Abstract
Twenty-seven extant reports from medieval Europe and the Middle East of the total solar eclipse of AD 1133 (+1133) are analysed to set limits on the Earth rotation parameter ∆T. We conclude that at the epoch +1133, ∆T is in the range +720 <ΔT<+1110 seconds.
Keywords
Introduction
Prior to the advent of accurate clocks in the 17th century, historical reports of the occurrence of total solar eclipses potentially provide the most accurate way of determining decade and long-term variations in the Earth’s rate of rotation. The paths of totality are narrow compared to the circumference of the Earth, and a definitive report of totality at a specific place fixes the observed longitude of the path and hence the rotational phase of the Earth at that epoch.
Professor Zawilski 1 has assembled an archive of reports of solar eclipses made from places in medieval Europe and the Near East. The eclipse of +1133 was widely observed and the archive contains 27 reports of that eclipse. Morrison et al. 2 used the two most explicit observations of totality to determine the value of the parameter ∆T, which is used to measure variations in the rate of rotation of the Earth. The purpose of the present paper is to examine the other 25 reports of the eclipse to determine whether tighter constraints can be placed on the value of ∆T obtained by Morrison et al. 3
An Appendix with the original historical reports of the solar eclipse of AD 1133 together with data on the greatest phase at the various places is available as Supplementary Material in the on-line edition of the Journal.
Path of totality and ∆T
We have developed our own programs for the calculation and plotting of the eclipse tracks in Figures 1 and 2. The basic coordinates of the Sun and Moon are extracted from the Jet Propulsion Laboratory’s long-term ephemerides DE 431 4 and the algorithms for finding their positions for the particular date and time and the position of the track of the eclipse on the Earth are taken from The Explanatory Supplement5,6 together with routines from the International Astronomical Union’s Standards of Fundamental Astronomy. 7 The map outlines in Figures 1 and 2 were downloaded from Natural Earth. 8

Track of totality western Europe for ∆

Track of totality across eastern Europe and the Middle East for
The computed longitude of the track of totality is obtained on the uniform time-scale Terrestrial Time (TT), which is the argument of time in the Solar System ephemerides. The difference in time
Thus, moving the computed track east in longitude by
Using this methodology, values of ∆T were derived by Morrison et al.
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for the historical period
The position of the umbral shadow cone is shown at 11:48 UT. Figure 2 covers southern Europe and the Middle East.
Penumbral phase and background brightness of sky
On either side of the track of totality there is a wide zone where the eclipse is partial. A measure of the size of the eclipse is given by the magnitude, which is the fraction of the solar diameter covered by the Moon at the time of greatest phase, expressed in units of the solar diameter. The greatest phase at a place in the penumbra occurs when the shadow cone passes closest to it.
To what extent stars are visible during totality and at places outside the belt of totality, depends on the sky brightness, the magnitude of the objects and the meteorological conditions. For example, haze will diminish the number of objects seen, and this could vary from place to place.
As a guide to the limiting stellar magnitude in a clear sky during the partial and total phases of an eclipse, we use the values in Table 2 of Können and Hinz,
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this shows that for an eclipse magnitude of
Figures 1 and 2 include the equal contours for eclipse magnitudes
Star field
Figure 3 shows the positions of the planets and stars brighter than first magnitude

Sky chart looking from the south at the bottom for a central location (Disibodenberg), showing planets and stars brighter than magnitude
For objects at an altitude of
Given Venus’s considerable brightness
Observational reports
The observational reports assembled by Zawilski are given in full in the Supplemental Appendix to this paper. Table 1 lists the names of the places of the observations, together with summaries of the critical comments appertaining to the greatest phase of the eclipse at each place. They are ordered by greatest phase, beginning to the west of the track of totality and progressing eastwards. In Figures 1 and 2 the place names are contracted to the first two letters of those listed in Table 1. Plots of the crescent Sun at greatest phase for
Critical comments in reports ordered by greatest phase from west to east, calculated for
The two asterisked reports were used in Morrison et al. (see Note 2).
Our objective is to deduce whether the reports are specific enough to fix the computed eclipse path in longitude, and hence the value of ∆T. We have adopted
where ∆λ measured in degrees is positive if the required shift is to the east, and negative to the west. We have rounded the results to the nearest 5 seconds.
The paper by Morrison et al.
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was restricted to the consideration of reports of totality. The two most explicit reports of totality were used to constrain ∆T. The upper boundary of the computed belt of totality in Figure 1 can not be moved further west than
In the present paper we expand on our derivation of the limits on ∆T by analysing reports of the eclipse from the penumbra as well as the umbra.
Discussion of individual reports
As a working hypothesis, we adopt the criteria that if a few bright stars are seen at a place, it is positioned somewhere between the
We begin with the discussion of the report from Monte Cassino (see Figure 2), which is furthest to the west of the computed path and proceed eastwards across the path of totality, ending with the easternmost report from Praha.
Monte Cassino (Figure 2)
The eclipse is definitely not total here. No sighting of stars is reported, which means that not even Venus was seen. This implies that Monte Cassino was either outside the phase boundary
Malmesbury (Ma, Figure 1)
William of Malmesbury was librarian at the monastery of Malmesbury, England at that time. He does not state that the eclipse was total, but reports seeing stars around the Sun. This implies that at least Venus and Mercury were visible, and therefore Malmesbury was somewhere in the zone between
Cambrai (Ca, Figure 1)
This report states that the Sun was suddenly obscured and there was darkness over all the Earth. Contrary to Malmesbury, no sighting of stars is reported, even though it has a slightly greater maximum phase. If Venus and Mercury were visible at Malmesbury, they should have been visible at Cambrai. The next report from Dover, with virtually the same greatest phase, does remark on the sighting of stars. This apparent inconsistency highlights the problem of variations in reporting, possibly due to differences in the local transparency of the atmosphere. As with Malmesbury, this observation does not produce useful constraints on ∆T.
Dover (probably) (Do, Figure 1)
The chronicle of John of Worcester records that the King and his army were assembled on the south coast of England in preparation to cross the channel to the continent. The likelihood is that they were at or near Dover, which is the nearest crossing point to the continent. The report states explicitly that the eclipse was not total, but that at greatest phase the Sun appeared like a new moon and many stars were seen. In that case, Dover would have to lie within the
On the other hand, the Anglo-Saxon Chronicle reports that the Sun was like a 3-day old moon with stars about it. For a 3-day old moon, the eclipse magnitude would be about
Bourbourg (Bo, Figure 1)
With a greatest phase similar to Cambrai and Dover, the report from Bourbourg concurs with Dover in seeing some stars, again, probably Venus, Mercury and Sirius. This does not usefully constrain ∆T.
Fosse, Floreffe, Gembloux (Fo, Fl, Ge, Figure 1)
None of this geographically close group of places asserts unequivocally that the eclipse was total. They are all consistent in sighting [some] stars; but as distinct from the first of the two reports for Dover, they do not assert that many stars were seen. The ‘stars’ could have been Venus, Mercury, Sirius, and possibly a few of the very brightest stars. So, we cannot be sure that these places were positioned inside or close to the
Liege (Li, Figure 1)
The report states that there was great darkness and stars were shining brightly. This suggests that Liege was within the 0.986 boundary, but not definitely total. To be within the
The lower boundary
Zwiefalten (Zw, Figure 1)
The report from Zwiefalten Monastery states that it darkened into night and the Sun was clearly without light. This definitely means that the eclipse was total. However, Liege, with nearly the identical greatest phase stops short of stating that the eclipse was total there. The problem with the report from Zweifalten is that its provenance is in doubt. The account may have been borrowed from another lost source. If the provenance were secure, totality would be possible if ∆T were less than
Brauweiler and Disibodenberg (Br, Di, Figure 1)
These two places are close to one another, and both state that the Sun was obscured and stars were seen, but this is not qualified by ‘many’. Therefore, we cannot be certain that they lay within the
Kloosterrade (Kerkrade) (Kl, Figure 1)
The report from Klooserrade supplies the supplementary information that the birds roosted and dew formed. This definitely indicates totality, and sets an upper limit of
Augsburg (Au, Figure 1)
The entry in the chronicle is definitely an account of totality. The Final sentence states: At length the Sun emerging from the darkness appeared in the manner of a star, then in the form of a new moon. The manner of a star is probably the appearance of a Baily’s bead, which is followed by a crescent shaped Sun. The only reservation with this report is its provenance. The exact place of observation is unknown. Our computation with
Freising, Salzburg, Heilsbroon, Egmond, Würzburg, Admont and Reichersberg (Fr, Sa, He, Eg, Wu, Ad, Re, Figure 1)
Apart from Freising and Admont, all these places either definitely describe totality or at least strongly suggest it. Salzburg (Sun disappeared; darkness; stars), Heilsbroon (Sun black as pitch; many stars), Egmond (Sun eclipsed; day turned to night; stars), Würzburg (as middle of night; stars), Reichersberg (Sun entirely concealed; many stars). These places, which strongly indicate totality, set the following lower and upper limits on ∆T:
Freising and Admont (darkness and stars) were probably within the
The value in brackets is outside the range of interest for ∆T
Hirschau, Paderborn, Corvei and Melrose (Hi, Pa, Co, Me, Figure 1)
None of these places states that the Sun was completely covered. On the other hand, they are explicit enough to put them inside the
Jerusalem (Figure 2)
The chronicle of St Andrew of Cambrai contains the following report:
After a long time it has been told much after returning home from Jerusalem, on that very day and that hour of darkness four hundred soldiers of the temple except five were killed by the Saracens on the other side of the river. And no wonder because of the killing of his members God had pleasure to introduce darkness to the world, and in this death of the Sun also the whole world was certainly darkened.
This is an intriguing report relayed from Jerusalem. It cannot be used to constrain ∆T because it does not say precisely where the eclipse was witnessed nor whether or not it was total. However, it is noteworthy that the computed northern limit of totality passes over the River Jordan close to Jerusalem. So, we could surmise that the report emanated from the east of the Jordan, looking towards Jerusalem, where the eclipse was either total or very nearly so.
Collected results
We collect together the dependable constraints on ∆T discussed in the previous section. These are plotted in Figure 4. The two dashed lines show the solution space for ∆T common to all these results.

Constraints on ∆T from discussion of places with reliable reports.
The results constrained by the
Conclusion
We conclude that
This is the tightest constraint on ∆T from consideration of all 27 reports, and thereby constitutes a moderate tightening over our previous result of
for the solution space for ∆T at the epoch
We note that ∆T has to be greater than
Supplemental Material
sj-pdf-1-jha-10.1177_00218286231209030 – Supplemental material for Total solar eclipse of AD 1133 and ΔT
Supplemental material, sj-pdf-1-jha-10.1177_00218286231209030 for Total solar eclipse of AD 1133 and ΔT by Leslie V. Morrison, Catherine Y. Hohenkerk, Marek Zawilski and F. Richard Stephenson in Journal for the History of Astronomy
Footnotes
Acknowledgements
The authors acknowledge HM Nautical Almanac Office and the International Astronomical Union’s Standards of Fundamental Astronomy. We thank the two referees for their helpful criticisms and suggestions, which have led to an improvement in the presentation of this paper.
Supplemental material
Supplemental material for this article is available online.
Notes
Notes on Contributors
Supplementary Material
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