Publications of the Astronomical Society of Japan, (2014), Vol. 00, No. 0∆T from solar eclipses around1415 ADTANIKAWA, Kiyotaka1 , SÔMA,
Mitsuru1 ,SIMMONDS, Ockie2 , andIWAHASHI, Kiyomi3
1National Astronomical Observatory ofJapan
2The Society of Māori Astronomy
Research and Traditions
3
National Institute of Japanese
Literature1

uniform. We know that the spin rate of the earth
decreases steadily. This is confirmed directly in ashort timescale by the Lunar laser ranging started
in 1969 (Chapront et al. 2002), and is confirmed
in a long timescale by using the ancient lunar
and solar eclipses and occultations of stars by
the Moon (Tanikawa & Sôma 2004; Stephenson,1997).
In the present report, our purpose is to obtainnarrow ranges of ∆T at around the beginning of
the fifteenth century. We have good records ofdeep solar eclipses in Asia and in Europe.
2 Solar eclipses and ∆T
2.1 ∆T from eclipses of years 1361, and 1366
2.1.1 Eclipse on 1361 May 5

At Shanghai (total)
Abstract. We look for the values of ∆T at around1415 AD. There are eclipses on 1406 June, 16
and 1415 June 7 which were observed in many
cities. In particular, the latter was observed bothin Japan and in Europe. The supposed arrivalof the Māori at Aotearoa (New Zealand) was in
1408 AD. The adventurers of Māori watched thetotal or almost total eclipse when they exploredthe central valcanic plateau of the North Islandof Aotearoa. This eclipse was that on 1409 Oct.
9. Our study shows that the range of ∆T is
168 s < ∆T < 675 s. ∆T of the neighboring
years are 738 s < ∆T < 830 s for 1390-1397 and540 s < ∆T < 679 s for 1431-1433. So the valueof ∆T for 1409 AD may be larger than 500 s.
Adopting this value, we obtain that lake Taupō
belonged to the area of total eclipse. This exactly
correspnds to what the Māori traditions tell.

日将没、忽無光、作蕉叶様、天黒如夜、星斗燦然、食頃、天再明、又少時乃没。(上海『松江府志』)(Translation)
Before the sunset, suddenly the light went
away, as covered by plantain leaves, thesky became dark like a night, stars shonebright, after a mealtime, the sky becamebright again, and then in a short time the sunset. (Sh‘anghăi “Sōngjiāngfŭ-zhı̀”)We judge that the eclipse was total atSōngjiāngfŭ (松江府), Sh‘anghăi. We plot the
shadow band of the eclipse in Fig.1 with ∆T =1000 s. We get the range of ∆T so that theeclipse was total at Sōngjiāngfŭ as
530 sec < ∆T < 1800 sec.
2.1.2 Eclipse on 1366 Aug. 7

1 Introduction

We have been interested in the short term variations in the long term trend of ∆T through ourhistory, where ∆T = TT − UT expresses the retardation of the Universal Time (UT) measured
by the rotation of the Earth compared with theTerrestrial Time (TT) which is supposed to flow

Kaesong
恭愍王十五年七月辛巳朔, 日食既 (高麗史)(Translation)
King Gonggong reign period, fifteenth year,
seventh month, Sinhwa [18], Pus, total solar
eclise (Goryeo-sa)

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Publications of the Astronomical Society of Japan, (2014), Vol. 00, No. 0

Name
Perugia
Neider Alteich
Braunschweig
Hamburg
PragueFolignoCelle
Nurnberg
Karlstejn
Kaesong
Hanseongbu
NanjingShanghai
Kyoto
Aizu
会津坂下町塔寺

Langitude12◦ 23′12◦ 42′10◦ 30′10◦ 0′
14◦ 25′12◦ 43′10◦ 4′
11◦ 5′
14◦ 12′126◦ 34′126◦ 59′118◦ 47′
121◦ 14′135◦ 48′139◦ 56′139◦ 48′

Latitude43◦ 7′
48◦ 52′52◦ 15′53◦ 33′50◦ 6′
42◦ 57′52◦ 38′49◦ 27′49◦ 57′37◦ 58′37◦ 35′32◦ 2′
31◦ 2′
35◦ 0′
37◦ 29′37◦ 34′Seoul(1368 - 1421)Jianye(松江府)

福島県 河沼郡

For Kaesong, totality is realized for−890 s < ∆T < −810 s.

Solar Eclipse

1361

5

5

50

The magnitude is 0.95 if ∆T = 300 s, and 0.90 if∆T = 1380 s. As for the observations in Kyoto,
we obtain ∆T > 50 s so that Kyoto is out of thetotality band. We obtain ∆T > 300 s
2.1.3 ∆T

Eclipse in 1366 does not give us good information for the range of ∆T . Thus two eclipses in1361 and 1366 give us the range of ∆T as

40

Kaesong

Luoyang

which is given only by the eclipse in 1361. We
can say that the other eclipse give us informationconsistent with this range.

Songjianfu

30

530 sec < ∆T < 1800 sec.

2.2 ∆T from eclipses of 1385 Dec. 31, 1390 Oct. 9,
and 1397 May 26
20

2.2.1 Eclipse on 1385 Dec. 31
110
TT - UT = 1000.0 sec

120

130

Corr. to tidal term
- - -0.00 "/cy^2
Magnitude 0.900

Fig. 1. The shadow of eclipse on 1361 May 5.

All the records quoted in Ginzel(1884) say thatthe eclipse was deep, but not total. Our calculation for a reasonable value of ∆T shows that themagnitude at Perugia and Milano was larger than
0.99. However, the totality band is nearly parallel to the latitude lines. We cannot get a good
restriction to the values of ∆T .

Publications of the Astronomical Society of Japan, (2014), Vol. 00, No. 0

Solar Eclipse

1366

8

7

40

3

2.2.4 ∆T

The record of 1390 Oct. 9 may be not reliablebecause the Goryeo Dynasty perished in 1392.
However, Goryeo and Choseon Dynasties are almost continuously connected, so the astronomers
might have been not so much affected by outside
political and military disturbances.

Kaesong

Kyoto
Mizushima30

130
TT - UT = 300.0 sec

140
Corr. to tidal term
- - -0.00 "/cy^2
Magnitude 0.990
0.950

Fig. 2. The shadow band of the eclipse on 1366 Aug. 7 in Korea andJapan. Dashed curves are equi-magnitude ones. Kyoto was on 0.99 andKaesong was 0.95 for ∆T = 300 s.

2.2.2 Eclipse on 1390 Oct. 9

At Kaesong
恭譲王二年九月庚寅朔, 日食既 (高麗史)(Translation)
King Gongsu reign period, second year,
ninth month, Gengin [27], Pus, a total eclipse(Goryeo-sa)
For Kaesong,
738 s < ∆T < 830 s.
2.2.3 Eclipse on 1397 May 26

Fig. 3. eclipses of 1390 Oct. 9 at Kaesong, 1397 May 26 at Seoul.

2.3 ∆T from eclipses of years 1406, 1413, and 1415
2.3.1 Asian observations of eclipse on 1406 June 16

All the records in China, Korea, and Japan say
the eclipse was partial. These are Ming-shi (明史)、(Ming, Huı̀yào (明会要)、Èrshēnyĕlù (二申野録) for China, Choseon wangjo Shillok (朝鮮王朝実録) for Korea, and Zoku-Honchou-Tsugan(続本朝通鑑), Zoku-Shigu-Shou (続史愚抄), andNoritokikyo-ki (教言卿記) for Japan. Our calculation shows that the east Asian sities weredeeply in the partial eclipse band. So we cannot get stringent restrictions to the range of ∆Tvalue.

at Hanseongbu (Seoul)
2.3.2 European observations of eclipse on 1406 June 16

太祖六年五月壬子朔, 日有食之既 (朝鮮王朝実録)(Translation)
Taijeu reign period, sixth year, fifth month,
Renja [49], there was an eclipse, total.
(Sillok)For Hanseongbu (Seoul),
266 s < ∆T < 1619 s.

The Eouropean record of Braunschweig says thatthe eclipse was total, and the record of Hirschau
suggests that it may be deep but non-total.
According to Stephenson(1997), the eclipse wastotal in Hamburg. This gives −838 s < ∆T < 736
s. The totality in Braunschweig gives us 168 s <∆T < 1698 s. The partiality of the eclipse in
Hirschau gives us ∆T < 1350 s. We obtain the
final range of ∆T as a common range

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Publications of the Astronomical Society of Japan, (2014), Vol. 00, No. 0

168 s < ∆T < 736 s(鏖永十二年) 五月朔日、如夜闇、半時許。
(曾津四家合考)from the data of Hamburg, Braunschweig, andHirschau.

(Translation)(Ouei reign period, twelfth year) fifth month,
Saku, for about one hour, it was dark like anight. (Aizu Sike Goukou: History of FourFamilies of Aizu)

2.3.3 Japanese observations of eclipse on 1413 Feb. 1

At Kyoto
正月一日辛巳、朝程天陰、已後小雪時々降、
但陰晴不定、未初刻ヨリ天晴、蝕始、申半
刻加持、酉半刻複末。(満濟准后日記)(Translation)
First month, first day Kanoto-mi [18]. In themorning, it was cloudy, and every now andthen light snow after that, and the weather
was not stable. From the first thirty minutesof Hitsuji-sho koku, the sky became clear
and, (according to the prediction) the eclipse
started, magnitude is deepest at the middle ofSaru Koku, and the eclipse ends at the middle of Tori koku. (Diaries of monk Mansai
Jugou)
春正月朔、日有食之既、薩戒記、文正年代記 (倭史後篇二)Spring, First month, Saku, there was a total solar eclipse. Satsukai Diary, Bunshou
Chronicles (The Latter volume Two of theHistory of Wa)
This eclipse has been recorded in thirteen literatures. Most literatures do not say ’total’. Only
Satsukai Diary and Bunshou Chronicles say thatthe eclipse was total. We judge the eclipse wasdeep but not total. Assuming Kyoto as the observation site,∆T < 950 s(鏖永十二年) 五月朔日、酉刻如闇、半時許。
(曾津土宜考)(Translation)(Ouei reign period twelfth year) fifth month,
Saku, for about one hour in Tori Koku, it
was dark. (Aizu Dogikou: Study of Aizu’
Products)(福島県 河沼郡会津坂下町塔寺)(鏖永十二年) 五月一日、酉刻許一天下入黒闇、半時許也。(塔寺長帳)(Translation)(Ouei reign period twelfth year) fifth month,
first day, around Tori Koku, the world
became in darkness for nearly one hour.
(Toudera Nagachou, Fukushima Prefecture,
KawanumaCounty,Aizu-Sakashita,
Toudera)
The above three records say that the eclipse
was total in Aizu. The records were written
nearly two hundred years before the Tokugawa
Shogunate established the government in 1600.
Kyoto(鏖永十二年) 五月丁酉朔、日食。(続本朝通鑑)(Translation)(Ouei reign period twelfth year) fifth month,
Hinoto-tori [34], Saku, eclipse. (ZokuHonchou-Tsugan)
The totality in Aizu gives us
50 s < ∆T < 1400 s
The record says the eclipse was partial in Kyoto.
The above range satisfies the partiality conditionof the eclipse in Kyoto.

2.3.4 Japanese observations of eclipse on 1415 June 7
2.3.5 European observations of eclipse on 1415 June 7

At Aizu

Neider AlteichPublications of the Astronomical Society of Japan, (2014), Vol. 00, No. 01415. Facta est eclipsis solis tenebrosa,
itaquod sol omnino emisit lumen suum quasi
ad duo Miserere-mei, hora sexta diei, septima die mensis Junii, (Notae Altahense)
quoted in Ginzel (1884).
(Translation)
1415. A dark eclipse of the Sun occurredwith the result that the Sun entirely lost its
light for twice the duration of the Miseremei(Psalm 51) at the 6th hour of the day on
the 7th day of June.
(Notae Altahenses; MGH, XVII, 424.)
The meaning of “for twice the duration of the
Meisere-mei” is unclear.
Prague1415.
Item septima die menses Junii,
quae erat feria VI. post Bonifacii hora XI.
eclipsatus est totus sol, itaquod non poterant misse sine luminibus celebravi. In
signum quod sol iustitie Christus in cordibus
Prelatorum multorum ad mortem magistri
Johannis Hus de proximo per Concilium
mortificandi anlielantium, fuit obscuratus.
(Magister Laurentiusde Brezina. De gestis
et variis accidentibus regni Boemiae. quoted
in Ginzel(1884))(Translation)
1415. At the same time, on the 7th day ofJune, which was the sixth day of the week,
after the Feast of S. Boniface (jun 5), at the
11th hour of the day, the whole Sun was
eclipsed. As a result, the Mass could not becelebrated without lights... (This happened)on account of the death of Master Jan Hus(which occurred) soon afterwards...
(Magister Laurentius de Brezina. De gestis
et variis accidentibus regno Boemiae).

51415. Anno quo supra feria sexta post
Corporis Christi, hora tertiarum, adeo notabilis eclipsis solis fuit, ut alites subita caligine deterrite, in terram deciderent. Et sidera
non secus,. quam nocte collucerent. (Math,de Michova Chron. Polonorum, lib. IV c. LI.
quoted in Ginzel(1884))(Translation)
1415 Year on the Friday after Corpus Christi(= oct. 6) at the third hour of the day, a notable eclipse of the Sun appeared. As a result of this unexpected and unfamiliar event,such a degree that to be birds, terrified by thesudden darkness, fell to the ground, and thestars were shining as if by night.
The above sentences contain real observationsof the surroundings such as “birds, terrified by
the sudden darkness,”, “the stars were shining as
if by night”.
2.3.6 ∆T

For Aizu, 39 s < ∆T < 1410 s, for Touji, 45 s <∆T < 1417 s, for Nieder Alteich, −796 s < ∆T <955 s, and For Prague, −1164 s < ∆T < 675 s.
We obtain
45 s < ∆T < 675 sfrom the data of Aizu, Touji, Nieder Alteich, andPrague.
From eclipses on 1406 June 16 and 1415 June
7, the range of ∆T is obtained as
168 s < ∆T < 675 s
2.4 ∆T from eclipse on 1420 Sept. 8

Eclipse on 1420 Sept. 8 has records in Ming-Shi.
The description is simple:
明成祖永楽十八年八月丁酉朔、日有食之。
(明史、成祖三)The description “the Mass could not be celebrated without lights” suggests that the eclipse
was total at Prague.

(Translation)
Emperor Cheng, Yongle reign period, 18th
year, eighth month, dīngyŏu [34], the firstday, there was an eclipse.
(Ming-shi,Emperor Cheng, third volume)

KrakauOur preliminary calculation shows that the6

Publications of the Astronomical Society of Japan, (2014), Vol. 00, No. 0

eclipse was very deep at Nanjing. Strangely,
The Ming-shi states quietly the fact that there
was an eclipse. More strange is that the Mingshi does not systematically compile the recordsof eclipses. Anyway we plot the eclipse bandsof the eclipse in Fig. ??. We obtain either∆T > 500 s or ∆T < 300 s in order that theeclipse was not total at Nanjing.
2.5 ∆T from eclipses of years 1431 and 1433
2.5.1 Two European observations of eclipse on 1431 Feb. 12

For perugia, −188 s < ∆T < 679 sec For Foligno,−16 s < ∆T < 846 sec
We have−16 s < ∆T < 679 sec
from the condition that the eclipse was total bothat perugia and Foligno.

Fig. 5. eclipses of 1431 Feb. 12 at Foligno and Perugia, and 1433 June 17
at Celle, Nurnberg and Karlstejn. We do not plot the data of Nurnberg and
Foligno because they are redundent.

Together with the data on 1431 Feb. 12, wehave a narrow range

2.5.2 Three observations of eclipse on 1433 June 17

The record says the totality of the eclipse.
However, we postpone the conclusion until wedraw the Sôma diagram.

548 s < ∆T < 679 sec
for the period includin 1431 and 1433.

3 Variations of ∆T around year 1415

Fig. 4. eclipses of 1433 June 17 at Celle, Nurnberg, and Karlstejn.

2.5.3 ∆T

For Celle, 548 s < ∆T < 2287 sec, for Nurnberg,−524 s < ∆T < 1080 sec, and for Karlstejn,−422 s < ∆T < 2044 sec. We have548 s < ∆T < 1080 sec
from the condition that the eclipse was total at
Celle, Nurnberg, and Karlstejn.

Fig. 6. Variations of ∆T during AD 1350 and 1450. 534 s < ∆T < 1794 s
for 1354 and 1366, 738 s < ∆T < 830 s for 1390 and 1397,
168 s < ∆T < 675 s for 1406 and 1415, 540 s < ∆T < 679 s for 1431 and1433,

Publications of the Astronomical Society of Japan, (2014), Vol. 00, No. 0

4 Magnitudes of eclipses of 15 June 1368, 9October 1409, 2 January 1424, and 25
March 1438 in North Island of Aotearoa(New Zealand)

7

Solar Eclipse

1409 109-30

4.1 Eclipse on 1368 June 15

We show in Fig. 7 the totality and partiality
bands of the eclipse on 1368 June 15 assuming ∆T = 600 s. The totality band runs northwest of Lake Taupo and passes across the northPenninsula. Around Taupo, the magnitude of theeclipse was 0.91 – 0.92. The sky was not dark.

-35

-40

-45

Solar Eclipse

1368

6 15

-30
160

165

TT - UT = 600.0 sec

170

175

Corr. to tidal term
- - -0.00 "/cy^2
Magnitude 0.950
0.900

Fig. 8. The shadow band of the eclipse on 1409 Oct. 9 in Aotearoa - New
Zealand. Dashed curves are equi-magnitude ones. 0.90, 0.80. ∆T = 600
s.

-35

-40

island. The magnitude of the eclipse was 0.8
around Lake Taupo. So, the sky became not dark.
-45

4.4 Eclipse on 1438 March 25
160

165

TT - UT = 700.0 sec

170

175

Corr. to tidal term
- - -0.00 "/cy^2
Magnitude 0.900
0.800Fig. 7. The shadow band of the eclipse on 1368 June 15 in Aotearoa - New
Zealand. Dashed curves are equi-magnitude ones. 0.90, 0.80. ∆T = 600s.

We show in Fig. 10 the totality and partiality
bands of the eclipse on 1438 Mar. 25 assuming∆T = 600 s. The totality band was grazing thesouth island and off the north island. The magnitude of the eclipse was 0.85 around Lake Taupo.
So, the sky became not dark.

Acknowledgements
4.2 Eclipse on 1409 Oct. 9

The totality and partiality bands of the eclipse on
1409 Oct. 9 are shown in Fig. 8. ∆T is set
to 600 s. The totality band of the eclipse runs
across the North Island from the north-west to thesouth-east. Lake Taupo is on the north edge ofthe totality band. So, the sky became dark around
Lake Taupo.

The authors are grateful to Mr. Hisashi
Hayakawa for information on European literature.
The authors express thanks to Dr. Chijou Udou
(kokugakuin University) for the knowledge on
Chinese sentences. This work has been partially supported by Grants-in-Aid for Scientific
Research (C), 2015 - 2018 (JP15K05038,
Mitsuru Soma) ”Variations of Earth Rotation andClimates”.

4.3 Eclipse on 1424 Jan. 2

References

We show in Fig. 9 the totality and partiality
bands of the eclipse on 1424 Jan. 2 assuming∆T = 600 s. The totality band was off the north(1) J. Chapront, M. Chapront-Touzé, and G. Francou: 2002,
A new determination of lunar orbital parameters, precession constant and tidal acceleration from LLR measurements, Astronomy& Astrophysics 387, 700 -.

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Solar Eclipse

1424

1

2

-30

-35

-40

-45

160

165

TT - UT = 600.0 sec

170

175

Corr. to tidal term
- - -0.00 "/cy^2
Magnitude 0.900
0.800Fig. 9. The shadow band of the eclipse on 1424 Jan. 2 in Aotearoa - New
Zealand. Dashed curves are equi-magnitude ones. 0.90, 0.80. ∆T = 600s.

Solar Eclipse

1438

3 25

-30

-35

-40

-45

160

165

TT - UT = 600.0 sec

170

175

Corr. to tidal term
- - -0.00 "/cy^2
Magnitude 0.900
0.800
0.700

Fig. 10. The shadow band of the eclipse on 1438 March 25 in Aotearoa New Zealand. Dashed curves are equi-magnitude ones. 0.90, 0.80, 0.70
from the right. ∆T = 600 s.

(2) F.K. Ginzel: 1884, Astronomische Untersuchungen über
Finsternisse, Sitzungsberichte der Kaiserlichen Akademie desWissenschaften in Wien, Math.-naturwiss. Kl. Abt. II, 88, 629–755.
(3) H. Th. R. Oppolzer: 1887, Canon der Finsternisse,
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(4) F.R. Stephenson: 1997, Historical Eclipses and the Earth’s
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(6) A.N. Vyssotsky: 1949, Astronomical Records in the
Russian Chronicles from 1000 to 1600 A.D. (as collectedby D. O. Sviatsky), Meddelande Fran Lunds Astronomiska
Observatorium, Ser. II, Nr. 126, Published by the Observatory,
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MUKAI, Yoshishige and KIKUCHI,
Shigemasa (向井吉重、菊池重匡校), The Old
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records of the temple from 1350 t0 1636 AD.
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Eds. HAYASHI, Tadashi, HAYASHI Hiroshi (林忠, 林恕)
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