The blue box in the left picture of Japan (from Visible Earth of NASA) corresponds to the area of the right map.

  It was the 7th century that the full-scale capital was constructed for the first time in the history of Japan. The capital was called Fujiwara kyo (kyo means capital; not shown in above map), and after that, capitals were transferred to Heijyou (Nara), Nagaoka, and Heian (Kyoto). These capitals, planed after Chinese ones, were rectangular in shape, and four sides face almost exactly to the cardinal points. But with precise measurements of the excavation sites, it is found that the directions of ancient capitals deviate slightly from the cardinal points. Below is the list of the deviations (errors) of the north-south lines of capitals from the true north, which was informed by Mr. Miyahara (Kyoto City Archaeological Research Institute).

the name of capital	the year of transfer	empress/ emperor	the deviation from the true north
Heijyou (Nara)	710	Genmei	21'6"W *1
Nagaoka	784	Kanmu	7'W
Heian (Kyoto)	794		22'55"W

*1: Kenji Uchiyama, 'Averaging calculation for the reconstruction of the plan of Nagaoka kyo', in "Bulletin of the excavation research institute of Nakaoka kyo"(Japanese) No. 31 (1984)

  1' (minute) is 1/60 of 1° (degree). 1" (second) is 1/60 of 1' and hence, 1/3600 of 1°. For example, the north-south direction of Heian-kyo is 22'55" West from the true north. If you walk 1000m to the true north, turn to the west, and walk 7m to the west, then the deviation will be the same as that of Heian-kyo. Notice that both Heijyou and Heian-kyo have the similar deviations. In the above right map, the deviations of orientation of capitals are rather exaggerated. Actually, the deviations are negligible in such a small scale.

  The questions are summarized as follows.

1. What is the method to measure the direction?
2. How much is the error involved by the method?
3. Is the similar deviations of Heijyou and Heian-kyo just a coincidence, or is there some connection between them?

2. How to measure the direction?

  You may think a compass was used for pointing to the true north. Compass had been known in China at the time, but the direction to which a compass points is different from the true north. The difference (called declination) changes in ages and locations, and can be up to 15 degree. It is concluded that the measurement using a compass is not accurate enough for the ancient Japanese capitals.

  Other possibility is to use the North Star (Polaris). But due to the wobbling of the earth's spin axis (called precession), the North Star was about 10 degree away from the celestial north pole (the center about which the stars rotate once a day) when the ancient Japanese capitals were constructed. So this naive method using the North Star is not accurate enough for the ancient Japanese capitals, but there are also ingenious mothod using the circumpolar star (see 2-2, below).

  The key is found in the old Chinese literature called Shuuhi Sankei (Japanese pronunciation) or Zhoubi Suanjing (Chinese pronunciation; though Japan adopted Chinese characters, the pronunciation is somewhat different between the two countries). This literature contains two methods for pointing to the true north.

2-1. The method using the Sun

  Kiyoshi Yabuuchi introduces the similar method (called the Indian circle method) as in Shuuhi Sankei, which uses the movement of the Sun. Let a pole (black line in the left figure, which is the view from the north) stand perpendicular to the level ground. Then draw a circle whose center is the root of the pole. As the sun rises in the morning (upper left), the shadow of the pole gets shorter. When the shadow of the top of the pole just falls on the circle, mark the point. In the afternoon, the shadow of the pole gets longer, and again mark the point where the shadow falls on the circle. The line through the two marked points is the true east-west direction, so the line perpendicular to this line is the true north-south direction.
  Theoretically, the Indian circle method leads to the error up to 7' in the time near spring and autumn equinox (March and September).

2-2. The method using the circumpolar star

  This literature also presents ingenious method using the circumploar star. Circumpolar stars rotate once a day, whose center is the north celestial pole. If we measure the direction of the eastern and western elongation of the star, the bisector of the two direction will be the true north. It is hard to observe both the eastern and western elongation in one night, so this method requires two observations at intervals of three to six month.

  To execute this method, I arranged the method described in Shuuhi Sankei. First, drive a stake in the field. Then put a tripod to the south of the stake, suspending a string with a weight to secure perpendicular. In the night, move the tripod to the east-west direction so that a observer to the south of the tripod can see both the stake and the star on the string.
  The left of poorly-drawn figures is the view from the above sky, and the right is the view from the observer, sitting to the south of the tripod and looking to the north. As the star rotates, move the tripod, and if the star reaches the eastern/western elongation, mark the point of the string. The bisector of the angle formed by the eastern-elongation, the stake, and the western-elongation, will be the true north.

3. Experiments

  The accuracy of these methods can not be estimated until some experiments are conducted. Kyoto Tenmon Meguri (the society for the astronomical heritage in Kyoto) conducted the first and preliminary experiment for the Indian circle method in June, 2002, and I uploaded Web pages on this experiment. Mr. Miyahara (Kyoto City Archaeological Research Institute) looked at my Web page and contacted me. Then, he took part in the society and offered the archaeological data and measurement skills, and the second experiment was conducted in October, 2002.

  The details of the second experiment and data processing are skipped, and we only present the final results. The direction obtained by the Indian circle method was compared with the true direction obtained by GPS, and the two directions agree within a few minutes or 1/1000 (which corresponds to the error of 1 m when you go 1 km to the true north).
(In the picture, the author was watching the tip of the shadow. Photo by Yoshihiro Marukawa)

  This error is comparable with the deviation of Nagaoka kyo (see the table in Chapter 1 of this page), so it is possible that the Indian circle method was used for the orientation of the capital. Errors can be as large as those of Heijyo and Heian kyo, in case any of the procedure went wrong (e.g., the ground is not perfectly level, or the pole is not perfectly perpendicular to the level). But we can not tell whether the similarity of the deviations of Heijyo and Heian-kyo (about 22' west) is just a coincidence, or there is another method which leads to the systematic error of 22' west, though we have not hit upon such a method.

  We will try another method using the circumpolar star presented in Shuuhi Sankei (Chapter 2-2 of this page). Moreover the information of the orientation of Chinese and Korean capitals is also necessary, but the precise measurement has not been reported yet.

Related External Links

• Astronomy in Japan : by Steve Renshaw and Saori Ihara
• Pyramid Orientation : various methods to orient pyramids.

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