YY) \ 3 SY \ DK errr ACY 77# 210102100 225700 اا‎ ١ ot the Theologicas Sem; 37 PRINCETON, N. J. Division \_. Section....e. Number td TRUBNER’S ORIENTAL SERIES. ** A knowledge of the commonplace, at least, of Oriental literature, philo- sophy, and religion is as necessary to the general reader of the present day as an acquaintance with the Latin and Greek classics was a generation or so ago. Immense strides have been made within the present century in these branches of learning; Sanskrit has been brought within the range of accurate philology, and its invaluable ancient literature thoroughly investigated ; the language and sacred books of the Zoroastrians have been laid bare; Egyptian, Assyrian, and other records of the remote past have been deciphered, and a group of scholars speak of still more recondite Accadian and Hittite monu- ments ; but the results of all the scholarship that has been devoted to these subjects have been almost inaccessible to the public because they were con- tained for the most part in learned or expensive works, or scattered through- out the numbers of scientific periodicals. Messrs. TrUBNER & Co., ina spirit of enterprise which does them infinite credit, have determined to supply the constantly-increasing want, and to give in a popular, or, at least, a compre- hensive form, all this mass of knowledge to the world.”— Times. Second Edition, post 8vo, pp. xxxii.—748, with Map, cloth, price ars. THE INDIAN EMPIRE : ITS PEOPLE, HISTORY, AND PRODUCTS. By the Hon. Sim W. W. HUNTER, K.C.S.1., C.S.1, C.LE, LL.D., Member of the Viceroy’s Legislative Council, Director-General of Statistics to the Government of India. Being a Revised Edition, brought up to date, and incorporating the general results of the Census of 1881, “Tt forms a volume of more than 700 pages, and is a marvellous combination of literary condensation and research. It gives a complete account of the Indian Empire, its history, peoples, and products, and forms the worthy outcome of seventeen years of labour with exceptional opportunities for rendering that labour fruitful. Nothing could be more lucid than Sir William Hunter’s expositions of the economic and political condition of India at the present time, or more interesting than his scholarly history of the India of the past,”—The Times. TRUBNER'’S ORIENTAL SERIES. THE FOLLOWING WORKS HAVE ALREADY APPEARED :— Third Edition, post 8vo, cloth, pp. xvi.—428, price 16s. ESSAYS ON THE SACRED LANGUAGE, WRITINGS, AND RELIGION OF THE PARSIS. By MARTIN HAUG, Pu.D., Late of the Universities of Tiibingen, Géttingen, and Bonn; Superintendent of Sanskrit Studies, and Professor of Sanskrit in the Poona College. EDITED AND ENLARGED BY Dr. E. W. WEST. To which is added a Biographical Memoir of the late Dr. Hauce by Prof. E. P. Evans. I. History of the Researches into the Sacred Writings and Religion of the Parsis, from the Earliest Times down to the Present. II. Languages of the Parsi Scriptures. 111. The Zend-Avesta, or the Scripture of the Parsis. IV. The Zoroastrian Religion, as to its Origin and Development. ‘*< Essays on the Sacred Language, Writings, and Religion of the Parsis,’ by the late Dr. Martin Haug, edited by Dr. E. W. West. The author intended, on his return from India, to expand the materials contained in this work into a comprehensive account of the Zoroastrian religion, but the design was frustrated by his untimely death. We have, however, in a concise and readable form, a history of the researches into the sacred writings and religion of the Parsis from the earliest times down to the present—a dissertation on the languages of the Parsi Scriptures, a translation of the Zend-Avesta, or the Scripture of the Parsis, and a dissertation on the Zoroas- trian religion, with especial reference to its origin and development.” —Times. Post 8vo, cloth, pp. vili—176, price 7s. 6d. TEXTS FROM THE BUDDHIST CANON COMMONLY KNOWN AS “DHAMMAPADA.” With Accompanying Narratives. Translated from the Chinese by 8. BEAL, B.A., Professor of Chinese, University College, London. The Dhammapada, as hitherto known by the Pali Text Edition, as edited by Fausbéll, by Max Miiller’s English, and Albrecht Weber’s German translations, consists only of twenty-six chapters or sections, whilst the Chinese version, or rather recension, as now translated by Mr. Beal, con- sists of thirty-nine sections. The students of Pali who possess Fausbdll’s text, or either of the above-named translations, will therefore needs want Mr. Beal’s English rendering of the Chinese version; the thirteen above- named additional sections not being accessible to them in any other form ; for, even if they understand Chinese, the Chinese original would be un- obtainable by them. Beal’s rendering of the Chinese translation is a most valuable aid to the‏ عور“ critical study of the work. It contains authentic texts gathered from ancient‏ eanonical books, and generally connected with some incident in the history of‏ Buddha. Their great interest, however, consists in the light which they throw upon‏ everyday life in India at the remote period at which they were written, and upon‏ the method of teaching adopted by the founder of the religion. The method‏ employed was principally parable, and the simplicity of the tales and the excellence‏ of the morals inculcated, as well as the strange hold which they have retained upon‏ ihe minds of millions of people, make them a very remarkable study.”— Times.‏ “Mr. Beal, by making it accessible in an English dress, has added to the great ser- vices he has already rendered to the comparative study of religious history.”—Acodemy. “© Valuable as exhibiting the doctrine of the Buddhists in its purest, least adul- terated form, it brings the modern reader face to face with that simple creed and rule of conduct which won its way overthe minds of myriads, and which is now nominally professed by 145 millions, who have overlaid its austere simplicity with innumerable ceremonies, forgotten itsmaxims, perverted its teaching, and so inverted its leading principle that a religion whose founder denied a God, now worships that founder as a god himself.” —Scotsman. TRUBNER’S ORIENTAL SERIES. Second Edition, post 8vo, cloth, pp. xxiv.—360, price ros. 6d. THE HISTORY OF INDIAN LITERATURE. By ALBRECHT WEBER. Translated from the Second German Edition by JoHN Mann, M.A., and THEODOR ZACHARIAE, Ph.D., with the sanction of the Author. Dr. BUHLER, Inspector of Schools in India, writes :—‘* When I was Pro- fessor of Oriental Languages in Elphinstone College, I frequently felt the want of such a work to which I could refer the students.” Professor CowELL, of Cambridge, writes :—‘‘It will be especially useful to the students in our Indian colleges and universities. I used to long for such a book when I was teaching in Caleutta. Hindu students are intensely interested in the history of Sanskrit literature, and this volume will supply them with all they want on the subject.” Professor WHITNEY, Yale College, Newhaven, Conn., U.S.A., writes :— ‘©T was one of the class to whom the work was originally given in the form of academic lectures. At their first appearance they were by far the most learned and able treatment of their subject ; and with their recent additions they still maintain decidedly the same rank.” “Is perhaps the most comprehensive and lucid survey of Sanskrit literature extant. The essays contained in the volume were originally delivered as academic lectures, and at the time of their first publication were acknowledged to be by far the most learned and able treatment of the subject. They have now been brought up to date by the addition of all the most important results of recent research,”— Times. Post 8vo, cloth, pp. xii.—198, accompanied by Two Language Maps, price 7s. 6d. A SKETCH OF THE MODERN LANGUAGES OF THE EAST INDIES. By ROBERT N. CUST, The Author has attempted to fill up a vacuum, the inconvenience of which pressed itself on his notice. Much had been written about the languages of the East Indies, but the extent of our present knowledge had not even been brought to a focus. It occurred to him that it might be of use to others to publish in an arranged form the notes which he had collected for his own edification. “Supplies a deficiency which has long been felt.” —Times. “The book before us is then a valuable contribution to philological science. It passes under review a vast number of languages, and it gives, or professes to give, in every case the sum and substance of the opinions and judgments of the best-informed writers.”—Saturday Review. Second Corrected Edition, post 8vo, pp. xii.—116, cloth, price 5s. THE BIRTH OF THE WAR-GOD. A Poem. By KALIDASA. Translated from the Sanskrit into English Verse by امتفظ‎ T. 8. GrirrirH, M.A. >» ق‎ very spirited rendering of the Kumdrasambhava, which was first published twenty-six years ago, and which we are glad to see made once more accessible.” — Times. ‘*Mr. Griffith’s very spirited rendering is well known to most who are at all interested in Indian literature, or enjoy the tenderness of feeling and rich creative imagination of its author.”—Jndian Antiquary. ‘©We are yery glad to welcome a second edition of Professor Griffith’s admirable translation. Few translations deserve a second edition better.”—Atheneum. TRUBNER’S ORIENTAL SERIES. Post 8vo, pp. 432, cloth, price 16s. A CLASSICAL DICTIONARY OF HINDU MYTHOLOGY AND RELIGION, GEOGRAPHY, HISTORY, AND LITERATURE. By JOHN DOWSON, M.R.A.S., Late Professor of Hindustani, Staff College. “This not only forms an indispensable book of reference to students of Indian literature, but is also of great general interest, as it gives in a concise and easily accessible form all that need be known about the personages of Hindu mythology whose names are so familiar, but of whom so little is known outside the limited circle of savants.”—Times. “It is no slight gain when such subjects are treated fairly and fully in a moderate space ; and we need only add that the few wants which we may hope to see supplied in new editions detract but little from the general excellence of Mr. Dowson’s work.” —Saturday Review. Post 8vo, with View of Mecca, pp. cxii.—172, cloth, price gs. SELECTIONS FROM THE KORAN. By EDWARD WILLIAM LANE, Translator of ‘‘ The Thousand and One Nights;” &c., .عن‎ A New Edition, Revised and Enlarged, with an Introduction by ’ STANLEY LANE POOLE. ٠» . . . Has been long esteemed in this country as the compilation of one of the greatest Arabic scholars of the time, the late Mr. Lane, the well-known translator of the ‘Arabian Nights.” . . . The present editor has emhanced the value of his relative’s work by divesting the text of a great deal of extraneous matter introduced by way of comment, and prefixing an introduction.” —Times. ‘Mr. Poole is both a generous and a learned biographer. . . . Mr. Poole tells us the facts . . . so far as it is possible for industry and criticism to ascertain them, and for literary skill to present them in a condensed and readable form.”—English- man, Calcutta. Post 8vo, pp. vi.—368, cloth, price 14s. MODERN INDIA AND THE INDIANS, BEING A SERIES OF IMPRESSIONS, NOTES, AND ESSAYS. By MONIER WILLIAMS, D.C.L., Hon. LL.D. of the University of Caleutta, Hon. Member of the Bombay Asiatic Society, Boden Professor of Sanskrit in the University of Oxford. Third Edition, revised and augmented by considerable Additions, with Illustrations and a Map. “In this volume we have the thoughtful impressions of a thoughtful man on some of the most important questions connected with our Indian Empire. . . . An en- lightened observant man, travelling among an enlightened observant people, Professor Monier Williams has brought before the public in a pleasant form more of the manners and customs of the Queen’s Indian subjects than we ever remember to have seen in any one work. He not only deserves the thanks of every Englishman for this able contribution to the study of Modern India—a subject with which we should be specially familiar—but he deserves the thanks of every Indian, Parsee or Hindu, Buddhist and Moslem, for his clear exposition of their manners, their creeds, and their necessities.” — Times. Post 8vo, pp. xliv.—376, cloth, ‘price 14 METRICAL TRANSLATIONS FROM SANSKRIT WRITERS. With an Introduction, many Prose Versions, and Parallel Passages from Classical Authors. By J. MUIR, C.1E., D.C.L., LU.D., Ph.D. «©. | , An agreeable introduction to Hindu poetry.”— Times. «|. A volume which may be taken as a fair illustration alike of the religious and moral sentiments and of the legendary lore of the best Sanskrit writers.”— Edinburgh Daily Review, TRUBNER'S ORIENTAL SERIES. Second Edition, post 8vo, pp. xxvi.—244, cloth, price 205. tebe Go bho 2 ALN; Or, ROSE GARDEN OF SHEKH MUSHLIU’D-DIN SADI OF SHIRAZ, Translated for the First Time into Prose and Verse, with an Introductory Preface, and a Life of the Author, from the Atish Kadah, By EDWARD B. EASTWICK, C.B., M.A., F.R.S., M.R.A.S. “Tt is a very fair rendering of the original.” —Times. “The new edition has long been desired, and will be welcomed by all who take any interest in Oriental poetry. The Gulistan is a typical Persian verse-book of the highest order. Mr. Eastwick’s rhymed translation . . . has long established itself in a secure position as the best version of Sadi’s finest work.”—Academy. “It is both faithfully and gracefully executed.”— Tablet. In Two Volumes, post 8vo, pp. viii.—4o8 and viii.—348, cloth, price 28s, MISCELLANEOUS ESSAYS RELATING TO INDIAN SUBJECTS. By BRIAN HOUGHTON HODGSON, Esq,, F.R.S., Late of the Bengal Civil Service ; Corresponding Member of the Institute ; Chevalier of the Legion of Honour; late British Minister at the Court of Nepal, d&c., dc. CONTENTS OF VOL. J. Section I.—On the Kocch, 82604, and Dhimdl Tribes.—Part I. Vocabulary.— Part 11. Grammar.—Part 111. Their Origin, Location, Numbers, Creed, Customs, Character, and Condition, with a General Description of the Climate they dwell in. —Appendix. Section II.—On Himalayan Ethnology.—I. Comparative Vocabulary of the Lan- guages of the Broken Tribes of Népél.—II. Vocabulary of the Dialects of the Kiranti Language.—III. Grammatical Analysis of the Vayu Language. The Vayu Grammar. —IV. Analysis of the Béhing Dialect of the Kiranti Language. The Bahing Gram- mar.—V. On the Vayu or Hayu Tribe of the Central Himalaya.—VI. On tue Kiranti Tribe of the Central Himalaya. CONTENTS OF VOL. Il. Srction II].—On the Aborigines of North-Eastern India. Comparative Vocabulary of the Tibetan, 183006, and Garé Tongues. Section 1V.—Aborigines of the North-Eastern Frontier. Section V.—Aborigines of the Eastern Frontier. Srction VI.—The Indo-Chinese Borderers, and their connection with the Hima- layans and Tibetans. Comparative Vccabulary of Indo-Chinese Borderers in Arakan. Comparative Vocabulary of Indo-Chinese Borderers in Tenasserim. Srction VII.—The Mongolian Affinities of the Caucasians.—Comparison and Ana- lysis of Caucasian and Mongolian Words. Section VIII.—Physical Type of Tibetans. Section IX.—The Aborigines of Central India.—Comparative Vocabulary of the Aboriginal Languages of Central India.—Aborigines of the Eastern Ghats.—Vocabu- lary of some of the Dialects of the Hill and Wandering Tribes in the Northern Sircars. —Aborigines of the Nilgiris, with Remarks on their Affinities Supplement to the Nilgirian Vocabularies.—The Aborigines of Southern India and Ceylon. Section X.—Route of Nepalese Mission to Pekin, with Remarks on the Water- Shed and Plateau of Tibet. Section XI.—Route from Kathmandu, the Capital of Nep&l, to Darjeeling in Sikim.—Memorandum relative to the Seven Cosis of Nepal. Section XII.—Some Accounts of the Systems of Law and Police as recognised in the State of Nepal. SEcTIon XIII.—The Native Method of making the Paper denominated Hindustan, Népalese. SrecTion XIV.—Pre-eminence of the Vernaculars; or, the Anglicists Answered ; Being Letters on the Education of the People of India. ** For the study of the less-known races of India Mr. Brian Hodgson’s ‘Miscellane- ous Essays’ will be found very valuable both to the philologist and the ethnologist.” TRUBNER'’S ORIENTAL SERIES. Third Edition, Two Vols., post 8vo, pp. viii.—268 and viii.—326, cloth, price 2Is. THE LIFE OR LEGEND OF GAUDAMA, THE BUDDHA OF THE BURMESE. With Annotations. The Ways to Neibban, and Notice on the Phongyies or Burmese Monks. By THE Ricut Rev. 2. BIGANDET, Bishop of Ramatha, Vicar-Apostolic of Ava and Pegu. *«The work is furnished with copious notes, wnich not only illustrate the subject- matter, but form a perfect encyclopedia of Buddhist lore.”— Times. ‘*A work which will furnish European students of Buddhism with a most valuable help in the prosecution of their investigations.”—Edinburgh Daily Review. “‘Bishop Bigandet’s invaluable work.”—IJndian Antiquary. “Viewed in this light, its importance is sufficient to place students of the subject under a deep obligation to its author.”—Calcutta Review. “This work is one of the greatest authorities upon Buddhism.”—Dublin Review. Post 8vo, pp. xxiv. —420, cloth, price 18s. CHINESE BUDDHISM. A VOLUME OF SKETCHES, HISTORICAL AND CRITICAL. By J. EDKINS, D.D. 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By ROBERT NEEDHAM CUST, Late Member of Her Majesty’s Indian Civil Service ; Hon. Secretary to the Royal Asiatic Society ; eet and Author of ‘“‘ The Modern Languages of the East Indies. ‘© We know none who has described Indian life, especially the life of the natives, with so much learning, sympathy, and literary talent.”—Academy. “They seem to us to be full of suggestive and original remarks.” —St. James's Gazette. >“ His book contains a vast amount of information. The result of thirty-five years of inquiry, reflection, and speculation, and that on subjects as full of fascination as of food for thought.”—Tablet. “ Exhibit such a thorough acquaintance with the history and antiquities of India as to entitle him to speak as one having authority.”—Edinburgh Daily Review. “©The author speaks with the authority of personal experience. ...« . It is this constant association with the country and the people which gives such a vividness to many of the pages.” —Atheneum. TRUBNER’S ORIENTAL SERIES. Post 890, pp. civ.—348, cloth, price 18s. BUDDHIST BIRTH STORIES; or, Jataka Tales. The Oldest Collection of Folk-lore Extant : BEING THE JATAKATTHAVANNANA, For the first time Edited in the original Pali. By V. FAUSBOLL ; And Translated by T. W. Ruys Davips. Translation. Volume I. “‘These are tales supposed to have been told by the Buddha of what he had seen and heard in his previous births. They are probably the nearest representatives of the original Aryan stories from which sprang the folk-lore of Europe as well as India. The introduction contains a most interesting disquisition on the migrations of these fables, tracing their reappearance in the various groups of folk-lore legends. Among other old friends, we meet with a version of the Judgment of Solomon.” —Times. “Tt is now some years since Mr. Rhys Davids asserted his right to be heard on this subject by his able article on Buddhism in the new edition of the ‘ Encyclopedia Britannica.’”—Leeds Mercury. “All who are interested in Buddhist literature ought to feel deeply indebted to Mr. Rhys Davids. His well-established reputation as a Pali scholar is a sufficient guarantee for the fidelity of his version, and the style of his translations is deserving of high praise.” —Academy. ““ No more competent expositor of Buddhism could be found than Mr. Rhys Davids. In the Jataka book we have, then, a priceless record of the earliest imaginative literature of our race; and . . . it presents to us a nearly complete picture of the social life and customs and popular beliefs of the common people of Aryan tribes, closely related to ourselves, just as they were passing through the first stages of civilisation.” —St. James’s Gazette. Post 890, pp. xxviii.—362, cloth, price r4s. A TALMUDIC MISCELLANY; Orn, A THOUSAND AND ONE EXTRACTS FROM THE TALMUD, THE MIDRASHIM, AND THE KABBALAH. Compiled and Translated by PAUL ISAAC HERSHON, Author of ‘* Genesis According to the Talmud,” &c. With Notes and Copious Indexes. “To obtain in so concise and handy a form as this volume a general idea of the Talmud is a boon to Christians at least.” —Times. “Tts peculiar and popular character will make it attractive to general readers. Mr. Hershon is a very competent scholar. . . . Contains samples of the good, bad, and indifferent, and especially extracts that throw light upon the Scriptures.”— British Quarterly Review. “>> Will convey to English readers a more complete and truthful notion of the Talmud than any other work that has yet appeared.”—Daily News. ‘‘Without overlooking in the slightest the several attractions of the previous volumes of the ‘ Oriental Series,’ we have no hesitation in saying that this surpasses them all in interest.”—Edinburgh Daily Review. “Mr. Hershon has . . . thus given English readers what is, we believe, a fair set of specimens which they can test for themselves.”—The Record. ‘‘This book is by far the best fitted in the present state of knowledge to enable the general reader to gain a fair and unbiassed conception of the multifarious contents of the wonderful miscellany which can only be truly understood—so Jewish pride asserts—by the life-long devotion of scholars of the Chosen People.”—IJnquirer. ‘«The value and importance of this volume consist in the fact that scarcely a single extract is given in its pages but throws some light, direct or refracted, upon those Scriptures which are the common heritage of Jew and Christian alike.”—John Bull. _ ‘* It is a capital specimen of Hebrew scholarship ; a monument of learned, loving, light-giving labour.”—Jewish Herald. TRUBNER'S ORIENTAL SERIES. Post 890, pp. xii.—228, cloth, price 7s. 6d. THE CLASSICAL POETRY OF THE JAPANESE. By BASIL HALL CHAMBERLAIN, Author of ‘‘ Yeigo Hefikaku Shirafi.” “A very curious volume. The author has manifestly devoted much labour to the task of studying the poetical literature of the Japanese, and rendering characteristic specimens into English verse.”—Daily News. ““Mr, Chamberlain’s volume is, so far as we are aware, the first attempt which has been made to interpret the literature of the Japanese to the Western world. It is to the classical poetry of Old Japan that we must turn for indigenous Japanese thought, and in the volume before us we have a selection from that poetry rendered into graceful English verse.” — Tablet. “Tt is undoubtedly one of the best translations of lyric literature which has appeared during the close of the last year.”—Celestial Empire. **Mr. Chamberlain set himself a dificult task when he undertook to reproduce Japanese poetry inan English form. But he has evidently laboured con amore, and his efforts are successful to a degree.”—London and China Express. Post 8vo, pp. xii.—164, cloth, price tos. 6d. THE HISTORY OF ESARHADDON (Son of Sennacherib), KING OF ASSYRIA, B.c. 681-668. Translated from the Cuneiform Inscriptions upon Cylinders and Tablets in the British Museum Collection; together with a Grammatical Analysis of each Word, Explanations of the Ideographs by Extracts from the Bi-Lingual Syllabaries, and List of Eponyms, &c. By ERNEST A. BUDGE, B.A., M.R.A.S., Assyrian Exhibitioner, Christ's College, Cambridge. “Students of scriptural archeology will also appreciate the ‘History of Esar- haddon,’ ” Times. “‘There is much to attract the scholar in this volume. It does not pretend to popularise studies which are yet in their infancy. Its primary object is to translate, but it does not assume to be more than tentative, and it offers both to the professed Assyriologist and to the ordinary non-Assyriological Semitic scholar the means of controlling its results.”—Academy. ‘‘Mr. Budge’s book is, of course, mainly addressed to Assyrian scholars and students. They are not, it is to be feared, a very numerous class. But the more thanks are due to him on that account for the way in which he has acquitted himself in his laborious task.”— Tablet. Post 8vo, pp. 448, cloth, price 21s. THE MESNEVI (Usually known as THE MESNEVIYI SHERIF, or HoLY MESNEVI) OF MEVLANA (OUR LORD) JELALU ’D-DIN MUHAMMED ER-RUMI. Book the First. Together with some Account of the Life and Acts of the Author, of his Ancestors, and of his Descendants. Illustrated by a Selection of Characteristic Anecdotes, as Collected by their Historian, MEVLANA SHEMSU-’D-DIN AHMED, EL EFLAKI, EL ‘ARIFI. Translated, and the Poetry Versified, in English, By JAMES W. REDHOUSE, M.R.A.S., &c. “ لق‎ complete treasury of occult Oriental lore.” —Saturday Review. 1 J “This book will be a very valuable help to the reader ignorant of Persia, who is desirous of obtaining an insight into a very important department of the literature extant in that language.”—T7ablet. TRUBNER'S ORIENTAL SERIES. Post 8vo, pp. xvi.— 280, cloth, price 6s. EASTERN PROVERBS AND EMBLEMS ILLUSTRATING OLD TRUTHS. By Rev. J. LONG, Member of the Bengal Asiatic Society, F.R.G.S, “‘ We regard the book as valuable, and wish for it a wide circulation and attentive reading.”—RKecord. “* altogether. it is quite a feast of good things.”—Globe. “It is full of interesting matter.”—Antiquary. Post 8vo, pp. viii—270, cloth, price 7s. 6d. INDIAN POETRY; Containing a New Edition of the ‘‘ Indian Song of Songs,” from the Sanserit of the ‘‘Gita Govinda” of Jayadeva; Two Books from ‘‘The Iliad of India ” (Mahabharata), ‘‘ Proverbial Wisdom” from the Shlokas of the Hitopadesa, and other Oriental Poems. By EDWIN ARNOLD, C.S.L., Author of ‘‘The Light of Asia.” “In this new volume of Messrs. Triibner’s Oriental Series, Mr. Edwin Arnold does good service by illustrating, thirough the medium of his musical English melodies, the power of Indian poetry to stir European emotions. The ‘Indian Song of Songs’ is not unknown to scholars. Mr. Arnold will have introduced it among popular English poems. 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Post 8vo, pp. xvi.—296, cloth, price 205. 6d. THE MIND OF MENCIUS ; Or, POLITICAL ECONOMY FOUNDED UPON MORAL PHILOSOPHY. A SysTeMATIC DIGEST OF THE DOCTRINES OF THE CHINESE PHILOSOPHER MENCIUsS. Translated from the Original Text and Classified, with Comments and Explanations, By the Rev. ERNST FABER, Rhenish Mission Society. Translated from the German, with Additional Notes, By the Rev. A. B. HUTCHINSON, C.M.S., Church Mission, Hong Kong. “Mr. Faber is already well known in the field of Chinese studies by his digest of the doctrines of Confucius. The value of this work will be perceived when it is remembered that at no time since relations commenced between China and the West has the former been so powerful—we had almost said aggressive—as now. For those who will give it careful study, Mr. Faber’s work is one of the most valuable of the excellent series to which it belongs.”— Nature. A2 TRUBNER’S ORIENTAL SERIES. Post 870, pp. 336, cloth, price 16s. THE RELIGIONS OF INDIA. By A. 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A SUMMARY DESCRIPTION OF THE ERAS, THE eras serve to fix certain moments of time which are Page 203. : 1 5 : . EB 1 mentioned in some historical or astronomical connection. tion of same The Hindus do not consider it wearisome to reckon with of the Fras huge numbers, but rather enjoy it. Still, in practical ™ use, they are compelled to replace them by smaller (more handy) ones. Of their eras we mention— 1. The beginning of the existence of Brahman. 2. The beginning of the day of the present nychthe- meron of Brahman, 2.6. the beginning of the kalpa, 3. The beginning of the seventh manvantara, in which we are now. 4. The beginning of the twenty-eighth catwryuga, in which we are now. 5. The beginning of the fourth yuga of the present caturyuga, called kalikdla, i.e. the time of Kali, The whole yuga is called after him, though, accurately speaking, fis time falls only in the last part of the yuga. Notwithstanding, the Hindus mean by kalikdla the beginning of the kaliyuga. 6. Pandava-kdla, 4.6. the time of the life and the wars of Bharata. All these eras vie with each other in antiquity, the VOI. IT, A 2 418121201715 4. one going back to a still more remote beginning than the other, and the sums of years which they afford go beyond hundreds, thousands, and higher orders of num- bers. Therefore not only astronomers, but also other people, think it wearisome and unpractical to use them. Tueidaither In order to give an idea of these eras, we shall use Lae ae , 3s a first gauge or point of comparison that Hindu atest-year. year the great bulk of which coincides with the year 400 of Yazdajird. This number consists only of hun- dreds, not of units and tens, and by this peculiarity it is distinguished from all other years that might possibly be chosen. Besides, it is a memorable time; for the breaking of the strongest pillar of the religion, the decease of the pattern of a prince, Mahmid, the lion of the world, the wonder of his time—may God have mercy upon him !—took place only a short time, less than a year, before it. The Hindu year precedes the Nauréz or new year’s day of this year only by twelve days, and the death of the prince occurred pre- cisely ten complete Persian months before it. Now, presupposing this our gauge as known, we shall compute the years for this point of junction, which is the begmning of the corresponding Hindu year, for the end of all years which come into question coincides with it, and the Nauréz of the year 400 of Yazdajird falls only a little latter (viz. twelve days). How much The book Vishnu-Dharma says: “ Vajra asked Mar- Trahwan Kandeya how much of the life of Brahman had elapsed ; Brahman Whereupon the sage answered : ‘That which has elapsed‏ وري تي is 8 years, 5 months, 4 days, 6 manvantaras, 7 saridhi,‏ “ل ير caturyugas, and 3 yugas of the twenty-eighth catur-‏ 27 yuga, and 10 divya-years up to the time of the afvamedha‏ which thou hast offered.’ He who knows the details of‏ this statement and comprehends them duly is a sage‏ man, and the sage is he who serves the only Lord and‏ strives to reach the neighbourhood of his place, which is‏ called Paramapada.” Page 204. The time of Rama ac- cording to Vishnu- Dharma. CHAPTER XLIX. 3 Presupposing this statement to be known, and refer- ring the reader to our explanation of the various mea- sures of time which we have given in former chapters, we offer the following analysis. Of the life of Brahman there have elapsed before our gauge 26,215,732,948,132 of our years. Of the nych- themeron of Brahman, we. of the kalpa of the day, there have elapsed 1,972,948,132, and of the seventh manvan- tara 120,532,132. The latter is also the date of the imprisoning of the King Bali, for it happened in the first caturyuga of the seventh manvantara. In all chronological dates which we have mentioned already and shall still mention, we only reckon with ‘complete years, for the Hindus are in the habit of dis- regarding fractions of a year. Further, the Vishnu-Dharma says: “Markandeya says, in answer to a question of Vajra, ‘I have already lived as long as 6 kalpas and 6 manvantaras of the seventh kalpa, 23 tretdyugas of the seventh manvantara. In the twenty-fourth tretdyuga Rama killed Ravana, and Lakshmana, the brother of Rama, killed Kumbha- karna, the brother of Ravana. The two subjugated all the Rakshasas. At that time Valmiki, the Rishi, com- posed the story of Rama and Ramayana and eternalised it in his books. It was I who told it to Yudhishthira, the son of Pandu, in the forest of Kamyakavana.’ ” The author of the Vishnu-Dharma reckons here with tretdyugas, first, because the events which he mentions occurred in a certain trefdyuya, and secondly, because it is more convenient to reckon with a simple unit than with such a unit as requires to be explained by reference to its single quarters. Besides, the latter part of the tretdyuga is a more suitable time for the events men- tioned than its beginning, because it is so much nearer to the age of evil-doing (v.i. pp. 379, 380). No doubt, the date of Rima and Ramayana is known among the 4 ALBERUNI’S INDIA. Hindus, but I for my part have not been able to ascer- tain it. Twenty-three caturyugas are 99,360,000 years, and, together with the time from the beginning of a caturyuga till the end of the tretdyuga, 102,384,000 years. If we subtract this number of years from the number of years of the seventh manvantara that have elapsed before our gauge-year, viz. 120,532,132 (v. p. 3), we get the remainder of 18,148,132 years, 1.6. so many years before our gauge-year as the conjectural date of Rama; and this may suffice, as long as it is not supported by a trustworthy tradition. The here-mentioned year corresponds to the 3,892,132d year of the 28th catur- Yuga. All these computations rest on the measures adopted by Brahmagupta. He and Pulisa agree in this, that the number of kalpas which have elapsed of the life of Brahman before the present kalpa is 6068 (equal to 8 years, 5 months, 4 days of Brahman). But they differ from each other in converting this number into catwr- yugas. According to Pulisa, it is equal to 6,116,544; according to Brahmagupta, only to 6,068,000 catur- yugas. Therefore, if we adopt the system of Pulisa, reckoning I manvantara as 72 caturyugas without samdhi, 1 kalpa as 1008 caturyugas, and each yuga as the fourth part of a caturyuga, that which has elapsed of the life of Brahman before our gauge-year is the sum of 26,425,456,204,132(!) years, and of the kalpa there have elapsed 1,986,124,132 years, of the manvan- tara 119,884,132 years, and of the caturyuga 3,244,132 years. Regarding the time which has elapsed since the beginning of the kaliyuga, there exists no difference amounting to whole years. According to both Brahma- gupta and Pulisa, of the kaliyuga there have elapsed before our gauge-year 4132 years, and between the How much time has elapsed be- tore o of the present kalpa, ac- cording to Pulisa and Brahma- gupta. Page 205. How much time has elapsed of the current kaliyuge. The era Kalayavana, Era of Sri Harsha, Era of Vik- ramaditya, GHAPTER XETX. 5 wars of Bharata and our gauge-year there have elapsed 3479 years. The year 4132 before the gauge-year is the epoch of the kalikdla, and the year 3479 before the gauge-year is the epoch of the Pandavakdla. The Hindus have an era called Kdlayavana, regard- ing which I have not been able to obtain full infor- mation. They place its epoch in the end of the last dvdparayuga. The here-mentioned Yavana (JMN) severely oppressed both their country and their religion. To date by the here-mentioned eras requires in any case vast numbers, since their epochs go back to a most remote antiquity. For this reason people have given up using them, and have adopted instead the eras of— (1.) Srt Harsha. (2.) Vikramaditya. (3.) Saka. (4.) Valabha, and (5.) Gupta. The Hindus believe regarding Sri Harsha that he used to examine the soil in order to see what of hidden treasures was in its interior, as far down as the seventh earth ; that, in fact, he found such treasures; and that, in consequence, he could dispense with oppressing his subjects (by taxes, &c.) His era is used in Mathura and the country of Kanoj. Between Sri Harsha and Vikra- mAditya there is an interval of 400 years, as I have been told by some of the inhabitants of that region. How- ever, in the Kashmirian calendar I have read that Sri Harsha was 664 years later than Vikramaditya. In face of this discrepancy I am in perfect uncertainty, which to the present moment has not yet been cleared up by any trustworthy information. Those who use the era of Vikramaditya live in the southern and western parts of India. It is used in the following way: 342 are multiplied by 3, which gives 6 418112 10/171:5 1 4. the product 1026. To this number you add the years which have elapsed of the current shashtyabda or sexa- gesimal samvatsara, and the sum is the corresponding year of the era of Vikramaditya. In the book Srda- hava by Mahadeva I find as his name Candrabiya. As regards this method of calculation, we must first say that it is rather awkward and unnatural, for if they began with 1026 as the basis of the calculation, as they begin—without any apparent necessity—with 342, this would serve the same purpose. And, secondly, admit- ting that the method is correct as long as there is only one shashtyabda in the date, how are we to reckon if there is a number of shashtyabdas ? The epoch of the era of Saka or Sakakdla falls 135 years later than that of Vikramaditya. The here-men- tioned Saka tyrannised over their country between the river Sindh and the ocean, after he had made Arya- varta in the midst of this realm his dwelling-place. He interdicted the Hindus from considering and repre- senting themselves as anything but Sakas. Some main- tain that he was a Sidra from the city of Almanstira ; others maintain that he was not a Hindu at all, and that he had come to India from the west. The Hindus had much to suffer from him, till at last they received help from the east, when Vikramaditya marched against him, put him to flight and killed him in the region of Kari, between Multan and the castle of Loni. Now this date became famous, as people rejoiced in the news of the death of the tyrant, and was used as the epoch of an era, especially by the astronomers. They honour the conqueror by adding Sri to his name, so as to say Sri Vikramaditya. Since there is a long interval between the era which is called the era of Vikramaditya (v. .م‎ 5) and the killing of Saka, we think that that Vik- ramaditya from whom the era has got its name is not identical with that one who killed Saka, but only a namesake of his. The Saka- kala. CHAPTER XLIX. 7 The era of Valabha is called so from Valabha, the ruler Era of of the town Valabhi, nearly 30 yojanas south of Anhil- Me eases vara. The epoch of this era falls 241 years later than Page 206. the epoch of the Saka era. People use it in this way. They first put down the year of the Sakakdla, and then subtract from it the cube of 6 and the square of 5 (216 + 25 = 241). The remainder is the year of the Valabha era. The history of Valabha is given in its proper place (cf. chap. xvii.) As regards the Guptakala, people say that the Guptas Guptakala. were wicked powerful people, and that when they ceased to exist this date was used as the epoch of an era. It seems that Valabha was the last of them, be- cause the epoch of the era of the Guptas falls, like that of the Valabha era, 241 years later than the Saka- kala. The era of the astronomers begins 587 years later than kra of the the Sakak4la. On this era is based the canon Khanda- hes” khaddyaka by Brahmagupta, which among Muhammadans is known as Al-arkand. Now, the year 400 of Yazdajird, which we have Comparison 2 of معطا‎ epochs chosen as a gauge, corresponds to the following years of the In- ° dian eras of the Indian eras :— with the test-year. (1) To the year 1488 of the era of Sri Harsha, (2) To the year 1088 of the era of Vikramaditya, (3) To the year 953 of the Sakakdla, (4) To the year 712 of the Valabha era, which is identical with the Guptakala, (5) To the year 366 of the era of the canon Khanda- khadyaka, (6) To the year 526 of the era of the canon Pajica- siddhéntikéd by Varahamihira, (7) To the year 132 of the era of the canon Kara- nasdra; and (8) To the year 65 of the era of the canon Karana- tilaka, 8 ALBERUNIS INDIA. The eras of the here-mentioned canones are such as the authors of them considered the most suitable to be used as cardinal points in astronomical and other cal- culations, whence calculation may conveniently extend forward or backward. Perhaps the epochs of these eras fall within the time when the authors in question them- selves lived, but it is also possible that they fall within a time anterior to their lifetime. On the popu- Common people in India date by the years of a cen- of dating by tenntwm, which they call samvatsara. If a centennium sanvatsaras. 15 finished, they drop it, and simply begin to date by a new one. This era is called lokakdla, 1.6. the era of the nation at large. But of this era people give such totally different accounts, that I have no means of making out the truth. In a similar manner they also differ among themselves regarding the beginning of the year. On the latter subject I shall communicate what I have heard myself, hoping meanwhile that one day we shall be able to discover a rule in this apparent confusion. Different Those who use the Saka era, the astronomers, begin bene ves, the year with the month Caitra, whilst the inhabitants of Kanir, which is conterminous with Kashmir, begin it with the month Bhadrapada. The same people count our gauge-year (400 Yazdajird) as the eighty-fourth year of an era of theirs. All the people who inhabit the country between Bardari and Marigala begin the year with the month Karttika, and they count the gauge-year as the 110th year of an era of theirs. The author of the Kashmirian calendar maintains that the latter year corresponds to the sixth year of a new centennium, and this, indeed, is the usage of the people of Kashmir. The people living in the country Nirahara, behind Marigala, as far as the utmost frontiers of Takeshar and Lohavar, begin the year with the month Margasirsha, and reckon our gauge-year as the 108th year of their Popular mode of dating in use among the Hindus, and criti- cisms there- on. Page 207. CHAPTER XLIX. 9 era. The people of Lanbaga, 2.6. Lamghan, follow their example. I have been told by people of Multan that this system is peculiar to the people of Sindh and Kanoj, and that they used to begin the year with the new moon of Margagirsha, but that the people of Multan only a few years ago had given up this system, and had adopted the system of the people of Kashmir, and followed their example in beginning the year with the new moon of Caitra. I have already before excused myself on account of the imperfection of the information given in this chap- ter. For we cannot offer a strictly scientific account of the eras to which it is devoted, simply because in them we have to reckon with periods of time far exceeding a centennium, (and because all tradition of events farther back than a hundred years is confused (v. p. 8).) So I have myself seen the roundabout way in which they compute the year of the destruction of Somanath in the year of the Hijra 416, or 947 Sakakdla. First, they write down the number 242, then under it 606, then under this 99. The sum of these numbers is 947, or the year of the Sakakdla. Now I am inclined to think that the 242 years have elapsed before the beginning of their centennial system, and that they have adopted the latter together with the Guptakala; further, that the number 606 represents complete samvatsaras or centennials, each of which they must reckon as 101 years; lastly, that the 99 years represent that time which has elapsed of the current centenmium. That this, indeed, is the nature of the calculation is confirmed by a leaf of a canon composed by Durlabha of Multan, which I have found by chance. Here the author says: “ First write 848 and add to it the laukika- kdla, 4.6. the era of the people, and the sum is the Sakakala.” If we write first the year of the Sakak4la correspond- 10 ALBERUNI’S INDIA. ing to our gauge-year, viz. 953, and subtract 848 from it, the remainder, 105, is the year of the lawkika-kdla, whilst the destruction of Somanath falls in the ninety- eighth year of the centennium or laukika-kdla. Durlabha says, besides, that the year begins with the month Margasirsha, but that the astronomers of 0 begin it with Caitra. The Hindus had kings residing in Kabul, Turks who were said to be of Tibetan origin. The first of them, Barhatakin, came into the country and entered a cave . in Kabul, which none could enter except by creeping on hands and knees. The cave had water, and besides he deposited there victuals for a certain number of days. It is still known in our time, and is called Var. People who consider the name of Barhatakin as a good omen enter the cave and bring out some of its water with great trouble. Certain troops of peasants were working before the door of the cave. Tricks of this kind can only be carried out and become notorious, if their author has made a secret arrangement with somebody else —in fact, with confederates. Now these had induced per- sons to work there continually day and night in turns, so that the place was never empty of people. Some days after he had entered the cave, he began to creep out of it in the presence of the people, who looked on him as a new-born baby. He wore Turkish dress, a short tunic open in front, a high hat, boots and arms. Now people honoured him asa being of mira- culous origin, who had been destined to be king, and in fact he brought those countries under his sway and ruled them under the title of a shkdhiya of Kédbul. The rule remained among his descendants for gene- rations, the number of which is said to be about sixty. Unfortunately the Hindus do not pay much attention to the historical order of things, they are very careless Origin of the dynasty of the Shahs of Kabul. The story of Kanik, CHAPTER XLIX. 11 in relating the chronological succession of their kings, and when they are pressed for information and are at a loss, not knowing what to say, they invariably take to tale-telling. But for this, we should com- municate to the reader the traditions which we have received from some people among them. I have been told that the pedigree of this royal family, written on silk, exists in the fortress Nagarkot, and I much desired to make myself acquainted with it, but the thing was impossible for various reasons. One of this series of kings was Kanik, the same who is said to have built the viidra (Buddhistic monastery) of Purushavar. It is called, after him, Kanik-caitya. People relate that the king of Kanoj had presented to him, among other gifts, a gorgeous and most singular piece of cloth. Now Kanik wanted to have dresses made out of it for himself, but his tailor had not the courage to make them, for he said, “There is (in the embroidery) the figure of a human foot, and whatever trouble I may take, the foot will always lie between the shoulders.” And that means the same as we have already mentioned in the story of Bali, the son of Virocana (i.e. a sign of subjugation, cf. i. p. 397). Now Kanik felt convinced that the ruler of Kanoj had thereby intended to vilify and disgrace him, and in hot haste he set out with his troops marching against him. When the rdi heard this, he was greatly perplexed, for he had no power to resist Kanik. Therefore he consulted his Vazir, and the latter said, “ You have roused a man who was quiet before, and have done un- becoming things. Now cut off my nose and lips, let me be mutilated, that I may find a cunning device; for there is no possibility of an open resistance.” The rai did with him as he had proposed, and then he went off to the frontiers of the realm. 12 ALBERUNPS INDIA. There he was found by the hostile army, was recog- nised and brought before Kanik, who asked what was the matter with him. The Vazir said, “I tried to dissuade Aim from opposing you, and sincerely advised him to be obedient to you. He, however, conceived a suspicion against me and ordered me to be mutilated. Since then he has gone, of his own accord, to a place which a man can only reach by a very long journey when he marches on the highroad, but which he may easily reach by undergoing the trouble of crossing an intervening desert, supposing that he can carry with himself water for so and so many days.” Thereupon Kanik answered: “The latter is easily done.” He ordered water to be carried along, and engaged the Vazir to show him the road. The Vazir marched be- fore the king and led him into a boundless desert. After the number of days had elapsed and the road did not come to an end, the king asked the Vazir what was now to be done. Then the Vazir said, ‘No blame attaches to me that I tried to save my master and to destroy his enemy. The nearest road leading out of this desert is that on which you have come. Now do with me as you like, for none will leave this desert alive.” Then Kanik جره نامع‎ his horse and rode round a de- pression in the soil. In the centre of it he thrust his spear into the earth, and lo! water poured from it in sufficient quantity for the army to drink from and to draw from for the march back. Upon this the Vazir said, “I had not directed my cunning scheme against powerful angels, but against feeble men. As things stand thus, accept my intercession for the prince, my benefactor, and pardon him.” Kanik answered, “I march back from this place. Thy wish is granted to thee. Thy master has already received what is due to him.” Kanik returned out of the desert, and the Vazir went back to his master, the "04 of Kanoj. There he Page 208. End of the Tibetan dy- nasty, and origin of the Brahman dynasty. CHAPTER XLIX. 13 found that on the same day when Kanik had thrust his spear into the earth, both the hands and feet had fallen off the body of the rdi. The last king of this race was Lagatuérmdn, and his Vazir was Kallar,a Brahman. The latter had been for- tunate, in so far as he had found by accident hidden treasures, which gave him much influence and power. In consequence, the last king of this Tibetan house, after it had held the royal power for so long a period, let it by degrees slip from his hands. Besides, Laga- tirmfin had bad manners and a worse behaviour, on account of which people complained of him greatly to the Vazir. Now the Vazir put him in chains and imprisoned him for correction, but then he himself found ruling sweet, his riches enabled him to carry out his plans, and so he occupied the royal throne. After him ruled the Brahman kings Samand (Samanta), Kamali, Bhim (Bhima), Jaipil (Jayapala), Ananda- pala, Tarojanapala (Trilocanapala). The latter was killed AH. 412 (A.D. 1021), and his son Bhimapala five years later (A.D. 1026). This Hindu Shahiya dynasty is now extinct, and of the whole house there is no longer the slightest. rem- nant in existence. We must say that, in all their grandeur, they never slackened in the ardent desire of doing that which is good and right, that they were men of noble sentiment and noble bearing. I admire the following passage in a letter of Anandapala, which he wrote to the prince Mahmid, when the relations be- tween them were already strained to the utmost: “I have learned that the Turks have rebelled against you and are spreading in Khurasan. If you wish, I shall come to you with 5000 horsemen, 10,000 foot-soldiers, and 100 elephants, or, if you wish, I shall send you my son with double the number. In acting thus, I do not speculate on the impression which this will make on you. I have been conquered by you, and 14 ALBERUNPS INDIA. therefore I do not wish that another man should conquer you.” The same prince cherished the bitterest hatred against the Muhammadans from the time when his son was made a prisoner, whilst his son Tarojanapala (Triloca- napala) was the very opposite of his father. CHAPTER L. ” HOW MANY STAR-CYCLES THERE ARE BOTH IN A “KALPA AND IN A “CATURYUGA.” Ir is one of the conditions of a kalpa that in it the planets, with their apsides and nodes, must unite in o° of Aries, .6.ة‎ in the point of the vernal equinox. Therefore each planet makes within a kalpa a certain number of complete revolutions or cycles. These star-cycles as known through the canon of The tradi- Alfazirt and Ya‘kib Ibn Tarik, were derived from a zari nat gar Hindu who came to Bagdad as a member of the politi- Tak. Ne cal mission which Sindh sent to the Khalif Almansir, AH. 154 (=A.D. 771). If we compare these secondary statements with the primary statements of the Hindus, we discover discrepancies, the cause of which is not known to me. Is their origin due to the translation of Alfazari and Ya‘kiib? or to the dictation of that Hindu? or to the fact that afterwards these computa- tions have been corrected by Brahmagupta, or some one else? For, certainly, any scholar who becomes aware of mistakes in astronomical computations and takes an interest in the subject, will endeavour to correct them, Muhammad as, eg. Muhammad Ibn Ishak of Sarakhs has done. Sarakus. For he had discovered in the computation of Saturn a falling back behind real time (1.¢., that Saturn, accord- ing to this computation, revolved slower than it did in reality). Now he assiduously studied the subject, till at last he was convinced that his fault did not originate 16 ALBERUNIS INDIA. from the equation (i.e. from the correction of the places of the stars, the computation of their mean places). Then he added to the cycles of Saturn one cycle more, and compared his calculation with the actual motion of the planet, till at last he found the calculation of the cycles completely to agree with astronomical observa- tion. Inaccordance with this correction he states the star-cycles in his canon. Brahmagupta relates a different theory regarding the cycles of the apsides and nodes of the moon, on the authority of Aryabhata. We quote this from Brah- magupta, for we could not read it in the original work of Aryabhata, but only in a quotation in the work of Brahmagupta. The following table contains all these traditions, which will facilitate the study of them, if God will! Number of their revolutions in a Number of the revolutions of Number of the re- volutions of their Aryabhata quoted by Brahma- gupta, Number of the rota- tions of the planets ina nodes. Has no node. 232,311,168 232,312,138 232,316,000 The anomalistic revolution of the moon is_ here treated as if it were the apsis, being the differ- ence between the motion of the moon and that of the apsis. (See the notes.) 267 584 their apsides. 480 488,105,858 488,219,000 257,205,194,142 41 Kalpa. 4, 320,000,000 57753300, 000 2,296,828,522 364,226,455 7,022,389,492 146,567,298 | 146,569,284. 146,569,238 | 120,000 according to the translation of Alfazari. 17,936,998,984 kalpa. Page 209. The planets. Sun : : Brahmagupta . The translation , of Alfazari . = | Aryabhata 0 ( = = Coad ع‎ , The anomalistic al revolution of the moon ac- cording 1 Brahmagupta Mars Mercury Jupiter Venus ١ 1 Brahmagupta Thetranslation of AlfazAri The correction of Alsarakhsi The fixed stars Saturn. CHAPTER L, 17 The computation of these cycles rests on the mean cycles of the planets motion of the planets. As a caturyuga is, according to ina catur- Brahmagupta, the one-thousandth part of a kalpa, we tives have only to {divide these cycles by 1000, and the quotient is the number of the star-cycles in one catur- yuga. Likewise, if we divide the cycles of the table by 10,000, the quotient is the number of the star-cycles in a kaliyuga, for this is one-tenth of a caturyuga. The fractions which may occur in those quotients are raised to wholes, to catuwryugas or kaliyugas, by being multi- plied by a number equal to the denominator of the fraction. The following table represents the star-cycles speci- ally in a caturyuga and kaliyuga, not those in a man- vantara. Although the manvantaras are nothing but multiplications of whole caturyugas, still it is difficult to reckon with them on account of the samdhi which is attached both to the beginning and to the end of them. The names of the planets. Their revolutions. Their revolutions | Page 210. in a Caturyuga. in a Kaliyuga. Sun. 1 4,320,000 432,000 His apsis : و‎ 33 Moon . - ا‎ 57:753,300 55775;330 a | 10 5 488, 105433 48, 8102333 of a. z.) Aryabhata 488,219 48,821, Her anomalistic revolution | 57,265,194;735 5,726, 5195060 اج‎ 5 Brahmagupta 232,31 ج112‎ 23,23 1232, 5 The translation of 52 8 ( . Alfazari 212,112 2212+ Aryabhata 232,316 2230s: Mars . 1 1 2,296, s28505 064 220,4 His apsis Os مويه‎ His node Oxo0s Orso50 Mercury 17,936,99813 1,793,0991456 His apsis o835 مققره‎ His node يق‎ 07321, Jupiter — 364,226 22 His apsis oft مره‎ His node مويه‎ 0 VOL. II. B Cay 18 ALBERUNTIS INDIA. The names of the plancts Their revolutions Their revolutions 9 in a Caturyuga. in a Kaliyuga. gene - : : 1 7,022, 389355 702, 0 عه‎ : 5 0 007 0000 er node 5 1 4 كوه‎ 00 588611111 21605072 14,6562849 His apsis . 9070 0 His node 5 : : 0 Orso es The translation of 146,569,735 14,656323% 5 Alfazart : 8 )The correction of 146,569119 14,6562 2ت‎ Alsarakhsi : The fixed stars . 120 12 Page arr. as After we have stated how many of the star-cycles of star-cycles ٠. . . . ofakalpa a kalpa fall in a caturyuga and in a kaliyuga, according and catur- . yuga,ac- to Brahmagupta, we shall now derive from the number cording to . . Pulisa. of star-cycles of a caturyuga according to Pulisa the number of star-cycles of a kalpa, first reckoning a kalpa = 1000 caturyugas, and, secondly, reckoning it as 1008 caturyugas. These numbers are contained in the following table :— The Yugas according to Pulisa. Number of Number of their Number of their The names of the | their revolu- revolutions in a revolutions in a planets. tions ina Kalpa of Kalpa of Caturyuga. rooo Caturyugas, 1008 Caturyugas. Sun 4,320,000 4,320,000,000 4,354,560,000 Moon. . 575753336 | 57:753:336,000 | 58,215,362,688 Her apsis . 488,219 488,219,000 492,124,752 Her node . 232,226 232,226,000 21 85 Mars 2,296,824 2,296,824,000 2,315,198,592 Mercury . 17.937,000 17,937,000,000 18,080,496,000 Jupiter 364,220 364,220,000 367,133,760 Venus 7,022,388 7,022, 388,coo 7,078, 567,104 Saturn 146,564 146,564,000 147,730,512 Transforma- We meet in this context with a curious circumstance.‏ ا word Arya- Evidently Alfazari and Ya'ktib sometimes heard from‏ among the their Hindu master expressions to this effect, that his‏ 1 calculation of the star-cycles was that of the great Sid- dhanta, whilst Aryabhata reckoned with one-thousandth Star-cycles according to Abf-alhasan of AVahwaz. Page 212. CHAPTER L. 19 They apparently did not understand him part of it. properly, and imagined that dryabhata (Arab. drjabhad) meant a thousandth part. d of this word something between ad and anr. So the consonant became changed to an 7, and people wrote The Hindus pronounce the Afterwards it was still more mutilated, the drjabhar. first r being changed to a z, and so people wrote dza- bhar. If the word in this garb wanders back to the Hindus, they will not recognise it. Further, Abfi-alhasan of Al’ahw4z mentions the revo- lutions of the planets in the years of al-arjabhar, 2.e. in I shall represent them in the table such as I have found them, for I guess that they are directly derived from the dictation of that Hindu. Possibly, therefore, they give us the theory of Aryabhata. Some of these numbers agree with the star-cycles in a catur- yuga, which we have mentioned on the authority of Brahmagupta; others differ from them, and agree with the theory of Pulisa; and a third class of numbers differs from those of both Brahmagupta and Pulisa, as the examination of the whole table will show. Their Yugas as parts of a Caturyuga according to Abt-alhasan Al’ahwaz 4,320,000 575753; 336 488,219 232,226 2,296,828 17,937,020 364,224 7,022, 388 146, 564 The names of the planets. Sun Moon . Her apsis . Her node . Mars <". Mercury . Jupiter Venus. Saturn caturyugas. ( 20 ) CHAPTER LI. AN EXPLANATION OF THE TERMS “ADHIMASA,” “CNA- RATRA,” AND THE “ AHARGANAS,” AS REPRESENTING DIFFERENT SUMS OF DAYS. THE months of the Hindus are lunar, their years solar ; therefore their new year’s day must in each solar year fall by so much earlier as the lunar year is shorter than the solar (roughly speaking, by eleven days). If this precession makes up one complete month, they act in the same way as the Jews, who make the year a leap year of thirteen months by reckoning the month Adar twice, and in a similar way to the heathen Arabs, who in a so-called annus procrastinationis postponed the new year’s day, thereby extending the preceding year to the duration of thirteen months. The Hindus call the year in which a month is repeated in the common language malamdsa. Mala means the dirt that clings to the hand, As such dirt is thrown away, thus the leap month is thrown away out of the calculation, and the number of the months of a year remains twelve. However, in the literature the leap month is called adhimdsa. That month is repeated within which (it being con- sidered as a solar month) two lunar months finish. If the end of the lunar month coincides with the beginning of the solar month, if, in fact, the former ends before any part of the latter has elapsed, this month is re- peated, because the end of the lunar month, although On the leap month. CHAPTER LI. 21 it has not yet run into the new solar month, still does no longer form part of the preceding month. If a month is repeated, the first time it has its ordinary name, whilst the second time they add before the name the word durd to distinguish between them. If, e.g. the month Ashadha is repeated, the first is called Pase 2:3. Ashidha, the second Durdshddha. The first month is that which is disregarded in the calculation. The Hin- dus consider it as unlucky, and do not celebrate any of the festivals in it which they celebrate’in the other months. The most unlucky time in this month is that day on which the lunation reaches its end. The author of the Vishnu-Dharma says: “ Candra quotation (ména) is smaller than sdvana, i.e. the lunar year is Vern” smaller than the civil year, by six days, ic. dnardtra. *"™* Una means decrease, deficiency. Saura is greater than candra by eleven days, which gives in two years and seven months the supernumerary adhimdsa month. This whole month is unlucky, and nothing must be done in it.” This isa rough description of the matter. We shall now describe it accurately. The lunar year has 360 lunar days, the solar year has 37laso lunar days. This difference sums up to the thirty days of an adhimdsa in the course of 97677,5°, lunar days, 4.6. 12 32 months, or in 2 years, 8 months, 16 days, plus the fraction: {7;4% lunar day, which is nearly = 5 minutes, 15 seconds. As the religious reason of this theory of intercala- Quotation tion the Hindus mention a passage of the Veda, which veda. they have read to us, to the following tenor: “If the day of conjunction, ze, the first lunar day of the month, passes without the sun’s marching from one zodiacal sign to the other, and if this takes place on the following day, the preceding month falls out of the calculation.” The meaning of this passage is not correct, and the criticisms fault must have risen with the man who recited and “"°™ 22 ALBERUNTS INDIA. translated the passage to me. For a month has thirty lunar days, and a twelfth part of the solar year has 303235 lunar days. This fraction, reckoned in day- minutes, is equal to 551 19%22" 30%. If we now, for example, suppose a conjunction or new moon to take place at o° of a zodiacal sign, we add this fraction to the time of the conjunction, and thereby we find the times of the sun’s entering the signs successively. As now the difference between a lunar and a solar month is only a fraction of a day, the sun’s entering a new sign may naturally take place on any of the days of the month. It may even happen that the sun enters two consecutive signs on the same month-day (eg. on the second or third of two consecutive months). This is the case if in one month the sun enters a sign before 4' 40" 374 30” have elapsed of it; for the next follow- ing entering a sign falls later by 55' 19% 23 30, and both these fractions (ie. less than 4! 40% 3741 30" plus the last-mentioned fraction) added together are not sufficient to make up one complete day. Therefore the quotation from the Veda is not correct. I suppose, however, that it may have the following ;Proposed ‘explanation ‘of the Vedic correct meaning :—If a month elapses in which the sun does not march from one sign to another, this month is disregarded in the calculation. For if the sun enters a sign on the 29th of a month, when at least أل‎ 4o% 37% 30°" have elapsed of it, this entering takes place before the beginning of the succeeding month, and therefore the latter month is without an entering of the sun into a new sign, because the next following entering falls on the first of the next but one or third month. If you compute the consecutive enterings, beginning with a conjunction taking place in o° of a certain sign, you find that in the thirty-third month the sun enters a new sign at 30' 20" of the twenty-ninth day, and that he enters the next following sign at 25' 39" 22™ 30'" of the first day of the thirty-fifth month. passage. Page 214. Explanation of the terms universal or artial months and days. CHAPTER LI. 23 Hence also becomes evident why this month, which is disregarded in the calculation, is considered as un- lucky. The reason is that the month misses just that moment which is particularly adapted to earn in it a heavenly reward, viz. the moment of the sun’s entering a new sign. As regards adhimdsa, the word means the first month, for AD means beginning (i.e. ddi). In the books of Ya‘kib Ibn Tarik and of Alfaz4ri this name is written padamdsa. Pada (in the orig. P-Dh) means end, and it is possible that the Hindus call the leap month by both names ; but the reader must be aware that these two authors frequently misspell or disfigure the Indian words, and that there is no reliance on their tradition. I only mention this because Pulisa explains the latter of the two months, which are called by the same name, as the supernumerary one. The month, as the time from one conjunction to the following, is one revolution of the moon, which revolves through the ecliptic, but in a course distant from that f of the sun. This isthe difference between the motions of the two heavenly luminaries, whilst the direction in which they move is the same. If we subtract the revolutions of the sun, we. the solar cycles of a kalpa, from its lunar cycles, the remainder shows how many more lunar months a kalpa has than solar months. All months or days which we reckon as parts of whole kalpas we call here universal, and all months or days which we reckon as parts of a part of a kalpa, eg. of a caturyuga, we call partial, for the purpose of sim- plifying the terminology. ‘ The year has twelve solar months, and eames Universal adhimésa twelve lunar months. The lunar year is complete with mouths. twelve months, whilst the solar year, in consequence of the difference of the two year kinds, has, with the addition of the adhimdsa, thirteen months. Now evi- dently the difference between the universal solar and 24 ALBERUNPS INDIA. lunar months is represented by these supernumerary months, by which a single year is extended to thirteen months. These, therefore, are the universal adhimdsa months. The wniversal solar months of a kalpa are 51,840, 000,000 ; the wniversal lunar months of a kalpa are 53.433.300,000. The difference between them or the adhimdsa months is 1,593,300,000. Multiplying each of these numbers by 30, we get days, viz. solar days of a kalpa, 1,555,200,000,000 ; lunar days, 1,602,999,000,000 ; the days of the adhimdsa months, 47,799,000,000. In order to reduce these numbers to smaller ones we divide them by a common divisor, viz. 9,000,000. Thus we get as the sum of the days of the solar months 172,800; as the sum of the days of the lunar months, 178,111; and as the sum of the days of the adhimdsa months, 5 31 If we further divide the wniversal solar, civil, and lunar days of a kalpa, each kind of them separately, by the universal adhimdsa months, the quotient represents the number of days within which a whole adhimdsa month sums up, viz. in 9763454; solar days, in 10064; lunar days, and in 990;3,5°%% civil days. This whole computation rests on the measures which Brahmagupta adopts regarding a kalpa and the star- eycles in a kalpa. According to the theory of Pulisa regarding the caturyuga, a caturyuga has 51,840,000 solar months, 53,433,336 lunar months, 1,593,336 adhimdsa months. Accordingly a caturyuga has 1,555.200,000 solar days, 1,603,000,080 lunar days, 47,800,080 days of adhimdsa months. If we reduce the numbers of the months by the common divisor of 24, we get 2,160,000 solar months, 2,226,389 lunar months, 66,389 adhimdsa months. If we divide the numbers of the day by the common How many solar, lunar, and civil days are re- quired for the forma- tion of an adhimdasa month. The compu- tation of adhimdsa according to Pulisa. Page 215. CHAPTER LL 25 divisor of 720, we get 2,160,000 solar days, 2,226,389 lunar days, 66,389 days of the adhimdsa months. If we, lastly, divide the wniversal solar, lunar, and civil days of a caturyuga, each kind separately, by the uni- versal adhimdsa months of a caturyuga, the quotient represents the numbers of days within which a whole adhimdsa month sums up, viz. in 976¢'s3%s5 solar days, in 1006735; lunar days, and in 990%$$$ civil days. These are the elements of the computation of the adhimdsa, which we have worked out for the benefit of the following investigations, Regarding the cause which necessitates the dnardtra, Explanation lit. the days of the decrease, we have to consider the fol- anavatra. lowing. If we have one year or a certain number of years, and reckon for each of them twelve months, we get the corresponding number of solar months, and by multi- plying the latter by 30, the corresponding number of solar days. It is evident that the number of the lunar months or days of the same period is the same, plus an increase which forms one or several adhimdsa months. If we reduce this increase to adhimdsa months due to the period of time in question, according to the relation between the universal solar months and the universal adhimdsa months, and add this to the months or days of the years in question, the sum represents the partial lunar days, 4.6. those which correspond to the given number of years. This, however, is not what is wanted. What we want is the number of civil days of the given number of years which are /ess than the lunar days; for one civil day is greater than one /unar day. Therefore, in order to find that which is sought, we must subtract some- thing from the number of lunar days, and this element which must be subtracted is called uénardtra. The tnardtra of the partial lunar days stands in the same relation to the wniversal lunar days as the uni- 26 ALBERUNIS INDIA. versal civil days are less than the universal lunar days. The universal lunar days of a kalpa are 1,602,999,000,000. This number is larger than the number of universal civil days by 25,082,550,000, which represents the uni- versal dnardtra. Both these numbers may be diminished by the com- mon divisor of 450,000. Thus we get 3,562,220 uni- versal lunar days, and 55,739 universal winardtra days. According to Pulisa, a caturyuga has 1,603,000,080 lunar days, and 25,082,280 winardtra days. The com- mon divisor by which both numbers may be reduced is 360. Thus we get 4,452,778 lunar days and 69,673 unardtra days. These are the rules for the computation of the uéna- رهاق‎ which we shall hereafter want for the compu- tation of the ahargana. The word means sum of days ; for dh means day, and argana, sum. va‘ktib Ibn Tarik has made a mistake in the compu- tation of the solar days; for he maintains that you get them by subtracting the solar cycles of a kalpa from the civil days of a kalpa, i.e. the universal civil days. But this is not the case. We get the solar days by multiplying the solar cycles of a kalpa by 12, in order to reduce them to months, and the product by 30, in order to reduce them to days, or by multiplying the number of cycles by 360. In the computation of the lunar days he has first taken the right course, multiplying the lunar months of a kalpa by 30, but afterwards he again falls into a mistake in the computation of the days of the énardtra. For he maintains that you get them by subtracting the solar days from the lunar days, whilst the correct thing is to subtract the civil days from the lunar days. Computa- tion of the tnardtra according to Pulisa. Criticisms on Ya'kab Ibn Tarik. Page 216. General rule how to find the sdvand- hargand. G27} CHAPTER LII. ON THE CALCULATION OF “AHARGANA” IN GENERAL, THAT IS, THE RESOLUTION OF YEARS AND MONTHS INTO DAYS, AND, VICE VERSA, THE COMPOSITION OF YEARS AND MONTHS OUT OF DAYS. THE general method of resolution is as follows :—The complete years are multiplied by 12; to the product are added the months which have elapsed of the current year, [and this sum is multiplied by 30;] to this product are added the days which have elapsed of the current month. The sum represents the saurdhargana, 4.6. the sum of the partial solar days. You write down the number in two places. In the one place you multiply it by 5311, 4.6. the number which represents the universal adhimdsa months. The product you divide by 172,800, ae. the number which represents the wniversal solar months. The quotient you get, as far as it contains complete days, is added to the number in the second place, and the sum represents the candradhargana, i.e. the sum of the partial lunar days. The latter number is again written down in two different places. In the one place you multiply it by 55,739, 4.6. the number which represents the wniversal dinardtra days, and divide the product by 3,562,220, we. the number which represents the universal lunar days. The quotient you get, as far as it represents complete days, is subtracted from the number written in the second place, and the remainder is the sdvandhargana, i.e. the sum of civil days which we wanted to find. 28 ALBERUNI’S INDIA. However, the reader must know that this computa- tion applies to dates in which there are only complete adhimdsa and tinardtra days, without any fraction. If, therefore, a given number of years commences with the beginning of a kalpa, or a caturyuga, or a kaliyuga, this computation is correct. But if the given years begin with some other time, it may by chance happen that this computation is correct, but possibly, too, it may result in proving the existence of adhimdsa time, and in that case the computation would not be correct. Also the reverse of these two eventualities may take place. However, if it is known with what particular moment in the kalpa, caturyuga, or kaliyuga a given number of years commences, we use a special method of com- putation, which we shall hereafter illustrate by some examples, We shall carry out this method for the begin- ning of the Indian year Sakakfla 953, the same year which we use as the gauge-year in all these computa- tions. First we compute the time from the beginning of the life of Brahman, according to the rules of Brahma- gupta. We have already mentioned that 6068 kalpas have elapsed before the present one. Multiplying this by the well-known number of the days of a kalpa (1,577,916,450,000 civil days, vide i. p. 368), we get 9,574,797,018,600,000 as the sum of the days of 6068 kalpas. Dividing this number by 7, we get 5 as a remainder, and reckoning five days backwards from the Saturday which is the last day of the preceding kalpa, we get Tuesday as the first day of the life of Brahman. We have already mentioned the sum of the days of a caturyuga (1,577,916,450 days, v. i. p. 370), and have explained that a kritayuga is equal to four-tenths of it, 1.6. 631,166,580 days. A manvantara has seventy-one times as much, 24.6. 112,032,067,950 days. The days of More de- tailed rule for the same purpose. The latter method earried out for Saka- kAla 953. Page 217. CHAPTER LI. 29 six manvantaras and their samdhi, consisting of seven kritayuga, are 676,610,573,760. If we divide this number by 7, we get a remainder of 2. Therefore the six manvantaras end with a Monday, and the seventh begins with a Tuesday. Oftheseventh manvantara there have already elapsed twenty-seven catwryugas, 1.6. 42,603,744,150 days. If we divide this number by 7, we get a remainder of 2. Therefore the twenty-eighth caturyuga begins with a Thursday. The days of the yugas which have elapsed of the present caturyuga are 1,420,124,805. The division by 7 givesthe remainder 1. Therefore the kaliyuga begins with a Friday. Now, returning to our gauge-year, we remark that the years which have elapsed of the kalpa up to that year are 1,972,948,132. Multiplying them by 12, we get as the number of their months 23,675,377,584. In the date which we have adopted as gauge-year there is no month, but only complete years; therefore we have nothing to add to this number. By multiplying this number, by 30 we get days, viz. 710,261,327,520. As there are no days in the normal date, we have no days to add to this number. li, therefore, we had multiplied the number of years by 360, we should have got the same result, viz. the partial solar days. Multiply this number by 5311 and divide the pro- duct by 172,800. The quotient is the number of the adhimdsa days, viz. 21,829,849,01872%. If, in multi- plying and dividing, we had used the months, we should have found the adhimdsa months, and, multi- plied by 30, they would be equal to the here-mentioned number of adhimdsa days. If we further add the adhimdsa days to the partial solar days, we get the sum of 732,091,176,5 38, 2.6. the partial lunar days. Multiplying them by 55,739, and 30 ALBERUNTIS INDIA. dividing the product by 3,562,220, we get the partial dnardtra days, viz., 11,455,224, 575 في‎ 06 This sum of days without the fraction is 5 ed from the partial lunar days, and the remainder, 720,635,951,963, represents the number of the civil days of our gauge-date. Dividing it by 7, we get as remainder 4, which means that the last of these days is a Wednesday. Therefore the Indian year commences with a Thursday. If we further want to find the adhimdsa time, we divide the adhimdsa days by 30, and the quotient is the number of the adhimdsas which have elapsed, viz. 727,661,633, plus a remainder of 28 days, 51 minutes, 30 seconds, for the current year. This is the time which has already elapsed of the adhimdsa month of the current year. To become a complete month, it only wants 1 day, 5 minutes, 30 seconds more. We have here used the solar and lunar days, the‏ ال calculation‏ applied toa adhimdsa and ainardtra days, to find a certain past‏ caturyuga‏ according to portion of a kalpa. We shall now do the same to find‏ the theory‏ of Pulisa. the past portion of a caturyuga, and we may use the same elements for the computation of a caturyuga which we have used for that of a kalpa, for both methods lead to the same result, as long as we adhere to one and the same theory (e.g. that of Brahmagupta), and do not mix up different chronological systems, and as long as each gunakdra and its bhdgabhdra, which we here mention together, correspond to each other in the two computations. The former term means a muiltiplicator in all kinds of calculations. In our (Arabic) astronomical hand- books, as well as those of the Persians, the word occurs in the form gunedr. The second term means each divisor. It occurs in the astronomical handbooks in the form bahedr. It would be useless if we were to exemplify this com- putation on a catwryuga according to the theory of Brah- Page 218. A similar metiiod of computation taken from the Pulisa- siddhanta. CHAPTER LII. 31 magupta, as according to him a caturyuga is simply one- thousandth of a kalpa. We should only have to shorten the above-mentioned numbers by three ciphers, and in every other respect get the same results. Therefore we shall now give this computation according to the theory of Pulisa, which, though applying to the caturyuga, is similar to the method of computation used for a kalpa. According to Pulisa, in the moment of the beginning of the gauge-year, there have elapsed of the years of the caturyuga 3,244,132, which are equal to 1,167,887,520 solar days. If we multiply the number of months which corresponds to this number of days with the number of the adhimdsa months of a caturyuga or a corresponding multiplicator, and divide the product by the number of the solar months of a caturyuga, or a corresponding divisor, we get as the number of adhi- mdsa months 1,196,525 {4$83. Further, the past 3,244,132 years of the caturyuga are 1,203,783,270 lunar days. Multiplying them by the number of the dnardtra days of a caturyuga, and dividing the product by the lunar days of a caturyuga, we get as the number of dnardtra days 18,5 3 5,700 يليج‎ Accordingly, the civil days which have elapsed since the beginning of the caturyuga are 1,184,947,570, and this it was which we wanted to find. We shall here communicate a passage from the Pulisa-siddhdnta, describing a similar method of com- putation, for the purpose of rendering the whole subject clearer to the mind of the reader, and fixing it there more thoroughly. Pulisa says: “ We first mark the kalpas which have elapsed of the life of Brahman before the present kalpa, 1.6. 6068. We multiply this number by the number of the caturyugas of a kalpa, i.e. 1008. Thus we get the product 6,116,544. This number we multiply by the number of the yugas of a caturyuga, 4.6. 4,and get the product 24,466,176. This number we multiply by the number of years of a yuga, 32 ALBERUNI’S INDIA. 4.6. 1,080,000, and get the product 26,423,470,080,000. These are the years which have elapsed before the present kalpa. We further multiply the latter number by 12, so as to get months, viz. 317,081,640,960,000. We write down this number in two different places. In the one place, we multiply it by the number of the adhimdsa months of a caturyuga, 1.0. 1.593,336, or a corresponding number which has been mentioned in the preceding, and we divide the product by the num- ber of the solar months of a catwryuga, 1.6. 51,840,000. The quotient is the number of adhimdsa لاك‎ viz. 9,745,709,750,784. This number we add to the number written in the second place, and get the sum of 326,827,350,710,784. Multiplying this number by 30, we get the product 9,804,820, 521,323,520, viz. lunar days. This number is again written down in two different places. In the one place we multiply it by the wnardtra of a caturyuga, 4.6. the difference between civil and lunar days, and divide the product by the lunar days of a caturyuga. Thus we get as quotient 15 3,416,869,240,320, ic. Unardtra days. We subtract this number from that one written in the second place, and we get as remainder 9.65 1,403,652,083,200, i.e. the days which have elapsed of the life of Brahman before the present kalpa, or the days of 6068 kalpas, each kalpa having 1,590,541,142,400 days. Dividing this sum of days by 7, we get no remainder. This period of time ends with a Saturday, and the present kalpa commences with a Sunday. This shows that the beginning of the life of Brahman too was a Sunday. Of the current kalpa there have elapsed six manvan- taras, each of 72 caturyugas, and each caturyuga of 4,320,000 years. Therefore six manvantaras have 1,866,240,000 years. This number we compute in the Page 219. CHAPTER LII. 33 same way as we have done in the preceding example. Thereby we find as the number of days of six complete manvantaras, 681,660,489,600. Dividing this number by 7, we get as remainder 6. Therefore the elapsed manvantaras end with a Friday, and the seventh man- vantara begins with a Saturday. Of the current manvantara there have elapsed 27 caturyugas, which, according to the preceding method of computation, represent the number of 42,603,780,600 days. The twenty-seventh caturyuga ends with a Monday, and the twenty-eighth begins with a Tues- day. Of the current catwryuga there have elapsed three yugas, OY 3,240,000 years. These represent, according to the preceding method of computation, the number of 1,183,438,350 days. Therefore these three yugas end with a Thursday, and kaliyuga commences with a Friday. Accordingly, the sum of days which have elapsed of the kalpa is 725,447,708,550, and the sum of days which have elapsed between the beginning of the life of Brahman and the beginning of the present kaliyuga is 9,652,129,099,791,750. To judge from the quotations from Aryabhata, as we Themethoa of ahargana have not seen a book of his, he seems to reckon in the employed by A following manner :— ae = The sum of days of a caturyuga is 1,577,917,500. The time between the beginning of the kalpa and the beginning of the kaliyuga is 725,447,570,625 days. The time between the beginning of the kalpa and our gauge-date is 725,449,079,845. The number of days which have elapsed of the life of Brahman before the present kalpa is 9,651,401,817,120,000. This is the correct method for the resolution of years into days, and all other measures of time are to be treated in accordance with this. We have already pointed out (on p. 26) a mistake VOL, II, 0 34 ALBERUNI’S INDIA. of Ya‘kib Ibn Tarik in the calculation of the universal solar and dnardtra days. As he translated from the Indian language a calculation the reasons of which he did not understand, it would have been his duty to examine it, and to check the various numbers of it one by the other. He mentions in his book also the method of ahargana, 4.6. the resolution of years, but his descrip- tion is not correct; for he says :— “ Multiply the months of the given number of years by the number of the adhimdsa months which have elapsed up to the time in question, according to the well-known rules of adhimdsa. Divide the product by the solar months. The quotient is the number of complete adhimdsa months plus its fractions which have elapsed up to the date in question.” The mistake is here so evident that even a copyist would notice it; how much more a mathematician who makes a computation according to this method; for he multiplies by the partial adhimdsa instead of the unwersal. 3esides, Ya‘kib mentions in his book another and perfectly correct method of resolution, which is this: “When you have found the number of months of the years, multiply them by the number of the lunar months, and divide the product by the solar months. The quotient is the number of adhimdsa months toge- ther with the number of the months of the years in question. “This number you multiply by 30, and you add to the product the days which have elapsed of the current month. The sum represents the lunar days. “Tf, instead of this, the first number of months were multiplied by 30, and the past portion of the month were added to the product, the sum would represent the partial solar days ; and if this number were further computed according to the preceding method, we should get the adhimdsa days together with the solar days.” The akar- gana as given by Ya‘k ib [bn Tarik. A second method given by Ya‘kub. CHAPTER LII. 35 The rationale of this calculation is the following :—If Explication we multiply, as we have done, by the number of the mentioned universal adhimdsa months, and divide the product by the universal solar months, the quotient represents the portion of adhimdsa time by which we have multiplied. As, now, the lunar months are the sum of solar and adhimdsa months, we multiply by them (the lunar months) and the division remains the same. The quo- tient is the sum of that number which is multiplied . and that one which is sought for, 2.6. the lunar days. We have already mentioned in the preceding part that by multiplying the lunar days by the universal Page 220. dnardtra days, and by dividing the product by the universal lunar days, we get the portion of wdnardtra days which belongs to the number of lunar days in question. However, the civil days in a kalpa are less than the lunar days by the amount of the dnardtra days. Now the lunar days we have stand in the same relation to the lunar days minus their due portion of dnardtra days as the whole number of lunar days (of a kalpa) to the whole number of lunar days (of a kalpa) minus the complete number of 14411070170: days (of a kalpa) ; and the latter number are the wniversal civil days. If we, therefore, multiply the number of lunar days we have by the universal civil days, and divide the product by the universal lunar days, we get as quotient the number of civil days of the date in ques- tion, and that it was which we wanted to find. In- stead of multiplying by the whole sum of civil days (of a kalpa), we multiply by 3,506,481, and instead of dividing by the whole number of lunar days (of a kalpa), we divide by 3,562,220. The Hindus have still another method of calculation. Another method of It is the following :—“ They multiply the elapsed years ¢ ah toa eos of the kalpa by 12, and add to the product the com- plete months which have elapsed of the current year, The sum they write down above the number 69,120, 36 ALBERUNI’S INDIA. (Lacuna.) and the number they get is subtracted from the num- ber written down in the middle place. The double of the remainder they divide by 65. Then the quotient represents the partial adhimdsa months. This number they add to that one which is written down in the uppermost place. They multiply the sum by 30, and add to the product the days which have elapsed of the current month. The sum represents the partial solar days. This number is written down in two different places, one under the other. They multiply the lower number by 11, and write the product under it. Then they divide it by 403,963, and add the quotient to the middle number. They divide the sum by 703, and the quotient represents the partial énardtra days. This number they subtract from the number written in the uppermost place, and the remainder is the number of civil days which we want to find.” The rationale of this computation is the following :— If we divide the universal solar months by the uni- versal adhimdsa months, we get as the measure of one adhimdsa month 32,5344; solar months. The double of this is 65735°; solar months. If we divide by this number the double of the months of the given years, the quotient is the number of the partial adhimdsas. How- ever, if we divide by wholes plus a fraction, and want to subtract from the number which is divided a certain portion, the remainder being divided by the wholes only, and the two subtracted portions being equal por- tions of the wholes to which they belong, the whole divisor stands in the same relation to its fraction as the divided number to the subtracted portion. If we make this computation for our gauge-year, we get the fraction of ,وو ومح‎ and dividing both num- hens ‘by 15, we get موكؤيج‎ It would also Re, pos ine here to reckon by single adhimdsas instead of double ones, and in that case it a Edi 7 7 Explication of the latter methcd, The latter method applied to the gauge- year. Method for . the compu- tation of the ainardatra days accord- ing to Brahma- gupta, Page 221. CHAPTER LII. 37 would not be necessary to double the remainder. But the inventor of this method seems to have preferred the reduplication in order to get smaller numbers; for if we reckon with single adhimdsas, we get the fraction of =$344,, which may be reduced by 96 as a common divisor. Thereby we get 89 as the multiplicator, and 5400 as the divisor. In this the inventor of the method has shown his sagacity, for the reason for his computation is the intention of getting partial lunar days and smaller multiplicators. His method (7.c. Brahmagupta’s) for the computation of the wnardtra days is the following :-— Tf we divide the universal lunar days by the uni- versal dnardtra days, we get as quotient 63 and a fraction, which may be reduced by the common divisor 450,000. Thus we get 6339253 lunar days as the period of time within which one duane day sums up. um we change this fraction into eleventh parts, we get كر‎ and a 0 of > Sern which, if expres gséd in minutes, is equal to 0’ 59” 54”. Since this fraction is very near to one whole, people have neglected it, and use, in a rough way, +? instead. Therefore, according to the Hindus, one tinardtra day sums up in 6342 or 493 lunar days. If we now multiply the number of énardira days, which corresponds to the number of lunar days by 6322-253, the product is less than that which we get by multiplying by 6324. If we, therefore, want to divide the lunar days by 590, on the supposition that the quotient is equal to the. first number, a certain portion must be added to the lunar days, and this portion he (the author of Pulisa-Siddhdnta) had not computed accu- rately, but only approximatively. For if we multiply the universal énardtra days by 703, we get the product 17,63 3,032,650,000, which is more than eleven times the universal lunar days. And if we multiply the universal lunar days by 11, we get the product 17,632,989, 000, C00. Il 55 ALBERUNI’S INDIA. The difference between the two numbers is 43,650,000. If we divide by this number the product of eleven times the universal lunar days, we get as quotient 403,963. This is the number used by the inventor of the method. If there were not a small remainder beyond the last-mentioned quotient (403,963 + a fraction), his method would be perfectly correct. However, there remains a fraction of 93. or ثم‎ and this is the amount which is neglected. If he uses this divisor without the fraction, and divides by it the product of eleven times the partial lunar days, the quotient would be by so much larger as the dividendum has increased. The other details of the calculation do not require comment. Because the majority of the Hindus, in reckoning their years, require the adhimdsa, they give the pre- ference to this method, and are particularly painstaking in describing the methods for the computation of the adhimdsa, disregarding the methods for the compu- tation of the énardtra days and the sum of the days (ahargana). One of their methods of finding the ad- himdsa for the years of a kalpa or caturyuga or kaliyuga is this :— They write down the years in three different places. They multiply the upper number by 10, the middle by 2481, and the lower by 7739. Then they divide the middle and lower numbers by 9600, and the quotients are days for the middle number and avama for the lower number. The sum of these two quotients is added to the number in the upper place. The sum represents the number of the complete adhimdsa days which have elapsed, and the sum of that which remains in the other two places is the fraction of the current adhimdsa, Dividing the days by 30, they get months. Yakaib Ibn Tarik states this method quite correctly, We shall, as an example, carry out this computation for ourgauge-year, The years of thekalpa which haveelapsed Criticisms of this method, Method for finding the adhimasa for the years of a kalpa, caturyuga, or kaliyuga. CHAPTER 1 39 till the moment of the gauge-date are 1,972,948,132. The latter We write down this number in three different places. a the The upper number we multiply by ten, by which it “°° gets a cipher more at the right side. The middle number we multiply by 2481 and get the product 4,894,884,315,492. The lower number we multiply by page 222. 7739, and get the product 15,268,645,593,548. The latter two numbers we divide by 9600; thereby we get for the middle number as quotieut 509,883,782 and a remainder of 8292, and for the lower number a quo- tient of 1,590,483,915 and aremainder of 9548. The sum of these two remainders is 17,840. This fraction (i.e. *7s55°) is reckoned as one whole. Thereby the sum of the numbers in all three places is raised to 21,829,849.018, 2.6. adhimdsa days, plus +92 day of the current adhimdsa day (i.e. which is now in course of summing up). Reducing these days to months, we get 727,661,633 months and a remainder of twenty-eight days, which is called Sh-D-D. This is the interval between the beginning of the month Caitra, which is not omitted in the series of months, and the moment of the vernal equinox. Further, adding the quotient which we have got for the middle number to the years of the kalpa, we get the sum of 2,482,831,914. Dividing this number by 7, we get the remainder 3. Therefore the sun has, in the year in question, entered Aries on a Tuesday. The two numbers which are used as multiplicators Explanatory for the numbers in the middle and lower places are to Tater gest be explained in the following manner :— ik Dividing the civil days of a kalpa by the solar cycles of a kalpa, we get as quotient the number of days which compose a year, 1.6. 3052430 soe G00 keducing this fraction by the common divisor of 450,000, we get 365322. The fraction may be further reduced by being divided by 3, but people leave it as it is, in order 40 ALBERUNIS INDIA. that this fraction and the other fractions which occur in the further course of this computation should have the same denominator. Dividing the universal dnardtra days by the solar years of a kalpa, the quotient is the number of tinardtra days which belong to a solar year, viz. 52-582-350.000 days. Reducing this fraction by the common divisor of 450,000, we get 53338 days. The fraction may fur- ther be reduced by being divided by 3. The measures of solar and lunar years are about 360 days, as are also the civil years of sun and moon, the one being a little larger, the other a little shorter. The one of these measures, the lunar year, is used in this computation, whilst the other measure, the solar year, is sought for, The sum of the two quotients (of the middle and lower number) is the difference between the two kinds of years. The upper number is multiplied by the sum of the complete days, and the middle and lower numbers are multiplied by each of the two fractions. If we want to abbreviate the computation, and do not, like the Hindus, wish to find the mean motions of sun and moon, we add the two multiplicators of the middle and lower numbers together. This gives the sum of 10,220. - To this sum we add, for the upper place, the product of the divisor X 10 = 96,000, and we get 798220, Reducing this fraction by the half, we get 933). In this chapter (p. 27) we have already explained’ that by multiplying the days by 5311, and dividing the product by 172,800, we get the number of the adhimdsas. If we now multiply the number of years instead of the days, the product is 3¢5 of the product which we should get when multiplying by the number of days. If we, therefore, want to have the same quotient which we get by the first division, we must divide by sev Of the divisor by which we divided in the first case, viz. 480 (for 360 X 480 = 172,800). Simplifica- tion of the same me- thod. Page 223. A second method for finding the adhimdsa, accordiug to Pulisa. Explication of the me- thod of ulisa. Further quotation from Pulisa, CHAPTER LIT, 41 Similar to this method is that one prescribed by Pulisa : “ Write down the number of the partial months in two different places. In the one place multiply it by 1111, and divide the product by 67,500. Sub- tract the quotient from the number in the other place, and divide the remainder by 32. The quotient is the number of the adhimdsa months, and the fraction in the quotient, if there is one, represents that part of an adhimdsa mouth which is in course of formation, Mul- tiplying this amount by 30, and dividing the product by 32, the quotient represents the days and day-frac- tions of the current adhimdsa month.” The rationale of this method is the following :— If you divide the solar months of a caturyuga by the adhimdsa months of a caturyuga, in accordance with the theory of Pulisa, you get as quotient 32%#323. Ifyou divide the months by this number, you get the com- plete adhimdsa months of the past portion of the catur- yuga or kalpa. Pulisa, however, wanted to divide by wholes alone, without any fractions. Therefore he had to subtract something from the dividendum, as has already been explained in a similar case (p. 36). We have found, in applying the computation to our gauge- year, as the fraction of the divisor, 53230, Which may be reduced by being divided by 32. Thereby we get عا .07,500 Pulisa has, in this calculation, reckoned by the solar‏ days into which a date is resolved, instead of by months.‏ For he says: “You write this number of days in two‏ different places. In the one place you multiply it by‏ and divide the product by 4,050,000. The quo-‏ 271 tient you subtract from the number in the other‏ place and divide the remainder by 976. The quo-‏ tient is the number of adhimdsa months, days, and‏ day-fractions.”‏ Further he says: “The reason of this is, that by‏ dividing the days of a caturyuga by the adhimdsa‏ 42 ALBERUNDS INDIA. months, you get as quotient 976 days and a remainder of 104,064. The common divisor for this number and for the divisor is 384. Reducing the fraction thereby, we get جوج دج‎ days.” Here, however, I suspect either the copyist or the translator, for Pulisa was too good a scholar to commit similar blunders. .The matter is this :— Those days which are divided by the adhimdsa months are of necessity solar days. The quotient con- tains wholes and fractions, as has been stated. Both denominator and numerator have as common divisor the number 24. Jeducing the fraction thereby, we get 4336 3558+ If we apply this rule to the months, and reduce the number of adhimdsa months to fractions, we get 47,800,000 as denominator.