Book vI chapter 9

On the anomaly of the Præcession of the Equinoxes, and of the obliquity¹ of the Zodiack.

A t one time the shifting of the æquinoxes is quicker, at another slower, being not always equal: because the poles of the earth travel unequally in the arctick and antarctick circle of the Zodiack; and decline on both sides from the middle path: whence the obliquity of the Zodiack to the Æquator seems to change. And as this has become known by means of long observations, so also has it been perceived, that the true æquinoctial points have been elongated² from the mean æquinoctial points, on this side and on that, by 70 minutes (when the prostaphæresis is greatest): but that the solstices either approach the equator unequally 12 minutes nearer, or recede³ as far behind; so that the nearest approach is 23 degrees 28 minutes, and the greatest elongation 23 degrees 52 minutes. Astronomers⁴ have given various explanations to account for this inequality of the præcession and also of the obliquity of the tropicks. Thebit, with the view of laying down a rule for such considerable inequalities in the motion of the stars, explained that the eighth sphære does not move with a continuous motion from west to east; but is shaken with a certain motion of trepidation⁵, by which the first points of Aries and Libra in the eighth heaven describe certain small circles with diameters equal to about nine degrees, around the first points of Aries and Libra in the ninth sphære. But since many things absurd and impossible as to motion follow from this motion of trepidation, that theory of motion is therefore long since obsolete⁶. Others therefore are compelled to attribute the motion to the eighth sphære, and to erect⁷ above it a ninth heaven also, yea, and to pile up yet a tenth and an eleventh: In the case of mathematicians⁸, indeed, the fault may be condoned⁹; for it is permissible¹⁰ for them, in the case of difficult motions, to lay down some rule and law of equality by any hypotheses. But by no means can such enormous and monstrous¹¹ celestial¹² structures be accepted by philosophers. And yet here one may see how hard to please are those who do not allow any motion to one very small body, the Earth; and notwithstanding they drive and rotate the heavens, which are huge and immense above all conception and imagination: I declare that they feign¹³ the heavens to be three (the most monstrous of all things in Nature) in order that some obscure motions forsooth251 may be accounted for. Ptolemy, who compares with his own the observations of Timocharis and Hipparchus, one of whom flourished 260 years, the other 460 years before him, thought that there was this motion of the eighth sphære, and of the whole firmament¹⁴; and proved by help of numerous phenomena¹⁵ that it took place over the poles of the Zodiack, and, supposing its motion to be so far æquable, that the non-planetary stars in the space of 100 years completed just one degree beneath the Primum Mobile. After him 750 years Albategnius discovered that one degree was completed in a space of 66 years, so that a whole period would be 23,760 years. Alphonsus made out that this motion was still slower, completing one degree and 28 minutes only in 200 years; and that thus the course of the fixed¹⁶ stars went on, though unequally. At length Copernicus, by means of the observations of Timocharis, Aristarchus of Samos, Hipparchus, Menelaus, Ptolemy, Mahometes Aractensis, Alphonsus, and of his own, detected the anomalies of the motion of the Earth's axis¹⁷: though I doubt not that other anomalies also will come to light some ages hence. So difficult is it to observe motion so slow, unless extending over a period of many centuries; on which account we still fail to understand the intent of Nature, what she is driving after through such inequality of motion. Let A be the pole of the Ecliptick, B C the Ecliptick, D the Æquator; when the pole of the Earth near the arctick circle of the Zodiack faces the point M, then there is an anomaly of the præcession of the æquinox at F; but when it faces N, there is an anomaly of the præcession at E. But when it faces I directly, then the maximum obliquity G is observed at the solstitial colure; but when it faces L, there is

the minimum obliquity H at the solstitial colure.

Copernicus' contorted circlet in the Arctick circle of the Zodiack.

Let F B G be the half of the Arctick circle described round the pole of the Zodiack: A B C the solstitial colure: A the pole of the Zodiack; D E the anomaly of longitude¹⁸ 140 minutes at either side on both ends: B C the anomaly of obliquity 24 minutes: B the greater obliquity of 23 degrees 52 minutes: D the mean obliquity of 23 degrees 40 minutes: C the minimum obliquity of 23 degrees 28 minutes.

 

 

The period of motion of the præcession of the æquinoxes is 25,816 Ægyptian years; the period of the obliquity of the Zodiack is 3434 years, and a little more. The period of the anomaly of the præcession of the æquinoxes is 1717 years, and a little more. If the whole time of the motion AI were divided into eight equal parts: in the first eighth the pole is borne somewhat swiftly from A to B; in the second eighth, more slowly from B to C; in the third, with the same slowness from C to D; in the fourth, more swiftly again from D to E; in the fifth, with the same swiftness from E to F; again more slowly from F to G; and with the same slowness from G to H; in the last eighth, somewhat swiftly again from H to I. And this is the contorted circlet of Copernicus, fused with the mean motion into the curved line which is the path of the true motion. And thus the pole attains¹⁹ the period of the anomaly of the præcession of the æquinoxes twice; and that of the declination or obliquity once only. It is thus that by later astronomers, but especially by Copernicus (the Restorer of Astronomy)²⁵², the anomalies of the motion of the Earth's axis are described, so far as the observations of the ancients down to our own times admit; but there are still needed more and exact observations for anyone to establish aught certain about the anomaly of the motion of the præcessions, and at the same time that also of the obliquity of the Zodiack. For ever since the time at which, by means of various observations, this anomaly was first observed, we have only arrived at half a period of the obliquity. So that all the more all these matters about the unequal motion both of the præcession and of the obliquity are uncertain and not well known: wherefore neither can we ourselves assign any natural causes for it, and establish it for certain. Wherefore also do we to our reasonings and experiments magnetical here set an end and period.²⁵³

FINIS

1 obliquity   

n.倾斜度

参考例句：

• It is here that the obliquity factor makes a crucial difference. 正是在这里，倾斜因子构成了重要的差别。 来自辞典例句
• The obliquity of the ecliptic is the fundamental cause of the seasons. 黄道的倾角是季节的基本成因。 来自辞典例句

2 elongated   

v.延长，加长( elongate的过去式和过去分词 )

参考例句：

• Modigliani's women have strangely elongated faces. 莫迪里阿尼画中的妇女都长着奇长无比的脸。
• A piece of rubber can be elongated by streching. 一块橡皮可以拉长。 来自《用法词典》

3 recede   

vi.退(去)，渐渐远去；向后倾斜，缩进

参考例句：

• The colleges would recede in importance.大学的重要性会降低。
• He saw that the dirty water had begun to recede.他发现那污浊的水开始往下退了。

4 astronomers   

n.天文学者，天文学家( astronomer的名词复数 )

参考例句：

• Astronomers can accurately foretell the date,time,and length of future eclipses. 天文学家能精确地预告未来日食月食的日期、时刻和时长。 来自《简明英汉词典》
• Astronomers used to ask why only Saturn has rings. 天文学家们过去一直感到奇怪，为什么只有土星有光环。 来自《简明英汉词典》

5 trepidation   

n.惊恐，惶恐

参考例句：

• The men set off in fear and trepidation.这群人惊慌失措地出发了。
• The threat of an epidemic caused great alarm and trepidation.流行病猖獗因而人心惶惶。

6 obsolete   

adj.已废弃的，过时的

参考例句：

• These goods are obsolete and will not fetch much on the market.这些货品过时了，在市场上卖不了高价。
• They tried to hammer obsolete ideas into the young people's heads.他们竭力把陈旧思想灌输给青年。

7 erect   

n./v.树立，建立，使竖立；adj.直立的，垂直的

参考例句：

• She held her head erect and her back straight.她昂着头，把背挺得笔直。
• Soldiers are trained to stand erect.士兵们训练站得笔直。

8 mathematicians   

数学家( mathematician的名词复数 )

参考例句：

• Do you suppose our mathematicians are unequal to that? 你以为我们的数学家做不到这一点吗？ 来自英汉文学
• Mathematicians can solve problems with two variables. 数学家们可以用两个变数来解决问题。 来自哲学部分

9 condoned   

v.容忍，宽恕，原谅( condone的过去式和过去分词 )

参考例句：

• Terrorism can never be condoned. 决不能容忍恐怖主义。
• They condoned his sins because he repented. 由于他的悔悟，他们宽恕了他的罪。 来自辞典例句

10 permissible   

adj.可允许的，许可的

参考例句：

• Is smoking permissible in the theatre?在剧院里允许吸烟吗？
• Delay is not permissible,even for a single day.不得延误，即使一日亦不可。

11 monstrous   

adj.巨大的；恐怖的；可耻的，丢脸的

参考例句：

• The smoke began to whirl and grew into a monstrous column.浓烟开始盘旋上升，形成了一个巨大的烟柱。
• Your behaviour in class is monstrous!你在课堂上的行为真是丢人！

12 celestial   

adj.天体的；天上的

参考例句：

• The rosy light yet beamed like a celestial dawn.玫瑰色的红光依然象天上的朝霞一样绚丽。
• Gravity governs the motions of celestial bodies.万有引力控制着天体的运动。

13 feign   

vt.假装，佯作

参考例句：

• He used to feign an excuse.他惯于伪造口实。
• She knew that her efforts to feign cheerfulness weren't convincing.她明白自己强作欢颜是瞒不了谁的。

14 firmament   

n.苍穹；最高层

参考例句：

• There are no stars in the firmament.天空没有一颗星星。
• He was rich,and a rising star in the political firmament.他十分富有，并且是政治高层一颗冉冉升起的新星。

15 phenomena   

n.现象

参考例句：

• Ade couldn't relate the phenomena with any theory he knew.艾德无法用他所知道的任何理论来解释这种现象。
• The object of these experiments was to find the connection,if any,between the two phenomena.这些实验的目的就是探索这两种现象之间的联系，如果存在着任何联系的话。

16 fixed   

adj.固定的，不变的，准备好的；(计算机)固定的

参考例句：

• Have you two fixed on a date for the wedding yet?你们俩选定婚期了吗？
• Once the aim is fixed,we should not change it arbitrarily.目标一旦确定，我们就不应该随意改变。

17 axis   

n.轴，轴线，中心线；坐标轴，基准线

参考例句：

• The earth's axis is the line between the North and South Poles.地轴是南北极之间的线。
• The axis of a circle is its diameter.圆的轴线是其直径。

18 longitude   

n.经线，经度

参考例句：

• The city is at longitude 21°east.这个城市位于东经21度。
• He noted the latitude and longitude,then made a mark on the admiralty chart.他记下纬度和经度，然后在航海图上做了个标记。

19 attains   

（通常经过努力）实现( attain的第三人称单数 )； 达到； 获得； 达到（某年龄、水平、状况）

参考例句：

• This is the period at which the body attains maturity. 这是身体发育成熟的时期。
• The temperature a star attains is determined by its mass. 恒星所达到的温度取决于它的质量。