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The new rules introduced a refinement that had the effect of slightly shortening the calculated calendar year. The "real" value of the length of the tropical year is 365.2422 days. The Julian calendar, by introducing a leap year every fourth year, effectively calculated the length of the year as (3653 + 366)/4 = 365.25 days. This value is in error by 0.0078 days per year, or one day in 128.20512 years. This value is the same as (400.0/128.20512 =) 3.12 days in 400 years. It was this figure that was eventually used as the basis for the Gregorian leap year rule. |
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To shorten the Julian year by three days every 400 years, the simplest method was to eliminate the leap day every 100 years (a four-day reduction in 400 years) but preserve the leap day in one of those cases to eliminate one of the 4 days. This is exactly what was done. |
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The Gregorian leap year rule states that |
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every year evenly divisible by four is a leap year, except that |
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every year evenly divisible by 100 is not a leap year, except that |
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every year evenly divisible by 400 is a leap year. |
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The year A.D. 2000 exercises all three parts of the Gregorian rule. The year is evenly divisible by 4, 100, and 400, and therefore is a leap year. |
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The Gregorian reform, as it affected the solar year, turned out to be rather simple in the long run. The Sun, however, was not the only actor in Church astronomy. Recall that a primary ecclesiastical concern was the calculation of Easter date, and that adjustment of the lunar cycle to the length of the solar year was the major issue. By changing the length of the solar year, the Gregorian correction altered the relationship of the lunar cycle to the solar year. As always, the Moon proved to be a far more complex problem than the Sun. |
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9.1.4.4.1
Julian Lunar Cycle |
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First, I'll review the lunar cycle in the Julian calendar. The Council of Nicaea took lunations to consist alternately of 29 and 30 days and created a lunar cycle on that basis. The framers used the Metonic cycle to create an equivalence between lunations and solar years and therefore used the period of 19 Julian years as their starting point. This length of time is (19365.25 =) 6,939.75 days. |
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On the lunation side of the equivalence, numbers are built by observing that 19 Julian years of 12 lunations, alternating between 29 and 30 days, is (29.5 1219 =) 6,726 days. In this period were intercalated six months of 30 days and one month of 29 days, or (630 + 29 =) 209 days, giving a total of (6,726 + 209 =) 6,935 days. |
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Next, the extra days introduced by Julian leap years must be accounted for. This is a bit more complex, since the leap years can be distributed across the 19 years in four |
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