Huo Rong's Observation Programme of A.D. 102 and the Han Li Solar Table

The nearest approach so far is probably the series of separate writings brought together in Yabuuti Kiyosi , Chugoku no tenmon rekihō (Tokyo, 1969). The topic of mathematical astronomy was largely excluded from the treatment of Chinese astronomy in Needham Joseph Wang Ling , Science and civilisation in China, iii: Mathematics and the sciences of the heavens and of the earth (Cambridge, 1959).

Maeyama Yasukatsu , “On the astronomical data of ancient China (ca. −100 ∼ +200): A numerical analysis (Part I)”, Archives internationales d'histoire des sciences , xxv/xcvii (1975), 247–76; idem, “On the astronomical data of ancient China (ca. −100 ∼ +200): A numerical analysis (Part II)”, Archives internationales d'histoire des sciences, xxvi/xcviii (1976), 27–58.

Latour Bruno , Science in action: How to follow scientists and engineers through society (Cambridge, MA, 1987), 131.

For the original, see Hou Han shu “History of Eastern Han dynasty” by Ye Fan , c. A.D. 450; Beijing, 1963 edn, zhi 3 [the third section of the monograph on mathematical astronomy and harmonics], pp. 3077–8. This work originally lacked monographs of its own, but now incorporates those of the otherwise lost Xu Han shu “Extension of the Han History” of Sima Biao (c. A.D. 240 — c. 306). Two data in the original have been emended. The third figure in the seventh column from the left was 53 8/10 ke, which does not give 100 ke when added to the 46 8/10 ke in the day clepsydra column as required, nor is it consistent with the prescribed calculation; hence the emendation to 53 2/10 ke. The bottom figure in the extreme right-hand column was 14 11/12 (in the original conventionally worded as ‘15 weakened ruo [by 1/12]’), but for consistency with the clepsydra data the ruo should clearly be emended to shao ‘[with an addition] less than [half]’, thus giving 15 3/12 according to the usual conventions.

Maeyama , “Astronomical data (Part I)” (ref. 2), 247–8.

Ibid., 258.

For instance, the historical astronomical data used in this article are found directly from Starry Night Pro, which has high accuracy for the period in question.

Robson Eleanor , “Neither Sherlock Holmes nor Babylon: A reassessment of Plimpton 322”, Historia mathematica, xxviii (2001), 167–206, p. 168.

Maeyama , “Astronomical data (Part II)” (ref. 2), 34–36. Maeyama's value of 35° is about 0.3° too far north: See below.

This star marked the western beginning of the range of RA corresponding to the lodge Dipper.

This work has survived in quotations in an eighth-century A.D. compilation, the Kai yuan zhan jing “Kai yuan [reign period] divination canon”, compiled before 729 by Qutan Xida [Gautama Siddhartha], a member of a clan of Indian astronomers at the Tang court; reprinted Hunan, 1994.

Maeyama , “Astronomical data (Part 1)” (ref. 2), 249–50.

Hou Han shu 3082.

The Grand Inception system (Tai chu li) was the astronomical system whose basic constants had been in use since 104 B.C. It differed slightly from the Han li in a number of its constants, and, as can be seen here, the positions it gave for the sun at the 24 qi.

Shi guan; these were the working staff of the imperial observatory.

Hou Han shu 3026.

Hou Han shu 3028.

On the question of how the date of the solstices was determined, see below.

Hou Han shu 3057.

On the day of winter solstice at Luoyang, the umbra of an 80 cun gnomon (from sun's upper limb) is 128.7 cun and the end of the penumbra (from sun's lower limb) it extends a further 2.54 cun, just under 60 mm. However a three-day change in the sun's declination changes the length of noon shadow cast by the sun's centre by only about 0.18 cun or 4 mm. As shown below, the error in predicted winter solstices from A.D. 85 to 89 was about 1.75 days. This would not have produced any obvious difference in noon shadow. As Nakayama explains, increasing the accuracy of winter solstice determination requires careful observation over successive days (preferably with a larger gnomon) and the use of interpolation techniques: Nakayama Shigeru , A history of Japanese astronomy: Chinese background and Western impact (Cambridge, MA, 1969), 123–7. A method of this type was not used in China until the fifth century A.D.

Hou Han shu 3057.

We use mean solar midnight for convenience, which is appropriate enough since Han astronomers took all days to be of equal length.

Hou Han shu 3063.

Cullen Christopher , “Seeing the appearances: Ecliptic and equator in the Eastern Han”, Studies in the history of natural sciences, xix (2000), 352–82.

Hou Han shu 3028–30; see the translation in Cullen, op. cit., 359–63.

One is reminded here of what David Brown has written in the context of ancient Mesopotamian astronomy: One of the advantages of schematic predictions of celestial motions is that they automatically generate portents through their divergence from what is actually observed. Brown David , Mesopotamian planetary astronomy-astrology (Groningen, 2000), 146–56.

Cullen , “Seeing the appearances” (ref. 24), 371–9.

Hou Han shu 3073.

Ecliptic extensions of the lodges are first listed in Jia Kui's memorial, Hou Han shu 3029–30. An identical list is repeated at Hou Han shu 3075, preceded by a list of equatorial extensions. The latter gives ‘leads and lags’ for each lodge identical to those found in the main solar table discussed here.

Hou Han shu 3076. The process by which it was decided that day-length depended directly on solar north polar distance is discussed below.

The figures given here relate to the day on which the true winter solstice fell in A.D. 102, which was December 22. As we shall see below, the Han astronomical system in use in A.D. 102 took December 24 of that year as winter solstice, on which the sun rose at 07:11 and set at 16:56. The difference is not significant for our purposes.

Hou Han shu 3076.

Hou Han shu 3076.

In this context, the reference is apparently to some astronomical system known in the Eastern Han but not officially used; the only other mention of it in a similar context is by Zhang Heng around A.D. 130: See Cullen , “Seeing the appearances” (ref. 24), 370.

As the modern editors note, the end of this quotation seems garbled in some way; the last twenty words of this translation (after “sundial shadow”) are therefore somewhat tentative, although the overall sense is clear enough.

This view of the origin of the table is also given by the author of the monograph on mathematical astronomy and harmonics in the Song shu “History of the [Liu] Song dynasty (A.D. 420–479)” by Shen Yue, A.D. 488 (monographs added after A.D. 500); Beijing, 1974 edn, 229. I owe this reference to Professor Shi Yunli (private communication).

Hou Han shu 3057.

To do this, we have to assume that the programme of observation began before the formal memorial that launched the investigation officially. That memorial can have been no earlier that the first day of “the fourteenth year of the Yongyuan period”, which was 6 February A.D. 102. But since Huo Rong would hardly have sent in his memorial without a great deal of preliminary investigation, this is not at all implausible.

This may easily be done using the Excel spreadsheet method I have described in Cullen C. , “Translating ancient Chinese astronomical systems with Excel: How not to stew the strawberries?”, Journal for the history of astronomy, xxxvi (2005), 336–8. see also the webpage at http://www.nri.org.uk/lifa.html for a downloadable version.

The modern city of Luoyang is some distance from the capital city of the Eastern Han dynasty, and it is likely that observations would have been made at the astronomical observatory, ling tai on the southern outskirts of the ancient city. The most detailed archaeological map available to me shows the ling tai as about 1km to the south of the Luo river, about 9km to the east of the modern city, with latitude and longitude approximately 34.70°N, 112.63°E. See Dianli Liu (ed.), Luoyang shi zhi “History of Luoyang”, xiv (Zhengzhou, 1995), 36.

The greatest error introduced by this procedure would have occurred near the equinoxes, when the sun's NPD can change by about 0.2° in twelve hours. The maximum effect would have been produced only if the qi inception had fallen at or near midnight.

As Professor Shi Yunli has noted (private communication), an error of 0.73° is consistent with errors in polar altitude known to have been tolerated by Han astronomers. See for instance the value of 36 du (35.48°) given by Zhang Heng (c. A.D. 130), quoted in Kai yuan zhan jing 1, 3. This is an overestimate of about 0.78° for the likely location of the Luoyang observatory in latitude 34.7°, where Zhang Heng is known have held office twice as director of the Han astronomical establishment. Setting the polar axis of an armillary sphere too high will of course reduce the values of solar NPD obtained by observation, which is what seems to have happened here.

Kuhn Thomas S. , The structure of scientific revolutions (Chicago and London, 1970), 150–2.