Adjustments (known as the "Centurion Leap Day Rule" ie div.4/skip100th/count400th or div.4/skip700th/count2800th)
Further adjustments that are necessary because an average year is actually 365.2425 days rather than 365.25 days. Do you see where the problem is? We "over-rounded" by adding a leap day in every 4 years. Hence, we have to do more "subtractions".
(Leap days) Adjustments to Gregorian calendar:
365.25 - 365.2425 = .2425 days
.25 - .2425 = .0075
.0075 * 400 years = 3 days
.25 x 400 years = 100 days
.2425 x 400 years = 97 days
3 days were over-rounded in 400 years
400-year period:
-Leap years: Year 400
-Non-leap years: Year 100, 200, 300
2000-year period:
-Leap years: Year 400, 800, 1200, 1600, 2000
-Non-leap years: Year 100, 200, 300, 500, 600, 700...
Conclusion (in order of precedence):
-Rule #1: Years that are divisible by 400 are Leap Years
-Rule #2: Years that are divisible by 100 are not Leap Years
(Leap weeks) Adjustments to Double Leap calendar:
365.2425 - 364 = 1.2425 days
1.25 - 1.2425 = .0075
.0075 * 2800 years = 21 days
.25 x 2800 years = 700 days
.2425 x 2800 years = 679 days
21 days were over-rounded in 2800 years
We have to subtract "3 leap weeks" from a 2800-year period. The intervals reveal that:
-Double Leap Years: Year 2800
-Single Leap Years: Year 700, 1400, 2100
Conclusion (in order of precedence):
-Rule A: Years divisible by 2800, 2 Leap Weeks would occur (no subtractions!)
-Rule B: Years divisible by 700, 1 Leap Week would occur (1 wk subtracted every 700 yrs!)
(The most confusing part is that we were adding leap-days every 4 years to a 365-day calendar and we were applying the further reverse adjustments of .25 - .2425 = .0075 * 400 years = 3 days. But now we are adding leap-week every 7 years (double-leap-week every 28 years) to a 364-day calendar and we are now applying the further reverse adjustments of .25 - .2425 = .0075 * 2800 years = 21 days.)
© 2009-2013 Marcus W.