The World-Year of the Persians

Waerden, B.L.van der en E.S.Kennedy The World-Year of the Persians In: Journal of the American Oriental Society 83 - 1963 - p.515 -327 N ' SHAR es QNAEROÉA BSLV à. Ast val Voller World-Year of the Persiuns. J. TheDEN: “OES kesaroy € BL VANDER WALR Amer. Oriental Sov. 83 (1963) p. 315-327. Lan ¿ $ W _E.S. Kenneoy und B. L. van per WAERDEN: The World-Year of the Persians. J. of the Amer. Orient. Soc. 83, p. 323 und 325.

The World-Year of the Persians Source: Journal of the American Oriental Society, Vol. 83, No. 3 (Aug. - Sep., 1963), pp. 315327 Published by: American Oriental Society Stable URL: http://www.jstor.org/stable/598071 Accessed: 18/01/2010 12:55 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=aos. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. American Oriental Society is collaborating with JSTOR to digitize, preserve and extend access to Journal of the American Oriental Society. http://www.jstor.org

NAFF: Reform and Diplomacy And yet, despite failure, it cannot be concluded that the results of Selim's labors were all negative. Western innovations and particularly western ideas, did not end with Selim's reign. They found in the decayed Ottoman Empire a rich soil in which they eventually took root. Selim's diplomatic reforms made a particular contribution to this process. His establishment of permanent embassies in Europe did enable a few young Ottomans to learn a European language and to inform themselves about some of the revolutionary ideas current in Europe. Some, on their return, "became officials at the Porte, where they formed a Westward-looking minority among the bureaucratic hierarchy, similar to that created among the officers by the military and naval reforms." 69 new ideas from the west were perverted by many and "took the form of free-thinking, or were clothed in mysticism, and were displayed even among the dignitaries of the Palace and the Sublime Porte "; also Nuri, Netaic, IV, 41-42, on the resentment and opposition aroused by Selim's reforms. 9 Lewis, Emergence, 61; also d'Ohsson, VII, 513. in the Reign of Selim III 315 Many of the specific reforms were left unchanged, though some fell temporarily into disuse. This is true especially in the case of diplomacy. When Mahmud II recommenced the task of reforming the Empire, he successfully adopted many of Selim's diplomatic reforms, most conspicuously, continuous diplomacy through resident missions abroad. Selim III's reign generated the forces of change and produced the essential precedents, indeed, even the necessary failures. Examples of such men are " tngiliz" Mahmud Efendi and Galib Efendi (later Galib Pasa). On Mahmud Efendi see Mehmed Siireyya, Sicill-i Osmani (Istanbul, 1890-98), IV, 329-30, Cevdet, Tarih, VII, 5-6, A. Adnan, La science chez les Turcs ottomans (Paris, 1939), and Lewis, "The Impact of the French Revolution on Turkey," Journal of World History, I (1953), 112. On Galib Efendi see Uzuncarsill, "Amedi Galib Efendinin Murahhasli i ve Paristen Gonderdigi $ifreli Mektuplar," Belleten, I (1937), 357-410, F. Babinger, Die Geschichtsschreiber der Osmanen und ihre Werke (Leipzig, 1927), "Galib Paga," Islam Ansiklo331, and F. Kpriilii, pedisi, IV, 710-14. THE WORLD-YEAR OF THE PERSIANS E. S. KENNEDY B. L. VAN DER WAERDEN AMERICAN UNIVERSITY OF BEIRUT, AND BROWN UNIVERSITY ZURICH UNIVERSITY 1. INTRODUCTION The notion of cyclicly recurrent cosmic disasters, a catastrophe by flood alternating with one by fire, both accompanying conjunctions of all planets at the zero point of the zodiac, has been traced from ancient Babylonia and Iran through Pythagorean and Stoic philosophy, thence into the medieval world.1 Because of its essential connection with astronomy, the concept of the world-year is of interest and utility to historians of science. Its ramifications provide clues elucidating the role of Sasanian Iran in the origin and transmission of scientific theory, particularly towards India. Translated below are two fragmentary versions of a chapter descriptive of the world-year and stemming ultimately from Abi Ma'shar2 al-Balkhi, 1 See van der Waerden, B. L., "Das grosse Jahr und die ewige Wiederkehr," Hermes 80 (1952), pp. 129-155. 2 Brockelmann, C., G. A. L. (Leiden, 1943), Vol. I (2d. ed.), p. 250; suppl. Vol. I, p. 394. the ninth century astrologer widely known in medieval Europe as Albumasar. He wrote a treatise called Kitab al-Uluf (Book of the Thousands), no copy of which is presently available. It was summarized, however, by Ahmad 'Abd al-Jalil al-Sijzi3 (fl. 1000) and the summary, though mutilated, has come down to us. 2. THE SOURCES The first, referred to hereafter as A, appears on f.236 of the anonymous MS (Paris) BN Arabe 5968. This important document, to which our attention was called by Mr. Marcel Destombes, is a collection of astronomical and genealogical tables and treatises evidently compiled by a member of the Ismaili sect. In fact, Blochet 4 states that the 3 Brockelmann, C. op. cit., Vol. I (2d. ed.), p. 246; suppl. Vol. I, p. 388. 4 Notices et extraits des manuscripts de la Bibliotheque Nationale, XLI (1923), pp. 391-398.

KENNEDY manuscript is a holograph of the unknown author, that it was written in the fortress of Alamut during the time of HIasan-i Sabbah, and that it is one of the books found in the Alamut library by the historian Juvaini when the place was taken and destroyed by Hulagu Khan 5 in 1256. Our passage is said to be from a work called Al-Jami' al-Shdhl. The same name is attached to British Museum MS Or. 1346, a collection of astrolgoical writings by al-Sijzl. Among these is his summary of the "Book of the Thousands," and a cursory examination of the latter showed that its first section, which we will call B, is a version of A. There is so little material identical between the two, they evidently having suffered the mistakes and omissions of independent successions of scribes, that it seems best to translate both without attempting to piece together a single original. Doubtless we will still be lacking some phrases set down by al-Sijzi in the first place, and what we have will differ somewhat from his original version. 3. THE TRANSLATIONS Numbers in parentheses indicate the beginnings of lines in the Arabic text. Words in parentheses do not appear in the original, but are added for clarification. The translations follow: A A line 1). world-year, according to the (f.23a: of the astrologers, is from the time of generality arrival of the planets at the first of Aries until the time of their return (2) to the end of Pisces, without there being a difference in their amounts (i.e., longitudes). As for those in a region of India (3) and their adherents, they say that the seven planets and their apogees and nodes (4) begin the motion from the first of Aries, and they conjoin at the end of Pisces in (5) 4,320,000,000 years. As for the partisans of the year of Arjabhaz (Aryabhata), (6) they differ from them and make the world-year 4,320,000 years. (7) The partisans of the years of the Arkand said differently from this. The Persians (ahl Fars) and some of (8) the Babylonians said that the world-years are 36[0],000 solar years, of which there are 365 days, (9) 15 minutes, 3[2] seconds, (and) 24 thirds, without requiring their apogees and nodes (to be The History of the World-Conqueror, by 5See: 'Ala-ad-Din Juvaini (transl. by J. A. Boyle), Manchester, 1958, Vol. II, p. 719. The World-Year of the Persians at Aries 0?). (10) If we divide the years of the Sindhind by a thousand there come out the Arjabhaz years. If we divide (11) by twelve thousand there comes out the year of the Persians. It is necessary to know that if the motions of (12) the apogees and nodes are the same it prevents their conjunction in one degree because they are scattered. (13) For the years of the Persians there are two characteristics. In the first place, if the mean motions are computed (14) by these years, one solar year by one year, there will be with the mean motions (15) a number which will increase an integer number of degrees in each thousand years, without a fraction. So if we take multiples of the mean motions (16) for each thousand years until the end of the world-year they all become degrees without fractions. This is not found (17) for the other cycles. The second characteristic is that the degrees elevated from the fractions of the sun, (18) especially if they are made days, the amount is 259 days, and these days are the base for the duration of (19) the child in the womb for a nine (month pregnancy?) and thereby the horoscope of the nativity is verified. The most famous and oldest of events is the Deluge, (20) in the time of Jam. Its time was at the mean conjunction of the seven planets (21) at the last (point) of Pisces on a Thursday, and verily half of the world-year had passed according to the belief of (22) the Persians. And what passed from the Deluge until the end of three thousand years was 1,095,776 (days), (23) and what passed of the fourth thousand until the Tuesday, the first of the reign of Yazdigerd (24) was 267,821 days, in solar years [733 and 86: 9, 10, 48 days . . .] which is two hundred and sixty-six (25) years of Yazdigerd and 348 days upon the entry of the sun into the first minute (26) of Aries at the time of its rising, at the position of Kankdidh (i.e. Kangdezh) on the morning of the day, it being a place to the east of (27) China, if it is opposite the middle of the earth appearing to it, it would rise, and when it arrives (28) at the midheaven of that place it would rise at the middle of the apparent earth. And what passed from the Deluge (29) until the first day on which Yazdigerd arose is 3,735 Persian years and ten months (f. 236b: line 1) and twenty[-three] days and twenty-two hours. From the date of the Deluge to the first of the year of (2) the Hijra is [3,725] (the text has 37,350) Persian years and eleven months and fourteen (3) days. The conjunction indicating the Deluge was

before it two hundred and seventy-six years, and (4) between the Deluge and the Saturn-Jupiter conjunction indicating the religion (of Islam) is 3,679 years. B (f.80b: line 22) A J STATEMENT CONCERNING WORLD-YEARS AND THE CHRONOLOGY (tawdrl7ch) (23) USED IN THIS BOOK. Verily, the generality of the learned among the people of India, and China, (24) and Rfm (the Byzantines), and Fars, and the people of Babylon, and those who follow them among the peoples are agreed (on the fact) that the seven planets were in conjunction (25) at the first minute of Aries and that they conjoin at the end of Pisces at the end of the world. As for the Hindus, they claim that the planets (f. 81a: line 1) their apogees and nodes, were in conjunction in the first minute of Aries, and that they conjoin at the last (2) (point) of Pisces at the end of the world, and the years of the world are from the time of the conjunction of the planets at the first minute of Aries until the time of (3) their conjunction at the end of Pisces, it being one and the same place, except that they differ among themselves as to the travel of the planets in the heaven. (4) As for those of one of the regions of India, they claim that the years of the world are 4,320,000,000 (5), they being the partisans (ashab) of the Sindhind. However, the other group of them, they being the partisans of the years of Arjabhaz, they (6) claim that the years of the world are 4,32[0],000. But the author ($ahib) of the " Book of the Thousands" used the years of the Persians for the cycles and (7) tasyrdat. However, some of the moderns used the world-years according to the way the partisans of the Sindhind explained them, (8) but we now, in this book, will utilize what the author of the "Book of the Thousands " used. So if you want to extract (9) the world-years and their days, look at the (number of) days and their fractions in which one of the planets rotates once around the heavens (10) in its mean motion, and multiply it by the days and fractions thereof in which another of the planets rotates once. (11) Then what results is the number of days in which the two will conjoin at the same position from which they started moving. (12) Then multiply what resulted of those days and fractions by the days and fractions in which another planet rotates (back) to the position in (13 which it was at the beginning of the motion, and thus according to World-Year of the Persians 317 this manner. Then multiply what you obtain for all seven of the planets (14) and the nodes and apogees, and it will be the days of the world. Verily the author of the " Book of the Thousands " mentioned the revolutions of the planets in days of (15) the world and the quantity of each of their revolutions in days and hours and minutes. At any rate, the days of the world utilized in this book are (16) [131], 493, 240 (text has 313, 493, 240) that being in solar years 36[0],000 according to a year of three hundred (17) and sixty-five days and fifteen minutes and thirty-two seconds and twentyfour thirds. That which passed from (18) the first day of the world-year until the first day of the Deluge [. . . and what passed of the fourth thousand] until the Tuesday, the first day of the reign of Yazdigerd was two hundred thousand (19) and sixty-seven thousand and eight hundred and twenty-one days, and its depiction in the Hindu (numerals) is 267,821. That will be (20) in solar years seven hundred and thirty-three years and eighty-six days and nine minutes and ten seconds and (21) forty-eight thirds. And what remains of days until the fourth thousand finishes is 97,438 days. That will be in two hundred and (22) sixty-six years of Yazdigerd and three hundred and forty[-eight] days upon the entry of the sun into the first minute of Aries, at the time of (23) its rising, at the position of Kankdiz, it being a place to the east of China. And that which passed from the Deluge until the first day (24) on which Yazdigerd arose (is) three thousand years and [seven] hundred and thirty-five Persian years and ten months and (25) twenty-three days and twenty-two hours. And that which passed from the Deluge until the first day of the year in which (26) the Prophet, the prayers of God upon him and peace, fled from Mecca to Medina in Persian years is three thousand and seven hundred and twenty-five (27) years and eleven months and fourteen days. That will be, in solar years, three thousands and seven hundred and twenty-three (28) years and three months and twenty-eight days and eight hours and fourteen minutes. So this is the saying concerning the world-years (29) and chronology used in this book. 4. COMMENTARY References to the sources give an A or a B followed by a colon and a number to identify the line of the text. Folio numbers will be given only when necessary to avoid ambiguity.

of the Persians A:2, B:4. places 10 attributes the 360,000 year cycle to Abui This span of time is the Kalpa, the fundamental Macshar,and Abui Ma'shar himself in his book on Hindu period upon which the Brahma-sphuta- conjunctions11 repeats the same numbers. Thus we have: siddhanta6 and the new Suirya-siddhanta7 are The world-year of the Persians = 360,000 years based. = 131,493,240 days, hence one solar year in this 1 Kalpa = 1,000 Mahagugas system is = 1,000 X 4,320,000 years. 131,493,240 At the beginning of a Kalpa all seven planets, as well as their apogees and nodes, were supposed to be at 0? Aries, just as our texts say. There is good reason for thinking that the Sindhind of the Islamic astronomers was an Arabic translation of the Brahma-sphuta-siddhanta,so that all is well thus far. Curiously enough, the scribe of B used the symbol for sexagesimal zeroes to denote the zeros in his decimal numerals. A:5-6, B:5-6. In the system of Aryabhata the fundamental unit is indeed taken as the Mahayuga, a thousandth of the Kalpa, and except for the missing zero to be restored in B the texts are still reliable. = 365.259 = 365;15,32,24 days. 360,000 These numbers can be verified by direct division, but all of them either occur in or are restorable from our A and B, or from the writings referred to above. Concerning " some of the Babylonians " Biruni 12 says, "The astrologers have tried to correct these years, beginning from the first of the conjunctions of Saturn and Jupiter, for which the sages among the inhabitants of Babel, and the Chaldaeans have constructed astronomical tables, the Deluge having originated in their country." A:12. Since, in the Kalpa system, the apogees are all at Aries 0? at the beginning of the Kalpa, it folA:7. lows that not only the mean planets, but also the The Arkand is the name of an early Islamic true planets are then at Aries 0?. On the other translation9 into Arabic of Brahmagupta's Khan- hand, in Aryabhata's system and in the Sasanian dakhadyaka. The ahargana of the latter is reck- astronomical handbook,the Zlj-i Shah, the apogees oned from the ~aka year 587, i.e., it does differ are fixed, hence at the beginning of the world-year from the system first named. the true planets will not be in conjunction, but will be "scattered." A:8, B:6,16. A:15. In spite of the omission of a zero in the length and The Persian system assumes that each planet in A both as of the Persian world-year given an integer number of revolutions in themtexts from the derived considerations accomplishes B, selves, reinforced by statements in other sources, 360,000 years, i.e., its advance in degrees during enable us to make the restoration with complete this period is an integer multiple of 360. It folconfidence. For one thing, if we perform the lows that in each thousand years the planet will by the same integer number of degrees, operation prescribed in A: 11 and divide the years advance of the Sindhind, 4,320,000,000, by 12,000, we ob- and " this is not found for the other cycles." tain 360,000, not 36,000. Birunil in several A:18. Duration of pregnancy computations were of This work has been published as: Brdhmasphutasidinterest to astrologers because by many of them dhanta, by Brahmagupta, edited with his own commentary by M. S. Dvivedin, Benares (Medical Hall Press), the instant of conception was considered to be of 1900, reprinted from Pandit, vol. 24. more importance for casting a horoscope than the 7Translated by E. Burgess, JAOS, 6 (1860), pp. 141instant of birth. We have seen that the length of Santhe of edition new 498; reprinted Calcutta, 1935; skrit text by K. S. Shukla: The Sirya-siddhanta with the commentary of Paramesvara, Lucknow Univ., 1957. 8 See the translation of Birunni's " India " by E. Sachau (London, 1910), Vol. I, p. 368; also Al-Biruini on Transits (Beirut, 1959), p. 141. 9 See, e. g., Birfini's " India " (transl.), Vol. II, p. 7. 10Cf. The Chronology of Ancient Nations, translated by E. Sachau (London, 1879), p. 29; also Al-Qdnun al-Mas'idi (Hyderabad-Deccan,1956), Vol. III, p. 1475. 11Escorial MS Arabe 937, f. 4r. Chron., transl., p. 28.

World-Year of the Persians 319 a Persian solar year, written as a pure decimal is al-Khwarizimi14 and al-BIruni15 to Tuesday, 16 365.259 days. "To elevate" in a medieval Arabic June, 632, the first day of the Yazdigerd calendar. mathematical context is to perform an operation A:24, B: 20-22. analogous to moving the decimal (or sexagesimal) To convert 267,821 days into Persian solar years to the that to some point is, right; multiply by integer power of the base, here ten. Elevation of we divide this number by 365.259, the number of the fractions of the number above (the "fractions days per year, and obtain 733 as a quotient and a of the sum" of A) by a thousand gives 259 the remainder of 86.153 = 86;9,10,48. Thus the number in is and it is shown B duration that of verified, given alleged pregnancy. the restoration made in A, which is lacking in the A:20. text, is valid. In the three versions of the Persian traditional The number of days given until the end of the chronology reported by Birfini13 the reign of the fourth thousand in B: 21, when added to the legendary Jam(shid), son of Tahmurath of the elapsed days of the fourth thousand is Pishdadian dynasty, falls approximately between the years - 3400 and - 2800 of the Christian era. 97,438 + 267,821 = 365,259, We will see presently that Abf Ma'shar puts the the number of days in a thousand Persian solar Deluge in -3101, hence it occurred during the years. So it has been transmitted without error. reign of Jam. Furthermore, since Yazdigerd years have just 365 B:14. days, We can only regret that al-Sijzi neglected to 97,438 days = 266 Yazdigerd years and pass on Abi Ma'shar's mean motion parameters 348 days. for the planets. Fortunately, as in so many other instances, most of them have been preserved for us So the statement in A: 24,25 is correct, and that by the incomparable Biruni, and they are discussed of B:21,22 is restored with the addition of an in Section 6 below. "eight." A:22. A:26, B:23. The number of days in three thousand Persian Kangdezh was a mythical Iranian castle built by solar years is Jam, evidently regarded as being at the eastern 3,000 X 365.259 = 1,095,777 days, edge of the habitable part of the globe. Birfni that Abf Ma'shar used it as the base locality which is the same as the text, except that the says for his zij.16 The habitable part of the earth was terminal digit of the latter is 6. thought of as extending through 180? of longitude. The idea seems to be that noon at Kangdezh would A:23, B:18. In these sections gaps in each of the two versions be sunrise in the middle of the inhabited regions. can be filled, but only partially, by utilizing one A: 29, B: 24. against the other. B: 18 does not make sense as it stands. But at least it is clear that a passage is Recalling that the "Persian" (or Egyptian) missing, as indicated by the square brackets, and calendaric year has 365 days and each Persian that the end of the missing passage should be month thirty days, we have for the span from restored as shown in the translation. Now the Deluge to Yazdigerd sum of the number of days in three thousand astr. Tafeln des Muh ibn Misa al-KhwaPersian solar years plus the number of days given rizmiSee:. ."Die ." herausgeg. von H. Suter (Kopenhagen, in both versions is 1914), Kgl. Danske Vidensk. Skrifter, 7. R., Hist. 14 1,095,777 + 267,821 = 1,363,598 days. This is precisely the span in days from Thursday, 17 February -3101, the Deluge date of 13 Chron., Transl., pp. 109-114, 200-203, 220. og. filos. Afd. 3, 1; "The Astronomical Tables of al-Khwarizmi," transl. w. comm. by O. Neugebauer, Hist. filos. Skr. Dan. Vid. Selsk. 4, no. 2, (Kopenhagen, 1962). 15 Chron. (transl.), p. 133. 1 In the "India" (transl), Vol. I, p. 304, Sachau writes "his geographical canon," but the text (Hyderabad-Deccan, 1958), p. 259, simply says "his zij."

of the Persians 1,363,598 days = 3,735 Persian years, 10 months, 23 days. in the text is too low for a fourteen conjunction interval and out of the question for any other. This number enables us to restore scribal omissions in A and B made in different places in the two versions. So the matter is settled down to integer days, but the additional twenty-two hours appearing in both A and B pose a difficulty. Quite plausibly the mention of Kangdezh just preceding was to account for a time difference due to geographical location and to the time of day taken as epoch. Now the time difference from Kangdezh to a place of longitude 90? is six hours; that between noon and sunrise epoch or between sunset and noon, is of the same order of magnitude, but no combination of these gives anything near twenty-two hours. A: f.236b: 4. The conjunction indicating the rise of Islam (qiran al-milla) the 185th conjunction of Saturn and Jupiter since that of the Deluge year, took place in 571 A.D. Testifying to this are horoscopes cast for the instant of the sun's entry into Aries on that year, several being versions of computations by AbiuMa'shar himself.17 The interval from Deluge to this conjunction is 3,672 years, not 3,679 as claimed by our text. A: f.236b: 1, B:26. The number of days from the Deluge date given above to 15 July, 622, the beginning of the Hijra This contains 3,725 Percalendar, is 1,359,974. sian 365-day years plus a remainder of 349 days. The latter contains eleven Persian months plus a remainder of nineteen days. Before 1006, however, it was customary to insert the five epagomenal days at the end of the eighth month instead of at the end of the year. If the former is done the remainder will be reduced to 14 days, the number given in both versions. Calculated thus, the result is reported correctly in B, but A has been garbled. B:28. To convert 1,359,974 days into Persian solar years we divide by 365.259. The quotient is 3,723, as in the text, with a remainder of 114.743 days, or three thirty-day months, twenty-four days, and 17:50 hours. We see no way of reconciling the last part of this result with the twenty-eight days and 8; 14 hours of the text. A: f.236b: 3. Our source states that 276 years before the Deluge there was a conjunction. In such a context usually means a Saturn-Jupiter "conjunction" conjunction. It will be shown in Section 5 below that the time between mean conjunctions of this sort, according to the parameters of Abu Ma'shar's book of conjunctions is 360,000 19.848 years, 18,138 where a year is 365.259 days. Fourteen conjunctions will take about 277.9 years, and the number 5. THE DOCTRINE OF ABU MA'SHAR We shall now compare the Persian system our sources mention with the doctrine of Abi Ma'shar, which is also based upon the assumption of a cycle of 360,000 years. This doctrine is known from several passages in the writings of Biruni and from various versions of Abul Ma'shar's book of conjunctions. In his Chronology (transl., p. 29), Birfni writes about Abf Ma'shar: He supposed that the Deluge had taken place at the conjunction of the stars in the last part of Pisces, and the first part of Aries, and he tried to compute their of places for that time. Then he found that they-all them-stood in conjunction in the space between the twenty-seventh degree of Pisces and the end of the first degree of Aries. Further, he supposed that between that time and the epoch of the Aera Alexandri, there is an interval of 2,790 intercalated years, 7 months and 26 days . . . Now, when he thought that he had well established the computation of this sum according to the method, which he has explained, and when he had arrived at the result, that the duration of those periods, which astronomers call 'star-cycles,' was 360,000 years, the beginning of which was to precede the time of the Deluge by 180,000 years, he drew the inconsiderate conclusion that the Deluge had occurred once in every 180,000 years, and that it would again occur in future at similar intervals. This man, who is so proud of his ingenuity, had computed these star-cycles only from the motions of the stars, as they had been fixed by the observations of the Persians; but they (the cycles) differ from the cycles, which have been based upon the observations of the Indians, known as the 'cycles of Sindhind,' and likewise they differ from the days of Arjabhaz, and the days of Arkand. Here, we see that Birfni distinguishes, just as our sources do, three kinds of cycles: The Persian 17 E. g. in MS PB20.B41, School of Theology, Beirut. f. 29a, of the Near East

cycle of 360,000 years, of which Biruni says that it is based upon the observations of " the Persians," the cycle of Aryabhata or Mahayuga of 12 Persian cycles, and the "cycle of Sindhind" or Kalpa of 1000 Mahayugas, which is said to be "based upon the observations of the Indians." In fact we know that the mean motions of the "Sindhind" are the same as those of Brahmagupta's Brahma-sphutasiddhanta,l8 and that the fundamental period of the Sindhind is just the Kalpa of Brahmagupta. Hence, Biruni's testimony confirms several statements of our sources. As we have seen, the duration of the year: 365;15,32,24 days is also the same in Abu Ma'shar's book of conjunctions and in the Persian System. Still, we have to be careful in using the evidence from Abf Ma'shar for the reconstruction of the " Persian system." According to Birfni's account, Ab-u Ma'shar had computed the places of the planets for the time of the Deluge and found positions between 27? Pisces and 1? Aries. Now, in the Persian system, the mean longitudes of the planets are exactly zero at this epoch, and the true places, calculated by the "Method of the Persians," are not at all between 27? and 1? Aries. It seems that Abu Ma'shar used, in his calculations, tables that were not in accordance with the Persian system.19 We have checked some horoscopes 20 ascribed to Abu Ma'shar and found that he assumed the numbers of revolutions of Jupiter and Saturn in 12 times 360,000 years to be 364,220 and 146,568. These are just the figures of the new Sirya-siddhanta. The number for Jupiter is not divisible by 12. In the Persian system, the numbers must be divisible by 12, because all planets return to their original positions in a period of 360,000 years. It seems that Abfu Ma'shar, in his theoretical expositions, uses the Persian System, but in his calculations a mixture of several systems. 18 Burckhardt, J. J., Vierteljahresschrift der naturf. Ges., Ziirich, 106, p. 213 (1961). " 19 The mean positions at Abi Ma'shar's epoch of the Deluge," as calculated by Brahmagupta's Brahmasphuta-siddanta, are just between 27 Pisces and 1 Aries. Possibly Abu Ma'shar used this system. 20 From MSS: Paris BN Arabe 2581; British Museum Or. 1346; Near East School of Theology, Beirut, PB20. B41. of the Persians 321 For this reason, we shall calculate the numbers of revolutions of the planets not from Abu Ma'shar's text, but from other sources, and use his text only as a check. 6. THE NUMBERS OF REVOLUTIONS Aryabhata's fundamental period, the Mahayuga, contains just 12 times 360,000 years. Therefore, if we divide the number of revolutions of any planet in a Mahayuga by 12, we obtain the number of revolutions in a Persian World Year (according to Aryabhata). The numbers of revolution in Aryabhata's first system the "midnight system," are the same as those in the Khandakhadyaka and in the Old Suiryasiddhanta.21 The numbers are quite near to reality and to those of Babylonian planetary theory (see Table 2 in B. L. van der Waerden, Vierteljahresschrift der naturf. Ges., Zurich 100, p. 165). Hence, if we divide these numbers by 12, we ought to get at least approximately the same numbers as in the Persian System. The division gives Saturn Jupiter Mars Venus 12,214 -i 30,352 - i 191,402 585,199 1,494,750 Mercury Moon 4,812,778 its apogee 40,685 its node 19,352 + J. It is a remarkable fact that four of the eight numbers are actually divisible by 12. The last two numbers are nearly divisible by 12, the remainders of the divisions being - 1 and + 2 respectively. For Jupiter and Saturn we have to add 4 to the numbers of revolutions in a Mahayuga in order to obtain divisibility by 12. If we neglect the fractions, the resulting numbers for Saturn, Jupiter, Mars and the Moon are even. This means that not only at the beginning and end, but also in the middle of the period of 360,000 years, at the "epoch of the Deluge," the planets are in conjunction with the sun, as they should be in the Persian system. For Venus the number is odd, but this does not matter: if we have an inferior conjunction in the beginning, we shall have a superior conjunction in the middle of the period, and vice-versa. How far can the numbers of revolutions in the Persian system differ from those calculated by division? The mean longitudes of the planets at the vernal equinox of - 3101 are zero in the Per21 See Sengupta, P. C., The Khandakhddyaka Brahmagupta, Univ. of Calcutta, 1934.

sian system as well as in Aryabhata's. Now, if we add one unit to the number of revolutions of any planet in 360,000 years, the motion in 3,600 years, and hence the longitude in the year 499 is increased by 3.6 degrees. If we add 2 units in order to keep the number even (as we must for the upper planets and the moon), the longitude in 499 is increased by 7.2 degrees. Now, Aryabhata's longitudes are in good accordancewith modern calculations, and a shift of 7.2 degrees would disturb this agreement altogether. Hence, the numbers given for Saturn, Jupiter, Mars and the Moon (without the fractions) are most probably the correct numbers of the Persian system, and the numbers computed for Venus and Mercury cannot differ from the correct numbers by more than 1 for Venus and 2 at most for Mercury. Birini, in his "Book of Instruction in Astrology," translated by R. R. Wright (London 1934), gives the numbers of revolutions of the planets according to Abu Ma'shar (p. 114 of the translation). The figures for Saturn, Jupiter, Mars, Venus and the Moon agree exactly with the results of our division. For Mercury Biruni gives 751 instead of 750. Possibly 751 is the correct figure, although 750 agrees exactly with Babylonian planetary theory and with Rhetoriius (Catal. Cod. astrol. Graec. I, p. 163). For the lunar apogee Biruni gives 19,365, which is quite impossible. Still, the 5 at the end agrees with our calculation. The preceding digits 19 3 6 are probably copied from the number for the node. For the lunar node, Biruni gives 19,360 revolutions. This number would give an error of 28.8 degrees in the position of the node for 499. Such an error would spoil all calculations of eclipses. Therefore, our number 19,352 is much more likely. The numbers of revolutions of Jupiter and Saturn, 30,352 and 12,214, are just the same as in the book of conjunctions of Abfu Ma'shar.22 The difference between these numbers is 18,138. This implies that there are 18,138 Jupiter-Saturn conjunctions in every cycle of 360,000 years. From one conjunction to the next, the motion of Saturn is The World-Year of the Persians The lapse of time from one conjunction to the next is 360,000 18,138 years. Starting with the assumed conjunction of the year - 3101, the times of the successive mean conjunctions can be calculated. For these calculated times, the mean longitudes of Jupiter and Saturn may be calculated by modern tables. If the mean motions of the Persian system were correct, the differences of the mean longitudes ought to be zero at the times of the calculated mean conjunctions. Actually, they are not zero. The error is approximately 5? in the 3rd century A. D., 4? in the 4th century A.D., 2? in the 5th century A.D., 1? in the 6th century A.D. From these errors we conclude that the Persian system in the form in which we know it, with 18,138 mean conjunctions in 360,000 years, cannot have originated before the 5th century. Errors of 1 or 2 degrees are tolerable, but errors of 4 or 5 degrees would spoil the calculation of the conjunctions altogether. This gives us 400 A.D. as a lower limit to the date of invention of the Persian system. To obtain an upper limit, we shall compare it with the system of Aryabhata. 7. ARYABBATA AND THE PERSIAN SYSTEM Aryabhata was just 23 years old in March 499, at the time of the spring equinox, as 3,600 years of the Kaliyuga had passed.23 He developed two slightly different astronomical systems, the "midnight system" and the "sunrise system." The latter, known to us from his own treatise Aryabhatlya, is based upon the assumption of a mean conjunction of all planets at 0? Aries on Friday, Febr. 18, - 3101, at sunrise. In the midnight system, known from the Paichasiddhantika of Varaha Mihira and from the Khandakhadyaka, the mean conjunction of all planets is 6 hours earlier, at midnight in the night 12,214 360? 242 ;25,17,10,6 from Thursday to Friday. In both systems, the 18,138 great conjunction marked the beginning of the degrees. This number is also given in Abui present Kaliyuga, the last quarter of the Mahayuga Ma'shar'sbook of conjunctions. 22 Escorial MS Arabe 937, f.4a. 23Clark, W. E., The Iryabhatiya of Aryabhata (Chicago, 1930).

of 4,320,000 years. Aryabhata himself calls the Mahayuga Caturyuga, i. e., fourfold cycle. The Caturyuga is 12 times the Persian cycle, and the numbers of revolution in the midnight system are 12 times the Persian numbers; only for Saturn and Jupiter they are 12 times the Persian numbers minus 4, as we have seen. Moreover, Aryabhata's date for the great conjunction of - 3101 differs only by 1 day from the Persian date. Obviously, the Persian system and the astronomy of Aryabhata are not independent. Either the Persians modified the system of Aryabhata or Aryabhata modified the Persian system. For several reasons, the second possibility seems more probable. To begin with, astronomical periods usually become longer and not shorter in the course of time. Kallippos multiplied the 19year cycle of Meton by 4 in order to obtain an integer number of days. The Babylonians used a lunar period of 248 days, Hellenistic texts made use of periods of 248 and 3,031 days, and in Tamil astronomy both periods were combined to a larger period of 12,372 days.24The old Surya-siddhanta is based upon the Mahayuga, but the new Suryasiddhanta is based upon the Kalpa. The examples could be multiplied still more. The tendency to longer periods is easy to explain. Longer periods give the astronomer more freedom to adapt the elements of his system to the observations. An example will illustrate this. In the Persian system, the mean motion of a planet in 1,000 years is an integer number of degrees. Hence, the mean motion in 3,000 years is a multiple of 3?. For Saturn, Jupiter, Mars and the moon, it is even a multiple of 6?. Now suppose an astronomer, who made observations in the year - 101, i.e. 3,000 years after the great conjunction of - 3101, wants to fix the number of revolutions in such a way that the positions of the planets agree with his observation. He has to round off the observed mean places to multiples of 3? or even 6?. If he observes in the year 499, he has to make his mean longitudes multiples of 36? or 72?. This means he cannot attain any great accuracy. On the other hand, in the system of Aryabhata, the mean positions in 499, March 21st at noon had to be multiples of 12? only. This advantage was a consequence of his using a larger period. 24 See van der Waerden, B. L., Centaurus 4, p. 221, and 5, p. 177. World-Year 323 of the Persians If the "Persians" had modified Aryabhata's system by reducing his period, they had to sacrifice this advantage and to make the system less flexible and less accurate. This is improbable. It is more probable that Aryabhata, who was an excellent theorist and who had rather accurate observations at his disposal, modified the Persian system, making it more flexible. According to Ibn Yunis 25 the Persians observed the solar apogee about 450 A.D. Aryabhata lived 50 years later. Hence, Persian astronomy existed before Aryabhata and may have influenced him. In classical Greek and Hellenistic literature, the doctrine of the "Great Year" was already connected with the myths of the Deluge and Ekpyrosis.26 These catastrophes were supposed to return periodically when the planets came together in certain signs of the zodiac. In the Persian system, we still find the Deluge connected with a conjunction of the planets. Aryabhata does not mention the Deluge; he only alludes to the "battle of Bharata" on Thursday, February 17, - 3101. The idea of a Deluge in the middle of a cycle of 360,000 years cannot be derived from India; it must have come to Persia from the West. 8. THE EPOCH OF THE PERSIAN SYSTEM We shall now investigate, at what time of the day the Great Conjunction of the year - 3101 was supposed to take place in the Persian system. In Aryabhata's first system this conjunction was at midnight between Thursday and Friday, February 18. Both systems of Aryabhata yield excellent values for the moments of New Moon in the 5th and 6th centuries. The differences between the mean longitudes of the moon and the sun agree with modern calculation within a tenth of a degree. For the Persian system, the agreement may be less good, but still the moments of Full Moon must be expected to come out without large systematic errors. Lunar eclipses are easily observable phenomena. In Aryabhata's first system, 3,600 years contain 6,5,15,31;30 days. In the Persian system they contain 6,5,15,32;24 days, i.e. nearly one day more. The number of revolutions of the moon is 25 The statement occurs in the Leiden fragment of his Hakimi Zij, Leiden Cod. Or. 143, p. 124. See also Taqizadeh, S. H., Gdh shumdri dar Irdn-i qadim, Tehran, 1316 (Hijri-i shamsi), p. 322. 26 See van der Waerden, B. L., Hermes, 80, p. 129.

of the Persians the same, hence, the mean longitudes of the sun and the moon at the end of 3,600 years after the conjunction of - 3101 are exactly the same in both systems. If the date of this conjunction were the same, the moments of New Moon and Full Moon would come out nearly one day too late in the Persian system, which is impossible. Hence, the conjunction of - 3101 must be shifted to the early morning of Thursday February 17, say between two and three hours Western India time, i. e. near midnight Babylon time. According to Biruni, Babylon was the base location of the Persian Zij-i Shah. Biruni also informs us that, in contrast to most zijes, the Zlj-i Shah reckons the nychthemeron from midnight to midnight.27 This agrees well with our conclusion that the Persians assume the conjunction of - 3101 at midnight in the night from February 16 to 17. Mashallah" (more properly md shd'allh). Both names, in Persian and Arabic, respectively, mean "what God desired." The question now arises, what was the relation between the Persians of our text, who used the cycle of 360,000 years, and the Persians of Birfni, who composed the Zik-i Shatro-ayar. From the common designation "the Persians" we may tentatively conclude that in both cases approximately the same group of people was meant, and that they lived in Sasanian Persia. This is fully confirmed by a closer examination of the evidence. First, both groups were very much interested in planetary conjunctions. Abf Ma'shar, in his book of conjunctions, deals at length with the calculation of Saturn-Jupiter conjunctions and their astrological significance.28 Ibn Hibinta 29 copying from a lost book on conjunctions by Mashallah, gives the time between two successive conjunctions as 19y 10m1ld, and the gain in the zodiac as 9. PERSIAN TABLES The latter figure is in agreement with 242;25?. Islamic astronomy starts with two translations, Abfi Ma'shar's calculation and with the Persian one from Sanskrit and one from Pahlavi, viz: Ibn Hibinta system, as we have seen already. an Indian a of translation the with the connected Sindhind, (i) important events conjunctions Siddhanta, most probably the Brahma-sphuta-sid- such as the Deluge, the birth of Christ, the religion of Islam, etc. Just so, our sources A and B condhanta of Brahmagupta, (ii) The Z-j-i Shah, a set of tables translated nect the Deluge and the religion with conjunctions. The conjunction of all planets in - 3101, which from the Persian Zkl-i Shatro-ayar. forms the basis of the Persian System, is a A z-j is a set of tables for calculating solar, in the sense of the astrolunar and planetary positions, eclipses etc. In "mighty conjunction" Birini's Rasa'il (Hyderabad-Deccan, 1948) zijes logical theory. we see that there are many points of conbased upon the Sindhind are called Sindhind zijes, tactThus, between the "Persian system" and Birfini's and zijes related to the Zij-i Shah are called Per- "Persians." Still, the Persian system is not sian zijes. Among the Persian zljes Biruni in- identical with the of the Zij-i Shah. There cludes those of Ya'qub ibn Tariq, al-Khwarizml, are differences in system the numbers of revolutions and Abu Ma'shar and the Shah. He repeatedly states the duration of the year. that Abfi Ma'shar depends on "the Persians." In The year of the Zij-i Shah has, according to the Rasa'il (iii) 89;10 he states that Ibn al-Farrukhan Escorial manuscript of the Tabulae Probatae,30 and AIashallah are intermediate between Abfi Ma'shar and the Persians. Since Ibn al-Farrukhan lived about 780, we must conclude that "the Persians" lived before 780 A.D. This is also clear from the fact that the Zlj-i Shah was translated about 790. The Jewish astrologer called Mashallah (Messehalla in the West) was closely connected with the Persian tradition. He, like Abf Ma'shar, came from Balkh, the city associated with Zoroaster. In a British Museum manuscript (Add. 23400, f. 2a) he is referred to as "Yazdankhwast, known as 27 Kennedy, E. S., JAOS 78 (1958), p. 260. 365;15,32,30 days. The same value is mentioned by HSshimi,31 who says it was used by the Persians and Mashallah. Blruni (Chron. Transl., p. 121) also confirms that 28 Kennedy, E. S., JAOS, 78, p. 259. The only extant fragment of this work is Munich MS Cod. Arab. 852. o3Kennedy, E. S., Trans. Amer. Philos. Soc., 45 (1956), no. 51, p. 132 and 147. On the Escorial codex Arabe 927 see also J. Vernet, "Las Tabulae probatae," Homenaje a Millas Vallicrosa, II, p. 501 (Consejo sup. de invest. cient., Barcelona, 1956). s Kitab 'ilal al-zijat, Bodl. MS Seld. All.1

World-Year of the Persians However, in the 325 Two stages of Persian astronomy are also mentioned by Ibn Yfunis. In the passage quoted under footnote no. 25, Ibn Yunis states that the Persians 365;15,32,24 days, observed the solar apogee at 77? 55' about 450 A.D. and again at 80? about 610 A.D. Now, the sun's and the same value is used by Abu Ma'shar. The fragment of Ibn Hibinta's astrology con- agogee cannot be "'observed" in the strict sense. tains a run of horoscopes calculated by Mashallah, Ibn Yunis knew this; he was a competent astronusing the Zij-i Shah, for years in which conjunc- omer, who collected many ancient observations and tions of Saturn and Jupiter took place.32 The made observations himself. So he must have mean motions of the planets and the duration of meant that the Persians determined the solar the year can be calculated from these horoscopes apogee about 450 and again about 610, both times on the assumption that the mean longitudes at the from observations. Possibly Ibn Yunis had this epoch - 3101 were zero. The calculation, made by information from the introduction of the Zlj-i J. J. Burckhardt and B. L. van der Waerden, con- Shah. In fact, the Zlj-i Shah located the solar firmed this assumption and yielded the following apogee at 80?, as we know from BIruni. In Aryabhata's midnight system, the solar numbers of revolutions of Saturn and Jupiter in was also located at 80?. Moreover, Birfni apogee 360,000 years: informs us that the maximum equations of the sun Saturn 12,214and the moon in the Zij-i Shah have passed from Jupiter 30,352. India to the Persians.33 These facts and testimonies suggest that the Zij-i Shah in its latest The numbers are just the same as in the Aryawhich was translated into Arabic about 790, form, bhatiya. The number for Saturn is definitely not the same as in the Persian system, for in the Per- may have been influenced by Aryabhata in some details such as the solar apogee and the number of sian system it must be an integer. revolutions of Saturn. Hence we may distinguish two stages of Persian The testimony of Ibn Yunis seems to indicate one "Persian the astronomy, represented by system " of our text, and the other by the Zij-i Shah. the existence of an earlier redaction, composed The following table shows the differences between about 450 or a little later, in which the solar apogee was placed at 77? 55'. the two systems: The existence of an earlier redaction of the Number of Zlk-i Shatro-ayar is also implied by a statement of Revolutions Saturn Year Jupiter Blruini in the Masudic Canon 34 to the effect that Persian System Khosro AnushIrvan (531-578) convoked an assem365; 15,32,24 12,214 30,352 12,214-i 30,352 365;15,32,30 Zij-i Shah bly of astronomers for the purpose of correcting 30,352 12,214-i 365;15,31,15 Aryabhatiya the Zlk. Possibly this information was also drawn from the introduction of the Zi,j-i Shah. The difference between the two Persian years is We now combine the results of Section 7 with very small. Aryabhata differs from the Shah by those of the present section. In Section 7 we 0;0,1,15 days, which means that 3,600 years of adduced reasons for supposing that the "Persian Aryabhata differ from the Shah by 0,0,1 ;15 days, system," with its cycle of 360,000 years, existed which means that 3,600 years of Aryabhata contain before 500 A.D. We also know that the already one and a quarter day less than 3,600 years of the Zlj-i Shah differed from the Persian system in the Shah. number of revolutions of Saturn and the duration The difference of - revolution of Saturn or 120 of the year, but that the differences are only small, degrees in 360,000 years means a shift of 1.2 de- and that both systems were based upon the assumpgrees in the position of Saturn at the time of tion of a conjunction of all in - 3101. planets Aryabhata, and a better agreement between theory In the present section we found that an earlier and observation. It is possible that the Zlij-i Shah redaction of the Zij-i Shah, in which the solar was influenced by Aryabhata and that this influwas placed at 77? 55' probably existed beapogee ence explains why the Zij-i Shah deviated from the original Persian system. on Transits (Rasa'il III) " 24:9, Amer. 33,"Al-Biruini it was used by the Persians. Persian system, the year has 2 Kennedy, E. S., JAOS, 78 (1958), pp. 259 and 262. Univ. of Beirut Oriental Series, 32 (1959). 34AI Qiann al-Mas'udi, p. 1423.

fore 500 A.D. and that the final redaction used a slightly different apogee. The sources used in the present section, viz. Ibn Yunis and al-Birufni, are quite different from the sources used in Section 7, viz. our A,B, and Aryabhata. Still, the results agree extremely well. All available evidence seems to support the conclusion that the latest Zik-i Shatro-aydr was preceded by an earlier redaction, composed about 450 and based upon the Persian system. 10. THE TABLES OF KHWARIZMI Of the "Persian" zljes mentioned by Islamic astronomers, only one is extant, viz the zij of Khwarizmi in the redaction of Maslama al-Majrlti, translated into Latin by Adelard of Bath.35 Maslama's main contribution to this zlj seems to have been, according to Sa'id al-Andalusi, the use of the Hijra calendar. The original zlj of Khwarizmi used the Yazdigerd calendar. Khwarizmi's zij is sometimes classified as a Persian zij, sometimes a Sindhind zij. Both classifications are justified, for Ibn al-Qifti, informs us that Khwarizmi "based his tables upon the mean positions of the Sindhind, but deviated from it in the equations and the inclination (of the ecliptic). He fixed his equations according to the methods of the Persians, and the declination of the sun according to Ptolemy." In fact, KhwarizmI's mean motions are just those of the Brahma-sphutasiddhanta,36 and his table of solar declination is just Ptolemy's. The maximum equations of the planets in Khwarizml's tables are nearly equal to those of the ZIj-i Shah, as the following Table 1 shows. For comparison, we have also given the maximum equations of the Khandakhadyaka. TABLE 1. Planetary equations Moon Sat. Jup. Mars Venus Mere. 2;14 4;56 9;37 5;6 11;12 2;13 4;0 2;14 4;56 9;36 5;6 11;13 2;14 4;2 2;14 4;56 9;34 5;6 11;10 2;14 4;28 Sun Shah Khwar. Khand. For the sun and the moon, the three treatises agree: In fact, we know from Biruni that these numbers "passed from India to the Persians." 85 See note 14 and the "Survey" of E. S. Kennedy, Trans. Amer. Philos. Soc., 46 (1956), notably p. 128 (no. 21) and 148 (? 6), also Sa'id al-Andalusi, Kitab Tabakat al-Umam, transl. by R. Blachere (Paris, 1935), pp. 102 and 130. 86 See note 18. The World-Year of the Persians For Jupiter too we find perfect agreement, and for Venus the difference is only 1'. In the other three cases, we see that Khwarizmi follows the Zij-i Shah, with deviations of only 1 or 2 minutes. The maximum values of the "equation with respect to the sun" or "Sighra equation," are displayed in Table 2: Shah Khwar. Khand. TABLE2. Second correction Sat. Jup. Mars Venus Mere. 5;44 5;44 6;20 10;52 10;52 11;30 40;30 40;31 40;30 47;11 47;11 46;15 1 21;30 21;30 21;30 Here too, Khwarizmi follows the Shah and not the Khand., except in the case of Mars. In the calculation of the true places of the planets, Khwarizmi follows the "method of the Persians" as Ibn al Qifti informs us. We may assume that this method was taught in the Zij-i Shah. For a detailed account of the method and its relation to Greek and Indian methods see B. L. van der Waerden, Archive for Hist. of Exact Sci., 1, p. 107 (1961). Still more important is the general form of Khwarizml's zlj. The central part of this zij is a table of mean motions in years, months, days and hours. Every Greek "Kanon" such as the "Handy Tables " of Ptolemy, and every Arabic zij contains such a table of mean motions. In India no such tables are known. The Hindu treatises known to the Muslims and to us are either Siddhdntas or theoretical treatises without tables, or Karana treatises such as the Khandakhadyaka, containing instructions for practical calculations. Neither kind contains tables of mean motions. Hence, the Muslims could get the idea of such a table only from the Greeks or Persians, not from India. Now the earliest Arabic set of tables showing clear signs of direct Greek influence is the set called Tabula Probata (see footnote 30), written by Yahya about 810. The zijes 2, 71, 30, and 100 of Kennedy's Survey (see footnote 35), based upon Indian and Persian methods, are about half a century older. Of these, the first two (2 and 71) are closely related to the zij of Khwarizmi. They must have contained tables of mean motions. Hence, it seems that the Muslims got the idea of such a table set starting with mean motions not from the Greeks, but from the Persians. This is confirmed by the fact that the most usual word for such a table set, the word zij, is derived from Pahlavi zck.

KENNEDY Our conclusion is that the Persian original of the Zij-i Shah contained a table of mean motions, followed by tables for computing corrections to obtain the true places of the planets according to the "Method of the Persians." This gives us a pretty clear idea of the general form of the tables. The The World-Year 327 of the Persians earlier redactions of the tables may have differed in the constants of the mean motions and in the maximum equations, but the general form of the tables must have been the same. Ultimately, the Persians must have got the idea of a Kanon from the Greeks. RAMAYANA STUDIES I THE KRAUNCA-VADHA EPISODE IN THE VALMIKI RAMAYANA CH. VAUDEVILLE PARIS THE KRAUNCA-VADHA EPISODE, narrated in sarga 2 of the Balakianda of the Valmiki Ramayana, is connected with the birth of the first sloka, uttered by sage Valmlki when he was afflicted by grief, sokca, on hearing the piteable cries of a female krauncZ-bird, deprived from her mate.' Just as sargas 1 and 3 in the Balakanda of the vulgate Ramayana purport to "explain" why and how the Ramayan.acame into existence, and which were the circumstances which induced Valmlki to begin his great tale, so the Kraufica-vadhaepisode, in sarga 2, is supposed to account for the birth of the slokca,the principal metre used in the Ramayana. This pretty tale appears at first sight as a kind of fancy, a flight of imagination due to one of the later rhapsodists who composed the Balakanda. Scholars and translators in general did not attach much importance to the episode, and contented themselves with a passing remark on the 1The episode is famous in Indian tradition, and is referred to in Asvaghosa's Buddhacarita, Kalidasa's Raghuvamsa and in the works of the Kashmirian poeticians, but the latter seem to have understood that it was the female bird which had been killed by the Nisada, and the male bird which was lamenting its loss. (On the interpretation of this divergence, see G. H. Bhatt, "The Krauficavadha in Dhvanyaloka and Kavyamimamsa," JOI vol. IX (1959), p. 148 f., and Ch. Vaudeville, "A further note on Krauficavadha in Dhvanyaloka and Kavyamimamsa," JOI vol. XI (1961), p. 122 f.). The story was also famous outside India, as it is alluded to in a 7th century inscription found in a Valmiki temple in Cambodia, cf. C. Bulcke, Rama-katha, Prayag, 1950, p. 240, who refers to BEFEO, vol. 28, p. 147 and JOI vol. VI, p. 117. Our references to the Valmiki text of the Balakanda are to the Baroda edition of the Valmiki Ramayana (Oriental Institute, Baroda, 1958). invraisemblance and fanciful character of the derivation sloka < sotcawhich seems to be hinted at in the episode, while crediting Valmiki with having given its final form to the epic slokca,or having been the first to write an epic entirely in sloka.2 A closer examination of the Kraufica-vadha episode, however, suggests that the passage is not so meaningless as it appears and that it does not concern the origin of the epic sloca metre as such. It rather refers to an ancient tale or popular belief concerning the origin of lyrical poetry, which has a bearing on the origins of the Valmiki Ramayana itself. PLACE OF THE KRAUNCA-VADHA VAL. R. I. 2. EPISODE IN The Ramayana scholars, Holzmann, H. Jacobi, followed by C. Bulcke, have convincingly shown 2 P. V. Kane, in History of Sanskrit Poetics, 1951, p. 320, note 1, is very affirmative: "Thus the Balakanda states the origin of the classical Sanskrit sloka and also contfins the germs of the rasa theory." H. Jacobi, in Das Rimayana, Bonn, 1893 [English translation of the same by S. N. Ghosal, Baroda, 1960; our references are to the latter] says: " If this legend is based on any fact, the same appears to be that the epic sloka in its regular form first emerges in the poem of Valmiki." (Jacobi, o. c., p. 62). Jacobi's view seems to have been accepted by Winternitz (A History of Indian Literature, I, p. 480). Hopkins, in The Great Epic of India, p. 65, rejects the idea that Valmiki is the "inventor" of the sloka: "We must let pass the statement of the Ramayana itself that Valmiki invented the sloka verse, though Valmiki may have been the first to set out to write an epic in Slokas . . ." Also, in note 2 to the same page: "That Valmiki could not have "invented the sloka" is shown by the presence of an earlier form of sloka in the Brahmanic literature retained in the Mahabharata."