The Indian Calendar (With Tables for the Conversion of Hindu and Muhammadan Into A. D. Dates, and Vice Versa)
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The Indian Calendar (With Tables for the Conversion of Hindu and Muhammadan Into A. D. Dates, and Vice Versa)

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Item Code: IDJ996
Author: Robert Sewell, Sankara Balkrishna Dikshit, With Tables of Eclipses Visible in India by Dr. Robert Schram
Edition: 1996
ISBN: 9788120812079
Pages: 183
Cover: Hardcover
Other Details 11.0" X 8.6"
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During the past decades considerable progress has been made in understanding and evaluating Indian astronomy and mathematics, due primarily to the researches carried out by David Pingree. In this connection his monumental Census of the Exact Sciences in Sanskrit, Series A. Vol. I (1970), II(1971), III(1976), IV(1981) published in Philadelphia deserves to be mentioned side by side with the "History of Mathematical Astronomy in India" in the Dictionary of Scientific Biography, Vol. XV. New York 1978, pp. 533-633, "Jyotihsastra. Astral and Mathematical Literature", A History of Indian Literature, Vol. VI, 4, Wiesbaden 1981, and finally "Jyotihsastra", Part I of A Descriptive Catalogue of the Sanskrit and other Indian Manuscripts of the Chandra Shum Shere Collection in Bodleian Library, Oxford 1983. Further R. Billard: L'astronomie indienne: Investigation des texts sanscritset des donnees numeriques, Paris 1971, Publications de 1'Ecole Francaise d'Extreme-Orient LXXXIII, and H. -G. Turstig: Jyotisa: Das System der indischen Astrologies, Wiesbaden 1980, Beitrage zur Sudasien-Forschung 57 my be mentioned here, although both these later books came under some criticism from D. Pingree.

In spite of the advanced knowledge of the system and the history of Indian astronomy and mathematics, comparatively little attention has been paid to the more practical side of astronomy, that is to say to the calendar. In particular the non-technical literature has hardly ever been taken into consideration. The wealth of information found in Buddhist sources reflecting the difficulties encountered in ancient time, when it became necessary to determine and to keep correct dates in every day life, has been almost completely neglected. Nevertheless the rules laid down for fixing the date of the uposatha or the beginning of the rainy season are highly interesting in many respects: Here we learn for instance that intercalary months were enforced by royal decree: Vinaya-Pitaka: Mahavagga can be gleaned from literature is aptly demonstrated by the very informative article by C. Vogel: "Die Jahreszeiten im Spiegel der altindischen Literature", Zeitschrit der; Deutschen Morgenlandischen Gesellschaft 121. 1971, pp. 284-326 (with an addendum ibidem 122.1972, p. *12*).

In a way practical difficulties similar to those experienced by the early Buddhists in India are not altogether alien to the present historian when it come to calculating dates mentioned in inscriptions themselves, and different calendar systems being in use at the same time, create problems, as the discussion by D. Pingree: " A Note on the calendars Used in Early Indian Inscriptions", Journal of the American Oriental Society 102-1982, pp. 355-359 shows.

Some help in solving such problems can be found in rather old publications: the pioneering articles by Hermann Jacobi (1850-1937) reprinted in his Kleine Schriften, Wiesbaden 1970 are still valuable today, and the publications by Robert Sewell (1845-1925) have been used by generations of epigraphists and historians. As these still important research tools have been out of print for a long time and are very hard to find, the general introduction to the Indian calendar is reprinted here as a first step. It has been supplemented by R. Sewell in two further books, which also deserve to be reissued in the course of time: Eclipses of the Moon in India, London 1898, and: Indian Chronography. An Extension of the 'Indian Calendar' with Working Examples, London 1912. Finally a series of articles by the same author, which originally appeared in Epigraphia Indica, has been collected as: The Siddhantas and the Indian Calendar Being a Continuation of 'Indian Chronography', Calcutta 1924.

In contrast to researches on the calendar in India proper, which have been somewhat neglected since R. Sewell's days, closely related systems borrowed from India have also been described more recently. First, as an old publication, A.M.B. Irwin: The Burmese Calendar, London 1901 can be mentioned. The Laotian time reckoning has been described after an early attempt by L. Finot: "Recherches sur la literature Laotienne", Bulletin de 1'Ecole Fracaise D'Extreme-Orient 17, 1917, pp.1-221 (on the calendar pp. 30-34) by Prince Phetsarath: "Le calendrier laotien", Bulletin des Amis de Laos, 4.1940, pp. 107-140, also in English as: "Tiao Maha Upahat Phetsarath: The Laotian Calendar", in: The Kingdom of Laos, Saigon 1959, pp. 97-125, and: S. Duperuis: "Le calcul du calendrier laotien", Peninsule, Etudes Interdisciplinaires sur 1'Asie du Sud-Est peninsulaine, 2/3, Paris, April 1981, pp. 25-118. For Thailand, where a rather old and probably highly interesting manuscript copied in AD 1578 under the title Adhikamasvinischaya (text in Lanna: Thai Yuan, describing Buddhist ecclesiastic chronology) and many colophons virtually untouched still await investigation, J. C. Eade: Southeast Asian Ephemeris, Solar and Planetary Positions, AD 638-2000, Ithaca/New York 1989 is a most helpful book. Indian influences on Indonesian chronology have been traced by J. G. de Casparis: Indonesian Malaysia und die Philippinen, I. Band Geschichte, 1. Lieferung, and finally the Tibetan chronology, also heavily indepted to India, has been described by D. Schuh: Untersuchungen zur Geschichte der tibetischen Kalenderrechnung, Wiesbaden 1973, Verzeichnis der Orientalischen Handschriften in Deutschland, Suplementband 16.


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 Sankara 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 earlier stages of my labours I had the advantage of receiving much support and assistance from Dr. J. Burgess (late Director-General of the Archaeological 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.

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 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.



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, 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 tithes 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 toad 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.

From the Jacket

The practical difficulties in calculating dates mentioned in inscriptions or in the colophons to manuscripts are considerable. Among the books offering help to historians and editors alike, the works of R. Sewell stand out as excellent introductions to this intricate subject. The book reprinted here was first published in 1897. However, in spite of its age, The Indian Calendar has retained its usefulness for the benefit of scholars working on the chronology of Ancient India.

Robert Sewell (1845-1925) has written extensively on Indian history, Besides his works on the Indian calendar and on chronology, his book a Forgotten Empire: Vijayanagara (1900) is one of the pioneering efforts to describe South Indian history, and The Historical Inscriptions of Southern India (1923) is still a valuable took for research.


The Hindu Calendar.
Art. I. Introductory I
Art. 4 The panchanga 2
Art. 5 The vara, or week day Days of the week 2
Art. 6 Time divisions 2
  Subdivisions of the day 2
Art. 7 The tithi, amavasya, purnima 3
Art. 8 The nakshatra 3
Art. 9 The yoga 3
Art. 10 The karana 3
Art. 11 The paksha 4
Art. 12 Lunar months 4
Art. 13 Amanta and purnimanta systems 4
Art. 14 Luni-solar month names 5
Art. 15 The solar year, tropical, sidereal, and anomalistic 5
Art. 16 The Kalpa. Mahayuga. Yoga. Julian Period 6
Art. 17 Siddhanta year-measurement 6
Art. 18 Siddhantas now used for the same 7
  The Siddhantas and other Astronomical Works.  
Art. 19 Siddhantas, Karanas, bija, Hindu schools of astronomers 7
Art. 20 Note on the Siddhantas, and their authors and dates 7
Art. 21 Authorities at present accepted by Hindus 9
  Further details. Contents of the Panchanga.  
Art. 22 The Indian Zodiac, rasi, amsa 9
Art. 23 The Sankrantis. Names given to solar months 9
Art. 24 Length of months 10
  Duration of solar months. Table 10
Art. 25 Adhika masas. Calendar used 11
Art. 26 True and mean sankrantis. Sodhya 11
Art. 28 The beginning of a solar month 12
  Rule I. (a) The midnight Rule (Bengal).  
  Rule I (b) The any-time Rule (Orissa).  
  Rule II. (a) The sunset Rule (Tamil).  
  Rule II. (b) The afternoon Rule (Malabar).  
Art. 29 Panchangs, tithis 13
Art. 30 Extract from an actual panchanga 13
  The Ahargana 16
Art. 31 Correspondence of tithis and solar days 16
  Performance of religious ceremonies, sraddhas, vratas 17
Art. 32 Adhika and kshaya tithis 17
Art. 34 Variation on account of longitude 18
Art. 35 Examples of the same 19
Art. 36 True and mean time 19
  Mean sun, mean moon, true and mean sunrise 19
Art. 37 Basis of calculation for the Tables 20
  Elements of uncertainty 20
Art. 38 Nakshatras 21
  Yoga-taras. Equal and unequal space systems. Garga and Brahma Siddhanta systems 21
  Table. Longitude of Ending-points of Nakshatras 22
Art. 39 Auspicious Yogas 22
Art. 40 Karanas 23
Art. 40a Eclipses 23
  Oppolzer's Canon. Note by Professor Jacobi 23
Art. 41 Lunar months and their names 24
  Season-names, star-names 24
Art. 42-44 Modern names of, derived from the nakshatras 24
  Table shewing this derivation 25
Art. 45 Adhika and kshaya masas. Rules 25
  Table 26
Art. 46 Their names. Rules 26
Art. 47 Their determination according to true and mean systems 27
  Change of practice about A. D. 1100 27
  Sripati. Bhaskaracharya 28
Art. 48 Rules given in another form 28
Art. 49 Different results by different Siddhantas 29
Art. 50 Some peculiarities in the occurrence of adhika and kshaya masas. 29
Art. 51 Intercalation of months by purnimanta scheme 30
Years and Cycles
Art. 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
Art. The sixty-year cycle of Jupiter 32
Art. 54-55 Kshaya samvatsaras 33
Art. 56-57 Variations in expunction of samvatsaras 33
  Jyotisha-tattva Rule 33
Art. 58 To find the current samvatsara 34
Art. 59 Rules for the same 34
  (a) By the Surya Siddhanta 34
  (b) By the Arya Siddhanta 34
  (c) By the Surya Siddhanta with the bija 35
  (d) Brihatsamhita and Jyotishatattva Rules 35
Art. 60 List of Expunged Samvatsaras by different authorities. Table 36
Art. 61 Earliest use of Jupiter's cycle 36
Art. 62 The southern (luni-solar) sixty-year cycle 36
Art. 63 The twelve-year cycle of Jupiter 37
  Two kinds of Do. 37
Art. 64 The Graha-paravritti and Onko cycles 37
The Various Eras.
Art. 65 General remarks 39
Art. 66 Importation of eras into different tracts 39
Art. 67 Examples of Do 39
Art. 68 Eras differently treated by the same author 39
Art. 69 Only one safe deduction 40
Art. 70 Current and expired years. Explanation 40
Art. 71 Description of the several eras 40
  The Kali-Yuga 40
  The Saptarshi Kala Era 41
  The Vikrama Era 41
  The Christian Era 42
  The Saka Era 42
  The Chedi or Kalachuri Era 42
  The Gupta Era 43
  The Valabhi Era 43
  The Bengali San 43
  The Vilayati Year 43
  The Amli Era of Orissa 43
  The Fasali Year 44
  The Luni-solar Fasali Year 44
  The Mahratta Sur San, or Shahur San 45
  The Harsha Kala 45
  The Magi San 45
  The Kollam Era, or Era of Parasurama 45
  The Nevar Era 45
  The Chalukya Era 46
  The Simha Samvat 46
  The Lakshmana Sena Era 46
  The Ilahi Era 46
  The Mahratta Raja Saka Era 47
Art. 72 Names of Hindi and N. W. Fasali months 47
Description and Explanation of the Tables
Art. 73-102 Table I. (general) 47
Art. 80 "Lunation-parts" or "tithi indices", or "t." explained. 49
Art. 81 Relation of "tithi-index" and "tithi-part" 50
Art. 82 To convert "t." into solar time 50
Art. 83-86 Lunar conditions requisite for the intercalation or suppression of a month 50
Art. 87 Reasons for adopting tithi-index notation 51
Art. 90 Method for arriving at correct intercalated and suppressed months 52
Art. 91 Plan of work adopted for Table I 52
Art. 96 Moments of Mesha-sankranti differ according to Arya and Surya Siddhantas. 54
  Table shewing difference 55
Art. 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
Art. 103 Table II., Parts i. and ii. Correspondence of amanta and purnimanta months, and of months in different eras 57
Art. 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
Art. 105 Table III. (Collective duration of months) 59
Art. 106 Tables IV., V. (w, a, b, c, for every day in a year, and for hours and minutes) 59
Art. 107-110 Tables VI., VII. (Lunar and solar equations of the centre) 60
  Equation of the centre explained 60
Art. 111 Tables VIII., VIIIA., VIIIB 62
Art. 112-117 Tables IX. To XVI 62
Use of the Tables.
Art. 118 Purposes for which the Tables may be used 62
Art. 119 To find the corresponding year and month of other eras 63
Art. 120 To find the samvatsara 63
Art. 121 To find the added or suppressed month 63
Art. 122-129 to convert a Hindu date into a date A. D. and vice versa 63
  By methods A, B, Or C, 63
Art. 131-133 To find the nakshatra, yoga, and karana current on any date 64
  Explanation of work for nakshatras and yogas. 64
Art. 134 To convert a solar date into a luni-solar date, and vice versa 65
Art. 135-136 Details for work by Method A 65
Art. 135 (A) Conversion of a Hindu  
  (B) Do. Of a date A. D. into a Hindu solar date 66
Art. 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
Art. 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
Art. 138 (B) Conversion of dates A. D. into Hindu dates 74
  (a) Luni-solar Dates 75
  (b) Solar Dates 76
Art. 139-160 Details for work by Method C. 77
Art. 139 (A) Conversion of Hindu luni-solar dates into dates A. D. 77
Art. 142 A clue for finding when a tithi is probably repeated or expunged 78
Art. 144 To find the moment of the ending of a tithi 78
Art. 145 Do. Of its beginning 78
Art. 149 (B) Conversion of Hindu solar dates into dates A. D. 86
Art. 150 (C) Conversion into dates A. D. of tithes which are coupled with solar months 89
Art. 151 (D) Conversion of dates A. D. into Hindu luni-solar dates 90
Art. 152 (E) Conversion of dates A. D. into Hindu solar dates 93
Art. 153 (F) Determination of Karanas 96
Art. 156 (G) Do. Of Nakshatras 97
Art. 159 (H) Do. Of Yogas. 97
Art. 160 (I) Verification of Indian dates 98
  The Muhammadan Calendar.  
Art. 161 Epoch of the Hijra 101
Art. 162 Leap-years 102
Art. 163 The months. Table 102
Art. 164 A month begins with the heliacal rising of the moon 102
Art. 165 Occurrence of this under certain conditions 103
Art. 166 Difference in,-caused by difference in longitude 103
Art. 167 Days of the Week. Table 103
Art. 168 Compensation for New Style in Europe 103
Art. 169 Rules for conversion of a date A. H. into a date A. D. 104
Art. 170 Rules for conversion of a date A. D. into a date A. H. 105
  Dr. Burgess's Perpetual Muhammadan Calendar 105-106
Table I I to cii.
Table II ciii to cvi
Table III cvii
Table IV cviii to cx
Table V cxi
Table VI cxii
Table VII cxiii
Table VIII cxiv
Table IX cxv, cxv
Table X cxvi, cxvii,
Table XI cxviii
Table XII cxix, cxx
Table XIII cxxi
Table XIV cxxiii
Table XV cxxiv
Table XVI cxx, cxxxvi
  Eclipses of the Sun in India by Dr. Robert Schram 109 to 116
  Table A. 117 to 127
  Table B. 128 to 137
  Table C. 138
  Table D. 139 to 148
  Additions and Corrections 149 to 161
  Index 163 to 169

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