卷六·第 268–272 问　平日与真日、月与年、闰法与“纳西”

BOOK VI. CHRONOLOGY

卷六　历法

§268. What are the mean days and the true days?

第二百六十八问　何谓平日与真日？

If the Sun were not moving with the second motion, and the first motion took it from some circle, it would bring it back to it in the period of a revolution of the whole equator, which is 360 times. But the Sun is not fixed; it moves in this period by its own amount. So the Sun does not return to the circle it left, whether that be the horizon, or the orb of midday and midnight, or another, except after a revolution of 360 times plus what it has travelled. Its course is not uniform but varies in speed and slowness, and that distance does not pass over all the circles in equal times: it passes over the eastern horizon by the ascensions of the town, over the western horizon by its descensions, and over the orb of midday and midnight by the ascensions of the right orb, because the meridian in every place stands in the place of one of the horizons of the equinoctial line, which pass through the two poles of the universe. It is thus clear that the amount of the true day is a revolution of 360 times together with the ascensions of the Sun's course, and that the amount of the mean day is a revolution of 360 times together with the ascensions of an arc equal to the mean motion of the Sun in one day.

假如太阳不以第二运动运行，第一运动把它从某个圈带走，就会在整个赤道转一周的时间里把它带回那个圈，那是三百六十时度。但太阳并非固定不动；它在这段时间里以它自己的量移动。所以太阳回到它离开的那个圈——不论那是地平，还是正午与午夜之圈，还是别的圈——要等转过三百六十时度，再加上它所走过的那一段。它的行程并不均匀，而是快慢不一，而那段距离通过各圈所用的时间也不相等：它通过东方地平按本城的上升时间，通过西方地平按本城的下降时间，通过正午与午夜之圈按正球的上升时间，因为每一处的子午圈都相当于赤道线上的一条地平，这些地平都通过宇宙的两极。由此可见，真日的长度是转过三百六十时度，再加上太阳所走那一段的上升时间；平日的长度是转过三百六十时度，再加上与太阳一日平均运动相等的一段弧的上升时间。

§269. What is the month?

第二百六十九问　何谓月？

The month is either natural or conventional. The natural month is the return of the Moon from the Sun to its first distance from it on one and the same of the two sides, east and west. But since the shapes of the light on the body of the Moon correspond to its distances from the Sun, custom has taken the crescent from among them, because it is as it were the beginning of the shapes. From one crescent to the next is 29½ days and a little more. But since it was not possible to use half a day, they counted the two months together as 59 days, one of them full, 30 days, and the other deficient, 29 days; and that is according to the mean course of the two luminaries. As for the true course, it happens, when the month is used by the sighting of the crescent with the eye, that two or three full months follow one another, and likewise deficient ones follow one another. The conventional month is one twelfth part of the natural year, or of something close to it.

月或是自然的，或是约定的。自然月是月亮离开太阳后，在东西两侧中的同一侧，回到它与太阳最初的距离。但由于月亮本体上光的形状对应于它与太阳的距离，习俗便从中取了新月，因为它好比诸形状的开端。从一次新月到下一次新月是二十九日半又多一点。但由于不便使用半日，人们把两个月合计为五十九日，其中一个是满的，三十日，另一个是缺的，二十九日；这是按两颗发光体的平均行程而言。至于按真实行程，用肉眼看新月来定月份时，会出现两三个满月相连，缺月也同样相连的情形。约定月是自然年的十二分之一，或接近于此的长度。

§270. What is the natural year, and what others are there?

第二百七十问　何谓自然年？另外还有哪些年？

The natural year is an expression for a period that includes the cycle of heat and cold, of tillage and breeding. It begins from the Sun's being at some point of the orb of the signs and ends at its return to it, and for this reason this year is ascribed to the Sun. Its amount is 365 days and a fraction which falls short of a quarter of a day by something, according to what we have found, and exceeds it by something, according to what the ancients found. This is the natural year; its month, which is a half of a sixth of it, is conventional, not natural. The conventional year is 12 months, multiples of the natural month; it is called lunar, and its amount is 354 days and nearly a fifth and a sixth of a day, I mean 11 parts out of 30 parts of the whole day.

自然年是对一段周期的称呼，这段周期包含冷热的循环、耕种与繁育的循环。它从太阳在黄道上的某一点开始，到它回到该点结束，因此这种年归属于太阳。它的长度是三百六十五日又一个零头，按我们所测得的，这零头比四分之一日少一点；按古人所测得的，比四分之一日多一点。这就是自然年；它的月是它的六分之一的一半，是约定的，不是自然的。约定年是十二个月，是自然月的倍数；它称为太阴年，它的长度是三百五十四日又将近一日的五分之一加六分之一，我是指一整日三十份中的十一份。

§271. How are these fractions used in the years?

第二百七十一问　年中的这些零头是怎样使用的？

In the solar year the quarter of a day is left aside until in 4 years a whole day is made up from it; this is added to the year, so that its days become 366. That is the practice of the Greeks, the Romans, the Syrians and the Copts of Egypt since the time of Augustus Caesar, king of the Romans. That year is called in Greek 'the measure' (al-miqyās) [text uncertain], and in Syriac kbīsā, which is Arabicized as kabīsa (intercalary), because the quarters of the day are pressed together (tankabis) in it into a whole day. As for the Persians, it was not permitted to them, on account of Magianism, to intercalate the year by a single day, so they used to put it off until in 120 years a whole month was made up from it; they added it to the year, so that its months became 13, the name of one of them being repeated in it, and that year was called bahīzak. They have neglected this since the end of their kingdom and the eclipse of their religion. The Copts before Augustus used to leave the quarter until the days of a whole year were gathered from it, and that is in 1460 years; then they dropped one year from the total of their years. It is all the same whether that was done or the year was repeated, so that two years were counted as one. In the lunar year, from the fifth and the sixth of a day a day is made up in the third year, by which the year becomes 355 days; and something is still left over, from which, together with the fifth and the sixth of a day that begin afresh, another day is made up in the sixth year; and so on until the fraction is entirely used up in 11 days at the completion of 30 years. These years are called the intercalary years of the Arabs, not because they used them or use them [corrected: MS omits 'not'], but because the makers of the zījes need them when they base the zījes on the years of the Arabs.

在太阳年里，四分之一日先搁在一边，等到四年里由它凑成一整日，就把这一日加到年上，于是那一年的日数成为三百六十六。这是希腊人、罗马人、叙利亚人和埃及科普特人自罗马人之王奥古斯都·恺撒的时代以来的做法。这样的年在希腊语里称为“尺度”（米格亚斯）〔原文疑有讹误〕，在叙利亚语里称为“克比萨”，阿拉伯化为“卡比萨”（闰），因为日的四分之一在其中被压聚（坦卡比斯）成一整日。至于波斯人，由于祆教的缘故，不许他们用单独一日来闰年，所以他们一直推延，直到一百二十年里由它凑成一整月；他们把它加到年上，于是那一年的月数成为十三，其中一个月的名字重复一次，那一年称为“巴希扎克”。自从他们的王国终结、他们的宗教衰落以来，他们就把这事荒废了。奥古斯都以前的科普特人把四分之一日搁在一边，直到由它聚成一整年的日数，那需要一千四百六十年；然后他们从年数的总和中去掉一年。不论是这样做，还是把那一年重复，使两年算作一年，都是一样的。在太阴年里，由日的五分之一与六分之一，到第三年凑成一日，那一年便成为三百五十五日；仍有些余下，它与重新开始的日的五分之一与六分之一一起，到第六年又凑成一日；依此类推，直到三十年满时，零头在十一日中全部用尽。这些年称为阿拉伯人的闰年，并不是因为他们用过或在用它们〔抄本无“不”字，据文义改正〕，而是因为编历表（齐吉）的人以阿拉伯人的年为基础编历表时需要它们。

§272. What is the nasīʾ?

第二百七十二问　何谓“纳西”？

The meaning of nasīʾ is postponement. The lunar year runs ahead of the solar year by about 11 days, and therefore the months of the Arabs go round through all the seasons of the year in about 33 years; any month of them that is assumed may be found in whatever season it happens to be, and at whatever place in it. The Jews were commanded in the Torah to use the natural months and years together, so they were obliged to intercalate the year with the month made up from the excess between the lunar and the solar years. They called that year ʿibbūr, which in Hebrew is derived from 'the pregnant woman', because they likened the additional thirteenth month in the year to the additional burden a woman carries in her womb; by the addition of this month the year returns to its place after having run ahead. The Jews had been neighbours of the Arabs at Yathrib, the city of the Prophet, and the Arabs wished their pilgrimage to fall at the most fruitful time of the year and the easiest for going to and fro in trade, and not to move from its place. So they learned intercalation from the Jews, by a method bearing little resemblance to that of the two nations [text uncertain], and they entrusted it to a group of men known by a particular name, who inherited it from their forefathers. They were called the postponers (nasaʾa) of al-Muḥarram and its permitters (ḥalala), because when they postponed al-Muḥarram, the first became permitted and the second sacred; until Islam abolished that in the year of the Farewell Pilgrimage, which is the year 9 of the Hijra [sic]. Whoever used lunar months and solar years together could not do without it; and the Ḥarrānians, known as the Ṣābians, who are the remnants of the pagans, were likely to have done so, but I have not ascertained their practice in it. As for the Indians, they repeat a month in whatever year the reckoning completes it, and they call that year malamāsa. Mal is the surplus that remains over between the two fractions, like dirt that is thrown away, and māsa is the month, so that it is as it were 'the discarded month'; in their classical language it is adhimāsa.

“纳西”的意思是推延。太阴年比太阳年约早十一日，因此阿拉伯人的月约三十三年就轮遍一年中的所有季节；他们的任何一个月，都可能落在恰好遇到的任何季节、季节中的任何位置。犹太人在《讨拉》里受命同时使用自然的月与年，所以他们不得不用太阴年与太阳年之差所积成的月来闰年。他们称那一年为“伊布尔”，这个词在希伯来语里出自“孕妇”，因为他们把年中增加的第十三个月，比作妇人腹中多怀的负担；靠增加这个月，年在跑到前面之后又回到原位。犹太人曾在先知之城叶斯里卜与阿拉伯人为邻，而阿拉伯人希望他们的朝觐落在一年中物产最丰、最便于往来经商的时候，不离其位。于是他们向犹太人学了置闰，所用的方法与这两个民族的方法很少相似〔原文疑有讹误〕，并把它交给一群以特定名称著称的人，这些人从祖先那里世袭此事。他们被称为穆哈兰姆月的“推延者”（纳萨阿）与“解禁者”（哈拉拉），因为当他们推延穆哈兰姆月时，第一个月就成为解禁的，第二个月成为神圣的；直到伊斯兰在辞别朝觐那一年废除了此事，那是希吉拉第九年〔原书如此〕。凡同时使用太阴月与太阳年的人，都离不开此法；以“萨比教徒”著称的哈兰人，是异教徒的遗民，很可能也这样做过，但我没有查实他们在这方面的做法。至于印度人，在推算凑满一个月的任何一年里，他们就重复一个月，称那一年为“马拉马萨”。“马拉”是两种零头之间余下的盈余，就像被丢弃的污垢，“马萨”是月，所以它好比“被丢弃的月”；在他们的雅言里，它称为“阿迪马萨”。