Dating Methods for theAncient Chinese Star Charts[Appendix: SHIBUKAWA Harumi's star charts]

Dating Methods for theAncient Chinese Star Charts[Appendix: SHIBUKAWA Harumi's star charts]
竹迫 忍
TAKESAKO Shinobu
日本数学史学会会員
http://www.kotenmon.com
takesako@mrj.biglobe.ne.jp

２０２３年１月２１日
第24回 天文文化研究会[格子月進図(3 colored)]Contents
Ⅰ． Overview of the ancient Chinese star charts

4 0:00

1. Overview of Dating Methods for Ancient Star chart
2. Style of Chinese star charts
3. Introduction of ancient Chinese star charts

Ⅱ． Dating of original star chart

32 17:10

4. Dating by constellation shapes and names

Ⅲ． Dating of the Observations and 1st Chart

62 33:00

5. Dating by the star positions
6. Dating by the vernal and autumnal equinox (ecliptic)
7. Dating by 12th order (12sings)
8. Summary of dating of 『格子月進図』
9. Summary of dating of the Ancient Chinese star chart

Ⅳ． Star Chart of SHIBUKAWA Harumi

3

90 47:50

This presentation summarizes the following papers and some new findings.
⚫ 『中国古代星図の年代推定の研究』数学史研究 (228号) p.1-21(2017)⚫ 『最小二乗法による古代星図の年代推定』数学史研究 (232号)p.1-22(2019)⚫ 『『格子月進図』の原図となった星図の年代推定』数学史研究(Ⅲ期 第1巻1号)(2022)⚫ 『渋川春海の星図の研究』数学史研究 (231号)p.1-48 (2018)2023/01/21

I． Overview of the ancient Chinese
star charts4１． Overview of Dating Methods forAncient Star chart

5

Date of 『キトラ天文図』 (Kitora Astronomical Map)
is not yet confirmed
An astronomical map drawn on the Kitora
Tumulus. Discovered in 1998 and excavated in
2004. More than 350 stars in 74 constellations
are depicted, centering on the North Pole.

Kitora Astronomical Map

Dating by M. Soma(2015)
Date：AD300±90 years
Place： Latitude 33.9 ± 0.7°
Dating by T. Nkamura(2015)
Date： BC80±aprox. 40 years
Place：There is no necessity toregard the latitude calculated
from the internal and external
circle as the latitude of the starobservation site.

6[「キトラ古墳天文図 星座写真集」PL.3より]2023/01/21

There was no dating method for the ancient Chinese
star charts⚫ 『天象列次分野之図』 is a star chart carved instone that was created in the 4th year of King Taejo
and the 28th year of Hongmu (1395) of Yi Dynasty
Korea (1392-1897).
⚫ According to the inscription, the original star map isbelieved to be from the Goguryeo period (668AD).⇒As a result, it was thought to be the original
map of the Kitora astronomical chart(700AD).
⚫ The tale inscribed on the inscription reads, "`When
Goguryeo was attacked by the allied forces of Tangand Silla and fell, the stone carved star map was
sunk in the Taedong River. However, a rubbed copy
was handed down, and there was one that waspresented to Taejo when he was enthroned, and thatrubbed copy was used as the original drawing"➢ Some researchers suspected it was a fiction basedon political background, but until now there was noway to ascertain the date of the original star chart.
7『天象列次分野之図(再刻)』（京都大学附属図書館所蔵）
2023/01/21

Incorrect dating of 『格子月進図』(Koshi Gettshins)『格子月進図』(Koshi Gettshins) End of Kamakura - Northern and Southern Courts period Private collection.
This is Japan's oldest star chart, created around AD 1100, and consists of two charts: the North Pole chart and the
Middle sky chart. This manuscript is from the first half of the 14th century and is a copy of a star chart handed
down in the family of Yasuyo Tsuchimikado, who worked as a professor of Yin and Yang. This painting wasstored in Tokyo Tennichikan, but it was destroyed by fire in the Tokyo air raid on April 25, 1945, and only a few
photographic prints remain. The grid refers to graph paper made from longitude and latitude lines, and the title
includes the Japanese , "A chart showing the movement of the moon at night.''(from "Bessatsu Taiyo" No. 73 (1991) p.39 including the figure below, )Mr.Imoto*：average 1101AD (Vernal(奎5.9°):1548 Autum(角3.9°):654) Corrected 330AD (Vernal:620 Autum:39)*： Without correction. However, the average year remains the same.

Dating by equinox
奎宿(Kui xiu) (HR215
Year

RA(°)

1548

5.9

1088

0.0

620

354.1

Vernal equinox
奎宿 -5.9°
奎宿 +5.9°角宿(Jiao xiu) (HR5056
Year

34ζ An)67α Vir)

RA(°)

Autumnal equinox

654

183.9

角宿 -3.9°

347

180.0

39

176.1

角宿 +3.9°82023/01/21

Dating methods of ancient star charts and targets
Existing Cart
Relative dates by comparison among the star charts
Absolute date by precession
(①②)

(③④⑤)

Observation
Same
dates

1st edition
star chart(⑥⑦)

transcribedstar charttranscribedstar chart

Absolute date by precession

Target①Shape of the constellation②Name of the constellation③Position of star (right ascension)④Position of star (declination)⑤Position of star (both)⑥Vernal & autumnal equinoxes⑦12th order (12 signs)

Date of thetranscribedstar chart

2017'paper 2018'paper 2022'paper○○○

Date of the
Observation
for the positionof the stars
Date of 1stedition of chart○○△(w/o correction)○(w correction)○

9

Each star chart has two dates.

2023/01/21

２．Style of Chinese star charts

10Measurements of star positions in China
去極度
(赤緯)
0°

east direction

秋
分
点

鬼
宿
距
星
(Gui xiu)

井宿
距星(Jing xiu) 春
分
点
91.5°
vernalequinoxautumnal
equinox28 leading stars
Longitude is measured from leading star as the 0 degree.

360 western degree＝365.25 Chinese degree

鬼
宿
経
線

井
宿
経
線

183°

11

2023/01/21

Chinese constellation systemHan
漢/後漢
3 systems
石氏
石氏星経(星表)
甘氏

三国

Jin
晋/南北朝

Upper limit of
the observation

Tang
Song
隋/唐 五代 宋『格子月進図』『天象列次分野之図』『敦煌天文図』

Integration of
3 system andmade star chart(呉/晋・陳卓)

巫(フ)氏(283constellations 1464stars)

五官

中官・２８宿・外官

元/明

太史令：in charge ofastronomy, calendars,
rituals, the drafting of
national document.

From 『歩天歌』
唐末

三垣・２８宿
２８宿

北官

12

紫微垣

西官 中官 東官

中官

南官

２８宿
外官
Organization of constellations

太微垣

天市垣

2023/01/21

銭楽之(Senrakshi) in the 5th century [Northern andSouthern Dynasties] made copper celestial globe『宋元嘉中(424-453)、太史令・銭楽之(センラクシ)所鋳揮天銅儀、以朱・黒・白三色、用殊三家、而合陳卓之数。』(「隋書」天文志)

渾天儀(明・北京古観象台)
13『格子月進図』(赤・黒・黄で彩色)
2023/01/21

『キトラ天文図』(Kitora Astronomical Map) is also a star
map after the integration of the three systems
The Kitora Astronomical
Map is also composed ofthree constellation systems.
⇒Since the star chart
depicting the constellationsof the three systems is basedon the star chart after Chen
Zhuo (end of 3rd century),
this period is the upper limitof the estimated year.

:甘氏:巫氏
Others:石氏
14[「キトラ古墳天文図 星座写真集」PL.3に加筆] 2023/01/21

Differences Between Chinese and Western Star chart⚫ Features of Chinese Chart： ・Many constellations and stars.
・no classification by star magnitude
・many faint stars of 5 to 6th magnitude⚫ No bright star near the Pole, the ancient Pole Star is a faint star.

15

Chinese constellation(『格子月進図』)

Western Constellation(『Almagest』)

Number of constellation

283(+235)

48

Number of stars

1467(+532)

935

1st mag. (>1.5 mag.)

16

20

2nd mag.

61

62

3rd mag.

149

159

4th mag.

352

359

5th mag.

518(west+220)299

6th mag.(<5.5mag.)

371(west+330)36
2023/01/21

Style of Ancient Chinese Star Chart (1/2)
Circular Star Chart
Circular Star Chart Centered on Pole Star
内規(Naiki, Inner Circle):Range always
visible from the observation point

Sun at the winter solstice（α=270°）Equator

North PoleNo classification bystar magnitude in the
Chinese star chart.

外規(Gaiki, Outer Circle):
The southernmost point visible
from the observation site

Ecliptic: path of the sun
16

2023/01/21

Explanation of inner and outer circles
A star never setson the horizon

内規(Naiki, Inner circle)
Stars on the horizon
North Pole
Celestial sphere(Observer's
Latitude)

North

HorizonEarth's
axis

West

East

ObserverSouth(Observer's
Latitude)EquatorSouth Pole
外規(Gaiki,Outer circle)

Stars always below
the horizon
17

2023/01/21

Style of ancient Chinese star chart (2/2)
Square star chart
内規 Naiki(Inner Circle)
Circular chart inside
the internal circle
北極星

内規 Naiki(Inner circle)

Square chart from internal
circle to external circle
黄道

赤道

18

外規 Gaiki(Outer circle)2023/01/21

Example of Square star chart 『格子月進図』
12th order line (every 31.5 degrees)： Based on season, later changed.

The angle fromthe North Pole
内規
(35°)
Inner
Circle約31.5度黄道

Equator赤道(91.5°)

距星

翼宿
18度

19

張宿
19度

Outer
Circle外規(148°)
28 constellation line：angel from leading star ⇒ Little influence of precession(Total lange is 366 degrees in this chart.) Observation site：35x360/366=34.43°[画像は『別冊太陽』73号(1991)p.39より]2023/01/21

陽城(Yangcheng, Reference site of Calendar)

20

Observatory of Yuan Dynasty
at Yangcheng (34.4°N, 113.1°E)

Instrument for measuring shadowsat Beijing Ancient observatory[http://www.kamakura-worldheritage.com/?cat=1 より][https://zh.wikipedia.org/wiki/圭表 より]

陽城:河南省登封市告成鎮（About 60km southeast of Luoyang）

2023/01/21

３．Introduction of ancient Chinese star charts

21

『格子月進図』(Koshi Gettshins)『格子月進図』 is a star chart handed downin the Tsuchimikado family. It wastranscribed from the original by Abe Yasuyo
around 1317. It was destroyed in an air raid
in 1945 when it was on display, but thephotographs remain. It is a star map thatremains as it was at the time of introduction.

22[『別冊太陽』73号(1991)p.38-39より]

Pei Xiu (224-271) of the Jin Dynasty produced a grid map.
2023/01/21

『高松塚古墳星宿図』(Constellation map of Takamatsuzuka Tumulus)
28 constellation map drawn on the
Takamatsuzuka Tumulus. Excavated in 1972.
28 constellations are drawn around theconstellation of North Pole and the 四補.

No figure in the left map

Maybe trash[「キトラ古墳天文図 星座写真集」PL.5より]

Cross

Should be
3 parts

SquareNo horizontal bar
in Tang's map

North-south reverse

23[高松塚壁画館パンフレットより]2023/01/21

『キトラ天文図』(Kitora Astronomical Map) (1/2)
An astronomical map drawn on the Kitora
Tumulus. Discovered in 1998 and excavated in
2004. More than 350 stars in 74 constellations
are depicted, centering on the North Pole.

Kitora Astronomical Map

24

Circular star chart drawn basedon 『 格 子 月 進 図 』. (It is drawn
reflecting the grade of brightness )(283 constellations, 1464 stars)

Outer circle of Kitora map

A mural drawing about 1/4 of theconstellations in a deformed form.

[「キトラ古墳天文図 星座写真集」PL.3より]2023/01/21

『キトラ天文図』(Kitora Astronomical Map) (2/2)
The constellations
around the outercircle are not drawn.

In-correct ecliptic

Correct ecliptic
Yi xiu (翼宿,enlarged)：Leading stars of
28 constellations
Inner：38.1°
Outer：44.5°

Two maps arealigned with Spica.

The old man's star isforced into the map.

25

2023/01/21

『敦煌天文図』 (Dunhuang astronomical map)
In 1900, a large number of documents were discovered in the Dunhuang Mogao Grottoes (17caves), and British explorer Stein bought some of them and brought them back to the British
Museum (1907). This map was included in these document. It is a celestial map of a square star
chart similar to 『格子月進図』, and is divided into 12 degrees according to field theory(分野説).
Needham, who discovered and introduced this star map, estimated that it was made around940AD, but he did not show no evidence.

Internal Circle
莫高窟(17窟)

12次の範囲は(発見当時)「開元占経」
によっている。

[http://www.atlascoelestis.com/Dunhuang%20VII%20sec%20base.htmlより]
26[https://www.youtube.com/watch?v=gOy6x6CfL7M&t=216より]2023/01/21

『敦煌天文図』 is similar to 『格子月進図』『敦煌天文図』『格子月進図』(３家彩色)[http://www.atlascoelestis.com/Dunhuang%20VII%20sec%20base.htmlより]

27

2023/01/21

Wrong Constellations in 『敦煌天文図』• The constellation of 「天皇」 is 「御女」.
• There is name of 「勾陳」, but constellation figure is missing.
• The constellation of「天一・太一」 is 「内厨」.
『敦煌天文図』『格子月進図』

内厨

28[http://www.atlascoelestis.com/Dunhuang%20VII%20sec%20base.htmlより]2023/01/21

『天象列次分野之図』 (Tenshou retsuji bunyanozu)
A stone carved star map made in the 28th
year of Hongmu (1395AD) in the 4th yearof King Taejo of Yi Dynasty Korea.
According to the inscription,"When
Goguryeo was attacked by the allied
forces of Tang and Silla and fell to ruin
(668AD), the star map was sunk in the
Taedong River. However, a rubbed copy
was handed down, and there was one thatwas presented to Taejo when he wasenthroned, and that rubbed copy was usedas the original drawing".

HakkokuArrow

Old man
29

Inner：37.7°
Outer：33.1°[『天象列次分野之図(再刻)』（京都大学附属図書館所蔵）及び
千葉市立郷土博物館 『東西の天球図』 (2002)p.18 より]2023/01/21

『蘇頌天文図』 (Su Song Star chart)『蘇頌天文図』 is a square star chart created by
Su Song, an astronomer from the Northern Songdynasty of China, and was published in the book
『 新 儀 象 法 要 』 published in the Tianyu era
around 1090. It is said to have been drawn basedon observations made during the Yuanfeng era(1078-85).

30[『中国の星座の歴史』 雄山閣出版 (1987) p.232-234より]2023/01/21

『蘇州天文図』(淳祐天文図)(The Suzhou Astronomical chart)
Based on a star map produced by
Huangsu of the Northern Songdynasty around 1190, this star
map was created by Wang
Zhiyuan in the 7th year of 淳祐
era(1247). It is also estimated to
be based on stellar observations
made during 元豊era(1078-1085).

31

Inner：33.9°
Outer：34.3°[『東西の天球図』千葉市郷土博物館(2002)p.15より] 2023/01/21

Ⅱ．Dating of original star chart

32

４．Dating by constellation shapes and names

33

Dating by constellation 「塁壁陣」(Leibizhen)(Tang dynasty or Song dynasty)(1/3)
The feature of the star charts after the Sung
dynasty is that the 「塁壁陣」 extends to the
虚宿(Xu xiu). Discovered by Mr. Kiyohiko
Ogawa (1932) by verifying the records of staroccultations.

『蘇頌星図』(宋)哭星34『格子月進図』(唐)

危Wei
宿 xiu

虚 Xu
宿 xiu

危
宿

虚
宿

From the 11th century onwards,
the "哭星" replaced the "塁壁陣"in Chinese records of occultationof star crimes. The record in Japanremains "Crying Star". Goryeo
records contain a mixture of both.
2023/01/21

Dating by constellation 「塁壁陣」(Tang dynasty or Song dynasty)『天象列次分野之図』（唐）

危 Wei
宿 xiu
Tang Dynasty star map
because it is in the Wei xiu.

虚 Xu
宿 xiu

(2/3)

『蘇州天文図』(宋)

危 Wei
宿 xiu
Song Dynasty star map
because it extends to Xu xiu.

虚 Xu
宿 xiu

35

2023/01/21

Dating by constellation 「塁壁陣」(Tang dynasty or Song dynasty)(3/3)

『敦煌天文図』(唐) (The Dunhuang Astronomical map)

危
宿

虚
宿

The range of 12 order inthe figure on the right is "8degrees of 女宿(Nu xiu)"
to "15 degrees of 危宿(Weixiu)". The range of the 12thorder of this star chart isthe same as the value of『開元占経』.

It is unknown how far the
塁壁陣 extend. But since theshape of the constellations issimilar to 『格子月進図』, itis judged to be a chart of
the Tang Dynasty.
36

2023/01/21

『敦煌天文図』の12次の範囲の比較
The 12th order of the "Dunhuang Astronomical Map" is based on field theory(分野説) and is similar to the 12 signs in the West. Also, its range is the sameas the value of 『開元占経』. It differs from the value in older documents.
⇒It is presumed that this map is after the Tang/Kaiyuan period (713-741)
when 『開元占経」 was written.

37

月

12次

季節

十二支

11

星紀

冬至

12

玄袴

1

敦煌天文図

開元占経(8世紀前半)

晋書天文志(7世紀)

乙巳占(7世紀)

始点

終点

始点

終点

始点

終点

始点

終点

丑

斗12度

女７度

斗12度

女７度

斗12度

女７度

斗12度

女７度

大寒

子

女８度

危15度

女８度

危15度

女８度

危15度

女８度

危15度

娵訾

雨水

亥

危16

奎４度

危16

奎４度

危16

奎４度

危16

奎４度

2

降婁

春分

戌

奎５度

胃６度

奎５度

胃６度

奎５度

胃６度

奎５度

胃６度

3

大梁

穀雨

酉

胃７度

畢11度

胃７度

畢11度

胃７度

畢11度

胃７度

畢11度

4

実沈

小満

申

畢12度

井15度

畢12度

井15度

畢12度

井15度

畢12度

井15度

5

鶉首

夏至

未

井16度

柳８度

井16度

柳８度

井16度

柳８度

井16度

柳８度

6

鶉火

大暑

午

柳９度

張17度

柳９度

張17度

柳９度

張16度

柳９度

張16度

7

鶉尾

処暑

巳

張18度

軫11度

張18度

軫11度

張17度

軫11度

張17度

軫11度

8

寿星

秋分

辰

軫12度

氐４度

軫12度

氐４度

軫12度

氐４度

軫12度

氐４度

9

大火

霜降

卯

氐５度

尾９度

氐５度

尾９度

氐５度

尾９度

氐５度

尾９度

10

析木

小雪

寅

尾10度

斗11(2)度

尾10度

斗11度

尾10度

斗11度

尾10度

斗11度

Same as 『開元占経』

Differ from 7th century document.

2023/01/21

Changes of constellation shapes over time(1/4)
Same shaped

Shape of 『翼宿』(Yi xiu) (3 divisions)『キトラ天文図』

Middle of change(3 divisions)『格子月進図』 『高松塚星宿図』 『敦煌天文図』 『天象列次分野之図』 『蘇頌星図』

Shape of 『天淵』(Tian Yuan)

Same shape

Middle of change『格子月進図』

38

Same shape(3 connected)『敦煌天文図』『天象列次分野之図』『蘇頌星図』

Direction of change
2023/01/21

Changes of constellation shapes over time(2/4)
Shape of 『天将軍』(Tian jiangjun)Same shape （Vertical direction）

Same shape（horizontal direction）『格子月進図』『敦煌天文図』

『天象列次
分野之図』

『蘇頌星図』『蘇州天文図』

Direction of change392023/01/21

Changes of constellation shapes over time(3/4)
Shape of 『井宿』(Jin xiu)
Same shape（No Horizontal line）

Same shape（Two Horizontal lines）

Middle of change(One Horizontal line）『格子月進図』『敦煌天文図』

『天象列次
分野之図』

『蘇頌星図』『蘇州天文図』『高松塚古墳星宿図』 『キトラ天文図』

40

Direction of change
2023/01/21

Changes of constellation shapes over time(4/4)
Shape of 『鬼宿』(Gui xiu)
Same shape（Square）

Same shape（Cross）『格子月進図』『敦煌天文図』『天象列次分野之図』 『蘇頌星図』『高松塚古墳星宿図』

41『蘇州天文図』『キトラ天文図』

Direction of change
2023/01/21

Dating by the shape of constellation North Pole(1/3)
The Pole Star was not ”帝星”, but changed along with the movement of the North Pole.

勾陳(Little bear)

帝星

北極星(HR424)
(現代)

北極

Wrong ancient
Pole star

北極星(HR4852) 北極星(HR4893)(後漢⇒晋⇒南北朝)(隋/唐⇒宋/明)天皇

Movement of north pole四輔

北極星(HR4927)(北辰) (春秋⇒漢)42

Note：Base of star table of 「SKY2000 Master Catalog、 Version 5」 (2006). up to 6.6 magnitude。
Sky at AD300. Number on the star is magnitude. Orange points are place of pole at that year.
Declination scale interval is 2°. HR number is number of 「Bright Star Catalogue」.

2023/01/21

Dating by the shape of constellation North Pole(2/3)
North pole at 300AD(晋)North Pole at 1100AD(宋)Straight line

Curved line
New Pole star
(HR4893)

Constellation
North Pole:5 stars Old Pole star
(HR4852)

Constellation
North Pole:5 stars

The 5 stars of constellations
North Pole are in a straight line.

The 5 stars of constellations
North Pole are aligned in a
curved line.

432023/01/21

Dating by the shape of constellation North Pole(3/3)
5 stars in straight line

5 stars in curved line
『格子月進図』

『天象列次
分野之図』

HR4852『高松塚星宿図』『蘇州天文図』『キトラ天文図』

HR4893

Not a star of
constellation
North Pole
『蘇頌星図』『敦煌天文図』
442023/01/21

Tail of 軒轅(Xuanyan) and 爟(Guan)of 『格子月進図』
Added later

Tail
軒轅(Xuanyan)

The composition of 『格子月進図』consistent with thedescription in 『開元占経』

Belly
Head
Left
hone

45

爟 on other star charts
are at this position

爟 in the modern chart.
爟

Right
hone

(Guan)柳宿
Liu xiu

鬼宿(Gui xiu)爟(かん)[『別冊太陽』73号(1991)p.38-39より]

唐開元占経(718～726)「爟星旧図軒轅腹内，今測軒轅尾南近柳宿北四星」(reference[43]p.767)「軒轅，舊尾漸斜向上，今測其尾勢迤邐向西」(reference[43]p.764)
2023/01/21

Changes in constellation shapes over time
Charts in Tang Dynasty
Constellation

格子
月進図

塁壁陣

Kisyuku

高松塚 キトラ
星宿図 天文図(Around 700AD)－－

翼宿(Yi xiu)

3parts(3parts) 3parts

天淵

W＋M

－

－

Hexagonal Hexagonal Hexagonal＋square with 4line with 4line

Hexagonal
with 4line

Horizontal－－

Horizontal

VerticalVerticalVertical

井宿(Jing xiu)

Non

(None)None

None

１ line２ lines

２ lines

鬼宿(Gui xiu)

cross

cross

squaresquaresquaresquaresquare

北極

line

line

line

line

curve

curve

curve

(North Pole)(HR4852)(HR4852)(HR4893)(HR4893)(HR4893)

爟(Guan)

North of
柳宿

(Leibizhen)(Tian Yuan)

大将軍(Tian jiangjun)

46

Charts in Song Dynasty(HR4852) (HR4852)－－

敦煌 天象列次 蘇州
天文図 分野之図 天文図蘇頌星図kisyuku

kyosuku

3parts(tentacles)

kisyuku kyosyuku

Integrated Integrated Integrated

Northeast Northeast Northwest Northwest
of 鬼宿
of 鬼宿
of 鬼宿
of 鬼宿

Orange：Beginning of Tang, Yellow：Tang, Green：Song2023/01/21

The shape of the constellation of theChinese Grave Chamber Constellation Map
Constellation figure(ceiling)47【遼・張世卿墓室】(1116, refer to p.53)[The Grave Chamber isunderground down the stairs][https://new.qq.com/omn/20211210/20211210A00LMN00.htmlより]

Grave Chamber Constellation Map (1/6)
Astana Burial Mounds in Turpan
65TAM38 (Middle of 8 century)翼⚫ 翼宿： letter U⚫ 井宿： 1 Horizontal line
⚫ 鬼宿： Square鬼井[潘鼎著『中国古天文図録』p.42より]
48

2023/01/21

Grave Chamber Constellation Map (2/6)
【銭寛墓星図】(900)【水邱氏墓星図】(901)

呉越王家族墓室星図
呉越国(907-978)⚫ 翼宿： Integrated⚫ 井宿： No Horizontal line
⚫ 鬼宿： Square
A slightly older than
『天象列次分野之図』

井
翼
翼

鬼

(東西逆)

49

[潘鼎著『中国古天文図録』p.47より]2023/01/21

Grave Chamber Constellation Map (3/6)
呉越王家族墓室星図
呉越国(907-978)【銭元瓘墓星図】(942)鬼【銭元瓘馬王后星図】(940) 【銭元次妃・呉漢月墓星図】(952)井翼⚫ 翼宿： 3parts⚫ 井宿： No horizontal line
⚫ 鬼宿： square[潘鼎著『中国古天文図録』p.48より]
50

北極・五星
(North Pole)

2023/01/21

Grave Chamber Constellation Map (4/6)
五代・後梁(907-923)・王処直墓(924)
唐朝末年和五代後梁・義武軍節度使・王処直（863年—923年）之墓。

https://www.163.com/dy/article/
DVA6F2HV0523G0SJ.html

河北省曲陽県
西燕川村付近井⚫ 翼宿： 3parts(with tentacles)⚫ 井宿： One Horizontal line
⚫ 鬼宿： Square

翼
鬼

51

[庄蕙芷『再論日本奈良的両座壁画墓及其天象図』p.208より]2023/01/21

Grave Chamber Constellation Map (5/6)
五代・南唐(937-975)初期
墓誌函蓋に描かれた星宿図⚫ 翼宿： Integrated⚫ 井宿； 3 Horizontal lines⚫ 鬼宿： Square
墓
誌
函
蓋
の
例

井
翼宿

翼

鬼

52

[潘鼎著『中国古天文図録』p.46より]2023/01/21

Grave Chamber Constellation Map (6/6)
【張世卿墓星図】(1116)【張恭诱墓星図】(1117)

Western 12sings

翼
鬼

翼

鬼

井

井

53

⚫ 翼宿： 3parts⚫ 井宿： 2 Horizontal lines⚫ 鬼宿： Square⚫ Western 12 signs

河北・宣化遼墓室星図[星図は潘鼎著『中国古天文図録』 口絵p.7より]2023/01/21

Tentative restored map of 高松塚古墳[Current][Restored map]

軫宿

翼宿

張宿 星宿

柳宿

鬼宿

井宿

： Remaining stars： Added stars： Remaining line
542023/01/21

Changes in constellation names「鼓旗」(Gu qi)⇒「右旗」(You qi)

左
旗

左
旗
左
旗

河
鼓

河
鼓

鼓
旗
鼓
旗

『格子月進図』

右
旗『天象列次分野之図』『敦煌天文図』

55

2023/01/21

Changes in constellation names「天矢」(Tian shi)⇒「屎」(Shi)

天天
矢矢

屎

天
矢

『格子月進図』『天象列次分野之図』『蘇州天文図』

562023/01/21

Chronological changes in constellation names
Star Charts and Documents in Tang Dynasty
星座 格子
名称 月進図隋書
晋書(648編纂)

鼓旗

鼓旗

天矢

天矢

天矢

武賁

武賁

虎賁

開元占経
(718～726)

河鼓/旗 河鼓並旗In Song Dybasty

敦煌 天象列次唐
蘇州
天文図 分野之図 歩天歌 天文図

蘇頌
天文図

鼓旗

右旗
右旗
右旗
右旗
(Changes corresponding to 左旗)

天矢

－

天矢

天屎
屎
屎
(Pronunciation is same)

虎賁

虎賁

虎賁

虎賁

虎賁

虎賁

天淵

天淵

天淵

天淵

天淵

天淵

(character replacement
by 避諱* )天淵 (character天泉 replacement
天池
by 避諱* )57*避諱(taboo): Prohibit the use of the personal names of the emperor and his relatives.
2023/01/21

taboo related to『格子月進図』⚫ 避諱(taboo): Prohibit the use of the personal names of the emperor and his relatives.
⚫ 避諱 is an important factor in the dating of ancient Chinese documents.

「晋書」「隋書」 compiled at the sametime, has replacement to 「武賁」「天池」.

李虎status of taboo of『格子月進図』

虎賁⇒武賁

天淵⇒天泉

右民角

天
泉

武
賁

李昞
唐
代
皇
帝

高祖・李淵(618～626)
太宗・李世民(626～649)
高宗・李治(649～683)「虎」と「淵」areprohibited. 「民」
is not prohibited.

『格子月進図』
was transcribed
during this period.
(618～649)「虎」、「淵」、「民」
All prohibited.

58

2023/01/21

taboo related to 『敦煌天文図』
The "Dunhuang Astronomical Map" is also presumed to have been written in the
period of King Gojong (649-683), based on the character of the "民" (reference[46]). However, the character that is avoided is not the star map, but the cloud(weather) forecast part.
『雲(気象)占い』⇒ “虎(Tiger)” and “淵(Yuan)” are used in star charts,
I think that they were copied from different originals.
李虎李昞
高祖・李淵(618～626)

虎賁(

太宗・李世民(626～649)

誤
字

)

唐
代
皇
帝

『星図』

(

誤
字

)

高宗・李治(649～683)「虎」、「淵」、「民」
の使用制限

天
淵

民の一画を
欠いている。
(避諱の方
法の一つ)

59

[http://www.atlascoelestis.com/Dunhuang%20VII%20sec%20base.htmlより]2023/01/21

The scroll containing 『敦煌天文図』 consists of two parts
The Dunhuang Astronomical Map has a title that has not yet been deciphered. In the paper(Reference [45]), for example, it is read as "The interpretation of the dream and thunder sutra one
volume, and there is an interpretation of "The interpretation of dreams and the book of lightning".
⇒The person who copied "Dunhuang Astronomical Map" did not speak Chinese as their native
language, and made many mistakes. The title of the book can be read as 『具解象及雲経一巻』(Detailed Interpretation of Celestial Phenomena and Cloud Divination). The first half and the second
half are connected without any context, and are probably copies from two books.

其
解
夢
及
雷
誤
経 写
一 復
元
巻

具
解
象
及
雲
経
一
巻

Second half：
Forecast by heavenFirst half：
Forecast by Cloud60

Recovery from the error[http://www.atlascoelestis.com/Dunhuang%20VII%20sec%20base.htmlより]2023/01/21

Date Estimation Results Based on
Constellation Shapes and Names
Related document

Ancient Chinese Star Chart

晋書・隋書天文志(648)

格子月進図(618～649)

開元占経(718～726)
Value of 12 order is same

Based on taboo.
高松塚星宿図/キトラ天文図(700頃)

敦煌天文図(800頃)

Chart of Tang
Dynasty

天象列次分野之図(900頃)
唐・歩天歌(唐末)The author is said to be "TanYuanzi" of the Sui Dynasty, but thename of the constellation wasaround the end of the Tang dynasty.

Similar to chart of Song Dynasty

蘇頌天文図(1086～93頃)
蘇州天文図(1190頃)

Chart of Song
Dynasty61

2023/01/21

Ⅲ．Dating of the Observations
and 1st Chart

62

５．Dating by the star positions

63

How to use the least squares method
for the Western star catalog
Observed value(αo,δo)
Diff ofdeclination
Shortest
angle

Change the year of calculation
and use the year with the lowest
error as the estimated year.
Movement of stars by precession

Diff. of right Theoretical value(α ,δ )c cascension

α：right ascension
δ：declination

In the case of the Western star catalog, since the right longitude is the absolutevalue from the vernal equinox, the year that minimizes the error in thefollowing formula is the estimated central year.

・Declination method： ΔL＝∑ (δo-δc)2・Right ascension method： ΔL＝∑ (αo-αc)2 cos 2 δc・Declination and ascension method ： ΔL＝∑ ( (δo-δc)2 + (αo-αc)2 cos 2 δc)64

2023/01/21

How to use the least squares method
for the Chinese star catalog (1/2)
Leading star１
Leading star 2
Ovserved value(α2o,δ2o) Observed value(α1o, δ1o)

Change the year of calculation
and use the year with the lowest
error as the estimated year.

Width of house(S1o )= (α2o-α1o)Width of house(S1c)= (α2c-α1c)
Theoretical value(α2c,δ2c)

Movement of stars by precession

Theoretical value(α1c,δ1c)

In the case of the Chinese star catalog, the right ascension is theangle from the leading star, so the absolute position in the rightascension direction is not determined. The right ascension direction
is compared by the width of house, which is from leading star tonext leading star. Declination is the same.
The year that minimizes the error in the following formula is theestimated central year.

65

・Declination method： ΔL＝∑ (δo-δc)2・House width method： ΔL＝∑ (So- Sc)2
2023/01/21

Example of least squares simulation (1/2)
『格子月進図』(Calculation by 28 Stars)

2

Residual error(°) = root(ΔL/(n-1))

1.8
1.6

1.4

Declination
method：1.2
1417AD±57.7(σ)(Residual error：1.21°)

0.8

House width
method0.6464AD±168.5(σ)(Residual error：0.76°)

0.4
0.2
0
0

100

200

300

400

500

600

700

800

Year
66

2023/01/21

Example of least squares simulation (2/2)

Residual error(°) = root(ΔL/(n-1))『キトラ天文図』(Calculation by 28 Stars)

67

Declination
method：House width
methodDeclination +House width
method：523AD
549AD±268.4(σ)(Residual error：5.58°)-732AD±708.7(σ)(Residual error：2.99°)『格子月進図』
level of error

西暦

2023/01/21

How to use the least squares method
for the Chinese star catalog (2/2)
Even in the case of the Chinese star catalog, if the right ascension can beassumed, the year that minimizes the error of the following formula will be
the estimated central year.
Declination and ascension method： ΔL＝∑ ( (δo-δc)2 + (αo-αc)2 cos 2 δc)
Method of MR. Tsugo Nakamura (28 constellations bootstrap method)①First, assuming that the right ascension of the first star is 0 degrees(reference star), calculate the right ascension of each star. Let Year1 be the yearthat minimizes ΔL1.
②Next, let Year2 be the year that minimizes ΔL2 with the right longitude of
the next stellar leading star at 0 degrees (datum star).
③After calculating 28 constellations, the average of Year1 to Year28 is taken as
the estimated central year.

Since the bootstrap method is not used as a calculation method here, it iscalled the declination/estimated right ascension method.

68

Note: The right ascension of the reference star has a true value of 0 degrees,
so the error is 0.
2023/01/21

Example of virtual right ascension (『格子月進図』)
Size of house Declination

69

宿名
角
亢
氐
房
心
尾
箕
斗
牛
女
虚
危
室
壁
奎
婁
胃
昴
畢
觜
参
井
鬼
柳
星
張
翼
軫

HR
5056
5315
5531
5944
6084
6247
6746
7039
7776
7950
8232
8414
8781
39
215
553
801
1142
1409
1876
1852
2286
3357
3410
3748
3903
4287
4662

距星
67α Vir98κ Vir
9α2 Lib
6π Sco20σ Scoμ1 Sco10γ2 Sgr
27φ Sgr
9β Cap2ε Aqr22β Aqr
34α Aqr
54α Peg
88γ Peg
34ζ And
6β Ari35 Ari17(b) Tau
74ε Tau37φ1 Ori
34δ Ori
13μ Gem
31θ Cnc4δ Hya30α Hya39υ1 Hya
7α Crt4γ Crv

宿広度
12.00
9.00
16.00
5.00
5.00
18.00
11.00
26.00
8.00
12.00
10.00
17.00
16.00
9.00
16.00
12.00
14.00
11.00
16.00
1.00
10.00
33.00
3.00
15.00
7.00
19.00
18.00
17.00

去極度
仮定赤経(1) 仮定赤経(2) 仮定赤経(3)93.00
0354.00345.00
90.50
12.00
0.00
357.00
97.25
21.00
9.00
0.00
109.00
37.00
25.00
16.00
110.00
42.00
30.00
21.00
123.00
47.00
35.00
26.00
Secondreference star
120.00
65.00
53.00
44.00
117.00
76.00
64.00
55.00
108.75102.0090.00
81.00
105.50110.0098.00
89.00
101.00122.00110.00101.0098.50
132.00120.00111.0083.25
149.00137.00128.00First
reference
Star
82.75
165.00153.00144.0071.25
174.00162.00153.0076.00
190.00178.00169.0071.00
202.00190.00181.0072.00
216.00204.00195.0075.00
227.00215.00206.0083.00
243.00231.00222.0092.50
244.00232.00223.0068.00
254.00242.00233.0067.00
287.00275.00266.0081.00
290.00278.00269.0095.00
305.00293.00284.00100.75312.00300.00291.00101.00331.00319.00310.0098.00
349.00337.00328.002023/01/21

estimated central ( σ, year )Standard Deviation from σ(年)Simulation results using each estimation method
900
800

House width
method

600
500
400
300

Declination and estimatedright ascension method

Declination
method：200

Declination and rightascension method

100
0
0

70

The declination and estimatedright ascension method is a moreerror-free estimation methodthan the declination method.

700

1

2

3

4

5

6

7

8

残差(度)
Residual error(°)= root(ΔL/(n-1))
2023/01/21

Estimated years of ancient star charts by
various estimation methods
The error is large and cannot
be used for estimation.

Star chart with the smallest error
Declination
ChartsCenterΣ
year (year)

Declination & estimatedright ascension

House width
error
(°)

Centerσ
year (year)

error
(°)

error
Centerσ
year (year) (°)

格子月進図

417

57.7

1.2

464 168.5

0.8

336

62.5

2.33

天象列次分野之図

472

182.8

3.8

-18 459.9

2.0

375 118.8

4.49

キトラ天文図(*)

549

268.4

5.6

-732 708.7

3.0

445 191.5

7.29

蘇州天文図

1108

114.9

2.4

1018 501.7

2.2

1124

88.6

3.33

蘇頌星図

1087

149.1

3.1

947

0.4

1080

83.8

3.15

95.2

Song Dynasty star charts are consistent with the presumption of"observations during the Yuanfeng era (1078-85)71

Note : *For the Kitora astronomical chart, 3-range stars with large errors have been corrected.
2023/01/21
See the papers for the data used.

６．Dating by the vernal and autumnal
equinox (ecliptic)

72

Dating by the vernal and autumnal equinox (ecliptic)
winter solstice

The eccentric circles in Chinese
star charts are drawn with thesame diameter as the equator, so
the vernal and autumnal equinoxes
are not 180 degrees apart. (θ)
must be shifted for correction.
(*Note: Kazuhiko Miyajima (2019) points outthat the ecliptic in the Suzhou astronomical
map may be in 300s AD.)

Center of
ecliptic

23°

eclipticθautumnal
equinox（Unit : western degree

星図
蘇州天文図(*)
天象列次分野之図
格子月進図(右秋分)
格子月進図(左秋分)
キトラ天文図(反転)VernalAutumn.

奎宿
3.6
3.7
5.9
5.9
3.7

角宿
5.4
5.1
3.9
－7.9
19.6

Diff.
(°)
168.2
169.2
173.1
184.9
163.2

Correction

(°)
5.9
5.4
3.4
－
－

θ

vernalequinoxequator

Summer solsticevernal equinox
Autumnal equinox average
year
奎宿
year
角宿
year
9.5
331
－0.5
386
359
9.1
363
－0.3
370
367
9.3
347
0.5
307
327
(presumed mis transcription )(Not estimated due to large error)

The ecliptic drawn in the 300s star charts were passed down to Song dynasty
73

2023/01/21

７．Dating by 12th order (12sings)

74

Dating by 12th order for『格子月進図』
玄枵

星紀
冬至

31度
15.5度 7度
22.5度

⚫ Center of 星紀 is winter solstice➢ 斗宿(Dou xiu) 22.5°➢ BC163⚫ Mr. Osaki's estimation➢ 12th order：BC190±21(Including other season)➢ Declination method：AD500±50➢ Mysterious star chart which has
two epochs

星紀
経線⇒Mystery of 『格子月進図』
There was a reason for this.

斗宿
経線

Note：「格子月進図」is the oldest star chart drawn in the 12thorder of the seasons, and the other star charts are drawn in"field theory" and cannot be estimated.
75[『別冊太陽』73号(1991)p.38-39より]2023/01/21

The position of the winter solstice in calendars
暦法記載の値
暦法

太初暦

暦修成

冬至の

年代

斗宿度**

-103 26(牛初)The position of the winter solstice at 斗宿(Dou xiu)(°)
計算値（270°との差）
大崎計算『歴代天文律暦

西洋度 斗距星 斗宿度
(A)

赤経

(B)

25.6

248.7

21.3

誤差

等志彙編』
対応年

記載項

4.3

－450

5冊p.1431－70

5冊p.1518

(A-B)

四分暦

85

21.25*

20.9

251.6

18.4

2.5

乾象暦

182頃

22

21.7

253.1

16.9

4.8

景初暦

237

21少

20.9

253.9

16.1

4.9

－80

5冊p.1632

元嘉暦

443

14強

13.9

257.1

12.9

1.0

377

6冊p.1735

大明暦

463

11

10.8

257.4

12.6

-1.8

6冊p.1743

興和暦

540

14

13.8

258.6

11.4

2.4

6冊p.1843

大象暦

579

12

11.8

259.2

10.8

1.0

6冊p.1892

麟徳暦

664

10

9.9

260.5

9.5

0.4

639

月進図

－

22.5

22.2

247.8

22.2

0.0

－162

76

5冊p.1580

7冊p.2199

2023/01/21

Chronological change in the position of thewinter solstice in the calendar

Potion at 斗宿(Dou xiu) (°)

The position of the winter solstice in the calendar was fixed at approximately 21.5 degrees of 斗宿.
The 景初暦 was enforced until 451, and is almost consistent with the position of 『格子月進図』.

太初暦
乾象暦
四分暦

景初暦

『格子月進図』

BC163年
Estimation by
Mr. Osaki Seiji

10 days shift of winter solitude
元嘉暦

Theoretical position of the winter solstice

Year
77

Calendar

Theory(Dating by the position of star)

2023/01/21

12th order after 『格子月進図』『格子月進図』 Based on season
玄枵

星紀『敦煌天文図』 Based on the astrology

冬至

星紀

玄枵
中点

斗12度
31度

15.5度

12度

15.5度 7度
22.5度

27.5度

5°Difference

(

星
記
誤
字

斗宿
経線

78

[『別冊太陽』73号(1991)p.38-39より]

)⇒

星紀
経線

星
紀
斗宿
経線

(It was not transcribed by Chinese)

2023/01/21

8．Summary of dating of 『格子月進図』

79

『格子月進図』 Comparison of date of Original chart

Imoto(1942,1972)

Watanabe(1987)p.764

Osaki(1987)
p.270-271

Nakamura

Position of the star (the least squares method)vernal andautumnal
equinox

12th
order

1100 *1(2019,2022)

Estimated RA

more stars

28 stars

28 stars－－－

After 一行(720)*2－

δAnd(814)
ζAnd(653)*3
ηAnd(466)－－－

After 一行(720)*2－

Recognized as
lunar path

BC190
±21

AD319±58[σ: 1.22°]481±38(163 stars)[σ: 1.84°]

－

－

－

AD545±90(21stars)[90%、
σ： 2.1°]－

AD485±20
(28宿)
[90%、
σ: 0.8°]－Before
AD451

AD417±58[1σ]
417±18[90%][σ:1.21°]

AD397±23(1346stars)[σ: 3.12°]

AD464±52(28stars)[90%、
σ: 0.76°]

AD336±19(28 stars)[90%、
σ: 2.33°]－

AD327(freehanddrawing)

A star chart based on observationfrom the mid 300s to 400AD.
80

House width

28 stars(2018)p.163

AuthorDeclination method*1：The direction of precession was opposite. There is no correction.
*2：The estimate date of 一行 is 440AD±37。
*3：Leading star isζAnd. There is no correction.
2023/01/21

Estimated History of 『格子月進図』
Existing Cart

Chen Zhuo's(陳卓)Star Chart

Relative dates by comparison among the star charts
Absolute date by precession(①②)

Latter halfof 300s

Observation

1st edition
star chart(③④⑤)

transcribedstar chart(⑥⑦)

Absolute date by precession②Name of the constellation③Position of star (right ascension)④Position of star (declination)⑤Position of star (both)⑥Vernal & autumnal equinoxes⑦12th order (12 signs)
81around 1317AD

618～649AD

Target①Shape of the constellation(To Japan)

Date of thetranscribedstar chart

2017'paper 2018'paper 2022'paper○○○

Date of the
Observation
for the positionof the stars
Date of 1stedition of charttranscribedstar chart○○△(w/o correction)○(w correction)○*：The vernal and autumnal equinox points and the 12th order are directly copied from the original chart. 2023/01/21

Tenno star in 『格子月進図』 is origin of the name "Tenno"
四輔

星座・北極
極星

勾陳
天皇

"tenno" is the center of theheavens and is the god of east.
【 別冊 太陽 No.73(1991) p.38より】

82

The star name of Great Emperor (天皇大帝)
is in the 晋書, but the 晋書 was completed
after the 640s. So, it was not completed
during the reign of Emperor Jomei (舒明).

2023/01/21

９．Summary of dating of theAncient Chinese star chart

83

Dates of Observation and 1st Star chartof Tang Dynasty Star Charts by precession
The stars in the Tang Dynasty
star charts were most likely
observed and 1st chart was madein last half of 300s AD.

Year: 12th order: Dating by thevernal andautumnal equinox『格子月進図』『天文列次分野之図』

Declination method『キトラ天文図』 『蘇州天文図』

Declination and estimatedright ascension method

Upper limit ofestimation(Integration of 3
constellations by
Chen Zhuo)

84

2023/01/21

Summary of Dating of Ancient Chinese Star Charts⚫ The first edition of chart was produced based on observations in the last half of 300s AD.
⚫ The dating by numerical calculation using precession just confirm it.
⚫ The dating by names and shapes is important to know their position in the system of star charts.
Dating by nameand shape

Dating by position vernal and12thof star [90%]autumnal
order(estimated RA)
equinox (season)

格子月進図

Bigging of Tang
(618-649AD)

336AD±19(2.3°)

327AD

Before451AD

HR4852高松塚古墳星宿図(around 700AD)

－

－

－

HR4852

キトラ天文図(around 700AD)

445AD±59(7.3°)－－

HR4852

敦煌天文図

Middle of Tang(around 800AD)－－(Astrology)

HR4852

天象列次分野之図

End of Tang(around 900AD)

375AD±37(4.5°)

367AD(Astrology)

HR4893

蘇州天文図Song (1247AD)

1124AD±27(3.3°)

359AD(Astrology)

HR4893Charts85

Pole Star

Around 310AD, it was at north pole
2023/01/21

Records of Occultations by Moons and Planetsin the Book of Jin(晋書)Accurate star charts were born from observations.
100
90
80

魏(220-265)

西晋(265-317)

陳卓(230-330,呉/晋・太史令)Jin destroys Wu(

cases (every 10years)

70
60
50

東晋(317-420)
The period when theoriginal chart of theTang Dynasty star
chart was produced

The accuracy of therecords is extremely
high at over 80%.

Capital of east Jin(南京)Latitude：32.0°
Longitude：118.8°

２
８
０

40

)

30

太史令：in charge ofastronomy, calendars,
rituals, the drafting of
national document.

20
100
220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390 400 410

Moon
86

Bw Planets

PlanetYear

記録件数は斎藤国治/小沢賢二『中国古代の天文記録の検証』 雄山閣 (1992)による2023/01/21

Family tree of ancient Chinses star chart
Dunhuang

China
AD300sJin
Observation

Chen Zhuo'sStar Map

KoreanPeninsulaJapan

1st edition ofChart (300s)
三家簿讃
格子月進図
(618-649)
Astronomical
mural drawing(sketch)

7th envoy to Tang (AD704 returns to Japan)

開元占経
敦煌天文図
(Copy of map)
・Shapes and names: Middle of Tang

Chart ofend of Tang
唐歩天歌
Song
Observation

87

キトラ天文図高松塚星宿図・Shape of bigging of Tang

AD800s

AD1080s

格子月進図(Original Chart)

隋書/晋書

Chart ofmiddle of Tang
AD900s

1st envoy to Tang (AD632 returns to Japan)

Lost due to war, only
photographs remain.

(around biggening of 900s)

GoryeoChart of Goryeo(918～1392)(Revisions)蘇頌星図(1086-93)

・Star positions : Song's observations
・Shapes and names: Late Tang
・Expansion of "塁壁陣"
・Song's Ecliptic

蘇州天文図(1247)

・Star positions : Song's observations
・Shapes and names: Late Tang
・Expansion of "塁壁陣"
・Jin's Ecliptic

天象列次分野之図(1395)

格子月進図(around 1317)
・Star positions : Jin's observations
・Shapes and names: Bigging of Tang
・Jin's Ecliptic and 12th order・No Expansion of "塁壁陣"・taboo of Bigging of Tang(618-649)

・Star positions : Jin's observations
・Shapes and names: Late Tang
Dot line is・No Expansion of "塁壁陣"
assumption.
・Jin's Ecliptic
・Unique reorganization in the shape of constellations

『格子月進図』was introduced alongwith Destiny Thought and Surveying Methods
Azimuth line by Pole star (HR4893) and direction of the ruins of Japan

Direction from true north.(min. ,+: west -: East)

Winter Sky

(

真
北
か
ら
の
方
位
分
、
正
は
西
偏
、
負
は
東
偏

水落遺跡
Mizuochi

中ツ道
Nakatsumichi

唐・長安城の方位
Tang's Chang'an

藤原京
Fujiwara

下ツ道
Shimotsumichi
Replacement of
Appointed Star
(Enthronement ofemperorSaimei,655)

前期難波宮
Early Naniwa)

88

Arrival ofmeasurement methos

The true north direction capital city is the stage
for dynastic ceremonies that embody theexistence of the destiny and prove thelegitimacy of those in power on earth.
(reference[13] )平城京
Heijyou

平安京
Heian

長岡京
Nagaoka

後期難波宮
Later Naniwa

Replacement of
Appointed Star
(around 780)

石神遺跡
Ishigamo
Summer sky

1st Envoy 2nd Envoy 詳細は、「古代の正方位測量法(第三版)」PDF版(2022/04/01)を参照。
to Tang
to Tang【Latitude：34.75°(Nara/Kyoto)】 ©2022 S.Takesako

Conclusion forthe dating of ancient Chinese star charts• The origin of the existing ancient
Chinese star charts is the Jin
Dynasty star chart in the 300s.
• The『格子月進図』 is the oldest
star chart that best conveys thecharacteristics of the star chartsof the Jin Dynasty, and it ishoped that it will be preserved
and restored as a world heritage.
【 別冊 太陽 No.73(1991) p.38より】

89

2023/01/21

Ⅳ．Star Chart of
SHIBUKAWA Harumi

90The Mystery of Harumi's Star Chart
Compilation of the Jokyo calendar to
replace the Senmyo calendar (1684).
⚫ He also observed the stars, identified thestars in the Chinese constellations, andproduced star charts and celestial globes.
⚫

⇒The star charts referred to in the observations
and the creation of the star charts were unknown.

91

2023/01/21

Charts of SHIBUKAWA Harumi 『天文列次之図』と『天文分野之図』①『天文列次之図』(1670)②『天文分野之図』(1677)『天象列次分野之図』(1395)[京都大学附属図書館所蔵]

92[国立公文書館][早稲田大学図書館]

2023/01/21

Correction of leading stars by SHIBUKAWA Harumi
Errored Leading stars 『天象列次分野之図』

93

No

宿

HR
番号

距星名

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21

角
亢
氐
房
心
尾
箕
斗
牛
女
虚
危
室
壁
圭
楼
胃
昴
畢
嘴
参

5056
5315
5531
5944
6084
6247
6746
7039
7776
7950
8232
8414
8781
39
215
553
801
1142
1409
1876
1852

α Vir
κ Vir
α Lib
π Sco
σ Sco
μ1 Sco
γ Sgr
φ Sgr
β Cap
ε Aqr
β Aqr
α Aqr
α Peg
γ Peg
ζ And
β Ari
35 Ari17 Tauε Tau
φ1 Ori
δ Ori

22

井

2286

μ Gem

23
24
25
26
27
28

鬼
柳
星
張
翼
珍

3357
3410
3748
3903
4287
4662

θ Cnc
δ Hya
α Hya
υ1 Hya
α Crt
γ Crv

合計

Charts of Harumi

天象図(Stone)

天象図(Wood)

列次図

分野図

ι Lib

ι Lib

ι Lib

ι Lib

天文瓊統
(天文成象)

Error due to referenceof woodblock chart.

δ3 Tauδ3 Tau

ν Gem

ν Gem

σ Hya

η Cnc*σ Hya

κ Hya*ν Hya

κ Hya*
ν Hya

6件

7件

γTau*

δ1 Tau

η Cnc

η Cnc
σ Hya

3件

3件

1件
2023/01/21

Celestial globe and 『天文瓊統』 (chart and table)『天球儀』(1690)『天文瓊統・星表』(1698)『③天文瓊統・星図』(1698)[伊勢神宮・徴古館HPより][国立公文書館][国立公文書館]
942023/01/21

Charts of SHIBUKAWA Harumi 『③天文成象』(1699)
Harumi's final star chart is based on a star chart of mainland China.

95[和泉市久保惣記念美術館蔵]

2023/01/21

The influence of 『天象列次分野之図』『天象列次分野之図』

作成年代
春海の星座
「宋大夫」の有無「弧」の形「軒轅」の形(獅子座の頭)「軒轅」の形
中央凹部

元星表

明天井図

常熟図

麟祥寺図

現代星図

列次図

分野図

神宮天球儀

天文瓊統
(成象図)

元朝
(13-14世紀)

明朝(1453年頃)

明朝(1506)

明朝(16世紀)

清朝以降(1981)

寛文10年(1670)

延宝5年(1677)

元禄3年(1690)

元禄11年(1698)

無
無
弓と矢1本

無
無
弓と矢1本

無
無
弓と矢1本

無
無
弓と矢1本

無
無
弓と矢1本

無
有
弓と矢1本

無
有
弓と矢1本

無
無
－

有
無
弓と矢1本

明確

明確

明確

明確

明確

明確

不明確

不明確

不明確

明確

角型

角型

角型

角型

角型

浅い丸型

浅い丸型

浅い丸型

角型

蘇頌図型

蘇頌図型

蘇頌図型

古代図型

蘇州図型

古代図型

蘇頌図型

－

蘇頌図型

米型
米型

六角形
米型

米型
米型

米型
米型

米型
六角形

六角形
六角形

米型
米型

－
－

米型
米型

天象図

蘇頌星図

蘇州星図

李氏朝鮮
洪武28年
(1395)
無
有
弓と矢2本

北宋
天佑年間
(1086～93)
無
無
弓と矢1本

北宋
淳祐7年
(1247)
無
無
弓と矢1本

明確

不明確

丸型

浅い角型

角型

独自
(3列)
六角形
六角形
北が大きい
台形
6
V字の重ね
正
不入壁度
5星入虚度
米型
長方形
V字の重ね

独自
(2列)
六角形
六角形
蘇頌図型

蘇頌図型

蘇頌図型

蘇頌図型

蘇頌図型

無

天象図型

蘇頌図型

－

2星のみ

「文晶」の星数「芻藁」を結ぶ線
珍宿(左轄右轄)「塁壁陣」の形・東「塁壁陣」の形・西「市楼」の形「八穀」の形「天床」の形

古代図型(「代」が南)六角形
六角形
中央が大きい箱型
7
連続
誤(左右逆)
3星入壁度
6星入危度
８の字
五角形
連続

6
V字の重ね
正
不入壁度
5星入虚度
箱型
長方形
V字の重ね

6
V字の重ね
正
不入壁度
5星入虚度
米型
V字の重ね
V字の重ね

6
V字の重ね
－
不入壁度
4星入虚度
米型
V字の重ね
V字の重ね

6
V字の重ね
－
不入壁度
5星入虚度
米型
V字の重ね
V字の重ね

6
V字の重ね
正
不入壁度
5星入虚度
米型
V字の重ね
V字の重ね

7
連続
誤(左右逆)
3星入壁度
6星入危度
８の字崩れ
五角形
連続

6
V字の重ね
正
3星入壁度
6星入危度
８の字崩れ
五角形
連続

6
(不明)
－
－
－
米型
－
V字の重ね

6
連続(独自)
正
不入壁度
5星入虚度
米型
V字の重ね
V字の重ね

「天囷」の形⊃型

クラゲ型原型

クラゲ型

クラゲ型

クラゲ型

クラゲ型

クラゲ型

⊃型

⊃型

－

クラゲ型

「天厨」の向き「酒旗」の向き「狼」の位置「老人」の位置「爟」の位置「積薪」の位置「列肆」の位置「六甲」の位置「哭星」の位置「外屏」の位置「人」の線「羽林」と「騎官」の三角をつなぐ線「天記」の名称

南北
東
井15.0度
井25.9度
鬼東北
積水東南
斗北西
華蓋西
虚宿線上
全星赤道南
直線

東西
西
井10.7度
井9.8度
鬼西北
鬼西
斗西
華蓋西
塁壁陣南
赤道上
直線(人形)

(4星)
西
井9.8度
井9.8度
鬼西北
鬼西北
斗南西
華蓋西
塁壁陣北
赤道上
直線(人形)

南北
西
井8度
－
－
鬼西
斗南西
－
－
赤道上
曲線

東西
西
井7.3度
井6.3度
鬼西北
鬼西北
斗南西
華蓋東
塁壁陣南
赤道上
曲線

東西
西
井8.7度
井6.2度
鬼北
鬼西北
斗西
華蓋東
塁壁陣北
全星赤道南
曲線

6
V字の重ね
正
4星入壁度
4星入虚度
米型
長方形
V字の重ね
クラゲ型で
閉じず
東西
西
井13.8度
井6.2度
鬼西北
鬼西北
斗西
華蓋東
塁壁陣南
赤道上
箱型

(丸型)
西
井5.7度
井0.8度
鬼西北
鬼西北
斗南
華蓋東
塁壁陣北
全星赤道北
箱型

南北
東
井18.0度
井22.0度
鬼東北
積水東南
斗北西
華蓋西
虚宿距星線上
全星赤道南
直線

南北
東
井15.3度
井14.6度
鬼東北
積水東南
斗北西
華蓋西
虚宿距星線上
全星赤道南
曲線

東西
西

東西
西
井8.5度
井3.0度
鬼西北
鬼西
斗南西
華蓋東
塁壁陣南
全星赤道北
曲線

「諸国」の形「天牢」の形「六甲」の形「器府」の形「天阿」の名称

96

Charts of Harumi「尿」の名称「三師」の名称
円環に12宮の有無

－
－
－
斗南西
－
－
－
－

有

無

無

無

無

無

無

無

有

有

－

有

無
復刻:天阿
木版:阿
天矢
三公
有

天記

天紀

天記

有

有

有

天記

天紀

天紀

天記

阿星

天阿

天阿

有

有

阿

天阿

天河

天阿

天阿

尿
三師
－

尿
三師
無

尿
三師
-

有
－
無

有
有
無

尿
三師
有

尿
三師
-

天紀
天讒⇒天河
阿⇒附耳
天矢
三公
無

尿
三師
無

無
三師
－

天矢
三師
－

: 網掛けは『天象図』と同じ特徴を示す。

2023/01/21

Evolution of constellations "諸国(Syokoku)"
in Harumi's chart①天文列次之図(1670)

天文瓊統・星表(1698)

Format of the catalogue
is same.
(Fill in the values in
the constellation chart)
Yuan Dynasty starcatalogue(around 1363)

国立公文書館蔵/内閣文庫[特003-0017]

Revised②天文分野之図(1677)97

早稲田大学図書館蔵[文庫08 C0998]『天文匯抄十一種』
北京図書館古籍珍本叢刊78(1988) p.343

国立公文書館蔵/内閣文庫
2023/01/21[特003-000917]

Comparison results between Harumi's star catalog
and Yuan Dynasty's star catalog
・The Yuan Dynasty Star Table lists the positions of about 740 stars.
・Among them, 626 stars are consistent with the Harumi's star catalog(1698).
・The display unit is 0.1°for Yuan catalog and 0.5° for the Harumi star catalog.
There are 14 stars within ±0.25. 4 of them are in exactly the same position.
Distribution of difference between two catalogs
There is a strong
correlation between
the two catalogs.

Difference of Declination

6.0

-6.0

4.0

2.0
0.0
-4.0

-2.0

0.0

2.0

4.0

6.0

-2.0
-4.0
-6.0

98

Difference of Right ascension

2023/01/21

Star Chart of 麟祥院(Kyoto)
An astronomical chart dedicated to
Rinshoin in 1636 by the third shogun,
Iemitsu. A star chart presented by the
Korean envoy. Based on a star map from
the Ming Dynasty. Harumi used thecentral part of this star map.

99

「大地の肖像 : 絵図・地図が語る世界」京都大学学術出版会 (2007)口絵より

2023/01/21

Comparison with『天文成象』 and 『麟祥院図』
It is believed that Harumi
used this 『麟祥院図』 as areference when observing
the star and creating thestar map for internal Circle.

HR:4893

α UMi(Pole star of Tang)

Line:『天文成象』
Dot line:『麟祥院図』
1002023/01/21

Relation diagram of Harumi's star charts
China
Obs.
宋

Lee Dynasty Korea(1078～85)蘇頌星図(1086-93)

Chart of Harumi

天象列次分野之図(1395)
天象列次分野之図(木版、1571)

Star Chart of china

Inference of Korean peninsula①天文列次之図(1670)

蘇州天文図(1247)
Obs.
元
元朝・星表(1363頃)②天文分野之図(1677)

Ming Celling
chart(1453頃)(1526-67)?
麟祥院天文図(16C)

常熟天文図(1506)
天象列次分野之図(再刻、1687)(1623-36)?
Obs.
神宮天球儀
(1690)
Obs.

101----； assumption

天文瓊統
③天文成象
(1698/99)

Kyoto(1684-86)

Edo(1687-97)

Inference of main land China

Chart of Ming
(15～16C)

2023/01/21

Estimated Year of Observation of Star Catalog
by Least Squares Method
The value of 『貞享暦』 (Jokyo reki).
The refer value from 『授時暦』(Jyujireki).

Star Catalogue
28 stars

Harumi's『Temon Keito』『天文瓊統』

Chineseconstellation
Harumi's new
constellation

It is also possible that he had
obtained Qing astronomical
documents.

number House Width Declenation Observation
28

1279±28.1

1654±19.4

1063

1681.5±6.8

2501712.5±14.5『授時暦』(jyujireki)

28 stars

28

Yuan star catalog
元・星表『三垣列舎入宿去極集』

28 stars

28

1363±6.0

All stars733

1357±5.7

1684～86(京都)
1687～97(江戸)

1272±15.3

(±1σ)

102

Harumi was actually observing the stars.
The identification of Chinese constellations ismuch better than that of the missionaries(16th-18th centuries)
2023/01/21

Thanks

103

参考文献

104

[ 1]安部泰世(書写)『格子月進図』 国立天文台蔵 貴重資料・広瀬秀雄文庫0100 及び、『別冊太陽』 平凡社 73号 (1991) p.38-39[ 2]井上充幸「東アジアにおける楊子器図の展開」 「大地の肖像：絵図・地図が語る世界」 京都大学学術出版会(2007)p.282-297,口絵13[ 3]井本進「まぼろしの星宿図」天文月報 65巻11号(1972) p.290-292[ 4]井本進「続本朝星図略考」天文月報 35巻6号(1942) p.64-69[ 5]大崎正次「『格子月進図』の調査報告」 『中国の星座の歴史』 雄山閣出版 (1987) p.256-282[ 6]小川清彦「哭星の同定について」天文月報 25巻7号 (1932) p.121-126[ 7]神奈川県立金沢文庫 『中世の占い』(1989)[ 8]川原秀城「東洋の星図」 『東西の天球図』 千葉市立郷土博物館 (2002) p.6-14[ 9]斎藤国治/小沢賢二『中国古代の天文記録の検証』 雄山閣 (1992)[10]佐々木英治 『格子月進図』 私家版 (1983)[11]渋川春海『天文瓊統』 国立公文書館蔵(15巻本)(WEB版)[12]相馬充「キトラ古墳天文図の観測年代と観測地の推定」 国立天文台報 18 (2015) p.1-12[13]妹尾達彦『長安の都市計画』 講談社 (2001)[14]大東文化大学東洋研究所『若杉家文書『三家簿讃』の研究』 大東文化大学東洋研究(2004)[15]竹迫忍「中国古代星図の年代推定の研究」 数学史研究 228 (2017) p.1-21[16]竹迫忍「渋川春海の星図の研究」 数学史研究 231 (2018) p.1-46[17]竹迫忍「最小二乗法による中国古代星図の年代推定」 数学史研究 232 (2019) p.1-22[18]竹迫忍「北極星による古代の正方位測定法の復元」 数学史研究 239 (2021) p.1-22[19]竹迫忍「『格子月進図』の原図となった星図の年代推定」 数学史研究 Ⅲ期 第1巻1号 (2022) p.1-18[20]辻正博「唐代寫本における避諱と則天文字の使用」敦煌寫本研究年報 第十号(2016) p.437-446[21]千葉市立郷土博物館『星座の文化史』 平成7年度特別展展示解説資料(1995)[22]千葉市立郷土博物館『東西の天球図』 天文資料解説集 No.3 (2002)[23]中村士「キトラ古墳星図及び関連史料の成立年の数理的再検討」 科学史研究 275 (2015) p.192-214[24]中村士『古代星座を読み解く』 東京大学出版会 (2018)[25]奈良文研「キトラ古墳天文図 星座写真資料」奈良文化財研究所研究報告16 (2016)[26]野尻抱影『星と東方美術』 恒星社厚生閣 (1971)[27]前原あやの 「星座の三家分類の形成と日本における受容」 東アジア文化交渉研究 8 (2015) p.295-311[28]宮島一彦「日本の古星図と東アジアの天文学」京都大学 人文学報82 (1999) p.45-96[29]宮島一彦「蘇州天文図に関する若干の検討と碑文の訳注」大阪市立科学館研究報告 29 (2019) p.49-64[30]安田辰馬「神宮徴古館農業館所蔵の天球儀」 天文月報 第31巻 第8号(1938） p.154-160[31]薮内清『改定増補 中国の天文暦法』 平凡社 (1990)[32]渡辺敏夫『近世日本天文学史〈下〉観測技術史』 恒星社厚生閣(1987)[33]渡辺敏夫「保井春海星図考」東京商船大学研究報告 自然科学 14号(1963) p.7-50
海外文献[34]孙小淳「《天文匯抄》星表研究」 陳美東主編 『中国古星図』 遼寧教育出版 (1996) p.79-108[35]伊世同「中西対照 恒星図表1950.0」 科学出版社 (1981)[36]四庫全書「欽定四庫全書・子部玉海巻３ 『唐歩天歌』 」(電子版)[37]中華書局編集部編『歴代天文律暦等志彙編第1/2/3/5/6/7冊』 中華書局(1975/75/76/76/76/76)[38]中国天文学史整理研究小組『中国天文学史』 科学出版社 (1981)[39]馬世長「敦煌星図的年代」 『中国古代天文文物論集』 中国社会科学院考古研究所 (1989) p.195-222[40]北京圖書館古籍出版編輯組編「三垣列舎入宿去極集」 『天文匯抄十一種』 北京図書館古籍珍本叢刊78 書目文獻出版社 (1988)p.331-350[41]潘鼎『中国古天文図録』 上海科技教育出版社 (2009)[42]潘鼎『中国恒星観測史』 学林出版社(1989)[43]瞿曇悉達編 『唐開元占経』 中国書店出版(1989)[44]鄧文寛『敦煌天文暦法文獻輯校』 江蘇古籍出版社(1996)[45]庄蕙芷
『再論日本奈良的両座壁画墓及其天象図』 中国科技史杂志(中国科技史雑誌) 第42卷 2021 第 2 期 p.200-214[46]Jean-Marc Bonnet-Bidaud,Françoise Praderie and Susan Whitfield「The Dunhuang Chinese Sky: A Comprehensive Study of The Oldest Known Star Atlas」Journal of Astronomical History and Heritage, 12(1), 39-59 (2009).

Reference material105

28 constellation map in the old document
The old document in 金沢文庫 (Kanazawa bunko)『二十八宿図并五行法』( transcribed in 1278)(It is said to be an excerpt from the text of 六壬占.
From the shape of the constellations, it is believed that the
document dates back to the Tang dynasty.

翼

106

鬼

⚫ 翼宿: 3 part
⚫ 井宿: no line
⚫ 鬼宿: square井[神奈川県立金沢文庫 『中世の占い』(1989)p.39より]2023/01/21

黄一農, he points out that HR4852 is pole star over
several centuries around 300 in his paper(1992).

HR4852

Translation:
Estimates by the author.
From the 1st century to the 5th
century, among the stars visible to thenaked eye, G(HR4852) was the only
star closest to the celestial pole.
Around 310 A.D., the angular leading
between the two was close, at 0.05°.
The star's luminosity was rather faint(magnitude 6.3), but in the clear nightskies of antiquity without light
pollution, astronomers of the time had
no difficulty seeing it.
Therefore, in these centuries, the PoleStar (i.e., string star) is most likely the
G Star.

黄一農著『極星與古度考』清華学報 第2期第22巻(1992)
1072023/01/21

Date of observation records other than star charts

The date ofobservation isaround 370AD.
Observation of 景祐年間
(1030)

大衍暦(720年代)

1082023/01/21

Dating Methods of Ancient
Chinese Star Charts[Appendix: SHIBUKAWA Harumi's star charts]