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History of the

in Different Countries Through the Ages

M.N. Saha and N.C. Lahiri

COUNCIL OF SCIENTIFIC & INDUSTRIAL RESEARCH Rafi Marg, New Delhi- 1 10001 1992 Part C of Report of Committee, Government of

First published: 1955 Reprinted: 1992

© Council of Scientific & Industrial Research, New Delhi

Printed by Publications & Information Directorate Dr K.S. Krishnan Marg, New Delhi -110012 FOREWORD

The Council of Scientific & Industrial Research (CSIR) of the Government of India appointed a Calendar Reform Committee under the chairmanship of Prof. Meghnad Saha in November 1952. The Committee was entrusted with the task of 'examining all the existing which are being followed in the country at and after a scientific study of the subject, submit proposals for an accurate and uniform calendar for the whole of India'. The following were the members of the Committee:

Prof. M.N. Saha, D.Sc, RR.S., M.P. (Chairman) Prof. A.C. Banerji, Vice-Chancellor, Allahabad University Dr. K.L. Daftari, Nagpur Shri J.S. Karandikar, Ex-Editor, The Kesari, Poona Dr. Gorakh Prasad, D.Sc., Allahabad University Prof. R.V. Vaidya, Madhav College, Ujjain Shri N.C. Lahiri, Calcutta (Secretary)

Dr. Gorakh Prasad and Shri N.C. Lahiri came in place of Prof. S.N. Bose and Dr. Akbar Ali who were originally appointed but were unable to serve.

The Committee's Report was submitted to CSIR in 1955 and the Government, in accepting the recom- mendations of the Committee, decided that 'a unified National Calendar' (the Calendar) be adopted for use with effect from 21 March 1956 A.D., i.e., 1 1878 Saka. The Report of the Calendar Reform Committee was published by CSIR in 1955. Part C of the Report consisting of a review of ' of the calendar in different countries through the ages' by Prof. M.N. Saha and Shri N.C. Lahiri was also published separately. This useful publication has been out of print for some and scientists in general, and astronomers in particular, have been conscious of the non-availability of this valuable review. Therefore, the CSIR has decided to reprint it. No changes have been made from the original except that 'Corrigenda and Addenda' have been incorporated into the text, and consequently the bibliography and the index (which pertain to the whole report) have been repaginated. The title page of the Report, Jawaharlal Nehru's message, and Saha & Lahiri 's preface have also been included in the present volume.

I hope that this reprinted volume will be found useful and informative by calendaric astronomers, historians and scientists in general.

S.K. Joshi New Delhi Director-General 15 1992. Council of Scientific & Industrial Research and Secretary, Department of Scientific & Industrial Research FACSIMILE OF ORIGINAL COVER

REPORT

OF THE

CALENDAR REFORM COMMITTEE

GOVERNMENT OF INDIA

Council of Scientific and Industrial Research, Old Mill Road, New Delhi. 1955 MESSAGE

I am glad that the Calendar Reform Committee has started its labours. The Government of India has entrusted to it the work of examining the different calendars followed in this country and to submit proposals to the Government for an accurate and uniform calendar based on a scientific study for the t^hole of India. I am told that we have at present thirty different calendars, differing from each other in various ways, including the methods of time reckoning. These calendars are the natural result of our political and cultural history and partly represent past political* divisions in the country. Now that we have attained independence, it is obviously desirable that there should be a certain uniformity in the calendar for our civic, social and other purposes and that this should be based on a scisntific approach to this problem.

It is true that for governmental and many other public purposes we follow the , which is used in the greater part of the world. The mere fact that it is largely used, makes it important. It has many virtues, but even this has certain defects which make it unsatisfactory for universal use.

It is always difficult to change a calendar to which people are used, because it affects social practices. But the attempt has to be made even though it may not be as complete as desired. In any , the present confusion in our own calendars in India ought to be removed.

I hope that our Scientists will give a lead in this matter.

New Delhi, February 18, 1953. MEMBERS OF THE CALENDAR REFORM COMMITTEE

CHAIRMAN

Prof. M. N. Saha, D. Sc., F. R. S., M, P., Director, Institute of Nuclear Physics, 92, Upper Circular Road, Calcutta-9.

MEMBERS

Prof, A. C. Banerji, M. A M M. Sc., F. N. I., Vice-Chancellor, Allahabad University, Allahabad.

Dr. K. L. Daftari, B. A., B. LM D. Litt., Mahal, Nagpur.

Shri J. S. Karandikar, B. A., LL. B., Ex -Editor, The Kesari, 568 Narayan Peth, Poona-2.

Dr. Gorakh Prasad, D. Sc., Reader in Mathematics, Allahabad University, Beli Avenue, Allahabad,

Prof. R. V. Vaidya, M. A., B. TM Senior Lecturer in Mathematics, Madhav College, Ujjain, 78, Ganesh Bhuvan, Freegunj, Ujjain.

Shri N. C. Lahiri, M. A., 55A, Raja Dinendra Street, Calcutta-6.

Shri N. C. Lahiri acted as the Secretary of the Committee. —

TRANSLITERATION

The scheme of transliteration of alphabets into Roman script adopted in this publication is the same as generally followed. The corresponding scripts are given below :

VOWELS CONSONANTS

k P kh

g b gh bh

c ch

3 jh

t th d dh n

o

au t th d dh n

N* B. Diacritical marks have not generally been used in names of persons belonging to recent as well as in well-known geographical names. PREFACE

The Calendar Reform Committee was appointed suggested by Dr. Hashim Amir Ali of the Osmania in November, 1952, by the Council of Scientific and University, and Janab Mohammed Ajmal Khan of the Industrial Research (of the Government of India) with Ministry of Education. It is for the Islamic world to give its the following terms of reference : verdict on these suggestions. If these sugges- tions are accepted, the "To examine all the existing calendars which are fceing would fall in line with other luni-solar calendars. followed in the country at present and after a scientific study of the subject, submit proposals for an accurate and As these two important systems of calendars had uniform calendar for the whole of India". to be left out, the Committee's labours were confined to an In accordance with its terms of reference, the examination of the different systems of calendars used by Hindus, Bauddhas Committee (for personnel, see p. 4) has scientifically and Jainas in the different states of India, chiefly examined all the calendars prevalent in India (vide for the fixing up of the dates and moments of their religious Part C, Chap. V), viz*,— festivals, and for certain civil purposes as well. Gregorian Calendar*.. which is used for civil and For the administrative purposes (vide purpose of examining all the existing calendars of India, as per terms of p. 170) all over the world. reference, an appeal was issued to the Paricanga (Almanac) makers for Islamic Calendar used for fixing up the dates furnishing the Committee with three copies of their of Islamic festivals (vide Pancangas. In reply to our request 60 Pancangas p. 179). (Almanacs) were received from different parts of the Indian Calendars country and were examined (p. 21). To facilitate or Pancangas used for fixing up dates and examination of the calendars, a questionnaire was moments of Hindu, Bauddha issued to which 51 replies were received (pp. 23-31). and Jaina festivals in different In addition to the above, 48 persons offered their States of India* and in many suggestions (pp. 32-38) for reform of the Indian cases for civil purposes also. calendar. These views were very divergent in They are about 30 in number. character. Some quoted ancient scriptures to prove (vide Chap. V, p. 258). that the is flat, with a golden mountain in the It has been pointed out (p. 171) that the Gregorian centre round which move the and the planets, calendar, which is used all over the world for civil others tried to refute the of . and administrative purposes, is a very unscientific and All opinions were taken into consideration in arriving inconvenient one. The (p* 173), at the decisions of the Committee. proposed by the World Calendar Association of New Principles in followed fixing up the Calendar : —The , has been examined and found suitable for calendar has got two distinct uses—civil and religious. modern life. The proposal for its adoption by all the The Indian Calendars are used not only for fixing up of the world for civil and administrative countries the dates and moments of religious observances but purposes was sponsored by the Indian Government also for the purpose of dating of documents and for before the U. N. O. and debated before the ECOSOC certain civil purposes not only by the rural, but also (Economic and Social Council) at Geneva in June, by a large section of the urban population. There is 173) and its recommendations have been 1954 (p. great divergence in practice in different parts of the transmitted to the Governments of the World for country in this respect. Therefore a unified solar their opinion. It is hoped that the World Calendar calendar has been proposed for all-India use for civil great will be ultimately adopted. It will lead to a purposes. This has been based on the correct length simplification of modern life. of the (viz. the ) and the popular

The introduction of the World Calendar in place -names, vix. % Caitra, , etc. have been of the Gregorian is a matter for the whole world, retained (see p. 6). which has now to look for decision by the U, N. O. Calendars are based partly on SCIENCE which The Islamic (Hejira) calendar has been discussed nobody is permitted to violate and partly on on p, 179, along with some proposals for reform CONVENTIONS which are man-made and vary from — —

X PREFACE place to place. The Indian calendars put up by (scientific) evolved by Indian astronomers almanac-makers commit the violation of the following on the basis of old Indian calendaric conceptions, principles of science : which were put on scientific basis by blending with They take the length of the year to be 365.258756 them astronomical conceptions prevalent in the West, from the days (p. 240, Part C of Report) as given by the ~ third B.C.

Biddhdnta about 500 A. D. ; while the correct length The is also used exclusively for horoscope of the tropical year, which alone can be used according making, a practice introduced into India since the to the Surya-SiddJ&nta and modern astronomy for first century A.D. by the Sakadvlpi . calendarical use, is 365.242196 days. The difference The Calendar Committee has devised a solar of .01656 days is partly due to errors of observation, calendar with fixed lengths of for all-India use, not infrequent in those days, and to their failure to in which it has been proposed to give, up the recognize the precession of equinoxes. As the Surya- calculations of the Surya- in which the Siddhanta value of the year-length is still used in solar months vary from 29 to 32 days. almanac-making, the year-beginning is advancing by Religious Calendar—The Committee's task resolved .01656 days per year, so that in the course of nearly itself into a critical examination of the different 1400 , the year-beginning has advanced by 23.2 Indian local calendars, about 30 in number, which days, with the result that the- -Indian solar year, use different methods of calculation. This produces instead of starting on the following the vernal great confusion. , i.e., on March 22, as prescribed in the Surya- As already stated the Siddhanta (see Chap. V, p. 239), starts on April 13 or Surya-Siddhanta year being longer than the tropical 14. The situation is the same as happened in year by about 24 mins., the due to the acceptance of 365.25 days as the length of months have gone out of the to which they conformed when the Siddhantic rules the year at the time of ; the

were framed ; as a result, the religious originally linked to the preceded it festivals are by 10 days by 1582 A.D., when the error was being observed not in the seasons for which they were intended but in seasons. rectified by the promulgation of a bull by Pope wron* The Committee felt that the error should be Gregory XIII. By this, , October 5 was corrected once for all and proclaimed as Friday, October 15, and new leap-year the months brought back to their original seasons. But with a view to avoiding violent in rules were introduced. any break the present day practices, the desired shifting has not Unlike Europe, where the Pope in the medieval been effected, but any further increase of the error has times possessed an authority which every one in been stopped by adopting the tropical year for our Catholic Europe respected, India had a multiplicity religious calendar also (sec p. 7). of and year^beginnings due to her history during

the years 500-1200 A. D. But for calendaric calcula- Before the rise of Siddhanta Jyotisa ( 400 A.D. ), tions, our astronomers all over India have been using India used only the calculated according only the Saka era since (500 A.D.) certainly to the Vcdahga Jyotifa rules and most religious festi- probably from much earlier times, and in local and vals ( e.g. the Janm3ftami, the birthday of Sri Krsna ) almanacs other eras are simply imposed on it. The used to be fixed up by the lunar calendar which used

: Calendar Committee has therefore recommended only t i tli i and naksatra. The Calendar Committee

That for all official purposes, the Central as well could not find out any way of breaking off with the as State Governments should use the Saka era along lunar affiliation short of a religious revolution and with the civil calendar proposed by the Committee has, therefore, decided to keep them. For this

(p.6). -It is suggested that the change-over may take purpose, the lunar year is to be pegged on to the solar place from the Saka year 1878, Caitra 1 (1956, March year by a number of conventions. The Committee has adhered to the ancient conventions as far as possible. 21}. If this is accepted, the last month of the year, viz. % 1877 Saka, the solar , which has a normal But the erroneous calculations of and naksatras length of 30 days, will have an extra number of 6 or have been replaced by modern calculations given in

7 days. - the nautical almanacs and modern ephemcrides, and the religious holidays have been fixed for a central The pre-eminence of the Saka era is due, as station of India ( page 40 ). historical evidences cited on pp. 228-238 and 255-257

show, that it was the earliest era introduced in India, The present practice is to calculate the for by Saka ruling powers, and have been used exclusively each locality and the result is that the same tithi by the Sakadvlpi (forming the astrologer may not occur on the same day at all places. The caste) for calendar-making on the basis of Siddhantic Calendar Committee has found that the continuance —

PREFACE xi

of different lunar calendars for different places is a (ii) But there are other holidays, which are given relic of medieval practice when communication was according to the position of the Sun (vide difficult, the printing press did not exist and pp. 117-118). astrologers of each locality used to calculate the (iii) Others which are given according to thb luni- calendar for that locality based on Siddhantic rules (pp. 119-124). and used to proclaim it on the first day of the year (iv) Holidays for Moslems and Christians 125 to their clients. In these days of improved communi- (pp. and 126). cation, free press, and radio, there is not the slightest justification for continuance of this practice and the * It is a task for the Central as well as State Govern- to Committee has fixed up the holidays for the central ments calculate in advance dates for the holidays it 30' gives. This is done on the advice of station (82° E, 23° 11' N, see Report p. 40); Pancanga-makers attached to each and recommended that these holidays may be used for Government. In addition, numerous indigenous pancangas arc the whole of India. The dates of festivals of the prepared on the Siddhantic system Hindus, Jainas and Bauddhas have been determined on of calculations, the elements of which arc now found to be the above basis. This will put an end to the calendar completely erroneous. There is a wide confusion. movement in the country first sponsored by the great savant, patriot and political leader, the late The confusion is symbolic of India's history. Lokamanya B. G. Tilak, for making the pancaiiga While all Christendom comprising people of Europe, calculations x>n the basis of the correct and up-to and America, follows the Gregorian calendar, astronomical elements. As a result, there are and the whole of the Islamic world follows the Hejira almost in every State different schools of pancariga calendar for civil and religious purposes, India uses 30 calculations, differing in the durations of tithis, different systems for fixing up the same holidays in naksatras, etc., and consequently in the dates of different parts of the country and frequently, two religious festivals. The problem before the Govern- rival schools of pancanga-makers in the same city fix ment is : which one of the divergent systems is to be up different dates for the same festival. This is a adopted. The Committee has suggested a system of state of affairs which Independent India cannot calculations for the religious calendar also, based on tolerate. A revised national calendar, as proposed most up-to-date elements of the motion of the sun and by us, should usher a new element of unity in the . Calendars for five years from 1954-55 India. to 1958-59 have been prepared on this basis showing The Committee has therefore gone deeply into the therein inter alia the dates of important festivals of history of calendar making in all countries from the different States (vide pp. 41-100). The lists of holidays earliest times particularly into the history of calendar- for the Government of India and of each separate making in India (vide Chap. V) and has arrived at their State for the five years have also been prepared from conclusions. Its recommendations are entirely in this calendar for the use of the Governments. The agreement with the precepts laid down by the Siddhan- Committee hopes that the Government of India as well tic astronomers, as given in the Stirya-Siddhanta and as the State Governments would adopt these lists in other standard treatises (see p. 238 et seq.). declaring their holidays in . The Ephcmerides Committee which has been formed by the Government The Committee has also compiled a list of all reli- pi India, consisting of 'astronomers versed in the gious festivals observed in diffirent parts of India and principles of calendar-making would act as advisers to listed them under the headings (i) Lunar, and (ii) Solar, the Central as well as State Governments. It may be with their criteria for fixing the dates of their obser- assisted by an advisory committee to help it in its vances (pp. 102-106). deliberations.

Where does the Government come in : Though India The responsibility of preparation of the five-yearly is a secular state, the Central Government and the calendar and the list of holidays on the basis of State Governments have to declare a number of - recommendations adopted by the Committee has been days in advance, a list of which. will be found on pages shared by Sri N. C. Lahiri and Sri R. V. Vaidya, 117-154 for the Central Government as well as for the aided by some assistants and several pandits of notjc, States. These holidays are of four different kinds, amongst whom the following may be mentioned : viz. : Sri A. K. Lahiri, Sri N. R. Choudhury, Pandit (i) Holidays given according to the Gregorian Narendranath Jyotiratna, and Joytish Siddhanta

calendar, e.fi,, Mahaima Gandhi's birthday, Kesari Venkata.Subba Sastry of Madras. which falls on Oct. 2. These present no We have received great help from C. G. Rajan, problem to any government. B.A., Sowcarpet, Madras. He has kindly furnished xii us with valuable suggestions regarding 'Rules for We have reproduced figures from certain books fixing the dates of festivals for South India*. and our acknowledgement is due to the publishers. It We are indebted to the Astronomer Royal of Great was however not possible to obtain previous permission Britain, Sir Harold Spencer Jones, and to Mr. Sadler, from them, but the sources have been mentioned at head of the Ephemcrides divison of the Royal the relevant places. Observatory of U. K. for having very kindly supplied It is a great pleasure and privilege to express our us with certain advance data relating to the sun and gratitude to our colleagues of the Calendar Committee the moon which have facilitated our calculations. We for their active co-operation in the deliberations of the have to thank the great oriental scholar, Otto Ncuge- Committee, and ungrudging help whenever it was bauer for having helped us in clearing many obscure sought for. astronomy. wish to points in ancient calcndaric We M. N. Saha thanks to Prof. P. C. Scngupta for helping express our Calcutta, Chairman us in clearing many points of ancient and medieval The 10th Nov., 1955. N. C. Lahiri . Secretary REPORT

OF THE

CALENDAR REFORM COMMITTEE

PART C

History of the Calendar in different Countries through the Ages

BY

Prof. M. N. SAHA, d. sc., f. r. s.

Professor Emeritus, University of Calcutta, Chairman, Calendar Reform Committee, AND

Sri N. C. LAHIRI, m. a.

Secretary, Calendar Reform Committee. CONTENTS

PART C

History of the Calendar in different countries through the ages

CHAPTER PAGE CHAPTER PAGE

I—General Principles of Calendar Making 157-163 4.6 The and the Signs 192

1.1 Introduction ... 157 4.7 Chaldean contributions to astronomy: Rise of planetary and horoscopic 1.2 The natural periods of time astrology 194 1.3 The problems of the Calendar ... 158 4.8 Greek contributions to astronomy 201 1.4 Subdivisions of the day ... 159 4.9 Discovery of the precession of the 1.5 Ahargana or heap of days: Julian days ... 161 equinoxes 204

164-173 11—The Solar Calendar Appendix:

2.1 Time reckonings in ancient ... 164 4-A-—Newton's explanation of the precession

2.2 Solar calendars of other ancient nations ... 165 of the equinoxes ... 207

2.3 The Iranian Calendar ... 166 4-B— of the lunar mansions ... 210

2.4 The French Revolution Calendar ... 167 V—Indian Calendar 212-270 2.5 The ... 168 5.1 The periods in Indian history 212 2.6 The Gregorian Calendar ... 170

5.2 Calendar in the Rg-Vedic 214 2.7 The World Calendar ... 171 5.3 Calendaric references in the

Yaj -Vedi c 1 i terature 218 III—The Luni-Solar and Lunar Calendars 174-180 5.4 Vedanga Jyotisa Calendar 221 3.1 Principles of Luni -solar calendars 174 The 5.5 Critical review of the inscriptional 3.2 Moon's synodic period or lunation: records about calendar 226 Empirical relation between the year and

the month ... 175 5.6 Solar Calendar in the Siddhanta Jyotisa period 234 3.3 The Luni-solar calendars of the

Babylonians the Macedonians, the 5.7 Lunar Calendar in the Siddhanta Jyotisa

Romans and the ... 176 period 245

3.4 The introduction of the era ... 177 5.8 Indian Eras 251

3.5 The Jewish Calendar ... 179 Appendix: 3.6 The Islamic Calendar • ... 179

5-A — The Seasons . 259

IV—Calendaric Astronomy 181-211 5-B — The Zero-point of the Hindu Zodiac 262

4.1 The Moon's movement in the sky ... 181 5-C — measurements in the Aitareya

Brahmana .. 266 4.2 Long period observations of the moon:

The Chaldean Saros ... 184 5-D — Precession of the Equinoxes amongst Indian Astronomers 267 4.3 The Gnomon ... 188

Jovian years .. 4.4 Night observations: the celestial pole 5-E-— The 270

and the equator ... 190

Bibliography . 271 4.5 The apparent path of the sun in the sky:

The ... 191 Index . 273 CHRONQ1 OGjCAL TABLE * SYR!A EGYPT Asia minor EUROPE '3500 India -3500

•3000 -3000 INDUS - VALLEY CIVILISATION SOTHfC CYCLE -2500 -2500 PYRAMIDS VED1C AKKAD OLD KINGDOM PERIOD

Urfll -2000 2000 MIDDLE KBiSWM

\\

KA5SSTES HYK SOS -1500 -1500 HITTITES VEDANGA CALENDAR NEW KINGDOM HOMERIC GREEKS -1000 -WOO GREEK NABONASSAfi\ ALPHABET ) OLYMPIC FOUNDATION CHALDEAN ERA OF \BUDDHA C H E M E N i D ITALIAN -500 A f 1" -500 — GREEK CITY STATES STATES E M P / RE CITY MAURYA PTOLEMA/C \ALEXAliDER\ BACTRIAN DYNASTY GREEK \ \rAESAR\ SAKA \CHRIST)r EMPIRE OF H O M KUSHAN \PTOLEMAlOS\

GUPTA S ASS ANID EMPIRE BYZA NTiNE_ E_MPJPE, END OF ROMAN 500 500 AftYABHAm EMPIRE MEDIEVAL /SLA MIC C A L / PHA \f£ DARK DYNASTIES AGE

1000 WOO \BNASKARA 1 RENAISSANCE ISLAMIC PERIOD \COPERNICUS 1500 1500 \GREGORY2M \AKBAR\ INDUSTRIAL BRITISH REVOLUTION PERIOD 2000 2000 THE ZODIAC THROUGH THE AGES

MAGNITUDES positions or the: first point or (T) IN Dl TFE.RENT TIMES. First • V = VeJic Times ahoul 2300 B.C. • /f = Hipparchoj UO B.C. Third • PiU Ptolemy 150 A.D.

Fourth . Sj - Surya SicJdhan/a 2.85 A.D.

F\FTH S 2 « , 500 A.D. Sj =r 510 AD. M = Modern 1950 A.D. CHAPTER I

General Principles : Calendar Making

1.1 INTRODUCTION The Day* :

The Flux of Time, of which we are all conscious, is The day, being the smallest unit, has been taken as apparently without beginning or end, but it is cut up the fundamental and the lengths of months,

periodically by several : natural phenomena, vix. the year and the seasons are expressed in terms of the (1) by the ever-recurring alternation of daylight day as the unit. and night, But the day is to be defined. Many early nations (2) by the recurrence of the moon's phases, defined the day as the time-period between sunrise to sunrise (savana day in India) or (3) by the recurrence of seasons. sunset to sunset (Babylonians and Jews). But the length of the day, If is these recurring phenomena which are used to so defined, when measured with even the rough measure time. chronometers of early days, was found to be variable. These phenomena have the greatest importance for This is due to the fact that except at the equator, the man, for they determine all human and animal life. sun does not rise or set at the same time in different Even prehistoric men could not help noticing these seasons of the year. So gradually the practice arose time-periods, and their effect on life. of defining the day as the period from midnight to When human communities started organized social midnight, i. e., when the sun is at the nadir to its next life in the valleys of the Indus and the Ganges (India), passage through the nadir. Even then the length of the Nile (Egypt), the Tigris and the the day is found to be variable when measured by an

(Mesopotamia) and the Hoang Ho (), several accurate chronometer. The reasons are set forth in all millenia before Christ (vide Chronological Table), these astronomical text books. Then came the idea of the phenomena acquired new importance. For these early mean solar day, and it is now taken as the funda- societies were founded mental unit of time. The solar on ; and agricultural mean day is -the practices depend on seasonal weather conditions. average interval between the two successive passages With these practices, therefore, grew national and of the sun over the meridian of a place derived from a religious festivals, necessary for the growth of social very large number of observations of such meridian life, and of civilization. People wanted to know in passages. The time between two passages is measured advance when to expect the or the , by an accurate chronometer. when most of the ancient festivals were celebrated ; In addition to the solar day, the astronomers define when to expect the onset of the winter or the also a sidereal day, which is the time period between ; when to prepare the ground for sowing ; two successive transits of a fixed . It measures the for sowing and for harvesting. the time of rotation of the earth round its axis.t Calendars are nothing but predictions of these events, The solar and were early framed on the basis of past experiences. day is larger than the sidereal day, because by the time the earth completes a rotation about its axis, the sun slips nearly a degree to the east,

due to the motion of the earth in its orbit, and it takes a little more time for the sun to come to the 1.2 THE NATURAL PERIODS OF TIME

The three events mentioned in (1), (2) and (3) above * Day here means 'Day and Night'. In ancient times, the define the natural divisions of time. : They are : of day-light from sunrise to sunset, and of the night from sunset to sunrise, were measured separately with the aid of water- The Day : defined by the alternation of daylight . It was comparatively late that the length of the Day, meaning and night. day-light and night, was measured. It was distinguished by the ahoratra in Sanskrit, ahna meaning daylight time, and rain meaning The Month : the complete cycle of moon's changes night time. In Greece, this was known as Nychthemeron. of phase, from end of new-moon to next end of new- + Actually speaking, the sidereal day is defined in astronomy as moon (amdnta months), or end of full-moon to end the period between two successive meridian passages of the First of next full-moon {purnimUnta months). point of Aries. As this point has a slow westward motion among the fixed The stars, the duration of the so called sidereal day is very Year : and its smaller subdivisions, viz., the slightly less than the actual sidereal day or the period of rotation of seasons. the earth. CALENDAR REFORM COMMITTEE 158 REPOKT OF THE early It appears that the Egyptians found very the place. We have the relation : meridian of recurrence (as related in the next section) from the solar days«366J sidereal days. 365J mean of 365 b the Nile floods that the year had a length the earth =23 56™ 4M00 mean . of Rotation of nearer days. Later they found the true length to be Sidereal day = 23 56 4.091 „ » » time 365.25 days. Mean solar day =24 3 56.555 sidereal ancient Babylonians, or Chaldeans as they period The The actual sidereal day, which measures the been were called from about 600 B.C., appear to have taken to be cons- of rotation of the earth is generally correct the earliest people who tried to obtain solar day comes from tant. The variable part of the the year, measures of the time-periods ; the month, two factors : and the seasons in terms of the day, and its subdivi- the sun's path to the equator, to (1) Obliquity of sions. Their determinations were transmitted and the Greeks who refined both the notions and measure- the sun in different parts This story will be told in (2) Unequal motion of ments very greatly. of the year. Chapter II. 45). length df the (See H. Spencer Jones, General Astronomy p. At present it is known that the that even the year) is given by :— It has however been recently found seasonal year (tropical constant but 365-24219879—'0*614 (t—1900) days, period of rotation of the earth is not Tropical year = amounts fluctuates both regularly and irregularly by where t= Gregorian year. tropical year is of the order of 10- • . & The present duration of a h m 365*2421955 days or 365d 5 48 45-7.

The Month : The : and The month is essentially a lunar phenomenon, of new moon countries, the ancients took the year to is the time-period from completion In some to the same {conjunction of moon with the sun) to the next new be the period when the sun returned This is the time of moon. But the length of the month so defined varies point in its path (the ecliptic). orbit round the sun. from 29.246 to 29.817 days, owing to the eccentricity revolution of the earth in its or of seasons, is the time of the moon's orbit and other causes. The month The tropical year, or the year synodic one vernal equinox lunation used in astronomy is the mean of passage of the sun from within The two years would period, which is the number of days comprised to the next vernal equinox. the number of if the vernal equinoctial point a large number of lunations divided by have been the same, point) were fixed. But lunations. Its value is given by (hereafter called the vernal d d narrated in Chapter IV, it recedes to the west at 1 lunation = 29. 5305882—O. 0000002 T as the rate of 50" per year. The tropical year is there- where T = no. of after 1900 A.D. fore less than the sidereal year by the time taken by The present duration of a lunation *= 29*5305881 to traverse 50% i.e., by .014167 days or d h m s the sun or 29 12 44 2. 8. There are other kinds of days m s 20 24 . months derived from the moon and the sun which For calendarical purpose, it is unmeaning to use will be discussed later. d the dates the sidereal year (365 . 256362), as then correspond to seasons. The use of the The Year and the Seasons : would not tropical year is enjoined by the Hindu astronomical year is the period taken by the seasonal The treatises like the and the PaMca to recur. The early people had but a characteristics Siddhantika. But these passages have been misunder- notion, of the length of the year in terms of vague stood, and Indian calendar makers have been using In the earliest mythology of most nations, the day. the sidereal year with a somewhat wrong length year was taken to have comprised 360 days, consis- the since the fifth century A.D. ting of 12 months each of 30 days. They apparently thought that the moon's phases recur at intervals of days. 30 1.3 THE PROBLEMS OF THE CALENDAR But experience soon showed that these measures Whatever may be the correct lengths of the astro- of the month and the year were wrong, but they have nomical month and the year, for application to human their stamp on history. The sexagesimal measure left in life, the following points have to be observed used in astronomy and trigonometry, as well as fanci- calendar. ancient framing a civil ful cycles of life of the Universe, invented by civil year and the month must have an nations, appear to have been inspired by these (a) The numbers. integral number of days. GEHERAL PEINCIPLES OF CALENDAR MAKING 159

during comparatively recent times. The ancient people (b) The starting day of the year, and of the month primitive devices. should be suitably defined. The dates must correspond used very ancients were strictly to seasons. The time-keeping apparatus of the the gnomon, the , and the water- or the (c) For purposes of continuous dating, an era the clepsydra. The first two depend on the motion of should be used, and it should be properly defined. sun, and require correction. The water-clock which (d) The civil day, as distinguished from the probably was first invented in Egypt, appears to have , should be defined for use in the been used down to the time of Galileo, when the

calendar. 1 discovery of pendulum motion led to the invention of months have to be kept, there (e) If the lunar clocks based on pendulum motion or use of the balance devices for luni-solar adjustment. should be convenient wheel. satisfactory solution of these pro- A correct and Subdivisions of time can be measured by the motion has not yet been obtained, though in the form regularly at the blems of any substance, which repeats itself ; calendars which have been used by of hundreds of present time in addition to pendulum clocks, quartz- of the world during historical times, different people clocks, and ammonia clocks have been used. The so attempted solutions. The early the we have many latter depend upon harmonic motions within on insufficient knowledge of the calendars were based ammonium molecule, giving rise to spectral lines whose duration of the natural time cycles—day, month and frequency can fcfe accurately measured. facts, year—an^ le(l to gross deviations from actual The present divisions of the solar day have which had to be rectified from time to time by the interesting history. Julius Caesar, Pope intervention of dictators like Sumerians It is stated by Sarton that the ancient Gregory XIII, or a founder of religion like Mohammed, dwellers of ) divided the day-time and Shah the Seljuk, or (original or by great monarchs like Melik night-time into three watches each. The Akber, the great Indian emperor. were naturally of unequal lengths and varied through- the historical order of development, that the Owing to out the year. It was only during equinoxes been used for the double purpose : calendars have watches were of equal length, each of our 4 . adjustment of the civic and adminis- (i) of the These unequal watches continued down to medieval trative life of the nation, -wise as times. The life of a medieval monk was socio-religious life of the (ii) of the regulation of follows. people. the night. The monk (1) Matins—last watch of In ancient and medieval times, society, state and got up nearly two hours before sun- church were intermingled, and the same calendar rise and started his work, served all purposes. The modern tendency is to (2) Prima—at sunrise, socio- dissociate civic life and administration from sunrise and noon- (3) Tertia—half-way between due to the enormous growth of religious life. Also time of saying , the world, the need intercourse amongst all nations of (hence the word, Siesta- (4) Sexta—at noon felt for a World Calendar dissociated from has been midday rest), bias. Owing to historical all religious and social whence our word Noon, (5) Nona—mid-afternoon, calendar is now used inter- reasons, the Gregorian before sunset, (6) Vespers—an civic and administrative purposes, but nationally for sunset. (7) Compline— at it is very inconvenient, and proposals have been made The watches were variable in duration and in their to the U. N. O. for the adoption of a simple World starting moments. Sarton remaks : Calendar (vide § 2.7). the day into A clock regularly running and dividing been, at first, more periods of equal duration would have than useful. For monastic purposes, a human SUBDIVISIONS OF THE DAY disturbing 1.4 or lay brother variable clock {e. g. a bell rung by a monk irregular intervals) was more practical than For pactical prurposes, the day is divided into 24 at the needed into an automatic one.* hours, an hour into sixty and a But even in ancient times, the need for measure- sixty seconds. ancient ment of equal intervals of time was felt. The 1 mean solar day « 24 x 60 x 60 = 86, 400 seconds. Babylonians used the Nychthemeron (Day and Night The subdivisions of time are measured by highly Science, Vol. Ill, Part I, developed mechanical contrivances (clocks, watches *Sarton, Introduction to the History of and chronometers), but they have come into use only p. 716. THE CALENDAR REFORM COMMITTEE 160 REPORT OF lipiika in of minutes ( kola or ) each, the same as the number into 12 hours of 30 Qesh combined- JMrafro) (astronomical treatises of the the day- a circle. In -4 minutes. The Egyptians divided nomenclatures of Qesh being there are conceptions with into 12 hours. Hindus) time into 12 hours, and the night no practi- light smaller divisions of time, but they had 24-hour division for the still Later in medieval times, the adopted. The cal utility. whole day (day and night) has been time-periods of the sun, and the moon, A.M. and P.M. were for the sake of None of the division into the lunations and times a year and the , and that the maximum number of m%. the convenience, so the day on the an hour, half-lunations are integral multiples of ; be rung, on the completion of bell has to several places of bell 24 the figures run to for apparently ringing a other hand, would not exceed 12, who quickly dis- decimals. How did the ancients, be a torture of the flesh. times would not integral multi- covered that the time-periods were secured by the divisions of the day were findings ? The broad ples of the day, express their the day-time (from in two ways. They divided into the history of Hindus will take us a long dive parts each called a It to sunset) into 4 equal story. The sunrise mathematical notation to elucidate this also similarly or . The night time was Exact prahara reader may consult Neugebauer's prahara is so curious 4 equal praharas. The Awakening divided into van der Waerden's Science measurement that even in Antiquity or popular a unit in Indian time very cumbrous 51-61). In fact, the symbolism was terms of praharas and (pp the lay man expresses time in notation about the discovery of the decimal system of division of the before half praharas. An alternative replaced the old 600 A.D. in India, where it quickly obtained by dividing the daytime time is the 'muhurta' quickly adopted notation. The discovery was determined by gnomon shadow cumbrous into 15 muhurtas purposes, but was first made measured from by the Arabs for certain The day muhurtas were treatise on lengths by Leonardo of Pisa in a The night muhurtas known to Europe lengths of shadows of the gnomon. but a few more Arithmetic published in 1202 A.D., part of the night time. ate similarly the fifteenth universally adopted. centuries passed before it was and night are not equal by means of As the durations of day practice of expressing fractions the The and autumnal equinox days, India and Europe. In except on the vernal decimals came later, both in not the muhurta of the day-time have wrote an astronomical Prahara and India an astronomer who counterparts. as those of their nocturnal in 1099 A. D. was called same durations treatise called 'Bhasvati* they are however equal, when hundreds) because he On equinox days, Satananda, (i.e. revelling in hundredths i.e. i as 25 =3* 30- used to write fractions in 1 Prahara

civilization have been described. We have described say the birth-day of , it can be in Chap. II, the purely solar calendars, in which the seen from an inspection of his birth register that it moon is altogether discarded as a time-marker. This took place on Feb.ll, of the year 1732. But this practice originated in Egypt about 3000 B.C. These practice by itself does not enable a scientific chrono- calendars require only a correct knowledge of the logist to fix up the event unambiguously on the length of year, and are therefore comparatively simpler. absolute Scale of Time, unless the whole history of

They required very little or almost no knowledge the particular method of date-recording is completely of astronomy. and accurately known One must know the lengths of the individual months, the leap-year rules, and We have described in Chap. Ill, the luni-solar the history of calendar reform. In the particular case calendars, prevalent in ancient Mesopotamia, India, mentioned, though George Washington * according to China and most other countries. In these calendars, his birth register is stated to have been born on Feb. both the sun and the moon are used as time-markers, 11, 1732, his birth-day is celebrated on Feb. 22. Why ? and therefore precise knowledge of their motion in Because Feb. 11 was the date according to the Julian the was essential for the formulation of a calendar. But in 1752, England (America was then correct calendar. We mark two stages : first the a colony of England) adopted the reformed Gregorian formulation of a calendar from a knowledge of only calendar, and by an Act of Parliament, declared Sept. the length of the year, and of the mean lunar 3 to be Sept. 14, a difference of 11 days. Following month. This was an older phase. It did not work the Gregorian calendar, Washington's birth-day had satisfactorily, because it depended on the mean motion to be shifted to Feb. 22. A scientific chronologist, say of the two luminaries. Actually, the time-predictions of China, would find it difficult to locate Washington's have to be verified by actual comparison of the birth-day unless he knew the whole history of the predicted happenings (say of the vernal equinox Gregorian calendar. day in the case of the sun, or the first appearance This difficulty is more pronounced Of the crescent of the moon after new moon on the when we have to deal a luni-solar calendar, western horizon) with the time of actual happenings. say that of Babylon. Many records of lunar occuring in This gave rise to the need for watching the daily Babylon were known to the Alexandrian astronomer, Claudius motion of the two luminaries, and invention of Ptolemy, but they were dated in Seleucidean era, and methods for recording and storing these observations ; Babylonian months, say year 179, 10th of . in other words/ this led to the science of astronomy. Now the Babylonian months were lunar, had lengths of 29 Early astronomy is almost completely calendarical. or 30 days, but the year could have lengths of At a later stage, the five planets attracted attention, 353, 354

383, 384 ( vide § 3'3 ). Therefore when two on account of their association with astrology. datings were compared, it was impossible to calculate We have therefore devoted Chap. IV to calendaric the number of days between them, unless the investi- astronomy, which was evolved by the Chaldeans and gator had before him a record showing the lengths of taken over from them by the Greeks, and in time years and months between the two events. Ptolemy diffused to other countries. expressed his datings according to the Egyptian calen- In Chap. V, we have described the various stages of dar, which enables one to calculate the interval far the development of the Indian calendar : —the empiri- more easily. He must have taken lot of pains to carry out the conversion from the Babylonian cal stage (Rg-Vedic), the mean motion stage ( Vedanga to Egyptian Jyoti$a), and the scientific stsfge (Siddhanta Jyoti$a). dates.

From 1200 A.D., astronomical studies became decadent How much better it would have been if a great in India, and we have analysed the cause of decadence. genius at the beginning of civilization, say near about We have given a full account of precession, as most 3000 B.C., started with a zero day, and started the Indian calendar makers still believe in the false theory practice of dating events by the number of days of Trepidation which disappeared from Europe after elapsed since this zero date, to the date when this 1687 A. D. particular event took place. Such a great genius did not appear and a confusing number of calendars came

into existence. The scientific chronologist is now

1.5 AHARGANA OR HEAP OF DAYS : JULIAN DAYS faced with the reverse problem : Suppose two ancient or medieval events are found dated according to two Though the Flux of Time is a continuous process, different calendars. How to reduce these dates to an it is divided for the sake of convenience and for absolute chronological scale ? natural reasons too, into years, months and days. The years are mostly counted from the beginning of For this purpose, a medieval French scholar, Joseph an era, so that if we wish to date a memorable event, Scaliger introduced in 1582 A. D., a system known as —

THE CALENDAR REFORM COMMITTEE 162 REPORT OP uniform time scale The For this purpose a continuous and Days' after his father, Julius Scaliger. 'Julian was necessary, and this was served by the ahargaQa. Julian period in years is Sryabhata had somehow the idea that the planets, 7980 years -19x28x15 planets and the two nodes (which were treated as years of the , point of Aries 19 being the length ia in Hindu astronomy) return to the first Indiction, - c „ of the Cycle of 6 was a unique after every 4.32 x 10 years, and there Solar Cycle, A Oo , of the of the Hindu and 28 » » » n » assemblage of planets at the first point that these three cycles he called the beginning It was found by calculation sphere at some past date which 4713 B.C. So the Julian assigned to the beginning started together on Jan. 1, of Kali . The date numbers started from February 17-18. The as well as the is now known to be 3102 B.C., period 6 all x-10 is intended to include revolution of planets of 4.32 that date. The Julian period common period of the future to which refe- consiting of dates both in the past and in years constitute a Mahayuga has an to be made and to that extent it rence is likely yuga of 1.728 x 10° years lies within the an era whose 6 advantage over of 1.296 x 10 " time. The years of the Julian " limits of historical of 0.864 x 10* now, but the day of the period are seldom employed 0.432 x 10 6 " and of frequently used in astronomy 6 Julian period is Total 4.32 x 10 years day, the Julian day calendaric tables. Unlike the civil It may be noticed that number is completed at noon. 4.32 xl0 c ~ 12000 x 360 number of world- Let us give the Julian days for a Sryabhata gave tables showing the number of asgivenbyGinzel, in his Eandbuch der Mathe- events, in the period of sidereal revolutions of planets . Technischen Chronologic matischm und in a 4.32xl0 6 years. The total number of days the length of a Table 1—Julian day numbers. Mahayuga- 1,577,917,800 which gives = 365.25875 days. Date Julian day year was evidently not satisfied that B.C. .. 588,465 ... 17 February, 3102 were Kaliyuga Sryabhatas figures for the periods of planets 747 B.C. 1,448,638 ... 26 February, 1000Mahayugas - correct. He introduced a = 324 B.C. 1,603,398 ' ... 12 November, 9 supposed to consti- Philippi 4.32 xlO years. The Kalpa was A.D. 1,749,621 ... 15 March, 78 . Saka era tute a 'Day of the Creator, Grand-father A.D. 1,825,030 ... 29 August 284 the Diocletian He gave the number of. sidereal revolutions of 622 A.D. 1,948,440 ... 16 July, had improved Hejira planets in a Kalpa, and thought he 16 June, 632 A.D. 1,952,063 Jezdegerd Sryabhatas figure for the year. (Persian) = 365.25844 days. A.D. 1,954,167 Brahmagupta s year Burmese era 21 March, 638 879 A.D. 2,042,405 'Ahargana' or heap of days, Newar era 20 October, Sryabhata calculated 1079 A.D. 2,115,236 of the Mahayuga as the zero-day. Jelali era 15 March, from the beginning very large (Iran) But evidently this practice involves the that the ideas underlying is inconvenient to use. Therefore It may be mentioned here numbers, and earlier to modifications of the system continuous reckoning of days occurred much later astronomers used Sryabhata I (476- from other convenient epochs, the celebrated Indian astronomer, by counting Ahargaw designation different epochs which 525A.D.), who introduced it under the within historical reach. The

celebrated Arya- : ''AharganJ* or heap of days in his have been used are of idea of counting ahar^V^ or heaps bha\\ya. The The beginning of the Kali era or 3102 B.C. upto the given date (1) days elapsed from a specified epoch 505 A.D. as is found in necessity for (2) 427 Saka era or dawned upon the Hindu astronomers as a of . for that date. They FaftcasiddhanUka calculating the position of planets calendar for dating era or 665 A.D. as is found in the followed the cumbrous luni-solar (3) 587 Saka any simple rules. of Brahmagupta. purposes, which was not based upon Kha^iakhUyaka a of 29 or 30 days, and occasionally A.D, as is found in the It contains months (4) 854 Saka era or 932 which was deter- thirteenth month, the recurrence of Laghurn&nasa of Muiijala. methods. The dates of the months mined by elaborate 961 Saka era or 1039 A.D. in the Siddhftnta the (5) numbered serially, but designated by are not Sehhara of Srlpati. It was accordingly found tithi current at sunrise. The astronomical treatises of the Hindus have been impossible to work out the mean positions of almost categories according to the initial calendar alone. divided into three planets on the basis of the luni-solar GENERAL PRINCIPLES OF CALENDAR MAKING 163

disturbing discontinuity. The curious reader may go> epoch employed for calculation. In which the calcula- places through his article published in the Centaurus. tions of ahargay,a as well as the planetary mean when give below the corresponding Julian are made from the Kalpa, is called a Siddhanta ; We, however, certain modern the calculations start from a Mdhayuga or Kali' day numbers and Kali ahargana for it is done beginning it is called a Tantra, and when dates. from a recent epoch it is called a Karaw. In any Julian days Kali ahargaipa case, the mean places of the planets with their nodes (elapsed at and apsides are given for the epoch of the treatise (elapsed at following midnight) from which calculations are to be started, with rules mean noon) for finding the aharga^a for any later date. This 1900, Jan. 1 2,415,021 1,826,556 later ahargaya is then made use of in finding for that 1947, Aug. 15 2,432,413 1,843,948 date the positions of planets from their given initial 1956, Mar. 21 2,435,554 1,847,089 positions and their daily motions, for, The difference between the two numbers 588,465 The mean position at any epoch represents the Julian day number on the Kali epochs = the mean position at the initial epoch as already stated. + daily motion x ahargana. The use of ahargana plays a very important part in Due to the complexity of the Hindu luni-solar modern epigraphical researches when the date recorded calendar, one has to go through complicated rules in the in an inscription is required to be converted into determining the ahargaria for any particular day. corresponding date of the . If the Dr. Olaf Schmidt of the Brown University and the Kali aharga<$a for the recorded date can be determined, Institute of Advanced Study, in discussing the method then the problem of ascertaining the corresponding. of computation of the Aharga<$a at length, has pointed Julian or Gregorian date becomes a very easy task. out that the present Hindu method suffers from a CHAPTER II The Solar Calendar

2.1 TIME-RECKONINGS IN Julian Calendar

Like other nations of antiquity the early Egyptians 1 Thoth (30) 29 August had a year of 360 days divided into 12 months, each 1 Phaophi (30) d,o September early from the 1 of 30 days ; but they found very Athyr (30) 28 October recurrence of the Nile flood, that the seasonal year 1 Choiak (30) 27 November consisted approximately of 365 days, and that a month 1 Tybi (30) 27 December or lunation (period from one new-moon to another) 1 Mechir (30) 26 January was nearly 29| days (real length 29.531 days). But 1 Phamenoth (30) 25 February they had already framed a calendar on the 30-day 1 Pharmuthi (30) 27 March month, and 360-day year, which had received religious 1 Pachon (30) 26 April sanction. Hence arose the first necessity for calendar- 1 Payni (30) 26 May reform recorded in ancient history. To persuade the 1 Epiphi (30) 25 June people to agree to this reform their priests invented 1 Mesori (30) 25 July the following myth : (1 Epagomenai 5) 24 August

"The Earth god Seb and the sky goddess Nut had once The year was divided into three seasons, each of illicit union. The supreme god Ra, the Sun, thereupon four months : Flood time, Seed time and Harvest time. that the children of the cursed the sky goddess Nut But the Egyptians soon found that even a year of union would be born neither in any year nor in any month. 365 days did not represent the correct length of the Nut turned to the god of wisdom, Thoth, for counsel. Thoth year, which, as we now know, is nearly 365J days. played a game of dice with the Moon-goddess, and won This fact they appear to have discovered in two from her y^th part of of her light out of which he made different ways : five extra days. To appease Ba the Sun-god, these five (1) from their measurement of the length of the days were given to him, and his year gained by five days year from heliacal risings of Sirius, and while the Moon-goddess's year lost five days. The extra five days in the solar year were not attached to any month, (2) from their long record of floods extending which continued to have 30 days as before ; but these days over centuries. came at the end of the year, and were celebrated as the The fixed star Sirius, which is the most brilliant birthdays of the gods born of the union of Seb and Nut, star in the heavens, was early associated with the chief viz., Osiris, Iais, Nephthys, Set and Anubis, five chief gods * goddess of the Egyptian pantheon, Isis> and was the of the Egyptian pantheon." subject of observation by her priests. The day of its Let us scrutinize the implications of this myth. first appearance on the eastern horizon at day-break

This is tantamount to discarding the moo?i altogether as a (heliacal rising) appeared to have been carefully time-maker, and basing the calendar entirely on the sun. observed, and then on every subsequent day, its posi- This was a very wise step, for as has been found from tion in the sky at sunrise used to be noted. It was ancient times, the moon is a very inconvenient time- found that gradually it got ahead of the sun, so its marker. The Egyptians maintained the old custom appearance on the horizon would be observed sometime of keeping months of 30 days' duration, and 12 months before sunrise, and on every successive sunrise, it made a year. But five days (Epagomenai in Greek) were would be found higher up in the . After about added to the year at the end, which were not attached a year it would be seen in the western horizon at to any month. They were celebrated as national sunset for a few days till it could no longer be traced. holidays. Each month of the Egyptian calendar was The Egyptians found as a result of long periods of divided into 3 , each of 10 days (Decads). observation, that it came again to the horizon at day break at the end of 365^ days, not 365 days. If on one The names of the Egyptian months together with year, the heliacal rising of Sirius took place on Thoth 1, the dates of beginning of each month as they stood in (Thoth was the name of the first month of the year) 22 B.C., are as follows : four years later it would take place on Thoth 2, and

* Zinner— Qeschichte der Sternkunde, p. 3, forty years later on Thoth 11. As the mean interval THE SOLAB CALENDAB 165

of heliacal rising of Sirius at the latitude of Memphis On account of its simplicity, the Egyptian calen- was 365.25 days, the Egyptians concluded that the dar was adopted by many nations of antiquity, and heliacal rising of Sirius would continue to move round even sometimes by the learned Chaldeans and Greeks,.

Fotheringham : the year in a complete cycle of ecu 1460 years ; called observes

the , after Sothis (Isis). They also appear "The Egyptian calendar was, upto the time of Julius- to have found from observations over long periods of Caesar's reform of the Roman calendar in 46 B.C., the only years that the Nile flood occurred not at intervals of civil calendar in which the length of each month and of 365 days, but of 365^ days. each year was fixed by rule instead of being determined by the discretion of officials or by direct observation. If the On account of the deficiency of i day in the year, number of years between two astronomical observations, the year-beginning lost touch with the arrival of the dated by the Egyptian calendar, was known, the exact Nile flood, though the temple priests had devised a number of days could be determined by a simple calculation. method of finding out the interval between Thoth 1, No such comparison could be made between dates referred and arrival of the Nile flood by observations of the to any other civil calendar unless the computer had access heliacal rising of the bright star Sirius, identified with to a record showing the number of days that had actually their chief goddess Isis. But they kept the knowledge been assigned to each month and the number of months that to themselves. had actually been assigned to each year. It is true that the Egyptians did not use a continuous era, but were content to If the Egyptians carried out a reform of their calen- number the years of each reign separately, so that there was. dar incorporating this fact, that the tropical year had a a difficulty in identifying a particular year, but the astronomers length of days, their calendar could have been 365* of the Ptolemaic age rectified this by the introduction of almost perfect. All that they had to do teas to take 6 eras.* The simplicity and regularity of the Egyptian extra days instead of 5 every fourth year. But the 365- calendar commended it to astronomers, who found it day year had so much soaked into the Egyptian mind, excellently adapted to the construction of tables that could that this move for calendar reform was never adopted be readily applied and used even for a remote past or for inspite of serious attempts by earlier Pharoahs, and a distant future without any fear that the system by which later, serious a more one by the Graeco-Egyptian time was reckoned in the tables might not coincide with the ruler system in Ptolemy Euergetes ( 238 B.C. ). But it became actual use. In the second century B.C. we find generally Chaldean known that the correct length of the year observations, sometimes nearly six centuries old, reduced to was 365^ days. Fotheringham in his article on 'The the Egyptian calendar in the works of Hipparchus B.C.), Calendar" observes : (126 who observed not in Egypt but at Ehodes, and cited from him by the Egyptian Ptolemy in An additional day was inserted at the close of the the second century of our era ; we also find in the second Egyptian year 23-22 B.C. on August 29 of what we call the century B.C., an Athenian observation of 432 B.C. reduced Julian calendar, and at the close of every fourth year after- to the Egyptian calendar oh an inscription found at , wards, so that the reformed or Alexandrian year began which appears to represent the work of the astronomer on August 30 of the Julian calendar in the year preceding Epi genes", t a Julian and on August 29 in all other years. The effect of this reform was to keep each Egyptian This calendar survives in a slightly modified form in the month fixed to the place in the natural year which it , the three first months of happened to occupy under the old calendar in the years the old Egyptian year corresponding exactly with the 2G-22 B.C. But the old calendar was not easily suppressed, three last months of the Armenian year. The and we find the two used side by side till A.D. 238 at least. Alexandrian calendar is still the calendar of Abyssinia The old calendar was probably the more popular, and and of the Coptic Church, and is used for agricultural was preferred by astronomers and astrologers. Ptolemy purposes in Egypt and other parts of northern . (150 A.D.) always used it, except in his treatise on annual phenomena, for which the new calendar was obviously more convenient. Theon in the fourth century A.D., though 2.2. SOLAR CALENDARS OF OTHER ANCIENT NATIONS mentioning the old calendar, habitually used the new. The story of the calendar in Egypt has been given Though not quite perfect, the Egyptian calendar in full, because the ancient Egyptians evolved a very was greatly admired in antiquity on account of its . simple and convenient calendar which, as mentioned simplicity, for the length of the year and the months before, would have been almost perfect (provided the were fixed by definite rules and not by officials or year was taken to consist of 365J days instead of 365 days). pandits. The religious observances fell on fixed days This was rendered possible by their bold initia* of the month and at stated hours, which were fixed * The Nabonassar Era—vide § 3.4. about 1200 B.C. + Article on *The Calendar', Nautical Almanac, 1935. , — —

OF TflE CALENDAR REFORM COMMITTEE 166 REPORT

time-marker. But 7. Bagayadi tive of discarding the moon as a civilized world 8 people in the remaining parts of the Atriyadija India and China) in ancient 9. (e.g., in Babylon, Greece, preferred 10. Anamaka and moderm times, retained tne moon and calendars described 11. Margazana the more complex luni-solar fortunate, for if their 12. Viyachna in Chap. III. This was rather the Egyptian calendar, the priest- rulers had adopted The Persians did not have weeks or decads, but ancient nations, particularly of astronomers of named * the successive days of the month serially never have taken to observation as Babylon, would according to their gods or religious principles, planets, and tried of the sun, the moon, and the below : for predicting their to evolve mathematical formulae (the Ephemerides) positions amongst stars in advance astronomical Nearest Vedic which form the basis on which our Zend Pehlewi for the Egyptian knowledge has been built up ; results of 1. Ahurahe mazdao AGharmazd calendar was evolved simply from and required 2. Vanheus mananho VohGman experiences extending over centuries, observations either 3. Ashahe vahistahe" Ardavahisht almost no astronomical sense, or except the heliacal 4. Kshathrahe vairjghe* Shatvalro of the sun, the moon and stars, and convenient, but O. opeiltd.J

THE SOLAR CALENDAR 167 471- 16th March, 1079 A.D. There are many Mordan-mah (31) begins 23 or 24 July interpretations of the Jelali reform, the modern Shartvar-mah (31) 23 or 24 August interpretation being 8 intercalary days in 33 years, Mehr-mah (30) 23 or 24 September giving the length of the year as 365.24242 days. The Aban-mah (30) 23 or 24 October year started from the day of or next to vernal equinox. Azar-mah (30) 22 or 23 November Dai-mah The Parsees in India, the followers of the Prophet (30) 22 or 23 December Bahman-mah (30) 21 Zarathustra are the descendants of Iranians who took or 22 January Esfand-mah (29, 30) or shelter in India on the. conquest of Persia by the 20 21 February Arabs. The following details about their calendar is reproduced from Encyclopaedia Britannica (14th 2.4 THE FRENCH REVOLUTION CALENDAR

edition), Parsees : The Egyptian calendar attracted the notice of The Parsees of India are divided into two sects, the the calendar committee of the French Revolutionary Shahanshahis and the Kadmis. differ to the correct They as Government (1789-1795) who wanted to replace chronological date for the computation of the era of Religion by Reason. The committee consisted, amongst Yazdegerd, the last king of Sassanian dynasty, who was others, the great mathematicians Laplace and Lagrange dethroned by the caliph Omar about A.D. 640. This led to and the poet d'Eglantine. Laplace proposed that the the variation of a month in the celebration of the festivals. year 1260 A.D,, when according to his calculations the The Parsees compute time from the fall of Yazdegerd. Their equinoctial line ivas perpendicular to the apse line of calendar is divided into twelve months of thirty each days ; the Earth's orbit should be taken the starting point of the other five days, being added for holy days, are not the French Revolution Era in place of a hypothetical counted. Each day is named after some particular angel of year of Chrisfs birth. But the calendar committee bliss, under whose special protection it is passed. On feast did not agree with him but started the era of the days a division of five watches is made under the protection glorious French revolution, with the autumnal of five different divinities. In midwinter a feast of six days equinox day of 1792 A.D., as this was nearest in date is held in commemoration of the six periods of creation. to the outbreak of the revolution. Sentiment proved About March 21, the vernal equinox, a festival is held in stronger than cold scientific reasoning. honour of agriculture, when planting begins. In the middle

of April a feast is held to celebrate the creation of trees, French Revolution Calendar shrubs and flowers. On the fourth day of the sixth month ( 1792 Sept. 22 to 1806 a feast is held in honour of Sahrevar, the presiding ) The consist over mountains and mines. On the sixteenth day of the ( Months of 30 days each ) seventh month a feast is held in honour of , the deity Month Season Month beginning presiding over and directing the course of the sun, and also a festival to celebrate truth and friendship. On the tenth Vendemiaire Grape gathering Sept. 22 day of the eighth month a festival is held in honour of Brumaire : Fog Oct. 22 Farvardin, the deity who presides over the departed souls of Frimaire : Frost Nov. 21 men. This day is especially set apart for the performance

of ceremonies for the dead. The people attend on the hills WINTER

where the *' towers of silence" are situated, and in the sagris Nivose : Snow Dec. 21 pray for the departed souls. The Parsee scriptures require Pluviose : Rain Jan. 20 the last ten days of the year to be spent in doing deeds Ventose : Wind Feb. 19 of charity. In modern Iran when Riza Shah Pahlavi came to 7. Germinal Seed March 21 power in 1920, he instituted a reform of the existing 8. Floreal : Blossom April 20 Muslim calendar abandoning the strictly lunar 9. Prairial : Pasture May 20 reckoning and introducing purely solar year restoring the early Persian names which had never fallen

entirely out of use. 10. Messidor : Harvest June 19 11. Thermidor Heat July 19 The names of the months, and their lengths are 12. Fructidor : Fruit Aug. 18 as follows : Day of Virtue Sept. 17 Parvardin-mah (31) begins 21 or 22 March „ Genius * 18 Ardibahisht-mah (31) „ 21 or 22 April „ Labour ,, 19 Khordad-mah/{31) „ 22 or 23 May „ Opinion » 20. Tir-aiah (31) M 22 or 23 June „ Rewards « 21 COMMITTEE 168 REPORT OF THE CALENDAR REFORM

and so the year-length would have been 366£ days, The seven-day was abandoned for a week of the poet only one day in excess of the correct length. But as 10 days. The month names were invented by were the intercalation was applied tather arbitrarily some- member of the committe. The last five days Sans-Culottides times after two years and sometimes after three years, dedicated to the service of the poor ( ) year-beginning gradually bhifted and the year and did not form part of any month. the started before the arrival of the proper seasons. After 13 years of service, the French Revolution The days of the month in the Roman calendar were calendar was abolished by Napoleon Bonaparte, then enumerated backwards from the next following Kalends (1st part of his bargain with the emperor of , as months, of month), Nones (5th of month, except in the 31-day Roman Catholic Church for his coronation by the Pope. when the 7th of month), or Ides (13th of month, except in the 31 -day months, when the 15th of month). Ihe day after the , for instance, would be expressed as 2.5 THE ROMAN CALENDAR 17 days before the Kalends of April. (The Christian Calendar) The Romans upto 45 B.C. apparently had rather and correct length of the year. What is now known as the Christian calendar, a vague idea of the originally conquest of Egypt in 44 B. C. used all over the world for civil purposes, had Julius Caesar after his the advice of nothing to do with Christianity. It was, according to introduced the leap-year system on that one view, originally the calendar o£ semi-savage tribes Egyptian astronomer Sosigenes, who suggested should be fixed of Northern Europe, who started their year sometime the mean length of the year length of the before the beginning of Spring (March 1 to 25) and had at 365i days, by making the normal only ten months of 304 days ending about the time of year 365 days and inserting an additional day every the (December 25), the remaining 61 days fourth year. At the same time the lengths of forming a period of hybernation when no work could months were fixed at their present durations. The be done due to the onset of winter, and were not extra day in leap years was obtained by repeating the counted at all. The city state of Rome also had sixth day before the Kalends of March. The name originally this calendar, but several corrections were Quintilis, the 5th month from March, was changed to made by the Roman Governments a -^t epochs July (Julius) in 44 B.C. in honour of Julius Caesar, and and the final shape was given to it by Julius Caesar in the name Sextilis was changed to August in 8 B.C. so revised is known as the Julian reign of his successor, , and in 46 B:C ; the calendar during the calendar. honour of him. There is a very widespread idea that the durations, of July and August were fixed at 31 days As already stated, this calendar originally had each in order to please 1 the two Roman dictators contained ten months from March to December Julius Caesar, and Octavious Caesar, also called comprising 304 days. It may be regarded as certain Augustus, and for this purpose the two extra days were that the months were lunar. The second Roman king cut off from February, thus reducing its duration to of the legendary period, Numa Pompilius, is supposed 28 days. It is a nice story, but does not appear to to have added two months (51 days) to the year in been critically probed. January have about 673 B.C., making a total of 355 days ; Owing to the drifting of the year-beginning, the (named from the god Janus, who faced both ways) now year 46 B.C. started about 90 days before the proper began the year, and February preceded March, which seasons. The months were first brought back to their became the third month. The number of days of the correct seasons by giving the year corresponding to months were 29, 28, 31, 29, 31, 29, 31, 29, 29, 31, 29, 29. 46 B.C., a normal intercalation of 23 days after February Adjustment of the year to the proper seasons was and then inserting 67 additional days between obtained by intercalation of a thirteenth month of November and December. This year therefore contai- actually 22 or 23 days* length (called Mercedonius) ned 445 days in all and is known as the 'year of after two years or three years as was considered nece- confusion. ssary, and was inserted between February and March.* But the perfect calendar was still a long way off. Had the intercalation been applied regularly at alter- Caesar wanted to start the on the 25th nate years the additional days in four years would December, the winter solstice day. But people resisted have been 45 (22 + 23) or Hi days per year on average, that choice because a new-moon was due on , * Id fact, the intercalary month consisted sometimes of 27 day $ 45 B.C. and some people considered that the new-moon sometimes of 28 days and was inserted after February and 23. Th was lucky. Caesar had to go along with them in their last five days of February, which were due to be repeated after ti i desire to start the new reckoning on a traditional lunar close of the intercalary month, were not actually repeated, result-h-.g in the intercalation of 22 or 23 days only. landmark. . ..

THE BOLAB CALENDAR 169

The Julian calendar spread throughout the Roman Invention of the Seven-day Week empire and survived th$ introduction of Christianity. Much of ancient astronomical knowledge is due to But the Christians introduced their c^wn holidays Chaldean astronomers who flourished between the which were partly Jewish in origin and for, this, luni 4- seventh century B.C. and the third century A.D., as solar and week-day reckonings had to be adopted. related in §4*7. They gave particular attention to the study of the movement of the sun, the moon and the planets, which they identified with their gods, Origin of the Seven-day Week because they thought that destiny of kings and states

were controlled by the gods, i.e., by the planets, Historical scholarship has shown that unlike, the and attached the greatest importance to the observa- year and the month, the seven-day week is an artificial tion of the position and movement of planets. They man-made cycle. The need for having this short attached magical value to the number 'Seven' which cycle arose out of the psychological need oi mankind was the number of planets or gods controlling human for having a day of rest and religious service after destiny. protracted labour extending over days. The seven-day week with a sabbatical day at the end, or something In 'Planetary Astrology', the sun, the moon and

similar to it, is needed not only by God Almighty, but the five planets, were identified with the chief gods of there no also by humbler toiling men. But has been the Babylonian pantheon^as given below : unanimity of practice.

Planets Babylonian As already stated, the ancient Egyptians had a ten- day week. The Vedic Indians had a six-day week God-names Iheir function started the month on the Pestilence and Babylonians . of The ancient who (1) . .Ninib God day after new-moon, had the first, eighth, fifteenth, Misery. marked out for religious of Gods. twenty-second day . King and the (2) Jupiter. . . , week with services. This was a kind of seven-day of (3) Mars . . God War. , but the last week might be of eight or nine of Order or . . & , Law (4) Sun . Shamash God days' duration, according as the month which was Justice. lunar had a length of 29 or 30 days. The ancient (5) Goddess of Fertility. Iranians had a separate name for each day of the God of Writing. month, but some days, at intervals of approximately (6)

seven, were marked out as Din-i-Parvan, for religious (7) God of Agriculture. practices. The pattern followed appears to have been were similar to the Babylonian practice. The continuous These seven gods, sitting in solemn conclave, seven-day week came into general use sometime after supposed to control the destinies of kings and their will and the first century A.D. It was unknown to the writers countries, and it was believed that country or its of the New Testament who do not mention anything judgement with respect to a particular the about the week day on which Christ was crucified or ruler could be obtained from an interpretation of the the week day on which he is alleged to have ascended position of the seven planets in the heavens, anfl retrograde). to Heaven. The fixing of Friday and for these nature of motion of the planets (direct or dating from the fifth incidents is a later concoction, The Chaldean god-names are given in the second century after Christ. All that the New Testament column, and the functions they control in the third b(Qoks say is, that He was crucified on the day before the column. Their identification with the Roman gods .is Hebrew festival of which used to be celebrated given in the first column. The planets* * were put and is still celebrated on the full-moon day of the in the order o^ their 'supposed distances from .the earth. month of Nisan. Further, the day was divided into 24 hours, and The continuous seven-day week was evolved on each of the seven gods was supposed to keep watch astrological grounds by unnamed astronomers who on the world over each hour of the day in rotation. may have been Chaldean or Greek at an unknown The particular day was named after the god who epoch, butbefore the first century A.D. The Jews kept watch at the first hour. Thus on , the ad&pted it as a cardinal part of their faith during watching god on the first hour was Saturn, and days of their contact with the Chaldeans. It is not their the day was named after him. The succeeding invention. We give a short story of this invention, as quite old sense of tvavderr it is generally believed. But it may riot be Planets used nol in modern sense but m the & accurate in all details. ing heavenly body. '

REFORM COMMITTEE 170 REPOBT OF THE CALENPAB They gods the classics like the great epic . hours of Saturday Were watched by the seven occur in inscriptions only from 484 A.D., but not in in rQtation as- follows :~ inscriptions of 300 A.D. Even now, they form but an Saturday unimportant part in the religious observances of the which are determined by the moon s phases. Hours 12 3 4 5 6 7 8.. .14 15 22 23 24 25 Hindus (Sun) It can therefore be said that the unbroken seven- God Watching 1 2 3 4 5 6 7 1... 7 1 1 2 3 4 day week was not a part of the religious life of any The table shows the picture for Saturday. On ancient nation, and it is not, even now, part of the so the day, Saturn keeps watch at the first hour, this religious life of many modern nations. It is a man-made is watched is named after him. The second hour day institution introduced on psychological grounds, and and so on. by (2) Jupiter, third by (3) Mars over therefore can be or should be modified if that leads 15th and is thus seen to preside at the 8th, Saturn to improvement and simplification of human life. 24th and 22nd hours of Saturday. Then for the 23rd, Mars 25th hours come in succession (2) Jupiter, (3) The Christian Era the first hour of the and (4) Sun. The 25th hour is vogue much accordingly named after the The present Christian era came into next . day, which was is About 530 A.D., the era-beginning was fixed presiding planet of the hour, vwrM No. 4 which later. If from the birth year of Christ which was fixed after Sun. We thus get Sunday following Saturday. amount of research by the Scythian we now repeat the process, we get the names of the a certain Exiguus and Christ's birth day (Christmas) . Dionysius week days following each other, as follows was fixed on December 25 which was the Julian date Saturday, Sunday, , , birth for the winter solstice day and the ceremonial , , and Friday. day of the Persian god Mithra in the first century B.C. The discovery of a Roman inscription at shows that King Herod of the who is said to have ordered the massacre of innocents was dead for four years at 1 A.D., and therefore Christ must have been born on 4 B.C., ox somewhat earlier.

Saturn

2.6 THE GREGORIAN CALENDAR

The Julian year of 365.25 days was longer than the true year of 365.2422 by .0078 days, so the winter A.D. solstice day which fell on December 21 in 323 f 1582 A.D. and the Christmas C Moon fell back by 10 days in day appeared to be losing all connections with the noticed winter solstice. Similar discrepancy was also the .* in connection with the observance of Various proposals were made for correcting the derived from the order of planets. assembled in Fig. 1—The order of week-days error and the Council of Trent which by Sunday, then Monday and so on. Saturday followed 1545 authorised the Pope to deal with the matter. XIII became Pope, these the days When in 1572, Gregory Jews, it may be mentioned*, reckon The plan that was most seventh schemes were considered and the by ordinal numbers—the first, seconds festivals, is observed day. The "first day is Saturday. V * Easter, the^nost joyous of the Christian Christendom in commemoration of the resurrec- of its origin annually throughout The seven-day week, from the account full-moon Christ, on the first Sunday after the The conti- tion of based on astrological ideology. last days of Christ coincided is clearly following the vernal equinox day. The to the classical his death fell upon the day nuous seven-day week was unknown with the Passover fast of the Jews and Christians. on the 14* day of the month of Nisan. Greeks, the Romans, the Hindus, and early of the feast of the Passover, as well Easter is associated with the moon's phased into the Christian world by an edict As the date of It was introduced falling anywhere equinox day, it is a movable festival, Constantine, about 323 A.D., as the vernal the Roman emperor movement is going on for of between March 22 and April 25. A (Sunday), 1928 to the Lord's Day the Easter day ; m who cbanged the narrowing down the range of variation of Sabbath. Its Easter Act, which contingent the week-day next to the Jewish the British Parliament passed the fixed Easter day as the first into India is about the same time and upon its acceptance internationally, introduction between April the second Saturday in April, falling sources. The week-days are not Sunday after from the same Britannica> Easter). Veda or 9 and 15. {Vide Encyclopaedia found in earlier Hindu scriptures like the s THE SOLAE CALENDAR 171

favoured was the one that had been proposed by Easter day, based on the mean length of the lunar Aloysrus Lilius, a Neapolitan physician. In 1582, Pope month, and the determination does not require any Gregory XIII published a bull instituting the revised advance calculation of moon's position. The following calendar and ordained that Friday, October 5 of that are the principal holidays dependent on the date of year was to be counted as Friday, October 15. For Easter. the future, centurial years that were not divisible by Days before Easter Days after Easter 400 were not to count as leap-years ; in consequence the number of leap-years in 400 years was reduced Septuagesima Sunday 63 Low Sunday 7 from 100 to 97 and the year-length of the calendar Quinquagesima „ 49 Rogation Sunday 35 thus became 365*2425 days, the error being only one Ash Wednesday 46 Ascension Day 39 day in 3300 years. Quadragesima Sunday 42 Whit Sunday 49 7 The Gregorian reformation of the calendar was Trinity Sunday 56 at once adopted by the Catholic states of Europe, 2 Corpus Christi 60 but other Christian states took longer time to accept it. In Great Britain it was officially introduced in 2.7 THE WORLD CALENDAR 1752. As the error had by that time amounted to already As stated the Gregorian calendar is' a most 11 days, the September of 1752 was deprived of these inconvenient system of time-reckoning. The days days and 3rd September was designated as the 14th of the months vary from 28 to 31 ; quarters consist September. In some countries the Gregorian calendar of 90 to days 92 ; and the two half-years contain 181 was not adopted until the present century. China and 184 days. The week-days wander about the month from and Albania adopted it in 1912, Bulgaria in 1916, year to year, so the year and month beginnings may fall Soviet Russia in 1918, Roumania and Greece in 1924, on any week-day, and this causes serious inconvenience and in 1927. The rules for Easter which to civic and economic activities. The number were revised on the basis of the Gregorian calendar of working days per month varies from have not been adopted by the Greek orthodox 24 to 27, which creates considerable Church. confusion and uncertainty in economic dealings and in the preparation and analysis Inspite of its wide use, the Christian or Gregorian of statistics and accounts. The present Gregorian calendar is a clumsy and inconvenient system of time- calendar is therefore in dire need of reform. reckoning on account of the arbitrary length of its months ranging from 28 to 31. With a view to The question of resolving these difficulties had reforming it many schemes have been proposed, but been under consideration for more than the last 100 years. the one deserving of serious consideration is the new In 1834, the Italian Padre Abbe' Mastrofini World Calendar advocated originally by the Italian proposed the Thirteen-Month Calendar, which was astronomer Armellini in 1887 and adopted by the strongly advocated by the positivist philosopher August World Calendar Association, Inc., which has its head- Comte. But this calendar could not attract much quarters in New York (630, Fifth Avenue,, New York attention and consequently it was abandoned. The 20, N. Y), under the able presidentship of Miss plan of reform which has received the most favourable Elisabeth Achelis * comments is, as mentioned earlier, that of the World Calendar Association. In the ecclesiastical calendar some holy days are observed on fixed days of the year, others known as Let us explain the ideas behind this movement : movable festivals are observed on fixed days of the Calendars are used for regulating two essentially week. Most of these are at fixed intervals before or distinct types of human activities, after Easter day. When the Easter day of any year viz., is fixed, the dates of other movable festivals can (a) Civic and administrative, accordingly be ascertained. The Council of Nice (b) Social and religious. convened in 325 A.D. adopted the rule for fixing the In ancient and medieval times, different countries date of Easter—it was to fall on the first Sunday after and religions had developed their characteristic calen- the 14th day of the moon (nearly full moon) which dars to serve both purposes, but in the modern age, occurs on or immediately after March 21. In fact due to historic reasons, almost all countries use : there are certain special tables for determining the (a) the Gregorian calendar for regulation of

civic and administrative life, * She had been devoting her services ungrudgingly for the (b) their own characteristic calendars for regu- cause of calendar reform for the last twenty-five years, and also been publishing a 'Journal of Calendar Reform* since then. lation of social and religious observances.

0. B.— 80 172 BEPORT OF THE CALENDAR REFORM COMMITTEE

For example, India uses the Gregorian calendar for additional day, the Leap- Year Bay, is inserted at the civic and administrative purposes, but various,luni-solar end of June, and have the usual Worldsday at the end 1965 will also start on a Sunday. calendars for fixing up dates for religious festivals of of the year ; then Hindus in different states. The Islamic countries also So, by this simple device of having a Worlds-day follow the same practice Gregorian calendar for civic — at the end of every year and a Leap-Year Day at the and administrative purposes, but the lunar calendar end of June every fourth year, both without any for religious purposes. week-day denomination, every year can be made to Even in Christian countries, which apparently use start on a Sunday, This will prove to be an inestimable the Gregorian calendar for both purposes, in actual advantage for the civic life of mankind. practice, some additional time-reckonings have to be It is needless to add illustrations of the chaotic way fixing the date of Easter and other holi- done for in which the starting week-days of months vary. They it. These reckonings constitute days which move with are chaotic, because lengths of months vary from 28 ecclesiastic calendar, and are survival of earlier the to 31. There is not the slightest scientific justifica- luni-solar calendars. tion for these varying lengths. They are said to have The disadvantages of the Gregorian calendar as been due to the caprice of two Roman dictators, or

used for, civic and administrative purposes are : some other historical cause not yet clear. How much

better it would be for civic purposes, if each month (a) that the years and months begin on different start on a fixed day of the week ? week days, could

(b) that months are of unequal length—from 28 The World Calendar plan proposes to put this right to 31 days—and they start on week-days by dividing the year into four quarters, each of three which are most changeable. months of 31, 30, 30 days' duration. According to this This happens because a normal year of 365 days plan, April, July, October would have each consists of 52 weeks plus one day ; and a leap-year January, coming every fourth year, has 366 days, and consists of 31 days, and start on Sunday, 52 weeks plus 2 days. If a normal year begins on a February, May, August, November would have each Sunday, the next year will start on Monday, and the 30 days, and start on Wednesday, leap-year will jump two week-days. year after a March, June, September, December would have This causes a most undesirable wandering of the each 30 days, and start on Friday. ^week-day on which the year begins, as is seen for the If this plan be adopted, the calendar will be perpe- Tiext few years. This year 1954, has started on a tual and fool-proof. What a welcome change it would shall have Friday. We prove when compared to the present chaotic and 1955 starting on Saturday wandering calendar ? Sunday 1956 „ „ The year has to conform to the period of the sun, 1957 „ „ Tuesday and this is covered by the leap-year rules, amended Wednesday 1958 „ „ by Pope Gregory XIII in 1582. The leap-year rules Thursday 1959 „ „ introduced by the Iranian poet-astronomer Omar 1960 Friday „ „ Khayyam in 1079, were more accurate, but less 1961 Sunday „ „ convenient. The Gregorian leap-year rules will How much better it would be for civic and adminis- cause a mistake of only one day in 3,300 years, which if devised that every year trative life a system could be is trivial. should start on a Sunday ? As regards the duration of months, the World marked improvement on the The World Calendar Plan Calendar plan is a chaotic lengths and starting days of months, inherited This is how the World Calendar Plan proposes to from the Julian calendar, which has been tolerated prevent this wandering of the starting-day of the * year. too long. The months of all the quarters are identical simple device. It is a very and have got 31, 30 & 30 days, commencing on If from 1961, which starts on a Sunday, the last day Sundays, Wednesdays and Fridays respectively. Each of the year (ix. Dec. £1) which would be under the month has thus got exactly 26 working days. It has present system a Sunday, is called the Worldsday, that retained the present 12 months, thus the four quarters

is, no week-day denomination is attached to it, then are always equal, each quarter has 3 months or 13 1962 also will start on a Sunday, and so will every year weeks or 91 days beginning on Sunday and ending till the next leap-year 1964. On that year another with Saturday. THE SOLAB CALENDAR 173

The objections to the World Calendar plan come fraction of people who would want to observe their from several Jewish organizations, on the ground that religious rites accprding to established usage. the World Calendar plan interferes with the But these inconveniences can be adjusted by unbroken seven-day week, by introducing Worlds- agreement, and it would be egoistical on the part of day and Leap-year - Day without any week-day a particular community or communities to try to denomination. This, they say, will interfere with impede the passage of a measure of such great useful- their religious life. ness to the whole of mankind on the plea that the World Calendar plan interferes with the As already shown, the religious sanction for the continuous seven-day week. Calendars are based on Science, seven-day cycle is either non-existent, or slight, which everybody must bow to amongst communities other than the Jews, and even ; and on Convention, which may be altered by mutual consent. The amongst them, it dates only from the first century A. D. unbroken seven-day week is a Convention^ but the The claims of certain Jewish Rabbis to prove that the World Calendar plan has proposed seven-day week cycle has been ordained by God a far better Conven- tion, which should be examined its Almighty from the of creation which event, on own merits.* took place on the according to these Jewish Rabbis, As a result of a request from the Government of day of the autumnal equinox, also a new moon day, India, the proposal of the World Calendar Reform is a fantastic conception of medieval scholars, which had become the subject of discussion at the eighteenth and no sane man can entertain in these days of Darwin session of the Economic and Social Council of the Einstein. United Nations held at Geneva during June-July, 1954. Professor M. N. Saha, F. The World Calendar plan has no intention of R. S., Chairman, Calendar Reform Committee, attended the interfering with, the characteristic calendars of ECOSOC meeting at Geneva to explain communities or nations. They can exist side by side the desirability of the proposed with the World Calendar. For such communities as reform. intend to maintain the continuous seven-day week, * Being the full text of the address in support of the Indian their religious week-days, including Sundays, would proposal for World Calendar reform, by Prof. M. N. Saha, F.R.S- at week- no doubt wander through the World Calendar the 18th Session of the Economic and Social Council of the United days, and cause some inconvenience to the very small Nations, held at Geneva in June-July, 1954.

THE WORLD CALENDAR JANUARY FEBRUARY MARCH S M T W T F S S M T W T F S S M T W T F S In this Improved Calendar : 1 2 3 4 5 6 7 12 3 4 1 2 8 9 10 11 12 13 14 5 6 7 8 9 10 11 3 4 5 6 7 8 9 15 16 17 18 19 20 21 12 13 14 15 16 17 18 10 11 12 13 14 15 16 Every year is the same. 22 23 24 25 26 27 28 19 20 21 22 23 24 25 17 18 19 20 21 22 23 29 30 31 26 27 28 29 30 24 25 26 27 28 29 30 The quarters are equal : each quarter has exactly 91 days, 13 weeks or 3 months APRIL MAY JUNE ; the S M T W T F S M T T F S M T W T F S four quarters are identical in form.

12 3 4 5 6 7 12 3 4 1 2 8 9 10 11 12 13 14 5 6 7 8 9 10 11 3 4 5 6 7 8 9 Each month has 26 weekdays, plus Sundays. 15 16 17 18 19 20 21 12 13 14 15 16 17 18 10 11 12 13 14 15 16

22 23 24 25 26 27 28 19 20 21 22 23 24 25 17 18 19 20 21 22 23 L, Each year begins on Sunday, 1 January ; each 29 30 31 26 27 28 29 30 24 25 16 27 28 29 30 W| working year begins on Monday, 2 January. JULY AUGUST SEPTEMBER Each quarter begins on Sunday,, ends on S M T W T F S S M T W T F s m T w t f s Saturday.

1 2 3 4 5 6 7 12 3 4 1 2 8 9 10 11 12 13 14 5 6 7 8 9 10 11 3 4 5 6 7 8 9 The calendar is .stabilized and perpetual, by 15 16 17 18 19 20 21 12 13 14 15 16 17 18 10 11 12 13 14 15 16 22 23 24 25 26 27 28 19 20 21 22 23 24 25 17 18 19 20 21 22 23 ending the year with a 365th day that follows 29 30 31 26 27 28 29 30 24 25 26 27 28 29 30 30 December each year, called Worldsday dated "W" or 31 December, a year-end world . OCTOBER NOVEMBER DECEMBER Leap-year day is similarly added, at the end of S M T W T F S S M T W T F S S M T W T F S

1 2 3 4 5 6 7 12 3 4 1 2 the second quarter, called Leapyear Day dated 8 9 10 11 12 13 14 5 6 7 8 9 10 11 3 4 5 6 7 8 9 15 16 17 18 19 20 21 12 13 14 15 16 17 18 10 11 12 13 14 15 16 "W" or 31 June, another world holiday in 22 23 24 25 26 27 28 19 20 21 22 23 24 25 17 18 19 20 21 22 23L- 29 30 31 26 27 28 29 30 24 25 26 27 28 29 30 W| leap years.

W

The Luni-Solar and Lunar Calendars

Twelve lunar months of 29£ days each, making a 3.1 PRINCIPLES OF LUNI-SOLAR CALENDARS short of the solar total of 354 days, fall nearly 11 days Egyptians appear to have been the only of each month The year. In the next year, the beginning nation of antiquity who discarded the moon days will be cultural occurs 11 days earlier, in three years 33 entirely as a time-marker. Other contemporaneous the same season lost.* To fix the same month to of nations, e.g., the Sumero-Akkadians two or cultural always, there are no other means than after Babylon, and the Vedic Indians retained both the sun number three years to intercalate a Thirteenth Month, year, the and the moon as time-markers, the sun for the the year. 13, by repeating the last month of moon for the month. taken up The luni-solar adjustment which is next The Indian astronomers called the moon masakrt, problems stated by is the first step to the solution of (month-maker) and before the Siddhanta Jyotw time, whole solution, Pannekoek, but it is not however the important as a time- the moon was considered more of correct predic- for it leaves untouched the problem same with marker than the sun (tide §5). It was the first tion of the day when the crescent of the moon other nations too, for as Pannekoek remarks, we find This appears after new moon in the western horizon. the opinion written in the sacred books of many will be taken up later (vide §4). nations "For regulating time, the moon has been Luni-solar adjustment can be satisfactorily made created'*. of the length of the if we have accurate knowledge and the moon, The retention of both the sun lunation. tropical year, and of the mean length of the of which however, gives rise to a multitude of problems, were Let us see how these fundamental periods follows.* a fair summary is given by Pannekoek as determined in ancient times. Babylonians, "With all peoples of antiquity, the Indians, the period the moon-calendar used ; Jews, Greeks, we find Length ot Seasons and the Year the first appearance of of the moon, the regular sequence of as sky, its growth to first length of the year was obtained in Egypt, the fine crescent moon in the evening The up later and from the recurrence of the Nile quarter, to full moon, at the same time coming we have already seen, decrease to last quarter till such striking natural filling the whole night, then the flood. In , no crescent before sunrise It is very probable that its disappearance after the last thin phenomena were available. moon's phases in the gnomon, was seen,—this regular cycle of the the Babylonians early learnt the use of the the first basis of the period of 29i days was everywhere with the aid of which they could determine summer and winter ". cardinal days of the year :

174 THE LUNI-SOLAE AND LUNAR CALENDARS 175

Table 2.—Showing the length of seasons. 3.2 MOON'S SYNODIC PERIOD OR LUNATION : EMPIRICAL RELATION BETWEEN THE YEAR Euctemon Calippos Chaldean Correct AND THE MONTH values for (432 B.C.) (370 B.C.) B.C.) 1384 B.C. (200 The solar year has thus a pretty nearly constant days days days days value, but even the earliest astronomers appear to have observed, that the lunation, or the synodic period Spring 93 94 94.50 94.09 of the moon is not a constant, but is variable. As a Summer 90 92 9273 91*29 matter of fact, the period varies from 29*246 to 29.817 days—nearly fourteen hours. The observation of the Autumn 90 89 88*59 88.58 actual motion of the moon formed the most formidable

Winter 92 90 89'44 91'29 problem in ancient astronomy {vide §4).

But all ancient nations show knowledge of Total — 365 365 365.26 365.25 an astonishingly correct value of the mean synodic period,

which is known to be 29.530588 days. This is probably because they could count the The length of the year was also found by the same number of days with fractions comprising a very large number of lunations, method. The solar year is the period between and therefore the mean value came out successive transitions of the sun through the same to be very correct. cardinal point, Neugebauer thinks that summer

solstice was first used for this purpose in ancient With the aid of the knowledge of correct values of times. But subsequently evidences are found of the the length of the tropical year, and of the mean points. use of other cardinal synodic period of the moon, it is possible to find out correct rules for luni-solar adjustment, Thus we find that during the classical period in as narrated below. But this could happen Babylon, the solar year started with the vernal only at a later stage. The first stage was certainly equinox. But the Macedonian Greeks and the Jews empirical as is clearly indicated from a record of the great started with the autumnal equinox. The west Babylonian king and law-giver Hammurabi (1800 B. C), European countries appear to have started the solar which says that the thirteenth month was proclaimed by royal year with the winter solstice. order throughout the empire on the advice of priests. All The number of days in a solar year would vary religious observances were forbidden during this between 365 and 366. Probably the exact length was period.* determined by counting the number of days between the It is not known however, year-beginnings separated by a large number of years what principles, if any, guided the king or rather his advisers and taking the mean. The Indian practice, followed in in their selection of the thirteenth month, but most probably the the Siddhantas, is to give the number of days in a adjustment was empirical, i.e., the month discarded Kalpa (a period of 4.32x10° years) from which one was wlien the priests found 'from can find out the number of days in a year by simple actual experience that the festival was going out of season. division. This appears in modern times to be a rather Many ancient nations who used the luni-solar calendar, do not cumbrous practice, but is probably reminiscent of appear to have gone beyond the empirical taking the mean for a large number of years. stage.

In ancient times, people had not learnt to follow the motion of the sun in the starry heavens, so they Empirical Relations between the Solar and Lunar were unaware of the difference between the sidereal ( Periods : The Intercalary Months. year and the tropical year. But from their method of measurement, they unconsciously chose the correct, or The Chaldean astronomers (as the Babylonians the tropical year. were called after 600 B.C.) appear to have striven incessantly to obtain very accurate values for the Modern measurements show that the length of the

mean lunation and the length of the solar . year, and tropical year is not constant, but is slowly varying.

It is becoming shorter at the rate of "0001 days or 8*6 * It is said that in ancient , the custom was that the sees, in 1600 years. Rabbis went to tjie fields and watched the time by their calendar for

the ripening of wheat. * If the lunar month of Addaru (last month So that in Sumerian times, the tropical year had of the year) fell back too much towards winter, they would proclaim a a length of 365.2425 days. The present length is second Addaru in that year, so that the first of Nisan would coincide 365-2422 days. roughly with the ripening of wheat THE CALENDAR REFORM COMMITTEE 176 REPORT OF 3.—The 19-year cycle. mathematical relation- Table work oat at the discovery of showing Intercalary Months periods having the form- Cycle of 19 years ships between these two (Compiled from Pannekoek' 9 calculation of dates in Babylonian Tables of planets) m lunar months =w solar years the Year in the Total no. of Tears of where both

Table 4.—Corresponding Lunar months. month-lengths were also the same as in the Chaldean Lunar Month-Names 19-year system. When the and Kushans began to rule in India, from first century B.C., they used (1) (2) (3) (4) the Macedonian months alternatively with the Indian Indian Chaldean Macedonian Jewish months which are shown in the first column. The first CAITRA Addaru Xanthicos Indian season, Spring, however according to imme- Vai&akha NISANNU (30) Artemesios Nissan morial Indian custom, has been on both sides of the Jyai§£ha Aim (29) Daisios Iyyar vernal equinox (—30° to 30°), while in the Graeco- A§adha Sivannu Pancmps (30) Chaldean system, the Spring started with vernal Sravana Duzu (29) Loios Tararauz equinox (0°). The first Indian month is Caitra, the Abu (30) Gorpiaios Ab first of the spring months, and according to rules Asvina Ululu (29) Hyperberetrios Ellui prevalent in Siddhantic times (300 A.D.), the month Kartika Tasritu (30) DIOS TISHRI was to be always on the lower side of the vernal Margaslrsa Arah equinox, i.e., the beginning of lunar Caitra was to be on Samnah (29) Appclaios Marheshvan a date before the vernal equinox. It may be added that Pausa Kisilibu Audynaios (30) the Indian lunar months mentioned here are amanta Dhabitu (29) Peritios Tebeth or new moon ending. Phalguna Shabat (30) Dystros Shebat Caitra Addaru (29) Xanthicos and 3.4 THE INTRODUCTION OF THE ERA Veadar For accurate date-recording, we require besides The first Babylonian month Nisannu, started with the month and the day, also a continuously running 30 days, and other months were alternately 29 and 30 era. But the era came rather late in human history. days. A normal year thus consisted of 354 days, but We find dated records of kings in Babylon from about occasionally an extra day was added to the last month, 1700 B.C. (Kassite kings). They used regnal years, and it became a year of 355 days. lunar months, and the day of the lunar month. The The effect of these intercalations was that the first ancient Egyptian records do not use any era, but

month, viz., the month of Nisannu, never strayed for sometimes the regnal years. But the use of regnal more than 30 days beyond the day of vernal equinox. years is very inconvenient for purposes of exact because one has to locate the As the table shows, the Babylonian year might be chronology, beginning of the reign of the king on the time-scale which often of 354, 355, 383, or 384 days duration, and occasio- proves to be an extremely difficult problem, e.

in column (3) in their home land. When they settled astronomers who were the earliest systematic observers in Babylon as rulers (313 B.C.), they continued to use of the heavenly bodies, get tired of the use of the the same months, but got them linked to Chaldean regnal years, and felt the need of a continuously months. Their first month was Dios, which was running era for precision in time-reckoning. They the seventh month of Chaldeans. This was probably took advantage of a unique gathering of planets about linked to the autumnal equinox in the same way as Feb. 26, 747 B.C. when Nabu Nazir was reigning in Nisannu was to the vernal equinox. The Macedonian Babylon to proclaim that the gods have ordained the year started six months earlier than the Chaldean year. 'introduction of a continuously running era' ( Shy and

I, April, The Macedonian months were used by the Telescope, Vol. p. 9, 1942). Parthians, the early Sakas, and the Kushans in India But the use of the Nabonassar era appears to have wihout change of name (vide § 5-5), and probably the been confined to astronomers. The kings continued THE CALENDAR REFORM COMMITTEE 178 REPORT OF these countries, as is apparent from regnal years as this had spread over all to record events, in their inscriptions and -datings mentioned royal family which contemporary great propaganda value for the a amanta, i.e., started after in § 5*5. The months were they were unwilling to forego. pegged on to the new-moon was completed and were other ancient eras, like is now known that the of the vernal It the solar year which started on the day the era of the Greek (776 B.C.) or after that of equinox. The Nisan was the first lunar month Rome (753 B.C.) are extrapolated eras. months Foundation of the vernal equinox. There were 7 intercalary Olympiads is ancient Greek method of dating by correspondence between The in a period of 19 years. The critically origin, but the system was the of uncertain Chaldean and Greek months and the position of Alexandrian chronologists, parti- examined by the months have been worked out by Prof. of intercalary (3rd century B.C.), the founder cularly Eratosthenes Pannekoek between the years 134-247 of the Seleuci- the Encyclopaedia chronology. According to 3-2 and 3-3) along scientific dean era, as already given (vide § is not 14th edition, Greek chronology Britannica, with their Indian equivalent lunar months. (i.e. 576 B.C.). The reliable till the 50th time after its alleged Era era was therefore invented a long The Parthian Foundation of Rome of starting. The era of the the year the introduction of the Seleucidean era, Britannic* 14th Since similar history (see Encyclopaedia had a a nation or a dynasty to start eras eras practice arose for Chronology). The starting years of these edition, commemorating some great event in their national or that of the Nabonassar era are suspiciously close to Parthian era, dynastic life. The first in record is the eras were plagiarized (747 B.C.). Probably both these the story of its starting is well-known. The the savants of and the era of Nabonassar after from Seleucid emperors ruled the from 312 B.C. the time-sense. and Rome acquired imposing on the countries under their domination Hipparchos and Ptolemy used It is noteworthy that Greek culture, the Seleucidean era, and the Graeco- nor the era of Foundation neither the era of Olympiads Chaldean system of time-reckoning. About 250 B.C., or Chaldean months which were in of Rome, nor Greek there were wide-spread revolts against Seleucid rule Nabonassar era and the more con- other parts lunar, but the , in (Eastern Persia), and solar months. They preferred led by venient Egyptian of the Near East. The revolt in Parthia was chauvinism. science to nationalistic one Arsaces and his brother Tiridates who belonged culture. to an Iranian tribe, which had adopted Greek derived Eras The Seleucidean and other To commemorate their liberation from Seleucidean introduced an era, beginning era) : The first the Parthians The Seleucidean Era (the S. E. rule, into general after the (i.e. 248 B.C.). But continuously running era which ran 64 years only rarely used. to commemorate the at first this era (Arsacid era) was circulation is that introduced from the Parthian emperors preferred to use on foundation of Seleucus's dynasty and dates The early .Babylon the Seleucidean era, the Macedonian year when Seleucus occupied the city of their methods months, and the Graeco-Chaldean system of time- after defeating his rivals. There were two In the first the first reckoning inscribed in Greek letters. of counting, differing in the initial year and century A.D., there was a Zoroastrian revival, the day of the year. era and S.E. was dropped in favour of the Parthian According to the official (Macedonian) reckoning, be used in place of Greek, though Dios (near Pehlevi began to the era started from the lunar month of Macedonian month-names were still kept. autumnal equinox) in the year (—311) A.D. or 312 B.C. Parthian names ruled at The months had Macedonian names. Though kings bearing Taxila about the first century B.C. to first century A.D., According to the native Babylonian reckoning, the no clear evidence of the (near e.g., king Gondophernes, era started from the lunar month of Nisan yet use of the Parthian era on Indian soil has vernal equinox) six months later than the starting of been found. the Macedonian year. The months had Chaldean that the Saka era, with its methods names, as given in Table No. 4. It is very likely in of calendar-reckoning, which came into vogue The Seleucid monarchs ruled over a vast empire India during the Siddhctnta Jyotisa times, was started from Syria to the borders of Afghanistan from 311 B.C. they attained prominence, under their by the Saka tribes when to 65 B.C. i.e., nearly for 250 years and and started an era of their own, in imitation of the rule, the knowledge of Graeco-Chaldean astronomy Parthians. They, however, retained the Graeco- and time-calculations spread far and wide, ultimately Chaldean method of lunar month-reckoning and reaching India, and profoundly modifying the indige- probably the same system of intercalary months. nous system in India. The use of Macedonian months THE ljUNT-SOLAK A&D LtTNAK CALENDARS 179

two, i.e., 2nd day of week), ha (he, five, i.e., fifth hour after

3.5 THE JEWISH CALENDAR sunset) and Bad (Besh, dalet, 204 minims after the hour).

(2) In the Bible various eras occur, e.g., the Mood, the The ancient Jewish calendar was lunar, the Exodus, the Earthquake in the days of King Uzziah, the beginning of the month being determined by the first regnal years of monarchs and the Babylonian exile. During visibility of the lunar crescent. As the month-names the exile and after, Jews reckoned by the years of the show (col. 4 of the table No. 4 ), they were evidently Persian kings. Such reckonings occur not only in the Bible derived from the Babylonian month-names excepting (e.g., Daniel viii, I) but also in the Assouan papyri. After one or two, viz., Marheshvan and . The day Alexander, the Jews employed the Seleucid era (called began in the evening and probably at sunset. The year Minyan Shetaroth, or era of deeds, since -legal deeds were begin with the spring month Abib or Nisan, used to dated by this era). So great was the influence exerted by the the latter being the Babylonian name of month Alexander, that this era persisted in the East till the 16th post-exilic which was adopted by the Jews in the century, and is still not extinct in south Arabia. This is the times. Intercalation was performed, when necessary, only era of antiquity that has survived. Others, which fell f repeating the twelfth month Adar which was then into disuse, were the Maccabaean eras, dating from the known as 'Veadar' followed by Adar. The year- accession of each prince, and the national era (143-142 B.C.), beginning was subsequently changed and in the last when Judaea became free under Simon. That the era century before Christ, it became the month of Tishri, described in Jubilees was other than hypothetical, is corresponding to the Macedonian month of Bios. This probable. Dates have also been reckoned from the fall of must have been due to the desire or need to follow the* second Temple [Le-Horban hab-bayyith). The equation the practice of the ruling race. of the eras is as follows.:

Originally there were no definite rules for inter- Year 1 after destruction = A.M. 3831 calation and for fixing up the beginning of the months. = 383 Seleucid Because various religious festivals and sacrifices were = A.D. 71 fixed with reference to the beginning of the month, The 'Era of Creation* is supposed to have started information about it was spread throughout the from the day of autumnal equinox of the year 3761 B.C. messengers and by signal fires on hilltops. country by So the sun and the moon must have existed before the fixed rules were About the A.D., day of creation !! introduced in the calendar and nothing was left to observation or discretion. Intercalation is governed by a 19-year cycle in which the 3rd, 6th, 8th f 11th, 14th, 17th and 19th years have got an extra month. 3.6 THE ISLAMIC CALENDAR The actual beginning of the initial month of the year, The Mohammedan calendar is purely lunar and vix., Tishri is obtained from the mea'n new-moon by has no connection with the solar year. The year complicated rules which are designed to prevent consists of 12 lunar months, the beginning of each certain solemn days from falling on inconvenient month being determined by the firtt observation of the days of the week. As a result, a may crescent moon in the evening sky. The months have consist of 353, 354 or 355 days and an embolismic or accordingly got 29 or 30 days and the year 554 or 355 leap-year of 383, 38*4 or 385 days. Ten of the months days. The new-year day of the Mohammedan calendar have got fixed durations of 29 or 30 days, as well as thus retrogrades through the seasons and completes the intercalary month which contains 30 days, the the cycle in a period of about 32-J solar years. other two varying according to the requisite length of the year. The era of the Mohammedan calendar, viz., the Hejira (A.H.), which was probably introduced by the The Jewish Era of Creation Caliph Umar about 638-639 A.D., started from the of 622 A.D., July 15, Thursday*, when the The Jews use an Era {Anno Mun&i, libriath olum) evening crescent moon of the first month Muharram of or 'Era of Creation which is supposed to have been the Mohammedan calendar was first visible. This started from the day of creation of the world. We was the new-year day preceding the emigration quote the following passages from Encyclopaedia of from Mecca which took place about Britanmca; 14th edition, 'Chronology, Jewish'. Sept. 20 (8 Rabi I), 622 A D. (l) The era is supposed to begin, according to the mnemonic Beharad, at the beginning of the lunar cycle on

commences from 4unset r the night between Sunday and Monday, Oct. 7, 3761 B.C., *As the. day of the Islamic calendar Friday started from the evening of that day. at 11 hours Hi minutes P.M. This is indicated by be (beth,

C. B.-31 —

180 REPORT OF THE CALENDAR REFORM COMMITTEE

been shown by Dr. Hashim Amir Ali of For astronomical and chronological purposes the It has now the Osmania University, Hyderabad, that the Moha- lengths of the months are however fixed by rule and calendar was originally luni-solar in which not by observation. The lengths of the months in days mmedan intercalation was made when necessary, and not for this purpose are as follows : purely lunar. This view-point has now been strongly rviunariaiii ...30 supported by Mohammed Ajmal Khan of the Ministry udldl 29 of Education, Govt, of India. They emphasize that Rabi-ul awwal 30 upto the last year of the life of Mohammed, i.e., upto Rabi-us sani 29 A.H. 10 or A.D. 632, a thirteenth month was inter- Jamada'L awwal 30 calated when necessary. The Arabs, among whom Jamada-s sani 29 there were relatively few men conversant with astro- Rajab 30 nomical calculations^ had a system in which a family Shaban 29 of astronomers, known as Qalammas was responsible Ramadan 30 for proclaiming at the Hajj (falling in the last month 29 Shawal would or of the year : Zilhijja) that a thirteenth month Zilkada 30 would not be added. Astronomically such intercala- Zilhijja 29 (or 30) tion should be made 3 times in 8 years or 7 times in 19 The leap-year, in which Zilhijja has one day more, years. The elder of the Qalamma had a certain amount contains 355 days and is known as Kabishah, In a cycle of discretion in determining when this intercalation practice afterwards of 30 years, there are 19 common years of 354 days and was to be practised, and this very 11 leap-years of 355 days. Thus 360 lunations are made caused great confusion. '012 than equivalent to 10,631 days or only days less According to this view, proper intercalation was for determining the leap- its actual duration. The rule applied in all the years where necessary upto A.H. 10 the year of this fixed calendar is that, if after dividing and consequently the year A.H. 11 (coming next, to 10, 13, 16, Hejira year by 30, the remainder is 2, 5, 7, the Hajj of A.H. 10) which started on March 29, 632 or 29, then it is a leap-year. to have 18, 21, 24, 26 A.D. {i.e., after the vernal equinox day) seems The only purely lunar calendar is the 'Islamic been a rather normal year, and as such all the previous the the calendar', which has been in vogue amongst new-year days appear to have been celebrated on followers of Islam since the death of the Prophet visibility of the crescent moon after the vernal equinox occupy Muhammad (632 A.D.). But it is well-known that day. The Muslim months should accordingly before this period Mecca observed some kind of luni- permanent places in the seasons as follows* ; countries of the solar calendar in common with all Muharram... Mar.—April Rajab ...Sept—Oct- story is that when pilgrims Near East. The common Safar April—May Shaban ...Oct.—Nov. countries and other parts of Arabia came Dec. distant . . Nov. from Rabi I ... May —June Ramadan — Hajj at Mecca (Hajj is a pre-Islamic ...Dec. Jan. to perform Rabi II ... June —July Shawal — often found that it was an intercalary they . practice), Jamadi I ... July —Aug. Zilkada . Jan. —Feb. to Meccan calculation, when no ...Feb. month according Jamadi II ... Aug.—Sept. Zilhijja —Mar. wait religious festival could be performed, and had to then be necessary to shift the to perform the ~^Mi this view is accepted, it would for a month before they were allowed is commonly accepted as July starting epoch of the Hejira era, which great hardships for distant visitors rites. This meant as 4 intercalary months or 118 days 16, 622 A.D., to an earlier date, recurrence of such incidents the the new-year days of A.H. 1 and and to prevent will then have to be inserted between or 13th month 29, 632 A.D. The initial epoch of the Prophet forbad^ the use of intercalary of A.H. 11, which is March at is the evening of March 19, 622 A.D., and decreed that the calendar should henceforth be Hejira era thus arrived equinox. Friday, the day following the vernal purely lunar. CHAPTER IV

Calendaric Astronomy

4.1 THE MOON'S MOVEMENT IN THE SKY and the moon move uniformly in the same great The scheme of lunar months given in Table No* 4 circle in the heavens. But even the, most primitive in a nineteen-year period, which came into vogue in observers could not fail to notice that neither do the Babylon about 383 B.C. did not however, completely two luminaries move in the same path, nor do they satisfy the needs of the , because move uniformly, each in its own path. for religious purposes, the month was to start on the The motion of the moon amongst the stars is the day the crescent moon was first visible in the western easiest to observe. This is illustrated in the two horizon after conjunction with the sun (the new- figures reproduced from the Sky and Telescope, giving

Fig. 2—Showing the positions of the sun, moon and planets among the stars in June. 1953, moon), a custom which is still followed in the Islamic positions of the moon, the sun, and the planets in the- countries. But the first visibility may not occur on field of fixed stars in the months of June and July,* the predicted day for manifold reasons. 1953.

Fig. 3—Showing the positions of the sun, moon- and planets among the stars in July, j;j53. The table given on p. 176 is based on mean values The central horizontal line is the line of the Of the lengths of the year and the synodic month, celestial equator (§ 4.4), and the sinuous line represents which is equivalent to the assumption that the sun the ecliptic or the sun's path (§ 4.5) but we -mav 181 :

OF THE CALENDAR REFORM COMMITTEE 182 EEPOKT Orionis iMrgosiras) to the west of concentrate on the bright star-group ignore these now, and simply on Jun; 11th, the day of the new- which it Castor and Pollux moon and the stars or star-clusters near moon. But on the next new-moon day, July 11th, she passes. about has moved near Castor and Pollux (Piutarvam) western moon begins as a thin crescent on the The 30° to the east. on the evening of June 12, the day of the first horizon found that the moon takes 11°, from The ancients must have after the new-moon, at an angle of visibility of the moon), a little over 27.3 days (sidereal period which has just set, below the bright stars the sun to overtake the notice the to return to the same star, but Castor and Pollux (Punarvam). Then we little over 29.5 days at sunset. sun, it takes a little longer, a position of the moon on successive evenings of the moon). Exactly i at the rate of about (the synodic period We find she is moving eastward phase). She sidereal period -27.321661 days 13° and becoming fuller (increasing in the mean h m B on the 17th, on =27d 7 43 11 .5 passes the bright star Regulus (Magha) Leonis (Uttara with a variation of ± 3J hours the 19th, she is half and passes north. Then she synodic period = 29.530588 days Phalgunt) leaving it a good deal to the and the mean d h m fl or Citra) on the = 29 12 44 2 . passes the bright star Spica ( a Virginis the 23rd near the star variation of ±7 hours. 21st, and is then gibbous on with a {Vimkha). Then she passes the well known a-lAbra The Lunar Mansions : 27th, near Scorpion-cluster and becomes full on the ancient nations developed the habit of be seen on the night of Many a star-cluster which cannot (or night-to-night) position designating the day-to-day full-moon, but can be detected later as the by the stars or star-clusters it passed on she rises nearly of the moon . On the full moon day, successive nights. The number of such stars or star- 180° from the sun (opposition). On each at sunset, at ambiguity was due clusters was either 27 or 28 ; the full moon she rises later and successive night after the moon to the fact that the mean sidereal period of passes the phases in the reverse order, i.e., later, and having a variation is about 27 £ days, the actual period becomes gibbous on June 30, when she has the bright hours, and the ancients who did not know how and is half on of seven star Altair (Srava

Later during Siddhanta Jyoti$a times the enumeration At one time the brilliant star Vega (a Lyme) was started with Aivini (a? fcA*Mtis)>- and this is still also included making 28 toahsairas. But this has a reckoned to be the first of the naksairas, although the latitude of 62° N and was later discarded. vernal point has now receded to the UUarabhMrapadd No satisfactory argument has been given for the group which should accordingly he taken as the first inclusion of such distant stars in the lunar zodiac. The naksatra. But the change has not been done because Arabs and the Chinese do not include these distant the Indian astrologers have failed to correct the stars in their lunar zodiac, but fainter ones near the

calendar for the precession of equinoxes. ecliptic. Prof. P. C. Sengupta is of the opinion that The Chinese start their Hsius with Citra or Indians generally preferred bright stars, but when such brighter a Virginis. This refers probably to the time when were not available near the ecliptic, they chose a Virginis was near the autumnal equinoctial point ones away from the ecliptic, which could be obtained (285 A.D.). The Arabs start their Manxils with on the line joining the moon's cusps. Arietis (Ash-Sharatani). The naksatras were used to name the 'days' in

There has been a good deal of controversy regarding the earliest strata of Indian literature. Thus when the the place of origin of the lunar zodiac. Many savants moon is expected to be found in the Magha naksaira were inclined to ascribe the origin of the 27 nak^atra (it Leonis), the day would be called the Magha day. system to ancient Babylon, like all other early astro- This is the oldest method of designating the day, for it nomical discoveries. But as far as the authors of this is found in the Rg-Vedas. Other methods of the book are aware, there is no positive evidence in favour designating the day by tithis or lunar days, or by of this view. Thousands of clay tablets containing seven week-days, came later. The system has continued astronomical data going back to 2000 B.C., and to the present times. In old times, astrology was based extending up to the first century A D. have been almost entirely on the nak§atra$i e.g., in Asoke's records, obtained, but none of them are known to have any the Pusya naksatra day was regarded as auspicious reference to 27 or 28 lunar mansions. when Braltiiiavm and Sramanas were fed, in order to enhance the king's punya (religious merits). In the On the other hand (as mentioned before) some of Mahabharaia also we find that the days are designated the nak§aira names are found in the oldest strata of by naksatras which apparently mean the star or star- the Rg-Vedas {ride § 5 2), which must be dated before cluster near which the moon is expected to be seen 1200 B.C., and a full list with some difference in names during the night. is found in the Yajur-Veda, which must be dated before

600 B.C. Nobody has yet been able, to refute yet Max As is apparent from Table No. 5, die naksatras dire Muller's arguments in favour of the indigenous origin at rather unequal distances, i.e., they rarely follow the of the Indian nak$alra system given in his preface ideal distance of 13 % \ This is rather inconvenient for to the Rg-Veda Samhita, page xxxv. precision time-reckoning. We find in the Vedaiiga precise definition of the It should be admitted that the lunar zodiac was pre- Jyotisa times an attempt at a nak$atra, which was detined as 800' scientific, i.e., it originated before astronomers became two limits of a conscious of the celestial equator and the ecliptic, and (-13° 20') of the ecliptic. The naksaira was named began to give positions of steller bodies with these as according to the most prominent star {Yogatdra) reference planes. The nak$attas give very roughly contained within these limits. These are given in the night-to-night position of the moon, by indicating column (2) of Tabte 5.

its proximity to stars and star-groups. Many of the We do not, however, have any idea as to how the identified as nak$atras are not at all near Indian stars beginnings and endings of the naksatra divisions were the ecliptic or the moon's path which, on account of fixed in India. The prominent ecliptic stars which were obliquity, is contained in a belt within ±5° of the its used as Yogatdras (junction-stars) in pre-Siddhantic ecliptic. Such are for example : period, are not distributed at regular intervals along

so it was found very difficult to (15) Svatu which is identified with Arcturus the ecliptic ; and in their respective equal divisions. {a Booiis\. which has a latitude of 31° N. include the stars clear table (No. 5) where the junction (22) &rava

REPOBT Of THE CALENDAR REEOBM COMMITTEE 184 Table 5.-fctar s of the Nakaafcra divisions. lAviaiona of the Siddhantaa Poeitions of the Junction Stars of Naksatra Beginning point Position of the star star Latitude of Junction Nam© S&yana of the naksatra in the naksatra (Yogatard) nakaatras division. (1956) division (1956) of naksatra s (6) (4) (5) (2) (3) (1) 10° 7' 99.' lu Arietis AO oo h Aayipt j3 11 1 0.7 4-7 36 oo 41 Arietis i 1U 2. Bharani oo 9 28 •+1 Am 23 7} Tauri m 3. Krttika 1 5 56 X X Do a Tauri ^ a) 0*7 4. A 7A 35 6 31 A Orionis JJSa 5. Mrgasiras QQ 46 ftp Q& OO a Orionis ID oo 6. Ardra 1lUoOQ LO 9 22 4- A ix4-1 1 1 9 37 Punarvasu j8 Geminorum 7. lib oo 11 32 4- fi X198-lie 7 S Cancri I u 8. Pusya oo 3 7 O o xoo1 33 2 Aslesii a Cancri 9. 1 4.3 1 5 58 1 4°, 1 X 'J a Leonis + 28 10. Maghn 160 42 15fi 35 4 7 I -L 20 Phalguni 8 Leonis ^ 11. Purva 1 6 1 1 fi°y 55 Leonis 4-19 1XUfi 171 12. Uttara Phalguni (3 1 (33 xo1 *i 9 36 — 12 12 192 51 J.OO 5 Corvi J 13. Hasfca 4 \jA 39 on ^ 1x 4*± OJ a Virginis — 2 3 14. Citra 17 4-30 46 203 38 209 55 Svati a Bootis 15. 1 13 4- 20 224 28 223 15 16. Visaklm a 236 35 5 23 — 1 59 241 58 17. Anuradhn 8 Scorpii 55 (-)o 46 - 4 34 249. 9 249 18, Jyestha a Scorpii 15 44 -13 47 263 59 263 19. Mula \ Scorpii 276 35 (")2 37 Sagittarii - 6 28 273 58 20. PurvHsadha 8 (")8 8 289 . 55 o - 3 27 281 47 21. Uttarasadha Sagittarii 303 15 (-)2 5 29 18 301 10 22. Sravana a Aquilae + 316 35 (-)o 51 31 55 315 44 Dhanistha )3 Delphini + 23. 55 11 3 - 23 340 58 329 24. Satabhisaj X Aquarii 352 53 343 15 9 38 la a Pegasi +19 24 25. Purva 11 58 8 33 356 35 Uttara la y Pegasi + 12 36 26. 55 9 21 - 13 19 16 9 27. Revati f Piscium The divisions of nak^atras shown in the table, as position of the autumnal equinox at the time the that already stated, has been based on the assumption the table was compiled. The figures in the last when of the lunar the star Spica occupies the 180th degree column represent the position of the star in the naksatra agrees with the statement of the zodiac. This arrangement division of that name. It seems that a few that the Dhanis\ha star No. 18 of the Vedaitga Jyoiisa Yogataras, viz.. No. 6 Ardra, No. 15 Srati, beginning of the (a or Delphini) marked the Jye$iha, No. 20 Purvasaiha, No. 21 Uttarasaolha, j8 l)ha>«sthA division, and also of the 's Surya No. 22 Sravana, and No. 23 Dhanistha fall outside the (x Leonis) is situated at the 6th the Siddhanta that Regulus naksatra division of which they are supposed to form degree of pe Magha division. Yogatara. Matters do not improve much, if we shift the beginning of each division so as to place ( Fiscium division or in the end of the Revati : (Revati) at 4.2 LONb PERIOD OBSERVATIONS OF THE MOON other words at the beginning of the Asriui division. THE CHALDEAN SAROS This will mean that the figures in col. (6) will The moon gains on the sun at the average rate of then have to be increased by 3° 59', which will per day, but it did not take the ancients long to push up the Yogataras of 1 Aivini, 2 Bharani, 12J° discover that the daily gain of the moon on the sun 3 KrtHka, 8 Pusya, 13 HaSta, 25 P. Bhadrapada, and fact as know now, it is far from uniform ; in we 26 U. Bhadrapada, so as to go outside the naksatra varies from approximately 10|° to 14|° per day. It was' division of which they form the Yogatara. In fact no therefore not possible to say beforehand whether arrangement at any time appears to have been the crescent moon would appear on the 29th or on the satisfactory enough for all the Yogataras to fall within 30th day after the beginning of the previous month. their respective naksatra divisions. -

CALENDARIC ASTRONOMY 185

conjunction of trie stin and But the exact prediction of the day was a necessity ( newr moon ), but every from the socio-religious point of view. In India, the the moon is not the occasion for a . A month was measured from full-moon to fMl-moon, and takes place only near opposition (full- in the Mah&bharata, the great epic which was compiled moon ), but every opposition of the sun and the moon from older materials about 400 B. C, it is recorded is not the occasion for a lunar eclipse. that sometimes the full moon occurred on the In many ancient countries, China and Babylon for thirteenth day after the new-moon, This was taken example, records of occurrence of eclipses had been to forebode great calamities for mankind. There were kept. The celebrated Greek astronomer, Ptolemy of similar ideas in Babylon of which Pannekoek says : ( ca. 150 A. D. ) had before him a record

"When the Moon is full on the night of the 14th, the of eclipses kept at the Babylonian archives dating from 747 B. C. They gave date of occurrence, time, normal time, it was a lucky omen ; when full-moon happened on the night of the 13th, 15th or 16th, it wag abnormal, and features of the eclipse, whether they were partial hence a bad omen. Here astrology and calendar were merged ; or total. From an analysis of these records, the deviation in the calendar was considered an unlucky sign Chaldean astronomers tried to discover the laws of and had to be restored at the end of the month."* periodicity of eclipses, which ultimately resulted in the discovery of the Saros cycle of 18 years and 10 or 11 Neugebauer says :

days. The basis of the Saros cycle is as follows : "The months of the Babylonian calendar are always real

" lunar months, the first day of which begins with the first We do not exactly know when the ancient visibility of the new crescent. The exact prediction of astronomers outgrew the myth of demons periodically this phenomenon is the main problem of the devouring the sun and the moon during eclipse times, as known to us from about 250 B. C. onwards, "t and arrived at the physical explanations now known to every student of astronomy, and reproduced in the This is rather comparatively late date. The reason diagrams given below. is that the accomplishment of this objective depends on the evolution of methods of exact astronomical observations, and of a method of recording them in precise mathematical language. Some ancient people never reached this stage. As far as we are aware, the ancient Babylonians were the first to evolve methods of observational astronomy. They also arrived at the principles of angular measurements, found the apparent paths of the moon, the sun, and the planets in the heavens, and discovered that it was only the sun's path (the ecliptic) which was fixed, and the Fig. 4—Showing an eclipse of the moon. paths of the moon, and the planets deviated somewhat from it. How this was done will be related later. But when they arrived at physical explanation of But even before these accurate methods had been ellipses, they had an understanding as to why there discovered, the Babylonian astronomers had learnt a are no eclipses during every full moon and new moon. lot more about the moon from long period observa- The paths of the two luminaries must be in different tions. The most remarkable of these discoveries is planes. This we take up in a subsequent section more that of the Chaldean Saros, or a period of 18 years fully, when we describe how the sun's path or ecliptic 10J days, in which the eclipses of the sun and the was discovered. moon recur. Suffice it to say that at some ancient epoch, some The occurrence of solar or lunar eclipses, when the Chaldean astronomer discovered that the moon's path two great luminaries disappear suddenly, either partially was different from the sun's, and therefore cuts the or wholly, were very striking phenomena for the sun's path at two points, now called Nodes. The ancient and medieval people, and gave rise to gloomy condition for an es&pse to happen is that the full- forebodings. There were all kinds of speculations moon and new-moon must take place sufficiently close about the cause of the eclipses, e.g., that the sun and to the Nodes, otherwise the luminaries would be too the moon were periodically devoured by demons or far aipart, for an eajipse to take- place. dragons. The ancient astronomers, however, found The 'Nodes* now take the place of the mythical dra- that a solar eclipse takes place only near conjunction gons which were supposed to waylay the sun and the moon, periodically, and swallow and disgorge them. * A. Pannekoek : The Origin of Astronomy. ascending node is called t G. Neugebauer : Babylonian Planetary Theory. In Hindu astronomy, the 186 REPORT OF THE CALENDAR' REFORM COMMITTEE

Hcchu with the symbol arrd the descending' node is month, because the nodes regress to the west. Its called' Keiu with the symbol ft, the names of the two value is 27.21222 days.

APPEARS SMALLER THAN SUN

r EARTH EARTH Fig. 6—Showing a total eclipse of the sun.

Fig. f> Showing an annular eclipse ot the sun. — The Chaldeans appear to have found, about 400 B. C, that 223 synodic months = 242 draconitic months. halves of the demon, who was cut in two by gods, so The reader can verify that the sun and the moon could get out. 223 synodic month =6585.321 days

In very ancient times, it was found that the two 242 draconitic months — 6585.357 days 'Nodes' were not fixed, but moved steadily to the west, From their long observations of eclipses, the so that the sun took less than a year to return to the Chaldean astronomers must have found that eclipses same node. This time is known as the * Draconitic year' recur after an interval of 6585 J days or 18 years llf or year of the Dragons, and its length is 346.62005 days (or 18 years 10 J days if 5 leap-years intervene). days. The time in which the moon returns to the This cycle has been known as the Chaldean Saros*

same node is known as the draconitic month or the The extent to which a knowledge of the cycle is useful

month of dragons. It is slightly less than the sidereal is given in the following modern table.

Table 6. —List of Lunar Eclipses of the Sa,ros cycle.

Lunar Eclipses

1914, Mar. 12 1932, Mar. 22 1950, Apr. 2 Asc. Part. -Total Sept. 4 Sept. 14 Sept. 26 Des. Part.-Total 1916, Jan. 20 1934, Jan. 30 1952, Feb. 11 Asc. Partial July 15 Aug. 5 Des. Partial 1917, Jan. 8 1935, Jan. 19 1953, Jan. 29 Asc. Total July 4 July 16 July 26 Des. Total Dec. 28 1936, Jan. 8 1954, Jan. 19 Asc. Total 1918, June 24 July 4 July 16 Des. Partial 1919, Nov. 7 1937, Nov. 18 1955, Nov. 29 Asc. Partial 1920, May 3 1938, May 14 1956, May 24 Des. Total-Part. Oct. 27 Nov. 7 Nov. 18 Asc. Total 1921, Apr. 22 1939, May 3 1951, May 13 Des. Total Oct. 16 Oct. 28 Nov. 7 Asc. Part.-Total 1923, Mar. 3 1941, Mar. 13 1959, Mar. 24 Des. Partial Aug. 26 Sept. 5 Asc. Partial 1924, Feb. 20 1942, Mar. 3 1960, Mar. 13 Des. Total Aug. 14 Aug. 26 Sept. 5 Asc. Total 1925, Feb. 8 1943, Feb. 20 1961, Mar. 2 Des. Partial Aug. 4 Aug. 15 Aug. 26 Asc. Part.-Total 1927, June 15 1945, June 25 1963, July 6 Asc. Total-Part. Dec. 8 Dec 19 Dec. 30 Des. Total 1928, June 3 1946, June 14 1964, June 25 Asc. Total Nov. 27 Dec. 8 Dec. 19 Des. Total 1947, June 3 1965, June 14 Asc. Partial 1930, Apr. 13 1948, Apr. 23 Asc. Partial Oct. 7 Des. Partial 1931, Apr. 2 1949, Apr. 13 1967, Apr. 24 Asc. Total

Sept. 26 (Jet. 1 Oct. 18- Des. Total CALENDABIC ASTBONOMY 187

Table 7.—List of Solar Eclipses.

Eclipses of the Saros cycle

Solar Eclipses

The dates of recurrence of the corresponding eclipses in three cycles from 1914 to 1967, the node at which the eclipse occurs, and the nature of the eclipse are shown below.

1914, Feb. 25 1932, Mar. 7 1950, Mar. 18 Asc. Annular Aug. 21 Aug. 31 Sept. 12 Des. Total 1915, Feb. 14 1933, Feb. 24 1951, Mar. 7 Asc. Annular Aug, 10 Aug. 21 Sept. 1 Des. Annular 1916, Feb, 3 1934, Feb. 14 1952, Feb. 25 Asc. Total July 30 Aug. 10 Aug. 20 Des. Annular Dec. 24 1935, Jan. 5 1953, — Asc. Partial 1917, Jan. 23 Feb. 3 Feb. 14 Asc. Partial June 19 June 30 July 11 Des. Partial July 19 July 30 Aug. 9 Des. Partial Dec, 14 Dec. 25 1954, Jan. 5 Asc. Annular 1918, June 8 1936, June 19 June 30 Des. Total Dec. 3 Dec. 13 Dec. 25 Asc. Annular 1919, May 29 1937, June 8 1955, June 20 Des. Total Nov. 22 Dec. 2 Dec. 14 Asc. Annular 1920, May 18 1938, May 29 1956, June 8 Des. Part .-Total Nov. 10 Nov. 22 Dec. 2 Asc. Partial 1921, Apr. 8 1939, Apr. 19 1957, Apr. 29 Des. Annular Oct. 1 Oct. 12 Oct. 23 Asc. Total-Part. 1922, Mar. 28 1940, Apr, 7 1958, Apr. 19 Des. Annular Sept. 21 Oct. 1 Oct. 12 Asc. Total 1923, Mar. 17 1941, Mar. 27 1959, Apr. 8 Des. Annular Sept. 10 Sept. 21 Oct. 2 Asc. Total 1924, Mar. 5 1942, Mar. 16 1960, Mar.— 27 Des. Partial July 31 Aug. 12 Asc. Partial Aug. 30 Sept. 10 Sept. 20 Asc. Partial 1925, Jan. 24 1943, Feb. 4 1961, Feb. 15 Des. Total July 20 Aug. 1 Aug. 11 Asc. Annular 1926, Jan. 14 1944, Jan. 25 1962, Feb. 5 Des. Total July 9 July 20 July 31 Asc. Annular 1927, Jan. 3 1945, Jan. 14 1963, Jan. 25 Des. Ann. -Total June 29 July 9 July 20 Asc. Total Dec. 24 1946, Jan. 3 1964, Jan. 14 Des. Partial 1928, May 19 May 30 June 10 Asc. Total-Part. June 17 June 29 July 9 Asc. Partial Nov. 12 Nov. 23 Dec. 4 Des. Partial 1929, May 9 1947, May 20 1965, May 30 Asc. Total Nov. 1 Nov. 12 Nov. 23 Des. Annular 1930, Apr. 28 1948, May 9 1966, May 20 Asc. Ann.-Total Oct. 21 Nov. 1 Nov. 12 Des. Total 1931, Apr. 18 1949, Apr. 28 1967, May 9 Asc. Partial Sept. 12 Des. Partial Oct. 11 Oct. 21 Nov. 2 Des. Part.-Total

The problem of first visibility of the £ the sky were discovered moon with in ancient times. This is which we started cannot therefore be taken up unless taken up in the succeeding sections, we describe how the path of the sun and the moon in

C. £.—32 188 BEPOUT OF THE CALENDAR REFORM COMMITTEE

into the sand, might have noticed that its shadow turned 4.3 THE GNOMON around during the day and that it varied in length as it Observations of the positions of the sun, the moon, turned. The gnomon in its simplest form was the experiment. Instead of a planets and stars are now made very accurately with systematization of that casual spear, a measured stick was established solidly in a vertical elaborate instruments installed in observatories. But position in the middle of a horizontal plane, well smoothed these instruments have been evolved after thousands out and unobstructed all around in order that the shadow of years of experience and application of human could be seen clearly from sunup to sundown. The astro- ingenuity, and have undergone radical changes in nomer (the systematic user of the gnomon deserves that design and set-up with every great technological name) observing the shadow throughout the year would see discovery. But let us see how the early astronomers that it reached a minimum every day (real noon), and that who had no instruments or very primitive ones made minimum varied from day to day, being shortest at one time observations, collected the fundamental data, and of the year {) and longest six months later evolved the basic astronomical ideas. {winter solstice^. Moreover, the direction of the shadow earliest instrument used by primitive astrono- The turned around from West to East during each day, to have been the gnomon, which we mers appears describing a fan the amplitude of which varied througout

now describe. the year"'.*

From the observation of the shadows cast by the gnomon, many useful deductions could be made. — These are : the (1) Mark the points in the morning and in evening when the shadows are equal in length and draw the lines showing the shadows. Then bisect the angle between the two shadow lines. This gives us the meridian or the north-south direction of the place.

The process of bisection was done by taking a rope gnomon Fig. 7—The attaching extreme points to the end points of the the rope, ; take the mid-point of the place, obliquity equal shadows then The ancients determined the latitude of year and the time of day by stretch the rope, and mark the position of of the ecliptic, the length of the and of the gnomon. gives us measuring the length and direction of shadow the mid-point. This connected to the pole noon-shadow of the gnomon AB, AE The figure ehows the the meridian line. If we draw a circle, with the pole the shadow on being the equinoctial shaoow and AO and AD as centre, and draw the meridian, the point where it two solstice-days, at a place on latitude - 0. strikes the northern semi-circle is the North point, the change in direction Nobody can fail to see opposite is the South point. The East and West objects throughout and length of shadows of vertical points are found by drawing a line at right angles to year. When these the day-time, and throughout the the north-south direction. observations are carefully made, by means of the So the cardinal directions are found. which is simply a gnomon ( &anku in Sanskrit ), (2) Observe the position of the sunrise from day vertical stick planted into the ground, and standing the obstruc- to day. If observations are carried on throughout on fairly level ground of large area, without 3'ear, there will be found two days in the year when tions from any direction, a good deal of astronomical the sun will arise exactly on the east point. Then it knowledge can be easily deduced. These observations is found that the day and night are equal in length. appear to have been made in all ancient countries. These days are called the Equinoctial days. Let us We have the following description, by George start from the equinoctial day in Spring (vernal Sarton, of observations made in ancient times in equinox). This happens on March 21st. Then we Greece with the aid of the gnomon.* observe that the sun at sunrise is steadily moving to stick or a pole planted "It (the gnomon) is simply a the north, at first rapidly, then more slowly. Near might use a column built for vertically in the ground, or one the extreme north, the sun's movement is very slow,

purpose or for any other ; the Egyptian obelisks would the that so this point is called the 'Solstice which means perfect if sufficiently isolated from other have been sun standing still. Actually the sun reaches its person, having driven his spear buildings. Any intelligent northern-most point on June 22 (summer solstice). as * Sarton mentions ( c 610-545 B.C.) of Miletus the 174. * : History Science, p. the gnomon in Greater Greece. George Barton A of earliest Ionian philosopher who used *

CALENDABIC ASTRONOMY 189

The day is longest on this date. Then the sun begins to According to Neugebauer : move south till it crosses the east point on September " ( during Seleucid periods, 23, when day and night again become equal (the autum- 300 B.C. -75 A.D. ) waa satisfied with an exact four-division nal equinox day). It continues to move south, till of the seasons as far as solstices and equinoxes are the extreme south is reached on December (the concerned, with the 22, summer solstice ( and not the vernal winter solstice day), when daylight is shortest for point ) as the fixed point."* places on the northern hemisphere. Then the sun At a later stage, they however found that the four turns back towards the east point reaching it on seasons had unequal lengths ( vide § 3*1). March 21, and the year-cycle is complete. The above definition of 'seasons' has come down The gnomon thus enabled the to ancient astronomers modern astronomy. The Hindu definition of (in Babylon; India, Greece, and China) to determine : seasons was different 5-6 ( vide § and 5-A ) (a) The Cardinal points : Fast, North, West, and The observation of the Cardinal days of the year South ; the north-south line is the meridian line (the appear to have been carried out all over the ancient Yamyottaia-rekha in Indian astonomy). world by other methods, and often in a far more elaborate manner. People (b) The Cardinal days of the Year : vix., would observe the day-to-day The Vernal Equinox (V.E.) day, when day and rise of the sun on the eastern horizon, and night are equal. mark out the days when the sun was farthest north (summer solstice day), or farthest south (winter solstice The Summer Solstice (S.S.) day, when the day day). The time period taken by the sun to pass from is the longest for observers on the northern hemisphere. the southern solstitial point to the northern The Autumnal Equinox (A.E.) day, when day solstitial point was known in the Vedas as the and night are again equal. Uttardyana (northern passage), and that taken by the sun to The Winter Solstice (W.S.) day, when the day pass from the northern solstitial point to the southern is the shortest for observers on the northern hemisphere. solstitial point was known as the Daksinayana All early astronomical work was done in the (southern passage). Exactly northern hemisphere. midway between these points the sun rises on the vernal and autumnal These methods are fully described in the Surya- equinoctial days. From the passage in the fcatapatha ShWianta, Chap. Ill, but they appear to have been Brahma^ quoted later ( vide §53), we see clearly that practised from far more ancient times. In the the point on the eastern horizon, where the sun rose appendix (5-C), we have quoted passages from the on these days, was recognized to be the true east. Aitareija which shows that the gnomon was Doubt has been expressed about the ability of used to determine the cardinal days of the year at the Vedic Aryans to make these * observations, but to these time when this ritualistic book was compiled. The objections, B. G. Tilak replied in his Orion, pp. 16-17. date is at least 600 B.C., i.e., before India had the "Prof. Weber and Dr. Schrader appear to doubt the Greek contact. It may be considerably older even. conclusion on the sole ground that we cannot suppose the

(c) To mark out the : Seasons We have primitive Aryans to have so far advanced in civilization mentioned earlier that in countries other than Egypt, as to correctly comprehend such problems. This means there were no impressive physical phenomenon like that we must refuse to draw legitimate inferences from

the arrival of the annual flood - of the Nile to mark plain facts when such inferences conflict with our precon- the ceived notions beginning of the solar year, or of the seasons. The about the primitive Aryan civilization. I seasons pass imperceptibly from the one to the other. am not disposed to follow this method, nor do I think that people, who knew and worked in The gnomon observations probably enabled the metals, made clothing of wool, constructed boats, built houses and early astronomers of Babylon and Greece to define the chariots, performed sacrifices, and had made some onset of the seasons, and the length of the year with advance in agriculture, were incapable greater precision. of ascertaining the solar and the lunar years. They could not have determined it In Graeco-Chaldean astronomy, we have four correct to a fraction of a second as modern astronomers seasons : have done but a ; rough practical estimate was, certainly, Spring from V.E. to S.S. not beyond their powers of comprehension. Summer S.S. to A.E. The best example of the ability of the ancient Autumn*- „ A.E. to W.S. people to observe the cardinal points of the sun's Winter- „ W.S. to V.E. motion is afforded by the Stonehenge in the Salisbury Thus every season starts immediately after a plains of England, of which detailed accounts cardinal day of t,he year and ends on the next * Neugebauer : Babylonian Planetary Theory, Proc. Amer. Philoa. cardinal day. Soc. Vol. 98 : 1, 1954, p. 64. REPOBT OF THE CALENDAR BEFOBM COMMITTEE 190 In the last, the book of Job (the Bible) and in . in Scientific American ( 188, have recently appeared find out their the star-groups are used by sailors to Discovery (1953, Vol. XIV, p.276). 6-25, 1953 ) and star-groups are found orientation. Representations of that not a related in these two publications, of about It is ancient Babylonian boundary stones 1500-1200 in time subsequent to 1800 B.C., say about long 1300 B.C. (see Fig. 15). Britain, who had not even B.C., the then inhabitants of were see how these observations used only stone Let us now learnt the use of any metal, but area made. implements, could construct a huge circular forming lintels moonless evening in early enclosed by large upright monoliths Suppose, on a clear central area having its about 8-30 P.M., we take and with a horse-shoe shaped Spring (say March ) and at the summer solstice field undisturbed by city lights, axis in the direction of sunrise on our stand in a wide almost beyond any doubt, day. It has been proved, the ceremonial that the Stonehenge was used for Sir Norman observation of sunrise on this day. direction of the axis of Lockyer in 1900 found that the angle of about H° with the horse-shoe actually makes an the summer solstice the present direction of sunrise on that it was a mistake on the day. He did hot think but that on account part of the original builders ; (angle between equator and of the change in obliquity direction of sunrise had changed ecliptic), the present using the rate of change of to the extent of H° and the time of construction at obliquity, he could fix up has been brilliantly 1800 ± 200 B.C. This estimate 14 some wood charcoal confirmed by C -analysis of pits which are presumed to be found in the local burial the Stonehenge. contemporary with the erection of of Lockyer's After this brilliant confirmation hoped that there will be less hesitation hypothesis, it is NORTH scholars to admit that it was possible on the part of i knew the use of metal and HORIZON for the Vedic Aryans who the stone-age people of far more advanced than at were 8-Showing the positions of Ursa Major (Saptar.fi) for the observation of the Fig. Britain, to devise methods interval of 3 hours. cardinal points of the year. unobstructed in all directions. We Probably in the and our vision is did they observe these points ? appearance How north. We shall find the by observing now face the way as the Britishers of 1500 B.C., same as shown in Fig. (8) : of sunrise on the of the heavens from a central place, the directions The directions high up to our right hand eastern horizon throughout the year. In the north, a little marked. Probably to observe the conspicuous the solstitial rises could be easily side we cannot fail of the found by bisecting the stars, called in Europe the equinoctial points were of seven seers. by means of ropes India, the Saptanti or seven angle between these two directions Great Bear, but in we shall Sutras. the heavens 3 hours later, as described in the Sulva- If we observe position as observe that the group has changed its our attention on the shown in Fig. (8). Let us fix Bear CELESTIAL (the pointers) of the Great 4.4 NIGHT OBSERVATIONS : THE two front stars The line joining these POLE AND THE EQUATOR and join a line through them. the hands of a watch, two stars appear to behave like nations were familiar with the Almost all ancient through a star half as bright for if produced they pass shepherds, travellers or navigators, night-sky either as appear to have revolved about it knowledge at some distance, and acquainted with more detailed Polans, and were is called the Pole Star or stars as centre. This star blue firmament studded with we of the revolving Sanskrit which means fixed. If constell- or Dhruva in modern city dweller. The striking that the than the throughout the night, we shall find the Orion could observe the Great.Bear, the Pleiades, the line of tions like remains approximately fixed, and and references to these star- Polaris not but catch their fancy it. The next day, at pointers continues to go round literature, in the Vedas, m groups arc found in ancient .

CALENDARIO ASTRONOMY 191

8-26 P.M., nearly 24 hours later they are again almost equator, like the parallels of latitude on the earth, exactly at the same position. are called parallels of . A star's parallel of We naturally come to the conclusion that the declination is identical with its diurnal circle. whole starry heavens have been rotating round an The great circles of the , which pass axis passing through the observer and the Pole Star through the poles in the same way as the meridians on

from east to west, and the rotation is completed in the earth, and which are therefore perpendicular to nearly 24 hours (exactly 23h 56m 4 8 of mean solar time). the celestial equator, are called hour-circles. Each star has its own hour-circle, which at the moment Definition of the Poles when the star passss the north-south line through the zenith of the observer, coincides with the celestial The celestial poles, or the poles round which meridian of the place. the rotation of the celestial sphere takes place may therefore be defined as those two points in the sky where a star would have no diurnal motion. The

IN SKY : exact position of either pole may be determined with 4.5 THE APPARENT PATH OF THE SUN THE proper instruments by finding the centre of the small THE ECLIPTIC

star near it, as for diurnal circle described by some The apparent path of the sun in the sky is known group. instance, the stars belonging to the Ursa Minor in astronomical language as the ecliptic. It is a great Actually the so-called pole star is at present 57 circle cutting the celestial equator at an angle of ca minutes away from the correct position of the pole 23J° (exactly 23° 26' 43" in 1955, but the angle varies star. which is not actually occupied by any from 22° 35' to 24° 13'). This is known as the Since the two poles are diametrically opposite in obliquity of the ecliptic. one of them is usually visible from a the sky; only The ecliptic is the most important reference circle north of the equator see only given place : observers in the heavens, and let us see how a knowledge of it in the southern the north pole, and vice versa was obtained in ancient times. hemisphere. The south pole is not marked by any It is obvious that a knowledge of the stars marking prominent star. the sun's path could not be obtained directly as in the Knowing as we now do, that the apparent revolu- case of the moon ; for when the sun is up, not even tion of the celestial sphere is due to the rotation of the brightest stars are visible. The knowledge must the earth on its axis, we may also define the poles as have been obtained indirectly. Early observers were the two points where the earth's axis of rotation (or accustomed to observe the heliacal rising of stars, i.e., any set of lines parallel to it), produced indefinitely, observe the brilliant stars lying close to the sun which would pierce the celestial sphere. are on the horizon just before sunrise. This must have given them a rough idea of the stars lying close to The Celestial Equator and Hour Circles the sun's path. From these observations, as well as

The celestial equator is the great circle of the from successive appearances of the moon on the first celestial sphere, drawn halfway between the poles days of the month as narrated in § 41, they must have also deduced that the sun was slipping from the west Z R to the east with reference to the fixed stars, and completing a revolution in one year. But how ivas

this path rigorously fixed ?

It appears that a knowledge of the stars lying on, or close to the moon's path was obtained from observa- tions made during lunar, rarely of solar eclipses.

They must have realized, as narrated in § 4.2, that during a total lunar eclipse, the moon occupies a position in the heavens opposite the sun, and the stars close to the moon, which become visible during Fig. 9—The celestial sphere. totality, approximately mark out points on the sun's

* (and therefore everywhere 90° from each of them), and path. So the word Ecliptic* which means the locus of eclipsas, came to denote the sun's path. is the great circle in which the plane of the earth's equator cuts the celestial sphere, as illustrated in The two points of intersection of the ecliptic

Fig, (9). Small circles drawn parallel to the celestial with the celestial equator are called respectively the X

THE CALENDAR REFORM COMMITTEE 192 KEPOBT OF

Celestial longitude « point Libra. The rC« Firsi point of Aries, and the First of latitude = node, when the CS ~ Celestial p first point of Aries is the ascending at B. Then north the first Let PS cut the ecliptic sun passes from the south to the > dhruvaka = I when the sun rB K Polar longitude or point of Libra is the descending node, have vernal BS=* Polar latitude or vik$epa=*d passes from the north to the south. We Aries, peculiar co-ordinates, now no longer equinox when the sun is at the first point of These last two point of the Surya Siddhanta to denote star summer solstice when the sun is at the first used, were used by is the first have been traced by Neugebauer to , autumnal equinox when the sun at positions. They the sun is centuries earlier. point of Libra, and winter solstice when Hipparchos five the origin of by at the first point of . To The position of a stellar body may be defined nomenclature, we return later. either its (a) and declination (8), and latitude(0). the most or its celestial longitude(x) The celestial equator and the ecliptic are The of stars in these co-ordinates began to important reference planes in astronomy. The positions terms of time of Claudius Ptolemy (150 A.D.) positions of all heavenly bodies are given in be given from the Aries as the in his Syntaxis. these planes, taking the first point of who used them scientific defini- initial point. We explain below the denote the tions of spherical co-ordinates used to on the celestial . position of a body 4 6 THE ZODIAC AND THE SIGNS

The early astronomers must have found that the sun's path in the heavens was almost fixed, while that of the moon, and of the planets, which acquired for astrological reasons great importance from about 1200 B.C., strayed some degrees to the north and south of the ecliptic.

In case of the moon the deviation from the ecliptic was found to be not much greater than 5°, but some of the planets strayed much more; in. the case of Venus, her perpendicular distance from the ecliptic rises sometimes as high as 8° degrees. So a belt was imagined straying about 9° north and 9° south of the ecliptic, in which the planets would always remain in course of their movement. This belt came to be known as the 'Zodiac*

The complete cycle of this belt was divided into 12 equal sectors each of 30°, and each sector called a

Fig. 10.—Stowing the spherical co-ordinates of a «ar. 'Sign'. The signs started with one of the points of intersection of the ecliptic and the equator, and the " Aries* after the constellation of In this figure : first sign was called

within it. The names of the succeeding signs are P= Celestial pole (dhnud). stars given in Table No. 8 on the next page, in which : rQi. =• Celestial equator. K>Pole of the ecliptic (kadamba). The first column gives the beginning and ending of X s = Plane of the ecliptic. the signs, the vernal equinoctial point being taken as T = First point of Aries (vernal equinox), the origin. r s = First point of Cancer (summer solstice). The second column gives the international names ^ = First point of Libra (autumnal equinox). which are in Latin with the symbols used to denote (winter solstice). Vf «= First point of Capricorn the signs. S = heavenly body. A The third column gives their English equivalent. PS^=Great circle thro'P,S cutting equator at Q. The fourth column gives the Greek names. They rQ^Right ascension — a synonimous with the international names. QS« Declination *S are set of alternative name* KS^ Great circle through K, S cutting ecliptic The fifth column gives a at C. for the signs given by Vartthamihira. CALENDARIC ASTBONOMY 193

Table 8 —Zodiacal Signs.

Different Names of Zodiacal Signs

Babylonian Beginning and Name of the English Greek Varaha Indian Mihira names names ending of the Signs & equivalent names Signs Symbol (6) (7) (1) (2) (3) (4) or Iku (Earn) 0°- 30° T Aries Bam Ki-ios Kriya Mesa, Ku Taburi Vrsibha Te-te (Bull) 30 - 60 B Bull Tauros Masmasu (Tsvins) 60 - 90 n Twins Didumoi Jituma Karka or Karkata Nangaru (Crab) 90 -120 s Cancer Crab Karxino; Kuli r a Leva Sim ha Aru (Lion) 120 -150 Q. Lion Leon (Virgin) 11 Parfchenosj Pathona Kanya Ki 150 -180 JP Virgin Balance Zugos Jiika Tula Nuru (Scales) 180 -210 . ^ Libra Kaurpa Vi/seika Akrabu (Scorpion) 210 -240 i'l Scorpion Scorpios Tanks ika Dhanuh Pa (Archer) 240 -270 t Sagittarius Archer Tozeutes Sahu (Goat) 270 -300 V/ Capricornus Goat Ligoxeros Akokera Gu (Water carrier) 300 -330 - Water Bearer Gdroxoos Hrdroga Zib (Fish) 330 -360 K Fish Ichthues Antvabha Mlna

The sixth column gives the Indian names. But why was such an odd assortment of animal The seventh column gives the Babylonian names. names chossn for the 'Signs' ? There have been

It can be easily inferred from the table that the interesting speculations. The reader may consult names are of Babylonian origin, but their exact Brown's Researches into the Origin of Ike Primitive significance is not always known. It has been assumed of the Greeks, Phoenicians and Babylonians, that the symbols used to denote the signs have been London, 1900. devised from a representation of the figure of the These signs were taken up by almost all nations in animal or object after which the sign has been named, the centuries before the Christian era on account of for example, the mouth and horns of the Ram, the same the significance attached to them by astrologers. In of the Bull, and so on. Greece, they were first supposed to have been Varahamihira's alternative names It is seen that introduced by the early Greek astronomer Cleostratos, are simply the Greek names given in column ( 5 ) an astronomer who observed about 532 B.C. in the course of transmission and as adopted for corrupted in island of Tenedos off the Hellespont who introduced the exception of the name for Sanskrit ; with the designation 'Zodiac* to describe the belt of stars l given as Kaurpa". This has phonetic Scorpion, which is about the ecliptic. The twelve 'Zodical Signs' are corresponding Babylonian sign name analogy' with the not known in older ritualistic Indian literature like The purely Sanskrit names Akrabu for Scorpion. the Brahmanas. They appear to have come to India are all of Greek names given in column (6) in the wake cf the Macedonian Greeks or of nations

of : with the exceptions like the Sakas who were intermediaries for trans- Miihuna or Amorous (3) Twins, which become mission of Greek culture to India. couple',

(9) the Archer, which becomes the 'Bow', Confusion in the starting point of the Zodiac (10) the Goat, which becomes the 'Crocodile', the 1 Waterpot'. (11) Water bearer, which becomes The Initial Point' of the zodiac should be the been translations of Some of them appear to have Vernal Point or the point of intersection-of the ecliptic Babylonian names. and the equator, but as will be shown in the next The Babylonian names, as interpreted by Ginzel* section, this point is not fixed, but moves west-ward 50- are given in the seventh column, with their meanings. along the ecliptic at the rate of approximately per year (precession o£ the equinoxes). This motion is It is thus seen that the names of the zodiacal signs unidirectional, but bsfore Newton proved it to be so in are originally of Babylonian origin. They were taken and the law of gravitation, there over almost without change by the Greeks, and 1687 from dynamics genuine astronomers subsequently by the Romans, and the Hindus, from was no unanimity even among&t nature of precessional

The attention of mankind was drawn in remote The hesitation of the medieval astronomers in antiquity to the five star-like bodies : precession can be easily understood. Most accepting Saturn and Mercury. practising the Venus, Jupiter, Mars, of them earned their livelihood by the basis that and Jupiter and occasionally Mars are more 'Astrological Cult' which was reared on Venus later it was and coincident with brilliant than ordinary stars. Sooner or the signs of the zodiac are fixed, ordinary stars remain fixed on this assumption crumbles to found that while the certain star-groups ; but creep along But as historical the revolving heavens these five stars the ground if precession is accepted. had clearly them, as a modern author puts it, 'like gloio-ivorms records now show, though astronomers the point ivhirling globe', each in its own way. Venus recognized that the initial point should be on a ecliptic, there appears as a morning and evening star, the maximum of intersection of the equator and the 47°. early drew the attention of was no unanimity even amongst ancient astronomers elongation being It horizon the location of this 'sea-faring people, its appearance on the eastern of different ages regarding not occupied by indicating early sunrise to persons on lonely seas. point in the heavens, because it was the ancients mankind some time to discover that it was any prominent star at any epoch and But it took motion which appeared for some period as were unaware of the importance of its the same luminary brilliance a morning star, then as an evening star. Its (vide § 4-9). could not but strike the imagination of mankind. Mercury also appears regularly as morning and evening have been discovered later than ASTRONOMY : star, and it must 4.7 CHALDEAN CONTRIBUTIONS TO such a remote age in antiquity that RISE OF PLANETARY AND HOROSCOPIC ASTROLOGY Venus, but still at all traces of its discovery are lost. We have seen that it was the needs of the motion of the brilliant luminary, Jupiter calendar which gave rise to scientific astronomy— The attention Mars across the sky attracted early ; which in the earliest times covered :

.MOV. 24

MAR. £4

The Path of Mart Among the Stars in 1939.

Fig. 11—Showing the retrograde motion of Mars. apparent motion among Although the planets always move in the same direction round the suti, their: direction. They sometimes the fixed stars as seen from the earth, is not always in the same forward this is known as the retrograde appear to move also in the backward direction among the stars, and Astronomy by Alter and Cleminshaw motion of a planet. The above figure reproduced from Pictorial August 24. illustrates how Mars was seen to retrograde during June 24 to

occasionally bursts into brilliance with fierce, red (a) Systematic observation of the movements of could not but attract notice. The three the moon, and the sun, light, which planets, Mars, Jupiter, and Saturn though generally (b) Recording of the observations in some moving to the east, from time to time reverse their convenient form on permanent materials, direction of motion (retrograde motion), as shown to deal (c) Invention of mathematical methods in Fig. 11. with the observations, with a view to predict From very early times and amongst widely astronomical events. separated communities, mystifcal importance was It is not, however, correct to say that it was the ascribed to the wandering of the Janets. calendar based on the sun and the moon which studies. mystical ideas took & very definite form in provided tfae sole stimulus for astronomical These which grew in planets strongly captured the attention the shape of 'Planetar^ AslroUW fa one t&ftft, "the Mesopotamia dUring the period B.C. to 800 B.C. rim*?* from This Planetary Astrology i* *» m distinguished Astronomy, p. 351. / A. Pjg$#<^C0ek : Origin of CALENDAEIG ASTRONOMY 195

Vedic emerged in Babylonian history from the time of older form of Astrology widely found in an these appeared moon, and the Assyrian supremacy (ca. 1300 B.C.), for India, which centred mainly round the mysteries of Heaven itself, the sun. to be linked up with the lunar mansions, and to a lesser extent on astrologer enjoyed very great prestige amongst the moon with certain nak$atras and the The conjunction of power the public, for did he not possess the mysterious was considered lucky, others unlucky (vide § 4'1). of foretelling correctly the dates of eclipses ! Planetary Astrology took the world by the samples o£ astronomical strongest Here are some of the storm after 300 B.C. and its influence was the last centuries of Assyrian power the rise of omina during during in Europe, till completely (900 B.C.-600 B.C.). rationalism and modern science almost 1 "Jupiter went back as far as the Pleiades' ; undermined this influence. But it still survives amongst "Mercury is appears in the East" ; "Mars greater extent enters Cancer" ; "Venus the credulous in the West, but to a far appears in the region of Orion" ; very bright" ; "Jupiter than amongst the eastern nations. EAST

to the earth. Fig. 12—Showing the motion of Mars relative

around earth and the other planets revolve in circles By placing the sun at the centre and having the the stars much explain the backward motion of the planets among it Copernicus (1473-1543) was able to taken from This is illustrated in the above figure, Phonal more simply than in the Ptolemaic system. while that The earth's speed is IB* miles a second Astronomy, in the case of Mars as seen from the earth. backward The earth overtakes Mars, the latter seems to move of Mars is onlv 15 miles a second. As the motion to the positions 1, 2 and 3, backward or retrograde direct motion of Mars to the east is shown at to the east again at 6 and 7. west at 4 and 5, and direct motion

turns and goes forth with What was the reason for the strong fascination "Mars stands in Scorpio, appeared in the Lion" ; brilliancy" ; "Saturn has which man has for astrology ? diminished and so on. "Mars approached Jupiter" ; Mankind has always a psychological weakness texts can predict future of scientific interest in these ; for omina, i.e., some signs which There is not a trace

of omina occupied by the omens : events, good or bad. The older form the mind of the reporters is entirely birds like the were rather crude, viz., flight of certain When such or such happens, animals like the jackal or the lord" crow, or movements of "it is lucky for the king, my ; animals. In many snake, howlings of certain birds and or, "copious floods will come" ; sacrificed to gods on countries, sheep and goats were "there will be devastation" ; claimed to diminished" the eve of great enterprises, and Augurs "the crops will be ; gods the besieged" ; be able to interpret the intentions of "the king will be

on will be slain" ; from an examination of lines and convolutions "the enemy fiepatoscopy ). "there will be raging of lions and wolves" ; the liver of the sacrificial animal (

lightning "the gods intend Akkad for happiness" ; Meteorological phenomena such as a were also and so on. discharge, haloes round the moon, aurora represent regardefas 'omens'. Yet, with all those observations, these reports first time very a considerable astronomical activity. For the The older forms of omina were all apparently had been gradually in history a large number of data on the planets crude compared to planetary omina which

C.R.—33 CALENDAR REFORM COMMITTEE 196 REPORT OF THE

the planets, and compilation of tables detailed knowledge of facts about the moon, and collected ; it implies a of positions, which afforded the basis on which modern their motion."* astronomy has been built up. In the large number of huge temples, called Ziggurats, ruins of which The ancient horoscopes which have been studied by been found in Mesopotamia, are supposed to have have scholars, and in the astronomical tables compiled by dedicated to the planetary gods, each storey being been ancient and medieval scholars, we have a huge temple to a particular god. It was the duty of assigned amount of data on planets. and priests to keep the planets under observation, material Pannekoek observes : record their positions on the only writing thousands circumstance that made this possible for astro- available then viz* clay-tablets. Hundreds of "The ruins of was the occurrence of extremely simple and striking such clay tablets have been discovered in the nomy patiently periodicities in the celestial phenomena. What looked Ziggurats, royal palaces and libraries, and irregular on occasional and superficial observing revealed interpreted by western scholars like Kugler.

Fig. 13— Ziggurat.

(Reproduced from Zinner's Gesckichte der Hternkunde)

continuous abundance of data. appear to have baen its regularity in a At first, planetary astrology SOUTH confined to states, and kings or powerful officials representing the state. But after the conquest of Babylon by the Persian conqueror Cyrus (538 B.C.), they appear to have been extended to private individuals. Thus came into existence 'Horoscopic Astrology', in which a chart is made of the 12 signs of the zodiac with the position of the planets shown therein, for the time of his birth, from which are foretold the events of his life and career. We are not interested in 'Horoscopic Astrology' at all, but wish only to remark that but for the stimulus provided by astrology, there would not have been that intense NORTH activity during ancient and (from about 500 B.C.) in the European method. medieval times, for large scale observations of the sun, Fig. 14—Showing a horoscope cast is in the east. The:£sign Aries, the first house or ascendant, Capricornus, the 10th house, is on the meridian at the Astronomy—reprinted from the The sign * Pannekoek : The Origin of occupying time of birth and so is in the south. The planets Notices of the Royal Astronomical Society, Vol III, ; Monthly symbols. the different signs are shown by the respective No. 4, 1951, pp. 351-52. *

CALENDARIG ASTEONOMY 197

regularities imposed No. of anomalistic No. of Length of the Regularities were not sought for ; but days anomalistic month themselves, without giving surprise. They aroused certain months derived expectations. Expectation is the first unconscious form of generalized knowledge, like all technical knowledge in daily D 9 248 27.555,556 days Then gradually the life growing out of practical experience. A 11 303 27.545,455 an indication that the expectation develops into prediction, C-11D+ A... 110- 3031 27.554,545 consciousness. In the rule, the regularity, has entered Actual value = 27.554,550 periods, celestial phenomena the regularities appear as fixed at the It is not sure whether these figures were arrived after which the same aspects return. Knowledge of by the Babylonians or by astronomers of other places. periods was the first form of astronomical theory". But these and the more accurate approximation of the The astronomical knowledge which the Chaldean moon's motion is found in the Paftca Siddhantika of

astronomers bequeathed to the world are : Varahamihira and is found used by Tamil astronomers.

equator and In the Paftca Siddhantika the synodic revolutions of (1) Conception of the celestial they apparently differ much racognition of the ecliptic as the sun's path. planets are given, but from the actual figures. The figures are quoted in (2) A number of relations between the synodic col. (2) of the table No. 9 below. The actual periods of and other periods of the moon and planets, vix., the synodic revolutions in days are given in col. (3).

1 year = 12.36914 lunar months ; modern value = 12.36827 lunar months. Tahle 9. — Synodic revolutions of planets from Panca-SiddhnntikiL — 59' 9" Mean daily motion of the sun ; given Actual Converted from modern value = 59' 8'\3. Planet As in P.S. (days) Col. (2) of -=13° 10' 35" Mean daily motion the moon ; (days) modern value = 13° 10' 35".0 (1) (2) (3) (4)

Extreme values of the true motion of the moon : Mars 768f 779.936 779.944 14' 6' 15° 35" to. IF 35 . Mercury 114A 115.878 115.870 Jupiter 393£ 398.884 398.868 According to modern determination these limits Venus 575| 583.921 583.880 are about 15° 23' to 11° 46'. Saturn 372| 378.092 378.093 — Length of the anomalistic month 27.55555 days ; modern value = 27.55455 days. Dr. Thibaut in his Paftca Siddhantika could not explain the figures in col. (2). It can be verified that

Or 9 anomalistic months = 248 days ; we can obtain the figures in col. (3) if we multiply the modern value = 247.991 days. corresponding figures in col. (2) by = Length of the synodic month 29.530594 days ; 365.2422 5.2422, u ^ , r by + > modern value = 29.530588 days. 360 ° - 360 obtained by such multiplication 223 synodic months = 242 draconitic months. The figures are col. which are found to be very close This gave rise to the Chaldean Saros cycle shown in (4), to the fgures in col. (3). The figures in col. (2) can be of eclipses. explained in another way, vi%., they are in degrees 269 anomalistic months = 251 synodic months. representing the arc through which the sun moves The length of the anomalistic month between two conjunctions. In other words, the deduced from this relation = 27.554569 days, figures in col. (2), not being ordinary mean solar days, value being .27.554550 days. the modern are 'saura days* of Indian astronomy, a snxra day being the time taken by the sun to move through one The Greek papyri gives longitudes of the moon for degree by mean motion, or 360 saura days = 365.2422 dates 248 days apart. This period is based on the mean solar days. This explanation has been found by Babylonian relation : 9 anomalistic months = 248 days. O. Neugebauer (ride his Exact Sciences in Antiquity). After eleven such steps of 248 days, there is a big step Most of these data were known to Hipparchos and also of 303 days in the . The length of the to Geminus, a Greek astronomer, who flourished about anomalistic month derived from these steps are as 70 B.C. follows. The "astronomical science'' as evolved by the Chaldean astronomers, is seen to be in reality the by- *Pannekoek : The Origin of Astronomy, p. 352. CALENDAR REFORM COMMITTEE 198 KEPOBT OF THE west points as deter- nonsense, cuts the horizon at the east and product of the huge amount of astrological dung, as Alberuni mined by the gnomon. a few pearls in a huge mass of us see when The Ecliptic :_From archaeological records, it is observed nearly ten centuries ago. Let out of the generally held that a knowledge of the star-groups lying these "pearls" gradually crystallized dung-heap. round about Two texts called 'Mul Afiri dated contain summary 700 B.C. have been discovered which of the time. Here is of the astronomical knowledge from Neugebauer's one of the pertinent passages Exact Sciences in Antiquity (p. 96). They They *re undoubtedly based on older material. knowledge of their contain a summary of the astronomical concerned with the fixed time. The first tablet is mostly in three "roads", the middle stars which are arranged about 30° width. The one being an equatorial belt of the moon, the seasons, second tablet concerns the planets, problems. These texts are lengths of shadow, and related the published parts are incompletely published and even detail- So much, however, is clear : full of difficulties in of elementary astronomical we find here a discussion in character but on a purely concepts, still quite descriptive risings and settings, though rational basis. The data on form, are our main basis for still in a rather schematic sculptured stones of ancient Babylon displaying the of the Babylonian constellations." Fig. 15—Two the identification astro- Sun, the Moon, Venus and Scorpion—symbols of a primitive astro- indicates that the Chaldean conception of astronomy. The passage logical science which fathered the modern north pole, and nomers of this period could locate the obtained in Babylon as early as equator, and could close to the ecliptic was had come to an idea of the celestial

numbers (Plimpton 322). Rg. J&—Babylonian Boundary Btone showing Pythagorian (Reproduced from Nengefaauer*B Enact Sciences in Antiquity)

when 1300 B.C for some of the ecliptic star-groups like the in the heavens. We do not know trace it found portrayed on boundary celestial equator Cancer, or Scorpion are they came to the knowledge that tW CALENDABIC ASTRONOMY 199 stones which can be dated 1300 B.C. Neugebauer Probably the first stage was to determine the and Sachs maintain that the ecliptic is first found angular distance of heavenly bodies from some mentioned in a Babylonian text of 419 B.C., but its 'Normal Stars' as indicated by Sachs.* These normal use as a reference plane must have started much stars were stars either on the ecliptic, like Regulus, earlier, probably before 550 B.C. But the steps by Spica, or a Librae or some other stars close to it. Sachs which the knowledge of stars marking the ecliptic gives a list of 34 such normal stars. Probably the

Fig. 17—Babylonian Boundary stone showing lunar epheroeris engraved on it (A. 3412 Rev.) {Exact Sciences in Antiquity)

was obtained, are not yet known with precision. ecliptic positions of these normal stars were Only some guesses can be made. determined after some effort by some method not yet known, and then the positions of other heavenly The early astronomers probably observed that the

bright stars Regulus ( a Leonis ), Spica ( a VtrginisU the conspicuous group Pleiades, and certain fainter stars a Librae, a Scorvii were almost on tne path. The ecliptic could be roughly constructed by joining these stars.

'Regulus* or a Leonis was the 'Royal Star' in Babylonian mythology. In Indian classics, it is known

as Magha (or the Great ) and the presiding deity is Jndra, the most powerful Vedic god. It is almost 2° exactly on the ecliptic. Citra ( or a Virginis ) is to the south.

The First Point of Aries :—The first point of Aries

is the fiducial point from which all astronomical measurements are made. But how was this point, or any other cardinal point, say the first point of Cancer first point of Capricornus ( summer solstice ), the first point of Libra, were ( winter solstice ) and the Fig. 18—. located on the circle of the ecliptic in early times ? (Reproduced from Kwyclopardia Britamniea). For rarely have the first point of Aries nor any bodies referred to the first point of Aries or the other of the cardinal points been occupied by prominent beginning of a sign could be found. The early stars during historical times. Even if for measurement, observations are rough accuracy of less the ancient astronomers used some kind of astrono- and no than a degree is claimed by any classical scholar for them. mical instrument, say the armillary sphere, it would first of be difficult for them to locate the point Aries * A. Sachs, Babylonian Horoscopes, p. 53, Journal of Cuneiform correct within a degree. Studies, VoL VI, No. 2. 200 REPORT OF THE CALENDAR REFORM COMMITTEE

4° the west Precession of Equinoxes :—But the first point of Ptolemy's first point of Arias T is to all Hipparchcs's. Aries is not a fixed point on the ecliptic, though of been obtained in ancient astronomers belived it to be fixed once for all. Clay tablet records have 50" Mesopotamia which have been interpreted as represen- It moves steadily to the west at the rate of per

--"-^ POSITIONS OF THE FIRST POINT OF ARIES (T) IN DIFFERENT TIMES. MAGNITUDES. =. Vedic Times aboul 2300 B.C. 140 B.C. First H=Hipparchoj Pi.= Ptolemy 150 A.a Second 185 AD. Si = SuryaSicfdhonfa Third 500 A£. Fourth 570 A.D. Fifth M= Modern 1S5Q A.D.

Fig. 19—The Zodiac through ages. and given ting two systems of Ephemeris known as Systems A year. Astronomers of different ages must have System B indicates that the vernal point is Aries 8°. measurements of stellar positions from observations B. This indicates that the observations were taken about made either during their own times, or from years before Ptolemy. This coincides approxi- observations made by their predecessors, quite 550 mately with the time of the Chaldean astronomer unconscious of the fact that the reference point had at Borsippa near Babylon, and of stars given Kidinnu, who observed shifted. The result is that the positions of the nineteen-year cycle. tally, and is taken to be the author by different astronomers of antiquity do not 10° the vernal point ; the always System A uses Aries as the positions given by the same astronomer are not might have flourished 120-150 of the Zodiac. author of this system consistent This is illustrated in Fig. 19 be identified with Aries T as years before Kidinnu, and may Let us take Hipparchos's First point of Naburiannu, son of Balatu, who flourished about 490 our standard point. CALENDABIC ASTRONOMY 201

for perfecting the 15° by Eudoxus of science, the use of astronomy B.C. Older still is the use of Aries to have come to a stop start a geometri- calender appears in the West the first Greek astronomer to Cnidus, conquered the This refers to after the Seleucidean era. For Rome cal theory of planetary motion. whole western Asia up to the Euphrates by about dating from about 810 B.C. These dates, observations replaced the independent 80 A. D., and the Julian calendar before they are accepted, should receive Babylonian luni-solar calendar, which have, however, verification. like continued to currency probably in limited regions Arabia and amongst certain communities. The Use of Spherical Co-ordinates Syria, The Sassanid Persians also followed their own solar primarily But the The ancient astronomers were interested calendars inherited from Acheminid times. later about 150 B.C., luni-solar calendar have in the moon and the planets but elements of the Chaldean with their Christian Hipparchos gives lists of fixed stars as well been used in a limited way, for the in Palestine positions. ecclesiastic calendar for Christianity arose these planets the most important event in Christ's It was clearly observed that though and Syria, and amounts* is recorded in terms of the keep near the ecliptic, they deviate by small life, His crucifixion, In prevalent in Palestine about the sometimes to the north, sometimes to the south. luni-solar calendar amounts A.D. the case of the moon, the maximum deviation first century orbit to the to nearly 5° (inclination of the moon's of planets, excepting in the case ecliptic). In the case 4.8 GREEK CONTRIBUTION TO ASTRONOMY deviation was not large. of Mercury and Venus, the to give a short of the moons It has been considered necessary In the case of the moon, a knowledge astronomy, because of account of Greek contributions to latitude was necessary for prediction celestial was Greek astro- and there is a widespread vi>w that it and therefore both the celestial longitude eclipses calendar reform in Chaldean astro- nomy which formed the basis of latitude used to be recorded by the 400 A.D. ( Siddhanta the case of planets, India which took place about nomers of the Seleucidean period. In far this view is used. Jyotisa calendar). Let us see how the celestial longitude appear to have been only appear to have made correct. The Greeks themselves the first to frame The Chaldean astronomers were their own no use of astronomy for the reform of and planetary ephemerides (i.e. calculation in lunar was done later in India. They cultivated positions—the pre- calendars, as advance of lunar and planetary an astronomy partly as pure science, partly as modern Nautical Almanacs and Ephemerides) cursor of adjunct to astrology. neither indispensable from about 500 B.C. But during these times, civilization had a or is now well-known that Greek knowledge of the sphere nor of spherical It the The ^remains The Chaldeans long past going back to at least 1500 B.C. plane trigonometry had developed. civilization have been found in Crete (itfinoan), developed the ideas of angular measurement of this had only (Mycenean). seconds, on the Greek mainland itself they expressed in degrees, minutes and and which scripts (Linear 360° degrees. Inscriptions have been found in strange the whole circle being divided into till 1952. We elucidated by A, and B) which defied decipherment Their methods, which have been the calendar in arithemetical. have therefore as yet no knowledge of Neugebauer, Sachs and others were B.C.), astrono- Mycenean age of Greece (1400 B.C.—1000 They took maximum and minimum values of the an inter- probably they will now be forthcoming. nomical quantities, and interpolated for but be linear 'Odyssey' written mediate period, assuming the change to The Homeric poems 'Iliad' and Exact Sciences in Hesiod writing about 700 (zigzag function, vide Neugebauer, about 900 B.C., as well as Astronomy). acquaintance of stars and Antiquity, Chap. V, Babylonian B.C. show considerable sea-faring people, to find out introduced geometrical constellations needed for It was the Greeks who heavenly bodies, their orientation when out at sea. methods to deal with positions of astronomy- But B.C., the Greek city-states began and made the next great advance in From about 750 only to a rudimentary they were engaged in maritime trade over they developed trigonometry to emerge ; activities they also used Babylonian whole Mediterranean basin. These stage ( vide § 4-8). But the while Ptolemy into contact with many older nations arithmetical methods alternately. Thus brought them his Syntaxis, attained a high standard of civilization, e.g., uses the trigonometric chord functions in who had East, vix., the Teirabiblos, he uses Egyptians, the nations of the Near in the astrological text, called the and the Assyrians and Babylonian arithmetical methods. Lydians, the Phoenicians, the The imbibed many elements of their civilization. Though the calendar, as we have seen, gave the scholars themselves admit that the Greeks of the astronomical older Greek first stimulus for the cultivation ;

CALENDAR REFORM COMMITTEE 202 REPORT OF THE have besides philosophers of the Pythagorian the Phoenicians, their We borrowed their script* from brotherhood 500-300 B. C. ), a religious their preliminary ideas of school ( coinage from the Lydians, cultivated geometry, astronomy, physics and and of astronomy from which geometry from the Egyptians to mathematics. They are cited by later writers enriched all these sciences the Chaldeans. But they was have propagated the view that the earth own original thoughts beyond measure by their bodies sphere, and the planets were also spherical As Plato (428-348 B.C.) proudly a and contributions. state when, and like the earth, but it is difficult to the Greeks acquire from foreigners, remarks : "...whatever on what grounds these theories were first propounded. something nobler" is turned by them into periods of tutelage. Greek genius in than Thales These were the science goes no further back Greek began to flower only after 400 B.C., and reckoned to be the astronomy Miletus (624-548 B.C. ), who is of aided by a number of causes. Greece. Considerable was of the seven sages of first geometry as a physics was ascribed to first was the development of knowledge of astronomy and The school supposed to have predicted by philosophers of the Pythagorean him by later writers. He is science scholars, notably total solar eclipse, which 500-300 B. C. ), and other the occurrence of an almost ( and Democritos on the basis of his of ( 450-430 B.C. ), occurred on May 28, 585 B.C., great impetus to both These stories are Abdera ( 460-370 B.C.). A knowledge of the Chaldean Saros. of Plato 428- versed in Assynology, and solid geometry was given by ( now disbelieved by scholars well plane them- philosopher and founder of a the Chaldeans 348 B.C. ), famous for according to their finding, the world as knowledge of the Saros school of studies and research known to selves before 400 B.C., had no amongst his contem- later to predict the eclipses, the 'Academy*. Plato counted of 18 years 10J days used distinction. only partial success. poraries and juniors several geometers of but they used other methods with methods, but not Archytas of Tarentum (first half of fourth Thales might have used one of these viz.. of Athens ( c. 380 B.C. ), Considering the crude century B.C. ), Theaitetus certainly the Chaldean Saros. several others. Thales' times, these of Cnidos ( d. 355 B.C. ), and of Greek civilization in Eudoxus state by these and fairytale of modern times All tha geometrical knowledge developed scholars think that it is a rewritten into a about the Saros. Thales other scholars was compiled, and that Thales knew anything contributions of his own by Minor which had active logical system with rich lived in a coastal city of Asia Near East, lived in the Museum of Alexandria with the great civilizations of the Euclid, who contact to the world in ascribed to him 280 B.C. And was bequeathed probably much of the knowledge ( X and known as the Elements thirteen ( or fifteen ) books were picked up from Babylon and Egypt. this day the basis of Euclid, which have remained to astronomy is Anaximander, of The next figure in Greek There is no teaching of elementary geometry. a junior contem- the ), likewise of Miletus ( 610-545 B.C. remained current other book of science which have to have introduced the porary of Thales, who is said time, now authoritative for such a long stretch" of 4"3). This may be conceded, and of the gnomon ( vide § use over two thousand years. most probably from the extending but this practice was derived much earlier factor was political. During the sixth Chaldeans, who used the gnomon from The second Christ, the Greek savants ) of Tenedos was cited fifth centuries before times. Cleostratos ( 530 B.C. and educational the knowledge of scholars had indeed undertaken by later authors to have introduced and of intercalations in the Near East in search of knowledge the zodiac, of the eight-year cycle journeys to transmitted the which were made possible and safe under Greece, but probably he merely —journeys Athens of the Acheminid empire (Persian). Babylonian knowledge and practice. Meton of the orderly regime the Persian empire by nineteen-year cycle of it was the conquest of said to have introduced the But is rendered in 432 B.C., but as of Macedon in 330 B.C., which 7 intercalary months in Athens Alexander calendars cannot contacts easier and more fruitful. The Greek remarked earlier, its use in Greek these dynasty in it was known in dynasties, viz., the Ptolemaic be dated before 342 B.C., though successor question of Seleucid dynasty in Babylon and other Babylon from at least 383 B.C. The Egypt, and the great patrons of still to be decided, in Asia Minor were all priority of this discovery is dynasties of ancient encouraged and maintained scholars probably by fresh finds and interpretation learning and the famous Museum at Alexandria, astronomical records. the former set up institution with a great library, linear A was a research "Ttl^pearT^t^Greekfl of Homeric poems used which equipment. It the simpler Phoenician observatory and other necessary andB but about 900 B.C., they borrowed an vowels. their use by the addition of from all parts of Greater Greece script' and adopted it to attracted scholars script and history, which became myth lodge and a salary. Thereby they forgot their old and provided them with free board, Minoan Linear B has been The decipherment of geniuses : and legend. place nurtured a number of great Greek Chadwick. This achieved in 1952 by Ventris and CALBNDAEIC ASTBONOMY 203

of epicycles, and eccentrics to account for planetary Euclid, already mentioned; Eratosthenes who first motion. He was a junior contemporary of two measured correctly the diameter of the earth and mentioned and great figures : Eratosthenes already was the founder of scientific chronology ; and others of Syracuse (287-212 B.C.), a great whom we shall meet presently. figure in mechanics, hydrostatics and other sciences, On the Asiatic side, under the centralized rule of but to astronomy, he is remembered as originator of the Seleucids, the later Chaldean and Greek astrono- the idea of Planetarium— a revolving open sphere mical efforts became very much intermingled. A with internal mechanisms with which he could imitate Chaldean priest, Berossus, who lived during the reign the motions of the sun, the moon, and the five planets. of the second Seleucidean king Antiochos Soter Archimedes is also credited with attempts for ( 282-261 B.C. ), translated into Greek the standard planets from the Chaldean works on astronomy and astrology. The finding out the actual distances of the whether this is correct or not, period from 340 B.C. to 150 A.D. may be called the earth. We do not know time, find the planets arranged accord- most flourishing period of astronomical studies in but about this we of their distances from the earth : antiquity. The Chaldeans figured prominently during ing to the order the earlier part of this period but their methods Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn were based on a primitive form of algebra and or if we take the reverse order : According to Neugebauer, their contri- arithmetic. Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon. butions in mathematics and astronomy were as good This last order was taken up by astrology and formed as those of the contemporary Greeks who used the basis of the seven-day week, which came into geometry, but they gradually faded into obscurity about the first century A.D. and vogue on account of their infatuation with astrology ; greatest name in Greek astronomy is the Greeks, though they were great believers in The of Nicaea, in who settled in the astrology, freed themselves at least from astrolatry, Hipparchos and had an observatory there and cultivated astronomy as part of astrology, and island of 161-127 B.C.J. He probably corresponded with the emerged as leaders in astronomical science. (ft. savants at the Museum of Alexandria. Not much of The earliest Greek astronomer to use geometrical his writings have come down to us, except through ideas in astronomy is, if we leave aside the Pytha- quotations and remarks by Claudius Ptolemy, the goreans, probably Eudoxus of Cnidos ( d. 355 B.C. ), famous Alexandrian astronomer who flourished three a junior contemporary, friend and pupil of Plato. centuries later. Sarton writes about Hipparchos : He made great original discoveries in geometry, and instruments, except Books V and VI of Euclid are ascribed to him. It "It is possible that all the Ptolemaic by him (e.g. was probably his knowledge of geometry which led the mural quadant, had already been invented and meridian instruments). He was the him to make the first scientific attempt to give a diopter, parallactic observer who divided the circles of his instru- geometrical explanation for the irregular motions of first Greek ments into 360 degrees. He constructed the first celestial the sun, the moon, and the planets. Twenty-seven globe on record. spheres, all concentric to the earth were needed to used and probably invented the stereographic account for these motions. This theory had but a He projection. He made an immense number of astronomical short life, but it is remarkable as the first instance, with amazing accuracy". when heavenly bodies, connected with great gods, observations were treated on a human level. The principle of measurement of angles was the Chaldeans. Hipparchos gave Eudoxus is supposed to be the inventor of certainly derived from geometrical methods for determining the sizes and a catalogue of 850 stars with their positions which found distances of the sun and the moon, usually ascribed is reproduced in Ptolemy's Syntaxis. Vogt preserved numbers giving position, to Aristarchus of Samos (ft. 280 B.C.), who is known to that of the 471 have taught that the daily revolution of the celestial 64 are , 67 are right ascensions, 340 are sphere was due to the rotation of the earth round its in polar longitudes and latitudes, which reappear in six hundred years later. axis. He is also said to have first put forward the the Surya Siddhanta,

heliocentric theory of the universe. Neither of these It is suggested that after his discovery of precession used celestial longi- theories was accepted by contemporary astronomers. ( vide § 4.9 ), Hipparchos probably The world had to wait for the appearance of a Coper- tudes and latitudes. But these co-ordinates had been nicus (1473-1543), for the acceptance of these views. already used by the Chaldeans at least a century earlier.

Apollonius of Perga (born about 262 B.C.) known Hipparchos had probably some knowledge of plane necessary for the solution more for his treatise on Conies, originated the theory and spherical trigonometry

C. B.-34 COMMITTEE 204 BBPOET OF THE CALENDAB KEFOBM has been long the time Arabic translation as the Almagest. It of astronomical problems, e. g., finding out it rendered all previous treatises in year, a problem supposed that of rise of zodiacal signs during the remained a standard text, It is the astronomy obsolete, and great importance to horoscopic astrology. of ancient and medieval double chord, which fertilized the brains of all current opinion that he used the astronomers, Greek, Jew, Arab, and European, till below : illustrated universe the rise of the heliocentric theory of the a to have Chord (2 a)«2 R rendered it obsolete. This opinion appears been rather exaggerated. Strangely enough, the Syntaxis appears to have been quite unknown to Hindu astronomers of the A.D. Ptolemy's chief contribution to astronomy was his elaborate theory of planetary motion and discovery of now a second inequality in the motion of the moon, stars called Evection. He gave a catalogue of 1028 Fig. 20 with their positions, most of which have been shown 3° to 0° 90°, have been taken from Hipparchos by adding and gave a table of double-chords from to to longitudes given by him. This represents the which was later improved by Ptolemy in his Syntaxis. the Hipparchos's 'Sine function shift of the first point of Aries since It is suggested by Neugebauer, that the time according to Ptolemy's calculation. The actual (Jy& in Hindu astronomy) was introduced 600 years is 4°. later by Xryabhata, and replaced the double chord. value The Hindu astronomers used Utkramajya which is the Ptolemy wrote a treatise on astrology known as the Bible of ver sine function, 1—cos a, but do not appear to have the "Tetrabiblos" which long remained used the cosine function as such. Neither the Greeks the astrologers. and the cotangent, nor the Hindus used the tangent, After Ptolemy, there were no great figure in astronomers about the which were introduced by Arab astronomy except few commentators and workers of (al-Batt3M, 858-929 A.D.), and were ninth century mediocre ability like Theon of Alexandria (about early days as Umbra Versa, and known in Latin in 370 A.D.), who initiated the false theory of trepidation ( extent of shadow ) respectively. Umbra Extensa of the equinoxes, and Paulus of Alexandria (fl. 378 of the practice of designating These are reminiscent A.D.) who wrote an astrological introduction. He is the sun by the length I of the the zenith distance Z of supposed to have been the inspirer of the Indian gnomon, l = tan Z, p being the height 7 5'6 shadow of the p Siddhanta known as 'PauliM Sid&hania {vide § ), of the gnomon. but this hypothesis started by Alberuni has never Between Hipparchos and Claudius Ptolemy been proved. With the of Christianty, and A.D.). the (150 A.D.), who lived at the Alexandrian Museum after murder of the learned Hypatia (415 from 128 A.D. to 151 A.D., there is a gap of 300 light' goes out of Greece. the phenomenal rise of horoscopic years, which saw The Greek contributions to astronomy are : however, very few great names astrology. There are, A geocentric theory of the universe, with the Menelaos, a Greek astronomer who in astronomy. planets in the order given on page 203. A.D.> laid the foundation of lived in Rome about 98 The treatment of planets as spherical bodies trigonometry, but it was confined to a spherical similar to the earth. proposition from which Ptolemy deduced transversal Geometrization of astronomy, development of solutions for only right angled spherical triangles, the concepts of the equator, the ecliptic and of of which either two sides or an angle and one declination, spherical co-ordinates (right ascension and side are given. The Hindu astronomers likewise used know- celestial latitude and longitude), some elementary only solutions of right angled spherical triangles. deal with ledge of plane and spherical trigometry to discovery of general relations in spherical The astronomical problems. triogonometry was the work of Arabic astronomers Knowledge of planetary orbits, and attempts to (al-Battanl). explain them with the aid of epicyclic theories. Claudius Ptolemy who worked at Alexandria 128-151 A.D., was, as Sarton says, a man of between 4.9 DISCOVERY OF THE PRECESSION OF the Euclidean type. Great equally as an astronomer, THE EQUINOXES mathematician, geographer, bhysicist, and chronologist, the previous sections, we have stated how the his main work is the great mathematical and astro- In started giving 'Syntaxis? and in Chaldean and Greek astronomers nomical treatise known in Greek as , CALENDARIC ASTRONOMY 205

positions of planets, and stars, with the point of but is subject to variations which we may disregard at intersection of the ecliptic and the equator—the first this stage. The shift is accumulative and in 100 years point of Aries—as the fiducial point. We shall now would amount to 1° 24'; and in about 26000 years the relate how the discovery was made that this point is first point will go completely round the ecliptic.

not fixed in the heavens, but has a slow motion The period depends upon certain factors and is not along the ecliptic, to the west at the rate of ca. 50" constant.

per year. The rate is very small* but as it is unidirec- The tropical year, or the year which decides the tional and cumulative, it is of immense importance recurrence of seasons, is the time-interval for the to astronomy, and incidentally is very damaging to return of the sun in its orbit, starting from the year's astrology. vernal equinoctial point to the next vernal equinoctial point. If these points When the sun, in course of its yearly journey were fixed on the ecliptic, the tropical year arrives at the first point of Aries, we have the vernal would be the same as the sidereal year, which is the same as the equinox. The first point of Aries is therefore also time of revolution of the earth in its orbit. called the vernal point. But since the vernal equinoctial point slips to the west, the sun has to travel 360° 0' 0"-50" The position of the vernal point has rarely in the = 359° 59' 10" to arrive at the new vernal equi- course of history, been occupied by a prominent star, noctial point, hence the duration of the tropical year is but in India, as narrated in § 5*4, its nearness to star- less than that of the sidereal year by about r 20 minutes. groups as well as the nearness of other cardinal

In exact terms : points to star-groups have been noted from very early times. Traditions of different epochs record different duration of the sidereal year -365.25636 mean solar days stars as being near to the cardinal points. But tropical „ =365.24220 nobody app?ard to have drawn any conclusion from at the present time.

these records {vide for details § 5'4 ). Further Consequences of the Precession In Babylon also, different sets of positions of

1 of the Equinoxes stars and planets record Aries 15 , Aries 10°, and

Aries 8° (the zero is of Ptolemy's) as being the vernal We may now consider some consequences of the point. But no Chaldean astronomer to our knowledge precession of the equinoxes. appears to have drawn any conclusion from these data. Hipparchos appears first to have marked out the The first astronomer known to have drawn beginning of the astronomical first point of Aries. It attention to the precession of the equinoxes was started 8° west of the star a Arietis. Ptolemy had Hipparchos. He particularly mentions that the found that it had shifted by his time by about 3°, distance of the bright star Spica (a Virginis or Citra) and gave the rate of precession as 36" per year. In has shifted by 2° from the autumnal equinoctial this, he was wrong, the true shift being about 4\ point since the time of his predecessor Timocharis Ptolemy in his 'Uranometry' gives the starting point who observed at Alexandria about 280 B.C. He of the sign 6° of Aries as to the west of (3 Arietis, and concluded that the autumnal point, and therefore also the other constellations marked at intervals of 30° the vernal point, was moving westward at the rate of may be marked out on the zodiac. The picture (Fig. 19) seconds per year. 51J gives the boundaries of the different signs according to It is not known whether Hipparchos considered Hipparchos. The boundaries cf the signs of Ptolemy the motion as unidirectional. It was impossible for would be 4° to the west of those of Hipparchos. him to say anything definite on this point, as By the time of Ptolemy, (and probably much obeservations extending over centuries are required to earlier), a complex system of astrology had developed enable one to make a definite statement on this which connected men's destiny in life with the point. position of planets in the different signs at the time Though Hipparchos made, as time showed, one of of his birth (horoscopy). It was claimed that even the greatest astronomical discoveries of all times, the fortunes of nations and countries could be which is all-invportant for the calendar, well as as for calculated in advance from planetary positions in the astronomy, its great importance does not appear to signs. Though a few rational men like Seneca and have been realized by either his contemporaries or were as much sceptical about the claims followers for thousands of years. of astrology as the modern man, the general mass Let us, therefore, dwell a little on the consequences became converted to its claims, even astronomers not of this discovery. Later and more accurate observa- excepted. Even the great Ptolemy wrote a treatise tions have shown that the rate is nearly 50" per year, *The Tetrabiblos 3 exposing the principles of Astrology. COMMITTEE 206 BBPOBT OF THE CALENDAR. BEFORM

precession, main Ptolemy's Almagest into Arabic ; he noted In fact, belief in astrology was one of the upheld the theory of trepidation. But the other incentives for the observation of the positions of but Arabic astronomers like al-Farghanl (861- heavenly bodies in ancient and medieval times which great (858-Syria), Abd al-RahamSn were carried out by medieval astronomers with so Baghdad), al-Battanl al-Sufl (903-986-Teheran) and Ibn Yunus (d. 1009— much zeal under the willing patronage of influential Cairo), all noted precession and rejected the theory persons. of trepidation. In fact al-Battani gave the rate of of precession is very disconcerting The discovery precession as 54" per year, which is far more correct for in the astrological lore, the signs to astrologers, than the rate given by Ptolemy, vh., 36" per year. whereas are identified with certain fixed star-clusters ; But unfortunately, Europe recovering from the precession tends to take them entirely out of these slumbers of dark ages were more influenced by the star-clusters. Thus since Hipparchoss time, the shift Spanish-Muslim astronomers al-Zarquali (L029-1087 of has been nearly 30 degrees, and what was the sign of al-Bitruji (ca 1150, living at Seville), sign Cordova), and Pisces in Hipparchos's time has now become the the theory of trepidation. As their has who upheld of Aries, and the astronomical sign of Aries now influence was considerable, they were largely nothing to do with the Aries constellation. responsible for its diffusion among the Muslim, Jewish This consequence must have been foreseen by the and Christian astronomers, so much so that Johann followers of Ptolemy, and they probably started, more Werner (1522) and Copernicus himself (1543) were still than on scientific grounds, to find and Kepler had doubts on psychological accepting it ; Tycho Brahe out theories to mitigate the devastating influence of concerning the continuity and regularity of the immediately precession on astrology. Astronomers precession, but they finally rejected the trepidation. precession. It following Ptolemy barely mentioned The theory of trepidation was completely given up in Alexandria (ca. 370 was first referred to by Theon of Europe after 1687, when Newton gave a physical of Trepidation, i.e., he A.D.) who invented the theory explanation of it from dynamics and the law of was not unidirec- said that the precessional motion gravitation. This is given in appendix (4- A), for the gave the amplitude of tional, but oscillatory. He benefit of Indian astrologers and almanac-makers who 8°. Probably this figure was suggested oscillation as still believe in the theory of trepidation and oppose s time the first point of by the fact that at Theon' reform of the wrong calendar they are using for than 8° from Aries had shifted by a little less centuries. that it Hipparchos s position, and Theon thought Sarton from whose writings much of this account would go back and save astrology. has been compiled, writes* : A.D.), head of the Proclos the successor (410-485 "The persistence of the false theory of trepidation is Athens, a very learned man and Platonic Academy at difi&cult to understand. At the very beginning of our era, denied the one of the founders of Neoplatonism, the time span of the observations was still too small to existence of precession ! measure the precession with precision and without ambiguity, but as the centuries passed there could not After the sixth century A.D„ the dark age set in remain any ambiguity. Between the stellar observations Europe and the mantle of scientific investigation fell registered in the Almagest and those that could be made by on the Hindus and the Arabs. Let us see how the Copernicus, almost fifteen centuries had elapsed, and the precession. Arab astronomers regarded the 21°" difference of longitudes would amount to Thabit ibn Qurra (826-901 A.D.), who flourished * Sarton, A Eisiory of Science, p. 446. at Baghdad under the early Abbasides, translated =

APPENDIX 4-A

Newton's Explanation of the Precession of the Equinoxes

In view of the prevailing confusion in the minds of the ecliptic. The celestial equator assumes a new position

Indian almanac makers regarding precession of the equinoxes, E 2 T 2 Q* in year 2. a short sketch of the physical explanation of the phenomenon The celestial pole P therefore goes round the pole of the originally given first by Newton is given here in the ecliptic C, and it makes a complete cycle in a period of about hope that those amongst Indian calendar makers who 26000 years as shown in fig. 22. believe in science, may be persuaded to give up their belief At present (1950 A. D.), the celestial pole is 58' from in the theory of trepidation and be converted to the Polaris (a Ursce Minoris) which is a star of the second sayana reckoning advocated in these pages. This magnitude. CP, i.e., the line joining the pole of the ecliptic explanation will be found in any standard book on Dynamics G to the celestial pole P continues to approach the Polaris or Dynamical Astronomy, e.g., in Webster's Dynamics. up to 2105 A. D., when the pole would be only 30' away from We have now to regard the earth as a material sphere, the star and will then begin to recede from it. spinning rapidly round its axes, which is inclined at an Polaris angle of ? — w to the plane of the ecliptic, where « = obliquity Qf Rotation of the ecliptic to the equator.

The earth is kept in its orbit by the gravitational pull of

the sun, which is situated at one of the foci of the earth's orbit

which is an ellipse. Dynamics shows that the plane of the Former ecliptic is almost invariant, i.e., does not change with time, Pole Star except a very small oscillation due to attraction of other

planets on the earth. What is then precession due to ?

This is explained by means of the following figure. 4600 B.a c P,

d Cygni

14 800 A.D. ^aLyrce

Fig. 22—Showing the precessional path of the celestial

pole among the stars, 4 (Taken from Astronomy by Russell & others)

It will be seen that the celestial pole has not been marked with a prominent star for most part of this period of 26000 years. About 2700 B. C, the second magnitude star a Draconis was the pole-star, as was probably known to the ancient Egyptians, the Chinese and the Rg-Vedic Hindus. Conscious human history hardly goes beyond this Fig. 21 —Showing the precession of the equinoxes. period. The prominent stars which will become pole stars

in future are : In the above figure (No. 21), C is the pole of the ecliptic

EL'L. Let T ± midway between E and L be the firsj; 7 Cephei 4500 A.D.

of 1. a Cephei... 7500 point Aries for year Then the celestial pole is P 1( A.D. and the celestial equator is 8 Cygni 11200 A.D. E X T X Q X . Due to precession of

the equinoxes, the first point of Aries is slowly moving in a Lyrse (Vega) . . .13600 A.D. the backward direction 1/ T along r E the ecliptic. If T ± The last *is a first magnitude star, the brightest in the ahtfts to T in year the , % celestial pole shifts to P 2 northern heavens and can be easily picked up with the *long the small circle P* P* P B ...where CP obliquity of naked eye.

207 208 EEPORT OF THE CALENDAR REFORM COMMITTED

The phenomenon of precession of the equinoxes tells us where : 10- 8 = gravitational constant = 6.67 X c. g. s. units ; that in addition to rotation, the earth has another motion, y polar axis the pole of C = moment of inertia of the earth round the ; viz., a slow conical motion of its axis round A = moment of inertia of the earth round an equatorial axis ; the ecliptic which causes the equinoxes to move bakward. ~ 23° 26' 45" = ecliptic ; The phenomenon can be visualized by reference to the w obliquity of the = X 33 = of the sun 1.99 10 gms ; motion of tops played by boys (Fig. 23). m mass 13 r ^distance of the earth from the sun = 1.497 X 10 cms ; It is a matter of common experience with those who when the top is thrown spinning tide-raising have played with tops that ~— term ; r 3 on the earth, the axis round which the top is spinning very 1 = longitude of the sun ; and it is also having a often is not vertical, but is oblique ; — n angular velocity of the earth ; slow motion in a circle round the vertical as shown £ — angular rotational speed of the earth in radians. motion. The in fig, 23. This last motion is precessional If the earth were a homogeneous sphere, C would be — A r top may be likened to the earth, and the vertical direction ecliptic. The and — 0. But taking the polar radius c~a (1- «), where of gravity, corresponds to the pole of the € = ellipticity of the earth, it can be shown that for the earth, in which concentric layers are taken to be homogeneous

(G-A) 1 / , *

Q But actually ——— is the mechanical ellipticity of the earth, C

the value of which has been found by observation as — 304 Substituting the values as given above in the expression

- d\pft Sym C A "(!-«»*)07 \ • «» lU Mr* "C" we get the progressive part of the solar precession 12 -2-46X10- .

This is in radians per second of time. To convert it to

seconds of arc per year, we have to multiply the expression s 7 by 2.063x10 X3.156X10 . Fig. 23—Motion of a top. 2.063 X 10 5 being the number of seconds of angle in earth causes 7 The spinning top, which is likened to the , a radian, and 3.156 X 10 the number of seconds of precessional motion of its axis. time in the year. We have therefore the rate of solar precession top would have fallen but for its spin. When it slows down, = 16."0 per year. of the top is the top falls down ; the precessional motion We have now to calculate the action of the moon which, due to the pull exerted by the gravity. in spite of its much smaller mass, exerts a far larger that a first Now turning to the earth, we see as perturbing force as the lunar distance is much smaller. In approximation, we may take it as a point of mass concentrated fact the tide raising force * or * ne raoon * s m^Te than at the centre, and then deduce its orbit as is done in (^r~)

classical planetary theory. This would have been all right, double that of the sun. This makes the rate of lunar

if the earth were a homogeneous sphere. But the earth is not precession = 34". 4 per year. a sphere, but a spheroid, having its polar axis shorter than But there is another . The moon's orbit is

the equatorial axis by 43 kms. ( — 27 miles). There is an not coincident with he sun's path (ecliptic) but is inclined equatorial bulge of matter. The pull due to the sun, is now at an average angle of 5° 9', the extreme values being 5° 19' to a force in the ecliptic passing through the centre equivalent and 4° 59'. Further the points of intersection of the moon's the "earth defining the orbital motion, plus a couple, which of orbit with the ecliptic travel round the ecliptic in a period of to turn the equator of the earth into the plane of the tends 18.6 years. The pole of the moon's orbit M therefore moves ecliptic. It is this couple which produces precessional motion. round the pole of the ecliptic C as shown in fig. 24 in a calculation reader refer to a book For details of the may period of 18,6 years. The lunar precessional angle \p», has

on Rigid Dynamics, say A.G. Webster, Dynamics, pp. 298-302, therefore to be defined from the instantaneous position of Jf.

We mention only the results here : Combination of the two precessional motions* If ^ be the angle of precession, i.e., the angle P ± CP a in

fig. 21. we have due to the sun s attraction The two can be combined as in fig. 24. Here

— . . sin C, are the poles of the ecliptic and of the 3ym V C A a ( 2 ^ M moon's orbit. P is the celestial pole. The solar precession can be — —

CALENDARIC ASTRONOMY 209

otherwise have been uniform. represented by the vector ^, along the line PS perpendicular the ecliptic, which would (period = 18*6 years) variations are known to CP, but the lunar precession is represented by the vector These periodic PJR, which goes up and down as M goes round G in a as Nutation.

_,- :-JF R Annual Rate of Precessional Motion

The solar and lunar precessions amount to 50. "37 per tropical year, with a very small centurial variation. After making necessary corrections for the slight motion of the plane of the ecliptic due to attraction of planets, the annual rate of general precession in longitude is obtained as

follows :

Rate of precession = 50."2564 +0."0222 T per trop. year, where T— Tropical centuries after 1900 A.D. "2 The nutation in longitude may amount to ±17. according to different positions of the , but its effect on the annual rate of precession does not exceed ±5. 8, so that the actual precession rate per year may vary between 44. "5 to 56. "0. The average rate of annual precession is not constant,

it is very slowly increasing. The annual rate for certain motions. Fig. 24—Combination of two precessional epochs along with the period taken by the equinoxes to move

through 1°, are however stated below : complete cycle of 18.6 years (period of moons node). Therefore the motion is equivalent to Hate of precession No. of years per degree = Cos MPG... parallel to PS. 2000 B.C. 49."391 72.89

$n =^m gin MPG...perpendicular to PS. 49.835 72.24 50.256 71.63 This causes certain irregularities in the precessional 1900 A.D. 50.279 71.60 motion and also in the annual variation of the obliquity of 2000 A.D. I u 1

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B.C. successive streams between 2500 B.C. and 1500 5.1 THE PERIODS IN INDIAN HISTORY Others would go further back in time-scale from Indian history necessary for The time-periods in certain astronomical evidences. our purpose are shown in the Chronological Table. Few, almost none of the material records or The earliest civilization so far discovered in India of the early Aryans except some potteries (sometimes artefacts is the Harappa-Mohenjo-Daro civilization been tentatively ascribed to them, have so far after also called the Indus-Valley civilization) named about discovered. Almost the whole of our knowledge the two ancient buried cities of Harappa in the Rg-Vedas them are derived from the hymns of the Punjab and Mohenjo-Daro in Sind. They were first which were composed by priestly families amongst brought to light by the late R.D. Baner jee, Superinten- Sanskrit), them in an archaic form of Sanskrit (Vedic of India in dent of the Western Circle of in these in honour of the gods they worshipped ; that this 1924. It has now been ascertained the hymns are found occasional references to the sun, civilization extended right upto Rupar on the Sutlej moon, certain stars, and to months and seasons. Some the east and to the Narmada valley in the south. in think that there are also references to planets, i.e., the was certainly contemporaneous with This civilization Vedic Aryans could distinguish between fixed stars Mesopotamian civilizations of about 2500 B.C., the and planets, but this is doubtful. From certain years before the city of Babylon had risen nearly 500 references which we discuss in § 5.2, we may conclude amongst the cities of Sumer and Akkad ; to supremacy that they used an empirical luni-solar calendar. the first dynastic civilization of Egypt. How not and with Probably this was used till 1300 B.C. We do projected into the time-scale is not yet far back it come across sufficient material records until we but certainly many thousand years back. known, come to the time of Asoka about 270 B.C. . records of the Indus-valley From the material What was the calendar during the period civilization, it is obvious that the Harappa-Mohenjo- 1330 B.C. — 250 B.C. ? The Yajur-Veda, the Brahmanas, people had attained to as high a standard of Daro the Upani$ads and other post Rg-Vedic literature, and if not higher, as the contemporary people civilization, the early Buddhistic literature contain occasional Egypt. But the script has not yet been deci- of Iraq and astronomical references, from which the nature of chronological it is therefore difficult to give a phered ; the calender used for ceremonical and other purposes a study of the but it is not so difficult to make is history, can be inferred. The interpretation of the texts of this civilization in arts and sciences ; attainments neither easy, nor unambiguous. The latter part of drainage could build well planned cities, used a pioneer they this period has been called by S. B. Dlksit, our Egypt or Iraq, system superior to that of contemporary period. in calendar research, as the Vedahga Jyotisa copper and bronze, and had evidently evloved a used This is discussed in § 5.4. highly complex social organization. calendar appears to have to have The Vedanga Jyotisa All civilized communities have been found from foreign influence, measures and been almost completely free evolved accurate systems of weights and though this point of view has been contested. The some kind of calendar for the regulation of social Persian conqueror Darius conquered Afghanistan, and have some evidences of the use of standard life. We appears to have Gandhar, about 518 B.C. ; this region weights and measures in the Indus valley. continued under the Achemenids for nearly two they evolved a calendar ? The presump- But had centuries. The Achemenids used a solar calendar they must have, but nothing has yet been tion is that probably adopted from Egypt in contrast to the amongst the artefacts left by these people so discoverd luni-solar calendar of India, but this does not appear to by the Archaeological Survey which far recovered have disturbed the indigenous luni-solar calendancal of time- light on the calendar, or the system throws system. measurement they used. The Vedahga Jyotisa period, which as we shall quite sound grounds that the Harappa- It is held on dynasts up to the time Punjab show, was continued by Indian Mohenjodaro people were succeeded in the (200 A.D.), was succeeded by the Sarasvati river by of the Satavahanas and in the valley of the now lost Siddhania Jyotisa period, but the first record of this people who were either autochthonous or the Aryan only about 400 A.D. The transi- or period is available more probably came through Afghanistan in single 212 INDIAN CALENDAB 213

the (175 150 B.C.), who controlled the whole of Iran and tional period from 100 A.D. to 400 A.D. is one of — wrested Bactria from the line of Eukratidas in 138 B.C. darkest periods in Indian chronology. Due to happenings, Greek successive by Macedonian and Bactrian But inspite of these political Pallavas Sakas and language of culture throughout the Greeks ( Tavanas ), Parthians ( X remained the Kusanas, the period from 300 B.C. to 200 A.D. is one whole Near East, from Asia Minor to North-Western called themselves of large foreign contacts which profoundly modified India. The Parthians since 128 B.C. state-craft. culture and used Greek Indian life in arts, sciences, and Thilhellens* or lover of Greek But the history of this period was entirely forgotten on their coins, and the Graeco-Chaldean method of inscriptions, their inscriptions. But about 140 and is being recovered bit by bit from date-recording on in move, vix., the Sakas foreign references, and from artefacts recovered B.C., a new power was on the of this they began to emerge as a ruling excavations of the sites occupied by invaders from ; of they attacked period. Let us give a bird's eye view of the* history race from about 138 B.C. In 129 B.C. they wrested it completely this period, imperfect as it is, so that the reader may Bactria, and by 123 B.C. killing follow without strain our account of the transition of out of the Parthian empire, after defeating and Parthian emperors, the Vedanga Jyoti$a calendar to Siddhantic calendar. on the battlefield two successive vix., Phraates II (128 B.C.) and Artabanus I (123 B.C.). In 323 B.C., Alexander of Macedon raided the coins have Punjab, but this incident by itself had no such The early Sakas appear from their to profound influence on Indian life as is generally made been under the spell of Greek civilization, and of culture and put motifs out. Its influence was rather indirect. In India, it used Greek as a language their coins. Pressed gave rise to a great national movement of unification taken from Greek mythology on under Candragupta and-Canakya. In the former by the next Parthian emperor, Mithradates II B.C., into the empire of Darius, it gave rise to a number of Greek (123—90 B.C.), they poured by 80 states which became the focus of radiation of Greek whole of what is modern Afghanistan, except the culture throughout the East. The most important Kabul valley, which the Greeks held for sometime. were Egypt under the rule of the Ptolemies, with Their new territory became known as 'Sakasthan* of capital at Alexandria, and the Near East under the comprising modern Afghanistan and parts N.W. poured in successive Seleucids with capital at Babylon, which was India. From Afghanistan, they Taxila about 70 B.C., and succeeded a few years later by a few miles streams to Malwa, Guzrat, later had put an end to distant from later Baghdad. In 306 B.C., Candragupta to Mathura, somewhat and in the Punjab. and Seleucus faced each other, but the Greek army the numerous Greek principalities was barred by the Satavahanas was rolled back to the borders of modern Iran, and Their further progress small kingdoms which almost the whole of modern Afghanistan except in the South, and numerous the break-up of the Bactria (modern Balkh) constituting the four satrapies arose in the Gangetic valley on empires A.D.). After 50 A.D., of the old Persian empire were ceded to India. They Sunga and Kanva (45 by the Kusanas continued to be politically and culturally parts of the Sakas of the North were supplanted a kindred race, and speaking the Saka India till the tenth century A.D. belonging to India their language ; they ruled Northern from till B.C., The Mauryas kept out the Greeks 186 capitals at Peshawar and Mathura up to at least 170 when on the break-up of their empire, the Greek A.D. Contemporaneously with them, were the Saka their settlers in Bactria who had revolted from houses of Ujjain, who started ruling from to inroads ipto overlords, the Seleucids, began make about first century of the Christian era. India. There -were two rival Greek houses, the A chart of these historical incidents is attached earlier, the Euthydemids who under Demetrius and for the sake of elucidation as they are necessary (175 B.C.) took possession of the Punjab for the comprehension of the extent and amount of and Sind between 180 B.C. to 150 B.C. and threatened Greek culture, which was propagated into India, not even but were rolled back beyond the through the Greeks directly, but as it appears line of Eukratidas who so much Jamuna by the Sungas ; the now, indirectly through the early Sakas and their ousted Demetrius and his line from Bactria and successors, the Kusanas. Afghanistan proper about 160 B.C., reigned in Afghanistan up to 50 B.C. But there rose about It now appears very probable that it was during the and Kusana ruler s (100 B.C.- 226 B.C., a great barrier between the Eastern Greeks the regime of Saka of the Graeco-Chaldean (Bactrians and Indian Greeks) and the Western 200 A.D.) that a knowledge which had developed in the Grecian world Greeks in the shape of the Parthian empire (248 B.C.), astronomy, with the astronomer which became very powerful under Mithradates I after 300 B.C., and ended 214 KBPORT OF THE CALENDAR REFORM COMMITTEE

: The Rkt Sama, Yajus Ptolemy (150 A.D.), and in the Near East under the comprising the four Vedas Seleucids (300 B.C. to 100 A.D.), penetrated into and Atharva.

India, being brought by astronomers belonging to the (b) The Brdhmanas which are prose texts contai- Saka countries, who later were absorbed into Indian ning theological matter, particularly observations on society as &akadvipi or Scythian Brahmins. The sacrifices and their mystical significances ; attached borrowings appear to be more from Seleucid Babylon to the Brahmanas, but reckoned also as independent than from the west. The knowledge of Graeco- works are the Aranyakas or Upanisads containing Chaldean astronomy was the basis on which the meditations of forest hermits and ascetics on* God. the calendar prescribed by the Surija Siddhanta and other world, arid mankind. These treatises are attached to Siddhantas were built up. It completely replaced the each of the individual Vedas. Jyotisa calendar and by about 400 A.D, former Vedanga (c) The Sutras or Aphorisms, or Veddngas. when the Vedanga Jyotisa calendar had completely 'Vedaiigas\ lit. limbs of Vedas, are post-Vedic disappeared from all parts of India. Sutra or aphorism literature which grew as results of A.D., almost the whole of From 400 A.D. to 1200 attempts to understand the Vedas in their various based on Siddhanta Jyotisa for India used calendars aspects, and sometimes to develop the ideas contained Indian astronomers used the date-recording. All in the Vedas. According to the orthodox view, there era for purposes of accurate calculations, but its Saka are six Veddngas as follows : was * use for date-recording by kings and writers (1) Siksd : or phonetics ; texts explaining how generally confined to parts of the South. In general, the Vedic literature proper is to be pronounced, and regnal the Indian dynasties used eras of their own, or memorized. years, though the annual calendar was compiled Kalpa : or ritualistic literature, of which according to rules laid down either in the Surya (2) four types are known : Srauta Sutras dealing with Siddhanta, the Arya Siddhanta or the Brahma with domestic duties sacrifices ; Qrhya Sutras dealing Siddhanta, These did not much differ in essentials. with of a householder ; Dharrna Sutras dealing When India since 1200 A.D. fell under Islamic religious and social laws ; Sftlva Sutras dealing with domination, the rulers introduced the lunar Hejira the construction of sacrificial altars. well. calendar for civil and administrative purposes as (3) Vyakarana : or Grammar, e. g. 9 Panini's famous Indian calendars were retained only in isolated their Astddhyayii which once fpr all fixed up the Sanskrit localities where Hindus happened to maintain language. The As\adhyayi is however the culmination ndependence, or used only for religious purposes. attempts by large number of older authors, whose The emperor Akber in 1584 tried to suppress the of works were rendered obsolete by Pacini' masterpiece. Hejira calendar for administrative purposes by the of the Vedic Tarikh-llahi, a modified version of the solar calendar (4) Nirukla or : explanation 1630. Since lived before Panini. of Iran, but this fell in disuse from about words ascribed to one Yaska, who British rule in 1757, the Gregorian the advent of (5) Chandas—Metrics ascribed to Pingala. calendar has been used for civil and administrative (6) Jyotisa—Astronomy: the Rg-Jyotisa is ascribed purposes, which is still being continued. to one Lagadha, of whom nothing is known. attempted to give below short accounts We have Only the sixth Vedanga or Jyotisa interests* us, in use in different epochs of history. of calendars though there are occasional references to the calendar in all Satra literatures.

5.2 CALENDAR IN THE MG-VEDIC AGE * ( —1200 B.C. ) Age of the Vedic Literature

of the calen- the 'Philologists' stratification of The Vedic Literature : The knowledge The above gives only from the Vedic Vedic literature. About the actual dar in this age can be obtained the age of the of different strata, is great divergence of opinion, literature which consists however age of each strata, there to the great that the oldest in point of age greatly differing in age. According though it is admitted presupposing then come the Brahrnanas and orientalist Max MUller four periods each are the Safnhitcis. are the preceding can be distinguished. They is taken from Mantras composing the * Much of the substance-matter of this section (a) The Chandas and Indian Literature Vol. I, published by the prayers, incantations, Winternitz's A History of Safnhiias or collections of hymns, Calcutta. Chap. I, on Vedic literature. and litanies University of benedictions, sacrificial formulas, INDIAN CALENDAR 215

Upanisads, next the Sutras or the Ved&figas. Of The first and the tenth books are miscellaneous the four Vedas, the Rg-Vedas are by common consent collections ascribed to different authors. They are taken to be the earliest in age and as Winternitz taken to be the latest in age. remarks, though all subsequent Indian literature refers The Rg-Vedas consist of 1028 hymns, containing to the Rg-Vedas, they presuppose nothing extant. over 40,000 lines of verses. Max Mtiller made a rough assignment of age to 4 The Vedas are regarded as '&rutis' or revealed the different strata as follows on the assumption that knowledge preserved by hearing." According to the BrSThmanic and Upanisadic literature predated savants, they were the outpourings of the heart and the rise of , and that the Sutra literature mind, of ancient priestly leaders, to their gods which which may be synchronous with the Buddhistic were mostly forces of nature, intermingled very often literature may be dated 600 B.C. to 200 B.C. Working with secular matter. Priestly families were trained backwards he assigned the Brahmanic literature to to memorize the texts and pass them on to succeding 600 B.C. to 800 B.C., the interval 800 B.C. to 1000 B.C. generations in ways which guaranteed their transmi- as the period in which the collections of hymns were ssion without error or alteration of the text. arranged, and 1000 B,C. to 1200 B.C, as the period of Savants are almost unanimous in their opinion that the beginning of Vedic poetry. He always regarded the Rg-Vedic texts which were composed in an archaic these periods as terminus ad quern, and in his Gifford form of Sanskrit, which was not completly understood Lectures on Physical Religion in 1889, he expressly even in 500 B.C„ have come to us without change. states "that we connot hope to fix' a terminus a quo. The orthodox Indian view that they are revealed Whether the Vedic hymns were composed 1000, 1200, knowledge is of course not shared by scholars, both 2000 or 3000 years B.C., no power on earth will ever eastern and western, who point out that very often determine. * in the text of the Vedas themselves and in Anukramatyis It is not correct therefore to say, as some people or introductions to texts, the authors of each hymn say, that Max Mtiller had proved that 1200-1000 B.C. are mentioned by name and family. is the date of the Rg-Vedas. t To which locality are the Vedas to be ascribed ? Other authorities, Schrader, Tilak, Jacobi, and As regards locality, they are certainly to be P. C. Sengupta have found much older age for Rg-Vedic ascribed to parts of Afghanistan, east of the Hindukush Indians : in fact, even as early as 4000 B.C., for some and the Punjab. The rivers of the Punjab, the incidents described in the Rg-Vedas.* But their Indus and its tributaries on both sides and the now arguments, being based on interpretations of vague lost SarasvatI are frequently mentioned, the Ganges passages assumed to refer to astronomical phenomena only once in a later text. The authors call themselves have not commanded general recognition. Aryas or Aryans, in contrast to the Dasas or Dasyus Let us first look at the strata within the Rg-Veda who were alien to them, and with whom they came itself. The Rg-Vedas are divided into 10 Mandalas in frequent clash. The Dasyus are now taken to be ( lit circles ) or books. Of these, the 2nd to the 8th partly Indus valley people, partly aboriginals. books are ascribed to certain priestly families, eg, The Rg-Vedas describe a highly complex society the 2nd book is ascribed to Gritsamadas, the 3rd to of priests, warriors, merchants and artisans, and slaves the Vi§v&mitras, etc. These are agreed to be the but the rigid caste system had not yet developed. oldest parts of the Vedas. There are also references to cities, but no artefacts The ninth book is devoted to Soma which is an except some pottery, have yet been discovered which intoxicating drink pressed out of a plant. The drink can be referred to the Rg-Vedic Aryans. was dear to the Aryans and is also mystically The Rg-Vedic Aryans, it appears, were con- identified with the Moon. temporaneous (if not older) with the great civilizations

* For details about Vedic antiquity, see Ancient Indian of Mesopotamia, both Sumerian, and later Accadian, Chronology by P. C. Sengupta. and according to one view, some of the royal families

+ It appears that Max Midler lias been a bit. dogmatic in his of Asia Minor, were probably 'Vedic, Aryans'. It is opinion. Shortly after his death the names of the Vedie gods, Indi a, therefore quite probable that they had attained as Varufta, Mitra and the Nasatyas in their Kg-Vedic forms were high a stage of civilization as that of Egypt of the discovered in the Hittitc clay tablets discovered at Hoghnz Knei in Pyramid builders (2700 BC), or of Sumer and Accad Aeia Minor. They have been assigned to about 145U B.C. More evidences about the Vedic Aryans were discovered in the excavations in under Sargon I. SarasvatI valley now being undertaken by the Arehaelogical Dept. the Let us see what information we can gather about of the Govt, of India. Further, fresh evidences are expected also in the calendar which they must have used, for no the archaelogical work undertaken in Afghanistan, Iran and Central be without Asia. civilized community can a calendar. :

COMMITTEE REPORT OF THE CALENDAR REFORM 216 wheel spoke-boards : One centred Translation : Twelve life of Vedic Aryans was there Further, the whole understands these ? In these sacrifices had three navels. Who gods ; and sacrifices to their great pegs which do not round are 360 sankus (rods) put in like with respect to seasons and to be carefully timed were year-long, get loosened". moon's phases. In fact, some sacrifices wheel, whose great Vedic scholar remarks is compared to a revolving as Dr. Martin Haug. the The year (twelve months). 46) to Ailareya Brahmana is divided into 12 parts in his introduction (p. circumference grouped into three navels (seasons). (affiliated to the Rg-Veda). They are which lasted for one year, days, divided into- "The Sattras [or sacrifices] Here also we have a year of 360 imitation of the sun's yearly course. constituting a season, as we were nothing but an 12 months, four months of six into two distinct parts, • each They were divided find in the oldest inscriptions. midst of both was the each ; in the months of thirty days the last passage is correct, If the interpretation of central day, cutting the whole Vwvan, i.e., equator, or later caturmasy* we have the earliest reference to the Sattra into two halves*. seasons each or division of the year into three times than the system, refers to somewhat later This four months. early times, the of but even during these Aryans, Rg-Veda, from these passages that Vedic developed. Let us see what It appears sacrificial cult was fully Egyptians also- from the once a year of 360 days as ancient get about the calendar had references we that this was not the had but they discovered later Rg-Vedic times. months, or for a correct value either for 12 lunar following reference shows that References seasonal year. For the Calendarie and Astronomical they used also a thirteenth month. in the Rig-Vedas 1.25.8 along with other Jig-Veda, These are few, and interspersed prajavatah wondered at, for the hymns dhvtavrato dvadasa matter This is not to be Veda maso vedaya upajayate. the gods, Agni (sacrificial are addressed chiefly to other national warrior god), etc., and knows the fire) (the Translation: Dhftavrata ( Vamna) The direct references that references are only incidental. the animals created during twelve months : (and) which are later in found only in Books 1 and 10 knows (the intercalary month> are period ; (and) he family books. twelve months). age than the which is created (near the texts of a few hymns and their the calendar Let us give the This passage makes it clear that English. the adjustment made ? translations in was luni-solar. But how was noted by Tilak Rg-Veda. 1.164.11 A hymn in the Gg-Veda first cakram our help. Dvadasararh nahi tajjaraya varvarti comes to paridyamvtasya Ilg-Veda, 4.33.7 agne mithunaso atra sapta satani A putra ranannrbhabat vimsatisca tasthuh. Dvadasa dyun yadagohyasya tithye sasantab- wheel (or time) having twelve Translation : The Suksetrakrnvannanayam ta sindhun dhanvatistha heavens, but it does not spokes revolve round the nnosadhir nimnamapalj. pairs of sons nde this out. Oh Agni! 720 wear sleeping for Translation: When the #bh™ (wheel). made themselves comfortable as likened to a wheel, having 12 twelve days have Here the year is the fields the unconcealable (sun), they bring the 720 pairs of sons are 360'-days guests of spokes (or months) ; The plants ^grow in good order and direct the rivers. and nights. \ and lowland is spread with water that the in wildernesses, The interpretation commonly accepted is into 12 Tilak, the Ifbhus are the genii of taken to consist of 360 days divided According to year was of the day (following or They are said to enjoy the hospitality months, and the night and seasons. verse. This for twelve days in the above preceding) constituted a couple. the sun the adjustment of passage, according to Tilak means Ifg-Veda. 1.164.48. 366—354 = 12 the solar year with the lunar (i.e., pradhayaseakramekam trini nabhyani Dvadasa days).* ka u tacciketa

trisata na sankavo'rpitah Tasmin tsakam VI. * Ancient Indian Chronology, Chapter sa?tirna calacalasah. r/. INDIAN CALENDAR 217

Another hymn from Atharva Veda (4.11.11) states Atharva Safnhita, 14.1.13 of yearly sacrifices after that : 'PrajSpati, the lord Suryaya vahatmi pragat savita yam avasrjat finishing one year's sacrifice, prepared himself for the Maghasu hanyante gavah phalgumsu vyuhyate. sacrifice*. next year's Translation : The first line is identical. In the line, the only change is Magha for Agha, and The sacrificial literature of India still preserves second In the lunar zodiac, Magha the memory of these days by ordaining that a person Phalgunl for Arjunz. for lunar No. 10, of which the chief star wishing to perform a yearly sacrifice should devote stands is Leonis. The two Phalgunl stars, Uttara Phalgunl 12 days (dvadasaha) before its commencement to the a (No.12) and Purva Phalgunl (No. 11) stand for Leonis preparatory rites. and 8 Leonis. Did the Rg-Vedic Aryans have any knowledge This verse shows that the custom of designating of the lunar zodiac, or designate the days by the lunar the day (it means day and night) by the lunar asterism mansions, as we find widely prevalent during later in which the moon is found in the night, which is times ? found widely in vogue in later times, and is used even

There is no explicit reference to this point, but to-day for religious purposes, was in use at the time words which are now used to denote the lunar when this hymn was written. The practice therefore mansions are found in several verses of the Rg- dates earlier than 1200 B.C. at least.

Vedas, e.g.,

Longer periods of Time : The Yuga in RV. 4-51-2 Citra" ( rt Virginia) is mentioned 'Yuga is a very common word used in Indian Magna" (a Leonis ) is mentioned in RV. 10-85-13 literature of all times to denote an integral number of but in these passages the meaning of these words is years when certain astronomical events recur. It not very clear. exactly corresponds to the Chaldean word 'Saros' The following references are more explicit. which has gone into international vocabulary. In

later Indian literature we have of all kinds : the J?g- Veda, 5. 54. 13 five yearly yuga, sixty yearly yuga, and Mahayugas of Yusma dattrasya Maruto vicetaso rayall syama 4*32 xlO 6 years. Was any Yuga, known in Rg-Vedic rathyo vayasvatah na yo yucchati tisyo yatha times ? divo'sme raranta Marutah sahasrinam. There is evidence that some kind of a short period Translation : You wise Maruts, we would like to yuga, probably the five yearly yuga of later times, in be disposer of the wealth conferred by you on us it which the moon's phases roughly recur, and which should not deviate (from us) as Tisya does not deviate was the chief theme of the Vedanga Jyotisa was from the heavens. known in Rg-Vedic times as the following quotation one is tempted to identify the word 'Tisya' with Here shows : (S Cancri). the lunar asterism of that name, vi% t , Pusya Rg-Safnhita, 1.158.6 The following reference is more explicit. Dirghatama mamateyo jujurvan dasame yuge apamartham yatinam Brahma bhavati sarathhS. Rg- Veda, 10. 85. 13 Translation : Dirghatama the son of Mamata Suryaya vahatuh pragat savita yamavasrjat having grown old in the tenth yuga became the Aghaau hanyante gavo'rjunyori paryuhyate. charioter of the karma which leads to semi-result.

; (dowry) of cows which was Translation The The most rational explanation of the word yuga given by Savita (Sun) had already gone ahead of Surya. here is probably the five yearly yuga of Vedanga the Agha-day, the cattle were slain (acc. to Sayana On Jyotisa for it is rational to expect that a man becomes departed), on the two Arjuni- days, she was led had old after he attains the 50th year. But there have bridegroom's house. to the been other explanations.

This passage occurs in the famous bridal hymn, The Seasons and the Year where the Sun god (Savitr) gives away his daughter The most commonly used word for year in the Surya to Soma (Moon) in marriage. It says that on the Indian literature is Varsa or Vatsara. The word are, Agha~day the cows, given as bridal dowry driven 4 Versa is very similar to Varsa, the rainy season, and away ; on the two Arjunl-d&y% the bride goes to the is probably derived from it. But curiously enough, bridegroom's house. this word is not found in Rg-Vedas. But the words This hymn is repeated in the Atharva Safnhitd &arad (Autumn), Hemanta (early Winter) etc., ate very as follows : often found to denote Reasons' and sometimes years, 218 REPORT OF THE CALENDAR REFORM COMMITTEE

l according to their practical purposes, in exactly the order in just as in English we very often say A young lady of which they were used at the sacrifice. These are, in fact, eighteen '. nothing more than prayer-books and song-books for the that the Summary : The above passages show practical use of certain sacrificial priests—not indeed Rg-Vedic Aryans, who must be placed at least before written books, but texts, which existed only in the heads of had a luni-solar calendar, and used 1200 B.C., teachers and priests and were preserved by means of oral months. do not have, however, their intercalary We teaching and learning in the priests' schools.* names for the 12 months, and there is no clue to find The Yajurvedas were compiled for the use of the out how the intercalary month which is mentioned " Adhvaryu priest Executor of the Sacrifice" who performs all at one place was introduced. It appears ihat they the sacrificial acts, and at the same time uttering prose individual days by the naksaira i.e., by the denoted prayers and sacrificial formulae (Yajus). They are the asterism in which the moon is found at the lunar liturgical Samhitas, and prayer books of the priests. night, and hence it is permissible to deduce that they Winternitz gives reasons to believe that the used the lunar zodiac for describing the motion of Sarhhitas of the Black Yajurveda school are older than the moon. There is no mention of the tithi ^or the those of the White school. lunar day) widely used in Indian calendars, in the Even such a conservative thinker as Berriedale Rg-Vedas. The solar year was probably taken to Keith gives 600 B.C. as the terminus ad quern for the consist of 366 days, of which 12 were dropped for verses of the Yajurveda Samhita". As we shall see, luni-solar adjustment. there are references which point to a much earlier origin. The Yajur-Veda gives the names of twelve months, 5 3 CALENDARIC REFERENCES IN THE and the names of the lunar mansions with their LITERATURE YAJUR VEDIC presiding , and talks of the sun's northernly and The Atharva Veda consisting mostly of magic southernly motion. We do not give the texts here, Keith's translation. incantations also contain calendaric references, but but only Dr. Berriedale we shall make only occasional use of them, as the text Taittiriya Safnhita, 4.4.11 of this Veda has not probably come to us in unadul- terated form, for the Atharva Veda was not regarded (a) (Ye are) Madhu and , the months of Spring. as holy as the Rg-Veda. (Ye are) Sukra and Suci, the months of Summer. Of the two other Vedas, the Sama-Vedas contain no (b) (c) (Ye are) Nabha and Nabhasya, the months new matter than what is contained in the Rg-Veda. of Rain. But there are copious calendaric reference in the (Ye are) Isa and Drja, the months of Autumn. Yajurveda for obvious reasons, which are clearly (d) (e) (Ye are) Sahas and Sahasya, the months brought out in the following extracts from Winternitz's of (Early) Winter (Hemanla). introductry remarks to Yajurvedic studies (p. 158-159) : (f) (Ye are) Tapas and Tapasya, the months of two Sarhhitas [Rk and Atharva] which have so far "The cool season. been discussed have in common the fact that they were not compiled for special liturgical purposes. Although most * are schools of the Yajurveda Samhita each with of the hymns of the rJg-Veda could be, and actually were There two a number of recensions as shown below : used for sacrificial purposes, and although the songs and Black Yajurveda School, with the following recensions : spells of the were almost throughout employed 1. The fa) TheKathaka for ritualistic and magic purposes, yet the collection and (b) The Kapisthala-Katha-Samhita, which is preserved only agrrangement of the hymns in these Samhitas have nothing in a few fragments of manuscript. the various liturgical and ritualistic purposes. called M. 6. to do with (c) The Maitrayani-Samhita—shortly also called "Apastamba- The hymns were collected for their own sake and arranged (d) The Taittiriya-Samhita, Apastamba-School, one of the chief and placed, in both these collections, with regard to their Samhita" after the which this text was taught—shortly called T. S. supposed authors or the singer- schools to which they schools in closely inter-related, and are designated belonged, partly also according to their contents and still These four recensions are belonging to the "Black Yajurveda*'. Differing from them is the more their external form-number of verses and such like. as White Yajurveda which is known as 6ukla Yajurveda. They are as we may say, collections of songs which pursue a called S. which takes its 2. The Vajasaneyi-Samhita shortly V. literary object. name from Yajfiavalkya Vajasaneya, the chief teacher of this Veda. of the other recensions, that of the It is quite different with the Samhitas two Of this Vajasaneyi-Samhita there are two which however differ- Vedaa, the and the Yajurveda. In these collections Kanva and that of the Mfidhyandina-Bchool, very little from each other. we find the songa, verses, and benedictions arranged INDIAN CALENDAR 219

The month-names which are- given here and There are several points to be noticed in this list,, repeated in many other verses of the Yajur-Veda which may.be compared with the list given on p. 210. have been interpreted by all authorities to be tropical. First, the naksatras start with Kfttikas which all

Further this is probably the earliest mention of month- authorities identify with the conspicuous group Pleiades. What is the significance of this ? names in Indian literature ; these names are no longer in use, and have been replaced by lunar month-names At the present times, the naksatras start with {Caitra, Vai&akha, etc,) which are, however, found at a AMni, of which the junction star is a or Arietis. later stage. This custom, Asvinyadi, was introduced in Siddhanta

Jyotisa time ( 500 A.D. when the astronomical first Madhu and Madhava have been taken in later ), point of Aries was near the end of the Revatt literature to correspond to the time-period when the naksatra ( ( Pisdum ), or the beginning of ASvini. sun moves from -30° to 30° along the ecliptic, and We do not enter into the controversy about the exact so on for the other months. But we have no reason location of this point by the Siddhanta astronomers, to believe that the Yajurvedic priests had developed which is fully discussed in Appendix 5-B. At present, such a fine mathematical sense of seasonal definition. the astronomical first point had shifted by as much as But it is almost certain that they must have developed 19° from £ Piscium, but the orthodox Indian calendar some method of observing the cardinal points of the makers do not admit in the continued precession of the sun's yearly -course, viz., the two solstices and the equinoxes, and still count the naksatras from Asvini. equinoxes. From these observations, they must have In all older literatures, on the other hand, including counted that the number of days in a year was 366 in the great epic Mahabhdrata, whose composition round numbers. or compilation may be dated about 400 B.C., the first The Yajur-Veda speaks in many places of the naksatra is Kfttikd. It therefore stands to reason to UttarViyana, the northernly course of the sun from assume that at one time, when the naksatra enumeration winter solstice to summer solstice and the Daksinayana started, the Pleiades were close to the astronomical or the southernly course from summer solstice to first point of Aries, or rose near the true east. This winter solstice and the Visuvan, or the equinoctial is implied in the following verse which S. B. Dlksit point. The ayanas or courses must have received picked out of the j&atapatha Brahmana : their designation from daily notings of sunrise on the eastern horizon. The year-long observation of shadows &atapatha Brahmana, 2.1.2.

cast by a gnomon, of which we have evidences, may Ekarh dve trini catvariti va anyani

have formed an alternative method for fixing up the naksatranyathaita eva bhfiyistha yat krtfcika.... solstitial days, and the cardinal points on the horizon, Eta ha vai pracyai diso na cyavante (vide Appendix 5-C), where some passages from the sarvani ha va anyani nalisatrani Aitareya Brahmaiia attached to the Rg-Veda are pracyai disascyavante. that the cardinal points stated in favour of the view Translation : —Other naksatras have one, two, of the gnomon. were observed by means three or four ( stars ) only ; these Kfttikas have many

Once they learnt to anticipate the cardinal days, ( stars ).. .They do not deviate from the east; all determination of the month-beginnings marking seasons other naksatras deviate from the east* would not be difficult. The Madhu-month (the first The names as given in this list are somewhat month of spring) would begin 30 or 31 days before the different from those now adopted, which have come for vernal equinox day or 61 days after the winter solstice into vogue since 500 A.D.; example, we have : day, and the Madhava month on the day after the No. 6 Tisya for Pusya equinoctial day and so on. Average length of 30£ No. 16 Rohini for Jyestha days would be given to each month, or 30 and ( There are thus two Rohinls, No. 2, and No. 16 31 days to the two months forming a season. No. 17 Vicrtau for Mala No. 20 Srona for Sravana The No. 21 Sravistha for Dhanistha No. 23 Prosthapada for Bhadrapada One of the peculiar features of the Indian No. 26 Asvajuya for Asvini calendars is the use of the Naksatras as explained in No. 27 ApabharanI for Bharanl § 41. Evidences have been given that the custom started from Rg-Vedic times. But we come across a The more important question is whether the lunar

full list of Naksatras only in the Yajurveda with mansions denote definite clusters of stars, or the names of presiding deities as given in Table No. 10 naksatra-divisions of later times, amounting t6 13° 20' 800' This point has been discussed in 4*1. ( p. 220 ), taken from Dlksit's Bharatiya Jyotifastra. or minutes ? 3

C. E.-36 .

BEFOBM COMMITTEE 220 EEPOBT OF THE CALENDAK

Table 10.

their Presiding Deities Names of Nakshatras in the Yajurveda with

Number* Principal Longitude Latitude Name of Presiding No, Star (1950'0) Naksatra Deity ( Grammatical) 2' 46" Tauri 59° 17' 39" + 4° Agni P 7] 1. - S a Tauri 69 5 25- 5 28 14 2. Bohini - 32 s \ Orionis 83 31 13 22 3. Mrgasirsa Soma p Invaka >> - 59 s a Orionis 88 3 22 16 1 Ardra Rudra D Bahil )» 112 31 29 + 6 40 51 D j8 Geminorum Puttarvasu o. 4 32 S 8 Cancri 128 1 23 + Tisya Brhaspati 6. 131 38 59 - 11 6 25 Sarpa P € Hydrae 7. Airesa 27 48 P a Leonis 149 8 1 + Magha Pifri ILL 8. 160 36 52 + 14 19 58 Aryama u S Leonis 9. Phalguni Purva Phalguni 170 55 23 + 12 16 13 f D (3 Leonis 10. Phalgun Bhaga Phalguni Uttara - 12 11 31 S 8 Oorvi 192 45 23 11. Hasta Savita 203 8 37 - 2 3 4 Tndvn. Tvasta s a Virginis 12. Citra 30 46 3 s a Bootis 203 32 8 + 13. Svati

Nis^ya 20' 19 D a Librae 224 23 7 + Visakha Indragni 14. 241 52 23 - 1 58 49 Mitra P S Scorpii 15. Anuradha 249 3 51 - 4 33 50 Indra s a Scorpii 16. Bohini Jyestha 263 53 14 - 13 46 56 Pitr D X Scorpii 17. Vioftau a Prajapati D Mulabarhani, Mula, Nirrti, 273 52 55 - 6 27 58 pah P S Sagittarii 18. Asadha A Purvasadha 281 41 11 - 3 26 36 Visvedeva P a Sagittarii 19. Asadha Uttarasadha + 61 44 7 Brahma s a Lyrae 284 36 54 Abhijit 29 18 18 s a Aquilae 301 4 16 + $rona Visnu 20. 315 38 38 + 31 55 21 Yasu p £ Delphini 21. $ravistha - 23 8 s X Aquarii 340 52 38 Satabhisak Indra, Varuna 22 352 47 19 + 19 24 25 Ajaekapad p a Pegasi 23. Prosthapada

i 8 27 32 + 12 35 55 Ahirbudhniya p 7 Pegasi 24. Prosthapada la 19 10 40 - 12 52 s f Piscium Bevati Pusa 25. 33 16 18 + 8 29 7 Asvin D /? Arietis 26. Asvayuja + 10 ~ 26 48 Yama P 41 Arietis 47 30 19 27. Apabharani

* = = Plural. ; P S= Singular ; D Dual Taittirtya Safnhita, 7.4.8. purnamaso mukhata The Lunar Month-Names Sarhvatsarasya yat phalguni kaiva eva sarhvatsaramarabhya diksante tasyai earlier have not solar month-names given The nirya-yat sammedhye visuvant sampadyate general currency. The month-names samvatsarasya gone into Citra purnamaso dikseran mukharh va etat lunar origin as given in § 5-7. are of . generally used yat citra purnamaso mukhata eva. the Taittirtya Safnhita These names are first found in consecrated on the Translation .—One should get many other places of the Yajur-Veda 7.4.8, and in day because Phalgima full moon form. We Phalguni full-moon but in a somewhat different are literature, year. Hence, ( such people ) is the "mouth" of the quote parts of the passage. ))) )

INDIAN CALENDAR 221

taken as consecrated from the very beginning of the is completed when the moon is ahead of the sun by year. But such 12°, 12° people have to accept one 'nirya' or integral multiples of ( vide § 57). (draw back), viz., that the 'Visuvan' occurs in Thus the first tithi ( Pratipada, lit. when the moon the cloudly season ( sammedhya ). Hence, one should is regenerated ) in the waxing half starts when the consecrate on the Citra full-moon day. The Citra full moon is in conjunction with the sun, and ends when J moon month is the *mouth of the year. she has gone ahead of the sun by 12°, when the From these passages, we learn that the lunar month second tithi of the waxing moon begins. The tithis came gradually. The ancient Indians reckoned by are numbered ordinally from 1 to 15, the end of the the paksa or the , and distinguished the fifteenth tithi being full-moon. Then begins the tithis of the closing full moon day of the pak$a by the naksatra waning moon, numbered from 1 to 15, the end of the 15th tithi where the moon was full. Thus Phalguni Paurnamasi being the new-moon. There are thirty tithis in a is that full moon when the moon gets full near the lunar month, and though the average duration is less than a solar day, being Uttara Phalguni star ( (3 Leonis \ one of the lunar 23,62 hours, the length of individual mansions. Caitri Paurnamasi is that full moon, when tithis may vary from 26.8 to 20.0 hours., on account of irregularity in the the moon gets full near the Citra star ( a Virginis ), which is the 14th lunar mansion. Later, as the months moon's motion.

were always full-moon ending, the word paurnamasi This is the definition of the tithi given in was dropped, and, e.g., the first part of Caitra-Paurna- Siddhdntas or scientific astronomy which started about masi, i.e., Caitra became the lunar month-name. The 400 A.D. But this presupposes knowledge of measure- above passage says that the Phalguna Paurnamasi ment of angles, and precise scientific observation, of was regarded as the last day of the year and less which we find no trace in the Vedic literature. What

frequently the Caitra Paurnamasi. This system still was then the origin of this system ? continues, and the first lunar month Caitra of the lunar We have no reference to tithi in the Rg-Veda. year begins on the day after Phalguni Paurnamasi. The first reference is found in Yajurvedic literature, There are twenty-seven naksatras and so only 12 and the Brahmanas. The Taittiiiya Safnhitd talks of can be selected for lunar month-names. the pa%cadasi tithi, which shows that the lunar paksa was divided into 15 tithis, counted by ordinal numbers The twelve names which we have got are : from 1 to 15 for each paksa. But what was the time- Caitra from Citra (No. 14) period meant by a tithi ? The Vaisakha „ Visakha ( „ 16) attached to the Rg-Veda gives the following definition Jyai§tha „ Jyestha ( „ 18) of the tithi.

Asa<}ha „ Asacjha ( „ 20 & 21 Sravana Aitareya Brahmana, 32.10 „ Sravana ( „ 22 ) Bhadra „ Bhadrapada ( „ 25 & 26 ) Yam paryastamiyad abhyudiyaditi sa tithih. Asvina „ Asvini „ 1 ( The tithi is that time-period about which the Kartika „ Krttika ( „ 3 ) moon sets or rises. Margaslrsa „ Mrgasiras ( „ 5 This has been interpreted by Prof. Pausa P. C. Sengupta „ Pusya ( „ 8 as follows : Magna „ Magha („ 10) During the Phalguna waxing moon ( sukla paksa ), the tithi „ Phalguni ( „ 11 & 12) was reckoned from moon-set to moon-set ; and during Of course, full moon takes the place by turn in all waning moon ( kfsna paksa ), the tithi was the naksatras. But only 12 at approximately equal reckoned from moon-rise to moon-rise. The tithis intervals could be selected. But we have too Rauhinya were thus of unequal length, as shown by Prof. P. C. paurnamasi etc. the paksa when the moon becomes Sengupta in Table No. 11 on page 222. full near Rohini, or Aldebaran ( lunar mansion No. 4). But Rauhinya was not selected for the name of a lunar month, because it was too near Krttika-Paurna- 5.4 THE CALENDAR masi. The history of the Indian calendar from the end of the Yajurveda Tithi period to the beginning of the Siddhanta Jyotisa period is very imperfectly known 'Tithi' or 'Lunar Day' is a very important concep- though there are plenty of calendaric references ition in Hindu astronomy, for holidays are always dated in the Brahmanas, Sutras, and the epic Mahahharata by the tithi. According to Siddhantic definition, a iiihi and various literature. On time-scale, it extends from 1

REFORM COMMITTEE 222 REPORT OF THE CALENDAR

Table 11.

Duration of Vedic Tithi

Ending of Vedic Tithi Duration Vedic Elapsed English Modern of Time of Event Event Vedic Tithi Tithi No. Date Tithi (L. M. T.-

(1936 A.D.) h m Moonset or Sunset Oct. 15 Amavasya 17 34 16 Pratipad 17 33 25 3 1 17 Dvi tiya Moonset 18 36 24 40 2 i ft TrHvn 19 16 3 C^.a 4-11 20 3 24 45 wcu U Lllv^Vltill 1 4 on Pq T"l/"»a TYlT 20 53 24 50

01 21 46 24 53 5 00 22 41 24 55 6 23 38 24 57 7 AO Afl+QTYl 1 OA 24 36 24 58 8 OK 25 35 24 59 9 Jib Dasami 35 25 10 2o Ekadasi 26 art 27 37 25 11 27 Dvadasi 42 25 12 28oo TrayodasI 28 25 13 OQ Caturdasi Moonset 29 49 22 11 33 14 Oil Moonrise or 17 Sunset 18 24 56 15 ol Pratipad & Moonrise 18 Dvitiya 19 18 25 16 Nov. 1 Trtiya 20 20 25 17 2 Caturthi 21 23 25 18 3 Paricam I 22 23 25 19 4 Sasthi 23 21 24 58 20 5 24 14 24 53 21 6 Astami 25 7 24 53 22 7 Navami 25 58 51 23 8 Dasami 24 26 47 24 49 24 9 Ekadasi 27 37 24 50 25 10 Dvadasi 28 27 24 50 26 11 Trayodasi 29 17 24 50 27 12 Caturdasi Moonrise 30 14 24 57 28 13 Sunrise 17 15 11 1 29 14 Amavasya Sunset 18 24 45 1 Nov. 15 Pratipad Moonset amavasya at moonset in the light half and at moonrise in the dark half. Near Note : —The Vedic tithi ends There are 29 or 30 such tithis in a lunar month, and all when the moon remains invisible, the ending is at sunset. duration except amavasya and purnima which are of about 12 hours' duration. tithis are of more than 24 hours'

attached to set by some at 1300 as mentioned earlier, the Yajus Jyotisa an unknown antiquity, which is the Yajurveda and consisting of 43 verses, and there B.C. to 300 A.D. to one Somakara, a commentator of this is a text ascribed The VeddTiga Jyotisa is generally assigned to the Vedas. The dffferent texts collection of unknown age of period. It may be said to be a sort of contain about the same matter, but the verses are aphorisms giving mathematical rules for fixing short showing that the original texts three haphazardly arranged calendar in advance, and is known in the unadulterated form. verses, have not come down to us in an versions: the Rg-Jyotisa consisting of 36 Lagadha The number of independent verses in all the versions attached to the Rg-Veda and ascribed to one INDIAN CALENDAE 223

The Vedaiiga Jyotisa further describes measure- is not more than 49, and some of the verses have subdivisions of the day by means of the not been interpreted. ments of the clepsydra, as well as by gnomon- shadows. There are several other calendarical treatises which is the assumption that the can be assigned to this period. The Surya Prajnapli, One particular feature the length of.ifche day to that of the night on a Jaina astronomical work, the Jyothakaranda, and ratio of

solstice day^rs as 3 : 2. the Kdlalokapralcasa. the summer Let us now examine these points critically. A short account of the calendaric rules followed observe that all the mathematical rules point in these treatises is given in Varahamihira's Paftca We

motions of the sun and the moon, i.e , Siddhantika, Chap. XII, where the rules are collected out only to mean <% of the sun and the moon were obtained by as Paitdmaha Siddhanta" or Astronomical Calendar the periods number of savana days in a large number according to Grandfather Brahma, the Creator, in counting the and dividing the number by the Hindu mythology. That shows the high antiquity of of years and months, of periods (year or month). No evidence is the rules. Varahamihira, as well as Brahmagupta number the systematic cfay to day observations of describe the rules as very "inaccurate" {Duravibhrastau, found of and the moon. Only the lunar zodiac was furthest from truth in Varahamihira's language) though the sun describing the positions of the sun and the they pay a formal courtesy to the supposed authors. used for have been divided into 27 But such has been the case with calendars of all moon, which appears to

naksatras ; in other words the naksatras ancient nations, including the Babylonians at this equal parts or denoted star-clusters but equal divisions of period and a critical account of the Vedaiiga Jyotisa no longer the lunar belt. is important from the historical point of view. There is no mention of the zodiac or twelve signs It may be remarked here that there are minor of the zodiac, or of week days, or of planetary motion. differences between Vedaiiga Jyotisa, the Jain systems, look critically into the rules. and the Paitamaha Siddhanta, which appear to be Let us now older treatises have a x = days the latest of this group. The 5 solar years = 365.2422 5 1826.2110 ; Siddhanta has x days year of 366 days, while the Paitamaha 62 synodic months = 29 .53059 62 = 1830.8965 ; a year of 365*3569 days (Dlksit). 67 sidereal months = 27.32166x67 -1830.5512 days. Jyotisa There is an extensive literature on Vedaiiga Therefore, regarded as a measure for luni-solar B. Dlksit, ^hich has been studied by Dr. G. Thibaut, S. adjustment, the error is 4.685 days in a period of 5 Sastry, amongst others. the ;S. K. Pillai, and Dr. R. Shama years, i.e., if we started a yuga with the sun and We here give an account of the calendar according moon together on the winter solstice day, the to the Paitamaha Siddhanta. beginning of the next yuga (6th year) would occur 4.685 days later than the winter solstice and in 5 to 6 yugas the discrepancy would amount to a month or half of the Contents Summary season. This cannot escape notice, and therefore have been some way of bringing back the "Five years constitute a Yuga or Saros of the sun there must the winter solstice day. Otherwise the calendar and the moon. yuga to becomes useless. But how could it have been The yuga comprises 1830 savana days (civil days) done ? and 1860 tithis (lunar days). several This is a matter for conjecture and In the yuga, there are 62 lunar months and 60 solar hypotheses have been proposed. According to S. B. months. So two months are omitted as intercalary Dlksit, we should have in 95 years : months, in a period of 5 years. according to the F. J.,f x 95 = 38 intercalary months, of omitted tithis in the period The number months. while actually we have, T\ x 95 = 35 intercalary is 30. So the Verfanga Jyotisa rules introduce 3 more are 67 naksatra-months (sidereal months) in There years, and if intercalary months than necessary in 95 moon passes through 67x27 = 1809 the yuga. The adjustment. This these are dropped, we can have good naksatras within this period. could have been done as follows : begins at winter solstice with the sun, The yuga = yugas, suppose In the first period of 30 years 6 and the moon together at the Bham-siha asterism they had 11 intercalary months instead of 12. or j3 Delphini)" (< the The beginning of the yuga would go ahead of the main points from which the five These are 4'685 x 6 -28.110 days. winter solstice in 30 years by yearly calendar can be constructed. OF THE CALENDAR REFORM COMMITTEE 224 KBPOBT on the lower side or intercalary month on the The mistake was .000305 days But if we do not have the back to 1 naksatra in 3279 days or about 9 years. 30th year, the s/wgcr-beginning is brought 29.53-28.110^1.421 days before the W.S. day. The the next period of 30 same process is repeated for The Time of the Vedanga Jyotisha back to years. The ?/wga-beginning is thus brought All recensions of the Veglanga Jyotisa contain the 2.842 days before the W.S. day. following verses : The next period may be taken to consist of 35 in which the yuga- somarkau yada sakarii savasavau years, i.e., 7 yttgas each of five years, Svarakramete hyudak. beginning goes ahead by 3.264 days. The combined Syatfcadadiyugam maghastapah suklo'yanarh (6) years is to sravisthadau suryacandramasavudak result of the three periods of 30, 30, and 35 Prapadyete 0.422 maghasravanayoh sada. (7) put the yuga beginning ahead of the W.S. day by Sarpardhe daksiiiarkastu cycles are described by days only. Other conjectural These two verses taken together yield the following : Dr. Shama Sastry. The winter solstice took place at the lunar practice really followed ? We But was any such asterism &mm\ha, which is later called Dhani$\ha\. S. B. Dlksit have no evidence from the verses ; but system This is the 21st naksatra in the Kfitikadi mentions that intercalary months were inserted only and 23rd in the Asvinyadi system and its component probably they were 'dropped when needed, and hence stars are far stars are a, 0, y and 8 DelphinL* These when not needed. 1 away from the ecliptic. We have for 1950 : Tithis 41' -+33° 2' a Delphini, Long. = 316° Lat. Jyotisa calendar The main object of the Vedaiiga -+31 55 p m „ =315 39 y) been the correct prediction of the appears to have 40 =+32 41 y „ -318 n (civil) day within the tithi and nalcsatra on any savana 57 a „ „ -318 35 „ =+31 yuga. In this respect, the rules were more accurate. month. The A tithi is defined as /^th of the lunar The Arabs have and i Aquarii which also correct measure is represent the Chinese Hsiu. = ^0588 = 984353 daySi ! uthi the It has been stated in the Vedaiiga Jyoii$a that the while the measure taken = .983871 days. The junction star of the asterism was placed at tithi the beginning mistake is .000482 days on the lower side or one beginning of the division and it marked the star in 2075 days or in 5f years. of Uttarayana or the W.S. day. Thus the Dhani§thd division had 270° as the The five yearly period consists of 1830 civil days representing longitude at the time when the tradition of the Vedaiiga in which there are 62 synodical months. Jyotisa calendar was formulated. If a Delphini is taken 62x29.53059 = 1830.8965 days. Hence We know longitude as the principal star of the asterism, then its to make the tithi calculations correct, one day in order in 1950, was 270° at the time of the Vedaiiga Jyotisa and (exactly 0.8965 days) had to be added to the total 41'. solstices take about its longitude is 316° As the civil days in the period. number of the time of 72 years to retrograde through one degree, 41'—270°) x 72- Nakshatras Vedanga Jyotisa is found to be (316° = before 1950 A.D. or 1413 B.C. The days were named according to the naksatras or 46 °7 x72 3362 years however, yields a somewhat lower lunar astensms in which the moon was found, and a The star Delphini, B.C. lot of crude astrology* had grown up round this period, i.e., about 1338

system. So it was necessary to predict the naksatra in advance. The Vedanga Jyotixa calendar prescribed The Plan of the Calendar some methods for such predictions. :— In a five yearly period of 1830 days, the sidereal In a period of 5 years, there are revolutions of the moon amounted to 67 in which 1830 civil days, there are 1809 aak^ntras* 62 lunar months, and so 1860 tithis, 27 166 67 sidereal months and so 1809 nak§atras. Actually 1 naksatm day - 'g = 1 .011913 days, As the period contains 60 solar months, there are while the measure taken = H§§ = 1.011608 days. every 2 intercalary months which are placed after

Astrology based only on the sun and the moon. Later post- both the * On a Dhani?tha day the moon got conjoined with Siddhantic astrology in India is largely (J race o- Chaldean, and makes motion. and a Delphinis at interval of 2 hours. use of the si^ns of the -zodiac, and of planetary position and j3 INDIAN CALENDAR 225

30 lunar months. Thus in the third year, the month period, and when it was added the last month adhika Sravana is adhika which is followed by Buddha Magha contained 30 days instead of 29 days which was

& ; and in the fifth year the last month is also otherwise its due. adhika which is adhika Magha, The ratio 1 for the duration of the longest day to that of the shortest night given in the Vedahga Jyotisa There are 1860 tithis while the number of civil was first noted by Dr. Thibaut. Later the same ratio days is 1830 ; so there are 30 omitted tithis {tithi ksaya). was found by Father Kugler from Babylonian cunei- Each period of 61 days contains 62 tithis, so one tithi form records of the Seleucidean period. The ratio is is omitted after 61 civil days. From this consideration characteristic of a latitude of 35° N, which is nearly the number of civil days per month can be obtained that of Babylon (for Babylon

distinctive names, vi%., (1) , (2) Parivatsara, Table 13.

(3) Idavatsara, (4) Anuvatsara, and (5) Idvatsara. Longest day and shortest night The plan of the five yearly calendar is shown (Calculated with obliquity of ecliptic as 23° 51' vhiqji is below : for 1300 B. C. The results for 500 B. C. are also almost tha same.)

Table 12. Latitude Longest day Shortest night Ratio

Number of days in each month of the Vedanga 30° N 13h 58m 10b 2m 1,39 Jyotisa Calendar 31° N 14 3 9 57 1.41 31° 32' N 14 6 9 54 1.42 Sain vat- Parivat- Idavat- Anuvat- Idvat- 32° N 14 8 9 52 1.43 sara sara sara sara sara 32°40' N 14 12 9 48 1.45 Magha 30 29 29 29 29 33° N 14 14 9 46 1.46 Phalguna 30 30 30 30 30 34° N 14 19 9 41 1.48 Caitra 29 29 29 29 29 35° N 14 24 9 36 1.50 Vaisakha 30 30 30 30 30 It is seen from the above table, that even at the Jyais^ha 29 29 29 29 29 latitude of Babylon, the ratio is not 1.50 but 1.45. At Asadha 30 30 30 30 30 Gandhar, it is 1.42. The difference is not very large. $ravana {adhika) — 29 But there is another factor to which attention must ^ravana 29 29 30 29 29 be drawn. Bhadrapada 30 30 30 30 30 Asvina 29 29 29 29 29 Both Babylonians and Indians measured subdivisions Kartika 30 30 30 30 30 of the day by means of some kind of Clepsydra. A Margasirsa 29 29 29 29 29 description of the Clepsydra used by Indians during Pausa 30 30 30 30 30 the Ved&nga Jyotisa-petiod will be found in S.B. Dlksit*s

Magha {adhika) — 29 or 30 Bharatiya Jyoti&dtstra (Sec. II, Chap. I). But the day- measured from the observed Total No. of 355 354 384 354 383 length must have been observed time of sunset. This is days in the year or 384 time of sunrise to the somewhat larger than the astronomical time of sunrise As already shown, the actual length of 62 lunar on account of refraction. Assuming that the effect of

months is 1830.8965 days, while there are 1830 civil refraction is to elevate a celestial body near the horizon days in the five yearly period. It is therefore very by about 35', and the sun's semi-diameter is about 16', likely that one civil day was added to the period the sun's upper limb appears on the horizon at a place when necessary to make it conform to the phases of on 32° latitude, about 4J minutes before the centre of the moon which were regularly observed. This the sun is due on the horizon. For the same reason, additional day was no doubt placed at the end of the the sunset takes place 4£ minutes after the astronomical 226 KBPOBT OF THE CALENDAR REFORM COMMITTEE

this the time of composition of the calculated sunset. So the apparent length of the day We get from Therefore Mahabharata as about 450 B.C. or sometime earlier. is increased by 2 x min. or by 9 minutes. for the latitude of Babylon we have the length of Varahamihira also notes that the winter solstice h m h m the maximum day-light 14 l2 + 9- = 14 21 , and no longer took place at Bhanis\ha, h m is 1.49. Taking the night is 9 39 . The ratio now PaHca SiddMntika, III, 21 effect of refraction into consideration the ratio for Gandhar also becomes 1.46, which is not much A slesardhadaslt yada nivrttih kilosnakiranasya different from 1.50 as for Babylon. So it is not Yuktamayanaih tadasife sampratamayanam punarvasutalj. necessary to assume that the ratio was obtained from sources. Babylonian Translation : When the return of the sun towards

the south ( i.e., the summer solstice ) took place from Effect of Precession the middle of Aslesa, the ayana was right : at the was prevalent for a long time The Vedaiiga Jyotisa present time ayana begins from Funarvasu. over India, for over 1300 years (1000 B.C. to 300 A.D.). In his Bvhat Safnhita, an astrological treatise, he Hence it is likely that the subsequent astronomers records : noticed the gradual shift of the solstitial colure in the several references are found to lunar zodiac. In fact, Bfhat Safnhita, . Ill, 1 whose name is this effect. Garga, an astronomer Aslesardhatdaksinam uttaramayanam raverdbaniflthadyam he is described as found in the Mahabharata, where Nunam kadacidasit yenoktam purvasastresu. having an astronomical school at a place called Translation : The beginning of the southern motion Gargasrota in the Sarasvatl basin, is the reputed author when the sun has passed half of Aslesa and the begin- of a pre-Siddhantic calendaric treatise called Oarga ning of the northern motion when the sun has passed Sainhita. He notes : the beginning of Bhanis\ha, must have taken place Yada mvartate'praptal.i sravisthamuttarayane at some epoch ; for these are recorded in old treatises. Aslesam daksine'praptab tada vindyanmaHad bhayam. From the time of Vedaiiga Jyotisa to Varahamihira's time of Uttarayana Translation : When at the time the summer solstice moved through more than reaching the 1| the sun is found turning (north) without naksatras of Aslesa + Fusya ) which indicated a lapse turning { i Sravisthas, and (at the time of Bahsinayana) of more than 1500 years from the time of Vedaiiga it should be (south) without reaching the Mlesa, Jyotisa. taken to indicate a period of calamity. It is thus seen that the Hindu astronomers observed It shows that at the time of Garga the W.S. did the shifting of the cardinal points due to precession no longer occur in &ravis\ha, neither the S.S. occurred of the equinoxes ; but as they had not developed the Jyotisa in the Aslesa division. At the time of Vedaiiga sense of era, they were unable to find out the time- the two solstices were marked by the starting point of interval between different records, and obtain a rate &ravistha and the middle point of Mlesa respectively. for precession, as was done by Hipparchos. Their therefore observed that the solstices were reced- Garga observations were also crude, as they used only the ing back over the lunar calendar, and had shifted at lunar zodiac. The shifting of the solstitial colures least by half a na/c$a*ra-division from the middle of remained to them an unsolved mystery. 480 A&lesa. His observations are therefore at least years labst'than those of the Vedaiiga Jyotisa. 5 5 CRITICAL REVIEW OF THE INSCRIPTIONS In the MaMbharata we get the following verse : Asvamedha, Chap. 44,2 RECORDS ABOUT CALENDAR

Ahal.i purvam tatoratrirmasah sukladayali smytali In this chapter, we are undertaking a critical Sravanadini rksani rtavab sisiradayali review of the references to the calendar in ancient night inscriptions, because, from the point of view of Translation : Day comes first and then the ; accurate history, inscriptional records are far more months are known to commence with the bright valuable than any references in ancient scriptures or half, the naksatras with fcrpvana* and the seasons classics, as they are contemporary documents, which with &iiira. have remained unaltered since the framers left them*. Here the asterism &ravana is described as the one Sravana is where the winter solstice takes place. * Sometimes inscriptions and copper plate records have been such instances are just preceding &rav%8\ha and the solstices take about found to have been forged at a latter date but by an experienced archaeologist 960 years to retrograde through one naksaira division. rare and can not escape detection )

INDIAN CALENDAR 227

References in ancient scriptures, poems, epics and 3. The months are not mentioned by name, except other literatures are, on the other hand, very often in one case where the month of Magha is liable to alterations, interpolations and errors in the mentioned. They are purnimditta, i.e., they hands of latter-day copyists and are, therefore, less started after full moon and ended in full moon. trust-worthy. This is not expressly mentioned but can be The oldest inscriptional records bearing a date inferred from the fact that the 14th, the 15th

( barring those belonging to the Ind^is-valley period (PaTicadasi) and the Pratipada, i.e., the first which have tithi arc enjoined to be the not been deciphered ) belong to the reign days on which of certain actions are the Emperor Asoka ( 273-236 B.C. ). From these, forbidden. These must be wc can make fairly accurate deductions regarding the the three days of invisibility of the moon, the calendar then in use. 14th being before new moon, the 15th the new moon, and the first, the day after new We take the Fifth Pillar Edict, Rampurva version moon, which were observed as unsuitable for found at the Champarai) district, . The many particular performances. language is Asokan Prakrt, the script is the oldest

form of Brahmi. ( 4. The day reckoning was by the tithi (lunar Sircar pp, 62-63 ) day), but the word tithi is probably not to be taken

Fifth Pillar Edict—Rampurva Version in the sense of the present Siddhantlc tithi, but in the sense of the Vedanga Jyotisa (1) Sadtmsatilva2mbhisitena(Sadv^ tithi or the old Brahmanic tithi. In the latter ktena)— * After twenty-six years had elapsed system, a tithi was counted from moon-set since coronation'. to moon- set during the bright half, and from (2) Ti&u cdtufnmdlsl^u tisyafn pufnnamdsiyarn tint- moon-rise to moon-rise during the dark-half. divasdni cdvudasafn painnadasafn 2>atipadafn There was the same tithi for the whole day. Tisrsu ( cdtunndsisu tisydydfti pur^amdsydfn, Prof. P. C. Sen Gupta has discussed this trisu divasenu-caturdase pancadase pratipadi method of tithi reckoning ( see p. 222 ). 'On the three cdturmdsl days, on the tisya full 5. Two days are mentioned by the lunar asterisms moon day, on the 14th, 15th and the first Tisya (

Again, in the same : naksatra. This system is found in vogue in the epic Mahabhdrata, e.g., in the following (3) Athami-pakhdye cdvudasdye painnadawye passage : tisd ye pundvasune (Astami-pakse, Balarama, the elder brother of Krsna, after returning catur-dahjdfn, paftcadasydfn, tixydyd/n, from pilgrimage on the eighteenth day of the punarvasau battle ) j states : 'On the eighth paksa, on the 14th, and the M. Bh., Salya Parra, Ch. 34, 6 15th ( new moon ) on the Tisya and CatvariiiiHadalianyadya dve ca me nii.isi'tasya Pimarvasu vai NaJcsatra days , Pusyena saihpraySfco'smi Sravane punaragafcah. (On these days, he forbids the castration of bulls). Translation : It is forty-two days since I left the house. I started on the Pusya From these passages, we (day) and have returned conclude that : on the Sravana.

1. , No era was used, but regnal years ( number of 6. There is no mention of the year-beginning. years elapsed since the king's coronation The Tisya were used for dating. Purnamasu i.e., the full-moon day ending the lunar month of Paw$a is marked 2. The time-reckoning was by seasons, each of out particularly.

8 paksas. The seasons are : It appears from the records that in Asoka's Grlsrna time, (Summer) : Comprising Caitra, Vaisdkha, the principles followed in framing the calendar were Jyai$tha, A$a4ha. those given in the Vedafiga Jyotisa. No era was used. Var$a (Rains) : Comprising Srdvaya, Bhddra, From the inscriptions, we can make no inference about Asvina, Kartika. the luni-solar adjustment, but there is no doubt that Hemanta (Winter) : Comprising , the year was seasonal as given in the inscription of the Pausa, Magha, Phdlguna. Satavahanas (see next page).

a R.—37 COMMITTEE OP THE CALENDAR REFORM 228 REPORT of Gautami- According to our calculations, the date date of the imperial dynasties records bearing a the first century A.D. No Kanvas putra Satakarni would be about Mauryas, the Sungas, and following the later records. next imperial We take some still are known. But the (Sircar, (186B.C.-45 A.D.) Raja Vlrapuru§adattaof Nagarjunlkon4a plenty of dated (2) the Satavahanas have left dynasty, pp. 220-221) same system of date-recording records. In these, the VirapurisadaUw Sava d va pa 6 di 10 and Uthis are llainTto Siri the seasons, the paksas, safnvaisme by regnal years, (Rajnuh &rt Vtrainmt.yt divase from to 8. The were serially numbered 1 Virapuru§adatta on and they On the sixth year of King Sri the even ones bukla ones were KfW paksas, on the tenth day. odd the 6th pah-va of the rarsa season, of Ssvina, second or pak§as. The sixth of var*a pakta is month examples are given below : Some (Sulda paksa). Emperor, light half Inscription of the Satavahana inscriptional evidences, (1) Nasik It is obvious from the above (Sircar, pp. 192-93). not used by Indian Gautamiputra Sri Satakarni that continuous era-recording was vasapakhe 2 dimse 1 of the Satavahanas, and no Data paiika Savachare 10 + 8 dynasts up to the time a^Uase 18 Varsapakse even the Mahabharata mentions (datta pa\tika Sar'nvatsare ancient books, not divtiye 2 divase prathame 1). an era. in the eighteenth it has been difficult to work the inscription was recorded As no era is mentioned, i c including coronation on the first day of the early Indian dynasts year elapsed since the out a chronology in the of the Vam season, i.e., Satavahanas. of the second Pak$a the on the first day after new lunar month of Sravaw> Coming of the Era to India moon (&ukla pak$a). The been inscriptions similarly 3.5, the era reckoning had There are other Satavahana As we have seen in § and the Seleucidean below : since 747 B.C., dated as summarized in the table in use in Babylon to power ot Selcucus era which marked the accession Table 14. was widely current m the at Babylon in 312 B.C., Satavahana Kings, both by the royalty and Table of Inscriptions of whole of the Middle East, date-recording. showing the public. says that as Asoka's Girnar inscription Lliders But though with five Greek he was in diplomatic correspondence Ratio Gotamiputasa Sami-Siriyaiia- 1024 Antiochus I and II of 16_G 1-5 kings of the West, including Satakanisa ^ sent Buddhist 7-G 5-1 and the Ptolemy of Egypt, and Vasithiputaaa Sami-Sm-Pulumavisa Babylon, 1100 Ba5o clear from his 2^-H 3-2 missionaries to these countries, it is 1106 R. V. Siri-Pulumavisa to use the purely Indian <>G continued •-• records that he V. Siri-Pulumayisa . 1122 B. the Vedaiiga-Jyotw* • iy "^ methods of date-recording based on 1123 R. V. Siri-Pulumayisa indication that any of the •• u-vi^-i* is not the slightest 1124 R. V. Siri-Pulumavisa There followed the Mauryas, 22-G 1-7 Indian imperial dynasties which the 24 A ' 6 Sungas and Kanvas (186 B.C.-45 A.D.). 1126 R. G. Satakanisa ^ "^ ti*, the themselves to be Satakanisa ... 7-H ( 100 A.D.) allowed 1146 R. G. Sami Siriyatia Satavahanas ' luni-solar calendar ... 2 H 8 the Graeco-Chaldean 1147 R. y. Sami Siri-Pulumaisa influenced by " 2 ' 1 East. ... 8 H then in vogue in the Near 90 (Sircar )- Siri-Pulumavisa which was G -Gotamiputasa. having B means ratio, V-Vasithiputasa, From about 180 B.C., North-Western India indicates the serial Bactrian Greeks. The number in the first column Taxila as capital passed under the The last the inscription in Lliders list. though we have plenty of number of It is rather strange that form e.g., in contains dates, in an abridged ; ruled in Afghanistan column coins of the Bactrian Greeks who 2-13. Here 19' is the , and 50 B.C., from 1123, we have 19, G and N.W. India between 160 B.C., or summer season, *2' following G and some G denotes Orima which their names have been recovered, half of the second prim i.e., the second worked out, not a single denotes the kind of chronology has been constituting the &ukla pak$a, and the which bears a date, month of Caitra, record has yet been discovered it is not clear 13' denotes the day. But is the coin of a last numeral except two doubtful ones. One the the lunar day, i.e., the tithi or valley, which bears whether the day is certain Plato, found in the Kabul not it be the tithi, it is probably interpreted as 147 solar day. Even if certain symbols which have been Brahmanic or Vedafiga tithi, but the old i.e., 165 B.C., Plato has been the Siddhantic of the Seleucidean era, tithi. INDIAN CALENDAR 229

century A.D. The inscriptions are mostly in Kharo'sthl identified by Tarn to be a brother of Eucratidas, and later ones found on Indian soil are in Brahml. The founder of the second Greek ruling house (175 B.C.- is Kharosthl inscriptions are collected by Dr.Sten Konow 139 B.C.) in Bactria. But the interpretation in his monumental work Cm*pus Inscriptionum doubtful. Indicarum, Vol. II., Part I., and are reproduced below time of The second one is an inscription of the in Groups A and B. king of the Euthydemid king Menander, the great (with the Group A is identical with Konow's A house who ruled over the Punjab, Sind and Rajputana omission of Nos. 20-23) and contains dates from year about 150 B.C., on the Shinkot Steatite Casket, the 58 to 200. Group B, identica with Konow's B-Group, only one of the Greek kings who has found a contains the inscriptions of Kusana period bearing permanent place in Indian literature in the celebrated between 3C0 and 400. meaning dates of years Milinda Pafhho, a philosophical treatise questions of king Menander. The inscription referred Indian month of GROUP A to mentions regnal year 5, the the date- Vaisakha, and the twenty-fifth day. Thus 1. Maira : [sain different from the recording is Indian, but slightly no Damijadasa saka-sa. 2. Sahdaur A : ra\_ja] in Asokan or Satavahana inscriptions system used [$a${«\..6'0]. because the. paksa is omitted. (Reading uncertain.) a mathe- Our studies gi ven in § 3 3, shows that sain .... : [ maharayasa ? ] Ayasa based on 3 . Sahdaur B matically accurate luni-solar calendar,

. .aq[hasathi.... Seleucid 4. Mansehra : astronomical knowledge, was first evolved in V>\9 Prothavatasa masasa divase 5. Fatehjang : sain Babylon between 300 B.C. to 200 B.C. by Chaldean sodase 10. were : astronomers. The features of this calendar athasatatimae Taxila copper-plate : sainratsaraye era for numbering 6. (a) The use of the Seleucidean 78 maharayasa mahaintasa Mogasa Panemasa years in place of the regnal years. masasa divase pafneame 5 etayc purvaye. the lunar month (b) The beginning of the year with 8 I. 7. Mucai : vase ekasitimaye which was to start on a date not later than .of Nisan Reading uncertain. 8. Kala Sang : [sain 10i)\ the vernal eqxinox. a month of 102. 9. Mount Banj : sainvatsaraye corresponds to the Indian month of Vaisakha (This Guduvharasa vasa 10. Takht-i-Bahi : maharayasa later defined in Siddhantic calendars). 26 safnvatsarae tisatimae 103 Vesakhasa alternative method of starting with (c) There was an masasa divase [praiha] »ne [di 1 atra pwria'] month of Dios which was to begin on a the Greek pak ne. equinox. not later than a month of the autumnal date ekadasa [*a»] timaye 111 11. Paja : safnvatsaraye Kartika, (This corresponds to the Indian month of Sravanasa masasa di [m*] se painlcada^se 15. calendars). as later defined in Siddhantic Sravanasa 20. 12. Kaldarra : vasa 113 done by the nineteen- (d) Luni-solar adjustment was 1*~\17. 13. Marguz : [vase (vide 3*2 — 3'4). year cycle § Sravanasa masasa di praclhame 14. Pan j tar : sain 122 of date-recording spread far and wide This system 1 maharayasa Ousanasa rajami. adopted by other ruling in the Near East and was scroll : sa 130 ayasa Asa4asa used an era 15. Taxila silver dynasties, viz., the Parthians, who however . 15 isa divase . maharajasa Macedonian months masasa divase starting from 248 B.C. They used rajatirajasa devaputrasa Khttsanasa aroga\ without alteration. daksinae. that this system penetrated I* can now be shown Je\hamase 16. Pesawar Museum, No. 20 : sain 108 gradually into India. divase pafneadase. to be Era or eras of unknown origin began maharajasa Uvimaka [vthi~\ 17. Khalatse : sain 187 certain inscriptions found in the North- mentioned in sasa. the Kabul valley about the first Western Punjab and ibhrata vase : ka 191 maharaja belonging to 18. Taxila silver century B.C. Some of them mention kings Manigulasa putrasa^Jihonikasa Cvkhsasa (west and southern the Saka tribes who ruled Ariana the k$atrapasa. Afghanistan comprising the regions-Area), Vesakhasa masasa divase (N.W. 19. Dewai : sain 200 Kandahar regions (Arachosia), and Gandhara itra khavasa. and the first athame 8 Punjab) between the second century B.C. 230 REPORT OF THE CALENDAR REFORM COMMITTEE

The Method of Date Recording which is supposed to stand for Azes. But this has been disputed- A record fully dated in Group A gives : This series starts with the year 58, if Cunningham's

The year of the era in figures and words ; though reading of (1) with the additional reading of the king's it does not give any particular designation to the era. name 'Moasa' is accepted. But even if we reject it, its The month, mostly in Sanskrit ; the day, by the series certainly starts with the year 68 in No. 5, ordinal number, e.g., No. 11, which means in the year and goes up to 136 at fairly small intervals, then to 111 on the 15th day of the month of Sravaria. 168, 187, 191, 200 containing names of rulers known The months are all in Sanskrit, except in No. 6, in from coins, viz., besides Maues above mentioned, which the month is in Greek (Panemos = Asatfha). No. Gondophernes (103 = 20 B.C.), some Kusana king (122 6 alone of this group contains the rather mysterious = 1 B.C.), Devaputra Kusana (136 = 14 A.D.), Maharaj- phrase 'Etaye purvaye' which means, 'before these*. bhrata Jehonika (191=69 A.D.). They are held to be This phrase, the meaning of which is not clear, occurs dated in the same era, which is usually called "the Old in Kusana (Group B) and even in Gupta inscriptions. Saka Era, shortly called O.S.E. But up to this time, no unanimity amongst scholars about This method of dating is quite different from that there has been the starting date of the era used in inscriptions of the contemporary Indian dynasts, viz., the Satavahanas, which mentioned regnal years, the season, grouped under A. the paksa, and then probably the old tithi or the lunar We now take the second group of inscriptions day. But it agrees with the method followed in which are those of the Kusanas, who ruled in North contemporary Parthia, which mentions the year India in the second century A-D. usually in the Seleucidean era, rarely in the Arsacid era, the name of the month in Greek, and the ordinal GROUP B number of the day, which ranges from 1 to 30 (see

Debevoise, 1938). From No. 10, it appears that The Ku§ana Inscriptions after Kaniska : whenever Indian months were used they were 24. Kaniska casket : sain 1 ma[ harayasa ] Purnwianta, following the classical Indian custom. Kaniskasa.

25. Sui Vihar : maharajasya rajatiraja&ya devapu- trasya Kaniskasya safnvatsare ekadase sain Date of records of Group A 11 Baisi{rn)kasya masas[ y ]a divase( in)

1 None of the inscriptions of Group A appear to athavise 28 [ aya ] tra divase. be 'Royal Records' but some contain names of kings, 26. Zeda : sain 11 Asa4asa masasa di 20 Utara- phagune isa kswnami murotiasa e.g., No, 6, which mentions a Maharaja Mahainta Moga, Kaniskasa rajami. who is taken to be identical with a king whose coins marjhakasa majh e divase have been found in large numbers in Gandhara. He 27. Manikiala : saM 18 Kartiyasa [ ] Kaneskasa. calls himself 'Maues' in the Greek inscription on the 20 etra purvae maharajasa Arthamisiya sastehi 10 obverse, and Moasa (i.e. of Moa) in Kharosthl on 28. Box lid : sain 18 masye the reverse. The title given there usually is is [ e ] ksunaftimri. Maharajasa Eajatirajasa Mahafntasa. It is held that 29. Kurram : sain 20 masasa Avadunakasa di 20 King Moga was Saka leader who starting from a base is [ e ] ksunainmi.

; maharajasa [Vajus] in Seistan or Arachosia, invaded Gandhara through the 30. Pesawar Museum, No. 21 southern route, sailed up the Indus, and ousted the kasa sain [24 Jethasa*!] masasadi ise Greek rulers Archebius from Taxila, Artemidorus ksunaMmi. from Puskalavati and Telephos from Kapsa (Bachhofer, 31. Hidda : sainvatsarae athaviinsatihi 28 masye 1936) and founded a large empire comprising parts of Apelae sasiehi dasahi 10 is [ e ] ksunainmi,

Afghanistan, Gandhara and the Punjab. 32. Sakardarra : sain 40 P [ r ~\o\havada$a masasa divas[ami~\ visami di 20 atra divasakale. He is generally held to have been a Saka, but some

: maharajasa rajatirajasa devaputrasa kaisa- hold without sufficient reason that he was a Tarthian. 33. Sra rasa Vajheskaputrasa Kaniskasa sainvatsarae He is the first of Indo-Scythian kings known to ekacapar[ i )sa[ i ] sain 4 1 Jethasa masasa di numismatics. He was followed by other Indo-Scythian 25 is [e] divasaksuiiami. kings in Gandhara; who are known from wide variety

34. Wardak : sain 51 masy[ e ] Arthamisiya of coins issued, viz., Azes I, Azilises and Azes II. sastehi 15 imena ga

athanii This is a deviation from Satavahana method of 35. Ui)4 : sain 61 Cetrasa mahasa divase closely the Graeco-Chal- di S iia k§unami Purvaxa4e. date-recording and follows dean method. Some inscriptions mention Greek 36. Mamane Dheri : sain S9 Margasirasra masi 5 ise months ( e. g. Gorpiaios which is Asvina or Bhadra Jc§unami. in Sircar's No. 49, p. 146 ) others Indian lunar months An incomplete date, makasa di 25, is further is small ( e. g. Srarana in No. 51 ), but their number found in the Kaniza Dheri inscription. compared with the seasonal mode of recording months. The second group Nos. 34-36 contains Kharosthi These inscriptions give no indication as to whether inscriptions of the Kusana kings after the first Kaniska. the month is Purijimanta or Amanita. The Indian These and Kusana Brahmi inscriptions mention : months are Puruiviattta. Years from '1 to 9a the kings Kaniska I from But the Zeda inscription of year 11 ( No. 26 of lto24, Group B) mentions that the imhsatra was TJUaraphalgurd II of the Vajheska from 24-28, Kaniska in on the 20th of Asdiiha, and ( 35 ) mentions that year 41> the year 61, the mikmtra on the 8th day of Caitra was from 33-60, Huviska Pnrvasadha. A comparison with tables of naksatra* from 62-98 Vasudeva shows that the months ended in full moon {Purr^imdnid). and the titles are given in full, The King's name As purnimanta months were unknown outside India, genitive. The era is generally ascribed and in the the Kusanas must have yielded to Indian influence as we have a record of his first to the famous Kaniska and adapted their original time-reckonings to the year. Indian custom; at least in their use of Indian months. date-recording is the same as in Their method of Historians and chronologists now almost unani- viz., see No. 25 ) the year of the era, the Group A, ( mously hold that all these inscriptions of Group B are Greek or Sanskrit, the ordinal number month name in dated in the same era which is sometimes called the then the phrase equivalent to asyai'n of the day* Kusana era, which was founded by King Kaniska. inscriptions, purvayaM ( before these ), but in these This is said to be proved by the fact that the inscrip- expressed in the form ise kxunawi or its variant, it is tions range from year 1, and we have phrases as in interpreted by Konow as equivalent which has been No. 25 of the Maharaja Bdjddhirdja Devaputra etasijafn pUrvatjain in the Khotani Saka of asyafn or Kani$Jca, in the year 11. But a little more scrutiny Konow thinks was the mother tongue language which shows that it is only a conventional phraseology, used Kaniska group and which they use in of kings of the in almost all Kusana inscriptions, for even in as late their inscriptions. In fact kings of this group use 'of a^s an inscription of year 98 of this group, we read

words, and from their wide ' a number of Khotani Saka the Maharaja Vasudeva in the year 98\ It is therefore put in a medley range of coins are known to have by no means clear that such phrases can be interpreted including Buddha of Greek, Iranian, and Indian gods to *nean that Kaniska started an entirely new era. coins, the names of the gods are not in on their but In fact, from Kaniska s profuse use of Greek months or Greek form but invari- their original Indian, Iranian and Greek gods, in his inscriptions and coins, language. ably in the form used in the Khotani Saka Cunningham was led to the belief that Kaniska dated The method of date-recording followed by the his inscriptions in the Seleucidean era, with hundreds Kusanas, in spite of its identity with that of Group A omitted, so that year 1 of Kaniska, is the year 401 shows some interesting variations. In the Kharosthi of S. E. and year 90 of the Christian era. of the Kusanas, the months are mostly that the inscriptions But it has been known for some time Vaisdkha, etc. ). Greek, less so in Sanskrit ( Caitra, Kusana empire did not stop with that Vasudeva who to 30 and clearly they are not The days run from 1 comes after Huviska. Dr. L. Bachhofer (1936) has solar days. When we turn to Brahmi inscrip- tithis but proved from numismatics the existence of : find that the month names are mostly tions, we Kaniska III, reigning apparently after Vasudeva I, Var$d, or Hemanta as in the Satava- seasonal : Oiima, Vasudeva II, reigning after Kaniska III. hana records. But since 4 is the maximum number The kings appear to -have retained full control of attached to these, and the day numbers run from the whole of modern Afghanistan including Bactria 1 to 30, the number after the season denotes a month, which appears to have been the home land of the not a pak$a and the days are solar. Thus G 4 denotes Kusanas and some parts of the Punjab, right up to the fourth month of the Gri$ma season, viz, A$a

is not mentioned. it is clearly impossible that era. Herzfeld had established that Vasudeva II, Now the person would occupy such an important who appears to have come after Kanaka III .about same the year 15 to 86, a period of 71 years. 210 A.D., was deprived of Bactria by Ardeshir I, the position from L. de Leeuw therefore suggests that while 86 is the founder of the Sasanid dynasty of 'Persia. The year (reckoning from year 1 of Kaniska), Sjsanids converted Bactria into a royalvprovince under usual Ku$ana '15' is really with hundred omitted and represents the charge of the crown prince, who struck coins actually the year 115 of Kaniska, i.e., dates of the two. closely imitating those of the Kus5nas. Vasudeva II of inscriptions differ by 115-86 = 29 years, which is much is also mentioned in the Armenian records of Moise plausible. In other words, after the year 100 of Khorene, a Jewish scholar, under the name Vehsadjan, more the Kanaka era was passed, hundreds were dropped as an Indian king who tried to form a league with in inscriptions found near about Mathura. and other older powers against the rising imperialism of Ardeshir. Vasudeva II is also thought The author has sustained her ground by numerous doubt to have sent an embassy to China about 230 A.D *. other illustrations, and there seems to be no that this is a brilliant suggestion and it can be taken The second Sassanian king Shapur I, claims to have l as proved that in numbering years of an era, hundreds conquered sometime after 240 A.D. PSKVR% which has were omitted in certain parts of the Kusana dominion been identified with Puru§apura or Peshawar, the in the second century of the Kaniska era. L. de capital of the KusSnas. This has also been confirmed Leeuw has found such dates in no less than 7 instances by the French excavations at Begram (Kapi£i) in bearing years 5, 12, 15, 22, 35, 50, 57 in which Afghanistan, which was destroyed by Shapur between apparently 103 has been omitted, so that 57 really 242 and 250 A.D. But this probably was not a stands for 157, and if we take the Kaniska era to have permanent occupation but a raid, as a Ku§ana king started from 78 A.D., the date of the last one is A.D. or Shah is mentioned in 'the Paikuli inscription of the 235 = (157 + 78). Probably the name of the reigning Sasanid king Narseh (293-302 A.D.). king was not mentioned, as he had either lost

Kushana Method of Date-recording In India : control over these regions, or as the inscriptions were

religious, it was not considered necessary. The second It appears rather strange that the Kusana way of alternative appears to be more correct. date-recording should suddenly come to a dead stop

I, and no on Indian soil with the year 98 of Vasudeva This is supported by the inscription on an image records containing a year number exceeding 100 should discovered by Dayaram Sahni in Mathura in 1927. be found on Indian soil. It mentions Maharaja Devaputra Kaniska. But on The mystery appears now to have been successfully palaeographic grounds, he can neither he Kaniska I solved by Mrs. Van Lohuizen de Leeuw in her book (1-24) nor Kani§ka II (41), but a later Kaniska, coming The Scythian Period (pub. 1949). She has proved that after Vasudeva I, and 14 is really year 114 of the several Biahml inscriptions in the Mathura region bear Kaniska era. We may identify him with Kaniska dates from years 5 to 57 in which, following an old III of Bachhofer. practice, the figure for hundred has been Indian So we come to this conclusion : k T omitted. Thus 5 stands for 105, '14' stands for 114 The records of Ku?ai)a kings, after Kaniska I of the Kusana era. The following example will suffice range from year 1 to 98. In the second century of (vide pp. 242-43 of the Scythian Period). the Kaniska era, hundreds are omitted and such

Cue and the same person Arya Vasula, female records have been found up to year 157, i.e., year 235 pupil of Arya Sangamika, holding the important of the Christian era. position of a religious preacher in the Jaina community, This raises a strong presumption that Kaniska is mentioned in two Brahmi inscriptions (No. 24 and was not the founder of the era, but he used one 70 of Lliders) bearing the year designations of 15 No. already in vogue, but omitted the hundreds. Thus and 86 respectively, the date-recording being in the year 1 of Kaniska is really year 1 plus some hundred, typical Kusana style. The palaeographical evidence may be 1, 2, or 3. L. de Leeuw does not expressly also shows that the inscriptions were recorded in the suggest this, though it is apparent from her reasoning Kusana age, though the name of the reigning monarch that year I of King Kaniska is year 201 of the Old &aka

* Ghirshman thought that the Viisudev* Kusana of these era*. If this suggestion be correct, since the old Saka is equated references is Vasudeva I, whose last reference year 98. He era is taken to have started in 123 B.C. (—122 A.D.) 242-250 and arrived at the year 98 of Kanaka's era to year A.D., instead of in 129 B.C.,-as postulated by L. de Leeuw, date 144 to 152 A.D. for the initial year of the Kanaka era. But the Kaniska started reigning in ( 201-123 )«78 A.D. equation of this Vasudeva with Vasudeva I is certainly wrong. This * must be Vasudeva II, or may be a still later Vasudeva. The suggestion is of Prof. M. N. Saha. .

INDIAN CALENDAE 233

used and The senior author has shown that Nahap3na above review of inscriptional records From the so that been the old Saka era with one hundred omitted, history, the following story has contemporary the old the year 46 of Nahapana was the year 146 of Teconstructed. about 24 A.D. first started in 123 B.C. Saka era or (1) The Saka era was Asia due to the kings Gautamlputra Satakarni and when the Sakas coming from Central The Satavahana from the Parthian Vasisthlputra Pulumavi, whose records are pressure of HOnas wrested Bactria his son The leader was the typical Indian fashion, reigned emperors after a seven years' war. found dated in the era was also hypothesis from about 40 A.D. to 80 probably one 'Azes', and therefore according to his least This Azes is not to epigraphical record, Nahapana is at alternately called the 'Azes' era. A.D. From Azes who succeeded by about 100 years from the next group of be confounded with the two later separated B. C. Sakas of U]jain belonging to Maues and reigned between 45 B. C. to 20 Saka rulers, the months and Graeco- of Castana, Earlier Sakas used Macedonian the house prevalent of date recording, Chaidean method The Saka of Ujjain. Indian whole of Near East. In throughout the another Saka ruling were equated to We come across the records of- dominions, Indian months which in Ujjain. As their coins show, the family, reigning Greek months were used. of (Cutch) stone inscriptions of the time culture. [Andau class had adopted Greek xuling / Sircar, p. 167]. i.e., Castana and Rudradaman, spread from 'Sakasthan , (2) When the Sakas India, Jdmotika-putrasya rajfiah Jludra- Afghanistan into contiguous parts of Rajnah Castanasya modern 52 culture. During Jaymldma-putrasya [ca] var$e diipaftcase they began to be influenced by Indian damnah dvillya vare Greek in their Phalguna-bahulasya { = krsna-pak$asya) stage, they exclusively used the first bhaginyah to use Kharosthi and {^divase) 2 tnadanena Sifnhila-putrena coins, but later they began aupasati sagotraya h Maues (80 B.C.-45 B.C.), thaviraya h Sifn hila-duhitu h Brahml as well. The coins of Jyes •• II show increasing influence yastih utthdpita- Azes I, Azilises, Azes southern Sakas who penetrated Castana, son of Jamotika of Indian culture. The Translation: Of king show Indian influence to Jayadaman, in the year into Saurashtra and Malwa and of king Rudradaman son of Phalguna and on a greater degree. 52, on the dark half of the month of centuries, they (Maues group, *' (3) In the first three the 2nd day era Kusanas) used the old Saka the second Nahapana group and This inscription mentions the year 52, of date- hundreds, and using a method of Phalguna. -omitting day of the Kfsna paksa of the month an exact copy of the contem- recording which was mentioned is that There is no doubt that the year Graeco-Chaldean system prevalent throughout porary as now known. For this satrapal house (Macedonian months, and of the &aka era the Parthian empire left a continuosly for nearly 300 years and has But they also began to use reigned ordinal number of days). name of the era is wealth of dated records. But the they did it, the month Indian months. Whenever records. They are Hindu not mentioned in the earlier Purnimania, as was the custom with old was merely as years so and so. mentioned ^ dynasts (Mauryas and Satavahanas). the use of Saka 78 A.D. earliest authentic instance of The classical Saka era starting from The (4) inscription of from 123 B.C. name is supplied by the Badami nothing but the old Saka era, starting era by is of the Calukya is Vallabhesvara (Pulakesin I omitted, SO/ that the year 1 of Kaniska Calikya with 200 {&aka-Varsesu dated 465 of the Saka era 201 of the Old Saka era. dynasty), year Epigraphia Indica Catus-s-atesu paftca-sasthi-yutesu : literature the use of the era by name &aka Era in the South- West. XXVII, p. 8J. In SimhasOri, a earlier. The Lokavibhaga of belonging to the Maues appears still Besides the earlier Sakas stated in a Digambara Jaina work in Sanskrit is there was another groupof Saka group, and the Kusanas, 80 beyond 300 manuscript to have been completed in who penetrated into the south-western part of kings, the Saka years (Ep. ImU XXVII, p. 5). group was (i.e. 380) of The earliest representative of this India! that the era used in the records of Their There is no doubt and his son-in-law Usavadata. Nahapana house beginning with Castana an unknown era. the western satrapal records are dated in years 41 to 46 of Rudradaman have come down to the present times Indian lunar months and days (probably tithis). and They use 'Era' par excellence the Saka Era, which is the ruled in Rajputana, Malwa, and northern as These Sakas purposes of calculation. warfare used by Indian astronomers for Maharastra and were engaged in continuous more 'Eras' which have been in use Gautamlputra Satakarni There ere 30 or with the Satavahana ruler been 5*8), but none of them have branch. in India {vide § who claim to have destroyed them root and CALENDAR REFORM COMMITTEE 234 REPORT OF THE

by the Indian used for calendarical calculation 5.6 SOLAR CALENDAR IN THE SIDDHANTA astronomers. / the origin of the Saka JYOTISHA PERIOD Yet it is difficult to assign satraps. An era can be founded era to the western Rise of Siddhantas or Scientific Astronomy Seleucids, the only by an imperial dynasty like the satraps never The Vedahga Jyotisa calendarical rules appear, Parthians or the Guptas. The western imperial position. from inscriptional records, to have been used right up claim, in their numerous records, any subordinate titles the end of the reign of the SatavShanas (200 A.D.). They are always satisfied with the to (Great Satrap) The analysis of inscriptional data on methods of date- like Ksatmpa {Satrap) or Maha Ksatrapa by their recording given in § 5*5 shows that it was the Saka while the imperial position is claimed KusSna rulers (50 B.C. - 100 A.D.). who introduced northern contemporaries, the Kusanas. and Ksatrapas the Graeco-Chaidean methods of date-recording,, The conclusion is that the western so that year prevalent in the Near East into India. These methods used the old Saka era, with 200 omitted ; of astronomy, of the old Saka require a knowledge of the fundamentals 1 of the present Saka era is year 201 which must have been available to the Saka and era, i.e., (201—122) = 79 A.D. Kusana rulers. In India, as the inscriptional records The gradual adoption of characteristic Indian dynasts probably accepted the of Satrap show, some purely Indian ideas by the Sakas is shown in a record system in full from about 248 A.D. (date of foundation Rudrasimha dated 103 S.E. or 181 A.D. of the Kalachuri era, the earliest era founded by Indian [Gunda Stone Inscription of the time of kings, leaving aside the Saka era which is admittedly'of I, Sircar, p. 176] Rudrasimha foreign origin and the Vikrama era whose origin is still svdwi-Castana- Siddham. Rajnah mahdksatrapasya shrouded in mystery). During the time of the Guptas prapautrastja rajnah kmtravasya svaml Jayaddmavaittrasya who founded an era commemorating their accession to srdmi-Rudraddma'Putrasya rajnah mahdksatrapasya power in 319 A.D. the integration of the western rajnah ksatrapasya svdmi-Rudrasifnhasya varse tryutta- system with the Indian appears to have been complete. Vaisdkha snddhe (tame) ( = adhika) 103 ra&ata Indian astronomical treatises, explaining the rules Rohint naksatra- ( = suklapakse) paftcama-dhanya tithatt of calendaric astronomy, are known as Siddhantas, but muhurte abhirena senapati Bappakasya put rem senapati it is difficult to find out their dates. The earliest Rudrabhutind grame rasapadrake vapi ( = kvpah) Indian astronomer who gave a date for himself was the bandhitd [stladibhih] ca sarva sattvanafn hita- khanita, celebrated Aryabhata who flourished in the ancient mkharthaw iti. city of Pataliputra and was born in 476 A.D. of Svaml Translation : Of king Mahaksatrapa It is necessary to reply to a question which has in the year 103 in the light half of the Rudrasimha very often been asked, but never satisfactorily month of Vaisakha on the 5th tithi and in the Rohirji answered, vi,\., naksatra muhurta, Why did the Indian savants who were in touch with The Saka satrap Rudrasimha, reigning in 181 A.D. the Greeks, and probably with Greek science since the time thus dates his inscriptions using an era (the Saka era), of Alexander's raid (323 B.C.\ take about 500-600 years purely Indian months, tithis and naksatras. This is to assimilate Greek astronomy, and use it for their own in full Siddhantic style, because the characteristic calendar- framing ? features of Siddhantic method of date recording which The Indians of 300 B.C. to 400 A.D., were quite mention ////// and naksatra are first found in this vigorous in body as well as in intellect as is shown by inscription. The 'week day' is however not mentioned. their capacity to resist successive hordes of foreign This is first mentioned in an inscription of the invaders, and their remarkable contributions to emperor Budhagupta (484 A. D.). religion, art, literature and certain sciences. Why did Sate pauaiyixtyadhike varsauam bhupatau ca they ,not accept the fundamentals of Greek astronomy ' Budhagupie Asddha rndsa [sukla~] —[f/m] dasyain calculations earlier ? miagurordhase for calendarical

(Iran- Stone Pillar Inscription of Bndha Gupta— The reply to this query appears to be as follows : Gupta year 165-484 A.D.). The Greeks of Alexander's time had almost nothing in calendaric astronomy, for Translation ; In the year 165 of the Gupta era to give to the Indians during the reign of emperor Budhagupta in the month their own knowledge of astronomy at this period was of Asadha and on the 12th tithi of the light half which extremely crude and far inferior to that of the was a Thursday (i.e. day dedicated to the preceptor contemporary Chaldeans. The remarkable achieve- of Gods). ments of the Greeks in astronomy, and geometry,. INDIAN GALEUMfl 235 though they started from the time of Alexander seyyathidam "canda-ggaho bhavissati, bhavissati, nakkhatta-ggaho bhavissati. (Plato's Academy), really flowered in full bloom in the suriyaggaho pathagamanarh bhavissati, century following Alexander (330 B.C. -200 B.C.). Candima suriyanarh candima suriyanarh uppathagamanarh, bhavissati, The culmination is found in. Hipparchos of Rhodes wrote treatises nakkhattanam pathagamanam bhavissati, who flourished from 160—120 B.C. ; he nakkhattanam uppathagamanarh bhavissati. on astronomy. Simultaneously in Seleucid Babylon, Ukkapato bhavissati. Disa-daho bhavissati. Chaldean and Greek astronomers made scientific Bhiimicalo bhavissati. Devadundubhi bhavissati. contributions of the highest order to astronomy ( vide Candima suriya nakkhattanam uggamanam have survived, but § 4.7 & 4.8 ), but none of their works ogamajaam samkilesarh vodanam bhavissati."* are now being found by archaeological explorations.

It is therefore obvious that the Indians of the age (Digha Nikaya, Vol. 1, p. 68, Pali Text Book Society) of Asoka (273 B.C.—200 B.C.), who were in touch with kingdoms of Babylon and Egypt, had not the Greek Translation : Some brahmanas and §ramatyas earn much to learn from the Greeks in astronomy. their livelihood by taking to beastly professions and

the Suhgas to out of fear they say : The Mauryas were succeeded by eating food brought them ; (186 B.C.—75 B.C.), but Indians during this age were in "there will be a solar eclipse, a lunar eclipse, occulta- touch only with the Bactrian Greeks. But by this time, tion of the stars, the sun and the moon will move in the Parthian empire had arisen (250 B.C.), producing the correct direction, in the incorrect direction, the a wedge between western and eastern Greeks. The naksatras will move in the correct path, in the only dated record of the Indo-Bactrian king, incorrect path, there will be precipitation of Menander (150 B.C.), is purely Indian in style. meteors, burning of the cardinal directions (?), earth- quakes, roar of heavenly war drums, the sun, the By about 150 B.C., direct contact between India and the stars will rise and set wrongly producing and Greater Greece which included Babylon had almost moon, distress amongst all beings, etc." ceased, due to the growth of the Parthian empire. wide Whatever ideas came, was through the Saka-Kusana This attitude to astrology and astrolatry on the kingdoms which came into existence after 90 B. C. By part of Indian leaders of thought during the period of that time, astronomy was regarded as only secondary 500 B.C. to 100 A.D., was undoubtedly a correct one, to planetary and horoscopic astrology, which had and would be welcomed by rationalists of all ages and grown to mighty proportions in the West. This may countries. But such ideas had apparently a very have been probably one of the main reasons for late deterrent effect on the study of astronomy in India. acceptance of Graeco-Chaldean astronomy in India, Pursuit of astronomical knowledge was confused with for Indian thought during these years ivas definitely astrology, and its cultivation was definitely forbidden hostile to astrology. in the thousands of monasteries which sprang all over within few hundred years of the Nirv5na It will surprise many of our readers to be told the country B.C). Yet monasteries were exactly the that astrology was not liked by Indian leaders of (544 B.C./ 483 astronomical studies could be quietly thought, which dominated Indian life during the period places where monks were, on account of their leisure 500 B.C.- 1 A. D. Nevertheless, it is a very correct pursued and eminently fitted for taking up such view. and temparament, studies, as had happened later in Europe, where some The Great Buddha, Whose thoughts and ideas of the most eminent astronomers came from the dominated India from 500 B.C. to the early centuries monkist ranks, e.g., Copernicus and Fabricius. of the Christian era, was a determined foe of astro- leaders, opposed to Buddhism, logy. In Buddha's time, and for hundreds of years Neither did Hindu and astrolatry. The after Buddha, there was in India no elaborate planetary encourage astrology practical that the practice of astrology or horoscopic astrology, but a crude kind of astrology politician thought was based on conjunctions of the moon with stars and not conducive to the exercise of personal initiative on various kinds of omina such as appearance and condemned it in no uncertain terms. In the a treatise on statecraft, of comets, eclipses, etc. But Buddha appears to Arthasa&tra of Kautilya, which have held even such astrological forecasts in great took shape between 300 B.C. and 100 A.D., and is contempt, as is evident from the following passage ascribed to Canakya, the following passage is

: ascribed to him : found

Yatha va pan'eke bhonto, Samana-brahmana

saddha-deyyani bhoianani bhurijitva te evarupaya * Acknowledgement is due to Prof. Mm. Bidhusekhar Sastri,. tiracchana-vijjaya micchajivena-jibdkam kappenti- who supplied these passages.

C. B.—38 236 REPORT OF THE CALENDAR REFORM COMMITTEE

in many Kautiliya Artha& to the Sungod. Professional astrologers, parts of India, admit to being descendants of these Nakflatram atiprcchantam balam artho'tivartate &ahadvipi Brahmanas and probably many of the Arfcho hyarthasya nakaatram kirii karisyanti tarakab. eminent astronomers like Aryabhata and Varahamihira eludes the who made great scientfic contributions to astronomy Translation : The objective (artha) belonged to this race. The planetary Sungod is always foolish man {balam) who enquires too much from the shown with high boots on, as in the case of Central stars. The objective should be the naksatra of the Asian kings (e.g., Kaniska). objective, of what avail are the stars ? the historian to trace how the steps This may be taken to represent the views of the It is a task for in which the importation of western astronomical practical politician about astrology and astrolatry, knowledge took place for the Siddhantas, which during the period 500 B.C. to 100 B.C. incorporate this knowledge and are all a few centuries Canakya was the great minister of Candragupta, later, and many of them bear no date. and history says that these two great leaders rolled y good point d appui for discussion is Varahamihira's back the hordes of the Macedonians, who had con- A

Pa%ca Siddhantikd ; for Varahamihira's date is known. quered the Acheminid Empire of Iran comprising He died in 587 A.D., in ripe old age so he must have the whole of the Near East to the borders of Iran, written his book about 550 A.D. This is a compendium and thereafter laid the foundation of the greatest reviewing the knowledge contained in the five empire India has ever seen. They clearly not only did Siddhantas which were current at his time. These not believe in astrology, but openly, and uithout reserve, were regarded as 'Apauruseyd or "knowledge revealed ridiculed its pretensions. by gods or mythical persons". But the influence of original Buddhism waned after Mahayanist Buddhism, which received the rise of The five Siddhantas are : encouragement during the reign of Kaniska great Paitarnaha ••Ascribed to Grandfather Brahma. A,D.) and other Kusana and Saka <78 A.D. to 102 Vasistha •••Ascribed to the mythical sage Buddhist iconography, coins, and kings. Then came Vasistha, a Vedic patriarch, and methods of western date-recording knowledge of the revealed by him to one Mandavya. and Kusanas used. They blended which the Sakas Romaka •••Revealed by god Visnu to Rsi Romasa indigenous Indian system slowly. with the or Romaka. astronomical The focus of diffusion of western Paulisa •••Ascribed sometimes to the sage UjjayinI, knowledge appears to have been the city of Pulastya, one of the seven seers or capital of the western Satraps who were apparently patriarchs forming the Great Bear era and the first to use a continuous era ( the Saka ), constellation of stars (but see later). purely a method of date-recording which was at first Surya -Revealed by the Sungod to A sura Seleucid Babylon, Graeco-Chaldean as prevalent in Maya, architect of gods, who the tithi and the but gradually Indian elements like propounds them to the Rsis. first time naksatra were blended, as we find for the 181 The five Siddhantas are given in the increasing in the inscription of Satrap Rudrasimha, dated order of their accuracy according to Varahamihira. A.D. (vide§5-5). t Thus Varahamihira considers the Surya Siddhanta as This city of Ujjayini was later adopted as the the most accurate, and next in order are the Paulisa, Indian Greenwich, for the measurement of longitudes and the Romaka. The Vasistha and Paitarnaha arc, of places. The borrowal of astronomical knowledge was according to Varahamihira, not accurate. therefore from Greece direct, but as now becomes not *' were those Siddhantas regarded as Apauru- increasingly clearer, from the West, which included Why (i.e. not due to any mortal man) ? Dlksit says Seleucid Babylon, and probably through Arsacid seya" {Bharatiya Jyotisdstra, Part II r Chap. 1) : Persia. The language of culture in these regions was Greek, and we therefore find Greek words like "The knowledge of astronomy as seen developed kendra (centre), lipiikd (lepton), hora (hour) in use by during the Vedic and Vedanga Jyotisa periods and Indian astronomers. described in Part I, was wide as compared with the

length of the period ; but it is very meagre, when com- This view is supported by the Indian myth that present position***. The oldest of astrolatry and astrology were brought to India by a pared with the knowledge (given in the oldest Siddhantas) party of Sakadvipi Brahmanas (Scythian Brahmins), astronomical the of astronomical who were invited to come to India for curing Samba, reveal a sudden rise in standard Those who raised the standard as given the son of Krsna, of leprosy by means of incantations knowledge. —

INDIAN CALENDAR 237

into the contents of in these works, were naturally regarded as superhuman We need not go any further indicates, the knowledge and hence the available ancient works on astronomy this Siddhanta. As the name the West, which was vaguely are regarded as 'apawuseyd (i.e. not compiled by was borrowed from 'Romaka* after the first century A.D. The mortal men) and it is clear that the belief has been known as un-Indian, but appears to be a formed later". yttga taken is quite blending of the nineteen-year cycle of Babylon, the This statement, made by Dlksit nearly sixty years five-yearly yuga of Veddiiga Jyoti§a, and the number 30 ago, really singles out only one phase of the issue, viz., which is the number of tithis in a month. The length the wide gulf in the level of astronomical knowledge of of the year is identical with Hipparchos's (365.2467), the Siddhantas and that in the Veddnga Jyotisa ; and this alone of the Siddhantas gives a length of the but leaves the question of actual authorship open. In year which is unmistakeably tropical. our opinion the Siddhantas were regarded as Apauruseya because they appear to have been com- The Romaka Siddhanta appears to represent a western astro- pilations by different schools of the knowledge of distinct school who tried to propagate Hipparchos. calendaric astronomy, as they diffused from the West nomical knowledge on the lines of One during the period 100 B.C.—400 A.D. But let us look of the later propounders was Srisena, who flourished

Brahmagupta ; the latter into them a little more closely. between Aryabhata and ridicules him roundly for having made a "kantha", i.e. five The Paitamaha Siddhanta : described in a wrapper made out of discarded rags of all types stanzas in Chap. XII. of the Paftea Siddhantika* meaning probably Srlsena's attempt to blend two already discussed it is a revised edition of the As incongruous systems of knowledge, western and Veddiiga Jyotisa ,but later authors say that it contained eastern. rules for the calculation of motions of the sun, the also the planets which were not given by moon and The Paulisa Siddhanta : the Veddiiga Jyoli$a. As the full text of the original This Siddhanta was at one time regarded as the Siddhanta has not been recovered, it is difficult to say rival of the Surya Siddhanta, but no text is available how the borrowal took place. now. But it continued to be current up to the time The Vasistha Siddhanta : as known to Varahamihira of Bhattotpala (966 A.D.), who quotes from it. is described in 13 couplets in Chap. II of the Pa%ca Alberuni (1030-44 A.D.) who was acquainted with Siddhantika. It describes methods of calculating tithi it, said that it was an adaptation from an astronomical and nak?aira, which are inaccurate. Besides it mentions treatise of Paulus of Sainthra, i.c, of Alexandria. But liasi (zodiacal signs), angular measurements, discusses it is not clear whether he had actually seen Paulus's length of the day, and the lagna (ascendant part of the treatise, and compared it with the Paulisa Siddhanta zodiac). Apparently this represents one attempt by a or simply made a guess on the analogy of names merely. school to propagate western astronomical knowledge. The name of one Paulus is found in the Alexandrian The school persisted and we have Vddsiha Siddhantas list of savants (378 A.D.) but his only known work is later than Varahamihira. One of the most famous was one on astrology, and it has nothing in common with Visnucandra (who was somewhat later than Aryabhata) Paulisa Siddhanta, which appears to have been purely who was conscious of the phenomenon of precession an astronomical treatise as we can reconstruct it from of the equinoxes. No text of the Siddhanta is the PaTtca Siddhantika (vide infra). The ascription to available, except some quotations. Paulus of Alexandria is not therefore proved. There Varahamihira pays a formal courtesy to Paitamaha is, however, reference in the Pau'isa Siddhanta to and VasiMa; this does not prevent him from Alexandria, or Yavanapura, as it was known to Hindu describing these two as 'duravibhrasiau\ i.e., furthest savants. The longitudes of Ujjaini and Banaras are from truth. given with reference to Alexandria (P. S., Chap. III).

The Romaka Siddhanta : The Pa%ca Siddhantika devotes a few stanzas of to this exposition of the The Bomaka Siddhanta as reviewed by Varahamihira Chaps. I, III, VI, VII, and VIII Paulisa Siddhanta. Nobody seems to have gone critically uses : x x years into the contends of these chapters after Dr. Thibaut A Yuga of 2850 years -19 5 30 ; who tried to explain these in his introduction to the 150 years = 54787 days ; left of them unexplained 1 year =365.2467 days. Paftca Siddhantika, but most owing to their obscurity. The number of intercalary months in the yuga is I, (verses 24—25), 30 Lords of the days of given as 1050, i.e., there are 7 intercalary months in In Chap. mentioned. This is quite un-Indian 19 years. the month are REFORM COMMITTEE 238 REPORT OF THE CALENDAR Chap. XII—Cosmogony, Geography, Dimension and reminds one of the Iranian calendar in which each of the Creation. one of thirty days of the month is named after a god of the „ XIII—Armillary Sphere, and other or principle (see § 2.3). The names of the lords Instruments. days as given in the Paulisa Siddhanta are of course XIV—Different modes of reckoning Time. all Indian.

A scrutiny of the text shows that it is, with the completely astro- The Surya Siddhanta exception of a few elements, almost 9-12 nomical. A few verses in Chap. Ill, viz., Nos. Of all the Siddhantas mentioned by Varahamihira deal with the trepidation theory of the precession of alone has survived and is still regarded with this equinoxes. These are regarded by all critics of the by Indian astrologers. This Siddhanta was veneration Surya Siddhanta to be interpolations made after the with annotations by Rev. E. Burgess, in 1860, published 12th century. and has been republished by the Calcutta University It will take us too much away from bur main theme editorship of P. L. Gangooly, with an intro- under the but every to give a critical account of this treatise, duction by Prof. P. C. Sengupta. critic has admitted that the text does not show any the This is supposed to have been described by influence of Ptolemy's Almagest. Prof. P. C. Sen- Sungod to Asura Maya, the architect of the gods, who This gupta's introduction is particularly valuable. revealed it to the Indian Rsis. These legends certainly Siddhanta indicates that longitudes should be calculated represent some sort of borrowing from the West, but from Ujjain and makes no mention of Alexandria. it would be fruitless to define its exact nature unless 400 Prof. Sengupta thinks that it dated from about the text is more critically examined. Varahamihira stars A.D., but a scrutiny of the co-ordinates of certain describes in Chapters IX, X, XI, XVI, XVII of the in marking the ecliptic, which we have discussed Paftca Siddhantika the contents of the Surya Siddhanta data Appendix 5-B, shows that it might have utilized are somewhat different from as known to him ; they Citra collected about 280 A.D., when the star those as found in the modern text. It appears that equinoctial (a Virginia), was close to the autumnal this Siddhanta was constantly revised with respect to point, and is therefore subsequent to 280 A.D. the astronomical constants contained in it as all The rules of framing the calendar are found in astronomical treatises should be. The text as we Chapter XII of which we give an account in the next have now was fixed up by Ranganatha in 1603 after section. which there have been no changes. Burgess, from 500 A.D., the Indian astronomers gave a study of the astronomical constants, thought that After about to Prof. pretext of ascribing astronomical treatises the final text referred to the year 1091 A.D. up the mythical sages and began to claim authorship P. C. Sengupta shows that the S.S. as reported by gods or that has written ; the earliest Varahamihira borrowed elements of astronomical data of the treatises they had Aryabhata (476—523 A.D.). The from Aryabhata, and the S.S. as current now has survived is that of were to frame rules for borrowed elements from Brahmagupta (628 A.D.). objects of their treatises astronomy calendaric calculations, knowledge of The modern Surya Siddhanta is a book of 500 which these rules were are forming the basis on verses divided into 14 chapters, contents of which framed. described briefly below : other In addition to the Surya Siddhanta only two Chap. I—Mean motions of the Planets. systems have survived, viz-, II—True places of the Planets. II, an n The Arya Siddhanta- due to Aryabhata Ill—Direction, Place, and Time. to be astronomer of the 10th century,_and supposed IV Eclipses, and especially Lunar who claims n — related to the of Aryabhata, Eclipses. Creator. to have derived it from Brahma, the Parallax in a Solar Eclipse. V— related to the The Brahma Siddhanta—vaguely Projection of Eclipses. n VI— authorship is Paitamaha Siddtenta, but the human VII—Planetary Conjunctions. Brahmagupta ascribed to the celebrated astronomer VIII—The Asterisms. (628 A.D.). IX—Heliacal Risings and Settings. astronomical treatises like that of X—Moon's Risings -and Settings, and But a number of by Bhaskaracarya and many the Elevation of her Cusps. Siddhanta kirormni either on account of their own XI—Certain malignant Aspects of the others, have survived with astrology. Sun and the Mocn-. merit or their connection INDIAN CALENDAR 239

Lanka, which is technically the name of a locality The Solar Calendar according to the on the equator lying in the meridian of Ujjayini, which Surya Siddhanta was the Greenwich of ancient India. This had

The first few verses of Chap. XII deal with the nothing to do with Ceylon, but is a fictitious name ; creation of the world according, to Hindu conception, 90° west of Lanka the city called Romaka, and of sun, the and the creation of the elements ; the 90° east of Lanka the city known as Yamakoti. moon, and the planets. The universe is taken to be The name Romaka vaguely refers to the capital of geocentric, and the planets in order of their decreasing the . ' Yamakoti' is quite fanciful. distances from the earth are given as (vide verse 3 J,) : The Surya Siddhanta takes it for granted that the Saturn, Jupiter, Mars, the Sun, Venus, Mercury sun's yearly motion through the ecliptic is known to and the Moon. the reader and now proceeds to explain the Signs of The fixed stars are placed beyond the orbit of Saturn. the Zodiac. Surya Siddhania> XII, Verse 32 Surya Siddhanta XII, 45 Mauhye samantat dandasya bhugolo byomni tisthati Mesadau devabhagasthe devanarii yati darsanam Bibhranati paramam sakfcim brahmarto dharanatmikaiii. Asuranam tuladau tu suryastadbhaga saficarah. of the celestial Translation : Quite in the middle Translation : In the half revolution beginning egg (Brahmano)a\ the earth sphere (Bhugola) stands in with Mesadi (lit. the initial point of Aries), the sun the ether, bearing the supreme might of Brahma being in the hemisphere of gods, is visible to the gods, ; which has the nature of a self supporting force. but while in that beginning with Tuladi (lit. the initial The astronomers are thus conscious that the earth point of Libra) he is visible to the demons moving in is a spherical body suspended in ether {byomni) their hemesphere.

Verse 34 : Describes the earth's polar axis, which This means that when the sun reaches Mesadi, the passing through the earth's centre emerges as initial point of the sign of Aries, the gods who are mountains of gold on either side. supposed to be in the north pole just witness the

: are supposed to dwell Verse 35 Gods and Rsis rising of the sun and has the sun over the horizon for the demons are on the upper (northern) pole, and six months. All these six months, the demons who are supposed to dwell on the nether (south) pole. supposed to be at the south pole are in the dark. It the for whom, Verse 43 : Describes two pole-stars (Dhruva*taras) is vice versa for their enemies Asuras which are fixed in the sky. dwelling in the south pole, the sun rises for them (beginning of the Tula sign i.e., The author could have been aware only of the when it is at Tuladi first point of Libra) and remains above the horizon for Polaris. By analogy he inferred the existence of a months. southern pole-star which, as is well-known, does six not exist. He had apparently no knowledge of the sky According to the S.S., therefore, the first point of far south of the equator. Aries is coincident with the vernal equinoctial point, and

the first point of Libra tuith the auturtinal equinoctial The remaining verses describe the equator : As in modern astronomy, it says that the polar star is on the point. person on the equator and the co-latitude horizon of a Surya Siddhanta, XIV, 9 and 10 (Lambaka) of the equator is 90°. Bhanormakarasamkranteb sanmasa uttarayanarii The Siddhantic astronomers thus completely Karkadestu tathaiva syat sanmasa daks in ayanam. 9 , the geocentric theory of the solar system. It accepted Dvirasinatha rtava stato'pi sisiradayat improvement on the ideas of the world was a great Mesadayo dvadasaite masastaireva vatsarah. 10, prevalent in India at the time of the great epic Mahabharata (date about 300 B.C.), in which the earth Translation: From the moment of the sun's entrance the sign of Capricorn, six is described to be a flat disc, with the Sumeru (safnkrdnti) into Makara, progress (uttarayana) mountain as a protruding peg in the centre, round months make up his northward ; which the diurnal motion of the celestial globe carrying so likewise from the moment of entrance into Karkata, are his southward the stars, planets, the sun and the moon takes place. the sign of Cancer, six months This idea of the world is also found in the Jatakas and progress (daksinayana). (9) other Buddhist scriptures. Thence also are reckoned the seasons (rtu), the In the subsequent verses four cardinal points on the cool season (siUra) and the r£st, each prevailing signs. These twelve, commencing with equator are recognized, these are : through two 240 REPOBT OF THE CALENDAR REFORM COMMITTEE

precession of the equinoxes, they were unaware of the Aries, are the months ; of them is made up tke the sidereal year and the tropical year (10). distinction^ between year. They had to obtain the year-length either from These quotations leave not the slightest doubt that observation or from outside sources. If they obtained according to the compilers of the S.S., the first point it from observations, they must have counted the of the zodiac is the point of intersection of the ecliptic number of days passed between the return of the sun and the equator, and the signs of the zodiac cover 30° to the same point in the sky over a number of years. each of the ecliptic. Such observations would show that the year had not It is supposed on good grounds that much of the the traditional value of 366 days given in Vedanga astronomical knowledge found in the Surya Siddhanta Jyotisa, but somewhat less. In fact, the Paitamaha it is is derived from Graeco-Chaldean sources. But length is 365.3569 days and there is no reason to clear from the text that the compilers of the S.S. had believe that it was derived from foreign sources. no knowledge of the precession of equinoxes, but they Successive observations must have enabled the Indian took the first point of Aries to be fixed. This is not to savants to push the accuracy still higher. be wondered at, for as shown in § 4.9, inspite of the Or alternatively they might have borrowed the works of Hipparchos and Ptolemy, precession was value from Graeco-Chaldean astronomy, but we cannot either not accepted or no importance was attached to their value is larger than Ptolemy's. It then explain why it by the astronomers of the Roman empire. may be We have seen that the Romaka Siddhanta gives a value added that the compilers of the S.S. were not aware which is Hipparchos's, and tropical, but the three more of the theory of trepidation of equinoxes which correct SiddhSntas reject it, as being too small. This appears to have been first formulated in the West by however indicates that they probably tried to derive Theon of Alexandria (ca. 370 A.D.). It is also important the length from observations as stated in the previous to note that the Indian astronomers did not take the paragraph and found the Romaka SiddhantaAength. too first point of Aries to be identical with that given small. If they had taken it from some other source, either by Hipparchos, Ptolemy or any other western we have still to discover that source. It is certainly authority as would have been the case if there was not Ptolemy's Almagest blind-folded borrowing. They assimilated the astro- nomical knowledge intelligently and took the first The ex-cathedra style of writing adopted by the point of Aries as the point of intersection of the Siddhantic astronomers, e.g., the number of days in a successive attempts equator and the ecliptic, and made Kalpa (a period of 4.32 x 10* years) is 1,577,917,828,000 to determine it by some kind of actual observations, according to Grandfather Brahma, or the Sungod, appear as shown in appendix 5-B. These observations does not enable one to trace the steps by which these first to have been made about 280 A.D. conclusions were reached.

The two problems of (i) distinguishing between the Length of the Year tropical year, and the sidereal year and of (ii) deter- The length of the year, according to the different mining the correct length of the year in terms of authorities are as follows, the mean solar days are very exacting ones.

Surya Siddhanta of days We have seen how it took the West the whole d U 3000 B.C. to 1582 A.D. to arrive Varahamihira ... 365 6 12- 36" =365.25875 time-period between that the true length of the tropical year Current S.S. ... 365 6 12 36.56 = 365.258756 at the idea Probably Iranian astrono- Ptolemy (sidereal) 365 6 9 48.6 = 365.256813 was close to 365.2425 days. A.D.), who had the Correct length of mers of Omar Khayam's time (1072 of the great Arabian observations by al- the sidereal year. .. 365 6 9 9.7 = 365.256362 advantage correct knowledge of Correct length of Battanl and others had a more acceptance of the distinction the tropical year- 365 5 48 45.7 = 365.242196 this length. The final between the tropical and the sidereal year dates only N. B. Varahamihira's length of the year is also found in from 1687 A.D., when Newton proved the theory of Aryabhata's ardhardtrika, or midnight system, and in to be wrong. Brahmagupta's Khari^ix Khadyaka. trepidation How did the. Indian savants manage to have such a The Siddhantic astronomers of 500-900 A.D. cannot wrong value for the length of the year ? therefore be blamed for their failure to grasp the two problems. But what to say of their blind followers The year, according to the Surya Siddh&nta, is the twentieth century, would continue to meant to be clearly tropical, but as the Indian savants who, in their belief in the theory of trepidation ? compiling the S.S. were ignorant of the phenomenon of proclaim INDIAN CALENDAB 241

Effect of continuance of the mistake (a) Starting the astronomical year from the moment the sun crosses the vernal equinoctial point. is The Surya Siddh&nta value, vix. t 365.258756 days (b) Starting the civil year on the day following. larger than the correct sidereal value by "002394 days and larger than the tropical length by .016560 days. The Siddhantic astronomers thus brought the Indian calendar on a line with the Graeco-Chaldean As the S.S. value is still used in almanac-framing, calendar prevalent in the Near East during the the effect has been that the year-beginning is advancing Seleucid times. >y .01656 days per year, so that in course of nearly 1400 years, the year-beginning has advanced by 23.2 days, In a few cases, e.g., in the case of the Vikrama so that the Indian solar year, instead of starting on the era reckoning as followed in parts of Guzrat, the year- day after the vernal equinox (March 22) now starts on beginning is in Kartika. This seems to be reminiscent April 13th or 14th. The situation is the same as of the custom amongst the Macedonian Greek rulers happened in Europe, where owing to the use of a of Babylon to* start the year on the autumnal equinox year-length of 365.25 days, since the time of Julius day. Caesar, the Christmas preceded the winter solstice by The First Month of the Year : 10 days, when the error was rectified by a Bull of Gregory XIII, and the calendar was stabilized by This has to be defined with respect to the defini- introducing revised leap-year rules. tion of the seasons. The Calendar Reform Committee has proposed that According to modern convention, which is derived the Indian New Year should start on the day after the from Graeco-Chaldean sources, the first season of the of vernal equinox, vernal equinox day. Most of the Indian calendar year is spring ; it begins on the day makers belong to the no-changer school, or the as shown in fig. 25 which shows also the other seasons. is, however, nirayana school (i.e., school not believing in the The Indian classification of seasons precession of the equinoxes). But this school does different as the following table shows. not realize that even if the sidereal length of the year Table 15 Indian Seasons. be acceped, the Indian year-length used by them is —

larger by nearly '0024 days, which cannot be tolerated. — 30° to 30°... Spring (Vasanta) Caitra & Vaisakha has to be made, it is better to do it Jyaistha A^iidha if a change . (Grisma) & So 30 to 90 . .Summer the year-length to be tropical, and Sravana Bhadra whole-hog, i.e., take 90 to 150 ...Rains (Varsa) ^ & start the year on the day after the vernal equinox. 150 to 210 ...Early Autumn (Sarat) Asvina & Kartika 270 ...Late Autumn Agrahayana & Pausa This is the proposal of the Indian Calendar Reform 210 to (Hemanta) Committee, and it is in full agreement with the canons 270 to 330 ...Winter (Sisira) Magna & Phalguna laid down in the Surya Siddhanta. The Siddhantic astronomers, therefore, found themselves in a difficulty. If they were to follow 'the the Year-beginning Historical Note on Indian convention, Caitra would be the first month follow Graeco- The Indian year, throughout ages, has been of two of the solar year. If they were to tfie they had to take VaUakha as kinds, the solar and the lunar, each having its own Chaldean covention, solar year. starting day- The year-beginning for the two kinds the first month of the of years, for different eras* is shown in Table No. 27. They struck a compromise. For defining the solar year, they took Vaisakha as the first month and for defining the lunar year they took Caitra as the first The Starting Day of the Solar Year month (see § 5*7). But this rule has been followed only in North In the Vedic age, the year-beginning was related India. In South India, they had different practices, probably to one of the cardinal days of the year, but as shown in the list of solar month-names (Table we do not know which cardinal day it was. The No. 16). Ved&iiga Jyotisa started the year from the winter In North India the first month is Vaisakha as solstice day, Brdhmaws started the year from the the S.S. which starts just after sun's Indian Spring (Vasanta) when the tropical (Sayana) laid down in through the V.E. point. longitude of the sun amounted to 330°. passage to see that in Tamil Nad, some of The Siddhantic astronomers must have found a It is interesting are of Sanskritic origin, others are of Tamil confusion, and so fixed up a rule for fixing the year- the names the most striking fact is that the first mouth, beginning, which we have just now dicussed. These origin. But in the starting after vernal equinox is not Vaisakha as rules amount to : 242 BEPOKT OF THE CALENDAR REFORK COMMITTEE

Table 16.

Corresponding Names of Solar Months.

Indian Names Bengal Assam Tamil Tinnevelly N. Malayalam of Signs Orissa or S. Malayalam (Orissa) VAISAKHA BAHAG CITTIRAI MESA MEDAM Vrsava Jyaistha Jeth Vaikasi Vrsava Edavam Mithuna A s^dha Ahar Ani Mithuna Midhunam Karkata Sravana Saon Adi Karkitaka Karki$aka Siriiha Bbadra Bhad Avani SIMHA Cingam Kanya Asvina Ahin Pura^tasi Kanya KANNI Tula Kartika Kati Arppisi (Aippasi) Thula Thulam Vrscika Agrahayana Aghon Karthigai Vrscika Vrscikam Dhanul.i Pausa Puha Margali Dhanug Makara Magha Magh Thai Makara Makaram Kumbha Phalguna Phagun Masi Kumbha Kumbham Mina Caitra Ca'fc Panguni Mina Minam

(The first month of the year has been distinguished by capitals).

N.B. The Bengali or Oriya names of solar months are taken without change from Sanskrit. The Assamese names are the same, but have local pronunciations.

rest of India but Ghittirai or Caitra, and so on. We do The mean length of a solar month not know why Tamil astronomers adopted a different -30.43823 according to S.S.

convention. We can onlv guess : probably they wanted =* 30.43685 according to modern data. to continue the old Indian usage that Caitra is to The actual lengths of the different solar months* remain the first month of the year. however, differ widely from the above mean values. In Tinnevelley and Malayalam districts the solar This is due to the fact that the earth does not move months are named after the signs of the zodiac. with uniform motion in a circular orbit round the sun, There is, therefore, no uniformity of practice in the but moves in an , one focus of which is nomenclature of the solar months, and in fixing up occupied by the sun, and according to Kepler's second the name of the first month of the solar year. law, it sweeps over equal areas round the sun in equal intervals of time. When the earth is farthest from Solar Months : Definition the sun, i.e. at aphelion (sun at apogee) of the elliptic orbit, the actual velocity of the After having defined the solar year, and the year earth becomes slowest, and the apparent angular beginning, the Surya Siddhanta proceeds to define the velocity of the sun becomes minimum, "Solar Month." and consequently the length of the solar month is greatest. This happens about Surya Siddhanta, Chap. 1,13 3rd or 4th July, i.e., about the middle of the solar Aindavastithibhi-stadvat samkrantya saura ucyate month of Asadha (Mithuna), and consequently this Masairdvadasabhirvarsarii divyam tadaharucyate. month has got the greatest length. The circumsfances six Translation : A lunar month, of as many lunar become reversed months later on about 2nd or 3rd January, when the earth is nearest to the days, (fithi) ; a solar (saura) month is det2rmined by sun, i.e., at perihelion (sun perigee), the entrance of the sun into a sign of the zodiac, i.e. at the angular velocity of the the length of the month is the time taken by the sun sun at that time becomes maximum, and consequently in passing 30° of its orbit, beginning from the the solar month of Pausa (Dhanufy) which is opposite to Ssadha, has got the initial point of a sign ; twelve months make a year, minimum length.

this is called a day of the gods. The following two figures ( Nos. 25 & 26 ) will explain This definiton is accepted by the Arya, and the position. Brahma Siddhantas as well. The durations of the different months, which are The working of this rule gives rise to plenty of different from each other due to the above reason, are

difficulties, which are described below : also not fixed for all time. The durations of the solar INDIAN CALENDAB 243

months undergo gradual variations on account of two made up of the precessional velocity of 50."27 per year

reasons ; v%%.$ in the retrograde direction and the perihelion velocity of 11."62 per year in the direct direction due to planetary attraction. This movement of the apse line with respect to the V.E. point causes variation in the lengths of the different months.

(ii) The second reason is that the ellipticity

of the earth's orbit is not constant ; it is gradually

changing. At present the eccentricity of the orbit is diminishing and the elliptic orbit is tending to become circular. As a result, the greatest duration of the month is diminishing in length and the least one increasing. Similarly the lengths of other months are also undergoing variation.

The modern elliptic theory of planetary orbits was Fig. 25 not known to the makers of Indian Siddhantas, but they knew that the sun's true motion was far (i) the line of apsides of the earth's elliptic orbit from uniform. They conceived that the sun has (i.e. the aphelion and perihelion points) is not fixed uniform motion in a circle, with the earth not exactly at the centre of that circle, but at a small distance from it. The orbit therefore becomes- an eccentric circle or an epicycle. Here also the angular motion of the sun becomes minimum when at apogee or farthest from the earth, and maximum when nearest to the eartn or at perigee. In this case the size and eccentricity of the circle are invariable quantities, and consequently the maximum and minimum limits of the months are constant. The apse line advances in this case also, but with a very slow motion, which according to the Surya Siddhanta amounts to a degree of arc in 31,008 years, or 11" in a

Fig. 26 century. The variations of the durations of months

due to this slow motion of the apse line is quite in but is advancing along the ecliptic at the negligible and the lengths of the months according to rate of 61".89 per year or l.°72 per century. This is the Surya Siddhanta are practically constant over ages.

Table 17—Lengths of different solar months reckoned from the vernal equinox. Lengths of Solar months.

According to Modern value SUrya Siddhanta (1950 A.DJ {as proposed)

(1) (2) (3) (4) (5) d h m d h m cJ -30° 30 22 26.8 30 11 25.2 Vaisakha (Me$a) ( o ) Caitra 31 10 5.2 30 23 29.6 Jyais^ha (Vftfa) ( 30 -60 ) Vaisakha 15 28.4 31 A$adha (Mithuna) ( 60 -90 ) 31 8 101 Jyaistha 31 11 24.4 31 10 t^ravana (Karka^a) ( 90 -120 ) 54.6 A sad ha 31 26.8 31 6 53.1 Bhadra (Simha) (120 -150 ) J^ravana 35.6 Asvina (Kanya) (150 -180 ) 30 10 30 21 18.7 Bhadra

Kartika (Tula) (180 -210 ) 29 21 26.4 30 8 58.2 Asvina 11 46.0 21 Agrahayana (Vrscika) (210 -240 ) 29 29 14.6 Kartika 29 7 37.6 29 13 8.7 Pausa (Dh&nub) (240 -270 ) Agrahayana 10 45.2 10 38.6 Magna (Makara) (270 -300 ) 29 29 Pauga 29 19 41.2 29 14 18.5 Phalguna (Kumbha) (300 -330 ) Magha 30 8 29.0 29 23 18.9 Caitra (Mina) (330 -360 ) Phalguna 365 6 12'6 365 5 48*8

O.B.—39 — J

244 REPORT OF THE CALENDAR REFORM COMMITTEE

In the Surya Siddhdnta, a formula is given for finding the true longitude of the sun from its mean Different conventions for fixing up the longitude. As the length of a month is the time taken beginning of the solar month by the sun to traverse arcs of 30° each along the The safnkranti or ingress of the sun into the ecliptic by its true motion, the lengths of the different different signs may take place at any hour of the day. months can be worked out when its true longitudes on Astronomically speaking the month starts from that different dates of the year are known. The true moment. But for civil purposes, the month should longitude is obtained by the Surya Siddhdnta with the start from a sunrise ; it should therefore start either

help of the following formula : on the day of the safnkranti or the next following True Long. — Mean Long. — 133. '68 sin K day according to the convention adopted for the + 3.18 sin 2 K locality. There are four different conventions in different States of India for determining the beginning where K~ Mandakendra of the sun, of the civil month. i.e., — mean sun — sun's apogee.

At the approximate time of each safnkranti, the Rules of Samkranti true longitude of the sun is calculated by the above The formula for two successive days, one before the Bengal rule : In Bengal, when a safnkranti takes attainment of the desired multiple of 30° of longitude place between sunrise and midnight of a civil day, the solar month begins on the following and the other after it, and then the actual time of day ; and when it occurs after crossing the exact multiple of 30th degree is obtained midnight, the month begins on the next following by the rule of simple proportion. This is called the day, i.e., on the third day. This is the general rule time of safnkranti or solar transit. The time interval j but if the safnkranti occurs in the period between 24 between the two successive safnkrdntis is the actual minutes before midnight to 24 minutes after length of the month, The lengths of the months thus midnight, then the duration of tithi derived from the Surya Siddhdnta compared with the current at sunrise will have to be examined. If the tithi at sunrise extends modern values, i.e., the values which we get after up to the moment of safnkranti, the month begins taking the elliptic motion of the sun, and the shift of on the next day : if the tithi ends before the first point of Aries are shown in Table No. 17, safnkranti, the month begins on the next following or the third day. on p. 243, in which : But in case of Karkata and Makara safnkrdntis, the criterion of tithi is not to be considered. If the Column (1) gives the names of months. Karkata safnkranti falls in the above period of 48 minutes about the midnight, the „ (2) gives the arc measured from the first month begins on the next day, and if the Makara point of Aries (the V.E. point) safnkranti falls in that period, the month begins covered by the true longitude on the third day. of the sun.

„ (3) gives the lengths of the months The Orissa rule : In Orissa the solar months of the derived from the Surya- Amli and Vilayati eras begin civilly on the same day Siddhdnta rules. (sunrise to next sunrise) as the safnkranti, irrespective of whether this takes place before after (4) gives the correct lengths of the or midnight.

months as in 1950 A.D. The Tamil rule : In the Tamil districts the rule is that when a safnkranti takes place (5) gives the corresponding names of the before sunset, the months as proposed by the month begins on the same day, while if it takes place Committee. after sunset the month begins on the following day.

The Malabar rule : The rule observed in the North

It would appear from table No. 17 that the and South Malayalam country is that, if the samkranti takes place between sunrise 18 h U1 lengths of the months of the Surya Siddhdnta are no and ghatykds (7 12 ) or more correctly fth of the duration of day from longer correct ; they greatly differ from their corres- sunrise (about 1-12^ P.M.) the month begins on the ponding modern values, sometimes by as much as 11 same day, otherwise it begins on the following hours. The Surya Siddhdnta value s, which the day.

almanac makers still use, are therefore grossly It will be observed that as a result of the different incorrect. Moreover, the lengths of the months are conventions combined with the incorrect month- undergoing gradual variation with times due to reasons lengths of the Surya Siddhdnta we are faced with the already explained. following problems INDIAN CAItENDAB 245

(1) the civil day of the solar month-beginning from such rules vary from 29 to 32, which is very

may differ by 1 to 2 days in different parts of India. inconvenient from various aspects of civil life.

(2) The integral number of days of the different The Committee has therefore felt that there is no solar months also vary from 29 to 32. need for keeping the solar months as astronomically

The months of Kartika, Agrahayatya, Pau§a, Magha defined. The length of 30 and 31 days are quite and Phalguna contain 29 or 30 days each, of which enough for civil purposes. Moreover, fixed durations two months must be of 29 days, and others of 30 days. of months by integral number of days is the most The months Caitra, Vai&akha and Asvina contain 30 convenient system in calendar making. The five or 31 days. months from the second to the sixth have the lengths of over 30| days, and so their lengths have been The • rest, vix., Jyaistha, Asa4ha, Sravana and

rounded to 31 days each ; and to the remaining Bhadra have got 31 to 32 days each, of which one or months 30 days have been allotted. two months will contain 32 days every year.

(3) The length of the month by integral number of civil days is not fixed, it varies from year to year. 5.7 THE LUNAR CALENDAR IN THE SIDDHANTA JYOTISHA PERIOD

Justification of the Solar Calendar as proposed The broad divisions of the year into seasons or the Committee by months are obtained by the solar calendar, but since

It has been shown that the intention of the maker for religious and social puposes the lunar calendar had of Surya Siddhanla and of other Siddhantas was to been used in India from the Vedic times, it becomes start the year from the moment of sun's crossing the incumbent to devise methods for pegging on the lunar vernal equinoctial point and to start the civil year calendar to the solar.

from the day following. The Committee has also The extent to which the lunar calendar affects adopted this view and proposed that the civil year Indian socio-religious life will be apparent from the for all-India use should start from the day following tables of holidays we have given on pp. 117-154. There the V. E. day, i.e., from March 22. In the Vedic the religious and social ceremonies and observances literature also it is found that the starting of the year and holidays of all states and communities are classified was related with one or other of the cardinal days of under the headings : the year. The Vedafiga Jyotisa started the year from (1) Regulated by the solar calendar of the the winter solstice day, the Brahmanas started the Siddhantas ; year from the Indian spring (Vasanta) when the

(2) Regulated by Gregorian dates ; tropical {Sayana) longitude of the sun amounted to Regulated by the lunar calendar. 330°, but in the Siddhantic period the year-beginning (3) coincided with the V.rE. day. So in adopting the The tables show that by far the largest number of Sayana system in our calendar calculations, the religious holidays and other important social ceremonies Indian tradition, from the Vedic times up to the are regulated by the lunar calendar. It is difficult to

Siddhantic times, has been very faithfully observed. see how the lunar affiliation, inconvenient as it is, can This has ensured that the Indian seasons would be replaced altogether, short of a revolution in which occupy permanent places in the calendar. we break entirely with our past. The -lunar calendar will therefore continue to play a very As regards the number of days per month, although important part as we continue to keep Our connection the Surya Siddhanta defines only the astronomical with the past, and with our cherished traditions. solar month as the time taken by the sun to traverse 30° of arc of the ecliptic, four different conventions Let us now restate the problems which arise when, have been evolved in different States of India for with reference to India, we want to peg the lunar determining the first day of the civil month from the calendar to the solar, how it was tackled in the past, actual time of transit as narrated earlier. None of and how the Calendar Reform Committee wants to the conventions is perfect. Such rules do not yield tackle it. fixed number of days for a month, as a result of The lunar month consists of 29.5306 days and 12 which it becomes extremely difficult for a chrono- such lunar months fall short of the solar year by 10.88 logist to locate any given date of this calendar, days. After about 2 or 3 years one additional or inter- unambiguously, in the Gregorian calendar, without calary lunar month is therefore necessary to make up going through lengthy and laborious calculations. the year ; and in 19 years there are 7 such intercalary Moreover, the number of days of months obtained months. In Babylon and Greece there were fixed rules =—

246 BEPOBT OF THE CALENDAB BEFOBM COMMITTEE

at have been introduced. Taking the mean vaules of the for intercalation ; the intercalary months appeared the length of the solar year, stated intervals and were placed at fixed positions in lunation-period and of the time when one extra month (i.e., intercalary month) the calendar (vide § 3.2). It appears that some kind of be determined. rough rules of intercalation of lunar months were will have to be introduced can easily uniform angular followed in India up to the first or second century But the luminaries do not move with and so A.D. when the calendar was framed according to motions [throughout their period of revolution the intercalary month on the the rules of Vedaiiga Jyoti§a (vide § 5.4). Thereafter the determination af the moon the Siddhantic system of calendar-making began basis of the actual movement of the sun and calculations according to develop, replacing the old Vedaiiga calendar. is a very difficult problem. The to the mean motions are however shown below. The Vedaiiga calendar as we have seen was crude and was based on approximate values of the lunar and Table 18—Calculation of intercalary months in a solar periods, the calendar was framed on the mean 19-year cycle. motions of the luminaries, and as such an intercalary month was inserted regularly after every period of Surya Modern- Modern- Siddhanta Sidereal Tropical 30 months. days days days The Siddhanta Jyotisa introduced the idea of true Length of year 365.258756 365.256361 365.242195 positions of the luminaries as distinct from their mean Solar month 30.438230 30.438030 30.436850 positions, and devised rules for framing the calendar Lunation 29.53Q581 29.530588 29 530588 on the basis of the true positions, and adopted more No. of solar months correct values for the periods of the moon and the after which a lunar sun. But some time elapsed before new rules were month is added 32.5355 32.5427 32.5850 adopted, and intercalary months continued to be 6939.60171 calculated on the basis of the mean motions of the 19 years 6939.91636 6939.86896 sun and the moon, employing however more correct 235 lunations = 19x12 6939.68818 6939.68818 6939.68818 values of their periods as given by the Siddhantas. In ( + 7) this connection the following remarks by Sewell and Error in the - 0.18078 0.08617 Dlksit, in the Indian Calendar (p. 27) are worth noting. 19-year cycle -0.22818 +

"It must be noted with regard to the intercalation and It would appear from the above figures that the suppression of months, that whereas at present these are cycle with 7 mala masas is a better approxi- regulated by the sun's and moon's apparent motion,—in other 19-year the tropical year, and the error words, by the apparent length of the solar and lunar months mation if we adopt with the sidereal year and the —and though this practice has been in use at least from gradually increases cycles, i.e., in 220 years, 1100 A.D. and was followed by Bhaskaracaryn, there is Surya Siddhanta year. In Hi in the evidence to show that in earlier times they were regulated the discrepancy would amount to only a day by the mean length of months. It was at the time of the case of the tropical year. celebrated astronomer (1039 A.D.) that the change It is also seen that one intercalary month is to be of practice took place". added at intervals of 32* solar months, or in other words an intercalary month recurs alternately after 32 and 33 solar months. According to this scheme the Intercalary months or Malamasas. intercalary months in a period of 19 years would be as

The length of the Surya Siddhanta year is 365.258756 follows : days and of a lunar month according to the S. S. is 29.5305879 days. Twelve such lunar months fall short Year Intercalary month Year Intercalary month of the S. S. year by 10.891701 days. The lunar year 1 11 10 Pausa therefore slides back on the solar scale each year by 2 12 — about 11 days. If the months were allowed to slide 3 9 Margaslrsa 13 — back continuously it would have completed the cycle 4 14 7 Ssvina in 33.5355 years, and the festivals attached to the lunar 5 15 ~ calendar would have moved through all the seasons 6 5 SrSvana 16 — of the year within this period, as now happens with the 7 17 3 Jyestha Islamic calendar. 8 18 — To prevent the occurrence of this undesirable 9 2 Vaisakha 19 12 Phal^^a feature, the system of intercalary months or mala m&sas 10 —

INDIAN CALENDAR 247

But the makers of Indian calendars have not new-moon ending month, it may begin on any day followed any scheme for intercalation based on mean during the last half of the preceding solar month and motions. They evolved a plan for distinguishing an the first half of the solar month in question. It will intercalary month from a normal month based on the therefore be seen that while the new*moon ending or

true motions of the sun and the moon. This plan is mukhya month sometimes falls almost entirely out-

also followed in giving the name to a lunar month, as side (i.e, % after) the relative solar month, the full-moon

explained below : ending or a gauna month always covers at least half of the solar month' of that name.

Siddhantic rules for the Lunar Calendar The months used for civil purposes in the Hindi calendar are the full-moon ending lunar months, and There are two kinds of lunar months used in India, are sub-divided into two halves kf$na pak$a covering the new-moon ending and the full-moon ending. In the period from full-moon to new-moon and termed calendarical calculations only the new-moon ending as vadi, and sukla paksa covering the period from new- months are used. moon to full-moon and termed as sudi. As these (i) The new-moon ending lunar month covers the months are on the gaum mana, the vadi half of a period from one new-moon to the next. This is known month comes first followed by the sudi half. The last as amanta or mukhya candra mdsa. It gets the same day of the year is therefore a full-moon day, the name as the solar month in which the moment of initial Phalgunl (or Holi ) Purnima, in keeping with the new-moon of the month falls. For this purpose the ancient Indian custom. solar month is to be reckoned from the exact moment The Samvat and Saka years in the Hindi calendar of one safnkranti of the sun to the moment of the next begins with Caitra Sukla Pratipad. For astronomical safnkranti. When a solar month completely covers purposes, however, the year begins a few days later a lunar month, i.e., when there are two moments of with the entrance of the sun into Mesa. new-moon (amanta), one at the beginning and the other at the end of a solar month, then the lunar month The calendars of Asaq^hi Safnvat and Karlikl Safnvat beginning from the first new-moon is the intercalary are, on the other hand, based on the new-moon ending month, which is then called an adhika or mala masa, months, and consequently the months begin 15 days and the lunar month beginning from the second new- later than the months of the Caitradi full-moon ending begins with Asa4ha moon is the normal month which is termed as suddha calendar. The A sa^hl calendar or nija in the Siddhantic system. Both the months Sukla 1, and the Kartikl calendar with Kartika bear the name of the same solar month but are prefixed Sukla 1. by adhika or suddha as the case may be. In an adhika The table (No. 20 on p. 249) shows the scheme of month religious observances are not generally allowed. the different calendars for the year ^aka 1875 or adhika month. If on the other hand, a lunar month completely (1953-54). The year contains a mala covers solar month, no new-moon having occurred a It may be seen from the above mentioned table in that solar month, the particular lunar month is then that in case of the light half of the month (sudi half) or decayed month. called a ksaya the month has the same name for the two systems of As the mukhya or new-moon ending lunar month month-reckoningsi but in the dark half of the month begins from the Amavasyd or the new-moon occurring (vadi half) the names of the months in the two systems in the solar month bearing the same name, the lunar are different. month may begin on any day during that solar month The year-beginnings of the Samvat era in the three — it may begin on the first or even on the last day of systems of luni -solar calendar are also different, as may that solar month. be seen from the following table. (ii) The full-moon ending lunar month known as purnirnanta or gauna candra masa, covers the period from one full-moon to the next, and is determined on Table 19—Showing the year-beginnings of the the basis of the corresponding new-moon ending month different systems of Samvat era. as defined above. It begins from the moment of full- Calendar Caitradi Agadhadi Kartikadi moon just a fort-night before the initial new-moon of system system system it of an amanta month, and also takes the name that Safnvat era 2010 2010 2010 month. Beginning Kartika S 1 But in the gaunamdna (i.e., full-moon ending lunar of year Caitra S 1 Asadha S 1 Mar., 1953) (12 July, 1953) (7 Nov., 1953) month), as the month starts 15 . days earlier than the (16 . —

248 REPORT OF THE CALENDAR REFORM COMMITTEE

Counting of the Succession of Days 'adhiha*. For example if the third tithi is repeated, of days of the half-month would be In all the calendars used in India, days are counted then the sequence according to the solar reckoning, as well as according 1, 2, 3, 3 adhiha, 4, etc.

the lunar reckoning {i.e., by tithi or lunar day). to Some improvement in the use of tithi for dating But there is a difference in emphasis. purposes is, however, observed in the Fusli calendar

In the eastern regions (Bengal, Orissa and Assam), in vogue in some parts of Northern India. In this following the and in Tamil Nad and Malabar, the solar reckoning is calendar the month begins from the day given more prominence. The almanacs give solar full- moon and dates are counted consecutively months and count the days serially from 1 to 29, 30, from 1 to 29 or 30 without any break at new-moon, or 31 or 32 as the case may be. The tithi endings are any gapping or over-lapping of dates with k$aya tithi 'this calendar given for every day, and the tithi may start at any or adhiha tithi. In fact the dates of starting of moment of the day. have no connection with iithis after the the month has been determined. The year of Fusli In other parts of India (except Bengal, Orissa, begins after the full-moon day of lunar Bhadra Assam and Tamil Nad), the counting of days is based on the lunar reckoning, and the number of the tithi current at sunrise is used as the ordinal number of Mala Masa and Kshaya Masa the date necessary in civil affairs. So there are 29 or It has been stated before that even at the beginning 30 days in a month, but the days are not always of the Siddhanta Jyotisa period, the intercalary months counted serially from 1 to 29 or 30. {mala or adhiha) were determined on the basis of the The month in the lunar calendar is divided into mean motions of the sun and the moon, and as such two half-months, the sudi and vadi halves in the new- there was no possibility of the occurrence of any so moon ending system, and the vadi and kudi halves in called ksaya or decayed month. But as already the full-moon ending system. In fact the year is mentioned, from about 1100 A.D., the intercalary divided into 24 half-months instead of 12 months. So months are being determined on the basis of the there are 14 to 15 days in a half-month {vide Table 20). true motions of the luminaries, i,e., on the actual

The tithi or lunar day is measured by the positions lengths of the new-moon-ending lunar month and of the moon and the sun. When they are in conjunc- of the different solar months as obtained from tion, i.e., at new-moon the 30th tithi or amavasya ends Siddhantic rules. This gave rise to the occurrence and the first tithi starts which continues upto the of ksaya months, and the intercalary months moment when the moon gains on the sun by 12° in were also placed at very irregular intervals. longitude. Similarly when the difference between the The period from new-moon to new-moon (the lunar moon and the sun is 24° the second tithi ends, and so period of fixed duration ; it varies h m month ) is not a on. The average duration of a tithi is 23 37 5, but within certain limits according to the different the actual duration of a particular tithi undergoes positions of the apse line of the lunar and solar orbits, wide variations from the above average according to as follows : the different positions of the sun, the moon and the lines of their apsides. It may become as great as h m b m every 26 47 and as small as 19 59 . So generally to Length of the Lunation day there is a tithi. But sometimes a tithi begins and By mean motion According to S.S. Modern is ends on the same civil day, and such a tithi dropped ; a li d h d h and some religious ceremonies of auspicious character 29 6.3 29 5.9 are not allowed to take place on such a tithi, and the 29 12.73 to to following day begins with the next following tithi. 29 19.1 29 19.6 For example, if the third tithi is dropped, the sequence of the half-month is 1, 2, 4, 5 etc., thus the of days Comparing these values with the actual lengths of seriality is broken here. solar months given in Table 24, it is observed that the As opposed to the above-mentioned case, the tithi minimum length of the lunar month falls short of all sometimes extends over two days, there being no tithi the solar months, even of the shortest month of Pawa. ending in a day (from sunrise to next sunrise). As the But as a mala masa is not possible in that month, the limits of the lunar months are same tithi remains current on two successive sunrises, maximum and minimum both the days recalculated for each of the solar months from the same tithi-numbex is allotted to j the separately. in the second day, however, it is suffixed by term Kartika to Fhalguna INDIAN CALENDAR 249

Table 20.

Scheme of the Lani-Solar Calendar

( Saka 1875 = 1953-54 A.D. )

Initial date reckoned on the Religious Calendar Civil Luni-Solar Calendar Solar Calendar as is now in use. Mukkya or new- Gauna or full- Full-moon New-moom Indian Solar moon ending moon ending Gregorian ending ending date

Caitra S Caitra S Caitra S Caitra S 2 Caitra 16 Mar. Caitra K Vaisakha K Vaisakha Caitra V V 17 Caitra 31 Mar. Vai&akha S Vai&ahha S Vaiixkha S Vamkha S 1 Vaisakha 14 Apr. (mala) (mala) (adhika) (adhika) Vamkha K Vaisakha K Vaisakha Vaiiakha V V 17 Vaisakha 30 Apr. (mala) (mala) (adhika) (adhika) Vaisakha S Vaisakha S Vaisakha 3 Vaisakha S 31 Vaisakha 14 May (suddha) (suddha) Vaisakha K Jyestha K Jyestha V Vaisakha V 15 Jyestha 29 May (suddha)

Jyestha S Jyestha Jyestha S Jyestha S 29 Jyestha 12 June Jyestha K Asadha K Asadha Jyestha V 14 Asadha 28 June Asadha S Asadha Asadha Asadha S S 28 Asadha 12 July Asadha K travaila oravana V Asadha E V 11 Sravana 27 July Sravana S Sravana Sravana S Sravana S S 25 Sravana 10 Aug. Sravana K Bhadra Bhadra V Sravana V 9 Bhadra 25 Aug. Bhadra S Bhadra s Bhadra Bhadra s 24 Bhadra 9 Sep. Bhadra K Asvina Asvina V Bhadra V 8 Asvina 24 Sep. Asvina S Asvina Asvina s Asvina s 23 Asvina 9 Oct. Asvina K Kartika Kartika V Asvina V 6 Kartika 23 Oct. Kartika S Kartika Kartika s Kartika s 21 Kartika 7 Nov. Kartika K Marga. K Marga. V Kartika V 5 Agrah. 21 Nov. Marga. S Marga. S Marga. s Marga. s 21 Agrah. 7 Dec. Marga K Pausa K Pausa V Marga. V 6 Pausa 21 Dec. Pausa S Pausa S Pausa s Pausa s 22 Pausa 6 Jan, 1954 Pausa K Magha K Magha V Pausa V 6 Magha 20 Jan. Magha S Magha S Magha s Magha 6 21 Magha 4 Feb. Magha K Phalguna K Phalguna V Magha V 6 Phalguna 18 Feb. Phalguna S Phalguna S Phalguna S Phalguna S 22 Phalguna 6 Mar. Phalguna K Caitra K Caitra V Phalguna V 6 Caitra 20 Mar. S — $ukla paksa or Sudi. K = Krsna paksa.

V= . or Vadi.

When the lunar month Length of the lunar month. Comparing the above limits with the nearly covers the Minimum Maximum actual lengths of months stated before, it Solar month of is found that the minimum length of the lunar month falls short of all the Kartika solar or Phalguna 29 9.7 29 18.0 months except Pausa. So a malamdsa or intercalary Agrahayana or Magha 29 10.5 29 18.8 month is possible in all the months except * the Pausa month 29 10.8 29 19.1 of ibtisd only. 250 REPORT OF THE CALENDAR REFORM COMMITTEE

month Adhika month The maximum duration of a lunar month, on the Saka A.D. Ksaya other hand, exceeds the lengths of the solar months 1115 1193-94 Pausa Asvina, Caitra Kartika, Caitra only in case of solar Agrahdyana, Pausa and Magha. So 1180 1258-59 Pausa Pausa Kartika, Phalguna a ksaya month is possible only in these three months. 1199 1277-78 Pausa Marga., Phalguna actual intercalary 1218 1296-97 A list is given below showing the 1237 1315-16 Margasirsa Kartika, PhlUguna months occurring during the period Saka 1823 (1901-2 1256 1334-35 L ausa Asvina, Phalguna D. ) on the basis of A. D. ) to Saka 1918 (1996-97 A. 1302 1380-81 Margasirsa Kartika, Vaisakha Surya Siddhanta calculations. 1321 1399-1400 Pausa Kartika, Caitra 1397 1475-76 Magha Asvina, Phalguna Table 21. 1443 1521-22 Margasirsa Kartika, Vaisakha Asvina, Caitra Intercalary months in the present century 1462 1540-41 Pausa 1603 1681-82 Pausa Asvina, Caitra tvaka Saka 1744 1822-23 Pauga Asvina, Caitra 1872 Asadha 1823 bravana 1885 1963-64 Pausa Asvina, Caitra 1826 Jyaistha 1875 Vaisakha It will be observed from the above table that 1828 Caitra 1877 Bhadra according to Surya Siddhanta calculations one ksaya 1831 Sravana 1880 Sravana month occurs on average after 63 years. But one 1834 Asadha 1883 Jyaistha repeat as soon as after 19 years and as late as 1837 Vaisakha 1885* Asvina, Caitra may years. In rare cases they recur after 46, 65> 1839 Bhadra 1888 Sravana after 141 1842 Sravana 1891 Asadha 76 and 122 years. 1894 Vaisakha 1845 Jyaistha Intercalary months according to 1847 Caitra 1896 Bhadra modern calculations 1850 Sravana 1899 Asadha for 1853 Asadha 1902 Jyaistha The lunar calendar proposed by the Committee 1856 Vaisakha l904**Asvina-Phal. religious purposes is based on the most up-to-date 1858 Bhadra 1907 Sravana value of the tropical year and the correct timings of 1861 Sravana 1910 Jyaistha new-moon. As such the intercalary months according 1864 Jyaistha 1913 Vaisakha to these calculations would not always be the same 1866 Caitra 1915 Bhadra as determined from Surya Siddhanta-Cd\cu\aX.ions and 1969 Sravana 1918 Asadha shown above, The intercalary {mala or adhika) and * + these calculations Pausa is Ksaya, Magha is Ksaya. decayed {ksaya) months according to are shown below for Saka years 1877 to 1902. As regards the ksaya months that occurred and according will be occurring during the period from 421 Saka Table 23—Intercalary month (49S-500 A D.) to 1885 iSaka (1963"64 A.D.) a statement to modern calculations. mentioning the is given below showing all such years Saka A.D Intercalary Saka A.D Intercalary Month Month month which is ksaya and also the months which are 1955-56 Bhadra 1896 1974-75 Bhadra adhika in these years. The calculations are based on 1877 Sravana 1899 1977-78 Sravana Surya Siddhanta without bija corrections upto 1500 1880 1958-59 1883 1961-62 Jyaistha 1902 1980-81 Jyaistha A. D. arid with these corrections after that year. 1885 1963-64 Kartika & Caitra (A.grahayana ksaya s Table 22—K§aya or decayed months 1888 1966-67 Sravana 1891 1969-70 Asadha &aka A.D. Ksaya month Adhika months before and after the Ksaya 1894 1972-73 Vaisakha month the 448 526-27 Pausa Kartika, Phalguna Proposal of the Committee about Lunar Calendar 467 545-46 Pausa Kartika, Phalguna According to the Siddhantic rules, the lunar 486 564-65 Pausa Asvina, Phalguna calendar is pegged on to the solar calendar, and so 532 610-11 Margasirsa Kartika, Vaisakha it is the luni-solar calendar with which we are at 551 629-30 Pausa Asvina, Caitra present concerned. It has already been shown that 692 770-71 Pausa Asvina, Caitra the length of the Surya Siddhanta year is greater than 814 892-93 Margasirsa Kartika, Caitra the year of the seasons {i.e., the tropical year) by 838 911-12 Pausa Asvina, Caitra 24 minutes. As a result of this the seasons have 974 1052-53 Pausa Asvina, Caitra. about —

INDIAN CALENDAR 251

the religious fallen back by about 23 days in our solar calendar. The luni-solar calendar by which to the The lunar calendar, being pegged on to the Siddhantic festivals are determined has been pegged on a point 23° 15' solar calendar, has also gone out of seasons by about religious solar calendar starting from solar the same period, and consequently religious festivals ahead of the V. E. point. As this religious year, the luni-solar are not being observed in the seasons originally calendar is based on the tropical go out of the intended. calendar pegged on to it would not seasons to which they at present conform, and so the the religious calendar The solar (saura) month for religious festivals would continue to be observed in the Although the Committee considers that the solar present seasons and there would be no further shifting. be year to which the religious lunar calendar is to The Committee has proposed that the luni-solar the V. E. day, it felt pegged on should also start from calendar should no longer be used for civil purposes a view be too violent ; with that the change would in any part of India. In its place the unified solar in the present day to avoiding any such great changes calendar proposed by the Committee should be used it has been considered expedient religious observances, uniformly in all parts of India irrespective of whether sometime to come any discon- not to introduce for the luni-solar or solar calendar is in vogue in any but only to stop further -increase tinuity in this system, particular part of the country. religious of the present error. The solar year for the calendar with Vaisakha as its first taura month should tropical longitude of the sun now commence when the 5.8 INDIAN ERAS amounts to 23° 15\ This saura month will determine the date precisely we the corresponding lunar months required for fixing Whenever we wish to define a of an era, dates of religious festivals. The lengths of such have to mention the year, generally current month, months, which are also fractional, are stated below, besides the month and the particular day of the well- giving the lengths according to the Surya Siddhanta and the week-day. This, enables an astronomer, place the event calculations compared with the corresponding modern versed in technical chronology, to In international practice values. correctly on the time-scale. the Christian era is used, which is supposed to have Table 24—Lengths of Solar months started from the birth -year of Jesus' Christ. But as of the Religious Calendar. mentioned in Chapter II, it is an extrapolated era which Months Lengths of came in use five hundred years after the birth of the to Surya Modem Saura Long, of Accorditig Founder of Christianity, and its day of starting may be Siddhanta Value Mdsa Sun widely different from the actual birthday of Christ, (1950 A.D.) about which there exists no precise knowledge. d h d 20h 55m Vaisakha 23° 15'— 30 22 30 In India, nearly 30 different eras were or are used 31 6 39 Jyaistha 53 15— 31 10 5 be classified as follows : 10 53 which can Afladha 83 15— 31 15 28 31 8 22 Eras of foreign origin, e.g., the Christian era, Sravana 113 15— 31 11 24 31 (1) and the Tarikh Ilahi of Akber. Bhadrapada 143 15— 31 27 30 23 51 the Hejira era, 10 36 30 11 51 list Asvina 173 15— 30 (2) Eras of purely Indian origin, given. 29 21 27 29 23 41 Kartika 203 15— into existence in the (3) Hybrid eras which came Margasirsa 233 15— 29 11 46 29 14 33 wake of Akber's introduction of Tarikh Ilahi. 40 Pausa 263 15— 29 7 38 29 10 Table 27 shows purely Indian eras, with their Magna 293 15— 29 10 45 29 12 57 starting years in terms of the Christian era, the elapsed Phalguna 323 IS- 29 19 41 29 20 54 30 8 33 year of the era*, the year-beginning, solar, lunar or Caitra 353 IS— 30 8 29 both solar and the lunar as the case may be, the parti- 365 6 13 365 5 49 cular regions of India where it is current. Inspite of the ages of the eras, the The. lengths of the months according to the Surya the apparent diversity in earlier, as the of calendarical calculations associated with Siddhanta are the same as shown . methods

; to be more accurate same month was used by the S. S. for both the each era are almost identical follow the rules given in purposes. But the modern value, is different from only slightly different and Siddhantas, Surya, Arya and that shown before, due to the fact that a different either cf the three of months. three methods differ but slightly. point is taken here for the beginning Brahma. The for all eras have "elapsed The modern value is, however, not fixed * Generally, but not always the Indian 1876 of 6aka era would be, if we followed times, but it undergoes slight variation as explained years". Thus year western convention, year 1877 6aka (current). previously. the

C. E. —40 REFORM COMMITEE 252 EEPORT OF THE CALENDAR Each cen- the centuries in the total period of the cycle. The apparent antiquity of certain eras, e.g., Asvinl, Bharayi, rather deceptive, tury is named after a nak§atrai viz., Kaliyuga or the Saptar& are however of years within the century is either in the Vedic etc ; and the'number for these eras are not mentioned of year of the a work of the generally mentioned, so that the number literature or even in the Mahabharata ( was in use in proof, however, era never exceeds 100. This era 4th to B.C. ). The best fact this era has in ancient Kashmir and neighbouring places. In that no eras were used in date-recording Great Bear) in the which give 'con- no relation with the seven gsis (the India is obtained from "Inscriptions" There is date-recording sky or with any actual nak?atra division. temporary evidence' of the method of era. composed. of opinion as to the beginning of the the time when the inscription was difference in use at the According to Vrddha Garga and the the oldest inscriptions so far discovered In India, tenth century named after Magha the Emperor starting year of the and deciphered satisfactorily are those of are 3177 B.C., 477 B.C. and 2224 A.D. of the different the earlier Indus valley Asoka (273 to 227 B.C.) ; for according to Varahamihira the third deciphered and no cycles, when seal recordings have not yet been century named Krttika begins. The beginning can be referred to the time- inscriptions or seals which the years of Varahamihira s Magha century of between 2500 B.C. (time of Indus valley civili- period however 2477 B. C, 224 A. D. have yet been different cycles are zation) and 250 B.C. ( time of Asoka ) inscriptions and 2924 A.D. brought to light. Asoka mentions in his his coronation. the Yudhisthira era started only the number of years elapsed since The Pancjava Kala or the day No month, week-day or the serial number of from 2449 B.C. according to Varahamihira. Asokan ins- month is mentioned. A typical in the The so-called Yudhisthira era (2449 B.C.) is given time references is given in § 5. 5. cription giving by Kalhana, chronicler of Kashmir (1150 A.D.), who used in the re- Continuous erak first began to be quotes the date from Vrddha Garga, an astronomer kings who reigned in occur cords of the Indo-Scythian whose time is unknown. This era also does not North-Western India bet- prior to modern Afghanistan and in any inscription or any ancient treatise ween 100 B.C. to 100 A.D. Kalhana (1150 A.D.). Prof. M. N. Saha has shown that the Kaliyuga or Saptam the Krttikas are in many places What is then the origin of in the Mahabharata go back to thousands of first of the naksatras and are very nearly era given in Table 27 which taken as the - to show presently the vernal equinox. If we calculate years before Christ ? We are going coincident with invented much later incidents on this basis, the date that they are extrapolated eras the date of the M.Bh. nearly 2449 B.C. than the alleged starting year. comes out to be very records that date-recor- incidents It is clear from historical It, however, niether proves that the the time of the ding by an era in India started from mentioned in the M.Bh., if they were actual of Ujjain. But epic was Kusana emperors and Saka satraps occurrences, took place in 2449 B.C., for the this respect, for none B.C. as we India cannot be singled out in not certainly put to writing before 400 viz., Egypt, Babylon, on 226. It is of the great nations of antiquity, know from a verse already mentioned p. used a continuously could be Assyria or later Greece and Rome, inconceiveable to think that the dates their history. The when running era till rather late in remembered correctly for over 2000 years, with the develop- astro- introduction of the era is connected writing was in a very primitive state. The which came rather late which ment of the sense of 'History* nomical references in the battle scenes, from the date of to all civilized nations. certain writers very laboriously deduce these occurrences, are most probably later interpola- occurred tions, on the supposition that the incidents about 2449 B.C. There is no inscriptional record Critical Examination of Indian Eras regarding the use of Yudhisthira era or Pan(}avakala.

Here we are examining critically the claims of a earlier, e.g., Kaliyuga Era few eras, which are supposed to date much (a) The believed to have the Kaliyuga era which is commonly which It is easy to show that the Kaliyuga era introduced in 3102 B.C., the Saptar$i era, and heen purports to date from 3102 B.C. is really an extra- the historian the Pa^ava-Kala mentioned by KalWa, polated era just like the Christian era, introduced and supposed to of Kashmir, who wrote in 1150 A.D., long long after the supposed year of its beginning. be dating from 2449 B.C., and others. It is first mentioned by Xryabha{a, the great The Saptarsi era commoly known as Lokakala or 3600 has such astronomer of ancient Pataliputra, who says that Laukika Kala is measured by centuries and 27 INDIAN CALENDAR 253

years of the Kaliyuga had passed when he was 23 should also bo a total eclipse of the Sun ; but no such

years old which is Saka year 421 (499 A. D.). It is not things happened at that time. The beginning of the mentioned earlier either in books or in inscriptions. Kaliyuga was the midnight at UjjayinI terminating the The first mention of this era in an inscription is found 17th February of 3102 B.C., according to Surya Siddhanta in the year 634-35 A.D., the inscription being that and the ardltanttrika system of Aryabhata's astronomy as of king Pulakesln II of the Calukya dynasty of described in the Khatjdaklmdyaka of Brahmagupta. Again this Kaliyuga is BadSml, or somewhat earlier in a Jain treatise. It said to have begun, according to the was most probably an era invented on astrological A.ryabha\iya from the sunrise at Lanka (supposed to be on the equator and on the same meridian with Ujjain) grounds just like the era of Nabonassar, by Sryabhata —from the mean sunrise on the 18th Feb., 3102 B.C. or some other astronomer, who felt that the great antiquity of Indian civilization could not be described Now astronomical events of the type described above by the eras then in use (Saka, Chedi or Gupta era), and more specially the conjunction of the sun and the moon as they were too recent. cannot happen both at midnight and at the next mean sunrise. This shows that this Kaliyuga had an unreal beginning. What were these astrological grounds ? The researches of Bailey, Bentley and Burgess have The astrological grounds were that at the beginning shown that a conjunction of all the 'planets' did not happen of the Kaliyuga, the sun, the moon and the planets at the beginning of this Kaliyuga. Burgess rightly

were in one zodiacal sign near the fixed Siddhantic observes : 'It seems hardly to admit of a doubt that tlie Mesadi which according to some authorities is epoch (the beginning of the astronomical Kaliyuga) was 180° arrived at by astronomical calculation carried backward. ( Piscium % but according to others is from Citra or a Virginis. This was probably a back calculation We also can corroborate the findings of above research- based on the then prevailing knowledge of planetary ers in the following way and by using the most up-to-date motion, but has now been found to be totally wrong, equations for the planetary mean elements. recalculated with the aid of more accurate when Now the precession of the equinoxes from 3102 B. C. motion. modern data on planetary We quote from to 499 A. D. or Aryabhata's time works out to have been Ancient Indian Chronology, pp. 35 39 by Prof. P. C. = 49° 32' 39". The mean planetary elements at the beginning

Sengupta, who has given a full exposition of Burgess's of the Kaliyuga, i.e., 17th Feb., 3102 B.C., UjjayinI mean views on this point, with recalculations of his own. time 24 hours, are worked out and shown below. We have

Table 25—Longitudes of Planets at Kali-beginning.

Mean Tropical Longitude at the same The same as assumed in Error in the assumption longitudes on time measured from the the Ardhardtrika system of Aryabhata and also of Planet Feb. 17, U.M.T. Vernal Equinox of 499 at the same time as the modern Surya- j 24 hrs., 3102 B.C. A.D,, i.e., Aryabhata's before and also at next Siddhanta and the time. j (Moderns.) sunrise. KUandakhadya ka . mean j

Sun 301° 40' 9.22" 351° 12' 48" 0° 0' 0" + 8° 47' 12" Moon 305 38 13.81 355 10 53 + 4 49 7 Moons Apogee 44 25 27.66 93 58 7 90 - 3 58 7 Moon's Node 147 20 15.05 196 52 54 180 -16 52 54 Mercury 268 24 1.65 317 56 41 + 42 3 19 Venus 334 44 50.25 24 17 29 -24 17 29 Mars 290 2 54.67 339 35 34 + 20 24 26 Jupiter 318 39 45.74 8 12 25 - 8 12 25 282 24 15.07 331 56 54 3 6 Saturn I + 28

" 9 ' Astronomical Kaliyuga an Astronomical Fiction added 49° 32' 39" to these mean tropical longitudes arrived at from the rules used, so aw to got tho longitudes measured At the beginning of the astronomical Kaliyuga, all the from the vernal equinox of Aryabhata's time. mean places of the planets, viz., the Sun, Moon, Mercury, Venus, Mars, Jupiter and Saturn, are taken to have been in Hence we see that tho assumed positions of the moan

conjunction at the beginning - of the Hindu sphere, the planets at the beginning of the astronomical Kaliyuga tvoro moon's apogee and her ascending node at respectively a really incorrect and the assumption was not a reality. But quarter circle and a half circle ahead of the same intial of what use this assumption was in Aryabhata's time, i.e.,

point. Under such a conjunction of all the planets, there 499 A.D., is now set forth below. :

254 REPORT OF THE CALENDAR REFORM COMMITTEE

Aryabha^a says that when he was 23 years old, 3600 about 57 B. C. Moreover a critical examination of years of Kali had elapsed. According to his Ardharatrika inscriptions show the following details about this era. system The earliest mention of this era, where it is 3600 years=»'l/l200 of a Mahayuga = 1314931.5 days. definitely connected with the name of king Vikramtf-

Again according to his Audayika system : ditya is found in an inscription of one king Jaikadeva 3600 years =1/1200 of a Mahayuga^ 1314931.25 days. who ruled near Okhamandal in the Kathiawar State.

Hence according to both these systems of astronomy of The year mentioned is 794 of Vikrama era, i.e., 737 Aryabhata, by counting 3600 years from the beginning of A.D. In a subsequent inscription, dated 795 V.E. it the astronomical Kali epoch, we arrive at the date March is also called the era of the lords of Mslava. So the 21, 499 A.D., tjjjayini mean time, 12 noon. The unreality Vikrama era and the era of Malava lords are one and

of the Kali epoch is also evident from this finding. the. same. Tracing back, we find the Malavagana era However, the position of mean planets at this time work in use by a family of kings reigning at Mandasor, out an given in table 26 below. Rajputana between the years 461-589 V.E., as feuda-

Table 26—Longitudes of Planets at 3600 Kaliyuga era.

Date : March 21, 499 A.D Ujjayini Mean Midday.

Long. Mean Long. Mean . Error in the Mean Long. Planet Ardharatrika Audayika Audayika Moderns. system. system. system. Sun 0° 0' 0" 0° 0' 0" 359° 42' 5" +17' 55" Moon 280 48 280 48 280 24 5a +23 8 Moon's Apogee 35 42 35 42 35 24 38 +17 22 Moon's Node 352 12 352 12 352 2 26 + 9 34 Mercury 180 186 183 9 51 +2° 50' 9" Venus 356 24 356 24 356 7 51 +16 9 Mars 7 12 7 12 "6 52 45 + 19 15 Jupiter 186 187 12 187 10 47 + 1 13 Saturn 49 12 49 12 48 21 13 +50 47

the beginning of the It is thus clear that Hindu tories to the Imperial Guptas ( 319-§50 A.D. ). They astronomical Kaliyuga was the result of a hack calculation call it not only the era of the Malava tribe* but also wrong in its data, and was thus started wrongly. alternatively as the Krta era. A number of inscrip-

It is also established that the astronomical Kaliyuga- tions bearing dates in the Krta era have been found in

reckoning is a pure astronomical fiction created for facilita- Rajasthan, and the earliest of them goes back to the ting the Hindu astronomical calculations and was designed year 282 of the Krta era (The Nandsa Yupa inscription to be correct only for 499 A.D. This Kali-reckoning described by Prof. Altekar, Epigraphia Indica, Vol.

cannot be earlier than the date when the Hindu scientific XXVII, p. 225). Siddhantas really came into being. As this conclusion From these evidences, it has been concluded by

JUjasthan, conquered the city of Kanauj about 824 (c) The Saka Bra A.D., they brought the Vikrama era from their original Hie Saka Era is the era par excellence home, and it which has became the current era all over northern been used by Indian astronomers Inciia except the all over India in their eastern region, and was used by all calculations since the time of the astronomer Rajput dynasties of medieval times. Varaha- mihira (died 587 A.D.) and probably earlier. The The months of the Vikrama era are all lunar, and Indian almanac-makers, even now, use the Saka era the first month is Caitm. The months begin after the for calculations, and then convert the calculations to full-moon but the year begins 15 days after the full- their own systems. moon of Phalguna, i.e. after the new-moon of Caitra* This era is extensively But for used over the whole of India astronomical calculations, it is pegged on to a except in Tinnevelly and part of Malabar, and is more solar year, which starts on the first of solar Vaisakha, widely used than any other era. It is also called Saka theoretically the day after the vernal equinox. The Vikrama Kala, Saka Bhtlpa Kala, Sakendra Kala, and Salivahana era is current also in parts of Gujrat, but Saka and also Saka Samvat. there the year Its years are Caitradi for begins in KSrttka and the months are luni-solar reckoning and Me$adi for solar reckoning. amanta, which corresponds to the Macedonian month In the luni-solar reckoning the months of Dios, the are purnirnanta and epoch is just six months later. in the North and amanta in Southern Thus the India. The western and northern varieties of the reckoning of the Saka era begins with the vernal equi- Vikrama era follow respectively the Macedonian and nox of 78 A.D., and is measured by expired years, so Babylonian reckonings (see § 3.3), the year of starting the year between the vernal equinox of 78 A.D. to that is years later 255 than that of the Seleucidean era. of 79 A.D. is zero of Saka era. In some pancangas or The conclusion is that the champions of the Southern India the current year is however seen to be Vikrama era have still to prove the existence of king used instead of the elapsed year, where the number of Vikrama of Ujjain. Early inscriptions show that the year of the era is one more than the era in general use method of date-recording is not typically Indian as in But we are not yet sure about the origin of this the Satavahana inscriptions but follow the Saka-KusSna era. It has been traced back to the Saka satraps of method, which fpllows the contemporary Graeco- Ujjain, from the year 52 (130 A.D.) to the end of the Chaldean method. It was therefore a foreign recko- dynasty about 395 A.D. But in their own records, ning introduced either by the Greeks or Sakas, or they merely record it as year so and so, but there is an Indian prince or tribe who had imbibed some not the slightest doubt that the era used by them Graeco-Chaldean culture, but was adopted by the subsequently became known as the Saka era (vide § 5.5). Malava tribes who migrated from the Punjab to Rajas- The Old and the New Saka era. than about the first century B.C. The association with king The dates given by different authorities about the a Vikrama occured 800 years later, and is starting year of the old Saka era mentioned in probably due to lapse of historical memory, for the § 5.5

vary from 155 B.C. to 88 B.C. as given below : only historical king VikramSditya who is known to have crushed the Saka power in Ujjain, was king Konow ; 88 B.C. (date of death of Mithradates II, the Candragupta II of the Gupta dynasty powerful Parthian emperor who is / (about 395 A.D.). Before this, the Saka dynasty in Ujjain had said to have subjugated the Sakas). reigned almost in unbroken sequence from about 100 Konow has proposed a number of other dates.

A.D. to 395 A.D., and ^had used an era of their Jayaswal : 120 B.C. :

own, later known as the 'Saka' era. All the Gupta Herzfeld : 110 B.C. : Settlement of the Sakas in

emperors from Samudragupta, had an "Aditya" title, Seistan by Mithradates II.

and many of them had the title "Vikramaditya" so Rapson : 150 B.C. : Establishment of the 8aka that the Gupta age was par excellence the age of kingdom of Seistan.

Vikramadityas. But all the Gupta emperors use in Tarn : 155 B.C. : Date of settlement of the Saka their inscriptions the family era called the Guptakala immigrants in Seistan by which commemorated the foundation of Gupta empire Mithradates I. (319 A.D.). The association of the Malava era with king Recently Dr. Van Lohuizen de Leeuw has discus- VikramSditya, and assignment of king VikramSditya sed the starting point of this era in her thought-provok- to Ujjain, was due to confusion of historical memory ing book 'The Scythian Period of Indian History*. She has not infrequent in Indian history. It may be' mentioned rejected all the above dates, and fixed up 129 B.C. as that the Vikrama era is never used by Indian astro- the starting date of the old Saka era. She identifies this nomers for their calendaric calculations, for which year as the one in which the Sakas, descending from puapose the Saka era is exclusively used. the Trans-Oxus region, attacked the Parthian empire —

OF THE CALENDAR REFORM COMMITTEE 256 REPORT be The points given in § 5.5 and above may emperor Phraates II was defea- in which the Parthian was summarized as follows : and the rich province of Bactna ted and killed, attacked to com- Sakas starting from Central Asia the Sakas. They founded an era (a) The occupied by overcame which their the Parthian empire in 129 B.C., and their victory over the Parthians memorate probable expanded and put an Parthian resistance by 123 B.C. It is very successors took to India, as they their principalities in Afghanistan that they started an era to commemorate end to the Bactrian Greek that the old to power in Bactria from 123 B.C. They used north-west Punjab. She suggests accession and methods of the Kusanas, who were Macedonian months and Graeco-Chaldean Saka era was also used by of as prevalent in the Seleucid tribe, but from the time calendaric calculations after all a Sakish ruling and Parthian dominions. Probably the era was some- Kaniska with hundreds omitted. leader. times named after Azes, who was probably their in its Saha has supported this theory with later Dr. M. N. But this Azes is not to be confounded era was founded features, but he thinks that the between 40 main Azes I or Azes II, who reigned in Taxila records that he shows from historical of its in 123 B C , for B.C. and 20 B.C. Within the first 200 years entered Bactria first in 129 B.C. and era. I the Sakas assailed era was alternatively called the Azes and starting/the year conflict with the Parthians, ! into a seven archaeologists as the 123 B.C., when the Par- (b) This Saka era ( known to finally conquered Bactria in ! emperors and Saka and killed. Saka era ) was used by the Saka emperor Artabanus II, was defeated old thian the time- This Was satraps in their Indian territories, but Probably the Sakas then founded their era. influenced by Indian Dr. Van Lohuizen de reckoning began to ba gradually also called the era of Azes. They began to use Indian months alter- accepted Sana's suggestion. customs. Leeuw has Pur'nimanta natively with Macedonian months and settled appears the first This hypothesis, though not finally months in place of Am&nta months. During the following in good deal of probability, for years, the hundreds were sometimes omitted, to- have , a 200 the era. reasons : the use of is nothing but the (c) The so-called Kaniska era Saha points to the fact that Indian classics, Dr. omitted. B.C. to the old Saka era with 200 which can be dated from the third century races in what is The Saka era was used by the house of Castana second century A.D., mentions three (d) the Sakas, with 200 omitted, but gradually they forgot modern Afghanistan and N. W. India, viz., of Ujjain attained to the origin of the era and continued their own reckoning the Yavanas, and the Pallavas, who the order in which they are without further omission of hundreds upto the end of status of ruling races. The over UjjainI about 395 A.D. As mentioned denotes correct chronological sequence, for the Saka satrapal rule of their chronological Indian astronomers were mostly of foreign they are arranged in the order the early mentioned as a Brahmana) the astronomical appearance in history, the gakas being origin (viz. Sakadvlpi (518 B.C.). But necessary for compiling the calendar were subject race in Darius's inscription reckonings first to attain the status using the Saka era and Graeco-Chaldean the Yavanas (Greeks) were the carried out the date of foundation The blending of Graeco-Chaldean of a ruling race, from 312 B.C., astronomy. in the west was about the early years of the of the Seleucid empire, whose power astronomy as known calendarica^ features overthrown by the Parthians, or Pehlevis (Pallavas of Christian era with older Indian Jyotisa. The Sakadvlpi Indian classics) in 248 B.C. formed the basis of Siddhanta Brahmins also brought to India horoscopic astrology ruling races of Yavanas and Pallavas a custom Both these using the Saka era exclusively in horoscopes, own, viz., the Seleucidean era from used eras of their which has persisted to this day. These facts explain the Parthian era from 248 B.C. Did the 312 B.C., and the pre-eminence of the Saka era. the last to attain third race, the Sakas who were their own ? It status of a ruling race ever use an era of it became the would be surprising if they did not, for (d) Other Eras status of ruling fashion for all races, who attained the .—The Buddhists of Ceylon Sakas, Buddha Nirvana Era people, to have eras of their own. The early the first century B.C. the influenced by their have been using since as their records show, were deeply Buddhist Nirvana* era, having its era-beginning in 544 neighbours to the west, viz., the Parthians who adopted found in use on they B.C. This era has not however been Greek culture, and their coin-records show that for a solitary instance in therefore most the Indian soil, except also adopted Greek culture, and inscription of Asokachalla Dev found at Gaya the Graeco-Chaldeah method of date an prbbably. Buddhist Nirvana dated in the year 1813 of the recording. :

INDIAN CALENDAB 257 era — 1270 A.D. Most of the antiquarians however called Parganati'AMa, reckoned from the time of put the date of Nirvana in 483 B.C. The origin of disappearance of Hindu rule. the Buddha Nirvana era used in Ceylon has not yet After the introduction of Tarikh Ilahi, the people been satisfactory explained. of Bengal began to use the Sarya Siddhanta reckoning,

: and the solar year. Bengali thus The Gupta Era —This era was clearly ] established The San had a by the founder of the Gupta dynasty (Candragupta I) hybrid origin ; to find' the current year of the Bengali to commemorate the accession to imperial power of San, we take Hejira year elasped in 1556, i.e., 963 and his family, about 319 A.D., and was in vogue over the add to it the number of solar years. Thus 1954 whole of Northern India from Saurashtra to Bengal A. D. is 963 A.D. + (1954 -1556) -1361 of Bengali San, during the days of their hegemony (319 A.D.-550 A.D.). After the decay of their empire, the era was continued hybri eras by their former vassals, the Maitrakas of Vallabhi and Other was in use in parts of Guzrat and Rajputana up to A number of other hybrid eras formed in a similar the thirteenth century. Its use in Bengal was discon- way to Bengali San is mentioned in the table (No. 27) tinued from about 510 A.D. with the disappearance Amli and Vilayati in Bengal and Orissa, the various of Gupta rule first in South Bengal, then over the Fasli or harvest years in Bengal, Deccan, and whole of Eastern India. In the (ancient Bombay. Madhyadesa), it was driven out by the Harsa era, All the other eras mentioned as hybrid in the which had a short period of existence, 606-824 A.D., chart were formed in a similar way, and the slight when the city of Kanauj was occupied by king differences are due to mistakes in calculation, or Nagabhata of the PratihSr dynasty, who hailed from differences in the time of introduction. While the Rajasthan. The Pratihars brought with them the Bengali San has Mesadi as year-beginning, others Vikrama era, . which had been current in Rajasthan, have taken the year-beginning to be coincident with and this became the great era of the north, used by some important mythical event of local provenance, all medieval Rajput dynasties, except those belonging e.g., the year-beginning of the Amli era used in to the eastern region. Orissa, viz., the 12th lunar day of the light half of the

month of Bhadra is said to represent the birth date in Eastern India Eras of king Indradyumna, the mythical king who is said

Most parts of Bengal were under the Gupta to have discovered the site of modern Puri. The emperors, and used the Gupta era during their great temple of Puri was actually built by king hegemony (319-510 A.D.). But Gupta rule disappeared Anyanka Bhim Dev of the dynasty about 1119 held in as mentioned above from major parts of Bengal from A.D., and kings of this dynasty who sway Orissa from 1035-1400 A. D, used the Ganga era,

Palas ; the Senas were migrants from the south thousands from their previous reckonings. In South it solar { Karnata-Ksatriyas ), where they were familiar with Malabar begins with the month Simha and the Saka era, but it was not used in royal records in North Malabar with the solar month Kanya. which continued to use regnal years. The Vikrama The era started from 825 A.D.

Samvat never became popular in Bengal, or Eastern The Jovian cycle : In Southern India the years are

India. After Mohamedan conquest, Bengal was left named after the name of the Jovian year and so it also without an era. For official purposes, Hejira was serves the purpose of an era of a short period, viz., 60 used, But the learned men used the Saka era, and the years, after which the years recur. Details about common people in certain parts used a rough reckoning, Jovian years will be found in Appendix 5-E. ( <

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The Seasons

We have seasons because the celestial equator is oblique The amount of daylight received at any place determines to the sun's path (or the ecliptic), or in modern parlance, the season. When we have maximum , we have

the axis of rotation of the earth is not perpendicular to its the hot season. When we have minimum sunlight, we shall orbit, but inclined at an angle of 66*°. This causes varying have winter. The other seasons come in-between. Bain, amounts of sunlight to fall on a particular locality through- frost, etc., are secondary effects produced by varying out the year. If the earth's axis were perpendicular to the amounts of sunlight, and of the atmospheric conditions

ecliptic, in other words the obliquity were zero, every stimulated by the sunlight received. The sun is the sole portion of the earth from the equator to the pole would arbiter of the seasons. shade. have had 12 hours of sunlight, and 12 hours of Hence the definitions of seasons as given by the ancient There would have been no seasons on any part of the earth, astronomers, whether Western and Indian, which base them just as we have now for places on the earth's equator, where on the cardinal days of the year, are the only correct

we have no variation of season throughout the year, because definitions. A system which deviates from this practice is the day and night are equal for all days of the year. wrong.

It can be proved from spherical trigonometry that the The majority of the Indian calendar makers have not,

duration of sunlight for a place having the latitude is however, followed this definition. The reason is more given by psychological than scientific. For along with astronomy, 1 12+tV Sin" ( tan

where 8= declination of the sun on that day ; 8 being up its canons on the basis of a fixed zodiac commonly known counted positive when it is north of the equator, and as the Nirayana system. The effect of this will be clear negative when south. from the following example.

If S is negative, i.e., when the sun is south of the The winter season (ki&ira) begins on the winter solstice- equator, the second term of the above equation is negative, day which date is also marked in all the Siddhdntas by and daylight will be of less than 12 hours' duration. sun's entry (safnkranti) into Makara. This event occurs on This holds up to the latitude of ^— € = 66*°, i.e., the the 22nd December. But the Indian calendar makers, following the nirayana system, state that the Makara beginning of the arctic zone. Between the arctic circle Safnkranti happens not on the 22nd December but on the and the north pole, the sun will remain constantly above 14th January and the winter season also begins on that the horizon more than twenty-four hours for several days date. Similar is the case with other seasons also. The result together during the year. Thus at a place on 70° north is that there is a* clear difference of 23 days in the reckoning latitude, the continuous day is observed for 64 days from of seasons. The later Hindu savants tried to reconcile the 21st May to 24th July, at 80° north latitude it is for 133 two points of view by adopting a theory of trepidation, days from 17th April to 28th August, at the north pole it which after Newton's explanation of precession, has been is for six months from 21st March to 23rd September. - definitely shown to be false. It is therefore absolutely For a person on the north pole, the sun will appear on. wrong to stick to the nirayana system. the horizon on the vernal equinox day, and will go on circling round the sky parallel to the horizon and rising It is however refreshing to tfnd that a few Indian savants definitely stood against the false every day a little up, till on the solstitial day, he attains have nirayana the maximum altitude, viz., 23° 27'. After that the sun system. The earliest were MuSjala Bha^a (932 A.D.), a will begin to move down and on the day of autumnal South Indian astronomer and Prthudaka Svami (950 A.D.), equinox, will pass below the horizon. Thus for six who observed at Kuruksetra. One of the latest was Mm. months, from 21st March '(V.E.) there will be continuous Bapudev Sastri, 0. I. R, Professor in the Sanskrit College, day for a person on the north pole, and from the 23rd Sept, Banaras, who wrote in 1862, as follows :

(A.B.) to the. next 21st March (V.E.), there will be a "Since the nirayana safnkrantis cannot be determined continuous night for six months. with precision and without doubt and since the nirayana

The position described above is for the northern hemis- raiis have no bearing on the ecliptic and its northern and phere, viz.j for those dwelling north of the equator. In the southern halves, we must not hanker after nirayana system

southern hemisphere the position is just reversed ; when for the purposes of our religious and other rites. We must the day is longer in the northern hemisphere, it is shorter accept sayana and our religious and other rites should be in the southern hemisphere. performed in accordance with the sayana .system".

0. R. -41 259 260 REPORT OF THE CALENDAR REFORM COMMITTEE

great man who The figures in the third column of the table below denote It is not generally known that another the angular distance of the sun from the astronomical first probably felt that the nirayaria system gave us wrong point of Aries (the V.E. point) indicating the beginning of seasons, was Pandit Ishwar Chandra Vidyasagar. We in Indian the month. learn from his biography that he had a course College, astronomy while he was a student of the Sanskrit The two months constituting the 'Spring Season' would Vasanta r Spring Calcutta about 1840. Before him, the thus include the day from Feb. 19 or 20 to April 19 or 20. Madhava, i.e., Caitra insisted of the months Madhu and The Vernal Equinox day (March 21) would be just in the India. But from 1850, and Vai&akha, as in other parts of middle. The same is the case with other seasons each of Vidyasagar began to bring out text books in Bengali in two months. which he retarded the seasons by a month, e.g., he said that the spring consists of Phalguna and Caitra, and no one Table 28. notion goes, questioned it. So in Bengal, as far as popular parts it -30° season starts on Feb. 12, while in other Madhu 1 Honey or sweet spring Vasanta Spring while the correct Madhava J o The sweet one starts on March 14, a month later, is Feb. 19. Sukra 1 30 Illuminating astronomical date according to Hindu Siddhantas Summer l^uci J 60 Burning Bengal thus commits a negative mistake of 7 days while days. Nabhas ) 90 Cloud other parts of India has a positive mistake of 23 Rains Nabbasya J 120 Cloudy position in respect of all the seasons is stated The 1 150 Moisture Autumn Isa below : Urja J 180 Force Sahas \ 210 Power Late Autumn! 240 Powerful Sun's longitude Correct date Present date Sahasya f Penance, mortification, 30° Apr. 19 Mar. 14 to May 13 Tapas 270 Vasanta ( ) 30° to Feb. 19 to - Winter fire (Spring) Tapasya 300 Pain (produced by heat) Grisma 30° to 90° Apr. 20 to June 20 May 14 to July 15 by the common people, (Summer) These names were seldom used 15 but they were very popular with poets. Varsa 90° to 150° June 21 to Aug. 22 July 16 to Sep.

(Rains) The figures in the second column of table No. 29 210° Aug. 23 to Oct. 22 Sep. 16 to Nov. 15 Sarat 150° to denote the angular distance of the sun on the ecliptic, the (Autumn) origin being the first point of Aries, We have described 210° 270° Oct. 23 to Dec. 21 Nov. 16 to Jan. 12 Hemanta to in § 4.5 how an idea of the ecliptic was derived from night (Late Autumn) observations of the sky and observation of eclipses, and 270° 330° Dec. 22 to Feb. 18 Jan. 13 to Mar. 14 Sisira to how it came to be used as a reference plane from very (Winter) ancient times.

The Indian definition of the seasons, though was based In continuing to follow the nirayana system, the Hindu on the cardinal days, was different from the definition of the calendar makers are under delusion that they are following westerners who divided the year into four seasons each of the path of . They are aerially committing the three months Winter, Spring, Summer and Autumn, starting whole Hindu society to Adharma. from*the four cardinal days. The ancient Indians divided covering the north-ward journey of the sun The period the year into six seasons each of two months as given in in Indian astronomy as the UttarayaT^a was known the table below. The spring season did not start with the north-ward passage and it consisted of the Winter, i.e., vernal equinox, as already stated but a month earlier and it Spring and Summer. It is the period from winter solstice was extended a month later, and so for every season. to summer solstice, and vice-versa, the period from summer solstice to winter solstice was known as the Daksii^ayana, Rains, Autumn i.e., southward passage and it consisted of Table 29. and Hemanta. Indian Seasons Tropical Month-names Lunar Month-names The names of months given in the second column of Spring (-30° to 30°) Madhu & Madhava Caitra-Vaisfikha Table No. 28 are found first in Taittiriya Safnhita, and they Summer (30° to 90°) &ukra & f§uci Jyaig^ha-Agatha are tropical, because they attempt to define the physical RainB (90° to 150°) Nabhas & Nabhasya Sravana-Bhadra months. characteristics of the Autumn (150P to 210°) Isa & Orja Asvina-Kartika Madhu means. 'Honey' and the name indicates Late Autumn 5 that the month was pleasant like honey. (210 to27(P) Sahas & Sahasya Agrahayana-Pausa Winter (270°to330e) Tapas & Tapasya Magha-Phalguna Madhava... means - Honeylike' or 'Sweet one'.

The names are thus expressive of the pleasantness of the The early Greek astronomers have left records about of the year spring season. their successive attempts to measure the length INDIAN CALENDAK 261

as is evident used the gnomon. the sun crossed the summer solstice (June 22), correctly. It is now known that they all Cloud-Messenger. seasons and of the from the lines in Kalidasa's MeghadUta or Measures of the length of the different are 'given in the year by some of their eminent astronomers Pratyasanne Nabhasi dayitajivita lambanarthi table (No. 30) below. Jimutena svakusalamayim harayi^yan pravrttim. measured ' the length ot The Chaldeans must have also was imminent, Translation : When the month of Nabhas somewhat earlier or the year by the same method, either just marking the onset of monsoon ), etc.** their names, ( simultaneously with the early Greeks, but survived. But if in Or in the Bamayana, Ayodhyakay> in the case of Spring, by whole sky was overcast day to the days from the day next to the yernal equinox in);.-.. variable from summer solstice day. The number would be WiDter solstice set in with the month of Tapas, - which taking the year, but a correct value was found by year t6 means penance. The winter solstice as mentioned above the mean. observations for a number of years and taking was the time from which the yearly sacrifices started. The lengths obtained by early astronomers are : The month names in the last column of table (No. 29) Table 30. are 'lunar', but they were linked to the solar months. They Total Spring Summer Autumn Winter are now in universal use all over India to denote days days days days days the two varieties are solar as well as lunar months ; but 94.50 92.73 88.59 89.44 365,26 Chaldean ... distinguished by the adjectives 'Solar' or 'Lunar*. Euctemon(432B.C) 93 90 90 92 365 90 365 Calippos (370B.C) 94 92 89 Both the European and Indian definitions of seasons Correct values are scientific as they are based on the cardinal days. The 88.58 91.29 365.25 1384 B.C. ... 94.09 91.29 for difference in nomenclature is trivial. The ancients early discovered that the seasons were of The Length of the Year : The length of the year, as unequal length, but they were ignorant of the physical found counting the in India mentioned earlier, must have been by reasons. These exact definitions of seasons, both another, or one solstice and are very number of days from one equinox to and in the West, were arrived at very early, but the true to another. important for accurate calendar-making ; the succeed- meaning of these definitions were forgotten in In actual practice, the number of days of the year, ing periods in India. counted in this way would vary between 365 and 366. In whole-numbered, In European astronomy, which is derived from Graeco- the early stages, the length of the year was of Vedanga Jyotisa period had a year of : 366 Chaldean astronomy, we have : but Indians days. Later when they came to a rigorous definition of the Spring 0°— 90° from V.E. to S.S. year, they realized that the number of days was not whole, Summer 90°—180° " S.S. to A.E. involved fractions. Probably the attempt at determin- Autumn 180°—270° " A.E. to W.S. but ing the exact length of the year involving fractional Winter 270°—360° " W.S. to V.B. numbers was obtained by adding up the lengths for a According to this scheme, the Bainy season consisting and taking the mean. formally set in when number of years, of months of Nabhas and Nabhasya APPENDIX 5-B

The Zero-point of the Hindu Zodiae

position of the V.E. point at the The Zero-point of the Hindu Zodiac : By this is meant have been given taking the possible to the Vernal Equinoctial Point (first point of Aries) at the observer's time as. the fiducial point. It is the S.S., if time when the Hindu savants switched on from the old locate it, as Burgess had shown in his edition of longitude of Vedaiiga-Jyoti$a calendar to the Siddhantic calendar (let with the aid of the data given, X, i.e., celestial calculated, and us eel this the epoch of the Siddhanta-Jyotisa or S. J.). the junction- stars in the epoch of S.J. is the stars for 1950. Let the There is a wide spread belief that a definite location can be compare it with the X of same \± and X \ being the value found for this point from the data given in the Surya- two values of X be denoted by a , x ThenX -X Siddhanta and other standard treatises. This impression is at the epoch of S. J., X t for the year 1950. a x which is the celestial however wrong. should have a constant value, longitude of the V.E. point at the epoch of the S.J. on the Its location has to be inferred from the co-ordinates assumption that they refer to observations at a definite given for known stars in Chap. VIII of the SUrya Siddhanta. point of time. The following is a short exposition of From these data Diksit thought that he had proved that it Burgess's calculations. but another school was very close to Bevati (C Piscium) ; S.S. gives the position of the junction-stars in thinks that the autumnal equinoctial point (first point of The terms of Dhruvaka and Vik$epa, two co-ordinates peculiar Libra) at this epoch was very close to the star Citra (Spica, to Surya- Siddhanta. Their meaning and relation to the < Virginis), and therefore the first point of Aries at the usually adopted co-ordinates is illustrated by means of epoch of S.J was 180° behind this point. The celestial 19° 10' 39" of fig, 27 and for convenience of the reader, the standard longitude in 1950 of f Piscium was and * Virginis was 203° 8' 36". The longitudes of the first K therefore point of Aries, according to the two schools 11'= 3° 58' differ by 23° 9'(-)l9° and they cannot be identical. Bevati or f Piscium was closest to T (the V.E. closest point) about 575 A.D., and Citra or < Virginis was clear difference to ^ (the A.E. point) about 285 A.D., a of 290 years. Thus even those who uphold the nirayarta school are not agreed amongst themselves regarding the exact location of the vernal point in the age of the Sftrya-Siddh&nta and though they talk of the Hindu zero-point, they do not know where it is. Still such is the intoxication warfare for partisanship that for 50 years, a wordy regarding the adoption of either of these two points as the the zero-point of the Hindu zodiac has gone on between Bevafl-Pak§a two rival factions known respectively as the and Citr3,-Pak$a, but as we shall show the different parties are simply beating about the bush for nothing. Kg. 27 Chapter VIII of the S.S gives a table of the celestial co- used for the different systems of ordinates (Dhruvaka and Vik$epa) of the junction-stars designations, symbolisms co-ordinates along with their Hindu equivalents (identifying stars) of 27 asterisms forming the Hindu lunar celestial

are shown in the table below : zodiac. It is agreed by all that these co-ordinates must

Table 31—Siddhantic designation of celestial co-ordinates.

Co-ordinate Hindu Symbol Figure Bemarks Designation

in Celestial longitude Bhoga X rC As Surya Siddhanta Celestial latitude $ara CS Used by Bhaskara Eight Ascension Visuvarhsa a rQ Modern Declination Kranti 8 QS As in Surya Siddhanta » Polar longitude Dhruvaka I TB » Polar latitude Viksepa d BS 262 —

INDIAN CALENDAR 263

With the aid of spherical trigonometry, the following certain. The values of X a — Xi are in three groups as relations may be deduced : follows :

No X.—Xi Average sin £ = sin d sin B ...(l) Group 1. -.2 22° 53' sm (X— I)— tan j8 cot B \ \ T KA)((X or tan (X-l)=tan d cos B J 8 22 1 1-22° 33' where, cot\B=cos I tan « (3) 9 22 57 14 22 21 }

The objective is to deduce the values of X and j8 of a Group 2. .21 16 1 .20 10 star whose Z, d are to be found from Chap. VIII of S.S. 4 20 57 As the formulae show, the key angle is B, which is deter- 10 20 8 h 20° 48' mined with the aid of relation (3). Then (l) gives us j3 12 20 47 21 21 18 and (2) gives us X— I. So X and J8 for the star are found. 24 21 2

Proceeding in this way, Burgess calculated the values Group 3. ..7 19 40 of X and of the junction-stars given in the S.S. We have 18 18 58 20 19 14 h 19° 9' •hacked these calculations. These are reproduced in table 22 18 34 No. 32 on pp. 264-65 in which : 27 19 21

Column 1 gives us the serial no. of the naksatra. (N.B. In giving the Dhruvaka and Viksepa, the S.S. * 2 " their names. uses a unit called Liptika, which means a minute of arc. * 3 " " the name of the junction star as This is traced to Greek "Lepton'*. Prof, B. V. Vaidya accepted see however later ( thinks that some of the figures for asterisms, as they are remarks). given by cryptic Sanskrit words, have not been properly m " " the magnitude of the star. 4 interpreted). " 6 " " the celestial longitude of the star We are not aware how the Hindu savants determined in 1950 from data given in a the dhruvakas and vik§epas. It appears that they had a modern Ephemeris. kind of armillary sphere with an ecliptic circle which they 6 " the celestial latitude of the star. used to set to the ecliptic with the aid of standard stars * 7 " " the dhruvaka or polar longitude like Pu$ya (S Gancri), Magha {

deduced, from the relation : " 12- " " the difference between the lati- Declination latitude of place tudes. = minus zenith distance.

Since Viksepa (BS) = QS-QB i.e., declination of the It iB evident that 0-/3' ought to be zero for all stars, star minus declination of a point B on the ecliptic not the fact as may be seen from the [which which is however x is sin- (sin I sin «)], the polar longitude (dhruvaka) and the table. In the time of the S.S., the observations cannot be

declination give the viksepa which is thus : expected to have been very precise. But yet we cannot probably hold that an identification is correct when the S — sin'^sin I sin «)

difference is too large. We are therefore rejecting all Anyhow the above analysis seems to show that the — 0' 2°. identifications where j8 exceeds Probably these stars co-ordinates of stars were determined at different epochs. correctly identified from the description have not been Firstly when T was respectively 22° 21' ahead of the given for them, or the co-ordinates given in the Surya- 20° 8' present T , secondly when it was ahead, and Siddh&nta were erroneously determined or wrongly handed 19° 21 thirdly when it was ' ahead. The epochs come out down to us. In the case of other stars, we find that X a — X x to be 340 A.D., 500 A.D., and 560 A.D., respectively. u ' 47' 10° 52'), 16° 58' 18' is 16° (or and 26 for three stars. The first epoch is nearly 200 years from the time of We are also rejecting these three identifications. This Ptolemy, and if it is assumed that Hindu astronomers identification of stars leaves us with the 16 as somewhat assumed Citra (Spica or < Virginia) to occupy the first point I 264 J [ 265 ]

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of Bibra, the epoch comes out to be 285 A.D., and the But he did not err on the fundamental point. He had 2° corresponding Vernal point to the west of Ptolemy's. clearly laid down that Mesadi, i.e., the first point of Aries from which the year was to be started was to be This analysis shows that the Indian astronomers had identified with the vernal equinoctial point. arrived at the idea that the equinoctial point should he It is to be noticed that properly located with reference to some standard stars and though the maker of the S.S. has absorbed many of the ideas there were probably three attempts, one about 285 A.D., from Greek astronomy including the use of technical terms like hora, the next about 500 A.D., and the last one about 570 A.D. liptikd, kendra, etc., he did not either blindly copy the They had not accepted the first point given by Ptolemy or Graeco -Chaldean data. From whichever source he any western astronomer. might have got the ideas, he absorbed it correctly and made an attempt to fix up the actual V.K The compiler (or compilers) of the S.S. was clearly point, as required in Chaldean astronomy, otherwise his unconscious of the precession of equinoxes, and while in his zero-point would have been coincident with Ptolemy's. report, he made a selection of these data, he did not perceive We have shown that whatever the Hindu zero-point of the that they were inconsistent with the idea of a fixed V.E, point. zodiac might be, it is not coincident with that of Ptolemy.

APPENDIX 5-C

Gnomon Measurements in the Aitareya Brahmaaa

References to the observation of the solstice are found The Vedic year-long sacrifices were begun in the earliest in very early literature as the following passage from the times on the day following the winter solstice. Hence the Aitareya Brdhmana : shows Visuvan which means the middle day of the year was the 'They perform the Ekavimsa day, the summer solstice day. Vi^uvan^ in the The above passage shows that the

middle of the year : by this sun was EkavimU day the gods raised observed by the Vedic Hindus to remain stationary up the sun towards the world of heaven (the e., without any highest region 1 change in the merdian zenith distance of the heavens, viz., the zenith). for days near Eor this , reason this sun 21 the summer solstice. The argument was (as raised up) is (called) Ekavimsa, of this this that if the Ekavimsa sun sun remained stationary for 21 days, he the (or day), the ten days before are ordained for the must have had 10 days of northerly motion, 10 days of hymns to be chanted during the day ; the ten southerly days after motion, and the middle (eleventh) day was are also ordained in the same way ; in the middle lies the' certainly the day of the summer solstice ; hence the sun Ekavimsa established on both sides going over these in the Viraj (a period worlds, in the interval between the two of ten days). It is certainly periods established in the Virdj. of 10 days on either side, did not waver'. Thus Therefore he going between (the two periods from a rough observation, of 10 days) the Vedic Hindus could find the over these worlds, does not waver.' real day of the summer or winter solstice. 'The gods were afraid of this Aditya (the sun) falling The next passage from the Aitareya Brahma\ia from this (not world of heaven (the highest place in the quoted) divides the Viraj of 10 days = thus ; 10 6 3- heavens) him with + 1 + ; three worlds (diurnal circles) of heaven the first days were set apart 6 for a Sadaha (six day-) period, (in the heavens) from below they propped up ; the Stomas followed by an atir&tra or extra day and then are the three came the worlds of heaven (diurnal circles in the three days of the three Stomas or heavens). Svarasamans. \The They were also afraid of his falling away atiratra days before and after the upward solstice day were ; him with three worlds of heaven (diurnal circles respectively styled Abhijit and Visvajit days. It may thus in the heavens) from above they propped up ; the Stomas be inferred that the Vedic Hindus by are the more accurate three worlds of heaven (diurnal circles in the observation found later on that the sun remained heavens) stationary indeed. Thus three below are the Saptadasas at the summer solstice for 7 and not 21 days. (seventeen), three above ; in the middle is the EkavifnSa on both Question may now be asked how could they sides supported by Svarasamans. Therefore he observe fchat the sun going between these remained stationary for 21 days and Svarasamans over these worlds does not for 23, 27, 29, or 31 days. This not waver*. depended on the degree of accuracy of observation possible for the Vedic Hindus This obscure passage has been interpreted by as follows their methods of measurement. by They probably observed Prof. P.C. Sengupta in his Ancient Indian Chronology. the noon-shadow of a vertical pole. APPENDIX 5-D

Precession of the Equinoxes amongst Indian Astronomers

On p. 226, we have given references to pre-Siddhantic The surmise that the early Siddhantic astronomers were notices of the location of the vernal point in the sky. We ignorant of the movement of the equinoxes is supported by

saw that ancient Indian savants noticed its gradual shift the fact that neither of the early eminent astronomers Aryabhata I (476 523 A.D.) Lalla ( due to precession ), but were only puzzled by the pheno- — nor (748 A.D.) whose menon. Let us see what was the experience of the dates are known, mention anything about precession of the Siddhantic astronomers in this respect. equinoxes in their writings which have come down to us. If they derived their knowledge of astronomy from the West, Dlksit, in his Bharatiya Jyolisastra, has summarized the- they followed the current western practice of ignoring the adventures of the idea of Preeession of the Equinoxes precession. The astronomer Varahamihira, who wrote amongst Indian astronomers of the Siddhanta period. The about 550 A. left following D., and has us a compendium of the five account draws heavily on his Chap. 3 ( p. 326 ) on Siidhantas, makes no mention of the phenomenon. This Ai/ana-Calana, which literally means 'the movement of the * proves that the original SUrya solstitial points'. SiddhSmta as known to Varahamihira contained no reference" to the movement of The 'Solstitial points' were known amongst Indians as the equinoctial points. In his Bfhat SaUhita as mentioned 'Ayanas' anth Siddhantic astronomers regarded them as on 226, Varahamihira, p. however, noted that the solstices 'imaginary planets' as they used to do in the case of the were receding back, but he could not say anything about the nodes of the lunar orbit. Though the nomenclature is cum- actual nature of the precession or assign any rate to it. brous, the chapter actually deals with the precession of But it is obvious that once the Indian astronomers the equinoxes, as this point is 90° behind the summer recognized T as the starting point of the zodiac, solstitial point. and started giving co-ordinates of stars in terms of T Q as the starting Before the Siddhantic period, the lunar calendar was of point, they could not avoid noticing the movement of the primary importance, hence the exact fixation of the vernal equinoxes, just as it happened with Hipparchos in Greece. equinoctial point ( T Q ) was not very important. It became According to Brahmagupta (628 A.D.), the first astronomer important from the time the Indian astronomers of the who made a pointed reference to it was one Visnu Candra Siddhanta period first realized that T Q should form the author of the Vasitfha Siddhanta whose date is given as' zero-point of the zodiac ; and made attempts at different ca. 578 A.D. He was supported by one &isena of whom epochs 285 A.D.-600 ( A.D. ) to give co-ordinates of stars only the name survives. For holding these views these (Dhruvaka and Vik$epa) with respect to this as the initial astronomers were roundly abused by Brahmagupta whose point. Chapter VIII of modern SUrya- Siddhanta gijves a views on these points appear to have been confused. But resume' of these co-ordinates for, the junction-stars of the undeterred by the great prestige of Brahmagupta, later lunar asterisms. Our analysis of these data as given in astronomers continued to make references to the movement Appendix 5-B shows that these co-ordinates must have of the equinoctial points. been obtained by actual observations at different epochs, and We cite some examples. as the compiler of the SUry a- Siddhanta was ignorant of the MuSjala Bhata, a south Indian phenomenon of precession of the equinoxes, he made an astronomer, wrote a treatise called Laghumanasa in 854 $aka or uncritical selection of these data compiled at different times 932 A.D. A later commentator, Munisvara, ascribes and included them in his Chap. VIII. the following verses to him. From these data, it is impossible to determine the exact Uttarato yamyadisam yamyantattadanu location of T at the time when the SUrya- Siddhanta was complied. saumyadigbhagam So the wordy warfare between the upholders of parisaratam gaganasadam calanam kincid bhave- the Citra-pak$a and the Bevati-pak$a becomes meaningless as pointed out on p. 262. dapame. 1. Visuvadapakramamandala-sampate praci mesadih l * The word Ayana Galana* strictly means the movement of the pascattula^iranayo-rapakramasambhavat proktafc. 2. "Solstitial Points". Bhaskaracarya uses the word 'Sampat-Galcma' Basitrayantaresmat karkadiranukramanmrgadisca for movement of the equinoctial points ( T and £t ). Mathematically tatra ca parama the two krantirjinabhagamitatha tatraiva. denominations are equivalent, but it has become the practice 3 NirdiB^o-yanasandhiscalanam tatraiva in Hindu astronomy to render the term 'Precession of the Equinoxes' sambhavati tadbhaganab kalpe by the words 'Ayana Calana*. We shall follow this practice through- syu-go-rasa-rasago-'nka-candra out. mitatu 4.

C.R.—42 267 ;

268 REPORT of the oalendab reform committee

Thereafter it diminishes in like Translation declination of the sun. the lapse of 3736 years, i.e. the half period, from manner and after 1. While the celestial bodies move in the sky again becomes zero and goes on the other side. The annual small it north to south and again from south to north, a very rate of motion, which on the average amounts to 46 .3 variation takes place in their declination. seconds, varies fromzfc 70"*5 to ' equator 2. The (ascending) node in which the celestial now come to a very controversial passage in the (Me§idi\ We and the ecliptic intersect is the first point of Aries modern SUrya Siddkcinta, Chap. Ill, verses 9 to 12. is the first point and it gives the 'East'. The second node These are : change their of Libra (Tuladi), and these two points never Trimsat krtyo yuge bhanarii cakrarii prak parilamvate -declination value (which is zero). tadgunad bhudinairbhaktat dyuganat yadabapyate. 9 at a distance 3. The first point of Cancer (KarkZdi) is Taddostrighna dasaptamsa vijtieya ayanabhidhat of three three signs (i.e. 90°) from it, and at a distance oi tatsamskrtadgrahat kranticohaya caradaiadikam of in the reverse order is the position of the first point signs sphutam drktulyatam gacchedayane visuvadvaye. 10 Capricorn (Makaradi), These give the positions of maximum Prak cakram calitam hine chayarkat karanagate declination which is 24 degrees. antaramsai rathavrtya pascacchesaistathadhike. 11 ayanas) show 4. The solstitial points (which mark the Evaih visuvaticchaya svadese ya dinardhaja in a Kalpa a movement, and the number of their revolutions dak^inottara rekhayaih sa tatra visuvat prabha. 12 199669. is counted as Translation The last passage recognizes processional motion, says 9. In an Age [yuga\ the circle of the asterisms (bha) 59".9 that it is continuous, and gives^the rate as per year. falls back eastward thirty score of revolutions. Of the Munjala Bhata makes no mention of trepidation. He noticed result obtained after multiplying the sum of days (dyugatya) that the Ayanas had processed by about 6° from the position by this number, and dividing by the number of natural given in the Surya-Sidtlh&nta. days in an Age, Prthudaka Svami (born 928 A.D.), an astronomer who 10. Take the part which determines the sine, multiply Kuruksetra, commenting on a observed at Peihowa, near found the degrees it by three, and divide by ten ; thus are passage of Brahmagupta says : called those of the precession (ayana). From the longitude 189411. "The revolution of Ayana in one Kalpa is of a planet as corrected by these are to be calculated the This is called the Ayana Yugd". declination, shadow, ascensional difference (caradala) etc. nature of This passage recognizes the continuous 11. The circle, as thus corrected, accords with its ob- and gives the rate of processional it precessional motion, served place at the solstice (ayana) and at either equinox ; motion as 56".82 seconds per year. has moved eastward, when the longitude of the sun, as obtain- ed by calculation, is less than that derived from the shadow. So far we have no mention of the 'Theory of Trepidation' then, ascribed to 12. the number of degrees of the difference ; This is first mentioned in the Arya Siddhanta t By it has moved westward by the amount of Aryabhata II, whose date is 1028 A.D. It says : turning back, difference, when calculated longitude is greater. Ayanagrahadot krantijyacapam kendravat dhanarnam syat Ayanalavastat samskrta khetadayana carapamalagnani. 12. These verses occur in the chapter on astronomical measurements by the gnomon, and are misfits there {krantijya) of Translation : —Find the sine declination according to all authorities, these verses did not exist in the the ayanagraha (in a way similar to that of the sun's original SUrya-Siddhanta, but have been extrapolated there, declination, declination) ; from it deduce the amount of and have no reference to the context of the chapter. The plus (north) or minus (south), which is the amount of extrapolation must, however, have taken place before the ayanafnsa* After applying this ayanafn§a-corToction to time of Bhaskaracarya II (1114-1178 A.D.), because he the planet, the values of cava (half the difference between comments on this passage. the lengths of day and night), declination of planets, lagna The passage supports the theory of trepidation and says (the orient ecliptic point), etc., are to be calculated. that the amplitude of precessional oscillation is 27° and the This has been interpreted as follows (Dlkgit, p.330). period of one complete oscillation is stated to be 7200 years. The equinox oscillates between ±24°, and the number of The rate of precession is given as 54" per year, which is revolutions of the Ayana-pl&Tiet in a Kalpa is 578159, which uniform and the same throughout the oscillation. These gives the period of revolution as 7472 years and the annual stanzas are quoted by Indian astrologers who are advocates rate of motion as 173 "A. During a quarter period viz,, 1868 of the nirayana system, in support of their arguments for years, the ayanafn§a increases from 0° to 24°, at first, sticking to the sidereal year. They say that the present rapidly, then gradually more slowly like the increase of ayanafnia is about 22°, and T will go on processing for

another 350 years till ayan&?ri§a becomes 27° and will" then, * This is a technical term used by Indian astronomers to denote the distance of the vernal point from the fixed Hindu Zodiac, turn back on its return journey. INDIAN CALENDAR 269

This is sufficient argument to them to turn down all Atha ca ye va te va bhaganah bhavantu yada ye'msa proposals lor S&yana reckoning taking the length of the nipunairupa labhyante tada sa eva krantipatab- year to be tropical. — Translation : "What Munjala and others have mention-

1 We now take the opinion of the last great Indian ed as Ayana Calana ', is nothing but the motion of this astronomer Bhaskaracarya II (1150 A.D.). equinoctial point. According to their view the number of

* revolution in a Kalpa is 199669 (yielding annul rate of He uses the term Sampat-Calana* i.e., movement of the 59".9). intersection of the ecliptic and the equator, instead of the Let whatsoever be the number of revolutions, whatever amount is obtained by expert observers is the classical term Ayana. He says : angle of precession for that time."

Siddhanta &iromani f Goladliyaya, From this it is clear that he recommends one to accept Golabandhadfii k&ra the ayanafnia which one would actually get by observation [visuvatkrantivalayapatasya] api calanamasti. Tasya of sun's place at any particular time. Dlksit says : Ye'ayanacalana bhagah prasiddhasta eva vilomagasya I have not come across single statement in which krantipatasya bhagah Bhaskaracarya has clearly said that equinoctial point makes TranslatiXm : —It (the equinox) has also movement. a complete "circular revolution", nor does be say that "it the of precession What is commonly known as amount does not make it". (ayanafn&a) is the same as the longitude of the equinoctial He has taken 1 minute per year as the ayana-motion point measured backwards. and has supposed 11° as th« ayandlh&a in l^aka 1105. He This evidently shows that he regarded the change as due thus means to take Saka 445 as the zero-precession year. to the retrograde motion of the node (i.e. equinoctial point) We thus perceive that Indian astronomers up to the time like modern European astronomers. of Bhaskaracarya were as much divided in their ideas about He criticises Brahmagupta for his views on Ayana precesssion of the equinoxes as the contemporary Arab

Calana and says : "One can observe that at the time of astronomers of the West (Hispano-Muslim), and the East. Brahmagupta, the ayanain&a value was very small and It is only after 1024 A.D. that they adopted a theory of hence it is likely that it could not have come to his notice ; trepidation. The earlier-astronomers like Munjala and yet how is it that he did not take the rate of revolution of Prthudaka merely noticed precession and gave their own equinoxes as given by the Sury a- Siddhanta, just as he has rates for it. Bhaskaracarya is non-committal about taken figures for rates in some other cases on the basis (or trepidation. The Indian astronomers do not appear to have authority) of already proved and accepted rates". been influenced by the views of the western astronomers,

He further says : the earlier Greeks or later Arabs.

Ayanacalanam yaduktam Munjaladyaib sa evayam It will be sheer stupidity to hold to the theory of (krantipatab) trepidation of equinoxes 270 years after it has been definitely* tatpakse tadbhaganafr kalpe go'ngartu-nanda-go-candrah proved to be wrong. The law of universal gravitation will (199669;. not be changed by God Almighty to oblige astrologers. APPENDIX 5-E

The Jovian Years

{Barhaspatya Var§a)

sixty-year The sidereal period of Jupiter, according to the SUrya The cycle is at present'in daily use in Southern India (south of Narmada) year (the solar year or Siddhanta is 4332.32 days which is nearly 11.86 sidereal where each the luni-solar years. Therefore Jupiter roughly stays for one year in one year) is named after that of the corresponding Jovian year. The years are counted there in regular succes- zodiacal sign, if we calculate by mean motion. sion and no safnvatsara is expunged. This practice is being This was taken advantage of to devise a cycle of 12 followed since about 905-06 A.D. (827 Saka), as a result of Jovian years. If we divide the Sury a- Siddhanta period by which the number of Northtlndian Safnvatsara has been 12, we get 361.026721 days which is taken as the length of gradually gaining over that of the South from that time. a Jovian year. This is 4.232 days Ie3s than the Surya The Saka year 1876 (1954-55 A.D.) is named 41 Plavanga Siddhanta solar year. So if a Jovian year and an ordinary in the North while in the South it is 28 Jaya. solar year begin on the same day, the Jovian year will begin to fall back, completing a complete retrogression The following are the names of the different years ; 65 in 85 — solar years, according to the SUrya- Siddhanta. Ala. (1) Prabhava (21) Sarvajit (41) Plavanga

(2) Vibhava (22) Sarvadharin (42) Kilaka So 85— solar years — 86^^ Jovian years, and one Jovian 2i 1 1 All (3) Sukla (23) Virodhin (43) Saumya

65 (4) Pramoda (24) Vikrta (44) Sadharana year year is expunged in every 85^[ years. The expunged (5) Prajapati (25) Khara (45) Virodhakrfc

(6) Angiras (26) Nandana (46) Paridhavin is called the Kmya year. In actual practice, the interval Srimukha (27) Vijaya (47) Pramadin between two expunctions is sometimes 85 and sometimes (7) Bhava (28) Jaya (48) Ananda 86 years. (8) (9) Yuvan (29) Manmatha (49) Kuksasa There was indeed at one time a period of 12 Jovian (10) Dhatri (30) Durmukha (50) Anala (Nala) years, but at some past epoch, a fivefold multiple, a cycle of (11) Isvara (31) Hemalamba (51) Pingala 60 Jovian years, each with a special name suffixed by the (12) Bahudhanya (32) Yilamba (52) Kalayukfca word 'Saihvatsara', came into use. (13) Pramathin (33) Vikarin (53) Siddharthin The beginning of the Jovian years is determined by the (14) Vikrama (34) ^arvarl (54) Eaudra entry of Jupiter into an Indian sign by mean motion, the (15) Vrsa (35) Plava (55) Durmati

1st, 13th, 25th, 37th and 49th years 'being marked by the (16) Chitrabhanu (36) Subhakrt (56) Dundubhi entry of Jupiter into the sign Kumbha, and not Mesa which (17) Subhanu (37) ^obhana (57) Rudhirodgarin is otherwise the first of the signs of the Siddhantas. It (18) Tarana (38) Krodhin (58) Baktaksa thus appears that the system of counting Jovian years is a (19) Parthiva (39) Visvavasu (59) Krodhana pre-Siddhilntic practice (20) Vyaya (40) Parabhava (60) Ksaya (Aksaya) —

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INDEX

Abbe Mastrofini, 171 Artemidorus of Puskalavati, 230 Brahmanas, 193, 214, 221, 241, 245 Abd al-Rahaman al-Ruff, 206 ArthakUstra of Kautilya, 235, 236 Brahrm, 227, 229, 231, 232, 233 Achelis, Miss Elisabeth, 12, 171 Aruiiodaya, 108 Brhat Samhita, 226, 267 Adar, 179 Aryabhata 1, 204, 234, 236, 237, 238, 240, 2c !, Brown, 193 Addaru, 175,176 253, 254, 267 Buddha, 231,235;

Adhika ( = mala) month, 7, 247, 230 Aryabhata II, 238, 268 nirvana of, 256, 257 Agni, 210 Iryabhatlya of Aryabhata, 162 238, 253 views on astrology. 235 Ahargana, 9, 11, 101, 102, 163 Arya Saiigamika, 232 Budhagupta, Gupta emperor, 234 Ahoratra, 157, 100 Irya Siddhanta, 1, 214, 251, 268 Burgess, Rev. E., 238, 253, 262, 263 Aitarcya BrTihmana, |89, 216, 219, 22], 266 Arya Vasula, 232 Akber, 1,159, 214, 251 Asokachalla Deva, 256 Aksaya ti tiya, 18, 39 Asoke, 177, 212, 227, 228, 252 Calendar, defined, 1, 157 Al-BattanT, 204, 200, 240 ; ; Assouan papyri, 179 civil, 6 , rate of precession, 206 Jjitadhyayl, 214 compilation according Alberuni,198,204, to S. S., 1 237-; Astrolatry, 235, 236 confusion in Indian, 10 Al-Bitruji, 206 ; Astrology, 12. 194, 196, 205, 206, 235, 236, 256 Egyptian, 164 Alexander of Macedon, ; 202, 213, 234, 235 Atharva Sathhita, 217, 218 French revolution, 167 Al-Fargham, 206 Atharm Veda, 214, 217, 218 Fusli, 248 Almagest, ; 204, 206, 238, 240 Audayika system, 254 Gregorian, 1, 3, 11, 170-172 Aloysius ; LiliuB, 171 August Gompte, French positivist philosopher Hejira, 1, 166, 179, 180, 214; Altekar, Prof., 254 171 history of reform movement, 10, 11 Al-Zarquali, 206 Augustus, 168 Iranian (Jelali) 1, 166 167 ; Amanta month, 101, 157, 177, 247 Ayanamsa, 5, 7, 16, 17, 20, 268, 269 ; Islamic, 179, 180 Ammonia clock, 32, 159 amount of acc. to Aryabhata II, 268 Jewish 179 ; Anaximander of Miletus, 188, 202 ; amount of fixed, 16, 17 lunar, 3,179, 245,247 gnomon. 202 ; (see also calendar for five years) * luni solar, 1, 3, 174, 249, 251 ; Ancient Indian Chronology, 215, 253,-266 definition, 268 calendar in Siddhantas 245-251 Andan (inscription), 233 rate of, 7 of Babylonians, Macedonians, Roma* Antiochus Sorter, 203 rate of Bhaskaracarya, 269 and the Jews, 176, 177 ; Antiochus I, II of Babylon, 228 value of, 7, 17 principles of 174 Anubis, Egyptian god, 164 Ayanas, 267. 268, 269 Siddhantie rules for 247 ; Anuvatsara, 225 Azes, 256 National, 12-14 ; Anyanka Bhlma Deva of Ganga dynasty, 257 Azes I, 230, 233, 256 Paitamaha Siddhanta, 223, Aparabna, 108 Azes II, 230, 233, 256 problems of the, 158, 159 Jpastamba Samhita, 218 Azilises, 230, 233 Reformed, 4 Aphelion, 242 ; movement of, 243 Religious 7 Apolloniu s of Perga, 203 Roman, 168 Ara (inscription), 230 Babylon, 225, 226, 228 latitude ; of, 225 Seleucid Babylonian, 229 ; Arachosia, 229, 230 Bachhofer, Dr. L., 230, 231, 232 Siddhanta Jyotisa Aranyaka, 214 period, 245, 246 Badami (inscription), 233, 253 Solar, 1,2, 164-173, 245; Archebius of Taxi la, 230 Bailey, 253 Siddhanta Jyotisa period, 234-245 Archimedes of Syracuse, 203 Balarama, 227 Tarikh-i-Jelali, 166, 167 Archytas of ; Tare n turn, 202 Banerjce, late R. D,, 212 Tarikh-Ilahi, Ardeshir I of 1, 214, 251, 257, 258 Persia, 232 Bentley, 253 ; Vedanga Jyotisa, 9, 221, 222, Ardharatrika system, 223 ; 1, 253,^254 BeroHsus, Chaldean priest, 203 World, 1, 171-173 Ariana, Herat regions, 229 Bharatiya JyotilQstra, 11, 160, 219, 225, 236, Aries Calendar of India, Reformed (as (zodiacal sign), 392, 193 267 recommended by the Committee), 41-100 Aries, first, point uf ; , 157, 192, 199, 207, 239, 240, Bhaskaracarya, 238, 246, 262, 267, 268, 269 ; explanation 262, 268 of terms used, 40 ; a van a calana, 269 Calendar Reform, Hipparcho's, 200, 205, 206 ; BkCtsmtl 160 suggestion movement of received, 5 200, 205, 206 Bhattotpala, 237 summary of position in different times, suggestions, 32-38 200 (fig). Bhoga (celestial longitude), 262 Ptolemy's, 200 Calikya Vallabhesvara, 233 Bija (correction), 3 Caliph Omar, Aristaivhos nf Samos, 203 167, 179 Box lid (inscription), 230 Calippos, Armellini, 171 length of season, 175, 261 Brahma. Creator in Hindu mythology, 223, Canakya, 213, 235, 236 Armillary sphere, 199 (fig.), 263 236,238, 239, 240 Cancer, Arsaces of Parthia, first point of, 192, 199 178 Brahmagupta, 223, 237, 238, 240, 253, 267, 268, Candragupta, Maurya, Artabanus I of Parthia, 213 213, 236, 257 269 Candragupta II, Vikramiiditya, Artabanus II of Parthia, 256 254, 255 Brahma Siddhanta, 1, 214 Capricorn, first point of, 192

273 ;;; ; ; ; ; ; ; ; ;; ; ; ; — ;; ; ;;; ;;; ; ; ; ;; ; ; ; ;

INDEX 274 Era eoHtd* Decad, 164 268 Christian, 170, 251, 258; Cara , correction , D' Eglantine, 167 Cardinal days, 189 current, 251 Declination, 192, 204, 263 Cardinal points, 189, 190, 219; Diocletion, 162 Demetrius, 213 determination of, 190 elapsed, 251 Abdera, 202 256 Democritos of Castana, 6aka Satrap, 233, #asli,257,258; I?ewai (inscription), 229 Revolution, 167 Centauries. 163 French Dkarma Sindhu, 19, 101 Central Station, 3, 4, 7, 14, 40 Gahga,257,258; Dhruva (celestial pole), 190, 192 Chadwick, 202 Gupta, 255, 257,258; Dhruvaka (polar long.), 192, 262, 263, 267 Chaldean Saras, 184,135, 186,202 Harsa, 254, 258; of junction stars, 264, 265 Jesus, 157, 201 Hojira, 162,180, 258; Christ, Dlgha NikZya, 235 introduction of, 177 ; Chronometer, 157 224, 225, Diksit, S. B., 11, r9, 160, 212, 219, 223, Jelali (Iranian), 162 ; Cicero, 205 236,237,246,262,267.268,269 202 era of Creation, 179 ; Cleostratos of Tenedos, 193, ; Jewish Diopter, 203 Jezdegerd (Persian), 162 ; zodiac, 193. 202 ; 255 Dios, Macedonian month, 179, 229, intercalation, 202 (Chedi), 234 8-year cycle of Kalachuri ; motion, 169, 195 Direct 254, 258 Clepsydra, 159, 223, 225 Kaliyuga, 13, 162, 252, ; Discovery, 190 Reform— 232, 256 Committee, Indian Calendar Kanaka, ; DurgastamT, 108 appointment of, 4 Kollam, 257, 258 ; 217 Dvadasaha, 257 dissenting note, 8, 18 ; Kollam Andu, ; of civil, 6, 7 ; Krta, 254 final recommendations ; of religious, 7, 8 ; final recoromandations Earth- Kusana.231,232 ; equatorial axis of, 208 inscription of, 230 members of, 4 ;

meeting, 9 ; rotation, 12 232 proceedings of the first period of ; method of date-recording, ;

meeting, 15 ; * proceedings of the second polar axis of, 208 ; Laksmana Sena, 258 proceedings of the third meeting, 17 ; speed in a second, 195 *, Laukika kala, 258 4 spinning of, 208 terms of reference. Maccabaean, 179 ; and Nautical Committee, Indian Ephemeris Easter, 170, 171 Magi, 258 Almanac, 8 Eclipses- Nirvana, 258 of o resolutions 4, condition of, 185 ; Committee meetings, 4, 5 ; Malavagana, 254

of day), 159 list of lunar, 186 ; Compline (division Nabonassar, 162, 177, 178, 253 ; 187 Roman emperor, 170 list of solar, ; Constantine, Newar, 162, 258 ; designation of, 185 celestial, Siddhantic periodicity ; Co-ordinate, Old 6aka, 230, 232-234, 236, 255, 256 ;

recurrence of, 186 ; of, 262 Olympiads, 178 184-187 195, 203, 206, 235 saros cycle, Copernicus, Pan«Java kala, 252 ; 259; 229 181. 191, 192, 197, 198, 207, Corpus'lnscriptionum Indicantm, Ecliptic, 158, Parasurama, 257 of, 191 Ctujamani yoga, 108 definition Parganati Abda, 257 earliest mention of, 199 ; Cunningham, 230, 231 Parthian, 178, 256 of Indiction, 162 fixing of, 191 Cycle Philippi, 162 ; 192,207; plane Of, Raja 6aka, 258 192,208; pole of, 6aka,2,4,6, 13, 162, 178, 214, 233,234, of, 191,207, 208,225 obliquity of, 233 260 255-258 ; earliest records Dak?inayana, 189. 219, 226, 239, 236, Ekadasi, observance of, 105 ghatika), 160 Saptar^i, 190, 252, 258 ; Panda ( = n&4i or Euclid, 202 emperor, 166, 176, 212, Elements of Seleucidean, 161, 176, 178, 179, 229, 230, Darius I, Achemenid Elliptic theory, 243 231, 255, 256 ; 256 199 Encyclopaedia Britannica, 170, 179, Vallabhi, 258 ; Day, 164 Epagomenai, Vikrama, 13, 234, 247, 254, 255. 257, 258 apparent length of, 226 ; 201 Ephemerides, Vilayati,244, 257,258; astronomical, 159 ; Committee, 4, 6 Ephemerides Yudhist-Mra, 252, 258 civil, 159 ; Epicycle, 203 earth, ; on diameter of the counting of the Eratosthenes, 178 Epigehis, 165 203 succession of, 248 ; Indica, 233, 254 Epiqraphia 202, 203 of, 157, 217 ; Euclid, definition Ml, 192, 197, 207, 239, 259 Equator, celestial, 229 designation in ancient Eucratidas, days, 188 Equinoctial Euctemon, length of season, 175, 261 time, 183 Equinoxes, 188 geometry 203 160 Eudoxus of Cnidus, 201, 202 ; on , division among Egyptians, ; 189, 192 ; autumnal, Euphrates, river, 157 among Hindus, 160 ; division 268 oscillation of, Euthydemids, 213 Julian, 161, 162 188, 189,192, 205, 253, vernal, 2, 11, 13, Evection,204 length of, 157, 159,259; 260 Exact Sciences in Antiquity, 3, 197, 198, 201 length at Babylon, 226 ; 252, 258 ; 13, 177, 228-231, 236, 251, shortest, 225 ; Era, length of longest and 159,197 Amli,244,257,258 ; mean solar, 157, 158, ; 178,230; Arsacid, Fabricious, 235 reckoning of 13, 14 ; Azes,232,256; (inscription), 229 saura, 197 Fatehjang Bengali San, 257, 258; 157, 158 Festivals, Religious- sidereal, Nirvana, 256-258 Buddha Alphabetical list of, 111-115 solar. 157 162 Burmese, ; Christian, 126 starting of, 1 ( 5, 7 ; Cfclukya Vikrama^258 101 sub-divisions of, 159 general rules for, Chedi(KalficurI),258; Debevoise, 230

ft H —43 ; ; ; ; ; ; ;—; ; ; ; ; ; ; ;;;; ;;; ;; ; ; ;; ;

INDEX 275

Introduction to the History Science, 159 festivals, Religious—eontd. Holidays, list of contd. of Isis, Egyptian god, 164, 165 Lunar—general rules for, 102-105 ; Bombay, 130

dates of, 119-124 Christian festivals, 126 ; Moslem, 125; Coorg, 148 Delhi, 149 Jacobi, 215 Solar—general rules for, 106 ;

dates of, 117-118 East Punjab, 134 ; Jaikadeva, 254 South Indian—general rules for 106 Fixed holidays & solar festivals, 117, 118 Jai Singh of Amber, 10 India, 127 Jamotika, 6aka king, 233 Fotheringham, Dr. J. K., 165 Govt, of ; Himachal Pradesh, 150 JanmaHamI, 19 Hyderabad, 137 Jatakas, 239

Galilio, 159 Jammu & Kashmir, 138 ; Jayanti, names of, 107 aswall, Gandhara, 225, 226, 229, 230 ; latitude of 225 Kutch, 151 Jay 255 Ganesa caturthT, 108 Lunar festivals, 119-124 Jehonika, 230 Oanges, river, 157 Madhya Bharat, 139 Jelaluddin, Melik Shah, 166 Gangooly.P. L.,238 Madhya Pradesh, 131 Johann Werner, 206 solstices, 226 Madras, 132 Jones, Sir Harold Spencer, 6, 12, 158 Garga, 226 ; receding of ; Garga Samkita, 226 , 152 Jovian cycle, 257

Gargasrota, river, 226 Moslem festivals, 125 Jovian (Barhaspatya) years, 270 ; Gauna (mana), 247, 248 Mysore, 140 names of, 270 Julian days. 161, 162 Geminus, 197 Orissa, 133 ; General Astronomy, 158 Patiala & East Panjab States Union, 141 Julian days of important events, 162, 163 period, 162 Geocentric theory, 204, 239 Kajasthan, 142 ; Julian .Julius Caesar, 2, 10, 159, 165, 168, 241 George Washington, birthday of, 161 Saurashtra, 143 ;

Gesh (division of time), 160 Travancore-Cochin, 144 Junction stars, of'naksatra, 184, 210, 211*. 900 ; 160 262-265 Ghatika, Tripura, 153 ; ;

Ghirshmnn 232 Pradesh, 135 dhruvaka of, 261, 205 ; ) Uttar ; 162, 193 latitude oi (1950), 220, 264, 265 Ginzel, F. K. Vindhya Pradesh, 154 ; ; 210, Gnomon, 159, 174, 188, 189, 202, 219, 223, 268 ; West Bengal, 136 (1956), 184, 211 meat in Aitareya a, 266 long, of (1956), 230, 264. 265 measure Hora, 236, 266 ; 210. Gondophernes, 178, 230 Horoscope, 196, 205, 256 (1956), 184. 211 ; Gorpiaios, Greek month, 231 Horoscopic astrology, 194, 196, 204, 256 magnitude of, 210, 211, 264, 265 tarsi), planet, Great Hear (Sap 190 Hour circle, 191 Jupiter, 194, 195, 203, 239 ; Greek Olympiads, 178 Hsiu, Chinese lunar mansion, 182, 183, 210, sidereal period of. 270 (chord), 204 Greenwich time (U. T.), 14 211, 224 ; Jya names with stars, 210, Jyoti>a Karanda, 223 Gregory XIII, Pope, 2, 10, 11, 170, 171 component 211 ; Gunda (inscription), 234 starting of, 183 Guptas, 254, 255, 257 Huviska, 231 Hypatia, 204 Kabishak, 180 Kadamba, pole of the ecliptic, 192 Hajj, 180 Kala or liptika, 160 Hammurabi, Babylonian king, 175 206 Ibn Yunus, Krdaloka Prakasa, 223 Harappa, 212 Idavataara, 225 Kalasang (inscription), 229 Harsa Vardhana, 254 Ides, 168 KalastamT, 108 Hashim, Amir AH, 180 Idvatsara, 225 Kaldarra (inscription), 229 Haug, Dr. Martin, 216 Iliad, 201 Kalends, 168 Heliacal rising, 164, 191 Indian Calendar,246 Kalhana, Historian of Kashmir, 252 Heliocentric theory, 203 Indian Ephemeris, An, 101 Kali, 162 ; long, of planets at Kali beginning Herzfeld, 232, 255 Indian Ephemeris and Nautical Almanac, 253 Heeiod, 201 5, 8, 12, 14, 17 Kalidasa, 7, 261 Hidda (inscription), 230 Indra, Indian god, 199, 215, 216 Kalpa, 162, 175, 214, 240, 268, 269 Hipparchos of Nicaea, 165, 166, 177, 178, 192, Indus, river, 157 Kalpadi, names of, 107 197, 200, 201, 203, 205, 206, 226, 235, Intercalary month ( = malamasa), 175, 176, Kandahar, 229 •237, 240 ; 245, 246j Kaniska, 230, 231, 236, 256 stars, 203 catalogue of ; Babylonian calendar, 176 Kanaka I, 231 precession, discovery of 205, 267 ; calculation of, 246, 249 ; Kaniska II, 232 first point of Aries, 200, 205, 206 definition of 247 ; Kaniska III, 231, 232 geometry & spherical trigonometry, 203, eight-year cycle, 202 Kaniska Casket (inscription), 230 204 Islamic calendar, 180 Kaniza Dheri (inscription), 231 Hippocrates of Chios, 202 Jewish calendar, 179 Kanva, 213, 228 History of Science , 206 list of acc. to modern calculations, 250 ; Kapisthala Ka^ha Samhita, 218 Hoang Ho, river, 157 list of according to S. S., 250 Kapsa, 230

Holidays, 5, 6 ; list of, 117-154 19-year cycle, 176, 200, 202, 229, 245, 246 ; ; Karana, 163 Ajmer, 145 Paitamaha Siddhanta, 223 ; Karanas, definition, names and calculation of, Assam, 128 Rg-Veda^lMlS;. 110 ; lords of, 110 Bhopal,146; Romaka Siddhanta, 237 Kanaka, 218 Bihar, 129 Siddhanta Jyotisa, 246, 248 ; Kaurpa (name of a sign), 193 Bilaspur, 147 Vedanga Jyoliga, 223, 224, 225, 246 ; ; ; ; ; ; ; ; , ; ;

276 INDEX

Kautllja, views on astrology, 236 Miinikiala (inscription), 230 Month, Solar— contd, Keith, Or. Berriedale, 218 M&nsehra (inscription), 229 Iranian names, 166 Kendra, 236. 266 Manvadi, names of, 107 length of, 211, 242-246, 251

Kepler, 2, 206, 242 Manzil, Arabian lunar mansion, 182, 183, length recommended by the 210, 211 Ketu (node), 186 ; Committee 2, 5, 6, 13, 15 Kbalatse (inscription), 229 names with component stars, 210, 211 names in French Revolution 240- starting of, 183 calendar, Khav4akhadyaka of Brahmagupta, 162. 167 j Marguz (inscription), 229 names in Yajur-Veda, 253 218 ;

(inscription), 231, 233 Mars, planet, 194, 195, 203, 239 ; names of, Indian 7, Kharorthi 229, 230, 5, 6, 14, 15 ; retrograde motion of, 194 names, Persian 166, Khotani 6a ka (language), 231 167 ; Kidinnu, 200 Masakrt, 174 number of days in Vedanga Jyotisa, Konow, Dr. Sten, 229, 231, 255 Matins, 159 225; Kranti (declination), 262 Maues, 230, 233 variation in length, 1 Krttikas, 182, 219, 252 Mauryas, 228 Synodic period, 197, 223

Miiller, 215 Moon, crescent . Ksaya month, 247, 248 250 Max 183, 214, of, 182 ; deviation Kugler, 176, 196, 225 Maya, 236, 238 of path from the ecliptic, 192, Kumbha mela, 6 Mean solar day, 157, 158 208;

Kumbha yoga, 108 Mean solar time, 158 inclination of path to the ecliptic, 201 ; Kurram (inscription), 230 MeghadTda of Kalidasa, 261 limiting values of true motion, 197 Kuruksetra, latitude of, 225 Melik Shah the Seljuk, 159 mean daily motion, 197 ; KuSanas, 213, 230-234, 236, 252, 256 Menander, 213, 229, 235 motion of, 182 204 movement Menelaos (Greek astronomer), ; of, 31, 181, 182 ; Spherical trigonometry, 204 rate of motion over the sun, 184 Lagadha, 214, 222 ; Mercedonius, 168 sidereal period of, 182 ; Laghumanasa of Mnnjala, 162, 267 Mercury, planet, 194, 195, 203, 239 synodic period of. 182 Lagna (orient ecliptic point), 237, 268 Meridian passage, 57 Mount Banj (inscription), 229 Lagrange, 167 Mesadi, 239 Mucai (inscription), 229 Lalla, on precession 267 Mesadi, sidereal, 16, 17, 40 Muhurta, 100, 108, 160 ; lords of, 109 Lambaka (co-latitude), 239 , 176, 202 Mukhya a, ; man 247, 249 Lanka. Greenwich of ancient India, 239, 253 ninetcen-year 202 cycle, Mtd Apin, Babylonian astrological text, 198 Laplace, 167 Metonic cycle, 162, 176 Munievara, commentator, 267 Latitude, celestial, 192,203, 204, 210, 211, 264 Milimla Panho (philosophical treatise), 229 Munjala Bhata, 11, 259 265; Mithra (Persian god), 167, 170 on precession, 267-269 polar, 192, 263, 264, 265 Mithradates I, 213, 255 Mural quadrant, 203

Leap year, 6, 13, 15 ; of Islamic calendar, 180 ; Mithradates II, 213, 255 Reformed Calendar of India, 186 of Mitra, Indian god, 215 Nabu Nazir, 177 Leonardo of Pisa, 160 Moga, £aka king, 230 Naburiannu, 200 Lohuizen, 256 Leeuw, Mrs. Van 232, 255, Mohammed Ajmal Khan, 180 Nadir, 157 libra, first point of, 192, 199, 239, 262, 268 Mohammed, Prophet, 159, 179, 180 Nagabha^a, 257 266 liptika, 160, 236, 263, Mohenjodaro, 212 Nahapana, 233 Lockyer, Sir Norman, 190 Naksatra, average length of, Moise of Khorene, 232 224 ; Lokambhaga of Simhasuri, 233 beginning of, 14, 229 Month, anomalistic, 197 ; ; Longitude, celestial, 7, 192, 203, 204, 210, 211 calculation of (acc. beginning in Babylonian calendar, 185 ; to the recommenda- 253, 264, 265 of, 185 tions of the definition 157, 158, ; Committee), 5, 7, 16, 17 polar, 192, 263, 264, 265 ; draconitic, 197 component stars of, 186, ; 210, 21 1^ Longitudes of planets at Kali-beginning, 253 def. intercalary {sec intercalary month) of in earliest times, 183. ,218, 227 Ltiders, 232 228, def. of in Lunar, 220, 221, 225, 245, 246 ; Vedanga Jyotisa, 183, 223-225 Lunar eclipse, 185 ; designation of, 182, commencement of as recommended 183 ; Lunar mansions, 182 ; division of, 183, 219 by the Committee, 7 ; 184, ;

of Rg Veda, 217 ; names of Indian, Chaldean and junction-stars of, 184, 210, 211, 220 stars of, 210, 211 r 264,265; Jewish, 177 ; Macedonian, 177, 229 Lunar year, beginning of, 220, 221 ; lords of, 109 ; length of Islamic, 180 ; Lunation, duration of, 158, 174, 175, 246 ; meaning of Indian, interpretation of month names, 221 ; 182, 210, 211 length of, 164, 248 , length acc. to S. S-, 246 names of-general 210, 211, 263 ; Tamil, reckoning in Mahabharata, 185 ; „ 109; Madhyahna, 101, 108 relation between draconitic and synodic, „ „ -Yajur Vedic with presiding 170, 183, 185,219, 221, 227, 228, 186; deities, 220 239, 252 number of, 182 ; sidereal, 223 ; ; month reckoning in, 185 Kg-Vedic, 183 ; Solar, causes of variation in length, 243 ; ; time of compilation, 226, 252 commencement of, shifting of the beginning of, 7 ; 18, 19 ; Mahadvadasi, defined, 107 starting of 182, 183 definition of, 242 ; Mahftyuga, 160, 162, 217, 254 different conventions in beginning Nandsa Yupa inscription, 254 Maira (inscription), 229 of, 244; Napolean Bonaparti, 168

Maitrayanl Sarhhita, 218 duration of, 243 *, Narseh, Sassanid king, 232 Mal&m&sa, 246, (see also intercalary month), Egyptian, 164 Nasatya,215 Mamine Pherl (inscription), 231 first month of the year, 5, 6 Nasik,228 ; ; ; ;; ; ; ; ; ; ; ;

INDEX 277

National Observatory, 5, 8, 12, 14 Phraates 1, 213 Puskalavati, 230 Nautical Almanac, 3, 165 Pictorial Astronomy, 194, 195 Pythagorean number, 198 ;(fig.) Nepthys, 164 PUlai, a K., 101, 223 Neugebauer, O., 3, 160, 175, 185, 189, 192, Pingala, 214 198, 199, 201, 203, 204 Planet, 169 order Quartz clock, 12, ; of distance, 203 ; 159 New Testament, 169 Questionnaire, references in Rg-Veda, 212 ; regarding calendar, 22 ; Newton, Isaac, 2, 193, 206, 240, 259 ; Planetarium, 203 replies to, 23-31 precession of the equinoxes, 207 Planetory Astrology, 169, 194—196 Night, definition of, 157 Plato, 202, 203, 228, 229 ; geometry, 202 Nile flood, 158, 164, 165, 174, 189 Pleiades, 182, 190, 195, 199, 219 Ha, Egyptian sun-god, 164 Nineteen-year cycle, 176, 200 Polar axis, 208 Kahu, ascending node, 186 Nirayaua, 259, 260, 262, 268 Polaris {< Ursae Minoris), 190, 207, 239 Ramaya^ta, 261 Nirt,iaya Sindhu, 101 celestial, Kampurva (inscription), 227 Pole, 191, 192, 207 ; Nirukta, 214 definition of, 191 Rahganatha, 233 Nirvana, Buddha, 235, 257 motion of, 207 Kapson, 255 Nisan, 161, 170, 175, 178, 229 179, observation of, 190, 191 Refraction, 225, 226 ; effect of, 225 Nisitha, 108 precessional path of, 207 Retrograde motion, 169, 194, 195 Nodes, 185, 186, 187, 269 Pope, Gregory XIII, 159, 172 -ttg-Samhita, 217, 218 Nona, 159 Pradosavrata, 108 Biy-Vedas,V&, 212, 214, 216, 217, 218, 221, Nones, 168 Prahara, 160 222 Numa Pompilius, 168 Prajapati, 217 calendaric references in, 216-218 ; Nut, 164 Prana (division of time), 160 description of, 215 Nutation, 209 Pratali, 108 Ribhus, 216

Nychthemeron, 157, 159 Precession of the equinoxes, 2, 7, 8, 193, liOO, Right ascension, 192, 204 204-206, 238, Riza Pahlavi 237, 240, 253, 259, 267 ; Shah ; 167 rate of, Romaka, 236,*239 Al-Baftani's 206 ; Obliquity, of the ecliptic, 158, 191, 207, 208, 225 among Hindus, 226 Rome, Era of foundation of, 178 amount of, 191 among Indian astronomers, 267 ; Rotation of the earth, 157, 158

definition of , 191 amplitude of precessional oscillation Rudiadanian, 233 ^Vctaeteris, 176 to Rudra Simha,' satrap, according S. S., 268 ; baka 231, 236

Octavious Caesar, 168 ; Bhaskariicarya's rate of, 269 ; Odyssey, 201 consequences of, 205, 206 ; Olympiads, 178 Sachs, A., 199, 201 discovery of, 204, 205 ; Omar Khayyam, 166, 172, 240 calendar, Saha, Prof. M. N„ 173, 232, 252, 256 effect in Indian 7, 11, 18 ; Omina, 19,3, 235 Siddhfuitas, 226 Sahdaur A (inscription), 229 effect in Indian ; Orbit, of the earth, 207 Sahdaur B (inscription), 229 explanation by Neffton, 207, 208 ; Orion, 189 Sahni, Dayaram, 232 Hipparchos's rate of, 205 ; Orion, 190, 195 6akas, 236 motion of (precessional), 208, 268 ; 213, 230, 233, Osiris, Egyptian god, 164 Sakadvipl Brahmanas, 214, 236, 256 Munjala Bhata's rate of, 268 ; 6a ka samvat, numerical value of, 209 ; 2o5 physical fiakasthan, 213. 233 explanation of, 207, 208 ; Paikuli (inscription), 232 Prthudaka Svaml's rate of, 268 6akendra kala, 255 Paitamaka Siddhanta, 223 Ptolemy's rate of, £alivahana &aka, 255 205 206 ; Paja (inscription), 229 rate Samarkand, 10 of annual, 209 ; Pakaa, 227-231 Sama Veda, 214, 218 rate of lunar, 208, 209 ; krsna or vahula, 15, 221, 228, 233, 247 Samhitas, 214, 218 ; rate of solar, 208, 209 ; iukla, 15, 228, 247 239, 244 221, ; Surya Siddhanta's rate of, 268 Samkranti, 2, 7, ; Pala, 160 215 Prthudaka Svami, 259, 268, 269 Mahavisuva, ; Palas, 257 Proclos, on precession, 206 Makara, 215 Pallavas, 256 rules 247, Ptolemy, Claudius, 161, 165, 166, 177, 178, 185, of, 244, 259 ; Pancangas,. list of, 21, 22 Uttarayana, 215 192, 200, 201, 203-206, 214, 228, 238, 24C, j Panca Siddhlntifca of Varahamihira, 158, 162, Sampat calana, 269 263, 266 ; 197,223,226, 236, 237, 238 on astrology, 205 Samudragupta* 255 Panemos, Greek month, 230 Samvatsara, 255, 270 „ evection, 204 ; Panini,2l4 Sangava, 108 „ rate of precession, 205 ; Panjtar (inscription), 229 188 „ theory of planetary motion, 204 6anku (gnomon), Pannekoek, Dr. Anton, I'M, 176,178.185,194, Ptolemies, 213 6ara (celestial latitude), 262 196, 197 Ptolemy, Euergetes, 165 .Sargon I, 215 202,217 Paraviddha, 101, 108 ; rules for, 109 Pulakesin I, 233 Saros, 184, 185, 159, 203, 204, 206 Parivatsara, 225 Pulakesb-It,'35ff Sarton, George, 188, Passpv^r last, 170 Pulastya, 236 Wastry, Mm. ;Bapudev, 259 Bidhusekhar, 235 Pataliputra, 10, 213, 234, 252. Puranas, 101, 252 pastry, Prof. Mm. 228, 233 Paultia Siddkinta^ffli Purnimfinta; moath, 157, 227,, 230, 231, 2S3, fSatakarni, Paulus of Alexandriav204* 23? 247, 256 (Satananda, 160 Perihelion, 242*, mbkfem^m.t ofj.S*3 Puruspur, 232 Satapatha Brahma^a, 18, 189, 219 Peshawar Museum (inscription), 229. 230 Purvahna, 101, 108 ^yljha^aa, 212+213, 227-231, 233, 234, 255, Philhellens, 213 PurvavidttBa^Wt,a08-p«iA» *rt?3fl9 Saturn, planetx,^, 195, 203^239 ;; ; ;; ; ; ; ; ; ; ; ;;

278 INDEX

Saura day, 197 Somakara, 222 Tithi. 183, 218, 227, 228, 230, 234, 236, 248 duration S&vana, 2, 157, 223, 224 Soaigenes, 168 average of, 221, 222, 224, 248 S&yahna, 106 Sothic cycle, 165 comparison of Siddhantic and modern, 3 defined, 3, Sayana, 1, 11, 12, 13, 217, 259 grlpati. 11,246 221 definition in Aitareya Brahmana, 221 Bcaliger, Joseph, 9, 11, 161 Srlsena, 237 ; on precession, 267 Scaliger, Julius, 162 Stone-henge, 189, 190 „ „ Siddhantas, 221 Vedanga Jyotisa, 224, 225 Schmidt, Dr. Olaf, 163 gudi, 247, 248 ,, ,, ; duration of Vedic tithi, 221 Schrader, 215 Suddha, 7, 247 error in the old method, 3, 14 Scientific American, 190 Sui Vihar (inscription), 230 ; lords of, 109 Scorpion, 193, 195, 198 Sulva-Sutras, 190, 214 ; measurement of, 248 Period Indian History, 232, 255 ; Scythian of Sun, distance from the earth, 208 ; names of, 222 239 ; Seasons, 157, 158, 174, 189, 216, 217, 227,230, entry into naksatras, 15, 40 ; numbers of, 15, 221, 222 causes of, 259 ; mass of, 208 189 Tiihitatvam, 101 determination by gnomon, mean daily motion, 197 ; Trepidation, theory of, 204, 206, 207,238, 240, error in counting, 260 ; semi-diameter of, 225 259, 268, 269 length of, 174, 175, 261 Sun-dial, 159 Tuladi, 239 moving back of, 18 ; Sun-rise, 15 ; Indian, Tycho Bvahe, 206 names of 217, 241, 260 ; timings of certain important places, 116

position of, 1, 6, 260 ; Sun-set, 15

relation of months with seasons in Vedic timings of certain important places, 116 ; age, Ullulu, 170 216, 218 ; Sunga, 213, 228, 235 in £g-Veda, 216, 217 Surya Pra/napti, 223 Ulugh Begh, 10 Seb, Egyptian god 164 Surya Siddhanta, 1, 2, 158, 189, 192, 203, 214, Umbra Extensa, 204 Seleucus, 178, 213, 228 236-240, 242-46, 250, 251, 253, 262-264, Umbra Versa, 204 Senas, Hindu ruling dynasty, 257 267, 268, 270 Und (inscription), 231 Seneca, 225 in, 240 Upanisads, 214, 215 calendar 239, ; 215, 221, 227, 238, 253, Urcmometry, 205 Sengupta, P. C, 183, description of, 238, 244 ; 266 error in length of year, 2, 241 Usavadata, Saka prince, 233 164 Ua-alafotlika, 101 Set, Egyptian god, length of the year, 2, 240, 241 ; Utkramajya, 204 Sewell, K. S., 246 star positions of, 264, 205 ; Sezta, 159 theory of trepidation, 268 Uttarfiyana. 189, 219, 224, 22G, 239, 260 (Sassanid king), 232 Shahpur I Sutras, 214. 215, 221 ; Shama Sastry, Dr. R., 223, 224 Srauta. Urhya, Dharma, Sulva, 214 Shin Kot (inscription), 229 Synodic period, 158, 175, 182 ; Vadi, 247, 248 Siddhanta Jyotisa, 161, 221 of planets acc. to P. 197 revolution S., Vaidya, Prof. R.V., 203 Siddhantas, 1, 2, 3, 163, 234, .236,237, 238, Syntaxis or Almagest, 192, 201, 203, 204 I Vt i dynna tht Di hs i f lyan h 101 245; Vajasancyi Swihhita, 218 Arya,238, 242,251; Vajheska, 231 Brahma, 238, 242, 251 Van dcr Waerdcn , 160 definition of, 234 Taittiriya Brahmana, 182 Varahamihira, 2, 7, 192, 193, 197, 223, 226, 236, Paitamaha, 236-238 ; Taittirlya Samhita, 218, 220, 221, 260 237, 238, 240, 252, 255, 267 Paulisa, 236-238 Takht-i-Bahi (inscription), 229 Varuna, Indian god, 215, 216 Roinaka, 236, 237, 240 ; Tantra, 163 Vasistha, Indian sage, 236 236, 238-244 Surya, 267 Tarn, 229, 255 Vasistha Siddhanta, 236, 237, Vasistha, 236, 237 Jaxila, 213, 228, 230, 256 Vasudcva I, 231, 232 Siddhanta Bokhara of 6rlpati, 162 Taxila copper plate (inscription), 229 Vasudcva II, 231, 232 Si<* V-Sada Siromatii of Bbaskaracarya, 238, and literature, 214 ; Taxila silver scroll (inscription), 229 Vedas, description _69 214, 215 Taxila silver vase (inscription), 229 age of its literature, , 158 Telephos of Kapsa, 230 Vedfingas, 214, 215 of the zodiac, 192, 193, 194, 196, 206, t Signs, 217, 224, 226, 237, 240, Tertia, 159 Vedanga Jyotisa, 101, 223, 224, 237, 239, 240 Tetrabibhs, 201, 204, 205 241,245,246; foksa, 214 Thabit-ibn-Qurra, 206 description of, 221-225 Sircar, 1>.C.,22*. 231, 233, 234 , 202 Vehsadjan, 232 Sirius, 104 Ventris, 202 prediction of solar eclipse, 202 ; givaratri, 108 planet, 194, 195, 198, 203, 239 Theaitetus of Athens, 202 Venus, ; Sky and Telescope, 177 ; heliacal rising and setting of, 6, 15 Thcon of Alexandria, 204, 206, 240 ; Solar day, mean, 157, 158 ; sec also Calendar for five years). on trepidation, 206, 240 ( division of, 159 ; equinox, 2, 158, 226, 239, 241, 267 Thibaut, Dr. G., 197, 223, 225, 237 Vernal Solar cycle, 162 ; point, 1, 158, 205 Thirteen- month calendar, 171 Vernal ; Solar time, mean, 158 ; movement of, 193, 194, 205, 267 Thoth, Egyptian god, 164 Solstices, 188, 189, 226 ; 159 Tigris, river, 157 Vespers, determination by Vedic Hindus, 266 ; Chandra, 260 215, 216 Vidyasagar, Pandit Ishwar observation in Aitareya Brahmana, 266 Tilak, B. G., 11, 189, 160 Time, natural divisions of, 157-160 Vighati, summer, 188, 189- 192, 226, 266 ; 255 Timocharis, 205 Vikramaditya, 254, winter, 13, 189, 192, 223, 224, 226, 241, Viksepa, 192,262-265,267 259 Tiridatcs, 178 ; 228 217, 227 Virapurusadatta, Solstitial colure, 226 Tisya, ; ; ;; ;; ; ; ; ;

INDEX 279

Visnu Candra,:237 ; on precession, 267 Year, 216 beginning of, 1, 6, ; 4, 13, 175 ; Year—contd. Visuvfin, 216, 219, 221, 266 beginning of in Brahmanas, 241, 245 ; starting day of the solar, 241 Viguvansa, 262 beginning of lunar. 221 ; Yoga, names and lords of, 110 Vogt, 203 "in Paitamaha, ; 223 ; calculation of, 110 Vrddha Garga, 252 *' in S. S., 239 Yogatara (junction star), 183, 184, 210, 211 Vyakarana, 214 " religious calendar , 251 Yuga, 217 " Siddhantic, 11, 241, 245 ; ofEomaka Siddhanta 237 " Solar, 2, 241 ; of Vedanga Jyotisa, 223, 224 Wardak (inscription), 230 " " Vedanga Jyotisa, 241, 245 ; Yugadi, 107 Water-clock, 157, 159 " Vedic Aryan, 216, 218 ; Webster, A. G., 207, 208 definition of, 157, 158 ; Week, 169, 170, 203, 223, 234. 251, 252 ; draconitic (eclipse), 186 Zarathustra, 167 origin and invention of, 169, 170 error in beginning of, 1, 13, 15, 241 Zeda (inscription), 230, 231 Winternitz, 214, 215, 218 error in beginning of Indian solar, 2 Ziggurat, 196 ; World Calendar Association, 10, 12, 171 first month of, Zinner, 4, 6, 241, 242, 251 ; Dr. Ernest, 164, 196 Worlds' day, 172, 173 Jovian (Barhaspatya), Zodiac, definition 270 ; of, 192, 193, 202 ;

length (average) of Babylonian, first point of , 14 161, 177 ; ; length of as foundby ancient lunar, astronomers, 182, 183, 223, 226 ; Vajasaneya, 218 174, 261 ; Arabian, 182, 183 Yajur Veda, 182, 183, 214, 218-222 " ; Brahmagupta, 162 Chinese, ; 182, 183 ; Black, 218; " Gregorian, 12, 13 ; Indian ( see naksatra) 6ukla, 218 " " Paitamaha, 223, 240 place of origin, 183 Yajurveda ; ; Samhita, 218 " " Ptolemy, 240 Kg Vedic, 217 ; Yajus Jyotisa, 222 " " sidereal, 158, 205, 240, position through ages, 246 ; 200 Yama, division of day, 55 160 " solar, 223 signs ; of the, 193 ; Yamakoti, 239 *' Surya " Siddhanta, 2,240, 241, 246'. starting point of, 193 Yamardha. 108 ; " " tropical, 1, 2, 4, 12, 158, 174, zero point of the Hindu, 262, 266, 287 Yaska, 214 175, f 205, 240, 246 269; Yavanapuri, 237 " Varahamihira, 240 Zodiacal signs, different names of, 193/see also Yavanas, 213, 256 *** " Vedic Aryan, 216 ; signs of the zodiac).