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Bharatiya Jyotihshastra (History of Indian Astronomy), translated by R. V. Vaidya v2: Volume 2

Bhāratīya Jyotiḥśāstra (History of Indian Astronomy), translated by R. V. Vaidya v2

Language
English

Contents

Volume 2

Front matter

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PART II

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History of Astronomy during the Siddhantic and Modern Periods

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Emblem of India

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PRINTED BY THE GENERAL MANAGER, GOVT. OF INDIA PRESS (PUB. UNIT), SANTRAGACHI, HOWRAH-4 AND PUBLISHED BY THE CONTROLLER OF PUBLICATIONS, CIVIL LINES, DELHI, 1981

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English Translation

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of

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(History of Indian Astronomy)

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by

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Sankar Balakrishna Dikshit

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[Translated by Prof. R. V. Vaidya, M. A. B. T.]

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PART II

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History of Astronomy during the Siddhantic and Modern periods

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PRINTED BY THE GENERAL MANAGER, GOVT. OF INDIA PRESS (PUB. UNIT), SANTRAGACHI, HOWRAH-4 AND PUBLISHED BY THE CONTROLLER OF PUBLICATIONS, CIVIL LINES, DELHI, 1981.

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Sale Price: Inland Rs 45/- Foreign £ 11.55 or 35 $ 64 Cents.

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Issued under the authority of THE DIRECTOR GENERAL OF METEOROLOGY, NEW DELHI INDIA METEOROLOGICAL DEPARTMENT MINISTRY OF TOURISM AND CIVIL AVIATION, GOVERNMENT OF INDIA

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Editing done at POSITIONAL ASTRONOMY CENTRE INDIA METEOROLOGICAL DEPARTMENT NEW ALIPORE, CALCUTTA-700053

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Copies available from :—

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IN INDIA :

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The Controller of Publications, Civil Lines, Delhi-110054

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Government of India Book Depot, 8, K. S. Roy Road, Calcutta-700001

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Government of India Kitab Mahal, Baba Kharak Singh Marg, New Delhi

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Government of India Book Depot, New Marine Lines, Bombay-400020

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And other agents selling Government of India publications.

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OUTSIDE INDIA : The High Commission of India : India House, Aldwych, London, W. C. 2.

Preface

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A treatise in Marathi “Bharatiya Jyotish Sastracha Prachin Ani Aryachin Itihas” by Sankar Balakrishna Dikshit, first published in the year 1896, is perhaps the only book on the history of the Indian Astronomy from ancient to modern times. Publication of an English translation of this monumental work was undertaken by the Meteorological Department of India in accordance with a recommendation by the late Professor M. N. Saha, D.Sc., F.R.S., Chairman of the Calendar Reform Committee. The first part of the English translation of this treatise, namely, “Bharatiya Jyotish Sastra, Part I” containing a history of Indian Astronomy in the Vedic and Vedanga period from ancient times upto 1000 B.C. was published by this department in 1968. The present volume contains an English translation of the remaining parts of the original treatise on the Siddhantic and the Modern periods.

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The translation of this treatise from Marathi to English was made by the late Professor R. V. Vaidya, a Marathi scholar and former Superintendent of Shree Jiwaji Observatory of Ujjain. He was also a member of the Calendar Reform Committee. This translation was also touched up by the late Professor P. C. Sen Gupta, a renowned Professor of Hindu Astronomy of the Calcutta University. The final editing of this volume has been made under the supervision of Shri A. Bandyopadhyay, Director, Positional Astronomy Centre of the Department at Calcutta. We expect this English translation of Dikshit’s excellent treatise will help scholars, both in India and abroad, to appreciate the remarkable achievement of Indian Astronomy during the ancient and medieval periods.

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India Meteorological Department, Mausam Bhavan, Lodi Road, New Delhi-110003. 16 September, 1981 (25 Bhadra, 1903 S.E.)

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P. K. DAS, Director General of Meteorology.

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PART II

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History of Astronomy during the Siddhantic and Modern Periods

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PART TWO

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HISTORY OF ASTRONOMY IN JYOTIṢA SIDDHĀNTA PERIOD

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1. GAṆITA SKANDHA (MATHEMATICAL BRANCH)

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(A) : MADHYAMĀDHIKĀRA (ADHIKĀRA ON MEAN PLACES)

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Chapter I.—History of Astronomical Works and Computation of Mean Places of Planets etc. 1

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Foreword 2

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The Group of Five Ancient Siddhāntas 3

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Pitāmaha Siddhānta 6, 47

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Vasiṣṭha Siddhānta 6

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Different Versions of Vasiṣṭha and Romaka Siddhāntas 9

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Romaka Siddhānta . 13

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Measures of the Year According to Different Works on Astronomy 14

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Puliśa Siddhānta 20, 36

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Sūrya Siddhānta 25, 26, 39

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The Pauruṣa (Human) Authors of Astronomical Works Before Śaka 420 (Lāṭa, Siṃha, Pradyumna, Vijayanandi) 26

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The Five Modern Siddhāntas 27

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Apauruṣeya, i.e., Divine 27

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The Numbers of Revolutions and Other Elements Mentioned by All the Five Siddhāntas 28

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The Yuga System 29

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General Description 30

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The Dates of the Five Siddhāntas 36

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Sūrya Siddhānta 37

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Subject Matter and Date 38, 65

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Maya 38

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Ptolemy 39

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A Relation Between the Two Sūrya Siddhāntas 41

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Lāṭa 41

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When Held in Reverence 41

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Works Following Modern Sūrya Siddhānta 41

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Anantadeva (Śaka 1144) . . . . . . . . . . 123

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Ādityapratāp Siddhānta . . . . . . . . . . 123

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Vāvilāla Koccannā (Śaka 1220) . . . . . . . . . 123

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Grahasiddhi (Śaka 1238) . . . . . . . . . . 123

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Nārmada (About Śaka 1300) . . . . . . . . . . 125

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Padmanābha (About Śaka 1320) . . . . . . . . . 125

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Dāmodara (Śaka 1339) . . . . . . . . . . 125

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Makaranda (Śaka 1400) . . . . . . . . . . 127

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Keśava . . . . . 127, 194

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Keśava II (Śaka 1418) . . . . . . . . . . 128

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Observations . . . . . . . . . . . 129

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Gaṇeśa Daivajñya (Śaka 1442) . . . . . . . . . 130

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Grahalāghava . . . . . . . . . . . 132

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His Speciality . . . . . . . . . . . 133

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Planetary corrections . . . . . . . . . . 134

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Kalpadruma Karaṇa . . . . . . . . . . 139

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Lakṣmīdāsa (Śaka 1422) . . . . . . . . . . 139

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Jñānarāja (Śaka 1425) . . . . . . . . . . 140

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Sūrya (Birth Śaka 1430) . . . . . . . . . . 144

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Dhuṇḍhirāja . . . . . . . . . . . 146

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Ananta (About Śaka 1480) . . . . . . . . . . 147

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Raghunātha (Śaka 1484) . . . . . . . . . . 149

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Raghunātha (Śaka 1487) . . . . . . . . . . 149

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Kṛpārāma . . . . . 149

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Dinkara (Śaka 1500) . . . . . . . . . . 149

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Gaṅgādhara (Śaka 1508) . . . . . . . . . . 150

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Rāmabhaṭa (Śaka 1512) . . . . . . . . . . 151

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Śrīnātha (Śaka 1512) . . . . . . . . . . 151

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Viṣṇu (Śaka 1530) . . . . . . . . . . 151

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Mallāri (About Śaka 1524) . . . . . . . . . . 155

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Viśvanātha . . . . . 156

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Other Works and Authors Belonging to Periods Later Than Śaka 950 . . . 193

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Śrīpati . . . 193

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Keśava . . . 194

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Graha Siddhi by Mahādeva . . . 194

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Kāmadhenu Karaṇa by Mahādeva (Saka 1289) . . . 194

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Gaṅgādhara (Saka 1356) . . . 195

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Nṛsiṃha (Śaka 1480) . . . 195

Chapter II—The Universe.

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Orbital Length in Yojanas . . . 196

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Moon’s Distance from the Earth . . . 196

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Distance of Planets from the Earth . . . 196

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Earth’s Radius . . . 199

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What Distance Does ‘Yojana’ Indicate . . . 199

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To Calculate the Distance in Degrees . . . 200

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Support for Universe . . . 200

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Attraction . . . 201

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Description of the Earth . . . 201

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Views of the Sky . . . 201

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Meru and Seven Worlds . . . 202

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Atmosphere Enveloping Earth . . . 202

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Pravaha and Other Kinds of Winds . . . 202

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Revolutions of Planets . . . 203

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Light of Planets . . . 203

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Vikṣepas of Planets . . . 203

Chapter III—“Ayana Calana” or Displacement of Solstitial Points

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Measure of Displacement of Solstitial Points . . . 206

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Does the Equinoctial Point Oscillate or Revolve . . . 212

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Accuracy of Ayana Motion . . . 213

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Findings of Other Nations Regarding the Rate of Precession . . . 214

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Accuracy of Zero-Precession Year . . . 215

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How Ayana Motion and the rate of Zero-Precession Were Determined . . . 218

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Association of the Junction-Star of Revati with Ayanāṃśa-Problem . . . 218

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When was Precessional Motion Finally Determined . . . 220

Transliteration

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

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| अ | आ | इ | ई | उ | ऊ |
| a | ā | i | ī | u | ū |
| ऋ | लृ | ए | ऐ | ओ | औ |
| ṛ | ḷ | e | ai | o | ou |
| क् | ख् | ग् | घ् | ङ् | |
| k | kh | g | gh | ṅ | |
| च् | छ् | ज् | झ् | ञ् | |
| c | ch | j | jh | ñ | |
| ट् | ठ् | ड् | ढ् | ण् | |
| ṭ | ṭh | ḍ | ḍh | ṇ | |
| त् | थ् | द् | ध् | न् | |
| t | th | d | dh | n | |
| प् | फ् | ब् | भ् | म् | |
| p | ph | b | bh | m | |
| य् | र् | ल् | व् | श् | |
| y | r | l | v | ś | |
| ष् | स् | ह् | ं | ः | |
| ṣ | s | h | ṃ | ḥ | |

Part Two: History of Astronomy in Jyotiṣa Siddhānta Period

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HISTORY OF ASTRONOMY

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IN JYOTIṢA SIDDHĀNTA PERIOD

1 Gaṇita Skandha (Mathematical Branch)

A : Madhyamādhikāra (Adhikāra on Mean Places)

Chapter I

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*History of astronomical Works and Computation of mean places of Planets etc.*

Foreward

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As mentioned in the INTRODUCTION,[*] the author proposes to discuss the History of the science of Astronomy from about 500 years before Śaka era to this day; and in the beginning, this first chapter of the Madhyamādhikāra (i.e. a section on mean places) under the GAṆITA SKANDHA (i.e. a Branch of Mathematics) will deal with the history of astronomical works and the question of computing the mean motions and places of planets.

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The knowledge of astronomy as developed during the Vedic and Vedāṅga Jyotiṣa periods and described in Part I, was considerable as compared with the pace of general progress during the period; but it would appear very meagre, when compared with the ability (developed in a later period) to predict the true positions of planets. It appears that some works might have been compiled during the interval between these periods. There may be some Saṃhitā works of that type; but they are either not available now or have not been seen by him. The period of Siddhāntic astronomy can somehow be linked with the ancient period. This point will be discussed later on; but we have no information as to how the knowledge of astronomy reached the highest stage of calculating the true motions and places of planets, how observations used to be taken and how the motions of planets were finally fixed after comparing the different observations. The oldest of astronomical (Siddhānta) works reveal a sudden rise in the standard of astronomical knowledge. Those who raised the standard of such knowledge through their works were naturally regarded as superhuman, and thus arose the popular belief that the available ancient works on mathematical astronomy are regarded as ‘apauruṣeya’ (i.e. not compiled by any mortal man), and it is clear that this belief has been formed later.

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Because these works were regarded as superhuman, they naturally did not include the description of subjects like observations. There seems to be another very strong reason for this omission. Looking to the conditions of those days when as a rule ‘shorter the works, the easier they were to commit to memory’, such works dealt with only the rules of calculating the motions and places of planets, and they appear to have avoided length by omitting the underlying theory.

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∗ Pulished in part I of the book

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The author proposes to deal with all works on astronomy in chronological order in this chapter on mean places. Their points of differences, if any, with matters pertaining to other Adhikāras from different works, as also some special points worth mentioning, have been treated in subsequent chapters ; otherwise, all information about the works has been given in this very chapter on mean places. Some works are considered divine while some authors have more than one book to their credit ; hence, the following account is arranged under the names of authors, and at places, under the titles of their works.

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The oldest known works on astronomy are the five Siddhāntas—the Sūrya Siddhānta and others. These are regarded as divine. They are again of two kinds. The Pañcasiddhāntikā of Varāhamihira mentions the Saura and other four Siddhāntas ; but at present they are not available. The Pañcasiddhāntikā simply provides clues to their elements. The author calls them the ‘ancient Siddhānta Pañcaka’ or ‘group of five ancient Siddhāntas’. There are five other Siddhāntas likewise entitled the Saura, which are at present available. He calls them ‘the modern group of five Siddhāntas’. These will presently be dealt with. First he takes up for consideration the group of five ancient Siddhāntas. These belong to the 5th century before Śaka era. Some of them may belong to an even earlier period.

The group of five ancient Siddhāntas

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The following are the Siddhāntas mentioned by Varāhamihira :—

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पौलिशरोमकवसिष्ठसौरपैतामहास्तु पंचसिद्धांताः ।।

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Pauliśa, Romaka, Vasiṣṭha, Saura and Paitāmaha are the five Siddhāntas.

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The elements described by the Pañcasiddhāntikā show that the Siddhāntas were different from the five modern Siddhāntas. Not only are these not available at present, but even the original work, entitled Pañcasiddhāntikā is not available and so, not much is known to any one on this side. Two copies of the work brought from Kashmir by Dr. Buhler are preserved in the Government collection of Manuscripts in the Deccan College (See Reg. No. 37 of 1874-75 and No. 338 of 1879-80) ; but these are very incorrect and incomplete and one is unable to find, at places, where one āryā (couplet) ends and the next one begins. The author has written out for himself a copy from the two versions, and calculations made therefrom have shown that the Sūrya and other Siddhāntas described in it, are different from the modern ones, in that they differ in the length of the year and the motions of planets. The astronomical works compiled during the last 800 years do not show that any one knew that there existed before a Sūrya-Siddhānta different from the modern one. He came to know of their existence in 1887 and no doubt reed be entertained about it, since this can be proved by calculations and by other evidence. The booklet of the Pañcasiddhāntikā is very incorrect and the major portion of it is unintelligible for want of a commentary ; however mary important points have been understood.. *The author would, therefore, describe briefly the five Siddhāntas in the order of the dates of their compilation as found by him.

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∗ *Dr. Thibaut published in 1889 A.D. the Pañcasiddhāntikā based on the Deccan College versions. It also gives a new commentary by Sudhākara Dvivedī. The author could not find time to read the whole of it uptil now. However all the important information which he could glean from the Pañcasiddhāntikā has already been given above.

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Varāhamihira, in the very first chapter of Pañcasiddhāntikā, observes as follows ;—

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पौलिशाति* विस्फुटसौ तस्यासन्नस्तु रोमक: ।।
स्पष्टतर: सावित्र: परिशेषौ दूरविभ्रष्टौ ।। ४ ।।

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“The Siddhānta made by Pauliśa is accurate ; near to it stands the Siddhānta by Romaka ; more accurate still is the Sāvitra (Saura). The two remaining ones are far from truth.”

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This shows that the Pauliśa Siddhānta was very clear at the time of the compilation of Pañcasiddhāntikā, which means that its calculations very much agreed with the actual observed positions. The Romaka was nearer to it in correctness. The Sūrya-Siddhānta was better than both and the remaining two (Vasiṣṭha and Pitāmaha) were far removed from correctness meaning that their calculations did not agree with the observed results. The Pitāmaha Siddhānta and Vasiṣṭha Siddhānta must have been the oldest of the five, and of the these two, in the author’s opinion, Pitāmaha Siddhānta must have been the more ancient. The reasons for this will be given later on. Let us now consider the Pitāmaha Siddhānta.

Pitāmaha Siddhānta

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The Subject matter

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The basic principles underlying the Pitāmaha Siddhānta have been given in the 12th chapter of the Pañcasiddhāntikā. That chapter contains only five āryās (couplets). Nowhere else in the Pañcasiddhāntikā is found anything about this Siddhānta. The first two of the five couplets run thus :—

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रविशशिनो: पंच युगं वर्षाणि पितामहोपदिष्टानि ।। अधिमासस्त्रिंशद्भिर्मासैरवमस्त्रिषष्ट्याह्नां ।।
दूनं शकेन्द्रकालं पंचभिरुद्ध्य शेषवर्षाणि ।। युगं माघसितार्थं कुर्याद्युगुणस्तदन्युदयात् २ ।।

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“According to the teaching of Pitāmaha, five years constitute a yuga of the sun and the moon. The adhimāsas occur after thirty months and an omitted lunar day (avam) once in sixty three days. Lessen the time of the Śaka King by two and divide the remainder by five ; with the remaining years find the ahargaṇa, counting from the first day of the light half of Māgha. The Ahargaṇa thus found begins with sunrise”.

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The fifth couplet describes the method of calculating the length of the day :—

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द्विघ्नं शशिरस (६१) भवतं † द्वादशहीनं दिवसमानं ।।

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† The word ‘hinam’ in this couplet is incorrect ; the proper word must be ‘yuktam’. The first half of the couplet is incorrect and has not, therefore, been given here, but it means nothing more than that has been given above within brackets.

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“Multiplying (the number of days elapsed after winter solstice or the number of days to go before the end of the ayana beginning with summer-solstice) by 2 divide by 61. Add 12 (muhūrtas) to the quotient, and the result will be the length of the day”.

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∗ The author copied out the couplets from the Pañcasiddhāntikā, exactly as they are written in his book. Dr. Thibaut has introduced new readings in the next and he has accepted at places only such of them which were considered suitable.

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This verse and the following, describing the method of calculating the nakṣatra, and stating that the nakṣatra should be counted from the Dhaniṣṭhā onward, show that the Pitāmaha Siddhānta has some similarity with the Vedāṅga Jyotiṣa system.

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Date of Compilation

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The method followed by Varāhamihira in explaining the Pitāmaha Siddhānta involves Śaka era but it has been used simply to calculate the ‘ahargaṇa’. The methods attributed to other Siddhāntas also direct one to calculate the ‘ahargaṇa’ from Śaka 427. Just as this does not imply that the Siddhāntas were compiled (by Varāhamihira himself), in Śaka 427, it cannot be taken to imply that the Pitāmaha Siddhānta was compiled after the beginning of Śaka era. It is evident from its similarity with the Vedāṅga Jyotiṣa system that it must have been more ancient than the beginning of Śaka era. There are, however, no means to fix up the date of its compilation.

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Āryabhaṭa I has, in the beginning of *Daśagītikā* written the following benedictory verse :—

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प्रणिपत्यैकमनेकं कं सत्यां देवतां परं ब्रह्म ।। आर्यभटस्त्रीणि गदति गणितं कालक्रियां गोलं ।।१।।

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“After saluting the Pitāmaha (kam) who is manifold and one at the same time, the god of truth and the Parabrahma, Āryabhaṭa describes the three subjects viz. mathematics, method of calculating time and the celestial spheree and in his last couplet he observes,

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आर्यभटीयं नाम्ना पूर्वं स्वायंभुवं सदा सदसत् ।।

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“The science known as the Āryabhaṭīya is the same as the science originaly expounded by Brahmā himself”.

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This shows that the Pitāmaha Siddhānta must have been compiled long before Āryabhaṭa lived (i.e. Śaka 421)

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Brahmagupta (Śaka 550) , in his Siddhānta, observes,

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ब्रह्मोक्तं ग्रहगणितं महता कालेन यत्खिलीभूतं ।।३भिर्धृतं स्फुटं तत् जिष्णुसुतब्रह्मगुप्तेन ।।२।।

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“The calculation of planets’ places as propounded by Brahmā has, become disjointed on account of (lapse of) long time ; Brahmagupta, the son of Jiṣṇu, is describing the same in clearer terms”.

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There are three Brahma Siddhāntas available at present. One is the Brahma Siddhānta by Brahmagupta, the second, the Brahma Siddhānta mentioned in Śakalya Saṃhitā and the third that included in Viṣṇudharmottara tarapurāṇa. In the Author’s view, to be explained later, the Viṣṇudharmottara and the Śakalyokta Brahma Siddhāntas are not older than the Brahmagupta’s time, but compiled much later. The basic principles, propounded by the Śakalya Brahma Siddhānta, even it be more ancient than Brahmagupta, are exactly the same as those propounded by the modern Sūrya-Siddhānta. It may as well be said to be in current use and not antiquated or disjointed ; and it will be shown further that the Viṣṇudharmottara Brahma Siddhānta is not similar to the Brahmagupta Siddhānta. This shows that the Brahma Siddhānta to which Brahmagupta has referred as containing mathematics explained by Brahmā, must have been different from the Brahma Siddhāntas of Śakalya Saṃhitā and Viṣṇudharmottarapurāṇa and it must be the same as the Pitāmaha Siddhānta of the Pañcasiddhāntikā. The Vedāṅga Jyotiṣa does not deal with the calculation of planets other than the sun and the moon; and the Pitāmaha Siddhānta of the Pañcasiddhāntikā also describes the calculations of the sun and the moon only. Varāhamihira has given the calculations of all planets in the case of only the Sūrya-Siddhānta out of the five Siddhāntas and mentions nothing about the planetary calculations contained in the Pitāmaha Siddhānta. It must have, however, contained the calculations of planets as remarked by Brahmagupta, and Varāhamihira appears to have omitted it, on finding that it did not agree with the actual observed places on account of lapse of time. A Pitāmaha Siddhānta, different from the one described in the Pañcasiddhāntikā, does not appear to have ever existed before Brahmagupta. The words “planetary calculations given by Brahmā” occurring in Brahmagupta’s work must certainly be referring to the Pitāmaha Siddhānta of the Pañcasiddhāntikā, and the remark, “a long time has elapsed” also refers to the same Pitāmaha Siddhānta. It follows, therefore, that it must have been compiled long before the Śaka era.

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Āryabhaṭa and Brahmagupta appear to have expressed veneration for the Pitāmaha Siddhānta only as a formality, because their siddhāntas and the Pitāmaha Siddhānta of the Pañcasiddhāntikā have nothing in common. It has already been pointed out in the course of the study of the Vedāṅga Jyotiṣa that Brahmagupta has openly found fault with the five-year Yuga system. Still, these arguments in no way affect the inference that there existed a Siddhānta known as the Pitāmaha Siddhānta before these two astronomers lived.

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The System

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The Pañcasiddhāntikā gives in the beginning two couplets relating to the Pitāmaha Siddhānta, the first of which contains the expression,

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अधिमासस्त्रिंशद्विमसैः

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meaning, “an intercalary month to be reckoned after 30 months”. It has been shown in the study of Vedāṅga Jyotiṣa that the adoption of an intercalary month after 30 months causes a grave error; but this very couplet has been cited by Bhaṭṭotpala in his commentary on Vṛhatsaṃhitā in connection with the verse “ekaikamabdeṣu” in Chapter 8. The reading there is “adhimāso dwyagnisamāisaiḥ” which means that an intercalary month is to be reckoned after 32 months. Again the same couplet is found in the commentary (Chapter I) by Mahādeo on Śrīpati’s Ratnamālā and it also gives “adhimāso dwyagnisamāiḥ” as the reading. It is strange that there is room for confusion due to doubtful readings at such an important place.

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If it be assumed that Utpala and Mahādeo changed the original reading viz. “triṃśatbhirmāsaiḥ”, why should they have substituted “dwyagnisamāiḥ” as the reading? The intercalary month occurs after more than 32½ months, and hence, they could have as well substituted some words meaning 32½ or 33. It appears, therefore, that “dwyagnisamāiḥ” must have been the original reading. According to the Vedāṅga Jyotiṣa one day (tithi) is suppressed after 62 days, while the above couplet mentions the suppression of one day as occuring after 63 days (tithis). This shows that the Vedāṅga Jyotiṣa and the Pitāmaha Siddhānta are not similar to each other completely, and this also lends an additional support to the view that “dwyagnisamaiḥ” must have been the original reading.

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The number of intercalary months in 8 years comes to be 3 at the rate of one intercalary month in 32 months. This gives 99 as the number of lunar months in 8 years and 2970 as the number of tithis (lunar days); and 47 1/6 lunar days will be suppressed during this number of tithis at the rate of one suppressed tithi per 63 lunar days. Hence, 8 years will be equal to 2922 6/7 sāvana days or one year will be equivalent to 365 days and 21 3/4 ghaṭis. This measure of a year is more accurate than that found in the Vedāṅga Jyotiṣa.

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The Pitāmaha Siddhānta existed before Āryabhaṭa, Varāhamihira, and Brahmagupta. As it had fallen into disuse in their times it is evident that it must have beer compiled long before them. It is similar to the Vedāṅga Jyotiṣa but differs from it much. Brahmagupta’s statement shows that it (the Pitāmaha Siddhānta) contained the calculations of Mars and other planets, which is not given in the Vedāṅga Jyotiṣa. It proves that a more accurate work known as the Pitāmaha Siddhānta was compiled sometime after the Vedāṅga Jyotiṣa and this is an important fact. If it were known how the places of Mars and other planets used to be calculated according to the Pitāmaha Siddhānta, it would have been found very useful in tracing the growth of Indian astornomy; but we have almost no hopes of obtaining the Pitāmaha Siddhānta now in its original form.

Vasiṣṭha Siddhānta

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The Date

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The Pañcasiddhāntikā contains 13 āryās (couplets) relating to Vasiṣṭha Siddhānta. The system described by it is somewhat different from that met with in other siddhāntic works. This fact and also the statement of Varāhamihira that “Vasiṣṭha is very inaccurate” leads one to infer that it must have been more ancient than the remaining three siddhārtas excepting the Pitāmaha Siddhānta.

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The System

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The thirteen couplets show that they mention nothing about planets other than the sun and the moon. The method of calculating tithis and nakṣatras is not similar to that of the present day. It mentions the rāśi (sign), aṃśa (degree) and Kalā (minutes) as the units and the subject of ‘shadow’ has been considered at length. Something has been told about the length of the day and the word ‘lagna’ (ascendant) has been used in a somewhat present day sense. The Vasiṣṭha Siddhānta, available at present, is in no way similar to the one existing before Varāhamihira’s time and did not exist in his time. This question will be discussed again later on.

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Different versions of Vasiṣṭha and Romaka Siddhāntas

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Two versions of the Vasiṣṭha and Romaka Siddhāntas were known at the time of Brahmagupta (Śaka 550). The case of Romaka Siddhānta will automatically be considered along with the evidence on the basis of which it is to be proved that there were two kinds of Vasiṣṭha Siddhānta. Let both of them, therefore, be considered together.

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Brahmagupta says at one place in his Siddhānta,

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पौलिशरोमकवासिष्ठसौरपैतामहेषु यत्प्रोक्तं ।। तन्नक्षत्रयनं नार्यभटोक्तं तदुक्तितरतः ।। ४६ ।।

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“I describe the ‘nakṣatrānayana’ i.e. the method of calculating nakṣatras, which has been given by other Siddhāntas viz. Pauliśa, Romaka, Vāsiṣṭha, Saura and Paitāmaha but not given by Āryabhaṭa”.

v2.c12.s2.t5.10

He observes at another place,

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अयमेव कृतः सूर्येंदुपुलिशरोमकवसिष्ठयवनाद्यैः ।।

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“This very (beginning of a yuga) has been adopted by Sūrya, Indu, Puliśa Romaka, Vasiṣṭha and Yavana”.

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Brahmagupta has cited as authority of the Sūrya and other Siddhāntas because these were in his favour. The Brahmagupta Siddhānta as a whole, appears to have launched a vigorous attack against Āryabhaṭa and others. He is, as it were, showering volleys of vituperation. Even then he has not made any direct attack against the group of first (Sūryādi) five Siddhāntas except the Romaka, and he has explicitly found fault with the Pattern, ony once, as may be seen from the following couplet :—

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युगमन्वंतरकल्पाः कालपरिच्छेदकाः स्मृतायुक्ताः ।। यस्मान्न रोमके ते स्मृतिबाह्यो रोमकस्तस्मात् ।। १३ ।।

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“The smṛti works mention yuga, manvantara and kalpa as the broad units of time. The Romaka has violated the Smṛtis since it does not mention them”.

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Brahmagupta, at another place, observes,

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लाटात्सूर्यशशांकौ मध्याद्विद्वच्चचंद्रपातो च ।। कुजबुधशीघ्रबृहस्पतिसितशीघ्रशनैश्चरान् मघमान् ।। ४८ ।। युगयातवर्षभगणान् वासिष्ठान् विजयनांदिकृतपादान् ।। मंदोच्चपरिधिपातस्पष्टीकरणाद्यार्यभटात् ।। ४९ ।। श्रीषेणेन गृहीत्वा रत्नोच्चयरोमकः कृतः कंथा ।। एतान्येव गृहीत्वा वासिष्टो विष्णुचंद्रेण ।। ५० ।।

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*The gist*

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“Śrīṣeṇa has compiled a ‘kanthā’ (i.e. a patch work) entitled as Romaka, by borrowing elements from different Siddhāntas, e.g. (i) mean sun and moon, moon's apogee, moon's node, Mars, Mercury, Jupiter, Venus, and Saturn from Lāṭa's work (ii) elapsed years of yugas and bhagaṇa (sidereal revolutions) from Vasiṣṭha (iii) the pāda (quadrants) from Vijayanandi's works and (iv) mandocca, aphelia, paridhi (epicycle), nodes of planetary orbits and calculations of true places from Āryabhaṭiya. Viṣṇucandra has similarly, compiled the Vasiṣṭha Siddhānta by borrowing the same elements".

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It has been said above that Viṣṇucandra has borrowed the same elements from other works in compiling the Vasiṣṭha Siddhānta as Śrīṣeṇa had borrowed in compiling the Romaka Siddhānta, and it has also been observed that Śrīṣeṇa took the bhagaṇas and the elapsed years of yugas from the Vasiṣṭha This shows that Viṣṇucandra also adopted the same elements from the Vasiṣṭha Siddhānta and other information from other Siddhāntas and compiled another Vasiṣṭha Siddhānta. It, therefore, shows that there existed two kinds of Vasiṣṭha Siddhāntas and that this was known to Brahmagupta. One of them was the original Vasiṣṭha Siddhānta and the other was Viṣṇucandra's Vasiṣṭha Siddhānta, compiled by borrowing some elements from the first.

v2.c12.s2.t5.21

It has already been remarked before that Brahmagupta has abused Romaka Siddhānta as 'a violator of Smṛti', because it does not give the time units of yuga, manvantara and kalpa; but it has also been shown above that Brahmagupta himself says that Śrīṣeṇa picked up the figures for 'elapsed years of yuga', from the Vasiṣṭha Siddhānta while compiling the Romaka Siddhānta. Similarly, he again observes,

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तद्युगबधो महायुगमुक्तं श्रीषेणविष्णुचंद्राद्यैः ।।
अ० ११ आर्या १५.
मेषादितः प्रवृत्ता नार्यभटस्य स्फुटा युगस्यादौ ।। श्रीषेणस्य कुजाद्याः
अ० २ आ० ४६.

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"That Śrīṣeṇa, Viṣṇucandra and other authors have mentioned 'Mahāyugas as a multiplicity of yugas' ...

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"Śrīṣeṇa has not given true positions of Mars and others from the commencement of a yuga, as is done by Āryabhaṭa, but from the beginning of Meṣa".

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Thus, according to the statement of Brahmagupta himself, the Romaka Siddhānta by Śrīṣeṇa did contain the yuga system and from this (it can be inferred that) there were two siddhāntas named Romaka, at the time of Brahmagupta— the one known as the original Romaka Siddhānta and the other, that 'compiled by Śrīṣeṇa'.

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Most of the names of astronomers who lived before Brahmagupta and who have been mentioned in his Siddhānta, are found in the Pañcasiddhāntikā. However, the names of Śrīṣeṇa and Viṣṇucandra are not found in the Pañcasiddhāntikā which mentions only one Siddhānta each, named as Vasiṣṭha and Romaka. This goes to show that Śrīṣeṇa's Romaka Siddhānta and Viṣṇucandra's Vasiṣṭha did not exist before Śaka 427, and that only the original Romaka Siddhānta and the original Vasiṣṭha Siddhānta existed then and these are given in the Pañcasiddhāntikā only in summary form. According to Brahmagupta, Śrīṣeṇa and Viṣṇucandra borrowed the method of finding true places from Āryabhaṭa. This also shows that they compiled their respective Siddhāntas after Śaka 421 while the Pañcasiddhāntikā leads to the conclusion that they were compiled after the Śaka 427.

Romaka Siddhānta

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It has been pointed out above that out of the two Romaka Siddhāntas described, only the original Romaka Siddhānta existed at the time of the Pañcasiddhāntikā. Let us now consider this Romaka Siddhānta.

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A large portion of the Pañcasiddhāntikā has been devoted to Romaka Siddhānta. Three couplets of the first chapter beginning from the 8th describe the method of finding the ‘ahargaṇa’. The fifteenth couplet mentions the intercalary months and the suppressed tithi. All the 18 ‘āryās’ of the 8th chapter are devoted to Romaka Siddhānta. They describe the calculations of the sun and moon, their true places and the method of calculating solar and lunar eclipses.

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The very first couplet giving the method of calculating the ‘ahargaṇa’ according to the Romaka Siddhānta runs thus :—

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