卷三·第 204–209 问　世界之日、星体大小、地球大小与元素层

§204. What are these days that are called the days of the world?

第二百零四问　被称为“世界之日”的这些日子是什么？

This is a name for a number of days in which the planets, their apogees and their jawzahrs complete whole revolutions. Every school has worked them out in order to keep the motions, according to what it found of their motions by its observations. The well-known ones are those of the Indians, who call this period in their language kalpa, and its days kalpa-ahargaṇa, that is, the sum of the days of a kalpa. Our people call them the days of the Sindhind, which in their language is siddhānta, a name applied to every excellent book on astronomical reckoning; it is explained as 'the straight, which does not bend'. These siddhāntas are five among them: one is ascribed to Sūrya, the second to Vasiṣṭha, the third to the Romaka, the fourth to Pulisa, and the fifth to Brahmā. They are called the days of the world because for them this is a day of Brahmā with respect to nature; at its beginning the planets and the rest began to move from the beginning of Aries on a Sunday. A period equal to it is a night of Brahmā, in which what moves is at rest; and so on until his life is complete, which is 100 years of his years composed of his days. To set out their opinions on this subject would be lengthy. We have put the revolutions in tables according to what the Indians have, not what is in the zījes of our people, and with them what Abū Maʿshar reports from the Persians about the hazārāt, that is, the thousands.

这是一个名称，指一定数目的日子，在这些日子里，诸行星、它们的远地点和它们的交点都转满整周。每一派都根据自己观测所得的运动把它推算出来，以便保存诸运动。其中著名的是印度人的，他们在自己的语言里把这段时期称为“劫”，把它的日数称为“劫积日”，意思是一劫的日子之和。我们的人把它们称为“信德欣德之日”，信德欣德在他们的语言里就是“悉檀多”，这是对每一部优秀的天文推算之书的称呼，解释为“正直而不弯曲的”。他们的悉檀多有五部：一部归于苏利耶，第二部归于婆私吒，第三部归于罗摩迦，第四部归于补利沙，第五部归于梵天。它们之所以称为世界之日，是因为在他们看来，就自然而言，这是梵天的一个白昼；在它开始时，诸行星和其余诸物在一个星期日从白羊座起点开始运动。与之等长的一段时期是梵天的一个夜晚，在其中运动之物都静止；如此下去，直到他的寿命满了，那是由他的日子构成的他的一百年。要把他们在这一题目上的见解一一列出，就太冗长了。我们已把诸周数列成表，依照的是印度人所有的，而不是我们的人的历表里的；与之并列的，是阿布·马谢尔转述波斯人关于“哈扎拉特”即“诸千”的说法。

§205. Do we know the sizes of the bodies of the planets?

第二百零五问　我们知道诸行星星体的大小吗？

As for the Moon, its diameter is known in terms of a unit in which the radius of the earth is one; Ptolemy found that by means of parallax. The diameter of the Sun, likewise, is known in that unit; he found it by means of the eclipses in the fifth book of the Almagest. As for the diameters of the wandering planets and of the fixed stars, their ratio to the diameter of the Sun as seen by the eye is also known by observation, as we have mentioned in the book [illegible]. We have put that in a table according to the view of Ptolemy.

至于月亮，它的直径以一种单位为人所知，在这种单位里地球的半径是一；托勒密是借视差求得的。太阳的直径同样以那种单位为人所知；他是在《天文学大成》第五卷里借交食求得的。至于诸游星和诸恒星的直径，它们与肉眼所见太阳直径之比，也是借观测而知的，如我们在〔抄本此处字迹难辨〕一书中所提到的。我们已按托勒密的见解把它列成表。

§206. Are their volumes, then, known in terms of the diameter of the earth?

第二百零六问　那么，它们的体积以地球的直径来量是已知的吗？

We said that the distance of each of the Sun and the Moon from the centre of the world is known in terms of the radius of the earth, as is shown in the fifth book of the Almagest as well. What is laid down among the practitioners of the art is that the farthest distance of each planet is the nearest distance of the planet above it, and the ratios of the near distances to the far distances are known; so when one of these distances is known, the rest become known. Thus the sizes of all the planets relative to the earth are known in terms of the radius of the earth, and so are their diameters; and so the ratio of their spherical bodies to the sphere of the earth is known as well. It is in that table, according to the findings of Ptolemy and their corrections.

我们说过，太阳和月亮各自与世界中心的距离以地球半径为单位是已知的，这也在《天文学大成》第五卷中证明了。本行从业者所定的是：每颗行星的最远距离就是它上面那颗行星的最近距离，而近距离与远距离之比是已知的；所以这些距离中只要知道一个，其余的就都知道了。这样，一切行星相对于地球的大小以地球半径为单位都已知，它们的直径也已知；于是它们的球体与地球之球的比也就知道了。这都在那张表里，依照托勒密的所得及其修正。

§207. And what is the size of the earth?

第二百零七问　地球的大小是多少？

As for measurements, nothing absolute can be had for the size of the earth, because [illegible] the units of length, of capacity and of weight are by convention. But if we want it in the well-known distances, its diameter in farsakhs is 2163 7/11 farsakhs [corrected: MS has 2163 1/3], and its circumference in farsakhs 6800 farsakhs. On this basis the area of its surface is 14,712,727 1/4 farsakhs, and the measure of its solid 166,744,242 1/5 farsakhs [corrected: MS has 160,744,242 1/5] [sic]. Since that is so, if the distance of each planet is multiplied by the farsakhs of the radius of the earth, and the body of each planet by the volume of the body of the earth, its distances and bodies in farsakhs become known; and they are in this table.

至于量度，地球的大小得不到什么绝对之数，因为〔抄本此处字迹难辨〕长度、容量和重量的单位都是约定的。但如果我们要用通行的路程单位来表示，它的直径是二千一百六十三又十一分之七法尔萨赫〔抄本作二千一百六十三又三分之一，据算改正〕，它的周长是六千八百法尔萨赫。据此，它表面的面积是一千四百七十一万二千七百二十七又四分之一法尔萨赫，它立体的量是一亿六千六百七十四万四千二百四十二又五分之一法尔萨赫〔抄本作一亿六千零七十四万余，脱一“六”字，据下表改正；此数本身有误，见讲解〕。既然如此，若把每颗行星的距离乘以地球半径的法尔萨赫数，把每颗行星的星体乘以地球之体的体积，它的距离和星体以法尔萨赫计就都知道了；它们就在这张表里。

It is followed by what completes it of the table, so that [illegible] only [illegible] here. [text uncertain]

其后接着是补全此表的部分，以便〔抄本此处字迹难辨〕仅〔抄本此处字迹难辨〕于此。〔原文疑有讹误〕

§208. Has there been disagreement about the size of the earth?

第二百零八问　关于地球的大小，有过分歧吗？

There is bound to be, for it is a matter reached by inference, not by eyewitness, and then by reports; and each nation knows it in terms of the distances used in its own region, such as the stadion of the Greeks, the yojana of the Indians, and the mile [illegible]. But to get at its truth, according to what has been translated from the books [text uncertain], al-Maʾmūn ibn al-Rashīd ordered it to be tested. A group of scholars undertook it, and measurement was made in the desert of Sinjār; they found the share of a single degree in miles to be 56 2/3 miles, by the black cubit, and they multiplied that by 360, which came to 20,400; and those are the miles of the circumference of the earth, [illegible]. The miles are thirds of farsakhs, and every mile contains 4000 cubits, which in Iraq are called black cubits, each of 24 fingers. We have already set out, in what we mentioned from the Indians in [illegible], what makes it unnecessary to repeat it.

必然会有，因为这是靠推断而不是靠亲眼目睹得来的事，然后又靠传闻；而且每个民族都以自己地区通用的路程单位来认识它，比如希腊人的斯塔迪昂、印度人的由旬，以及〔抄本此处字迹难辨〕的里。但为求得它的真相，根据从诸书〔原文疑有讹误〕中译出的内容，拉希德之子马蒙下令对它加以检验。一群学者承担了此事，在辛贾尔荒原上进行了测量；他们得出一度所占的里数是五十六又三分之二里，用的是黑肘，他们把它乘以三百六十，得二万零四百；这就是地球周长的里数，〔抄本此处字迹难辨〕。里是法尔萨赫的三分之一，每一里含四千肘，这种肘在伊拉克称为黑肘，每肘二十四指。我们已在〔抄本此处字迹难辨〕中转述印度人的说法时，叙述了足以不必重复的内容。

§209. Are the diameters of the four elements of the said size?

第二百零九问　四元素的直径是上述的大小吗？

It is known that the surface of the earth is jagged and that the waters are gathered in its furrows, and that from the two together comes, on the whole, a single sphere of the size we have mentioned. When its radius is subtracted from the nearest distance of the Moon, there remains for the thickness of the air 35,213 2/11 farsakhs. When the volume of the sphere of the earth, which is 5,305,498,589 4/5 farsakhs, is subtracted from the volume of the lowest sphere of the Moon, which is 200,356,658,322,333 1/3 farsakhs, there remain 200,351,352,823,743 and 1/3 and 1/5 cubic farsakhs, which is the volume of the place of the air and the fire together. In its lower part there arise from the moist vapour of water the winds, clouds, rains, snows and hail, then the thunders, crashes, lightnings, thunderbolts, the rainbow, the haloes and the like; and in its upper part there arise from the dry, smoky vapour of the earth the stars with locks of hair and with tails, the falling shooting stars, and the like.

已知地球的表面是参差不平的，水汇聚在它的沟壑里，二者合起来大体上成为一个球，大小就是我们所说的那样。把它的半径从月亮的最近距离中减去，剩下的大气厚度是三万五千二百一十三又十一分之二法尔萨赫。把地球之球的体积，即五十三亿零五百四十九万八千五百八十九又五分之四法尔萨赫，从月亮最低天球的体积，即二百万亿三千五百六十六亿五千八百三十二万二千三百三十三又三分之一法尔萨赫中减去，剩下二百万亿三千五百一十三亿五千二百八十二万三千七百四十三又三分之一又五分之一立方法尔萨赫，这就是气与火两者所在之处的体积。在它的下部，由水的湿润蒸气生出风、云、雨、雪和冰雹，然后是雷鸣、霹雳、闪电、落雷、虹、晕之类；在它的上部，由土的干燥烟气生出带发之星与带尾之星、坠落的流星之类。