Shoushili was the official calendrical method promulgated in 1280 CE by the Yuan dynasty. It contains a list of the angular spans in right ascensions for the 28 lunar lodges. They are known to have been measured by Guo Shoujing with his advanced instruments with an unprecedented precision or reading error of 5′. Such precise data are useful to determine their observational epoch with an error range which is narrow enough to pinpoint on which historical occasion they were observed. Using the precise SIMBAD data based on eDR3 of GAIA and carefully identified determinative stars and considering the precession of equinoxes and proper motions, we apply linear regression methods to those data and obtain the observational epoch of 1271 ± 16 CE and the measurement error of 4.1′. We also have polar distances corresponding to declinations written in another manuscript of the Ming dynasty. Since the two data sets have similar significant digits, they were suggested to have the same origin. However, we obtain their observational epoch of 1364±5 CE and the measurement error of 5.7′. They must have been measured with different instruments and on a different occasion from the observations related to Shoushili. We review the history of the calendrical reform during the 13th century in the Yuan dynasty. We conclude that the observational epoch obtained from lodge spans in Shoushili agrees with the period of observations led by Guo Shoujing or 1276–1279 CE, which is also supported by the fact that the ecliptic lodge span values listed in Shoushili were calculated from the equatorial lodge spans.

Abstract
1. Introduction
2. Data Analyses
    2.1. Data
    2.2. Methods
    2.3. Epoch of the Lodge Spans in Shoushili
    2.4. Epoch of the Polar Distances in QJJ
    2.5. Comparisons with Previous Researches
3. Conclusions
Acknowledgments
References
Appendix A. Six Stars in Ling Tai Mi Yuan

• Sang-Hyeon Ahn(Theoretical Astronomy Center, Korea Astronomy and Space Science Institute) Corresponding Author