The Shixian calendar and seventeenth-century reform
The 1645 calendar
The Shixian (时宪历) calendar entered official use in 1645, early in the Qing dynasty. New astronomical procedures changed how celestial events were calculated, while the calendar retained its lunisolar structure of lunar months coordinated with the seasons. The reform did not introduce Gregorian civil dating.
Much of the preparatory work belonged to the preceding Ming dynasty. The solar eclipse of June 21, 1629, observed at Beijing, became an important test of competing predictions and helped prompt a new reform programme. Xu Guangqi was given responsibility for the work that year. Chinese scholars and officials collaborated with Jesuit specialists to translate astronomical works, compare methods and develop tables suitable for official use.
Johann Adam Schall von Bell, known in Chinese as Tang Ruowang, subsequently played a leading role in bringing this work into Qing service. The change of dynasty gave the project a new political setting, but it drew on years of late-Ming translation and calculation. The Qing court's adoption of the calendar established official support for methods that had already been developed and debated.
Astronomical books and solar terms
The collection called Chongzhen Lishu, the calendrical treatises of the Chongzhen reign, brought the reform's working knowledge together. It included explanations of astronomical theory and instruments, observational methods, and tables for the Sun, Moon, planets and eclipses. Such material allowed specialists to work through a prediction rather than simply consult a list of dates.
An early-Qing revision, Xiyang Xinfa Lishu, reorganized this material. Its 1645 edition used earlier Ming printing blocks with additions made by the Qintianjian, the imperial astronomical office. These technical works supplied procedures for producing annual calendars, as well as for predicting celestial events. The Shixian calculations continued to be revised during the Qing as new tables and astronomical models became available.
One consequential change concerned the solar terms. Earlier calendars commonly assigned them by pingqi (平气), dividing the adopted seasonal year into equal time intervals. The Shixian tradition used dingqi (定气), assigning terms by the Sun's calculated position along the ecliptic, its apparent annual path against the stars. Successive terms were set at 15-degree intervals of longitude.
| Feature | Mean solar terms: pingqi | Position-based solar terms: dingqi |
|---|---|---|
| What is divided equally? | Time within the adopted seasonal year | The Sun's ecliptic longitude |
| Step between successive terms | One twenty-fourth of the year | 15 degrees |
| Elapsed time between terms | Equal within the scheme | Unequal |
| Principal terms | Every second solar term | Every second solar term, at 30-degree steps |
The Sun's apparent annual motion is uneven. Moving through 15 degrees therefore takes different lengths of time in different parts of the year. The equinoxes and solstices fall at specified positions in this sequence. The twelve principal terms, which alternate with the other twelve solar terms, also help assign lunar months to the seasonal year.
Lunar months and leap months
Lunar months continued to begin on the civil day containing a calculated new moon. Each month contains 29 or 30 days. Solar terms have their own calculated times, so their position within a lunar month changes from year to year.
Changing from equal time intervals to equal angular intervals affected month numbering and intercalation. With position-based terms, a lunar month can contain two principal terms, and more than one month in a sequence can lack one. A month without a principal term is therefore not automatically a leap month.
The Shixian-derived Chinese rule gives priority to the winter solstice: the lunar month containing its date is month 11. Count the lunar months from the beginning of one such month 11 to the beginning of the next, including the first but excluding the next. If there are twelve months, no leap month is needed within that interval. If there are thirteen, the first month in the interval without a principal term is designated the leap month. It takes the number of the preceding month, with a leap designation, and ordinary month numbering then continues.
These rules operate on calendar days. When a principal term falls on the first day of a lunar month, it belongs to that month, even if its precise time precedes the new moon that day. The calculation must therefore establish both the astronomical events and the civil dates containing them. Together, the new-moon dates, winter-solstice month and leap-month rule keep the lunar sequence tied to the seasons.