The First Complete Chinese Theory of the Moon: The Innovations of LIU Hong c. A.D. 200

I am grateful for helpful comments and criticisms from Weixing Niu Sivin Nathan Swerdlow Noel and Taub Liba , who have seen material from various parts of this project. I remain responsible for all remaining errors and omissions.

I should also like to express my gratitude to SPACE.com Canada Inc. for the unsolicited gift of their desk-top astronomy software “Starry Night Pro”, which I have found extremely helpful in the course of this project. My unsystematic testing suggets that its retrodictions agree closely with the listings of lunar phases and solar and lunar eclipses from NASA websites such as Fred Espenak's http://sunearth.gsfc.nasa.gov/eclipse/eclipse.html, with which interested readers of this journal will no doubt be familiar.

Jin shu “History of the Jin dynasty” (c. A.D. 648, repr. Beijing, 1974), 17, 500.

Following a usage first proposed by Sivin Nathan , Cosmos and computation in early Chinese mathematical astronomy (Leiden, 1969), 7, n.l, I use the term “[astronomical] system” as my favoured translation of li (a word that may alternatively be written as ). There are times when the common translation “calendar” will do just as well, but it is generally not adequate to indicate to a modern reader the nature of the contents and function of a li. One of the basic meanings of li is “succession”, and I take advantage of this in some cases below to render li as “sequence” where this is more appropriate to the context than “system”.

The clearest and historically most aware account of the lunar inequalities known to me is to be found in Neugebauer O. , A history of ancient mathematical astronomy (Berlin, 1975), part 3, 1103–12. What counts as an inequality (or “anomaly” or “perturbation”) depends on what one's initial expectation of the “equal” motion of the Moon should be. In the ancient West, this was generally uniform motion with respect to the ecliptic. In ancient China around A.D. 100 the base expectation was of uniform motion of Moon (and Sun) with respect to the celestial equator, so that an initial “inequality” had to be dealt with to get to the Western starting position.

“Qian” here is the name of the masculine and heavenly principle which is paired with the feminine and earthly principle Kun in the cosmology of the Han commentaries on the Book of Changes Yi jing . This ancient text was a basic part of the intellectual heritage of Chinese thinkers in the time of Liu Hong. “Xiang” in this context has resonances that combine the notions of “phenomena” in the Greek sense with that of the existence of heavenly “counterparts” with things on Earth. Hence I have rendered it as “manifestation”. For non-sinologue readers, I will mention that an approximation to the correct pronunciation of the Chinese words represented in the official pinyin romanization as “Qian Xiang li” would be “cheeyen syang lee”.

For a more detailed introduction to such issues, see Cullen Christopher , Astronomy and mathematics in ancient China: The Zhou bi suan jing (Cambridge, 1996), chapter 1.

Detailed accounts of some these debates are to be found in Hanshu Hou “History of the Later [i.e. Eastern] Han dynasty” (A.D. 450, repr. Beijing, 1963), treatise 2, 3025–43. From Hou Han shu, treatise 3, 3082, it is clear that it was Liu Hong himself who compiled the collection of material on which this text draws. The complex background of the treatises now included in the Hou Han shu text is investigated in detail and with great clarity in The treatises of Later Han: Their author, sources, contents and place in Chinese historiography, by Beck Mansveldt B. J. (Leiden, 1990).

Jin shu 17, 503 has all these details.

Jin shu 17, 504–31.

Li Shi yi shu “Transmitted works of Mr. Li”; the material relating to astronomy is to be found in Zhongguo kexue jishu dianji tonghui “Compendium of classic Chinese texts on science and technology” (Henan Educational Press, 1995), Tianwen “Astronomy”, ii, 701 ff,.

Needham J. , Science and civilisation in China, iii (Cambridge, 1959), 390. Out of about 300 pages devoted to astronomy in this volume, mathematical astronomy in the sense that it is represented by such writers as Liu Hong is allotted only 19 pages.

Cullen , 'op. cit. (ref. 6).

Sivin , op. cit. (ref. 3).

The Sun's mean daily motion defines the unit of the du, which measures motion along a celestial great circle. Historians of Western astronomy usually take the inequality of the seasons as a rather obvious explanandum for any attempt at mathematicization of astronomy, and in that they are following the example of Ptolemy: See Almagest III.4, in Toomer G. J. (tr.), Ptolemy's Almagest (Princeton, 1998), 153–4. In China, however, the problem was not at all obvious, since observations of the precise instants of the equinoxes were not made as they seem to have been in the West: Interest was concentrated on the solstices, and it was at first assumed that the equinoxes were placed half-way between them. It was not until the sixth century A.D. that Zixin Zhang drew attention to the inequality: See Kiyoshi Yabuuchi Chûgoku no Temmon Rekihô “Chinese mathematical astronomy” (Tokyo, 1969), 308–9.

The sequential numbering of the sections of Liu Hong's text refers to my forthcoming translation.

Constants stated in this form are listed at the start of Liu Hong's text with their numerical values.

This equivalence had been the basis of intercalation procedures for several centuries before the time of Liu Hong, and is equivalent to the western Metonic cycle.

Both the tables given in this article have been slightly modified for ease of comprehension, as well as being rotated through ninety degrees. The + and — signs in the table represent words in the original such as “excess” or “deficit”, “add” or subtract”. Some minor annotations are not shown here.

In the original text the title of this section has been interchanged with that of Section 43 below. That section explains the movement of the Moon on the “Three Ways” (on the ecliptic, to the north of it and to the south), whereas this section clearly treats of the Moon's variations in speed.

It seems clear that the word yu “remainder” is a mistaken repetition from the previous sentence, since it is the whole days that should be counted off.

Ptolemy likewise decided that this effect was negligible in the course of his own discussion of the Moon's first inequality: See Almagest IV.6, p. 191 in Toomer's translation (ref. 14).

It is clear however that astronomers in his day were aware that different systems might need to use different positions for the solstice: But it was not yet seen as necessary or possible for a system to make provision for the position of the solstice to shift systematically.

Compare the discussion in Yabuuchi, op. cit. (ref. 14), 325ff., which begins the discussion no earlier than the Sui and Tang period (from c. A.D. 600).