Arithmetic
The following are Gregorian minus Revised Julian date differences, calculated for the beginning of March in each century year, which is where differences arise or disappear, until 8000 AD. These are exact arithmetic calculations, not depending on any astronomy. A negative difference means that the proleptic Revised Julian calendar was behind the proleptic Gregorian calendar. A positive difference means that the Revised Julian calendar will be ahead of the Gregorian calendar, which will first occur on 1 March 2800:
| Century Difference |
100 0 |
200 −1 |
300 −1 |
400 0 |
500 0 |
600 −1 |
700 −1 |
800 0 |
900 0 |
1000 0 |
|---|---|---|---|---|---|---|---|---|---|---|
| Century Difference |
1100 −1 |
1200 0 |
1300 0 |
1400 0 |
1500 −1 |
1600 0 |
1700 0 |
1800 0 |
1900 0 |
2000 0 |
| Century Difference |
2100 0 |
2200 0 |
2300 0 |
2400 0 |
2500 0 |
2600 0 |
2700 0 |
2800 +1 |
2900 0 |
3000 0 |
| Century Difference |
3100 0 |
3200 +1 |
3300 0 |
3400 0 |
3500 0 |
3600 +1 |
3700 +1 |
3800 0 |
3900 0 |
4000 +1 |
| Century Difference |
4100 +1 |
4200 0 |
4300 0 |
4400 +1 |
4500 +1 |
4600 +1 |
4700 0 |
4800 +1 |
4900 +1 |
5000 +1 |
| Century Difference |
5100 0 |
5200 +1 |
5300 +1 |
5400 +1 |
5500 +1 |
5600 +1 |
5700 +1 |
5800 +1 |
5900 +1 |
6000 +1 |
| Century Difference |
6100 +1 |
6200 +1 |
6300 +1 |
6400 +2 |
6500 +1 |
6600 +1 |
6700 +1 |
6800 +2 |
6900 +1 |
7000 +1 |
| Century Difference |
7100 +1 |
7200 +2 |
7300 +2 |
7400 +1 |
7500 +1 |
7600 +2 |
7700 +2 |
7800 +1 |
7900 +1 |
8000 +2 |
In 900 Julian years there are 900⁄4 = 225 leap days. The Revised Julian leap rule omits seven of nine century leap years, leaving 225−7 = 218 leap days per 900-year cycle. Thus the calendar mean year is 365+218⁄900 days, but this is actually a double-cycle that reduces to 365+109⁄450 = 365.242 days, or exactly 365 days 5 hours 48 minutes 48 seconds, which is exactly 24 seconds shorter than the Gregorian mean year of 365.2425 days, so in the long term the average the Revised Julian pulls ahead of the Gregorian calendar by one day in 3600 years.
The number of days per Revised Julian cycle = 900 × 365 + 218 = 328,718 days. Taking mod 7 leaves a remainder of 5, so like the Julian calendar the Revised Julian calendar cycle does not contain a whole number of weeks. Therefore, a full repetition of the Revised Julian leap cycle with respect to the seven-day day weekly cycle is seven times longer.
Read more about this topic: Revised Julian Calendar
Famous quotes containing the word arithmetic:
“I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori. Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction.”
—Gottlob Frege (1848–1925)
“Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build my arithmetic.... It is all the more serious since, with the loss of my rule V, not only the foundations of my arithmetic, but also the sole possible foundations of arithmetic seem to vanish.”
—Gottlob Frege (1848–1925)
“‘Tis no extravagant arithmetic to say, that for every ten jokes,—thou hast got an hundred enemies; and till thou hast gone on, and raised a swarm of wasps about thine ears, and art half stung to death by them, thou wilt never be convinced it is so.”
—Laurence Sterne (1713–1768)