DECADES. AFRICAN SYSTEMS. 16l< 168 PRIMITIVE TIME RECKONING. names Thus arises the division of the month into three decades, in which however the last decade may vary between 9 and 10 days. The division into decades is not so common as the halving of the month. I'he Zuni of Arizona divide the month into three decades, each of which is called a 'ten'2. I'he Ahanta of the western Gold Coast divide the moon-month into three periods, two of ten days each, the third which lasts until the new moon appears — of about 9 */» days more correctly, no doubt, varying between 9 and 10 days.) The Sofa, lese of East Africa must have done the same, since de Earia says that they divided the month into 3 decades and that the first day of the first decade was the feast of the new moon 3, I'he Masai, who number either the days of the whole month consecutively or the days of its two halves, nevertheless give special prominence to the initial days of the decades (alongside of other notable days), and’call them ncgcra*. Among the Greeks the division into decades displaced the older bisection. Of the names of the decades the first and third refer to the concrete form of the moon: /' zoranrros, older d/go/o rog \ literally 'the appearing, waxing moon', and 111/1’ (f Dirol', 'the waning moon'. Eor originally fu'/v must here have had the sense of 'moon’ which the etymology suggests. I'he second decade was called ui/v ia 6c'>v. 'the month at the middle’: the epithet shews that m'/v here means 'month', and not moon’. This name is therefore younger than the two others, which must once have been used to describe the two halves of the month, and do so still in Homer'’. I'he custom of reckoning on the fingers or on a notched stick has doubtless lent assistance to the counting of the days of the month. The W'a-Sania make a notch in a stick for every day, and when the month is ended they put this stick aside and begin a new one 7. At the southern corner of Lake Xyassa the days are counted by means of pieces of wood threaded on a string h. A complete enumeration of the days however 1 Below, pp. 188 and 206 f. 2 Stevenson, p. 10S. 3 Ellis, Yoruba, p. 144. 4 Merker, pp. 154 ff. 5 Hesiod, Op., v. 773. " See my remarks in .bch. /. Religiouswiss-, 14, p. 432. 7 Barrett, p. 35. * Stannus, p. 288. only exists among highly developed peoples who have discarded a more concrete time-reckoning in favour of an abstract system, just as the civilised peoples of modern Europe aban doned the Roman system of time-reckoning, which was still often used in the Middle Ages (though indeed it had long since departed from its concrete basis', in favour of a simple enumeration of the days of the month. Finally a couple of curious East African reckonings of the da vs of the month are to be mentioned, although they arc not primitive but have a lengthy development behind them. A common feature of both is that the day of the new moon is already the fourth day, so that the counting of the days begins with the moon's invisibility, which can hardly have been the original practice. The Wadschagga divide the month into four parts the days of which are numbered, the first and third parts consisting of ten days each, and the second and fourth of live days each. Accordingly they begin to count the new moon at 'the fourth day, which brings the moon', the day on which the slender delicate crescent of the moon first reappears after sunset: tor the rites of this day see above, p. 153. On the fourth day of the second division (the eleventh after new moon they say that ’the moon turns to the back of the house’: when twilight falls it is already seen beyond the culmination-point. The fourth day of the third division the 16th after new moon) is called 'the day that brings the moon up from below' i. e. from the eastern hori zon), where 'it appears like a pot’; the fourth day of the last division is called 'the four, which dismisses the moon’, and the first of the first division, when the moon vanishes, 'the one, which floats away the moon so that it is no longer visible’: it 'tramples into pieces the days of the God’ ’. 'I'he natural phases of the moon therefore make themselves felt in spite of the counting. With this, as is so often the case, is connected a fully developed superstition concerning the days of the month. The Masai in ordinary life reckon their moon-months as consisting of 30 days, and number the days from 1 to 30 or 1 (•iutinann, pp. 238 (f. SUMERIAN MONTHS. CHAPTER VIII. OLI) SEMITIC MONTHS. 1. BABYLONIA. In the much disputed questions of the ancient Babylonian astronomy and calendar the non expert is in a situation of despair: for whoever cannot himself make use of the sources is referred to the often directly contradictory statements of the experts. I cannot however shirk the task of investigating whether in Babylonian calendric systems traces of the primitive time-reckoning are not also to be found. Unfortunately I cannot limit myself to matters upon which a certain unity of opinion prevails, but must also touch upon burning questions, such as the intercalation. What is here offered is in the nature of things only an attempt: but I may perhaps be allowed to express the hope that competent specialists, not led astray by chronological hypotheses, may afterwards observe how far the few but obvious characteristics of the primitive time-reckoning recur also in the Babylonian system. I he multiplicity and variability of the names of the months are found once more in ancient Sumer. In so comparatively late a period as the kingdom of Ur (in the middle of the second half oi the third millenium B. C.) each minor state had its own list of months, which I here reproduce, together with the suggested explanations, chiefly from the latest work of Lands-berger '. At this time there was in use in Nippur a list of months the terms of which later served as general ideograms for the months. 1 he names are: — 1, bar-3ag-gar(-ra), month 1 The explanations given by Muss-Arnolt are known to me only through Ginzel, I, 117 ff. 227 of habitation or inhabitants of the sanctuary; 2. gn,d)-si-sa, the name is derived by the Babylonians themselves from an agricultural occupation, the driving of the irrigating-machine drawn by oxen: the moderns connect this name with the gu(d)-si-su festival celebrated in this month at Nippur; 3, seg-ga, shortened from seg-u-sub-bci-gar-ra, 'month in which the brick is laid in the mould’; 4, su-kul-na, probably 'sowing-month', although the time does not fit: for displacements see below p. 261; bjie-nc-gar(-ra), named from a festival; 6, kin~dInanna, named from an Istar festival; 7, du(l)-azag(-ga), from a festival; 8, aphi-du a, 'month of the opening of the irrigation-pipes’, which tits very well with the time of year; 6, kan-kait-na, probably ’ploughing-month’, which also agrees very well with the season; 10, ab(-ba)-e(-a), from a festival; 11, as-a(-an), 'month of the spelt’; 12, se-kin-kud-(du), 'month of the corn-harvest’. There are therefore some names of the familiar kind, taken from agricultural occupations, but more are borrowed from festivals. It is very natural that the list of months should be regulated by ecclesiastical points of view, since Nippur was a great and very ancient centre of the religious cult. Most interesting are the months from Girsu (Lagash). From the pre-Sargonic period about 25 names of months have hitherto been found, of which only 8 or 9 persisted up to the second and third periods. These 25 names of months are divided by Landsberger into the following groups: — (b occasional names of months, under which he includes those which are consciously named after the object or employment mentioned in the document itself, or even improvised from the domestic occupation in question. Four names are given but are not translated. (2) isolated and foreign names of months: 'month in which the shining (or white) star sinks down from the culmination-point’, a type familiar to us; 'month in which the third people came from Uruk’, doubtless an accidental description. Further, two months named from festivals at Lagash. (3) agricultural by-names: Hit sc-kin-kitd-dit, see above; 7/w gur-dub-ba-a, 'month in which the granary is covered with grain’; further a name not explained, perhaps identical with the foregoing. (4) terms belonging to the religious cult. 228 PRIMITIVE TIME-RECKONING. Of these no fewer than 17 exist, not counting those already mentioned: they are nearly all named after festivals. Great pains have been taken to arrange the months in their position in . the calendar, and the superfluous names have been set down merely as doublets, since they have been judged by the lists of months current among ourselves. When we compare the terms with those of the primitive time-reckoning, it becomes clear that the naming of the months is here in the same fluctuating state as e. g. among the Melanesians. According to circumstances, an agricultural occupation, the rising of a star, a festival, etc. is seized upon in order to describe the month. Certainly the months can be chronologically arranged, but to draw up a fixed series from these 25 names is impossible, even if tendencies towards the formation of such a series already exist. The development tends in this direction in order to facilitate a general understanding, and in the second period, at the time of the kingdom of Akkad in the 28th to 26th centuries, a list of this nature occurs.1: — 1, itu ezcn gan-mas, perhaps 'month of the reckoning’, i. e. of the profits of the agriculture, or 'mois oil la campagne resplendit'; 2, itu ezen har-ra-ue-sar-sar, 'month in which the oxen work'; 3, itu ezen dingir ne-su, of uncertain meaning but connected with the cult; 4, itu sit-kul, see above; 5, itu ezen dim-ku, month of the feast in which the dim consecrated to the deity was eaten; 6, itu ezen ,ll"' not certain , is referred to the splendour of the blossoming season, though this falls earlier. But in May the dry season begins, and so one would think rather of the splendour of the sun. Yerash ha-etanim, corresponding to the seventh, about September, means month of the flowing, i. e. of the perennial streams, which now at the end of the dry season are the only ones that have water. Yerash bid, the eighth, cannot be referred to the gathering of the fruit bid , which has already taken place, but probably means the rainy month, since the autumn rains now begin 2. The descriptions are therefore of the kind already sufficiently familiar. But in the writings of the Old Testament the numbering of the months, beginning at the Feast of the Passover, is the common method of description, which is only replaced by the 1 I Kings, Chap. VI and VIII. 2 Dillman, p. 926, Konig, p. 612 ft., and elsewhere. VUy. v\ - MxnouckoTi THE CHRONOLOGY At 7 <■ OF * - ANCIENT NATIONS ■ AN ENGLISH VERSION OF THE ARABIC- TEXT OF THE ATHAR-UL-BAKIYA OF ALBIRCNI, w OR !J.| “VESTIGES OF THE PAST,” COLLECTED AND REDUCED TO WRITING BY THE AUTHOR IN A.H. 390-----1, A.D. 1000. * TRANSLATED AND EDITED, WITII NOTES AND INDEX, BY Db. C. EDWARD SACIIAU PROFESSOR IN THE ROYAL UNIVERSITY OF BERLIN. LONDON: PUBLISHED FOR THE ORIENTAL TRANSLATION FUND OF GREAT BRITAIN & IRELAND By WILLIAM H. ALLEN AND CO. 13 WATERLOO PLACE, PALL MALL. PUBLISHERS TO THE INDIA OFFICE. 1879. PREFACE. It was Sir Henry Rawlinson who first directed public attention to this work of Albirfini, in his celebrated article on Central Asia in the “ Quarterly Review ” for 1866, in which he gave some valuable information derived from his own manuscript copy, now the property of the British Museum. In offering the book, both in text and translation, to the learned world, I feel bound to premise that it is scarcely of a nature to attract the interest of the general reader. It appeals to minds trained in the schools of various sciences. Even competent scholars will find it no easy matter to follow our author through all the mazes of his elaborate scientific calculations. Containing, as it does, all the technical and historical details of the various systems for the computation of time, invented and used by the Persians, Sogdians, Chorasmians, Jews, Syrians, Harranians, and Arabs, together with Greek traditions, it offers an equal interest to all those who study the antiquity and history of the Zoroastrian and Jewish, Christian and Muhammadan religions.* The work of Albirfini has the character of a primary source. Oriental philologists are accustomed to see one book soon superseded by another, Barhebraeus by Ibn-al’athirfc Ibn-al’athir by Al-Tabari. Although it is likely enough * By Christians, I understand the Melkite and Nestorian Churches, whilst the author does not seem to have known much more of the Jacobites than the name. vi PREFACE. that on many subjects in this book we shall one day find better authenticated and more ancient information, I venture to say, that, as a whole, it will scarcely ever bo superseded. It is a standard work in Oriental literature, and has been recognised as such by the East itself, representing in its peculiar line the highest development of Oriental scholarship. Perhaps we shall one day find the literary sources themselves from which Albirfini derived his information, and shall be enabled to dispense with his extracts from them. But there are other chapters, e.g. those on the calendars of the ancient inhabitants of Central Asia, regarding which we shall, in all likelihood, never find any more ancient information, because the author had learned the subject from hearsay among a population which was then on the eve of dying out. As the first editor and translator of a book of this kind, I venture to claim the indulgence of the reader. Generations of scholars have toiled to carry the understanding of Herodotus to that point where it is now, and how much is wanting still! The work of generations will be required to do full justice to Albiruni. A classical philologist can edit a Greek text in a correct form, even though he may have no complete understanding of the subject-matter in all possible relations. Not so an Arabic philologist. The ambiguity of the Arabic writing—prolt dolor !—is the reason why a manuscript expresses only three-quarters of the author’s meaning, whilst the editor is compelled to supply the fourth quarter from his own knowledge and discernment. No number in any chronological table can be considered correct, as long as it is not proved by computation to be so, and even in the simplest historical narrative the editor and translator may most lamentably go astray in his interpretation, if there is something wrong with the method of his research. PREFACE. vii I have boldly attacked the sometimes rather enigmatic style of the author, and if I have missed the mark, if the bewildering variety and multiplicity of the subject-matter have prevented me reaching the very bottom of every question, I must do what more or less every Oriental author does at the end of his work,—humbly ask the gentle reader to pardon my error and to correct it. I. The Author. The full name of the author is Abu-Raihan Muhammad b. ’Ahmad Albiruni. He quotes himself as Abu-Raihan (ride p. 134, 1. 29), and so he is generally called in Eastern literature, more rarely Albiruni. The latter name means, literally, extraneous, being a derivative from the Persian which means the outside as a noun, and outside as a preposition. In our time the word is pronounced Birun (or Beeroon), e.g. in Teheran, but the vowel of the first syllable is a yai-majhul, which means that in more ancient times it was pronounced Berun (or Bayroon). This statement rests on the authority of the Persian lexicographers. That the name was pronounced in this way in Central Asia about the author’s time, we learn from an indisputable statement regarding our author from the pen of Alsam‘am, a philologist and biographer of high repute, who wrote only one hundred years after the author’s death (yide Introduction to my edition of the text, p. xviii.). Ho was a native of Khwarizm, or Chorasmia, the modern Khiva; to speak more accurately, a native either of a suburb (Benin) of the capital of the country, both of which bore the same name KhwArizm, or of the country-district (also called Benin} belonging to the capital. Albirftni was born a.h. 362, 3. Dhu-alhijja (a.d. 973, 4 albTrCnJ. The matter standing thus, it is our duty to proceed from what is near to the more distant, from what is known to that which is less known, to gather the traditions from those who have reported them, to correct them as much as possible, and to leave the rest as it is, in order to make our work help him, who seeks truth and loves wisdom, in making independent researches on other subjects, and guide him to find out that which was denied to us, whilst we were working at this subject, by the will of God, and with his help. In conformity with our plan, we must proceed to explain the nature of day and night, of their totality, i.e. the astronomical day, and assumed 10 beginning. For day and night are to the months, years, and eras, what one is for the numerals, of which they are composed, and into which they are resolved. By an accurate knowledge of day and night, the progress towards learning that which is composed of them and built upon them, becomes easy. 5 CHAPTER I. ON THE NATURE OF DAY AND NIGHT, OF THEIR TOTALITY AND OF THEIR BEGINNINGS. I say : Day and night (i.e. vv^Orjp.epov) are one revolution of the sun in the rotation of the universe, starting from and returning to a circle, which has been assumed as the beginning of this same Nychthemeron, whichsoever circle it may be, it being determined by general consent. This circle is a “ great ” circle ; for each great circle is dynamically an horizon. By “ dynamically ” (rp Swa/xet), I mean that it (this circle) 10 may be the horizon of any place on the earth. By the “ rotation of the universe," I mean the motion of the celestial sphere, and of all that is in it, which we observe going round on its two poles from east to west. The Setting of the Sun as the beginning of the Day.—Now, the Arabs assumed as the beginning of their Nychthemeron the point where the setting sun intersects the circle of the horizon. Therefore their Nychthemeron extends from the moment when the sun disappears from the horizon till his disappearance on the following day. They were induced to adopt this system by the fact that their months are based upon the course of the moon, derived from her various motions, and . 20 that the beginnings of the months were fixed, not by calculation, but by the appearance of the new moons. Now, full moon, the appearance of which is, with them, the beginning of the month, becomes visible towards sunset. Therefore their night preceded their day ; and, there-fore, it is their custom to let the nights j>recede the days, when they p. 6. mention them in connection with the names of the seven days of the week. J Those who herein agree with them plead for this system, saying that darkness in the order (of the creation) precedes light, and that light suddenly came forth when darkness existed already ; that, therefore, 30 that which was anterior in existence is the most suitable to be adopted 6 ALBtRflNi. as the beginning. And, therefore, they considered absence of motion as superior to motion, comparing rest and tranquillity with darkness, and because of the fact that motion is always produced by some want and necessity; that weariness follows upon the necessity; that, therefore, weariness is the consequence of motion. Lastly, because rest (the absence of motion), when remaining in the elements for a time, does not produce decay; whilst motion, when remaining in the elements and taking hold of them, produces corruption. As instances of this they adduce earthquakes, storms, waves, &c. The Rising of the Sun as the beginning of the Day.—As to the 10 other nations, the Greeks and Romans, and those who follow with them the like theory, they have agreed among themselves that the Nych-themeron should be reckoned from the moment when the sun rises above the eastern horizon till the same moment of the following day, as their months are derived by calculation, and do not depend upon the phases of the moon or any other star, and as the months begin with the beginning of the day. Therefore, with them, the day precedes the night; and, in favour of this view, they argue that light is an Ent, whilst darkness is a Non-ena. Those who think that light was anterior in existence to darkness consider motion as superior to rest (the absence 20 of motion), because motion is an Ena, not a Non-ena—is life, not death. They meet the arguments of their opponents with similar ones, saying, e.g. that heaven is something more excellent than the earth; that a working man and a young man are the healthiest; that running water does not, like standing water, become putrid. Noon or Midnight as the beginning of the Day.—The greater part and the most eminent of the learned men among astronomers reckon the Nychthemeron from the moment when the sun arrives on the plane of the meridian till the same moment of the following day. This is an intermediate view. Therefore their Nychthemera begin from the' 30 visible half of the plane of the meridian. Upon this system they have built their calculation in the astronomical tables (the Canons), and have thereby derived the places of the stars, along with their equal motions and their corrected places, in the almanacks (lit. year-books). Other astronomers prefer the invisible half of the plane of the meridian, and begin, therefore, their day at midnight, as e.g. the author of the Canon (Zij) of Shahriyaran Shah. This does not alter the case, as both methods are based upon the same principle. People were induced to prefer the meridian to the horizon by many circumstances. One was, that they had discovered that the Nych- 40 themera vary, and are not always of the same length; a variation which, during the eclipses, is clearly apparent even to the senses. The reason of this variation is the fact that the course of the sun in the ecliptic varies, it being accelerated one time and retarded another ; and that the single sections of the ecliptic cross the circles (the horizons) 7 ON THE NATURE OF DAY AND NIGHT. at a different rate of velocity. Therefore, in order to remove that variation which attaches to the Nychthemera, they wanted some kind of equation ; and the equation of the Nychthemera by means of the -rising of the ecliptic above the meridian is constant and regular everywhere on the earth, because this circle is one of the horizons of the p. 7. • globe which form a right angle (with the meridian) ; and because its conditions and qualities remain the same in every part of the earth. This quality they did not find in the horizontal circles, for they vary for each place; and every latitude has a particular horizon of its own, 10 different from that of any other place, and because the single sections of the ecliptic cross the horizons at a different rate of velocity. To use the horizons (for the equation of the Nychthemera) is a proceeding both imperfect and intricate. Another reason why they preferred the meridian to the horizon is this, that the distances between the meridians of different places correspond to the distances of their meridians on the equator and the parallel circles ; whilst the distances between the horizontal circles are the same with the addition of their northern and southern declination. An accurate description of everything connected with stars and their 20 places is not possible, except by means of that direction which depends upon the meridian. This direction is called “ longitude,” which has nothing in common with the other direction, which depends upon the horizon, and is called “ latitude.” Therefore they have chosen that circle which might serve as a regular and constant basis of their calculations, and have not used others ; although, if they had wished to use the horizons, it would have been possible, and would have led them to the same results as the meridian, but only after a long and roundabout process. And it is the greatest mistake possible purposely to deviate from the direct route in order to 30 go by a long roundabout. Day, Night, and the Duration of the Day of Fast—This is the general definition of the day which we give, the night being included. Now, if we proceed to divide and to distinguish, we have to state that the words “ Yaum ” (day) in its restricted signification, and “ Nahdr ” (day), mean the same, viz., the time from the rising of the body of the sun till its setting. On the other hand, night means the time from the setting of the body of the sun till its rising. Thus these two terms are used among all nations by general consent, nobody disputing their meanings, except one Muslim lawyer, who has defined the beginning of 40 the day to be the rise of dawn, and its end to be the setting of the sun, because he presumed that the day and the duration of fasting were identical. Foi* this view of his he argues from the following word of God (Sura ii. 183) : “ Eat and drink till you can distinguish a white thread from a black thread at the light of dawn. Thereupon fast the entire day till the night.” Now, he has maintained that these two terms 8 albIr^n!. (dpat KaifHKal), not of the Horce rectce, which are also called oequinoctiales 20 ( an<^ the inner circle, the formula The cycles which we have mentioned hitherto, are derived from the moon, though not exclusively. The solar cycle consists of 28 years, and serves to indicate on what days of the week the solar years commence. For if the Jewish year had simply 365 days without the quarter-day, the beginning of the year would in every seven years return to the 10 same week-day. Since, however, they are intercalated once in four years, the beginning does not return to the same day, except in 28 years, i.e. 4x7 years. Likewise the other cycles, heretofore mentioned, do not, on being completed, return to the same week-day, except the largest cycle, on account of its arising from a duplication of the cycle of 19 years with the solar cycle. The three kinds of the Jewish Year.—I say further: If the Jewish years had simply the first two qualities, i.e. were either common years or leap-years, it would be easy to learn their beginnings, and to distinguish between the two qualities which are proper to them, provided 20 the above-mentioned formula of computation for the years of the Mahzor be known. The Jewish year, however, is a threefold one. For they have made an arrangement among themselves, that New Year shall not fall on a Sunday, Wednesday, or Friday, i.e. on the days of the sun and his two stars (Mercury and Venus) ; and that Passover, by which the beginning of Nisan is regulated, shall not fall on the days of the inferior stars, i.e. on Monday, Wednesday, and Friday, for reasons on which we shall hereafter enlarge as much as possible. Thereby they were compelled either to postpone or to advance New Year and Passover, when they happened to fall on one of the days mentioned. 30 For this reason their year consists of the following three species :— I. The year called ^1-% i.e. the imperfect one (HIDH), in which the months Marheshwan and Kislew have only 29 days. II. The year called i.e. the intermediate lit. secun- dum ordineni suum, in which Marheshwan has 29 days, and Kislew 30 days. III. The year called i.e. the perfect one *n which both Marheshwan and Kislew have 30 days. Each of these three species of years may be either a common year or a leap-year. So we get a combination of six species of years, as we 40 have here illustrated in the form of a genealogical diagram, and distributed in the following representation. ON THE NATURE OF MONTHS. 67 The Year. p. 57. Common year of 12 months. Leap-year of 13 months. Perfect, of 355 days. Marheshwan, 30 days. Kislew, 30 days. Perfect, of 385 days. Marheshwan, 30 days. Kislew, 30 days. Intermediate, of 354 days. Marheshwan, 29 days. Kislew, 30 days. Intermediate, of 384 days. Marheshwan, 29 days. Kislew, 30 days. Imperfect, of 353 days. 10 Marheshwan, 29 days. Kislew, 29 days. Imperfect, of 383 days. Marheshwan, 29 days. Kislew, 29 days. For the deduction of these differences they have many modes of computation as well as tables, which we shall not fail to explain hereafter. Determination Of New Moon.—Regarding their knowledge of the beginning of the month, and the mode in which it is computed and used, the Jews are divided into two sects, one of which are the Rabbanites. They derive the beginning of the month by means of calculation from the mean motions of the two luminaries (sun and moon), no regard being had as to whether new moon is visible already or not. For it was their 20 object to have a conventional time, that was to begin from the conjunction of sun and moon. By the following accident they were, as they relate themselves, induced to adopt this system: at the time when they returned to Jerusalem, they posted guards upon the tops of the mountains to observe new moon, and they ordered them to light a fire and to make a smoke, which was to be a signal for them that new moon in fact had been seen. Now, on account of the enmity which existed between them and the Samaritans, these latter went and sent up the smoke from the mountain one day before new moon was seen. This practice they continued during several months, at the beginnings of 30 which heaven always happened to be clouded. Finally, people in Jerusalem found out this, observing that new moon, on the 3rd and 4th of the month, rose above the horizon from the east. Hence it was evident that the Samaritans had deceived them. Therefore they had recourse to the scholars of their time, in order to be protected by a system of calculation against the deceitful practices of their enemies, to which they were exposed by their present method. Tn order to prove that it was legally permitted to fix the beginning of the month by calculation instead of observation, they referred to the duration of the deluge. For they assert that Noah computed and fixed 40 the beginnings of the months by calculation, because heaven was covered p. 58. 5 * 68 ALBiR^Ni. and clouded for so long as six months, during which time neither new mpon nor any other phase of the moon could be observed. The mathematicians, therefore, computed tor them the cycles, and taught them how to find, by calculation, the conjunctions and the appearance of new moon, viz. that between new moon and the con-junction the time of 24 hours must elapse. And this conies near the truth. For if it was the corrected conjunction, not the mean one, the moon would in these hours move forward about 13 degrees, and her elongation from the sun would be about 12 degrees. This reform was brought about nearly 200 years after Alexander. 10 Before that time they used to observe the Tekn/oth »•<’• the year-quarters, on the computation of which we shall enlarge hereafter, and to compare them with the conjunction of that month, to which the Tekufa in question was to be referred. If they found that the conjunction preceded the Tekufa by about 30 days, they intercalated a month in this year, e.g. if they found that the conjunction of Tammuz preceded the Tekufa of Tammuz, i.e. the summer-solstice by about 30 days, they intercalated in that year a month Tammuz, so that it had one Tammuz and a second Tammuz (TTSTH VT3J3). In the same way they acted with the other Tektifoth. 20 Some Rabbanites, however, deny that such guards were posted, and that they made a smoke as a signal. According to their opinion, the cause of the deduction of this system of calculation was the following: the scholars and the priests of the Israelites, feeling convinced that their people would be scattered and dispersed in consequence of the last destruction of Jerusalem, as thev thought, were afraid that their compatriots, being scattered all over the world, and solelv relying upon the appearance of new moon, which of course in different countries would be different for them, might, on account of this, fall into diss -nsioiis, and a schism in their doctrine might take place. Therefore they invented 30 these calculations,—a work which was particularly att nded to by Eliezer ben Paruah, and ordered people to adhere to them, to use them, to return to them, wherever and under whatever circumstances they lived, so that a schism among them might be avoided. The second sect are the Mihtdileg, who derive the boginning of the month from the conjunction; they are also called Alkner'i and Al’ndi-ma'iyya, because they demand that people shall only follow the wording of the text, no regard being had to considerations and analogies, etc., even if it may be illogical and impracticable. One party of them is called the *. I ib'iiih x. who derived their name 10 from ‘Anan, the head of thetmigration "ho lived between 100 and 110 years ago. A head of the emigration must of necessity be one of the descendants of David; an offspring of another family would not be fit for this office. Their common people relate, that only he is qualified who, standing upright, can reach his knees with the tops of his ON THE NATURE OF MONTHS. 69 \ V fingers; just as people relate such things of the prince of the true believers, ‘Alt hen ’Abi Talib, and of those of his descendants who are qualified for the Iiuaina and the rule of the community (the Muhammadan world). The genealogy of this ‘Anan is the following:— th 'n py h h p py 1 NTJM TOH n ^2FID2 ’’bHDH '1 -V1 1T2 N3N 'n JFC 'n NMH h fTtSEtT 3*1 2 X1 trym* h wpin 'n wt 'n N'cntf 'n h XVI 10 NW' 'n py h 'n pnv h 'n XXI p. 59. tmra 'n 3 mpy h n’O’-d h h xxvi prj’nm h h 1 ms 'n 'n XXXI tnvr h h nw h irwirr '2 irp’nrr 'n xxxvl n oynm 'n fton 'n hon h toEtthrr h XLI TH n XLVI Tie opposed a connnunity of Rabbanites in many of their observances. He fixed the beginning of the month bv the appearance of the new moon in a similar way, as is prescribed in Islam, not caring on what day of the week the beginning of the month happened to fall. He gave up 20 the system of computation of the Rabbanites, and made the intercalation of a month depend upon tin* observation of barley-seed in ‘Irak and Syria between the 1st and the 14th Nisan. If he found a first-fruit fit A for triction and reaping; he left the year as a. common year; if he did \ ! not find that, he intercalated the year. Tin* mode of prognosticating the state of the corn was practically this, that one of his followers went out on the 23rd Shebat, to examine—in Syria ami the countries of a similar climate the state of the l.arley-st ed. If he found that the Safa, i.e. the prickles of the beard of the ear of corn, had already come out, he counted I rom that day till Passover 50 davs ; if he found that it had 3<> not yet come out, he int rcalated a month into tin* year. Ami some added the intercalary month to Shefat. so that there was a Shefat and an U-Shefat ; whilst others added it to Adhar, so that there was an Arthur and a II < -.1 ilhir. The Ananiles mostly use Shefat, not Adhar, whilst the Rabbanites use exclusively Adhar. This system of prognostieating (he stat of the corn is a different one according to the difference of the air and the climate of the countries. . Therefore it would be necessary to make a special rule for every place, and not to rely upon the rub1 made for one certain place, because this would not be applicable elsewhere. 40 Syrian Months. -The Christians in Syria, ‘Irak, and Khurasan have '•ombined Greek and Jewish months. For they use the months of the (.•reeks, I mt h.i ve adopt ■ the 1st <> t t he G reel, (let ober as t!;< • begin ni u g 72 ALBinCxt. Ndjir is derived from najr, which means “ intense heat,” as it is used in the following verse:— “ A stinking water, on account of which a man turns his face aside, Even he who is tortured by thirst, if he tasted it in a ‘ boiling hot ’ month.” Khawwan is the form of the verb “ to deceive," and Suwon is the form Jbd of the verb “ to preserve, to take care." And these significations agreed with the natures of the months at the time when they were first employed as names for them. Zabbd means a " great and frequently occurring calamity." The month 10 was called so, because in it there was much and frequent fighting. Bd'id, too, received its name from the fighting in it, for many people used to perish ” in it. This circumstance is expressed in the following proverb: "All that is portentous happens between Jumddd and Rajab." For in this month people were in great haste and eagerness to carry out whatever blood revenge or warlike expeditions they wen' upon, before the month Rajab came in. 'Asamm was called so, because in it people abstained from fighting, so that the clash of weapons was not heard. Wdghil means “ one who conies to a drinking-party without having been 20 invited." This month was called so, because it suddenly comes in after Ramadan, and because in Ramadan there was much wine-drinking, on account of the next following months being the months of pilgrimage. Natil means “ a measure, a pot of wine." The month was called so, because in it people indulged in drinking debauches, and frequently used that pot. *Adil is derived from “ \adl ” (which means either “ to be just ” or “ to turn aside”). The month was called so, because it was one of the months of pilgrimage, when they used to abstain from the use of the Na(il, i.e. the wine-pot. 80 Banna was called so, because the sheep were “ crying ” on account of the drawing near of the time when they were to be killed. Burak was called so, because of the kneeling down of the camels on being led to the slaughtering-place. A better versification of these names than tin* above-mentioned one is that by the Wazir ’IsnuVil ben ‘Abbad:— “ You wanted to know the months of the pagan Arabs. Take them according to the order of Muharram (Safar, etc.), of which they partake. p. 62. First comes Mu'taniir, then Ndjir; and Khawwan and Suwon are 40 connected by one tie. Hanin, Zabbd. 'Asamm, ‘Adil, Ndfik with Waghl, and Banna with Burak." ON THE NATURE OF MONTHS. 73 If the etymologies of these two classes of names of the months are such as wo have related, we must suppose that between the two periods of giving the names there was a great interval of time. Or else our explanations and etymologies would not be correct. For in one class of the months the highest pitch of the heat is Safar, whilst in the other it is Ramac.hin ; and this (that the greatest heat should be either in Safar or in Ramaclan) is not possible at one and the same period, or at two periods which are not very far distant from each other. Intercalation of the Ancient Arabs.—At the time of paganism Id the Arabs used their months in a similar way to the Muslims ; their pilgrimage went wandering around through the four seasons of the year. But then they desired to perform the pilgrimage at such time as their merchandise (hides, skins, fruit, etc.) was ready for the market, and to fix it according to an invariable rule, so that it should occur in the most agreeable and abundant season of the year. Therefore they learned the system of intercalation from the Jews of their neighbourhood, about 200 years before the Hijra. And they used intercalation in a similar way to the Jews, adding the difference between their year and the solar year, when it had summed up to one complete month, to the months of 20 their year. Then their intercalators themselves, the so-called Kaldmis of the tribe Kimina, rose, after pilgrimage had been finished, delivered a speech to the people at the fair, and intercalated the month, calling the next following month by the name of that month in which they were. The Arabs consented to this arrangement and adopted the decision of the Kalammas. This proceeding they called “ Nasi’,” i.e. postponement, because in every second or third year they postponed the beginning of the year for a month, as it was required by the progression of the year. One of their poets has said:— “ We have an intercalator, under whose banner we march ; 39 He declares the months profane or sacred,, as he likes.” The first intercalation applied to Muharram; in consequence Safar was called Muharram, Rabi' I. was called Safar, and so on; and in this way all the names of all the months were changed. The second intercalation applied to Safar; in consequence the next following month (Rabi I.) was call' d Safar. And this went on till intercalation had passed through all twelve months of the year and returned to Muharram. Then they commenced anew what they had done the first time. The Arabs counted the cycles of intercalation and fixed thereby their dates. They said for instance : “ From the time x till the time y the 40 years have turned round one cycle.” But now, if notwithstanding intercalation it became evident -that a month progressed beyond its proper place in the four seasons of the year, in consequence of the accumulation of the fractions of the solar year, and of the remainder of the plus-difference between the Solar year , 74 ALBfR^Nt. and the lunar year, to which latter they had added this plus-difference, they made a second intercalation. Such a progression they were able to recognize from the rising and setting of the Lunar Mansions. This went on till the time when the Prophet fled from Makka to Madina, when the turn of intercalation, as we have mentioned, had come to Sha* ban. p. 63. Now, this month was called Muharram, and Ramadan was called Safar. Then the Prophet waited till the “farewell pilgrimage," on which occasion he addressed the people, and said:-** The season, the time has gone round as it was on the day of God’s creating the heavens and the earth.” (Sura ix. 38.) By which he meant that the months had returned 10 to their original places, and that they had been freed from what the Arabs used to do with them. Therefore, the “farewell pilgrimage," was also called “ the correct pilgrimage." Thereupon intercalation wras prohibited and altogether neglected. Months of the Themudeni.—’Abu-Bakr Muhammad ben Duraid Al azdi relates in his Kitdb-alwishdh, that the people Thamud called the months by the following names :— I. Mujib i.e. Muharram. VII. Haubal. Mujir. . Mauha. Murid. Daimur. 20 Mulzim. I Dabir. Mu?dir. Haifal. Haubar. Musbil. He says that they commenced their year with the month Daimur, i.e. ■ Ramadan. The following is a versification of these names by ’Abft-Sahl ‘tsa ben Yahya Almasihi:— “The months of Thamud are Miljib, Mujir, Murid; then follow Mulzim and Mus dir. Then come Haubar and Haubal, followed by Mauha and Daimur. Then come Dabir, and Haifal, and Musbil, till it is finished, the most 80 celebrated among them.” Arabic Names Of Days.—The Arabs did not, like the Persians, give special names to the single davs of the month, but they had special names for each three nights of every month, which were derived from the state of the moon and her light during them. Beginning with the first of the month, they called— The first three nights (lst-3rd) ghurar, which is the plural of ghurra, and means the first of everything. According to others they were called so, because during them the new moon appeared like a blaze on the forehead of a horse. 40 The second three nights (4tii-6th) nufal, from tanaffala, which means, “beginning to make a present without any necessity." Others call them shuhb, i.e. the white nights. ”Sed neomenia Judaica, Arabica, & Samaritana exoedit mo-dum (pao-Eiosut plurimu. ita oiviles neomenie mensium Lunariu sint tripliois generis: Attioae airo ~qs s:Judaicae, Samaritanae, & Arabicae, ano vrjs %i^aro5, a tertia, inquam, die."— Soaliger, Joseph, "De Emendation© Temporum," p. 6. Translation: But the Jewish, Arabic, and Samaritan new moon commonly exceeds the size of the phasis [moon’s first appearance], so that the civil new moons of lunar months are a triple kind: the Attic, from the conjunction; the Calip-pic, from the waxing; the Jewish, Arabic, and Samaritan, from the shape of the moon from the third day, I say. [Roman months seem to copy Greek moons] The Ides correspond to the 15th of March, May, July and October, and to the 13th of the other months. Webster. "Nonnullis placet, Idus diotas vocabulo Graeco, a specie quae apud illosei^ea vooatur, quod ea die plenam speciem luna demonstret.”— Venerabilis Bedae, "Opera Quae Supersunt Omnia," Edited,G.A. Giles, Vol. VI, Londini, 1843, p. 176. Translation: Some hold that in the Greek language, Ides was called from "specie," which with them is called "g’i&q" because on that day the moon shows a full face. ’kiJeuo corresponds to Latin "video." "In the beginnings of the Church, both the Apostles ■ and those who followed after them for a hundred years, always celebrated the Jewish passover, as testifies Eusebius and his ancient ecclesiastical history, and after all, Nioephorus Callistus. But under Coinmodus, those who were observing the Jewish passover, were condemned of heresy by Victor, bishop of Rome, and by others whom he himself had called into the synod. But the difference in this celebration is twofold, in fact, either in the calculation of the moon or in the rite. In like manner, the difference is twofold in reference to the calculation of the moon. For either in the new moon, to the extent the new moons were triply employed by the ancients, as we have discussed in the Greek year; or in the embolism. For the new moons are reckoned either according to the conjunction, as of the ancient At-.". > tics; or according to the waxing, as the Calippics; or according to the shape of the moon, such as of the Jews, Arabs, ancient Chaldeans, and Damascenes. [’In the first it was quite dark; in the second it did open itself to receive the sun-beams; in the last it did appear, oornic-ulata, horned.1— Godwyn, Thomas, "Moses and Aaron," London, 1685, p. 122.] The embolisms differ as to the calculation of the beginning of the cycles, since indeed some begin their cycles one way, and some another, so that the first year of the Jewish cycle is fourth in that of our Tisri, and fifth in Nisan. In this manner the Paschal month of the Christians often runs in Adar of the Jews. But the rite of the "fourteenth day" was differing from the rite of the Europeans in time alone, because the Europeans decree that the passover of the resurrection must be celebrated on the Lord’s day, but the "fourteenth day" people were celebrating the passover of the crucifixion on the 14th of the moon. I earnestly desire to weigh diligently these differences. For in ignorance of them, they who condemned the quartadeci-mans have followed this, so that pot only do they themselves not know the day of the passion of the Lord, but they have even left it hidden to posterity in great shadows of ignorance. But what, or of what kind the cycle of the quartadeoimans was, even if I keep silent, they who read Eusebius and the ecclesiastical writers of history know. For it is not hidden that the cycle of those who imitated in every way the Apostles in this thing — and very many of them had crossed over from Judaism to Christianity — was pure Jewish and Chalda-ic, whose earliest Nisan in the times of Dionysius was March 24, in the first Dionysian cycle of the moon. But 75 b the latest, was April 20, by the twelfth Dionysian cycle. Would that those enemies of the quartadecimans had carefully taken note of this fact. • • Page 105. ’’Although we have touched somewhat in the foregoing c chapter concerning the ancient rite of the Passover by the Christians, yet this place demands that we speak more fully concerning this. All the ancient Christians were regulating the Passover according to the lunar year, using the canon only for it, and thereby thinking that they trod in the footsteps of Moses and the Jews. But there was a twofold difference. One is, that some sooner, others later, were intercalating the months. For the Asians, who were following the footsteps of John the Evangelist, and of others who were the equal of the Apostles, were using the pure Jewish year. But the Europeans were placing their cycle at the equinox, and were celebrating the Passover on the full moon next after the equinox. This was the difference in the months. Another difference was in the day: because indeed some were appointing the paschal festival on the Jewish 14th of Nisan, others, on the next Lord* s day after the 14th of the moon. • • p. 106. ’’But those ancients [early Church], when they used this cycle, were thinking that they celebrated the Passover in the Jewish Nisan, which was Adar in the years 2,4, 5, 7, 10, 12, 13, 15, 16, 18, as the Table [page 107] indicates, which now will first teach our men how much those ancients erred in ignorance of a thing of no little moment, since from which the computation of the times of the preaching of Christ and of His passion was pending. We certainly know this from no Christian man, but of those who have either published the Jewish year, or have written concerning the day of the Lord’s passion that thus far have perceived the position and place of the Jewish new moons and their embolisms.”— Soaliger, Joseph, ”De Emendations Temporum,” p. 107. ON THE NATURE OF MONTHS. 75 10 20 80 40 The third three nights (7th-9th) tusa*, because the ninth night is the last of them. Others call them buhr, because in them the darkness of the night is particularly thick. The fourth three nights (10th-12th) *ushar, because the tenth night is the first of them. The fifth three nights (13th-15th) bid, because they are white by the shining of the moon from the beginning of the night till the end. The sixth three nights (16th-18th) dura*, because they are black at the beginning like the sheep with a black head and a white body. p. 64. Originally the comparison was taken from a coat of mail in which people' are clad, because the colour of the head of him who is dressed in it, differs from the colour of the rest of his body. The seventh three nights (19th-21st) zulam, because in most cases they were dark. The eighth three nights (22nd-24th) handdis (from Amd?s=extremely dark). Others call them duhm, on account of their being dark. The ninth three nights (25th-27th) da'ddi', because they are remainders (or last parts). Others derive it from the mode of walking of the camels, viz., stretching forth the one foot, to which the other is quickly following. Th.e tenth three nights (28th-30th) mihdk, on account of the waning of the moon and the month. Besides, they distinguished certain nights of the month by special names, e.g. the last night of the month was called sirdr, because in it the moon hides herself; it was also called fahama on account of there being no light in it, and bard', because the sun has nothing to do with it. Likewise the last day of the month was called nahir, because it is in the nahr (throat) of the month. The 13th night is called sawa, the 14th the night of “ badr," because in it the moon is full, and her light complete. For of everything that has become complete you say badara; e.g. 10,000 dirhams are called one badra, because that is supposed to be the most complete and the last number, although it is not so in reality. The Arabs used in their months also the seven days of the week, the ancient names of which are the following:— 1. ’Awwal, i.e. Sunday. 2. ’Ahwan. 3. Jubar. 4. Dubiir. 5. Mu’nis. 6. ‘Aruba. 7. Shiyar. They are mentioned by one of their poets in the following verse:— I strongly hope that I shall remain alive, and that my day (of death) will be either 'Awwal, or 'Ahican, or Jubar, ON THE NATURE OF MONTHS. 77 But, when they tried to fix thereby the beginning and end of fasting, their calculation, in most cases, preceded the legitimate time by one day. Whereupon they set about eliciting curious things from the following word of t he Prophet: “ Fast, when she (new-moon) appears, and cease fasting when she re-appears.” For they asserted, that the words “ last, , when sho appears ” mean the fasting of that day, in the afternoon of which new-ihooii becomes visible, as people say, “ prepare yourselves to meet him ” in which case the act of preparing precedes that of meeting. 10 Besides, they assert that the month of Ramadan has never less than thirty days. However, astronomers and all those who consider the subject attentively, are well aware that the appearance of now-moon does not proceed regularly according to one and the same rule for several reasons: the motion of the moon varies, being sometimes slower, sometimes faster; she is sometimes near the earth, sometimes far distant; she ascends in north and south, and descends in them; and each single one of these occurrences may take place on every point of the ecliptic. And besides, some sections of the ecliptic sink faster, others slower. All this varies according to the different latitudes of the countries, and 20 according to the difference of the atmosphere. This refers either to different places where the air is either naturally clear or dark, being always mixed up with vapours, and mostly dusty, or it refers to different times, the air being dense at one time, and clear at another. Besides, the power of the sight of the observers varies, some being sharp-sighted, others dim-sighted. And all these circumstances, however different they are, are liable to various kinds of coincidences, which may happen at each beginning of the two months of Ramadan and Shawwal under innumerable forms and varieties. For these reasons the month Ramadan is sometimes incomplete, sometimes complete, and all this varies accord- 30 ing to the greater or less latitude of the countries, so that, e.g. in northern countries the month may be complete, whilst the same month is incomplete in southern countries, and vie<\ verso. Further, also, these differences in the various countries do not follow one and the same rule; on the contrary, one identical circumstance may happen to one month several consecutive times or with interruptions. But even supposing that the use which they make of those tables and calculations were correct, and their computation agreed with the appearance of new-moon, or preceded it by one day, which they have made a fundamental principle, they would require special computations for each 40 degree of longitude, because the variation in the appearance of new-moon does not depend alone upon the latitudes, but to a great extent p. 66. also upon the longitudes of the countries. For, jfrequcntly^new-moon is not seen in some place, whilst she is seen in another place not far to the jvestj and frequently she js seen in both places at once. This is one of the reasons for which it would be necessary to have special calculations 78 and tables for every single degree of longitude. Therefore, now, their theory is quite utopian, viz. that the month of Ramadan should always be complete, and that both its beginning and end should be identical in the whole inhabited world, as would follow from that table which they use. . • • Compare with this the following saying of the Prophet: "We are illiterate people, we do not write nor do we reckon the month thus and thus and thus,” each time showing his ten fingers, meaning a complete month or thirty days. Then he repeated his words, saying, "and thus and thus and thus," and at the third time he held back one thumb, meaning an incomplete month or twenty-nine days. By this generally known sentence, the Prophet ordained that the month should be one time complete, and incomplete another time, and that this is to be regulated by the appearance of the new moon, not by calculation, as he says, we do not write, nor do we reckon (calculate). 153 For the same reason, three months which are perfect according to the appearance of new moon, can follow each other, whilst of the imperfect months not more than two can follow each other. And their following each other is possible only in consequence of the variation of the motions of the two great luminaries (sun and moon), and of the variation of the setting of the zodiacal signs (i.e. the varying velocity with which the sun moves through the various signs of the Ecliptic). In what Period the beginning of the Jewish Year returns to the same Date.—If the conjunctions at the beginnings of two consecutive great cycles (of 532 years) coincided with each other (i.e. if they were cyclical in such a way as to begin always at the same time of the week), we should be able to compute the qualities of the Jewish years by means of tables, comprising the years of a great cycle, similar to the Chronicon of the Christians. However, the moleds of these cycles do not return to the same time of the week except in 689,472 years, for the following reason: The Character of the small cycle, i.e. the remainder which you get by dividing its number of days by 7, is 2d. 16h. 595H. This fraction is not raised to one whole, except in a number of cycles, which is equal to the number of Halakim of one Nychthemeron, i.e. 25,920. Because fractions are not raised to wholes, except when multiplied by a number which is equal to the complete number of the same kind of fractions of one whole (i.e. by the denominator). But as both the number of the Halakim of the Nychthemeron 76 albirOnJ. Or the following day, Dubdr, or if I get beyond that, either Mu'nis or i Aruba or iShiydr." Afterwards the Arabs gave them the following new names :— Al-’ahad, i.e. one. Al-ithnan, „ two. Al-thulatha, „ three. . Al-'arbi'a, „ four. Al-khamis „ five. Al-jum‘a, „ gathering. Al-sabt, „ sabbath. 10 The Arabs fixed the beginning of the month by the appearance of new moon, and the same has been established as a law in Islam, as the Lord has said (Sura ii. 185) : “ They will ask thee regarding the new moons. Speak: they are certain moments of time for the use of mankind (in general) and for pilgrimage.” Determination of the length of Ramadan, the Month of Fasting.—Some years ago, however, a pagan sect started into existence somehow or other. They considered how best to employ the interpretation (of the Koran), and to attach themselves to the system of the exoteric school of interpreters who, as they maintain, are the Jews and 20 Christians. For these latter have astronomical tables and calculations, by means of which they compute their months, and derive the knowledge of their fast days, whilst Muslims are compelled to observe new moon, and to inquire into the different phases of the light of the moon, and into that which is common to both her visible and invisible halves. But then they found that Jews and Christians have no certainty on this subject, that they differ, and that one of them blindly follows the other, although they had done their utmost in the study of the places of the moon, and in the researches regarding her motions (lit. expeditions) and stations. 80 Thereupon they had recourse to the astronomers, and composed their Canons and books, beginning them with dissertations on the elements of the knowledge of the Arabian months, adding various kinds of compu-p. 65. tations and chronological tables. Now, people, thinking that these calculations were based upon the observation of the new-moons, adopted some of them, attributed their authorships to Ja‘far Al-sadik. and believed that they were one of the mysteries of prophecy. However, these calculations are based not upon the apparent, but upon the mean, i.e. the corrected, motions of sun and moon, upon a lunar year of 354,’ days, and upon the supposition that six months of the year are complete, six 40 incomplete, and that each complete month is followed by an incomplete one. So we judge from the nature of their Canons, and from the books which are intended to establish the bases on which the Canons rest. 144 albIrCnL IV. They determine this space of time (between the conjunction and the appearance of new moon) by wpai Kaipucal. Whilst it is well known that it is not allowed to use them for the computation of conjunction, except on the equator. V. They compute the conjunctions by the mean, not the apparent motion. Therefore passover frequently falls two complete days later than the real opposition—one day in consequence of the Equations, another day in consequence of their postponing passover from a Dies illicita to a Dies licita. Computation of the Moled of a Year according to the Jewish 10 System.—If we, now, want to find the M'ded of a year, which term the Jews apply to the conjunction at the beginning of each month as well as the conjunction at the beginning of every cycle, we take the complete years of the 2Era Adami, i.e. till the end of the year which is preceded by the month Tishri in question. We convert the number of years into Minor Cycles, and multiply the number of cycles by 2d. 16h. 595H, which you get as a remainder if you convert the days of the minor cycle into weeks. The product which arises we keep in mind. Thereupon, we consider the remainder of years that do not fill up one 20 complete minor cycle. How many of them are common years, how many leap years, we learn by the Ordo intercalation's, nwo (i.e. the 2nd, 5th, 7th, 10th, 13th, 16th, and 18th years of the cycle are leap years). The number of common years we multiply by 4d. 8h. 876n, the number of leap years by 5d. 21h. 589 . The product of these two multiplications we add to the sum we have kept in mind. To the sum we al wavs add 5d. 14h., 30 which represents the interval between the time of the conjunction and the beginning of the night of Sunday that was the commencement of the first year of the sEra Adami. Then we raise each 1,080 Halaks to 1 hour, and add it to the other hours ; each 24 hours we convert into 1 day, and add it to the other days. The sum of days that arises we convert into weeks, and the remainder of days that are less than a week is the distance of the from the beginning of the night of Sunday. Now, that time to which in the last instance our calculation leads us, is the time of the conjunc-p.147. tion at the beginning of Tishri. ’40 We have made such a computation for a year of the sEra Alexandra, in order to facilitate the process and to simplify the apparatus. If you want to find the conjunction at the beginning of Tishri, take the years of the JEra Alcxandri, and subtract therefrom always 12 years, which are the remainder of the minor cycle at the epoch of the Aira CYCLES, YEAR-POINTS, MOL^DS, AND LEAP-MONTHS. 145 Alexandri, according to the Ordo intercalationis 33,123.^. The remainder of years divide by 19 ; the quotient you get is the number of minor cycles. Convert these minor cycles into great cycles, if they are of a sufficient number to give complete great cycles, and keep in mind what remainder of years you have got. They are the current years of the cycle in question, according to the Ordo intercalationis The great cycles, if you get such, compare with the table of the great cycles, and take the number of days, hours, and Halakim which you find 10 opposite them. The small cycles compare with the table of the small cycles, and the number of days, hours, and Halakim which you find opposite them. These' two numbers add together, days to days, hours to hours, and Halakim to Halakim. ' This sum add to the Basis, which is written in the table uppermost, and which is the Moled of the 12th year of the xEra Alexandri. Convert each 1,080 Halakim into an hour, each 24 hours into a day, and the days into weeks. The remainder of days you get is the distance between the beginning of the night of Sunday and the time of the conjunction. 20 This is according to Jewish calculation. We have used as the starting-point in this our calculation the beginning of the night for no other reason but this, that they commence the Nychthemeron with sunset, as we have mentioned in the first part of this book. Here follows the fable, computed by that method of calculation which we have explained in the preceding pages:— p.148. The Numbers of the Small Cycles. The Years of the Small Cycles. Days. Hours. I Halakim. I r i 30 1 19 2 16 595 2 38 o 9 110 3 57 1 1 705 4 76 3 18 220 5 95 6 10 815 6 114 2 3 330 7 133 4 19 925 8 152 0 12 440 9 171 3 4 1,035 10 190 5 21 550 40 11 209 1 14 65 12 228 4 6 660 13 247 6 23 175 14 266 2 15 770 15 285 8 285 10 154 (25,920) and the number of the remainder of the Hala kirn of the cycles (595) may be divided by 5, the fractions will be raised to wholes if multiplied by a number of cycles, which is equal to 1/5 of the Halakim of the Nychthemeron, i.e. 5184. Now, the conjunction (at the beginning of the year) does not return to the same time of the week except in a number of cycles which is the sevenfold of this number (5184), i.e. 36,288. And this is the number of cycles which represent the above-mentioned number of years (viz. 689,472). In general, conjunction and opposition return to the same place (i.e. happen again at the same time of the week) in each 181,440 months, which is the product of the multiplication of the number of Halakim of one Nychthemeron (25,920) by 7. 159 Likewise there is a difference between Jews and Christians regarding the leap year, as we shall explain in the chapter on the Christian Fast, if God permits. If, now, there is a difference between them, and they are willing to accept our decision, we shall consider the two oppositions pf their two passovers. and shall say, that that opposition at which the moon moves in the middle part of Spica oroF’Cancer'* or^TReT sun is about to leave Aries, is to be' rejected according to both systems, whilst the contrary^is to be adopted. To the lover of truth, the correctness of these two assertions will be apparent, if the conditions we have mentioned are observed. 1 = Uhuqo’s “'-ccn Adhar II This is the original Adhar, which is called so in general (without the addition of I. or II.) in common years. There cannot be any ambiguity about what we just mentioned, speaking of another Adhar preceding this one (because this only relates to leap-years). It has two Rosh-Hodesh and 29 days. 302 The followers of Jesus wanted to know beforehand the Passover of the Jews, in order to derive thence the beginning of their Lent. So they consulted the Jews, and asked them regard-ing this subject, but the Jews, guided by the enmity which exists between the two parties, told them lies*in order to lead them astray. And besides, the eras of both parties differed. X C-G-Ax-cA I o—-(o. 302 Finally, many of the Christian mathematicians took the work in hand and made calculations with the various cycles and different methods. Now, that method which they at least agreed to adopt, is the table called X^oviKovjof which they maintain that it was calculated by Eusebius, Bishop of Caesarea, and the 318 bishops of the Synod of Nicaea. 314-315 As regards the Sabians, we have already explained that this name applies to the real Sabians, i.e. to the remnant of the captive Jews in Babylonia, whom Nebukadnezar had transferred from Jerusalem to that country. After having freely moved about in Babylonia, and having acclimatized themselves to the country, they found it inconvenient to return to Syria; therefore they preferred to stay in Babylonia. Their religion wanted a certain solid foundation, in consequence of which they listened to the doctrines of the Magians, and inclined towards some of them. So their religion became a mixture of Magian and Jewish elements like that of the so-called Samaritans who were transferred from Babylonia to Syria. Their day begins with sunrise, whilst all others, who use lunar months, make it begin with sunset. [This statement refers to the Harranians], Their lunar month begins with the second day after conjunction (new moon). If, now, conjunction precedes sunrise only by one minute, the third following day is the beginning of the month. But if conjunction coincides with sunrise or falls only a little later, the second day after conjunction is the beginning of the month. 319 (The author tries to form his information regarding the Har-ranian calendar into a system.)--Because their great fasting falls into the first phase (quadrature) of Hilal [new moon] Adhar, whilst sun and moon stand in two double-bodied signs (Pisces and Gemini?), and because the end of the fasting falls into the first phase of Hilal Nisan, whilst the sun and moon stand in certain two inclining signs (Aries and Cancer), their months must of necessity revolve in the solar year in a similar way to the Jewish months, that is to say; on an average. And between the causes of each of these two things there is a connection. For the Jewish Passover demands that the sun and moon should stand in the first opposition in two signs of the equinoxes— for they may stand in opposition, and not only once, but twice— and the Harranian fast-breaking demands that which we have men 319 tioned (in Hilal Adhar). Hence follows that the phase (quadrature) next preceding the Jewish Passover is the fast-breaking of the Harranians, and that the conjunction which falls next to the autumnal equinox is the beginning of their year, never falling beyond Ilul. If we compute these elements for a cycle of 19 years, we get a rough sort of computation, but only a rough one, for they themselves try to correct it by means of the time of^conjunction, as we have mentioned. The methods of both Jews and Christians for the computation of Passover are based upon such motions of the luminaries, of which we have found out that they remain back behind real time, especially as regards the sun (the precession of the equinoxes having been neglected). If we examine the oppositions according to the motions that have been found by recent observations, we find that some of them precede the Easter-limit according to both Jewish and Christian systems; they, however, disregard this precession, whilst it is really the case, and we find that others of them (the oppositions) fall near the end of the East-er-limit; these latter oppositions they adopt and rely upon Hit ■! ■■nil'll I f • -’rwro them, whilst they are utterly wrong; for the real time (or opposition) precedes that time already by one month. 386 p. 63, 1. 15. This view, that Adhar II. is the leap-month, was held by the Karaeans, according to Eliah ben Mose in Selden, "Dissertatio de civil! anno Judaico," cap. v. p. 166. 389 II. Enneadecateris Meton discovered that 235 synodical months pretty nearly correspond to 19 solar years. In constructing his cycle of 19 years, he reckoned the solar year at 365 and 5/19 d.,i.e. by 1/76 d. longer than it had been reckoned in the Ootaeteris (a mistake which afterwards Callippus strove to retrieve). More correct was the following Jewish calculation with Hipparchic measures: 235 lunations, each = 29d. 12h. 793 H., give the sum of— 6,939 d. 16^11 h. = i79,876,755 H. If we divide this sum of Halaks by the length of the solar year of — 365 g|79T. h< _ 9>467>190 we get as quotient 19 (years), and a remainder of only 145 H. According to this computation, the difference between the rotations of sun and moon at the end of the first Enneadecateris 389 29 would not be more than 145 H., or i.e. a little more than 1/7 h., or than 1/168 d., whilst, according to Callippus, this difference was greater, viz. 19/76 d. = 1/4 d. This reform of the Metonic Enneadecateris enabled the Jews to dispense with the 76 years cycle of Callippus, which he constructed of four-times the Enneadecateris with the omission of one day* The Jewish calculation is more correct than that of Callippus, who reckoned the solar year too long. 390 p. 66, 1. 23. The words that Passover by which the beginning of Nisan is regulated I understand in this way, that' Passover, i.e. the 15th Nisan, and the 1st Nisan always fall on the same week-day. 391 p. 68, 1. 35. If the Miladites commenced the month with the moment of the conjunction, they differed from the Rabbanites in this, that the latter made the beginning of the month (e.g. the beginning of the first month or New-year’s-day) depend not alone upon conjunction, but also upon certain other conditions, for example, the condition(Lazarus Bendavid, section 36). The Rabbanites tried in everything to assimilate their calendar, based upon the astronomical determination of conjunction, to the more ancient calendar which had been based upon the ob-seryation of New Moon. The conservative tendency of this reform of the Jewish calendar is pointed out by A. Schwarz, ”Der Judisohe Kalendar,” pp. 59-61. 438 p. 300, 1. 4. The Jews count 3,448 years between Adam and Alexander. If you divide this sum by 19, you get 9 as a remainder, i.e. the first year of the Aera Alexandri is the 10th year of the cycle. The division of 5180 by 19 gives a remainder of 12, i.e. the first year of the Aera Alexandri is, according to the Christians, the 13th year of the cycle.