The Indian Calendar, with Tables for the Conversion of Hindu and Muhammadan into A.D. Dates, and vice versa c3: Preface

The Indian Calendar, with Tables for the Conversion of Hindu and Muhammadan into A.D. Dates, and vice versâ c3

Language: English

Preface

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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 Offices 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 publications of Professor Jacobi, Dr. Schram, Professor Kielhorn, Dr. Fleet, Pandit Śaṅkara Bâlkṛiṣhṇa Dîkshit, 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.

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In the earlier stages of my labours I had the advantage of receiving much support and assistance from Dr. J. Burgess (late Director-General of the Archæological 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. Śaṅkara Bâlkṛiṣhṇa Dîkshit, 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.

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Tables XIV. and XV. were prepared by Mr. T. Lakshmiah Naidu of Madras.

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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.

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I must also tender my warm thanks for much invaluable help to Mr. H. H. Turner, Savilian Professor of Astronomy at Oxford, to Professor Kielhorn, C.I.E., of Göttingen, and to Professor Jacobi.

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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.

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R. SEWELL.

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II.

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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.

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The idea then occurred to me that by inserting the *a*, *b*, *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 karaṇa for any day of any year; and again, that by giving the exact moment of the Mesha saṅkrânti 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 saṅkrântis, 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.

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My calculation for the moments of Mesha saṅkrântis, 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.

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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.

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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.

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S. BALKRISHNA DÎKSHIT.

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TABLE OF CONTENTS.

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PART I.

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The Hindu Calendar.

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| | | | Page |
| Art. 1. | Introductory . . . . . | | 1 |

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*Elements and Definitions.*

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| Art. 4. | The pañchâṅga . . . . . | | 2 |
| ,, 5. | The vâra, or week day . . . . . | | 2 |
| | Days of the week . . . . . | | 2 |
| ,, 6. | Time divisions . . . . . | | 2 |
| | Subdivisions of the day . . . . . | | 2 |
| ,, 7. | The tithi, amâvâsyâ, pûrṇimâ . . . . . | | 3 |
| ,, 8. | The nakshatra . . . . . | | 3 |
| ,, 9. | The yoga . . . . . | | 3 |
| ,, 10. | The karaṇa . . . . . | | 3 |
| ,, 11. | The paksha . . . . . | | 4 |
| ,, 12. | Lunar months . . . . . | | 4 |
| ,, 13. | Amânta and pûrṇimânta systems . . . . . . . . . . . | | 4 |
| ,, 14. | Luni-solar month names . . . . . | | 5 |
| ,, 15. | The solar year, tropical, sidereal, and anomalistic . . . . . . | | 5 |
| ,, 16. | The Kalpa. Mahâyuga. Yuga. Julian Period . . . . . . . | | 6 |
| ,, 17. | *Siddhânta* year-measurement . . . . . | | 6 |
| ,, 18. | *Siddhântas* now used for the same . . . . . . . . . . | | 7 |

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*The Siddhântas and other Astronomical Works.*

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| Art. 19. | *Siddhântas*, *Karaṇas*, bîja, Hindu schools of astronomers . . . | | 7 |
| ,, 20. | Note on the *Siddhântas*, and their authors and dates . . . . | | 7 |
| ,, 21. | Authorities at present accepted by Hindus . . . . . . . . | | 9 |

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*Further details. Contents of the Pañchâṅga.*

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| Art. 22. | The Indian Zodiac, râśi, aṁśa . . . . . . . . . . . | | 9 |
| ,, 23. | The Saṅkrântis. Names given to solar months . . . . . . | | 9 |
| ,, 24. | Length of months . . . . . | | 10 |
| | Duration of solar months. *Table* . . . . . . . . . . | | 10 |
| ,, 25. | Adhika mâsas. Calendar used . . . . . . . . . . . | | 11 |
| ,, 26. | True and mean saṅkrântis. Śodhya . . . . . . . . . | | 11 |

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| | | Page |
| Art. 28. | The beginning of a solar month . . . . . | 12 |
| | Rule I. (*a*) The midnight Rule (Bengal). | |
| | „ I. (*b*) The any-time Rule (Orissa). | |
| | „ II. (*a*) The sunset Rule (Tamil). | |
| | „ II. (*b*) The afternoon Rule (Malabar). | |
| „ 29. | Pañchâṅgs, tithis . . . . . | 13 |
| „ 30. | Extract from an actual pañchâṅga . . . . . | 13 |
| | The Ahargaṇa . . . . . | 16 |
| „ 31. | Correspondence of tithis and solar days . . . . . | 16 |
| | Performance of religious ceremonies, śrâddhas, 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-târâs. Equal and unequal space systems. *Garga* and *Brahma Siddhânta* systems . . . . . | 21 |
| | *Table.* Longitude of Ending-points of Nakshatras . . . . . . . . | 22 |
| „ 39. | Auspicious Yogas . . . . . | 22 |
| „ 40. | Karaṇas . . . . . | 23 |
| „ 40*a*. | 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 mâsas. Rules . . . . . | 25 |
| | Table . . . . . | 26 |
| „ 46. | Their names. Rules . . . . . | 26 |
| „ 47. | Their determination according to true and mean systems . . . . . . | 27 |
| | Change of practice about A.D. 1100 . . . . . | 27 |
| | Śrîpati. Bhâskarâchârya . . . . . | 28 |
| „ 48. | Rules given in another form . . . . . | 28 |
| „ 49. | Different results by different Siddhântas . . . . . . . . . . . | 29 |
| „ 50. | Some peculiarities in the occurrence of adhika and kshaya mâsas . . | 29 |
| „ 51. | Intercalation of months by pûrṇimânta scheme . . . . . . . . . | 30 |

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Years and Cycles.

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| „ 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 sixty-year cycle of Jupiter . . . . . | 32 |

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| | | Page |
| Art. 54—55. | Kshaya saṁvatsaras . . . . . . . . . . | 33 |
| ,, 56—57. | Variations in expunction of saṁvatsaras . . . . . . . | 33 |
| | *Jyotisha-tattva* Rule . . . . . . . . . . | 33 |
| ,, 58. | To find the current saṁvatsara . . . . . . . . . | 34 |
| ,, 59. | Rules for the same . . . . . . . . . . | 34 |
| | (a) By the *Sûrya Siddhânta* . . . . . . . . . | 34 |
| | (b) By the *Ârya Siddhânta* . . . . . . . . . | 34 |
| | (c) By the *Sûrya Siddhânta* with the bîja . . . . . . . | 35 |
| | (d) *Bṛihatsaṁhitâ* and *Jyotishatattva* Rules . . . . . . . | 35 |
| ,, 60. | List of Expunged Saṁvatsaras by different authorities. *Table* . . . | 36 |
| ,, 61. | Earliest use of Jupiter's cycle . . . . . . . . . | 36 |
| ,, 62. | The southern (luni-solar) sixty-year cycle . . . . . . . | 36 |
| ,, 63. | The twelve-year cycle of Jupiter. . . . . . . . . | 37 |
| | Two kinds of Do. . . . . . . . . . | 37 |
| ,, 64. | The Graha-paravṛitti and Oṅko cycles . . . . . . . | 37 |

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PART II.

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The Various Eras.

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| Art. 65. | General remarks . . . . . . . . . . | 39 |
| ,, 66. | Importation of eras into different tracts . . . . . . . | 39 |
| ,, 67. | Examples of Do. . . . . . . . . . | 39 |
| ,, 68. | Eras differently treated by the same author . . . . . . | 39 |
| ,, 69. | Only one safe deduction . . . . . . . . . | 40 |
| ,, 70. | Current and expired years. Explanation . . . . . . . | 40 |
| ,, 71. | Description of the several eras . . . . . . . . | 40 |
| | The Kali-Yuga. . . . . . . . . . . | 40 |
| | The Saptarshi Kâla Era . . . . . . . . . | 41 |
| | The Vikrama Era . . . . . . . . . . | 41 |
| | The Christian Era . . . . . . . . . | 42 |
| | The Śaka Era . . . . . . . . . . | 42 |
| | The Chedi or Kalachuri Era . . . . . . . . | 42 |
| | The Gupta Era . . . . . . . . . . | 43 |
| | The Valabhî Era . . . . . . . . . . | 43 |
| | The Bengalî San . . . . . . . . . . | 43 |
| | The Vilâyatî Year . . . . . . . . . | 43 |
| | The Amli Era of Orissa. . . . . . . . . | 43 |
| | The Fasali Year . . . . . . . . . . | 44 |
| | The Luni-solar Fasali Year . . . . . . . . | 44 |
| | The Mahratta Sûr San, or Shahûr San . . . . . . | 45 |
| | The Harsha Kâla . . . . . . . . . . | 45 |
| | The Mâgi San . . . . . . . . . . | 45 |
| | The Kollam Era, or Era of Paraśurâma . . . . . . | 45 |
| | The Nevâr Era . . . . . . . . . . | 45 |
| | The Châlukya Era . . . . . . . . . | 46 |
| | The Siṁha Samvat . . . . . . . . . | 46 |

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| | Page |
| The Lakshmaṇa Sena Era . . . . . | 46 |
| The Ilâhi Era . . . . . | 46 |
| The Mahratta Râja Śaka Era . . . . . | 47 |
| Art. 72. Names of Hindî and N. W. Fasali months . . . . . . . . | 47 |

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PART III.

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Description and Explanation of the Tables.

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| | Page |
| Art. 73—102. Table I. (general) . . . . . | 47 |
| Art. 80. "Lunation-parts" or "tithi indices", or "*t.*" explained . | 49 |
| ,, 81. Relation of "tithi-index" and "tithi-part" . . . . . . | 50 |
| ,, 82. To convert "*t.*" into solar time . . . . . . . . . | 50 |
| ,, 83—86. Lunar conditions requisite for the intercalation or suppression of a month . . . . . . . . . . | 50 |
| ,, 87. Reasons for adopting tithi-index notation . . . . . . | 51 |
| ,, 90. Method for arriving at correct intercalated and suppressed months . . . . . | 52 |
| ,, 91. Plan of work adopted for Table I. . . . . . . . . . | 52 |
| ,, 96. Moments of Mesha-saṅkrânti differ according to *Ârya* and *Sûrya Siddhântas* . . . . . | 54 |
| Table shewing difference . . . . . . . . . . . | 55 |
| ,, 102. *a*, *b*, *c*, (cols. 23, 24, 25) fully explained . . . . . . . | 56 |
| *Table.* Increase of *a*, *b*, *c*, in a year and in a day . . | 57 |
| ,, 103. Table II., Parts i. and ii. Correspondence of amânta and pûrṇimânta months, and of months in different eras . . . . . . . . . | 57 |
| ,, 104. Table II., Part iii. Do. of years of different eras . . . . . . | 58 |
| Rules for conversion of a year of one era into that of another . | 58 |
| ,, 105. Table III. (Collective duration of months) . . . . . . . . | 59 |
| ,, 106. Tables IV., V. (*w*, *a*, *b*, *c* for every day in a year, and for hours and minutes) . . . . . | 59 |
| ,, 107—110. Tables VI., VII. (Lunar and solar equations of the centre . | 60 |
| Equation of the centre explained . . . . . . . . : | 60 |
| ,, 111. Tables VIII., VIIIA., VIIIB . . . . . | 62 |
| ,, 112—117. Tables IX. to XVI . . . . . | 62 |

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PART IV.

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Use of the Tables.

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| | Page |
| Art. 118. Purposes for which the Tables may be used . . . . . . . . | 62 |
| ,, 119. To find the corresponding year and month of other eras . . . . | 63 |
| ,, 120. To find the samvatsara . . . . . | 63 |
| ,, 121. To find the added or suppressed month . . . . . . . . . | 63 |
| ,, 122—129. To convert a Hindu date into a date A.D. and vice versâ . | 63 |
| By methods A, B, or C . . . . . | 63 |
| ,, 131—133. To find the nakshatra, yoga, and karaṇa current on any date | 64 |
| Explanation of work for nakshatras and yogas . . . . . . . | 64 |
| ,, 134. To convert a solar date into a luni-solar date, and vice versâ . | 65 |

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| | | Page |
| Art. 135–136. | Details for work by Method A | 65 |
| Art. 135. | (A) Conversion of a Hindu solar date into a date A.D. | 65 |
| | (B) Do. of a date A.D. into a Hindu solar date . | 66 |
| ,, 136. | (A) Do. of a Hindu luni-solar date into a date A.D. | 67 |
| | (B) Do. of a date A.D. into a Hindu luni-solar date | 68 |
| ,, 137–138. | Details for work by Method B . | 69 |
| Art. 137. | (A) Conversion of Hindu dates into dates A.D. | 69 |
| | (*a*) Luni-solar Dates . | 70 |
| | (*b*) Solar Dates . | 73 |
| ,, 138. | (B) Conversion of dates A.D. into Hindu dates | 74 |
| | (*a*) Luni-solar Dates. | 75 |
| | (*b*) Solar Dates . | 76 |
| ,, 139–160. | Details for work by Method C . | 77 |
| Art. 139. | (A) Conversion of Hindu luni-solar dates into dates A.D. | 77 |
| ,, 142. | A clue for finding when a tithi is probably repeated | |
| | or expunged . | 78 |
| ,, 144. | To find the moment of the ending of a tithi | 78 |
| ,, 145. | Do. of its beginning | 78 |
| ,, 149. | (B) Conversion of Hindu solar dates into dates A.D. | 86 |
| ,, 150. | (C) Conversion into dates A.D. of tithis which are | |
| | coupled with solar months | 89 |
| ,, 151. | (D) Conversion of dates A.D. into Hindu luni-solar dates | 90 |
| ,, 152. | (E) Conversion of dates A.D. into Hindu solar dates . | 93 |
| ,, 153. | (F) Determination of Karaṇas | 96 |
| ,, 156. | (G) Do. of Nakshatras | 97 |
| ,, 159. | (H) Do. of Yogas. | 97 |
| ,, 160. | (I) Verification of Indian dates | 98 |