Why 1903 Had a Leap Fifth Month: On Zhongqi Falling on the Same Day as Conjunction in the Chinese Calendar

In the calendar code I was writing, I noticed that the published calendar shows 1903 as having a leap fifth month, yet my calculation did not produce one. After careful investigation, I found the reason.

On July 24, 1903, the Major Heat (Dashu) solar term begins at 9:00, while the sun–moon conjunction occurs that evening at 20:00. Under a strict reading of time, this Major Heat belongs to the previous month, so no leap month should be inserted in that previous month.

However, the rules of the Chinese calendar are not precise down to the double-hour; a conjunction on July 24 is taken as meaning that the first day of the month begins at the zi hour of July 24—this is analogous to "catching up" (chaojie).

Although Major Heat arrives early, in the calendrical system it is assigned to this month's qi, and therefore the year is a leap fifth month.

In coding, this issue must be taken into account: if a month's zhongqi (mid-qi) falls on the same day as the first day of the next month, then that month should be treated as having no zhongqi, and a leap month should be inserted.