卷三·第 135–144 问　时辰、赤道、黄道与分至点

§135. What are the hours, and what are their kinds?

第一百三十五问　何谓时辰，时辰有哪几种？

The hours are of two kinds. One kind is the equal hours, each of which is one of twenty-four parts of the whole day; their sizes do not vary. When night and daytime are equal, the hours of each of them are twelve; when one of them grows longer, its hours become more than twelve, and the hours of the other fall short of twelve by the amount of that one's excess over it. The other kind of hours is the crooked hours, by which each of the daytime and the night is always twelve hours, each one being half of a sixth of the daytime or of the night; but they are longer in a long daytime than in a short one; indeed, whenever the daytime differs from its night, the hours of the one also differ from the hours of the other. So the equal hours vary in number in the daytime and the night and agree in size, while the crooked hours are those that vary in size in them and agree in number. The equal hours are also called equinoctial (muʿtadila), and the crooked temporal (zamāniyya).

时辰有两种。一种是等时，每一个都是整日的二十四分之一；它们的大小不变。夜与昼相等时，各有十二个时辰；其中之一变长时，它的时辰就多于十二，另一个的时辰就少于十二，所少之数正等于前者所多之数。另一种时辰是曲时，按这种时辰，昼和夜各自永远是十二个时辰，每一个是昼或夜的六分之一的一半；但它们在长昼中比在短昼中长；实际上，只要昼与它的夜不等，这一方的时辰也就与那一方的时辰不等。所以等时在昼夜中数目不同而大小一致，曲时则在昼夜中大小不同而数目一致。等时又称为赤道时（穆阿塔迪拉），曲时又称为季节时（扎马尼亚）。

§136. Into how many parts is the hour divided?

第一百三十六问　一个时辰分为几部分？

The hour, and indeed everything by which one measures length, volume or weight, is divided, as we have said, into sixty minutes and what follows them. The Jews divide the hour into eighteen times sixty, that is, 1080 parts, which they call in Hebrew ḥalaq; they do not go below these, except that they sometimes halve the ḥalaq.

时辰，乃至一切用来度量长度、容积或重量的东西，如我们说过的，都分为六十分以及其后的各级。犹太人把时辰分为十八乘六十，即一千零八十份，用希伯来语称为“哈拉克”；他们不再往下分，只是有时把哈拉克分成两半。

§137. How are the hours reckoned among the Indians?

第一百三十七问　印度人怎样计算时辰？

They call the hour by the name of half a sign, which in their language is horā, and they do not use the hour except in astrology. In common use, however, they take the day as one unit and divide it into sixty parts, each of which is called a gharī; and each gharī into sixty parts, which some of them call chasha and vijaka, and others pārī; and each pārī is six prāṇa, and they claim that a prāṇa is the duration of one breath of a man in a balanced state. This division corresponds to fractions of the equal hours, because the gharīs are equal in size and vary in number in the daytime and its night. Converting them into equal hours is done by doubling their fifth; and converting equal hours into gharīs is done by setting the number down in two places, doubling the one and halving the other, and then adding together what results in both. The Indians have another division which they call muhūrta, of which the day has thirty. Each muhūrta contains two gharīs when the daytime is equal to its night and each of them is fifteen muhūrtas; and when they differ, each muhūrta of the daytime differs in size from each muhūrta of the night.

他们用半个星座的名称称呼时辰，在他们的语言里是“霍拉”，而他们除了在占星中以外不用时辰。在日常使用中，他们把一日当作一个单位，分为六十份，每一份称为“伽利”；每一伽利又分为六十份，有些人称之为“恰沙”和“维贾卡”，另一些人称之为“帕利”；每一帕利是六“普拉纳”，他们声称一普拉纳是一个身体平和的人一次呼吸的时长。这种划分与等时的分数相当，因为伽利大小相等，在昼与其夜之中数目不同。把伽利换算成等时，是把它的五分之一加倍；把等时换算成伽利，是把这个数写在两处，一处加倍，另一处减半，再把两处所得相加。印度人另有一种划分，称为“牟呼栗多”，一日有三十个。昼与夜相等、各为十五个牟呼栗多时，每个牟呼栗多含两个伽利；二者不等时，昼的每个牟呼栗多就与夜的每个牟呼栗多大小不同。

§138. What is the equator?

第一百三十八问　何谓赤道？

The pole and the circle on the surface of a sphere belong to the category of correlatives; so too the motion of a sphere, for it requires two poles, and the two poles require a great circle midway between them. One of the two poles of the first motion is visible to the people of the north and the other is hidden from them in the south, and between them there is a great circle. When the sphere moves on the axis joining those two poles, the motion is referred to that middle circle, because its greatest speed is there, while on the other, small circles whose centres lie on the axis it is slower in proportion to their distance from it. Because the great circle lies in the middle, it is called a belt (minṭaqa), by way of comparison. The equator, then, is the great circle that is the belt of the first motion.

极与球面上的圆属于相关者一类；球的运动也是如此，因为它需要两个极，而两个极又需要在它们正中间的一个大圆。第一运动的两极中，一个北方的人看得见，另一个在南方，对他们隐而不见，两极之间有一个大圆。球绕连接这两极的轴运动时，运动就归于那个中间的圆，因为它的速度在那里最大；而在另外那些圆心位于轴上的小圆上，运动较慢，慢的程度与它们离那个大圆的距离成比例。因为这个大圆位于正中，所以按比喻称它为“带”（明塔卡）。因此，赤道就是作为第一运动之带的那个大圆。

§139. What is the zodiac (ecliptic)?

第一百三十九问　何谓黄道？

It is the great circle that is the belt of the second motion; it is also called the orb of the signs (falak al-burūj). The Sun, in its eastward motion, keeps to this circle and does not leave it. This belt is inclined to the equator, cutting it at two opposite points, so that half of it lies north of the equator and the other half south of it; and by the amount of this inclination the poles of the two motions are apart from each other, in each of the two directions, north and south. The circle that passes through the poles of the equator and the poles of the zodiac is known as the circle passing through the four poles.

它是作为第二运动之带的那个大圆；它又被称为“诸星座之天”。太阳在它的东向运动中始终沿着这个圆，从不离开。这条带与赤道斜交，在相对的两点上与它相截，所以它的一半在赤道之北，另一半在赤道之南；两种运动的极彼此相距的量，在北、南两个方向上，都正等于这个倾斜的量。穿过赤道两极与黄道两极的那个圆，称为过四极圈。

§140. What are the daily orbits?

第一百四十问　何谓日周圈？

They are the circles parallel to the equator, in the directions north and south, those that pass through the points of the zodiac and those that touch it; and if they are attributed to anything, they are attributed to the stars or the points that revolve on them.

它们是在赤道南北两侧、与赤道平行的圆，有的穿过黄道上的各点，有的与黄道相切；若要把它们归属于什么，就归属于在它们上面旋转的星或点。

§141. What are the orbits of latitude?

第一百四十一问　何谓黄纬圈？

They are the circles parallel to the zodiac, in the directions north and south of it.

它们是在黄道南北两侧、与黄道平行的圆。

§142. What are the almucantars?

第一百四十二问　何谓地平纬圈？

They are the circles parallel to the horizon. If they are above it, towards the zenith, they are the almucantars of altitude; and if they are below the horizon, towards the nadir, they are called the almucantars of depression.

它们是与地平平行的圆。若在地平之上、朝向天顶，就是高度地平纬圈；若在地平之下、朝向天底，就称为深度地平纬圈。

§143. What are the equinoctial and the solstitial points?

第一百四十三问　何谓分点与至点？

A great circle meets and cuts a great circle at two diametrically opposite places, and is farthest from it at two others likewise. Since the zodiac cuts the equator at two opposite points, it is farthest from it at two others. The two points of intersection are the equinoxes, because when the Sun reaches them daytime and night become equal for all the inhabitants of the earth, and neither exceeds the other. Of these two points, the one on leaving which the Sun comes into the northern half of the zodiac is the vernal equinoctial point, and the one on leaving which it comes into the southern half is the autumnal equinoctial point. The equinox (iʿtidāl) is also called 'equality' (istiwāʾ). The two points of greatest distance belong to the solstices: the one in the northern half of the zodiac is called the summer solstice and the summer turning-point, and the one in its southern half the winter solstice and the winter turning-point, because there the Sun turns back to climb northwards after descending, or to descend southwards after climbing.

一个大圆与另一个大圆在直径相对的两处相遇、相交，又在另外两处同样相对的地方离它最远。黄道既然在相对的两点上与赤道相交，就在另外两点上离它最远。两个交点是分点，因为太阳到达那里时，对地上所有居民来说，昼夜都变得相等，谁也不超过谁。这两点中，太阳离开它就进入黄道北半的那一点，是春分点；离开它就进入南半的那一点，是秋分点。分点（伊阿提达勒）又称为“均等”（伊斯提瓦）。两个最远点属于两至：在黄道北半的称为夏至，又称夏季转折点；在南半的称为冬至，又称冬季转折点，因为太阳在那里折返：下降之后转而向北攀升，或攀升之后转而向南下降。

§144. Into how many parts are the circumferences of circles divided?

第一百四十四问　圆周分为几部分？

The convention among the practitioners of the art is to divide the circuit of every circle, great or small, into 360 equal parts. On the equator they are called times (azmān), because in their revolution they run neck and neck with time, like two horses in a race, so that time is measured by the times and counted by them. On the zodiac they are called degrees (darajāt, 'steps'), because the Sun climbs and descends in the two directions by what it travels on it, and climbing and descending belong to steps. On the other circles they are called parts.

本行的从业者约定：每一个圆，不论大小，其周都分为三百六十等份。在赤道上，它们被称为“时度”（阿兹曼），因为它们在旋转中与时间并驾齐驱，如同赛跑的两匹马，所以时间以时度来量、以时度来数。在黄道上，它们被称为“度”（达拉贾特，意为“台阶”），因为太阳沿黄道所走的路程使它在两个方向上攀升、下降，而攀升与下降正属于台阶。在其他圆上，它们被称为“份”。