The Chinese lunisolar calendar – whose New Year occurred adjacent to Ash Wednesday this week – is, as all men know, a Jesuit production. For imperial decrees of 1611 and 1629 commanded those expert mathematicians and astronomers, being missionaries of the Society of Jesus then resident in Beijing, to correct the traditional calendar of the Ming Empire; the work was completed between 1642 and 1644; and, after an invasion and change of dynasty, was promulgated in the first year of the Qing (that is, Manchu) Empire, in 1645.
There was some contretemps back in Rome at the involvement of Fr Johann Adam Schall von Bell, S.J., in the composition of such a calendar, providing as it did for the various feasts and fasts of pagan idolatry, not to mention days of good and bad fortune as prescribed by oriental superstition; but his involvement was all carefully examined and approved by a curial commission, Fr Schall's role being revealed as simply providing the calculations upon which substructure native officials arranged their customary observances, without any acquiescence of that Jesuit in their non-Christian rites; and in the same year of 1664, Pope Alexander VII officially approved the good father's appointment as a mandarin and chief mathematician of the Empire of China.
Being a lunisolar calendar, its lunar months (stretching from new moon to new moon, with the full moon occurring, more or less, on the fifteenth day of each) are carefully disposed to correspond to the solar year, with the intercalation of an extra month from time to time (roughly every three years). Though its solar year is calculated between successive (northern hemisphere) winter solstices, it is interesting to note several convenient properties of the Chinese calendar that relate instead to the vernal equinox, which must always fall within the second lunar month.
I wonder if the Jesuits, who laboured for the Son of Heaven that he be converted and turn to worship the Son of Man, that he, too, and all the peoples of his Empire, become sons of God and co-heirs of heaven, did not spot the eminent suitability of their clever improvement of the Chinese calendar for the determination of the date of Easter, in conformity with the then-recent Gregorian calendrical reform?
For I have been checking if a simple algorithm applied to the Chinese calendar will correctly yield the date of Easter: and it seems it does, if two safeguards be applied.
To begin with, recall what the first Ecumenical Council decreed: that Easter falls on the first Sunday after the first (or "Paschal") full moon after the (northern) vernal equinox. The West (whether non-Chalcedonian, Greek or Latin) has always determined this date by the use of tables. However, in principle astronomical calculations would yield an equal or superior result.
The reformed Chinese calendar of 1645 is based upon observations of the true rather than the mean sun and moon. (Since early last century, it has not been based upon the meridian of Beijing, but upon that of 120 degrees East; this is about the only change made after the Jesuits' codification and improvement of ancient tradition.)
To determine the date of Easter by use of the Chinese calendar, first one finds the date of the vernal equinox in the relevant year (this always falls in the second lunar month), converting if necessary from the Gregorian to the Chinese date (though most Chinese calendars provide the "solar terms", including the relevant equinox). Then one notes if that equinox occurs before or after the fifteenth of the lunar month (when the full moon, in almost all cases*, occurs). If before, then the first Sunday after that fifteenth* day will be Easter Sunday. If after, then the first Sunday after the fifteenth* of the third month will be Easter.
I add an asterisk (*) above to signify that I have made a perhaps unwarranted simplification (though it works well enough in over 93% of cases): for, having downloaded a table of all lunar phases and their timings from 1600 to 2200 inclusive, it appears that the fifteenth day of the Chinese month is not always the date of the full moon: sometimes it is the sixteenth, or even the seventeenth.
For the eighty years from 1974 to 2053, four times (in 1994, 2021, 2025 and 2048) the calculation of the date of Easter requires not merely assuming that the fifteenth of the lunar month is the date of the full moon, but a careful checking of its exact date. Obviously, a truly comprehensive Chinese calendar table will include the exact date of the full moon each lunar month, so providing a wholly accurate method for finding Easter Sunday.
There is a further rule necessary: in 1981, this method would suggest that Easter falls on the 26th of April, but Easter can only fall between the 22nd of March and the 25th of April – so an added rule must prescribe that, in such a case, Easter be observed a week earlier.
If only the good fathers of the Society of Jesus (in those days, not merely great scholars, but staunchly orthodox too) had managed to convert the Emperor of China! If only the Chinese Rites controversy had been correctly resolved in 1704 (when instead those observances were banned, raising the wrath of the Kangxi Emperor, and resulting in the persecution of Chinese Christians), rather than only in 1939! If only Clement XI had been as well-informed and truly irenic as Pius XII – without in any way being syncretistic!
Ah, the might-have-beens of history: if only Matteo Ricci's understanding of Chinese customs had been upheld rather than spurned, then the conversion of China could have been effected centuries earlier, rather than postponed until the Sino-Japanese conflict and the Communist conquest of mainland China; or, to speak of another theatre of conflict, why did Mary, James II, the Old Pretender and the Young Pretender fail, and Elizabeth and the Prince of Orange succeed? We must bow before the inscrutable decrees of Providence.
In any case, once the men of Han are converted in God's good time – and there are many Christians and Catholics among them, despite all persecution – then indeed one providential convenience will be that the Chinese calendar is admirably adapted to the calculation of the date of Easter.