Study for the Dating of the Old Chinese Star Charts: The oldest star chart “Moon’s path chart in grid paper”[格子月進図] thatconveys the image of the constellation at the beginning of Tang[初唐]Sinobu TAKESAKO
1. Introduction
The dating of the ancient Chinese star chart, so far has been carried out by finding thedate at which the error with the width of 28 xiu [28 宿広度] (1) or the identified stars areminimized by the precession. These methods estimate the dates from the observation
date of star catalog used for star charts. However, the same value of width of 28 xiu
were used long time, and the value of Han Dynasty[漢朝] has been only revised at Tang
Dynasty[唐朝](618-907) and Song Dynasty[宋朝] (960–1279). In addition, the starcatalog is also used in Tang Dynasty, which was measured in Han Dynasty[漢朝] andJin Dynasty[晉朝] (265–420). Therefore, in the date estimation by the present method,
only the result with Han Dynasty or Jin Dynasty is obtained. (2)In this way, in the ancient China where the same star catalog was used for a long time,the dating when the star chart was actually drawn, for example, the estimation of thedate of the star chart draw in Tang Dynasty, it cannot be done by using the observation
date of star catalog in principle.
The date estimation method proposed in this paper is not an estimation method basedon one dimensional information based on the position of the stars so far, but it ismultidimensional, such as the shape, positional relationship, and name of constellations
drawn on each star chart. It is a comparative age estimation method based on
information. In this method, even if multiple star charts use the same star catalog, it ispossible to estimate the date using unique information of each star chart.
For example, although it has not been noted that the shape and positional relationshipof Chinese constellations changed according to the period of the time, K. Ogawa of theTokyo Astronomical Observatory points it out from the study of the occultations of stars
by the moon and the planet in the ancient record. K. Ogawa (1932) says that “(chapter
5.) The disappearance of the Ku 哭星 (γ, δ Cap) and expansion of the Leibizhen 塁壁陣.
In the China, Ku 哭星 was absorbed during the 11th century, probably as a result of theastrological advance of the Leibizhen 塁壁陣.” It is supposed that the constellation Ku 哭
星 is absorbed by the constellation Leibizhen 塁壁陣. By using this, it is possible toestimate that the star chart where the Leibizhen 塁壁陣 is not expanded to the positionof Ku 哭星 (γ, δ Cap) is a star chart before the middle of the 11th century.
In addition to this, in Kaiyuanzhanjing [開元占経] compiled by Gautama Siddha[瞿曇悉達] during the first half of the ‘period of Emperor Xuan Zong [開元年間](713-741). In
this text, here is document called "Star chart" [星図](Vol. 106-110), which summarize
the transition of the ancient constellation, although there are only few clearly changed
constellations. It can be used for dating the star charts, this document shows thedifference between the current shape of the constellation[今図] in Tang Dynasty’s andthe old shape in the old period[旧図].
In addition to Kaiyuanzhanjing [開元占経], astronomical related documents describe
the approximate positional relationship of constellations and the constellation name ofthat period. We will compare and estimate the creation date of star charts based on
those documents.
Note) The star charts in the following documents are used in this study.
Su Song star chart[蘇頌星図]: S.Osaki(1987)p.232-234
Moon’s path chart[格子月進図][格子月進図]: Photo of National Observatory andE.Sasaki(1984)
Dunhuang star chart[敦煌星図]: S. Whitfield (2009) p.41
Chart of sky[天象列次分野之図]: Nara cultural Labo.(2016) (PL.7)- 1 -Suzhiu shike xingtu[淳祐石刻天文図]: Nara cultural Labo. (2016) (PL.6)
Kitora Astronomical Diagram[キトラ古墳天文図]:Nara cultural Labo. (2016) (PL.3
Takamatsuzuka Astronomical Diagram[高松塚古墳星 宿図]:Nara cultural Labo.
(2016) (PL.5))
Sankebosan[三家簿讃]: Daito Univ. (2004)
The Chinese constellations are referred to as XingXiu[星宿] for 28 xiu constellations,and other constellations are referred to as XingGuan[星官], but in this paper they will
be unified and referred to as Constellations[星座].
2. Star chart for the datingThis study is based on Su Song star chart[蘇頌星図] in Song dynasty(960–1279), as amain reference, we make a comparative dating of three star charts older than that. In
addition, there is also a star chart called Suzhiu shike xingtu[蘇州石刻星図(淳祐星図)] inSong dynasty. (3) Su Song Star Chart[蘇頌星図] is a star chart created by astronomer Su
Song[蘇頌](1020-1101) in North Song dynasty(960–1127), and it is printed in the bookon the astronomical observation instrument called Xin yixiang fayao[ 新 儀 象 法
要](completed in 1086 to 93) K. Yabuuchi (1990) p.125-126 states that the Su Song star
chart[蘇頌星図] is drawn based on the observations during [元豊年間] (1078-85).
However, it is said that the original book has not been transmitted, and there may be amodification in the later version. In the Su Song star chart[蘇頌星図], the Ku 哭星 (γ, δCap) mentioned above was absorbed by the western end of the Leibizhen 塁壁陣
expanded to Xu xiu 虚宿 and becomes a star that composes the Leibizhen 塁壁陣.
1) Moon’s path chart in grid paper[格子月進図] (hereinafter abbreviated as Moon’s path
grid chart )Moon’s path chart[格子月進図] is a star chart of Tuchimikado [土御門], and it is a copyof the original drawing by Y. ABE [安倍泰世] around the first year of Bunpo[文保] (1317).
In addition, it is described as "moon grid figure" in the note of the book (1215) of thetranscription of the old document of the constellation "Sankebosan" [三家簿讃](4), and it
is said that the original drawing existed by this time. Moon’s path chart[格子月進図]
was discovered by Susumu Imoto during the 2nd world war, but it was destroyed by air
raids (1945) during the exhibition at Yurakucho Tonichi Kaikan[有楽町東日会館].
Luckily, there are still photos taken before the fire and a restored version of chart has
been published by E. Sasaki (1984). Moon’s path chart[格子月進図] consisted of acircular diagram of the northern sky and a square diagram of the mid latitude. The
square star chart was drawn on a sheet of 1degree interval grid. The constellations weredrawn in three colors of yellow, red and black according to the three family’sclassification. (5) In this star chart, the western end of the Leibizhen [塁壁陣] mentioned
earlier is in Wei xiu 危宿, and Ku 哭星(γ, δ Cap) has not been absorbed by the
Leibizhen 塁壁陣, so the original chart is drawn before the Song Dynasty[宋朝] .
About the date of the original drawing, S. Imoto (1942) p. 69 had suggested almost thesame age as Su Song star chart in the AD 1100 from the spring equinox, and it is
supposed to that the chat was based on the observation of Yuan Zhen period [元豊年間](1078-85). T. Watanabe (1987) p.762-764 suggested based on the width of 28 xiu [28 宿広度](1), it has a slight difference from the value of Yixing[一行] (about AD720) who madeDayan calendar[大衍暦], 2) Based on the description of Song Shi[宋史], the width of 28
xiu [28 宿広度] did not change from Han Dynasty to Yixing[一行]. Based on these,
Watanabe thought Moon’s path chart[格子月進図] was produced from 720 to 1215. S.
Osaki (1987) p.256-273 suggested, 1) From the analysis of the area of 12 section[12 次]
which represent season indicate the date is BC188 ± 21 years. 2) From the analysis of
declination of position of the stars, the date is AD 500 ± 50 years.
Since this star chart has been burned in the war, so detailed research has only been
conducted by S. Osaki, and identification work with the modern star catalog has notbeen conducted.

- 2 -2) Dunhuang star chart[敦煌天文図]In 1900, a large number of documents were found at the Mogao Caves[莫高窟] in
Dunhuang in western China, and the British explorer A. Stein bought part of them andbrought it back to the British Museum (1907). The documents contained star chartcalled Dunhuang star chart[ 敦 煌 天 文 図 ] (Stain, MS3326). Afterward, Needham
introduced a part of this chart in "Science and Civilization of China" (1959) andrevealed its existence. He estimated the date of the star chat is around AD940, but did
not show the basis of it. (6)Ma[馬世長](1989) p. 198 suggested based on ,1) in the divination part of MS 3326, thetaboo characters (avoid the characters of the emperor’s close relatives) of min 民 of [太宗・世民] is modified (one line of the character is deleted), 2) the text in the star chart
From the fact that the characters of tan[旦] of Ruizong [睿宗・旦] is not absconded, 3) the
nonuse of the Modified Chinese characters by Wu Zetian [則天文字], the date was during
Zhongzong 中宗 period (705～710) in the Tang Dynasty. Furthermore, S.I. Whitfield(2009) p.50 dates back to the Gao Zong 高宗 period (649 to 684) until the year when
Ruizong [睿宗] ranked in 684 by the same reason. However, these estimations are notbased on the star chart itself.
Dunhuang star chart[敦煌天文図] is composed of a circular diagram of the northern sky
and a square diagram of the mid latitude divided into 12th order (month). This star
chart is very similar to Moon’s path chart[格子月進図], and the shapes and names of
constellations are almost the same and can be compared easily. But there are manyerrors if it is copied by the person without knowledge of constellations. (7) This star
chart seems to have been copied from the original chart in a short time, and the picturesand letters are also rough. The Ku 哭星 (γ, δ Cap) in this star chart has not beenabsorbed by the Leibizhen 塁壁陣, so the original chart is drawn before the Song
Dynasty[宋朝] (960–1279).
3) Chart of the sky [天象列次分野之図] (hereinafter referred to as [天象図])
Chart of the sky is a stone shaped star chart transmitted to Korea, according to theinscription “When there was a stone caving star chart in the castle of Goguryeo Dynasty[高句麗], it was attacked by the coalition forces of Tang[唐] and Silla[新羅] and Goguryeo
was destroyed (668). The chart of the stone sculpture was sunk in the river. However,
the rubbed copy was remained. When Lee Chosun Taizu[太祖] (Reigned: 1392-1398) was
crowned, it was presented to him. He ordered to create an stone caving star chart withthe rubbed copy as an original drawing, and was completed in December of 1395 [太祖4, 洪武 28]. (8) This stone caving star chart was caved again on the back during SongSong 粛宋 period (1674 to 1720). The rubbed copy being distributed is said to be a recraved figure. However, the rubbed copy of the original, which is considered to be theGoguryeo period, has not been transmitted.
As for the date of the original drawing, T. Watanabe (1987) p. 772 suggested, the value
described in the inscription of Chart of the sky[天象図] and the value of Shi shi
xingjing[石氏星経] described in Jiu tang shu tianwenzhi[旧唐書天文志] and Kaiyuan
zhanjing [開元占経] based on the observation of AD 200 is almost the same. Based on
this, he believes the date of the chart is from AD 200 to 668 when Goguryeo wasdestroyed. However, this estimation has a problem, this estimation was not made basedon a star chart itself, and it was made based on the star position and legend in theinscription described on 1495 without examination of these newly described materials.
In this star chart, the western end of the Leibizhen 塁壁陣 is in the Wei xiu 危宿, andthe Ku 哭星 (γ, δ Cap) is not absorbed by the Leibizhen 塁壁陣, so it is a star chart
before the Song Dynasty[宋朝] (960–1279).

- 3 -3. Dating of Moon’s path chart[格子月進図]
We will start the dating of Moon’s path chart[格子月進図]. Fig. 1 shows the area around
Xuanyuan 軒轅 in chart.
Fig. 1 Moon’s path chart[格子月進図] (From “Bessats Taiyou” Vol.73 (1991) p.39)

1) The shape of Xuanyuan 軒轅
The first thing to notice when we look at Moon’s path chart[格子月進図] is that there isno number on the star in the row of stars extending northwest from Xuanyuan 軒轅 in
the middle of Fig. 1. Since it is in the same constellation, this portion of constellation isconsidered to be added later. The Xuanyuan[軒轅] of Su Song star chart [蘇頌星図] also
extends in the same northwest direction, but there is no branch at the end.
Xuanyuan[軒轅] is described as "Yellow Dragon" in Sankebosan [三家簿讃](Daito Univ.
(2004), 7th paper). the southern part is the head of a dragon, and the stars in the west
are tails. The description for the Xuanyuan 軒轅 in Kaiyuanzhanjing [開元占経] (Vol.
107) says that "軒轅，舊尾漸斜向上，今測其尾勢迤邐向西"( Xuanyuan 軒轅, the tail was
gradually turning upwards in the old chart. But we measure now, the appearance of the- 4 -tail is long sideways and heading west.) Therefore, the west facing tail is the tail of thestar chart of the period when Gautama Siddha [瞿曇悉達] editing Kaiyuan zhanjing [開元占経] , and the northwest facing diagonal tail is the tail of the old star chart.
Although the figure of the main constellation is drawn in Sankebosan [三家簿讃] andmost of them are in the same shape as Moon’s path chart[格子月進図], Xuanyuan 軒轅
has a branched tail extending to the northwest (see FIG. 2). In the back of the book of
Yasushi Abe (1215/2/21), who copied Sankebosan [三家簿讃] (on February 21,1215 ),wrote that “As for the figure, if the difference is large, just copy it according to Moon
path chart.” However, since Xuanyuan 軒 轅 has a large difference compared toSankebosan [三家簿讃], it may have been added in Moon’s path chart[格子月進図]. The
constellation with a branched end is one of the features of the constellations ofSankebosan [三家簿讃] and Moon’s path chart[格子月進図]. There are Tiangou 天狗 in
the lower right of Fig. 1, and Guki 鼓旗 and Zuoki 左旗 in addition to the above, havebranched end.
Summary of the tail of Xuanyuan[軒轅] is as follows.
Old chart: A tail extending to the northwest. (The end of the tail was divided in
Sankebosan [三家簿讃].)
Current chart (Period of Kaiyuan[開元年間]): A tail extending to west.
Song Dynasty (from Su Song star chart[蘇頌星図]): A tail extending to the northwest.
(The end of the tail is not branched.)
Therefore, the original shape of Xuanyuan 軒轅 in the Moon’s path chat conforms to thedescription in Kaiyuan zhanjing [開元占経].
Fig. 2 Shape of constellation of Xuanyuan 軒轅 (except Moon’s path chart[格子月進図])『三家簿讃 』

『敦煌図』

『天象図』

『蘇頌星図』

2) The position of Guan 爟
The square constellation in the south of the character of Xuanyuan 軒轅宮 in Fig. 1 isGuan 爟. It is a constellation that means a signal fire. About this constellation, Kaiyuan
zhanjing [開元占経] (Vol. 109) state “燿星,舊圖在軒轅腹內,今測在軒轅尾南,近柳北四星”(Guan 爟, it is in the belly of Xuanyuan 軒轅 in the old chart. Now we measure , it issouth of tail of Xuanyuan 軒轅. 4 stars are close to north of Liu xiu 柳宿) As it is unclear
where the belly of Xuanyuan 軒轅, if we look at the description of Neiping 内平 locatedin the north of Xuanyuan 軒轅, it says “舊云在中台南,舊圖在軒轅腹,又在柳七星度,今測在中台南,張七度,複與星經同.四星,中台南.” Kaiyuan zhanjing [開元占経] (Vol. 109) From
this description, the belly of Xuanyuan 軒轅 is south of Zhongtai 中台. Therefore it
locates north of Xuanyuan 軒轅. The description of Guan 爟 is translated as follows.
Guan 爟, was located north of Xuanyuan 軒轅 in the old chart, but now it is a four starsouth of the Xuanyuan 軒轅 and close to the north of Liu xiu 柳宿.
In the Su Song star chart[蘇頌星図], Guan 爟 has moved to the northwest of Gui xiu 鬼
宿. However, in Sankebosan [三家簿讃] (Daito Univ. (2004) No. 13 paper) says “爟四星在軒轅右角南、一曰在尾西”. (Guan 爟 is four stars, located in south of right hone of
Xuanyuan 軒轅, other says it is west of tail.) If we are supplementing the latter half with
“在[軒轅]尾西”(it was west of tail of Xuanyuan 軒轅), Therefore, it cannot be denied thatit may have been in the west of Xuanyuan[軒轅] tail (north of Gui xiu 鬼宿) in old
chart.(9) Fig. 3 shows the positional relationship between Guan 爟 and Gui xiu 鬼宿 in- 5 -each star chart. The summary of positions of Guan 爟 are as follows .
Old chart: North of Xuanyuan 軒轅. Or west of Xuanyuan 軒轅 tail (north of Gui xiu 鬼
宿).
Current chart (Period of Kaiyuan[開元年間]): Close to the north of Liu xiu 柳宿 in thesouth of Xuanyuan 軒轅 tail (southeast of Gui xiu 鬼宿).
Song Dynasty (from Su Song star chart[蘇頌星図]): Northwest of Gui xiu 鬼宿.
Therefore, the position of Guan 爟 in the Moon’s path chat conforms to the description of
the current figure in Kaiyuan zhanjing [開元占経].
Fig. 3 Positional relationship between Guan 爟 and Gui xiu 鬼宿

『月進図』

『敦煌図』

『天象図』

『蘇頌星図』

3) Direction of the mouth of Dou 中斗
As shown in Fig. 4, to the east of Dizuo 帝座, there are twin constellations in the northand south called Dou 中斗 and Hu 斛. There is a note in Sankebosan [三家簿讃] , it says
"one hundred" in red ink. (Daido Univ. (2004) sheet No. 12)
Kaiyuan zhanjing [開元占経] (Vol. 107) says “[中]斗,五星,在宦者西南.舊[中]斗星口仰兼
背斛,今視天,[中]斗口向下覆斛.” (The mouth of the old Dou 中斗 turned upwards and Hu
斛 turned to the back. If you look at the sky now, the mouth of Dou 中斗 will cover Hu
斛 downwards.) Since Dou 中斗 in Moon’s path chat is facing Hu 斛 downwards, itmatches the description in current figure in Kaiyuan zhanjing [開元占経]. Unlike thedescription of Kaiyuan zhanjing [開元占経], Su Song star chart[蘇頌星図] is facing east.
The summary of the direction of the mouth of Dou 中斗 is as follows.
Old chart: Upward with Hu 斛 in the back.
Current chart (Period of Kaiyuan[開元年間]): Downwards to cover the Hu 斛.
Song Dynasty (from Su Song star chart[蘇頌星図]): Facing east.
Fig. 4 Orientation of Dou 中斗 and Hu 斛.

『月進図』

『敦煌図』

『天象図』

『蘇頌星図』

4) The position of Jixin 積薪
Jisui 積水 and Jixin 積薪 are at the end of the tail extending to the west of Xuanyuan
軒轅 in Fig. 1. The position of these constellations are “積水,一星,北河西北.積薪,一星,積水東南”(Jisui 積水, one star, north west of Beihe 北河. Jixin 積薪, one star, southwest of
Jisui 積水) in Kaiyuan zhanjing [開元占経] (Vol. 107). There is no comparison with oldchart because they were the same position. In the case of the Su Song star chart[蘇頌星図], Jixin 積薪 has moved south, to the west of Gui xiu 鬼宿. Therefore, it is possible todetermine whether it is a pre Song Dynasty[宋朝] star chat based on whether Jixin 積薪
is located to the north or south of Beihe 北河. Moon’s path chart[格子月進図] is a chartof the pre Song Dynasty[宋朝], because Jixin 積薪 is east of Jisui 積水 and north of
Beihe 北 河 . In addition, it matches east of Jisui 積 水 described in Sui shu- 6 -tianwenzhi[隋書天文志]. The summary of the positions of Jixin 積薪 are as follows.
Old chat: Southeast of Jisui 積水 and north of Beihe 北河 .
Current chart (Period of Kaiyuan[開元年間]): Southeast of Jisui 積水, north of Beihe 北河.
Song Dynasty (from Su Song star chart[蘇頌星図]): South of Beihe 北河, West of Gui xiu
鬼宿. (However, Son shi [宋史] states that Jixin 積薪 is northeast of Jisui 積水)
5) The shape of Leibizhen 塁壁陣
The description of Kaiyuan zhanjing [開元占経] (Vol. 108) of Leibizhen 塁壁陣, which
was used to identify whether it is a pre Song Dynasty[宋朝] star chart, is as follows. “壘
壁 陣 , 東 頭 第 一 星 入 東 壁 度 , 又 西 頭 五 星 入 危 度 . 今 測 不 入 東 壁 度 , 又 西 頭 六 星 入 危 度 .”(Leibizhen 塁壁陣, in the old chart, one star of the east head was in Bi xiu 壁宿 and fivestars of west head are in Wei xiu 危宿. When we measure now, no star of the east head
was in Bi xiu 壁宿 and six stars of west head are in Wei xiu 危宿. Six stars are in the
hotel.) In case of Moon’s path chart, no star of the east head was in Bi xiu 壁宿 and six
stars of west head are in Wei xiu 危宿. Therefore, Moon’s path chat is in the middle ofthe old chart and current chart.
The summary of the form of Leibizhen 塁壁陣 is as follows.
Old chart: One star of the east head was in Bi xiu 壁宿 and five stars of west head are in
Wei xiu 危宿.
Current chart (Period of Kaiyuan[開元年間]): No star of the east head was in Bi xiu 壁宿and six stars of west head are in Wei xiu 危宿.
Song Dynasty (from Su Song star chart[蘇頌星図]): No star of the east head was in Bi
xiu 壁宿 and five stars of west head are in Xu xiu 虚宿.
6) The shape of Yi xiu 翼宿As shown in the lower left of Fig. 1, the Yi xiu 翼宿 is separated into three parts, upper,
middle, and lower, in Moon’s path chart[格子月進図]. This is exactly the same as thefigure of Sankebosan [三家簿讃] (Daito Univ. (2004) paper No. 5). In addition, although
Yi xiu 翼 宿 in Kitora tomb astronomy diagram[ キ ト ラ 古 墳 天 文 図 ] is designed
symmetrically, it is common to be divided into three parts. (See Fig. 5) When thisbecomes Su Song star chart[蘇頌星図], the three parts are in a series to change into an
image of a bird. In addition, about Yi xiu 翼宿 of Takamatsuzuka tomb astronomy
diagram[高松塚古墳星宿図], although the some of the restoration figure incorrectly
using Yi xiu 翼宿 of Su Song star chart, there is only a small part of the upper and lower
portion is remained (see Nara cultural property research Office (2016) (PL. 5)).
Although it is slight, the existing part overlaps with the design of Kitora tombastronomy diagram[キトラ天文図]. Therefore, it can be presumed that Moon’s pathchart[格子月進図] is a star chart of the same period as Kitora tomb around AD700.
Fig. 5 Shape of Yi xiu[翼宿]『キトラ天文図』 『月進図』『敦煌図』『天象図』 『蘇頌星図』

7) Shape of Tianyuan 天淵
There is a constellation with 10 stars named Tianyuan 天淵 to the south of Dou xiu 斗
宿. As shown in Fig. 6, the letters of “M” are facing each other in Moon’s path chart[格子月進図] and San Sankebosan [三家簿讃] (Daito Univ. (2004) paper17th), and they havethe shape of a constellation like a river. This is converted to a form in which the- 7 -mountains facing each other in the letter “M” are connected by a line and the four
vertices of the hexagon and the four-way star are connected in Su Song star chart[蘇頌星図]. The change is small, but the appearance is very different, so it can also be used
for the dating of the chart. The Suzhiu shike xingtu[蘇州石刻星図(淳祐星図)] is also thesame shape as the Su Song star chart[蘇頌星図].
Fig. 6 Shape of Tianyuan 天淵

『月進図』

『敦煌図』

『天象図』

『蘇頌星図』

8) The shape of Tianda jiangjun 天大将軍
There is a ship shaped constellation called Tianda jiangjun 天大将軍 in the northeastof Kui xiu 奎宿, and it is placed in horizontally in Moon’s path chart[格子月進図], butsince Su Song star chart[蘇頌星図] is place it almost vertical direction, this constellation
can also be used for the dating of the chart.
9) The shape of Hu 弧
The Hu 弧 in the lower right of Fig. 1 is the same as the Sankebosan [三家簿讃] (Daito
Univ. (2004) sheet No. 10), and the Hu 弧 in Kitora astronomy diagram is the same
shape of figure. The Su Song star chart[蘇頌星図] has also same form. Therefore, there
is no change with age in Hu 弧. In Suzhiu shike xingtu[蘇州石刻星図(淳祐星図)], there isa star between the bow of the arrow and the strings.
10) The name of Youqi 右旗
There are constellations called Hegu 河鼓 and Youqi 右旗 in Su Song star chart[蘇頌星図]. But there is no constellation name of Youqi 右旗 at the early days of Tang Dynasty
when Kaiyuan zhanjing [開元占経] was compiled. Kaiyuan zhanjing [開元占経](Vol. 107)
states ”河鼓並旗,十二星,在牽牛北.” (Hegu 河鼓 and qi 並旗, 12 stars, it is north of Nui xiu
牛宿.) In the case of Sankebosan [三家簿讃] (Daito Univ. (2004), No. 6), it is called
HeguGuqi 河鼓ゝ旗
（河鼓鼓旗）. Similarly, Youqi 右旗 is described as Guqi 鼓旗 in Moon’s
path chart[格子月進図]. That is, it can be estimated that Guqi 鼓旗 changed to Youqi 右旗 after the middle of Tang dynasty. This can be used for the dating of the chart.
11) The name of Huben 虎賁 and Tianyuan 天淵 related to taboo character
Kaiyuan zhanjing [開元占経] (Volume 110) states that ”虎賁,古今同,一星,下台南.”(Huben 虎賁, same as old chart, one star, south of Xiatai 下台. But the south of Xiatai“下台” in Fig. 1 is “武賁”. In the same way, this star was also called “武賁”in Jin shu
tianwenzhi[ 晉 書 天 文 志 ]( 歴 代 天 文 律 暦 等 志 彙 編 (Compilation of the Astronomical
document) Vol.1,p.179, hereinafter abbreviated as CA) and Sui shu tianwenzhi [隋書天文志](CA Vol.2,p.572) Osaki, M. (1987) p. 155 explained the reason that, because thesewas edited in the early Tang Dynasty, the character of Tiger “虎” was taboo characterand transformed the tiger into “武”. In fact, Taizu 太祖[李虎] is the grandfather of the
Gaozu 高祖[李淵] (reigned: 618-626) who is father of Taizong 太宗[李世民](reigned:
626-649).
In the same way, The name of Tianyuan 天淵 is also changed to Tianchi 天池 (pond in
the sky) to avoided taboo character of “淵” which is name of Lee Yuan 唐・高祖[姓・諱：李淵] in Jin shu tianwenzhi[晉書天文志] and Sui shu tianwenzhi [隋書天文志]. In case ofMoon’s path chart[格子月進図], Tianyuan 天淵 is changed to Tianquan 天泉 (spring of
the sky).
- 8 -In addition, there are stars named Youminjiao 右民角 and Zuominjiao 左民角 besidethe Ecliptic of Xuanyuan 軒轅 in Figure 1. The character of Min 民 is taboo character
for Taizong 太宗[李世民]. But because this character is frequently used, it was permitted
to use it alone during his reign. However, the following emperor Gaozong 高宗[李治].
(reigned: 649-683) made it taboo character on June 649. (10) Therefore, Original
drawing of Moon’ path chart was drawn between AD618 and 649, during this period, the“淵” is regarded as taboo character and "民" is not regarded as taboo character.
12) The dating by the spring equinox
There is a line that seems to be an ecliptic in Moon’s path chart[格子月進図], and thedate can be estimated from the spring equinox that intersect the equator. (11) But there
are two points for autumnal equinoxes at left and right side in Moon’s path chart[格子月進図] and they are not a same right ascension.
S. Imoto (1942) p. 69 first made an estimation with the spring equinox of this chart,
and the estimated date is roughly the same as Su Song star chart[蘇頌星図] in the AD
1100’s. However, there is an error in this estimation. AD1100 is when the reference starof Kui xiu 奎宿 (ζ And) is at the spring equinox, and the spring equinox of Moon’s pathchart[格子月進図] is 5.5 degrees east of it, so it is before AD700.
Watanabe Toshio (1987) p.762 calculates the potential 3 reference stars of Kui xiu 奎宿,
and gives the results of AD814 (δ And), AD653 (ζ And), AD466 (ηAnd) respectively. (12)However he has describes that “the only thing that matches, as a result of the dating bywidth of 28 xiu [28 宿広度] (after AD720, see section 2.1), is δ And only, and it is difficult
to decide which one to trust and we should investigate by other methods. “However, if we look at Kui xiu 奎宿 in Moon’s path chart[格子月進図], the star on thewest of the three stars is ζ And, and this star is considered to be a reference star of Kui
xiu 奎宿. This can also be confirmed from the Moon’s path chart[格子月進図], even if wecalculate with the star β And which is close to the spring equinox, it is AD696. Therefore,
the spring equinox of Moon’s path chart[格子月進図] is the year 653 calculated with thestar ζ And is 5.5 degrees east from the Spring equinox. As a matter of fact, whencalculated with the left and right autumnal equinoxes, it will be AD345 and AD988, andthe average will be AD666, which is a value close to the spring equinox.
13) Summary of dating of Moon’s path chart[格子月進図]Based on the above consideration, the most of the parts of original drawing of Moon’s
path chart[ 格 子 月 進 図 ] is same as Current chart (period of Kaiyuan[ 開 元 年 間 ])described in Kaiyuan zhanjing [開元占経] edited by Gautama Siddha[瞿曇悉達] except
some constellation name to avoid taboo character.
The original drawing is considered to be drawn during Gaozu 高祖(reigned: 618-626)
and Taizong 太宗(reigned: 626-649) period, base of the situation of taboo character. In
addition, considering the use of new width of 28 xiu [28 宿広度] and the dating of thespring equinox, the relationship with Li Ruifeng 李淳風(602-670) is also considered, andas the date of original chart, Taizong 太宗(reigned: 626-649) period is most suitable date.
4. Dating of Dunhuang star chart[敦煌天文図]1) The shape of Xuanyuan 軒轅
The tail of Xuanyuan 軒轅 extends northeast as shown in Fig. 2, but there is no branchat the end of the tail. Therefore, the date is estimated between period of Kaiyuan[唐・開元年間] and Song Dynasty[宋朝].
2) The position of Guan 爟
As shown in Fig. 3, Guan 爟 is located northeast of Gui xiu[鬼宿]. Therefore, the date isestimated to be the period before the current chart of Kaiyuan zhanjing [開元占経], or
between period of Kaiyuan[唐・開元年間] and Song Dynasty[宋朝].

- 9 -3) Direction of the mouth of Dou 中斗
Dou 中斗 is shown in the figure of October, but it is drawn to the east as shown in Fig.
4 and is different from the description of Kaiyuan zhanjing [開元占経] and it is the sameas Su Song star chart[蘇頌星図]. The date is estimated to be between period of
Kaiyuan[唐・開元年間] and Song Dynasty[宋朝].
4) The position of Jixin 積薪
Jixin 積薪 is located to the north of Beihe 北河 and is presumed to be a chart before
Song Dynasty[宋朝].
5) The shape of Leibizhen 塁壁陣
There is no line of 28 xiu reference star in Dunhuang star chart[敦煌天文図], so wecannot judge the position of the stars of Leibizhen 塁壁陣.
6) The shape of Yi xiu 翼宿Yi xiu 翼宿 is also divided into three parts as shown in Figure 5. However, unlike
Moon’s star chart[格子月進図], the number of stars in the central star group has
increased, and the tentacles are shaped to extend vertically. It is a state of one step
before three parts are connected like Su Song star chart[蘇頌星図]. From this, the age isestimated to be between period of Kaiyuan[唐・開元年間] and Song Dynasty[宋朝].
7) Shape of Tianyuan 天淵As shown in Fig. 6, Tianyuan 天淵 has a ring consisting of six stars (correcting fivestars in the original drawing) surrounded by a square gate consisting of four stars. It isa shape quite different from Tianyuan 天淵 in Moon’s path chart[格子月進図]. But it is aform where the four stars around in Su Song star chart[蘇頌星図] are connected insquare, and it is an age close to Su Song star chart[蘇頌星図] From the shape of the
figure, there is no evolution to be considered in the direction from Dunhuang star
chart[敦煌天文図] to Moon’s path chart[格子月進図].
8) The shape of Tianda jiangjun 天大将軍
There is no name of in Tianda jiangjun 天大将軍 at the south of Gedao 閣道 in the
figure in February, but there is jiangjun 天大将軍 put it in horizontally. Therefore, thedate can be estimated as a period close to Moon’s path chart[格子月進図].
9) The shape of Hu 弧
Hu 弧 has almost the same form as Sankebosan [三家簿讃] and Moon’s path chart[格子月進図], except that there is a star between the bow of the arrow and the strings. Thisis the same as Suzhiu shike xingtu[蘇州石刻星図(淳祐星図)].
10) The name of Youqi 右旗
Youqi 右旗 in July chart is written as Guqi 鼓旗 as same as Moon’s path chart[格子月進図]. Therefore, the age of Dunhuang star chart[敦煌天文図] is estimated to be earlier
than the age of Tan bu tian ge[唐歩天歌], which is close to period of Kaiyuan[唐・開元年
間].
11) The name of Huben 虎賁 and Tianyuan 天淵 related to taboo character
Huben 虎賁 is in the upper right of the figure in July as "虎賁" and Tianyuan 天淵 is inlower right in November as "天淵". The date can be estimated after the period when thetaboo character ended like Kaiyuan zhanjing [開元占経].
12) Text of Dunhuang star chart[敦煌天文図]According to 鄧文寛(1996) p.82-83 note (80) and (96), 『自栁九度至張十七度』(in June
chart) and 『自張十八度至軫[十]一度』(in July chart), are same value of Kaiyuan- 10 -

zhanjing [開元占経] (vol.64). Therefore, the text of Dunhuang star chart[敦煌天文図] is
considered to be taken from Kaiyuan zhanjing [開元占経], and it can be estimated as thetime after Kaiyuan zhanjing [開元占経].
13) Summary of dating of Dunhuang star chart[敦煌天文図]The shape of constellation of Dunhuang star chart[敦煌天文図] is similar to Moon’s
path chart[格子月進図], and it can be estimated to be between after the period of
Kaiyuan[唐・開元年間] and middle of Tang[唐] period.
5. Estimating the Age of Chart of Sky[天象図]1) The shape of Xuanyuan 軒轅
The tail of Xuanyuan 軒轅 extends to the northeast as well as Dunhuang star chart[敦煌天文図] as shown in Fig. 2. There is no branch at the end of tail. Therefore, the date isestimated between period of Kaiyuan[唐・開元年間] and Song Dynasty[宋朝].
2) The position of Guan 爟
As shown in Fig. 3, Guan 爟 is located northeast of Gui xiu 鬼宿 like Dunhuang star
chart[敦煌天文図]. Therefore, the date is estimated to be the period before the current
chart of Kaiyuan zhanjing [開元占経] or between period of Kaiyuan[唐・開元年間] andSong Dynasty[宋朝].
3) Direction of the mouth of Dou 中斗
As shown in Fig. 4, Dou 中斗 is drawn to the east almost the same way as Su Song star
chart[蘇頌星図], and it differs from the description of Kaiyuan zhanjing [開元占経].
Therefore, the date is estimated to be between period of Kaiyuan[唐・開元年間] and Song
Dynasty[宋朝]4) The position of Jixin 積薪
Jixin 積薪 is located to the north of Beihe 北河 and is presumed to be a chart before
Song Dynasty[宋朝].
5) The shape of Leibizhen 塁壁陣
There stars of the east head was in Bi xiu 壁宿 and six stars of west head are in Wei
xiu 危宿. The west head is the same as the figure of Kaiyuan zhanjing [開元占経].
Therefore, it is estimated from the west head of Leibizhen 塁壁陣 that the year is periodof Kaiyuan[唐・開元年間], but the east head is very different from that period.
6) The shape of Yi xiu 翼宿As shown in Figure 5, Yi xiu 翼宿 has the same figure which three parts are connected
as Su Song star chart[蘇頌星図]. Yi xiu 翼宿 of the two star charts of “呉越王銭氏家族墓
室星図”(Qian Chu Family Tomb Star Diagram, around AD900) published in 潘鼎(2009)p.47 are also connected with three parts. If this figure is a correct copy of a mural,Yi xiu 翼宿 has been integrated at the end of the Tang Dynasty. Therefore, the date isestimated to be after the period of Dunhuang star chart[敦煌天文図] and in the lastperiod of Tang Dynasty [唐] .
7) Shape of Tianyuan 天淵As shown in Fig. 6, Tianyuan 天淵" is similar to Su Song star chart[蘇頌星図] andestimated to be close to Song Dynasty[宋朝].
8) The shape of Tianda jiangjun 天大将軍
Tianda jiangjun 天大将軍 is placed vertically in the north and south, and it ispresumed to be the date similar to the Su Song star chart[蘇頌星図] and close to Song
Dynasty[宋朝].

- 11 -

9) The shape of Hu 弧
Hu 弧 has two arrows and is shaped differently from the other three star charts.
10) The name of Youqi 右旗 and Tianshi 天尿Youqi 右旗 is described as "右旗" as well as Tan bu tian ge[唐歩天歌], not Guqi 鼓旗. In
addition, Tianshi 天尿 is written as Tianshi 天矢 like other ancient star charts, unlike
Tang bu tian ge[唐歩天歌]. Therefore, it is presumed that the date is considered after
the Dunhuang star chart[敦煌天文図] and older than the Tang bu tian ge[唐歩天歌].
11) The name of Huben 虎賁 and Tianyuan 天淵 related to taboo character
There are Huben 虎賁 and Tianyuan 天淵 in the chart, therefore, no character fortaboo is used. It is estimated to be after Kaiyuan zhanjing [開元占経].
12) Peculiarity of this chart
There are many constellations that cannot be seen in other ancient star charts of thesame period.
・ In Hu 弧, there are two arrows instead of one.
・ In Bagu 八穀 in north sky, the shape is not a rectangle but a pentagon.
・ In Gang 紅 in north sky, the shape is not straight but curved.
・ Yulinjun 羽林軍 is not a combination of triangles but the whole is connected.
・ In Laoren 老人 is not west of Hu 弧 but east. This star cannot be seen from Seoul.
・ 宗太夫 4 stars is added to the east of Zongren 宋人.(13)・ A circle of 12 zodiac zone has been added. It is influence of Huihui Lee 回回暦.
K. Yabuuchi(1959) p. 146 states "The figure created by Wu Yunfu 伍允孚, who became
an official of the Observatory during King Zhonglie 忠烈王(1275-1308), was widely usedin the observatory.“ There is a possibility that the original image of this chart is not thesame as Tang’s original drawing, but after being transmitted to Goryeo 高麗, themodifications has been applied.
13) Dating by using spring and autumn equinox
The inscription is referred to as Jin shu tianwenzhi[晉書天文志], and it is said that”秋
分:角五小弱,春分:奎十四小強”(Autumn:Jiao xiu 5 and few degrees( BC52), Spring:Kui
xiu 14 and few degrees (BC48).) Reading from the star chart, Autumn equinox: 5degrees (BC44), spring equinox: 4 degrees (AD776 years), and spring distribution isadvancing, but autumn distribution is drawn as Jin shu tianwenzhi[晉書天文志].
K. Yabuuchi (1990) p. 124 says that the “Reading from Suzhiu shike xingtu[蘇州石刻星図(淳祐星図)], Autumn equinox is at Jiao xiu 角 5 degree and Vernal Equinox is at Kui
xiu 奎 3 degree, the date is around AD900 from the Neugebauer star list.” But, it has
also an error in the fall equinox, and in any case, the vernal equinox and fall equinox ofthe 天象図 are in almost the same position as the Suzhiu shike xingtu[蘇州石刻星図(淳祐星図)] and cannot be used for dating the chart.
14) Summary of dating of 天象図
The date of the original drawing of 天象図 can be estimated to be after Dunhuang star
chart[敦煌天文図] and before Tang bu tian ge[唐歩天歌]. However after transmitted toGoryeo 高麗, modifications were made to the original drawing.
6. Summary of estimated date each star chart
The results of dating of chart are summarized in Table 1. There were only few
contradictions of the times between items in each star chart. The estimated ages of theoriginal drawings are summarized in the following order.
Moon’s path chart[格子月進 図 ] ⇒ (Kaiyuan zhanjing [開元占経 ])⇒ Dunhuang star
chart[敦煌天文図]⇒Chat of sky[天象図]⇒(Tang bu tian ge[唐歩天歌])⇒Su Song star
chart[蘇頌星図]- 12 -

Among them, the establishment of the Tang bu tian ge[唐歩天歌] is considered from its
name to the Tang period, and assuming that each change requires 50 to 100 years, theapproximate dates are estimated to be as follows.
1) Moon’s path chart[格子月進図]: period of Taizong 太宗 (reigned: AD626-649)
2) (Kaiyuan zhanjing [開元占経]): period of Kaiyuan[開元年間] (AD713-741)
3) Dunhuang star chart[敦煌天文図]: Middle Tang[中唐期] (around AD800)
4) Chat of sky[天象図]: Late Tang [晩唐](around AD850-900)
5) (Tang bu tian ge[唐歩天歌]): End of Tang [唐末](around AD900)
The above estimated date is the date when the original chart of each chart was created.
7. The time of transmission of Moon’s path chart[格子月進図] chart to Japan and therelationship with the Kitora astronomy diagram
7.1 The time of transmission of the Moon’s path chart[格子月進図] to Japan
According dating of the chart, Moon’s path chart[格子月進図] is latest chart in Tang
during 7th to 8th centuries. Based on the consideration of taboo character, Moon’s pathchart[格子月進図] was transmitted to Japan at the early stage of that period. As thetransmission route, it is possible to think of the Japanese missions to Tang [唐] orSilla[新羅] who frequently traveled during Tennmu and Jitho[天武・持統] period. For
example,Linde Li[麟徳暦], which was compiled by Li Wei 李淳風 and enacted fromperiod of Linde[麟徳年間] (664-665), was transmitted to Silla[新羅] in 674, and in Japanin 690 as a name of Yifeng Li[儀鳳暦], it was used with Yuan Jia Li[元嘉暦]. (14) It isthought that Moon’s path chart[格子月進図] has been transmitted to Japan around thisperiod. In addition, it will also coincide with the time when the emperor Tenchi[天智]introduced a water clock(AD660) in Japan.
In period of emperor of Tenmu in Nihon Shoki[日本書紀], "Tenmu year 4, January 5th(675/2/5) Established Astronomical Observatory Place" is said. In addition, the first
appearance of the planet name is "Tenmu year 10, September 17(681/11/3), Mars
entered to Moon", and the first appearance of the constellation name is "Tenmu year 10,
November 13 (684/12) There is star, the center is bright, the star moves along with
Pleiades. “ In addition, in Syokunihongi[続日本紀] says Jinki[神亀] year 4, March 丁酉(727/4/20), Mars enter Westgate of east Jing (東井西亭門), east jing is alias of Jing xiu[井宿], but west gate is not unknown as the constellation name and star name. However,the note of Jing xiu 井宿 at the bottom right of Fig. 1 says "8 stars of Jing xiu[井宿],[Other name] Precious house[玉亭] [Other name] Precious gate[門玉]. Teimon[亭門] may
be an abbreviated star name from these names. (15) These records are supporting
evidence of the fact that Moon’s path chart[格子月進図] had already been transmitted toJapan around this time.
7.2 The relationship between Moon’s path chart[格子月進図] and Kitora astronomy
diagramSince Kitora astronomy diagram is a circular diagram centered on the North Pole, it isconsidered that the original chart was also a circular diagram. Therefore, Kitora
astronomy diagram is not a direct copy of Moon’s path chart[格子月進図]. It is thoughtthat there is another star chart in which Moon’s path chart[格子月進図] is drawn in acircle, and that is the original chart of Kitora astronomy diagram.
It is said that 283 constellations and 1464 stars are drawn in Moon’s star chart, but
Kitora astronomy diagram is drawn only about 74 constellations and 350 stars.
However, because Kitora astronomy diagram also fills the circular drawing area, one
constellation is drawn in two to three times the actual size. Therefore, Kitora astronomy
chart is not an astronomical star chart but a decorative astronomical chart designed formural paintings. As a result, constellations such as Kulou[庫楼], Qiguan[騎官] andJizu[積卒]have not kept their original shape.
The positions of the 28 xiu reference stars in Kitora astronomy diagram are relatively- 13 -

consistent compared with other constellations, so the drawing procedure in the sketch
for the wall is as follows. The half of the drawing area were fill with the important
constellations near the North Pole and the constellations of 28 xiu. Then the remaining
area is drawn with a distinctive constellation. Therefore, the concept of the star chart isthe same as those of the Takamatsuzuka Tomb[高松塚古墳] with the North Pole and 28
xiu constellations. In addition, the misplaced constellation between Zhang xiu 張宿 andYi xiu 翼宿 in Kitora astronomy diagram is considered to be an error at the time ofdrawing in the stone chamber. But if change the position of two constellation, lower partof Yi xiu 翼宿 will stick out by the outer circle 外規. Therefore, it is thought that it was
replaced from the design at the time of drawing creation. I think that the differences in
the positional relationship around Jiuzhou shukou 九州殊口 (I think it is Tianyuan 天苑), Tiancang 天倉, Tianyu 天庚 and Fuzhi 鉄鎖 are also the same. In addition,
astronomical accuracy is not much sought after because of its use for wall in tomb,
including the reversal of the Ecliptic. I think sketch for the drawing was designed inTang[唐] along with other mural figures and they were brought to Japan.
7.3 Situation after transmission of Moon’s path chart[格子月進図] to Japan
In China, a new star chart was made even after Moon’s star chart. For example, theoriginal drawing of Dunhuang star chart[敦煌天文図] is considered to have been edited
by dividing the revised version of Moon’s path chart[格子月進図] into 12 drawings.
However, the new star chart was not transmitted to Japan after Moon’s path chart[格子月進図], because of the termination of Japanese missions to Tang [唐]. Because of this, itis thought that Moon’s path chart[格子月進図] was used in Inyoudou 陰陽道 in the
Middle Ages and transmitted to the present while keeping the original shape of
constellation. This is the same situation as the Xuanming Li [宣明暦] used as original
until the Edo period for 800 years.
8. Conclusion
The order of the creation date of the star chart, that was not clear until now, have beenclarified to some extent by the comparative dating of the star chart. As a result, it waspossible to clarify that Moon’s path chart[格子月進図], which is photocopy of originals, isthe oldest and most refined astronomical chart that conveys the image of theconstellation of the beginning of Tang. At present, attention has been focused on Kitora
astronomical diagram, but due to inaccurate dating far Moon’s path chart[格子月進図] ,it was not used for the study of Kitora astronomical diagram. It is hoped that the precise
astronomical chart drawn in the older period than Kitora tomb construction will berecognized, and that an accurate restoration work will be created to convey its value tothe future. (16)Finally, the Identified star chat of Moon’s path chart[格子月進図] is attached as Figure
7. This chart shows same are as Figure 1.

- 14 -

- 15 -

Fig. 7 Identified star chart of Moon’s path chart[格子月進図]

Note: The same star area as in Fig. 1, drawn at AD 650. Identification was made from E.
Sasaki (1983).
The tail of the old age of Xuanyuan[軒轅] in Moon’s path chart[格子月進図] extends
from the 8th star, but it is extended from the 11th star in Fig. 7 because there is no
identifiable star in the vicinity. It seems that the tail of the old age of Xuanyuan[軒轅] in
Moon’s path chart[格子月進図] was roughly added in visually from the comparison withthe figure of Sankebosan [三家簿讃].
After the tail of Xuanyuan[軒轅] moves to the north like Dunhuang star chart[敦煌天文図] or Chat of sky[天象図], it is thought that Guan[爟] has moved to the square formedby the remaining stars 13, 15, 16, 17 in Fig. 7 『月進図の同定図』（軒轅周辺部分）- 16 -

Note(1) In modern astronomy, the longitude of the star is displayed at 360 degrees, with aspring equinox point of 0 degrees, but in ancient Greek astronomy, 360 degrees isdivided into 12 palaces every 30 degrees to make it easier to handle numbers. Similarly,
in China’s astronomy, the circumference of the equator was divided into 28
constellations, each of which was assigned a bright star (reference star) and represented
the longitude of the star at an angle from the star. The angle between the stars is called
the width of 28 xiu [28 宿広度]. Because the angle from the star to the specific star andthe width of 28 xiu [28 宿広度] are relative angles unlike the angle from the springequinox, the influence of precession is small. Therefore, the same star list has been usedin China for a long time. In China, the equator is set at 365.25 degrees according to the
speed of the sun. In addition, declination is expressed by the degree from the north pole.
(2) T. Nakamura (2015.10) uses 28 reference stars in Kitora astronomy diagram, and M.
Soma (2015) uses 11 stars that can be regarded as declination drawn correctly, andestimates the precession dates, the results are BC80 ± 40 years and AD 300 ± 90 years
respectively. T. Nakamura (2015.11) also analyzes using 28 stars in Chart of sky[天象図],
he got the results of BC 66 ± 12 years. By the result of both star charts, he has
assumed that they were based on Shi shi xingjing [石氏星経] (estimated as BC 54 years± 11 years).
(3) As a star chart of Song Dynasty[宋朝], there is also a Suzhiu shike xingtu[蘇州石刻星図(淳祐星図)] which is sculpted in 1247 by Wang Chihyuan 王致遠 based on the star
chart produced by Huang Shang 黄裳 of North Song Dynasty[北宋朝] around 1190 as astar chart. Osaki, M. (1987) p. 231-237 states that there are many errors compared withSu Song star chart[蘇頌星図]. He has also listed the locations of the error.
(4) Sankebosan [三家簿讃] is a document transmitted to the Wakasugi-ke 若杉家, who
has the job responsible for home affairs for Tsuchimikado-ke 土御門家. According to k.
Yamashita (2004) p.196, The book was established under the influence of followings.
1) Chen Zhuo (Taizi lìng in Jin(265-420) 晋 太 子 令 ) 陳 卓 who reorganized theconstellations established under the name of the three family (Shi 石・Gan 甘・Wu 巫)from the former Han’s end to the later Han
2) Sen Lezhi(Taizi lìng in Song(420-479)宋太子令) 銭楽之 who placed the threefamily’s constellation in three colors.
Sankebosan [三家簿讃] is considered as Chinese orthodox heavenly document that has
been augmented with some constellations before Tang[唐].
It is said that it was transmitted to Japan before 748, and the existing document is acopy of the early Kamakura[鎌倉時代] (1235). Specifically, in addition to individual
constellation names and positions, constellation diagrams are described. Sankebosan[三家簿讃] is also a document that only remained in Japan. For details, see Daito Univ.
(2004). The photocopy is also in S. Murayama (1987). Regarding to the three family
Classification, please refer to A. Maehara (2015).
(5) The photo copy of the Moon’s path chart[格子月進図] is black and white photograph,so the original color is unknown, but S. Imoto (1972) p.290 states that the stars of the 28
xui were plotted in yellow, red and black. In addition, there is also a description
regarding the three colors on Moon’s path chart[格子月進図],”三家簿讃 二百八十三官
一千四百六十四星 (略) 三色事 黄色殷巫咸 赤色魏石申 黒斉甘徳”.
The magazine “別冊 太陽”(Besstsu Taiyo)Heibon,73 (1991) also has a photograph ofMoon’ path chart, but there is no photograph for central part around Kui xiu 奎宿.
(6) Please refer to H. Nojiri (1971) p. 189-197 “14. The Dunhuang old star chart”.

- 17 -

(7) Please refer to the textbook of Deng Wenzhao 鄧文寛 (1996) pp. 58-93. However,there are the following mistakes in school textbooks compared to Moon’s path chart[格子月進図]. Also, from the content of the error, it is considered that there are also mistakes
when split into 12 figures.
1) (60) Shuifu 水府 and Sidu 四瀆 are placed opposite.
2) (69) "轝" is considered as Tiangou 天狗, but in fact "天車" is an error of Tianshe 天社.
3) (70) "天苗" is an error of Tiangou 天狗.
4) (76) There is no indication that the position of Neiping 内平 is the north of
Xuanyuan 軒轅.
5) (101) Corrected Pingdao 平道 to Ping 平, but Moon’s path chart[格子月進図] also
Pingdao 平道.
6) (126) There is no need to add Jingu 神宮. The position of Jingu 神宮 is also different,
and it is not in Moon’s path chart[格子月進図].
7) (146) "升" has been corrected without a note on Dou 斗.
8) (148) "甶" is commented as "no star on chart", but it is an error of Gou 狗, because it
is south of Dou 斗.
9) (156) It was assumed that [Gou 狗・Gouguo 狗国] is wrong, but [Tianji 天雉・Gouguo
狗国] is wrong.
(8) For the inscription and the written text in Japanese of Chat of the sky[天象図], refer
to Chiba City Folk Museum (2002) p.18-21.
(9) The other documents have the following descriptions about the position of Guan 爟
Jin shu tianwenzhi[晉書天文志]: “軒轅西四星曰爟”(4 stars at west of Xuanyuan 軒轅 isGuan[爟]. ) (edited in Tang, 彙編 vol.1, p.185)
Sui shu tianwenzhi [隋書天文志]: “軒轅西四星曰爟”(4 stars at west of Xuanyuan 軒轅
is Guan 爟.) (edited in Tang, 彙編 vol.2, p.579)
Kaiyuan zhanjing [開元占経]: “甘氏曰爟四星在軒轅尾南柳北”(Gan 甘 say Guan 爟 4stars at south of tail of Xuanyuan 軒轅 and north of Liu xiu 柳宿)(Vol. 69)
Son shi[宋史]: ”爟四星,在鬼宿西北,一曰軒轅西”(Guan 爟 4 stars, at northwest of Gui xiu
鬼宿. Another book say at west of Xuanyuan 軒轅.) (彙編 Vol.3 p.902)
In addition, the Dunhuang document No. 2512, brought in by French Perrier
introduced (Luo Zhenyu 羅振玉編(2004) includes as Astrology )by Y.Yamashita (2004)
p.380, says “爟四星軒轅尾西” (p.380) (Guan 爟 4 stars at west of tail of Xuanyuan 軒轅)and “爟星鬼上懸”(p.386)( Guan 爟 is located to the north of Gui xiu 鬼宿). It is considered
to be a transcript of around AD621［武徳四年］, because there is a description of “自天皇巳来至武徳四年二百七十六万一千一百八歳”(p.376)( The emperor came here to be 2, 761,
108 years with AD621.) However, this document has taboo character in Huben 虎賁 (p.
381) and Tianyuan 天淵 (p. 382), so it can only be regarded as a document after
AD621[武徳四年]. In addition, Youqi 右旗 (p.382) is a misprint of Zuoqi 左旗. There arealso two misprints for left and right name in Dunhuang star chart[敦煌天文図]. The
date of this document is considered to be the same age as Dunhuang star chart[敦煌天文図] from constellation names such as Guqi 鼓旗 and Tianshi 天矢.
There is also a “鬼上四星是爟” ( 4 stars over Gui xiu 鬼宿 is Guan 爟) in Tang bu tiange[唐歩天歌] (Yuhai 玉海 vol. 3), which has an essay made by Dan Yuanzi 丹元子 of Sui
隋, but in the Tang bu tian ge[唐歩天歌], Youqi 右旗 is described as "左旗右旗各九星河鼓両畔" (Zuoqi 左旗 and Youqi 右旗 are each nine star along with Hegu 河鼓.) Since theconstellation name of Youqi 右旗 is not in Kaiyuan zhanjing [開元占経], the date of Tangbu tian ge[唐歩天歌] is considered to be after the period of Kaiyuan[開元年間]. S. Osaki- 18 -

(1987) p.76-77 also says that the author of Tang bu tian ge[唐歩天歌] is Dan Yuanzi 丹元子 of Sui 隋 or 王希明 Wang Ximing of Tang 唐, but they are actually an unknown personwith the trace. However, in view of its contents, it shows a figure that lies between Jin
shu[晉書]/ Sui shu[隋書] and Son shi[宋史], so it is true that it is the one that describes
the constellations of the Tang Dynasty[唐朝]. Daito Univ. (2004) p.137/153 also says thatthe article Hegu 河鼓 Youqi 右旗 cannot be found in the documents of Jin shu[晉書] andKaiyuan zhanjing [開元占経]. In addition, Tianshi 天矢 located south of Shen xiu 参宿
has also changed its name to Tianshi 天尿 in Song Dynasty[宋朝], but it is also
considered as Tianshi 天尿 in Tang bu tian ge[唐歩天歌]. Therefore, it is estimated thatthe date of Tang bu tian ge[唐歩天歌] is the end of the Tang Dynasty[唐朝].
(10) Refer to M. Tsuji (2016) p.438. According to Wang 王諺坤 (1997) p. 314, “人” were
often used as a substitute for “民”(min). For the taboo character of "虎" and "淵", see
Wang (1997) p. 167 and p. 578. The situation of replace of taboo character is the same as
Jin shu tianwenzhi[晉書天文志] and Sui shu tianwenzhi [隋書天文志], which werecompiled in Taizong 太宗 period (reigned: 626-649). (Please refer to Y. Kegazawa (2005)
p. 354 for compilation time). In Moon’s path chart[格子月進図] restored version, E.
Sasaki (1984) states "天淵", but in the original picture, we can read it "天泉".

(This picture is added in English version only from Bessatus Taiyou 73(1991) p.39)(11) M. Osaki (1987) p. 261 points out the possibility of moon’s path, but there are many
researchers who consider it as ecliptic (sun’s path).
(12) T. Watanabe (1987) p. 762 does not describe the specific calculation method, but theresults agree if the spring equinox is calculated 5.5 degrees east of the reference star of
Kui xiu 奎宿 (ζ And).
(13) Zong Taifu 宗太夫 is in Sankebosan [三家簿讃] (Daito Univ. (2004) sheet No. 6), but
it is not recognized as a constellation by Tianwenzhi 天文志 in China or Kaiyuan
zhanjing [開元占経]. Please refer to Daito Univ. (2004) p.136.
14) It is a common theory that Linde Li[麟徳暦] is referred to as Yi Feng Li[儀鳳暦] inJapan because it was transmitted during period of Yi Feng 儀鳳(676-679) of Tang
Dynasty. However, in the “日本国見在書目録"(Japanese List of Bibliography) createdduring the Heian 平安 period, Linde Li[麟徳暦] and Yi Feng Li[儀鳳暦] are described as
different calendars and cannot be explained by common theory. H. Inoue (1980) p. 247(note 73) says that this is Yi Feng Li[儀鳳暦] because it has been modified in Silla 新羅and used since the period of Yi Feng 儀鳳(676-679). I agree with this, and I think that- 19 -

Silla revised the first line of the calendar to the following and named it Yi Feng 儀鳳
新唐書暦志二『麟徳暦 麟徳元年甲子、距上元積二十六萬九千八百八十算』(彙編 7,p.2141)
儀鳳暦書（my assumption）『儀鳳暦 儀鳳元年丙子、距上元積二十六萬九千八百九十二算』(12 years have been added to the accumulation year from the origination year to thecalendar origin because the origination year has been lowered by 12 years)(15) In K. Saito (1986) p.96 says that west house gete 西亭門 is unknown and it isrecorded that Mars enter Jing xiu 井宿. However, on this day (727/4/20), the Mars 熒惑
is near the northern star εGem of the four star rows of east of Jing xiu 井宿 and Mars ismoving in the direction of leaving from Jing xiu 井宿. The article says “熒惑東井西亭門ニ入ル”(Mars enter the west gate ), so the eastern star area adjacent to Jing xiu 井宿 isseems to called house gate 亭門 and Mars enter the west of house gate 西亭門.
(16) T. Nakamura (2014) p.206 says that the negative of Moon’s path chart[格子月進図]
is missing. Also, it should be noted that E. Sasaki (1984) has no grid (it cannot correct
thedistortion of chart). The following stars in the original photograph is notdescribed either. 1) 鉞星(axe) in Jing xiu 井宿, 2) Zongzheng 宋正 2 stars, 3)Liyu 離瑜 2stars. In addition, Zhangren 丈人 2 stars south of Dou xiu 斗宿 is an error of original
chart, it is Gouguo 狗 2 stars.
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Thid document is English translation version (ver.1 2019/May/18) from thefollowing paper isuued on November 2017,
Japanese title
中国古代星図の年代推定の研究－初唐の星座の姿を伝える最古の星図『格子月進図』－
竹迫 忍
数学史研究 No 228 (2017)
English title
Study for the Dating of the Old Chinese Star Charts
Shinobu TAKESAKO
Journal of History of Mathematics, Japan
No.228 August-November (2017)- 22 -