Yi Xing - 一行

Zhang Sui (张遂) was a native of Julu who lived and served during the Tang Dynasty (618-907). When he became a Buddhist monk he was known as Sēng Yīxíng 僧一行, or more commonly, just Yi Xing 一行. Seng is the title for a Buddhist monk.

Yi Xing was a gifted mathematician and was given the task with others to create a new calendar. To do so, he first set out to take new measurements of the stars and planets.

In 727, the year of his death, Yi Xing published the Da Yan calendar (大衍历 Dà Yǎn Lì,) which was a book explaining the calculations for the calendar as well as the calendar itself. There were seven sections or chapters dealing with the calendar and the observations supporting it. While formulating the calendar, Yi Xing used his new measurements for the stars in the 28 xiù or constellations. He also used the data he collected on the length of the Sun's shadow at summer solstice along the meridian. He used the quadratic interpolation method (不等间距二次内插法) to make corrections on observations in order to implement the dingqi to predict eclipses. The theory is called dingshuo and is based on the division of the ecliptic into 24 equal segments of 15 degrees. While Yi Xing was aware of the method and used it, he could not include it in his Da Yan calendar for political reasons. The traditionalists just couldn't stand that much change, even if it was more accurate. In addition, Yi Xing was able to measure the actual movement of the Sun -- to measure the variations of its speed on the ecliptic. The inclusion of all of these measures made the Da Yan calendar much more accurate than the Huang Ji calendar from the Suí Dynasty (隋朝 581-618), which it replaced.

It was used from 727 to 751 and served as a benchmark for calendar makers for many dynasties afterward. It was much more than a more accurate calendar. Along the way to greater accuracy, Yi Xing had made even more important observations of the celestial bodies. Among findings reported in the Da Yan and elsewhere were observations of the asymmetrical movements of the sun and moon, the calculation of the speed of the sun's movement along the path of the ecliptic, and the first estimation of the length of a degree on the meridian. Yi Xing measured it as 351.27 li or 123.7 kilometers.

As mentioned before, as part of his research, he worked with Liang Lingzan and others to create an elaborate water powered armillary sphere in his observatory on the palace grounds in Chang'an. Playing with the mechanics of the thing undoubtedly helped him work on the mathematics to describe the variations observed in the motions of various celestial objects.

One of his most impressive findings was the observation of what is now called proper stellar motion. Proper stellar motion is when stars which are closer to us move across the sky at a faster rate than do stars that are far away from us. The amount of movement is extremely small. Barnard's Star discovered by Edward Barnard in 1916 only moves 10.3 arc seconds annually in relation to the star field. For Yi Xing, one of the most important implications of this finding was that stars move by themselves and are not fixed to a celestial sphere as Zhang Heng's egg theory proposed.

Yi Xing writing the Da Yan calendar


This instrument 夏矩仪 (xiàjǔ yí) can be used to measure the height of the North Pole Star

In different places the eclipse occurs at different times - called 食差 shíchā - meaning that the full eclipse will be local and in other places it will be partial.

Calendars in China are major works of mathematics and astronomy. Because the calendar must take into account the motions of both the sun and the moon to calculate the date, and the sun and moon move independently of one another, and the sun and moon both have variable speeds on their orbits, and the month is measure by the moon and the year by the sun, and the earth is curved and tilted in its orbit, determining when Spring Festival will occur each year takes some calculation. The calendar must be calculated for years to come. The months will differ in length from year to year and corrections must be built in for variability. In addition to defining the dates, the calendar must predict the lunar and solar eclipses. The major new calendars also included significant new observations and theories of celestial motion. These are included in the calendar to explain the calculations.

The Da Yan calendar (大衍历 Dà Yǎn Lì) had seven volumes devoted to different observations and topics including Yi Xing's observations of proper stellar motion.

Last update: May 2007
© Marilyn Shea, 2007