The Provenance of Early Chinese Records of Large Solar Eclipses and the Determination of the Earth’s Rotation

Abstract

An analysis of the tracks of total and annular solar eclipses crossing China reveals that most of the reports of such eclipses in the treatises in the dynastic histories from 206 bc to ad 1368 were very probably recorded at the capital by the court astronomers. Some of the reports in the annals, on the other hand, could only have been based on observation if they originated from outside the capital, and in some cases from remote regions of China. Particular attention is paid to the eclipse of ad 454, which has importance for delineating the behaviour of the Earth’s rotation parameter ∆T.

Keywords

Chinese eclipses Earth rotation

Introduction

Historical records of the occurrence of large solar eclipses provide a vital data set for the determination of changes in the Earth’s past rate of rotation (Stephenson et al.).¹ Ancient records from China constitute the major part of this dataset before ad 800. In this article, we investigate the provenance of the Chinese records of large solar eclipses, using our recent solution for the Earth’s rotation to fix the tracks of totality relative to the Chinese capital of the time. We then explore which (if any) of the Chinese descriptive records from various sources best match these predictions. The most reliable and consistent subset of these data are then given greater weight when they are included in the revised derivation of changes in the Earth’s rate of rotation.

Care needs to be taken to avoid circularity in this methodology: eclipse observations are used to predict the behaviour of the Earth’s rotation, which in turn is used to select the most ‘reliable’ eclipse records. Two important factors mitigate against this potential shortcoming:

Independent observations of eclipses from Babylon and Greece have much greater weight than those of China before ad 200 in predicting the behaviour of the Earth’s rotation. The period most prone to circularity is around ad 200–500, where only Chinese observations are available, apart from a set of three Greek (timed) observations in ad 364. This problem is addressed in section “Implications for the behaviour of ∆T in the period −197 to +1292.”

In this article, we are principally concerned with a comparative study of the internal consistency of records of eclipses originating from different sources in China.

Early Chinese history is replete with records of solar eclipses (as well as accounts of other celestial phenomena). One of the principal reasons for observing these events and recording the observations was their perceived astrological importance. There are very few reliable Chinese records of solar eclipses prior to the late 8th century bc. However, an important set of 36 very early solar eclipse observations (along with occasional references to comets and meteors), covering the interval from 722 bc to 481 bc, is to be found in the Chunqiu (“Spring and Autumn Annals”). This work is a chronicle of the state of Lu, the home of Confucius. Over the next three centuries or so (largely encompassing the Warring States Period), until the start of the Former Han dynasty, astronomical records of any kind are fairly sporadic.

Over many centuries, from the beginning of the Former Han dynasty in 206 bc to the end of the Yuan dynasty in ad 1368, the main source of Chinese astronomical records (including eclipses) is the official dynastic histories. However, in later dynasties (the Ming and Qing), celestial observations are included in a variety of sources—such as the Ming shilu (“Veritable records of the Ming”) and Qing shilu (“Veritable records of the Qing”), in addition to the official histories, and also numerous chronicles of individual states. In the present article, we have restricted our attention to the observations of solar eclipses recorded in the Chinese dynastic histories, which were described as total or unusually large. In our study of the Earth’s rotation using these data, the proximity of the observer to the belt of totality is crucial in fixing the rotational phase of the Earth on the date of an eclipse. Observations which were simply recorded as ‘eclipse’ cannot be used in our studies of the Earth’s past rotation because the penumbral shadow on the Earth covers a wide area, and, without any further qualification, we cannot say where the observer was in relation to the comparatively narrow belt of totality.

The detailed Chinese records of eclipses in the period 198 bc to ad 761 form an important data set in studies of the Earth’s past rotation before about ad 800. Their reliability is the focus of this investigation. After ad 800, Arab and European observations become paramount.

Annals and treatises

In the official dynastic histories, there are two main sources of solar eclipse reports: the imperial annals (benji), which cover the first chapters of a history and the “treatise on astronomy” (tianwenzhi) or the “treatise on the five phases” (wuxingzhi). Not every dynastic history contains a treatise of specific relevance to the present paper. Treatises are absent in several dynastic histories, notably the Sanguozhi (“Records of the Three Kingdoms”), Liangshu (“History of the Liang dynasty”), Chenshu (“History of the Chen dynasty”), Nanshi (“History of the Southern Dynasties”) and Liaoshi (“Liao dynasty”).

Although most of the solar eclipse records in the dynastic histories merely mention the occurrence of an eclipse on a specific date, a small—but significant—proportion give additional details. Such information sometimes includes whether an eclipse was “total” (ji) or “almost complete” (jijin). Dual reports of most eclipses are found in both the annals and appropriate treatise of a dynastic history. However, the descriptions of the same large eclipses in both annals and treatises are frequently in discord.

The question arises as to why there are differences in the reports of the same event. First, there is good reason to assume that the accounts of eclipses (and other celestial phenomena) in the various treatises are based on the observations of the imperial astronomers at the appropriate capital. Many of the reports in these works contain technical details: for instance, the position of the Sun at a solar eclipse in relation to the equatorial reference system of 28 unequal lodges (xiu) into which the circuit of the heavens was divided (the right ascension (RA)) to the nearest degree (du); or detailed descriptions of the motion of a comet through the constellations and estimates of the length of its tail. Close conjunctions of the Moon with planets or stars are also frequently noted in the treatises. By comparison, such details are extremely rare in imperial annals.

However, an intriguing exception to this general rule occurs in the Tang dynasty (ad 618 to 907). There are two official Tang histories: The Jiu Tangshu (“Old History of the Tang dynasty”) and the Xin Tangshu (“New History of the Tang dynasty”). The Old History was compiled between ad 940 and 945, soon after the end of the Tang dynasty. About a century later (ad 1043–1060), it was felt desirable to compile a New History. Several of the solar eclipse records in the annals of the Old History contain astronomical information which is absent in the annals of the New History. For example, the Jiu Tangshu annals specifically state that in ad 702, the eclipse was “not complete and like a hook”, adding that “it was seen at the capital and in the four directions”. Comments on the appearance of the Sun (“like a hook”) occur in the annals of the Old History in both ad 729 and 754. Such descriptive details are absent in the annals of the New History; the brief eclipse records here are typical of those in the annals of other dynastic histories.

Dubs² in his discussion of the solar eclipse records in the Hanshu (206 bc to ad 23) compared the reports of the eclipses in 188 bc and 28 bc in both the treatise (chapter 27) and the annals (chapters 2 and 10). He noted that whereas in the treatise the eclipses were described as “almost complete” and “like a hook”, the annals state that the eclipse was “total”. Using the preliminary eclipse tables, which were available at the time, Dubs computed the magnitudes of the two eclipses at the Han dynasty capital of Chang’an and concluded that “The statement in the annals that the eclipse was total must have been taken from the report of places outside the capital.”

Dubs focused on the eclipses in the Former Han dynasty. In the present article, we revise Dubs’ work and extend our investigation to the end of the Yuan dynasty. Using our studies on Earth’s past rotation (Stephenson et al.³), we are able to accurately compute the local circumstances of any eclipse at any particular place as far back as about 700 bc. This has provided us with an opportunity to intercompare the dual accounts of specific solar eclipses in both the treatises and annals of a dynastic history.

In all, we have investigated reports of 35 solar eclipses, which were described as total or nearly total from the start of the Former Han dynasty (206 bc) to the end of the Yuan dynasty (ad 1368). These are listed in Table 1 with both the bc/ad and algebraic numbering of the year. These systems of date nomenclature are used interchangeably in this article.

Table 1.

Large solar eclipses reported in Chinese dynastic histories −197 to +1292.

FORMER HAN DYNASTY					CHEN DYNASTY
198	bc	−197	Aug	7	ad	562	+562	Oct	14
188	bc	−187	Jul	17	SUI DYNASTY
181	bc	−180	Mar	4	ad	616	+616	May	21
147	bc	−146	Nov	10	TANG DYNASTY
89	bc	−88	Sep	29	ad	702	+702	Sep	26
80	bc	−79	Sep	20	ad	729	+729	Oct	27
35	bc	−34	Nov	1	ad	754	+754	Jun	25
28	bc	−27	Jun	19	ad	756	+756	Oct	28
2	bc	−1	Feb	5	ad	761	+761	Aug	5
ad	2	+2	Nov	23	ad	822	+822	Apr	25
LATER HAN DYNASTY					ad	879	+879	Apr	25
ad	65	+65	Dec	16	ad	888	+888	Apr	15
ad	120	+120	Jan	18	(NORTHERN) SONG DYNASTY
THREE KINGDOMS (SANGUO) PERIOD					ad	977	+977	Dec	13
ad	243	+243	Jun	5	LIAO DYNASTY
JIN DYNASTY					ad	1005	+1005	Jan	13
ad	306	+306	Jul	27	ad	1122	+1122	Mar	10
ad	360	+360	Aug	28	(LATER) JIN DYNASTY
LIU SONG DYNASTY					ad	1214	+1214	Oct	5
ad	429	+429	Dec	12	(SOUTHERN) SONGDYNASTY
ad	454	+454	Aug	10	(SOUTHERN) SONGDYNASTY
LIANG DYNASTY					ad	1275	+1275	Jun	25
ad	516	+516	Apr	18	YUAN DYNASTY
ad	522	+522	Jun	10	ad	1292	+1292	Jan	21

Chinese calendar and dating of eclipses

Commencing with the Former Han dynasty, there are frequent solar eclipse records in Chinese history. The date of each event—in both the imperial annals and the treatises— follows a standard pattern: year of the appropriate imperial reign period, lunar month, day of the sexagenary cycle, day of the lunar month (almost invariably the first or last day). To give an example, the eclipse of −180 is reported as occurring in the “7th year of Empress Lu, first lunar month, day jichou, the last day of the month”. The day jichou was the 26th day of the appropriate 60-day cycle. When this date is converted to the Julian calendar, it corresponds to −180 March 4, which is precisely the date on which modern computation indicates that a large solar eclipse was visible in China. Such accord between historical and astronomical dating is typical of almost all Chinese eclipse records; exceptions are rare. The few instances where we find significant discord between the recorded date and our computed date (other than due to minor copying errors in the cyclical day) will be discussed in “Discussion of individual eclipse records −197 to +1292.”

Places of observation and historical background

Fortunately, in the early centuries, and again between about ad 600 and 900, the history of China (as relevant for the present purpose) was fairly uncomplicated. Chang’an was the capital from 206 bc until ad 23 (the Former Han dynasty), which covers the first 10 eclipses in our list. For the next four eclipses (down to ad 306), the capital was Luoyang (from the Later Han dynasty to midway through the earlier Jin dynasty). In ad 316, Luoyang was captured by invaders from the north-west and soon afterwards (in ad 317) Jiankang, far to the south-east, became the new capital; this continued through several short dynasties (Liu Song, Qi, Liang and Chen) in southern China until ad 589, when the Sui dynasty unified China. For much of the intervening period of more than two centuries, the north of China was ruled independently by the Wei, with its capital at the former Jin metropolis of Luoyang. Although several eclipses are reported in Weishu, (the official history of the Wei dynasty), none of these appear to have been particularly large (Table 2).

Table 2.

Place coordinates.

	N (°)	E (°)
Chang’an (Han dynasty)	34.35	108.88
Luoyang	34.75	112.47
Daxing	34.27	108.90
Guangling	32.45	119.45
Jiankang	32.06	118.79
Chang’an (Tang dynasty)	34.27	108.90
Kaifeng	34.72	114.40
Linan	30.25	120.17
Dadu (Zhongtu)	39.92	116.42
Dading^a	41.7	118.8

Coordinates interpolated in the charts of Hermann.⁴

At the beginning of the Sui dynasty, in ad 589, the Sui capital was Daxing, but on the death of the first emperor in ad 605, the capital was moved to Luoyang. This was a very turbulent period, and unity was not established until the Tang dynasty, which lasted from ad 618 to 907. The Tang capital was Chang’an, a few kilometres to the south of the Han city of the same name. Apart from a brief period between ad 756 and 757, when the emperor had to flee to the north-west because of a rebellion, Chang’an remained the capital until the end of the Tang dynasty; there are six Tang records of large solar eclipses—from ad 702 to 888.

From the point of view of eclipses, the period after ad 907 is again complex. The Tang dynasty was followed by a turbulent period known as the Wudai (“Five dynasties”), which lasted until ad 960. There are no records of large solar eclipses during this brief interval. Although the Song dynasty ruled from ad 960 to 1279, in ad 1127 the northern half of China was annexed by the Jin dynasty, which ruled mainly from the former Song capital of Kaifeng, while the Song transferred their capital to Linan (modern Hangzhou) in the far south.

Only a single large eclipse of the Sun is recorded in Jin history (in ad 1214). The Jin dynasty lasted until ad 1234, when it fell to the Mongols. For a while, from the early 10th century until ad 1125 the Liao, a semi-nomadic kingdom existed in the extreme north of China. Dading was the central residence of the Liao emperors, although other cities held the role of capital at this period. Two large solar eclipses are recorded in the Liaoshi annals. Soon after the total eclipse of ad 1275 (for which detailed records exist in the Songshi), the Mongols finally conquered the whole of China, establishing the Yuan dynasty with its capital at Dadu (Beijing). The Yuan dynasty lasted until ad 1368.

Discussion of individual eclipse records −197 to +1292

For each eclipse, we reproduce the report in the treatises and annals, as appropriate, together with the computed central magnitude at greatest phase. The accompanying maps show the path of the umbral shadow across the Earth’s surface and the location of the appropriate capital.

The times, associated quantities and locations on the Earth of the umbral shadow have been calculated using our own software based on the Besselian plane method as described in The Explanatory Supplement.^5,6 The basic coordinates of the Sun and Moon are from the Jet Propulsion Laboratory’s long-term ephemerides DE 431 (Folkner et al.⁷) and their apparent places uses the algorithm that is given in The Explanatory Supplement⁸ together with routines from the Standards Of Fundamental Astronomy.⁹ The correction to the rotational phase of the Earth is determined by the value of ∆T taken from our paper Historical Changes in UT/lod from Eclipses.¹⁰

−197 August 7 (Annular; central magnitude 0.95 ): Chang’an (Former Han dynasty)

Hanshu treatise [27]:

The Sun was eclipsed; it was total; it was 13° in (the lodge) Zhang.

Hanshu annals [1]:

The Sun was eclipsed.

Although this eclipse was annular, the report in the treatise describes it as “total”. We presume that at this period there was not a separate term for a central annular eclipse. In fact, not until as late as ad 1292 do we find a clear description of an annular solar eclipse: “the Sun was like a golden ring”. Thus, it seems reasonable to assume annularity at the Chinese capital of Chang’an. From the plot of the track, the eclipse was fully annular (magnitude 0.95) at Chang’an, in agreement with the treatise report. In contrast, the Hanshu annals merely note the occurrence of a solar eclipse. (NOTE: In a considerable number of records, we are told the position of the Sun in the lodge system. The positions given often correspond quite closely to the results of modern calculation, but they seem more likely to have been the result of calculation by the ancient Chinese astronomers rather than of direct measurement, given the limitations of available instrumentation and the difficulty of observation under eclipse conditions.)

−187 July 17 (Total; 1.02): Chang’an (Former Han dynasty)

Hanshu treatise [27]:

The Sun was eclipsed; it was almost complete. It was at the beginning of (the lodge) Qixing.

Hanshu annals [2]:

The Sun was eclipsed; it was total.

From the plot, the track of totality passed to the south of Chang’an. During maximum phase at Chang’an, 7% of the Sun’s diameter remained visible, thus agreeing with the treatise “almost complete”, but at variance with the annals “total”.

−180 March 4 (Total; 1.04): Chang’an (Former Han dynasty)

Hanshu treatise [27]:

The Sun was eclipsed; it was total; it was 9° in (the lodge) Yingshi, which represents the interior of the Palace chambers. At that time the (Dowager) Empress of Gao[-zu] was upset by it and said, ‘This is on my account’. The next year it was fulfilled. [The Empress Dowager died nearly 18 months after the eclipse.]

Hanshu annals [3]:

The Sun was eclipsed; it was total.

The plot shows that the eclipse was total at Chang’an, in agreement with both accounts.

−146 November 10 (Total; 1.01): Chang’an (Former Han dynasty)

Hanshu treatise [27]:

Emperor Jing, 3rd year of the Zhongyuan reign period, 9th month, day wuxi [35], the last day of the month. The Sun was eclipsed; it was almost complete. It was 9° in (the lodge) Wei.

Hanshu annals [5]:

The Sun was eclipsed.

The date, as found in the treatise is correct. But the Hanshu annals incorrectly give the date as the 4th year of the Zhongyuan reign period, 10th month, day wuwu [55]. This date corresponds to −145 November 30, on or near which no eclipse was visible in China. The plot shows the track in the north of China. Almost a quarter of the Sun’s diameter remained at maximum phase, slightly at variance with the treatise “almost complete”.

−88 September 29 (Annular-Total; 1.00): Chang’an (Former Han dynasty).

Hanshu treatise [27]:

The Sun was eclipsed; it was not complete and like a hook. It was 2° in (the lodge) Kang … it recovered before sunset.

Hanshu annals [6]:

The Sun was eclipsed.

The plot shows the track in the south of China. At Chang’an, about a 10th of the Sun’s diameter (magnitude 0.91) remained at maximum phase. This is in accord with the treatise “not complete and like a hook.” By comparison, the annals merely note the occurrence of an eclipse. This is the earliest known record which describes the partially eclipsed Sun as “like a hook”. In later years, this expression was frequently used in reports of partial eclipses.

−79 September 20 (Total; 1.02): Chang’an (Former Han dynasty)

Hanshu treatise [27]:

The Sun was eclipsed; it was almost complete. It was 20° in (the lodge) Zhang.

Hanshu annals [7]:

The Sun was eclipsed; it was total.

Almost a fifth of the Sun’s diameter (magnitude 0.79) remained at maximum phase. This is slightly at variance with the report “almost complete”, but at odds with “total” in the annals.

−34 November 1 (Annular; 0.99): Chang’an (Former Han dynasty)

Hanshu treatise [27]:

Emperor Yuan, Jianzhao reign period, 5th year, 6th month, day renshen [9], the last day of the month. The Sun was eclipsed; it was not complete and like a hook; then it set.

Hanshu annals [9]:

The Sun was eclipsed.

The date in both the treatise and annals is in error. It corresponds to −33 August 23, but no eclipse was visible on that date. It is very likely that the records refer to −34 November 1, since from the plot of the track it is seen that the Sun set eclipsed, which is in agreement with the statement “then it set”. About a fifth of the Sun remained at maximum phase, which agrees with the statement “not complete and like a hook”. The annals simply note the occurrence of an eclipse.

−27 June 19 (Total; 1.07): Chang’an (Former Han dynasty)

Hanshu treatise [27]:

The Sun was eclipsed; it was not complete and like a hook; it was 6° in (the lodge) Dongjing. When the eclipse first began, it started from the south-west.

Hanshu annals [10]:

The Sun was eclipsed; it was total.

At maximum phase in Chang’an, about 8% of the Sun’s diameter remained. This is in good agreement with the treatise “not complete and like a hook”, but at variance with the annals “total”.

−1 February 5 (Annular-Total; 1.00): Chang’an (Former Han dynasty)

Hanshu treatise [27]:

The Sun was eclipsed; it was not complete and like a hook. It was 10° in (the lodge) Yingshi.

Hanshu annals [11]:

The Sun was eclipsed.

At maximum phase in Chang’an (magnitude 0.85), 15% of the Sun’s diameter remained, in good agreement with the Hanshu treatise “not complete and like a hook”. The track of totality was very narrow. The annals are not specific on the magnitude of the eclipse.

+2 November 23 (Annular-Total; 1.00): Chang’an (Former Han dynasty)

Hanshu treatise [27]:

The Sun was eclipsed; it was total.

Hanshu annals [12]:

The Sun was eclipsed.

This eclipse is similar to that of −1 February 5, with a very narrow track of totality, and it is unlikely that it was seen as total anywhere in the vicinity of Chang’an. At Chang’an, nearly a tenth of the Sun’s diameter was unobscured at maximum phase, in contradiction to the treatise “total”, whereas the report in the annals is not specific. This is one of the few eclipses wrongly described in the treatises (see section “Implications for the behaviour of ∆T in the period −197 to +1292”).

+65 December 16 (Total; 1.02): Luoyang (Later Han dynasty) or Guangling?

Houhanshu treatise [28]:

The Sun was eclipsed; it was total; it was 11° in (the lodge) (Nan) Dou.

Houhanshu annals [2]:

The Sun was eclipsed; it was total.

Both the treatise and the annals assert that his eclipse was total. However, at the capital Luoyang, 5% of the Sun remained at maximum phase. As with the preceding eclipse (year +2), this is a rare instance where the report in the treatise is in error (see section “Implications for the behaviour of ∆T in the period −197 to +1292”).

+120 January 18 (Total; 1.03): Luoyang (Later Han dynasty)

Houhanshu treatise [28]:

The Sun was eclipsed. It was almost complete; on Earth it was like evening. It was 11° in (the lodge) Xunu.

Houhanshu annals [5]:

The Sun was eclipsed; it was total.

The record in the Houhanshu treatise agrees with the fact that Luoyang was just outside the track of totality (magnitude 0.99). Presumably, the report of totality in the annals originated from outside the capital.

+243 June 5 (Annular; 0.94): Luoyang (Three Kingdoms, Sanguo period)

Jinshu treatise [12]:

The Sun was eclipsed.

Sanguozhi annals [4]:

The Sun was eclipsed; it was total.

There is no treatise on astronomy in the Sanguozhi, but the Jinshu treatise contains astronomical records from the Wei kingdom (capital Luoyang) during the Sanguo period (ad 220 to 265). The eclipse was definitely not total at Luoyang: about a third of the Sun’s diameter was visible (magnitude 0.64) at maximum phase; the eclipse would only have been annular in the extreme north-west of China (outside the boundary of our plot). (Note: There is a minor dating error in the cyclical day in the treatise.)

+306 July 27 (Annular; 0.94): Luoyang (Jin dynasty)

Songshu treatise [34]:

The Sun was eclipsed; it was total.

Jinshu treatise [12]:

The Sun was eclipsed.

Jinshu annals [4]:

The Sun was eclipsed.

The plot shows a central annular eclipse (magnitude 0.94), in agreement with the report of totality in the Songshu treatise. The Songshu, which is much concerned with Jin as well as Song history, was compiled in ad 492/3, about 150 years before the Jinshu was compiled (ad 644). Hence, the Songshu may contain information which had been lost by the time the Jinshu was compiled.

+360 August 28 (Annular; 0.93): Jiankang (Jin dynasty)

Songshu treatise [34]:

The Sun was eclipsed. It was not complete and like a hook.

Jinshu treatise [12]:

The Sun was eclipsed; it was almost complete and was in (the lodge) Jiao.

Jinshu annals [8]:

The Sun was eclipsed; it was total.

The plot shows that Jiankang was just to the north of the track of annularity, in accord with the Songshu and Jinsh treatises, but not the annals.

+429 December 12 (Total; 1.03): Jiankang (Liu Song dynasty)

Songshu treatise [34]:

The Sun was eclipsed; it was not complete and like a hook. During the eclipse stars were seen. At the hour of fu (= 15 hours -17 hours), then it disappeared. In Hebei province the Earth was in darkness.

Songshu annals [5]:

The Sun was eclipsed.

Nanshi annals, section on Song annals [2]:

The Sun was eclipsed; stars were seen by day.

At maximum phase in Jiankang 6% of the solar diameter remained visible. (The magnitude is not sensitive to the precise value of ∆T in this case). “Stars seen” could only have been Venus and Jupiter. The Nanshi (“History of the Southern Dynasties”) covers the Song, Nanqi, Liang and Chen dynasties, which existed in South China from ad 420 to 589. It was compiled between ad 630 and 650—150 years or so after the Songshu was compiled. Since only the Nanshi annals mentions “stars seen by day”, the report probably came from the Hebei region (to the north of Jiankang), where the eclipse was reported as being total in the Songshu treatise.

+454 August 10 (Total; 1.04): Jiankang (Liu Song dynasty)

Songshu treatise [34]:

The Sun was eclipsed; it was total; all the constellations (i.e. the lodges) were brightly lit.

Songshu annals [6]:

The Sun was eclipsed.

Nanshi annals, section on Song annals [2]:

The Sun was eclipsed; it was total.

There is no doubt from the report in the treatise that Jiankang was actually in, or at least on the very edge of the track of totality.

The Songshu treatise also records a total eclipse on a date corresponding to +453 August 20. The record states that “The Sun was eclipsed it was total and all the stars were seen”. No eclipse was total in China for several years around this time, apart from that of +454 August 10. It is noteworthy that the date of the non-event in +453 (which is also reported in the annals of the Songshu and Nanshi, but without any mention of magnitude or the visibility of stars) is exactly 12 lunar months prior to the date of the eclipse of +454. Hence, it may reasonably be concluded that the earlier records represent misplaced reports of the total eclipse of +454.

+516 April 18 (Annular; 0.938): Jiankang (Liang dynasty)

Liangshu annals [2]:

The Sun was eclipsed.

Nanshi, section on Liang annals [6]:

The Sun was eclipsed; it was total.

This eclipse reached a computed magnitude of 0.93 at Jiankang, which was very close to the edge of the wide zone of annularity. It is unfortunate that neither the Liangshu nor the Nanshi contains a treatise, which might have resolved the issue of whether or not it was central at Jiankang.

+522 June 10 (Total; 1.07): Jiankang (Liang dynasty)

Liangshu annals [3]:

The Sun was eclipsed; it was total.

Nanshi annals [7]:

The Sun was eclipsed; it was total.

This eclipse reached a computed magnitude of 0.99 at Jiankang, which was close to the edge of the wide zone of totality. Once again, it is unfortunate that neither the Liangshu nor the Nanshi contains a treatise.

+562 October 14 (Annular; 0.98): Chang’an (Northern Zhou dynasty) or Jiankang (Chen dynasty)

Suishu treatise [21]:

The Sun was eclipsed; it was total.

Zhoushu annals [5]:

The Sun was eclipsed.

Beishi annals, section on Zhou annals [10]:

The Sun was eclipsed.

Chenshu annals [3]:

The Sun was eclipsed.

Nanshi annals, section on Chen annals [9]:

The Sun was eclipsed.

The entry in the Suishu treatise is a retrospective entry for the Northern Zhou dynasty. The eclipse was central in the Vietnam region, but reached a magnitude of only 0.33 at Chang’an (and 0.31 at Jiankang). The zone of annularity extended no further than latitude 17°Ν—far to the south of China. The source of the Suishu record of a total eclipse is thus obscure.

+616 May 21 (Annular; 0.97): Luoyang ? (Sui dynasty)

Suishu treatise [21]:

The Sun was eclipsed; it was total.

Suishu annals [4]:

The Sun was eclipsed; it was total.

Beishu annals [12]:

The Sun was eclipsed; it was total.

Although this eclipse was consistently reported as total, there is some doubt as to the place of observation due to several major rebellions around this time. As is clear from the plot of the track, it was not central at Daxing nor Luoyang.

+702 September 26 (Total; 1.03): Chang’an (Tang dynasty)

Xin Tangshu treatise [32]:

The Sun was eclipsed; it was almost total; it was in the first degree of (the lodge) Jiao.

Xin Tangshu annals [4]:

The Sun was eclipsed.

Jiu Tangshu annals [6]:

The Sun was eclipsed; it was not complete and like a hook. It was seen at the capital and in the four directions.

The eclipse was not total at the capital, reaching a magnitude of 0.97 there. This is in accord with the plot of the track and supports the records in both the Xin Tangshu treatise and the Jiu Tangshu annals. The detail in the Jiu Tangshu annals [6] is unusual. Not only does the report clearly describe a large partial eclipse, but it also asserts that the eclipse (evidently partial) was seen at both the capital and in the provinces. As shown in the plot, the provincial locations to the south and west of Chang’an experienced a partial eclipse.

+729 October 27 (Total; 1.05): Chang’an (Tang dynasty)

Xin Tangshu treatise [32]:

The Sun was eclipsed; it was not complete and like a hook. It was 9° in (the lodge) Di.

Jiu Tangshu treatise [36]:

The Sun was eclipsed.

Xin Tangshu annals [5]:

The Sun was eclipsed.

Jiu Tangshu annals [8]:

The Sun was eclipsed; it was like a hook.

This eclipse was not total at the capital, reaching a magnitude of 0.91 there. This is in accordance with the reports in both the Xin Tanshu treatise [32] and the Jiu Tangshu annals [8]. Once again (as in +702), there is no inconsistency between the description in the Xin Tangshu treatise and the Jiu Tangshu annals, other than the note of the RA of the Sun as cited in the treatise.

+754 June 25 (Total; 1.03): Chang’an (Tang dynasty)

Xin Tangshu treatise [32]:

The Sun was eclipsed; it was almost total; it was 19° in (the lodge) Dongjing.

Jiu Tangshu treatise [36]:

The Sun was eclipsed.

Xin Tangshu annals [5]:

The Sun was eclipsed.

Jiu Tangshu annals [9]:

The Sun was eclipsed; it was not complete and like a hook.

The computed eclipse magnitude at Chang’an was 0.84, which is in accord with both the reports of a large partial eclipse in the Xin Tangshu treatise and the Jiu Tangshu annals.

+756 October 28 (Total; 1.02): Chang’an (Tang dynasty)

Xin Tangshu treatise [32]:

The Sun was eclipsed; it was total; it was 10° in (the lodge) Di.

Jiu Tangshu treatise [36]:

The Sun was eclipsed.

Xin Tangshu annals [6]:

The Sun was eclipsed.

Jiu Tangshu annals [10]:

The Sun was eclipsed; it was total.

As noted in section “Places of observation and historical background,” there is doubt as to the place of observation of this eclipse. On account of the An Lushan rebellion and capture of Chang’an early in +756, the Tang Emperor Suzong and his court had fled to north-west China. They were unable to return to Chang’an until the following year. Computation reveals that this eclipse was total in the far north-west of China—see eclipse map. This temporary relocation of the court could be the origin of the “total” reports in the Xin Tangshu treatise and Jiu Tangshu annals.

+761 August 5 (Total; 1.05): Chang’an (Tang dynasty)

Xin Tangshu treatise [32]:

The Sun was eclipsed; the large stars were all seen; it was 4° in (the lodge) Zhang.

Jiu Tangshu treatise [36]:

The Sun was eclipsed; the large stars were all seen. The Astronomer Royal, Qutan, reported (to the emperor): “The Sun diminished. Precisely after 6 marks (ke) in the hour of chen the loss began; at 1 mark in the hour of si it was total; at 1 mark before the hour of wu it was restored to fullness. It was 4° in (the lodge) Zhang.”

Xin Tangshu annals [6]:

The Sun was eclipsed

Jiu Tangshu annals [10]:

The Sun was eclipsed; the large stars were all seen.

Both the treatises and the annals assert that this eclipse was total at the capital of Chang’an. The account in the Jiu Tangshu treatise, quoting the report of the Astronomer Royal is especially detailed.

+822 April 25 (Total; 1.07): Chang’an (Tang dynasty)

Xin Tangshu treatise [32]:

The Sun was eclipsed; it was 13° in (the lodge) Wei.

Jiu Tangshu treatise [36]:

The Sun was eclipsed; it was 12° in (the lodge) Wei. It was not complete by one quarter. In (the regions of) Yan and Zhao it was seen to be total.

Xin Tangshu annals [8]:

The Sun was eclipsed.

Jiu Tangshu annals [16]:

The Sun was eclipsed.

Only the Jiu Tangshu treatise mentions the magnitude of this eclipse, although the computed magnitude at Chang’an was 0.94, the recorded magnitude is very much underestimated. (Note: The difference is only 1° between solar RA as recorded in the Xin Tangshu and the Jiu Tangshu treatises.)

+879 April 25?

Xin Tangshu treatise [32]:

6th year of the Qianfu reign period of Emperor Xizong, 4th lunar month, day gengshen [57], the first day of the month, there was an eclipse of the Sun. The eclipse was total and the Sun was 8° in (the lodge) Wei.

Xin Tangshu annals [9]:

(same date as treatise) The Sun was eclipsed.

Although the Sun and Moon were indeed in conjunction on that day (corresponding to + 879 April 25), and the Sun was indeed in the lodge Wei, no eclipse occurred on or near that date and no eclipse was central in China for several years around that time. We interpret the records as an abortive prediction, noting that—for instance—in both +778 and +790 the astronomical treatise of the Jiu Tangshu records eclipses that were said to have been predicted, but not seen.

+888 April 15 (Annular; 0.94); Chang’an (Tang dynasty)

Xin Tangshu treatise [32]:

The Sun was eclipsed; it was 1° in (the lodge) Wei.

Xin Tangshu annals [9]:

The Sun was eclipsed; it was total.

There are no records of the event in the Jiu Tangshu treatise. This generally annular eclipse reached a magnitude of only 0.68 at Chang’an. The central zone was far to the east along the Chinese coast and also in Korea. Evidently, the treatise reports an observation made at the capital, whereas the annals report from a provincial location much to the east of Chang’an.

+977 December 13 (Total; 1.03); Kaifeng (Northern Song dynasty)

Songshi treatise [52]:

The Sun was eclipsed; it was total.

Songshi annals [4]:

The Sun was eclipsed; it was total.

This eclipse was barely visible at Kaifeng; at mid-eclipse the Sun was 8° below the western horizon, while at first contact the solar altitude was only 3°. The path of totality did not reach further north than latitude 18°N. The eclipse was total in Vietnam, and elsewhere in south-east Asia. Possibly, the record implies an attempt at prediction by the Song astronomers.

+1005 January 13 (Total; 1.04): Dading ? (Liao dynasty)

Liaoshi annals [5]:

The Sun was eclipsed; it was total.

The Liaoshi does not have an astronomical treatise. The history of the semi-nomadic kingdom of Liao is complex. Dading was the central residence of the emperors, but there were also several other imperial residences. Computation indicates that the eclipse was total at Dading, and also over a wide area of the Liao kingdom.

+1122 March 10 (Total; 1.06): Dading ? (Liao dynasty)

Liaoshi annals [25]:

The Sun was eclipsed; it was total.

Our plot shows that the eclipse was not total at Dading, reaching only magnitude 0.89. The eclipse was only total in the extreme north-west of China.

+1214 October 5 (Total; 1.05):

This eclipse was recorded independently in the Jin and Song empires.

1) Kaifeng or Zhongtu? (Jin dynasty)

Jinshi treatise [20]:

The Sun was eclipsed; the large stars were all seen.

Jinshi annals [14]:

The Sun was eclipsed.

Commencing nearly a century before the eclipse (in +1127), the Jin dynasty ruled much of the northern half of China. Jin armies occupied the Song dynasty capital of Kaifeng, and this city became the Jin southern capital; the Song court fled south to Linan. Until around the time of the eclipse, Zhongtu (modern name Beijing) was the Jin central capital. However, during the winter of +1213/1214, the Mongols under Genghis Khan blockaded the Jin central capital of Zhongtu and soon afterwards the Jin emperor decided to transfer his court to the southern capital of Kaifeng. There is thus some doubt as to the place of observation in +1214.

Although the eclipse seems to have been very large where it was observed, there is no direct indication of its magnitude. At Kaifeng, the eclipse reached a magnitude of 0.88, which would be hardly large enough to render “all the large stars” visible. Further north, at Zhongtu, the magnitude was even less (0.75).

2) Linan (Northern Song dynasty)

Songshi treatise [52]:

The Sun was eclipsed; it was in (the lodge) Jiao.

Songshi annals [39]:

The Sun was eclipsed; Venus was seen by day.

The eclipse reached a magnitude of 0.91 at Linan. This might have rendered Venus visible (the eclipse occurred around noon, while the planet was 43° west of the Sun), but there is nothing in the records to suggest totality.

+1275 June 25 (Total; 1.07): Linan (Southern Song dynasty)

Songshi wuxingzi treatise [67]:

The Sun was eclipsed; it was total. The sky and Earth were in darkness. People could not be distinguished within a foot. The chickens and ducks returned to roost … then it regained its brightness.

Songshi tianwen treatise [52]:

The Sun was eclipsed; it was total. Stars were seen. The chickens and ducks returned to roost. In the following year the Song dynasty was extinguished.

Songshi annals [47]:

The Sun was eclipsed; it was total. It became as dark as night.

This eclipse was indeed fully total at the Song capital of Linan, in accord with the various detailed descriptions. The allusion to the effect of the eclipse on birds is unique in Chinese history.

+1292 January 21 (Annular; 0.94): Dadu (Yuan dynasty)

Yuanshi trestise [48]:

The Sun was eclipsed. A darkness invaded the Sun, which was not totally covered. It was like a golden ring. There were vapours like golden earrings to left and right, and a vapour like a halo completely surrounding it.

Yuanshi annals [17]:

The Sun was eclipsed. Because the Sun was eclipsed, the normal daily greetings to the Emperor were not offered by the court. At the time of the solar eclipse, there were vapours like golden earrings to left and right, and a vapour like a halo completely surrounding it.

The report in the treatise is an unusually careful account of an annular eclipse. In particular, the reference to the Sun appearing like a “golden ring” is unique in Chinese history. This was mid-winter, and it would probably be very cold. It seems likely that a cloud of ice-crystals in the atmosphere produced the halo display, which is alluded to in both records. Computation reveals that at Dadu (Beijing), the Yuan capital, the eclipse (magnitude 0.94) was indeed annular. On this occasion, the imperial annals are clearly reporting from a source at the capital itself.

Comparison of the consistency of eclipse reports in the treatises and annals

In order to fix the phase of the Earth’s rotation at a particular date, we need to know with a good degree of certainty whether or not an eclipse was total, nearly total or central annular at a particular place. A simple report that the Sun was eclipsed is not sufficiently precise for our purposes, because the report may have emanated from anywhere in the extensive partial zone, thus giving a wide range for the parameter ∆T. This deficiency exists in many of the reports in the annals. Also, several of the Hanshu annals record that eclipses were total, when in fact in most cases the eclipse could not have been total at the capital, and there is no evidence of where these may have been observed. Therefore, again, these reports cannot be used in the study of the Earth’s rotation.

On the other hand, the annals in the two official histories devoted to the Tang dynasty generally give more details than the Hanshu annals. The earlier of these, the Jiu Tangshu (Old History of the Tang) was compiled less than 40 years after the end of the dynasty. The Xin Tangshu (New History of the Tang) was compiled about a century after the completion of the Jiu Tangshu. Occasionally, the Jiu Tangshu contains interesting detail omitted in the Xin Tangshu. However, we note that on other occasions the Jiu Tangshu treatise [36] fails to mention the occurrence of several eclipses—notably those of +702 and +709.

Apart from the eclipse of +756, the reports in the Jiu Tangshu annals (but not the Xin Tangshu annals) support the description in the Xin Tangshu treatise. In general, it does seem that, unlike the Xin Tangshu annals, and the annals of other official histories, the Jiu Tangshu annals are based on the records of the official astronomers, although they omit technical details such as the solar RA.

The large number of reports in the annals before the Tang dynasty claiming totality for eclipses which were in fact not total at the capital, strongly suggests that these reports came from the provinces rather than the capital itself. Indeed, two of the later reports of totality in the annals must have come from as far away as Vietnam (+977), or the most northern part of China (+1122).

By contrast, the reports in the treatises nearly always follow the statement ‘the Sun was eclipsed’ by the qualifications ‘it was total’ or ‘it was nearly total, and like a hook’. In general, there is very good agreement with calculation. Only in the eclipses of +2, +65, +562 and +1214 are the treatise reports significantly in error. The treatises also often contain supplementary information about which constellation (the lodge) the Sun was located. The eclipse of +562 does not contribute to the discussion of ∆T, so we do not consider it further. The other three are discussed further in the next section.

In conclusion, the generally close agreement of the treatises with calculation constitutes strong evidence that they contain reports by the court astronomers situated at the royal palace in the capital. They can be regarded with a high degree of reliability for the determination of ∆T.

It is interesting to investigate how many large eclipses could potentially have been observed at Chang’an during the settled period of the Former Han dynasty from −205 to +23. We find that there were 18 eclipses of magnitude greater than 0.80 that could have been witnessed at Chang’an in this period. This comprises 10 listed in Table 1, together with eclipses in the years −121, −95, −92 (−68), −53, −14, +6 and +16 where, unfortunately, there is no indication of the magnitude of the eclipse in the report. These are not considered by us in this article because they do not make a contribution to the discussion of ∆T. The eclipse in −68 is the only one that is not reported at all in the Former Han dynastic histories. Clearly, this implies that the court astronomers were assiduous in their recording of eclipses.

Besides these large eclipses which occurred in China during the Former Han dynasty, the Hanshu also records 12 ‘eclipses’ which were invisible in China in that period. We surmise that these were attempts at prediction. Indeed, later, in the Tang dynasty, there are many false sightings of eclipses, some not visible in China, which were cited as if they were observations, and this supports our conjecture that the reports of eclipses in +879 and +977 were in fact predictions and not observations.

Implications for the behaviour of ∆T in the period −197 to +1292

The ramifications for ∆T of adopting the Chinese treatise reports, while rejecting the annals, are considered in relation to contemporaneous results from other civilisations. Table 3 lists the range of solutions for the critical values of ∆T and their residuals $δ$ ∆T (rounded to the nearest 10 seconds ) with respect to the long-term parabolic fit to our standardised set of worldwide data. Note that the limits for partial eclipses are the inverse of total eclipses, in the sense that they define boundaries of ∆T where the eclipse was not total. The parabola and other data points are taken from Morrison et al.¹¹ and Stephenson et al.¹²

Δ T (p a r a b o l a) = - 320.0 + 32.5 ((y e a r - {1825) / 100)}^{2} seconds

Table 3.

Limitations on the value of ∆T from Chinese large solar eclipses.

Year	Type of eclipse	Limiting values					Difference from parabola
Year	Type of eclipse	Lower				Upper
Treatises
		seconds				seconds	seconds				seconds
−197	total	—		∆T	<	+13000	—		δ∆T	<	+30
−187	partial	+13830	>	∆T	>	+14140	+ 990	>	δ∆T	>	+1300
−180	total	+11780	<	∆T	<	+12700	− 970	<	δ∆T	<	0
−27	partial	—		∆T	>	+9530	—		δ∆T	>	−1300
+65	total (Lu)	+8450	<	∆T	<	+8900	− 1300	<	δ∆T	<	−850
+ 65	total (Gu)	+9150	<	∆T	<	+9630	− 600	<	δ∆T	<	−120
+120	partial	+8140	>	∆T	>	+8980	− 990	>	δ∆T	>	−150
+306	total	+6550	<	∆T	<	+7890	− 630	<	δ∆T	<	+710
+ 360	partial	+7100	>	∆T		—	+ 450	>	δ∆T		—
+454	partial	—		∆T	>	+6030	—		δ∆T	>	+240
+702	partial	—		∆T	>	+2720	—		δ∆T	>	−1060
+761	total	+1700	<	∆T	<	+3260	− 1660	<	δ∆T	<	−100
+822	partial	+4020	>	∆T		—	+1070	>	δ∆T		—
+1275	total	−740	<	∆T	<	+1280	−1400	<	δ∆T	<	+620
+1292	total	−60	<	∆T	<	+1820	−660	<	δ∆T	<	+1220
Annals
		seconds				seconds	seconds		δ∆T		seconds
+516	total	+3600	<	∆T	<	+5200	−1650	<	δ∆T	<	−50
+522	total	+3450	<	∆T	<	+5100	−1750	<	δ∆T	<	−100

Lu: Luoyang; Gu: Guangling.

Some eclipses, such as −146, do not impose any feasible constraints on ∆T. Values of $δ Δ T$ outside the range ±2000 seconds are not listed. The type of eclipse is as reported in the treatises or annals, as distinct from calculation.

Although the reports in the annals have been discounted, we include two reports from +516 and +522 in Table 3 because they impinge on the discussion of ∆T.

The values of $δ Δ T$ in Table 3 are plotted in Figure 1, together with results from Babylon, Greece, Arab Dominions and Europe, which are listed in the Supplement of Stephenson et al., (2016)¹³ and included in Figure 2 of Morrison et al. (2017).¹⁴ The main difference between Figure 15 of Stephenson et al. (2016), and Figure 2 of Morrison et al. (2017), is the inclusion of tighter constraints on the range of ∆T for the eclipse of +1239 resulting from a reconsideration of the observations from Toledo in that year.

Figure 1.

Differences, $δ Δ T$ , listed in Table 3, together with the results taken from Figure 2 of Morrison et al. (see Note 10), where the smooth black curve is the cubic spline that was fitted to the data.

The present analysis does not materially affect the results for ∆T before year 0. From year 0 to +800, there are relatively few critical observations, and apart from the Greek results for +71 and four timed observations, all the observations are Chinese.

If our published long-term spline fit to ∆T is accurate, then the reports in the years +2, +65 and +1214 in the treatises are anomalous. Also, the reports for +516 and +522 in the annals have a bearing on the discussion of +454. We discuss these in conjunction with Figure 1.

+2 November 23: For the remote chance that this eclipse was total at Chang’an, the value of ∆T would need to be about 8300 seconds, producing a residual $δ Δ T$ of absolute magnitude greater than 2000 seconds, and hence not included in Table 3. This result is completely impossible given contemporaneous reports of other eclipses, and therefore, the report is definitely wrong (for some unknown reason).

+65 December 16: The range of ∆T obtained from this treatise report on the assumption that it was total at the capital, Luoyang, is clearly at variance with the Greek result for +71, and it stands off from the general parabolic trend (straight line at zero) in Figure 1. Interestingly, it is further stated in the report in the Hou Hanshu treatise that the lodge Nandou was regarded as corresponding to Guangling province on astrological grounds, and it was reported that “the King of Guangling died”. This might suggest that the observation was made at Guangling, and not Luoyang. The result for Guangling overlaps the eclipse at +71 (see Figure 1). However, this argument is speculative, and we conclude that the report of totality at the capital is spurious.

+454 August 10: The lower firm bound of +6120 seconds for this eclipse is crucial to determining the behaviour of ∆T around this epoch. The upper bounds of +516 and +522 in Figure 1 suggest either a lower bound for +454, or a steeper increase in ∆T between them. This would lead to a greater fluctuation in ∆T around that epoch. The consequential change in the lod is not feasible. However, the reports of totality for +516 and +522 come from annals, and we have shown that we cannot assume that these observations were made at the capital. Therefore, we reject these two observations, and retain the lower bound of +454, which we have used in the past for fitting a curve by cubic splines to the values of ∆T.

+ 1214 October 5: Although the treatise does not specifically mention totality, the implication of the statement in the treatise report that “the large stars were all seen” is that the eclipse was total or nearly total at the place of observation. Therefore, we infer that this report in the Jinshi treatise would have come from the path of totality or very close to it, towards the west of the Jin empire. For totality at the capital (Kaifeng), ∆T would have to be greater than +2470 seconds ( $δ Δ T > + 1600 seconds$ ), which is at odds with the constraints imposed by other contemporaneous observations shown in Figure 1.

Summary of the reliability of the treatise observations of large solar eclipses for the determination of ∆T

In Table 4, we summarise our results regarding the reliability of the treatise reports of eclipses where the place of observation is not in doubt. This shows that of the 28 reports, only 5 are definitely in error.

Table 4.

Summary of the reliability of the treatise observations.

Year	Type	∆T (seconds)	Place of observation	Mag. at place		Treatise report	Reliable
−197	A	12760	Chang’an	0.95	c	total	yes
−187	T	12640	Chang’an	0.93		almost complete	yes
−180	T	12560	Chang’an	1.04	c	total	yes
−146	T	12160	Chang’an	0.77		almost complete	yes
−88	AT	11510	Chang’an	0.91		not complete	yes
−79	T	11410	Chang’an	0.79		almost complete	yes
−34	A	10910	Chang’an	0.82		not complete	yes
−27	T	10840	Chang’an	0.92		not complete	yes
−1	AT	10570	Chang’an	0.85		not complete	yes
+2	AT	10530	Chang’an	0.91		total	no
+65	T	9870	Chang’an	0.95		total	no
+120	T	9310	Chang’an	0.99		almost complete	yes
+306	A	7450	Luoyang	0.94	c	total	yes
+360	A	6920	Jiankang	0.92		not complete	yes
+429	T	6230	Jiankang	0.94		not complete	yes
+454	T	5980	Jiankang	1.04	c	total	yes
+562	A	4910	Jiankang	0.31		total	no
+ 702	T	3600	Chang’an	0.97		almost complete	yes
+729	T	3370	Chang’an	0.91		not complete	yes
+754	T	3160	Chang’an	0.84		almost complete	yes
+761	T	3100	Chang’an	1.05	c	total	yes
+822	T	2620	Chang’an	0.94		not complete	yes
+879	—	2220	Chang’an	—		total	no – prediction?
+977	T	1640	Kaifeng	—		total	no – prediction?
+1275	T	730	Linan	1.07	c	total	yes
+1292	A	680	Dadu	0.94	c	annular	yes

A = Annular, T = Total, c = central eclipse magnitude.

Conclusion

From a detailed analysis of the tracks of total and annular eclipses recorded in the dynastic histories in the period 206 bc to ad 1368, there is very good evidence that nearly all the detailed reports in the treatises were made at the capital by the court astronomers. By contrast, the reports of totality in the annals, were largely based on reports from places outside the capital, and in some cases from remote regions of China.

The long-term fluctuation shown in Figure 1 with its reliance on the lower bound of ∆T for the eclipse of +454, which we have published previously, is supported by this analysis.

Footnotes

Acknowledgements

The authors acknowledge HM Nautical Almanac Office and the International Astronomical Union’s Standards of Fundamental Astronomy.¹⁵ The map outlines were downloaded from Natural Earth at .

Notes on contributors

F. Richard Stephenson is an Emeritus Professor at the University of Durham, in the Physics department. His research concentrates on historical aspects of astronomy, in particular analysing ancient astronomical records to reconstruct the history of Earth’s rotation, as exemplified in his book Historical Eclipses and Earth’s Rotation (Cambridge University Press, 1997, ISBN 0-521-46194-4).

Leslie V. Morrison worked in the fields of astrometry and the Earth’s rotation at the Royal Greenwich Observatory, 1960–1998. He has collaborated with F. Richard Stephenson on several studies of the long-term variations in the Earth’s rotation, including, Measurement of the Earth’s rotation: 720 bc to ad 2015.¹⁶

Catherine Y. Hohenkerk worked at the Royal Greenwich Observatory from 1971 and in the late 1970s transferred to H.M. Nautical Almanac Office (HMNAO), where she worked on the Nautical and Astronomical Almanacs. She retired from the UK Hydrographic Office, latterly HMNAO’s host organisation, at the end of January 2017. She is a fellow of the Royal Institute of Navigation and chair of the International Astronomical Union’s Standards of Fundamental Astronomy (SOFA) Board. She collaborated with Stephenson and Morrison in the paper Measurement of the Earth’s rotation: 720 bc to ad 2015.¹⁷