 „ 58. To find the current for the same 34 ,, 59. Rules (a) By the Siirya Siddhanta 34 (b) By the Arya Siddhhita 34 bija 35 (c) By the Siirya Siddhanta with the Rules (d) Brihatsamhita and Jyotishatattva 35 authorities. Table . 36 60. List of Expunged Samvatsaras by different . 30 „ 61. Earliest use of Jupiter's cycle cycle 3° „ 62. The southern (luni-solar) sixty-year 37 „ 63. The twelve-year cycle of Jupiter Two kinds of Do 37 cycles 37 „ 64. The Graha-paravritti and Onko PART II. The Various Eras. Art. 65. General remarks 39 tracts 39 „ 66.