## 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.)

__(Leap days) Adjustments to Gregorian calendar:__

__(Leap weeks) Adjustments to Double Leap calendar:__

© 2009-2013 Marcus W.