A Discussion on the Literary Sources of the Method for Determining Cardinal Directions in Ancient China
1. Basis of the Discussion
The methods for determining cardinal directions were described in several ancient Chinese books, such as Kaogong ji（考工记，The Artificer's Record, c. 5th century BC）, Zhoubi suanjing（周髀算经，Arithmetical Classics of the Zhou Gnomon, c. 1st century BC）, Huainanzi（淮南子，Master Huainan, c. 2nd century BC）, and Huyi lun（狐疑论，On Fox Suspicion） in Zhen Luan（甄鸾）'s Commentary on Shushu jiyi（数术记遗，Memoir on Some Numerological Arts, c. 6th century AD）. All texts concerned have been discussed in my previous paper -- “The Method of Determining Cardinal Directions in Ancient India and China”, which was first presented to the 20th International Congress on History of Science took place two years ago in Liege, Belgium. A Chinese version was published in Vol. 17, no. 1 of the Hanxue yanjiu （汉学研究）.
The texts I have studied are:
 KGJ: When builders construct the（capital of）state,（they first）find a level plane using the leveling instrument, place a pole vertically and measure its shadow;（then）describe a circle（on the ground）, and observe the shadows of sunrise and sunset. Refer to the shadow at noon and to the Northern Star at midnight, so that the cardinal directions are determined.
 ZBSJ: Place a pole vertically and mark the shadows when the sun rises and sets, hence the line joining the two notes refers to the east-west direction; connect its middle point and the point where the pole is placed, the north-south direction is determined.
 HYL: It ought to set up a pole as gnomon, and to describe a circle on the ground by using a cord fastened to the pole. When the sun rises on morning, the shadow of the pole exceeds the circle; while the sun goes up, the shadow becomes shorter and shorter, once its end meets the circle to mark the point of intersection in the northwest. On afternoon the shadow becomes longer and longer, once its end meets the circle again to mark the point of intersection in the northeast. Take（the line joining）the two（marked）points to get the east-west direction. Take the middle（point of the line）connecting（the point where）the pole（is placed）to get the north-south direction.
2. Earlier Literary Sources
Where did the method come from?
There is a similar description in Sulbasutra of Katyayana, one of the ancient Indian Vedanta literatures compiled in the 3rd century BC, and it is called “Indian circle method”. On the other hand, the date of Kaogong ji was completed is uncertain, although someone assumed it could be as early as the 5th century BC. However, there is not any convincing evidence showing the emergence of cultural exchange between the two nations in that time. In my point of view, this kind of method originated in China and India separately.
Sulbasutra is a kind of manuals for the construction of various types of altars for fire-sacrifice in ancient India.“Sulba”means “string”or“cord”, and “sutra”means “canon”or“classic”.
Similarly, the Chinese texts also refer to that the method was used in construction. Like what is recorded in Kaogong ji:“When builders construct the（capital of）state ……”etc.
Now we come to one of more popular Chinese literatures, i.e. the Shijing（诗经，The Book of Songs）. According to its preface and Mao Heng' s annotation, the poem Dingzhi fangzhong（定之方中，Determining Directions）eulogized Duke Wen of the Wei State（卫文公，reigned 659-634 BC）in the Spring and Autumn Period（770-476 BC）, who led his people to reconstruct the capital in Chuqiu （楚丘） in 658 BC, under the protection of the Duke Huan of the Qi State（齐桓公，reigned 685－643 BC）.
It says: “To construct the palace in Chuqiu, （we）first choose the suitable location; to build the chambers in Chuqiu, （we）determine the directions by measuring the sun.”
Mao Heng' s note:“kui（揆）means‘measure’; to measure the sunrise and sunset so that we know the east and west.”
Yanzi chunqiu（晏子春秋，The Stories of Master Yanying）is a book assumed to be compiled in the Warring States Period（475-221 BC）, but it really reveals some words and deeds of Yanying（?- 500 BC）, the famous minister of Qi State. One story says:
“When Baiqin（柏寝）platform was completed, Duke Jing（齐景公，reigned 547-490 BC）ordered Shikai（师开，royal musician）to play music …… and Shikai found the chamber tended towards the west（according to harmonic theory）…… Therefore Duke called on Daijiang（大匠，Big Builder）and asked him:‘Why did you build the chamber westward?’Daijiang replied:‘We built it corresponding to the palace.’（Duke）then called on and asked Sikong（司空，the Minister of Works）:‘Why did you build the palace westward?’ Sikong replied:‘We built the palace corresponding to the town.’Next day Yanzi was presented at court, Duke asked him:‘In the past my ancestor was granted fief in Yingqiu（营丘）, why did people set up the town westward?’Yanzi answered:‘In the past when people establish（the capital of）state,（they）look from the south at the North Star, how did they possibly get the cardinal directions? But today we find it towards the west, because（your ancestor）wanted to worship to the Zhou court where was in the west.’Duke praised with surprise:‘Are you the（sage）minister in ancient time?’”
Although in the text, Yanzi seems to deny the possibility of using instrument to determine the cardinal directions, his words reflects the importance of direction in construction. And this paragraph can be competed with those in KGJ and ZZSJ.
3. About the Tools
According to Zhouli（周礼，The Rites of the Zhou Dynasty）, there was a special official section called tufangshi（土方氏）, and it was in charge of measure, land, and construction. In particular, “tufangshi mastered the method of tugui（土圭之法）to measure the shadow of the sun.”
There is no object tugui to be unearthed until now, but according to Zhouli and other relevant literatures, it could be assumed like this: a piece of square board with 1.5 chi（尺）on each side, a pole is set up at the center, and the most important -- a circle drawn on the board. Obviously, it is a model of the method that we are discussing; and conversely, an instrument like this could be used to determine the cardinal directions.
The form of tugui is very similar to guiyi（晷仪， sundial）. Now I would like show you two extant objects guiyi: the first was excavated in Jinchun, Luoyang in 1932, now is kept in Ontario Royal Museum, Canada; the second was excavated in Tuoketuo, Inner-Mongolia in 1897, now is kept in Chinese History Mesuem. Both are Western Han instruments.
In my opinion, at beginning a kind of tool was only used to determine the cardinal directions and particular time like noon; later on scale had been added and it could be also measure the time in general. Therefore tugui had been gradually developed into guiyi.