卷四·第 214–221 问　城市经纬度、日出方位与昼夜长短

§214. What is the latitude of a town?

第二百一十四问　何谓城市的纬度？

It is its shortest distance from the equinoctial line towards the north, because the towns are in this region. Facing it in the sky is a similar great-circle arc lying between the zenith and the equator, and the altitude of the north pole is equal to it; that is why the latitude is expressed by that altitude. The depression of the south pole, though it is equal to it as well, is hidden and not perceived.

它是城市向北离赤道线的最短距离，因为诸城都在这一区域。天上与它相对的，是天顶与天赤道之间一段与之相似的大圆弧，北极的高度与它相等；所以纬度就用这个高度来表示。南极的低落虽然也与它相等，但隐而不见，觉察不到。

§215. What is the longitude of a town?

第二百一十五问　何谓城市的经度？

It is its distance from the farthest end of habitation, whether taken on the equator, or on the equinoctial line, or on the line of the towns parallel to them; for the similarity between them makes one stand in place of the other. Since what we use of this art is derived from the views of the Greeks, and they began longitude from the nearer of the two ends of habitation to them, which is the western one, the longitude of a town is therefore its distance from the west. But on this end there is disagreement among them: some of them begin longitude from the shore of the western Ocean, and some from six islands lying far out in the sea, about 200 farsakhs, called the Islands of Happiness and the Eternal Islands (al-Khālidāt), which are opposite the west. So two kinds of longitude may be found in the books for one town, with 10 degrees between them, and to distinguish them requires discernment and practice.

它是城市离有人居住之地最远一端的距离，无论是在天赤道上量、在赤道线上量，还是在城市所在的、与二者平行的那条线上量；因为三者相似，所以可以互相代替。由于我们在这门学问中所用的，是从希腊人的见解中得来的，而他们是从有人居住之地两端中离他们较近的一端，也就是西端，开始起算经度的，所以城市的经度就是它离西方的距离。但在这一端上，他们之间有分歧：有些人从西方大洋的岸边起算经度，有些人则从远在海中约二百法尔萨赫的六座岛屿起算，这些岛称为幸福群岛和永生群岛，正对着西方。所以书中对同一座城市可能有两种经度，相差十度，要分辨它们，需要眼力和练习。

§216. What is called 'between the two longitudes'?

第二百一十六问　何谓“两经之间”？

It is the difference between the longitudes of the two towns, and it is equal to the times between their two meridians, whether on the equator or on each of the daily orbits of the two towns or on others.

它是两座城市经度之差，等于它们两条子午线之间的时度，无论是在天赤道上量、在两城各自的日周圈上量，还是在别的圈上量。

§217. What follows from the difference in longitude of two towns when their latitudes are equal?

第二百一十七问　两座城市纬度相等而经度不同，会生出什么来？

Nothing follows for them from that except the difference in rising and setting: the beginning of daytime or of night in the eastern of the two, which is the one of greater longitude, always comes before it comes in the western one by the amount between their longitudes; and midday and midnight are in them by the same reckoning. The nature of the air does not differ between them except through some accident affecting one of them from a difference of position with respect to seas, mountains, sands, lowland or highland; otherwise the two are alike.

由此对它们生出的，只有升起与落下的不同：白昼或黑夜的开始，在两城中偏东的那一座，也就是经度较大的那一座，总是比在偏西的那一座来得早，早的量就是两城的经度之差；正午和子夜在两城也照此计算。两城空气的性质并无不同，除非其中一城因在海、山、沙地、低地或高地方面位置不同，而受到某种偶然的影响；否则二者是一样的。

§218. What follows from the difference in latitude of two towns when their longitudes are equal?

第二百一十八问　两座城市经度相等而纬度不同，会生出什么来？

Midday or midnight comes to both of them at one time, and so does the rising and the setting of the Sun when it is at the beginning of Aries and of Libra; and in the same way the rising and setting of every star that is on the equator. But when the Sun or the star is not on the equator itself but has moved away from it to the south, its rising on the town of smaller latitude comes before its rising on the town of greater latitude, and its setting on the town of smaller latitude after its setting on the town of greater latitude. If the Sun or the star is north of the equator, the matter is the reverse of what we have said: I mean, its rising on the town of smaller latitude comes after its rising on the town of greater latitude, and its setting on the town of smaller latitude before its setting on the town of greater latitude. The 'before' and 'after' in this have no regular amount. Further, the lengths of one and the same daytime and of its night differ in the two, when they are unequal; the amplitude of the risings, the altitude at midday and its shadow differ; the stars that are always visible and those always hidden differ; and the one of greater latitude is colder in air, unless some circumstance of position arises in them, so that the preponderance goes to the one of greater latitude over the other in heat of air [text uncertain]; as with Ghazna among the cold lands and Baghdad among the hot lands, whose latitudes are equal.

正午或子夜同时到达两城，太阳在白羊座起点和天秤座起点时的升起与落下也是同时的；同样，凡在天赤道上的星，其升落也同时。但当太阳或星不在天赤道本身，而是离开它向南时，它在纬度较小之城的升起早于在纬度较大之城的升起，它在纬度较小之城的落下晚于在纬度较大之城的落下。若太阳或星在天赤道以北，情形就与我们所说的相反：我是说，它在纬度较小之城的升起晚于在纬度较大之城的升起，它在纬度较小之城的落下早于在纬度较大之城的落下。这里的“早”与“晚”没有固定的量。此外，在昼夜不等的时候，同一个白昼及其黑夜的长度在两城中也不同；日出方位的幅度、正午的高度及其影长都不同；恒显之星和恒隐之星也不同；纬度较大的一城空气较冷，除非两城出现某种位置上的情况，使纬度较大的一城在空气的热度上反而胜过另一城〔原文疑有讹误〕；例如寒冷之地中的伽色尼与炎热之地中的巴格达，二者纬度相等。

§219. What follows from a difference in both longitudes and latitudes of two towns together?

第二百一十九问　两座城市经度和纬度都不同，会生出什么来？

In them there occurs all that we have mentioned of the two kinds of difference, composed of the two taken singly; and the rising of a star in one and its setting in the other do not coincide in them except when it is on one of the two points at which their horizons intersect.

在它们之中，会出现我们所说两类差异的全部情形，由二者各自单独的情形合成；而且一颗星在其中一城的升起与在另一城的落下，除非它恰好在两城地平相交的两点之一上，否则不会同时发生。

§220. What is the amplitude of the rising?

第二百二十问　何谓日出方位的幅度？

When the Sun is at the beginning of Aries and of Libra, it rises and sets in line with the equinoctial line which we derived by means of the Indian circle. When it inclines to the north, its rising and setting are in line with two points on the northern half of the horizon, which are the ends of a line parallel to the equinoctial line; and they keep getting farther from it until the Sun reaches the beginning of Cancer, and then the two points of its rising and setting are called the summer rising and its setting. Likewise, when it inclines towards the south, its rising and setting are in line with two points on the southern half of the horizon, which keep getting farther from the equinoctial line until the Sun reaches the beginning of Capricorn, and then the two points of its rising and setting are called the winter rising and its setting. The amplitude of the rising, then, is what lies between the equinoctial line and its place of rising. On the equinoctial line it is equal to the declination, but in towns that have latitudes the amplitude of the rising or of the setting exceeds the declination, and the greater the latitude, the greater the amplitude. This is the figure of it.

太阳在白羊座起点和天秤座起点时，正对着我们用印度圆求出的春秋分线升起和落下。当它向北偏时，它的升起和落下正对着地平北半上的两点，这两点是一条与春秋分线平行之线的两端；它们离春秋分线越来越远，直到太阳到达巨蟹座起点，这时它升起和落下的两点就称为夏季的日出处和夏季的日落处。同样，当它向南偏时，它的升起和落下正对着地平南半上的两点，这两点离春秋分线越来越远，直到太阳到达摩羯座起点，这时它升起和落下的两点就称为冬季的日出处和冬季的日落处。所以，日出方位的幅度就是春秋分线与它的升起之处之间的那段。在赤道线上，它等于赤纬；但在有纬度的城市里，日出或日落方位的幅度大于赤纬，纬度越大，幅度越大。这是它的图。

§221. How do daytime and night lengthen in the towns?

第二百二十一问　城市里的白昼与黑夜怎样变长？

The Sun turns either on the equator or on an orbit parallel to it, and the pole of all of them is the pole of the universe. When the horizon passes through the pole, and that is on the equinoctial line, it cuts the equator and the orbits parallel to it in halves, so that what is above the horizon of them equals what is below it; and so night and daytime are always equal there. When a town moves away from the equinoctial line, so that it has a latitude in the north and the pole is raised by its amount, the horizon does not pass through the pole and does not cut any circle in halves except the equator, because the two are both great circles; and so night and daytime are equal in all dwelling places when the Sun enters the beginning of Aries and of Libra, for these two are on the equator. As for the other orbits, the horizon cuts them in such an arrangement that what is above the horizon of the northern ones is greater than what is below it; and so in the northern signs the daytime lengthens and the night shortens. As for the southern ones, what of them is above the horizon is smaller than what is below it; and so in the southern signs the daytime shortens and the night lengthens. When the distance of two orbits from the equator is the same, one of them in the north and the other in the south, the increase and decrease of daytime and night in them are the same, and they are reciprocal in daytime and night: I mean that the daytime of one of them is equal to the night of the other.

太阳或在天赤道上转，或在与之平行的轨道上转，这些轨道全都以宇宙之极为极。当地平通过极时，那是在赤道线上，它就把天赤道和与之平行的诸轨道都切成两半，于是诸轨道在地平以上的部分等于地平以下的部分；所以那里昼夜总是相等。当一座城市离开赤道线，在北方有了纬度，极按纬度的大小升高时，地平就不再通过极，除了天赤道，它不把任何圈切成两半，因为二者都是大圆；所以当太阳进入白羊座起点和天秤座起点时，一切住处昼夜都相等，因为这两点在天赤道上。至于其余的轨道，地平切它们的方式是：北方诸轨道在地平以上的部分大于地平以下的部分；所以在北方诸星座中，白昼变长，黑夜变短。至于南方诸轨道，在地平以上的部分小于地平以下的部分；所以在南方诸星座中，白昼变短，黑夜变长。当两条轨道离天赤道的距离相同，一条在北、一条在南时，它们的昼夜增减是相同的，而且在昼夜上互相对调：我是说，其中一条的白昼等于另一条的黑夜。