Ling Xian(Mystical Laws)
《灵宪》
A monumental astronomic works，Ling Xian，translated as Mystical Laws is a distillation of the years of practice and theoretical research by Zhang Heng，a famous astronomer of the Eastern Han Dynasty.Dealing with such topics as the formation and structure of the heaven and earth and the cosmicevolvement as well as the nature and movement of celestial bodies，the book pro-moted the level of ancient China’s astronomical level to a new high and cast a pro-found impact on the following generations.
《灵宪》是东汉著名天文学家张衡积多年的实践与理论研究写成的一部天文巨著。该书全面阐述了天地的生成、宇宙的演化、天地的结构、日月星辰的本质及其运动等诸多重大问题，将中国古代的天文学水平提升到了一个新阶段，并对后世产生了深远的影响。
The astronomical achievements of Lang Xian are as follows:
《灵宪》的天文学成就如下:
First, Ling Xian discusses the origin and structure of the cosmos. In terms of the formation of the heaven and earth，Ling Xian believes that the heaven .the earth，and all the other things have their origins in primitive and chaotic yuanqi(vi-tality).ft further holds that，instead of staying permanently unchanged，the struc-ture of the cosmos is constantly developing. These views，basically, are similar to modern theories on the evolution of the cosmos.
第一，论述了宇宙的起源和宇宙的结构。关于天地的生成问题，《灵宪》认为天地万物是从原始的浑沌未分的元气发展来的。这种天体演化思想，是从物质运动的本身来说明宇宙的形成，认为宇宙结构不是亘古不变的，而是不断发展变化的。这些观点，与现代宇宙演化学说在基本原理上是相通的。
Second，based on the theory of sphere heavens，the book scientifically elabo-rates on the lunar eclipse.、。。explanation of the phenomenon，Zhang Heng wrote in the book“The moon itself is not luminescent, but rather reflecting the sunlight. The part of the moon where the sunlight fails to reach will not give out light. If the moon into the shadow of the earth，a lunar eclipse occurs.
第二，在浑天说的基础上，科学地阐述了月食的原因。张衡在《灵宪》中写道:“月光生于日之所照;魄生于日之所蔽。当日则光盈，就日则光尽也。”(大意为:月亮本身是不发光的，而是太阳光照射到月亮上，月亮才折射出光，太阳光照不到的地方则出现亏缺。如果月亮进人地影，就会发生“月食”。)
Third，in relation of the finity and infinity of the cosmos，Zhang Heng com-pared the heaven to an eggshell，and the earth to the egg yolk.Zhang Heng，however , did not believe the eggshell to be the boundary of the cosmos.He viewed the cosmos that people could see with the naked eye as limited while the part that could not be seen as infinite.
第三，宇宙的有限性和无限性。张衡把天比作一个鸡蛋壳，把地比作蛋壳中的鸡蛋黄，但他并不认为硬壳是宇宙的边界。张衡认为，人们目之所及的宇宙世界是有限的，但在人们目之所及之外的宇宙世界则是无限的。
Fourth，Zhang recorded his measurement of both the sun and the moon’s an-gular diameter,which is 1 /736 of the celestial sphere，or rather 29度21(or 29度21)，an absolute difference of 20from the modern average value of 31度5(or 31度5).Considering the scientific level and observatory conditions of over 2000 years ago，the number is fairly precise.
第四，张衡实测出日、月的角直径是整个周天的1/736，即29021，这与近代天文测量所得的日和月的平均角直径值3105，相比，绝对误差仅有2。由于2000多年前的科学技术水平及观测条件，这个数值可以说是相当精确的。
Fifth，based on his careful observation of the celestial bodies，Zhang Heng sorted out the various star charts made by his predecessors and re-established a new chart, recording the position of over 3,000 stars.
第五，张衡在认真观察天体的基础上，对前人留传下来的好几种星表作了整理、汇总，建立了恒星多达三千的新星表。
The last but not the least, concerning the movement of the five planets，Zhang worte:‘The sun,the moon and the flue planets all move in-between the heaven and earth rather than on the wall of the celestial sphere. Moreover the seven ce-lestial bodies move at different speeds.’
第六，关于五星的运动问题，张衡提出:日、月、五星是在天地之间运行，而非在天球壁上运行。并且，这七个天体运动的速度各不相同。
Ling Xian,is one of the most outstanding astronomic works in the history of ancient Chinese astronomy，represents a milestone in the development of Chinese astronomy. Its importance in the astronomical history is not lessened at all by its mistakes and shortcomings.
《灵宪》是中国古代天文学史上最杰出的天文学著作之一，也是中国天文学发展的一个里程碑。虽然其中还有一些错误和不足，但在天文学史上、的意义并不因此而逊色。