佛祖歷代通載 2.15

2.15

From high antiquity onward, the four seasons were ordered, the length of days and nights was measured, and the equinoxes and solstices arose. The Book of Documents says: 'A year consists of three hundred and sixty-six days; by an intercalary month the four seasons are fixed and the year is completed.' (The body of Heaven is perfectly round, circumscribing 365 and 1/4 degrees. Reversing its rotation westward around the Earth, it regularly completes one circuit a day and exceeds it by one degree. The sun adheres to Heaven but moves slightly slower; thus the sun's travel in one day also completes one circuit around the Earth, yet relative to Heaven falls short by one degree. Accumulating 365 days and 235/940ths of a day, it meets with Heaven: this is the figure for the sun's travel in one year. The moon adheres to Heaven and moves still slower; in one day it regularly falls short of Heaven by 13 and 7/19ths degrees. Accumulating 29 days and 499/940ths of a day, it meets with the sun. Twelve meetings yield 348 whole days and an accumulated remainder of fractions; further, 5,988 divided by the day-divisor 940 yields 6 with a remainder of 348. Taken altogether, this yields 354 days and 348/940ths of a day: this is the figure for the moon's travel in one year. A year has twelve months; a month has thirty days; 360 is the regular number of a single storage. Thus, when the sun meets with Heaven and exceeds it by 5 days and 235/940ths of a day, this is the solar excess; when the moon meets with the sun and falls short by 5 days and 592/940ths of a day, this is the lunar deficit; and from this the intercalation arises. Hence the intercalary rate for one year is 10 days and 827/940ths of a day; in three years there is one intercalation of 32 days and 601/940ths of a day; in five years there are two intercalations of 54 days and 375/940ths of a day; in nineteen years there are seven intercalations, whereupon the solar terms and new moons coincide evenly: this constitutes one cycle. Therefore, if no intercalation is inserted for three years, one month of spring slips into summer, and the seasons gradually become unfixed; the month of zi slips into chou, and the year gradually becomes incomplete. If this accumulates for long until three intercalations are missed, all of spring slips into summer, and the seasons become entirely disordered. If twelve intercalations are missed, all of zi slips into chou, and the year becomes entirely incomplete.)